LMFDB - Embedded newform 37.7.d.a.6.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,7,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, 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:	$8.51200109393$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.3
Character	$\chi$	$=$	37.6
Dual form			37.7.d.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.48840 + 8.48840i) q^{2} +25.9060i q^{3} -80.1058i q^{4} +(25.7278 + 25.7278i) q^{5} +(-219.900 - 219.900i) q^{6} -623.749 q^{7} +(136.713 + 136.713i) q^{8} +57.8805 q^{9} +O(q^{10})$	\(q+(-8.48840 + 8.48840i) q^{2} +25.9060i q^{3} -80.1058i q^{4} +(25.7278 + 25.7278i) q^{5} +(-219.900 - 219.900i) q^{6} -623.749 q^{7} +(136.713 + 136.713i) q^{8} +57.8805 q^{9} -436.776 q^{10} -647.366i q^{11} +2075.22 q^{12} +(691.960 + 691.960i) q^{13} +(5294.63 - 5294.63i) q^{14} +(-666.504 + 666.504i) q^{15} +2805.83 q^{16} +(-621.958 - 621.958i) q^{17} +(-491.313 + 491.313i) q^{18} +(3140.76 + 3140.76i) q^{19} +(2060.95 - 2060.95i) q^{20} -16158.8i q^{21} +(5495.10 + 5495.10i) q^{22} +(-10112.6 - 10112.6i) q^{23} +(-3541.68 + 3541.68i) q^{24} -14301.2i q^{25} -11747.3 q^{26} +20384.9i q^{27} +49965.9i q^{28} +(-9140.49 + 9140.49i) q^{29} -11315.1i q^{30} +(-9012.81 + 9012.81i) q^{31} +(-32566.6 + 32566.6i) q^{32} +16770.7 q^{33} +10558.9 q^{34} +(-16047.7 - 16047.7i) q^{35} -4636.57i q^{36} +(1138.25 - 50640.2i) q^{37} -53320.1 q^{38} +(-17925.9 + 17925.9i) q^{39} +7034.65i q^{40} -57906.4i q^{41} +(137163. + 137163. i) q^{42} +(-98303.5 - 98303.5i) q^{43} -51857.8 q^{44} +(1489.14 + 1489.14i) q^{45} +171679. q^{46} -17015.2 q^{47} +72687.7i q^{48} +271414. q^{49} +(121394. + 121394. i) q^{50} +(16112.4 - 16112.4i) q^{51} +(55430.0 - 55430.0i) q^{52} -239178. q^{53} +(-173035. - 173035. i) q^{54} +(16655.3 - 16655.3i) q^{55} +(-85274.5 - 85274.5i) q^{56} +(-81364.5 + 81364.5i) q^{57} -155176. i q^{58} +(-89748.0 - 89748.0i) q^{59} +(53390.9 + 53390.9i) q^{60} +(-54818.0 + 54818.0i) q^{61} -153009. i q^{62} -36102.9 q^{63} -373304. i q^{64} +35605.2i q^{65} +(-142356. + 142356. i) q^{66} +194411. i q^{67} +(-49822.4 + 49822.4i) q^{68} +(261976. - 261976. i) q^{69} +272438. q^{70} -120174. q^{71} +(7913.01 + 7913.01i) q^{72} +440247. i q^{73} +(420192. + 439516. i) q^{74} +370485. q^{75} +(251593. - 251593. i) q^{76} +403794. i q^{77} -304324. i q^{78} +(-129856. - 129856. i) q^{79} +(72187.8 + 72187.8i) q^{80} -485896. q^{81} +(491532. + 491532. i) q^{82} -552715. q^{83} -1.29442e6 q^{84} -32003.2i q^{85} +1.66888e6 q^{86} +(-236793. - 236793. i) q^{87} +(88503.3 - 88503.3i) q^{88} +(-412193. + 412193. i) q^{89} -25280.8 q^{90} +(-431609. - 431609. i) q^{91} +(-810075. + 810075. i) q^{92} +(-233486. - 233486. i) q^{93} +(144432. - 144432. i) q^{94} +161610. i q^{95} +(-843670. - 843670. i) q^{96} +(1.07887e6 + 1.07887e6i) q^{97} +(-2.30387e6 + 2.30387e6i) q^{98} -37469.9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9} - 1876 q^{10} + 11104 q^{12} - 2904 q^{13} - 7678 q^{14} + 4288 q^{15} - 44824 q^{16} + 2064 q^{17} + 6222 q^{18} - 4954 q^{19} - 43084 q^{20} - 39810 q^{22} + 21966 q^{23} + 79188 q^{24} + 66604 q^{26} + 69500 q^{29} - 32418 q^{31} - 141992 q^{32} + 54752 q^{33} + 256508 q^{34} - 26164 q^{35} + 180242 q^{37} + 329032 q^{38} - 60088 q^{39} - 346014 q^{42} - 144514 q^{43} - 294896 q^{44} + 842152 q^{45} - 522736 q^{46} - 157076 q^{47} + 405652 q^{49} + 46176 q^{50} - 624984 q^{51} - 161884 q^{52} - 512988 q^{53} + 541150 q^{54} + 824640 q^{55} - 608488 q^{56} - 311992 q^{57} + 187582 q^{59} - 1156764 q^{60} - 1321908 q^{61} - 887284 q^{63} + 752126 q^{66} + 1244832 q^{68} + 41960 q^{69} - 1029284 q^{70} + 1316252 q^{71} + 777880 q^{72} + 1117260 q^{74} - 2148904 q^{75} - 814428 q^{76} - 56722 q^{79} + 3750844 q^{80} - 930796 q^{81} + 1462554 q^{82} - 841484 q^{83} + 5065540 q^{84} + 3992612 q^{86} + 2494224 q^{87} - 3796428 q^{88} - 1439724 q^{89} - 5618044 q^{90} - 8644 q^{91} + 7826980 q^{92} - 54064 q^{93} - 2057938 q^{94} - 8819328 q^{96} + 2578548 q^{97} - 6043946 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9 - 1876 * q^10 + 11104 * q^12 - 2904 * q^13 - 7678 * q^14 + 4288 * q^15 - 44824 * q^16 + 2064 * q^17 + 6222 * q^18 - 4954 * q^19 - 43084 * q^20 - 39810 * q^22 + 21966 * q^23 + 79188 * q^24 + 66604 * q^26 + 69500 * q^29 - 32418 * q^31 - 141992 * q^32 + 54752 * q^33 + 256508 * q^34 - 26164 * q^35 + 180242 * q^37 + 329032 * q^38 - 60088 * q^39 - 346014 * q^42 - 144514 * q^43 - 294896 * q^44 + 842152 * q^45 - 522736 * q^46 - 157076 * q^47 + 405652 * q^49 + 46176 * q^50 - 624984 * q^51 - 161884 * q^52 - 512988 * q^53 + 541150 * q^54 + 824640 * q^55 - 608488 * q^56 - 311992 * q^57 + 187582 * q^59 - 1156764 * q^60 - 1321908 * q^61 - 887284 * q^63 + 752126 * q^66 + 1244832 * q^68 + 41960 * q^69 - 1029284 * q^70 + 1316252 * q^71 + 777880 * q^72 + 1117260 * q^74 - 2148904 * q^75 - 814428 * q^76 - 56722 * q^79 + 3750844 * q^80 - 930796 * q^81 + 1462554 * q^82 - 841484 * q^83 + 5065540 * q^84 + 3992612 * q^86 + 2494224 * q^87 - 3796428 * q^88 - 1439724 * q^89 - 5618044 * q^90 - 8644 * q^91 + 7826980 * q^92 - 54064 * q^93 - 2057938 * q^94 - 8819328 * q^96 + 2578548 * q^97 - 6043946 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−8.48840	+	8.48840i	−1.06105	+	1.06105i	−0.0630388	+	0.998011i	$0.520079\pi$
$2$	−8.48840	+	8.48840i	−1.06105	+	1.06105i	−0.998011	+	0.0630388i	$0.979921\pi$
$3$			25.9060i			0.959481i	0.877411	+	0.479740i	$0.159269\pi$
$3$			25.9060i			0.959481i	−0.877411	+	0.479740i	$0.840731\pi$
$4$		−	80.1058i		−	1.25165i
$5$	25.7278	+	25.7278i	0.205823	+	0.205823i	0.802489	−	0.596667i	$-0.203509\pi$
$5$	25.7278	+	25.7278i	0.205823	+	0.205823i	−0.596667	+	0.802489i	$0.703509\pi$
$6$	−219.900	−	219.900i	−1.01806	−	1.01806i
$7$	−623.749			−1.81851			−0.909255	−	0.416240i	$-0.863348\pi$
$7$	−623.749			−1.81851			−0.909255	+	0.416240i	$0.863348\pi$
$8$	136.713	+	136.713i	0.267017	+	0.267017i
$9$	57.8805			0.0793971
$10$	−436.776			−0.436776
$11$		−	647.366i		−	0.486376i	−0.969979	−	0.243188i	$-0.921807\pi$
$11$		−	647.366i		−	0.486376i	0.969979	−	0.243188i	$-0.0781932\pi$
$12$	2075.22			1.20094
$13$	691.960	+	691.960i	0.314957	+	0.314957i	0.846826	−	0.531870i	$-0.178510\pi$
$13$	691.960	+	691.960i	0.314957	+	0.314957i	−0.531870	+	0.846826i	$0.678510\pi$
$14$	5294.63	−	5294.63i	1.92953	−	1.92953i
$15$	−666.504	+	666.504i	−0.197483	+	0.197483i
$16$	2805.83			0.685017
$17$	−621.958	−	621.958i	−0.126594	−	0.126594i	0.640971	−	0.767565i	$-0.278532\pi$
$17$	−621.958	−	621.958i	−0.126594	−	0.126594i	−0.767565	+	0.640971i	$0.778532\pi$
$18$	−491.313	+	491.313i	−0.0842443	+	0.0842443i
$19$	3140.76	+	3140.76i	0.457904	+	0.457904i	0.897967	−	0.440063i	$-0.145044\pi$
$19$	3140.76	+	3140.76i	0.457904	+	0.457904i	−0.440063	+	0.897967i	$0.645044\pi$
$20$	2060.95	−	2060.95i	0.257619	−	0.257619i
$21$		−	16158.8i		−	1.74482i
$22$	5495.10	+	5495.10i	0.516069	+	0.516069i
$23$	−10112.6	−	10112.6i	−0.831147	−	0.831147i	0.156527	−	0.987674i	$-0.449970\pi$
$23$	−10112.6	−	10112.6i	−0.831147	−	0.831147i	−0.987674	+	0.156527i	$0.949970\pi$
$24$	−3541.68	+	3541.68i	−0.256198	+	0.256198i
$25$		−	14301.2i		−	0.915274i
$26$	−11747.3			−0.668369
$27$			20384.9i			1.03566i
$28$			49965.9i			2.27614i
$29$	−9140.49	+	9140.49i	−0.374779	+	0.374779i	−0.869214	−	0.494435i	$-0.835375\pi$
$29$	−9140.49	+	9140.49i	−0.374779	+	0.374779i	0.494435	+	0.869214i	$0.335375\pi$
$30$		−	11315.1i		−	0.419078i
$31$	−9012.81	+	9012.81i	−0.302535	+	0.302535i	−0.842005	−	0.539470i	$-0.818625\pi$
$31$	−9012.81	+	9012.81i	−0.302535	+	0.302535i	0.539470	+	0.842005i	$0.318625\pi$
$32$	−32566.6	+	32566.6i	−0.993854	+	0.993854i
$33$	16770.7			0.466668
$34$	10558.9			0.268646
$35$	−16047.7	−	16047.7i	−0.374290	−	0.374290i
$36$		−	4636.57i		−	0.0993777i
$37$	1138.25	−	50640.2i	0.0224715	−	0.999747i
$37$	1138.25	−	50640.2i	0.0224715	−	0.999747i
$38$	−53320.1			−0.971717
$39$	−17925.9	+	17925.9i	−0.302195	+	0.302195i
$40$			7034.65i			0.109916i
$41$		−	57906.4i		−	0.840185i	−0.907481	−	0.420092i	$-0.861998\pi$
$41$		−	57906.4i		−	0.840185i	0.907481	−	0.420092i	$-0.138002\pi$
$42$	137163.	+	137163.i	1.85135	+	1.85135i
$43$	−98303.5	−	98303.5i	−1.23641	−	1.23641i	−0.961457	−	0.274956i	$-0.911337\pi$
$43$	−98303.5	−	98303.5i	−1.23641	−	1.23641i	−0.274956	−	0.961457i	$-0.588663\pi$
$44$	−51857.8			−0.608774
$45$	1489.14	+	1489.14i	0.0163417	+	0.0163417i
$46$	171679.			1.76378
$47$	−17015.2			−0.163887			−0.0819434	−	0.996637i	$-0.526113\pi$
$47$	−17015.2			−0.163887			−0.0819434	+	0.996637i	$0.526113\pi$
$48$			72687.7i			0.657260i
$49$	271414.			2.30698
$50$	121394.	+	121394.i	0.971152	+	0.971152i
$51$	16112.4	−	16112.4i	0.121465	−	0.121465i
$52$	55430.0	−	55430.0i	0.394217	−	0.394217i
$53$	−239178.			−1.60655			−0.803274	−	0.595610i	$-0.796910\pi$
$53$	−239178.			−1.60655			−0.803274	+	0.595610i	$0.796910\pi$
$54$	−173035.	−	173035.i	−1.09889	−	1.09889i
$55$	16655.3	−	16655.3i	0.100107	−	0.100107i
$56$	−85274.5	−	85274.5i	−0.485574	−	0.485574i
$57$	−81364.5	+	81364.5i	−0.439350	+	0.439350i
$58$		−	155176.i		−	0.795319i
$59$	−89748.0	−	89748.0i	−0.436987	−	0.436987i	0.454009	−	0.890997i	$-0.349993\pi$
$59$	−89748.0	−	89748.0i	−0.436987	−	0.436987i	−0.890997	+	0.454009i	$0.849993\pi$
$60$	53390.9	+	53390.9i	0.247180	+	0.247180i
$61$	−54818.0	+	54818.0i	−0.241509	+	0.241509i	−0.817474	−	0.575965i	$-0.804626\pi$
$61$	−54818.0	+	54818.0i	−0.241509	+	0.241509i	0.575965	+	0.817474i	$0.304626\pi$
$62$		−	153009.i		−	0.642009i
$63$	−36102.9			−0.144384
$64$		−	373304.i		−	1.42404i
$65$			35605.2i			0.129650i
$66$	−142356.	+	142356.i	−0.495158	+	0.495158i
$67$			194411.i			0.646393i	0.946332	+	0.323197i	$0.104758\pi$
$67$			194411.i			0.646393i	−0.946332	+	0.323197i	$0.895242\pi$
$68$	−49822.4	+	49822.4i	−0.158452	+	0.158452i
$69$	261976.	−	261976.i	0.797469	−	0.797469i
$70$	272438.			0.794281
$71$	−120174.			−0.335765			−0.167883	−	0.985807i	$-0.553693\pi$
$71$	−120174.			−0.335765			−0.167883	+	0.985807i	$0.553693\pi$
$72$	7913.01	+	7913.01i	0.0212004	+	0.0212004i
$73$			440247.i			1.13169i	0.824512	+	0.565845i	$0.191450\pi$
$73$			440247.i			1.13169i	−0.824512	+	0.565845i	$0.808550\pi$
$74$	420192.	+	439516.i	1.03694	+	1.08463i
$75$	370485.			0.878188
$76$	251593.	−	251593.i	0.573137	−	0.573137i
$77$			403794.i			0.884479i
$78$		−	304324.i		−	0.641287i
$79$	−129856.	−	129856.i	−0.263378	−	0.263378i	0.563047	−	0.826425i	$-0.309629\pi$
$79$	−129856.	−	129856.i	−0.263378	−	0.263378i	−0.826425	+	0.563047i	$0.809629\pi$
$80$	72187.8	+	72187.8i	0.140992	+	0.140992i
$81$	−485896.			−0.914299
$82$	491532.	+	491532.i	0.891478	+	0.891478i
$83$	−552715.			−0.966644			−0.483322	−	0.875443i	$-0.660570\pi$
$83$	−552715.			−0.966644			−0.483322	+	0.875443i	$0.660570\pi$
$84$	−1.29442e6			−2.18392
$85$		−	32003.2i		−	0.0521119i
$86$	1.66888e6			2.62379
$87$	−236793.	−	236793.i	−0.359593	−	0.359593i
$88$	88503.3	−	88503.3i	0.129871	−	0.129871i
$89$	−412193.	+	412193.i	−0.584697	+	0.584697i	−0.936190	−	0.351493i	$-0.885674\pi$
$89$	−412193.	+	412193.i	−0.584697	+	0.584697i	0.351493	+	0.936190i	$0.385674\pi$
$90$	−25280.8			−0.0346788
$91$	−431609.	−	431609.i	−0.572752	−	0.572752i
$92$	−810075.	+	810075.i	−1.04031	+	1.04031i
$93$	−233486.	−	233486.i	−0.290276	−	0.290276i
$94$	144432.	−	144432.i	0.173892	−	0.173892i
$95$			161610.i			0.188494i
$96$	−843670.	−	843670.i	−0.953584	−	0.953584i
$97$	1.07887e6	+	1.07887e6i	1.18210	+	1.18210i	0.979199	+	0.202903i	$0.0650377\pi$
$97$	1.07887e6	+	1.07887e6i	1.18210	+	1.18210i	0.202903	+	0.979199i	$0.434962\pi$
$98$	−2.30387e6	+	2.30387e6i	−2.44782	+	2.44782i
$99$		−	37469.9i		−	0.0386169i
$100$	−1.14561e6			−1.14561
$101$		−	2.00899e6i		−	1.94991i	−0.222410	−	0.974953i	$-0.571392\pi$
$101$		−	2.00899e6i		−	1.94991i	0.222410	−	0.974953i	$-0.428608\pi$
$102$			273537.i			0.257760i
$103$	848383.	−	848383.i	0.776391	−	0.776391i	−0.202825	−	0.979215i	$-0.565012\pi$
$103$	848383.	−	848383.i	0.776391	−	0.776391i	0.979215	+	0.202825i	$0.0650121\pi$
$104$			189200.i			0.168198i
$105$	415731.	−	415731.i	0.359124	−	0.359124i
$106$	2.03024e6	−	2.03024e6i	1.70463	−	1.70463i
$107$	−1.06170e6			−0.866665			−0.433333	−	0.901234i	$-0.642662\pi$
$107$	−1.06170e6			−0.866665			−0.433333	+	0.901234i	$0.642662\pi$
$108$	1.63295e6			1.29629
$109$	1.09201e6	+	1.09201e6i	0.843230	+	0.843230i	0.989278	−	0.146048i	$-0.0466554\pi$
$109$	1.09201e6	+	1.09201e6i	0.843230	+	0.843230i	−0.146048	+	0.989278i	$0.546655\pi$
$110$			282754.i			0.212437i
$111$	1.31188e6	+	29487.5i	0.959238	+	0.0215610i
$112$	−1.75013e6			−1.24571
$113$	9704.60	−	9704.60i	0.00672577	−	0.00672577i	−0.703736	−	0.710462i	$-0.748486\pi$
$113$	9704.60	−	9704.60i	0.00672577	−	0.00672577i	0.710462	+	0.703736i	$0.248486\pi$
$114$		−	1.38131e6i		−	0.932344i
$115$		−	520348.i		−	0.342137i
$116$	732207.	+	732207.i	0.469094	+	0.469094i
$117$	40051.0	+	40051.0i	0.0250067	+	0.0250067i
$118$	1.52363e6			0.927331
$119$	387945.	+	387945.i	0.230213	+	0.230213i
$120$	−182239.			−0.105463
$121$	1.35248e6			0.763438
$122$		−	930634.i		−	0.512507i
$123$	1.50012e6			0.806141
$124$	721979.	+	721979.i	0.378669	+	0.378669i
$125$	769935.	−	769935.i	0.394207	−	0.394207i
$126$	306456.	−	306456.i	0.153199	−	0.153199i
$127$	−3.95958e6			−1.93303			−0.966514	−	0.256615i	$-0.917393\pi$
$127$	−3.95958e6			−1.93303			−0.966514	+	0.256615i	$0.917393\pi$
$128$	1.08449e6	+	1.08449e6i	0.517124	+	0.517124i
$129$	2.54665e6	−	2.54665e6i	1.18631	−	1.18631i
$130$	−302231.	−	302231.i	−0.137565	−	0.137565i
$131$	−1.36974e6	+	1.36974e6i	−0.609292	+	0.609292i	−0.942761	−	0.333469i	$-0.891781\pi$
$131$	−1.36974e6	+	1.36974e6i	−0.609292	+	0.609292i	0.333469	+	0.942761i	$0.391781\pi$
$132$		−	1.34343e6i		−	0.584107i
$133$	−1.95905e6	−	1.95905e6i	−0.832702	−	0.832702i
$134$	−1.65024e6	−	1.65024e6i	−0.685856	−	0.685856i
$135$	−524459.	+	524459.i	−0.213162	+	0.213162i
$136$		−	170059.i		−	0.0676057i
$137$	2.15276e6			0.837209			0.418604	−	0.908169i	$-0.362519\pi$
$137$	2.15276e6			0.837209			0.418604	+	0.908169i	$0.362519\pi$
$138$			4.44751e6i			1.69231i
$139$			1.59523e6i			0.593988i	0.954879	+	0.296994i	$0.0959841\pi$
$139$			1.59523e6i			0.593988i	−0.954879	+	0.296994i	$0.904016\pi$
$140$	−1.28551e6	+	1.28551e6i	−0.468482	+	0.468482i
$141$		−	440796.i		−	0.157246i
$142$	1.02009e6	−	1.02009e6i	0.356264	−	0.356264i
$143$	447951.	−	447951.i	0.153187	−	0.153187i
$144$	162403.			0.0543884
$145$	−470330.			−0.154276
$146$	−3.73699e6	−	3.73699e6i	−1.20078	−	1.20078i
$147$			7.03123e6i			2.21350i
$148$	−4.05658e6	−	91180.6i	−1.25134	−	0.0281266i
$149$	−5.84990e6			−1.76844			−0.884219	−	0.467072i	$-0.845309\pi$
$149$	−5.84990e6			−1.76844			−0.884219	+	0.467072i	$0.845309\pi$
$150$	−3.14483e6	+	3.14483e6i	−0.931801	+	0.931801i
$151$			5.22353e6i			1.51717i	0.651575	+	0.758584i	$0.274108\pi$
$151$			5.22353e6i			1.51717i	−0.651575	+	0.758584i	$0.725892\pi$
$152$			858765.i			0.244536i
$153$	−35999.2	−	35999.2i	−0.0100512	−	0.0100512i
$154$	−3.42756e6	−	3.42756e6i	−0.938477	−	0.938477i
$155$	−463760.			−0.124537
$156$	1.43597e6	+	1.43597e6i	0.378243	+	0.378243i
$157$	1.53406e6			0.396409			0.198205	−	0.980161i	$-0.436489\pi$
$157$	1.53406e6			0.396409			0.198205	+	0.980161i	$0.436489\pi$
$158$	2.20453e6			0.558915
$159$		−	6.19614e6i		−	1.54145i
$160$	−1.67574e6			−0.409115
$161$	6.30770e6	+	6.30770e6i	1.51145	+	1.51145i
$162$	4.12448e6	−	4.12448e6i	0.970117	−	0.970117i
$163$	1.45668e6	−	1.45668e6i	0.336358	−	0.336358i	−0.518637	−	0.854995i	$-0.673560\pi$
$163$	1.45668e6	−	1.45668e6i	0.336358	−	0.336358i	0.854995	+	0.518637i	$0.173560\pi$
$164$	−4.63864e6			−1.05162
$165$	431472.	+	431472.i	0.0960508	+	0.0960508i
$166$	4.69166e6	−	4.69166e6i	1.02566	−	1.02566i
$167$	4.51364e6	+	4.51364e6i	0.969121	+	0.969121i	0.999537	−	0.0304166i	$-0.00968340\pi$
$167$	4.51364e6	+	4.51364e6i	0.969121	+	0.969121i	−0.0304166	+	0.999537i	$0.509683\pi$
$168$	2.20912e6	−	2.20912e6i	0.465898	−	0.465898i
$169$		−	3.86919e6i		−	0.801605i
$170$	271656.	+	271656.i	0.0552933	+	0.0552933i
$171$	181789.	+	181789.i	0.0363562	+	0.0363562i
$172$	−7.87468e6	+	7.87468e6i	−1.54756	+	1.54756i
$173$			6.90721e6i			1.33403i	0.745046	+	0.667013i	$0.232427\pi$
$173$			6.90721e6i			1.33403i	−0.745046	+	0.667013i	$0.767573\pi$
$174$	4.01999e6			0.763093
$175$			8.92033e6i			1.66443i
$176$		−	1.81640e6i		−	0.333176i
$177$	2.32501e6	−	2.32501e6i	0.419281	−	0.419281i
$178$		−	6.99773e6i		−	1.24079i
$179$	3.17252e6	−	3.17252e6i	0.553153	−	0.553153i	−0.374197	−	0.927349i	$-0.622081\pi$
$179$	3.17252e6	−	3.17252e6i	0.553153	−	0.553153i	0.927349	+	0.374197i	$0.122081\pi$
$180$	119289.	−	119289.i	0.0204542	−	0.0204542i
$181$	−7.44259e6			−1.25513			−0.627565	−	0.778565i	$-0.715948\pi$
$181$	−7.44259e6			−1.25513			−0.627565	+	0.778565i	$0.715948\pi$
$182$	7.32734e6			1.21544
$183$	−1.42011e6	−	1.42011e6i	−0.231723	−	0.231723i
$184$		−	2.76503e6i		−	0.443861i
$185$	1.33215e6	−	1.27358e6i	0.210396	−	0.201145i
$186$	3.96384e6			0.615995
$187$	−402634.	+	402634.i	−0.0615724	+	0.0615724i
$188$			1.36302e6i			0.205130i
$189$		−	1.27151e7i		−	1.88336i
$190$	−1.37181e6	−	1.37181e6i	−0.200001	−	0.200001i
$191$	1.36919e6	+	1.36919e6i	0.196501	+	0.196501i	0.798498	−	0.601997i	$-0.205628\pi$
$191$	1.36919e6	+	1.36919e6i	0.196501	+	0.196501i	−0.601997	+	0.798498i	$0.705628\pi$
$192$	9.67080e6			1.36634
$193$	−3.24554e6	−	3.24554e6i	−0.451455	−	0.451455i	0.444382	−	0.895837i	$-0.353423\pi$
$193$	−3.24554e6	−	3.24554e6i	−0.451455	−	0.451455i	−0.895837	+	0.444382i	$0.853423\pi$
$194$	−1.83158e7			−2.50854
$195$	−922388.			−0.124397
$196$		−	2.17418e7i		−	2.88754i
$197$	−4.79838e6			−0.627619			−0.313809	−	0.949486i	$-0.601605\pi$
$197$	−4.79838e6			−0.627619			−0.313809	+	0.949486i	$0.601605\pi$
$198$	318059.	+	318059.i	0.0409744	+	0.0409744i
$199$	−7.02522e6	+	7.02522e6i	−0.891457	+	0.891457i	−0.994660	−	0.103203i	$-0.967091\pi$
$199$	−7.02522e6	+	7.02522e6i	−0.891457	+	0.891457i	0.103203	+	0.994660i	$0.467091\pi$
$200$	1.95515e6	−	1.95515e6i	0.244394	−	0.244394i
$201$	−5.03641e6			−0.620202
$202$	1.70531e7	+	1.70531e7i	2.06895	+	2.06895i
$203$	5.70137e6	−	5.70137e6i	0.681540	−	0.681540i
$204$	−1.29070e6	−	1.29070e6i	−0.152032	−	0.152032i
$205$	1.48980e6	−	1.48980e6i	0.172929	−	0.172929i
$206$			1.44028e7i			1.64758i
$207$	−585320.	−	585320.i	−0.0659907	−	0.0659907i
$208$	1.94152e6	+	1.94152e6i	0.215750	+	0.215750i
$209$	2.03322e6	−	2.03322e6i	0.222713	−	0.222713i
$210$			7.05778e6i			0.762097i
$211$	−7.16053e6			−0.762251			−0.381125	−	0.924523i	$-0.624463\pi$
$211$	−7.16053e6			−0.762251			−0.381125	+	0.924523i	$0.624463\pi$
$212$			1.91596e7i			2.01084i
$213$		−	3.11323e6i		−	0.322160i
$214$	9.01215e6	−	9.01215e6i	0.919575	−	0.919575i
$215$		−	5.05827e6i		−	0.508963i
$216$	−2.78688e6	+	2.78688e6i	−0.276539	+	0.276539i
$217$	5.62173e6	−	5.62173e6i	0.550162	−	0.550162i
$218$	−1.85388e7			−1.78942
$219$	−1.14050e7			−1.08583
$220$	−1.33419e6	−	1.33419e6i	−0.125299	−	0.125299i
$221$		−	860739.i		−	0.0797434i
$222$	−1.13861e7	+	1.08855e7i	−1.04068	+	0.994922i
$223$	1.37335e7			1.23841			0.619206	−	0.785228i	$-0.287454\pi$
$223$	1.37335e7			1.23841			0.619206	+	0.785228i	$0.287454\pi$
$224$	2.03134e7	−	2.03134e7i	1.80733	−	1.80733i
$225$		−	827759.i		−	0.0726702i
$226$			164753.i			0.0142728i
$227$	3.44448e6	+	3.44448e6i	0.294473	+	0.294473i	0.838844	−	0.544371i	$-0.183232\pi$
$227$	3.44448e6	+	3.44448e6i	0.294473	+	0.294473i	−0.544371	+	0.838844i	$0.683232\pi$
$228$	6.51777e6	+	6.51777e6i	0.549914	+	0.549914i
$229$	6.00311e6			0.499885			0.249943	−	0.968261i	$-0.419588\pi$
$229$	6.00311e6			0.499885			0.249943	+	0.968261i	$0.419588\pi$
$230$	4.41692e6	+	4.41692e6i	0.363025	+	0.363025i
$231$	−1.04607e7			−0.848641
$232$	−2.49925e6			−0.200145
$233$		−	2.14272e7i		−	1.69394i	−0.531642	−	0.846969i	$-0.678425\pi$
$233$		−	2.14272e7i		−	1.69394i	0.531642	−	0.846969i	$-0.321575\pi$
$234$	−679938.			−0.0530666
$235$	−437765.	−	437765.i	−0.0337316	−	0.0337316i
$236$	−7.18934e6	+	7.18934e6i	−0.546957	+	0.546957i
$237$	3.36404e6	−	3.36404e6i	0.252706	−	0.252706i
$238$	−6.58607e6			−0.488535
$239$	−1.38506e7	−	1.38506e7i	−1.01455	−	1.01455i	−0.999893	−	0.0146585i	$-0.995334\pi$
$239$	−1.38506e7	−	1.38506e7i	−1.01455	−	1.01455i	−0.0146585	−	0.999893i	$-0.504666\pi$
$240$	−1.87010e6	+	1.87010e6i	−0.135279	+	0.135279i
$241$	1.57623e7	+	1.57623e7i	1.12608	+	1.12608i	0.990809	+	0.135270i	$0.0431901\pi$
$241$	1.57623e7	+	1.57623e7i	1.12608	+	1.12608i	0.135270	+	0.990809i	$0.456810\pi$
$242$	−1.14804e7	+	1.14804e7i	−0.810046	+	0.810046i
$243$			2.27299e6i			0.158409i
$244$	4.39124e6	+	4.39124e6i	0.302286	+	0.302286i
$245$	6.98288e6	+	6.98288e6i	0.474828	+	0.474828i
$246$	−1.27336e7	+	1.27336e7i	−0.855356	+	0.855356i
$247$			4.34656e6i			0.288440i
$248$	−2.46433e6			−0.161564
$249$		−	1.43186e7i		−	0.927476i
$250$			1.30710e7i			0.836546i
$251$	−1.21887e7	+	1.21887e7i	−0.770787	+	0.770787i	−0.978244	−	0.207457i	$-0.933481\pi$
$251$	−1.21887e7	+	1.21887e7i	−0.770787	+	0.770787i	0.207457	+	0.978244i	$0.433481\pi$
$252$			2.89205e6i			0.180719i
$253$	−6.54653e6	+	6.54653e6i	−0.404250	+	0.404250i
$254$	3.36105e7	−	3.36105e7i	2.05104	−	2.05104i
$255$	829075.			0.0500004
$256$	5.48030e6			0.326651
$257$	−1.55220e7	−	1.55220e7i	−0.914424	−	0.914424i	0.0821929	−	0.996616i	$-0.473808\pi$
$257$	−1.55220e7	−	1.55220e7i	−0.914424	−	0.914424i	−0.996616	+	0.0821929i	$0.973808\pi$
$258$			4.32339e7i			2.51748i
$259$	−709983.	+	3.15868e7i	−0.0408647	+	1.81805i
$260$	2.85219e6			0.162277
$261$	−529056.	+	529056.i	−0.0297564	+	0.0297564i
$262$		−	2.32539e7i		−	1.29298i
$263$		−	6.90022e6i		−	0.379311i	−0.981851	−	0.189656i	$-0.939263\pi$
$263$		−	6.90022e6i		−	0.379311i	0.981851	−	0.189656i	$-0.0607372\pi$
$264$	2.29276e6	+	2.29276e6i	0.124608	+	0.124608i
$265$	−6.15353e6	−	6.15353e6i	−0.330664	−	0.330664i
$266$	3.32583e7			1.76708
$267$	−1.06783e7	−	1.06783e7i	−0.561006	−	0.561006i
$268$	1.55735e7			0.809061
$269$	−1.51125e7			−0.776391			−0.388195	−	0.921577i	$-0.626901\pi$
$269$	−1.51125e7			−0.776391			−0.388195	+	0.921577i	$0.626901\pi$
$270$		−	8.90364e6i		−	0.452352i
$271$	−2.77306e7			−1.39332			−0.696660	−	0.717401i	$-0.745331\pi$
$271$	−2.77306e7			−1.39332			−0.696660	+	0.717401i	$0.745331\pi$
$272$	−1.74511e6	−	1.74511e6i	−0.0867192	−	0.0867192i
$273$	1.11813e7	−	1.11813e7i	0.549544	−	0.549544i
$274$	−1.82735e7	+	1.82735e7i	−0.888320	+	0.888320i
$275$	−9.25809e6			−0.445167
$276$	−2.09858e7	−	2.09858e7i	−0.998155	−	0.998155i
$277$	2.06753e7	−	2.06753e7i	0.972776	−	0.972776i	−0.0268626	−	0.999639i	$-0.508552\pi$
$277$	2.06753e7	−	2.06753e7i	0.972776	−	0.972776i	0.999639	+	0.0268626i	$0.00855167\pi$
$278$	−1.35409e7	−	1.35409e7i	−0.630251	−	0.630251i
$279$	−521666.	+	521666.i	−0.0240204	+	0.0240204i
$280$		−	4.38785e6i		−	0.199884i
$281$	8.52341e6	+	8.52341e6i	0.384144	+	0.384144i	0.872593	−	0.488449i	$-0.162437\pi$
$281$	8.52341e6	+	8.52341e6i	0.384144	+	0.384144i	−0.488449	+	0.872593i	$0.662437\pi$
$282$	3.74165e6	+	3.74165e6i	0.166846	+	0.166846i
$283$	807117.	−	807117.i	0.0356104	−	0.0356104i	−0.689077	−	0.724688i	$-0.741984\pi$
$283$	807117.	−	807117.i	0.0356104	−	0.0356104i	0.724688	+	0.689077i	$0.241984\pi$
$284$			9.62664e6i			0.420262i
$285$	−4.18666e6			−0.180856
$286$			7.60478e6i			0.325079i
$287$			3.61190e7i			1.52788i
$288$	−1.88497e6	+	1.88497e6i	−0.0789092	+	0.0789092i
$289$		−	2.33639e7i		−	0.967948i
$290$	3.99235e6	−	3.99235e6i	0.163695	−	0.163695i
$291$	−2.79492e7	+	2.79492e7i	−1.13420	+	1.13420i
$292$	3.52663e7			1.41648
$293$	2.85164e6			0.113369			0.0566843	−	0.998392i	$-0.481947\pi$
$293$	2.85164e6			0.113369			0.0566843	+	0.998392i	$0.481947\pi$
$294$	−5.96839e7	−	5.96839e7i	−2.34863	−	2.34863i
$295$		−	4.61804e6i		−	0.179884i
$296$	7.07878e6	−	6.76755e6i	0.272950	−	0.260950i
$297$	1.31965e7			0.503720
$298$	4.96563e7	−	4.96563e7i	1.87640	−	1.87640i
$299$		−	1.39950e7i		−	0.523550i
$300$		−	2.96781e7i		−	1.09919i
$301$	6.13167e7	+	6.13167e7i	2.24843	+	2.24843i
$302$	−4.43394e7	−	4.43394e7i	−1.60979	−	1.60979i
$303$	5.20449e7			1.87090
$304$	8.81243e6	+	8.81243e6i	0.313672	+	0.313672i
$305$	−2.82070e6			−0.0994161
$306$	611152.			0.0213297
$307$			1.01743e7i			0.351631i	0.984423	+	0.175816i	$0.0562563\pi$
$307$			1.01743e7i			0.351631i	−0.984423	+	0.175816i	$0.943744\pi$
$308$	3.23463e7			1.10706
$309$	2.19782e7	+	2.19782e7i	0.744932	+	0.744932i
$310$	3.93658e6	−	3.93658e6i	0.132140	−	0.132140i
$311$	3.62820e7	−	3.62820e7i	1.20617	−	1.20617i	0.233916	−	0.972257i	$-0.424846\pi$
$311$	3.62820e7	−	3.62820e7i	1.20617	−	1.20617i	0.972257	−	0.233916i	$-0.0751541\pi$
$312$	−4.90140e6			−0.161382
$313$	2.91171e6	+	2.91171e6i	0.0949545	+	0.0949545i	0.752988	−	0.658034i	$-0.228612\pi$
$313$	2.91171e6	+	2.91171e6i	0.0949545	+	0.0949545i	−0.658034	+	0.752988i	$0.728612\pi$
$314$	−1.30217e7	+	1.30217e7i	−0.420610	+	0.420610i
$315$	−928849.	−	928849.i	−0.0297176	−	0.0297176i
$316$	−1.04022e7	+	1.04022e7i	−0.329658	+	0.329658i
$317$			3.14466e7i			0.987178i	0.869695	+	0.493589i	$0.164315\pi$
$317$			3.14466e7i			0.987178i	−0.869695	+	0.493589i	$0.835685\pi$
$318$	5.25953e7	+	5.25953e7i	1.63556	+	1.63556i
$319$	5.91725e6	+	5.91725e6i	0.182284	+	0.182284i
$320$	9.60429e6	−	9.60429e6i	0.293100	−	0.293100i
$321$		−	2.75044e7i		−	0.831548i
$322$	−1.07085e8			−3.20744
$323$		−	3.90684e6i		−	0.115936i
$324$			3.89231e7i			1.14439i
$325$	9.89583e6	−	9.89583e6i	0.288272	−	0.288272i
$326$			2.47298e7i			0.713785i
$327$	−2.82895e7	+	2.82895e7i	−0.809062	+	0.809062i
$328$	7.91655e6	−	7.91655e6i	0.224344	−	0.224344i
$329$	1.06132e7			0.298030
$330$	−7.32502e6			−0.203829
$331$	−8.18407e6	−	8.18407e6i	−0.225676	−	0.225676i	0.585208	−	0.810884i	$-0.301013\pi$
$331$	−8.18407e6	−	8.18407e6i	−0.225676	−	0.225676i	−0.810884	+	0.585208i	$0.801013\pi$
$332$			4.42757e7i			1.20990i
$333$	65882.6	−	2.93108e6i	0.00178418	−	0.0793771i
$334$	−7.66272e7			−2.05657
$335$	−5.00178e6	+	5.00178e6i	−0.133042	+	0.133042i
$336$		−	4.53389e7i		−	1.19523i
$337$			2.45997e7i			0.642746i	0.946953	+	0.321373i	$0.104144\pi$
$337$			2.45997e7i			0.642746i	−0.946953	+	0.321373i	$0.895856\pi$
$338$	3.28433e7	+	3.28433e7i	0.850543	+	0.850543i
$339$	251407.	+	251407.i	0.00645325	+	0.00645325i
$340$	−2.56365e6			−0.0652261
$341$	5.83459e6	+	5.83459e6i	0.147146	+	0.147146i
$342$	−3.08619e6			−0.0771516
$343$	−9.59105e7			−2.37675
$344$		−	2.68787e7i		−	0.660287i
$345$	1.34801e7			0.328274
$346$	−5.86311e7	−	5.86311e7i	−1.41547	−	1.41547i
$347$	5.64528e7	−	5.64528e7i	1.35113	−	1.35113i	0.466731	−	0.884399i	$-0.345432\pi$
$347$	5.64528e7	−	5.64528e7i	1.35113	−	1.35113i	0.884399	−	0.466731i	$-0.154568\pi$
$348$	−1.89685e7	+	1.89685e7i	−0.450086	+	0.450086i
$349$	−7.36768e7			−1.73322			−0.866611	−	0.498984i	$-0.833707\pi$
$349$	−7.36768e7			−1.73322			−0.866611	+	0.498984i	$0.833707\pi$
$350$	−7.57193e7	−	7.57193e7i	−1.76605	−	1.76605i
$351$	−1.41055e7	+	1.41055e7i	−0.326188	+	0.326188i
$352$	2.10825e7	+	2.10825e7i	0.483387	+	0.483387i
$353$	−4.49695e6	+	4.49695e6i	−0.102234	+	0.102234i	−0.756374	−	0.654140i	$-0.773031\pi$
$353$	−4.49695e6	+	4.49695e6i	−0.102234	+	0.102234i	0.654140	+	0.756374i	$0.273031\pi$
$354$			3.94712e7i			0.889756i
$355$	−3.09182e6	−	3.09182e6i	−0.0691080	−	0.0691080i
$356$	3.30191e7	+	3.30191e7i	0.731839	+	0.731839i
$357$	−1.00501e7	+	1.00501e7i	−0.220885	+	0.220885i
$358$			5.38592e7i			1.17385i
$359$	−5.21505e7			−1.12713			−0.563566	−	0.826071i	$-0.690571\pi$
$359$	−5.21505e7			−1.12713			−0.563566	+	0.826071i	$0.690571\pi$
$360$			407169.i			0.00872704i
$361$		−	2.73171e7i		−	0.580649i
$362$	6.31757e7	−	6.31757e7i	1.33175	−	1.33175i
$363$			3.50373e7i			0.732504i
$364$	−3.45744e7	+	3.45744e7i	−0.716887	+	0.716887i
$365$	−1.13266e7	+	1.13266e7i	−0.232927	+	0.232927i
$366$	2.41090e7			0.491740
$367$	3.16422e7			0.640131			0.320066	−	0.947395i	$-0.396295\pi$
$367$	3.16422e7			0.640131			0.320066	+	0.947395i	$0.396295\pi$
$368$	−2.83741e7	−	2.83741e7i	−0.569349	−	0.569349i
$369$		−	3.35165e6i		−	0.0667083i
$370$	−497161.	+	2.21184e7i	−0.00981503	+	0.436666i
$371$	1.49187e8			2.92152
$372$	−1.87036e7	+	1.87036e7i	−0.363325	+	0.363325i
$373$			6.74834e7i			1.30038i	0.759772	+	0.650190i	$0.225311\pi$
$373$			6.74834e7i			1.30038i	−0.759772	+	0.650190i	$0.774689\pi$
$374$		−	6.83544e6i		−	0.130663i
$375$	1.99459e7	+	1.99459e7i	0.378234	+	0.378234i
$376$	−2.32620e6	−	2.32620e6i	−0.0437606	−	0.0437606i
$377$	−1.26497e7			−0.236078
$378$	1.07931e8	+	1.07931e8i	1.99834	+	1.99834i
$379$	7.69574e6			0.141362			0.0706810	−	0.997499i	$-0.477483\pi$
$379$	7.69574e6			0.141362			0.0706810	+	0.997499i	$0.477483\pi$
$380$	1.29459e7			0.235929
$381$		−	1.02577e8i		−	1.85470i
$382$	−2.32445e7			−0.416994
$383$	−1.30408e7	−	1.30408e7i	−0.232117	−	0.232117i	0.581459	−	0.813576i	$-0.302482\pi$
$383$	−1.30408e7	−	1.30408e7i	−0.232117	−	0.232117i	−0.813576	+	0.581459i	$0.802482\pi$
$384$	−2.80947e7	+	2.80947e7i	−0.496171	+	0.496171i
$385$	−1.03887e7	+	1.03887e7i	−0.182046	+	0.182046i
$386$	5.50988e7			0.958033
$387$	−5.68986e6	−	5.68986e6i	−0.0981677	−	0.0981677i
$388$	8.64240e7	−	8.64240e7i	1.47958	−	1.47958i
$389$	4.48567e7	+	4.48567e7i	0.762041	+	0.762041i	0.976691	−	0.214650i	$-0.0688610\pi$
$389$	4.48567e7	+	4.48567e7i	0.762041	+	0.762041i	−0.214650	+	0.976691i	$0.568861\pi$
$390$	7.82960e6	−	7.82960e6i	0.131991	−	0.131991i
$391$			1.25792e7i			0.210437i
$392$	3.71057e7	+	3.71057e7i	0.616003	+	0.616003i
$393$	−3.54846e7	−	3.54846e7i	−0.584604	−	0.584604i
$394$	4.07306e7	−	4.07306e7i	0.665935	−	0.665935i
$395$		−	6.68181e6i		−	0.108418i
$396$	−3.00156e6			−0.0483349
$397$		−	6.55443e7i		−	1.04752i	−0.851865	−	0.523761i	$-0.824528\pi$
$397$		−	6.55443e7i		−	1.04752i	0.851865	−	0.523761i	$-0.175472\pi$
$398$		−	1.19266e8i		−	1.89176i
$399$	5.07510e7	−	5.07510e7i	0.798961	−	0.798961i
$400$		−	4.01266e7i		−	0.626978i
$401$	5.53288e7	−	5.53288e7i	0.858061	−	0.858061i	−0.133049	−	0.991110i	$-0.542477\pi$
$401$	5.53288e7	−	5.53288e7i	0.858061	−	0.858061i	0.991110	+	0.133049i	$0.0424766\pi$
$402$	4.27511e7	−	4.27511e7i	0.658065	−	0.658065i
$403$	−1.24730e7			−0.190571
$404$	−1.60932e8			−2.44061
$405$	−1.25010e7	−	1.25010e7i	−0.188183	−	0.188183i
$406$			9.67910e7i			1.44630i
$407$	−3.27828e7	−	736866.i	−0.486253	−	0.0109296i
$408$	4.40555e6			0.0648664
$409$	3.36262e7	−	3.36262e7i	0.491482	−	0.491482i	−0.417291	−	0.908773i	$-0.637020\pi$
$409$	3.36262e7	−	3.36262e7i	0.491482	−	0.491482i	0.908773	+	0.417291i	$0.137020\pi$
$410$			2.52921e7i			0.366972i
$411$			5.57693e7i			0.803285i
$412$	−6.79604e7	−	6.79604e7i	−0.971772	−	0.971772i
$413$	5.59802e7	+	5.59802e7i	0.794666	+	0.794666i
$414$	9.93687e6			0.140039
$415$	−1.42201e7	−	1.42201e7i	−0.198957	−	0.198957i
$416$	−4.50696e7			−0.626042
$417$	−4.13259e7			−0.569920
$418$			3.45176e7i			0.472620i
$419$	−1.05897e8			−1.43960			−0.719798	−	0.694183i	$-0.755766\pi$
$419$	−1.05897e8			−1.43960			−0.719798	+	0.694183i	$0.755766\pi$
$420$	−3.33025e7	−	3.33025e7i	−0.449499	−	0.449499i
$421$	−7.28790e7	+	7.28790e7i	−0.976689	+	0.976689i	−0.999734	−	0.0230453i	$-0.992664\pi$
$421$	−7.28790e7	+	7.28790e7i	−0.976689	+	0.976689i	0.0230453	+	0.999734i	$0.492664\pi$
$422$	6.07815e7	−	6.07815e7i	0.808786	−	0.808786i
$423$	−984850.			−0.0130122
$424$	−3.26987e7	−	3.26987e7i	−0.428976	−	0.428976i
$425$	−8.89472e6	+	8.89472e6i	−0.115868	+	0.115868i
$426$	2.64263e7	+	2.64263e7i	0.341828	+	0.341828i
$427$	3.41927e7	−	3.41927e7i	0.439187	−	0.439187i
$428$			8.50485e7i			1.08476i
$429$	1.16046e7	+	1.16046e7i	0.146980	+	0.146980i
$430$	4.29366e7	+	4.29366e7i	0.540035	+	0.540035i
$431$	−1.19008e7	+	1.19008e7i	−0.148643	+	0.148643i	−0.777511	−	0.628869i	$-0.783518\pi$
$431$	−1.19008e7	+	1.19008e7i	−0.148643	+	0.148643i	0.628869	+	0.777511i	$0.283518\pi$
$432$			5.71965e7i			0.709445i
$433$	−3.35531e7			−0.413304			−0.206652	−	0.978415i	$-0.566257\pi$
$433$	−3.35531e7			−0.413304			−0.206652	+	0.978415i	$0.566257\pi$
$434$			9.54390e7i			1.16750i
$435$		−	1.21844e7i		−	0.148025i
$436$	8.74761e7	−	8.74761e7i	1.05543	−	1.05543i
$437$		−	6.35223e7i		−	0.761170i
$438$	9.68103e7	−	9.68103e7i	1.15212	−	1.15212i
$439$	−8.44388e6	+	8.44388e6i	−0.0998041	+	0.0998041i	−0.755246	−	0.655442i	$-0.772482\pi$
$439$	−8.44388e6	+	8.44388e6i	−0.0998041	+	0.0998041i	0.655442	+	0.755246i	$0.272482\pi$
$440$	4.55399e6			0.0534607
$441$	1.57096e7			0.183167
$442$	7.30630e6	+	7.30630e6i	0.0846117	+	0.0846117i
$443$			6.03427e7i			0.694086i	0.937849	+	0.347043i	$0.112814\pi$
$443$			6.03427e7i			0.694086i	−0.937849	+	0.347043i	$0.887186\pi$
$444$	2.36212e6	−	1.05090e8i	0.0269869	−	1.20063i
$445$	−2.12097e7			−0.240688
$446$	−1.16575e8	+	1.16575e8i	−1.31402	+	1.31402i
$447$		−	1.51547e8i		−	1.69678i
$448$			2.32848e8i			2.58963i
$449$	−7.44941e6	−	7.44941e6i	−0.0822968	−	0.0822968i	0.664760	−	0.747057i	$-0.268534\pi$
$449$	−7.44941e6	−	7.44941e6i	−0.0822968	−	0.0822968i	−0.747057	+	0.664760i	$0.768534\pi$
$450$	7.02634e6	+	7.02634e6i	0.0771067	+	0.0771067i
$451$	−3.74866e7			−0.408646
$452$	−777395.	−	777395.i	−0.00841834	−	0.00841834i
$453$	−1.35321e8			−1.45569
$454$	−5.84762e7			−0.624902
$455$		−	2.22087e7i		−	0.235770i
$456$	−2.22471e7			−0.234628
$457$	2.02681e7	+	2.02681e7i	0.212356	+	0.212356i	0.805267	−	0.592912i	$-0.202022\pi$
$457$	2.02681e7	+	2.02681e7i	0.212356	+	0.212356i	−0.592912	+	0.805267i	$0.702022\pi$
$458$	−5.09568e7	+	5.09568e7i	−0.530403	+	0.530403i
$459$	1.26785e7	−	1.26785e7i	0.131109	−	0.131109i
$460$	−4.16829e7			−0.428238
$461$	−6.23340e7	−	6.23340e7i	−0.636242	−	0.636242i	0.313385	−	0.949626i	$-0.398537\pi$
$461$	−6.23340e7	−	6.23340e7i	−0.636242	−	0.636242i	−0.949626	+	0.313385i	$0.898537\pi$
$462$	8.87944e7	−	8.87944e7i	0.900450	−	0.900450i
$463$	4.00374e6	+	4.00374e6i	0.0403388	+	0.0403388i	0.726988	−	0.686650i	$-0.240919\pi$
$463$	4.00374e6	+	4.00374e6i	0.0403388	+	0.0403388i	−0.686650	+	0.726988i	$0.740919\pi$
$464$	−2.56466e7	+	2.56466e7i	−0.256730	+	0.256730i
$465$		−	1.20142e7i		−	0.119491i
$466$	1.81883e8	+	1.81883e8i	1.79735	+	1.79735i
$467$	1.01381e8	+	1.01381e8i	0.995422	+	0.995422i	0.999990	−	0.00456799i	$-0.00145404\pi$
$467$	1.01381e8	+	1.01381e8i	0.995422	+	0.995422i	−0.00456799	+	0.999990i	$0.501454\pi$
$468$	3.20832e6	−	3.20832e6i	0.0312997	−	0.0312997i
$469$		−	1.21264e8i		−	1.17547i
$470$	7.43184e6			0.0715819
$471$			3.97413e7i			0.380347i
$472$		−	2.45394e7i		−	0.233366i
$473$	−6.36384e7	+	6.36384e7i	−0.601362	+	0.601362i
$474$			5.71106e7i			0.536268i
$475$	4.49165e7	−	4.49165e7i	0.419107	−	0.419107i
$476$	3.10767e7	−	3.10767e7i	0.288147	−	0.288147i
$477$	−1.38437e7			−0.127555
$478$	2.35138e8			2.15298
$479$	1.05683e8	+	1.05683e8i	0.961607	+	0.961607i	0.999290	−	0.0376824i	$-0.0119975\pi$
$479$	1.05683e8	+	1.05683e8i	0.961607	+	0.961607i	−0.0376824	+	0.999290i	$0.511998\pi$
$480$		−	4.34116e7i		−	0.392538i
$481$	3.58286e7	−	3.42534e7i	0.321955	−	0.307800i
$482$	−2.67594e8			−2.38965
$483$	−1.63407e8	+	1.63407e8i	−1.45021	+	1.45021i
$484$		−	1.08341e8i		−	0.955561i
$485$			5.55141e7i			0.486606i
$486$	−1.92940e7	−	1.92940e7i	−0.168079	−	0.168079i
$487$	5.71284e7	+	5.71284e7i	0.494613	+	0.494613i	0.909756	−	0.415143i	$-0.136269\pi$
$487$	5.71284e7	+	5.71284e7i	0.494613	+	0.494613i	−0.415143	+	0.909756i	$0.636269\pi$
$488$	−1.49887e7			−0.128974
$489$	3.77367e7	+	3.77367e7i	0.322729	+	0.322729i
$490$	−1.18547e8			−1.00763
$491$	9.65906e7			0.816001			0.408000	−	0.912982i	$-0.366226\pi$
$491$	9.65906e7			0.816001			0.408000	+	0.912982i	$0.366226\pi$
$492$		−	1.20168e8i		−	1.00901i
$493$	1.13700e7			0.0948898
$494$	−3.68953e7	−	3.68953e7i	−0.306049	−	0.306049i
$495$	964019.	−	964019.i	0.00794822	−	0.00794822i
$496$	−2.52884e7	+	2.52884e7i	−0.207241	+	0.207241i
$497$	7.49584e7			0.610592
$498$	1.21542e8	+	1.21542e8i	0.984099	+	0.984099i
$499$	1.01661e8	−	1.01661e8i	0.818187	−	0.818187i	−0.167658	−	0.985845i	$-0.553621\pi$
$499$	1.01661e8	−	1.01661e8i	0.818187	−	0.818187i	0.985845	+	0.167658i	$0.0536205\pi$
$500$	−6.16763e7	−	6.16763e7i	−0.493410	−	0.493410i
$501$	−1.16930e8	+	1.16930e8i	−0.929852	+	0.929852i
$502$		−	2.06924e8i		−	1.63569i
$503$	−5.39737e7	−	5.39737e7i	−0.424110	−	0.424110i	0.462506	−	0.886616i	$-0.346950\pi$
$503$	−5.39737e7	−	5.39737e7i	−0.424110	−	0.424110i	−0.886616	+	0.462506i	$0.846950\pi$
$504$	−4.93573e6	−	4.93573e6i	−0.0385532	−	0.0385532i
$505$	5.16869e7	−	5.16869e7i	0.401335	−	0.401335i
$506$		−	1.11139e8i		−	0.857858i
$507$	1.00235e8			0.769124
$508$			3.17186e8i			2.41948i
$509$			1.56281e8i			1.18510i	0.805535	+	0.592548i	$0.201878\pi$
$509$			1.56281e8i			1.18510i	−0.805535	+	0.592548i	$0.798122\pi$
$510$	−7.03752e6	+	7.03752e6i	−0.0530529	+	0.0530529i
$511$		−	2.74603e8i		−	2.05799i
$512$	−1.15926e8	+	1.15926e8i	−0.863718	+	0.863718i
$513$	−6.40241e7	+	6.40241e7i	−0.474233	+	0.474233i
$514$	2.63513e8			1.94050
$515$	4.36541e7			0.319597
$516$	−2.04001e8	−	2.04001e8i	−1.48485	−	1.48485i
$517$			1.10151e7i			0.0797106i
$518$	−2.62094e8	−	2.74148e8i	−1.88568	−	1.97240i
$519$	−1.78938e8			−1.27997
$520$	−4.86769e6	+	4.86769e6i	−0.0346189	+	0.0346189i
$521$			1.31507e8i			0.929896i	0.885338	+	0.464948i	$0.153927\pi$
$521$			1.31507e8i			0.929896i	−0.885338	+	0.464948i	$0.846073\pi$
$522$		−	8.98168e6i		−	0.0631461i
$523$	−5.71217e7	−	5.71217e7i	−0.399297	−	0.399297i	0.478688	−	0.877985i	$-0.341112\pi$
$523$	−5.71217e7	−	5.71217e7i	−0.399297	−	0.399297i	−0.877985	+	0.478688i	$0.841112\pi$
$524$	1.09725e8	+	1.09725e8i	0.762623	+	0.762623i
$525$	−2.31090e8			−1.59699
$526$	5.85718e7	+	5.85718e7i	0.402468	+	0.402468i
$527$	1.12112e7			0.0765983
$528$	4.70556e7			0.319675
$529$			5.64920e7i			0.381610i
$530$	1.04467e8			0.701701
$531$	−5.19466e6	−	5.19466e6i	−0.0346956	−	0.0346956i
$532$	−1.56931e8	+	1.56931e8i	−1.04225	+	1.04225i
$533$	4.00689e7	−	4.00689e7i	0.264622	−	0.264622i
$534$	1.81283e8			1.19051
$535$	−2.73153e7	−	2.73153e7i	−0.178379	−	0.178379i
$536$	−2.65785e7	+	2.65785e7i	−0.172598	+	0.172598i
$537$	8.21872e7	+	8.21872e7i	0.530739	+	0.530739i
$538$	1.28281e8	−	1.28281e8i	0.823789	−	0.823789i
$539$		−	1.75704e8i		−	1.12206i
$540$	4.20122e7	+	4.20122e7i	0.266805	+	0.266805i
$541$	−1.40069e8	−	1.40069e8i	−0.884604	−	0.884604i	0.109394	−	0.993998i	$-0.465109\pi$
$541$	−1.40069e8	−	1.40069e8i	−0.884604	−	0.884604i	−0.993998	+	0.109394i	$0.965109\pi$
$542$	2.35388e8	−	2.35388e8i	1.47838	−	1.47838i
$543$		−	1.92808e8i		−	1.20427i
$544$	4.05101e7			0.251632
$545$			5.61899e7i			0.347111i
$546$			1.89822e8i			1.16619i
$547$	1.00065e7	−	1.00065e7i	0.0611394	−	0.0611394i	−0.675876	−	0.737015i	$-0.736235\pi$
$547$	1.00065e7	−	1.00065e7i	0.0611394	−	0.0611394i	0.737015	+	0.675876i	$0.236235\pi$
$548$		−	1.72449e8i		−	1.04790i
$549$	−3.17289e6	+	3.17289e6i	−0.0191751	+	0.0191751i
$550$	7.85864e7	−	7.85864e7i	0.472345	−	0.472345i
$551$	−5.74162e7			−0.343226
$552$	7.16309e7			0.425876
$553$	8.09974e7	+	8.09974e7i	0.478956	+	0.478956i
$554$			3.51001e8i			2.06433i
$555$	3.29933e7	+	3.45106e7i	0.192995	+	0.201871i
$556$	1.27787e8			0.743467
$557$	−2.69406e7	+	2.69406e7i	−0.155899	+	0.155899i	−0.780747	−	0.624848i	$-0.785161\pi$
$557$	−2.69406e7	+	2.69406e7i	−0.155899	+	0.155899i	0.624848	+	0.780747i	$0.285161\pi$
$558$		−	8.85622e6i		−	0.0509737i
$559$		−	1.36044e8i		−	0.778833i
$560$	−4.50271e7	−	4.50271e7i	−0.256395	−	0.256395i
$561$	−1.04306e7	−	1.04306e7i	−0.0590775	−	0.0590775i
$562$	−1.44700e8			−0.815192
$563$	5.65227e7	+	5.65227e7i	0.316736	+	0.316736i	0.847512	−	0.530776i	$-0.178099\pi$
$563$	5.65227e7	+	5.65227e7i	0.316736	+	0.316736i	−0.530776	+	0.847512i	$0.678099\pi$
$564$	−3.53103e7			−0.196818
$565$	499356.			0.00276863
$566$			1.37023e7i			0.0755689i
$567$	3.03077e8			1.66266
$568$	−1.64293e7	−	1.64293e7i	−0.0896551	−	0.0896551i
$569$	−1.92514e8	+	1.92514e8i	−1.04502	+	1.04502i	−0.0460824	+	0.998938i	$0.514674\pi$
$569$	−1.92514e8	+	1.92514e8i	−1.04502	+	1.04502i	−0.998938	+	0.0460824i	$0.985326\pi$
$570$	3.55380e7	−	3.55380e7i	0.191897	−	0.191897i
$571$	1.23541e8			0.663597			0.331798	−	0.943350i	$-0.392345\pi$
$571$	1.23541e8			0.663597			0.331798	+	0.943350i	$0.392345\pi$
$572$	−3.58835e7	−	3.58835e7i	−0.191737	−	0.191737i
$573$	−3.54703e7	+	3.54703e7i	−0.188539	+	0.188539i
$574$	−3.06593e8	−	3.06593e8i	−1.62116	−	1.62116i
$575$	−1.44621e8	+	1.44621e8i	−0.760727	+	0.760727i
$576$		−	2.16070e7i		−	0.113065i
$577$	−2.14055e7	−	2.14055e7i	−0.111429	−	0.111429i	0.649194	−	0.760623i	$-0.275106\pi$
$577$	−2.14055e7	−	2.14055e7i	−0.111429	−	0.111429i	−0.760623	+	0.649194i	$0.775106\pi$
$578$	1.98322e8	+	1.98322e8i	1.02704	+	1.02704i
$579$	8.40788e7	−	8.40788e7i	0.433162	−	0.433162i
$580$			3.76762e7i			0.193100i
$581$	3.44755e8			1.75785
$582$		−	4.74489e8i		−	2.40689i
$583$			1.54836e8i			0.781386i
$584$	−6.01874e7	+	6.01874e7i	−0.302181	+	0.302181i
$585$			2.06085e6i			0.0102939i
$586$	−2.42059e7	+	2.42059e7i	−0.120290	+	0.120290i
$587$	2.16449e8	−	2.16449e8i	1.07014	−	1.07014i	0.0727936	−	0.997347i	$-0.476809\pi$
$587$	2.16449e8	−	2.16449e8i	1.07014	−	1.07014i	0.997347	−	0.0727936i	$-0.0231914\pi$
$588$	5.63243e8			2.77054
$589$	−5.66142e7			−0.277064
$590$	3.91998e7	+	3.91998e7i	0.190866	+	0.190866i
$591$		−	1.24307e8i		−	0.602188i
$592$	3.19374e6	−	1.42088e8i	0.0153934	−	0.684844i
$593$	−2.26318e8			−1.08531			−0.542657	−	0.839954i	$-0.682582\pi$
$593$	−2.26318e8			−1.08531			−0.542657	+	0.839954i	$0.682582\pi$
$594$	−1.12017e8	+	1.12017e8i	−0.534472	+	0.534472i
$595$			1.99620e7i			0.0947660i
$596$			4.68612e8i			2.21347i
$597$	−1.81995e8	−	1.81995e8i	−0.855336	−	0.855336i
$598$	1.18795e8	+	1.18795e8i	0.555513	+	0.555513i
$599$	−1.77704e8			−0.826829			−0.413415	−	0.910543i	$-0.635664\pi$
$599$	−1.77704e8			−0.826829			−0.413415	+	0.910543i	$0.635664\pi$
$600$	5.06501e7	+	5.06501e7i	0.234491	+	0.234491i
$601$	8.33678e7			0.384039			0.192019	−	0.981391i	$-0.438496\pi$
$601$	8.33678e7			0.384039			0.192019	+	0.981391i	$0.438496\pi$
$602$	−1.04096e9			−4.77139
$603$			1.12526e7i			0.0513218i
$604$	4.18436e8			1.89897
$605$	3.47963e7	+	3.47963e7i	0.157133	+	0.157133i
$606$	−4.41778e8	+	4.41778e8i	−1.98512	+	1.98512i
$607$	5.52860e7	−	5.52860e7i	0.247201	−	0.247201i	−0.572620	−	0.819821i	$-0.694073\pi$
$607$	5.52860e7	−	5.52860e7i	0.247201	−	0.247201i	0.819821	+	0.572620i	$0.194073\pi$
$608$	−2.04568e8			−0.910179
$609$	1.47700e8	+	1.47700e8i	0.653924	+	0.653924i
$610$	2.39432e7	−	2.39432e7i	0.105485	−	0.105485i
$611$	−1.17739e7	−	1.17739e7i	−0.0516173	−	0.0516173i
$612$	−2.88375e6	+	2.88375e6i	−0.0125807	+	0.0125807i
$613$			1.23250e7i			0.0535064i	0.999642	+	0.0267532i	$0.00851682\pi$
$613$			1.23250e7i			0.0535064i	−0.999642	+	0.0267532i	$0.991483\pi$
$614$	−8.63632e7	−	8.63632e7i	−0.373099	−	0.373099i
$615$	3.85948e7	+	3.85948e7i	0.165922	+	0.165922i
$616$	−5.52038e7	+	5.52038e7i	−0.236171	+	0.236171i
$617$			2.70639e8i			1.15222i	0.817372	+	0.576110i	$0.195430\pi$
$617$			2.70639e8i			1.15222i	−0.817372	+	0.576110i	$0.804570\pi$
$618$	−3.73119e8			−1.58082
$619$		−	3.54778e7i		−	0.149584i	−0.997199	−	0.0747920i	$-0.976171\pi$
$619$		−	3.54778e7i		−	0.149584i	0.997199	−	0.0747920i	$-0.0238293\pi$
$620$			3.71499e7i			0.155877i
$621$	2.06144e8	−	2.06144e8i	0.860786	−	0.860786i
$622$			6.15951e8i			2.55962i
$623$	2.57105e8	−	2.57105e8i	1.06328	−	1.06328i
$624$	−5.02970e7	+	5.02970e7i	−0.207008	+	0.207008i
$625$	−1.83838e8			−0.753001
$626$	−4.94316e7			−0.201503
$627$	5.26726e7	+	5.26726e7i	0.213689	+	0.213689i
$628$		−	1.22887e8i		−	0.496167i
$629$	−3.22040e7	+	3.07881e7i	−0.129407	+	0.123718i
$630$	1.57689e7			0.0630637
$631$	−7.40683e6	+	7.40683e6i	−0.0294812	+	0.0294812i	−0.721694	−	0.692213i	$-0.756636\pi$
$631$	−7.40683e6	+	7.40683e6i	−0.0294812	+	0.0294812i	0.692213	+	0.721694i	$0.256636\pi$
$632$		−	3.55059e7i		−	0.140653i
$633$		−	1.85501e8i		−	0.731365i
$634$	−2.66931e8	−	2.66931e8i	−1.04745	−	1.04745i
$635$	−1.01871e8	−	1.01871e8i	−0.397861	−	0.397861i
$636$	−4.96347e8			−1.92936
$637$	1.87807e8	+	1.87807e8i	0.726598	+	0.726598i
$638$	−1.00456e8			−0.386824
$639$	−6.95574e6			−0.0266588
$640$			5.58030e7i			0.212872i
$641$	4.01576e8			1.52473			0.762367	−	0.647145i	$-0.224037\pi$
$641$	4.01576e8			1.52473			0.762367	+	0.647145i	$0.224037\pi$
$642$	2.33469e8	+	2.33469e8i	0.882314	+	0.882314i
$643$	−3.45514e8	+	3.45514e8i	−1.29967	+	1.29967i	−0.371062	+	0.928608i	$0.621006\pi$
$643$	−3.45514e8	+	3.45514e8i	−1.29967	+	1.29967i	−0.928608	+	0.371062i	$0.878994\pi$
$644$	5.05284e8	−	5.05284e8i	1.89181	−	1.89181i
$645$	1.31039e8			0.488340
$646$	3.31628e7	+	3.31628e7i	0.123014	+	0.123014i
$647$	−3.32741e8	+	3.32741e8i	−1.22855	+	1.22855i	−0.264041	+	0.964512i	$0.585055\pi$
$647$	−3.32741e8	+	3.32741e8i	−1.22855	+	1.22855i	−0.964512	+	0.264041i	$0.914945\pi$
$648$	−6.64282e7	−	6.64282e7i	−0.244134	−	0.244134i
$649$	−5.80999e7	+	5.80999e7i	−0.212540	+	0.212540i
$650$			1.67999e8i			0.611741i
$651$	1.45636e8	+	1.45636e8i	0.527870	+	0.527870i
$652$	−1.16689e8	−	1.16689e8i	−0.421004	−	0.421004i
$653$	2.10075e8	−	2.10075e8i	0.754459	−	0.754459i	−0.220849	−	0.975308i	$-0.570883\pi$
$653$	2.10075e8	−	2.10075e8i	0.754459	−	0.754459i	0.975308	+	0.220849i	$0.0708829\pi$
$654$		−	4.80265e8i		−	1.71691i
$655$	−7.04811e7			−0.250812
$656$		−	1.62475e8i		−	0.575540i
$657$			2.54817e7i			0.0898529i
$658$	−9.00893e7	+	9.00893e7i	−0.316225	+	0.316225i
$659$		−	8.31747e6i		−	0.0290626i	−0.999894	−	0.0145313i	$-0.995374\pi$
$659$		−	8.31747e6i		−	0.0290626i	0.999894	−	0.0145313i	$-0.00462562\pi$
$660$	3.45635e7	−	3.45635e7i	0.120222	−	0.120222i
$661$	−1.40967e7	+	1.40967e7i	−0.0488106	+	0.0488106i	−0.731091	−	0.682280i	$-0.760988\pi$
$661$	−1.40967e7	+	1.40967e7i	−0.0488106	+	0.0488106i	0.682280	+	0.731091i	$0.260988\pi$
$662$	1.38939e8			0.478907
$663$	2.22983e7			0.0765122
$664$	−7.55632e7	−	7.55632e7i	−0.258111	−	0.258111i
$665$		−	1.00804e8i		−	0.342778i
$666$	2.43210e7	+	2.54394e7i	0.0823300	+	0.0861162i
$667$	1.84868e8			0.622993
$668$	3.61569e8	−	3.61569e8i	1.21300	−	1.21300i
$669$			3.55779e8i			1.18823i
$670$		−	8.49141e7i		−	0.282329i
$671$	3.54873e7	+	3.54873e7i	0.117464	+	0.117464i
$672$	5.26238e8	+	5.26238e8i	1.73410	+	1.73410i
$673$	8.59355e7			0.281921			0.140961	−	0.990015i	$-0.454981\pi$
$673$	8.59355e7			0.281921			0.140961	+	0.990015i	$0.454981\pi$
$674$	−2.08812e8	−	2.08812e8i	−0.681985	−	0.681985i
$675$	2.91528e8			0.947913
$676$	−3.09945e8			−1.00333
$677$			1.60900e8i			0.518549i	0.965804	+	0.259275i	$0.0834835\pi$
$677$			1.60900e8i			0.518549i	−0.965804	+	0.259275i	$0.916517\pi$
$678$	−4.26809e6			−0.0136944
$679$	−6.72945e8	−	6.72945e8i	−2.14966	−	2.14966i
$680$	4.37525e6	−	4.37525e6i	0.0139148	−	0.0139148i
$681$	−8.92326e7	+	8.92326e7i	−0.282541	+	0.282541i
$682$	−9.90527e7			−0.312258
$683$	−2.54749e8	−	2.54749e8i	−0.799560	−	0.799560i	0.183466	−	0.983026i	$-0.441268\pi$
$683$	−2.54749e8	−	2.54749e8i	−0.799560	−	0.799560i	−0.983026	+	0.183466i	$0.941268\pi$
$684$	1.45624e7	−	1.45624e7i	0.0455054	−	0.0455054i
$685$	5.53858e7	+	5.53858e7i	0.172316	+	0.172316i
$686$	8.14126e8	−	8.14126e8i	2.52185	−	2.52185i
$687$			1.55517e8i			0.479630i
$688$	−2.75823e8	−	2.75823e8i	−0.846963	−	0.846963i
$689$	−1.65501e8	−	1.65501e8i	−0.505993	−	0.505993i
$690$	−1.14425e8	+	1.14425e8i	−0.348315	+	0.348315i
$691$		−	1.80230e8i		−	0.546252i	−0.961978	−	0.273126i	$-0.911942\pi$
$691$		−	1.80230e8i		−	0.546252i	0.961978	−	0.273126i	$-0.0880575\pi$
$692$	5.53308e8			1.66974
$693$			2.33718e7i			0.0702251i
$694$			9.58388e8i			2.86723i
$695$	−4.10417e7	+	4.10417e7i	−0.122256	+	0.122256i
$696$		−	6.47454e7i		−	0.192035i
$697$	−3.60153e7	+	3.60153e7i	−0.106363	+	0.106363i
$698$	6.25398e8	−	6.25398e8i	1.83904	−	1.83904i
$699$	5.55093e8			1.62530
$700$	7.14571e8			2.08330
$701$	−6.81434e7	−	6.81434e7i	−0.197820	−	0.197820i	0.601245	−	0.799065i	$-0.294672\pi$
$701$	−6.81434e7	−	6.81434e7i	−0.197820	−	0.197820i	−0.799065	+	0.601245i	$0.794672\pi$
$702$		−	2.39467e8i		−	0.692204i
$703$	1.62624e8	−	1.55474e8i	0.468078	−	0.447498i
$704$	−2.41664e8			−0.692619
$705$	1.13407e7	−	1.13407e7i	0.0323648	−	0.0323648i
$706$		−	7.63439e7i		−	0.216950i
$707$			1.25311e9i			3.54592i
$708$	−1.86247e8	−	1.86247e8i	−0.524795	−	0.524795i
$709$	−1.91820e8	−	1.91820e8i	−0.538215	−	0.538215i	0.384789	−	0.923004i	$-0.374274\pi$
$709$	−1.91820e8	−	1.91820e8i	−0.538215	−	0.538215i	−0.923004	+	0.384789i	$0.874274\pi$
$710$	5.24891e7			0.146654
$711$	−7.51612e6	−	7.51612e6i	−0.0209115	−	0.0209115i
$712$	−1.12704e8			−0.312249
$713$	1.82285e8			0.502902
$714$		−	1.70619e8i		−	0.468740i
$715$	2.30496e7			0.0630588
$716$	−2.54137e8	−	2.54137e8i	−0.692356	−	0.692356i
$717$	3.58812e8	−	3.58812e8i	0.973442	−	0.973442i
$718$	4.42674e8	−	4.42674e8i	1.19594	−	1.19594i
$719$	2.62911e8			0.707330			0.353665	−	0.935372i	$-0.384935\pi$
$719$	2.62911e8			0.707330			0.353665	+	0.935372i	$0.384935\pi$
$720$	4.17827e6	+	4.17827e6i	0.0111943	+	0.0111943i
$721$	−5.29178e8	+	5.29178e8i	−1.41187	+	1.41187i
$722$	2.31879e8	+	2.31879e8i	0.616097	+	0.616097i
$723$	−4.08338e8	+	4.08338e8i	−1.08045	+	1.08045i
$724$			5.96195e8i			1.57099i
$725$	1.30720e8	+	1.30720e8i	0.343026	+	0.343026i
$726$	−2.97410e8	−	2.97410e8i	−0.777224	−	0.777224i
$727$	2.96797e7	−	2.96797e7i	0.0772424	−	0.0772424i	−0.667430	−	0.744672i	$-0.732606\pi$
$727$	2.96797e7	−	2.96797e7i	0.0772424	−	0.0772424i	0.744672	+	0.667430i	$0.232606\pi$
$728$		−	1.18013e8i		−	0.305869i
$729$	−4.13102e8			−1.06629
$730$		−	1.92289e8i		−	0.494295i
$731$			1.22281e8i			0.313046i
$732$	−1.13759e8	+	1.13759e8i	−0.290037	+	0.290037i
$733$			2.13412e8i			0.541885i	0.962596	+	0.270942i	$0.0873353\pi$
$733$			2.13412e8i			0.541885i	−0.962596	+	0.270942i	$0.912665\pi$
$734$	−2.68592e8	+	2.68592e8i	−0.679211	+	0.679211i
$735$	−1.80898e8	+	1.80898e8i	−0.455588	+	0.455588i
$736$	6.58664e8			1.65208
$737$	1.25855e8			0.314390
$738$	2.84502e7	+	2.84502e7i	0.0707808	+	0.0707808i
$739$			1.22419e8i			0.303330i	0.988432	+	0.151665i	$0.0484635\pi$
$739$			1.22419e8i			0.303330i	−0.988432	+	0.151665i	$0.951537\pi$
$740$	−1.02021e8	−	1.06713e8i	−0.251764	−	0.263343i
$741$	−1.12602e8			−0.276752
$742$	−1.26636e9	+	1.26636e9i	−3.09988	+	3.09988i
$743$		−	6.71148e7i		−	0.163626i	−0.996648	−	0.0818130i	$-0.973929\pi$
$743$		−	6.71148e7i		−	0.163626i	0.996648	−	0.0818130i	$-0.0260710\pi$
$744$		−	6.38410e7i		−	0.155018i
$745$	−1.50505e8	−	1.50505e8i	−0.363984	−	0.363984i
$746$	−5.72826e8	−	5.72826e8i	−1.37977	−	1.37977i
$747$	−3.19914e7			−0.0767488
$748$	3.22534e7	+	3.22534e7i	0.0770673	+	0.0770673i
$749$	6.62235e8			1.57604
$750$	−3.38618e8			−0.802649
$751$		−	3.98841e8i		−	0.941630i	−0.882232	−	0.470815i	$-0.843960\pi$
$751$		−	3.98841e8i		−	0.941630i	0.882232	−	0.470815i	$-0.156040\pi$
$752$	−4.77418e7			−0.112265
$753$	−3.15759e8	−	3.15759e8i	−0.739555	−	0.739555i
$754$	1.07376e8	−	1.07376e8i	0.250491	−	0.250491i
$755$	−1.34390e8	+	1.34390e8i	−0.312267	+	0.312267i
$756$	−1.01855e9			−2.35731
$757$	−2.26175e8	−	2.26175e8i	−0.521383	−	0.521383i	0.396606	−	0.917989i	$-0.370188\pi$
$757$	−2.26175e8	−	2.26175e8i	−0.521383	−	0.521383i	−0.917989	+	0.396606i	$0.870188\pi$
$758$	−6.53245e7	+	6.53245e7i	−0.149992	+	0.149992i
$759$	−1.69594e8	−	1.69594e8i	−0.387870	−	0.387870i
$760$	−2.20941e7	+	2.20941e7i	−0.0503311	+	0.0503311i
$761$		−	1.40959e8i		−	0.319844i	−0.987130	−	0.159922i	$-0.948876\pi$
$761$		−	1.40959e8i		−	0.319844i	0.987130	−	0.159922i	$-0.0511242\pi$
$762$	8.70713e8	+	8.70713e8i	1.96793	+	1.96793i
$763$	−6.81138e8	−	6.81138e8i	−1.53342	−	1.53342i
$764$	1.09680e8	−	1.09680e8i	0.245951	−	0.245951i
$765$		−	1.85236e6i		−	0.00413754i
$766$	2.21391e8			0.492576
$767$		−	1.24204e8i		−	0.275264i
$768$			1.41972e8i			0.313415i
$769$	1.25788e8	−	1.25788e8i	0.276605	−	0.276605i	−0.555147	−	0.831752i	$-0.687338\pi$
$769$	1.25788e8	−	1.25788e8i	0.276605	−	0.276605i	0.831752	+	0.555147i	$0.187338\pi$
$770$		−	1.76367e8i		−	0.386319i
$771$	4.02112e8	−	4.02112e8i	0.877372	−	0.877372i
$772$	−2.59986e8	+	2.59986e8i	−0.565065	+	0.565065i
$773$	−1.12294e8			−0.243118			−0.121559	−	0.992584i	$-0.538789\pi$
$773$	−1.12294e8			−0.243118			−0.121559	+	0.992584i	$0.538789\pi$
$774$	9.65956e7			0.208322
$775$	1.28894e8	+	1.28894e8i	0.276902	+	0.276902i
$776$			2.94991e8i			0.631283i
$777$	−8.18286e8	−	1.83928e7i	−1.74438	−	0.0392089i
$778$	−7.61523e8			−1.61713
$779$	1.81870e8	−	1.81870e8i	0.384724	−	0.384724i
$780$			7.38887e7i			0.155702i
$781$			7.77966e7i			0.163308i
$782$	−1.06777e8	−	1.06777e8i	−0.223284	−	0.223284i
$783$	−1.86328e8	−	1.86328e8i	−0.388144	−	0.388144i
$784$	7.61540e8			1.58032
$785$	3.94680e7	+	3.94680e7i	0.0815899	+	0.0815899i
$786$	6.02414e8			1.24059
$787$	6.25448e8			1.28312			0.641560	−	0.767073i	$-0.278288\pi$
$787$	6.25448e8			1.28312			0.641560	+	0.767073i	$0.278288\pi$
$788$			3.84378e8i			0.785561i
$789$	1.78757e8			0.363942
$790$	5.67179e7	+	5.67179e7i	0.115037	+	0.115037i
$791$	−6.05323e6	+	6.05323e6i	−0.0122309	+	0.0122309i
$792$	5.12262e6	−	5.12262e6i	0.0103114	−	0.0103114i
$793$	−7.58637e7			−0.152130
$794$	5.56366e8	+	5.56366e8i	1.11147	+	1.11147i
$795$	1.59413e8	−	1.59413e8i	0.317265	−	0.317265i
$796$	5.62761e8	+	5.62761e8i	1.11580	+	1.11580i
$797$	−1.04457e8	+	1.04457e8i	−0.206331	+	0.206331i	−0.802706	−	0.596375i	$-0.796607\pi$
$797$	−1.04457e8	+	1.04457e8i	−0.206331	+	0.206331i	0.596375	+	0.802706i	$0.296607\pi$
$798$			8.61589e8i			1.69548i
$799$	1.05828e7	+	1.05828e7i	0.0207471	+	0.0207471i
$800$	4.65740e8	+	4.65740e8i	0.909649	+	0.909649i
$801$	−2.38580e7	+	2.38580e7i	−0.0464233	+	0.0464233i
$802$			9.39306e8i			1.82089i
$803$	2.85001e8			0.550427
$804$			4.03446e8i			0.776278i
$805$			3.24567e8i			0.622180i
$806$	1.05876e8	−	1.05876e8i	0.202205	−	0.202205i
$807$		−	3.91505e8i		−	0.744932i
$808$	2.74655e8	−	2.74655e8i	0.520659	−	0.520659i
$809$	−2.67867e8	+	2.67867e8i	−0.505911	+	0.505911i	−0.913269	−	0.407358i	$-0.866450\pi$
$809$	−2.67867e8	+	2.67867e8i	−0.505911	+	0.505911i	0.407358	+	0.913269i	$0.366450\pi$
$810$	2.12228e8			0.399344
$811$	−2.07327e8			−0.388681			−0.194341	−	0.980934i	$-0.562257\pi$
$811$	−2.07327e8			−0.388681			−0.194341	+	0.980934i	$0.562257\pi$
$812$	−4.56713e8	−	4.56713e8i	−0.853052	−	0.853052i
$813$		−	7.18388e8i		−	1.33686i
$814$	2.84528e8	−	2.72018e8i	0.527536	−	0.504342i
$815$	7.49544e7			0.138460
$816$	4.52087e7	−	4.52087e7i	0.0832054	−	0.0832054i
$817$		−	6.17496e8i		−	1.13232i
$818$			5.70865e8i			1.04297i
$819$	−2.49818e7	−	2.49818e7i	−0.0454748	−	0.0454748i
$820$	−1.19342e8	−	1.19342e8i	−0.216447	−	0.216447i
$821$	4.92480e8			0.889937			0.444968	−	0.895546i	$-0.353215\pi$
$821$	4.92480e8			0.889937			0.444968	+	0.895546i	$0.353215\pi$
$822$	−4.73392e8	−	4.73392e8i	−0.852326	−	0.852326i
$823$	−5.59978e8			−1.00455			−0.502275	−	0.864708i	$-0.667504\pi$
$823$	−5.59978e8			−1.00455			−0.502275	+	0.864708i	$0.667504\pi$
$824$	2.31970e8			0.414619
$825$		−	2.39840e8i		−	0.427129i
$826$	−9.50365e8			−1.68636
$827$	4.42654e8	+	4.42654e8i	0.782614	+	0.782614i	0.980271	−	0.197657i	$-0.0633334\pi$
$827$	4.42654e8	+	4.42654e8i	0.782614	+	0.782614i	−0.197657	+	0.980271i	$0.563333\pi$
$828$	−4.68876e7	+	4.68876e7i	−0.0825975	+	0.0825975i
$829$	5.65450e8	−	5.65450e8i	0.992501	−	0.992501i	−0.00747148	−	0.999972i	$-0.502378\pi$
$829$	5.65450e8	−	5.65450e8i	0.992501	−	0.992501i	0.999972	+	0.00747148i	$0.00237827\pi$
$830$	2.41412e8			0.422207
$831$	5.35614e8	+	5.35614e8i	0.933360	+	0.933360i
$832$	2.58311e8	−	2.58311e8i	0.448511	−	0.448511i
$833$	−1.68808e8	−	1.68808e8i	−0.292050	−	0.292050i
$834$	3.50790e8	−	3.50790e8i	0.604713	−	0.604713i
$835$			2.32252e8i			0.398934i
$836$	−1.62873e8	−	1.62873e8i	−0.278760	−	0.278760i
$837$	−1.83725e8	−	1.83725e8i	−0.313323	−	0.313323i
$838$	8.98894e8	−	8.98894e8i	1.52748	−	1.52748i
$839$		−	8.34916e8i		−	1.41370i	−0.707364	−	0.706850i	$-0.750116\pi$
$839$		−	8.34916e8i		−	1.41370i	0.707364	−	0.706850i	$-0.249884\pi$
$840$	1.13672e8			0.191785
$841$			4.27726e8i			0.719081i
$842$		−	1.23725e9i		−	2.07263i
$843$	−2.20807e8	+	2.20807e8i	−0.368579	+	0.368579i
$844$			5.73601e8i			0.954074i
$845$	9.95459e7	−	9.95459e7i	0.164988	−	0.164988i
$846$	8.35980e6	−	8.35980e6i	0.0138065	−	0.0138065i
$847$	−8.43606e8			−1.38832
$848$	−6.71092e8			−1.10051
$849$	2.09092e7	+	2.09092e7i	0.0341675	+	0.0341675i
$850$		−	1.51004e8i		−	0.245884i
$851$	−5.23613e8	+	5.00592e8i	−0.849614	+	0.812260i
$852$	−2.49388e8			−0.403233
$853$	4.36744e8	−	4.36744e8i	0.703688	−	0.703688i	−0.261512	−	0.965200i	$-0.584221\pi$
$853$	4.36744e8	−	4.36744e8i	0.703688	−	0.703688i	0.965200	+	0.261512i	$0.0842211\pi$
$854$			5.80482e8i			0.931998i
$855$			9.35406e6i			0.0149659i
$856$	−1.45148e8	−	1.45148e8i	−0.231415	−	0.231415i
$857$	−8.35425e8	−	8.35425e8i	−1.32729	−	1.32729i	−0.907728	−	0.419559i	$-0.862185\pi$
$857$	−8.35425e8	−	8.35425e8i	−1.32729	−	1.32729i	−0.419559	−	0.907728i	$-0.637815\pi$
$858$	−1.97009e8			−0.311907
$859$	6.91579e8	+	6.91579e8i	1.09109	+	1.09109i	0.995412	+	0.0956820i	$0.0305032\pi$
$859$	6.91579e8	+	6.91579e8i	1.09109	+	1.09109i	0.0956820	+	0.995412i	$0.469497\pi$
$860$	−4.05197e8			−0.637046
$861$	−9.35699e8			−1.46597
$862$		−	2.02037e8i		−	0.315434i
$863$	−4.77975e8			−0.743658			−0.371829	−	0.928301i	$-0.621269\pi$
$863$	−4.77975e8			−0.743658			−0.371829	+	0.928301i	$0.621269\pi$
$864$	−6.63867e8	−	6.63867e8i	−1.02930	−	1.02930i
$865$	−1.77707e8	+	1.77707e8i	−0.274573	+	0.274573i
$866$	2.84812e8	−	2.84812e8i	0.438536	−	0.438536i
$867$	6.05265e8			0.928727
$868$	−4.50334e8	−	4.50334e8i	−0.688613	−	0.688613i
$869$	−8.40642e7	+	8.40642e7i	−0.128101	+	0.128101i
$870$	1.03426e8	+	1.03426e8i	0.157062	+	0.157062i
$871$	−1.34525e8	+	1.34525e8i	−0.203586	+	0.203586i
$872$			2.98583e8i			0.450314i
$873$	6.24457e7	+	6.24457e7i	0.0938555	+	0.0938555i
$874$	5.39203e8	+	5.39203e8i	0.807640	+	0.807640i
$875$	−4.80246e8	+	4.80246e8i	−0.716868	+	0.716868i
$876$			9.13608e8i			1.35909i
$877$	−3.06879e8			−0.454956			−0.227478	−	0.973783i	$-0.573048\pi$
$877$	−3.06879e8			−0.454956			−0.227478	+	0.973783i	$0.573048\pi$
$878$		−	1.43350e8i		−	0.211794i
$879$			7.38746e7i			0.108775i
$880$	4.67320e7	−	4.67320e7i	0.0685750	−	0.0685750i
$881$		−	1.28555e8i		−	0.188002i	−0.995572	−	0.0940008i	$-0.970034\pi$
$881$		−	1.28555e8i		−	0.188002i	0.995572	−	0.0940008i	$-0.0299656\pi$
$882$	−1.33349e8	+	1.33349e8i	−0.194350	+	0.194350i
$883$	3.79357e8	−	3.79357e8i	0.551018	−	0.551018i	−0.375717	−	0.926735i	$-0.622603\pi$
$883$	3.79357e8	−	3.79357e8i	0.551018	−	0.551018i	0.926735	+	0.375717i	$0.122603\pi$
$884$	−6.89502e7			−0.0998111
$885$	1.19635e8			0.172595
$886$	−5.12213e8	−	5.12213e8i	−0.736460	−	0.736460i
$887$		−	7.94457e8i		−	1.13841i	−0.822195	−	0.569206i	$-0.807251\pi$
$887$		−	7.94457e8i		−	1.13841i	0.822195	−	0.569206i	$-0.192749\pi$
$888$	1.75320e8	+	1.83383e8i	0.250376	+	0.261890i
$889$	2.46978e9			3.51523
$890$	1.80036e8	−	1.80036e8i	0.255382	−	0.255382i
$891$			3.14553e8i			0.444693i
$892$		−	1.10013e9i		−	1.55006i
$893$	−5.34408e7	−	5.34408e7i	−0.0750444	−	0.0750444i
$894$	1.28640e9	+	1.28640e9i	1.80037	+	1.80037i
$895$	1.63244e8			0.227703
$896$	−6.76448e8	−	6.76448e8i	−0.940396	−	0.940396i
$897$	3.62553e8			0.502336
$898$	1.26467e8			0.174642
$899$		−	1.64763e8i		−	0.226768i
$900$	−6.63083e7			−0.0909579
$901$	1.48759e8	+	1.48759e8i	0.203380	+	0.203380i
$902$	3.18202e8	−	3.18202e8i	0.433593	−	0.433593i
$903$	−1.58847e9	+	1.58847e9i	−2.15732	+	2.15732i
$904$	2.65349e6			0.00359180
$905$	−1.91482e8	−	1.91482e8i	−0.258334	−	0.258334i
$906$	1.14866e9	−	1.14866e9i	1.54456	−	1.54456i
$907$	5.94120e8	+	5.94120e8i	0.796255	+	0.796255i	0.982503	−	0.186248i	$-0.0596328\pi$
$907$	5.94120e8	+	5.94120e8i	0.796255	+	0.796255i	−0.186248	+	0.982503i	$0.559633\pi$
$908$	2.75923e8	−	2.75923e8i	0.368579	−	0.368579i
$909$		−	1.16281e8i		−	0.154817i
$910$	1.88516e8	+	1.88516e8i	0.250164	+	0.250164i
$911$	4.60050e8	+	4.60050e8i	0.608485	+	0.608485i	0.942550	−	0.334065i	$-0.108420\pi$
$911$	4.60050e8	+	4.60050e8i	0.608485	+	0.608485i	−0.334065	+	0.942550i	$0.608420\pi$
$912$	−2.28295e8	+	2.28295e8i	−0.300962	+	0.300962i
$913$			3.57809e8i			0.470152i
$914$	−3.44087e8			−0.450640
$915$		−	7.30729e7i		−	0.0953878i
$916$		−	4.80885e8i		−	0.625683i
$917$	8.54376e8	−	8.54376e8i	1.10800	−	1.10800i
$918$			2.15241e8i			0.278226i
$919$	−5.39878e8	+	5.39878e8i	−0.695583	+	0.695583i	−0.963455	−	0.267872i	$-0.913680\pi$
$919$	−5.39878e8	+	5.39878e8i	−0.695583	+	0.695583i	0.267872	+	0.963455i	$0.413680\pi$
$920$	7.11383e7	−	7.11383e7i	0.0913566	−	0.0913566i
$921$	−2.63574e8			−0.337384
$922$	1.05823e9			1.35017
$923$	−8.31556e7	−	8.31556e7i	−0.105751	−	0.105751i
$924$			8.37961e8i			1.06220i
$925$	−7.24214e8	−	1.62783e7i	−0.915043	−	0.0205676i
$926$	−6.79707e7			−0.0856030
$927$	4.91048e7	−	4.91048e7i	0.0616432	−	0.0616432i
$928$		−	5.95350e8i		−	0.744952i
$929$			1.21416e8i			0.151436i	0.997129	+	0.0757180i	$0.0241249\pi$
$929$			1.21416e8i			0.151436i	−0.997129	+	0.0757180i	$0.975875\pi$
$930$	1.01981e8	+	1.01981e8i	0.126786	+	0.126786i
$931$	8.52445e8	+	8.52445e8i	1.05637	+	1.05637i
$932$	−1.71644e9			−2.12022
$933$	9.39919e8	+	9.39919e8i	1.15730	+	1.15730i
$934$	−1.72113e9			−2.11238
$935$	−2.07178e7			−0.0253460
$936$			1.09510e7i			0.0133544i
$937$	7.70931e8			0.937123			0.468562	−	0.883431i	$-0.344772\pi$
$937$	7.70931e8			0.937123			0.468562	+	0.883431i	$0.344772\pi$
$938$	1.02934e9	+	1.02934e9i	1.24723	+	1.24723i
$939$	−7.54308e7	+	7.54308e7i	−0.0911070	+	0.0911070i
$940$	−3.50675e7	+	3.50675e7i	−0.0422203	+	0.0422203i
$941$	7.43878e8			0.892756			0.446378	−	0.894844i	$-0.352714\pi$
$941$	7.43878e8			0.892756			0.446378	+	0.894844i	$0.352714\pi$
$942$	−3.37340e8	−	3.37340e8i	−0.403567	−	0.403567i
$943$	−5.85582e8	+	5.85582e8i	−0.698317	+	0.698317i
$944$	−2.51818e8	−	2.51818e8i	−0.299344	−	0.299344i
$945$	3.27131e8	−	3.27131e8i	0.387638	−	0.387638i
$946$		−	1.08038e9i		−	1.27615i
$947$	−1.24291e8	−	1.24291e8i	−0.146349	−	0.146349i	0.630136	−	0.776485i	$-0.282999\pi$
$947$	−1.24291e8	−	1.24291e8i	−0.146349	−	0.146349i	−0.776485	+	0.630136i	$0.782999\pi$
$948$	−2.69479e8	−	2.69479e8i	−0.316301	−	0.316301i
$949$	−3.04633e8	+	3.04633e8i	−0.356433	+	0.356433i
$950$			7.62539e8i			0.889388i
$951$	−8.14654e8			−0.947178
$952$			1.06074e8i			0.122942i
$953$		−	3.20204e8i		−	0.369954i	−0.982743	−	0.184977i	$-0.940779\pi$
$953$		−	3.20204e8i		−	0.369954i	0.982743	−	0.184977i	$-0.0592211\pi$
$954$	1.17511e8	−	1.17511e8i	0.135343	−	0.135343i
$955$			7.04527e7i			0.0808886i
$956$	−1.10951e9	+	1.10951e9i	−1.26987	+	1.26987i
$957$	−1.53292e8	+	1.53292e8i	−0.174898	+	0.174898i
$958$	−1.79416e9			−2.04063
$959$	−1.34278e9			−1.52247
$960$	2.48808e8	+	2.48808e8i	0.281223	+	0.281223i
$961$			7.25042e8i			0.816945i
$962$	−1.33713e7	+	5.94884e8i	−0.0150193	+	0.668201i
$963$	−6.14519e7			−0.0688107
$964$	1.26265e9	−	1.26265e9i	1.40946	−	1.40946i
$965$		−	1.67001e8i		−	0.185839i
$966$		−	2.77413e9i		−	3.07748i
$967$	8.94439e8	+	8.94439e8i	0.989171	+	0.989171i	0.999942	−	0.0107709i	$-0.00342854\pi$
$967$	8.94439e8	+	8.94439e8i	0.989171	+	0.989171i	−0.0107709	+	0.999942i	$0.503429\pi$
$968$	1.84901e8	+	1.84901e8i	0.203851	+	0.203851i
$969$	1.01211e8			0.111238
$970$	−4.71226e8	−	4.71226e8i	−0.516314	−	0.516314i
$971$	−3.22865e8			−0.352666			−0.176333	−	0.984331i	$-0.556424\pi$
$971$	−3.22865e8			−0.352666			−0.176333	+	0.984331i	$0.556424\pi$
$972$	1.82080e8			0.198273
$973$		−	9.95020e8i		−	1.08017i
$974$	−9.69858e8			−1.04962
$975$	2.56361e8	+	2.56361e8i	0.276591	+	0.276591i
$976$	−1.53810e8	+	1.53810e8i	−0.165438	+	0.165438i
$977$	4.65195e8	−	4.65195e8i	0.498828	−	0.498828i	−0.412245	−	0.911073i	$-0.635255\pi$
$977$	4.65195e8	−	4.65195e8i	0.498828	−	0.498828i	0.911073	+	0.412245i	$0.135255\pi$
$978$	−6.40649e8			−0.684863
$979$	2.66840e8	+	2.66840e8i	0.284383	+	0.284383i
$980$	5.59369e8	−	5.59369e8i	0.594320	−	0.594320i
$981$	6.32059e7	+	6.32059e7i	0.0669500	+	0.0669500i
$982$	−8.19900e8	+	8.19900e8i	−0.865817	+	0.865817i
$983$		−	1.24254e9i		−	1.30812i	−0.756441	−	0.654062i	$-0.773063\pi$
$983$		−	1.24254e9i		−	1.30812i	0.756441	−	0.654062i	$-0.226937\pi$
$984$	2.05086e8	+	2.05086e8i	0.215254	+	0.215254i
$985$	−1.23452e8	−	1.23452e8i	−0.129178	−	0.129178i
$986$	−9.65131e7	+	9.65131e7i	−0.100683	+	0.100683i
$987$			2.74946e8i			0.285954i
$988$	3.48185e8			0.361026
$989$			1.98820e9i			2.05528i
$990$			1.63660e7i			0.0168669i
$991$	−2.99324e8	+	2.99324e8i	−0.307553	+	0.307553i	−0.843960	−	0.536407i	$-0.819781\pi$
$991$	−2.99324e8	+	2.99324e8i	−0.307553	+	0.307553i	0.536407	+	0.843960i	$0.319781\pi$
$992$		−	5.87034e8i		−	0.601351i
$993$	2.12016e8	−	2.12016e8i	0.216532	−	0.216532i
$994$	−6.36277e8	+	6.36277e8i	−0.647869	+	0.647869i
$995$	−3.61487e8			−0.366964
$996$	−1.14700e9			−1.16088
$997$	6.87331e8	+	6.87331e8i	0.693554	+	0.693554i	0.963012	−	0.269458i	$-0.0868445\pi$
$997$	6.87331e8	+	6.87331e8i	0.693554	+	0.693554i	−0.269458	+	0.963012i	$0.586845\pi$
$998$			1.72588e9i			1.73627i
$999$	1.03230e9	+	2.32031e7i	1.03540	+	0.0232729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.d.a.6.3	✓	36
37.31	odd	4	inner	37.7.d.a.31.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.d.a.6.3	✓	36	1.1	even	1	trivial
37.7.d.a.31.3	yes	36	37.31	odd	4	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.48840 + 8.48840i) q^{2} +25.9060i q^{3} -80.1058i q^{4} +(25.7278 + 25.7278i) q^{5} +(-219.900 - 219.900i) q^{6} -623.749 q^{7} +(136.713 + 136.713i) q^{8} +57.8805 q^{9} +O(q^{10})\)	\(q+(-8.48840 + 8.48840i) q^{2} +25.9060i q^{3} -80.1058i q^{4} +(25.7278 + 25.7278i) q^{5} +(-219.900 - 219.900i) q^{6} -623.749 q^{7} +(136.713 + 136.713i) q^{8} +57.8805 q^{9} -436.776 q^{10} -647.366i q^{11} +2075.22 q^{12} +(691.960 + 691.960i) q^{13} +(5294.63 - 5294.63i) q^{14} +(-666.504 + 666.504i) q^{15} +2805.83 q^{16} +(-621.958 - 621.958i) q^{17} +(-491.313 + 491.313i) q^{18} +(3140.76 + 3140.76i) q^{19} +(2060.95 - 2060.95i) q^{20} -16158.8i q^{21} +(5495.10 + 5495.10i) q^{22} +(-10112.6 - 10112.6i) q^{23} +(-3541.68 + 3541.68i) q^{24} -14301.2i q^{25} -11747.3 q^{26} +20384.9i q^{27} +49965.9i q^{28} +(-9140.49 + 9140.49i) q^{29} -11315.1i q^{30} +(-9012.81 + 9012.81i) q^{31} +(-32566.6 + 32566.6i) q^{32} +16770.7 q^{33} +10558.9 q^{34} +(-16047.7 - 16047.7i) q^{35} -4636.57i q^{36} +(1138.25 - 50640.2i) q^{37} -53320.1 q^{38} +(-17925.9 + 17925.9i) q^{39} +7034.65i q^{40} -57906.4i q^{41} +(137163. + 137163. i) q^{42} +(-98303.5 - 98303.5i) q^{43} -51857.8 q^{44} +(1489.14 + 1489.14i) q^{45} +171679. q^{46} -17015.2 q^{47} +72687.7i q^{48} +271414. q^{49} +(121394. + 121394. i) q^{50} +(16112.4 - 16112.4i) q^{51} +(55430.0 - 55430.0i) q^{52} -239178. q^{53} +(-173035. - 173035. i) q^{54} +(16655.3 - 16655.3i) q^{55} +(-85274.5 - 85274.5i) q^{56} +(-81364.5 + 81364.5i) q^{57} -155176. i q^{58} +(-89748.0 - 89748.0i) q^{59} +(53390.9 + 53390.9i) q^{60} +(-54818.0 + 54818.0i) q^{61} -153009. i q^{62} -36102.9 q^{63} -373304. i q^{64} +35605.2i q^{65} +(-142356. + 142356. i) q^{66} +194411. i q^{67} +(-49822.4 + 49822.4i) q^{68} +(261976. - 261976. i) q^{69} +272438. q^{70} -120174. q^{71} +(7913.01 + 7913.01i) q^{72} +440247. i q^{73} +(420192. + 439516. i) q^{74} +370485. q^{75} +(251593. - 251593. i) q^{76} +403794. i q^{77} -304324. i q^{78} +(-129856. - 129856. i) q^{79} +(72187.8 + 72187.8i) q^{80} -485896. q^{81} +(491532. + 491532. i) q^{82} -552715. q^{83} -1.29442e6 q^{84} -32003.2i q^{85} +1.66888e6 q^{86} +(-236793. - 236793. i) q^{87} +(88503.3 - 88503.3i) q^{88} +(-412193. + 412193. i) q^{89} -25280.8 q^{90} +(-431609. - 431609. i) q^{91} +(-810075. + 810075. i) q^{92} +(-233486. - 233486. i) q^{93} +(144432. - 144432. i) q^{94} +161610. i q^{95} +(-843670. - 843670. i) q^{96} +(1.07887e6 + 1.07887e6i) q^{97} +(-2.30387e6 + 2.30387e6i) q^{98} -37469.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9	\( 36 q - 4 q^{2} - 256 q^{5} + 126 q^{6} - 4 q^{7} + 168 q^{8} - 7140 q^{9} - 1876 q^{10} + 11104 q^{12} - 2904 q^{13} - 7678 q^{14} + 4288 q^{15} - 44824 q^{16} + 2064 q^{17} + 6222 q^{18} - 4954 q^{19} - 43084 q^{20} - 39810 q^{22} + 21966 q^{23} + 79188 q^{24} + 66604 q^{26} + 69500 q^{29} - 32418 q^{31} - 141992 q^{32} + 54752 q^{33} + 256508 q^{34} - 26164 q^{35} + 180242 q^{37} + 329032 q^{38} - 60088 q^{39} - 346014 q^{42} - 144514 q^{43} - 294896 q^{44} + 842152 q^{45} - 522736 q^{46} - 157076 q^{47} + 405652 q^{49} + 46176 q^{50} - 624984 q^{51} - 161884 q^{52} - 512988 q^{53} + 541150 q^{54} + 824640 q^{55} - 608488 q^{56} - 311992 q^{57} + 187582 q^{59} - 1156764 q^{60} - 1321908 q^{61} - 887284 q^{63} + 752126 q^{66} + 1244832 q^{68} + 41960 q^{69} - 1029284 q^{70} + 1316252 q^{71} + 777880 q^{72} + 1117260 q^{74} - 2148904 q^{75} - 814428 q^{76} - 56722 q^{79} + 3750844 q^{80} - 930796 q^{81} + 1462554 q^{82} - 841484 q^{83} + 5065540 q^{84} + 3992612 q^{86} + 2494224 q^{87} - 3796428 q^{88} - 1439724 q^{89} - 5618044 q^{90} - 8644 q^{91} + 7826980 q^{92} - 54064 q^{93} - 2057938 q^{94} - 8819328 q^{96} + 2578548 q^{97} - 6043946 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 - 256 * q^5 + 126 * q^6 - 4 * q^7 + 168 * q^8 - 7140 * q^9 - 1876 * q^10 + 11104 * q^12 - 2904 * q^13 - 7678 * q^14 + 4288 * q^15 - 44824 * q^16 + 2064 * q^17 + 6222 * q^18 - 4954 * q^19 - 43084 * q^20 - 39810 * q^22 + 21966 * q^23 + 79188 * q^24 + 66604 * q^26 + 69500 * q^29 - 32418 * q^31 - 141992 * q^32 + 54752 * q^33 + 256508 * q^34 - 26164 * q^35 + 180242 * q^37 + 329032 * q^38 - 60088 * q^39 - 346014 * q^42 - 144514 * q^43 - 294896 * q^44 + 842152 * q^45 - 522736 * q^46 - 157076 * q^47 + 405652 * q^49 + 46176 * q^50 - 624984 * q^51 - 161884 * q^52 - 512988 * q^53 + 541150 * q^54 + 824640 * q^55 - 608488 * q^56 - 311992 * q^57 + 187582 * q^59 - 1156764 * q^60 - 1321908 * q^61 - 887284 * q^63 + 752126 * q^66 + 1244832 * q^68 + 41960 * q^69 - 1029284 * q^70 + 1316252 * q^71 + 777880 * q^72 + 1117260 * q^74 - 2148904 * q^75 - 814428 * q^76 - 56722 * q^79 + 3750844 * q^80 - 930796 * q^81 + 1462554 * q^82 - 841484 * q^83 + 5065540 * q^84 + 3992612 * q^86 + 2494224 * q^87 - 3796428 * q^88 - 1439724 * q^89 - 5618044 * q^90 - 8644 * q^91 + 7826980 * q^92 - 54064 * q^93 - 2057938 * q^94 - 8819328 * q^96 + 2578548 * q^97 - 6043946 * q^98

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