LMFDB - Embedded newform 177.7.c.a.58.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,7,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	177.c (of order $2$, degree $1$, 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:	$40.7195728007$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.41
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.65433i q^{2} +15.5885 q^{3} +19.7199 q^{4} +168.519 q^{5} +103.731i q^{6} +568.245 q^{7} +557.100i q^{8} +243.000 q^{9} +O(q^{10})$	\(q+6.65433i q^{2} +15.5885 q^{3} +19.7199 q^{4} +168.519 q^{5} +103.731i q^{6} +568.245 q^{7} +557.100i q^{8} +243.000 q^{9} +1121.38i q^{10} +433.875i q^{11} +307.403 q^{12} +1424.64i q^{13} +3781.29i q^{14} +2626.95 q^{15} -2445.05 q^{16} -3203.72 q^{17} +1617.00i q^{18} -480.820 q^{19} +3323.18 q^{20} +8858.06 q^{21} -2887.14 q^{22} -5842.85i q^{23} +8684.33i q^{24} +12773.6 q^{25} -9480.00 q^{26} +3788.00 q^{27} +11205.7 q^{28} -16081.4 q^{29} +17480.6i q^{30} -48586.3i q^{31} +19384.2i q^{32} +6763.43i q^{33} -21318.6i q^{34} +95759.9 q^{35} +4791.94 q^{36} -27263.4i q^{37} -3199.53i q^{38} +22207.9i q^{39} +93881.7i q^{40} -14615.3 q^{41} +58944.4i q^{42} +68476.3i q^{43} +8555.98i q^{44} +40950.0 q^{45} +38880.2 q^{46} -189784. i q^{47} -38114.5 q^{48} +205253. q^{49} +84999.4i q^{50} -49941.0 q^{51} +28093.8i q^{52} -263394. q^{53} +25206.6i q^{54} +73116.0i q^{55} +316569. i q^{56} -7495.24 q^{57} -107011. i q^{58} +(30685.3 - 203074. i) q^{59} +51803.2 q^{60} -68461.2i q^{61} +323309. q^{62} +138083. q^{63} -285472. q^{64} +240078. i q^{65} -45006.1 q^{66} +381209. i q^{67} -63177.1 q^{68} -91081.0i q^{69} +637218. i q^{70} -330328. q^{71} +135375. i q^{72} -63471.0i q^{73} +181419. q^{74} +199120. q^{75} -9481.73 q^{76} +246547. i q^{77} -147779. q^{78} +49824.6 q^{79} -412036. q^{80} +59049.0 q^{81} -97255.2i q^{82} +57827.2i q^{83} +174680. q^{84} -539887. q^{85} -455664. q^{86} -250685. q^{87} -241711. q^{88} +792215. i q^{89} +272495. i q^{90} +809543. i q^{91} -115221. i q^{92} -757386. i q^{93} +1.26289e6 q^{94} -81027.1 q^{95} +302170. i q^{96} -632824. i q^{97} +1.36582e6i q^{98} +105432. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			6.65433i			0.831791i	0.909412	+	0.415895i	$0.136532\pi$
$2$			6.65433i			0.831791i	−0.909412	+	0.415895i	$0.863468\pi$
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	19.7199			0.308124
$5$	168.519			1.34815			0.674075	−	0.738663i	$-0.264543\pi$
$5$	168.519			1.34815			0.674075	+	0.738663i	$0.264543\pi$
$6$			103.731i			0.480235i
$7$	568.245			1.65669			0.828345	−	0.560218i	$-0.189283\pi$
$7$	568.245			1.65669			0.828345	+	0.560218i	$0.189283\pi$
$8$			557.100i			1.08809i
$9$	243.000			0.333333
$10$			1121.38i			1.12138i
$11$			433.875i			0.325976i	0.986628	+	0.162988i	$0.0521132\pi$
$11$			433.875i			0.325976i	−0.986628	+	0.162988i	$0.947887\pi$
$12$	307.403			0.177895
$13$			1424.64i			0.648447i	0.945981	+	0.324223i	$0.105103\pi$
$13$			1424.64i			0.648447i	−0.945981	+	0.324223i	$0.894897\pi$
$14$			3781.29i			1.37802i
$15$	2626.95			0.778355
$16$	−2445.05			−0.596936
$17$	−3203.72			−0.652090			−0.326045	−	0.945354i	$-0.605716\pi$
$17$	−3203.72			−0.652090			−0.326045	+	0.945354i	$0.605716\pi$
$18$			1617.00i			0.277264i
$19$	−480.820			−0.0701006			−0.0350503	−	0.999386i	$-0.511159\pi$
$19$	−480.820			−0.0701006			−0.0350503	+	0.999386i	$0.511159\pi$
$20$	3323.18			0.415397
$21$	8858.06			0.956491
$22$	−2887.14			−0.271144
$23$		−	5842.85i		−	0.480221i	−0.970746	−	0.240110i	$-0.922816\pi$
$23$		−	5842.85i		−	0.480221i	0.970746	−	0.240110i	$-0.0771837\pi$
$24$			8684.33i			0.628206i
$25$	12773.6			0.817508
$26$	−9480.00			−0.539372
$27$	3788.00			0.192450
$28$	11205.7			0.510466
$29$	−16081.4			−0.659373			−0.329686	−	0.944090i	$-0.606943\pi$
$29$	−16081.4			−0.659373			−0.329686	+	0.944090i	$0.606943\pi$
$30$			17480.6i			0.647428i
$31$		−	48586.3i		−	1.63091i	−0.578823	−	0.815453i	$-0.696488\pi$
$31$		−	48586.3i		−	1.63091i	0.578823	−	0.815453i	$-0.303512\pi$
$32$			19384.2i			0.591560i
$33$			6763.43i			0.188203i
$34$		−	21318.6i		−	0.542403i
$35$	95759.9			2.23347
$36$	4791.94			0.102708
$37$		−	27263.4i		−	0.538238i	−0.963107	−	0.269119i	$-0.913268\pi$
$37$		−	27263.4i		−	0.538238i	0.963107	−	0.269119i	$-0.0867324\pi$
$38$		−	3199.53i		−	0.0583090i
$39$			22207.9i			0.374381i
$40$			93881.7i			1.46690i
$41$	−14615.3			−0.212059			−0.106030	−	0.994363i	$-0.533814\pi$
$41$	−14615.3			−0.212059			−0.106030	+	0.994363i	$0.533814\pi$
$42$			58944.4i			0.795600i
$43$			68476.3i			0.861262i	0.902528	+	0.430631i	$0.141709\pi$
$43$			68476.3i			0.861262i	−0.902528	+	0.430631i	$0.858291\pi$
$44$			8555.98i			0.100441i
$45$	40950.0			0.449383
$46$	38880.2			0.399443
$47$		−	189784.i		−	1.82796i	−0.405762	−	0.913979i	$-0.632994\pi$
$47$		−	189784.i		−	1.82796i	0.405762	−	0.913979i	$-0.367006\pi$
$48$	−38114.5			−0.344641
$49$	205253.			1.74462
$50$			84999.4i			0.679995i
$51$	−49941.0			−0.376484
$52$			28093.8i			0.199802i
$53$	−263394.			−1.76921			−0.884604	−	0.466343i	$-0.845571\pi$
$53$	−263394.			−1.76921			−0.884604	+	0.466343i	$0.845571\pi$
$54$			25206.6i			0.160078i
$55$			73116.0i			0.439465i
$56$			316569.i			1.80262i
$57$	−7495.24			−0.0404726
$58$		−	107011.i		−	0.548460i
$59$	30685.3	−	203074.i	0.149408	−	0.988776i
$59$	30685.3	−	203074.i	0.149408	−	0.988776i
$60$	51803.2			0.239830
$61$		−	68461.2i		−	0.301617i	−0.988563	−	0.150808i	$-0.951812\pi$
$61$		−	68461.2i		−	0.301617i	0.988563	−	0.150808i	$-0.0481876\pi$
$62$	323309.			1.35657
$63$	138083.			0.552230
$64$	−285472.			−1.08899
$65$			240078.i			0.874203i
$66$	−45006.1			−0.156545
$67$			381209.i			1.26747i	0.773549	+	0.633736i	$0.218480\pi$
$67$			381209.i			1.26747i	−0.773549	+	0.633736i	$0.781520\pi$
$68$	−63177.1			−0.200925
$69$		−	91081.0i		−	0.277256i
$70$			637218.i			1.85778i
$71$	−330328.			−0.922935			−0.461467	−	0.887157i	$-0.652677\pi$
$71$	−330328.			−0.922935			−0.461467	+	0.887157i	$0.652677\pi$
$72$			135375.i			0.362695i
$73$		−	63471.0i		−	0.163157i	−0.996667	−	0.0815787i	$-0.974004\pi$
$73$		−	63471.0i		−	0.163157i	0.996667	−	0.0815787i	$-0.0259962\pi$
$74$	181419.			0.447701
$75$	199120.			0.471988
$76$	−9481.73			−0.0215997
$77$			246547.i			0.540042i
$78$	−147779.			−0.311407
$79$	49824.6			0.101056			0.0505281	−	0.998723i	$-0.483910\pi$
$79$	49824.6			0.101056			0.0505281	+	0.998723i	$0.483910\pi$
$80$	−412036.			−0.804759
$81$	59049.0			0.111111
$82$		−	97255.2i		−	0.176389i
$83$			57827.2i			0.101134i	0.998721	+	0.0505671i	$0.0161029\pi$
$83$			57827.2i			0.101134i	−0.998721	+	0.0505671i	$0.983897\pi$
$84$	174680.			0.294718
$85$	−539887.			−0.879115
$86$	−455664.			−0.716389
$87$	−250685.			−0.380689
$88$	−241711.			−0.354690
$89$			792215.i			1.12376i	0.827219	+	0.561879i	$0.189921\pi$
$89$			792215.i			1.12376i	−0.827219	+	0.561879i	$0.810079\pi$
$90$			272495.i			0.373793i
$91$			809543.i			1.07428i
$92$		−	115221.i		−	0.147968i
$93$		−	757386.i		−	0.941604i
$94$	1.26289e6			1.52048
$95$	−81027.1			−0.0945060
$96$			302170.i			0.341537i
$97$		−	632824.i		−	0.693374i	−0.937981	−	0.346687i	$-0.887307\pi$
$97$		−	632824.i		−	0.693374i	0.937981	−	0.346687i	$-0.112693\pi$
$98$			1.36582e6i			1.45116i
$99$			105432.i			0.108659i
$100$	251894.			0.251894
$101$			1.61402e6i			1.56655i	0.621675	+	0.783276i	$0.286453\pi$
$101$			1.61402e6i			1.56655i	−0.621675	+	0.783276i	$0.713547\pi$
$102$		−	332324.i		−	0.313156i
$103$		−	801623.i		−	0.733599i	−0.930300	−	0.366799i	$-0.880454\pi$
$103$		−	801623.i		−	0.733599i	0.930300	−	0.366799i	$-0.119546\pi$
$104$	−793665.			−0.705566
$105$	1.49275e6			1.28949
$106$		−	1.75271e6i		−	1.47161i
$107$	188639.			0.153985			0.0769927	−	0.997032i	$-0.475468\pi$
$107$	188639.			0.153985			0.0769927	+	0.997032i	$0.475468\pi$
$108$	74699.0			0.0592985
$109$			137612.i			0.106261i	0.998588	+	0.0531307i	$0.0169200\pi$
$109$			137612.i			0.106261i	−0.998588	+	0.0531307i	$0.983080\pi$
$110$	−486538.			−0.365543
$111$		−	424994.i		−	0.310752i
$112$	−1.38939e6			−0.988938
$113$			952885.i			0.660397i	0.943912	+	0.330198i	$0.107116\pi$
$113$			952885.i			0.660397i	−0.943912	+	0.330198i	$0.892884\pi$
$114$		−	49875.8i		−	0.0336647i
$115$		−	984629.i		−	0.647410i
$116$	−317125.			−0.203169
$117$			346187.i			0.216149i
$118$	1.35132e6	+	204190.i	0.822455	+	0.124276i
$119$	−1.82050e6			−1.08031
$120$			1.46347e6i			0.846916i
$121$	1.58331e6			0.893739
$122$	455564.			0.250882
$123$	−227831.			−0.122432
$124$		−	958119.i		−	0.502521i
$125$	−480522.			−0.246027
$126$			918853.i			0.459340i
$127$	2.83971e6			1.38632			0.693159	−	0.720785i	$-0.256218\pi$
$127$	2.83971e6			1.38632			0.693159	+	0.720785i	$0.256218\pi$
$128$		−	659034.i		−	0.314252i
$129$			1.06744e6i			0.497250i
$130$	−1.59756e6			−0.727154
$131$		−	1.05300e6i		−	0.468395i	−0.972189	−	0.234198i	$-0.924754\pi$
$131$		−	1.05300e6i		−	0.468395i	0.972189	−	0.234198i	$-0.0752463\pi$
$132$			133374.i			0.0579897i
$133$	−273223.			−0.116135
$134$	−2.53669e6			−1.05427
$135$	638348.			0.259452
$136$		−	1.78479e6i		−	0.709530i
$137$	3.78035e6			1.47018			0.735090	−	0.677969i	$-0.237140\pi$
$137$	3.78035e6			1.47018			0.735090	+	0.677969i	$0.237140\pi$
$138$	606083.			0.230619
$139$	2.26731e6			0.844240			0.422120	−	0.906540i	$-0.361286\pi$
$139$	2.26731e6			0.844240			0.422120	+	0.906540i	$0.361286\pi$
$140$	1.88838e6			0.688184
$141$		−	2.95844e6i		−	1.05537i
$142$		−	2.19811e6i		−	0.767689i
$143$	−618114.			−0.211378
$144$	−594147.			−0.198979
$145$	−2.71002e6			−0.888933
$146$	422357.			0.135713
$147$	3.19958e6			1.00726
$148$		−	537631.i		−	0.165844i
$149$		−	352053.i		−	0.106426i	−0.998583	−	0.0532132i	$-0.983054\pi$
$149$		−	352053.i		−	0.106426i	0.998583	−	0.0532132i	$-0.0169463\pi$
$150$			1.32501e6i			0.392596i
$151$		−	6.04947e6i		−	1.75706i	−0.477687	−	0.878530i	$-0.658525\pi$
$151$		−	6.04947e6i		−	1.75706i	0.477687	−	0.878530i	$-0.341475\pi$
$152$		−	267865.i		−	0.0762754i
$153$	−778504.			−0.217363
$154$	−1.64060e6			−0.449202
$155$		−	8.18771e6i		−	2.19871i
$156$			437938.i			0.115356i
$157$		−	4.21637e6i		−	1.08953i	−0.838589	−	0.544765i	$-0.816619\pi$
$157$		−	4.21637e6i		−	1.08953i	0.838589	−	0.544765i	$-0.183381\pi$
$158$			331549.i			0.0840576i
$159$	−4.10591e6			−1.02145
$160$			3.26661e6i			0.797511i
$161$		−	3.32017e6i		−	0.795577i
$162$			392931.i			0.0924212i
$163$	−5.63329e6			−1.30077			−0.650383	−	0.759606i	$-0.725392\pi$
$163$	−5.63329e6			−1.30077			−0.650383	+	0.759606i	$0.725392\pi$
$164$	−288213.			−0.0653405
$165$			1.13977e6i			0.253725i
$166$	−384801.			−0.0841225
$167$	4.22418e6			0.906971			0.453485	−	0.891264i	$-0.350180\pi$
$167$	4.22418e6			0.906971			0.453485	+	0.891264i	$0.350180\pi$
$168$			4.93482e6i			1.04074i
$169$	2.79722e6			0.579517
$170$		−	3.59258e6i		−	0.731240i
$171$	−116839.			−0.0233669
$172$			1.35035e6i			0.265375i
$173$		−	3.51913e6i		−	0.679668i	−0.940485	−	0.339834i	$-0.889629\pi$
$173$		−	3.51913e6i		−	0.679668i	0.940485	−	0.339834i	$-0.110371\pi$
$174$		−	1.66814e6i		−	0.316654i
$175$	7.25851e6			1.35436
$176$		−	1.06084e6i		−	0.194587i
$177$	478336.	−	3.16561e6i	0.0862608	−	0.570870i
$178$	−5.27166e6			−0.934732
$179$			1.00294e7i			1.74871i	0.485291	+	0.874353i	$0.338714\pi$
$179$			1.00294e7i			1.74871i	−0.485291	+	0.874353i	$0.661286\pi$
$180$	807532.			0.138466
$181$	−5.10709e6			−0.861266			−0.430633	−	0.902527i	$-0.641710\pi$
$181$	−5.10709e6			−0.861266			−0.430633	+	0.902527i	$0.641710\pi$
$182$	−5.38696e6			−0.893573
$183$		−	1.06721e6i		−	0.174138i
$184$	3.25505e6			0.522521
$185$		−	4.59439e6i		−	0.725625i
$186$	5.03989e6			0.783218
$187$		−	1.39001e6i		−	0.212566i
$188$		−	3.74253e6i		−	0.563238i
$189$	2.15251e6			0.318830
$190$		−	539181.i		−	0.0786093i
$191$			1.03251e7i			1.48182i	0.671605	+	0.740909i	$0.265605\pi$
$191$			1.03251e7i			1.48182i	−0.671605	+	0.740909i	$0.734395\pi$
$192$	−4.45007e6			−0.628729
$193$	1.65636e6			0.230400			0.115200	−	0.993342i	$-0.463249\pi$
$193$	1.65636e6			0.230400			0.115200	+	0.993342i	$0.463249\pi$
$194$	4.21102e6			0.576742
$195$			3.74245e6i			0.504722i
$196$	4.04758e6			0.537560
$197$	−6.81276e6			−0.891096			−0.445548	−	0.895258i	$-0.646991\pi$
$197$	−6.81276e6			−0.891096			−0.445548	+	0.895258i	$0.646991\pi$
$198$	−701576.			−0.0903814
$199$	−544506.			−0.0690945			−0.0345473	−	0.999403i	$-0.510999\pi$
$199$	−544506.			−0.0690945			−0.0345473	+	0.999403i	$0.510999\pi$
$200$			7.11615e6i			0.889518i
$201$			5.94246e6i			0.731776i
$202$	−1.07402e7			−1.30304
$203$	−9.13820e6			−1.09238
$204$	−984834.			−0.116004
$205$	−2.46296e6			−0.285888
$206$	5.33426e6			0.610201
$207$		−	1.41981e6i		−	0.160074i
$208$		−	3.48331e6i		−	0.387081i
$209$		−	208615.i		−	0.0228511i
$210$			9.93324e6i			1.07259i
$211$		−	2.00834e6i		−	0.213791i	−0.994270	−	0.106895i	$-0.965909\pi$
$211$		−	2.00834e6i		−	0.213791i	0.994270	−	0.106895i	$-0.0340910\pi$
$212$	−5.19412e6			−0.545135
$213$	−5.14931e6			−0.532857
$214$			1.25526e6i			0.128084i
$215$			1.15395e7i			1.16111i
$216$			2.11029e6i			0.209402i
$217$		−	2.76089e7i		−	2.70191i
$218$	−915712.			−0.0883873
$219$		−	989416.i		−	0.0941990i
$220$			1.44184e6i			0.135410i
$221$		−	4.56414e6i		−	0.422846i
$222$	2.82805e6			0.258480
$223$	−1.11675e7			−1.00703			−0.503514	−	0.863987i	$-0.667960\pi$
$223$	−1.11675e7			−1.00703			−0.503514	+	0.863987i	$0.667960\pi$
$224$			1.10150e7i			0.980031i
$225$	3.10397e6			0.272503
$226$	−6.34081e6			−0.549312
$227$		−	8.43595e6i		−	0.721201i	−0.932720	−	0.360601i	$-0.882572\pi$
$227$		−	8.43595e6i		−	0.721201i	0.932720	−	0.360601i	$-0.117428\pi$
$228$	−147806.			−0.0124706
$229$			3.57189e6i			0.297435i	0.988880	+	0.148718i	$0.0475145\pi$
$229$			3.57189e6i			0.297435i	−0.988880	+	0.148718i	$0.952485\pi$
$230$	6.55204e6			0.538509
$231$			3.84329e6i			0.311793i
$232$		−	8.95897e6i		−	0.717454i
$233$			1.49908e7i			1.18511i	0.805530	+	0.592555i	$0.201881\pi$
$233$			1.49908e7i			1.18511i	−0.805530	+	0.592555i	$0.798119\pi$
$234$	−2.30364e6			−0.179791
$235$		−	3.19822e7i		−	2.46436i
$236$	605111.	−	4.00460e6i	0.0460362	−	0.304665i
$237$	776689.			0.0583448
$238$		−	1.21142e7i		−	0.898593i
$239$	−7.08836e6			−0.519221			−0.259610	−	0.965713i	$-0.583594\pi$
$239$	−7.08836e6			−0.519221			−0.259610	+	0.965713i	$0.583594\pi$
$240$	−6.42301e6			−0.464628
$241$	2.47456e7			1.76786			0.883928	−	0.467622i	$-0.154889\pi$
$241$	2.47456e7			1.76786			0.883928	+	0.467622i	$0.154889\pi$
$242$			1.05359e7i			0.743404i
$243$	920483.			0.0641500
$244$		−	1.35005e6i		−	0.0929353i
$245$	3.45890e7			2.35201
$246$		−	1.51606e6i		−	0.101838i
$247$		−	684994.i		−	0.0454565i
$248$	2.70674e7			1.77457
$249$			901437.i			0.0583898i
$250$		−	3.19755e6i		−	0.204643i
$251$	4.72593e6			0.298859			0.149429	−	0.988772i	$-0.452256\pi$
$251$	4.72593e6			0.298859			0.149429	+	0.988772i	$0.452256\pi$
$252$	2.72300e6			0.170155
$253$	2.53506e6			0.156541
$254$			1.88964e7i			1.15313i
$255$	−8.41600e6			−0.507557
$256$	−1.38848e7			−0.827598
$257$	−1.93357e7			−1.13910			−0.569549	−	0.821958i	$-0.692882\pi$
$257$	−1.93357e7			−1.13910			−0.569549	+	0.821958i	$0.692882\pi$
$258$	−7.10310e6			−0.413608
$259$		−	1.54923e7i		−	0.891693i
$260$			4.73432e6i			0.269363i
$261$	−3.90779e6			−0.219791
$262$	7.00697e6			0.389607
$263$	3.31759e7			1.82371			0.911855	−	0.410512i	$-0.134650\pi$
$263$	3.31759e7			1.82371			0.911855	+	0.410512i	$0.134650\pi$
$264$	−3.76791e6			−0.204780
$265$	−4.43869e7			−2.38516
$266$		−	1.81812e6i		−	0.0966000i
$267$			1.23494e7i			0.648802i
$268$			7.51741e6i			0.390539i
$269$			3.69340e7i			1.89745i	0.316109	+	0.948723i	$0.397623\pi$
$269$			3.69340e7i			1.89745i	−0.316109	+	0.948723i	$0.602377\pi$
$270$			4.24778e6i			0.215809i
$271$	9.48324e6			0.476484			0.238242	−	0.971206i	$-0.423429\pi$
$271$	9.48324e6			0.476484			0.238242	+	0.971206i	$0.423429\pi$
$272$	7.83325e6			0.389256
$273$			1.26195e7i			0.620233i
$274$			2.51557e7i			1.22288i
$275$			5.54212e6i			0.266488i
$276$		−	1.79611e6i		−	0.0854291i
$277$	2.02819e7			0.954267			0.477134	−	0.878831i	$-0.341676\pi$
$277$	2.02819e7			0.954267			0.477134	+	0.878831i	$0.341676\pi$
$278$			1.50874e7i			0.702231i
$279$		−	1.18065e7i		−	0.543635i
$280$			5.33478e7i			2.43020i
$281$	5.15301e6			0.232243			0.116121	−	0.993235i	$-0.462954\pi$
$281$	5.15301e6			0.232243			0.116121	+	0.993235i	$0.462954\pi$
$282$	1.96864e7			0.877849
$283$			3.44954e7i			1.52196i	0.648778	+	0.760978i	$0.275280\pi$
$283$			3.44954e7i			1.52196i	−0.648778	+	0.760978i	$0.724720\pi$
$284$	−6.51405e6			−0.284378
$285$	−1.26309e6			−0.0545631
$286$		−	4.11313e6i		−	0.175823i
$287$	−8.30509e6			−0.351317
$288$			4.71037e6i			0.197187i
$289$	−1.38738e7			−0.574779
$290$		−	1.80334e7i		−	0.739407i
$291$		−	9.86475e6i		−	0.400320i
$292$		−	1.25164e6i		−	0.0502727i
$293$	−2.59121e7			−1.03015			−0.515075	−	0.857145i	$-0.672236\pi$
$293$	−2.59121e7			−1.03015			−0.515075	+	0.857145i	$0.672236\pi$
$294$			2.12911e7i			0.837828i
$295$	5.17104e6	−	3.42217e7i	0.201424	−	1.33302i
$296$	1.51884e7			0.585649
$297$			1.64351e6i			0.0627342i
$298$	2.34268e6			0.0885246
$299$	8.32394e6			0.311398
$300$	3.92663e6			0.145431
$301$			3.89113e7i			1.42684i
$302$	4.02552e7			1.46151
$303$			2.51601e7i			0.904449i
$304$	1.17563e6			0.0418455
$305$		−	1.15370e7i		−	0.406624i
$306$		−	5.18042e6i		−	0.180801i
$307$	−5.13183e7			−1.77361			−0.886804	−	0.462147i	$-0.847079\pi$
$307$	−5.13183e7			−1.77361			−0.886804	+	0.462147i	$0.847079\pi$
$308$			4.86189e6i			0.166400i
$309$		−	1.24961e7i		−	0.423543i
$310$	5.44837e7			1.82886
$311$	−191017.			−0.00635025			−0.00317513	−	0.999995i	$-0.501011\pi$
$311$	−191017.			−0.00635025			−0.00317513	+	0.999995i	$0.501011\pi$
$312$	−1.23720e7			−0.407358
$313$		−	5.29245e7i		−	1.72593i	−0.505261	−	0.862966i	$-0.668604\pi$
$313$		−	5.29245e7i		−	1.72593i	0.505261	−	0.862966i	$-0.331396\pi$
$314$	2.80571e7			0.906262
$315$	2.32697e7			0.744489
$316$	982538.			0.0311378
$317$	−2.57744e7			−0.809117			−0.404558	−	0.914512i	$-0.632575\pi$
$317$	−2.57744e7			−0.809117			−0.404558	+	0.914512i	$0.632575\pi$
$318$		−	2.73221e7i		−	0.849635i
$319$		−	6.97733e6i		−	0.214940i
$320$	−4.81074e7			−1.46812
$321$	2.94059e6			0.0889035
$322$	2.20935e7			0.661754
$323$	1.54041e6			0.0457119
$324$	1.16444e6			0.0342360
$325$			1.81977e7i			0.530110i
$326$		−	3.74858e7i		−	1.08197i
$327$			2.14515e6i			0.0613500i
$328$		−	8.14220e6i		−	0.230739i
$329$		−	1.07844e8i		−	3.02836i
$330$	−7.58437e6			−0.211046
$331$	2.30935e7			0.636803			0.318401	−	0.947956i	$-0.396854\pi$
$331$	2.30935e7			0.636803			0.318401	+	0.947956i	$0.396854\pi$
$332$			1.14035e6i			0.0311619i
$333$		−	6.62499e6i		−	0.179413i
$334$			2.81091e7i			0.754410i
$335$			6.42408e7i			1.70874i
$336$	−2.16584e7			−0.570963
$337$			2.78790e7i			0.728428i	0.931315	+	0.364214i	$0.118662\pi$
$337$			2.78790e7i			0.728428i	−0.931315	+	0.364214i	$0.881338\pi$
$338$			1.86136e7i			0.482037i
$339$			1.48540e7i			0.381280i
$340$	−1.06465e7			−0.270876
$341$	2.10804e7			0.531637
$342$		−	777486.i		−	0.0194363i
$343$	4.97806e7			1.23361
$344$	−3.81481e7			−0.937126
$345$		−	1.53488e7i		−	0.373782i
$346$	2.34174e7			0.565342
$347$		−	3.17902e7i		−	0.760859i	−0.924810	−	0.380430i	$-0.875776\pi$
$347$		−	3.17902e7i		−	0.760859i	0.924810	−	0.380430i	$-0.124224\pi$
$348$	−4.94349e6			−0.117299
$349$			2.41409e7i			0.567906i	0.958838	+	0.283953i	$0.0916459\pi$
$349$			2.41409e7i			0.567906i	−0.958838	+	0.283953i	$0.908354\pi$
$350$			4.83005e7i			1.12654i
$351$			5.39652e6i			0.124794i
$352$	−8.41032e6			−0.192835
$353$		−	5.77487e7i		−	1.31286i	−0.754387	−	0.656430i	$-0.772066\pi$
$353$		−	5.77487e7i		−	1.31286i	0.754387	−	0.656430i	$-0.227934\pi$
$354$	2.10650e7	+	3.18300e6i	0.474844	+	0.0717509i
$355$	−5.56665e7			−1.24425
$356$			1.56224e7i			0.346257i
$357$	−2.83787e7			−0.623718
$358$	−6.67390e7			−1.45456
$359$	−4.80212e7			−1.03789			−0.518943	−	0.854809i	$-0.673674\pi$
$359$	−4.80212e7			−1.03789			−0.518943	+	0.854809i	$0.673674\pi$
$360$			2.28133e7i			0.488967i
$361$	−4.68147e7			−0.995086
$362$		−	3.39842e7i		−	0.716394i
$363$	2.46814e7			0.516001
$364$			1.59641e7i			0.331010i
$365$		−	1.06961e7i		−	0.219961i
$366$	7.10153e6			0.144847
$367$		−	7.19741e7i		−	1.45606i	−0.685547	−	0.728028i	$-0.740437\pi$
$367$		−	7.19741e7i		−	1.45606i	0.685547	−	0.728028i	$-0.259563\pi$
$368$			1.42860e7i			0.286661i
$369$	−3.55153e6			−0.0706864
$370$	3.05725e7			0.603568
$371$	−1.49672e8			−2.93103
$372$		−	1.49356e7i		−	0.290131i
$373$	−1.33221e6			−0.0256712			−0.0128356	−	0.999918i	$-0.504086\pi$
$373$	−1.33221e6			−0.0256712			−0.0128356	+	0.999918i	$0.504086\pi$
$374$	9.24959e6			0.176810
$375$	−7.49059e6			−0.142044
$376$	1.05729e8			1.98897
$377$		−	2.29102e7i		−	0.427568i
$378$			1.43235e7i			0.265200i
$379$	7.76840e6			0.142697			0.0713484	−	0.997451i	$-0.477270\pi$
$379$	7.76840e6			0.142697			0.0713484	+	0.997451i	$0.477270\pi$
$380$	−1.59785e6			−0.0291196
$381$	4.42667e7			0.800391
$382$	−6.87067e7			−1.23256
$383$	9.79995e6			0.174433			0.0872163	−	0.996189i	$-0.472203\pi$
$383$	9.79995e6			0.174433			0.0872163	+	0.996189i	$0.472203\pi$
$384$		−	1.02733e7i		−	0.181433i
$385$			4.15478e7i			0.728057i
$386$			1.10220e7i			0.191645i
$387$			1.66397e7i			0.287087i
$388$		−	1.24792e7i		−	0.213645i
$389$	−3.88967e7			−0.660791			−0.330396	−	0.943843i	$-0.607182\pi$
$389$	−3.88967e7			−0.660791			−0.330396	+	0.943843i	$0.607182\pi$
$390$	−2.49035e7			−0.419823
$391$			1.87188e7i			0.313147i
$392$			1.14346e8i			1.89830i
$393$		−	1.64146e7i		−	0.270428i
$394$		−	4.53343e7i		−	0.741205i
$395$	8.39638e6			0.136239
$396$			2.07910e6i			0.0334804i
$397$		−	5.11786e7i		−	0.817932i	−0.912550	−	0.408966i	$-0.865889\pi$
$397$		−	5.11786e7i		−	0.817932i	0.912550	−	0.408966i	$-0.134111\pi$
$398$		−	3.62332e6i		−	0.0574722i
$399$	−4.25913e6			−0.0670505
$400$	−3.12320e7			−0.488000
$401$		−	3.02513e7i		−	0.469148i	−0.972098	−	0.234574i	$-0.924630\pi$
$401$		−	3.02513e7i		−	0.469148i	0.972098	−	0.234574i	$-0.0753696\pi$
$402$	−3.95431e7			−0.608684
$403$	6.92179e7			1.05756
$404$			3.18283e7i			0.482692i
$405$	9.95086e6			0.149794
$406$		−	6.08086e7i		−	0.908629i
$407$	1.18289e7			0.175453
$408$		−	2.78221e7i		−	0.409647i
$409$		−	4.92500e7i		−	0.719841i	−0.932983	−	0.359921i	$-0.882804\pi$
$409$		−	4.92500e7i		−	0.719841i	0.932983	−	0.359921i	$-0.117196\pi$
$410$		−	1.63893e7i		−	0.237799i
$411$	5.89299e7			0.848809
$412$		−	1.58080e7i		−	0.226039i
$413$	1.74367e7	−	1.15396e8i	0.247523	−	1.63810i
$414$	9.44789e6			0.133148
$415$			9.74497e6i			0.136344i
$416$	−2.76155e7			−0.383595
$417$	3.53438e7			0.487422
$418$	1.38820e6			0.0190074
$419$		−	7.50637e7i		−	1.02044i	−0.860044	−	0.510220i	$-0.829564\pi$
$419$		−	7.50637e7i		−	1.02044i	0.860044	−	0.510220i	$-0.170436\pi$
$420$	2.94369e7			0.397323
$421$			2.32571e6i			0.0311680i	0.999879	+	0.0155840i	$0.00496074\pi$
$421$			2.32571e6i			0.0311680i	−0.999879	+	0.0155840i	$0.995039\pi$
$422$	1.33641e7			0.177829
$423$		−	4.61175e7i		−	0.609319i
$424$		−	1.46737e8i		−	1.92505i
$425$	−4.09229e7			−0.533089
$426$		−	3.42652e7i		−	0.443225i
$427$		−	3.89027e7i		−	0.499685i
$428$	3.71994e6			0.0474466
$429$	−9.63544e6			−0.122039
$430$	−7.67879e7			−0.965800
$431$		−	2.06821e7i		−	0.258323i	−0.991624	−	0.129161i	$-0.958771\pi$
$431$		−	2.06821e7i		−	0.258323i	0.991624	−	0.129161i	$-0.0412285\pi$
$432$	−9.26183e6			−0.114880
$433$	9.48112e7			1.16787			0.583937	−	0.811799i	$-0.301511\pi$
$433$	9.48112e7			1.16787			0.583937	+	0.811799i	$0.301511\pi$
$434$	1.83719e8			2.24742
$435$	−4.22451e7			−0.513226
$436$			2.71369e6i			0.0327417i
$437$			2.80936e6i			0.0336637i
$438$	6.58390e6			0.0783539
$439$	−1.73231e7			−0.204753			−0.102377	−	0.994746i	$-0.532645\pi$
$439$	−1.73231e7			−0.204753			−0.102377	+	0.994746i	$0.532645\pi$
$440$	−4.07329e7			−0.478175
$441$	4.98765e7			0.581541
$442$	3.03713e7			0.351719
$443$		−	3.20560e6i		−	0.0368722i	−0.999830	−	0.0184361i	$-0.994131\pi$
$443$		−	3.20560e6i		−	0.0368722i	0.999830	−	0.0184361i	$-0.00586872\pi$
$444$		−	8.38084e6i		−	0.0957500i
$445$			1.33503e8i			1.51499i
$446$		−	7.43123e7i		−	0.837637i
$447$		−	5.48797e6i		−	0.0614453i
$448$	−1.62218e8			−1.80412
$449$	3.81575e7			0.421542			0.210771	−	0.977536i	$-0.432403\pi$
$449$	3.81575e7			0.421542			0.210771	+	0.977536i	$0.432403\pi$
$450$			2.06549e7i			0.226665i
$451$		−	6.34122e6i		−	0.0691263i
$452$			1.87908e7i			0.203484i
$453$		−	9.43019e7i		−	1.01444i
$454$	5.61356e7			0.599889
$455$			1.36423e8i			1.44828i
$456$		−	4.17560e6i		−	0.0440376i
$457$			1.22414e7i			0.128258i	0.997942	+	0.0641289i	$0.0204269\pi$
$457$			1.22414e7i			0.128258i	−0.997942	+	0.0641289i	$0.979573\pi$
$458$	−2.37686e7			−0.247404
$459$	−1.21357e7			−0.125495
$460$		−	1.94168e7i		−	0.199482i
$461$	−1.13108e8			−1.15449			−0.577247	−	0.816570i	$-0.695873\pi$
$461$	−1.13108e8			−1.15449			−0.577247	+	0.816570i	$0.695873\pi$
$462$	−2.55745e7			−0.259347
$463$			1.06495e8i			1.07297i	0.843910	+	0.536485i	$0.180248\pi$
$463$			1.06495e8i			1.07297i	−0.843910	+	0.536485i	$0.819752\pi$
$464$	3.93199e7			0.393603
$465$		−	1.27634e8i		−	1.26942i
$466$	−9.97540e7			−0.985763
$467$			3.56008e7i			0.349550i	0.984608	+	0.174775i	$0.0559198\pi$
$467$			3.56008e7i			0.349550i	−0.984608	+	0.174775i	$0.944080\pi$
$468$			6.82678e6i			0.0666006i
$469$			2.16620e8i			2.09981i
$470$	2.12820e8			2.04983
$471$		−	6.57267e7i		−	0.629041i
$472$	1.13132e8	+	1.70948e7i	1.07587	+	0.162569i
$473$	−2.97101e7			−0.280751
$474$			5.16834e6i			0.0485307i
$475$	−6.14178e6			−0.0573077
$476$	−3.59001e7			−0.332870
$477$	−6.40048e7			−0.589736
$478$		−	4.71682e7i		−	0.431883i
$479$	−3.29980e7			−0.300249			−0.150124	−	0.988667i	$-0.547967\pi$
$479$	−3.29980e7			−0.300249			−0.150124	+	0.988667i	$0.547967\pi$
$480$			5.09213e7i			0.460443i
$481$	3.88404e7			0.349018
$482$			1.64665e8i			1.47049i
$483$		−	5.17563e7i		−	0.459327i
$484$	3.12228e7			0.275382
$485$		−	1.06643e8i		−	0.934772i
$486$			6.12519e6i			0.0533594i
$487$	1.60962e8			1.39359			0.696796	−	0.717269i	$-0.254608\pi$
$487$	1.60962e8			1.39359			0.696796	+	0.717269i	$0.254608\pi$
$488$	3.81397e7			0.328185
$489$	−8.78143e7			−0.750998
$490$			2.30166e8i			1.95638i
$491$	−9.28174e7			−0.784125			−0.392062	−	0.919939i	$-0.628238\pi$
$491$	−9.28174e7			−0.784125			−0.392062	+	0.919939i	$0.628238\pi$
$492$	−4.49280e6			−0.0377244
$493$	5.15204e7			0.429971
$494$	4.55817e6			0.0378103
$495$			1.77672e7i			0.146488i
$496$			1.18796e8i			0.973546i
$497$	−1.87707e8			−1.52902
$498$	−5.99846e6			−0.0485681
$499$	1.69869e8			1.36714			0.683569	−	0.729886i	$-0.260427\pi$
$499$	1.69869e8			1.36714			0.683569	+	0.729886i	$0.260427\pi$
$500$	−9.47585e6			−0.0758068
$501$	6.58485e7			0.523640
$502$			3.14479e7i			0.248588i
$503$		−	9.91155e7i		−	0.778821i	−0.921064	−	0.389410i	$-0.872679\pi$
$503$		−	9.91155e7i		−	0.778821i	0.921064	−	0.389410i	$-0.127321\pi$
$504$			7.69263e7i			0.600874i
$505$			2.71992e8i			2.11195i
$506$			1.68691e7i			0.130209i
$507$	4.36043e7			0.334584
$508$	5.59989e7			0.427158
$509$		−	9.96791e6i		−	0.0755876i	−0.999286	−	0.0377938i	$-0.987967\pi$
$509$		−	9.96791e6i		−	0.0755876i	0.999286	−	0.0377938i	$-0.0120330\pi$
$510$		−	5.60028e7i		−	0.422182i
$511$		−	3.60671e7i		−	0.270301i
$512$		−	1.34572e8i		−	1.00264i
$513$	−1.82134e6			−0.0134909
$514$		−	1.28666e8i		−	0.947491i
$515$		−	1.35089e8i		−	0.989001i
$516$			2.10498e7i			0.153214i
$517$	8.23425e7			0.595871
$518$	1.03091e8			0.741702
$519$		−	5.48578e7i		−	0.392407i
$520$	−1.33747e8			−0.951208
$521$	1.51073e8			1.06825			0.534126	−	0.845405i	$-0.320641\pi$
$521$	1.51073e8			1.06825			0.534126	+	0.845405i	$0.320641\pi$
$522$		−	2.60037e7i		−	0.182820i
$523$	7.08136e7			0.495007			0.247504	−	0.968887i	$-0.420390\pi$
$523$	7.08136e7			0.495007			0.247504	+	0.968887i	$0.420390\pi$
$524$		−	2.07650e7i		−	0.144324i
$525$	1.13149e8			0.781938
$526$			2.20764e8i			1.51695i
$527$			1.55657e8i			1.06350i
$528$		−	1.65369e7i		−	0.112345i
$529$	1.13897e8			0.769388
$530$		−	2.95365e8i		−	1.98395i
$531$	7.45652e6	−	4.93469e7i	0.0498027	−	0.329592i
$532$	−5.38794e6			−0.0357839
$533$		−	2.08216e7i		−	0.137509i
$534$	−8.21770e7			−0.539668
$535$	3.17892e7			0.207595
$536$	−2.12371e8			−1.37912
$537$			1.56343e8i			1.00962i
$538$	−2.45771e8			−1.57828
$539$			8.90541e7i			0.568706i
$540$	1.25882e7			0.0799432
$541$			2.84621e8i			1.79752i	0.438437	+	0.898762i	$0.355532\pi$
$541$			2.84621e8i			1.79752i	−0.438437	+	0.898762i	$0.644468\pi$
$542$			6.31046e7i			0.396335i
$543$	−7.96116e7			−0.497252
$544$		−	6.21016e7i		−	0.385750i
$545$			2.31901e7i			0.143256i
$546$	−8.39744e7			−0.515904
$547$	−2.31430e8			−1.41403			−0.707013	−	0.707200i	$-0.749958\pi$
$547$	−2.31430e8			−1.41403			−0.707013	+	0.707200i	$0.749958\pi$
$548$	7.45483e7			0.452998
$549$		−	1.66361e7i		−	0.100539i
$550$	−3.68791e7			−0.221662
$551$	7.73228e6			0.0462224
$552$	5.07412e7			0.301678
$553$	2.83126e7			0.167419
$554$			1.34963e8i			0.793751i
$555$		−	7.16194e7i		−	0.418940i
$556$	4.47111e7			0.260130
$557$	3.39669e6			0.0196558			0.00982788	−	0.999952i	$-0.496872\pi$
$557$	3.39669e6			0.0196558			0.00982788	+	0.999952i	$0.496872\pi$
$558$	7.85642e7			0.452191
$559$	−9.75539e7			−0.558482
$560$	−2.34138e8			−1.33324
$561$		−	2.16681e7i		−	0.122725i
$562$			3.42898e7i			0.193177i
$563$		−	1.40454e8i		−	0.787063i	−0.919311	−	0.393532i	$-0.871253\pi$
$563$		−	1.40454e8i		−	0.787063i	0.919311	−	0.393532i	$-0.128747\pi$
$564$		−	5.83402e7i		−	0.325185i
$565$			1.60579e8i			0.890314i
$566$	−2.29544e8			−1.26595
$567$	3.35543e7			0.184077
$568$		−	1.84026e8i		−	1.00423i
$569$			3.71990e7i			0.201927i	0.994890	+	0.100963i	$0.0321925\pi$
$569$			3.71990e7i			0.201927i	−0.994890	+	0.100963i	$0.967808\pi$
$570$		−	8.40500e6i		−	0.0453851i
$571$			1.77384e8i			0.952810i	0.879226	+	0.476405i	$0.158060\pi$
$571$			1.77384e8i			0.952810i	−0.879226	+	0.476405i	$0.841940\pi$
$572$	−1.21892e7			−0.0651307
$573$			1.60953e8i			0.855528i
$574$		−	5.52648e7i		−	0.292222i
$575$		−	7.46339e7i		−	0.392584i
$576$	−6.93697e7			−0.362997
$577$	1.78824e8			0.930890			0.465445	−	0.885077i	$-0.345894\pi$
$577$	1.78824e8			0.930890			0.465445	+	0.885077i	$0.345894\pi$
$578$		−	9.23205e7i		−	0.478096i
$579$	2.58201e7			0.133022
$580$	−5.34415e7			−0.273902
$581$			3.28600e7i			0.167548i
$582$	6.56432e7			0.332982
$583$		−	1.14280e8i		−	0.576720i
$584$	3.53597e7			0.177529
$585$			5.83390e7i			0.291401i
$586$		−	1.72428e8i		−	0.856869i
$587$			1.98303e8i			0.980428i	0.871602	+	0.490214i	$0.163081\pi$
$587$			1.98303e8i			0.980428i	−0.871602	+	0.490214i	$0.836919\pi$
$588$	6.30955e7			0.310360
$589$			2.33613e7i			0.114327i
$590$	2.27723e8	+	3.44098e7i	1.10879	+	0.167543i
$591$	−1.06200e8			−0.514474
$592$			6.66602e7i			0.321293i
$593$	1.33160e8			0.638574			0.319287	−	0.947658i	$-0.396557\pi$
$593$	1.33160e8			0.638574			0.319287	+	0.947658i	$0.396557\pi$
$594$	−1.09365e7			−0.0521817
$595$	−3.06788e8			−1.45642
$596$		−	6.94247e6i		−	0.0327925i
$597$	−8.48801e6			−0.0398917
$598$			5.53902e7i			0.259018i
$599$	2.83893e8			1.32091			0.660457	−	0.750864i	$-0.270363\pi$
$599$	2.83893e8			1.32091			0.660457	+	0.750864i	$0.270363\pi$
$600$			1.10930e8i			0.513564i
$601$			3.04660e8i			1.40344i	0.712455	+	0.701718i	$0.247583\pi$
$601$			3.04660e8i			1.40344i	−0.712455	+	0.701718i	$0.752417\pi$
$602$	−2.58929e8			−1.18684
$603$			9.26338e7i			0.422491i
$604$		−	1.19295e8i		−	0.541392i
$605$	2.66818e8			1.20489
$606$	−1.67423e8			−0.752312
$607$	−4.18672e8			−1.87201			−0.936005	−	0.351986i	$-0.885506\pi$
$607$	−4.18672e8			−1.87201			−0.936005	+	0.351986i	$0.885506\pi$
$608$		−	9.32032e6i		−	0.0414687i
$609$	−1.42450e8			−0.630684
$610$	7.67710e7			0.338226
$611$	2.70374e8			1.18533
$612$	−1.53520e7			−0.0669748
$613$			9.05013e7i			0.392892i	0.980515	+	0.196446i	$0.0629401\pi$
$613$			9.05013e7i			0.392892i	−0.980515	+	0.196446i	$0.937060\pi$
$614$		−	3.41489e8i		−	1.47527i
$615$	−3.83937e7			−0.165057
$616$	−1.37351e8			−0.587612
$617$	5.67251e7			0.241501			0.120751	−	0.992683i	$-0.461470\pi$
$617$	5.67251e7			0.241501			0.120751	+	0.992683i	$0.461470\pi$
$618$	8.31529e7			0.352300
$619$	−2.52861e8			−1.06613			−0.533065	−	0.846074i	$-0.678960\pi$
$619$	−2.52861e8			−1.06613			−0.533065	+	0.846074i	$0.678960\pi$
$620$		−	1.61461e8i		−	0.677474i
$621$		−	2.21327e7i		−	0.0924185i
$622$		−	1.27109e6i		−	0.00528208i
$623$			4.50172e8i			1.86172i
$624$		−	5.42994e7i		−	0.223481i
$625$	−2.80564e8			−1.14919
$626$	3.52177e8			1.43562
$627$		−	3.25199e6i		−	0.0131931i
$628$		−	8.31465e7i		−	0.335710i
$629$			8.73441e7i			0.350979i
$630$			1.54844e8i			0.619259i
$631$	3.87969e8			1.54422			0.772110	−	0.635489i	$-0.219201\pi$
$631$	3.87969e8			1.54422			0.772110	+	0.635489i	$0.219201\pi$
$632$			2.77573e7i			0.109958i
$633$		−	3.13069e7i		−	0.123432i
$634$		−	1.71512e8i		−	0.673016i
$635$	4.78544e8			1.86896
$636$	−8.09683e7			−0.314734
$637$			2.92411e8i			1.13130i
$638$	4.64294e7			0.178785
$639$	−8.02698e7			−0.307645
$640$		−	1.11060e8i		−	0.423659i
$641$	−7.22759e7			−0.274422			−0.137211	−	0.990542i	$-0.543814\pi$
$641$	−7.22759e7			−0.274422			−0.137211	+	0.990542i	$0.543814\pi$
$642$			1.95676e7i			0.0739491i
$643$	3.34141e8			1.25689			0.628445	−	0.777854i	$-0.283692\pi$
$643$	3.34141e8			1.25689			0.628445	+	0.777854i	$0.283692\pi$
$644$		−	6.54735e7i		−	0.245136i
$645$			1.79884e8i			0.670367i
$646$			1.02504e7i			0.0380227i
$647$	−7.18958e7			−0.265455			−0.132727	−	0.991153i	$-0.542373\pi$
$647$	−7.18958e7			−0.265455			−0.132727	+	0.991153i	$0.542373\pi$
$648$			3.28962e7i			0.120898i
$649$	8.81085e7	+	1.33136e7i	0.322317	+	0.0487035i
$650$	−1.21093e8			−0.440941
$651$		−	4.30381e8i		−	1.55995i
$652$	−1.11088e8			−0.400797
$653$	−4.95669e8			−1.78013			−0.890065	−	0.455833i	$-0.849341\pi$
$653$	−4.95669e8			−1.78013			−0.890065	+	0.455833i	$0.849341\pi$
$654$	−1.42745e7			−0.0510304
$655$		−	1.77449e8i		−	0.631467i
$656$	3.57352e7			0.126586
$657$		−	1.54235e7i		−	0.0543858i
$658$	7.17628e8			2.51896
$659$			2.59687e8i			0.907391i	0.891157	+	0.453696i	$0.149895\pi$
$659$			2.59687e8i			0.907391i	−0.891157	+	0.453696i	$0.850105\pi$
$660$			2.24761e7i			0.0781788i
$661$	−4.06459e8			−1.40738			−0.703691	−	0.710506i	$-0.748466\pi$
$661$	−4.06459e8			−1.40738			−0.703691	+	0.710506i	$0.748466\pi$
$662$			1.53671e8i			0.529687i
$663$		−	7.11479e7i		−	0.244130i
$664$	−3.22155e7			−0.110043
$665$	−4.60432e7			−0.156567
$666$	4.40849e7			0.149234
$667$			9.39614e7i			0.316645i
$668$	8.33006e7			0.279459
$669$	−1.74084e8			−0.581408
$670$	−4.27479e8			−1.42132
$671$	2.97036e7			0.0983199
$672$			1.71707e8i			0.565821i
$673$		−	5.55778e7i		−	0.182329i	−0.995836	−	0.0911645i	$-0.970941\pi$
$673$		−	5.55778e7i		−	0.182329i	0.995836	−	0.0911645i	$-0.0290589\pi$
$674$	−1.85516e8			−0.605900
$675$	4.83862e7			0.157329
$676$	5.51609e7			0.178563
$677$	1.89135e8			0.609545			0.304772	−	0.952425i	$-0.401420\pi$
$677$	1.89135e8			0.609545			0.304772	+	0.952425i	$0.401420\pi$
$678$	−9.88434e7			−0.317146
$679$		−	3.59599e8i		−	1.14871i
$680$		−	3.00771e8i		−	0.956552i
$681$		−	1.31503e8i		−	0.416386i
$682$			1.40276e8i			0.442211i
$683$			4.05073e8i			1.27137i	0.771949	+	0.635684i	$0.219282\pi$
$683$			4.05073e8i			1.27137i	−0.771949	+	0.635684i	$0.780718\pi$
$684$	−2.30406e6			−0.00719989
$685$	6.37060e8			1.98202
$686$			3.31256e8i			1.02611i
$687$			5.56803e7i			0.171724i
$688$		−	1.67428e8i		−	0.514118i
$689$		−	3.75242e8i		−	1.14724i
$690$	1.02136e8			0.310909
$691$		−	1.33571e8i		−	0.404835i	−0.979299	−	0.202418i	$-0.935120\pi$
$691$		−	1.33571e8i		−	0.404835i	0.979299	−	0.202418i	$-0.0648798\pi$
$692$		−	6.93970e7i		−	0.209422i
$693$			5.99109e7i			0.180014i
$694$	2.11542e8			0.632876
$695$	3.82084e8			1.13816
$696$		−	1.39657e8i		−	0.414222i
$697$	4.68234e7			0.138282
$698$	−1.60641e8			−0.472379
$699$			2.33684e8i			0.684223i
$700$	1.43137e8			0.417310
$701$		−	1.26831e8i		−	0.368190i	−0.982908	−	0.184095i	$-0.941065\pi$
$701$		−	1.26831e8i		−	0.368190i	0.982908	−	0.184095i	$-0.0589355\pi$
$702$	−3.59102e7			−0.103802
$703$			1.31088e7i			0.0377308i
$704$		−	1.23859e8i		−	0.354985i
$705$		−	4.98553e8i		−	1.42280i
$706$	3.84279e8			1.09202
$707$			9.17158e8i			2.59529i
$708$	9.43275e6	−	6.24255e7i	0.0265790	−	0.175899i
$709$	4.76626e8			1.33733			0.668666	−	0.743563i	$-0.266866\pi$
$709$	4.76626e8			1.33733			0.668666	+	0.743563i	$0.266866\pi$
$710$		−	3.70423e8i		−	1.03496i
$711$	1.21074e7			0.0336854
$712$	−4.41343e8			−1.22275
$713$	−2.83883e8			−0.783195
$714$		−	1.88841e8i		−	0.518803i
$715$	−1.04164e8			−0.284970
$716$			1.97779e8i			0.538818i
$717$	−1.10497e8			−0.299772
$718$		−	3.19549e8i		−	0.863304i
$719$		−	2.32671e8i		−	0.625972i	−0.949758	−	0.312986i	$-0.898671\pi$
$719$		−	2.32671e8i		−	0.625972i	0.949758	−	0.312986i	$-0.101329\pi$
$720$	−1.00125e8			−0.268253
$721$		−	4.55518e8i		−	1.21535i
$722$		−	3.11520e8i		−	0.827703i
$723$	3.85746e8			1.02067
$724$	−1.00711e8			−0.265377
$725$	−2.05417e8			−0.539042
$726$			1.64238e8i			0.429205i
$727$	−2.98682e8			−0.777332			−0.388666	−	0.921379i	$-0.627064\pi$
$727$	−2.98682e8			−0.777332			−0.388666	+	0.921379i	$0.627064\pi$
$728$	−4.50996e8			−1.16890
$729$	1.43489e7			0.0370370
$730$	7.11751e7			0.182961
$731$		−	2.19379e8i		−	0.561620i
$732$		−	2.10452e7i		−	0.0536562i
$733$	−3.16957e8			−0.804801			−0.402401	−	0.915464i	$-0.631824\pi$
$733$	−3.16957e8			−0.804801			−0.402401	+	0.915464i	$0.631824\pi$
$734$	4.78939e8			1.21113
$735$	5.39189e8			1.35794
$736$	1.13259e8			0.284079
$737$	−1.65397e8			−0.413166
$738$		−	2.36330e7i		−	0.0587963i
$739$		−	3.58559e8i		−	0.888438i	−0.895918	−	0.444219i	$-0.853481\pi$
$739$		−	3.58559e8i		−	0.888438i	0.895918	−	0.444219i	$-0.146519\pi$
$740$		−	9.06010e7i		−	0.223582i
$741$		−	1.06780e7i		−	0.0262443i
$742$		−	9.95970e8i		−	2.43800i
$743$	−6.56381e8			−1.60026			−0.800128	−	0.599829i	$-0.795235\pi$
$743$	−6.56381e8			−1.60026			−0.800128	+	0.599829i	$0.795235\pi$
$744$	4.21940e8			1.02455
$745$		−	5.93276e7i		−	0.143479i
$746$		−	8.86496e6i		−	0.0213531i
$747$			1.40520e7i			0.0337114i
$748$		−	2.74109e7i		−	0.0654967i
$749$	1.07193e8			0.255106
$750$		−	4.98448e7i		−	0.118151i
$751$			5.00869e8i			1.18251i	0.806485	+	0.591254i	$0.201367\pi$
$751$			5.00869e8i			1.18251i	−0.806485	+	0.591254i	$0.798633\pi$
$752$			4.64031e8i			1.09117i
$753$	7.36700e7			0.172546
$754$	1.52452e8			0.355647
$755$		−	1.01945e9i		−	2.36878i
$756$	4.24473e7			0.0982392
$757$	−4.64421e8			−1.07059			−0.535296	−	0.844664i	$-0.679800\pi$
$757$	−4.64421e8			−1.07059			−0.535296	+	0.844664i	$0.679800\pi$
$758$			5.16935e7i			0.118694i
$759$	3.95177e7			0.0903788
$760$		−	4.51402e7i		−	0.102831i
$761$	2.78011e8			0.630823			0.315412	−	0.948955i	$-0.397857\pi$
$761$	2.78011e8			0.630823			0.315412	+	0.948955i	$0.397857\pi$
$762$			2.94565e8i			0.665758i
$763$			7.81971e7i			0.176042i
$764$			2.03611e8i			0.456584i
$765$	−1.31192e8			−0.293038
$766$			6.52121e7i			0.145091i
$767$	2.89306e8	+	4.37154e7i	0.641168	+	0.0968831i
$768$	−2.16442e8			−0.477814
$769$		−	7.91607e8i		−	1.74073i	−0.492410	−	0.870363i	$-0.663884\pi$
$769$		−	7.91607e8i		−	1.74073i	0.492410	−	0.870363i	$-0.336116\pi$
$770$	−2.76472e8			−0.605591
$771$	−3.01414e8			−0.657658
$772$	3.26633e7			0.0709918
$773$		−	3.12941e8i		−	0.677523i	−0.940872	−	0.338761i	$-0.889992\pi$
$773$		−	3.12941e8i		−	0.677523i	0.940872	−	0.338761i	$-0.110008\pi$
$774$	−1.10726e8			−0.238796
$775$		−	6.20620e8i		−	1.33328i
$776$	3.52546e8			0.754450
$777$		−	2.41500e8i		−	0.514819i
$778$		−	2.58832e8i		−	0.549640i
$779$	7.02734e6			0.0148655
$780$			7.38008e7i			0.155517i
$781$		−	1.43321e8i		−	0.300855i
$782$	−1.24561e8			−0.260473
$783$	−6.09164e7			−0.126896
$784$	−5.01854e8			−1.04143
$785$		−	7.10537e8i		−	1.46885i
$786$	1.09228e8			0.224940
$787$	−4.78158e8			−0.980950			−0.490475	−	0.871455i	$-0.663177\pi$
$787$	−4.78158e8			−0.980950			−0.490475	+	0.871455i	$0.663177\pi$
$788$	−1.34347e8			−0.274568
$789$	5.17162e8			1.05292
$790$			5.58723e7i			0.113322i
$791$			5.41472e8i			1.09407i
$792$	−5.87359e7			−0.118230
$793$	9.75325e7			0.195582
$794$	3.40559e8			0.680348
$795$	−6.91923e8			−1.37707
$796$	−1.07376e7			−0.0212897
$797$		−	7.02073e8i		−	1.38678i	−0.720563	−	0.693389i	$-0.756117\pi$
$797$		−	7.02073e8i		−	1.38678i	0.720563	−	0.693389i	$-0.243883\pi$
$798$		−	2.83416e7i		−	0.0557720i
$799$			6.08015e8i			1.19199i
$800$			2.47606e8i			0.483605i
$801$			1.92508e8i			0.374586i
$802$	2.01302e8			0.390233
$803$	2.75385e7			0.0531855
$804$			1.17185e8i			0.225478i
$805$		−	5.59510e8i		−	1.07256i
$806$			4.60599e8i			0.879665i
$807$			5.75744e8i			1.09549i
$808$	−8.99170e8			−1.70454
$809$		−	2.04443e8i		−	0.386124i	−0.981187	−	0.193062i	$-0.938158\pi$
$809$		−	2.04443e8i		−	0.386124i	0.981187	−	0.193062i	$-0.0618419\pi$
$810$			6.62163e7i			0.124598i
$811$			4.79939e8i			0.899753i	0.893091	+	0.449877i	$0.148532\pi$
$811$			4.79939e8i			0.899753i	−0.893091	+	0.449877i	$0.851468\pi$
$812$	−1.80205e8			−0.336587
$813$	1.47829e8			0.275098
$814$			7.87132e7i			0.145940i
$815$	−9.49315e8			−1.75363
$816$	1.22108e8			0.224737
$817$		−	3.29248e7i		−	0.0603749i
$818$	3.27726e8			0.598757
$819$			1.96719e8i			0.358092i
$820$	−4.85694e7			−0.0880888
$821$			4.07583e8i			0.736524i	0.929722	+	0.368262i	$0.120047\pi$
$821$			4.07583e8i			0.736524i	−0.929722	+	0.368262i	$0.879953\pi$
$822$			3.92139e8i			0.706032i
$823$			9.34559e8i			1.67651i	0.545276	+	0.838257i	$0.316425\pi$
$823$			9.34559e8i			1.67651i	−0.545276	+	0.838257i	$0.683575\pi$
$824$	4.46584e8			0.798218
$825$			8.63931e7i			0.153857i
$826$	7.67880e8	+	1.16030e8i	1.36255	+	0.205887i
$827$	−9.49005e8			−1.67785			−0.838923	−	0.544250i	$-0.816814\pi$
$827$	−9.49005e8			−1.67785			−0.838923	+	0.544250i	$0.816814\pi$
$828$		−	2.79986e7i		−	0.0493225i
$829$	−8.62590e8			−1.51405			−0.757026	−	0.653385i	$-0.773348\pi$
$829$	−8.62590e8			−1.51405			−0.757026	+	0.653385i	$0.773348\pi$
$830$	−6.48462e7			−0.113410
$831$	3.16164e8			0.550947
$832$		−	4.06694e8i		−	0.706152i
$833$	−6.57573e8			−1.13765
$834$			2.35189e8i			0.405433i
$835$	7.11854e8			1.22273
$836$		−	4.11388e6i		−	0.00704098i
$837$		−	1.84045e8i		−	0.313868i
$838$	4.99498e8			0.848793
$839$			1.02168e9i			1.72993i	0.501832	+	0.864965i	$0.332660\pi$
$839$			1.02168e9i			1.72993i	−0.501832	+	0.864965i	$0.667340\pi$
$840$			8.31610e8i			1.40308i
$841$	−3.36210e8			−0.565227
$842$	−1.54760e7			−0.0259253
$843$	8.03275e7			0.134085
$844$		−	3.96043e7i		−	0.0658741i
$845$	4.71383e8			0.781275
$846$	3.06881e8			0.506826
$847$	8.99710e8			1.48065
$848$	6.44012e8			1.05610
$849$			5.37730e8i			0.878701i
$850$		−	2.72314e8i		−	0.443418i
$851$	−1.59296e8			−0.258473
$852$	−1.01544e8			−0.164186
$853$	−2.98558e8			−0.481040			−0.240520	−	0.970644i	$-0.577318\pi$
$853$	−2.98558e8			−0.481040			−0.240520	+	0.970644i	$0.577318\pi$
$854$	2.58872e8			0.415634
$855$	−1.96896e7			−0.0315020
$856$			1.05091e8i			0.167549i
$857$			7.59597e8i			1.20681i	0.797433	+	0.603407i	$0.206191\pi$
$857$			7.59597e8i			1.20681i	−0.797433	+	0.603407i	$0.793809\pi$
$858$		−	6.41174e7i		−	0.101511i
$859$		−	7.05646e8i		−	1.11329i	−0.830751	−	0.556644i	$-0.812089\pi$
$859$		−	7.05646e8i		−	1.11329i	0.830751	−	0.556644i	$-0.187911\pi$
$860$			2.27559e8i			0.357766i
$861$	−1.29464e8			−0.202833
$862$	1.37625e8			0.214870
$863$			8.60792e8i			1.33926i	0.742694	+	0.669631i	$0.233548\pi$
$863$			8.60792e8i			1.33926i	−0.742694	+	0.669631i	$0.766452\pi$
$864$			7.34274e7i			0.113846i
$865$		−	5.93039e8i		−	0.916295i
$866$			6.30905e8i			0.971427i
$867$	−2.16270e8			−0.331849
$868$		−	5.44446e8i		−	0.832522i
$869$			2.16176e7i			0.0329419i
$870$		−	2.81113e8i		−	0.426897i
$871$	−5.43084e8			−0.821889
$872$	−7.66634e7			−0.115621
$873$		−	1.53776e8i		−	0.231125i
$874$	−1.86944e7			−0.0280012
$875$	−2.73054e8			−0.407591
$876$		−	1.95112e7i		−	0.0290250i
$877$	−1.01938e9			−1.51126			−0.755630	−	0.654999i	$-0.772669\pi$
$877$	−1.01938e9			−1.51126			−0.755630	+	0.654999i	$0.772669\pi$
$878$		−	1.15273e8i		−	0.170312i
$879$	−4.03930e8			−0.594757
$880$		−	1.78772e8i		−	0.262332i
$881$		−	8.47546e8i		−	1.23947i	−0.784812	−	0.619734i	$-0.787240\pi$
$881$		−	8.47546e8i		−	1.23947i	0.784812	−	0.619734i	$-0.212760\pi$
$882$			3.31895e8i			0.483720i
$883$	1.07160e9			1.55651			0.778254	−	0.627950i	$-0.216106\pi$
$883$	1.07160e9			1.55651			0.778254	+	0.627950i	$0.216106\pi$
$884$		−	9.00045e7i		−	0.130289i
$885$	8.06086e7	−	5.33464e8i	0.116292	−	0.769618i
$886$	2.13311e7			0.0306699
$887$			4.74911e8i			0.680520i	0.940331	+	0.340260i	$0.110515\pi$
$887$			4.74911e8i			0.680520i	−0.940331	+	0.340260i	$0.889485\pi$
$888$	2.36764e8			0.338124
$889$	1.61365e9			2.29670
$890$	−8.88373e8			−1.26016
$891$			2.56199e7i			0.0362196i
$892$	−2.20223e8			−0.310290
$893$			9.12519e7i			0.128141i
$894$	3.65187e7			0.0511097
$895$			1.69014e9i			2.35752i
$896$		−	3.74493e8i		−	0.520618i
$897$	1.29757e8			0.179786
$898$			2.53912e8i			0.350634i
$899$			7.81339e8i			1.07538i
$900$	6.12102e7			0.0839645
$901$	8.43841e8			1.15368
$902$	4.21966e7			0.0574986
$903$			6.06567e8i			0.823789i
$904$	−5.30852e8			−0.718568
$905$	−8.60640e8			−1.16112
$906$	6.27516e8			0.843801
$907$	8.35818e8			1.12018			0.560092	−	0.828430i	$-0.310766\pi$
$907$	8.35818e8			1.12018			0.560092	+	0.828430i	$0.310766\pi$
$908$		−	1.66356e8i		−	0.222219i
$909$			3.92207e8i			0.522184i
$910$	−9.07804e8			−1.20467
$911$	−1.33831e7			−0.0177011			−0.00885055	−	0.999961i	$-0.502817\pi$
$911$	−1.33831e7			−0.0177011			−0.00885055	+	0.999961i	$0.502817\pi$
$912$	1.83262e7			0.0241595
$913$	−2.50898e7			−0.0329674
$914$	−8.14585e7			−0.106684
$915$		−	1.79844e8i		−	0.234765i
$916$			7.04375e7i			0.0916468i
$917$		−	5.98359e8i		−	0.775986i
$918$		−	8.07547e7i		−	0.104385i
$919$			1.02914e9i			1.32596i	0.748638	+	0.662979i	$0.230708\pi$
$919$			1.02914e9i			1.32596i	−0.748638	+	0.662979i	$0.769292\pi$
$920$	5.48537e8			0.704437
$921$	−7.99974e8			−1.02399
$922$		−	7.52659e8i		−	0.960297i
$923$		−	4.70598e8i		−	0.598474i
$924$			7.57893e7i			0.0960710i
$925$		−	3.48250e8i		−	0.440013i
$926$	−7.08655e8			−0.892487
$927$		−	1.94794e8i		−	0.244533i
$928$		−	3.11727e8i		−	0.390059i
$929$		−	5.47096e8i		−	0.682364i	−0.939997	−	0.341182i	$-0.889173\pi$
$929$		−	5.47096e8i		−	0.682364i	0.939997	−	0.341182i	$-0.110827\pi$
$930$	8.49316e8			1.05589
$931$	−9.86898e7			−0.122299
$932$			2.95618e8i			0.365161i
$933$	−2.97766e6			−0.00366632
$934$	−2.36900e8			−0.290753
$935$		−	2.34243e8i		−	0.286571i
$936$	−1.92861e8			−0.235189
$937$		−	7.06068e6i		−	0.00858278i	−0.999991	−	0.00429139i	$-0.998634\pi$
$937$		−	7.06068e6i		−	0.00858278i	0.999991	−	0.00429139i	$-0.00136600\pi$
$938$	−1.44146e9			−1.74660
$939$		−	8.25012e8i		−	0.996468i
$940$		−	6.30686e8i		−	0.759328i
$941$		−	8.79465e8i		−	1.05548i	−0.849406	−	0.527740i	$-0.823040\pi$
$941$		−	8.79465e8i		−	1.05548i	0.849406	−	0.527740i	$-0.176960\pi$
$942$	4.37367e8			0.523230
$943$			8.53952e7i			0.101835i
$944$	−7.50270e7	+	4.96525e8i	−0.0891870	+	0.590236i
$945$	3.62738e8			0.429831
$946$		−	1.97701e8i		−	0.233526i
$947$	−3.40905e7			−0.0401406			−0.0200703	−	0.999799i	$-0.506389\pi$
$947$	−3.40905e7			−0.0401406			−0.0200703	+	0.999799i	$0.506389\pi$
$948$	1.53163e7			0.0179774
$949$	9.04232e7			0.105799
$950$		−	4.08694e7i		−	0.0476681i
$951$	−4.01784e8			−0.467144
$952$		−	1.01420e9i		−	1.17547i
$953$	1.38270e9			1.59753			0.798764	−	0.601645i	$-0.205488\pi$
$953$	1.38270e9			1.59753			0.798764	+	0.601645i	$0.205488\pi$
$954$		−	4.25909e8i		−	0.490537i
$955$			1.73998e9i			1.99771i
$956$	−1.39782e8			−0.159984
$957$		−	1.08766e8i		−	0.124096i
$958$		−	2.19580e8i		−	0.249744i
$959$	2.14817e9			2.43563
$960$	−7.49920e8			−0.847620
$961$	−1.47313e9			−1.65986
$962$			2.58457e8i			0.290310i
$963$	4.58392e7			0.0513285
$964$	4.87982e8			0.544719
$965$	2.79128e8			0.310614
$966$	3.44403e8			0.382064
$967$			1.55069e9i			1.71492i	0.514548	+	0.857462i	$0.327960\pi$
$967$			1.55069e9i			1.71492i	−0.514548	+	0.857462i	$0.672040\pi$
$968$			8.82064e8i			0.972465i
$969$	2.40126e7			0.0263918
$970$	7.09635e8			0.777535
$971$	9.78420e8			1.06873			0.534365	−	0.845254i	$-0.320551\pi$
$971$	9.78420e8			1.06873			0.534365	+	0.845254i	$0.320551\pi$
$972$	1.81519e7			0.0197662
$973$	1.28838e9			1.39864
$974$			1.07109e9i			1.15918i
$975$			2.83674e8i			0.306059i
$976$			1.67391e8i			0.180046i
$977$		−	1.33799e9i		−	1.43472i	−0.696701	−	0.717362i	$-0.745349\pi$
$977$		−	1.33799e9i		−	1.43472i	0.696701	−	0.717362i	$-0.254651\pi$
$978$		−	5.84345e8i		−	0.624673i
$979$	−3.43722e8			−0.366319
$980$	6.82093e8			0.724711
$981$			3.34396e7i			0.0354205i
$982$		−	6.17638e8i		−	0.652228i
$983$			1.77728e9i			1.87110i	0.353198	+	0.935549i	$0.385094\pi$
$983$			1.77728e9i			1.87110i	−0.353198	+	0.935549i	$0.614906\pi$
$984$		−	1.26924e8i		−	0.133217i
$985$	−1.14808e9			−1.20133
$986$			3.42834e8i			0.357646i
$987$		−	1.68112e9i		−	1.74842i
$988$		−	1.35080e7i		−	0.0140062i
$989$	4.00097e8			0.413596
$990$	−1.18229e8			−0.121848
$991$			1.51518e9i			1.55684i	0.627747	+	0.778418i	$0.283977\pi$
$991$			1.51518e9i			1.55684i	−0.627747	+	0.778418i	$0.716023\pi$
$992$	9.41809e8			0.964779
$993$	3.59991e8			0.367658
$994$		−	1.24907e9i		−	1.27182i
$995$	−9.17595e7			−0.0931498
$996$			1.77763e7i			0.0179913i
$997$	9.43213e7			0.0951753			0.0475877	−	0.998867i	$-0.484847\pi$
$997$	9.43213e7			0.0951753			0.0475877	+	0.998867i	$0.484847\pi$
$998$			1.13036e9i			1.13717i
$999$		−	1.03273e8i		−	0.103584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.41	yes	60
59.58	odd	2	inner	177.7.c.a.58.20	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.20	✓	60	59.58	odd	2	inner
177.7.c.a.58.41	yes	60	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+6.65433i q^{2} +15.5885 q^{3} +19.7199 q^{4} +168.519 q^{5} +103.731i q^{6} +568.245 q^{7} +557.100i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+6.65433i q^{2} +15.5885 q^{3} +19.7199 q^{4} +168.519 q^{5} +103.731i q^{6} +568.245 q^{7} +557.100i q^{8} +243.000 q^{9} +1121.38i q^{10} +433.875i q^{11} +307.403 q^{12} +1424.64i q^{13} +3781.29i q^{14} +2626.95 q^{15} -2445.05 q^{16} -3203.72 q^{17} +1617.00i q^{18} -480.820 q^{19} +3323.18 q^{20} +8858.06 q^{21} -2887.14 q^{22} -5842.85i q^{23} +8684.33i q^{24} +12773.6 q^{25} -9480.00 q^{26} +3788.00 q^{27} +11205.7 q^{28} -16081.4 q^{29} +17480.6i q^{30} -48586.3i q^{31} +19384.2i q^{32} +6763.43i q^{33} -21318.6i q^{34} +95759.9 q^{35} +4791.94 q^{36} -27263.4i q^{37} -3199.53i q^{38} +22207.9i q^{39} +93881.7i q^{40} -14615.3 q^{41} +58944.4i q^{42} +68476.3i q^{43} +8555.98i q^{44} +40950.0 q^{45} +38880.2 q^{46} -189784. i q^{47} -38114.5 q^{48} +205253. q^{49} +84999.4i q^{50} -49941.0 q^{51} +28093.8i q^{52} -263394. q^{53} +25206.6i q^{54} +73116.0i q^{55} +316569. i q^{56} -7495.24 q^{57} -107011. i q^{58} +(30685.3 - 203074. i) q^{59} +51803.2 q^{60} -68461.2i q^{61} +323309. q^{62} +138083. q^{63} -285472. q^{64} +240078. i q^{65} -45006.1 q^{66} +381209. i q^{67} -63177.1 q^{68} -91081.0i q^{69} +637218. i q^{70} -330328. q^{71} +135375. i q^{72} -63471.0i q^{73} +181419. q^{74} +199120. q^{75} -9481.73 q^{76} +246547. i q^{77} -147779. q^{78} +49824.6 q^{79} -412036. q^{80} +59049.0 q^{81} -97255.2i q^{82} +57827.2i q^{83} +174680. q^{84} -539887. q^{85} -455664. q^{86} -250685. q^{87} -241711. q^{88} +792215. i q^{89} +272495. i q^{90} +809543. i q^{91} -115221. i q^{92} -757386. i q^{93} +1.26289e6 q^{94} -81027.1 q^{95} +302170. i q^{96} -632824. i q^{97} +1.36582e6i q^{98} +105432. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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