LMFDB - Embedded newform 287.3.g.a.132.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(132,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("287.132");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.g (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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			132.7
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.19098i q^{2} +(-0.547162 + 0.547162i) q^{3} -6.18236 q^{4} +3.96088 q^{5} +(1.74598 + 1.74598i) q^{6} +(6.79862 + 1.66698i) q^{7} +6.96386i q^{8} +8.40123i q^{9} +O(q^{10})$	\(q-3.19098i q^{2} +(-0.547162 + 0.547162i) q^{3} -6.18236 q^{4} +3.96088 q^{5} +(1.74598 + 1.74598i) q^{6} +(6.79862 + 1.66698i) q^{7} +6.96386i q^{8} +8.40123i q^{9} -12.6391i q^{10} +(5.67402 + 5.67402i) q^{11} +(3.38275 - 3.38275i) q^{12} +(15.7745 - 15.7745i) q^{13} +(5.31931 - 21.6942i) q^{14} +(-2.16724 + 2.16724i) q^{15} -2.50789 q^{16} +(14.0838 + 14.0838i) q^{17} +26.8082 q^{18} +(-8.40723 - 8.40723i) q^{19} -24.4876 q^{20} +(-4.63205 + 2.80783i) q^{21} +(18.1057 - 18.1057i) q^{22} +19.5486 q^{23} +(-3.81036 - 3.81036i) q^{24} -9.31140 q^{25} +(-50.3360 - 50.3360i) q^{26} +(-9.52129 - 9.52129i) q^{27} +(-42.0315 - 10.3059i) q^{28} +(-25.9476 - 25.9476i) q^{29} +(6.91563 + 6.91563i) q^{30} +3.79734i q^{31} +35.8581i q^{32} -6.20921 q^{33} +(44.9410 - 44.9410i) q^{34} +(26.9285 + 6.60272i) q^{35} -51.9394i q^{36} +4.85702 q^{37} +(-26.8273 + 26.8273i) q^{38} +17.2624i q^{39} +27.5830i q^{40} +(9.78616 - 39.8150i) q^{41} +(8.95974 + 14.7808i) q^{42} +25.5372i q^{43} +(-35.0788 - 35.0788i) q^{44} +33.2763i q^{45} -62.3793i q^{46} +(-16.4822 - 16.4822i) q^{47} +(1.37222 - 1.37222i) q^{48} +(43.4423 + 22.6663i) q^{49} +29.7125i q^{50} -15.4122 q^{51} +(-97.5233 + 97.5233i) q^{52} +(-13.2206 - 13.2206i) q^{53} +(-30.3822 + 30.3822i) q^{54} +(22.4741 + 22.4741i) q^{55} +(-11.6086 + 47.3446i) q^{56} +9.20023 q^{57} +(-82.7982 + 82.7982i) q^{58} +39.6785i q^{59} +(13.3987 - 13.3987i) q^{60} -39.1105 q^{61} +12.1173 q^{62} +(-14.0047 + 57.1167i) q^{63} +104.391 q^{64} +(62.4808 - 62.4808i) q^{65} +19.8135i q^{66} +(1.90926 - 1.90926i) q^{67} +(-87.0708 - 87.0708i) q^{68} +(-10.6963 + 10.6963i) q^{69} +(21.0692 - 85.9284i) q^{70} +(-30.1744 - 30.1744i) q^{71} -58.5050 q^{72} +57.8527 q^{73} -15.4987i q^{74} +(5.09484 - 5.09484i) q^{75} +(51.9765 + 51.9765i) q^{76} +(29.1170 + 48.0340i) q^{77} +55.0838 q^{78} +(92.2195 + 92.2195i) q^{79} -9.93347 q^{80} -65.1917 q^{81} +(-127.049 - 31.2274i) q^{82} -87.6716i q^{83} +(28.6370 - 17.3590i) q^{84} +(55.7841 + 55.7841i) q^{85} +81.4887 q^{86} +28.3950 q^{87} +(-39.5131 + 39.5131i) q^{88} +(62.0487 - 62.0487i) q^{89} +106.184 q^{90} +(133.540 - 80.9487i) q^{91} -120.857 q^{92} +(-2.07776 - 2.07776i) q^{93} +(-52.5943 + 52.5943i) q^{94} +(-33.3001 - 33.3001i) q^{95} +(-19.6202 - 19.6202i) q^{96} +(117.168 + 117.168i) q^{97} +(72.3279 - 138.624i) q^{98} +(-47.6687 + 47.6687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) $ 108 * q - 216 * q^4 - 2 * q^7	$ 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) $ 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	3.19098i		−	1.59549i	−0.602995	−	0.797745i	$-0.706026\pi$
$2$		−	3.19098i		−	1.59549i	0.602995	−	0.797745i	$-0.293974\pi$
$3$	−0.547162	+	0.547162i	−0.182387	+	0.182387i	−0.792395	−	0.610008i	$-0.791166\pi$
$3$	−0.547162	+	0.547162i	−0.182387	+	0.182387i	0.610008	+	0.792395i	$0.291166\pi$
$4$	−6.18236			−1.54559
$5$	3.96088			0.792177			0.396088	−	0.918212i	$-0.370367\pi$
$5$	3.96088			0.792177			0.396088	+	0.918212i	$0.370367\pi$
$6$	1.74598	+	1.74598i	0.290997	+	0.290997i
$7$	6.79862	+	1.66698i	0.971231	+	0.238140i
$7$	6.79862	+	1.66698i	0.971231	+	0.238140i
$8$			6.96386i			0.870482i
$9$			8.40123i			0.933470i
$10$		−	12.6391i		−	1.26391i
$11$	5.67402	+	5.67402i	0.515820	+	0.515820i	0.916304	−	0.400484i	$-0.131158\pi$
$11$	5.67402	+	5.67402i	0.515820	+	0.515820i	−0.400484	+	0.916304i	$0.631158\pi$
$12$	3.38275	−	3.38275i	0.281896	−	0.281896i
$13$	15.7745	−	15.7745i	1.21342	−	1.21342i	0.243525	−	0.969895i	$-0.421696\pi$
$13$	15.7745	−	15.7745i	1.21342	−	1.21342i	0.969895	−	0.243525i	$-0.0783036\pi$
$14$	5.31931	−	21.6942i	0.379951	−	1.54959i
$15$	−2.16724	+	2.16724i	−0.144483	+	0.144483i
$16$	−2.50789			−0.156743
$17$	14.0838	+	14.0838i	0.828456	+	0.828456i	0.987303	−	0.158847i	$-0.0507777\pi$
$17$	14.0838	+	14.0838i	0.828456	+	0.828456i	−0.158847	+	0.987303i	$0.550778\pi$
$18$	26.8082			1.48934
$19$	−8.40723	−	8.40723i	−0.442486	−	0.442486i	0.450361	−	0.892847i	$-0.351295\pi$
$19$	−8.40723	−	8.40723i	−0.442486	−	0.442486i	−0.892847	+	0.450361i	$0.851295\pi$
$20$	−24.4876			−1.22438
$21$	−4.63205	+	2.80783i	−0.220574	+	0.133706i
$22$	18.1057	−	18.1057i	0.822986	−	0.822986i
$23$	19.5486			0.849941			0.424971	−	0.905207i	$-0.360284\pi$
$23$	19.5486			0.849941			0.424971	+	0.905207i	$0.360284\pi$
$24$	−3.81036	−	3.81036i	−0.158765	−	0.158765i
$25$	−9.31140			−0.372456
$26$	−50.3360	−	50.3360i	−1.93600	−	1.93600i
$27$	−9.52129	−	9.52129i	−0.352640	−	0.352640i
$28$	−42.0315	−	10.3059i	−1.50112	−	0.368067i
$29$	−25.9476	−	25.9476i	−0.894744	−	0.894744i	0.100222	−	0.994965i	$-0.468045\pi$
$29$	−25.9476	−	25.9476i	−0.894744	−	0.894744i	−0.994965	+	0.100222i	$0.968045\pi$
$30$	6.91563	+	6.91563i	0.230521	+	0.230521i
$31$			3.79734i			0.122495i	0.998123	+	0.0612475i	$0.0195079\pi$
$31$			3.79734i			0.122495i	−0.998123	+	0.0612475i	$0.980492\pi$
$32$			35.8581i			1.12056i
$33$	−6.20921			−0.188158
$34$	44.9410	−	44.9410i	1.32179	−	1.32179i
$35$	26.9285	+	6.60272i	0.769386	+	0.188649i
$36$		−	51.9394i		−	1.44276i
$37$	4.85702			0.131271			0.0656354	−	0.997844i	$-0.479093\pi$
$37$	4.85702			0.131271			0.0656354	+	0.997844i	$0.479093\pi$
$38$	−26.8273	+	26.8273i	−0.705982	+	0.705982i
$39$			17.2624i			0.442624i
$40$			27.5830i			0.689576i
$41$	9.78616	−	39.8150i	0.238687	−	0.971097i
$41$	9.78616	−	39.8150i	0.238687	−	0.971097i
$42$	8.95974	+	14.7808i	0.213327	+	0.351923i
$43$			25.5372i			0.593888i	0.954895	+	0.296944i	$0.0959675\pi$
$43$			25.5372i			0.593888i	−0.954895	+	0.296944i	$0.904032\pi$
$44$	−35.0788	−	35.0788i	−0.797246	−	0.797246i
$45$			33.2763i			0.739473i
$46$		−	62.3793i		−	1.35607i
$47$	−16.4822	−	16.4822i	−0.350684	−	0.350684i	0.509680	−	0.860364i	$-0.329764\pi$
$47$	−16.4822	−	16.4822i	−0.350684	−	0.350684i	−0.860364	+	0.509680i	$0.829764\pi$
$48$	1.37222	−	1.37222i	0.0285880	−	0.0285880i
$49$	43.4423	+	22.6663i	0.886578	+	0.462578i
$50$			29.7125i			0.594250i
$51$	−15.4122			−0.302200
$52$	−97.5233	+	97.5233i	−1.87545	+	1.87545i
$53$	−13.2206	−	13.2206i	−0.249446	−	0.249446i	0.571297	−	0.820743i	$-0.306440\pi$
$53$	−13.2206	−	13.2206i	−0.249446	−	0.249446i	−0.820743	+	0.571297i	$0.806440\pi$
$54$	−30.3822	+	30.3822i	−0.562634	+	0.562634i
$55$	22.4741	+	22.4741i	0.408621	+	0.408621i
$56$	−11.6086	+	47.3446i	−0.207297	+	0.845439i
$57$	9.20023			0.161407
$58$	−82.7982	+	82.7982i	−1.42755	+	1.42755i
$59$			39.6785i			0.672516i	0.941770	+	0.336258i	$0.109161\pi$
$59$			39.6785i			0.672516i	−0.941770	+	0.336258i	$0.890839\pi$
$60$	13.3987	−	13.3987i	0.223311	−	0.223311i
$61$	−39.1105			−0.641156			−0.320578	−	0.947222i	$-0.603877\pi$
$61$	−39.1105			−0.641156			−0.320578	+	0.947222i	$0.603877\pi$
$62$	12.1173			0.195440
$63$	−14.0047	+	57.1167i	−0.222297	+	0.906615i
$64$	104.391			1.63111
$65$	62.4808	−	62.4808i	0.961243	−	0.961243i
$66$			19.8135i			0.300204i
$67$	1.90926	−	1.90926i	0.0284965	−	0.0284965i	−0.692715	−	0.721211i	$-0.743586\pi$
$67$	1.90926	−	1.90926i	0.0284965	−	0.0284965i	0.721211	+	0.692715i	$0.243586\pi$
$68$	−87.0708	−	87.0708i	−1.28045	−	1.28045i
$69$	−10.6963	+	10.6963i	−0.155018	+	0.155018i
$70$	21.0692	−	85.9284i	0.300988	−	1.22755i
$71$	−30.1744	−	30.1744i	−0.424991	−	0.424991i	0.461927	−	0.886918i	$-0.347158\pi$
$71$	−30.1744	−	30.1744i	−0.424991	−	0.424991i	−0.886918	+	0.461927i	$0.847158\pi$
$72$	−58.5050			−0.812569
$73$	57.8527			0.792502			0.396251	−	0.918142i	$-0.370311\pi$
$73$	57.8527			0.792502			0.396251	+	0.918142i	$0.370311\pi$
$74$		−	15.4987i		−	0.209441i
$75$	5.09484	−	5.09484i	0.0679312	−	0.0679312i
$76$	51.9765	+	51.9765i	0.683901	+	0.683901i
$77$	29.1170	+	48.0340i	0.378143	+	0.623818i
$78$	55.0838			0.706203
$79$	92.2195	+	92.2195i	1.16734	+	1.16734i	0.982832	+	0.184504i	$0.0590680\pi$
$79$	92.2195	+	92.2195i	1.16734	+	1.16734i	0.184504	+	0.982832i	$0.440932\pi$
$80$	−9.93347			−0.124168
$81$	−65.1917			−0.804836
$82$	−127.049	−	31.2274i	−1.54938	−	0.380822i
$83$		−	87.6716i		−	1.05628i	−0.849156	−	0.528142i	$-0.822889\pi$
$83$		−	87.6716i		−	1.05628i	0.849156	−	0.528142i	$-0.177111\pi$
$84$	28.6370	−	17.3590i	0.340917	−	0.206655i
$85$	55.7841	+	55.7841i	0.656284	+	0.656284i
$86$	81.4887			0.947543
$87$	28.3950			0.326380
$88$	−39.5131	+	39.5131i	−0.449012	+	0.449012i
$89$	62.0487	−	62.0487i	0.697176	−	0.697176i	−0.266624	−	0.963801i	$-0.585908\pi$
$89$	62.0487	−	62.0487i	0.697176	−	0.697176i	0.963801	+	0.266624i	$0.0859083\pi$
$90$	106.184			1.17982
$91$	133.540	−	80.9487i	1.46747	−	0.889546i
$92$	−120.857			−1.31366
$93$	−2.07776	−	2.07776i	−0.0223415	−	0.0223415i
$94$	−52.5943	+	52.5943i	−0.559514	+	0.559514i
$95$	−33.3001	−	33.3001i	−0.350527	−	0.350527i
$96$	−19.6202	−	19.6202i	−0.204377	−	0.204377i
$97$	117.168	+	117.168i	1.20791	+	1.20791i	0.971701	+	0.236213i	$0.0759062\pi$
$97$	117.168	+	117.168i	1.20791	+	1.20791i	0.236213	+	0.971701i	$0.424094\pi$
$98$	72.3279	−	138.624i	0.738039	−	1.41453i
$99$	−47.6687	+	47.6687i	−0.481502	+	0.481502i
$100$	57.5664			0.575664
$101$	−114.204	−	114.204i	−1.13073	−	1.13073i	−0.990055	−	0.140678i	$-0.955072\pi$
$101$	−114.204	−	114.204i	−1.13073	−	1.13073i	−0.140678	−	0.990055i	$-0.544928\pi$
$102$			49.1800i			0.482156i
$103$	−21.3967			−0.207735			−0.103867	−	0.994591i	$-0.533122\pi$
$103$	−21.3967			−0.207735			−0.103867	+	0.994591i	$0.533122\pi$
$104$	109.851	+	109.851i	1.05626	+	1.05626i
$105$	−18.3470	+	11.1215i	−0.174733	+	0.105919i
$106$	−42.1868	+	42.1868i	−0.397989	+	0.397989i
$107$	−37.6147			−0.351539			−0.175770	−	0.984431i	$-0.556241\pi$
$107$	−37.6147			−0.351539			−0.175770	+	0.984431i	$0.556241\pi$
$108$	58.8640	+	58.8640i	0.545037	+	0.545037i
$109$	−112.619	+	112.619i	−1.03320	+	1.03320i	−0.0337719	+	0.999430i	$0.510752\pi$
$109$	−112.619	+	112.619i	−1.03320	+	1.03320i	−0.999430	+	0.0337719i	$0.989248\pi$
$110$	71.7145	−	71.7145i	0.651950	−	0.651950i
$111$	−2.65758	+	2.65758i	−0.0239421	+	0.0239421i
$112$	−17.0502	−	4.18061i	−0.152234	−	0.0373269i
$113$	83.7110			0.740805			0.370402	−	0.928871i	$-0.379220\pi$
$113$	83.7110			0.740805			0.370402	+	0.928871i	$0.379220\pi$
$114$		−	29.3577i		−	0.257524i
$115$	77.4299			0.673304
$116$	160.417	+	160.417i	1.38291	+	1.38291i
$117$	132.525	+	132.525i	1.13269	+	1.13269i
$118$	126.613			1.07299
$119$	72.2726	+	119.227i	0.607333	+	1.00191i
$120$	−15.0924	−	15.0924i	−0.125770	−	0.125770i
$121$		−	56.6110i		−	0.467860i
$122$			124.801i			1.02296i
$123$	16.4306	+	27.1398i	0.133582	+	0.220649i
$124$		−	23.4765i		−	0.189327i
$125$	−135.903			−1.08723
$126$	182.258	+	44.6887i	1.44649	+	0.354672i
$127$	−173.547			−1.36652			−0.683258	−	0.730177i	$-0.739437\pi$
$127$	−173.547			−1.36652			−0.683258	+	0.730177i	$0.739437\pi$
$128$		−	189.677i		−	1.48185i
$129$	−13.9730	−	13.9730i	−0.108318	−	0.108318i
$130$	−199.375	−	199.375i	−1.53365	−	1.53365i
$131$	−235.410			−1.79702			−0.898511	−	0.438951i	$-0.855350\pi$
$131$	−235.410			−1.79702			−0.898511	+	0.438951i	$0.855350\pi$
$132$	38.3876			0.290815
$133$	−43.1428	−	71.1722i	−0.324382	−	0.535129i
$134$	−6.09243	−	6.09243i	−0.0454659	−	0.0454659i
$135$	−37.7127	−	37.7127i	−0.279353	−	0.279353i
$136$	−98.0772	+	98.0772i	−0.721156	+	0.721156i
$137$	46.0139	−	46.0139i	0.335868	−	0.335868i	−0.518942	−	0.854810i	$-0.673674\pi$
$137$	46.0139	−	46.0139i	0.335868	−	0.335868i	0.854810	+	0.518942i	$0.173674\pi$
$138$	34.1316	+	34.1316i	0.247330	+	0.247330i
$139$			251.182i			1.80707i	0.428516	+	0.903534i	$0.359036\pi$
$139$			251.182i			1.80707i	−0.428516	+	0.903534i	$0.640964\pi$
$140$	−166.482	−	40.8204i	−1.18916	−	0.291574i
$141$	18.0368			0.127921
$142$	−96.2858	+	96.2858i	−0.678069	+	0.678069i
$143$	179.009			1.25181
$144$		−	21.0694i		−	0.146315i
$145$	−102.775	−	102.775i	−0.708795	−	0.708795i
$146$		−	184.607i		−	1.26443i
$147$	−36.1721	+	11.3678i	−0.246069	+	0.0773322i
$148$	−30.0278			−0.202891
$149$	−148.077	+	148.077i	−0.993802	+	0.993802i	−0.999981	−	0.00617858i	$-0.998033\pi$
$149$	−148.077	+	148.077i	−0.993802	+	0.993802i	0.00617858	+	0.999981i	$0.498033\pi$
$150$	−16.2575	−	16.2575i	−0.108384	−	0.108384i
$151$	168.550	+	168.550i	1.11622	+	1.11622i	0.992291	+	0.123932i	$0.0395506\pi$
$151$	168.550	+	168.550i	1.11622	+	1.11622i	0.123932	+	0.992291i	$0.460449\pi$
$152$	58.5467	−	58.5467i	0.385176	−	0.385176i
$153$	−118.321	+	118.321i	−0.773339	+	0.773339i
$154$	153.275	−	92.9117i	0.995295	−	0.603323i
$155$			15.0408i			0.0970377i
$156$		−	106.722i		−	0.684115i
$157$	−89.3437	+	89.3437i	−0.569068	+	0.569068i	−0.931867	−	0.362799i	$-0.881821\pi$
$157$	−89.3437	+	89.3437i	−0.569068	+	0.569068i	0.362799	+	0.931867i	$0.381821\pi$
$158$	294.271	−	294.271i	1.86247	−	1.86247i
$159$	14.4677			0.0909916
$160$			142.030i			0.887685i
$161$	132.904	+	32.5873i	0.825489	+	0.202405i
$162$			208.025i			1.28411i
$163$	−28.2171			−0.173111			−0.0865554	−	0.996247i	$-0.527586\pi$
$163$	−28.2171			−0.173111			−0.0865554	+	0.996247i	$0.527586\pi$
$164$	−60.5015	+	246.150i	−0.368912	+	1.50092i
$165$	−24.5940			−0.149054
$166$	−279.758			−1.68529
$167$	−178.318	+	178.318i	−1.06777	+	1.06777i	−0.0702441	+	0.997530i	$0.522378\pi$
$167$	−178.318	+	178.318i	−1.06777	+	1.06777i	−0.997530	+	0.0702441i	$0.977622\pi$
$168$	−19.5533	−	32.2569i	−0.116389	−	0.192006i
$169$		−	328.667i		−	1.94477i
$170$	178.006	−	178.006i	1.04709	−	1.04709i
$171$	70.6310	−	70.6310i	0.413047	−	0.413047i
$172$		−	157.880i		−	0.917908i
$173$	−127.515			−0.737082			−0.368541	−	0.929611i	$-0.620143\pi$
$173$	−127.515			−0.737082			−0.368541	+	0.929611i	$0.620143\pi$
$174$		−	90.6080i		−	0.520736i
$175$	−63.3046	−	15.5219i	−0.361741	−	0.0886968i
$176$	−14.2298	−	14.2298i	−0.0808513	−	0.0808513i
$177$	−21.7105	−	21.7105i	−0.122658	−	0.122658i
$178$	−197.996	−	197.996i	−1.11234	−	1.11234i
$179$	−5.75577	+	5.75577i	−0.0321551	+	0.0321551i	−0.723002	−	0.690846i	$-0.757238\pi$
$179$	−5.75577	+	5.75577i	−0.0321551	+	0.0321551i	0.690846	+	0.723002i	$0.257238\pi$
$180$		−	205.726i		−	1.14292i
$181$	−114.047	−	114.047i	−0.630095	−	0.630095i	0.317997	−	0.948092i	$-0.396990\pi$
$181$	−114.047	−	114.047i	−0.630095	−	0.630095i	−0.948092	+	0.317997i	$0.896990\pi$
$182$	−258.306	−	426.124i	−1.41926	−	2.34134i
$183$	21.3998	−	21.3998i	0.116939	−	0.116939i
$184$			136.134i			0.739859i
$185$	19.2381			0.103990
$186$	−6.63010	+	6.63010i	−0.0356457	+	0.0356457i
$187$			159.823i			0.854668i
$188$	101.899	+	101.899i	0.542014	+	0.542014i
$189$	−48.8597	−	80.6034i	−0.258517	−	0.426473i
$190$	−106.260	+	106.260i	−0.559262	+	0.559262i
$191$	−55.5085	+	55.5085i	−0.290621	+	0.290621i	−0.837325	−	0.546705i	$-0.815882\pi$
$191$	−55.5085	+	55.5085i	−0.290621	+	0.290621i	0.546705	+	0.837325i	$0.315882\pi$
$192$	−57.1187	+	57.1187i	−0.297493	+	0.297493i
$193$	−180.932	−	180.932i	−0.937471	−	0.937471i	0.0606861	−	0.998157i	$-0.480671\pi$
$193$	−180.932	−	180.932i	−0.937471	−	0.937471i	−0.998157	+	0.0606861i	$0.980671\pi$
$194$	373.880	−	373.880i	1.92722	−	1.92722i
$195$			68.3742i			0.350637i
$196$	−268.576	−	140.131i	−1.37029	−	0.714956i
$197$		−	239.162i		−	1.21402i	−0.794694	−	0.607011i	$-0.792369\pi$
$197$		−	239.162i		−	1.21402i	0.794694	−	0.607011i	$-0.207631\pi$
$198$	152.110	+	152.110i	0.768232	+	0.768232i
$199$	−23.7058	−	23.7058i	−0.119125	−	0.119125i	0.645031	−	0.764156i	$-0.276844\pi$
$199$	−23.7058	−	23.7058i	−0.119125	−	0.119125i	−0.764156	+	0.645031i	$0.776844\pi$
$200$		−	64.8432i		−	0.324216i
$201$			2.08935i			0.0103948i
$202$	−364.423	+	364.423i	−1.80407	+	1.80407i
$203$	−133.153	−	219.662i	−0.655928	−	1.08208i
$204$	95.2836			0.467076
$205$	38.7618	−	157.702i	0.189082	−	0.769280i
$206$			68.2764i			0.331439i
$207$			164.233i			0.793394i
$208$	−39.5606	+	39.5606i	−0.190195	+	0.190195i
$209$		−	95.4055i		−	0.456486i
$210$	35.4885	+	58.5450i	0.168993	+	0.278786i
$211$	−46.6915	+	46.6915i	−0.221287	+	0.221287i	−0.809040	−	0.587753i	$-0.800013\pi$
$211$	−46.6915	+	46.6915i	−0.221287	+	0.221287i	0.587753	+	0.809040i	$0.300013\pi$
$212$	81.7348	+	81.7348i	0.385541	+	0.385541i
$213$	33.0205			0.155026
$214$			120.028i			0.560877i
$215$			101.150i			0.470465i
$216$	66.3049	−	66.3049i	0.306967	−	0.306967i
$217$	−6.33011	+	25.8167i	−0.0291710	+	0.118971i
$218$	359.365	+	359.365i	1.64846	+	1.64846i
$219$	−31.6548	+	31.6548i	−0.144542	+	0.144542i
$220$	−138.943	−	138.943i	−0.631559	−	0.631559i
$221$	444.327			2.01053
$222$	8.48027	+	8.48027i	0.0381994	+	0.0381994i
$223$		−	3.28799i		−	0.0147444i	−0.999973	−	0.00737218i	$-0.997653\pi$
$223$		−	3.28799i		−	0.0147444i	0.999973	−	0.00737218i	$-0.00234666\pi$
$224$	−59.7748	+	243.785i	−0.266852	+	1.08833i
$225$		−	78.2272i		−	0.347676i
$226$		−	267.120i		−	1.18195i
$227$	223.829	+	223.829i	0.986032	+	0.986032i	0.999904	−	0.0138713i	$-0.00441551\pi$
$227$	223.829	+	223.829i	0.986032	+	0.986032i	−0.0138713	+	0.999904i	$0.504416\pi$
$228$	−56.8791			−0.249470
$229$	−81.6871	−	81.6871i	−0.356712	−	0.356712i	0.505887	−	0.862600i	$-0.331165\pi$
$229$	−81.6871	−	81.6871i	−0.356712	−	0.356712i	−0.862600	+	0.505887i	$0.831165\pi$
$230$		−	247.077i		−	1.07425i
$231$	−42.2140	−	10.3506i	−0.182745	−	0.0448080i
$232$	180.695	−	180.695i	0.778858	−	0.778858i
$233$	25.7772	+	25.7772i	0.110632	+	0.110632i	0.760256	−	0.649624i	$-0.225074\pi$
$233$	25.7772	+	25.7772i	0.110632	+	0.110632i	−0.649624	+	0.760256i	$0.725074\pi$
$234$	422.884	−	422.884i	1.80720	−	1.80720i
$235$	−65.2840	−	65.2840i	−0.277804	−	0.277804i
$236$		−	245.306i		−	1.03943i
$237$	−100.918			−0.425814
$238$	380.452	−	230.621i	1.59854	−	0.968994i
$239$	100.497	+	100.497i	0.420489	+	0.420489i	0.885372	−	0.464883i	$-0.153904\pi$
$239$	100.497	+	100.497i	0.420489	+	0.420489i	−0.464883	+	0.885372i	$0.653904\pi$
$240$	5.43522	−	5.43522i	0.0226467	−	0.0226467i
$241$	88.4938			0.367194			0.183597	−	0.983002i	$-0.441226\pi$
$241$	88.4938			0.367194			0.183597	+	0.983002i	$0.441226\pi$
$242$	−180.645			−0.746466
$243$	121.362	−	121.362i	0.499432	−	0.499432i
$244$	241.795			0.990964
$245$	172.070	+	89.7788i	0.702327	+	0.366444i
$246$	86.6027	−	52.4298i	0.352043	−	0.213129i
$247$	−265.239			−1.07384
$248$	−26.4442			−0.106630
$249$	47.9705	+	47.9705i	0.192653	+	0.192653i
$250$			433.665i			1.73466i
$251$	184.882			0.736582			0.368291	−	0.929710i	$-0.379943\pi$
$251$	184.882			0.736582			0.368291	+	0.929710i	$0.379943\pi$
$252$	86.5820	−	353.116i	0.343580	−	1.40125i
$253$	110.919	+	110.919i	0.438416	+	0.438416i
$254$			553.787i			2.18026i
$255$	−61.0459			−0.239395
$256$	−187.692			−0.733171
$257$	252.644	−	252.644i	0.983052	−	0.983052i	−0.0168065	−	0.999859i	$-0.505350\pi$
$257$	252.644	−	252.644i	0.983052	−	0.983052i	0.999859	+	0.0168065i	$0.00534993\pi$
$258$	−44.5875	+	44.5875i	−0.172820	+	0.172820i
$259$	33.0210	+	8.09657i	0.127494	+	0.0312609i
$260$	−386.278	+	386.278i	−1.48569	+	1.48569i
$261$	217.991	−	217.991i	0.835216	−	0.835216i
$262$			751.188i			2.86713i
$263$	−265.667	+	265.667i	−1.01014	+	1.01014i	−0.0101909	+	0.999948i	$0.503244\pi$
$263$	−265.667	+	265.667i	−1.01014	+	1.01014i	−0.999948	+	0.0101909i	$0.996756\pi$
$264$		−	43.2401i		−	0.163788i
$265$	−52.3655	−	52.3655i	−0.197606	−	0.197606i
$266$	−227.109	+	137.668i	−0.853794	+	0.517548i
$267$			67.9013i			0.254312i
$268$	−11.8038	+	11.8038i	−0.0440439	+	0.0440439i
$269$			269.950i			1.00353i	0.865004	+	0.501765i	$0.167316\pi$
$269$			269.950i			1.00353i	−0.865004	+	0.501765i	$0.832684\pi$
$270$	−120.341	+	120.341i	−0.445706	+	0.445706i
$271$		−	173.800i		−	0.641329i	−0.947193	−	0.320664i	$-0.896094\pi$
$271$		−	173.800i		−	0.641329i	0.947193	−	0.320664i	$-0.103906\pi$
$272$	−35.3205	−	35.3205i	−0.129855	−	0.129855i
$273$	−28.7760	+	117.360i	−0.105407	+	0.429890i
$274$	−146.830	−	146.830i	−0.535874	−	0.535874i
$275$	−52.8330	−	52.8330i	−0.192120	−	0.192120i
$276$	66.1282	−	66.1282i	0.239595	−	0.239595i
$277$	72.9690			0.263426			0.131713	−	0.991288i	$-0.457952\pi$
$277$	72.9690			0.263426			0.131713	+	0.991288i	$0.457952\pi$
$278$	801.518			2.88316
$279$	−31.9024			−0.114345
$280$	−45.9804	+	187.526i	−0.164216	+	0.669737i
$281$	84.8226	−	84.8226i	0.301860	−	0.301860i	−0.539881	−	0.841741i	$-0.681531\pi$
$281$	84.8226	−	84.8226i	0.301860	−	0.301860i	0.841741	+	0.539881i	$0.181531\pi$
$282$		−	57.5552i		−	0.204096i
$283$			58.7529i			0.207607i	0.994598	+	0.103804i	$0.0331014\pi$
$283$			58.7529i			0.207607i	−0.994598	+	0.103804i	$0.966899\pi$
$284$	186.549	+	186.549i	0.656862	+	0.656862i
$285$	36.4410			0.127863
$286$		−	571.214i		−	1.99725i
$287$	132.903	−	254.373i	0.463077	−	0.886318i
$288$	−301.252			−1.04601
$289$			107.704i			0.372678i
$290$	−327.954	+	327.954i	−1.13088	+	1.13088i
$291$	−128.219			−0.440616
$292$	−357.666			−1.22488
$293$	−381.544	−	381.544i	−1.30220	−	1.30220i	−0.926908	−	0.375289i	$-0.877543\pi$
$293$	−381.544	−	381.544i	−1.30220	−	1.30220i	−0.375289	−	0.926908i	$-0.622457\pi$
$294$	36.2745	+	115.425i	0.123383	+	0.392601i
$295$			157.162i			0.532752i
$296$			33.8236i			0.114269i
$297$		−	108.048i		−	0.363798i
$298$	472.509	+	472.509i	1.58560	+	1.58560i
$299$	308.369	−	308.369i	1.03133	−	1.03133i
$300$	−31.4981	+	31.4981i	−0.104994	+	0.104994i
$301$	−42.5701	+	173.618i	−0.141429	+	0.576803i
$302$	537.839	−	537.839i	1.78092	−	1.78092i
$303$	124.976			0.412463
$304$	21.0844	+	21.0844i	0.0693567	+	0.0693567i
$305$	−154.912			−0.507909
$306$	377.559	+	377.559i	1.23385	+	1.23385i
$307$	−350.054			−1.14024			−0.570121	−	0.821561i	$-0.693104\pi$
$307$	−350.054			−1.14024			−0.570121	+	0.821561i	$0.693104\pi$
$308$	−180.012	−	296.963i	−0.584453	−	0.964166i
$309$	11.7074	−	11.7074i	0.0378882	−	0.0378882i
$310$	47.9950			0.154823
$311$	−239.122	−	239.122i	−0.768880	−	0.768880i	0.209029	−	0.977909i	$-0.432970\pi$
$311$	−239.122	−	239.122i	−0.768880	−	0.768880i	−0.977909	+	0.209029i	$0.932970\pi$
$312$	−120.213			−0.385297
$313$	−192.954	−	192.954i	−0.616468	−	0.616468i	0.328156	−	0.944624i	$-0.393573\pi$
$313$	−192.954	−	192.954i	−0.616468	−	0.616468i	−0.944624	+	0.328156i	$0.893573\pi$
$314$	285.094	+	285.094i	0.907942	+	0.907942i
$315$	−55.4710	+	226.233i	−0.176098	+	0.718199i
$316$	−570.134	−	570.134i	−1.80422	−	1.80422i
$317$	−168.969	−	168.969i	−0.533026	−	0.533026i	0.388446	−	0.921472i	$-0.373012\pi$
$317$	−168.969	−	168.969i	−0.533026	−	0.533026i	−0.921472	+	0.388446i	$0.873012\pi$
$318$		−	46.1660i		−	0.145176i
$319$		−	294.454i		−	0.923053i
$320$	413.480			1.29212
$321$	20.5813	−	20.5813i	0.0641162	−	0.0641162i
$322$	103.985	−	424.093i	0.322936	−	1.31706i
$323$		−	236.811i		−	0.733160i
$324$	403.038			1.24395
$325$	−146.882	+	146.882i	−0.451945	+	0.451945i
$326$			90.0401i			0.276197i
$327$		−	123.242i		−	0.376886i
$328$	277.266	+	68.1494i	0.845322	+	0.207773i
$329$	−84.5805	−	139.531i	−0.257083	−	0.424108i
$330$			78.4789i			0.237815i
$331$	379.585	+	379.585i	1.14678	+	1.14678i	0.987181	+	0.159603i	$0.0510213\pi$
$331$	379.585	+	379.585i	1.14678	+	1.14678i	0.159603	+	0.987181i	$0.448979\pi$
$332$			542.017i			1.63258i
$333$			40.8049i			0.122537i
$334$	569.010	+	569.010i	1.70362	+	1.70362i
$335$	7.56238	−	7.56238i	0.0225743	−	0.0225743i
$336$	11.6167	−	7.04175i	0.0345735	−	0.0209576i
$337$			436.431i			1.29505i	0.762045	+	0.647524i	$0.224195\pi$
$337$			436.431i			1.29505i	−0.762045	+	0.647524i	$0.775805\pi$
$338$	−1048.77			−3.10287
$339$	−45.8034	+	45.8034i	−0.135113	+	0.135113i
$340$	−344.877	−	344.877i	−1.01434	−	1.01434i
$341$	−21.5462	+	21.5462i	−0.0631853	+	0.0631853i
$342$	−225.382	−	225.382i	−0.659012	−	0.659012i
$343$	257.563	+	226.517i	0.750914	+	0.660401i
$344$	−177.837			−0.516969
$345$	−42.3667	+	42.3667i	−0.122802	+	0.122802i
$346$			406.899i			1.17601i
$347$	367.262	−	367.262i	1.05839	−	1.05839i	0.0602066	−	0.998186i	$-0.480824\pi$
$347$	367.262	−	367.262i	1.05839	−	1.05839i	0.998186	−	0.0602066i	$-0.0191760\pi$
$348$	−175.548			−0.504449
$349$	−50.2460			−0.143971			−0.0719856	−	0.997406i	$-0.522934\pi$
$349$	−50.2460			−0.143971			−0.0719856	+	0.997406i	$0.522934\pi$
$350$	−49.5302	+	202.004i	−0.141515	+	0.577154i
$351$	−300.386			−0.855801
$352$	−203.459	+	203.459i	−0.578009	+	0.578009i
$353$			102.390i			0.290056i	0.989428	+	0.145028i	$0.0463272\pi$
$353$			102.390i			0.290056i	−0.989428	+	0.145028i	$0.953673\pi$
$354$	−69.2779	+	69.2779i	−0.195700	+	0.195700i
$355$	−119.517	−	119.517i	−0.336668	−	0.336668i
$356$	−383.607	+	383.607i	−1.07755	+	1.07755i
$357$	−104.781	−	25.6918i	−0.293506	−	0.0719659i
$358$	18.3665	+	18.3665i	0.0513032	+	0.0513032i
$359$	−133.385			−0.371545			−0.185772	−	0.982593i	$-0.559479\pi$
$359$	−133.385			−0.371545			−0.185772	+	0.982593i	$0.559479\pi$
$360$	−231.731			−0.643698
$361$		−	219.637i		−	0.608413i
$362$	−363.922	+	363.922i	−1.00531	+	1.00531i
$363$	30.9754	+	30.9754i	0.0853317	+	0.0853317i
$364$	−825.593	+	500.454i	−2.26811	+	1.37487i
$365$	229.148			0.627802
$366$	−68.2863	−	68.2863i	−0.186575	−	0.186575i
$367$	585.638			1.59574			0.797871	−	0.602828i	$-0.205959\pi$
$367$	585.638			1.59574			0.797871	+	0.602828i	$0.205959\pi$
$368$	−49.0259			−0.133223
$369$	334.495	+	82.2158i	0.906489	+	0.222807i
$370$		−	61.3884i		−	0.165915i
$371$	−67.8435	−	111.921i	−0.182867	−	0.301673i
$372$	12.8455	+	12.8455i	0.0345308	+	0.0345308i
$373$	569.696			1.52734			0.763668	−	0.645609i	$-0.223396\pi$
$373$	569.696			1.52734			0.763668	+	0.645609i	$0.223396\pi$
$374$	509.992			1.36361
$375$	74.3612	−	74.3612i	0.198296	−	0.198296i
$376$	114.779	−	114.779i	0.305265	−	0.305265i
$377$	−818.617			−2.17140
$378$	−257.204	+	155.910i	−0.680433	+	0.412462i
$379$	−334.427			−0.882392			−0.441196	−	0.897411i	$-0.645446\pi$
$379$	−334.427			−0.882392			−0.441196	+	0.897411i	$0.645446\pi$
$380$	205.873	+	205.873i	0.541771	+	0.541771i
$381$	94.9585	−	94.9585i	0.249235	−	0.249235i
$382$	177.127	+	177.127i	0.463682	+	0.463682i
$383$	84.3829	+	84.3829i	0.220321	+	0.220321i	0.808634	−	0.588313i	$-0.200208\pi$
$383$	84.3829	+	84.3829i	0.220321	+	0.220321i	−0.588313	+	0.808634i	$0.700208\pi$
$384$	103.784	+	103.784i	0.270271	+	0.270271i
$385$	115.329	+	190.257i	0.299556	+	0.494174i
$386$	−577.350	+	577.350i	−1.49573	+	1.49573i
$387$	−214.544			−0.554377
$388$	−724.372	−	724.372i	−1.86694	−	1.86694i
$389$		−	111.842i		−	0.287512i	−0.989613	−	0.143756i	$-0.954082\pi$
$389$		−	111.842i		−	0.287512i	0.989613	−	0.143756i	$-0.0459181\pi$
$390$	218.181			0.559438
$391$	275.318	+	275.318i	0.704139	+	0.704139i
$392$	−157.845	+	302.526i	−0.402666	+	0.771751i
$393$	128.807	−	128.807i	0.327754	−	0.327754i
$394$	−763.162			−1.93696
$395$	365.271	+	365.271i	0.924737	+	0.924737i
$396$	294.705	−	294.705i	0.744205	−	0.744205i
$397$	266.842	−	266.842i	0.672146	−	0.672146i	−0.286065	−	0.958210i	$-0.592347\pi$
$397$	266.842	−	266.842i	0.672146	−	0.672146i	0.958210	+	0.286065i	$0.0923472\pi$
$398$	−75.6448	+	75.6448i	−0.190062	+	0.190062i
$399$	62.5488	+	15.3366i	0.156764	+	0.0384376i
$400$	23.3520			0.0583800
$401$			249.531i			0.622271i	0.950366	+	0.311136i	$0.100709\pi$
$401$			249.531i			0.622271i	−0.950366	+	0.311136i	$0.899291\pi$
$402$	6.66709			0.0165848
$403$	59.9010	+	59.9010i	0.148638	+	0.148638i
$404$	706.050	+	706.050i	1.74765	+	1.74765i
$405$	−258.217			−0.637572
$406$	−700.936	+	424.890i	−1.72644	+	1.04653i
$407$	27.5588	+	27.5588i	0.0677121	+	0.0677121i
$408$		−	107.328i		−	0.263059i
$409$		−	482.088i		−	1.17870i	−0.807878	−	0.589350i	$-0.799384\pi$
$409$		−	482.088i		−	1.17870i	0.807878	−	0.589350i	$-0.200616\pi$
$410$	−503.225	−	123.688i	−1.22738	−	0.301679i
$411$			50.3541i			0.122516i
$412$	132.282			0.321072
$413$	−66.1433	+	269.759i	−0.160153	+	0.653169i
$414$	524.063			1.26585
$415$		−	347.257i		−	0.836764i
$416$	565.641	+	565.641i	1.35971	+	1.35971i
$417$	−137.437	−	137.437i	−0.329586	−	0.329586i
$418$	−304.437			−0.728319
$419$	121.457			0.289872			0.144936	−	0.989441i	$-0.453702\pi$
$419$	121.457			0.289872			0.144936	+	0.989441i	$0.453702\pi$
$420$	113.428	−	68.7571i	0.270066	−	0.163707i
$421$	409.524	+	409.524i	0.972741	+	0.972741i	0.999638	−	0.0268970i	$-0.00856261\pi$
$421$	409.524	+	409.524i	0.972741	+	0.972741i	−0.0268970	+	0.999638i	$0.508563\pi$
$422$	148.992	+	148.992i	0.353061	+	0.353061i
$423$	138.470	−	138.470i	0.327353	−	0.327353i
$424$	92.0667	−	92.0667i	0.217138	−	0.217138i
$425$	−131.139	−	131.139i	−0.308563	−	0.308563i
$426$		−	105.368i		−	0.247342i
$427$	−265.897	−	65.1965i	−0.622710	−	0.152685i
$428$	232.547			0.543335
$429$	−97.9469	+	97.9469i	−0.228314	+	0.228314i
$430$	322.767			0.750622
$431$			478.260i			1.10965i	0.831966	+	0.554827i	$0.187215\pi$
$431$			478.260i			1.10965i	−0.831966	+	0.554827i	$0.812785\pi$
$432$	23.8784	+	23.8784i	0.0552740	+	0.0552740i
$433$		−	645.738i		−	1.49131i	−0.666331	−	0.745656i	$-0.732136\pi$
$433$		−	645.738i		−	1.49131i	0.666331	−	0.745656i	$-0.267864\pi$
$434$	82.3805	+	20.1992i	0.189817	+	0.0465420i
$435$	112.469			0.258550
$436$	696.251	−	696.251i	1.59691	−	1.59691i
$437$	−164.350	−	164.350i	−0.376087	−	0.376087i
$438$	101.010	+	101.010i	0.230616	+	0.230616i
$439$	58.9246	−	58.9246i	0.134225	−	0.134225i	−0.636802	−	0.771027i	$-0.719743\pi$
$439$	58.9246	−	58.9246i	0.134225	−	0.134225i	0.771027	+	0.636802i	$0.219743\pi$
$440$	−156.507	+	156.507i	−0.355697	+	0.355697i
$441$	−190.425	+	364.969i	−0.431803	+	0.827594i
$442$		−	1417.84i		−	3.20778i
$443$		−	805.387i		−	1.81803i	−0.416763	−	0.909015i	$-0.636836\pi$
$443$		−	805.387i		−	1.81803i	0.416763	−	0.909015i	$-0.363164\pi$
$444$	16.4301	−	16.4301i	0.0370047	−	0.0370047i
$445$	245.768	−	245.768i	0.552287	−	0.552287i
$446$	−10.4919			−0.0235245
$447$		−	162.044i		−	0.362514i
$448$	709.713	+	174.018i	1.58418	+	0.388432i
$449$			717.492i			1.59798i	0.601346	+	0.798988i	$0.294631\pi$
$449$			717.492i			1.59798i	−0.601346	+	0.798988i	$0.705369\pi$
$450$	−249.621			−0.554714
$451$	281.438	−	170.384i	0.624030	−	0.377791i
$452$	−517.531			−1.14498
$453$	−184.448			−0.407170
$454$	714.235	−	714.235i	1.57321	−	1.57321i
$455$	528.937	−	320.628i	1.16250	−	0.704678i
$456$			64.0691i			0.140502i
$457$	48.9394	−	48.9394i	0.107088	−	0.107088i	−0.651532	−	0.758621i	$-0.725874\pi$
$457$	48.9394	−	48.9394i	0.107088	−	0.107088i	0.758621	+	0.651532i	$0.225874\pi$
$458$	−260.662	+	260.662i	−0.569131	+	0.569131i
$459$		−	268.191i		−	0.584294i
$460$	−478.699			−1.04065
$461$		−	137.998i		−	0.299345i	−0.988736	−	0.149672i	$-0.952178\pi$
$461$		−	137.998i		−	0.299345i	0.988736	−	0.149672i	$-0.0478219\pi$
$462$	−33.0287	+	134.704i	−0.0714907	+	0.291567i
$463$	223.065	+	223.065i	0.481783	+	0.481783i	0.905701	−	0.423918i	$-0.139346\pi$
$463$	223.065	+	223.065i	0.481783	+	0.481783i	−0.423918	+	0.905701i	$0.639346\pi$
$464$	65.0737	+	65.0737i	0.140245	+	0.140245i
$465$	−8.22977	−	8.22977i	−0.0176984	−	0.0176984i
$466$	82.2546	−	82.2546i	0.176512	−	0.176512i
$467$		−	596.094i		−	1.27643i	−0.769857	−	0.638216i	$-0.779673\pi$
$467$		−	596.094i		−	1.27643i	0.769857	−	0.638216i	$-0.220327\pi$
$468$	−819.315	−	819.315i	−1.75067	−	1.75067i
$469$	16.1631	−	9.79765i	0.0344628	−	0.0208905i
$470$	−208.320	+	208.320i	−0.443234	+	0.443234i
$471$		−	97.7709i		−	0.207581i
$472$	−276.315			−0.585414
$473$	−144.899	+	144.899i	−0.306339	+	0.306339i
$474$			322.027i			0.679383i
$475$	78.2830	+	78.2830i	0.164806	+	0.164806i
$476$	−446.815	−	737.106i	−0.938687	−	1.54854i
$477$	111.070	−	111.070i	0.232851	−	0.232851i
$478$	320.684	−	320.684i	0.670886	−	0.670886i
$479$	148.147	−	148.147i	0.309283	−	0.309283i	−0.535348	−	0.844631i	$-0.679820\pi$
$479$	148.147	−	148.147i	0.309283	−	0.309283i	0.844631	+	0.535348i	$0.179820\pi$
$480$	−77.7132	−	77.7132i	−0.161902	−	0.161902i
$481$	76.6168	−	76.6168i	0.159287	−	0.159287i
$482$		−	282.382i		−	0.585854i
$483$	−90.5503	+	54.8893i	−0.187475	+	0.113643i
$484$			349.990i			0.723119i
$485$	464.088	+	464.088i	0.956882	+	0.956882i
$486$	−387.264	−	387.264i	−0.796839	−	0.796839i
$487$			899.405i			1.84683i	0.383806	+	0.923414i	$0.374613\pi$
$487$			899.405i			1.84683i	−0.383806	+	0.923414i	$0.625387\pi$
$488$		−	272.360i		−	0.558115i
$489$	15.4393	−	15.4393i	0.0315732	−	0.0315732i
$490$	286.482	−	549.072i	0.584658	−	1.12056i
$491$	147.591			0.300593			0.150296	−	0.988641i	$-0.451977\pi$
$491$	147.591			0.300593			0.150296	+	0.988641i	$0.451977\pi$
$492$	−101.580	−	167.788i	−0.206463	−	0.341033i
$493$		−	730.878i		−	1.48251i
$494$			846.372i			1.71330i
$495$	−188.810	+	188.810i	−0.381435	+	0.381435i
$496$		−	9.52333i		−	0.0192003i
$497$	−154.844	−	255.444i	−0.311557	−	0.513972i
$498$	153.073	−	153.073i	0.307376	−	0.307376i
$499$	186.266	+	186.266i	0.373279	+	0.373279i	0.868670	−	0.495391i	$-0.164975\pi$
$499$	186.266	+	186.266i	0.373279	+	0.373279i	−0.495391	+	0.868670i	$0.664975\pi$
$500$	840.204			1.68041
$501$		−	195.138i		−	0.389497i
$502$		−	589.956i		−	1.17521i
$503$	−628.644	+	628.644i	−1.24979	+	1.24979i	−0.293975	+	0.955813i	$0.594978\pi$
$503$	−628.644	+	628.644i	−1.24979	+	1.24979i	−0.955813	+	0.293975i	$0.905022\pi$
$504$	−397.753	−	97.5267i	−0.789192	−	0.193505i
$505$	−452.349	−	452.349i	−0.895741	−	0.895741i
$506$	353.942	−	353.942i	0.699489	−	0.699489i
$507$	179.834	+	179.834i	0.354702	+	0.354702i
$508$	1072.93			2.11207
$509$	−491.496	−	491.496i	−0.965610	−	0.965610i	0.0338180	−	0.999428i	$-0.489233\pi$
$509$	−491.496	−	491.496i	−0.965610	−	0.965610i	−0.999428	+	0.0338180i	$0.989233\pi$
$510$			194.796i			0.381953i
$511$	393.318	+	96.4394i	0.769703	+	0.188727i
$512$		−	159.787i		−	0.312083i
$513$			160.095i			0.312076i
$514$	−806.183	−	806.183i	−1.56845	−	1.56845i
$515$	−84.7497			−0.164563
$516$	86.3859	+	86.3859i	0.167415	+	0.167415i
$517$		−	187.040i		−	0.361780i
$518$	25.8360	−	105.369i	0.0498764	−	0.203416i
$519$	69.7715	−	69.7715i	0.134434	−	0.134434i
$520$	435.107	+	435.107i	0.836745	+	0.836745i
$521$	387.374	−	387.374i	0.743520	−	0.743520i	−0.229734	−	0.973254i	$-0.573786\pi$
$521$	387.374	−	387.374i	0.743520	−	0.743520i	0.973254	+	0.229734i	$0.0737855\pi$
$522$	−695.606	−	695.606i	−1.33258	−	1.33258i
$523$			342.942i			0.655720i	0.944726	+	0.327860i	$0.106327\pi$
$523$			342.942i			0.655720i	−0.944726	+	0.327860i	$0.893673\pi$
$524$	1455.39			2.77746
$525$	43.1309	−	26.1449i	0.0821540	−	0.0497997i
$526$	847.737	+	847.737i	1.61167	+	1.61167i
$527$	−53.4809	+	53.4809i	−0.101482	+	0.101482i
$528$	15.5720			0.0294925
$529$	−146.850			−0.277600
$530$	−167.097	+	167.097i	−0.315278	+	0.315278i
$531$	−333.348			−0.627774
$532$	266.724	+	440.012i	0.501361	+	0.827090i
$533$	−473.688	−	782.430i	−0.888720	−	1.46797i
$534$	216.672			0.405752
$535$	−148.987			−0.278481
$536$	13.2958	+	13.2958i	0.0248057	+	0.0248057i
$537$		−	6.29867i		−	0.0117294i
$538$	861.404			1.60112
$539$	117.883	+	375.102i	0.218708	+	0.695922i
$540$	233.153	+	233.153i	0.431766	+	0.431766i
$541$			171.317i			0.316667i	0.987386	+	0.158334i	$0.0506122\pi$
$541$			171.317i			0.316667i	−0.987386	+	0.158334i	$0.949388\pi$
$542$	−554.593			−1.02323
$543$	124.804			0.229843
$544$	−505.016	+	505.016i	−0.928338	+	0.928338i
$545$	−446.071	+	446.071i	−0.818478	+	0.818478i
$546$	374.494	+	91.8238i	0.685886	+	0.168175i
$547$	−291.403	+	291.403i	−0.532730	+	0.532730i	−0.921384	−	0.388654i	$-0.872940\pi$
$547$	−291.403	+	291.403i	−0.532730	+	0.532730i	0.388654	+	0.921384i	$0.372940\pi$
$548$	−284.475	+	284.475i	−0.519114	+	0.519114i
$549$		−	328.576i		−	0.598500i
$550$	−168.589	+	168.589i	−0.306526	+	0.306526i
$551$			436.294i			0.791822i
$552$	−74.4873	−	74.4873i	−0.134941	−	0.134941i
$553$	473.237	+	780.694i	0.855763	+	1.41174i
$554$		−	232.843i		−	0.420294i
$555$	−10.5263	+	10.5263i	−0.0189664	+	0.0189664i
$556$		−	1552.90i		−	2.79298i
$557$	−281.161	+	281.161i	−0.504777	+	0.504777i	−0.912919	−	0.408142i	$-0.866177\pi$
$557$	−281.161	+	281.161i	−0.504777	+	0.504777i	0.408142	+	0.912919i	$0.366177\pi$
$558$			101.800i			0.182437i
$559$	402.835	+	402.835i	0.720636	+	0.720636i
$560$	−67.5339	−	16.5589i	−0.120596	−	0.0295695i
$561$	−87.4490	−	87.4490i	−0.155881	−	0.155881i
$562$	−270.667	−	270.667i	−0.481615	−	0.481615i
$563$	43.2798	−	43.2798i	0.0768736	−	0.0768736i	−0.667625	−	0.744498i	$-0.732689\pi$
$563$	43.2798	−	43.2798i	0.0768736	−	0.0768736i	0.744498	+	0.667625i	$0.232689\pi$
$564$	−111.510			−0.197713
$565$	331.569			0.586849
$566$	187.479			0.331235
$567$	−443.213	−	108.673i	−0.781681	−	0.191664i
$568$	210.130	−	210.130i	0.369947	−	0.369947i
$569$		−	763.655i		−	1.34210i	−0.741412	−	0.671050i	$-0.765843\pi$
$569$		−	763.655i		−	1.34210i	0.741412	−	0.671050i	$-0.234157\pi$
$570$		−	116.283i		−	0.204005i
$571$	−303.734	−	303.734i	−0.531934	−	0.531934i	0.389213	−	0.921148i	$-0.372747\pi$
$571$	−303.734	−	303.734i	−0.531934	−	0.531934i	−0.921148	+	0.389213i	$0.872747\pi$
$572$	−1106.70			−1.93479
$573$		−	60.7443i		−	0.106011i
$574$	−811.700	−	424.091i	−1.41411	−	0.738835i
$575$	−182.025			−0.316566
$576$			877.011i			1.52259i
$577$	−584.022	+	584.022i	−1.01217	+	1.01217i	−0.0122453	+	0.999925i	$0.503898\pi$
$577$	−584.022	+	584.022i	−1.01217	+	1.01217i	−0.999925	+	0.0122453i	$0.996102\pi$
$578$	343.681			0.594605
$579$	197.998			0.341965
$580$	635.394	+	635.394i	1.09551	+	1.09551i
$581$	146.147	−	596.045i	0.251544	−	1.02590i
$582$			409.145i			0.702999i
$583$		−	150.028i		−	0.257339i
$584$			402.878i			0.689859i
$585$	524.915	+	524.915i	0.897291	+	0.897291i
$586$	−1217.50	+	1217.50i	−2.07764	+	2.07764i
$587$	−721.955	+	721.955i	−1.22991	+	1.22991i	−0.265907	+	0.963999i	$0.585671\pi$
$587$	−721.955	+	721.955i	−1.22991	+	1.22991i	−0.963999	+	0.265907i	$0.914329\pi$
$588$	223.629	−	70.2800i	0.380322	−	0.119524i
$589$	31.9251	−	31.9251i	0.0542023	−	0.0542023i
$590$	501.500			0.850001
$591$	130.860	+	130.860i	0.221422	+	0.221422i
$592$	−12.1809			−0.0205758
$593$	168.579	+	168.579i	0.284282	+	0.284282i	0.834814	−	0.550532i	$-0.185575\pi$
$593$	168.579	+	168.579i	0.284282	+	0.284282i	−0.550532	+	0.834814i	$0.685575\pi$
$594$	−344.779			−0.580436
$595$	286.264	+	472.246i	0.481115	+	0.793690i
$596$	915.462	−	915.462i	1.53601	−	1.53601i
$597$	25.9418			0.0434536
$598$	−984.000	−	984.000i	−1.64548	−	1.64548i
$599$	−317.692			−0.530371			−0.265186	−	0.964197i	$-0.585433\pi$
$599$	−317.692			−0.530371			−0.265186	+	0.964197i	$0.585433\pi$
$600$	35.4797	+	35.4797i	0.0591329	+	0.0591329i
$601$	629.061	+	629.061i	1.04669	+	1.04669i	0.998855	+	0.0478356i	$0.0152324\pi$
$601$	629.061	+	629.061i	1.04669	+	1.04669i	0.0478356	+	0.998855i	$0.484768\pi$
$602$	554.010	+	135.840i	0.920283	+	0.225648i
$603$	16.0402	+	16.0402i	0.0266006	+	0.0266006i
$604$	−1042.03	−	1042.03i	−1.72522	−	1.72522i
$605$		−	224.230i		−	0.370628i
$606$		−	398.797i		−	0.658080i
$607$	−378.223			−0.623102			−0.311551	−	0.950229i	$-0.600848\pi$
$607$	−378.223			−0.623102			−0.311551	+	0.950229i	$0.600848\pi$
$608$	301.467	−	301.467i	0.495834	−	0.495834i
$609$	193.047	+	47.3340i	0.316990	+	0.0777242i
$610$			494.322i			0.810364i
$611$	−519.994			−0.851055
$612$	731.501	−	731.501i	1.19526	−	1.19526i
$613$		−	788.654i		−	1.28655i	−0.765636	−	0.643274i	$-0.777576\pi$
$613$		−	788.654i		−	1.28655i	0.765636	−	0.643274i	$-0.222424\pi$
$614$			1117.02i			1.81925i
$615$	65.0797	+	107.498i	0.105821	+	0.174793i
$616$	−334.502	+	202.766i	−0.543022	+	0.329166i
$617$			11.9529i			0.0193726i	0.999953	+	0.00968631i	$0.00308330\pi$
$617$			11.9529i			0.0193726i	−0.999953	+	0.00968631i	$0.996917\pi$
$618$	−37.3582	−	37.3582i	−0.0604502	−	0.0604502i
$619$		−	607.237i		−	0.980997i	−0.871442	−	0.490498i	$-0.836815\pi$
$619$		−	607.237i		−	0.980997i	0.871442	−	0.490498i	$-0.163185\pi$
$620$		−	92.9879i		−	0.149980i
$621$	−186.128	−	186.128i	−0.299723	−	0.299723i
$622$	−763.033	+	763.033i	−1.22674	+	1.22674i
$623$	525.279	−	318.411i	0.843145	−	0.511093i
$624$		−	43.2921i		−	0.0693784i
$625$	−305.513			−0.488821
$626$	−615.714	+	615.714i	−0.983568	+	0.983568i
$627$	52.2022	+	52.2022i	0.0832572	+	0.0832572i
$628$	552.354	−	552.354i	0.879545	−	0.879545i
$629$	68.4051	+	68.4051i	0.108752	+	0.108752i
$630$	721.904	+	177.007i	1.14588	+	0.280963i
$631$	−552.239			−0.875180			−0.437590	−	0.899175i	$-0.644168\pi$
$631$	−552.239			−0.875180			−0.437590	+	0.899175i	$0.644168\pi$
$632$	−642.204	+	642.204i	−1.01615	+	1.01615i
$633$		−	51.0956i		−	0.0807198i
$634$	−539.178	+	539.178i	−0.850438	+	0.850438i
$635$	−687.401			−1.08252
$636$	−89.4443			−0.140636
$637$	1042.83	−	327.730i	1.63709	−	0.514490i
$638$	−939.597			−1.47272
$639$	253.502	−	253.502i	0.396716	−	0.396716i
$640$		−	751.288i		−	1.17389i
$641$	563.488	−	563.488i	0.879077	−	0.879077i	−0.114362	−	0.993439i	$-0.536482\pi$
$641$	563.488	−	563.488i	0.879077	−	0.879077i	0.993439	+	0.114362i	$0.0364825\pi$
$642$	−65.6746	−	65.6746i	−0.102297	−	0.102297i
$643$	−216.787	+	216.787i	−0.337149	+	0.337149i	−0.855293	−	0.518144i	$-0.826623\pi$
$643$	−216.787	+	216.787i	−0.337149	+	0.337149i	0.518144	+	0.855293i	$0.326623\pi$
$644$	−821.658	−	201.466i	−1.27587	−	0.312835i
$645$	−55.3454	−	55.3454i	−0.0858067	−	0.0858067i
$646$	−755.658			−1.16975
$647$	−584.343			−0.903157			−0.451579	−	0.892231i	$-0.649139\pi$
$647$	−584.343			−0.903157			−0.451579	+	0.892231i	$0.649139\pi$
$648$		−	453.986i		−	0.700595i
$649$	−225.136	+	225.136i	−0.346897	+	0.346897i
$650$	468.698	+	468.698i	0.721074	+	0.721074i
$651$	−10.6623	−	17.5895i	−0.0163784	−	0.0270192i
$652$	174.448			0.267558
$653$	−319.944	−	319.944i	−0.489960	−	0.489960i	0.418333	−	0.908294i	$-0.362614\pi$
$653$	−319.944	−	319.944i	−0.489960	−	0.489960i	−0.908294	+	0.418333i	$0.862614\pi$
$654$	−393.261			−0.601317
$655$	−932.431			−1.42356
$656$	−24.5426	+	99.8517i	−0.0374126	+	0.152213i
$657$			486.033i			0.739777i
$658$	−445.242	+	269.895i	−0.676660	+	0.410174i
$659$	755.575	+	755.575i	1.14655	+	1.14655i	0.987227	+	0.159321i	$0.0509305\pi$
$659$	755.575	+	755.575i	1.14655	+	1.14655i	0.159321	+	0.987227i	$0.449070\pi$
$660$	152.049			0.230377
$661$	125.874			0.190429			0.0952146	−	0.995457i	$-0.469646\pi$
$661$	125.874			0.190429			0.0952146	+	0.995457i	$0.469646\pi$
$662$	1211.25	−	1211.25i	1.82968	−	1.82968i
$663$	−243.119	+	243.119i	−0.366695	+	0.366695i
$664$	610.532			0.919477
$665$	−170.884	−	281.905i	−0.256968	−	0.423917i
$666$	130.208			0.195507
$667$	−507.240	−	507.240i	−0.760479	−	0.760479i
$668$	1102.43	−	1102.43i	1.65034	−	1.65034i
$669$	1.79906	+	1.79906i	0.00268918	+	0.00268918i
$670$	−24.1314	−	24.1314i	−0.0360170	−	0.0360170i
$671$	−221.914	−	221.914i	−0.330721	−	0.330721i
$672$	−100.683	−	166.096i	−0.149827	−	0.247167i
$673$	−163.119	+	163.119i	−0.242376	+	0.242376i	−0.817832	−	0.575457i	$-0.804824\pi$
$673$	−163.119	+	163.119i	−0.242376	+	0.242376i	0.575457	+	0.817832i	$0.304824\pi$
$674$	1392.64			2.06624
$675$	88.6565	+	88.6565i	0.131343	+	0.131343i
$676$			2031.93i			3.00582i
$677$	−156.857			−0.231694			−0.115847	−	0.993267i	$-0.536958\pi$
$677$	−156.857			−0.231694			−0.115847	+	0.993267i	$0.536958\pi$
$678$	146.158	+	146.158i	0.215572	+	0.215572i
$679$	601.261	+	991.894i	0.885510	+	1.46082i
$680$	−388.473	+	388.473i	−0.571283	+	0.571283i
$681$	−244.942			−0.359679
$682$	68.7535	+	68.7535i	0.100812	+	0.100812i
$683$	391.080	−	391.080i	0.572592	−	0.572592i	−0.360260	−	0.932852i	$-0.617312\pi$
$683$	391.080	−	391.080i	0.572592	−	0.572592i	0.932852	+	0.360260i	$0.117312\pi$
$684$	−436.666	+	436.666i	−0.638401	+	0.638401i
$685$	182.256	−	182.256i	0.266067	−	0.266067i
$686$	722.813	−	821.880i	1.05366	−	1.19808i
$687$	89.3921			0.130119
$688$		−	64.0446i		−	0.0930880i
$689$	−417.097			−0.605366
$690$	135.191	+	135.191i	0.195929	+	0.195929i
$691$	−288.055	−	288.055i	−0.416867	−	0.416867i	0.467256	−	0.884122i	$-0.345243\pi$
$691$	−288.055	−	288.055i	−0.416867	−	0.416867i	−0.884122	+	0.467256i	$0.845243\pi$
$692$	788.345			1.13923
$693$	−403.544	+	244.618i	−0.582315	+	0.352985i
$694$	−1171.93	−	1171.93i	−1.68866	−	1.68866i
$695$			994.905i			1.43152i
$696$			197.739i			0.284108i
$697$	698.570	−	422.918i	1.00225	−	0.606769i
$698$			160.334i			0.229705i
$699$	−28.2086			−0.0403557
$700$	391.372	+	95.9621i	0.559102	+	0.137089i
$701$	−663.247			−0.946144			−0.473072	−	0.881024i	$-0.656855\pi$
$701$	−663.247			−0.946144			−0.473072	+	0.881024i	$0.656855\pi$
$702$			958.526i			1.36542i
$703$	−40.8341	−	40.8341i	−0.0580854	−	0.0580854i
$704$	592.315	+	592.315i	0.841357	+	0.841357i
$705$	71.4418			0.101336
$706$	326.724			0.462781
$707$	−586.053	−	966.806i	−0.828930	−	1.36748i
$708$	134.222	+	134.222i	0.189580	+	0.189580i
$709$	508.764	+	508.764i	0.717579	+	0.717579i	0.968109	−	0.250530i	$-0.0806047\pi$
$709$	508.764	+	508.764i	0.717579	+	0.717579i	−0.250530	+	0.968109i	$0.580605\pi$
$710$	−381.377	+	381.377i	−0.537151	+	0.537151i
$711$	−774.757	+	774.757i	−1.08967	+	1.08967i
$712$	432.098	+	432.098i	0.606879	+	0.606879i
$713$			74.2329i			0.104114i
$714$	−81.9821	+	334.356i	−0.114821	+	0.468285i
$715$	709.034			0.991656
$716$	35.5842	−	35.5842i	0.0496986	−	0.0496986i
$717$	−109.976			−0.153384
$718$			425.627i			0.592796i
$719$	−239.727	−	239.727i	−0.333417	−	0.333417i	0.520465	−	0.853883i	$-0.325758\pi$
$719$	−239.727	−	239.727i	−0.333417	−	0.333417i	−0.853883	+	0.520465i	$0.825758\pi$
$720$		−	83.4534i		−	0.115907i
$721$	−145.468	−	35.6679i	−0.201758	−	0.0494700i
$722$	−700.858			−0.970717
$723$	−48.4204	+	48.4204i	−0.0669715	+	0.0669715i
$724$	705.080	+	705.080i	0.973868	+	0.973868i
$725$	241.608	+	241.608i	0.333253	+	0.333253i
$726$	98.8419	−	98.8419i	0.136146	−	0.136146i
$727$	798.326	−	798.326i	1.09811	−	1.09811i	0.103478	−	0.994632i	$-0.467003\pi$
$727$	798.326	−	798.326i	1.09811	−	1.09811i	0.994632	−	0.103478i	$-0.0329971\pi$
$728$	563.715	+	929.955i	0.774334	+	1.27741i
$729$		−	453.916i		−	0.622656i
$730$		−	731.206i		−	1.00165i
$731$	−359.660	+	359.660i	−0.492010	+	0.492010i
$732$	−132.301	+	132.301i	−0.180739	+	0.180739i
$733$	−1134.49			−1.54774			−0.773868	−	0.633347i	$-0.781681\pi$
$733$	−1134.49			−1.54774			−0.773868	+	0.633347i	$0.781681\pi$
$734$		−	1868.76i		−	2.54599i
$735$	−143.274	+	45.0267i	−0.194930	+	0.0612608i
$736$			700.977i			0.952414i
$737$	21.6664			0.0293981
$738$	262.349	−	1067.37i	0.355486	−	1.44629i
$739$	−422.469			−0.571676			−0.285838	−	0.958278i	$-0.592272\pi$
$739$	−422.469			−0.571676			−0.285838	+	0.958278i	$0.592272\pi$
$740$	−118.937			−0.160725
$741$	145.129	−	145.129i	0.195855	−	0.195855i
$742$	−357.137	+	216.487i	−0.481316	+	0.291762i
$743$		−	930.010i		−	1.25170i	−0.779945	−	0.625848i	$-0.784753\pi$
$743$		−	930.010i		−	1.25170i	0.779945	−	0.625848i	$-0.215247\pi$
$744$	14.4692	−	14.4692i	0.0194479	−	0.0194479i
$745$	−586.514	+	586.514i	−0.787267	+	0.787267i
$746$		−	1817.89i		−	2.43685i
$747$	736.549			0.986009
$748$		−	988.082i		−	1.32097i
$749$	−255.728	−	62.7030i	−0.341426	−	0.0837156i
$750$	−237.285	−	237.285i	−0.316380	−	0.316380i
$751$	769.335	+	769.335i	1.02441	+	1.02441i	0.999694	+	0.0247195i	$0.00786927\pi$
$751$	769.335	+	769.335i	1.02441	+	1.02441i	0.0247195	+	0.999694i	$0.492131\pi$
$752$	41.3355	+	41.3355i	0.0549675	+	0.0549675i
$753$	−101.160	+	101.160i	−0.134343	+	0.134343i
$754$			2612.19i			3.46444i
$755$	667.606	+	667.606i	0.884246	+	0.884246i
$756$	302.068	+	498.319i	0.399561	+	0.659152i
$757$	86.5594	−	86.5594i	0.114345	−	0.114345i	−0.647619	−	0.761964i	$-0.724235\pi$
$757$	86.5594	−	86.5594i	0.114345	−	0.114345i	0.761964	+	0.647619i	$0.224235\pi$
$758$			1067.15i			1.40785i
$759$	−121.382			−0.159923
$760$	231.897	−	231.897i	0.305127	−	0.305127i
$761$		−	1156.24i		−	1.51937i	−0.650293	−	0.759683i	$-0.725354\pi$
$761$		−	1156.24i		−	1.51937i	0.650293	−	0.759683i	$-0.274646\pi$
$762$	−303.011	−	303.011i	−0.397652	−	0.397652i
$763$	−953.387	+	577.919i	−1.24952	+	0.757430i
$764$	343.173	−	343.173i	0.449180	−	0.449180i
$765$	−468.655	+	468.655i	−0.612621	+	0.612621i
$766$	269.264	−	269.264i	0.351520	−	0.351520i
$767$	625.906	+	625.906i	0.816044	+	0.816044i
$768$	102.698	−	102.698i	0.133721	−	0.133721i
$769$			519.052i			0.674970i	0.941331	+	0.337485i	$0.109576\pi$
$769$			519.052i			0.674970i	−0.941331	+	0.337485i	$0.890424\pi$
$770$	607.106	−	368.013i	0.788450	−	0.477938i
$771$			276.475i			0.358592i
$772$	1118.59	+	1118.59i	1.44894	+	1.44894i
$773$	839.881	+	839.881i	1.08652	+	1.08652i	0.995884	+	0.0906367i	$0.0288902\pi$
$773$	839.881	+	839.881i	1.08652	+	1.08652i	0.0906367	+	0.995884i	$0.471110\pi$
$774$			684.605i			0.884503i
$775$		−	35.3586i		−	0.0456240i
$776$	−815.939	+	815.939i	−1.05147	+	1.05147i
$777$	−22.4980	+	13.6377i	−0.0289549	+	0.0175517i
$778$	−356.887			−0.458723
$779$	−417.008	+	252.459i	−0.535312	+	0.324081i
$780$		−	422.714i		−	0.541940i
$781$		−	342.420i		−	0.438438i
$782$	878.535	−	878.535i	1.12345	−	1.12345i
$783$			494.108i			0.631045i
$784$	−108.949	−	56.8448i	−0.138965	−	0.0725061i
$785$	−353.880	+	353.880i	−0.450802	+	0.450802i
$786$	−411.021	−	411.021i	−0.522928	−	0.522928i
$787$	762.661			0.969073			0.484537	−	0.874771i	$-0.338988\pi$
$787$	762.661			0.969073			0.484537	+	0.874771i	$0.338988\pi$
$788$			1478.59i			1.87638i
$789$		−	290.725i		−	0.368473i
$790$	1165.57	−	1165.57i	1.47541	−	1.47541i
$791$	569.119	+	139.545i	0.719493	+	0.176416i
$792$	−331.958	−	331.958i	−0.419139	−	0.419139i
$793$	−616.947	+	616.947i	−0.777991	+	0.777991i
$794$	−851.487	−	851.487i	−1.07240	−	1.07240i
$795$	57.3048			0.0720814
$796$	146.558	+	146.558i	0.184118	+	0.184118i
$797$			60.9149i			0.0764302i	0.999270	+	0.0382151i	$0.0121672\pi$
$797$			60.9149i			0.0764302i	−0.999270	+	0.0382151i	$0.987833\pi$
$798$	48.9388	−	199.592i	0.0613269	−	0.250115i
$799$		−	464.262i		−	0.581053i
$800$		−	333.889i		−	0.417361i
$801$	521.285	+	521.285i	0.650793	+	0.650793i
$802$	796.248			0.992828
$803$	328.257	+	328.257i	0.408788	+	0.408788i
$804$		−	12.9171i		−	0.0160661i
$805$	526.416	+	129.074i	0.653933	+	0.160341i
$806$	191.143	−	191.143i	0.237150	−	0.237150i
$807$	−147.706	−	147.706i	−0.183031	−	0.183031i
$808$	795.301	−	795.301i	0.984283	−	0.984283i
$809$	−625.026	−	625.026i	−0.772591	−	0.772591i	0.205968	−	0.978559i	$-0.433966\pi$
$809$	−625.026	−	625.026i	−0.772591	−	0.772591i	−0.978559	+	0.205968i	$0.933966\pi$
$810$			823.964i			1.01724i
$811$	301.350			0.371578			0.185789	−	0.982590i	$-0.440516\pi$
$811$	301.350			0.371578			0.185789	+	0.982590i	$0.440516\pi$
$812$	823.202	+	1358.03i	1.01380	+	1.67245i
$813$	95.0967	+	95.0967i	0.116970	+	0.116970i
$814$	87.9397	−	87.9397i	0.108034	−	0.108034i
$815$	−111.765			−0.137134
$816$	38.6521			0.0473678
$817$	214.697	−	214.697i	0.262787	−	0.262787i
$818$	−1538.33			−1.88060
$819$	680.068	+	1121.90i	0.830364	+	1.36984i
$820$	−239.640	+	974.973i	−0.292243	+	1.18899i
$821$	371.422			0.452402			0.226201	−	0.974081i	$-0.427369\pi$
$821$	371.422			0.452402			0.226201	+	0.974081i	$0.427369\pi$
$822$	160.679			0.195473
$823$	−1075.19	−	1075.19i	−1.30643	−	1.30643i	−0.923973	−	0.382458i	$-0.875078\pi$
$823$	−1075.19	−	1075.19i	−1.30643	−	1.30643i	−0.382458	−	0.923973i	$-0.624922\pi$
$824$		−	149.003i		−	0.180829i
$825$	57.8164			0.0700805
$826$	860.795	+	211.062i	1.04212	+	0.255523i
$827$	1104.01	+	1104.01i	1.33496	+	1.33496i	0.900868	+	0.434093i	$0.142931\pi$
$827$	1104.01	+	1104.01i	1.33496	+	1.33496i	0.434093	+	0.900868i	$0.357069\pi$
$828$		−	1015.34i		−	1.22626i
$829$	1116.70			1.34704			0.673521	−	0.739168i	$-0.264781\pi$
$829$	1116.70			1.34704			0.673521	+	0.739168i	$0.264781\pi$
$830$	−1108.09			−1.33505
$831$	−39.9259	+	39.9259i	−0.0480456	+	0.0480456i
$832$	1646.71	−	1646.71i	1.97922	−	1.97922i
$833$	292.604	+	931.058i	0.351265	+	1.11772i
$834$	−438.560	+	438.560i	−0.525852	+	0.525852i
$835$	−706.298	+	706.298i	−0.845866	+	0.845866i
$836$			589.831i			0.705539i
$837$	36.1556	−	36.1556i	0.0431967	−	0.0431967i
$838$		−	387.565i		−	0.462489i
$839$	290.266	+	290.266i	0.345966	+	0.345966i	0.858605	−	0.512638i	$-0.171332\pi$
$839$	290.266	+	290.266i	0.345966	+	0.345966i	−0.512638	+	0.858605i	$0.671332\pi$
$840$	−77.4485	−	127.766i	−0.0922007	−	0.152102i
$841$			505.552i			0.601132i
$842$	1306.78	−	1306.78i	1.55200	−	1.55200i
$843$			92.8234i			0.110111i
$844$	288.664	−	288.664i	0.342018	−	0.342018i
$845$		−	1301.81i		−	1.54060i
$846$	−441.857	−	441.857i	−0.522289	−	0.522289i
$847$	94.3696	−	384.877i	0.111416	−	0.454400i
$848$	33.1560	+	33.1560i	0.0390990	+	0.0390990i
$849$	−32.1473	−	32.1473i	−0.0378649	−	0.0378649i
$850$	−418.463	+	418.463i	−0.492310	+	0.492310i
$851$	94.9482			0.111572
$852$	−204.145			−0.239606
$853$	−891.784			−1.04547			−0.522734	−	0.852496i	$-0.675088\pi$
$853$	−891.784			−1.04547			−0.522734	+	0.852496i	$0.675088\pi$
$854$	−208.041	+	848.473i	−0.243608	+	0.993528i
$855$	279.761	−	279.761i	0.327206	−	0.327206i
$856$		−	261.943i		−	0.306009i
$857$			340.117i			0.396870i	0.980114	+	0.198435i	$0.0635858\pi$
$857$			340.117i			0.396870i	−0.980114	+	0.198435i	$0.936414\pi$
$858$	312.547	+	312.547i	0.364273	+	0.364273i
$859$	809.559			0.942443			0.471222	−	0.882015i	$-0.343813\pi$
$859$	809.559			0.942443			0.471222	+	0.882015i	$0.343813\pi$
$860$		−	625.345i		−	0.727145i
$861$	66.4638	+	211.903i	0.0771937	+	0.246112i
$862$	1526.12			1.77044
$863$		−	695.590i		−	0.806014i	−0.915197	−	0.403007i	$-0.867965\pi$
$863$		−	695.590i		−	0.806014i	0.915197	−	0.403007i	$-0.132035\pi$
$864$	341.415	−	341.415i	0.395156	−	0.395156i
$865$	−505.073			−0.583899
$866$	−2060.54			−2.37937
$867$	−58.9315	−	58.9315i	−0.0679718	−	0.0679718i
$868$	39.1350	−	159.608i	0.0450864	−	0.183880i
$869$			1046.51i			1.20427i
$870$		−	358.888i		−	0.412515i
$871$		−	60.2352i		−	0.0691564i
$872$	−784.262	−	784.262i	−0.899383	−	0.899383i
$873$	−984.352	+	984.352i	−1.12755	+	1.12755i
$874$	−524.437	+	524.437i	−0.600043	+	0.600043i
$875$	−923.955	−	226.549i	−1.05595	−	0.258913i
$876$	195.701	−	195.701i	0.223403	−	0.223403i
$877$	349.522			0.398543			0.199271	−	0.979944i	$-0.436142\pi$
$877$	349.522			0.398543			0.199271	+	0.979944i	$0.436142\pi$
$878$	−188.027	−	188.027i	−0.214154	−	0.214154i
$879$	417.532			0.475008
$880$	−56.3627	−	56.3627i	−0.0640485	−	0.0640485i
$881$	1324.28			1.50316			0.751579	−	0.659643i	$-0.229292\pi$
$881$	1324.28			1.50316			0.751579	+	0.659643i	$0.229292\pi$
$882$	1164.61	+	607.643i	1.32042	+	0.688938i
$883$	861.176	−	861.176i	0.975285	−	0.975285i	−0.0244170	−	0.999702i	$-0.507773\pi$
$883$	861.176	−	861.176i	0.975285	−	0.975285i	0.999702	+	0.0244170i	$0.00777296\pi$
$884$	−2746.99			−3.10745
$885$	−85.9929	−	85.9929i	−0.0971672	−	0.0971672i
$886$	−2569.98			−2.90065
$887$	−78.2717	−	78.2717i	−0.0882432	−	0.0882432i	0.661607	−	0.749850i	$-0.269875\pi$
$887$	−78.2717	−	78.2717i	−0.0882432	−	0.0882432i	−0.749850	+	0.661607i	$0.769875\pi$
$888$	−18.5070	−	18.5070i	−0.0208412	−	0.0208412i
$889$	−1179.88	−	289.301i	−1.32720	−	0.325422i
$890$	−784.240	−	784.240i	−0.881168	−	0.881168i
$891$	−369.899	−	369.899i	−0.415150	−	0.415150i
$892$			20.3276i			0.0227887i
$893$			277.139i			0.310346i
$894$	−517.078			−0.578387
$895$	−22.7979	+	22.7979i	−0.0254725	+	0.0254725i
$896$	316.188	−	1289.54i	0.352888	−	1.43922i
$897$			337.456i			0.376205i
$898$	2289.50			2.54956
$899$	98.5319	−	98.5319i	0.109602	−	0.109602i
$900$			483.628i			0.537365i
$901$		−	372.393i		−	0.413310i
$902$	−543.692	−	898.062i	−0.602763	−	0.995634i
$903$	−71.7042	−	118.290i	−0.0794066	−	0.130996i
$904$			582.951i			0.644858i
$905$	−451.728	−	451.728i	−0.499147	−	0.499147i
$906$			588.570i			0.649635i
$907$			1617.21i			1.78303i	0.452995	+	0.891513i	$0.350356\pi$
$907$			1617.21i			1.78303i	−0.452995	+	0.891513i	$0.649644\pi$
$908$	−1383.79	−	1383.79i	−1.52400	−	1.52400i
$909$	959.455	−	959.455i	1.05551	−	1.05551i
$910$	−1023.12	−	1687.83i	−1.12431	−	1.85476i
$911$		−	1329.11i		−	1.45896i	−0.684003	−	0.729479i	$-0.739762\pi$
$911$		−	1329.11i		−	1.45896i	0.684003	−	0.729479i	$-0.260238\pi$
$912$	−23.0732			−0.0252995
$913$	497.450	−	497.450i	0.544852	−	0.544852i
$914$	−156.165	−	156.165i	−0.170859	−	0.170859i
$915$	84.7620	−	84.7620i	0.0926361	−	0.0926361i
$916$	505.019	+	505.019i	0.551330	+	0.551330i
$917$	−1600.46	−	392.424i	−1.74532	−	0.427943i
$918$	−855.792			−0.932235
$919$	6.07145	−	6.07145i	0.00660658	−	0.00660658i	−0.703796	−	0.710402i	$-0.748513\pi$
$919$	6.07145	−	6.07145i	0.00660658	−	0.00660658i	0.710402	+	0.703796i	$0.248513\pi$
$920$			539.211i			0.586099i
$921$	191.536	−	191.536i	0.207966	−	0.207966i
$922$	−440.349			−0.477602
$923$	−951.968			−1.03138
$924$	260.982	+	63.9914i	0.282448	+	0.0692547i
$925$	−45.2256			−0.0488926
$926$	711.797	−	711.797i	0.768680	−	0.768680i
$927$		−	179.758i		−	0.193914i
$928$	930.430	−	930.430i	1.00262	−	1.00262i
$929$	819.752	+	819.752i	0.882402	+	0.882402i	0.993778	−	0.111376i	$-0.0355259\pi$
$929$	819.752	+	819.752i	0.882402	+	0.882402i	−0.111376	+	0.993778i	$0.535526\pi$
$930$	−26.2610	+	26.2610i	−0.0282377	+	0.0282377i
$931$	−174.669	−	555.791i	−0.187614	−	0.596983i
$932$	−159.364	−	159.364i	−0.170991	−	0.170991i
$933$	261.677			0.280468
$934$	−1902.12			−2.03654
$935$			633.040i			0.677048i
$936$	−922.884	+	922.884i	−0.985987	+	0.985987i
$937$	676.985	+	676.985i	0.722502	+	0.722502i	0.969114	−	0.246612i	$-0.0793173\pi$
$937$	676.985	+	676.985i	0.722502	+	0.722502i	−0.246612	+	0.969114i	$0.579317\pi$
$938$	−31.2641	−	51.5760i	−0.0333306	−	0.0549851i
$939$	211.154			0.224872
$940$	403.609	+	403.609i	0.429371	+	0.429371i
$941$	−1712.52			−1.81989			−0.909944	−	0.414730i	$-0.863876\pi$
$941$	−1712.52			−1.81989			−0.909944	+	0.414730i	$0.863876\pi$
$942$	−311.985			−0.331194
$943$	191.306	−	778.329i	0.202870	−	0.825375i
$944$		−	99.5094i		−	0.105412i
$945$	−193.528	−	319.261i	−0.204791	−	0.337842i
$946$	462.368	+	462.368i	0.488762	+	0.488762i
$947$	819.577			0.865445			0.432723	−	0.901527i	$-0.357553\pi$
$947$	819.577			0.865445			0.432723	+	0.901527i	$0.357553\pi$
$948$	623.911			0.658134
$949$	912.594	−	912.594i	0.961638	−	0.961638i
$950$	249.800	−	249.800i	0.262947	−	0.262947i
$951$	184.907			0.194434
$952$	−830.282	+	503.296i	−0.872145	+	0.528673i
$953$	−37.0426			−0.0388695			−0.0194347	−	0.999811i	$-0.506187\pi$
$953$	−37.0426			−0.0388695			−0.0194347	+	0.999811i	$0.506187\pi$
$954$	−354.421	−	354.421i	−0.371511	−	0.371511i
$955$	−219.863	+	219.863i	−0.230223	+	0.230223i
$956$	−621.308	−	621.308i	−0.649903	−	0.649903i
$957$	161.114	+	161.114i	0.168353	+	0.168353i
$958$	−472.733	−	472.733i	−0.493458	−	0.493458i
$959$	389.535	−	236.127i	0.406189	−	0.246222i
$960$	−226.240	+	226.240i	−0.235667	+	0.235667i
$961$	946.580			0.984995
$962$	−244.483	−	244.483i	−0.254140	−	0.254140i
$963$		−	316.010i		−	0.328151i
$964$	−547.100			−0.567531
$965$	−716.650	−	716.650i	−0.742643	−	0.742643i
$966$	175.151	+	288.944i	0.181316	+	0.299114i
$967$	−639.851	+	639.851i	−0.661687	+	0.661687i	−0.955777	−	0.294091i	$-0.904983\pi$
$967$	−639.851	+	639.851i	−0.661687	+	0.661687i	0.294091	+	0.955777i	$0.404983\pi$
$968$	394.231			0.407264
$969$	129.574	+	129.574i	0.133719	+	0.133719i
$970$	1480.89	−	1480.89i	1.52670	−	1.52670i
$971$	353.535	−	353.535i	0.364094	−	0.364094i	−0.501224	−	0.865318i	$-0.667117\pi$
$971$	353.535	−	353.535i	0.364094	−	0.364094i	0.865318	+	0.501224i	$0.167117\pi$
$972$	−750.303	+	750.303i	−0.771917	+	0.771917i
$973$	−418.717	+	1707.69i	−0.430336	+	1.75508i
$974$	2869.98			2.94659
$975$		−	160.737i		−	0.164858i
$976$	98.0850			0.100497
$977$	−39.2863	−	39.2863i	−0.0402111	−	0.0402111i	0.686715	−	0.726926i	$-0.259052\pi$
$977$	−39.2863	−	39.2863i	−0.0402111	−	0.0402111i	−0.726926	+	0.686715i	$0.759052\pi$
$978$	−49.2665	−	49.2665i	−0.0503747	−	0.0503747i
$979$	704.131			0.719235
$980$	−1063.80	−	555.044i	−1.08551	−	0.566372i
$981$	−946.138	−	946.138i	−0.964462	−	0.964462i
$982$		−	470.960i		−	0.479593i
$983$		−	175.087i		−	0.178115i	−0.996026	−	0.0890575i	$-0.971614\pi$
$983$		−	175.087i		−	0.178115i	0.996026	−	0.0890575i	$-0.0283855\pi$
$984$	−188.998	+	114.420i	−0.192071	+	0.116281i
$985$		−	947.294i		−	0.961719i
$986$	−2332.22			−2.36533
$987$	122.625	+	30.0671i	0.124241	+	0.0304631i
$988$	1639.80			1.65972
$989$			499.218i			0.504770i
$990$	602.490	+	602.490i	0.608576	+	0.608576i
$991$	1057.60	+	1057.60i	1.06720	+	1.06720i	0.997573	+	0.0696279i	$0.0221812\pi$
$991$	1057.60	+	1057.60i	1.06720	+	1.06720i	0.0696279	+	0.997573i	$0.477819\pi$
$992$	−136.165			−0.137264
$993$	−415.389			−0.418318
$994$	−815.117	+	494.103i	−0.820037	+	0.497086i
$995$	−93.8960	−	93.8960i	−0.0943678	−	0.0943678i
$996$	−296.571	−	296.571i	−0.297762	−	0.297762i
$997$	404.378	−	404.378i	0.405595	−	0.405595i	−0.474604	−	0.880199i	$-0.657409\pi$
$997$	404.378	−	404.378i	0.405595	−	0.405595i	0.880199	+	0.474604i	$0.157409\pi$
$998$	594.373	−	594.373i	0.595564	−	0.595564i
$999$	−46.2451	−	46.2451i	−0.0462914	−	0.0462914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.7	✓	108
7.6	odd	2	inner	287.3.g.a.132.8	yes	108
41.32	even	4	inner	287.3.g.a.237.48	yes	108
287.237	odd	4	inner	287.3.g.a.237.47	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.7	✓	108	1.1	even	1	trivial
287.3.g.a.132.8	yes	108	7.6	odd	2	inner
287.3.g.a.237.47	yes	108	287.237	odd	4	inner
287.3.g.a.237.48	yes	108	41.32	even	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.19098i q^{2} +(-0.547162 + 0.547162i) q^{3} -6.18236 q^{4} +3.96088 q^{5} +(1.74598 + 1.74598i) q^{6} +(6.79862 + 1.66698i) q^{7} +6.96386i q^{8} +8.40123i q^{9} +O(q^{10})\)	\(q-3.19098i q^{2} +(-0.547162 + 0.547162i) q^{3} -6.18236 q^{4} +3.96088 q^{5} +(1.74598 + 1.74598i) q^{6} +(6.79862 + 1.66698i) q^{7} +6.96386i q^{8} +8.40123i q^{9} -12.6391i q^{10} +(5.67402 + 5.67402i) q^{11} +(3.38275 - 3.38275i) q^{12} +(15.7745 - 15.7745i) q^{13} +(5.31931 - 21.6942i) q^{14} +(-2.16724 + 2.16724i) q^{15} -2.50789 q^{16} +(14.0838 + 14.0838i) q^{17} +26.8082 q^{18} +(-8.40723 - 8.40723i) q^{19} -24.4876 q^{20} +(-4.63205 + 2.80783i) q^{21} +(18.1057 - 18.1057i) q^{22} +19.5486 q^{23} +(-3.81036 - 3.81036i) q^{24} -9.31140 q^{25} +(-50.3360 - 50.3360i) q^{26} +(-9.52129 - 9.52129i) q^{27} +(-42.0315 - 10.3059i) q^{28} +(-25.9476 - 25.9476i) q^{29} +(6.91563 + 6.91563i) q^{30} +3.79734i q^{31} +35.8581i q^{32} -6.20921 q^{33} +(44.9410 - 44.9410i) q^{34} +(26.9285 + 6.60272i) q^{35} -51.9394i q^{36} +4.85702 q^{37} +(-26.8273 + 26.8273i) q^{38} +17.2624i q^{39} +27.5830i q^{40} +(9.78616 - 39.8150i) q^{41} +(8.95974 + 14.7808i) q^{42} +25.5372i q^{43} +(-35.0788 - 35.0788i) q^{44} +33.2763i q^{45} -62.3793i q^{46} +(-16.4822 - 16.4822i) q^{47} +(1.37222 - 1.37222i) q^{48} +(43.4423 + 22.6663i) q^{49} +29.7125i q^{50} -15.4122 q^{51} +(-97.5233 + 97.5233i) q^{52} +(-13.2206 - 13.2206i) q^{53} +(-30.3822 + 30.3822i) q^{54} +(22.4741 + 22.4741i) q^{55} +(-11.6086 + 47.3446i) q^{56} +9.20023 q^{57} +(-82.7982 + 82.7982i) q^{58} +39.6785i q^{59} +(13.3987 - 13.3987i) q^{60} -39.1105 q^{61} +12.1173 q^{62} +(-14.0047 + 57.1167i) q^{63} +104.391 q^{64} +(62.4808 - 62.4808i) q^{65} +19.8135i q^{66} +(1.90926 - 1.90926i) q^{67} +(-87.0708 - 87.0708i) q^{68} +(-10.6963 + 10.6963i) q^{69} +(21.0692 - 85.9284i) q^{70} +(-30.1744 - 30.1744i) q^{71} -58.5050 q^{72} +57.8527 q^{73} -15.4987i q^{74} +(5.09484 - 5.09484i) q^{75} +(51.9765 + 51.9765i) q^{76} +(29.1170 + 48.0340i) q^{77} +55.0838 q^{78} +(92.2195 + 92.2195i) q^{79} -9.93347 q^{80} -65.1917 q^{81} +(-127.049 - 31.2274i) q^{82} -87.6716i q^{83} +(28.6370 - 17.3590i) q^{84} +(55.7841 + 55.7841i) q^{85} +81.4887 q^{86} +28.3950 q^{87} +(-39.5131 + 39.5131i) q^{88} +(62.0487 - 62.0487i) q^{89} +106.184 q^{90} +(133.540 - 80.9487i) q^{91} -120.857 q^{92} +(-2.07776 - 2.07776i) q^{93} +(-52.5943 + 52.5943i) q^{94} +(-33.3001 - 33.3001i) q^{95} +(-19.6202 - 19.6202i) q^{96} +(117.168 + 117.168i) q^{97} +(72.3279 - 138.624i) q^{98} +(-47.6687 + 47.6687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \) 108 * q - 216 * q^4 - 2 * q^7	\( 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) \) 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Introduction

L-functions

Modular forms

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Database

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