LMFDB - Embedded newform 43.7.d.a.37.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, 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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.16
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.84004i q^{2} +(36.4833 + 21.0637i) q^{3} +2.53376 q^{4} +(-116.673 - 67.3609i) q^{5} +(-165.140 + 286.031i) q^{6} +(-385.031 + 222.298i) q^{7} +521.627i q^{8} +(522.856 + 905.613i) q^{9} +O(q^{10})$	\(q+7.84004i q^{2} +(36.4833 + 21.0637i) q^{3} +2.53376 q^{4} +(-116.673 - 67.3609i) q^{5} +(-165.140 + 286.031i) q^{6} +(-385.031 + 222.298i) q^{7} +521.627i q^{8} +(522.856 + 905.613i) q^{9} +(528.113 - 914.718i) q^{10} -327.603 q^{11} +(92.4399 + 53.3702i) q^{12} +(1051.90 + 1821.95i) q^{13} +(-1742.82 - 3018.66i) q^{14} +(-2837.74 - 4915.10i) q^{15} -3927.42 q^{16} +(2727.39 + 4723.97i) q^{17} +(-7100.05 + 4099.21i) q^{18} +(3872.49 + 2235.78i) q^{19} +(-295.620 - 170.676i) q^{20} -18729.6 q^{21} -2568.42i q^{22} +(8465.56 - 14662.8i) q^{23} +(-10987.4 + 19030.7i) q^{24} +(1262.49 + 2186.70i) q^{25} +(-14284.1 + 8246.95i) q^{26} +13342.2i q^{27} +(-975.575 + 563.248i) q^{28} +(12578.3 - 7262.09i) q^{29} +(38534.6 - 22248.0i) q^{30} +(25798.6 - 44684.4i) q^{31} +2593.02i q^{32} +(-11952.1 - 6900.53i) q^{33} +(-37036.1 + 21382.8i) q^{34} +59896.7 q^{35} +(1324.79 + 2294.60i) q^{36} +(70836.6 + 40897.5i) q^{37} +(-17528.6 + 30360.5i) q^{38} +88627.6i q^{39} +(35137.3 - 60859.6i) q^{40} -18379.1 q^{41} -146841. i q^{42} +(-23774.6 + 75869.2i) q^{43} -830.067 q^{44} -140880. i q^{45} +(114957. + 66370.3i) q^{46} -55823.4 q^{47} +(-143285. - 82725.9i) q^{48} +(40008.1 - 69296.0i) q^{49} +(-17143.8 + 9897.99i) q^{50} +229795. i q^{51} +(2665.26 + 4616.37i) q^{52} +(86428.0 - 149698. i) q^{53} -104604. q^{54} +(38222.3 + 22067.7i) q^{55} +(-115957. - 200843. i) q^{56} +(94187.6 + 163138. i) q^{57} +(56935.0 + 98614.4i) q^{58} +24253.5 q^{59} +(-7190.14 - 12453.7i) q^{60} +(-103219. + 59593.7i) q^{61} +(350328. + 202262. i) q^{62} +(-402632. - 232459. i) q^{63} -271684. q^{64} -283428. i q^{65} +(54100.4 - 93704.7i) q^{66} +(-246132. + 426314. i) q^{67} +(6910.53 + 11969.4i) q^{68} +(617704. - 356631. i) q^{69} +469593. i q^{70} +(318444. - 183854. i) q^{71} +(-472393. + 272736. i) q^{72} +(-517521. + 298791. i) q^{73} +(-320638. + 555361. i) q^{74} +106371. i q^{75} +(9811.95 + 5664.93i) q^{76} +(126137. - 72825.5i) q^{77} -694844. q^{78} +(79931.1 + 138445. i) q^{79} +(458222. + 264555. i) q^{80} +(100126. - 173423. i) q^{81} -144093. i q^{82} +(56714.5 - 98232.4i) q^{83} -47456.3 q^{84} -734877. i q^{85} +(-594817. - 186394. i) q^{86} +611865. q^{87} -170887. i q^{88} +(-255618. - 147581. i) q^{89} +1.10451e6 q^{90} +(-810029. - 467671. i) q^{91} +(21449.7 - 37151.9i) q^{92} +(1.88244e6 - 1.08683e6i) q^{93} -437658. i q^{94} +(-301209. - 521709. i) q^{95} +(-54618.5 + 94602.1i) q^{96} +1.59602e6 q^{97} +(543283. + 313665. i) q^{98} +(-171289. - 296682. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			7.84004i			0.980005i	0.871721	+	0.490003i	$0.163004\pi$
$2$			7.84004i			0.980005i	−0.871721	+	0.490003i	$0.836996\pi$
$3$	36.4833	+	21.0637i	1.35123	+	0.780136i	0.988423	−	0.151726i	$-0.0484833\pi$
$3$	36.4833	+	21.0637i	1.35123	+	0.780136i	0.362812	+	0.931862i	$0.381817\pi$
$4$	2.53376			0.0395900
$5$	−116.673	−	67.3609i	−0.933381	−	0.538888i	−0.0455014	−	0.998964i	$-0.514489\pi$
$5$	−116.673	−	67.3609i	−0.933381	−	0.538888i	−0.887879	+	0.460077i	$0.847822\pi$
$6$	−165.140	+	286.031i	−0.764537	+	1.32422i
$7$	−385.031	+	222.298i	−1.12254	+	0.648098i	−0.942048	−	0.335478i	$-0.891102\pi$
$7$	−385.031	+	222.298i	−1.12254	+	0.648098i	−0.180491	+	0.983577i	$0.557769\pi$
$8$			521.627i			1.01880i
$9$	522.856	+	905.613i	0.717224	+	1.24227i
$10$	528.113	−	914.718i	0.528113	−	0.914718i
$11$	−327.603			−0.246133			−0.123067	−	0.992398i	$-0.539273\pi$
$11$	−327.603			−0.246133			−0.123067	+	0.992398i	$0.539273\pi$
$12$	92.4399	+	53.3702i	0.0534953	+	0.0308855i
$13$	1051.90	+	1821.95i	0.478790	+	0.829288i	0.999704	−	0.0243205i	$-0.00774223\pi$
$13$	1051.90	+	1821.95i	0.478790	+	0.829288i	−0.520914	+	0.853609i	$0.674409\pi$
$14$	−1742.82	−	3018.66i	−0.635140	−	1.10009i
$15$	−2837.74	−	4915.10i	−0.840811	−	1.45633i
$16$	−3927.42			−0.958843
$17$	2727.39	+	4723.97i	0.555136	+	0.961525i	0.997893	+	0.0648826i	$0.0206673\pi$
$17$	2727.39	+	4723.97i	0.555136	+	0.961525i	−0.442756	+	0.896642i	$0.645999\pi$
$18$	−7100.05	+	4099.21i	−1.21743	+	0.702883i
$19$	3872.49	+	2235.78i	0.564585	+	0.325963i	0.754984	−	0.655743i	$-0.227645\pi$
$19$	3872.49	+	2235.78i	0.564585	+	0.325963i	−0.190399	+	0.981707i	$0.560978\pi$
$20$	−295.620	−	170.676i	−0.0369525	−	0.0213345i
$21$	−18729.6			−2.02242
$22$		−	2568.42i		−	0.241212i
$23$	8465.56	−	14662.8i	0.695780	−	1.20513i	−0.274137	−	0.961691i	$-0.588392\pi$
$23$	8465.56	−	14662.8i	0.695780	−	1.20513i	0.969917	−	0.243436i	$-0.0782745\pi$
$24$	−10987.4	+	19030.7i	−0.794805	+	1.37664i
$25$	1262.49	+	2186.70i	0.0807995	+	0.139949i
$26$	−14284.1	+	8246.95i	−0.812707	+	0.469217i
$27$			13342.2i			0.677856i
$28$	−975.575	+	563.248i	−0.0444413	+	0.0256582i
$29$	12578.3	−	7262.09i	0.515737	−	0.297761i	−0.219452	−	0.975623i	$-0.570427\pi$
$29$	12578.3	−	7262.09i	0.515737	−	0.297761i	0.735189	+	0.677863i	$0.237094\pi$
$30$	38534.6	−	22248.0i	1.42721	−	0.823999i
$31$	25798.6	−	44684.4i	0.865986	−	1.49993i	−7.95439e−5	−	1.00000i	$-0.500025\pi$
$31$	25798.6	−	44684.4i	0.865986	−	1.49993i	0.866065	−	0.499931i	$-0.166641\pi$
$32$			2593.02i			0.0791328i
$33$	−11952.1	−	6900.53i	−0.332584	−	0.192017i
$34$	−37036.1	+	21382.8i	−0.942299	+	0.544037i
$35$	59896.7			1.39701
$36$	1324.79	+	2294.60i	0.0283949	+	0.0491813i
$37$	70836.6	+	40897.5i	1.39847	+	0.807405i	0.994232	−	0.107250i	$-0.0342045\pi$
$37$	70836.6	+	40897.5i	1.39847	+	0.807405i	0.404235	+	0.914655i	$0.367538\pi$
$38$	−17528.6	+	30360.5i	−0.319446	+	0.553296i
$39$			88627.6i			1.49408i
$40$	35137.3	−	60859.6i	0.549020	−	0.950931i
$41$	−18379.1			−0.266669			−0.133335	−	0.991071i	$-0.542569\pi$
$41$	−18379.1			−0.266669			−0.133335	+	0.991071i	$0.542569\pi$
$42$		−	146841.i		−	1.98198i
$43$	−23774.6	+	75869.2i	−0.299025	+	0.954245i
$43$	−23774.6	+	75869.2i	−0.299025	+	0.954245i
$44$	−830.067			−0.00974440
$45$		−	140880.i		−	1.54601i
$46$	114957.	+	66370.3i	1.18103	+	0.681868i
$47$	−55823.4			−0.537678			−0.268839	−	0.963185i	$-0.586640\pi$
$47$	−55823.4			−0.537678			−0.268839	+	0.963185i	$0.586640\pi$
$48$	−143285.	−	82725.9i	−1.29562	−	0.748027i
$49$	40008.1	−	69296.0i	0.340063	−	0.589006i
$50$	−17143.8	+	9897.99i	−0.137151	+	0.0791839i
$51$			229795.i			1.73233i
$52$	2665.26	+	4616.37i	0.0189553	+	0.0328315i
$53$	86428.0	−	149698.i	0.580533	−	1.00551i	−0.414883	−	0.909875i	$-0.636178\pi$
$53$	86428.0	−	149698.i	0.580533	−	1.00551i	0.995416	−	0.0956378i	$-0.0304890\pi$
$54$	−104604.			−0.664302
$55$	38222.3	+	22067.7i	0.229736	+	0.132638i
$56$	−115957.	−	200843.i	−0.660285	−	1.14365i
$57$	94187.6	+	163138.i	0.508591	+	0.880906i
$58$	56935.0	+	98614.4i	0.291807	+	0.505425i
$59$	24253.5			0.118092			0.0590458	−	0.998255i	$-0.481194\pi$
$59$	24253.5			0.118092			0.0590458	+	0.998255i	$0.481194\pi$
$60$	−7190.14	−	12453.7i	−0.0332877	−	0.0576559i
$61$	−103219.	+	59593.7i	−0.454749	+	0.262549i	−0.709834	−	0.704369i	$-0.751230\pi$
$61$	−103219.	+	59593.7i	−0.454749	+	0.262549i	0.255085	+	0.966919i	$0.417897\pi$
$62$	350328.	+	202262.i	1.46994	+	0.848670i
$63$	−402632.	−	232459.i	−1.61022	−	0.929663i
$64$	−271684.			−1.03639
$65$		−	283428.i		−	1.03206i
$66$	54100.4	−	93704.7i	0.188178	−	0.325934i
$67$	−246132.	+	426314.i	−0.818360	+	1.41744i	0.0885307	+	0.996073i	$0.471783\pi$
$67$	−246132.	+	426314.i	−0.818360	+	1.41744i	−0.906890	+	0.421367i	$0.861550\pi$
$68$	6910.53	+	11969.4i	0.0219778	+	0.0380667i
$69$	617704.	−	356631.i	1.88032	−	1.08561i
$70$			469593.i			1.36908i
$71$	318444.	−	183854.i	0.889729	−	0.513685i	0.0158753	−	0.999874i	$-0.494947\pi$
$71$	318444.	−	183854.i	0.889729	−	0.513685i	0.873854	+	0.486189i	$0.161613\pi$
$72$	−472393.	+	272736.i	−1.26563	+	0.730710i
$73$	−517521.	+	298791.i	−1.33033	+	0.768066i	−0.985350	−	0.170544i	$-0.945448\pi$
$73$	−517521.	+	298791.i	−1.33033	+	0.768066i	−0.344980	+	0.938610i	$0.612114\pi$
$74$	−320638.	+	555361.i	−0.791261	+	1.37050i
$75$			106371.i			0.252138i
$76$	9811.95	+	5664.93i	0.0223519	+	0.0129049i
$77$	126137.	−	72825.5i	0.276294	−	0.159519i
$78$	−694844.			−1.46421
$79$	79931.1	+	138445.i	0.162119	+	0.280799i	0.935629	−	0.352986i	$-0.114834\pi$
$79$	79931.1	+	138445.i	0.162119	+	0.280799i	−0.773509	+	0.633785i	$0.781500\pi$
$80$	458222.	+	264555.i	0.894965	+	0.516708i
$81$	100126.	−	173423.i	0.188404	−	0.326325i
$82$		−	144093.i		−	0.261337i
$83$	56714.5	−	98232.4i	0.0991881	−	0.171799i	−0.812161	−	0.583434i	$-0.801709\pi$
$83$	56714.5	−	98232.4i	0.0991881	−	0.171799i	0.911349	+	0.411635i	$0.135042\pi$
$84$	−47456.3			−0.0800675
$85$		−	734877.i		−	1.19662i
$86$	−594817.	−	186394.i	−0.935165	−	0.293046i
$87$	611865.			0.929175
$88$		−	170887.i		−	0.250761i
$89$	−255618.	−	147581.i	−0.362595	−	0.209344i	0.307624	−	0.951508i	$-0.400466\pi$
$89$	−255618.	−	147581.i	−0.362595	−	0.209344i	−0.670218	+	0.742164i	$0.733800\pi$
$90$	1.10451e6			1.51510
$91$	−810029.	−	467671.i	−1.07492	−	0.620606i
$92$	21449.7	−	37151.9i	0.0275459	−	0.0477109i
$93$	1.88244e6	−	1.08683e6i	2.34030	−	1.35117i
$94$		−	437658.i		−	0.526928i
$95$	−301209.	−	521709.i	−0.351315	−	0.608496i
$96$	−54618.5	+	94602.1i	−0.0617343	+	0.106927i
$97$	1.59602e6			1.74873			0.874363	−	0.485272i	$-0.161279\pi$
$97$	1.59602e6			1.74873			0.874363	+	0.485272i	$0.161279\pi$
$98$	543283.	+	313665.i	0.577229	+	0.333263i
$99$	−171289.	−	296682.i	−0.176533	−	0.305763i
$100$	3198.85	+	5540.57i	0.00319885	+	0.00554057i
$101$	−790560.	−	1.36929e6i	−0.767310	−	1.32902i	−0.939017	−	0.343871i	$-0.888262\pi$
$101$	−790560.	−	1.36929e6i	−0.767310	−	1.32902i	0.171707	−	0.985148i	$-0.445072\pi$
$102$	−1.80160e6			−1.69769
$103$	231603.	+	401148.i	0.211949	+	0.367107i	0.952325	−	0.305087i	$-0.0986855\pi$
$103$	231603.	+	401148.i	0.211949	+	0.367107i	−0.740375	+	0.672194i	$0.765352\pi$
$104$	−950377.	+	548701.i	−0.844882	+	0.487793i
$105$	2.18523e6	+	1.26164e6i	1.88769	+	1.08986i
$106$	1.17364e6	+	677599.i	0.985407	+	0.568925i
$107$	39803.3			0.0324914			0.0162457	−	0.999868i	$-0.494829\pi$
$107$	39803.3			0.0324914			0.0162457	+	0.999868i	$0.494829\pi$
$108$			33806.0i			0.0268363i
$109$	−1.03903e6	+	1.79965e6i	−0.802323	+	1.38966i	0.115761	+	0.993277i	$0.463069\pi$
$109$	−1.03903e6	+	1.79965e6i	−0.802323	+	1.38966i	−0.918084	+	0.396387i	$0.870264\pi$
$110$	−173011.	+	299665.i	−0.129986	+	0.225142i
$111$	1.72290e6	+	2.98415e6i	1.25977	+	2.18199i
$112$	1.51218e6	−	873056.i	1.07634	−	0.621424i
$113$		−	2.50088e6i		−	1.73324i	−0.498971	−	0.866619i	$-0.666289\pi$
$113$		−	2.50088e6i		−	1.73324i	0.498971	−	0.866619i	$-0.333711\pi$
$114$	−1.27901e6	+	738434.i	−0.863293	+	0.498422i
$115$	−1.97540e6	+	1.14050e6i	−1.29886	+	0.749894i
$116$	31870.4	−	18400.4i	0.0204180	−	0.0117883i
$117$	−1.09999e6	+	1.90523e6i	−0.686799	+	1.18957i
$118$			190149.i			0.115730i
$119$	−2.10026e6	−	1.21258e6i	−1.24632	−	0.719566i
$120$	2.56385e6	−	1.48024e6i	1.48371	−	0.856621i
$121$	−1.66424e6			−0.939418
$122$	−467217.	−	809243.i	−0.257300	−	0.445656i
$123$	−670532.	−	387132.i	−0.360333	−	0.208038i
$124$	65367.3	−	113220.i	0.0342843	−	0.0593822i
$125$			1.76486e6i			0.903608i
$126$	1.82249e6	−	3.15665e6i	0.911074	−	1.57803i
$127$	2.18358e6			1.06600			0.533000	−	0.846115i	$-0.321065\pi$
$127$	2.18358e6			1.06600			0.533000	+	0.846115i	$0.321065\pi$
$128$		−	1.96406e6i		−	0.936538i
$129$	−2.46546e6	+	2.26718e6i	−1.14849	+	1.05613i
$130$	2.22209e6			1.01142
$131$			1.42783e6i			0.635128i	0.948237	+	0.317564i	$0.102865\pi$
$131$			1.42783e6i			0.635128i	−0.948237	+	0.317564i	$0.897135\pi$
$132$	−30283.6	−	17484.3i	−0.0131670	−	0.00760196i
$133$	−1.98804e6			−0.845025
$134$	−3.34232e6	−	1.92969e6i	−1.38910	−	0.801997i
$135$	898746.	−	1.55667e6i	0.365288	−	0.632698i
$136$	−2.46415e6	+	1.42268e6i	−0.979605	+	0.565575i
$137$			572173.i			0.222518i	0.993791	+	0.111259i	$0.0354883\pi$
$137$			572173.i			0.222518i	−0.993791	+	0.111259i	$0.964512\pi$
$138$	2.79600e6	+	4.84282e6i	1.06390	+	1.84273i
$139$	1.99697e6	−	3.45886e6i	0.743580	−	1.28792i	−0.207275	−	0.978283i	$-0.566460\pi$
$139$	1.99697e6	−	3.45886e6i	0.743580	−	1.28792i	0.950855	−	0.309636i	$-0.100207\pi$
$140$	151764.			0.0553075
$141$	−2.03662e6	−	1.17585e6i	−0.726530	−	0.419462i
$142$	1.44142e6	+	2.49661e6i	0.503414	+	0.871939i
$143$	−344606.	−	596876.i	−0.117846	−	0.204115i
$144$	−2.05348e6	−	3.55672e6i	−0.687705	−	1.19114i
$145$	−1.95672e6			−0.641838
$146$	−2.34253e6	−	4.05738e6i	−0.752709	−	1.30373i
$147$	2.91925e6	−	1.68543e6i	0.919009	−	0.530590i
$148$	179483.	+	103624.i	0.0553653	+	0.0319651i
$149$	−2.65414e6	−	1.53237e6i	−0.802352	−	0.463238i	0.0419408	−	0.999120i	$-0.486646\pi$
$149$	−2.65414e6	−	1.53237e6i	−0.802352	−	0.463238i	−0.844293	+	0.535882i	$0.819979\pi$
$150$	−833952.			−0.247097
$151$			3.49807e6i			1.01601i	0.861354	+	0.508005i	$0.169617\pi$
$151$			3.49807e6i			1.01601i	−0.861354	+	0.508005i	$0.830383\pi$
$152$	−1.16625e6	+	2.02000e6i	−0.332093	+	0.575201i
$153$	−2.85206e6	+	4.93991e6i	−0.796314	+	1.37926i
$154$	570955.	+	988923.i	0.156329	+	0.270770i
$155$	−6.01997e6	+	3.47563e6i	−1.61659	+	0.933338i
$156$			224561.i			0.0591507i
$157$	4.41630e6	−	2.54975e6i	1.14120	−	0.658869i	0.194469	−	0.980909i	$-0.437702\pi$
$157$	4.41630e6	−	2.54975e6i	1.14120	−	0.658869i	0.946726	+	0.322039i	$0.104368\pi$
$158$	−1.08541e6	+	626663.i	−0.275184	+	0.158878i
$159$	6.30636e6	−	3.64098e6i	1.56887	−	0.905789i
$160$	174668.	−	302535.i	0.0426437	−	0.0738610i
$161$			7.52750e6i			1.80374i
$162$	1.35964e6	+	784989.i	0.319801	+	0.184637i
$163$	1.55268e6	−	896439.i	0.358524	−	0.206994i	−0.309909	−	0.950766i	$-0.600299\pi$
$163$	1.55268e6	−	896439.i	0.358524	−	0.206994i	0.668433	+	0.743772i	$0.266965\pi$
$164$	−46568.2			−0.0105574
$165$	929652.	+	1.61020e6i	0.206952	+	0.358451i
$166$	770146.	+	444644.i	0.168364	+	0.0972049i
$167$	−150906.	+	261376.i	−0.0324008	+	0.0561199i	−0.881771	−	0.471678i	$-0.843649\pi$
$167$	−150906.	+	261376.i	−0.0324008	+	0.0561199i	0.849370	+	0.527797i	$0.176982\pi$
$168$		−	9.76988e6i		−	2.06045i
$169$	200411.	−	347123.i	0.0415205	−	0.0719155i
$170$	5.76147e6			1.17270
$171$			4.67597e6i			0.935155i
$172$	−60239.1	+	192234.i	−0.0118384	+	0.0377785i
$173$	6.71660e6			1.29721			0.648606	−	0.761124i	$-0.275352\pi$
$173$	6.71660e6			1.29721			0.648606	+	0.761124i	$0.275352\pi$
$174$			4.79704e6i			0.910596i
$175$	−972197.	−	561298.i	−0.181401	−	0.104732i
$176$	1.28664e6			0.236003
$177$	884850.	+	510868.i	0.159569	+	0.0921275i
$178$	1.15704e6	−	2.00406e6i	0.205158	−	0.355345i
$179$	3.47756e6	−	2.00777e6i	0.606340	−	0.350070i	−0.165192	−	0.986261i	$-0.552824\pi$
$179$	3.47756e6	−	2.00777e6i	0.606340	−	0.350070i	0.771532	+	0.636191i	$0.219491\pi$
$180$		−	356957.i		−	0.0612065i
$181$	−4.21134e6	−	7.29425e6i	−0.710206	−	1.23011i	−0.964780	−	0.263060i	$-0.915268\pi$
$181$	−4.21134e6	−	7.29425e6i	−0.710206	−	1.23011i	0.254573	−	0.967053i	$-0.418065\pi$
$182$	3.66656e6	−	6.35066e6i	0.608197	−	1.05343i
$183$	−5.02105e6			−0.819296
$184$	7.64850e6	+	4.41587e6i	1.22779	+	0.708863i
$185$	−5.50979e6	−	9.54323e6i	−0.870201	−	1.50723i
$186$	8.52075e6	+	1.47584e7i	1.32416	+	2.29351i
$187$	−893501.	−	1.54759e6i	−0.136638	−	0.236663i
$188$	−141443.			−0.0212867
$189$	−2.96595e6	−	5.13717e6i	−0.439317	−	0.760920i
$190$	4.09022e6	−	2.36149e6i	0.596329	−	0.344291i
$191$	3.89200e6	+	2.24705e6i	0.558564	+	0.322487i	0.752569	−	0.658513i	$-0.228814\pi$
$191$	3.89200e6	+	2.24705e6i	0.558564	+	0.322487i	−0.194005	+	0.981001i	$0.562148\pi$
$192$	−9.91195e6	−	5.72267e6i	−1.40041	−	0.808527i
$193$	−3.37851e6			−0.469951			−0.234976	−	0.972001i	$-0.575501\pi$
$193$	−3.37851e6			−0.469951			−0.234976	+	0.972001i	$0.575501\pi$
$194$			1.25128e7i			1.71376i
$195$	5.97004e6	−	1.03404e7i	0.805143	−	1.39455i
$196$	101371.	−	175579.i	0.0134631	−	0.0233187i
$197$	−6.56487e6	−	1.13707e7i	−0.858673	−	1.48726i	−0.873196	−	0.487370i	$-0.837956\pi$
$197$	−6.56487e6	−	1.13707e7i	−0.858673	−	1.48726i	0.0145229	−	0.999895i	$-0.495377\pi$
$198$	2.32600e6	−	1.34292e6i	0.299650	−	0.173003i
$199$		−	3.22237e6i		−	0.408899i	−0.978877	−	0.204450i	$-0.934460\pi$
$199$		−	3.22237e6i		−	0.408899i	0.978877	−	0.204450i	$-0.0655405\pi$
$200$	−1.14064e6	+	658550.i	−0.142580	+	0.0823188i
$201$	−1.79595e7	+	1.03689e7i	−2.21159	+	1.27686i
$202$	1.07353e7	−	6.19802e6i	1.30245	−	0.751967i
$203$	−3.22869e6	+	5.59226e6i	−0.385956	+	0.668496i
$204$			582245.i			0.0685828i
$205$	2.14434e6	+	1.23803e6i	0.248904	+	0.143705i
$206$	−3.14502e6	+	1.81578e6i	−0.359767	+	0.207711i
$207$	1.77051e7			1.99612
$208$	−4.13126e6	−	7.15555e6i	−0.459084	−	0.795157i
$209$	−1.26864e6	−	732450.i	−0.138963	−	0.0802304i
$210$	−9.89135e6	+	1.71323e7i	−1.06806	+	1.84994i
$211$		−	1.33613e6i		−	0.142233i	−0.997468	−	0.0711167i	$-0.977344\pi$
$211$		−	1.33613e6i		−	0.142233i	0.997468	−	0.0711167i	$-0.0226563\pi$
$212$	218988.	−	379298.i	0.0229833	−	0.0398082i
$213$	1.54905e7			1.60298
$214$			312060.i			0.0318417i
$215$	7.88446e6	−	7.25037e6i	0.793335	−	0.729533i
$216$	−6.95968e6			−0.690602
$217$			2.29399e7i			2.24498i
$218$	−1.41094e7	−	8.14605e6i	−1.36188	−	0.786280i
$219$	−2.51745e7			−2.39678
$220$	96846.1	+	55914.1i	0.00909524	+	0.00525114i
$221$	−5.73788e6	+	9.93830e6i	−0.531587	+	0.920737i
$222$	−2.33959e7	+	1.35076e7i	−2.13836	+	1.23458i
$223$		−	5.83307e6i		−	0.525996i	−0.964796	−	0.262998i	$-0.915289\pi$
$223$		−	5.83307e6i		−	0.525996i	0.964796	−	0.262998i	$-0.0847113\pi$
$224$	−576423.	−	998394.i	−0.0512858	−	0.0888296i
$225$	−1.32020e6	+	2.28666e6i	−0.115903	+	0.200749i
$226$	1.96070e7			1.69858
$227$	−6.69092e6	−	3.86301e6i	−0.572016	−	0.330254i	0.185938	−	0.982561i	$-0.440468\pi$
$227$	−6.69092e6	−	3.86301e6i	−0.572016	−	0.330254i	−0.757954	+	0.652308i	$0.773801\pi$
$228$	238648.	+	413351.i	0.0201351	+	0.0348750i
$229$	4.22606e6	+	7.31975e6i	0.351908	+	0.609522i	0.986584	−	0.163256i	$-0.0521997\pi$
$229$	4.22606e6	+	7.31975e6i	0.351908	+	0.609522i	−0.634676	+	0.772778i	$0.718866\pi$
$230$	−8.94153e6	−	1.54872e7i	−0.734900	−	1.27288i
$231$	6.13589e6			0.497784
$232$	3.78810e6	+	6.56119e6i	0.303360	+	0.525434i
$233$	476080.	−	274865.i	0.0376367	−	0.0217296i	−0.481064	−	0.876686i	$-0.659749\pi$
$233$	476080.	−	274865.i	0.0376367	−	0.0217296i	0.518700	+	0.854956i	$0.326416\pi$
$234$	−1.49371e7	−	8.62394e6i	−1.16579	−	0.673066i
$235$	6.51306e6	+	3.76032e6i	0.501859	+	0.289748i
$236$	61452.6			0.00467524
$237$			6.73457e6i			0.505900i
$238$	9.50670e6	−	1.64661e7i	0.705178	−	1.22140i
$239$	7.42657e6	−	1.28632e7i	0.543995	−	0.942227i	−0.454675	−	0.890658i	$-0.650244\pi$
$239$	7.42657e6	−	1.28632e7i	0.543995	−	0.942227i	0.998669	−	0.0515690i	$-0.0164222\pi$
$240$	1.11450e7	+	1.93037e7i	0.806205	+	1.39639i
$241$	3.46153e6	−	1.99852e6i	0.247296	−	0.142776i	−0.371230	−	0.928541i	$-0.621064\pi$
$241$	3.46153e6	−	1.99852e6i	0.247296	−	0.142776i	0.618525	+	0.785765i	$0.287730\pi$
$242$		−	1.30477e7i		−	0.920635i
$243$	1.57292e7	−	9.08127e6i	1.09620	−	0.632889i
$244$	−261533.	+	150996.i	−0.0180035	+	0.0103943i
$245$	−9.33568e6	+	5.38996e6i	−0.634816	+	0.366511i
$246$	3.03513e6	−	5.25700e6i	0.203879	−	0.353128i
$247$			9.40729e6i			0.624272i
$248$	2.33086e7	+	1.34572e7i	1.52814	+	0.882269i
$249$	4.13827e6	−	2.38923e6i	0.268053	−	0.154760i
$250$	−1.38366e7			−0.885540
$251$	1.23737e7	+	2.14319e7i	0.782489	+	1.35531i	0.930488	+	0.366323i	$0.119383\pi$
$251$	1.23737e7	+	2.14319e7i	0.782489	+	1.35531i	−0.147999	+	0.988988i	$0.547283\pi$
$252$	−1.02017e6	−	588996.i	−0.0637487	−	0.0368053i
$253$	−2.77334e6	+	4.80357e6i	−0.171255	+	0.296622i
$254$			1.71193e7i			1.04468i
$255$	1.54792e7	−	2.68108e7i	0.933530	−	1.61692i
$256$	−1.98946e6			−0.118581
$257$			2.01647e7i			1.18793i	0.804490	+	0.593966i	$0.202439\pi$
$257$			2.01647e7i			1.18793i	−0.804490	+	0.593966i	$0.797561\pi$
$258$	−1.77748e7	−	1.93293e7i	−1.03501	−	1.12553i
$259$	−3.63657e7			−2.09311
$260$		−	718138.i		−	0.0408590i
$261$	1.31533e7	+	7.59405e6i	0.739797	+	0.427122i
$262$	−1.11942e7			−0.622429
$263$	−527604.	−	304613.i	−0.0290029	−	0.0167448i	0.485428	−	0.874276i	$-0.338664\pi$
$263$	−527604.	−	304613.i	−0.0290029	−	0.0167448i	−0.514431	+	0.857532i	$0.671997\pi$
$264$	3.59950e6	−	6.23452e6i	0.195628	−	0.338838i
$265$	−2.01676e7	+	1.16437e7i	−1.08372	+	0.625684i
$266$		−	1.55863e7i		−	0.828129i
$267$	−6.21720e6	−	1.07685e7i	−0.326634	−	0.565746i
$268$	−623639.	+	1.08018e6i	−0.0323988	+	0.0561164i
$269$	−2.04452e7			−1.05035			−0.525174	−	0.850995i	$-0.676000\pi$
$269$	−2.04452e7			−1.05035			−0.525174	+	0.850995i	$0.676000\pi$
$270$	1.22044e7	+	7.04620e6i	0.620047	+	0.357984i
$271$	−4.31298e6	−	7.47030e6i	−0.216705	−	0.375345i	0.737093	−	0.675791i	$-0.236198\pi$
$271$	−4.31298e6	−	7.47030e6i	−0.216705	−	0.375345i	−0.953799	+	0.300446i	$0.902864\pi$
$272$	−1.07116e7	−	1.85530e7i	−0.532289	−	0.921951i
$273$	−1.97017e7	−	3.41244e7i	−0.968314	−	1.67717i
$274$	−4.48586e6			−0.218069
$275$	−413597.	−	716370.i	−0.0198874	−	0.0344461i
$276$	1.56511e6	−	903617.i	0.0744420	−	0.0429791i
$277$	1.52684e7	+	8.81522e6i	0.718380	+	0.414757i	0.814156	−	0.580646i	$-0.197200\pi$
$277$	1.52684e7	+	8.81522e6i	0.718380	+	0.414757i	−0.0957761	+	0.995403i	$0.530533\pi$
$278$	2.71176e7	+	1.56563e7i	1.26217	+	0.728712i
$279$	5.39558e7			2.48442
$280$			3.12438e7i			1.42328i
$281$	9.50646e6	−	1.64657e7i	0.428450	−	0.742097i	−0.568286	−	0.822831i	$-0.692393\pi$
$281$	9.50646e6	−	1.64657e7i	0.428450	−	0.742097i	0.996736	+	0.0807343i	$0.0257265\pi$
$282$	9.21867e6	−	1.59672e7i	0.411075	−	0.712003i
$283$	4.62910e6	+	8.01783e6i	0.204238	+	0.353751i	0.949890	−	0.312585i	$-0.101195\pi$
$283$	4.62910e6	+	8.01783e6i	0.204238	+	0.353751i	−0.745652	+	0.666336i	$0.767862\pi$
$284$	806859.	−	465841.i	0.0352243	−	0.0203368i
$285$		−	2.53783e7i		−	1.09629i
$286$	4.67953e6	−	2.70173e6i	0.200034	−	0.115490i
$287$	7.07653e6	−	4.08564e6i	0.299347	−	0.172828i
$288$	−2.34828e6	+	1.35578e6i	−0.0983041	+	0.0567559i
$289$	−2.80848e6	+	4.86443e6i	−0.116353	+	0.201529i
$290$		−	1.53408e7i		−	0.629005i
$291$	5.82280e7	+	3.36179e7i	2.36294	+	1.36424i
$292$	−1.31127e6	+	757063.i	−0.0526677	+	0.0304077i
$293$	−4.55625e6			−0.181136			−0.0905680	−	0.995890i	$-0.528868\pi$
$293$	−4.55625e6			−0.181136			−0.0905680	+	0.995890i	$0.528868\pi$
$294$	1.32139e7	+	2.28871e7i	0.519981	+	0.900634i
$295$	−2.82972e6	−	1.63374e6i	−0.110224	−	0.0636381i
$296$	−2.13333e7	+	3.69503e7i	−0.822587	+	1.42476i
$297$		−	4.37096e6i		−	0.166843i
$298$	1.20138e7	−	2.08086e7i	0.453976	−	0.786309i
$299$	3.56197e7			1.33253
$300$			269518.i			0.00998215i
$301$	−7.71159e6	−	3.44970e7i	−0.282777	−	1.26498i
$302$	−2.74250e7			−0.995695
$303$		−	6.66083e7i		−	2.39442i
$304$	−1.52089e7	−	8.78086e6i	−0.541348	−	0.312548i
$305$	1.60571e7			0.565938
$306$	−3.87291e7	−	2.23603e7i	−1.35168	−	0.780392i
$307$	−7.90956e6	+	1.36998e7i	−0.273361	+	0.473476i	−0.969720	−	0.244218i	$-0.921469\pi$
$307$	−7.90956e6	+	1.36998e7i	−0.273361	+	0.473476i	0.696359	+	0.717694i	$0.254802\pi$
$308$	319602.	−	184522.i	0.0109385	−	0.00631533i
$309$			1.95136e7i			0.661397i
$310$	−2.72491e7	−	4.71968e7i	−0.914676	−	1.58426i
$311$	1.43630e7	−	2.48774e7i	0.477489	−	0.827035i	−0.522178	−	0.852836i	$-0.674880\pi$
$311$	1.43630e7	−	2.48774e7i	0.477489	−	0.827035i	0.999667	+	0.0258012i	$0.00821370\pi$
$312$	−4.62306e7			−1.52218
$313$	3.76377e7	+	2.17301e7i	1.22741	+	0.708647i	0.966488	−	0.256713i	$-0.0826394\pi$
$313$	3.76377e7	+	2.17301e7i	1.22741	+	0.708647i	0.260924	+	0.965359i	$0.415973\pi$
$314$	1.99902e7	+	3.46240e7i	0.645695	+	1.11838i
$315$	3.13174e7	+	5.42433e7i	1.00197	+	1.73546i
$316$	202526.	+	350785.i	0.00641829	+	0.0111168i
$317$	−6.09350e7			−1.91289			−0.956443	−	0.291920i	$-0.905706\pi$
$317$	−6.09350e7			−1.91289			−0.956443	+	0.291920i	$0.905706\pi$
$318$	2.85454e7	+	4.94421e7i	0.887678	+	1.53750i
$319$	−4.12069e6	+	2.37908e6i	−0.126940	+	0.0732888i
$320$	3.16981e7	+	1.83009e7i	0.967349	+	0.558499i
$321$	1.45216e6	+	838404.i	0.0439035	+	0.0253477i
$322$	−5.90159e7			−1.76767
$323$			2.43914e7i			0.723817i
$324$	253694.	−	439411.i	0.00745891	−	0.0129192i
$325$	−2.65603e6	+	4.60039e6i	−0.0773720	+	0.134012i
$326$	7.02812e6	+	1.21731e7i	0.202855	+	0.351356i
$327$	−7.58147e7	+	4.37716e7i	−2.16825	+	1.25184i
$328$		−	9.58705e6i		−	0.271684i
$329$	2.14937e7	−	1.24094e7i	0.603565	−	0.348468i
$330$	−1.26241e7	+	7.28851e6i	−0.351283	+	0.202814i
$331$	−5.50411e7	+	3.17780e7i	−1.51776	+	0.876279i	−0.517979	+	0.855394i	$0.673315\pi$
$331$	−5.50411e7	+	3.17780e7i	−1.51776	+	0.876279i	−0.999782	+	0.0208860i	$0.993351\pi$
$332$	143701.	−	248897.i	0.00392685	−	0.00680151i
$333$			8.55340e7i			2.31636i
$334$	−2.04920e6	−	1.18311e6i	−0.0549978	−	0.0317530i
$335$	5.74338e7	−	3.31594e7i	1.52768	−	0.882007i
$336$	7.35591e7			1.93918
$337$	−1.63553e7	−	2.83282e7i	−0.427336	−	0.740167i	0.569300	−	0.822130i	$-0.307214\pi$
$337$	−1.63553e7	−	2.83282e7i	−0.427336	−	0.740167i	−0.996635	+	0.0819630i	$0.973881\pi$
$338$	2.72146e6	+	1.57123e6i	0.0704776	+	0.0406903i
$339$	5.26778e7	−	9.12405e7i	1.35216	−	2.34201i
$340$		−	1.86200e6i		−	0.0473743i
$341$	−8.45170e6	+	1.46388e7i	−0.213148	+	0.369183i
$342$	−3.66598e7			−0.916456
$343$		−	1.67314e7i		−	0.414620i
$344$	−3.95754e7	−	1.24015e7i	−0.972188	−	0.304648i
$345$	−9.60921e7			−2.34008
$346$			5.26584e7i			1.27127i
$347$	1.22705e7	+	7.08436e6i	0.293679	+	0.169556i	0.639600	−	0.768708i	$-0.279100\pi$
$347$	1.22705e7	+	7.08436e6i	0.293679	+	0.169556i	−0.345921	+	0.938264i	$0.612433\pi$
$348$	1.55032e6			0.0367860
$349$	7.53804e6	+	4.35209e6i	0.177330	+	0.102382i	0.586038	−	0.810284i	$-0.300687\pi$
$349$	7.53804e6	+	4.35209e6i	0.177330	+	0.102382i	−0.408708	+	0.912665i	$0.634020\pi$
$350$	4.40060e6	−	7.62206e6i	0.102638	−	0.177774i
$351$	−2.43088e7	+	1.40347e7i	−0.562138	+	0.324551i
$352$		−	849483.i		−	0.0194772i
$353$	−3.74563e7	−	6.48762e7i	−0.851531	−	1.47490i	−0.879826	−	0.475296i	$-0.842341\pi$
$353$	−3.74563e7	−	6.48762e7i	−0.851531	−	1.47490i	0.0282946	−	0.999600i	$-0.490992\pi$
$354$	−4.00523e6	+	6.93726e6i	−0.0902854	+	0.156379i
$355$	−4.95382e7			−1.10727
$356$	−647674.	−	373935.i	−0.0143551	−	0.00828793i
$357$	−5.10829e7	−	8.84782e7i	−1.12272	−	1.94461i
$358$	1.57410e7	+	2.72642e7i	0.343071	+	0.594216i
$359$	−1.21301e7	−	2.10099e7i	−0.262168	−	0.454088i	0.704650	−	0.709555i	$-0.251104\pi$
$359$	−1.21301e7	−	2.10099e7i	−0.262168	−	0.454088i	−0.966818	+	0.255467i	$0.917771\pi$
$360$	7.34870e7			1.57508
$361$	−1.35255e7	−	2.34268e7i	−0.287496	−	0.497957i
$362$	5.71872e7	−	3.30171e7i	1.20552	−	0.696006i
$363$	−6.07169e7	−	3.50549e7i	−1.26937	−	0.732874i
$364$	−2.05242e6	−	1.18496e6i	−0.0425561	−	0.0245698i
$365$	8.05073e7			1.65561
$366$		−	3.93652e7i		−	0.802914i
$367$	3.99405e6	−	6.91790e6i	0.0808008	−	0.139951i	−0.822793	−	0.568341i	$-0.807586\pi$
$367$	3.99405e6	−	6.91790e6i	0.0808008	−	0.139951i	0.903594	+	0.428390i	$0.140919\pi$
$368$	−3.32478e7	+	5.75869e7i	−0.667144	+	1.15553i
$369$	−9.60963e6	−	1.66444e7i	−0.191262	−	0.331275i
$370$	7.48193e7	−	4.31970e7i	1.47710	−	0.852802i
$371$			7.68510e7i			1.50497i
$372$	4.76964e6	−	2.75375e6i	0.0926524	−	0.0534929i
$373$	−1.48835e7	+	8.59297e6i	−0.286799	+	0.165583i	−0.636497	−	0.771279i	$-0.719617\pi$
$373$	−1.48835e7	+	8.59297e6i	−0.286799	+	0.165583i	0.349699	+	0.936862i	$0.386284\pi$
$374$	1.21332e7	−	7.00508e6i	0.231931	−	0.133905i
$375$	−3.71744e7	+	6.43879e7i	−0.704937	+	1.22099i
$376$		−	2.91190e7i		−	0.547789i
$377$	2.64623e7	+	1.52780e7i	0.493859	+	0.285130i
$378$	4.02757e7	−	2.32532e7i	0.745705	−	0.430533i
$379$	−1.20939e7			−0.222152			−0.111076	−	0.993812i	$-0.535430\pi$
$379$	−1.20939e7			−0.222152			−0.111076	+	0.993812i	$0.535430\pi$
$380$	−763190.	−	1.32188e6i	−0.0139086	−	0.0240903i
$381$	7.96641e7	+	4.59941e7i	1.44042	+	0.831624i
$382$	−1.76170e7	+	3.05135e7i	−0.316039	+	0.547396i
$383$			7.58296e7i			1.34972i	0.737947	+	0.674858i	$0.235795\pi$
$383$			7.58296e7i			1.34972i	−0.737947	+	0.674858i	$0.764205\pi$
$384$	4.13704e7	−	7.16556e7i	0.730627	−	1.26548i
$385$	−1.96224e7			−0.343850
$386$		−	2.64876e7i		−	0.460555i
$387$	−8.11388e7	+	1.81381e7i	−1.39990	+	0.312938i
$388$	4.04392e6			0.0692320
$389$		−	1.37218e7i		−	0.233111i	−0.993184	−	0.116556i	$-0.962815\pi$
$389$		−	1.37218e7i		−	0.233111i	0.993184	−	0.116556i	$-0.0371853\pi$
$390$	8.10692e7	+	4.68053e7i	1.36667	+	0.789045i
$391$	9.23553e7			1.54501
$392$	3.61467e7	+	2.08693e7i	0.600081	+	0.346457i
$393$	−3.00752e7	+	5.20918e7i	−0.495486	+	0.858207i
$394$	8.91467e7	−	5.14689e7i	1.45753	−	0.841504i
$395$		−	2.15369e7i		−	0.349456i
$396$	−434006.	−	751720.i	−0.00698892	−	0.0121052i
$397$	5.27569e6	−	9.13777e6i	0.0843156	−	0.146039i	−0.820784	−	0.571239i	$-0.806463\pi$
$397$	5.27569e6	−	9.13777e6i	0.0843156	−	0.146039i	0.905099	+	0.425200i	$0.139796\pi$
$398$	2.52635e7			0.400723
$399$	−7.25303e7	−	4.18754e7i	−1.14183	−	0.659234i
$400$	−4.95834e6	−	8.58809e6i	−0.0774740	−	0.134189i
$401$	2.00306e7	+	3.46941e7i	0.310643	+	0.538049i	0.978502	−	0.206239i	$-0.0661224\pi$
$401$	2.00306e7	+	3.46941e7i	0.310643	+	0.538049i	−0.667859	+	0.744288i	$0.732789\pi$
$402$	−8.12926e7	−	1.40803e8i	−1.25133	−	2.16737i
$403$	1.08550e8			1.65850
$404$	−2.00309e6	−	3.46945e6i	−0.0303778	−	0.0526158i
$405$	−2.33638e7	+	1.34891e7i	−0.351705	+	0.203057i
$406$	−4.38435e7	−	2.53131e7i	−0.655130	−	0.378239i
$407$	−2.32063e7	−	1.33982e7i	−0.344209	−	0.198729i
$408$	−1.19867e8			−1.76490
$409$			1.15542e8i			1.68876i	0.535743	+	0.844381i	$0.320032\pi$
$409$			1.15542e8i			1.68876i	−0.535743	+	0.844381i	$0.679968\pi$
$410$	−9.70624e6	+	1.68117e7i	−0.140831	+	0.243927i
$411$	−1.20521e7	+	2.08748e7i	−0.173594	+	0.300674i
$412$	586825.	+	1.01641e6i	0.00839107	+	0.0145338i
$413$	−9.33836e6	+	5.39151e6i	−0.132562	+	0.0765350i
$414$			1.38808e8i			1.95621i
$415$	−1.32340e7	+	7.64068e6i	−0.185161	+	0.106902i
$416$	−4.72435e6	+	2.72760e6i	−0.0656239	+	0.0378880i
$417$	1.45712e8	−	8.41271e7i	2.00950	−	1.16019i
$418$	5.74244e6	−	9.94619e6i	0.0786262	−	0.136185i
$419$			7.07193e7i			0.961382i	0.876890	+	0.480691i	$0.159614\pi$
$419$			7.07193e7i			0.961382i	−0.876890	+	0.480691i	$0.840386\pi$
$420$	5.53685e6	+	3.19670e6i	0.0747334	+	0.0431474i
$421$	−1.43862e7	+	8.30589e6i	−0.192797	+	0.111311i	−0.593291	−	0.804988i	$-0.702172\pi$
$421$	−1.43862e7	+	8.30589e6i	−0.192797	+	0.111311i	0.400494	+	0.916299i	$0.368838\pi$
$422$	1.04753e7			0.139390
$423$	−2.91876e7	−	5.05544e7i	−0.385636	−	0.667941i
$424$	7.80864e7	+	4.50832e7i	1.02442	+	0.591449i
$425$	−6.88661e6	+	1.19279e7i	−0.0897095	+	0.155381i
$426$			1.21446e8i			1.57093i
$427$	2.64951e7	−	4.58908e7i	0.340315	−	0.589443i
$428$	100852.			0.00128633
$429$		−	2.90347e7i		−	0.367744i
$430$	5.68432e7	+	6.18145e7i	0.714946	+	0.777472i
$431$	1.56678e8			1.95693			0.978466	−	0.206410i	$-0.0661782\pi$
$431$	1.56678e8			1.95693			0.978466	+	0.206410i	$0.0661782\pi$
$432$		−	5.24006e7i		−	0.649957i
$433$	−4.57815e7	−	2.64319e7i	−0.563931	−	0.325586i	0.190791	−	0.981631i	$-0.438895\pi$
$433$	−4.57815e7	−	2.64319e7i	−0.563931	−	0.325586i	−0.754722	+	0.656045i	$0.772228\pi$
$434$	−1.79849e8			−2.20009
$435$	−7.13878e7	−	4.12158e7i	−0.867274	−	0.500721i
$436$	−2.63265e6	+	4.55989e6i	−0.0317639	+	0.0550167i
$437$	6.55656e7	−	3.78543e7i	0.785654	−	0.453598i
$438$		−	1.97369e8i		−	2.34886i
$439$	−6.53778e7	−	1.13238e8i	−0.772746	−	1.33844i	−0.936053	−	0.351860i	$-0.885549\pi$
$439$	−6.53778e7	−	1.13238e8i	−0.772746	−	1.33844i	0.163307	−	0.986575i	$-0.447784\pi$
$440$	−1.15111e7	+	1.99378e7i	−0.135132	+	0.234056i
$441$	8.36738e7			0.975604
$442$	−7.79167e7	−	4.49852e7i	−0.902326	−	0.520958i
$443$	4.06510e7	+	7.04095e7i	0.467584	+	0.809879i	0.999314	−	0.0370347i	$-0.0117912\pi$
$443$	4.06510e7	+	7.04095e7i	0.467584	+	0.809879i	−0.531730	+	0.846914i	$0.678458\pi$
$444$	4.36542e6	+	7.56112e6i	0.0498743	+	0.0863848i
$445$	1.98824e7	+	3.44373e7i	0.225626	+	0.390796i
$446$	4.57315e7			0.515479
$447$	−6.45546e7	−	1.11812e8i	−0.722777	−	1.25189i
$448$	1.04607e8	−	6.03948e7i	1.16339	−	0.671685i
$449$	1.15268e7	+	6.65499e6i	0.127341	+	0.0735205i	0.562317	−	0.826921i	$-0.309910\pi$
$449$	1.15268e7	+	6.65499e6i	0.127341	+	0.0735205i	−0.434976	+	0.900442i	$0.643243\pi$
$450$	−1.79275e7	−	1.03504e7i	−0.196735	−	0.113585i
$451$	6.02106e6			0.0656362
$452$		−	6.33663e6i		−	0.0686188i
$453$	−7.36823e7	+	1.27621e8i	−0.792626	+	1.37287i
$454$	3.02861e7	−	5.24571e7i	0.323650	−	0.560579i
$455$	6.30055e7	+	1.09129e8i	0.668873	+	1.15852i
$456$	−8.50971e7	+	4.91308e7i	−0.897470	+	0.518155i
$457$		−	8.86056e7i		−	0.928351i	−0.885743	−	0.464176i	$-0.846351\pi$
$457$		−	8.86056e7i		−	0.928351i	0.885743	−	0.464176i	$-0.153649\pi$
$458$	−5.73871e7	+	3.31325e7i	−0.597335	+	0.344871i
$459$	−6.30283e7	+	3.63894e7i	−0.651775	+	0.376303i
$460$	−5.00517e6	+	2.88974e6i	−0.0514216	+	0.0296883i
$461$	4.90045e7	−	8.48782e7i	0.500187	−	0.866350i	−0.499813	−	0.866134i	$-0.666598\pi$
$461$	4.90045e7	−	8.48782e7i	0.500187	−	0.866350i	1.00000		0.000216483i	$-6.89085e-5\pi$
$462$			4.81056e7i			0.487831i
$463$	−1.32217e8	−	7.63354e7i	−1.33212	−	0.769100i	−0.346496	−	0.938051i	$-0.612629\pi$
$463$	−1.32217e8	−	7.63354e7i	−1.33212	−	0.769100i	−0.985624	+	0.168951i	$0.945962\pi$
$464$	−4.94003e7	+	2.85213e7i	−0.494510	+	0.285506i
$465$	−2.92838e8			−2.91252
$466$	2.15495e6	+	3.73248e6i	0.0212951	+	0.0368842i
$467$	−3.05612e7	−	1.76445e7i	−0.300068	−	0.173244i	0.342405	−	0.939552i	$-0.388758\pi$
$467$	−3.05612e7	−	1.76445e7i	−0.300068	−	0.173244i	−0.642473	+	0.766308i	$0.722092\pi$
$468$	−2.78710e6	+	4.82740e6i	−0.0271903	+	0.0470951i
$469$		−	2.18859e8i		−	2.12151i
$470$	−2.94810e7	+	5.10626e7i	−0.283955	+	0.491824i
$471$	2.14829e8			2.05603
$472$			1.26513e7i			0.120312i
$473$	7.78864e6	−	2.48550e7i	0.0736000	−	0.234871i
$474$	−5.27993e7			−0.495784
$475$			1.12906e7i			0.105351i
$476$	−5.32154e6	−	3.07239e6i	−0.0493420	−	0.0284876i
$477$	1.80758e8			1.66549
$478$	1.00848e8	+	5.82246e7i	0.923387	+	0.533118i
$479$	−8.04562e7	+	1.39354e8i	−0.732070	+	1.26798i	0.223927	+	0.974606i	$0.428112\pi$
$479$	−8.04562e7	+	1.39354e8i	−0.732070	+	1.26798i	−0.955997	+	0.293377i	$0.905221\pi$
$480$	1.27450e7	−	7.35831e6i	0.115243	−	0.0665357i
$481$			1.72081e8i			1.54631i
$482$	1.56684e7	+	2.71385e7i	0.139922	+	0.242351i
$483$	−1.58557e8	+	2.74628e8i	−1.40716	+	2.43727i
$484$	−4.21677e6			−0.0371915
$485$	−1.86211e8	−	1.07509e8i	−1.63223	−	0.942367i
$486$	7.11975e7	+	1.23318e8i	0.620235	+	1.07428i
$487$	−1.93829e7	−	3.35722e7i	−0.167816	−	0.290665i	0.769836	−	0.638242i	$-0.220338\pi$
$487$	−1.93829e7	−	3.35722e7i	−0.167816	−	0.290665i	−0.937652	+	0.347577i	$0.887005\pi$
$488$	−3.10857e7	−	5.38420e7i	−0.267486	−	0.463299i
$489$	7.55292e7			0.645934
$490$	−4.22575e7	−	7.31921e7i	−0.359183	−	0.622123i
$491$	1.51321e8	−	8.73655e7i	1.27837	−	0.738066i	0.301820	−	0.953365i	$-0.402406\pi$
$491$	1.51321e8	−	8.73655e7i	1.27837	−	0.738066i	0.976548	+	0.215299i	$0.0690725\pi$
$492$	−1.69896e6	−	980898.i	−0.0142656	−	0.00823623i
$493$	6.86117e7	+	3.96130e7i	0.572608	+	0.330596i
$494$	−7.37536e7			−0.611790
$495$			4.61529e7i			0.380525i
$496$	−1.01322e8	+	1.75495e8i	−0.830344	+	1.43820i
$497$	−8.17405e7	+	1.41579e8i	−0.665837	+	1.15326i
$498$	1.87317e7	+	3.24442e7i	0.151666	+	0.262693i
$499$	−3.69885e7	+	2.13553e7i	−0.297690	+	0.171872i	−0.641405	−	0.767203i	$-0.721648\pi$
$499$	−3.69885e7	+	2.13553e7i	−0.297690	+	0.171872i	0.343714	+	0.939074i	$0.388315\pi$
$500$			4.47172e6i			0.0357738i
$501$	−1.10111e7	+	6.35726e6i	−0.0875623	+	0.0505541i
$502$	−1.68027e8	+	9.70103e7i	−1.32821	+	0.766843i
$503$	−7.29923e7	+	4.21421e7i	−0.573552	+	0.331141i	−0.758567	−	0.651595i	$-0.774100\pi$
$503$	−7.29923e7	+	4.21421e7i	−0.573552	+	0.331141i	0.185015	+	0.982736i	$0.440767\pi$
$504$	1.21257e8	−	2.10024e8i	0.947144	−	1.64050i
$505$			2.13011e8i			1.65397i
$506$	−3.76602e7	−	2.17431e7i	−0.290691	−	0.167830i
$507$	1.46233e7	−	8.44279e6i	0.112208	−	0.0647832i
$508$	5.53265e6			0.0422029
$509$	−2.60794e7	−	4.51709e7i	−0.197763	−	0.342535i	0.750040	−	0.661393i	$-0.230034\pi$
$509$	−2.60794e7	−	4.51709e7i	−0.197763	−	0.342535i	−0.947803	+	0.318857i	$0.896701\pi$
$510$	2.10198e8	+	1.21358e8i	1.58459	+	0.914864i
$511$	1.32841e8	−	2.30087e8i	0.995565	−	1.72437i
$512$		−	1.41297e8i		−	1.05275i
$513$	−2.98303e7	+	5.16677e7i	−0.220956	+	0.382707i
$514$	−1.58092e8			−1.16418
$515$		−	6.24039e7i		−	0.456868i
$516$	−6.24688e6	+	5.74449e6i	−0.0454688	+	0.0418121i
$517$	1.82879e7			0.132341
$518$		−	2.85108e8i		−	2.05126i
$519$	2.45044e8	+	1.41476e8i	1.75284	+	1.01200i
$520$	1.47844e8			1.05146
$521$	7.34341e7	+	4.23972e7i	0.519259	+	0.299795i	0.736632	−	0.676294i	$-0.236415\pi$
$521$	7.34341e7	+	4.23972e7i	0.519259	+	0.299795i	−0.217372	+	0.976089i	$0.569749\pi$
$522$	−5.95377e7	+	1.03122e8i	−0.418582	+	0.725005i
$523$	3.93149e7	−	2.26985e7i	0.274823	−	0.158669i	−0.356255	−	0.934389i	$-0.615946\pi$
$523$	3.93149e7	−	2.26985e7i	0.274823	−	0.158669i	0.631077	+	0.775720i	$0.282613\pi$
$524$			3.61776e6i			0.0251447i
$525$	−2.36460e7	−	4.09561e7i	−0.163410	−	0.283035i
$526$	2.38817e6	−	4.13644e6i	0.0164100	−	0.0284230i
$527$	2.81451e8			1.92296
$528$	4.69408e7	+	2.71013e7i	0.318896	+	0.184114i
$529$	−6.93133e7	−	1.20054e8i	−0.468220	−	0.810980i
$530$	−9.12874e7	−	1.58114e8i	−0.613173	−	1.06205i
$531$	1.26811e7	+	2.19643e7i	0.0846981	+	0.146701i
$532$	−5.03721e6			−0.0334545
$533$	−1.93330e7	−	3.34858e7i	−0.127679	−	0.221146i
$534$	8.44255e7	−	4.87431e7i	0.554434	−	0.320103i
$535$	−4.64396e6	−	2.68119e6i	−0.0303268	−	0.0175092i
$536$	−2.22377e8	−	1.28389e8i	−1.44409	−	0.833748i
$537$	1.69164e8			1.09241
$538$		−	1.60291e8i		−	1.02935i
$539$	−1.31068e7	+	2.27016e7i	−0.0837008	+	0.144974i
$540$	2.27720e6	−	3.94423e6i	0.0144617	−	0.0250485i
$541$	2.84147e7	+	4.92158e7i	0.179453	+	0.310822i	0.941693	−	0.336472i	$-0.109234\pi$
$541$	2.84147e7	+	4.92158e7i	0.179453	+	0.310822i	−0.762240	+	0.647294i	$0.775900\pi$
$542$	5.85675e7	−	3.38140e7i	0.367840	−	0.212372i
$543$		−	3.54825e8i		−	2.21623i
$544$	−1.22494e7	+	7.07217e6i	−0.0760881	+	0.0439295i
$545$	2.42453e8	−	1.39980e8i	1.49774	−	0.864723i
$546$	2.67536e8	−	1.54462e8i	1.64363	−	0.948952i
$547$	−4.20473e7	+	7.28280e7i	−0.256907	+	0.444976i	−0.965412	−	0.260730i	$-0.916037\pi$
$547$	−4.20473e7	+	7.28280e7i	−0.256907	+	0.444976i	0.708505	+	0.705706i	$0.249370\pi$
$548$			1.44975e6i			0.00880948i
$549$	−1.07938e8	−	6.23178e7i	−0.652313	−	0.376613i
$550$	5.61637e6	−	3.24261e6i	0.0337573	−	0.0194898i
$551$	6.49458e7			0.388236
$552$	1.86029e8	+	3.22211e8i	1.10602	+	1.91568i
$553$	−6.15519e7	−	3.55370e7i	−0.363970	−	0.210138i
$554$	−6.91117e7	+	1.19705e8i	−0.406464	+	0.704016i
$555$		−	4.64225e8i		−	2.71550i
$556$	5.05984e6	−	8.76391e6i	0.0294383	−	0.0509886i
$557$	−2.21356e8			−1.28093			−0.640466	−	0.767987i	$-0.721259\pi$
$557$	−2.21356e8			−1.28093			−0.640466	+	0.767987i	$0.721259\pi$
$558$			4.23015e8i			2.43475i
$559$	−1.63238e8	+	3.64908e7i	−0.934515	+	0.208905i
$560$	−2.35240e8			−1.33951
$561$		−	7.52816e7i		−	0.426383i
$562$	1.29092e8	+	7.45311e7i	0.727259	+	0.419883i
$563$	−6.90867e7			−0.387141			−0.193571	−	0.981086i	$-0.562007\pi$
$563$	−6.90867e7			−0.387141			−0.193571	+	0.981086i	$0.562007\pi$
$564$	−5.16031e6	−	2.97931e6i	−0.0287633	−	0.0166065i
$565$	−1.68462e8	+	2.91784e8i	−0.934020	+	1.61777i
$566$	−6.28601e7	+	3.62923e7i	−0.346678	+	0.200155i
$567$			8.90308e7i			0.488417i
$568$	9.59031e7	+	1.66109e8i	0.523344	+	0.906459i
$569$	−8.22776e7	+	1.42509e8i	−0.446627	+	0.773581i	−0.998164	−	0.0605697i	$-0.980708\pi$
$569$	−8.22776e7	+	1.42509e8i	−0.446627	+	0.773581i	0.551537	+	0.834151i	$0.314042\pi$
$570$	1.98967e8			1.07437
$571$	2.56517e7	+	1.48100e7i	0.137787	+	0.0795514i	0.567309	−	0.823505i	$-0.307985\pi$
$571$	2.56517e7	+	1.48100e7i	0.137787	+	0.0795514i	−0.429522	+	0.903056i	$0.641318\pi$
$572$	−873149.	−	1.51234e6i	−0.00466552	−	0.00808092i
$573$	9.46622e7	+	1.63960e8i	0.503168	+	0.871512i
$574$	3.20316e7	+	5.54803e7i	0.169372	+	0.293361i
$575$	4.27508e7			0.224875
$576$	−1.42052e8	−	2.46041e8i	−0.743326	−	1.28748i
$577$	1.23899e8	−	7.15332e7i	0.644972	−	0.372375i	−0.141555	−	0.989930i	$-0.545210\pi$
$577$	1.23899e8	−	7.15332e7i	0.644972	−	0.372375i	0.786527	+	0.617555i	$0.211877\pi$
$578$	−3.81373e7	−	2.20186e7i	−0.197500	−	0.114027i
$579$	−1.23259e8	−	7.11638e7i	−0.635015	−	0.366626i
$580$	−4.95786e6			−0.0254103
$581$			5.04300e7i			0.257135i
$582$	−2.63566e8	+	4.56510e8i	−1.33697	+	2.31569i
$583$	−2.83141e7	+	4.90415e7i	−0.142888	+	0.247490i
$584$	−1.55857e8	−	2.69953e8i	−0.782509	−	1.35534i
$585$	2.56676e8	−	1.48192e8i	1.28209	−	0.740215i
$586$		−	3.57212e7i		−	0.177514i
$587$	1.46436e8	−	8.45448e7i	0.723991	−	0.417996i	−0.0922289	−	0.995738i	$-0.529399\pi$
$587$	1.46436e8	−	8.45448e7i	0.723991	−	0.417996i	0.816220	+	0.577742i	$0.196066\pi$
$588$	7.39668e6	−	4.27048e6i	0.0363835	−	0.0210061i
$589$	1.99809e8	−	1.15360e8i	0.977845	−	0.564559i
$590$	1.28086e7	−	2.21851e7i	0.0623657	−	0.108020i
$591$		−	5.53121e8i		−	2.67952i
$592$	−2.78205e8	−	1.60622e8i	−1.34091	−	0.774175i
$593$	−8.19797e7	+	4.73310e7i	−0.393135	+	0.226977i	−0.683518	−	0.729934i	$-0.739551\pi$
$593$	−8.19797e7	+	4.73310e7i	−0.393135	+	0.226977i	0.290382	+	0.956911i	$0.406217\pi$
$594$	3.42685e7			0.163507
$595$	1.63361e8	+	2.82950e8i	0.775530	+	1.34326i
$596$	−6.72495e6	−	3.88265e6i	−0.0317651	−	0.0183396i
$597$	6.78750e7	−	1.17563e8i	0.318997	−	0.552519i
$598$			2.79260e8i			1.30589i
$599$	−1.51159e8	+	2.61815e8i	−0.703321	+	1.21819i	0.263972	+	0.964530i	$0.414967\pi$
$599$	−1.51159e8	+	2.61815e8i	−0.703321	+	1.21819i	−0.967294	+	0.253658i	$0.918366\pi$
$600$	−5.54859e7			−0.256879
$601$		−	6.20051e7i		−	0.285630i	−0.989749	−	0.142815i	$-0.954385\pi$
$601$		−	6.20051e7i		−	0.285630i	0.989749	−	0.142815i	$-0.0456154\pi$
$602$	2.70458e8	−	6.04592e7i	1.23968	−	0.277123i
$603$	−5.14767e8			−2.34779
$604$			8.86327e6i			0.0402238i
$605$	1.94171e8	+	1.12105e8i	0.876835	+	0.506241i
$606$	5.22212e8			2.34655
$607$	−1.28816e8	−	7.43717e7i	−0.575973	−	0.332538i	0.183558	−	0.983009i	$-0.441238\pi$
$607$	−1.28816e8	−	7.43717e7i	−0.575973	−	0.332538i	−0.759532	+	0.650470i	$0.774572\pi$
$608$	−5.79743e6	+	1.00415e7i	−0.0257944	+	0.0446772i
$609$	−2.35587e8	+	1.36016e8i	−1.04304	+	0.602197i
$610$			1.25889e8i			0.554622i
$611$	−5.87207e7	−	1.01707e8i	−0.257435	−	0.445890i
$612$	−7.22643e6	+	1.25165e7i	−0.0315260	+	0.0546047i
$613$	−1.69967e8			−0.737875			−0.368937	−	0.929454i	$-0.620278\pi$
$613$	−1.69967e8			−0.737875			−0.368937	+	0.929454i	$0.620278\pi$
$614$	−1.07407e8	−	6.20113e7i	−0.464009	−	0.267895i
$615$	5.21551e7	+	9.03353e7i	0.224219	+	0.388358i
$616$	3.79878e7	+	6.57967e7i	0.162518	+	0.281490i
$617$	−8.77316e7	−	1.51956e8i	−0.373508	−	0.646936i	0.616594	−	0.787281i	$-0.288512\pi$
$617$	−8.77316e7	−	1.51956e8i	−0.373508	−	0.646936i	−0.990103	+	0.140346i	$0.955179\pi$
$618$	−1.52988e8			−0.648173
$619$	1.70453e8	+	2.95233e8i	0.718675	+	1.24478i	0.961525	+	0.274718i	$0.0885846\pi$
$619$	1.70453e8	+	2.95233e8i	0.718675	+	1.24478i	−0.242849	+	0.970064i	$0.578082\pi$
$620$	−1.52532e7	+	8.80641e6i	−0.0640007	+	0.0369508i
$621$	1.95634e8	+	1.12949e8i	0.816902	+	0.471639i
$622$	1.95040e8	+	1.12606e8i	0.810499	+	0.467942i
$623$	1.31228e8			0.542702
$624$		−	3.48078e8i		−	1.43259i
$625$	1.38609e8	−	2.40078e8i	0.567742	−	0.983359i
$626$	−1.70365e8	+	2.95081e8i	−0.694477	+	1.20287i
$627$	−3.08562e7	−	5.34444e7i	−0.125181	−	0.216820i
$628$	1.11898e7	−	6.46046e6i	0.0451799	−	0.0260846i
$629$			4.46173e8i			1.79288i
$630$	−4.25270e8	+	2.45529e8i	−1.70076	+	0.981933i
$631$	−1.46112e7	+	8.43577e6i	−0.0581564	+	0.0335766i	−0.528796	−	0.848749i	$-0.677356\pi$
$631$	−1.46112e7	+	8.43577e6i	−0.0581564	+	0.0335766i	0.470640	+	0.882325i	$0.344023\pi$
$632$	−7.22165e7	+	4.16942e7i	−0.286079	+	0.165168i
$633$	2.81438e7	−	4.87465e7i	0.110961	−	0.192191i
$634$		−	4.77733e8i		−	1.87464i
$635$	−2.54763e8	−	1.47088e8i	−0.994983	−	0.574454i
$636$	1.59788e7	−	9.22536e6i	0.0621116	−	0.0358601i
$637$	1.68338e8			0.651275
$638$	−1.86521e7	−	3.23064e7i	−0.0718234	−	0.124402i
$639$	3.33001e8	+	1.92258e8i	1.27627	+	0.736855i
$640$	−1.32301e8	+	2.29152e8i	−0.504689	+	0.874146i
$641$			1.50717e8i			0.572251i	0.958192	+	0.286126i	$0.0923675\pi$
$641$			1.50717e8i			0.572251i	−0.958192	+	0.286126i	$0.907633\pi$
$642$	−6.57313e6	+	1.13850e7i	−0.0248409	+	0.0430257i
$643$	−1.71716e8			−0.645917			−0.322959	−	0.946413i	$-0.604677\pi$
$643$	−1.71716e8			−0.645917			−0.322959	+	0.946413i	$0.604677\pi$
$644$			1.90728e7i			0.0714098i
$645$	4.40371e8	−	9.84421e7i	1.64112	−	0.366861i
$646$	−1.91229e8			−0.709344
$647$		−	4.60664e8i		−	1.70087i	−0.526079	−	0.850436i	$-0.676338\pi$
$647$		−	4.60664e8i		−	1.70087i	0.526079	−	0.850436i	$-0.323662\pi$
$648$	9.04620e7	+	5.22283e7i	0.332461	+	0.191947i
$649$	−7.94554e6			−0.0290663
$650$	−3.60672e7	−	2.08234e7i	−0.131333	−	0.0758249i
$651$	−4.83198e8	+	8.36923e8i	−1.75139	+	3.03349i
$652$	3.93411e6	−	2.27136e6i	0.0141940	−	0.00819489i
$653$		−	1.16862e8i		−	0.419693i	−0.977734	−	0.209847i	$-0.932704\pi$
$653$		−	1.16862e8i		−	0.419693i	0.977734	−	0.209847i	$-0.0672965\pi$
$654$	−3.43171e8	−	5.94390e8i	−1.22681	−	2.12490i
$655$	9.61797e7	−	1.66588e8i	0.342263	−	0.592816i
$656$	7.21825e7			0.255694
$657$	−5.41178e8	−	3.12449e8i	−1.90829	−	1.10175i
$658$	9.72903e7	+	1.68512e8i	0.341501	+	0.591497i
$659$	−1.08363e8	−	1.87691e8i	−0.378640	−	0.655824i	0.612224	−	0.790684i	$-0.290275\pi$
$659$	−1.08363e8	−	1.87691e8i	−0.378640	−	0.655824i	−0.990865	+	0.134860i	$0.956942\pi$
$660$	2.35551e6	+	4.07987e6i	0.00819320	+	0.0141910i
$661$	5.54803e8			1.92103			0.960516	−	0.278226i	$-0.0897463\pi$
$661$	5.54803e8			1.92103			0.960516	+	0.278226i	$0.0897463\pi$
$662$	−2.49141e8	−	4.31525e8i	−0.858758	−	1.48741i
$663$	−4.18674e8	+	2.41722e8i	−1.43660	+	0.829421i
$664$	5.12407e7	+	2.95838e7i	0.175029	+	0.101053i
$665$	2.31949e8	+	1.33916e8i	0.788730	+	0.455374i
$666$	−6.70590e8			−2.27005
$667$		−	2.45910e8i		−	0.828704i
$668$	−382359.	+	662264.i	−0.00128275	+	0.00222179i
$669$	1.22866e8	−	2.12810e8i	0.410349	−	0.710745i
$670$	2.59971e8	+	4.50283e8i	0.864372	+	1.49714i
$671$	3.38150e7	−	1.95231e7i	0.111929	−	0.0646221i
$672$		−	4.85663e7i		−	0.160040i
$673$	−2.03133e7	+	1.17279e7i	−0.0666399	+	0.0384746i	−0.532950	−	0.846147i	$-0.678917\pi$
$673$	−2.03133e7	+	1.17279e7i	−0.0666399	+	0.0384746i	0.466310	+	0.884621i	$0.345583\pi$
$674$	2.22094e8	−	1.28226e8i	0.725367	−	0.418791i
$675$	−2.91755e7	+	1.68445e7i	−0.0948651	+	0.0547704i
$676$	507794.	−	879524.i	0.00164379	−	0.00284713i
$677$			2.28403e8i			0.736098i	0.929806	+	0.368049i	$0.119974\pi$
$677$			2.28403e8i			0.736098i	−0.929806	+	0.368049i	$0.880026\pi$
$678$	7.15330e8	+	4.12996e8i	2.29518	+	1.32512i
$679$	−6.14516e8	+	3.54791e8i	−1.96301	+	1.13335i
$680$	3.83332e8			1.21913
$681$	−1.62738e8	−	2.81871e8i	−0.515286	−	0.892501i
$682$	−1.14769e8	−	6.62617e7i	−0.361801	−	0.208886i
$683$	9.21532e7	−	1.59614e8i	0.289233	−	0.500967i	−0.684394	−	0.729113i	$-0.739933\pi$
$683$	9.21532e7	−	1.59614e8i	0.289233	−	0.500967i	0.973627	+	0.228146i	$0.0732664\pi$
$684$			1.18478e7i			0.0370227i
$685$	3.85421e7	−	6.67569e7i	0.119912	−	0.207694i
$686$	1.31175e8			0.406330
$687$			3.56065e8i			1.09814i
$688$	9.33728e7	−	2.97970e8i	0.286718	−	0.914971i
$689$	3.63655e8			1.11181
$690$		−	7.53366e8i		−	2.29329i
$691$	1.34664e8	+	7.77481e7i	0.408146	+	0.235643i	0.689993	−	0.723816i	$-0.257614\pi$
$691$	1.34664e8	+	7.77481e7i	0.408146	+	0.235643i	−0.281847	+	0.959459i	$0.590947\pi$
$692$	1.70182e7			0.0513566
$693$	1.31903e8	+	7.61545e7i	0.396330	+	0.228821i
$694$	−5.55416e7	+	9.62009e7i	−0.166165	+	0.287807i
$695$	−4.65984e8	+	2.69036e8i	−1.38809	+	0.801412i
$696$			3.19165e8i			0.946647i
$697$	−5.01269e7	−	8.68224e7i	−0.148038	−	0.256409i
$698$	−3.41206e7	+	5.90985e7i	−0.100334	+	0.173784i
$699$	2.31586e7			0.0678081
$700$	−2.46331e6	−	1.42219e6i	−0.00718167	−	0.00414634i
$701$	−1.65826e8	−	2.87219e8i	−0.481392	−	0.833795i	0.518380	−	0.855150i	$-0.326535\pi$
$701$	−1.65826e8	−	2.87219e8i	−0.481392	−	0.833795i	−0.999772	+	0.0213554i	$0.993202\pi$
$702$	−1.10033e8	−	1.90582e8i	−0.318061	−	0.550898i
$703$	1.82876e8	+	3.16750e8i	0.526369	+	0.911698i
$704$	8.90047e7			0.255091
$705$	1.58412e8	+	2.74378e8i	0.452086	+	0.783036i
$706$	5.08632e8	−	2.93659e8i	1.44541	−	0.834505i
$707$	6.08780e8	+	3.51479e8i	1.72267	+	0.994584i
$708$	2.24200e6	+	1.29442e6i	0.00631735	+	0.00364732i
$709$	−4.75605e8			−1.33447			−0.667234	−	0.744849i	$-0.732522\pi$
$709$	−4.75605e8			−1.33447			−0.667234	+	0.744849i	$0.732522\pi$
$710$		−	3.88382e8i		−	1.08513i
$711$	−8.35849e7	+	1.44773e8i	−0.232551	+	0.402791i
$712$	7.69824e7	−	1.33337e8i	0.213281	−	0.369413i
$713$	−4.36799e8	−	7.56557e8i	−1.20507	−	2.08724i
$714$	6.93672e8	−	4.00492e8i	1.90572	−	1.10027i
$715$			9.28520e7i			0.254023i
$716$	8.81130e6	−	5.08721e6i	0.0240050	−	0.0138593i
$717$	5.41892e8	−	3.12862e8i	1.47013	−	0.848780i
$718$	1.64718e8	−	9.51001e7i	0.445009	−	0.256926i
$719$	−3.36176e8	+	5.82274e8i	−0.904441	+	1.56654i	−0.0827748	+	0.996568i	$0.526378\pi$
$719$	−3.36176e8	+	5.82274e8i	−0.904441	+	1.56654i	−0.821666	+	0.569969i	$0.806955\pi$
$720$			5.53296e8i			1.48238i
$721$	−1.78349e8	−	1.02970e8i	−0.475843	−	0.274728i
$722$	1.83667e8	−	1.06040e8i	0.488001	−	0.281747i
$723$	1.68384e8			0.445540
$724$	−1.06705e7	−	1.84819e7i	−0.0281170	−	0.0487001i
$725$	3.17600e7	+	1.83367e7i	0.0833425	+	0.0481178i
$726$	2.74832e8	−	4.76023e8i	0.718220	−	1.24399i
$727$			6.23850e8i			1.62359i	0.583940	+	0.811797i	$0.301510\pi$
$727$			6.23850e8i			1.62359i	−0.583940	+	0.811797i	$0.698490\pi$
$728$	2.43950e8	−	4.22533e8i	0.632275	−	1.09513i
$729$	6.19156e8			1.59815
$730$			6.31181e8i			1.62250i
$731$	−4.23246e8	+	9.46140e7i	−1.08353	+	0.242216i
$732$	−1.27221e7			−0.0324359
$733$		−	7.66890e8i		−	1.94725i	−0.228158	−	0.973624i	$-0.573270\pi$
$733$		−	7.66890e8i		−	1.94725i	0.228158	−	0.973624i	$-0.426730\pi$
$734$	5.42367e7	+	3.13135e7i	0.137153	+	0.0791852i
$735$	−4.54129e8			−1.14371
$736$	3.80209e7	+	2.19514e7i	0.0953650	+	0.0550590i
$737$	8.06338e7	−	1.39662e8i	0.201425	−	0.348879i
$738$	1.30493e8	−	7.53399e7i	0.324651	−	0.187437i
$739$		−	3.76954e8i		−	0.934018i	−0.884253	−	0.467009i	$-0.845332\pi$
$739$		−	3.76954e8i		−	0.934018i	0.884253	−	0.467009i	$-0.154668\pi$
$740$	−1.39605e7	−	2.41802e7i	−0.0344512	−	0.0596713i
$741$	−1.98152e8	+	3.43209e8i	−0.487017	+	0.843538i
$742$	−6.02515e8			−1.47488
$743$	3.96121e7	+	2.28700e7i	0.0965742	+	0.0557571i	0.547509	−	0.836800i	$-0.315576\pi$
$743$	3.96121e7	+	2.28700e7i	0.0965742	+	0.0557571i	−0.450935	+	0.892557i	$0.648909\pi$
$744$	5.66918e8	+	9.81930e8i	1.37658	+	2.38431i
$745$	2.06444e8	+	3.57571e8i	0.499267	+	0.864755i
$746$	−6.73692e7	−	1.16687e8i	−0.162272	−	0.281064i
$747$	1.18614e8			0.284560
$748$	−2.26391e6	−	3.92121e6i	−0.00540947	−	0.00936948i
$749$	−1.53255e7	+	8.84819e6i	−0.0364729	+	0.0210576i
$750$	−5.04804e8	−	2.91449e8i	−1.19657	−	0.690842i
$751$	−4.47102e8	−	2.58135e8i	−1.05557	−	0.609434i	−0.131366	−	0.991334i	$-0.541936\pi$
$751$	−4.47102e8	−	2.58135e8i	−1.05557	−	0.609434i	−0.924204	+	0.381900i	$0.875270\pi$
$752$	2.19242e8			0.515549
$753$			1.04254e9i			2.44179i
$754$	−1.19780e8	+	2.07465e8i	−0.279428	+	0.483984i
$755$	2.35634e8	−	4.08129e8i	0.547515	−	0.948324i
$756$	−7.51500e6	−	1.30164e7i	−0.0173926	−	0.0301248i
$757$	3.71013e8	−	2.14204e8i	0.855267	−	0.493788i	−0.00715774	−	0.999974i	$-0.502278\pi$
$757$	3.71013e8	−	2.14204e8i	0.855267	−	0.493788i	0.862424	+	0.506186i	$0.168945\pi$
$758$		−	9.48169e7i		−	0.217710i
$759$	−2.02362e8	+	1.16834e8i	−0.462810	+	0.267204i
$760$	2.72138e8	−	1.57119e8i	0.619938	−	0.357921i
$761$	2.28313e8	−	1.31817e8i	0.518056	−	0.299100i	−0.218083	−	0.975930i	$-0.569980\pi$
$761$	2.28313e8	−	1.31817e8i	0.518056	−	0.299100i	0.736139	+	0.676831i	$0.236647\pi$
$762$	−3.60596e8	+	6.24570e8i	−0.814996	+	1.41161i
$763$		−	9.23897e8i		−	2.07994i
$764$	9.86139e6	+	5.69348e6i	0.0221135	+	0.0127673i
$765$	6.65514e8	−	3.84235e8i	1.48653	−	0.858247i
$766$	−5.94507e8			−1.32273
$767$	2.55123e7	+	4.41887e7i	0.0565411	+	0.0979320i
$768$	−7.25823e7	−	4.19054e7i	−0.160231	−	0.0925095i
$769$	2.50031e7	−	4.33066e7i	0.0549812	−	0.0952302i	−0.837225	−	0.546859i	$-0.815823\pi$
$769$	2.50031e7	−	4.33066e7i	0.0549812	−	0.0952302i	0.892206	+	0.451629i	$0.149157\pi$
$770$		−	1.53840e8i		−	0.336975i
$771$	−4.24742e8	+	7.35675e8i	−0.926749	+	1.60518i
$772$	−8.56032e6			−0.0186054
$773$			6.73450e8i			1.45803i	0.684498	+	0.729015i	$0.260022\pi$
$773$			6.73450e8i			1.45803i	−0.684498	+	0.729015i	$0.739978\pi$
$774$	−1.42203e8	−	6.36132e8i	−0.306681	−	1.37191i
$775$	1.30282e8			0.279885
$776$			8.32526e8i			1.78161i
$777$	−1.32674e9	−	7.65995e8i	−2.82829	−	1.63291i
$778$	1.07580e8			0.228450
$779$	−7.11729e7	−	4.10917e7i	−0.150558	−	0.0869244i
$780$	1.51266e7	−	2.62001e7i	0.0318756	−	0.0552102i
$781$	−1.04323e8	+	6.02311e7i	−0.218992	+	0.126435i
$782$			7.24070e8i			1.51412i
$783$	9.68925e7	+	1.67823e8i	0.201839	+	0.349595i
$784$	−1.57128e8	+	2.72154e8i	−0.326067	+	0.564764i
$785$	−6.87015e8			−1.42023
$786$	−4.08402e8	−	2.35791e8i	−0.841047	−	0.485579i
$787$	1.15551e8	+	2.00140e8i	0.237055	+	0.410592i	0.959868	−	0.280452i	$-0.0904843\pi$
$787$	1.15551e8	+	2.00140e8i	0.237055	+	0.410592i	−0.722813	+	0.691044i	$0.757151\pi$
$788$	−1.66338e7	−	2.88106e7i	−0.0339948	−	0.0588807i
$789$	−1.28325e7	−	2.22266e7i	−0.0261265	−	0.0452524i
$790$	1.68850e8			0.342469
$791$	5.55940e8	+	9.62917e8i	1.12331	+	1.94563i
$792$	1.54757e8	−	8.93492e7i	0.311513	−	0.179852i
$793$	−2.17153e8	−	1.25373e8i	−0.435458	−	0.251412i
$794$	7.16405e7	+	4.13616e7i	0.143119	+	0.0826297i
$795$	−9.81039e8			−1.95247
$796$		−	8.16471e6i		−	0.0161883i
$797$	−2.06088e8	+	3.56955e8i	−0.407079	+	0.705081i	−0.994561	−	0.104156i	$-0.966786\pi$
$797$	−2.06088e8	+	3.56955e8i	−0.407079	+	0.705081i	0.587482	+	0.809237i	$0.300119\pi$
$798$	3.28305e8	−	5.68640e8i	0.646053	−	1.11900i
$799$	−1.52252e8	−	2.63708e8i	−0.298485	−	0.516991i
$800$	−5.67016e6	+	3.27367e6i	−0.0110745	+	0.00639389i
$801$		−	3.08655e8i		−	0.600586i
$802$	−2.72003e8	+	1.57041e8i	−0.527291	+	0.304432i
$803$	1.69542e8	−	9.78849e7i	0.327438	−	0.189047i
$804$	−4.55049e7	+	2.62723e7i	−0.0875568	+	0.0505510i
$805$	5.07059e8	−	8.78252e8i	0.972011	−	1.68357i
$806$			8.51038e8i			1.62534i
$807$	−7.45908e8	−	4.30650e8i	−1.41927	−	0.819415i
$808$	7.14259e8	−	4.12378e8i	1.35401	−	0.781738i
$809$	2.81481e8			0.531624			0.265812	−	0.964025i	$-0.414360\pi$
$809$	2.81481e8			0.531624			0.265812	+	0.964025i	$0.414360\pi$
$810$	−1.05755e8	−	1.83173e8i	−0.198997	−	0.344673i
$811$	4.53881e8	+	2.62049e8i	0.850902	+	0.491269i	0.860955	−	0.508681i	$-0.169867\pi$
$811$	4.53881e8	+	2.62049e8i	0.850902	+	0.491269i	−0.0100528	+	0.999949i	$0.503200\pi$
$812$	−8.18072e6	+	1.41694e7i	−0.0152800	+	0.0264657i
$813$		−	3.63389e8i		−	0.676239i
$814$	1.05042e8	−	1.81938e8i	0.194756	−	0.337327i
$815$	−2.41540e8			−0.446186
$816$		−	9.02501e8i		−	1.66103i
$817$	−2.61694e8	+	2.40648e8i	−0.479874	+	0.441281i
$818$	−9.05851e8			−1.65500
$819$		−	9.78098e8i		−	1.78045i
$820$	5.43323e6	+	3.13688e6i	0.00985410	+	0.00568927i
$821$	−6.62891e8			−1.19788			−0.598939	−	0.800795i	$-0.704411\pi$
$821$	−6.62891e8			−1.19788			−0.598939	+	0.800795i	$0.704411\pi$
$822$	−1.63659e8	−	9.44886e7i	−0.294662	−	0.170123i
$823$	2.87934e8	−	4.98717e8i	0.516528	−	0.894652i	−0.483288	−	0.875461i	$-0.660558\pi$
$823$	2.87934e8	−	4.98717e8i	0.516528	−	0.894652i	0.999816	−	0.0191909i	$-0.00610902\pi$
$824$	−2.09250e8	+	1.20810e8i	−0.374010	+	0.215935i
$825$		−	3.48474e7i		−	0.0620596i
$826$	−4.22696e7	−	7.32131e7i	−0.0750047	−	0.129912i
$827$	1.08037e8	−	1.87126e8i	0.191010	−	0.330840i	−0.754575	−	0.656214i	$-0.772157\pi$
$827$	1.08037e8	−	1.87126e8i	0.191010	−	0.330840i	0.945585	+	0.325374i	$0.105490\pi$
$828$	4.48603e7			0.0790263
$829$	3.29447e8	+	1.90206e8i	0.578258	+	0.333858i	0.760441	−	0.649407i	$-0.224983\pi$
$829$	3.29447e8	+	1.90206e8i	0.578258	+	0.333858i	−0.182183	+	0.983265i	$0.558316\pi$
$830$	−5.99033e7	−	1.03755e8i	−0.104765	−	0.181458i
$831$	3.71362e8	+	6.43217e8i	0.647133	+	1.12087i
$832$	−2.85785e8	−	4.94994e8i	−0.496215	−	0.859469i
$833$	4.36470e8			0.755125
$834$	6.59560e8	+	1.14239e9i	1.13699	+	1.96932i
$835$	3.52131e7	−	2.03303e7i	0.0604846	−	0.0349208i
$836$	−3.21443e6	−	1.85585e6i	−0.00550155	−	0.00317632i
$837$	5.96191e8	+	3.44211e8i	1.01674	+	0.587013i
$838$	−5.54442e8			−0.942159
$839$			3.05592e8i			0.517436i	0.965953	+	0.258718i	$0.0833000\pi$
$839$			3.05592e8i			0.517436i	−0.965953	+	0.258718i	$0.916700\pi$
$840$	−6.58108e8	+	1.13988e9i	−1.11035	+	1.92318i
$841$	−1.91936e8	+	3.32443e8i	−0.322677	+	0.558893i
$842$	−6.51185e7	−	1.12789e8i	−0.109086	−	0.188942i
$843$	6.93655e8	−	4.00482e8i	1.15787	−	0.668498i
$844$		−	3.38543e6i		−	0.00563102i
$845$	−4.67650e7	+	2.69998e7i	−0.0775088	+	0.0447497i
$846$	3.96349e8	−	2.28832e8i	0.654585	−	0.377925i
$847$	6.40783e8	−	3.69956e8i	1.05453	−	0.608835i
$848$	−3.39439e8	+	5.87926e8i	−0.556640	+	0.964128i
$849$			3.90023e8i			0.637334i
$850$	−9.35156e7	−	5.39913e7i	−0.152275	−	0.0879158i
$851$	1.19934e9	−	6.92440e8i	1.94605	−	1.12355i
$852$	3.92492e7			0.0634618
$853$	−1.34985e8	−	2.33801e8i	−0.217490	−	0.376703i	0.736550	−	0.676383i	$-0.236454\pi$
$853$	−1.34985e8	−	2.33801e8i	−0.217490	−	0.376703i	−0.954040	+	0.299680i	$0.903120\pi$
$854$	3.59786e8	+	2.07722e8i	0.577658	+	0.333511i
$855$	3.14978e8	−	5.45557e8i	0.503943	−	0.872855i
$856$			2.07625e7i			0.0331023i
$857$	−4.84639e8	+	8.39420e8i	−0.769974	+	1.33363i	0.167602	+	0.985855i	$0.446397\pi$
$857$	−4.84639e8	+	8.39420e8i	−0.769974	+	1.33363i	−0.937576	+	0.347779i	$0.886936\pi$
$858$	2.27633e8			0.360391
$859$			3.27615e8i			0.516873i	0.966028	+	0.258437i	$0.0832073\pi$
$859$			3.27615e8i			0.516873i	−0.966028	+	0.258437i	$0.916793\pi$
$860$	1.99773e7	−	1.83707e7i	0.0314081	−	0.0288822i
$861$	3.44234e8			0.539317
$862$			1.22836e9i			1.91780i
$863$	5.64888e8	+	3.26138e8i	0.878880	+	0.507422i	0.870289	−	0.492541i	$-0.163932\pi$
$863$	5.64888e8	+	3.26138e8i	0.878880	+	0.507422i	0.00859119	+	0.999963i	$0.497265\pi$
$864$	−3.45967e7			−0.0536406
$865$	−7.83643e8	−	4.52436e8i	−1.21079	−	0.699051i
$866$	2.07228e8	−	3.58929e8i	0.319076	−	0.552655i
$867$	−2.04925e8	+	1.18314e8i	−0.314440	+	0.181542i
$868$			5.81240e7i			0.0888785i
$869$	−2.61857e7	−	4.53549e7i	−0.0399029	−	0.0691139i
$870$	3.23133e8	−	5.59683e8i	0.490709	−	0.849933i
$871$	−1.03563e9			−1.56729
$872$	−9.38749e8	−	5.41987e8i	−1.41579	−	0.817409i
$873$	8.34487e8	+	1.44537e9i	1.25423	+	2.17239i
$874$	2.96779e8	+	5.14037e8i	0.444528	+	0.769945i
$875$	−3.92324e8	−	6.79525e8i	−0.585627	−	1.01434i
$876$	−6.37861e7			−0.0948886
$877$	−2.28537e8	−	3.95838e8i	−0.338811	−	0.586838i	0.645398	−	0.763846i	$-0.276691\pi$
$877$	−2.28537e8	−	3.95838e8i	−0.338811	−	0.586838i	−0.984209	+	0.177008i	$0.943358\pi$
$878$	8.87788e8	−	5.12565e8i	1.31167	−	0.757295i
$879$	−1.66227e8	−	9.59713e7i	−0.244757	−	0.141311i
$880$	−1.50115e8	−	8.66690e7i	−0.220281	−	0.127179i
$881$	−2.44002e8			−0.356834			−0.178417	−	0.983955i	$-0.557098\pi$
$881$	−2.44002e8			−0.356834			−0.178417	+	0.983955i	$0.557098\pi$
$882$			6.56006e8i			0.956097i
$883$	5.56171e8	−	9.63316e8i	0.807842	−	1.39922i	−0.106514	−	0.994311i	$-0.533969\pi$
$883$	5.56171e8	−	9.63316e8i	0.807842	−	1.39922i	0.914356	−	0.404911i	$-0.132698\pi$
$884$	−1.45384e7	+	2.51812e7i	−0.0210455	+	0.0364519i
$885$	−6.88252e7	−	1.19209e8i	−0.0992927	−	0.171980i
$886$	−5.52014e8	+	3.18705e8i	−0.793686	+	0.458235i
$887$			4.74098e8i			0.679355i	0.940542	+	0.339678i	$0.110318\pi$
$887$			4.74098e8i			0.679355i	−0.940542	+	0.339678i	$0.889682\pi$
$888$	−1.55662e9	+	8.98713e8i	−2.22302	+	1.28346i
$889$	−8.40744e8	+	4.85404e8i	−1.19663	+	0.690872i
$890$	−2.69990e8	+	1.55879e8i	−0.382982	+	0.221115i
$891$	−3.28015e7	+	5.68138e7i	−0.0463725	+	0.0803195i
$892$		−	1.47796e7i		−	0.0208242i
$893$	−2.16175e8	−	1.24809e8i	−0.303565	−	0.175263i
$894$	8.76609e8	−	5.06111e8i	1.22686	−	0.708326i
$895$	−5.40982e8			−0.754594
$896$	4.36607e8	+	7.56225e8i	0.606969	+	1.05130i
$897$	1.29953e9	+	7.50282e8i	1.80056	+	1.03955i
$898$	−5.21754e7	+	9.03704e7i	−0.0720504	+	0.124795i
$899$		−	7.49406e8i		−	1.03143i
$900$	−3.34507e6	+	5.79384e6i	−0.00458858	+	0.00794765i
$901$	9.42890e8			1.28910
$902$			4.72054e7i			0.0643238i
$903$	4.45289e8	−	1.42100e9i	0.604754	−	1.92988i
$904$	1.30453e9			1.76583
$905$			1.13472e9i			1.53089i
$906$	−1.00056e9	−	5.77672e8i	−1.34542	−	0.776778i
$907$	7.65946e8			1.02654			0.513270	−	0.858227i	$-0.328434\pi$
$907$	7.65946e8			1.02654			0.513270	+	0.858227i	$0.328434\pi$
$908$	−1.69532e7	−	9.78792e6i	−0.0226461	−	0.0130747i
$909$	8.26698e8	−	1.43188e9i	1.10067	−	1.90641i
$910$	−8.55573e8	+	4.93965e8i	−1.13536	+	0.655499i
$911$		−	4.48010e8i		−	0.592561i	−0.955101	−	0.296280i	$-0.904254\pi$
$911$		−	4.48010e8i		−	0.592561i	0.955101	−	0.296280i	$-0.0957463\pi$
$912$	−3.69914e8	−	6.40710e8i	−0.487659	−	0.844650i
$913$	−1.85799e7	+	3.21812e7i	−0.0244135	+	0.0422854i
$914$	6.94671e8			0.909789
$915$	5.85818e8	+	3.38222e8i	0.764715	+	0.441508i
$916$	1.07078e7	+	1.85465e7i	0.0139320	+	0.0241310i
$917$	−3.17402e8	−	5.49757e8i	−0.411625	−	0.712956i
$918$	−2.85295e8	−	4.94145e8i	−0.368778	−	0.638743i
$919$	−1.99788e8			−0.257408			−0.128704	−	0.991683i	$-0.541082\pi$
$919$	−1.99788e8			−0.257408			−0.128704	+	0.991683i	$0.541082\pi$
$920$	−5.94914e8	−	1.03042e9i	−0.763995	−	1.32328i
$921$	−5.77134e8	+	3.33209e8i	−0.738751	+	0.426518i
$922$	6.65449e8	+	3.84197e8i	0.849028	+	0.490186i
$923$	6.69943e8	+	3.86792e8i	0.851987	+	0.491895i
$924$	1.55468e7			0.0197073
$925$			2.06531e8i			0.260952i
$926$	5.98473e8	−	1.03658e9i	0.753722	−	1.30549i
$927$	−2.42190e8	+	4.19485e8i	−0.304030	+	0.526596i
$928$	1.88307e7	+	3.26158e7i	0.0235626	+	0.0408117i
$929$	7.50852e8	−	4.33505e8i	0.936499	−	0.540688i	0.0476377	−	0.998865i	$-0.484831\pi$
$929$	7.50852e8	−	4.33505e8i	0.936499	−	0.540688i	0.888861	+	0.458177i	$0.151497\pi$
$930$		−	2.29586e9i		−	2.85429i
$931$	3.09862e8	−	1.78899e8i	0.383989	−	0.221696i
$932$	1.20627e6	−	696440.i	0.00149004	−	0.000860273i
$933$	1.04802e9	−	6.05074e8i	1.29040	−	0.745013i
$934$	1.38334e8	−	2.39601e8i	0.169780	−	0.294068i
$935$			2.40748e8i			0.294529i
$936$	−9.93821e8	−	5.73783e8i	−1.21194	−	0.699713i
$937$	−9.17742e8	+	5.29858e8i	−1.11558	+	0.644082i	−0.940270	−	0.340431i	$-0.889427\pi$
$937$	−9.17742e8	+	5.29858e8i	−1.11558	+	0.644082i	−0.175313	+	0.984513i	$0.556094\pi$
$938$	1.71586e9			2.07909
$939$	9.15433e8	+	1.58558e9i	1.10568	+	1.91510i
$940$	1.65025e7	+	9.52773e6i	0.0198686	+	0.0114711i
$941$	5.94508e8	−	1.02972e9i	0.713492	−	1.23580i	−0.250046	−	0.968234i	$-0.580446\pi$
$941$	5.94508e8	−	1.02972e9i	0.713492	−	1.23580i	0.963538	−	0.267570i	$-0.0862208\pi$
$942$			1.68427e9i			2.01492i
$943$	−1.55589e8	+	2.69489e8i	−0.185543	+	0.321370i
$944$	−9.52538e7			−0.113231
$945$			7.99156e8i			0.946970i
$946$	1.94864e8	+	6.10632e7i	0.230175	+	0.0721284i
$947$	1.45933e9			1.71831			0.859157	−	0.511713i	$-0.170989\pi$
$947$	1.45933e9			1.71831			0.859157	+	0.511713i	$0.170989\pi$
$948$			1.70638e7i			0.0200286i
$949$	−1.08876e9	−	6.28597e8i	−1.27390	−	0.735485i
$950$	−8.85190e7			−0.103244
$951$	−2.22311e9	−	1.28351e9i	−2.58476	−	1.49231i
$952$	6.32517e8	−	1.09555e9i	0.733096	−	1.26976i
$953$	−1.29890e9	+	7.49919e8i	−1.50071	+	0.866434i	−0.500708	+	0.865616i	$0.666927\pi$
$953$	−1.29890e9	+	7.49919e8i	−1.50071	+	0.866434i	−1.00000		0.000818164i	$0.999740\pi$
$954$			1.41715e9i			1.63219i
$955$	−3.02727e8	−	5.24338e8i	−0.347569	−	0.602007i
$956$	1.88171e7	−	3.25922e7i	0.0215367	−	0.0373027i
$957$	−2.00449e8			−0.228701
$958$	−1.09254e9	−	6.30780e8i	−1.24263	−	0.717433i
$959$	−1.27193e8	−	2.20304e8i	−0.144214	−	0.249785i
$960$	7.70968e8	+	1.33536e9i	0.871411	+	1.50933i
$961$	−8.87381e8	−	1.53699e9i	−0.999862	−	1.73181i
$962$	−1.34912e9			−1.51539
$963$	2.08114e7	+	3.60464e7i	0.0233036	+	0.0403630i
$964$	8.77068e6	−	5.06375e6i	0.00979044	−	0.00565251i
$965$	3.94179e8	+	2.27579e8i	0.438644	+	0.253251i
$966$	−2.15310e9	−	1.24309e9i	−2.38854	−	1.37902i
$967$	4.05958e8			0.448954			0.224477	−	0.974479i	$-0.427933\pi$
$967$	4.05958e8			0.448954			0.224477	+	0.974479i	$0.427933\pi$
$968$		−	8.68112e8i		−	0.957083i
$969$	−5.13772e8	+	8.89879e8i	−0.564675	+	0.978046i
$970$	8.42876e8	−	1.45990e9i	0.923525	−	1.59959i
$971$	5.84471e8	+	1.01233e9i	0.638419	+	1.10577i	0.985780	+	0.168042i	$0.0537444\pi$
$971$	5.84471e8	+	1.01233e9i	0.638419	+	1.10577i	−0.347361	+	0.937731i	$0.612922\pi$
$972$	3.98540e7	−	2.30097e7i	0.0433984	−	0.0250561i
$973$			1.77569e9i			1.92765i
$974$	2.63208e8	−	1.51963e8i	0.284853	−	0.164460i
$975$	−1.93802e8	+	1.11892e8i	−0.209095	+	0.120721i
$976$	4.05385e8	−	2.34049e8i	0.436032	−	0.251743i
$977$	−2.77846e8	+	4.81243e8i	−0.297934	+	0.516037i	−0.975663	−	0.219275i	$-0.929631\pi$
$977$	−2.77846e8	+	4.81243e8i	−0.297934	+	0.516037i	0.677729	+	0.735312i	$0.262964\pi$
$978$			5.92152e8i			0.633019i
$979$	8.37413e7	+	4.83481e7i	0.0892466	+	0.0515266i
$980$	−2.36544e7	+	1.36569e7i	−0.0251323	+	0.0145102i
$981$	−2.17306e9			−2.30178
$982$	6.84949e8	+	1.18637e9i	0.723309	+	1.25281i
$983$	5.84005e8	+	3.37176e8i	0.614831	+	0.354973i	0.774854	−	0.632140i	$-0.217823\pi$
$983$	5.84005e8	+	3.37176e8i	0.614831	+	0.354973i	−0.160023	+	0.987113i	$0.551157\pi$
$984$	2.01938e8	−	3.49768e8i	0.211950	−	0.367108i
$985$			1.76886e9i			1.85091i
$986$	−3.10568e8	+	5.37919e8i	−0.323985	+	0.561159i
$987$	1.04555e9			1.08741
$988$			2.38358e7i			0.0247149i
$989$	9.11187e8	+	9.90876e8i	0.941930	+	1.02431i
$990$	−3.61840e8			−0.372916
$991$			1.15738e9i			1.18920i	0.804020	+	0.594602i	$0.202691\pi$
$991$			1.15738e9i			1.18920i	−0.804020	+	0.594602i	$0.797309\pi$
$992$	1.15868e8	+	6.68963e7i	0.118694	+	0.0685278i
$993$	−2.67745e9			−2.73447
$994$	−1.10998e9	−	6.40849e8i	−1.13020	−	0.652524i
$995$	−2.17062e8	+	3.75962e8i	−0.220351	+	0.381659i
$996$	1.04854e7	−	6.05373e6i	0.0106122	−	0.00612696i
$997$			1.27813e9i			1.28970i	0.764308	+	0.644851i	$0.223081\pi$
$997$			1.27813e9i			1.28970i	−0.764308	+	0.644851i	$0.776919\pi$
$998$	−1.67426e8	−	2.89991e8i	−0.168435	−	0.291738i
$999$	−5.45664e8	+	9.45118e8i	−0.547304	+	0.947959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.16	yes	42
43.7	odd	6	inner	43.7.d.a.7.6	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.6	✓	42	43.7	odd	6	inner
43.7.d.a.37.16	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+7.84004i q^{2} +(36.4833 + 21.0637i) q^{3} +2.53376 q^{4} +(-116.673 - 67.3609i) q^{5} +(-165.140 + 286.031i) q^{6} +(-385.031 + 222.298i) q^{7} +521.627i q^{8} +(522.856 + 905.613i) q^{9} +O(q^{10})\)	\(q+7.84004i q^{2} +(36.4833 + 21.0637i) q^{3} +2.53376 q^{4} +(-116.673 - 67.3609i) q^{5} +(-165.140 + 286.031i) q^{6} +(-385.031 + 222.298i) q^{7} +521.627i q^{8} +(522.856 + 905.613i) q^{9} +(528.113 - 914.718i) q^{10} -327.603 q^{11} +(92.4399 + 53.3702i) q^{12} +(1051.90 + 1821.95i) q^{13} +(-1742.82 - 3018.66i) q^{14} +(-2837.74 - 4915.10i) q^{15} -3927.42 q^{16} +(2727.39 + 4723.97i) q^{17} +(-7100.05 + 4099.21i) q^{18} +(3872.49 + 2235.78i) q^{19} +(-295.620 - 170.676i) q^{20} -18729.6 q^{21} -2568.42i q^{22} +(8465.56 - 14662.8i) q^{23} +(-10987.4 + 19030.7i) q^{24} +(1262.49 + 2186.70i) q^{25} +(-14284.1 + 8246.95i) q^{26} +13342.2i q^{27} +(-975.575 + 563.248i) q^{28} +(12578.3 - 7262.09i) q^{29} +(38534.6 - 22248.0i) q^{30} +(25798.6 - 44684.4i) q^{31} +2593.02i q^{32} +(-11952.1 - 6900.53i) q^{33} +(-37036.1 + 21382.8i) q^{34} +59896.7 q^{35} +(1324.79 + 2294.60i) q^{36} +(70836.6 + 40897.5i) q^{37} +(-17528.6 + 30360.5i) q^{38} +88627.6i q^{39} +(35137.3 - 60859.6i) q^{40} -18379.1 q^{41} -146841. i q^{42} +(-23774.6 + 75869.2i) q^{43} -830.067 q^{44} -140880. i q^{45} +(114957. + 66370.3i) q^{46} -55823.4 q^{47} +(-143285. - 82725.9i) q^{48} +(40008.1 - 69296.0i) q^{49} +(-17143.8 + 9897.99i) q^{50} +229795. i q^{51} +(2665.26 + 4616.37i) q^{52} +(86428.0 - 149698. i) q^{53} -104604. q^{54} +(38222.3 + 22067.7i) q^{55} +(-115957. - 200843. i) q^{56} +(94187.6 + 163138. i) q^{57} +(56935.0 + 98614.4i) q^{58} +24253.5 q^{59} +(-7190.14 - 12453.7i) q^{60} +(-103219. + 59593.7i) q^{61} +(350328. + 202262. i) q^{62} +(-402632. - 232459. i) q^{63} -271684. q^{64} -283428. i q^{65} +(54100.4 - 93704.7i) q^{66} +(-246132. + 426314. i) q^{67} +(6910.53 + 11969.4i) q^{68} +(617704. - 356631. i) q^{69} +469593. i q^{70} +(318444. - 183854. i) q^{71} +(-472393. + 272736. i) q^{72} +(-517521. + 298791. i) q^{73} +(-320638. + 555361. i) q^{74} +106371. i q^{75} +(9811.95 + 5664.93i) q^{76} +(126137. - 72825.5i) q^{77} -694844. q^{78} +(79931.1 + 138445. i) q^{79} +(458222. + 264555. i) q^{80} +(100126. - 173423. i) q^{81} -144093. i q^{82} +(56714.5 - 98232.4i) q^{83} -47456.3 q^{84} -734877. i q^{85} +(-594817. - 186394. i) q^{86} +611865. q^{87} -170887. i q^{88} +(-255618. - 147581. i) q^{89} +1.10451e6 q^{90} +(-810029. - 467671. i) q^{91} +(21449.7 - 37151.9i) q^{92} +(1.88244e6 - 1.08683e6i) q^{93} -437658. i q^{94} +(-301209. - 521709. i) q^{95} +(-54618.5 + 94602.1i) q^{96} +1.59602e6 q^{97} +(543283. + 313665. i) q^{98} +(-171289. - 296682. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more