LMFDB - Embedded newform 76.7.l.a.23.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(23,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$58$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.12
Character	$\chi$	$=$	76.23
Dual form			76.7.l.a.43.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.50920 + 4.65084i) q^{2} +(33.9040 - 5.97820i) q^{3} +(20.7395 - 60.5465i) q^{4} +(-158.311 + 132.839i) q^{5} +(-192.885 + 196.595i) q^{6} +(-237.498 - 137.119i) q^{7} +(146.594 + 490.565i) q^{8} +(428.710 - 156.038i) q^{9} +O(q^{10})$	\(q+(-6.50920 + 4.65084i) q^{2} +(33.9040 - 5.97820i) q^{3} +(20.7395 - 60.5465i) q^{4} +(-158.311 + 132.839i) q^{5} +(-192.885 + 196.595i) q^{6} +(-237.498 - 137.119i) q^{7} +(146.594 + 490.565i) q^{8} +(428.710 - 156.038i) q^{9} +(412.668 - 1600.95i) q^{10} +(1999.99 - 1154.70i) q^{11} +(341.193 - 2176.75i) q^{12} +(-126.423 + 716.981i) q^{13} +(2183.64 - 212.025i) q^{14} +(-4573.25 + 5450.19i) q^{15} +(-3235.75 - 2511.40i) q^{16} +(-6801.47 - 2475.53i) q^{17} +(-2064.85 + 3009.54i) q^{18} +(716.197 - 6821.51i) q^{19} +(4759.63 + 12340.2i) q^{20} +(-8871.87 - 3229.10i) q^{21} +(-7648.06 + 16817.8i) q^{22} +(12111.2 - 14433.6i) q^{23} +(7902.83 + 15755.8i) q^{24} +(4703.01 - 26672.1i) q^{25} +(-2511.65 - 5254.95i) q^{26} +(-8132.76 + 4695.45i) q^{27} +(-13227.7 + 11535.9i) q^{28} +(8660.86 - 3152.29i) q^{29} +(4420.29 - 56745.8i) q^{30} +(-22878.8 - 13209.1i) q^{31} +(32742.3 + 1298.29i) q^{32} +(60904.9 - 51105.3i) q^{33} +(55785.4 - 15518.8i) q^{34} +(55813.3 - 9841.39i) q^{35} +(-556.314 - 29193.0i) q^{36} -39469.9 q^{37} +(27063.8 + 47733.5i) q^{38} +25064.3i q^{39} +(-88373.5 - 58188.5i) q^{40} +(-20666.9 - 117208. i) q^{41} +(72766.8 - 20242.7i) q^{42} +(7518.77 + 8960.52i) q^{43} +(-28434.0 - 145040. i) q^{44} +(-47141.6 + 81651.7i) q^{45} +(-11706.2 + 150279. i) q^{46} +(-10078.3 - 27689.8i) q^{47} +(-124719. - 65802.8i) q^{48} +(-21221.0 - 36755.9i) q^{49} +(93434.6 + 195487. i) q^{50} +(-245396. - 43270.0i) q^{51} +(40788.7 + 22524.3i) q^{52} +(174814. + 146686. i) q^{53} +(31100.0 - 68387.8i) q^{54} +(-163233. + 448478. i) q^{55} +(32450.2 - 136609. i) q^{56} +(-16498.3 - 235558. i) q^{57} +(-41714.5 + 60799.1i) q^{58} +(41775.2 - 114777. i) q^{59} +(235143. + 389928. i) q^{60} +(144271. + 121058. i) q^{61} +(210356. - 20425.0i) q^{62} +(-123213. - 21725.8i) q^{63} +(-219164. + 143828. i) q^{64} +(-75228.7 - 130300. i) q^{65} +(-158760. + 615913. i) q^{66} +(-11676.7 - 32081.5i) q^{67} +(-290943. + 360464. i) q^{68} +(324333. - 561762. i) q^{69} +(-317530. + 323638. i) q^{70} +(-111509. - 132891. i) q^{71} +(139393. + 187436. i) q^{72} +(50165.7 + 284504. i) q^{73} +(256918. - 183568. i) q^{74} -932407. i q^{75} +(-398165. - 184838. i) q^{76} -633326. q^{77} +(-116570. - 163149. i) q^{78} +(-352757. + 62200.6i) q^{79} +(845866. - 32250.1i) q^{80} +(-502439. + 421597. i) q^{81} +(679638. + 666810. i) q^{82} +(-179112. - 103410. i) q^{83} +(-379508. + 470190. i) q^{84} +(1.40559e6 - 511594. i) q^{85} +(-90615.1 - 23357.3i) q^{86} +(274793. - 158652. i) q^{87} +(859642. + 811855. i) q^{88} +(-1104.09 + 6261.61i) q^{89} +(-72894.2 - 750736. i) q^{90} +(128337. - 152946. i) q^{91} +(-622724. - 1.03264e6i) q^{92} +(-854651. - 311068. i) q^{93} +(194382. + 133366. i) q^{94} +(792778. + 1.17506e6i) q^{95} +(1.11786e6 - 151722. i) q^{96} +(-1.31216e6 - 477588. i) q^{97} +(309077. + 140556. i) q^{98} +(677241. - 807104. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9}+O(q^{10}) $ 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9} + 2811 q^{10} - 3 q^{12} - 7572 q^{13} + 8217 q^{14} - 1392 q^{16} - 12 q^{17} - 12 q^{18} + 33618 q^{20} - 33546 q^{21} - 198 q^{22} - 7128 q^{24} - 12 q^{25} + 84453 q^{26} + 13464 q^{28} - 12 q^{29} + 75510 q^{30} + 9339 q^{32} - 366 q^{33} - 289248 q^{34} - 419349 q^{36} - 24 q^{37} + 158040 q^{38} + 264570 q^{40} + 27360 q^{41} + 206001 q^{42} - 525639 q^{44} - 6 q^{45} - 269328 q^{46} - 703179 q^{48} + 2319360 q^{49} + 264534 q^{50} + 130809 q^{52} - 182292 q^{53} + 607083 q^{54} - 705906 q^{56} - 12 q^{57} - 710004 q^{58} + 1060416 q^{60} - 325092 q^{61} - 1967868 q^{62} - 1611921 q^{64} + 398994 q^{65} - 2295684 q^{66} + 1125642 q^{68} - 1625190 q^{69} + 3496059 q^{70} + 4948626 q^{72} - 2224812 q^{73} + 2661159 q^{74} - 968262 q^{76} + 974412 q^{77} - 340743 q^{78} - 3996663 q^{80} + 4277754 q^{81} - 3214221 q^{82} - 872109 q^{84} - 3207900 q^{85} + 3189360 q^{86} + 827973 q^{88} - 2016084 q^{89} - 710406 q^{90} - 2545116 q^{92} + 4486254 q^{93} - 14322630 q^{94} + 2623530 q^{96} - 1223112 q^{97} + 10989009 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9 + 2811 * q^10 - 3 * q^12 - 7572 * q^13 + 8217 * q^14 - 1392 * q^16 - 12 * q^17 - 12 * q^18 + 33618 * q^20 - 33546 * q^21 - 198 * q^22 - 7128 * q^24 - 12 * q^25 + 84453 * q^26 + 13464 * q^28 - 12 * q^29 + 75510 * q^30 + 9339 * q^32 - 366 * q^33 - 289248 * q^34 - 419349 * q^36 - 24 * q^37 + 158040 * q^38 + 264570 * q^40 + 27360 * q^41 + 206001 * q^42 - 525639 * q^44 - 6 * q^45 - 269328 * q^46 - 703179 * q^48 + 2319360 * q^49 + 264534 * q^50 + 130809 * q^52 - 182292 * q^53 + 607083 * q^54 - 705906 * q^56 - 12 * q^57 - 710004 * q^58 + 1060416 * q^60 - 325092 * q^61 - 1967868 * q^62 - 1611921 * q^64 + 398994 * q^65 - 2295684 * q^66 + 1125642 * q^68 - 1625190 * q^69 + 3496059 * q^70 + 4948626 * q^72 - 2224812 * q^73 + 2661159 * q^74 - 968262 * q^76 + 974412 * q^77 - 340743 * q^78 - 3996663 * q^80 + 4277754 * q^81 - 3214221 * q^82 - 872109 * q^84 - 3207900 * q^85 + 3189360 * q^86 + 827973 * q^88 - 2016084 * q^89 - 710406 * q^90 - 2545116 * q^92 + 4486254 * q^93 - 14322630 * q^94 + 2623530 * q^96 - 1223112 * q^97 + 10989009 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.50920	+	4.65084i	−0.813650	+	0.581354i
$2$	−6.50920	+	4.65084i	−0.813650	+	0.581354i
$3$	33.9040	−	5.97820i	1.25571	−	0.221415i	0.494071	−	0.869422i	$-0.335508\pi$
$3$	33.9040	−	5.97820i	1.25571	−	0.221415i	0.761635	+	0.648007i	$0.224397\pi$
$4$	20.7395	−	60.5465i	0.324054	−	0.946039i
$5$	−158.311	+	132.839i	−1.26649	+	1.06271i	−0.271529	+	0.962430i	$0.587529\pi$
$5$	−158.311	+	132.839i	−1.26649	+	1.06271i	−0.994959	+	0.100280i	$0.968026\pi$
$6$	−192.885	+	196.595i	−0.892985	+	0.910164i
$7$	−237.498	−	137.119i	−0.692414	−	0.399765i	0.112102	−	0.993697i	$-0.464242\pi$
$7$	−237.498	−	137.119i	−0.692414	−	0.399765i	−0.804516	+	0.593932i	$0.797575\pi$
$8$	146.594	+	490.565i	0.286317	+	0.958135i
$9$	428.710	−	156.038i	0.588079	−	0.214043i
$10$	412.668	−	1600.95i	0.412668	−	1.60095i
$11$	1999.99	−	1154.70i	1.50263	−	0.867541i	0.502630	−	0.864502i	$-0.332366\pi$
$11$	1999.99	−	1154.70i	1.50263	−	0.867541i	0.999995	−	0.00303919i	$-0.000967406\pi$
$12$	341.193	−	2176.75i	0.197450	−	1.25970i
$13$	−126.423	+	716.981i	−0.0575435	+	0.326346i	−0.999967	−	0.00807524i	$-0.997430\pi$
$13$	−126.423	+	716.981i	−0.0575435	+	0.326346i	0.942424	+	0.334421i	$0.108541\pi$
$14$	2183.64	−	212.025i	0.795788	−	0.0772686i
$15$	−4573.25	+	5450.19i	−1.35504	+	1.61487i
$16$	−3235.75	−	2511.40i	−0.789978	−	0.613135i
$17$	−6801.47	−	2475.53i	−1.38438	−	0.503874i	−0.460878	−	0.887464i	$-0.652465\pi$
$17$	−6801.47	−	2475.53i	−1.38438	−	0.503874i	−0.923504	+	0.383590i	$0.874688\pi$
$18$	−2064.85	+	3009.54i	−0.354056	+	0.516039i
$19$	716.197	−	6821.51i	0.104417	−	0.994534i
$19$	716.197	−	6821.51i	0.104417	−	0.994534i
$20$	4759.63	+	12340.2i	0.594954	+	1.54252i
$21$	−8871.87	−	3229.10i	−0.957981	−	0.348677i
$22$	−7648.06	+	16817.8i	−0.718263	+	1.57943i
$23$	12111.2	−	14433.6i	0.995418	−	1.18629i	0.0129393	−	0.999916i	$-0.495881\pi$
$23$	12111.2	−	14433.6i	0.995418	−	1.18629i	0.982478	−	0.186376i	$-0.0596744\pi$
$24$	7902.83	+	15755.8i	0.571675	+	1.13974i
$25$	4703.01	−	26672.1i	0.300992	−	1.70701i
$26$	−2511.65	−	5254.95i	−0.142902	−	0.298984i
$27$	−8132.76	+	4695.45i	−0.413187	+	0.238554i
$28$	−13227.7	+	11535.9i	−0.602573	+	0.525504i
$29$	8660.86	−	3152.29i	0.355113	−	0.129251i	−0.158303	−	0.987391i	$-0.550602\pi$
$29$	8660.86	−	3152.29i	0.355113	−	0.129251i	0.513416	+	0.858140i	$0.328380\pi$
$30$	4420.29	−	56745.8i	0.163715	−	2.10170i
$31$	−22878.8	−	13209.1i	−0.767978	−	0.443392i	0.0641749	−	0.997939i	$-0.479558\pi$
$31$	−22878.8	−	13209.1i	−0.767978	−	0.443392i	−0.832153	+	0.554546i	$0.812892\pi$
$32$	32742.3	+	1298.29i	0.999215	+	0.0396208i
$33$	60904.9	−	51105.3i	1.69477	−	1.42208i
$34$	55785.4	−	15518.8i	1.41933	−	0.394839i
$35$	55813.3	−	9841.39i	1.30177	−	0.229537i
$36$	−556.314	−	29193.0i	−0.0119237	−	0.625707i
$37$	−39469.9			−0.779222			−0.389611	−	0.920979i	$-0.627391\pi$
$37$	−39469.9			−0.779222			−0.389611	+	0.920979i	$0.627391\pi$
$38$	27063.8	+	47733.5i	0.493217	+	0.869906i
$39$			25064.3i			0.422535i
$40$	−88373.5	−	58188.5i	−1.38084	−	0.909195i
$41$	−20666.9	−	117208.i	−0.299863	−	1.70061i	−0.646751	−	0.762702i	$-0.723873\pi$
$41$	−20666.9	−	117208.i	−0.299863	−	1.70061i	0.346887	−	0.937907i	$-0.387239\pi$
$42$	72766.8	−	20242.7i	0.982167	−	0.273226i
$43$	7518.77	+	8960.52i	0.0945674	+	0.112701i	0.811253	−	0.584696i	$-0.198786\pi$
$43$	7518.77	+	8960.52i	0.0945674	+	0.112701i	−0.716685	+	0.697397i	$0.754342\pi$
$44$	−28434.0	−	145040.i	−0.333795	−	1.70267i
$45$	−47141.6	+	81651.7i	−0.517329	+	0.896041i
$46$	−11706.2	+	150279.i	−0.120266	+	1.54392i
$47$	−10078.3	−	27689.8i	−0.0970717	−	0.266702i	0.881647	−	0.471910i	$-0.156435\pi$
$47$	−10078.3	−	27689.8i	−0.0970717	−	0.266702i	−0.978718	+	0.205208i	$0.934213\pi$
$48$	−124719.	−	65802.8i	−1.12774	−	0.595005i
$49$	−21221.0	−	36755.9i	−0.180376	−	0.312420i
$50$	93434.6	+	195487.i	0.747477	+	1.56389i
$51$	−245396.	−	43270.0i	−1.84994	−	0.326194i
$52$	40788.7	+	22524.3i	0.290088	+	0.160192i
$53$	174814.	+	146686.i	1.17422	+	0.985285i	1.00000		0.000577322i	$0.000183767\pi$
$53$	174814.	+	146686.i	1.17422	+	0.985285i	0.174217	+	0.984707i	$0.444261\pi$
$54$	31100.0	−	68387.8i	0.197506	−	0.434307i
$55$	−163233.	+	448478.i	−0.981113	+	2.69559i
$56$	32450.2	−	136609.i	0.184779	−	0.777885i
$57$	−16498.3	−	235558.i	−0.0890872	−	1.27196i
$58$	−41714.5	+	60799.1i	−0.213798	+	0.311611i
$59$	41775.2	−	114777.i	0.203406	−	0.558852i	−0.795483	−	0.605975i	$-0.792783\pi$
$59$	41775.2	−	114777.i	0.203406	−	0.558852i	0.998889	+	0.0471229i	$0.0150052\pi$
$60$	235143.	+	389928.i	1.08862	+	1.80522i
$61$	144271.	+	121058.i	0.635609	+	0.533339i	0.902666	−	0.430342i	$-0.141607\pi$
$61$	144271.	+	121058.i	0.635609	+	0.533339i	−0.267057	+	0.963681i	$0.586051\pi$
$62$	210356.	−	20425.0i	0.882634	−	0.0857010i
$63$	−123213.	−	21725.8i	−0.492761	−	0.0868871i
$64$	−219164.	+	143828.i	−0.836045	+	0.548660i
$65$	−75228.7	−	130300.i	−0.273932	−	0.474465i
$66$	−158760.	+	615913.i	−0.552217	+	2.14234i
$67$	−11676.7	−	32081.5i	−0.0388236	−	0.106667i	0.918766	−	0.394802i	$-0.129187\pi$
$67$	−11676.7	−	32081.5i	−0.0388236	−	0.106667i	−0.957590	+	0.288135i	$0.906965\pi$
$68$	−290943.	+	360464.i	−0.925298	+	1.14640i
$69$	324333.	−	561762.i	0.987289	−	1.71003i
$70$	−317530.	+	323638.i	−0.925742	+	0.943551i
$71$	−111509.	−	132891.i	−0.311555	−	0.371297i	0.587431	−	0.809274i	$-0.300139\pi$
$71$	−111509.	−	132891.i	−0.311555	−	0.371297i	−0.898986	+	0.437978i	$0.855695\pi$
$72$	139393.	+	187436.i	0.373459	+	0.502175i
$73$	50165.7	+	284504.i	0.128955	+	0.731340i	0.978880	+	0.204436i	$0.0655362\pi$
$73$	50165.7	+	284504.i	0.128955	+	0.731340i	−0.849925	+	0.526904i	$0.823353\pi$
$74$	256918.	−	183568.i	0.634015	−	0.453004i
$75$		−	932407.i		−	2.21015i
$76$	−398165.	−	184838.i	−0.907030	−	0.421065i
$77$	−633326.			−1.38725
$78$	−116570.	−	163149.i	−0.245642	−	0.343796i
$79$	−352757.	+	62200.6i	−0.715475	+	0.126158i	−0.519524	−	0.854456i	$-0.673891\pi$
$79$	−352757.	+	62200.6i	−0.715475	+	0.126158i	−0.195951	+	0.980614i	$0.562779\pi$
$80$	845866.	−	32250.1i	1.65208	−	0.0629885i
$81$	−502439.	+	421597.i	−0.945428	+	0.793309i
$82$	679638.	+	666810.i	1.23264	+	1.20937i
$83$	−179112.	−	103410.i	−0.313249	−	0.180854i	0.335131	−	0.942172i	$-0.391220\pi$
$83$	−179112.	−	103410.i	−0.313249	−	0.180854i	−0.648379	+	0.761317i	$0.724553\pi$
$84$	−379508.	+	470190.i	−0.640299	+	0.793297i
$85$	1.40559e6	−	511594.i	2.28877	−	0.833046i
$86$	−90615.1	−	23357.3i	−0.142464	−	0.0367221i
$87$	274793.	−	158652.i	0.417300	−	0.240928i
$88$	859642.	+	811855.i	1.26145	+	1.19133i
$89$	−1104.09	+	6261.61i	−0.00156615	+	0.00888210i	−0.985581	−	0.169205i	$-0.945880\pi$
$89$	−1104.09	+	6261.61i	−0.00156615	+	0.00888210i	0.984015	+	0.178087i	$0.0569910\pi$
$90$	−72894.2	−	750736.i	−0.0999920	−	1.02982i
$91$	128337.	−	152946.i	0.170305	−	0.202962i
$92$	−622724.	−	1.03264e6i	−0.799709	−	1.32613i
$93$	−854651.	−	311068.i	−1.06253	−	0.386728i
$94$	194382.	+	133366.i	0.234031	+	0.160569i
$95$	792778.	+	1.17506e6i	0.924658	+	1.37053i
$96$	1.11786e6	−	151722.i	1.26349	−	0.171489i
$97$	−1.31216e6	−	477588.i	−1.43771	−	0.523285i	−0.498582	−	0.866843i	$-0.666146\pi$
$97$	−1.31216e6	−	477588.i	−1.43771	−	0.523285i	−0.939132	+	0.343558i	$0.888368\pi$
$98$	309077.	+	140556.i	0.328389	+	0.149338i
$99$	677241.	−	807104.i	0.697971	−	0.831810i
$100$	−1.51736e6	−	837915.i	−1.51736	−	0.837915i
$101$	−272563.	+	1.54578e6i	−0.264547	+	1.50032i	0.505774	+	0.862666i	$0.331207\pi$
$101$	−272563.	+	1.54578e6i	−0.264547	+	1.50032i	−0.770321	+	0.637656i	$0.779904\pi$
$102$	1.79858e6	−	859645.i	1.69484	−	0.810063i
$103$	−461125.	+	266231.i	−0.421994	+	0.243639i	−0.695930	−	0.718109i	$-0.745008\pi$
$103$	−461125.	+	266231.i	−0.421994	+	0.243639i	0.273936	+	0.961748i	$0.411674\pi$
$104$	−370259.	+	43086.5i	−0.329159	+	0.0383038i
$105$	1.83346e6	−	667326.i	1.58381	−	0.576461i
$106$	−1.82011e6	−	141780.i	−1.52820	−	0.119041i
$107$	678422.	+	391687.i	0.553795	+	0.319734i	0.750651	−	0.660699i	$-0.229740\pi$
$107$	678422.	+	391687.i	0.553795	+	0.319734i	−0.196856	+	0.980432i	$0.563073\pi$
$108$	115624.	+	589791.i	0.0917860	+	0.468195i
$109$	−349520.	+	293282.i	−0.269894	+	0.226468i	−0.767682	−	0.640831i	$-0.778590\pi$
$109$	−349520.	+	293282.i	−0.269894	+	0.226468i	0.497789	+	0.867298i	$0.334146\pi$
$110$	−1.02328e6	−	3.67840e6i	−0.768808	−	2.76364i
$111$	−1.33819e6	+	235959.i	−0.978474	+	0.172531i
$112$	424121.	+	1.04014e6i	0.301881	+	0.740349i
$113$	−408072.			−0.282815			−0.141407	−	0.989952i	$-0.545163\pi$
$113$	−408072.			−0.282815			−0.141407	+	0.989952i	$0.545163\pi$
$114$	1.20293e6	+	1.45657e6i	0.811946	+	0.983140i
$115$			3.89385e6i			2.56027i
$116$	−11238.7	−	589761.i	−0.00720019	−	0.377835i
$117$	57677.2	+	327103.i	0.0360119	+	0.204234i
$118$	261883.	+	941394.i	0.159390	+	0.572961i
$119$	1.27589e6	+	1.52055e6i	0.757133	+	0.902316i
$120$	−3.34408e6	−	1.44451e6i	−1.93523	−	0.835944i
$121$	1.78087e6	−	3.08456e6i	1.00525	−	1.74115i
$122$	−1.50211e6	−	117009.i	−0.827222	−	0.0644376i
$123$	−1.40138e6	−	3.85026e6i	−0.753080	−	2.06907i
$124$	−1.27426e6	+	1.11128e6i	−0.668333	+	0.582854i
$125$	1.18401e6	+	2.05077e6i	0.606214	+	1.04999i
$126$	903065.	−	431627.i	0.451447	−	0.215773i
$127$	−1.67771e6	−	295826.i	−0.819043	−	0.144419i	−0.251599	−	0.967832i	$-0.580956\pi$
$127$	−1.67771e6	−	295826.i	−0.819043	−	0.144419i	−0.567444	+	0.823412i	$0.692068\pi$
$128$	757664.	−	1.95550e6i	0.361282	−	0.932456i
$129$	308484.	+	258849.i	0.143702	+	0.120581i
$130$	1.09568e6	+	498272.i	0.498718	+	0.226797i
$131$	123039.	−	338046.i	0.0547304	−	0.150370i	−0.909315	−	0.416109i	$-0.863394\pi$
$131$	123039.	−	338046.i	0.0547304	−	0.150370i	0.964045	+	0.265738i	$0.0856157\pi$
$132$	−1.83111e6	−	4.74747e6i	−0.796145	−	2.06415i
$133$	−1.10546e6	+	1.52189e6i	−0.469880	+	0.646886i
$134$	225212.	+	154518.i	0.0936001	+	0.0642193i
$135$	663768.	−	1.82369e6i	0.269783	−	0.741223i
$136$	217353.	−	3.69946e6i	0.0864072	−	1.47069i
$137$	−139818.	−	117322.i	−0.0543755	−	0.0456264i	0.615195	−	0.788375i	$-0.289077\pi$
$137$	−139818.	−	117322.i	−0.0543755	−	0.0456264i	−0.669570	+	0.742749i	$0.733522\pi$
$138$	501510.	+	5.16504e6i	0.190828	+	1.96533i
$139$	4.05123e6	+	714341.i	1.50849	+	0.265987i	0.865897	−	0.500222i	$-0.166748\pi$
$139$	4.05123e6	+	714341.i	1.50849	+	0.265987i	0.642592	+	0.766209i	$0.277859\pi$
$140$	561677.	−	3.58340e6i	0.204693	−	1.30591i
$141$	−507230.	−	878547.i	−0.180945	−	0.313406i
$142$	1.34389e6	+	346406.i	0.469352	+	0.120982i
$143$	575050.	+	1.57994e6i	0.196652	+	0.540296i
$144$	−1.77907e6	−	571764.i	−0.595807	−	0.191483i
$145$	−952363.	+	1.64954e6i	−0.312391	+	0.541077i
$146$	−1.64972e6	−	1.61858e6i	−0.530092	−	0.520087i
$147$	−939212.	−	1.11931e6i	−0.295673	−	0.352369i
$148$	−818586.	+	2.38977e6i	−0.252510	+	0.737174i
$149$	227416.	+	1.28974e6i	0.0687483	+	0.389891i	0.999694	+	0.0247336i	$0.00787376\pi$
$149$	227416.	+	1.28974e6i	0.0687483	+	0.389891i	−0.930946	+	0.365158i	$0.881015\pi$
$150$	4.33647e6	+	6.06922e6i	1.28488	+	1.79829i
$151$		−	4.97682e6i		−	1.44551i	−0.691104	−	0.722755i	$-0.742875\pi$
$151$		−	4.97682e6i		−	1.44551i	0.691104	−	0.722755i	$-0.257125\pi$
$152$	3.45138e6	−	648652.i	0.982794	−	0.184706i
$153$	−3.30213e6			−0.921977
$154$	4.12245e6	−	2.94549e6i	1.12874	−	0.806484i
$155$	5.37665e6	−	948049.i	1.44383	−	0.254587i
$156$	1.51756e6	+	519821.i	0.399734	+	0.136924i
$157$	1.47510e6	−	1.23776e6i	0.381173	−	0.319842i	−0.431990	−	0.901879i	$-0.642188\pi$
$157$	1.47510e6	−	1.23776e6i	0.381173	−	0.319842i	0.813163	+	0.582036i	$0.197744\pi$
$158$	2.00688e6	−	2.04549e6i	0.508804	−	0.518593i
$159$	6.80382e6	+	3.92818e6i	1.69263	+	0.977238i
$160$	−5.35593e6	+	4.14391e6i	−1.30760	+	1.01170i
$161$	−4.85553e6	+	1.76727e6i	−1.16348	+	0.423472i
$162$	1.30970e6	−	5.08102e6i	0.308055	−	1.19510i
$163$	−220730.	+	127438.i	−0.0509680	+	0.0294264i	−0.525267	−	0.850937i	$-0.676035\pi$
$163$	−220730.	+	127438.i	−0.0509680	+	0.0294264i	0.474299	+	0.880364i	$0.342701\pi$
$164$	−7.52513e6	−	1.17952e6i	−1.70601	−	0.267407i
$165$	−2.85316e6	+	1.61811e7i	−0.635146	+	3.60209i
$166$	1.64682e6	−	159901.i	0.360015	−	0.0349564i
$167$	−1.97896e6	+	2.35843e6i	−0.424901	+	0.506377i	−0.935444	−	0.353475i	$-0.885000\pi$
$167$	−1.97896e6	+	2.35843e6i	−0.424901	+	0.506377i	0.510543	+	0.859852i	$0.329444\pi$
$168$	283517.	−	4.82559e6i	0.0597931	−	1.01771i
$169$	4.03764e6	+	1.46958e6i	0.836502	+	0.304462i
$170$	−6.76996e6	+	9.86726e6i	−1.37797	+	2.00840i
$171$	−757370.	−	3.03620e6i	−0.151468	−	0.607214i
$172$	698463.	−	269399.i	0.137264	−	0.0529432i
$173$	−6.81949e6	−	2.48209e6i	−1.31708	−	0.479379i	−0.414561	−	0.910022i	$-0.636065\pi$
$173$	−6.81949e6	−	2.48209e6i	−1.31708	−	0.479379i	−0.902523	+	0.430642i	$0.858287\pi$
$174$	−1.05082e6	+	2.31071e6i	−0.199471	+	0.438630i
$175$	−4.77421e6	+	5.68969e6i	−0.890815	+	1.06163i
$176$	−9.37139e6	−	1.28648e6i	−1.71896	−	0.235974i
$177$	730193.	−	4.14113e6i	0.131679	−	0.746791i
$178$	−21934.9	−	45893.0i	−0.00388935	−	0.00813741i
$179$	527412.	−	304502.i	0.0919583	−	0.0530922i	−0.453316	−	0.891350i	$-0.649759\pi$
$179$	527412.	−	304502.i	0.0919583	−	0.0530922i	0.545274	+	0.838258i	$0.316426\pi$
$180$	3.96603e6	+	4.54767e6i	0.680047	+	0.779779i
$181$	1.18432e6	−	431056.i	0.199725	−	0.0726938i	−0.240221	−	0.970718i	$-0.577220\pi$
$181$	1.18432e6	−	431056.i	0.199725	−	0.0726938i	0.439946	+	0.898024i	$0.354998\pi$
$182$	−124045.	+	1.59243e6i	−0.0205762	+	0.264148i
$183$	5.61508e6	+	3.24187e6i	0.916226	+	0.528984i
$184$	8.85607e6	+	3.82547e6i	1.42163	+	0.614089i
$185$	6.24853e6	−	5.24314e6i	0.986876	−	0.828087i
$186$	7.00983e6	−	1.95004e6i	1.08935	−	0.303043i
$187$	−1.64614e7	+	2.90259e6i	−2.51734	+	0.443875i
$188$	−1.88554e6	+	35931.6i	−0.283767	+	0.00540759i
$189$	2.57535e6			0.381462
$190$	−1.06254e7	−	3.96161e6i	−1.54911	−	0.577579i
$191$		−	8.09114e6i		−	1.16121i	−0.814187	−	0.580603i	$-0.802817\pi$
$191$		−	8.09114e6i		−	1.16121i	0.814187	−	0.580603i	$-0.197183\pi$
$192$	−6.57072e6	+	6.18656e6i	−0.928345	+	0.874069i
$193$	829585.	+	4.70481e6i	0.115396	+	0.654441i	0.986554	+	0.163438i	$0.0522584\pi$
$193$	829585.	+	4.70481e6i	0.115396	+	0.654441i	−0.871158	+	0.491003i	$0.836631\pi$
$194$	1.07623e7	−	2.99393e6i	1.47401	−	0.410050i
$195$	−3.32952e6	−	3.96796e6i	−0.449032	−	0.535135i
$196$	−2.66555e6	+	522560.i	−0.354013	+	0.0694014i
$197$	5.50307e6	−	9.53160e6i	0.719791	−	1.24671i	−0.241292	−	0.970453i	$-0.577571\pi$
$197$	5.50307e6	−	9.53160e6i	0.719791	−	1.24671i	0.961082	−	0.276262i	$-0.0890956\pi$
$198$	−654590.	+	8.40334e6i	−0.0843284	+	1.08257i
$199$	−578626.	−	1.58976e6i	−0.0734241	−	0.201731i	0.897551	−	0.440910i	$-0.145344\pi$
$199$	−578626.	−	1.58976e6i	−0.0734241	−	0.201731i	−0.970976	+	0.239179i	$0.923122\pi$
$200$	1.37738e7	−	1.60284e6i	1.72173	−	0.200355i
$201$	−587676.	−	1.01789e6i	−0.0723686	−	0.125346i
$202$	−5.41501e6	−	1.13295e7i	−0.656970	−	1.37453i
$203$	−2.48918e6	−	438909.i	−0.297555	−	0.0524670i
$204$	−7.70924e6	+	1.39605e7i	−0.908073	+	1.64441i
$205$	1.88415e7	+	1.58099e7i	2.18703	+	1.83513i
$206$	1.76336e6	−	3.87756e6i	0.201716	−	0.443565i
$207$	2.94002e6	−	8.07764e6i	0.331466	−	0.910696i
$208$	2.20970e6	−	2.00247e6i	0.245552	−	0.222524i
$209$	−6.44438e6	−	1.44700e7i	−0.705899	−	1.58500i
$210$	−8.83076e6	+	1.28709e7i	−0.953543	+	1.38980i
$211$	−1.50933e6	+	4.14684e6i	−0.160670	+	0.441438i	−0.993738	−	0.111732i	$-0.964360\pi$
$211$	−1.50933e6	+	4.14684e6i	−0.160670	+	0.441438i	0.833068	+	0.553171i	$0.186582\pi$
$212$	1.25069e7	−	7.54217e6i	1.31263	−	0.791569i
$213$	−4.57505e6	−	3.83893e6i	−0.473432	−	0.397257i
$214$	−6.23766e6	+	605658.i	−0.636474	+	0.0617997i
$215$	−2.38061e6	−	419766.i	−0.239537	−	0.0422368i
$216$	−3.49564e6	−	3.30132e6i	−0.346869	−	0.327587i
$217$	3.62245e6	+	6.27426e6i	0.354506	+	0.614022i
$218$	911090.	−	3.53459e6i	0.0879411	−	0.341169i
$219$	3.40164e6	+	9.34593e6i	0.323859	+	0.889796i
$220$	2.37684e7	+	1.91844e7i	2.23219	+	1.80169i
$221$	2.63477e6	−	4.56356e6i	0.244099	−	0.422792i
$222$	7.61315e6	−	7.75961e6i	0.695834	−	0.709220i
$223$	2.09941e6	+	2.50198e6i	0.189314	+	0.225615i	0.852350	−	0.522972i	$-0.175177\pi$
$223$	2.09941e6	+	2.50198e6i	0.189314	+	0.225615i	−0.663036	+	0.748588i	$0.730732\pi$
$224$	−7.59820e6	−	4.79794e6i	−0.676031	−	0.426885i
$225$	−2.14562e6	−	1.21684e7i	−0.188367	−	1.06828i
$226$	2.65623e6	−	1.89788e6i	0.230112	−	0.164416i
$227$			9.85289e6i			0.842338i	0.906982	+	0.421169i	$0.138380\pi$
$227$			9.85289e6i			0.842338i	−0.906982	+	0.421169i	$0.861620\pi$
$228$	−1.46044e7	−	3.88644e6i	−1.23219	−	0.327904i
$229$	−2.34766e7			−1.95492			−0.977459	−	0.211123i	$-0.932288\pi$
$229$	−2.34766e7			−1.95492			−0.977459	+	0.211123i	$0.932288\pi$
$230$	−1.81096e7	−	2.53458e7i	−1.48842	−	2.08316i
$231$	−2.14723e7	+	3.78615e6i	−1.74198	+	0.307158i
$232$	2.81604e6	+	3.78661e6i	0.225514	+	0.303240i
$233$	9.34190e6	−	7.83879e6i	0.738529	−	0.619699i	−0.193913	−	0.981019i	$-0.562118\pi$
$233$	9.34190e6	−	7.83879e6i	0.738529	−	0.619699i	0.932442	+	0.361319i	$0.117674\pi$
$234$	−1.89674e6	−	1.86094e6i	−0.148033	−	0.145239i
$235$	5.27378e6	+	3.04482e6i	0.406367	+	0.234616i
$236$	−6.08292e6	−	4.90975e6i	−0.462781	−	0.373528i
$237$	−1.15880e7	+	4.21770e6i	−0.870493	+	0.316833i
$238$	−1.53768e7	−	3.96359e6i	−1.14061	−	0.294007i
$239$	−823133.	+	475236.i	−0.0602943	+	0.0348109i	−0.529844	−	0.848095i	$-0.677750\pi$
$239$	−823133.	+	475236.i	−0.0602943	+	0.0348109i	0.469550	+	0.882906i	$0.344416\pi$
$240$	2.84855e7	−	6.15017e6i	2.06058	−	0.444891i
$241$	1.56997e6	−	8.90376e6i	0.112161	−	0.636096i	−0.875956	−	0.482391i	$-0.839768\pi$
$241$	1.56997e6	−	8.90376e6i	0.112161	−	0.636096i	0.988117	−	0.153705i	$-0.0491204\pi$
$242$	2.75372e6	+	2.83605e7i	0.194301	+	2.00110i
$243$	−1.01138e7	+	1.20532e7i	−0.704851	+	0.840008i
$244$	1.03217e7	−	6.22443e6i	0.710531	−	0.428480i
$245$	8.24213e6	+	2.99989e6i	0.560455	+	0.203989i
$246$	2.70288e7	+	1.85445e7i	1.81561	+	1.24569i
$247$	4.80035e6	+	1.37590e6i	0.318553	+	0.0913050i
$248$	3.12602e6	−	1.31599e7i	0.204945	−	0.862777i
$249$	−6.69081e6	−	2.43526e6i	−0.433392	−	0.157742i
$250$	−1.72448e7	−	7.84223e6i	−1.10366	−	0.501903i
$251$	1.13473e7	−	1.35232e7i	0.717585	−	0.855184i	−0.276809	−	0.960925i	$-0.589277\pi$
$251$	1.13473e7	−	1.35232e7i	0.717585	−	0.855184i	0.994394	+	0.105741i	$0.0337213\pi$
$252$	−3.87080e6	+	7.00955e6i	−0.241880	+	0.438015i
$253$	7.55596e6	−	4.28520e7i	0.466582	−	2.64612i
$254$	1.22964e7	−	5.87717e6i	0.750373	−	0.358647i
$255$	4.45969e7	−	2.57480e7i	2.68958	−	1.55283i
$256$	4.16293e6	+	1.62525e7i	0.248130	+	0.968727i
$257$	1.02742e7	−	3.73949e6i	0.605267	−	0.220299i	−0.0211641	−	0.999776i	$-0.506737\pi$
$257$	1.02742e7	−	3.73949e6i	0.605267	−	0.220299i	0.626431	+	0.779477i	$0.284515\pi$
$258$	−3.21185e6	−	250192.i	−0.187024	−	0.0145685i
$259$	9.37403e6	+	5.41210e6i	0.539544	+	0.311506i
$260$	−9.44940e6	+	1.85248e6i	−0.537631	+	0.105398i
$261$	3.22112e6	−	2.70284e6i	0.181169	−	0.152019i
$262$	771313.	+	2.77265e6i	0.0428871	+	0.154167i
$263$	−3.02067e6	+	532626.i	−0.166049	+	0.0292789i	−0.256054	−	0.966662i	$-0.582423\pi$
$263$	−3.02067e6	+	532626.i	−0.166049	+	0.0292789i	0.0900055	+	0.995941i	$0.471312\pi$
$264$	3.39988e7	+	2.23861e7i	1.84778	+	1.21665i
$265$	−4.71606e7			−2.53420
$266$	117589.	−	1.50476e7i	0.00624772	−	0.799506i
$267$			218894.i			0.0115001i
$268$	−2.18459e6	+	41630.4i	−0.113492	+	0.00216275i
$269$	−2.69801e6	−	1.53012e7i	−0.138607	−	0.786082i	−0.972279	−	0.233822i	$-0.924877\pi$
$269$	−2.69801e6	−	1.53012e7i	−0.138607	−	0.786082i	0.833672	−	0.552260i	$-0.186234\pi$
$270$	4.16107e6	+	1.49578e7i	0.211404	+	0.759937i
$271$	−1.80574e7	−	2.15199e7i	−0.907291	−	1.08127i	−0.996360	−	0.0852419i	$-0.972834\pi$
$271$	−1.80574e7	−	2.15199e7i	−0.907291	−	1.08127i	0.0890692	−	0.996025i	$-0.471611\pi$
$272$	1.57908e7	+	2.50914e7i	0.784688	+	1.24686i
$273$	3.43681e6	−	5.95273e6i	0.168915	−	0.292569i
$274$	1.45575e6	+	113398.i	0.0707677	+	0.00551255i
$275$	−2.13922e7	−	5.87745e7i	−1.02862	−	2.82612i
$276$	−2.72862e7	−	3.12879e7i	−1.29782	−	1.48816i
$277$	4.89627e6	+	8.48060e6i	0.230370	+	0.399013i	0.957917	−	0.287045i	$-0.0926729\pi$
$277$	4.89627e6	+	8.48060e6i	0.230370	+	0.399013i	−0.727547	+	0.686058i	$0.759340\pi$
$278$	−2.96925e7	+	1.41918e7i	−1.38202	+	0.660546i
$279$	−1.18695e7	−	2.09291e6i	−0.546537	−	0.0963692i
$280$	1.30098e7	+	2.59374e7i	0.592646	+	1.18155i
$281$	1.45409e7	+	1.22013e7i	0.655349	+	0.549903i	0.908689	−	0.417474i	$-0.137085\pi$
$281$	1.45409e7	+	1.22013e7i	0.655349	+	0.549903i	−0.253340	+	0.967377i	$0.581529\pi$
$282$	7.38764e6	+	3.35960e6i	0.329426	+	0.149810i
$283$	4.97714e6	−	1.36746e7i	0.219594	−	0.603330i	−0.780158	−	0.625582i	$-0.784862\pi$
$283$	4.97714e6	−	1.36746e7i	0.219594	−	0.603330i	0.999752	+	0.0222523i	$0.00708372\pi$
$284$	−1.03587e7	+	3.99538e6i	−0.452222	+	0.174423i
$285$	3.39031e7	+	3.50999e7i	1.46455	+	1.51625i
$286$	−1.10912e7	−	7.60967e6i	−0.474109	−	0.325288i
$287$	−1.11631e7	+	3.06704e7i	−0.472215	+	1.29740i
$288$	1.42395e7	−	4.55243e6i	0.596098	−	0.190575i
$289$	2.16412e7	+	1.81592e7i	0.896579	+	0.752319i
$290$	−1.47262e6	−	1.51665e7i	−0.0603804	−	0.621857i
$291$	−4.73427e7	−	8.34780e6i	−1.92121	−	0.338761i
$292$	1.82661e7	+	2.86310e6i	0.733665	+	0.114997i
$293$	−1.65845e6	−	2.87252e6i	−0.0659324	−	0.114198i	0.831175	−	0.556011i	$-0.187669\pi$
$293$	−1.65845e6	−	2.87252e6i	−0.0659324	−	0.114198i	−0.897107	+	0.441813i	$0.854336\pi$
$294$	1.13192e7	+	2.91769e6i	0.445426	+	0.114815i
$295$	8.63329e6	+	2.37198e7i	0.336287	+	0.923941i
$296$	−5.78607e6	−	1.93626e7i	−0.223104	−	0.746600i
$297$	−1.08436e7	+	1.87818e7i	−0.413910	+	0.716913i
$298$	−7.47867e6	−	7.33751e6i	−0.282602	−	0.277268i
$299$	8.81749e6	+	1.05083e7i	0.329861	+	0.393114i
$300$	−5.64539e7	−	1.93376e7i	−2.09089	−	0.716208i
$301$	−557030.	−	3.15907e6i	−0.0204258	−	0.115840i
$302$	2.31464e7	+	3.23952e7i	0.840354	+	1.17614i
$303$			5.40377e7i			1.94254i
$304$	−1.94490e7	+	2.02740e7i	−0.692271	+	0.721638i
$305$	−3.89209e7			−1.37178
$306$	2.14942e7	−	1.53577e7i	0.750167	−	0.535995i
$307$	−2.45679e6	+	433198.i	−0.0849088	+	0.0149717i	−0.215941	−	0.976406i	$-0.569282\pi$
$307$	−2.45679e6	+	433198.i	−0.0849088	+	0.0149717i	0.131032	+	0.991378i	$0.458171\pi$
$308$	−1.31348e7	+	3.83456e7i	−0.449544	+	1.31239i
$309$	−1.40424e7	+	1.17830e7i	−0.475956	+	0.399374i
$310$	−3.05885e7	+	3.11770e7i	−1.02677	+	1.04652i
$311$	2.78492e7	+	1.60787e7i	0.925829	+	0.534528i	0.885490	−	0.464658i	$-0.153823\pi$
$311$	2.78492e7	+	1.60787e7i	0.925829	+	0.534528i	0.0403392	+	0.999186i	$0.487156\pi$
$312$	−1.22957e7	+	3.67429e6i	−0.404845	+	0.120979i
$313$	1.80576e7	−	6.57241e6i	0.588879	−	0.214334i	−0.0303573	−	0.999539i	$-0.509665\pi$
$313$	1.80576e7	−	6.57241e6i	0.588879	−	0.214334i	0.619236	+	0.785205i	$0.287442\pi$
$314$	−3.84513e6	+	1.49172e7i	−0.124200	+	0.481836i
$315$	2.23921e7	−	1.29281e7i	0.716412	−	0.413621i
$316$	−3.54997e6	+	2.26482e7i	−0.112503	+	0.717749i
$317$	−185521.	+	1.05214e6i	−0.00582393	+	0.0330292i	−0.987581	−	0.157109i	$-0.949783\pi$
$317$	−185521.	+	1.05214e6i	−0.00582393	+	0.0330292i	0.981757	+	0.190138i	$0.0608937\pi$
$318$	−6.25568e7	+	6.07407e6i	−1.94533	+	0.188885i
$319$	1.36817e7	−	1.63052e7i	0.421472	−	0.502291i
$320$	1.55902e7	−	5.18831e7i	0.475775	−	1.58335i
$321$	2.53429e7	+	9.22404e6i	0.766197	+	0.278873i
$322$	2.33863e7	−	3.40857e7i	0.700478	−	1.02095i
$323$	−2.17580e7	+	4.46233e7i	−0.645672	+	1.32420i
$324$	1.51059e7	+	3.91646e7i	0.444131	+	1.15149i
$325$	1.85288e7	+	6.74393e6i	0.539756	+	0.196455i
$326$	844079.	−	1.85610e6i	0.0243630	−	0.0535733i
$327$	−1.00968e7	+	1.20330e7i	−0.288764	+	0.344135i
$328$	5.44683e7	−	2.73204e7i	1.54356	−	0.774222i
$329$	−1.40325e6	+	7.95820e6i	−0.0394045	+	0.223474i
$330$	−5.66837e7	−	1.18595e8i	−1.57731	−	3.30009i
$331$	5.80881e6	−	3.35372e6i	0.160178	−	0.0924789i	−0.417768	−	0.908554i	$-0.637188\pi$
$331$	5.80881e6	−	3.35372e6i	0.160178	−	0.0924789i	0.577946	+	0.816075i	$0.303854\pi$
$332$	−9.97579e6	+	8.69990e6i	−0.272605	+	0.237739i
$333$	−1.69211e7	+	6.15879e6i	−0.458244	+	0.166787i
$334$	1.91277e6	−	2.45554e7i	0.0513362	−	0.659032i
$335$	6.11021e6	+	3.52773e6i	0.162526	+	0.0938342i
$336$	2.05976e7	+	3.27294e7i	0.542998	+	0.862819i
$337$	−1.65769e6	+	1.39097e6i	−0.0433125	+	0.0363435i	−0.664187	−	0.747567i	$-0.731222\pi$
$337$	−1.65769e6	+	1.39097e6i	−0.0433125	+	0.0363435i	0.620874	+	0.783910i	$0.286778\pi$
$338$	−3.31166e7	+	9.21259e6i	−0.857621	+	0.238579i
$339$	−1.38353e7	+	2.43954e6i	−0.355132	+	0.0626193i
$340$	−1.82397e6	−	9.57139e7i	−0.0464066	−	2.43522i
$341$	−6.10100e7			−1.53864
$342$	1.90507e7	+	1.62408e7i	0.476248	+	0.406004i
$343$			4.39032e7i			1.08796i
$344$	−3.29351e6	+	5.00201e6i	−0.0809066	+	0.122877i
$345$	2.32782e7	+	1.32017e8i	0.566881	+	3.21494i
$346$	5.59332e7	−	1.55599e7i	1.35033	−	0.375645i
$347$	3.31450e7	+	3.95007e7i	0.793286	+	0.945401i	0.999452	−	0.0331159i	$-0.0105431\pi$
$347$	3.31450e7	+	3.95007e7i	0.793286	+	0.945401i	−0.206166	+	0.978517i	$0.566099\pi$
$348$	−3.90675e6	−	1.99281e7i	−0.0926996	−	0.472855i
$349$	−1.12962e7	+	1.95655e7i	−0.265739	+	0.460273i	−0.967757	−	0.251886i	$-0.918949\pi$
$349$	−1.12962e7	+	1.95655e7i	−0.265739	+	0.460273i	0.702018	+	0.712159i	$0.252283\pi$
$350$	4.61453e6	−	5.92394e7i	0.107628	−	1.38168i
$351$	−2.33838e6	−	6.42465e6i	−0.0540747	−	0.148569i
$352$	6.69835e7	−	3.52108e7i	1.53582	−	0.807325i
$353$	2.78953e7	+	4.83161e7i	0.634172	+	1.09842i	0.986690	+	0.162613i	$0.0519921\pi$
$353$	2.78953e7	+	4.83161e7i	0.634172	+	1.09842i	−0.352518	+	0.935805i	$0.614675\pi$
$354$	1.45067e7	+	3.03515e7i	0.327009	+	0.684179i
$355$	3.53062e7	+	6.22544e6i	0.789162	+	0.139150i
$356$	356220.	+	196711.i	0.00789529	+	0.00435992i
$357$	5.23480e7	+	4.39252e7i	1.15052	+	0.965403i
$358$	−2.01685e6	+	4.43497e6i	−0.0439566	+	0.0966589i
$359$	1.46604e7	−	4.02790e7i	0.316855	−	0.870553i	−0.674373	−	0.738391i	$-0.735586\pi$
$359$	1.46604e7	−	4.02790e7i	0.316855	−	0.870553i	0.991228	−	0.132162i	$-0.0421919\pi$
$360$	−4.69662e7	−	1.11564e7i	−1.00665	−	0.239120i
$361$	−4.60200e7	−	9.77109e6i	−0.978194	−	0.207693i
$362$	−5.70418e6	+	8.31389e6i	−0.120245	+	0.175258i
$363$	4.19386e7	−	1.15225e8i	0.876787	−	2.40895i
$364$	−6.59872e6	−	1.09424e7i	−0.136822	−	0.226886i
$365$	−4.57349e7	−	3.83762e7i	−0.940523	−	0.789192i
$366$	−5.16271e7	+	5.01283e6i	−1.05302	+	0.102245i
$367$	−1.44081e7	−	2.54054e6i	−0.291481	−	0.0513959i	0.0259958	−	0.999662i	$-0.491724\pi$
$367$	−1.44081e7	−	2.54054e6i	−0.291481	−	0.0513959i	−0.317476	+	0.948266i	$0.602835\pi$
$368$	−7.54376e7	+	1.62874e7i	−1.51372	+	0.326819i
$369$	−2.71489e7	−	4.70232e7i	−0.540347	−	0.935909i
$370$	−1.62880e7	+	6.31895e7i	−0.321560	+	1.24750i
$371$	−2.14044e7	−	5.88080e7i	−0.419161	−	1.15164i
$372$	−3.65591e7	+	4.52948e7i	−0.710176	+	0.879871i
$373$	3.11746e7	−	5.39960e7i	0.600723	−	1.04048i	−0.391988	−	0.919970i	$-0.628213\pi$
$373$	3.11746e7	−	5.39960e7i	0.600723	−	1.04048i	0.992712	−	0.120513i	$-0.0384540\pi$
$374$	9.36510e7	−	9.54527e7i	1.79018	−	1.82462i
$375$	5.24027e7	+	6.24511e7i	0.993711	+	1.18426i
$376$	1.21062e7	−	9.00322e6i	0.227743	−	0.169369i
$377$	1.16520e6	+	6.60819e6i	0.0217459	+	0.123327i
$378$	−1.67635e7	+	1.19775e7i	−0.310377	+	0.221764i
$379$		−	1.04267e8i		−	1.91527i	−0.287986	−	0.957635i	$-0.592986\pi$
$379$		−	1.04267e8i		−	1.91527i	0.287986	−	0.957635i	$-0.407014\pi$
$380$	8.75874e7	−	2.36298e7i	1.59621	−	0.430636i
$381$	−5.86498e7			−1.06045
$382$	3.76306e7	+	5.26669e7i	0.675073	+	0.944816i
$383$	7.49428e7	−	1.32144e7i	1.33393	−	0.235208i	0.539204	−	0.842175i	$-0.318725\pi$
$383$	7.49428e7	−	1.32144e7i	1.33393	−	0.235208i	0.794727	+	0.606967i	$0.207614\pi$
$384$	1.39975e7	−	7.08289e7i	0.247205	−	1.25088i
$385$	1.00262e8	−	8.41302e7i	1.75694	−	1.47425i
$386$	−2.72812e7	−	2.67663e7i	−0.474354	−	0.465400i
$387$	4.62155e6	+	2.66825e6i	0.0797360	+	0.0460356i
$388$	−5.61298e7	+	6.95419e7i	−0.960945	+	1.19056i
$389$	9.58885e7	−	3.49005e7i	1.62899	−	0.592903i	0.643923	−	0.765091i	$-0.277306\pi$
$389$	9.58885e7	−	3.49005e7i	1.62899	−	0.592903i	0.985064	+	0.172188i	$0.0550837\pi$
$390$	4.01268e7	+	1.03432e7i	0.676458	+	0.174367i
$391$	−1.18105e8	+	6.81880e7i	−1.97578	+	1.14072i
$392$	1.49203e7	−	1.57985e7i	0.247696	−	0.262275i
$393$	2.15061e6	−	1.21967e7i	0.0354310	−	0.200939i
$394$	8.50928e6	+	8.76370e7i	0.139125	+	1.43284i
$395$	4.75827e7	−	5.67069e7i	0.772072	−	0.920120i
$396$	−3.48217e7	−	5.77434e7i	−0.560743	−	0.929859i
$397$	−9.19449e7	−	3.34652e7i	−1.46945	−	0.534838i	−0.521502	−	0.853250i	$-0.674628\pi$
$397$	−9.19449e7	−	3.34652e7i	−1.46945	−	0.534838i	−0.947952	+	0.318413i	$0.896850\pi$
$398$	1.11601e7	+	7.65699e6i	0.177019	+	0.121453i
$399$	−2.83813e7	+	5.82068e7i	−0.446800	+	0.916337i
$400$	−8.22020e7	+	7.44930e7i	−1.28441	+	1.16395i
$401$	−5.71668e7	−	2.08070e7i	−0.886566	−	0.322684i	−0.141709	−	0.989908i	$-0.545260\pi$
$401$	−5.71668e7	−	2.08070e7i	−0.886566	−	0.322684i	−0.744856	+	0.667225i	$0.767482\pi$
$402$	8.55932e6	+	3.89244e6i	0.131753	+	0.0599161i
$403$	1.23631e7	−	1.47338e7i	0.188891	−	0.225112i
$404$	8.79389e7	+	4.85615e7i	1.33363	+	0.736457i
$405$	2.35373e7	−	1.33487e8i	0.354317	−	2.00943i
$406$	1.82438e7	−	8.71980e6i	0.272608	−	0.130295i
$407$	−7.89397e7	+	4.55758e7i	−1.17088	+	0.676007i
$408$	−1.47469e7	−	1.26726e8i	−0.217131	−	1.86589i
$409$	−5.54585e7	+	2.01853e7i	−0.810585	+	0.295029i	−0.713865	−	0.700283i	$-0.753057\pi$
$409$	−5.54585e7	+	2.01853e7i	−0.810585	+	0.295029i	−0.0967195	+	0.995312i	$0.530835\pi$
$410$	−1.96172e8	−	1.52811e7i	−2.84634	−	0.221719i
$411$	−5.44179e6	−	3.14182e6i	−0.0783819	−	0.0452538i
$412$	6.55584e6	+	3.34410e7i	0.0937425	+	0.478175i
$413$	−2.56596e7	+	2.15310e7i	−0.364251	+	0.305642i
$414$	1.84306e7	+	6.62526e7i	0.259740	+	0.933688i
$415$	4.20922e7	−	7.42199e6i	0.588921	−	0.103843i
$416$	−5.07023e6	+	2.33115e7i	−0.0704284	+	0.323809i
$417$	1.41623e8			1.95311
$418$	1.09245e8	+	6.42162e7i	1.49580	+	0.879256i
$419$			4.00885e7i			0.544976i	0.962159	+	0.272488i	$0.0878465\pi$
$419$			4.00885e7i			0.544976i	−0.962159	+	0.272488i	$0.912154\pi$
$420$	−2.37919e6	−	1.24850e8i	−0.0321130	−	1.68515i
$421$	1.28786e7	+	7.30379e7i	0.172592	+	0.978818i	0.940887	+	0.338722i	$0.109995\pi$
$421$	1.28786e7	+	7.30379e7i	0.172592	+	0.978818i	−0.768294	+	0.640097i	$0.778894\pi$
$422$	−9.46176e6	−	3.40123e7i	−0.125903	−	0.452583i
$423$	−8.64131e6	−	1.02983e7i	−0.114172	−	0.136064i
$424$	−4.63324e7	+	1.07261e8i	−0.607838	+	1.40716i
$425$	−9.80149e7	+	1.69767e8i	−1.27681	+	2.21149i
$426$	4.76342e7	+	3.71053e6i	0.616155	+	0.0479962i
$427$	−1.76647e7	−	4.85333e7i	−0.226894	−	0.623385i
$428$	3.77854e7	−	3.29527e7i	0.481940	−	0.420300i
$429$	2.89417e7	+	5.01285e7i	0.366566	+	0.634911i
$430$	1.74481e7	−	8.33948e6i	0.219454	−	0.104890i
$431$	1.21488e8	+	2.14217e7i	1.51741	+	0.267560i	0.869415	−	0.494083i	$-0.164496\pi$
$431$	1.21488e8	+	2.14217e7i	1.51741	+	0.267560i	0.647996	+	0.761644i	$0.275607\pi$
$432$	3.81077e7	+	5.23133e6i	0.472674	+	0.0648875i
$433$	−4.13142e7	−	3.46667e7i	−0.508903	−	0.427020i	0.351840	−	0.936060i	$-0.385556\pi$
$433$	−4.13142e7	−	3.46667e7i	−0.508903	−	0.427020i	−0.860743	+	0.509040i	$0.830001\pi$
$434$	−5.27598e7	−	2.39931e7i	−0.645408	−	0.293506i
$435$	−2.24277e7	+	6.16195e7i	−0.272469	+	0.748601i
$436$	1.05083e7	+	2.72447e7i	0.126787	+	0.328718i
$437$	−8.97850e7	−	9.29543e7i	−1.07587	−	1.11385i
$438$	−6.56084e7	−	4.50141e7i	−0.780795	−	0.535706i
$439$	−5.43427e7	+	1.49305e8i	−0.642314	+	1.76474i	0.00201781	+	0.999998i	$0.499358\pi$
$439$	−5.43427e7	+	1.49305e8i	−0.642314	+	1.76474i	−0.644332	+	0.764746i	$0.722865\pi$
$440$	−2.43937e8	−	1.43319e7i	−2.86364	−	0.168247i
$441$	−1.48330e7	−	1.24463e7i	−0.172947	−	0.145119i
$442$	4.07409e6	+	4.19590e7i	0.0471807	+	0.485913i
$443$	−4.72314e7	−	8.32817e6i	−0.543275	−	0.0957940i	−0.104726	−	0.994501i	$-0.533396\pi$
$443$	−4.72314e7	−	8.32817e6i	−0.543275	−	0.0957940i	−0.438549	+	0.898707i	$0.644508\pi$
$444$	−1.34669e7	+	8.59164e7i	−0.153857	+	0.981583i
$445$	−656994.	−	1.13795e6i	−0.00745558	−	0.0129134i
$446$	−2.53018e7	−	6.52188e6i	−0.285198	−	0.0735137i
$447$	1.54206e7	+	4.23679e7i	0.172655	+	0.474367i
$448$	7.17727e7	−	4.10717e6i	0.798224	−	0.0456782i
$449$	−6.27494e7	+	1.08685e8i	−0.693220	+	1.20069i	0.277558	+	0.960709i	$0.410475\pi$
$449$	−6.27494e7	+	1.08685e8i	−0.693220	+	1.20069i	−0.970777	+	0.239982i	$0.922858\pi$
$450$	7.05596e7	+	6.92278e7i	0.774317	+	0.759701i
$451$	−1.76673e8	−	2.10551e8i	−1.92593	−	2.29523i
$452$	−8.46320e6	+	2.47073e7i	−0.0916472	+	0.267554i
$453$	−2.97524e7	−	1.68734e8i	−0.320057	−	1.81514i
$454$	−4.58242e7	−	6.41345e7i	−0.489697	−	0.685368i
$455$			4.12613e7i			0.438035i
$456$	1.13138e8	−	4.26250e7i	1.19320	−	0.449541i
$457$	8.43594e7			0.883863			0.441932	−	0.897049i	$-0.354293\pi$
$457$	8.43594e7			0.883863			0.441932	+	0.897049i	$0.354293\pi$
$458$	1.52814e8	−	1.09186e8i	1.59062	−	1.13650i
$459$	6.69384e7	−	1.18031e7i	0.692209	−	0.122055i
$460$	2.35759e8	+	8.07563e7i	2.42211	+	0.829665i
$461$	−7.39429e6	+	6.20455e6i	−0.0754734	+	0.0633297i	−0.679744	−	0.733450i	$-0.737909\pi$
$461$	−7.39429e6	+	6.20455e6i	−0.0754734	+	0.0633297i	0.604271	+	0.796779i	$0.293465\pi$
$462$	1.22159e8	−	1.24509e8i	1.23879	−	1.26263i
$463$	6.56674e7	+	3.79131e7i	0.661618	+	0.381985i	0.792893	−	0.609361i	$-0.208574\pi$
$463$	6.56674e7	+	3.79131e7i	0.661618	+	0.381985i	−0.131275	+	0.991346i	$0.541907\pi$
$464$	−3.59410e7	−	1.15509e7i	−0.359780	−	0.115627i
$465$	1.76623e8	−	6.42854e7i	1.75666	−	0.639372i
$466$	−2.43514e7	+	9.44719e7i	−0.240639	+	0.933566i
$467$	1.14323e8	−	6.60042e7i	1.12249	−	0.648069i	0.180453	−	0.983584i	$-0.442244\pi$
$467$	1.14323e8	−	6.60042e7i	1.12249	−	0.648069i	0.942035	+	0.335515i	$0.108910\pi$
$468$	2.10012e7	+	3.29180e6i	0.204883	+	0.0321141i
$469$	−1.62580e6	+	9.22038e6i	−0.0157597	+	0.0893779i
$470$	−4.84891e7	+	4.70814e6i	−0.467036	+	0.0453478i
$471$	4.26123e7	−	5.07833e7i	0.407823	−	0.486025i
$472$	6.24294e7	+	3.66790e6i	0.593695	+	0.0348812i
$473$	2.53842e7	+	9.23909e6i	0.239872	+	0.0873063i
$474$	5.58131e7	−	8.13480e7i	0.524084	−	0.763857i
$475$	−1.78575e8	−	5.11840e7i	−1.66625	−	0.477588i
$476$	1.18525e8	−	4.57153e7i	1.09898	−	0.423878i
$477$	9.78329e7	+	3.56083e7i	0.901426	+	0.328092i
$478$	3.14770e6	−	6.92166e6i	0.0288210	−	0.0633763i
$479$	8.79280e7	−	1.04788e8i	0.800056	−	0.953470i	−0.199595	−	0.979878i	$-0.563963\pi$
$479$	8.79280e7	−	1.04788e8i	0.800056	−	0.953470i	0.999651	+	0.0264088i	$0.00840715\pi$
$480$	−1.56815e8	+	1.72514e8i	−1.41796	+	1.55991i
$481$	4.98991e6	−	2.82992e7i	0.0448392	−	0.254296i
$482$	3.11907e7	+	6.52581e7i	0.278537	+	0.582765i
$483$	−1.54057e8	+	8.89448e7i	−1.36722	+	0.789367i
$484$	−1.49825e8	−	1.71797e8i	−1.32144	−	1.51524i
$485$	2.71172e8	−	9.86985e7i	2.37695	−	0.865138i
$486$	9.77557e6	−	1.25495e8i	0.0851595	−	1.09324i
$487$	−1.00103e8	−	5.77947e7i	−0.866686	−	0.500381i	−0.000440313	−	1.00000i	$-0.500140\pi$
$487$	−1.00103e8	−	5.77947e7i	−0.866686	−	0.500381i	−0.866245	+	0.499619i	$0.833473\pi$
$488$	−3.82374e7	+	8.85207e7i	−0.329025	+	0.761703i
$489$	−6.72178e6	+	5.64024e6i	−0.0574854	+	0.0482360i
$490$	−6.76017e7	+	1.88059e7i	−0.574605	+	0.159847i
$491$	−1.92488e8	+	3.39409e7i	−1.62615	+	0.286734i	−0.911051	−	0.412293i	$-0.864728\pi$
$491$	−1.92488e8	+	3.39409e7i	−1.62615	+	0.286734i	−0.715096	+	0.699027i	$0.753617\pi$
$492$	−2.62184e8	+	4.99628e6i	−2.20146	+	0.0419519i
$493$	−6.67101e7			−0.556738
$494$	−3.76455e7	+	1.33696e7i	−0.312271	+	0.110902i
$495$			2.17737e8i			1.79522i
$496$	4.08568e7	+	1.00199e8i	0.334826	+	0.821144i
$497$	8.26117e6	+	4.68514e7i	0.0672934	+	0.381640i
$498$	5.48778e7	−	1.52663e7i	0.444333	−	0.123608i
$499$	3.40026e7	+	4.05227e7i	0.273659	+	0.326134i	0.885317	−	0.464988i	$-0.153941\pi$
$499$	3.40026e7	+	4.05227e7i	0.273659	+	0.326134i	−0.611658	+	0.791123i	$0.709497\pi$
$500$	1.48723e8	−	2.91559e7i	1.18978	−	0.233247i
$501$	−5.29956e7	+	9.17911e7i	−0.421431	+	0.729940i
$502$	−1.09678e7	+	1.40800e8i	−0.0866981	+	1.11299i
$503$	5.36315e6	+	1.47351e7i	0.0421421	+	0.115784i	0.958979	−	0.283478i	$-0.0914884\pi$
$503$	5.36315e6	+	1.47351e7i	0.0421421	+	0.115784i	−0.916837	+	0.399263i	$0.869266\pi$
$504$	−7.40443e6	−	6.36291e7i	−0.0578363	−	0.497009i
$505$	−1.62190e8	−	2.80922e8i	−1.25936	−	2.18128i
$506$	1.50114e8	+	3.14074e8i	1.15870	+	2.42427i
$507$	1.45678e8	+	2.56869e7i	1.11781	+	0.197101i
$508$	−5.27061e7	+	9.54443e7i	−0.402040	+	0.728046i
$509$	−2.30241e6	−	1.93195e6i	−0.0174594	−	0.0146502i	0.634016	−	0.773320i	$-0.281405\pi$
$509$	−2.30241e6	−	1.93195e6i	−0.0174594	−	0.0146502i	−0.651476	+	0.758670i	$0.725850\pi$
$510$	−1.70540e8	+	3.75012e8i	−1.28563	+	2.82706i
$511$	2.70968e7	−	7.44477e7i	0.203074	−	0.557942i
$512$	−1.02685e8	−	8.64300e7i	−0.765065	−	0.643953i
$513$	2.62054e7	+	5.88405e7i	0.194106	+	0.435837i
$514$	−4.94849e7	+	7.21245e7i	−0.364404	+	0.531121i
$515$	3.76354e7	−	1.03402e8i	0.275534	−	0.757023i
$516$	2.20702e7	−	1.33093e7i	0.160641	−	0.0968734i
$517$	−5.21298e7	−	4.37421e7i	−0.377237	−	0.316540i
$518$	−8.61882e7	+	8.36861e6i	−0.620096	+	0.0602094i
$519$	−2.46047e8	−	4.33847e7i	−1.76001	−	0.310337i
$520$	5.28925e7	−	5.60058e7i	0.376170	−	0.398312i
$521$	1.18264e8	+	2.04839e8i	0.836256	+	1.44844i	0.893003	+	0.450050i	$0.148594\pi$
$521$	1.18264e8	+	2.04839e8i	0.836256	+	1.44844i	−0.0567470	+	0.998389i	$0.518073\pi$
$522$	−8.39645e6	+	3.25742e7i	−0.0590316	+	0.229014i
$523$	1.57028e7	+	4.31431e7i	0.109767	+	0.301582i	0.982399	−	0.186797i	$-0.0598106\pi$
$523$	1.57028e7	+	4.31431e7i	0.109767	+	0.301582i	−0.872632	+	0.488379i	$0.837588\pi$
$524$	−1.79158e7	−	1.44605e7i	−0.124521	−	0.100505i
$525$	−1.27851e8	+	2.21445e8i	−0.883541	+	1.53034i
$526$	1.71850e7	−	1.75156e7i	0.118084	−	0.120356i
$527$	1.22910e8	+	1.46478e8i	0.839761	+	1.00079i
$528$	−3.25419e8	+	1.24071e7i	−2.21076	+	0.0842889i
$529$	−3.59410e7	−	2.03831e8i	−0.242786	−	1.37691i
$530$	3.06978e8	−	2.19336e8i	2.06196	−	1.47327i
$531$		−	5.57243e7i		−	0.372187i
$532$	6.92184e7	+	9.84946e7i	0.459713	+	0.654150i
$533$	8.66484e7			0.572241
$534$	−1.01804e6	−	1.42483e6i	−0.00668562	−	0.00935704i
$535$	−1.59433e8	+	2.81123e7i	−1.04116	+	0.183584i
$536$	1.40263e7	−	1.04311e7i	0.0910854	−	0.0677388i
$537$	1.60610e7	−	1.34768e7i	0.103717	−	0.0870291i
$538$	8.87251e7	+	8.70505e7i	0.569770	+	0.559016i
$539$	−8.48838e7	−	4.90077e7i	−0.542074	−	0.312967i
$540$	−9.66517e7	−	7.80111e7i	−0.613802	−	0.495422i
$541$	4.41546e7	−	1.60709e7i	0.278858	−	0.101496i	−0.198805	−	0.980039i	$-0.563706\pi$
$541$	4.41546e7	−	1.60709e7i	0.278858	−	0.101496i	0.477663	+	0.878543i	$0.341484\pi$
$542$	2.17625e8	+	5.60958e7i	1.36682	+	0.352316i
$543$	3.75762e7	−	2.16946e7i	0.234700	−	0.135504i
$544$	−2.19481e8	−	8.98848e7i	−1.36333	−	0.558328i
$545$	1.63737e7	−	9.28596e7i	0.101148	−	0.573637i
$546$	5.31427e6	+	5.47315e7i	0.0326487	+	0.336248i
$547$	−1.24525e7	+	1.48404e7i	−0.0760844	+	0.0906739i	−0.802744	−	0.596324i	$-0.796627\pi$
$547$	−1.24525e7	+	1.48404e7i	−0.0760844	+	0.0906739i	0.726659	+	0.686998i	$0.241072\pi$
$548$	−1.00032e7	+	6.03233e6i	−0.0607850	+	0.0366558i
$549$	8.07400e7	+	2.93870e7i	0.487946	+	0.177598i
$550$	4.12597e8	+	2.83084e8i	2.47992	+	1.70148i
$551$	−1.53005e7	−	6.13377e7i	−0.0914642	−	0.366668i
$552$	3.23126e8	+	7.67555e7i	1.92112	+	0.456344i
$553$	9.23080e7	+	3.35974e7i	0.545838	+	0.198669i
$554$	−7.13127e7	−	3.24302e7i	−0.419409	−	0.190730i
$555$	1.80506e8	−	2.15119e8i	1.05587	−	1.25834i
$556$	1.27271e8	−	2.30472e8i	0.740466	−	1.34089i
$557$	−2.04815e7	+	1.16156e8i	−0.118521	+	0.672166i	0.866425	+	0.499306i	$0.166412\pi$
$557$	−2.04815e7	+	1.16156e8i	−0.118521	+	0.672166i	−0.984946	+	0.172860i	$0.944699\pi$
$558$	8.69947e7	−	4.15799e7i	0.500715	−	0.239321i
$559$	−7.37507e6	+	4.25800e6i	−0.0422212	+	0.0243764i
$560$	−2.05314e8	−	1.08325e8i	−1.16911	−	0.616831i
$561$	−5.40755e8	+	1.96819e8i	−3.06275	+	1.11475i
$562$	−1.51396e8	−	1.17932e7i	−0.852913	−	0.0664389i
$563$	1.87034e8	+	1.07984e8i	1.04808	+	0.605110i	0.922112	−	0.386924i	$-0.126462\pi$
$563$	1.87034e8	+	1.07984e8i	1.04808	+	0.605110i	0.125970	+	0.992034i	$0.459796\pi$
$564$	−6.37126e7	+	1.24904e7i	−0.355131	+	0.0696206i
$565$	6.46024e7	−	5.42078e7i	0.358181	−	0.300550i
$566$	3.12010e7	+	1.12159e8i	0.172076	+	0.618562i
$567$	1.77137e8	−	3.12341e7i	0.971765	−	0.171348i
$568$	4.88452e7	−	7.41835e7i	0.266549	−	0.404820i
$569$	−2.52195e8			−1.36899			−0.684494	−	0.729018i	$-0.739977\pi$
$569$	−2.52195e8			−1.36899			−0.684494	+	0.729018i	$0.739977\pi$
$570$	−3.83926e8	−	7.07942e7i	−2.07311	−	0.382273i
$571$			1.90759e8i			1.02465i	0.858790	+	0.512327i	$0.171216\pi$
$571$			1.90759e8i			1.02465i	−0.858790	+	0.512327i	$0.828784\pi$
$572$	1.07586e8	−	2.05020e6i	0.574867	−	0.0109549i
$573$	−4.83704e7	−	2.74322e8i	−0.257108	−	1.45813i
$574$	−6.99800e7	−	2.51558e8i	−0.370031	−	1.33015i
$575$	−3.28015e8	−	3.90913e8i	−1.72540	−	2.05626i
$576$	−7.15153e7	+	9.58583e7i	−0.374224	+	0.501606i
$577$	1.78976e8	−	3.09995e8i	0.931679	−	1.61372i	0.151227	−	0.988499i	$-0.451678\pi$
$577$	1.78976e8	−	3.09995e8i	0.931679	−	1.61372i	0.780452	−	0.625216i	$-0.214989\pi$
$578$	−2.25322e8	−	1.75518e7i	−1.16687	−	0.0908947i
$579$	5.62526e7	+	1.54553e8i	0.289806	+	0.796235i
$580$	8.01224e7	+	9.18728e7i	0.410648	+	0.470872i
$581$	2.83591e7	+	4.91193e7i	0.144598	+	0.250452i
$582$	3.46988e8	−	1.65846e8i	1.76013	−	0.841270i
$583$	5.19005e8	+	9.15145e7i	2.61918	+	0.461832i
$584$	−1.32214e8	+	6.63162e7i	−0.663801	+	0.332951i
$585$	−5.25830e7	−	4.41223e7i	−0.262650	−	0.220389i
$586$	2.41548e7	+	1.09846e7i	0.120036	+	0.0545874i
$587$	−8.41013e7	+	2.31067e8i	−0.415804	+	1.14241i	0.538252	+	0.842784i	$0.319085\pi$
$587$	−8.41013e7	+	2.31067e8i	−0.415804	+	1.14241i	−0.954056	+	0.299628i	$0.903137\pi$
$588$	−8.72490e7	+	3.36521e7i	−0.429169	+	0.165531i
$589$	−1.06492e8	+	1.46608e8i	−0.521159	+	0.717482i
$590$	−1.66513e8	−	1.14245e8i	−0.810758	−	0.556263i
$591$	1.29595e8	−	3.56058e8i	0.627804	−	1.72488i
$592$	1.27715e8	+	9.91249e7i	0.615568	+	0.477769i
$593$	−8.71961e7	−	7.31662e7i	−0.418151	−	0.350870i	0.409308	−	0.912396i	$-0.365770\pi$
$593$	−8.71961e7	−	7.31662e7i	−0.418151	−	0.350870i	−0.827459	+	0.561526i	$0.810214\pi$
$594$	−1.67673e7	−	1.72686e8i	−0.0800026	−	0.823945i
$595$	−4.03975e8	−	7.12317e7i	−1.91780	−	0.338160i
$596$	8.28057e7	+	1.29793e7i	0.391130	+	0.0613073i
$597$	−2.91217e7	−	5.04402e7i	−0.136865	−	0.237058i
$598$	−1.06267e8	−	2.73918e7i	−0.496930	−	0.128091i
$599$	−5.81456e7	−	1.59754e8i	−0.270543	−	0.743311i	−0.998344	−	0.0575225i	$-0.981680\pi$
$599$	−5.81456e7	−	1.59754e8i	−0.270543	−	0.743311i	0.727801	−	0.685788i	$-0.240542\pi$
$600$	4.57406e8	−	1.36685e8i	2.11762	−	0.632803i
$601$	1.08466e8	−	1.87869e8i	0.499657	−	0.865432i	−0.500343	−	0.865827i	$-0.666793\pi$
$601$	1.08466e8	−	1.87869e8i	0.499657	−	0.865432i	1.00000		0.000395746i	$0.000125970\pi$
$602$	1.83182e7	+	1.79724e7i	0.0839638	+	0.0823790i
$603$	−1.00118e7	−	1.19316e7i	−0.0456627	−	0.0544186i
$604$	−3.01329e8	−	1.03217e8i	−1.36751	−	0.468424i
$605$	1.27817e8	+	7.24888e8i	0.577196	+	3.27344i
$606$	−2.51321e8	−	3.51743e8i	−1.12930	−	1.58055i
$607$			3.33959e8i			1.49323i	0.665256	+	0.746615i	$0.268322\pi$
$607$			3.33959e8i			1.49323i	−0.665256	+	0.746615i	$0.731678\pi$
$608$	3.23062e7	−	2.22422e8i	0.143739	−	0.989616i
$609$	−8.70170e7			−0.385259
$610$	2.53344e8	−	1.81015e8i	1.11615	−	0.797488i
$611$	2.11272e7	−	3.72530e6i	0.0926229	−	0.0163319i
$612$	−6.84844e7	+	1.99932e8i	−0.298770	+	0.872225i
$613$	−8.80183e7	+	7.38561e7i	−0.382113	+	0.320631i	−0.813531	−	0.581521i	$-0.802458\pi$
$613$	−8.80183e7	+	7.38561e7i	−0.382113	+	0.320631i	0.431419	+	0.902152i	$0.358013\pi$
$614$	1.39770e7	−	1.42459e7i	0.0603822	−	0.0615439i
$615$	7.33318e8	+	4.23381e8i	3.15259	+	1.82015i
$616$	−9.28419e7	−	3.10687e8i	−0.397193	−	1.32917i
$617$	3.81868e8	−	1.38989e8i	1.62577	−	0.591731i	0.641298	−	0.767292i	$-0.278396\pi$
$617$	3.81868e8	−	1.38989e8i	1.62577	−	0.591731i	0.984469	+	0.175561i	$0.0561740\pi$
$618$	3.66042e7	−	1.42007e8i	0.155084	−	0.601650i
$619$	−1.41832e8	+	8.18868e7i	−0.598002	+	0.345257i	−0.768255	−	0.640144i	$-0.778875\pi$
$619$	−1.41832e8	+	8.18868e7i	−0.598002	+	0.345257i	0.170253	+	0.985400i	$0.445541\pi$
$620$	5.41079e7	−	3.45199e8i	0.227031	−	1.44842i
$621$	−3.07255e7	+	1.74253e8i	−0.128299	+	0.727621i
$622$	−2.56055e8	+	2.48622e7i	−1.06405	+	0.103316i
$623$	1.12081e6	−	1.33573e6i	0.00463518	−	0.00552399i
$624$	6.29467e7	−	8.11019e7i	0.259071	−	0.333793i
$625$	−6.22046e7	−	2.26406e7i	−0.254790	−	0.0927359i
$626$	−8.69731e7	+	1.26764e8i	−0.354537	+	0.516741i
$627$	−3.04995e8	−	4.52064e8i	−1.23734	−	1.83399i
$628$	−4.43489e7	−	1.14982e8i	−0.179062	−	0.464251i
$629$	2.68454e8	+	9.77091e7i	1.07874	+	0.392630i
$630$	−8.56283e7	+	1.88293e8i	−0.342449	+	0.753032i
$631$	−1.35233e8	+	1.61165e8i	−0.538263	+	0.641477i	−0.964797	−	0.262994i	$-0.915290\pi$
$631$	−1.35233e8	+	1.61165e8i	−0.538263	+	0.641477i	0.426534	+	0.904472i	$0.359734\pi$
$632$	−8.22256e7	−	1.63932e8i	−0.325729	−	0.649401i
$633$	−2.63816e7	+	1.49618e8i	−0.104014	+	0.589891i
$634$	−3.68575e6	−	7.71145e6i	−0.0144630	−	0.0302600i
$635$	3.04898e8	−	1.76033e8i	1.19078	−	0.687499i
$636$	3.78945e8	−	3.30479e8i	1.47301	−	1.28461i
$637$	2.90361e7	−	1.05683e7i	0.112336	−	0.0408870i
$638$	−1.32241e7	+	1.69766e8i	−0.0509219	+	0.653713i
$639$	−6.85410e7	−	3.95722e7i	−0.262693	−	0.151666i
$640$	1.39820e8	+	4.10225e8i	0.533371	+	1.56488i
$641$	3.41487e8	−	2.86542e8i	1.29658	−	1.08796i	0.305858	−	0.952077i	$-0.401057\pi$
$641$	3.41487e8	−	2.86542e8i	1.29658	−	1.08796i	0.990725	−	0.135885i	$-0.0433876\pi$
$642$	−2.07861e8	+	5.78242e7i	−0.785540	+	0.218527i
$643$	3.41479e8	−	6.02120e7i	1.28449	−	0.226490i	0.510605	−	0.859815i	$-0.329421\pi$
$643$	3.41479e8	−	6.02120e7i	1.28449	−	0.226490i	0.773886	+	0.633325i	$0.218310\pi$
$644$	6.30076e6	+	3.30637e8i	0.0235904	+	1.23792i
$645$	−8.32217e7			−0.310140
$646$	−6.59080e7	−	3.91655e8i	−0.244478	−	1.45280i
$647$			2.09851e8i			0.774814i	0.921909	+	0.387407i	$0.126629\pi$
$647$			2.09851e8i			0.774814i	−0.921909	+	0.387407i	$0.873371\pi$
$648$	−2.80475e8	−	1.84676e8i	−1.03079	−	0.678710i
$649$	−4.89819e7	−	2.77790e8i	−0.179185	−	1.01621i
$650$	−1.51973e8	+	4.22768e7i	−0.553382	+	0.153944i
$651$	1.60324e8	+	1.91067e8i	0.581108	+	0.692538i
$652$	3.13813e6	+	1.60074e7i	0.0113221	+	0.0577535i
$653$	−5.55693e7	+	9.62489e7i	−0.199570	+	0.345666i	−0.948389	−	0.317109i	$-0.897288\pi$
$653$	−5.55693e7	+	9.62489e7i	−0.199570	+	0.345666i	0.748819	+	0.662775i	$0.230621\pi$
$654$	9.75915e6	−	1.25284e8i	0.0348882	−	0.447880i
$655$	2.54273e7	+	6.98608e7i	0.0904848	+	0.248605i
$656$	−2.27483e8	+	4.31157e8i	−0.805818	+	1.52730i
$657$	6.58998e7	+	1.14142e8i	0.232374	+	0.402484i
$658$	−2.78783e7	−	5.83278e7i	−0.0978562	−	0.204738i
$659$	−3.76318e8	−	6.63549e7i	−1.31492	−	0.231855i	−0.528174	−	0.849136i	$-0.677123\pi$
$659$	−3.76318e8	−	6.63549e7i	−1.31492	−	0.231855i	−0.786743	+	0.617281i	$0.788234\pi$
$660$	9.20533e8	+	5.08335e8i	3.20190	+	1.76815i
$661$	−2.36802e8	−	1.98701e8i	−0.819938	−	0.688010i	0.133019	−	0.991113i	$-0.457533\pi$
$661$	−2.36802e8	−	1.98701e8i	−0.819938	−	0.688010i	−0.952958	+	0.303103i	$0.901977\pi$
$662$	−2.22131e7	+	4.88459e7i	−0.0765660	+	0.168366i
$663$	6.20476e7	−	1.70474e8i	0.212904	−	0.584949i
$664$	2.44727e7	−	1.03025e8i	0.0835944	−	0.351916i
$665$	−2.71598e7	−	3.87779e8i	−0.0923552	−	1.31862i
$666$	8.14997e7	−	1.18786e8i	0.275888	−	0.402109i
$667$	5.93948e7	−	1.63186e8i	0.200157	−	0.549927i
$668$	1.01752e8	+	1.68732e8i	0.341362	+	0.566067i
$669$	8.61358e7	+	7.22765e7i	0.287677	+	0.241390i
$670$	−5.61795e7	+	5.45486e6i	−0.186790	+	0.0181367i
$671$	4.28326e8	+	7.55255e7i	1.41778	+	0.249992i
$672$	−2.86293e8	−	1.17246e8i	−0.943414	−	0.386359i
$673$	1.24937e8	+	2.16397e8i	0.409869	+	0.709914i	0.994875	−	0.101115i	$-0.0322411\pi$
$673$	1.24937e8	+	2.16397e8i	0.409869	+	0.709914i	−0.585006	+	0.811029i	$0.698908\pi$
$674$	4.32108e6	−	1.67637e7i	0.0141128	−	0.0547509i
$675$	8.69890e7	+	2.39000e8i	0.282848	+	0.777118i
$676$	1.72716e8	−	2.13986e8i	0.559105	−	0.692701i
$677$	−2.58994e8	+	4.48590e8i	−0.834686	+	1.44572i	0.0595999	+	0.998222i	$0.481018\pi$
$677$	−2.58994e8	+	4.48590e8i	−0.834686	+	1.44572i	−0.894286	+	0.447496i	$0.852316\pi$
$678$	7.87109e7	−	8.02252e7i	0.252549	−	0.257408i
$679$	2.46149e8	+	2.93349e8i	0.786301	+	0.937077i
$680$	4.57022e8	+	6.14539e8i	1.45349	+	1.95444i
$681$	5.89025e7	+	3.34053e8i	0.186506	+	1.05773i
$682$	3.97127e8	−	2.83748e8i	1.25192	−	0.894497i
$683$			9.49105e7i			0.297887i	0.988846	+	0.148944i	$0.0475873\pi$
$683$			9.49105e7i			0.297887i	−0.988846	+	0.148944i	$0.952413\pi$
$684$	−1.99539e8	−	1.71130e7i	−0.623532	−	0.0534760i
$685$	3.77197e7			0.117354
$686$	−2.04186e8	−	2.85775e8i	−0.632491	−	0.885221i
$687$	−7.95952e8	+	1.40348e8i	−2.45480	+	0.432848i
$688$	−1.82538e6	−	4.78767e7i	−0.00560516	−	0.147014i
$689$	−1.27272e8	+	1.06794e8i	−0.389112	+	0.326504i
$690$	−7.65512e8	−	7.51063e8i	−2.33026	−	2.28628i
$691$	−3.66349e8	−	2.11512e8i	−1.11035	−	0.641063i	−0.171432	−	0.985196i	$-0.554840\pi$
$691$	−3.66349e8	−	2.11512e8i	−1.11035	−	0.641063i	−0.938921	+	0.344133i	$0.888173\pi$
$692$	−2.91714e8	+	3.61419e8i	−0.880318	+	1.09067i
$693$	−2.71513e8	+	9.88226e7i	−0.815813	+	0.296932i
$694$	−3.99459e8	−	1.02966e8i	−1.19507	−	0.308046i
$695$	−7.36246e8	+	4.25072e8i	−2.19315	+	1.26622i
$696$	1.18112e8	+	1.11546e8i	0.350322	+	0.330848i
$697$	−1.49586e8	+	8.48345e8i	−0.441767	+	2.50538i
$698$	−1.74670e7	−	1.79893e8i	−0.0513633	−	0.528990i
$699$	2.69866e8	−	3.21614e8i	0.790164	−	0.941681i
$700$	2.45476e8	+	4.07063e8i	0.715673	+	1.18677i
$701$	2.26194e8	+	8.23278e7i	0.656639	+	0.238997i	0.648785	−	0.760972i	$-0.275278\pi$
$701$	2.26194e8	+	8.23278e7i	0.656639	+	0.238997i	0.00785451	+	0.999969i	$0.497500\pi$
$702$	4.51010e7	+	3.09439e7i	0.130369	+	0.0894466i
$703$	−2.82683e7	+	2.69244e8i	−0.0813642	+	0.774963i
$704$	−2.72249e8	+	5.40724e8i	−0.780277	+	1.54973i
$705$	1.97005e8	+	7.17040e7i	0.562225	+	0.204633i
$706$	−4.06286e8	−	1.84763e8i	−1.15456	−	0.525049i
$707$	2.76690e8	−	3.29746e8i	0.782952	−	0.933086i
$708$	−2.35587e8	−	1.30095e8i	−0.663822	−	0.366575i
$709$	3.47351e7	−	1.96993e8i	0.0974608	−	0.552728i	−0.896505	−	0.443034i	$-0.853902\pi$
$709$	3.47351e7	−	1.96993e8i	0.0974608	−	0.552728i	0.993965	−	0.109693i	$-0.0349869\pi$
$710$	−2.58769e8	+	1.23681e8i	−0.722997	+	0.345563i
$711$	−1.41525e8	+	8.17094e7i	−0.393753	+	0.227333i
$712$	−3.23358e6	+	376287.i	−0.00895867	+	0.00104251i
$713$	−4.67746e8	+	1.70246e8i	−1.29045	+	0.469686i
$714$	−5.45032e8	−	4.24560e7i	−1.49736	−	0.116639i
$715$	−3.00914e8	−	1.73733e8i	−0.823236	−	0.475295i
$716$	−7.49825e6	−	3.82481e7i	−0.0204278	−	0.104201i
$717$	−2.50665e7	+	2.10333e7i	−0.0680042	+	0.0570623i
$718$	9.19037e7	+	3.30367e8i	0.248290	+	0.892531i
$719$	1.85834e8	−	3.27675e7i	0.499964	−	0.0881571i	0.0820211	−	0.996631i	$-0.473863\pi$
$719$	1.85834e8	−	3.27675e7i	0.499964	−	0.0881571i	0.417942	+	0.908474i	$0.362751\pi$
$720$	3.57599e8	−	1.45813e8i	0.958073	−	0.390659i
$721$	1.46022e8			0.389593
$722$	3.44997e8	−	1.50429e8i	0.916651	−	0.399688i
$723$		−	3.11259e8i		−	0.823583i
$724$	−1.53682e6	−	8.06460e7i	−0.00404957	−	0.212504i
$725$	−4.33461e7	−	2.45828e8i	−0.113746	−	0.645086i
$726$	2.62907e8	+	9.45075e8i	0.687057	+	2.46977i
$727$	3.29877e7	+	3.93133e7i	0.0858518	+	0.102314i	0.807260	−	0.590196i	$-0.200949\pi$
$727$	3.29877e7	+	3.93133e7i	0.0858518	+	0.102314i	−0.721408	+	0.692510i	$0.756505\pi$
$728$	9.38437e7	+	4.05367e7i	0.243226	+	0.105064i
$729$	−3.17724e7	+	5.50314e7i	−0.0820101	+	0.142046i
$730$	4.76179e8	+	3.70926e7i	1.22406	+	0.0953496i
$731$	−2.89566e7	−	7.95576e7i	−0.0741303	−	0.203671i
$732$	3.12738e8	−	2.72739e8i	0.797346	−	0.695366i
$733$	−2.11021e7	−	3.65499e7i	−0.0535813	−	0.0928056i	0.837991	−	0.545685i	$-0.183730\pi$
$733$	−2.11021e7	−	3.65499e7i	−0.0535813	−	0.0928056i	−0.891572	+	0.452879i	$0.850397\pi$
$734$	1.05601e8	−	5.04730e7i	0.267043	−	0.127635i
$735$	2.97375e8	+	5.24353e7i	0.748933	+	0.132057i
$736$	4.15289e8	−	4.56866e8i	1.04164	−	1.14592i
$737$	−6.03977e7	−	5.06797e7i	−0.150875	−	0.126599i
$738$	3.95415e8	+	1.79819e8i	0.983748	+	0.447369i
$739$	2.43113e8	−	6.67947e8i	0.602385	−	1.65504i	−0.144041	−	0.989572i	$-0.546010\pi$
$739$	2.43113e8	−	6.67947e8i	0.602385	−	1.65504i	0.746426	−	0.665468i	$-0.231768\pi$
$740$	−1.87862e8	−	4.87066e8i	−0.463601	−	1.20197i
$741$	1.70977e8	+	1.79510e7i	0.420225	+	0.0441199i
$742$	4.12832e8	+	2.83245e8i	1.01056	+	0.693348i
$743$	−1.93029e8	+	5.30342e8i	−0.470604	+	1.29297i	0.446664	+	0.894702i	$0.352612\pi$
$743$	−1.93029e8	+	5.30342e8i	−0.470604	+	1.29297i	−0.917267	+	0.398272i	$0.869610\pi$
$744$	2.73120e7	−	4.64863e8i	0.0663184	−	1.12877i
$745$	−2.07330e8	−	1.73970e8i	−0.501410	−	0.420733i
$746$	4.82046e7	+	4.96459e8i	0.116111	+	1.19582i
$747$	−9.29227e7	−	1.63848e7i	−0.222926	−	0.0393078i
$748$	−1.65659e8	+	1.05688e9i	−0.395831	+	2.52534i
$749$	−1.07416e8	−	1.86050e8i	−0.255637	−	0.442776i
$750$	−6.31550e8	−	1.62791e8i	−1.49701	−	0.385874i
$751$	−9.70806e7	−	2.66727e8i	−0.229199	−	0.629719i	0.770774	−	0.637109i	$-0.219870\pi$
$751$	−9.70806e7	−	2.66727e8i	−0.229199	−	0.629719i	−0.999973	+	0.00739012i	$0.997648\pi$
$752$	−3.69295e7	+	1.14908e8i	−0.0868401	+	0.270207i
$753$	3.03876e8	−	5.26329e8i	0.711725	−	1.23274i
$754$	−3.83182e7	−	3.75949e7i	−0.0893903	−	0.0877031i
$755$	6.61115e8	+	7.87886e8i	1.53616	+	1.83072i
$756$	5.34114e7	−	1.55928e8i	0.123614	−	0.360878i
$757$	−1.00859e8	−	5.72002e8i	−0.232503	−	1.31859i	−0.847809	−	0.530302i	$-0.822078\pi$
$757$	−1.00859e8	−	5.72002e8i	−0.232503	−	1.31859i	0.615306	−	0.788289i	$-0.289033\pi$
$758$	4.84929e8	+	6.78696e8i	1.11345	+	1.55836i
$759$		−	1.49803e9i		−	3.42605i
$760$	−4.60226e8	+	5.61166e8i	−1.04841	+	1.27835i
$761$	−3.14685e6			−0.00714039			−0.00357019	−	0.999994i	$-0.501136\pi$
$761$	−3.14685e6			−0.00714039			−0.00357019	+	0.999994i	$0.501136\pi$
$762$	3.81763e8	−	2.72770e8i	0.862838	−	0.616499i
$763$	1.23225e8	−	2.17279e7i	0.277412	−	0.0489152i
$764$	−4.89890e8	−	1.67806e8i	−1.09855	−	0.376294i
$765$	5.22764e8	−	4.38651e8i	1.16767	−	0.979794i
$766$	−4.26360e8	+	4.34562e8i	−0.948615	+	0.966864i
$767$	7.70113e7	+	4.44625e7i	0.170674	+	0.0985389i
$768$	2.38301e8	+	5.26140e8i	0.526069	+	1.16150i
$769$	−1.53457e8	+	5.58538e7i	−0.337449	+	0.122821i	−0.505186	−	0.863010i	$-0.668576\pi$
$769$	−1.53457e8	+	5.58538e7i	−0.337449	+	0.122821i	0.167737	+	0.985832i	$0.446354\pi$
$770$	−2.61353e8	+	1.01392e9i	−0.572474	+	2.22092i
$771$	3.25980e8	−	1.88205e8i	0.711260	−	0.410646i
$772$	3.02065e8	+	4.73468e7i	0.656521	+	0.102906i
$773$	3.38897e7	−	1.92198e8i	0.0733718	−	0.416112i	−0.925893	−	0.377785i	$-0.876686\pi$
$773$	3.38897e7	−	1.92198e8i	0.0733718	−	0.416112i	0.999265	−	0.0383273i	$-0.0122029\pi$
$774$	−4.24922e7	+	4.12586e6i	−0.0916402	+	0.00889799i
$775$	−4.59913e8	+	5.48103e8i	−0.988031	+	1.17749i
$776$	4.19326e7	−	7.13713e8i	0.0897359	−	1.52735i
$777$	3.50172e8	+	1.27452e8i	0.746480	+	0.271697i
$778$	−4.61841e8	+	6.73136e8i	−0.980739	+	1.42943i
$779$	−8.14334e8	+	5.70354e7i	−1.72262	+	0.120651i
$780$	−3.09299e8	+	1.19297e8i	−0.651769	+	0.251389i
$781$	−3.76466e8	−	1.37023e8i	−0.790265	−	0.287633i
$782$	4.51639e8	−	9.93137e8i	0.944433	−	2.07677i
$783$	−5.56352e7	+	6.63035e7i	−0.115895	+	0.138118i
$784$	−2.36429e7	+	1.72227e8i	−0.0490629	+	0.357399i
$785$	−6.91027e7	+	3.91901e8i	−0.142852	+	0.810153i
$786$	4.27261e7	+	8.93929e7i	0.0879884	+	0.184092i
$787$	4.74818e8	−	2.74136e8i	0.974098	−	0.562396i	0.0736150	−	0.997287i	$-0.476546\pi$
$787$	4.74818e8	−	2.74136e8i	0.974098	−	0.562396i	0.900483	+	0.434891i	$0.143213\pi$
$788$	−4.62974e8	−	5.30872e8i	−0.946189	−	1.08495i
$789$	−9.92288e7	+	3.61163e7i	−0.202026	+	0.0735314i
$790$	−4.59913e7	+	5.90416e8i	−0.0932812	+	1.19750i
$791$	9.69163e7	+	5.59547e7i	0.195825	+	0.113059i
$792$	4.95217e8	+	2.13914e8i	0.996827	+	0.430589i
$793$	−1.05035e8	+	8.81351e7i	−0.210628	+	0.176738i
$794$	7.54129e8	−	2.09789e8i	1.50655	−	0.419103i
$795$	−1.59893e9	+	2.81935e8i	−3.18221	+	0.561110i
$796$	−1.08255e8	+	2.06295e6i	−0.214639	+	0.00409025i
$797$	9.42907e8			1.86249			0.931245	−	0.364393i	$-0.118724\pi$
$797$	9.42907e8			1.86249			0.931245	+	0.364393i	$0.118724\pi$
$798$	−8.59707e7	−	5.10877e8i	−0.169177	−	1.00533i
$799$			2.13281e8i			0.418130i
$800$	1.88615e8	−	8.67198e8i	0.368389	−	1.69375i
$801$	503712.	+	2.85669e6i	0.000980132	+	0.00555860i
$802$	4.68881e8	−	1.30436e8i	0.908948	−	0.252857i
$803$	4.28847e8	+	5.11080e8i	0.828239	+	0.987057i
$804$	−7.38175e7	+	1.44713e7i	−0.142034	+	0.0278446i
$805$	5.33922e8	−	9.24780e8i	1.02351	−	1.77276i
$806$	−1.19496e7	+	1.53404e8i	−0.0228217	+	0.292975i
$807$	−1.82947e8	−	5.02643e8i	−0.348100	−	0.956398i
$808$	−7.98263e8	+	9.28929e7i	−1.51326	+	0.176096i
$809$	1.91879e8	+	3.32344e8i	0.362395	+	0.627686i	0.988354	−	0.152169i	$-0.0486259\pi$
$809$	1.91879e8	+	3.32344e8i	0.362395	+	0.627686i	−0.625960	+	0.779855i	$0.715293\pi$
$810$	4.67616e8	+	9.78361e8i	0.879902	+	1.84096i
$811$	−9.17650e7	−	1.61806e7i	−0.172034	−	0.0303343i	0.0869675	−	0.996211i	$-0.472282\pi$
$811$	−9.17650e7	−	1.61806e7i	−0.172034	−	0.0303343i	−0.259002	+	0.965877i	$0.583393\pi$
$812$	−7.81985e7	+	1.41608e8i	−0.146060	+	0.264496i
$813$	−7.40868e8	−	6.21662e8i	−1.37870	−	1.15687i
$814$	3.01869e8	−	6.63798e8i	0.559686	−	1.23073i
$815$	1.80152e7	−	4.94963e7i	0.0332787	−	0.0914324i
$816$	6.85373e8	+	7.56300e8i	1.26141	+	1.39195i
$817$	6.65092e7	−	4.48718e7i	0.121959	−	0.0822825i
$818$	2.67113e8	−	3.89318e8i	0.488016	−	0.711287i
$819$	3.11540e7	−	8.55950e7i	0.0567104	−	0.155811i
$820$	1.34800e9	−	8.12898e8i	2.44482	−	1.47433i
$821$	1.66468e8	+	1.39683e8i	0.300816	+	0.252415i	0.780684	−	0.624926i	$-0.214871\pi$
$821$	1.66468e8	+	1.39683e8i	0.300816	+	0.252415i	−0.479868	+	0.877341i	$0.659315\pi$
$822$	5.00338e7	−	4.85812e6i	0.0900840	−	0.00874688i
$823$	−2.62869e7	−	4.63510e6i	−0.0471564	−	0.00831495i	0.150020	−	0.988683i	$-0.452066\pi$
$823$	−2.62869e7	−	4.63510e6i	−0.0471564	−	0.00831495i	−0.197177	+	0.980368i	$0.563177\pi$
$824$	−1.98202e8	−	1.87184e8i	−0.354263	−	0.334570i
$825$	−1.07665e9	−	1.86481e9i	−1.91739	−	3.32103i
$826$	6.68867e7	−	2.59488e8i	0.118686	−	0.460445i
$827$	−1.76766e7	−	4.85662e7i	−0.0312524	−	0.0858652i	0.923085	−	0.384596i	$-0.125659\pi$
$827$	−1.76766e7	−	4.85662e7i	−0.0312524	−	0.0858652i	−0.954338	+	0.298730i	$0.903437\pi$
$828$	−4.28098e8	−	3.45534e8i	−0.754141	−	0.608695i
$829$	1.44180e8	−	2.49727e8i	0.253071	−	0.438332i	−0.711299	−	0.702890i	$-0.751893\pi$
$829$	1.44180e8	−	2.49727e8i	0.253071	−	0.438332i	0.964370	+	0.264558i	$0.0852261\pi$
$830$	−2.39468e8	+	2.44075e8i	−0.418807	+	0.426864i
$831$	2.16702e8	+	2.58256e8i	0.377625	+	0.450035i
$832$	−7.54146e7	−	1.75320e8i	−0.130944	−	0.304411i
$833$	5.33437e7	+	3.02527e8i	0.0922886	+	0.523395i
$834$	−9.21856e8	+	6.58667e8i	−1.58915	+	1.13545i
$835$		−	6.36249e8i		−	1.09287i
$836$	−1.00976e9	+	9.00853e7i	−1.72822	+	0.154183i
$837$	2.48091e8			0.423091
$838$	−1.86445e8	−	2.60944e8i	−0.316824	−	0.443420i
$839$	4.37398e8	−	7.71251e7i	0.740613	−	0.130590i	0.209402	−	0.977830i	$-0.432848\pi$
$839$	4.37398e8	−	7.71251e7i	0.740613	−	0.130590i	0.531211	+	0.847240i	$0.321737\pi$
$840$	5.96142e8	+	8.01607e8i	1.00580	+	1.35246i
$841$	−3.90588e8	+	3.27742e8i	−0.656645	+	0.550990i
$842$	−4.23516e8	−	4.15523e8i	−0.709470	−	0.696079i
$843$	5.65937e8	+	3.26744e8i	0.944682	+	0.545412i
$844$	2.19774e8	+	1.77388e8i	0.365552	+	0.295050i
$845$	−8.34420e8	+	3.03704e8i	−1.38298	+	0.503362i
$846$	1.04144e8	+	2.68445e7i	0.171997	+	0.0443347i
$847$	−8.45906e8	+	4.88384e8i	−1.39210	+	0.803732i
$848$	−1.97266e8	−	9.13668e8i	−0.323492	−	1.49831i
$849$	8.69959e7	−	4.93378e8i	0.142159	−	0.806226i
$850$	−1.51558e8	−	1.56090e9i	−0.246787	−	2.54166i
$851$	−4.78030e8	+	5.69694e8i	−0.775652	+	0.924386i
$852$	−3.27318e8	+	1.97386e8i	−0.529238	+	0.319152i
$853$	2.44048e8	+	8.88261e7i	0.393213	+	0.143118i	0.531057	−	0.847336i	$-0.321795\pi$
$853$	2.44048e8	+	8.88261e7i	0.393213	+	0.143118i	−0.137844	+	0.990454i	$0.544017\pi$
$854$	3.40704e8	+	2.33758e8i	0.547020	+	0.375312i
$855$	5.23225e8	+	3.80056e8i	0.837125	+	0.608064i
$856$	−9.26953e7	+	3.90230e8i	−0.147787	+	0.622155i
$857$	8.71413e8	+	3.17168e8i	1.38446	+	0.503904i	0.923528	−	0.383530i	$-0.125292\pi$
$857$	8.71413e8	+	3.17168e8i	1.38446	+	0.503904i	0.460936	+	0.887434i	$0.347514\pi$
$858$	−4.21527e8	−	1.91694e8i	−0.667365	−	0.303491i
$859$	4.98038e8	−	5.93538e8i	0.785747	−	0.936417i	−0.213431	−	0.976958i	$-0.568464\pi$
$859$	4.98038e8	−	5.93538e8i	0.785747	−	0.936417i	0.999178	+	0.0405415i	$0.0129083\pi$
$860$	−7.47879e7	+	1.35432e8i	−0.117581	+	0.212924i
$861$	−1.95121e8	+	1.10659e9i	−0.305699	+	1.73371i
$862$	−8.90422e8	+	4.25585e8i	−1.39019	+	0.664453i
$863$	−2.67515e8	+	1.54450e8i	−0.416212	+	0.240300i	−0.693456	−	0.720499i	$-0.743913\pi$
$863$	−2.67515e8	+	1.54450e8i	−0.416212	+	0.240300i	0.277243	+	0.960800i	$0.410579\pi$
$864$	−2.72381e8	+	1.43181e8i	−0.422314	+	0.221996i
$865$	1.40932e9	−	5.12950e8i	2.17751	−	0.792550i
$866$	4.30151e8	+	3.35072e7i	0.662320	+	0.0515923i
$867$	8.42285e8	+	4.86293e8i	1.29241	+	0.746176i
$868$	4.55012e8	−	8.92016e7i	0.695767	−	0.136400i
$869$	−6.33689e8	+	5.31728e8i	−0.965644	+	0.810272i
$870$	−1.40596e8	−	5.05401e8i	−0.213508	−	0.767500i
$871$	2.44780e7	−	4.31613e6i	0.0370443	−	0.00653191i
$872$	−1.95112e8	−	1.28469e8i	−0.294262	−	0.193753i
$873$	−6.37058e8			−0.957495
$874$	1.01674e9	+	1.87483e8i	1.52292	+	0.280820i
$875$		−	6.49404e8i		−	0.969373i
$876$	6.36411e8	−	1.21277e7i	0.946729	−	0.0180413i
$877$	−2.05525e7	−	1.16559e8i	−0.0304695	−	0.172801i	0.965776	−	0.259379i	$-0.0835179\pi$
$877$	−2.05525e7	−	1.16559e8i	−0.0304695	−	0.172801i	−0.996245	+	0.0865781i	$0.972407\pi$
$878$	−3.40667e8	−	1.22460e9i	−0.503322	−	1.80930i
$879$	−7.34006e7	−	8.74754e7i	−0.108077	−	0.128801i
$880$	1.65449e9	−	1.04122e9i	2.42782	−	1.52790i
$881$	6.05784e8	−	1.04925e9i	0.885911	−	1.53444i	0.0412440	−	0.999149i	$-0.486868\pi$
$881$	6.05784e8	−	1.04925e9i	0.885911	−	1.53444i	0.844666	−	0.535293i	$-0.179799\pi$
$882$	1.54436e8	+	1.20300e7i	0.225084	+	0.0175332i
$883$	−1.10161e8	−	3.02665e8i	−0.160009	−	0.439622i	0.833617	−	0.552342i	$-0.186266\pi$
$883$	−1.10161e8	−	3.02665e8i	−0.160009	−	0.439622i	−0.993627	+	0.112720i	$0.964044\pi$
$884$	−2.21664e8	−	2.54172e8i	−0.320876	−	0.367935i
$885$	4.34505e8	+	7.52585e8i	0.626852	+	1.08574i
$886$	3.46172e8	−	1.65456e8i	0.497726	−	0.237892i
$887$	−6.46476e8	−	1.13991e8i	−0.926363	−	0.163343i	−0.309938	−	0.950757i	$-0.600308\pi$
$887$	−6.46476e8	−	1.13991e8i	−0.926363	−	0.163343i	−0.616425	+	0.787414i	$0.711420\pi$
$888$	−3.11924e8	−	6.21880e8i	−0.445462	−	0.888111i
$889$	3.57890e8	+	3.00305e8i	0.509382	+	0.427423i
$890$	9.56891e6	+	4.35156e6i	0.0135735	+	0.00617270i
$891$	−5.18059e8	+	1.42336e9i	−0.732397	+	2.01224i
$892$	1.95026e8	−	7.52221e7i	0.274789	−	0.105987i
$893$	−1.96104e8	+	4.89176e7i	−0.275380	+	0.0686928i
$894$	−2.97422e8	−	2.04062e8i	−0.416256	−	0.285595i
$895$	−4.30456e7	+	1.18267e8i	−0.0600426	+	0.164966i
$896$	−4.48081e8	+	3.60537e8i	−0.622920	+	0.501217i
$897$	3.61769e8	+	3.03560e8i	0.501250	+	0.420599i
$898$	−9.70281e7	−	9.99291e8i	−0.133989	−	1.37995i
$899$	−2.39789e8	−	4.22813e7i	−0.330028	−	0.0581928i
$900$	−7.81254e8	−	1.22457e8i	−1.07168	−	0.167979i
$901$	−8.25864e8	−	1.43044e9i	−1.12910	−	1.95567i
$902$	2.12924e9	+	5.48840e8i	2.90138	+	0.747870i
$903$	−3.77711e7	−	1.03775e8i	−0.0512976	−	0.140939i
$904$	−5.98211e7	−	2.00186e8i	−0.0809746	−	0.270975i
$905$	−1.30229e8	+	2.25564e8i	−0.175697	+	0.304315i
$906$	9.78421e8	+	9.59953e8i	1.31565	+	1.29082i
$907$	3.76926e6	+	4.49202e6i	0.00505166	+	0.00602033i	0.768564	−	0.639772i	$-0.220971\pi$
$907$	3.76926e6	+	4.49202e6i	0.00505166	+	0.00602033i	−0.763513	+	0.645793i	$0.776527\pi$
$908$	5.96558e8	+	2.04344e8i	0.796884	+	0.272963i
$909$	1.24350e8	+	7.05222e8i	0.165559	+	0.938932i
$910$	−1.91899e8	−	2.68578e8i	−0.254653	−	0.356407i
$911$		−	3.27375e8i		−	0.433003i	−0.976282	−	0.216502i	$-0.930535\pi$
$911$		−	3.27375e8i		−	0.433003i	0.976282	−	0.216502i	$-0.0694646\pi$
$912$	−5.38197e8	+	8.03641e8i	−0.709507	+	1.05944i
$913$	−4.77629e8			−0.627594
$914$	−5.49113e8	+	3.92342e8i	−0.719156	+	0.513838i
$915$	−1.31958e9	+	2.32677e8i	−1.72255	+	0.303731i
$916$	−4.86892e8	+	1.42143e9i	−0.633500	+	1.84943i
$917$	−7.55742e7	+	6.34143e7i	−0.0980089	+	0.0822392i
$918$	−3.80822e8	+	3.88148e8i	−0.492259	+	0.501729i
$919$	7.87671e8	+	4.54762e8i	1.01484	+	0.585919i	0.912606	−	0.408841i	$-0.134067\pi$
$919$	7.87671e8	+	4.54762e8i	1.01484	+	0.585919i	0.102236	+	0.994760i	$0.467400\pi$
$920$	−1.91018e9	+	5.70815e8i	−2.45308	+	0.733047i
$921$	−8.07054e7	+	2.93744e7i	−0.103306	+	0.0376001i
$922$	1.92746e7	−	7.47763e7i	0.0245920	−	0.0954050i
$923$	1.09378e8	−	6.31493e7i	0.139099	−	0.0803088i
$924$	−2.16086e8	+	1.37859e9i	−0.273912	+	1.74751i
$925$	−1.85627e8	+	1.05275e9i	−0.234540	+	1.33014i
$926$	−6.03770e8	+	5.86242e7i	−0.760394	+	0.0738319i
$927$	−1.56147e8	+	1.86088e8i	−0.196017	+	0.233604i
$928$	2.87669e8	−	9.19689e7i	0.359955	−	0.115079i
$929$	−1.12816e9	−	4.10615e8i	−1.40709	−	0.512139i	−0.476817	−	0.879003i	$-0.658209\pi$
$929$	−1.12816e9	−	4.10615e8i	−1.40709	−	0.512139i	−0.930275	+	0.366863i	$0.880432\pi$
$930$	−8.50692e8	+	1.23989e9i	−1.05760	+	1.54147i
$931$	−2.65929e8	+	1.18435e8i	−0.329546	+	0.146768i
$932$	−2.80865e8	−	7.28191e8i	−0.346936	−	0.899493i
$933$	1.04032e9	+	3.78646e8i	1.28092	+	0.466217i
$934$	−4.37175e8	+	9.61331e8i	−0.536555	+	1.17986i
$935$	2.22044e9	−	2.64622e9i	2.71647	−	3.23736i
$936$	−1.52010e8	+	7.62459e7i	−0.185373	+	0.0929799i
$937$	−8.20082e7	+	4.65091e8i	−0.0996869	+	0.565353i	0.893523	+	0.449017i	$0.148226\pi$
$937$	−8.20082e7	+	4.65091e8i	−0.0996869	+	0.565353i	−0.993210	+	0.116335i	$0.962885\pi$
$938$	−3.22998e7	−	6.75787e7i	−0.0391373	−	0.0818844i
$939$	5.72933e8	−	3.30783e8i	0.692002	−	0.399527i
$940$	2.93729e8	−	2.56161e8i	0.353641	−	0.308411i
$941$	2.43073e8	−	8.84715e7i	0.291722	−	0.106178i	−0.192014	−	0.981392i	$-0.561502\pi$
$941$	2.43073e8	−	8.84715e7i	0.291722	−	0.106178i	0.483735	+	0.875214i	$0.339280\pi$
$942$	−4.11871e7	+	5.28742e8i	−0.0492729	+	0.632544i
$943$	−1.94203e9	−	1.12123e9i	−2.31591	−	1.33709i
$944$	−4.23424e8	+	2.66474e8i	−0.503338	+	0.316766i
$945$	−4.07707e8	+	3.42106e8i	−0.483117	+	0.405383i
$946$	−2.08200e8	+	5.79185e7i	−0.245928	+	0.0684139i
$947$	5.03518e8	−	8.87838e7i	0.592878	−	0.104540i	0.130844	−	0.991403i	$-0.458231\pi$
$947$	5.03518e8	−	8.87838e7i	0.592878	−	0.104540i	0.462033	+	0.886863i	$0.347120\pi$
$948$	1.50372e7	+	7.89088e8i	0.0176499	+	0.926191i
$949$	−2.10326e8			−0.246090
$950$	1.40043e9	−	4.97357e8i	1.63340	−	0.580093i
$951$			3.67810e7i			0.0427644i
$952$	−5.58889e8	+	8.48811e8i	−0.647761	+	0.983784i
$953$	4.12788e7	+	2.34104e8i	0.0476923	+	0.270477i	0.999324	−	0.0367648i	$-0.0117052\pi$
$953$	4.12788e7	+	2.34104e8i	0.0476923	+	0.270477i	−0.951632	+	0.307241i	$0.900594\pi$
$954$	−8.02423e8	+	2.23223e8i	−0.924183	+	0.257096i
$955$	1.07482e9	+	1.28092e9i	1.23403	+	1.47066i
$956$	1.17025e7	+	5.96939e7i	0.0133939	+	0.0683214i
$957$	3.66390e8	−	6.34605e8i	0.418030	−	0.724049i
$958$	−8.49871e7	+	1.09103e9i	−0.0966622	+	1.24091i
$959$	1.71195e7	+	4.70355e7i	0.0194104	+	0.0533298i
$960$	2.18403e8	−	1.85225e9i	0.246857	−	2.09356i
$961$	−9.47913e7	−	1.64183e8i	−0.106807	−	0.184995i
$962$	9.91346e7	+	2.07413e8i	0.111352	+	0.232975i
$963$	3.51964e8	+	6.20608e7i	0.394112	+	0.0694926i
$964$	−5.06531e8	−	2.79716e8i	−0.565425	−	0.312238i
$965$	−7.56314e8	−	6.34623e8i	−0.841628	−	0.706210i
$966$	5.89120e8	−	1.29545e9i	0.653540	−	1.43711i
$967$	2.12904e8	−	5.84948e8i	0.235453	−	0.646901i	−0.764545	−	0.644571i	$-0.777036\pi$
$967$	2.12904e8	−	5.84948e8i	0.235453	−	0.646901i	0.999997	−	0.00233023i	$-0.000741737\pi$
$968$	1.77424e9	+	4.21454e8i	1.95608	+	0.464648i
$969$	−4.70919e8	+	1.64298e9i	−0.517577	+	1.80577i
$970$	−1.30608e9	+	1.90363e9i	−1.43105	+	2.08577i
$971$	−4.04907e8	+	1.11247e9i	−0.442280	+	1.21515i	0.495709	+	0.868489i	$0.334908\pi$
$971$	−4.04907e8	+	1.11247e9i	−0.442280	+	1.21515i	−0.937989	+	0.346666i	$0.887314\pi$
$972$	5.20023e8	+	8.62334e8i	0.566271	+	0.939024i
$973$	−8.64208e8	−	7.25156e8i	−0.938166	−	0.787215i
$974$	9.20387e8	−	8.93667e7i	0.996078	−	0.0967161i
$975$	6.68518e8	+	1.17878e8i	0.721272	+	0.127180i
$976$	−1.62800e8	−	7.54036e8i	−0.175108	−	0.811040i
$977$	6.64207e8	+	1.15044e9i	0.712229	+	1.23362i	0.964019	+	0.265835i	$0.0856476\pi$
$977$	6.64207e8	+	1.15044e9i	0.712229	+	1.23362i	−0.251789	+	0.967782i	$0.581019\pi$
$978$	1.75216e7	−	6.79753e7i	0.0187308	−	0.0726666i
$979$	5.02208e6	+	1.37981e7i	0.00535224	+	0.0147052i
$980$	3.52570e8	−	4.36816e8i	0.374599	−	0.464109i
$981$	−1.04080e8	+	1.80271e8i	−0.110245	+	0.190950i
$982$	1.09509e9	−	1.11616e9i	1.15642	−	1.17867i
$983$	−9.20125e8	−	1.09656e9i	−0.968693	−	1.15444i	−0.987973	−	0.154629i	$-0.950582\pi$
$983$	−9.20125e8	−	1.09656e9i	−0.968693	−	1.15444i	0.0192794	−	0.999814i	$-0.493863\pi$
$984$	1.68337e9	−	1.25189e9i	1.76683	−	1.31396i
$985$	3.94969e8	+	2.23998e9i	0.413289	+	2.34388i
$986$	4.34230e8	−	3.10258e8i	0.452990	−	0.323662i
$987$			2.78204e8i			0.289342i
$988$	1.82862e8	−	2.62109e8i	0.189607	−	0.271776i
$989$	2.20394e8			0.227830
$990$	−1.01266e9	−	1.41730e9i	−1.04366	−	1.46068i
$991$	9.00608e8	−	1.58802e8i	0.925369	−	0.163168i	0.309395	−	0.950934i	$-0.399874\pi$
$991$	9.00608e8	−	1.58802e8i	0.925369	−	0.163168i	0.615974	+	0.787766i	$0.288762\pi$
$992$	−7.31955e8	−	4.62199e8i	−0.749807	−	0.473472i
$993$	1.76893e8	−	1.48431e8i	0.180660	−	0.151592i
$994$	−2.71672e8	−	2.66544e8i	−0.276621	−	0.271400i
$995$	3.02785e8	+	1.74813e8i	0.307372	+	0.177462i
$996$	−2.86210e8	+	3.54599e8i	−0.289672	+	0.358889i
$997$	6.64053e8	−	2.41696e8i	0.670066	−	0.243884i	0.0154896	−	0.999880i	$-0.495069\pi$
$997$	6.64053e8	−	2.41696e8i	0.670066	−	0.243884i	0.654576	+	0.755996i	$0.272847\pi$
$998$	−4.09794e8	−	1.05630e8i	−0.412262	−	0.106266i
$999$	3.21000e8	−	1.85329e8i	0.321965	−	0.185886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.l.a.23.12	✓	348
4.3	odd	2	inner	76.7.l.a.23.25	yes	348
19.5	even	9	inner	76.7.l.a.43.25	yes	348
76.43	odd	18	inner	76.7.l.a.43.12	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.l.a.23.12	✓	348	1.1	even	1	trivial
76.7.l.a.23.25	yes	348	4.3	odd	2	inner
76.7.l.a.43.12	yes	348	76.43	odd	18	inner
76.7.l.a.43.25	yes	348	19.5	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.50920 + 4.65084i) q^{2} +(33.9040 - 5.97820i) q^{3} +(20.7395 - 60.5465i) q^{4} +(-158.311 + 132.839i) q^{5} +(-192.885 + 196.595i) q^{6} +(-237.498 - 137.119i) q^{7} +(146.594 + 490.565i) q^{8} +(428.710 - 156.038i) q^{9} +O(q^{10})\)	\(q+(-6.50920 + 4.65084i) q^{2} +(33.9040 - 5.97820i) q^{3} +(20.7395 - 60.5465i) q^{4} +(-158.311 + 132.839i) q^{5} +(-192.885 + 196.595i) q^{6} +(-237.498 - 137.119i) q^{7} +(146.594 + 490.565i) q^{8} +(428.710 - 156.038i) q^{9} +(412.668 - 1600.95i) q^{10} +(1999.99 - 1154.70i) q^{11} +(341.193 - 2176.75i) q^{12} +(-126.423 + 716.981i) q^{13} +(2183.64 - 212.025i) q^{14} +(-4573.25 + 5450.19i) q^{15} +(-3235.75 - 2511.40i) q^{16} +(-6801.47 - 2475.53i) q^{17} +(-2064.85 + 3009.54i) q^{18} +(716.197 - 6821.51i) q^{19} +(4759.63 + 12340.2i) q^{20} +(-8871.87 - 3229.10i) q^{21} +(-7648.06 + 16817.8i) q^{22} +(12111.2 - 14433.6i) q^{23} +(7902.83 + 15755.8i) q^{24} +(4703.01 - 26672.1i) q^{25} +(-2511.65 - 5254.95i) q^{26} +(-8132.76 + 4695.45i) q^{27} +(-13227.7 + 11535.9i) q^{28} +(8660.86 - 3152.29i) q^{29} +(4420.29 - 56745.8i) q^{30} +(-22878.8 - 13209.1i) q^{31} +(32742.3 + 1298.29i) q^{32} +(60904.9 - 51105.3i) q^{33} +(55785.4 - 15518.8i) q^{34} +(55813.3 - 9841.39i) q^{35} +(-556.314 - 29193.0i) q^{36} -39469.9 q^{37} +(27063.8 + 47733.5i) q^{38} +25064.3i q^{39} +(-88373.5 - 58188.5i) q^{40} +(-20666.9 - 117208. i) q^{41} +(72766.8 - 20242.7i) q^{42} +(7518.77 + 8960.52i) q^{43} +(-28434.0 - 145040. i) q^{44} +(-47141.6 + 81651.7i) q^{45} +(-11706.2 + 150279. i) q^{46} +(-10078.3 - 27689.8i) q^{47} +(-124719. - 65802.8i) q^{48} +(-21221.0 - 36755.9i) q^{49} +(93434.6 + 195487. i) q^{50} +(-245396. - 43270.0i) q^{51} +(40788.7 + 22524.3i) q^{52} +(174814. + 146686. i) q^{53} +(31100.0 - 68387.8i) q^{54} +(-163233. + 448478. i) q^{55} +(32450.2 - 136609. i) q^{56} +(-16498.3 - 235558. i) q^{57} +(-41714.5 + 60799.1i) q^{58} +(41775.2 - 114777. i) q^{59} +(235143. + 389928. i) q^{60} +(144271. + 121058. i) q^{61} +(210356. - 20425.0i) q^{62} +(-123213. - 21725.8i) q^{63} +(-219164. + 143828. i) q^{64} +(-75228.7 - 130300. i) q^{65} +(-158760. + 615913. i) q^{66} +(-11676.7 - 32081.5i) q^{67} +(-290943. + 360464. i) q^{68} +(324333. - 561762. i) q^{69} +(-317530. + 323638. i) q^{70} +(-111509. - 132891. i) q^{71} +(139393. + 187436. i) q^{72} +(50165.7 + 284504. i) q^{73} +(256918. - 183568. i) q^{74} -932407. i q^{75} +(-398165. - 184838. i) q^{76} -633326. q^{77} +(-116570. - 163149. i) q^{78} +(-352757. + 62200.6i) q^{79} +(845866. - 32250.1i) q^{80} +(-502439. + 421597. i) q^{81} +(679638. + 666810. i) q^{82} +(-179112. - 103410. i) q^{83} +(-379508. + 470190. i) q^{84} +(1.40559e6 - 511594. i) q^{85} +(-90615.1 - 23357.3i) q^{86} +(274793. - 158652. i) q^{87} +(859642. + 811855. i) q^{88} +(-1104.09 + 6261.61i) q^{89} +(-72894.2 - 750736. i) q^{90} +(128337. - 152946. i) q^{91} +(-622724. - 1.03264e6i) q^{92} +(-854651. - 311068. i) q^{93} +(194382. + 133366. i) q^{94} +(792778. + 1.17506e6i) q^{95} +(1.11786e6 - 151722. i) q^{96} +(-1.31216e6 - 477588. i) q^{97} +(309077. + 140556. i) q^{98} +(677241. - 807104. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9}+O(q^{10}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9} + 2811 q^{10} - 3 q^{12} - 7572 q^{13} + 8217 q^{14} - 1392 q^{16} - 12 q^{17} - 12 q^{18} + 33618 q^{20} - 33546 q^{21} - 198 q^{22} - 7128 q^{24} - 12 q^{25} + 84453 q^{26} + 13464 q^{28} - 12 q^{29} + 75510 q^{30} + 9339 q^{32} - 366 q^{33} - 289248 q^{34} - 419349 q^{36} - 24 q^{37} + 158040 q^{38} + 264570 q^{40} + 27360 q^{41} + 206001 q^{42} - 525639 q^{44} - 6 q^{45} - 269328 q^{46} - 703179 q^{48} + 2319360 q^{49} + 264534 q^{50} + 130809 q^{52} - 182292 q^{53} + 607083 q^{54} - 705906 q^{56} - 12 q^{57} - 710004 q^{58} + 1060416 q^{60} - 325092 q^{61} - 1967868 q^{62} - 1611921 q^{64} + 398994 q^{65} - 2295684 q^{66} + 1125642 q^{68} - 1625190 q^{69} + 3496059 q^{70} + 4948626 q^{72} - 2224812 q^{73} + 2661159 q^{74} - 968262 q^{76} + 974412 q^{77} - 340743 q^{78} - 3996663 q^{80} + 4277754 q^{81} - 3214221 q^{82} - 872109 q^{84} - 3207900 q^{85} + 3189360 q^{86} + 827973 q^{88} - 2016084 q^{89} - 710406 q^{90} - 2545116 q^{92} + 4486254 q^{93} - 14322630 q^{94} + 2623530 q^{96} - 1223112 q^{97} + 10989009 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9 + 2811 * q^10 - 3 * q^12 - 7572 * q^13 + 8217 * q^14 - 1392 * q^16 - 12 * q^17 - 12 * q^18 + 33618 * q^20 - 33546 * q^21 - 198 * q^22 - 7128 * q^24 - 12 * q^25 + 84453 * q^26 + 13464 * q^28 - 12 * q^29 + 75510 * q^30 + 9339 * q^32 - 366 * q^33 - 289248 * q^34 - 419349 * q^36 - 24 * q^37 + 158040 * q^38 + 264570 * q^40 + 27360 * q^41 + 206001 * q^42 - 525639 * q^44 - 6 * q^45 - 269328 * q^46 - 703179 * q^48 + 2319360 * q^49 + 264534 * q^50 + 130809 * q^52 - 182292 * q^53 + 607083 * q^54 - 705906 * q^56 - 12 * q^57 - 710004 * q^58 + 1060416 * q^60 - 325092 * q^61 - 1967868 * q^62 - 1611921 * q^64 + 398994 * q^65 - 2295684 * q^66 + 1125642 * q^68 - 1625190 * q^69 + 3496059 * q^70 + 4948626 * q^72 - 2224812 * q^73 + 2661159 * q^74 - 968262 * q^76 + 974412 * q^77 - 340743 * q^78 - 3996663 * q^80 + 4277754 * q^81 - 3214221 * q^82 - 872109 * q^84 - 3207900 * q^85 + 3189360 * q^86 + 827973 * q^88 - 2016084 * q^89 - 710406 * q^90 - 2545116 * q^92 + 4486254 * q^93 - 14322630 * q^94 + 2623530 * q^96 - 1223112 * q^97 + 10989009 * q^98

Introduction

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