LMFDB - Embedded newform 287.3.g.a.132.16

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			132.16
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73155i q^{2} +(2.85212 - 2.85212i) q^{3} +1.00173 q^{4} -4.47811 q^{5} +(-4.93859 - 4.93859i) q^{6} +(5.62348 + 4.16852i) q^{7} -8.66075i q^{8} -7.26914i q^{9} +O(q^{10})$	\(q-1.73155i q^{2} +(2.85212 - 2.85212i) q^{3} +1.00173 q^{4} -4.47811 q^{5} +(-4.93859 - 4.93859i) q^{6} +(5.62348 + 4.16852i) q^{7} -8.66075i q^{8} -7.26914i q^{9} +7.75408i q^{10} +(-4.70640 - 4.70640i) q^{11} +(2.85705 - 2.85705i) q^{12} +(10.0575 - 10.0575i) q^{13} +(7.21800 - 9.73734i) q^{14} +(-12.7721 + 12.7721i) q^{15} -10.9896 q^{16} +(-19.3478 - 19.3478i) q^{17} -12.5869 q^{18} +(-10.5848 - 10.5848i) q^{19} -4.48586 q^{20} +(27.9279 - 4.14972i) q^{21} +(-8.14938 + 8.14938i) q^{22} +20.4618 q^{23} +(-24.7015 - 24.7015i) q^{24} -4.94651 q^{25} +(-17.4150 - 17.4150i) q^{26} +(4.93661 + 4.93661i) q^{27} +(5.63320 + 4.17573i) q^{28} +(32.3802 + 32.3802i) q^{29} +(22.1156 + 22.1156i) q^{30} +50.2490i q^{31} -15.6139i q^{32} -26.8464 q^{33} +(-33.5018 + 33.5018i) q^{34} +(-25.1826 - 18.6671i) q^{35} -7.28172i q^{36} +29.5649 q^{37} +(-18.3280 + 18.3280i) q^{38} -57.3701i q^{39} +38.7838i q^{40} +(22.5580 - 34.2365i) q^{41} +(-7.18545 - 48.3586i) q^{42} +74.9758i q^{43} +(-4.71454 - 4.71454i) q^{44} +32.5520i q^{45} -35.4307i q^{46} +(-8.59188 - 8.59188i) q^{47} +(-31.3437 + 31.3437i) q^{48} +(14.2470 + 46.8831i) q^{49} +8.56513i q^{50} -110.365 q^{51} +(10.0749 - 10.0749i) q^{52} +(16.4924 + 16.4924i) q^{53} +(8.54799 - 8.54799i) q^{54} +(21.0758 + 21.0758i) q^{55} +(36.1025 - 48.7035i) q^{56} -60.3779 q^{57} +(56.0680 - 56.0680i) q^{58} -3.81468i q^{59} +(-12.7942 + 12.7942i) q^{60} -4.31241 q^{61} +87.0088 q^{62} +(30.3015 - 40.8779i) q^{63} -70.9948 q^{64} +(-45.0384 + 45.0384i) q^{65} +46.4860i q^{66} +(80.1024 - 80.1024i) q^{67} +(-19.3813 - 19.3813i) q^{68} +(58.3595 - 58.3595i) q^{69} +(-32.3230 + 43.6049i) q^{70} +(-29.7478 - 29.7478i) q^{71} -62.9563 q^{72} +5.88004 q^{73} -51.1932i q^{74} +(-14.1080 + 14.1080i) q^{75} +(-10.6031 - 10.6031i) q^{76} +(-6.84763 - 46.0851i) q^{77} -99.3393 q^{78} +(-89.2277 - 89.2277i) q^{79} +49.2128 q^{80} +93.5818 q^{81} +(-59.2822 - 39.0604i) q^{82} +122.374i q^{83} +(27.9762 - 4.15689i) q^{84} +(86.6417 + 86.6417i) q^{85} +129.825 q^{86} +184.704 q^{87} +(-40.7610 + 40.7610i) q^{88} +(-39.5686 + 39.5686i) q^{89} +56.3655 q^{90} +(98.4826 - 14.6332i) q^{91} +20.4972 q^{92} +(143.316 + 143.316i) q^{93} +(-14.8773 + 14.8773i) q^{94} +(47.3997 + 47.3997i) q^{95} +(-44.5327 - 44.5327i) q^{96} +(70.3650 + 70.3650i) q^{97} +(81.1805 - 24.6693i) q^{98} +(-34.2115 + 34.2115i) 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 $

$2$		−	1.73155i		−	0.865776i	−0.901448	−	0.432888i	$-0.857495\pi$
$2$		−	1.73155i		−	0.865776i	0.901448	−	0.432888i	$-0.142505\pi$
$3$	2.85212	−	2.85212i	0.950706	−	0.950706i	−0.0481351	−	0.998841i	$-0.515328\pi$
$3$	2.85212	−	2.85212i	0.950706	−	0.950706i	0.998841	+	0.0481351i	$0.0153278\pi$
$4$	1.00173			0.250432
$5$	−4.47811			−0.895623			−0.447811	−	0.894128i	$-0.647796\pi$
$5$	−4.47811			−0.895623			−0.447811	+	0.894128i	$0.647796\pi$
$6$	−4.93859	−	4.93859i	−0.823098	−	0.823098i
$7$	5.62348	+	4.16852i	0.803354	+	0.595502i
$7$	5.62348	+	4.16852i	0.803354	+	0.595502i
$8$		−	8.66075i		−	1.08259i
$9$		−	7.26914i		−	0.807683i
$10$			7.75408i			0.775408i
$11$	−4.70640	−	4.70640i	−0.427855	−	0.427855i	0.460042	−	0.887897i	$-0.347834\pi$
$11$	−4.70640	−	4.70640i	−0.427855	−	0.427855i	−0.887897	+	0.460042i	$0.847834\pi$
$12$	2.85705	−	2.85705i	0.238088	−	0.238088i
$13$	10.0575	−	10.0575i	0.773651	−	0.773651i	−0.205092	−	0.978743i	$-0.565749\pi$
$13$	10.0575	−	10.0575i	0.773651	−	0.773651i	0.978743	+	0.205092i	$0.0657493\pi$
$14$	7.21800	−	9.73734i	0.515571	−	0.695524i
$15$	−12.7721	+	12.7721i	−0.851473	+	0.851473i
$16$	−10.9896			−0.686851
$17$	−19.3478	−	19.3478i	−1.13811	−	1.13811i	−0.988789	−	0.149318i	$-0.952292\pi$
$17$	−19.3478	−	19.3478i	−1.13811	−	1.13811i	−0.149318	−	0.988789i	$-0.547708\pi$
$18$	−12.5869			−0.699272
$19$	−10.5848	−	10.5848i	−0.557092	−	0.557092i	0.371386	−	0.928479i	$-0.378883\pi$
$19$	−10.5848	−	10.5848i	−0.557092	−	0.557092i	−0.928479	+	0.371386i	$0.878883\pi$
$20$	−4.48586			−0.224293
$21$	27.9279	−	4.14972i	1.32990	−	0.197606i
$22$	−8.14938	+	8.14938i	−0.370426	+	0.370426i
$23$	20.4618			0.889644			0.444822	−	0.895619i	$-0.353267\pi$
$23$	20.4618			0.889644			0.444822	+	0.895619i	$0.353267\pi$
$24$	−24.7015	−	24.7015i	−1.02923	−	1.02923i
$25$	−4.94651			−0.197860
$26$	−17.4150	−	17.4150i	−0.669808	−	0.669808i
$27$	4.93661	+	4.93661i	0.182837	+	0.182837i
$28$	5.63320	+	4.17573i	0.201186	+	0.149133i
$29$	32.3802	+	32.3802i	1.11656	+	1.11656i	0.992243	+	0.124317i	$0.0396740\pi$
$29$	32.3802	+	32.3802i	1.11656	+	1.11656i	0.124317	+	0.992243i	$0.460326\pi$
$30$	22.1156	+	22.1156i	0.737185	+	0.737185i
$31$			50.2490i			1.62094i	0.585782	+	0.810468i	$0.300787\pi$
$31$			50.2490i			1.62094i	−0.585782	+	0.810468i	$0.699213\pi$
$32$		−	15.6139i		−	0.487935i
$33$	−26.8464			−0.813528
$34$	−33.5018	+	33.5018i	−0.985346	+	0.985346i
$35$	−25.1826	−	18.6671i	−0.719502	−	0.533345i
$36$		−	7.28172i		−	0.202270i
$37$	29.5649			0.799052			0.399526	−	0.916722i	$-0.369175\pi$
$37$	29.5649			0.799052			0.399526	+	0.916722i	$0.369175\pi$
$38$	−18.3280	+	18.3280i	−0.482317	+	0.482317i
$39$		−	57.3701i		−	1.47103i
$40$			38.7838i			0.969596i
$41$	22.5580	−	34.2365i	0.550195	−	0.835036i
$41$	22.5580	−	34.2365i	0.550195	−	0.835036i
$42$	−7.18545	−	48.3586i	−0.171082	−	1.15140i
$43$			74.9758i			1.74362i	0.489841	+	0.871812i	$0.337055\pi$
$43$			74.9758i			1.74362i	−0.489841	+	0.871812i	$0.662945\pi$
$44$	−4.71454	−	4.71454i	−0.107149	−	0.107149i
$45$			32.5520i			0.723379i
$46$		−	35.4307i		−	0.770232i
$47$	−8.59188	−	8.59188i	−0.182806	−	0.182806i	0.609771	−	0.792577i	$-0.291261\pi$
$47$	−8.59188	−	8.59188i	−0.182806	−	0.182806i	−0.792577	+	0.609771i	$0.791261\pi$
$48$	−31.3437	+	31.3437i	−0.652993	+	0.652993i
$49$	14.2470	+	46.8831i	0.290754	+	0.956798i
$50$			8.56513i			0.171303i
$51$	−110.365			−2.16401
$52$	10.0749	−	10.0749i	0.193747	−	0.193747i
$53$	16.4924	+	16.4924i	0.311177	+	0.311177i	0.845365	−	0.534189i	$-0.179383\pi$
$53$	16.4924	+	16.4924i	0.311177	+	0.311177i	−0.534189	+	0.845365i	$0.679383\pi$
$54$	8.54799	−	8.54799i	0.158296	−	0.158296i
$55$	21.0758	+	21.0758i	0.383197	+	0.383197i
$56$	36.1025	−	48.7035i	0.644687	−	0.869706i
$57$	−60.3779			−1.05926
$58$	56.0680	−	56.0680i	0.966690	−	0.966690i
$59$		−	3.81468i		−	0.0646556i	−0.999477	−	0.0323278i	$-0.989708\pi$
$59$		−	3.81468i		−	0.0646556i	0.999477	−	0.0323278i	$-0.0102920\pi$
$60$	−12.7942	+	12.7942i	−0.213237	+	0.213237i
$61$	−4.31241			−0.0706952			−0.0353476	−	0.999375i	$-0.511254\pi$
$61$	−4.31241			−0.0706952			−0.0353476	+	0.999375i	$0.511254\pi$
$62$	87.0088			1.40337
$63$	30.3015	−	40.8779i	0.480977	−	0.648855i
$64$	−70.9948			−1.10929
$65$	−45.0384	+	45.0384i	−0.692899	+	0.692899i
$66$			46.4860i			0.704333i
$67$	80.1024	−	80.1024i	1.19556	−	1.19556i	0.220076	−	0.975483i	$-0.429369\pi$
$67$	80.1024	−	80.1024i	1.19556	−	1.19556i	0.975483	−	0.220076i	$-0.0706305\pi$
$68$	−19.3813	−	19.3813i	−0.285019	−	0.285019i
$69$	58.3595	−	58.3595i	0.845790	−	0.845790i
$70$	−32.3230	+	43.6049i	−0.461757	+	0.622927i
$71$	−29.7478	−	29.7478i	−0.418983	−	0.418983i	0.465870	−	0.884853i	$-0.345741\pi$
$71$	−29.7478	−	29.7478i	−0.418983	−	0.418983i	−0.884853	+	0.465870i	$0.845741\pi$
$72$	−62.9563			−0.874392
$73$	5.88004			0.0805484			0.0402742	−	0.999189i	$-0.487177\pi$
$73$	5.88004			0.0805484			0.0402742	+	0.999189i	$0.487177\pi$
$74$		−	51.1932i		−	0.691800i
$75$	−14.1080	+	14.1080i	−0.188107	+	0.188107i
$76$	−10.6031	−	10.6031i	−0.139514	−	0.139514i
$77$	−6.84763	−	46.0851i	−0.0889303	−	0.598507i
$78$	−99.3393			−1.27358
$79$	−89.2277	−	89.2277i	−1.12946	−	1.12946i	−0.990264	−	0.139201i	$-0.955547\pi$
$79$	−89.2277	−	89.2277i	−1.12946	−	1.12946i	−0.139201	−	0.990264i	$-0.544453\pi$
$80$	49.2128			0.615159
$81$	93.5818			1.15533
$82$	−59.2822	−	39.0604i	−0.722954	−	0.476346i
$83$			122.374i			1.47439i	0.675681	+	0.737194i	$0.263850\pi$
$83$			122.374i			1.47439i	−0.675681	+	0.737194i	$0.736150\pi$
$84$	27.9762	−	4.15689i	0.333050	−	0.0494868i
$85$	86.6417	+	86.6417i	1.01931	+	1.01931i
$86$	129.825			1.50959
$87$	184.704			2.12304
$88$	−40.7610	+	40.7610i	−0.463193	+	0.463193i
$89$	−39.5686	+	39.5686i	−0.444591	+	0.444591i	−0.893552	−	0.448961i	$-0.851794\pi$
$89$	−39.5686	+	39.5686i	−0.444591	+	0.444591i	0.448961	+	0.893552i	$0.351794\pi$
$90$	56.3655			0.626284
$91$	98.4826	−	14.6332i	1.08223	−	0.160804i
$92$	20.4972			0.222796
$93$	143.316	+	143.316i	1.54103	+	1.54103i
$94$	−14.8773	+	14.8773i	−0.158269	+	0.158269i
$95$	47.3997	+	47.3997i	0.498945	+	0.498945i
$96$	−44.5327	−	44.5327i	−0.463882	−	0.463882i
$97$	70.3650	+	70.3650i	0.725413	+	0.725413i	0.969702	−	0.244290i	$-0.0785548\pi$
$97$	70.3650	+	70.3650i	0.725413	+	0.725413i	−0.244290	+	0.969702i	$0.578555\pi$
$98$	81.1805	−	24.6693i	0.828372	−	0.251728i
$99$	−34.2115	+	34.2115i	−0.345571	+	0.345571i
$100$	−4.95506			−0.0495506
$101$	65.6992	+	65.6992i	0.650487	+	0.650487i	0.953110	−	0.302623i	$-0.0978623\pi$
$101$	65.6992	+	65.6992i	0.650487	+	0.650487i	−0.302623	+	0.953110i	$0.597862\pi$
$102$			191.102i			1.87355i
$103$	117.150			1.13738			0.568690	−	0.822552i	$-0.307450\pi$
$103$	117.150			1.13738			0.568690	+	0.822552i	$0.307450\pi$
$104$	−87.1052	−	87.1052i	−0.837550	−	0.837550i
$105$	−125.064	+	18.5829i	−1.19109	+	0.176980i
$106$	28.5574	−	28.5574i	0.269409	−	0.269409i
$107$	−125.129			−1.16943			−0.584713	−	0.811240i	$-0.698793\pi$
$107$	−125.129			−1.16943			−0.584713	+	0.811240i	$0.698793\pi$
$108$	4.94514	+	4.94514i	0.0457884	+	0.0457884i
$109$	−62.6657	+	62.6657i	−0.574915	+	0.574915i	−0.933498	−	0.358583i	$-0.883260\pi$
$109$	−62.6657	+	62.6657i	−0.574915	+	0.574915i	0.358583	+	0.933498i	$0.383260\pi$
$110$	36.4939	−	36.4939i	0.331762	−	0.331762i
$111$	84.3226	−	84.3226i	0.759663	−	0.759663i
$112$	−61.7999	−	45.8104i	−0.551784	−	0.409021i
$113$	23.1964			0.205278			0.102639	−	0.994719i	$-0.467271\pi$
$113$	23.1964			0.205278			0.102639	+	0.994719i	$0.467271\pi$
$114$			104.547i			0.917083i
$115$	−91.6303			−0.796785
$116$	32.4362	+	32.4362i	0.279623	+	0.279623i
$117$	−73.1091	−	73.1091i	−0.624864	−	0.624864i
$118$	−6.60531			−0.0559772
$119$	−28.1503	−	189.454i	−0.236557	−	1.59205i
$120$	110.616	+	110.616i	0.921800	+	0.921800i
$121$		−	76.6995i		−	0.633880i
$122$			7.46715i			0.0612062i
$123$	−33.3084	−	161.985i	−0.270800	−	1.31695i
$124$			50.3360i			0.405935i
$125$	134.104			1.07283
$126$	−70.7821	−	52.4687i	−0.561763	−	0.416418i
$127$	193.317			1.52218			0.761089	−	0.648648i	$-0.224665\pi$
$127$	193.317			1.52218			0.761089	+	0.648648i	$0.224665\pi$
$128$			60.4754i			0.472464i
$129$	213.840	+	213.840i	1.65767	+	1.65767i
$130$	77.9864	+	77.9864i	0.599895	+	0.599895i
$131$	−73.3426			−0.559867			−0.279934	−	0.960019i	$-0.590312\pi$
$131$	−73.3426			−0.559867			−0.279934	+	0.960019i	$0.590312\pi$
$132$	−26.8929			−0.203734
$133$	−15.4004	−	103.646i	−0.115792	−	0.779292i
$134$	−138.701	−	138.701i	−1.03509	−	1.03509i
$135$	−22.1067	−	22.1067i	−0.163753	−	0.163753i
$136$	−167.567	+	167.567i	−1.23211	+	1.23211i
$137$	12.9929	−	12.9929i	0.0948384	−	0.0948384i	−0.658096	−	0.752934i	$-0.728638\pi$
$137$	12.9929	−	12.9929i	0.0948384	−	0.0948384i	0.752934	+	0.658096i	$0.228638\pi$
$138$	−101.052	−	101.052i	−0.732264	−	0.732264i
$139$			70.5142i			0.507296i	0.967297	+	0.253648i	$0.0816305\pi$
$139$			70.5142i			0.507296i	−0.967297	+	0.253648i	$0.918370\pi$
$140$	−25.2261	−	18.6994i	−0.180187	−	0.133567i
$141$	−49.0101			−0.347589
$142$	−51.5098	+	51.5098i	−0.362745	+	0.362745i
$143$	−94.6690			−0.662021
$144$			79.8851i			0.554758i
$145$	−145.002	−	145.002i	−1.00002	−	1.00002i
$146$		−	10.1816i		−	0.0697369i
$147$	174.350	+	93.0821i	1.18605	+	0.633211i
$148$	29.6161			0.200109
$149$	−42.0632	+	42.0632i	−0.282303	+	0.282303i	−0.834027	−	0.551724i	$-0.813970\pi$
$149$	−42.0632	+	42.0632i	−0.282303	+	0.282303i	0.551724	+	0.834027i	$0.313970\pi$
$150$	24.4288	+	24.4288i	0.162858	+	0.162858i
$151$	−178.083	−	178.083i	−1.17936	−	1.17936i	−0.979908	−	0.199448i	$-0.936085\pi$
$151$	−178.083	−	178.083i	−1.17936	−	1.17936i	−0.199448	−	0.979908i	$-0.563915\pi$
$152$	−91.6719	+	91.6719i	−0.603105	+	0.603105i
$153$	−140.642	+	140.642i	−0.919230	+	0.919230i
$154$	−79.7987	+	11.8570i	−0.518173	+	0.0769937i
$155$		−	225.021i		−	1.45175i
$156$		−	57.4693i		−	0.368393i
$157$	−134.046	+	134.046i	−0.853798	+	0.853798i	−0.990599	−	0.136801i	$-0.956318\pi$
$157$	−134.046	+	134.046i	−0.853798	+	0.853798i	0.136801	+	0.990599i	$0.456318\pi$
$158$	−154.502	+	154.502i	−0.977863	+	0.977863i
$159$	94.0763			0.591675
$160$			69.9209i			0.437005i
$161$	115.067	+	85.2954i	0.714699	+	0.529785i
$162$		−	162.042i		−	1.00026i
$163$	152.240			0.933987			0.466993	−	0.884261i	$-0.345337\pi$
$163$	152.240			0.933987			0.466993	+	0.884261i	$0.345337\pi$
$164$	22.5970	−	34.2957i	0.137787	−	0.209120i
$165$	120.221			0.728614
$166$	211.897			1.27649
$167$	−5.93594	+	5.93594i	−0.0355446	+	0.0355446i	−0.724656	−	0.689111i	$-0.758001\pi$
$167$	−5.93594	+	5.93594i	−0.0355446	+	0.0355446i	0.689111	+	0.724656i	$0.258001\pi$
$168$	−35.9397	−	241.877i	−0.213927	−	1.43974i
$169$		−	33.3051i		−	0.197071i
$170$	150.025	−	150.025i	0.882498	−	0.882498i
$171$	−76.9421	+	76.9421i	−0.449954	+	0.449954i
$172$			75.1055i			0.436660i
$173$	−198.807			−1.14917			−0.574587	−	0.818443i	$-0.694837\pi$
$173$	−198.807			−1.14917			−0.574587	+	0.818443i	$0.694837\pi$
$174$		−	319.825i		−	1.83808i
$175$	−27.8166	−	20.6196i	−0.158952	−	0.117826i
$176$	51.7216	+	51.7216i	0.293873	+	0.293873i
$177$	−10.8799	−	10.8799i	−0.0614684	−	0.0614684i
$178$	68.5151	+	68.5151i	0.384916	+	0.384916i
$179$	−28.6827	+	28.6827i	−0.160238	+	0.160238i	−0.782672	−	0.622434i	$-0.786144\pi$
$179$	−28.6827	+	28.6827i	−0.160238	+	0.160238i	0.622434	+	0.782672i	$0.286144\pi$
$180$			32.6083i			0.181157i
$181$	−150.226	−	150.226i	−0.829979	−	0.829979i	0.157535	−	0.987513i	$-0.449645\pi$
$181$	−150.226	−	150.226i	−0.829979	−	0.829979i	−0.987513	+	0.157535i	$0.949645\pi$
$182$	−25.3381	−	170.528i	−0.139221	−	0.936965i
$183$	−12.2995	+	12.2995i	−0.0672103	+	0.0672103i
$184$		−	177.215i		−	0.963123i
$185$	−132.395			−0.715649
$186$	248.159	−	248.159i	1.33419	−	1.33419i
$187$			182.117i			0.973890i
$188$	−8.60674	−	8.60674i	−0.0457805	−	0.0457805i
$189$	7.18256	+	48.3392i	0.0380030	+	0.255763i
$190$	82.0751	−	82.0751i	0.431974	−	0.431974i
$191$	−125.729	+	125.729i	−0.658266	+	0.658266i	−0.954970	−	0.296703i	$-0.904113\pi$
$191$	−125.729	+	125.729i	−0.658266	+	0.658266i	0.296703	+	0.954970i	$0.404113\pi$
$192$	−202.485	+	202.485i	−1.05461	+	1.05461i
$193$	−115.749	−	115.749i	−0.599735	−	0.599735i	0.340507	−	0.940242i	$-0.389401\pi$
$193$	−115.749	−	115.749i	−0.599735	−	0.599735i	−0.940242	+	0.340507i	$0.889401\pi$
$194$	121.841	−	121.841i	0.628045	−	0.628045i
$195$			256.910i			1.31749i
$196$	14.2716	+	46.9642i	0.0728143	+	0.239613i
$197$		−	254.736i		−	1.29307i	−0.762882	−	0.646537i	$-0.776216\pi$
$197$		−	254.736i		−	1.29307i	0.762882	−	0.646537i	$-0.223784\pi$
$198$	59.2390	+	59.2390i	0.299187	+	0.299187i
$199$	132.820	+	132.820i	0.667435	+	0.667435i	0.957122	−	0.289686i	$-0.0935510\pi$
$199$	132.820	+	132.820i	0.667435	+	0.667435i	−0.289686	+	0.957122i	$0.593551\pi$
$200$			42.8405i			0.214202i
$201$		−	456.923i		−	2.27325i
$202$	113.762	−	113.762i	0.563176	−	0.563176i
$203$	47.1119	+	317.067i	0.232079	+	1.56191i
$204$	−110.555			−0.541938
$205$	−101.017	+	153.315i	−0.492767	+	0.747877i
$206$		−	202.852i		−	0.984716i
$207$		−	148.740i		−	0.718550i
$208$	−110.528	+	110.528i	−0.531383	+	0.531383i
$209$			99.6323i			0.476710i
$210$	32.1772	+	216.555i	0.153225	+	1.03122i
$211$	−67.3598	+	67.3598i	−0.319241	+	0.319241i	−0.848475	−	0.529235i	$-0.822479\pi$
$211$	−67.3598	+	67.3598i	−0.319241	+	0.319241i	0.529235	+	0.848475i	$0.322479\pi$
$212$	16.5209	+	16.5209i	0.0779287	+	0.0779287i
$213$	−169.688			−0.796659
$214$			216.666i			1.01246i
$215$		−	335.750i		−	1.56163i
$216$	42.7547	−	42.7547i	0.197938	−	0.197938i
$217$	−209.464	+	282.574i	−0.965271	+	1.30219i
$218$	108.509	+	108.509i	0.497747	+	0.497747i
$219$	16.7706	−	16.7706i	0.0765779	−	0.0765779i
$220$	21.1123	+	21.1123i	0.0959648	+	0.0959648i
$221$	−389.180			−1.76100
$222$	−146.009	−	146.009i	−0.657698	−	0.657698i
$223$			218.148i			0.978243i	0.872216	+	0.489121i	$0.162682\pi$
$223$			218.148i			0.978243i	−0.872216	+	0.489121i	$0.837318\pi$
$224$	65.0869	−	87.8045i	0.290566	−	0.391984i
$225$			35.9569i			0.159808i
$226$		−	40.1658i		−	0.177725i
$227$	−122.660	−	122.660i	−0.540353	−	0.540353i	0.383280	−	0.923632i	$-0.374795\pi$
$227$	−122.660	−	122.660i	−0.540353	−	0.540353i	−0.923632	+	0.383280i	$0.874795\pi$
$228$	−60.4824			−0.265273
$229$	36.8056	+	36.8056i	0.160723	+	0.160723i	0.782887	−	0.622164i	$-0.213746\pi$
$229$	36.8056	+	36.8056i	0.160723	+	0.160723i	−0.622164	+	0.782887i	$0.713746\pi$
$230$			158.663i			0.689837i
$231$	−150.970	−	111.910i	−0.653551	−	0.484458i
$232$	280.437	−	280.437i	1.20878	−	1.20878i
$233$	156.661	+	156.661i	0.672365	+	0.672365i	0.958261	−	0.285896i	$-0.0922910\pi$
$233$	156.661	+	156.661i	0.672365	+	0.672365i	−0.285896	+	0.958261i	$0.592291\pi$
$234$	−126.592	+	126.592i	−0.540992	+	0.540992i
$235$	38.4754	+	38.4754i	0.163725	+	0.163725i
$236$		−	3.82128i		−	0.0161919i
$237$	−508.976			−2.14758
$238$	−328.049	+	48.7437i	−1.37836	+	0.204806i
$239$	148.005	+	148.005i	0.619267	+	0.619267i	0.945343	−	0.326077i	$-0.105727\pi$
$239$	148.005	+	148.005i	0.619267	+	0.619267i	−0.326077	+	0.945343i	$0.605727\pi$
$240$	140.361	−	140.361i	0.584836	−	0.584836i
$241$	282.725			1.17313			0.586565	−	0.809902i	$-0.300480\pi$
$241$	282.725			1.17313			0.586565	+	0.809902i	$0.300480\pi$
$242$	−132.809			−0.548798
$243$	222.477	−	222.477i	0.915543	−	0.915543i
$244$	−4.31987			−0.0177044
$245$	−63.7995	−	209.948i	−0.260406	−	0.856930i
$246$	−280.485	+	57.6751i	−1.14018	+	0.234452i
$247$	−212.912			−0.861990
$248$	435.194			1.75482
$249$	349.026	+	349.026i	1.40171	+	1.40171i
$250$		−	232.208i		−	0.928831i
$251$	−257.266			−1.02497			−0.512483	−	0.858698i	$-0.671274\pi$
$251$	−257.266			−1.02497			−0.512483	+	0.858698i	$0.671274\pi$
$252$	30.3539	−	40.9486i	0.120452	−	0.162494i
$253$	−96.3016	−	96.3016i	−0.380639	−	0.380639i
$254$		−	334.738i		−	1.31786i
$255$	494.225			1.93814
$256$	−179.263			−0.700245
$257$	−37.1124	+	37.1124i	−0.144406	+	0.144406i	−0.775614	−	0.631208i	$-0.782560\pi$
$257$	−37.1124	+	37.1124i	−0.144406	+	0.144406i	0.631208	+	0.775614i	$0.282560\pi$
$258$	370.275	−	370.275i	1.43517	−	1.43517i
$259$	166.258	+	123.242i	0.641921	+	0.475837i
$260$	−45.1163	+	45.1163i	−0.173524	+	0.173524i
$261$	235.377	−	235.377i	0.901826	−	0.901826i
$262$			126.996i			0.484719i
$263$	−161.674	+	161.674i	−0.614731	+	0.614731i	−0.944175	−	0.329444i	$-0.893139\pi$
$263$	−161.674	+	161.674i	−0.614731	+	0.614731i	0.329444	+	0.944175i	$0.393139\pi$
$264$			232.510i			0.880721i
$265$	−73.8546	−	73.8546i	−0.278697	−	0.278697i
$266$	−179.468	+	26.6666i	−0.674692	+	0.100250i
$267$			225.709i			0.845350i
$268$	80.2410	−	80.2410i	0.299407	−	0.299407i
$269$		−	164.820i		−	0.612714i	−0.951917	−	0.306357i	$-0.900890\pi$
$269$		−	164.820i		−	0.612714i	0.951917	−	0.306357i	$-0.0991101\pi$
$270$	−38.2788	+	38.2788i	−0.141774	+	0.141774i
$271$			310.635i			1.14626i	0.819466	+	0.573128i	$0.194270\pi$
$271$			310.635i			1.14626i	−0.819466	+	0.573128i	$0.805730\pi$
$272$	212.625	+	212.625i	0.781710	+	0.781710i
$273$	239.148	−	322.619i	0.876001	−	1.18176i
$274$	−22.4978	−	22.4978i	−0.0821088	−	0.0821088i
$275$	23.2803	+	23.2803i	0.0846555	+	0.0846555i
$276$	58.4604	−	58.4604i	0.211813	−	0.211813i
$277$	−115.751			−0.417874			−0.208937	−	0.977929i	$-0.567000\pi$
$277$	−115.751			−0.417874			−0.208937	+	0.977929i	$0.567000\pi$
$278$	122.099			0.439205
$279$	365.268			1.30920
$280$	−161.671	+	218.100i	−0.577396	+	0.778928i
$281$	230.626	−	230.626i	0.820733	−	0.820733i	−0.165480	−	0.986213i	$-0.552917\pi$
$281$	230.626	−	230.626i	0.820733	−	0.820733i	0.986213	+	0.165480i	$0.0529173\pi$
$282$			84.8635i			0.300934i
$283$		−	319.675i		−	1.12959i	−0.825230	−	0.564797i	$-0.808954\pi$
$283$		−	319.675i		−	1.12959i	0.825230	−	0.564797i	$-0.191046\pi$
$284$	−29.7993	−	29.7993i	−0.104927	−	0.104927i
$285$	270.379			0.948699
$286$			163.924i			0.573161i
$287$	269.570	−	98.4946i	0.939267	−	0.343187i
$288$	−113.500			−0.394097
$289$			459.677i			1.59058i
$290$	−251.079	+	251.079i	−0.865790	+	0.865790i
$291$	401.379			1.37931
$292$	5.89021			0.0201719
$293$	−311.388	−	311.388i	−1.06276	−	1.06276i	−0.997894	−	0.0648625i	$-0.979339\pi$
$293$	−311.388	−	311.388i	−1.06276	−	1.06276i	−0.0648625	−	0.997894i	$-0.520661\pi$
$294$	161.176	−	301.896i	0.548219	−	1.02686i
$295$			17.0826i			0.0579070i
$296$		−	256.055i		−	0.865049i
$297$		−	46.4673i		−	0.156456i
$298$	72.8345	+	72.8345i	0.244411	+	0.244411i
$299$	205.794	−	205.794i	0.688274	−	0.688274i
$300$	−14.1324	+	14.1324i	−0.0471081	+	0.0471081i
$301$	−312.538	+	421.625i	−1.03833	+	1.40075i
$302$	−308.359	+	308.359i	−1.02106	+	1.02106i
$303$	374.764			1.23684
$304$	116.322	+	116.322i	0.382640	+	0.382640i
$305$	19.3114			0.0633162
$306$	243.529	+	243.529i	0.795847	+	0.795847i
$307$	−1.91460			−0.00623650			−0.00311825	−	0.999995i	$-0.500993\pi$
$307$	−1.91460			−0.00623650			−0.00311825	+	0.999995i	$0.500993\pi$
$308$	−6.85947	−	46.1648i	−0.0222710	−	0.149886i
$309$	334.126	−	334.126i	1.08131	−	1.08131i
$310$	−389.635			−1.25689
$311$	321.503	+	321.503i	1.03377	+	1.03377i	0.999409	+	0.0343624i	$0.0109401\pi$
$311$	321.503	+	321.503i	1.03377	+	1.03377i	0.0343624	+	0.999409i	$0.489060\pi$
$312$	−496.868			−1.59253
$313$	−277.304	−	277.304i	−0.885956	−	0.885956i	0.108176	−	0.994132i	$-0.465499\pi$
$313$	−277.304	−	277.304i	−0.885956	−	0.885956i	−0.994132	+	0.108176i	$0.965499\pi$
$314$	232.108	+	232.108i	0.739197	+	0.739197i
$315$	−135.694	+	183.056i	−0.430774	+	0.581129i
$316$	−89.3821	−	89.3821i	−0.282855	−	0.282855i
$317$	−271.906	−	271.906i	−0.857749	−	0.857749i	0.133324	−	0.991073i	$-0.457435\pi$
$317$	−271.906	−	271.906i	−0.857749	−	0.857749i	−0.991073	+	0.133324i	$0.957435\pi$
$318$		−	162.898i		−	0.512258i
$319$		−	304.789i		−	0.955451i
$320$	317.923			0.993508
$321$	−356.881	+	356.881i	−1.11178	+	1.11178i
$322$	147.693	−	199.244i	0.458675	−	0.618769i
$323$			409.584i			1.26806i
$324$	93.7437			0.289332
$325$	−49.7493	+	49.7493i	−0.153075	+	0.153075i
$326$		−	263.611i		−	0.808623i
$327$			357.460i			1.09315i
$328$	−296.514	−	195.369i	−0.904005	−	0.595638i
$329$	−12.5008	−	84.1316i	−0.0379965	−	0.255719i
$330$		−	208.169i		−	0.630817i
$331$	−242.227	−	242.227i	−0.731804	−	0.731804i	0.239173	−	0.970977i	$-0.423124\pi$
$331$	−242.227	−	242.227i	−0.731804	−	0.731804i	−0.970977	+	0.239173i	$0.923124\pi$
$332$			122.586i			0.369234i
$333$		−	214.912i		−	0.645380i
$334$	10.2784	+	10.2784i	0.0307736	+	0.0307736i
$335$	−358.708	+	358.708i	−1.07077	+	1.07077i
$336$	−306.917	+	45.6038i	−0.913444	+	0.135726i
$337$			47.5106i			0.140981i	0.997512	+	0.0704905i	$0.0224564\pi$
$337$			47.5106i			0.140981i	−0.997512	+	0.0704905i	$0.977544\pi$
$338$	−57.6694			−0.170620
$339$	66.1589	−	66.1589i	0.195159	−	0.195159i
$340$	86.7916	+	86.7916i	0.255269	+	0.255269i
$341$	236.492	−	236.492i	0.693526	−	0.693526i
$342$	133.229	+	133.229i	0.389559	+	0.389559i
$343$	−115.315	+	323.035i	−0.336197	+	0.941792i
$344$	649.347			1.88764
$345$	−261.340	+	261.340i	−0.757508	+	0.757508i
$346$			344.245i			0.994927i
$347$	−30.5475	+	30.5475i	−0.0880332	+	0.0880332i	−0.749752	−	0.661719i	$-0.769827\pi$
$347$	−30.5475	+	30.5475i	−0.0880332	+	0.0880332i	0.661719	+	0.749752i	$0.269827\pi$
$348$	185.024			0.531678
$349$	412.592			1.18221			0.591106	−	0.806594i	$-0.298692\pi$
$349$	412.592			1.18221			0.591106	+	0.806594i	$0.298692\pi$
$350$	−35.7039	+	48.1658i	−0.102011	+	0.137617i
$351$	99.2994			0.282904
$352$	−73.4854	+	73.4854i	−0.208765	+	0.208765i
$353$			496.470i			1.40643i	0.710977	+	0.703216i	$0.248253\pi$
$353$			496.470i			1.40643i	−0.710977	+	0.703216i	$0.751747\pi$
$354$	−18.8391	+	18.8391i	−0.0532179	+	0.0532179i
$355$	133.214	+	133.214i	0.375251	+	0.375251i
$356$	−39.6370	+	39.6370i	−0.111340	+	0.111340i
$357$	−620.632	−	460.056i	−1.73847	−	1.28867i
$358$	49.6655	+	49.6655i	0.138731	+	0.138731i
$359$	343.055			0.955586			0.477793	−	0.878472i	$-0.341437\pi$
$359$	343.055			0.955586			0.477793	+	0.878472i	$0.341437\pi$
$360$	281.925			0.783126
$361$		−	136.926i		−	0.379296i
$362$	−260.124	+	260.124i	−0.718575	+	0.718575i
$363$	−218.756	−	218.756i	−0.602634	−	0.602634i
$364$	98.6529	−	14.6585i	0.271024	−	0.0402706i
$365$	−26.3315			−0.0721410
$366$	21.2972	+	21.2972i	0.0581891	+	0.0581891i
$367$	−579.594			−1.57928			−0.789638	−	0.613573i	$-0.789732\pi$
$367$	−579.594			−1.57928			−0.789638	+	0.613573i	$0.789732\pi$
$368$	−224.868			−0.611053
$369$	−248.870	−	163.977i	−0.674444	−	0.444383i
$370$			229.249i			0.619592i
$371$	23.9957	+	161.493i	0.0646785	+	0.435291i
$372$	143.564	+	143.564i	0.385925	+	0.385925i
$373$	−400.629			−1.07407			−0.537036	−	0.843559i	$-0.680456\pi$
$373$	−400.629			−1.07407			−0.537036	+	0.843559i	$0.680456\pi$
$374$	315.346			0.843170
$375$	382.480	−	382.480i	1.01995	−	1.01995i
$376$	−74.4121	+	74.4121i	−0.197905	+	0.197905i
$377$	651.326			1.72765
$378$	83.7018	−	12.4370i	0.221433	−	0.0329021i
$379$	−98.4012			−0.259634			−0.129817	−	0.991538i	$-0.541439\pi$
$379$	−98.4012			−0.259634			−0.129817	+	0.991538i	$0.541439\pi$
$380$	47.4817	+	47.4817i	0.124952	+	0.124952i
$381$	551.361	−	551.361i	1.44714	−	1.44714i
$382$	217.706	+	217.706i	0.569911	+	0.569911i
$383$	−214.818	−	214.818i	−0.560882	−	0.560882i	0.368676	−	0.929558i	$-0.379811\pi$
$383$	−214.818	−	214.818i	−0.560882	−	0.560882i	−0.929558	+	0.368676i	$0.879811\pi$
$384$	172.483	+	172.483i	0.449175	+	0.449175i
$385$	30.6645	+	206.374i	0.0796480	+	0.536037i
$386$	−200.425	+	200.425i	−0.519236	+	0.519236i
$387$	545.010			1.40829
$388$	70.4867	+	70.4867i	0.181667	+	0.181667i
$389$			193.109i			0.496424i	0.968706	+	0.248212i	$0.0798430\pi$
$389$			193.109i			0.496424i	−0.968706	+	0.248212i	$0.920157\pi$
$390$	444.853			1.14065
$391$	−395.892	−	395.892i	−1.01251	−	1.01251i
$392$	406.043	−	123.389i	1.03582	−	0.314769i
$393$	−209.182	+	209.182i	−0.532269	+	0.532269i
$394$	−441.088			−1.11951
$395$	399.572	+	399.572i	1.01157	+	1.01157i
$396$	−34.2707	+	34.2707i	−0.0865422	+	0.0865422i
$397$	−139.534	+	139.534i	−0.351470	+	0.351470i	−0.860656	−	0.509186i	$-0.829946\pi$
$397$	−139.534	+	139.534i	−0.351470	+	0.351470i	0.509186	+	0.860656i	$0.329946\pi$
$398$	229.984	−	229.984i	0.577849	−	0.577849i
$399$	−339.534	−	251.686i	−0.850962	−	0.630793i
$400$	54.3602			0.135901
$401$		−	658.767i		−	1.64281i	−0.570345	−	0.821405i	$-0.693190\pi$
$401$		−	658.767i		−	1.64281i	0.570345	−	0.821405i	$-0.306810\pi$
$402$	−791.186			−1.96812
$403$	505.378	+	505.378i	1.25404	+	1.25404i
$404$	65.8128	+	65.8128i	0.162903	+	0.162903i
$405$	−419.070			−1.03474
$406$	549.018	−	81.5767i	1.35226	−	0.200928i
$407$	−139.145	−	139.145i	−0.341878	−	0.341878i
$408$			955.840i			2.34274i
$409$		−	461.105i		−	1.12740i	−0.825981	−	0.563699i	$-0.809378\pi$
$409$		−	461.105i		−	1.12740i	0.825981	−	0.563699i	$-0.190622\pi$
$410$	265.472	+	174.917i	0.647494	+	0.426626i
$411$		−	74.1143i		−	0.180327i
$412$	117.353			0.284837
$413$	15.9016	−	21.4518i	0.0385025	−	0.0519413i
$414$	−257.551			−0.622103
$415$		−	548.005i		−	1.32049i
$416$	−157.036	−	157.036i	−0.377491	−	0.377491i
$417$	201.115	+	201.115i	0.482289	+	0.482289i
$418$	172.518			0.412724
$419$	−278.288			−0.664173			−0.332086	−	0.943249i	$-0.607753\pi$
$419$	−278.288			−0.664173			−0.332086	+	0.943249i	$0.607753\pi$
$420$	−125.281	+	18.6150i	−0.298287	+	0.0443215i
$421$	−47.6632	−	47.6632i	−0.113214	−	0.113214i	0.648230	−	0.761444i	$-0.275509\pi$
$421$	−47.6632	−	47.6632i	−0.113214	−	0.113214i	−0.761444	+	0.648230i	$0.775509\pi$
$422$	116.637	+	116.637i	0.276391	+	0.276391i
$423$	−62.4556	+	62.4556i	−0.147649	+	0.147649i
$424$	142.836	−	142.836i	0.336878	−	0.336878i
$425$	95.7041	+	95.7041i	0.225186	+	0.225186i
$426$			293.824i			0.689728i
$427$	−24.2507	−	17.9763i	−0.0567932	−	0.0420991i
$428$	−125.345			−0.292862
$429$	−270.007	+	270.007i	−0.629387	+	0.629387i
$430$	−581.369			−1.35202
$431$		−	34.3919i		−	0.0797956i	−0.999204	−	0.0398978i	$-0.987297\pi$
$431$		−	34.3919i		−	0.0797956i	0.999204	−	0.0398978i	$-0.0127032\pi$
$432$	−54.2514	−	54.2514i	−0.125582	−	0.125582i
$433$			228.364i			0.527399i	0.964605	+	0.263699i	$0.0849427\pi$
$433$			228.364i			0.527399i	−0.964605	+	0.263699i	$0.915057\pi$
$434$	489.292	+	362.698i	1.12740	+	0.835709i
$435$	−827.127			−1.90144
$436$	−62.7741	+	62.7741i	−0.143977	+	0.143977i
$437$	−216.583	−	216.583i	−0.495614	−	0.495614i
$438$	−29.0391	−	29.0391i	−0.0662993	−	0.0662993i
$439$	363.493	−	363.493i	0.828003	−	0.828003i	−0.159238	−	0.987240i	$-0.550904\pi$
$439$	363.493	−	363.493i	0.828003	−	0.828003i	0.987240	+	0.159238i	$0.0509036\pi$
$440$	182.532	−	182.532i	0.414846	−	0.414846i
$441$	340.800	−	103.563i	0.772789	−	0.234837i
$442$			673.885i			1.52463i
$443$			883.315i			1.99394i	0.0777938	+	0.996969i	$0.475212\pi$
$443$			883.315i			1.99394i	−0.0777938	+	0.996969i	$0.524788\pi$
$444$	84.4685	−	84.4685i	0.190244	−	0.190244i
$445$	177.193	−	177.193i	0.398186	−	0.398186i
$446$	377.735			0.846939
$447$			239.938i			0.536774i
$448$	−399.237	−	295.943i	−0.891155	−	0.660587i
$449$			64.0657i			0.142685i	0.997452	+	0.0713427i	$0.0227284\pi$
$449$			64.0657i			0.142685i	−0.997452	+	0.0713427i	$0.977272\pi$
$450$	62.2612			0.138358
$451$	−267.298	+	54.9636i	−0.592678	+	0.121870i
$452$	23.2365			0.0514082
$453$	−1015.83			−2.24244
$454$	−212.392	+	212.392i	−0.467824	+	0.467824i
$455$	−441.016	+	65.5291i	−0.969266	+	0.144020i
$456$			522.918i			1.14675i
$457$	24.4227	−	24.4227i	0.0534413	−	0.0534413i	−0.679881	−	0.733322i	$-0.737969\pi$
$457$	24.4227	−	24.4227i	0.0534413	−	0.0534413i	0.733322	+	0.679881i	$0.237969\pi$
$458$	63.7307	−	63.7307i	0.139150	−	0.139150i
$459$		−	191.025i		−	0.416177i
$460$	−91.7888			−0.199541
$461$		−	55.9924i		−	0.121459i	−0.998154	−	0.0607293i	$-0.980657\pi$
$461$		−	55.9924i		−	0.121459i	0.998154	−	0.0607293i	$-0.0193426\pi$
$462$	−193.778	+	261.413i	−0.419432	+	0.565829i
$463$	−265.837	−	265.837i	−0.574161	−	0.574161i	0.359127	−	0.933289i	$-0.383074\pi$
$463$	−265.837	−	265.837i	−0.574161	−	0.574161i	−0.933289	+	0.359127i	$0.883074\pi$
$464$	−355.846	−	355.846i	−0.766910	−	0.766910i
$465$	−641.786	−	641.786i	−1.38018	−	1.38018i
$466$	271.267	−	271.267i	0.582118	−	0.582118i
$467$		−	62.6089i		−	0.134066i	−0.997751	−	0.0670331i	$-0.978647\pi$
$467$		−	62.6089i		−	0.134066i	0.997751	−	0.0670331i	$-0.0213533\pi$
$468$	−73.2356	−	73.2356i	−0.156486	−	0.156486i
$469$	784.362	−	116.546i	1.67241	−	0.248499i
$470$	66.6221	−	66.6221i	0.141749	−	0.141749i
$471$			764.631i			1.62342i
$472$	−33.0380			−0.0699958
$473$	352.867	−	352.867i	0.746018	−	0.746018i
$474$			881.318i			1.85932i
$475$	52.3576	+	52.3576i	0.110226	+	0.110226i
$476$	−28.1990	−	189.781i	−0.0592416	−	0.398700i
$477$	119.885	−	119.885i	0.251332	−	0.251332i
$478$	256.278	−	256.278i	0.536146	−	0.536146i
$479$	270.176	−	270.176i	0.564041	−	0.564041i	−0.366412	−	0.930453i	$-0.619414\pi$
$479$	270.176	−	270.176i	0.564041	−	0.564041i	0.930453	+	0.366412i	$0.119414\pi$
$480$	199.423	+	199.423i	0.415464	+	0.415464i
$481$	297.348	−	297.348i	0.618187	−	0.618187i
$482$		−	489.552i		−	1.01567i
$483$	571.456	−	84.9107i	1.18314	−	0.175799i
$484$		−	76.8322i		−	0.158744i
$485$	−315.103	−	315.103i	−0.649696	−	0.649696i
$486$	−385.230	−	385.230i	−0.792655	−	0.792655i
$487$		−	454.377i		−	0.933012i	−0.884518	−	0.466506i	$-0.845513\pi$
$487$		−	454.377i		−	0.933012i	0.884518	−	0.466506i	$-0.154487\pi$
$488$			37.3487i			0.0765342i
$489$	434.206	−	434.206i	0.887946	−	0.887946i
$490$	−363.535	+	110.472i	−0.741909	+	0.225453i
$491$	3.00168			0.00611340			0.00305670	−	0.999995i	$-0.499027\pi$
$491$	3.00168			0.00611340			0.00305670	+	0.999995i	$0.499027\pi$
$492$	−33.3660	−	162.265i	−0.0678170	−	0.329806i
$493$		−	1252.97i		−	2.54153i
$494$			368.667i			0.746290i
$495$	153.203	−	153.203i	0.309501	−	0.309501i
$496$		−	552.218i		−	1.11334i
$497$	−43.2819	−	291.290i	−0.0870862	−	0.586097i
$498$	604.356	−	604.356i	1.21357	−	1.21357i
$499$	363.344	+	363.344i	0.728144	+	0.728144i	0.970250	−	0.242106i	$-0.0778381\pi$
$499$	363.344	+	363.344i	0.728144	+	0.728144i	−0.242106	+	0.970250i	$0.577838\pi$
$500$	134.336			0.268672
$501$			33.8600i			0.0675848i
$502$			445.470i			0.887390i
$503$	−350.168	+	350.168i	−0.696159	+	0.696159i	−0.963580	−	0.267421i	$-0.913829\pi$
$503$	−350.168	+	350.168i	−0.696159	+	0.696159i	0.267421	+	0.963580i	$0.413829\pi$
$504$	−354.033	−	262.434i	−0.702446	−	0.520703i
$505$	−294.208	−	294.208i	−0.582591	−	0.582591i
$506$	−166.751	+	166.751i	−0.329548	+	0.329548i
$507$	−94.9899	−	94.9899i	−0.187357	−	0.187357i
$508$	193.651			0.381203
$509$	143.752	+	143.752i	0.282421	+	0.282421i	0.834074	−	0.551653i	$-0.186003\pi$
$509$	143.752	+	143.752i	0.282421	+	0.282421i	−0.551653	+	0.834074i	$0.686003\pi$
$510$		−	855.776i		−	1.67799i
$511$	33.0662	+	24.5110i	0.0647089	+	0.0479668i
$512$			552.304i			1.07872i
$513$		−	104.506i		−	0.203714i
$514$	64.2620	+	64.2620i	0.125023	+	0.125023i
$515$	−524.612			−1.01866
$516$	214.210	+	214.210i	0.415135	+	0.415135i
$517$			80.8737i			0.156429i
$518$	213.400	−	287.884i	0.411968	−	0.555760i
$519$	−567.021	+	567.021i	−1.09253	+	1.09253i
$520$	390.067	+	390.067i	0.750128	+	0.750128i
$521$	−518.554	+	518.554i	−0.995305	+	0.995305i	−0.999989	−	0.00468391i	$-0.998509\pi$
$521$	−518.554	+	518.554i	−0.995305	+	0.995305i	0.00468391	+	0.999989i	$0.498509\pi$
$522$	−407.567	−	407.567i	−0.780779	−	0.780779i
$523$			82.1864i			0.157144i	0.996908	+	0.0785721i	$0.0250361\pi$
$523$			82.1864i			0.157144i	−0.996908	+	0.0785721i	$0.974964\pi$
$524$	−73.4694			−0.140209
$525$	−138.146	+	20.5266i	−0.263134	+	0.0390983i
$526$	279.947	+	279.947i	0.532219	+	0.532219i
$527$	972.210	−	972.210i	1.84480	−	1.84480i
$528$	295.032			0.558773
$529$	−110.314			−0.208533
$530$	−127.883	+	127.883i	−0.241289	+	0.241289i
$531$	−27.7295			−0.0522212
$532$	−15.4270	−	103.825i	−0.0289982	−	0.195160i
$533$	−117.456	−	571.208i	−0.220367	−	1.07169i
$534$	390.826			0.731884
$535$	560.340			1.04736
$536$	−693.747	−	693.747i	−1.29430	−	1.29430i
$537$			163.613i			0.304679i
$538$	−285.394			−0.530473
$539$	153.599	−	287.703i	0.284970	−	0.533771i
$540$	−22.1449	−	22.1449i	−0.0410091	−	0.0410091i
$541$			53.1619i			0.0982660i	0.998792	+	0.0491330i	$0.0156458\pi$
$541$			53.1619i			0.0982660i	−0.998792	+	0.0491330i	$0.984354\pi$
$542$	537.881			0.992400
$543$	−856.925			−1.57813
$544$	−302.095	+	302.095i	−0.555322	+	0.555322i
$545$	280.624	−	280.624i	0.514907	−	0.514907i
$546$	−558.632	−	414.097i	−1.02314	−	0.758420i
$547$	16.6584	−	16.6584i	0.0304542	−	0.0304542i	−0.691716	−	0.722170i	$-0.743145\pi$
$547$	16.6584	−	16.6584i	0.0304542	−	0.0304542i	0.722170	+	0.691716i	$0.243145\pi$
$548$	13.0153	−	13.0153i	0.0237506	−	0.0237506i
$549$			31.3475i			0.0570993i
$550$	40.3110	−	40.3110i	0.0732927	−	0.0732927i
$551$		−	685.474i		−	1.24405i
$552$	−505.437	−	505.437i	−0.915647	−	0.915647i
$553$	−129.823	−	873.717i	−0.234761	−	1.57996i
$554$			200.429i			0.361785i
$555$	−377.606	+	377.606i	−0.680372	+	0.680372i
$556$			70.6361i			0.127043i
$557$	−255.146	+	255.146i	−0.458072	+	0.458072i	−0.898022	−	0.439950i	$-0.854996\pi$
$557$	−255.146	+	255.146i	−0.458072	+	0.458072i	0.439950	+	0.898022i	$0.354996\pi$
$558$		−	632.479i		−	1.13348i
$559$	754.067	+	754.067i	1.34896	+	1.34896i
$560$	276.747	+	205.144i	0.494191	+	0.366329i
$561$	519.420	+	519.420i	0.925883	+	0.925883i
$562$	−399.341	−	399.341i	−0.710571	−	0.710571i
$563$	−355.197	+	355.197i	−0.630901	+	0.630901i	−0.948294	−	0.317393i	$-0.897193\pi$
$563$	−355.197	+	355.197i	−0.630901	+	0.630901i	0.317393	+	0.948294i	$0.397193\pi$
$564$	−49.0948			−0.0870476
$565$	−103.876			−0.183852
$566$	−553.534			−0.977975
$567$	526.255	+	390.097i	0.928140	+	0.688002i
$568$	−257.638	+	257.638i	−0.453589	+	0.453589i
$569$			134.168i			0.235796i	0.993026	+	0.117898i	$0.0376156\pi$
$569$			134.168i			0.235796i	−0.993026	+	0.117898i	$0.962384\pi$
$570$		−	468.175i		−	0.821360i
$571$	51.6605	+	51.6605i	0.0904737	+	0.0904737i	0.750895	−	0.660421i	$-0.229622\pi$
$571$	51.6605	+	51.6605i	0.0904737	+	0.0904737i	−0.660421	+	0.750895i	$0.729622\pi$
$572$	−94.8327			−0.165791
$573$			717.187i			1.25164i
$574$	−170.548	−	466.774i	−0.297123	−	0.813195i
$575$	−101.214			−0.176025
$576$			516.071i			0.895957i
$577$	220.514	−	220.514i	0.382173	−	0.382173i	−0.489711	−	0.871885i	$-0.662898\pi$
$577$	220.514	−	220.514i	0.382173	−	0.382173i	0.871885	+	0.489711i	$0.162898\pi$
$578$	795.954			1.37708
$579$	−660.259			−1.14034
$580$	−145.253	−	145.253i	−0.250436	−	0.250436i
$581$	−510.119	+	688.168i	−0.878001	+	1.18445i
$582$		−	695.008i		−	1.19417i
$583$		−	155.239i		−	0.266277i
$584$		−	50.9255i		−	0.0872013i
$585$	327.391	+	327.391i	0.559643	+	0.559643i
$586$	−539.184	+	539.184i	−0.920109	+	0.920109i
$587$	−55.7618	+	55.7618i	−0.0949946	+	0.0949946i	−0.753007	−	0.658012i	$-0.771397\pi$
$587$	−55.7618	+	55.7618i	−0.0949946	+	0.0949946i	0.658012	+	0.753007i	$0.271397\pi$
$588$	174.652	+	93.2431i	0.297027	+	0.158577i
$589$	531.874	−	531.874i	0.903012	−	0.903012i
$590$	29.5793			0.0501345
$591$	−726.536	−	726.536i	−1.22933	−	1.22933i
$592$	−324.907			−0.548830
$593$	−196.228	−	196.228i	−0.330908	−	0.330908i	0.522023	−	0.852931i	$-0.325177\pi$
$593$	−196.228	−	196.228i	−0.330908	−	0.330908i	−0.852931	+	0.522023i	$0.825177\pi$
$594$	−80.4606			−0.135455
$595$	126.060	+	848.395i	0.211866	+	1.42587i
$596$	−42.1359	+	42.1359i	−0.0706978	+	0.0706978i
$597$	757.634			1.26907
$598$	−356.343	−	356.343i	−0.595891	−	0.595891i
$599$	−368.010			−0.614374			−0.307187	−	0.951649i	$-0.599388\pi$
$599$	−368.010			−0.614374			−0.307187	+	0.951649i	$0.599388\pi$
$600$	122.186	+	122.186i	0.203643	+	0.203643i
$601$	−646.809	−	646.809i	−1.07622	−	1.07622i	−0.996845	−	0.0793774i	$-0.974707\pi$
$601$	−646.809	−	646.809i	−1.07622	−	1.07622i	−0.0793774	−	0.996845i	$-0.525293\pi$
$602$	730.065	+	541.175i	1.21273	+	0.898963i
$603$	−582.276	−	582.276i	−0.965632	−	0.965632i
$604$	−178.391	−	178.391i	−0.295349	−	0.295349i
$605$			343.469i			0.567717i
$606$		−	648.923i		−	1.07083i
$607$	885.026			1.45803			0.729016	−	0.684496i	$-0.239978\pi$
$607$	885.026			1.45803			0.729016	+	0.684496i	$0.239978\pi$
$608$	−165.270	+	165.270i	−0.271825	+	0.271825i
$609$	1038.68	+	769.943i	1.70555	+	1.26427i
$610$		−	33.4388i		−	0.0548176i
$611$	−172.825			−0.282856
$612$	−140.885	+	140.885i	−0.230205	+	0.230205i
$613$			353.654i			0.576924i	0.957491	+	0.288462i	$0.0931439\pi$
$613$			353.654i			0.576924i	−0.957491	+	0.288462i	$0.906856\pi$
$614$			3.31524i			0.00539941i
$615$	149.159	+	725.385i	0.242534	+	1.17949i
$616$	−399.131	+	59.3056i	−0.647941	+	0.0962754i
$617$			962.721i			1.56033i	0.625576	+	0.780163i	$0.284864\pi$
$617$			962.721i			1.56033i	−0.625576	+	0.780163i	$0.715136\pi$
$618$	−578.556	−	578.556i	−0.936175	−	0.936175i
$619$			567.474i			0.916760i	0.888756	+	0.458380i	$0.151570\pi$
$619$			567.474i			0.916760i	−0.888756	+	0.458380i	$0.848430\pi$
$620$		−	225.410i		−	0.363565i
$621$	101.012	+	101.012i	0.162660	+	0.162660i
$622$	556.699	−	556.699i	0.895015	−	0.895015i
$623$	−387.455	+	57.5707i	−0.621919	+	0.0924089i
$624$			630.476i			1.01038i
$625$	−476.869			−0.762991
$626$	−480.166	+	480.166i	−0.767039	+	0.767039i
$627$	284.163	+	284.163i	0.453210	+	0.453210i
$628$	−134.278	+	134.278i	−0.213819	+	0.213819i
$629$	−572.017	−	572.017i	−0.909407	−	0.909407i
$630$	316.970	+	234.961i	0.503127	+	0.372953i
$631$	639.495			1.01346			0.506731	−	0.862104i	$-0.330854\pi$
$631$	639.495			1.01346			0.506731	+	0.862104i	$0.330854\pi$
$632$	−772.779	+	772.779i	−1.22275	+	1.22275i
$633$			384.236i			0.607008i
$634$	−470.820	+	470.820i	−0.742618	+	0.742618i
$635$	−865.693			−1.36330
$636$	94.2390			0.148174
$637$	614.813	+	328.237i	0.965170	+	0.515285i
$638$	−527.758			−0.827206
$639$	−216.241	+	216.241i	−0.338405	+	0.338405i
$640$		−	270.816i		−	0.423150i
$641$	128.425	−	128.425i	0.200351	−	0.200351i	−0.599799	−	0.800150i	$-0.704753\pi$
$641$	128.425	−	128.425i	0.200351	−	0.200351i	0.800150	+	0.599799i	$0.204753\pi$
$642$	617.958	+	617.958i	0.962552	+	0.962552i
$643$	562.313	−	562.313i	0.874515	−	0.874515i	−0.118445	−	0.992961i	$-0.537791\pi$
$643$	562.313	−	562.313i	0.874515	−	0.874515i	0.992961	+	0.118445i	$0.0377910\pi$
$644$	115.266	+	85.4429i	0.178984	+	0.132675i
$645$	−957.599	−	957.599i	−1.48465	−	1.48465i
$646$	709.216			1.09786
$647$	738.567			1.14153			0.570763	−	0.821115i	$-0.306648\pi$
$647$	738.567			1.14153			0.570763	+	0.821115i	$0.306648\pi$
$648$		−	810.489i		−	1.25075i
$649$	−17.9534	+	17.9534i	−0.0276632	+	0.0276632i
$650$	86.1435	+	86.1435i	0.132528	+	0.132528i
$651$	208.519	+	1403.35i	0.320306	+	2.15568i
$652$	152.503			0.233901
$653$	244.164	+	244.164i	0.373911	+	0.373911i	0.868899	−	0.494989i	$-0.164828\pi$
$653$	244.164	+	244.164i	0.373911	+	0.373911i	−0.494989	+	0.868899i	$0.664828\pi$
$654$	618.960			0.946422
$655$	328.436			0.501430
$656$	−247.904	+	376.246i	−0.377902	+	0.573545i
$657$		−	42.7428i		−	0.0650576i
$658$	−145.678	+	21.6458i	−0.221395	+	0.0328964i
$659$	488.984	+	488.984i	0.742008	+	0.742008i	0.972964	−	0.230956i	$-0.0741853\pi$
$659$	488.984	+	488.984i	0.742008	+	0.742008i	−0.230956	+	0.972964i	$0.574185\pi$
$660$	120.429			0.182469
$661$	−237.247			−0.358922			−0.179461	−	0.983765i	$-0.557435\pi$
$661$	−237.247			−0.358922			−0.179461	+	0.983765i	$0.557435\pi$
$662$	−419.428	+	419.428i	−0.633578	+	0.633578i
$663$	−1109.99	+	1109.99i	−1.67419	+	1.67419i
$664$	1059.85			1.59616
$665$	68.9647	+	464.138i	0.103706	+	0.697952i
$666$	−372.131			−0.558755
$667$	662.558	+	662.558i	0.993341	+	0.993341i
$668$	−5.94621	+	5.94621i	−0.00890151	+	0.00890151i
$669$	622.184	+	622.184i	0.930021	+	0.930021i
$670$	621.121	+	621.121i	0.927046	+	0.927046i
$671$	20.2959	+	20.2959i	0.0302473	+	0.0302473i
$672$	−64.7933	−	436.064i	−0.0964186	−	0.648905i
$673$	−71.9433	+	71.9433i	−0.106899	+	0.106899i	−0.758533	−	0.651634i	$-0.774084\pi$
$673$	−71.9433	+	71.9433i	−0.106899	+	0.106899i	0.651634	+	0.758533i	$0.274084\pi$
$674$	82.2670			0.122058
$675$	−24.4189	−	24.4189i	−0.0361762	−	0.0361762i
$676$		−	33.3627i		−	0.0493530i
$677$	−1143.77			−1.68946			−0.844732	−	0.535190i	$-0.820240\pi$
$677$	−1143.77			−1.68946			−0.844732	+	0.535190i	$0.820240\pi$
$678$	−114.557	−	114.557i	−0.168964	−	0.168964i
$679$	102.378	+	689.014i	0.150778	+	1.01475i
$680$	750.383	−	750.383i	1.10350	−	1.10350i
$681$	−699.681			−1.02743
$682$	−409.499	−	409.499i	−0.600438	−	0.600438i
$683$	815.483	−	815.483i	1.19397	−	1.19397i	0.218029	−	0.975942i	$-0.430037\pi$
$683$	815.483	−	815.483i	1.19397	−	1.19397i	0.975942	−	0.218029i	$-0.0699628\pi$
$684$	−77.0752	+	77.0752i	−0.112683	+	0.112683i
$685$	−58.1835	+	58.1835i	−0.0849394	+	0.0849394i
$686$	559.351	+	199.675i	0.815380	+	0.291071i
$687$	209.947			0.305600
$688$		−	823.956i		−	1.19761i
$689$	331.742			0.481484
$690$	452.524	+	452.524i	0.655832	+	0.655832i
$691$	249.169	+	249.169i	0.360593	+	0.360593i	0.864031	−	0.503439i	$-0.167932\pi$
$691$	249.169	+	249.169i	0.360593	+	0.360593i	−0.503439	+	0.864031i	$0.667932\pi$
$692$	−199.151			−0.287790
$693$	−334.999	+	49.7764i	−0.483404	+	0.0718274i
$694$	52.8946	+	52.8946i	0.0762170	+	0.0762170i
$695$		−	315.770i		−	0.454346i
$696$		−	1599.68i		−	2.29839i
$697$	−1098.85	+	225.953i	−1.57654	+	0.324179i
$698$		−	714.424i		−	1.02353i
$699$	893.632			1.27844
$700$	−27.8647	−	20.6553i	−0.0398067	−	0.0295075i
$701$	963.601			1.37461			0.687304	−	0.726370i	$-0.258794\pi$
$701$	963.601			1.37461			0.687304	+	0.726370i	$0.258794\pi$
$702$		−	171.942i		−	0.244932i
$703$	−312.938	−	312.938i	−0.445146	−	0.445146i
$704$	334.130	+	334.130i	0.474617	+	0.474617i
$705$	219.473			0.311309
$706$	859.664			1.21765
$707$	95.5897	+	643.326i	0.135205	+	0.909938i
$708$	−10.8987	−	10.8987i	−0.0153937	−	0.0153937i
$709$	120.071	+	120.071i	0.169352	+	0.169352i	0.786695	−	0.617342i	$-0.211791\pi$
$709$	120.071	+	120.071i	0.169352	+	0.169352i	−0.617342	+	0.786695i	$0.711791\pi$
$710$	230.667	−	230.667i	0.324883	−	0.324883i
$711$	−648.609	+	648.609i	−0.912249	+	0.912249i
$712$	342.694	+	342.694i	0.481312	+	0.481312i
$713$			1028.19i			1.44206i
$714$	−796.611	+	1074.66i	−1.11570	+	1.50512i
$715$	423.938			0.592921
$716$	−28.7323	+	28.7323i	−0.0401289	+	0.0401289i
$717$	844.254			1.17748
$718$		−	594.018i		−	0.827323i
$719$	643.328	+	643.328i	0.894754	+	0.894754i	0.994966	−	0.100212i	$-0.0319520\pi$
$719$	643.328	+	643.328i	0.894754	+	0.894754i	−0.100212	+	0.994966i	$0.531952\pi$
$720$		−	357.735i		−	0.496854i
$721$	658.791	+	488.342i	0.913719	+	0.677312i
$722$	−237.094			−0.328385
$723$	806.363	−	806.363i	1.11530	−	1.11530i
$724$	−150.486	−	150.486i	−0.207854	−	0.207854i
$725$	−160.169	−	160.169i	−0.220923	−	0.220923i
$726$	−378.787	+	378.787i	−0.521746	+	0.521746i
$727$	930.388	−	930.388i	1.27976	−	1.27976i	0.338964	−	0.940799i	$-0.389924\pi$
$727$	930.388	−	930.388i	1.27976	−	1.27976i	0.940799	−	0.338964i	$-0.110076\pi$
$728$	−126.735	−	852.933i	−0.174086	−	1.17161i
$729$		−	426.824i		−	0.585492i
$730$			45.5943i			0.0624579i
$731$	1450.62	−	1450.62i	1.98443	−	1.98443i
$732$	−12.3208	+	12.3208i	−0.0168316	+	0.0168316i
$733$	−476.649			−0.650272			−0.325136	−	0.945667i	$-0.605410\pi$
$733$	−476.649			−0.650272			−0.325136	+	0.945667i	$0.605410\pi$
$734$			1003.60i			1.36730i
$735$	−780.759	−	416.832i	−1.06226	−	0.567118i
$736$		−	319.489i		−	0.434088i
$737$	−753.989			−1.02305
$738$	−283.935	+	430.931i	−0.384736	+	0.583917i
$739$	−831.570			−1.12526			−0.562632	−	0.826708i	$-0.690211\pi$
$739$	−831.570			−1.12526			−0.562632	+	0.826708i	$0.690211\pi$
$740$	−132.624			−0.179222
$741$	−607.249	+	607.249i	−0.819499	+	0.819499i
$742$	279.633	−	41.5498i	0.376865	−	0.0559971i
$743$		−	425.691i		−	0.572935i	−0.958090	−	0.286467i	$-0.907519\pi$
$743$		−	425.691i		−	0.572935i	0.958090	−	0.286467i	$-0.0924810\pi$
$744$	1241.23	−	1241.23i	1.66831	−	1.66831i
$745$	188.364	−	188.364i	0.252837	−	0.252837i
$746$			693.710i			0.929906i
$747$	889.556			1.19084
$748$			182.432i			0.243894i
$749$	−703.657	−	521.600i	−0.939462	−	0.696395i
$750$	−662.283	−	662.283i	−0.883045	−	0.883045i
$751$	−176.349	−	176.349i	−0.234818	−	0.234818i	0.579882	−	0.814700i	$-0.303099\pi$
$751$	−176.349	−	176.349i	−0.234818	−	0.234818i	−0.814700	+	0.579882i	$0.803099\pi$
$752$	94.4215	+	94.4215i	0.125560	+	0.125560i
$753$	−733.754	+	733.754i	−0.974440	+	0.974440i
$754$		−	1127.80i		−	1.49576i
$755$	797.475	+	797.475i	1.05626	+	1.05626i
$756$	7.19499	+	48.4228i	0.00951718	+	0.0640513i
$757$	−191.376	+	191.376i	−0.252809	+	0.252809i	−0.822121	−	0.569312i	$-0.807210\pi$
$757$	−191.376	+	191.376i	−0.252809	+	0.252809i	0.569312	+	0.822121i	$0.307210\pi$
$758$			170.387i			0.224785i
$759$	−549.327			−0.723751
$760$	410.517	−	410.517i	0.540154	−	0.540154i
$761$			169.426i			0.222637i	0.993785	+	0.111318i	$0.0355073\pi$
$761$			169.426i			0.222637i	−0.993785	+	0.111318i	$0.964493\pi$
$762$	−954.711	−	954.711i	−1.25290	−	1.25290i
$763$	−613.622	+	91.1761i	−0.804223	+	0.119497i
$764$	−125.946	+	125.946i	−0.164851	+	0.164851i
$765$	629.811	−	629.811i	0.823283	−	0.823283i
$766$	−371.968	+	371.968i	−0.485598	+	0.485598i
$767$	−38.3660	−	38.3660i	−0.0500209	−	0.0500209i
$768$	−511.278	+	511.278i	−0.665727	+	0.665727i
$769$			24.4605i			0.0318082i	0.999874	+	0.0159041i	$0.00506265\pi$
$769$			24.4605i			0.0318082i	−0.999874	+	0.0159041i	$0.994937\pi$
$770$	357.347	−	53.0971i	0.464088	−	0.0689573i
$771$			211.698i			0.274575i
$772$	−115.949	−	115.949i	−0.150193	−	0.150193i
$773$	−140.273	−	140.273i	−0.181466	−	0.181466i	0.610529	−	0.791994i	$-0.290957\pi$
$773$	−140.273	−	140.273i	−0.181466	−	0.181466i	−0.791994	+	0.610529i	$0.790957\pi$
$774$		−	943.713i		−	1.21927i
$775$		−	248.557i		−	0.320719i
$776$	609.414	−	609.414i	0.785327	−	0.785327i
$777$	825.687	−	122.686i	1.06266	−	0.157897i
$778$	334.378			0.429792
$779$	−601.156	+	123.614i	−0.771702	+	0.158683i
$780$			257.354i			0.329941i
$781$			280.010i			0.358528i
$782$	−685.507	+	685.507i	−0.876607	+	0.876607i
$783$			319.697i			0.408297i
$784$	−156.569	−	515.227i	−0.199705	−	0.657178i
$785$	600.274	−	600.274i	0.764681	−	0.764681i
$786$	362.209	+	362.209i	0.460825	+	0.460825i
$787$	−954.470			−1.21280			−0.606398	−	0.795162i	$-0.707386\pi$
$787$	−954.470			−1.21280			−0.606398	+	0.795162i	$0.707386\pi$
$788$		−	255.176i		−	0.323828i
$789$			922.227i			1.16886i
$790$	691.879	−	691.879i	0.875796	−	0.875796i
$791$	130.444	+	96.6946i	0.164911	+	0.122243i
$792$	296.298	+	296.298i	0.374113	+	0.374113i
$793$	−43.3719	+	43.3719i	−0.0546934	+	0.0546934i
$794$	241.610	+	241.610i	0.304294	+	0.304294i
$795$	−421.284			−0.529917
$796$	133.049	+	133.049i	0.167147	+	0.167147i
$797$		−	679.761i		−	0.852900i	−0.904511	−	0.426450i	$-0.859764\pi$
$797$		−	679.761i		−	0.852900i	0.904511	−	0.426450i	$-0.140236\pi$
$798$	−435.808	+	587.920i	−0.546125	+	0.736742i
$799$			332.468i			0.416105i
$800$			77.2343i			0.0965429i
$801$	287.630	+	287.630i	0.359088	+	0.359088i
$802$	−1140.69			−1.42231
$803$	−27.6738	−	27.6738i	−0.0344631	−	0.0344631i
$804$		−	457.713i		−	0.569295i
$805$	−515.281	−	381.962i	−0.640100	−	0.474487i
$806$	875.088	−	875.088i	1.08572	−	1.08572i
$807$	−470.086	−	470.086i	−0.582511	−	0.582511i
$808$	569.005	−	569.005i	0.704214	−	0.704214i
$809$	254.839	+	254.839i	0.315005	+	0.315005i	0.846845	−	0.531840i	$-0.178499\pi$
$809$	254.839	+	254.839i	0.315005	+	0.315005i	−0.531840	+	0.846845i	$0.678499\pi$
$810$			725.641i			0.895854i
$811$	1122.62			1.38425			0.692123	−	0.721780i	$-0.256676\pi$
$811$	1122.62			1.38425			0.692123	+	0.721780i	$0.256676\pi$
$812$	47.1934	+	317.615i	0.0581200	+	0.391152i
$813$	885.968	+	885.968i	1.08975	+	1.08975i
$814$	−240.936	+	240.936i	−0.295990	+	0.295990i
$815$	−681.747			−0.836500
$816$	1212.86			1.48635
$817$	793.601	−	793.601i	0.971360	−	0.971360i
$818$	−798.428			−0.976073
$819$	−106.371	−	715.884i	−0.129879	−	0.874095i
$820$	−101.192	+	153.580i	−0.123405	+	0.187293i
$821$	−1164.30			−1.41814			−0.709072	−	0.705136i	$-0.750886\pi$
$821$	−1164.30			−1.41814			−0.709072	+	0.705136i	$0.750886\pi$
$822$	−128.333			−0.156123
$823$	800.699	+	800.699i	0.972903	+	0.972903i	0.999642	−	0.0267399i	$-0.00851259\pi$
$823$	800.699	+	800.699i	0.972903	+	0.972903i	−0.0267399	+	0.999642i	$0.508513\pi$
$824$		−	1014.61i		−	1.23132i
$825$	132.796			0.160965
$826$	−37.1448	−	27.5344i	−0.0449695	−	0.0333346i
$827$	−227.275	−	227.275i	−0.274819	−	0.274819i	0.556218	−	0.831036i	$-0.312252\pi$
$827$	−227.275	−	227.275i	−0.274819	−	0.274819i	−0.831036	+	0.556218i	$0.812252\pi$
$828$		−	148.997i		−	0.179948i
$829$	−1615.16			−1.94832			−0.974160	−	0.225858i	$-0.927482\pi$
$829$	−1615.16			−1.94832			−0.974160	+	0.225858i	$0.927482\pi$
$830$	−948.900			−1.14325
$831$	−330.135	+	330.135i	−0.397275	+	0.397275i
$832$	−714.027	+	714.027i	−0.858206	+	0.858206i
$833$	631.438	−	1182.73i	0.758029	−	1.41985i
$834$	348.240	−	348.240i	0.417554	−	0.417554i
$835$	26.5818	−	26.5818i	0.0318345	−	0.0318345i
$836$			99.8046i			0.119384i
$837$	−248.060	+	248.060i	−0.296368	+	0.296368i
$838$			481.871i			0.575025i
$839$	−406.759	−	406.759i	−0.484814	−	0.484814i	0.421851	−	0.906665i	$-0.361380\pi$
$839$	−406.759	−	406.759i	−0.484814	−	0.484814i	−0.906665	+	0.421851i	$0.861380\pi$
$840$	160.942	+	1083.15i	0.191597	+	1.28947i
$841$			1255.96i			1.49341i
$842$	−82.5313	+	82.5313i	−0.0980182	+	0.0980182i
$843$		−	1315.55i		−	1.56055i
$844$	−67.4763	+	67.4763i	−0.0799482	+	0.0799482i
$845$			149.144i			0.176502i
$846$	108.145	+	108.145i	0.127831	+	0.127831i
$847$	319.723	−	431.318i	0.377477	−	0.509230i
$848$	−181.245	−	181.245i	−0.213732	−	0.213732i
$849$	−911.751	−	911.751i	−1.07391	−	1.07391i
$850$	165.717	−	165.717i	0.194961	−	0.194961i
$851$	604.952			0.710872
$852$	−169.982			−0.199509
$853$	791.176			0.927521			0.463761	−	0.885961i	$-0.346500\pi$
$853$	791.176			0.927521			0.463761	+	0.885961i	$0.346500\pi$
$854$	−31.1270	+	41.9914i	−0.0364484	+	0.0491702i
$855$	344.555	−	344.555i	0.402989	−	0.402989i
$856$			1083.71i			1.26601i
$857$			1152.87i			1.34524i	0.739989	+	0.672619i	$0.234831\pi$
$857$			1152.87i			1.34524i	−0.739989	+	0.672619i	$0.765169\pi$
$858$	467.531	+	467.531i	0.544908	+	0.544908i
$859$	1060.95			1.23510			0.617550	−	0.786532i	$-0.288125\pi$
$859$	1060.95			1.23510			0.617550	+	0.786532i	$0.288125\pi$
$860$		−	336.331i		−	0.391082i
$861$	487.926	−	1049.76i	0.566697	−	1.21924i
$862$	−59.5513			−0.0690851
$863$		−	1710.54i		−	1.98209i	−0.133523	−	0.991046i	$-0.542629\pi$
$863$		−	1710.54i		−	1.98209i	0.133523	−	0.991046i	$-0.457371\pi$
$864$	77.0797	−	77.0797i	0.0892127	−	0.0892127i
$865$	890.281			1.02923
$866$	395.423			0.456609
$867$	1311.05	+	1311.05i	1.51217	+	1.51217i
$868$	−209.826	+	283.063i	−0.241735	+	0.326109i
$869$			839.884i			0.966494i
$870$			1432.21i			1.64622i
$871$		−	1611.25i		−	1.84989i
$872$	542.732	+	542.732i	0.622399	+	0.622399i
$873$	511.493	−	511.493i	0.585903	−	0.585903i
$874$	−375.025	+	375.025i	−0.429091	+	0.429091i
$875$	754.130	+	559.014i	0.861862	+	0.638873i
$876$	16.7996	−	16.7996i	0.0191776	−	0.0191776i
$877$	309.611			0.353034			0.176517	−	0.984298i	$-0.443517\pi$
$877$	309.611			0.353034			0.176517	+	0.984298i	$0.443517\pi$
$878$	−629.407	−	629.407i	−0.716865	−	0.716865i
$879$	−1776.23			−2.02074
$880$	−231.615	−	231.615i	−0.263199	−	0.263199i
$881$	−914.596			−1.03813			−0.519067	−	0.854734i	$-0.673720\pi$
$881$	−914.596			−1.03813			−0.519067	+	0.854734i	$0.673720\pi$
$882$	−179.325	−	590.113i	−0.203316	−	0.669062i
$883$	386.202	−	386.202i	0.437375	−	0.437375i	−0.453753	−	0.891128i	$-0.649915\pi$
$883$	386.202	−	386.202i	0.437375	−	0.437375i	0.891128	+	0.453753i	$0.149915\pi$
$884$	−389.853			−0.441010
$885$	48.7215	+	48.7215i	0.0550525	+	0.0550525i
$886$	1529.51			1.72630
$887$	−806.725	−	806.725i	−0.909498	−	0.909498i	0.0867333	−	0.996232i	$-0.472357\pi$
$887$	−806.725	−	806.725i	−0.909498	−	0.909498i	−0.996232	+	0.0867333i	$0.972357\pi$
$888$	−730.297	−	730.297i	−0.822407	−	0.822407i
$889$	1087.11	+	805.843i	1.22285	+	0.906460i
$890$	−306.818	−	306.818i	−0.344740	−	0.344740i
$891$	−440.434	−	440.434i	−0.494314	−	0.494314i
$892$			218.525i			0.244984i
$893$			181.886i			0.203680i
$894$	415.465			0.464726
$895$	128.444	−	128.444i	0.143513	−	0.143513i
$896$	−252.093	+	340.082i	−0.281354	+	0.379556i
$897$		−	1173.90i		−	1.30869i
$898$	110.933			0.123533
$899$	−1627.08	+	1627.08i	−1.80987	+	1.80987i
$900$			36.0191i			0.0400212i
$901$		−	638.182i		−	0.708305i
$902$	95.1723	+	462.840i	0.105513	+	0.513126i
$903$	311.128	+	2093.92i	0.344550	+	2.31885i
$904$		−	200.898i		−	0.222233i
$905$	672.730	+	672.730i	0.743348	+	0.743348i
$906$			1758.95i			1.94145i
$907$			1704.09i			1.87882i	0.342794	+	0.939411i	$0.388627\pi$
$907$			1704.09i			1.87882i	−0.342794	+	0.939411i	$0.611373\pi$
$908$	−122.872	−	122.872i	−0.135322	−	0.135322i
$909$	477.577	−	477.577i	0.525387	−	0.525387i
$910$	113.467	+	763.642i	0.124689	+	0.839167i
$911$			823.795i			0.904275i	0.891948	+	0.452138i	$0.149338\pi$
$911$			823.795i			0.904275i	−0.891948	+	0.452138i	$0.850662\pi$
$912$	663.530			0.727555
$913$	575.942	−	575.942i	0.630824	−	0.630824i
$914$	−42.2891	−	42.2891i	−0.0462682	−	0.0462682i
$915$	55.0785	−	55.0785i	0.0601951	−	0.0601951i
$916$	36.8692	+	36.8692i	0.0402502	+	0.0402502i
$917$	−412.440	−	305.730i	−0.449771	−	0.333402i
$918$	−330.770			−0.360316
$919$	518.304	−	518.304i	0.563987	−	0.563987i	−0.366450	−	0.930438i	$-0.619427\pi$
$919$	518.304	−	518.304i	0.563987	−	0.563987i	0.930438	+	0.366450i	$0.119427\pi$
$920$			793.587i			0.862595i
$921$	−5.46068	+	5.46068i	−0.00592907	+	0.00592907i
$922$	−96.9538			−0.105156
$923$	−598.375			−0.648293
$924$	−151.231	−	112.103i	−0.163670	−	0.121324i
$925$	−146.243			−0.158101
$926$	−460.310	+	460.310i	−0.497095	+	0.497095i
$927$		−	851.581i		−	0.918642i
$928$	505.582	−	505.582i	0.544808	−	0.544808i
$929$	584.961	+	584.961i	0.629668	+	0.629668i	0.947984	−	0.318317i	$-0.103118\pi$
$929$	584.961	+	584.961i	0.629668	+	0.629668i	−0.318317	+	0.947984i	$0.603118\pi$
$930$	−1111.29	+	1111.29i	−1.19493	+	1.19493i
$931$	345.446	−	647.047i	0.371048	−	0.695002i
$932$	156.932	+	156.932i	0.168382	+	0.168382i
$933$	1833.93			1.96563
$934$	−108.411			−0.116071
$935$		−	815.542i		−	0.872238i
$936$	−633.180	+	633.180i	−0.676474	+	0.676474i
$937$	−614.371	−	614.371i	−0.655679	−	0.655679i	0.298676	−	0.954355i	$-0.403455\pi$
$937$	−614.371	−	614.371i	−0.655679	−	0.655679i	−0.954355	+	0.298676i	$0.903455\pi$
$938$	−201.805	−	1358.16i	−0.215144	−	1.44794i
$939$	−1581.81			−1.68457
$940$	38.5419	+	38.5419i	0.0410021	+	0.0410021i
$941$	−1067.14			−1.13405			−0.567023	−	0.823702i	$-0.691905\pi$
$941$	−1067.14			−1.13405			−0.567023	+	0.823702i	$0.691905\pi$
$942$	1324.00			1.40552
$943$	461.578	−	700.540i	0.489478	−	0.742885i
$944$			41.9219i			0.0444088i
$945$	−32.1643	−	216.468i	−0.0340363	−	0.229067i
$946$	−611.007	−	611.007i	−0.645884	−	0.645884i
$947$	−201.990			−0.213295			−0.106647	−	0.994297i	$-0.534012\pi$
$947$	−201.990			−0.213295			−0.106647	+	0.994297i	$0.534012\pi$
$948$	−509.856			−0.537823
$949$	59.1382	−	59.1382i	0.0623164	−	0.0623164i
$950$	90.6598	−	90.6598i	0.0954314	−	0.0954314i
$951$	−1551.02			−1.63093
$952$	−1640.81	+	243.803i	−1.72354	+	0.256095i
$953$	−688.861			−0.722834			−0.361417	−	0.932404i	$-0.617707\pi$
$953$	−688.861			−0.722834			−0.361417	+	0.932404i	$0.617707\pi$
$954$	−207.588	−	207.588i	−0.217597	−	0.217597i
$955$	563.028	−	563.028i	0.589558	−	0.589558i
$956$	148.261	+	148.261i	0.155084	+	0.155084i
$957$	−869.294	−	869.294i	−0.908353	−	0.908353i
$958$	−467.823	−	467.823i	−0.488333	−	0.488333i
$959$	127.226	−	18.9041i	0.132665	−	0.0197123i
$960$	906.753	−	906.753i	0.944534	−	0.944534i
$961$	−1563.97			−1.62744
$962$	−514.874	−	514.874i	−0.535212	−	0.535212i
$963$			909.577i			0.944525i
$964$	283.214			0.293790
$965$	518.337	+	518.337i	0.537137	+	0.537137i
$966$	−147.027	−	989.505i	−0.152202	−	1.02433i
$967$	−22.1237	+	22.1237i	−0.0228786	+	0.0228786i	−0.718454	−	0.695575i	$-0.755150\pi$
$967$	−22.1237	+	22.1237i	−0.0228786	+	0.0228786i	0.695575	+	0.718454i	$0.255150\pi$
$968$	−664.275			−0.686235
$969$	1168.18	+	1168.18i	1.20555	+	1.20555i
$970$	−545.616	+	545.616i	−0.562491	+	0.562491i
$971$	−420.577	+	420.577i	−0.433138	+	0.433138i	−0.889694	−	0.456557i	$-0.849083\pi$
$971$	−420.577	+	420.577i	−0.433138	+	0.433138i	0.456557	+	0.889694i	$0.349083\pi$
$972$	222.862	−	222.862i	0.229282	−	0.229282i
$973$	−293.939	+	396.535i	−0.302096	+	0.407538i
$974$	−786.777			−0.807779
$975$			283.782i			0.291058i
$976$	47.3917			0.0485571
$977$	268.551	+	268.551i	0.274873	+	0.274873i	0.831058	−	0.556185i	$-0.187736\pi$
$977$	268.551	+	268.551i	0.274873	+	0.274873i	−0.556185	+	0.831058i	$0.687736\pi$
$978$	−751.850	−	751.850i	−0.768763	−	0.768763i
$979$	372.452			0.380441
$980$	−63.9098	−	210.311i	−0.0652141	−	0.214603i
$981$	455.526	+	455.526i	0.464349	+	0.464349i
$982$		−	5.19757i		−	0.00529284i
$983$			1523.00i			1.54934i	0.632364	+	0.774672i	$0.282085\pi$
$983$			1523.00i			1.54934i	−0.632364	+	0.774672i	$0.717915\pi$
$984$	−1402.91	+	288.475i	−1.42572	+	0.293166i
$985$			1140.74i			1.15811i
$986$	−2169.59			−2.20039
$987$	−275.607	−	204.299i	−0.279237	−	0.206990i
$988$	−213.280			−0.215870
$989$			1534.14i			1.55120i
$990$	−265.279	−	265.279i	−0.267959	−	0.267959i
$991$	−1149.43	−	1149.43i	−1.15986	−	1.15986i	−0.984504	−	0.175359i	$-0.943891\pi$
$991$	−1149.43	−	1149.43i	−1.15986	−	1.15986i	−0.175359	−	0.984504i	$-0.556109\pi$
$992$	784.584			0.790912
$993$	−1381.72			−1.39146
$994$	−504.384	+	74.9448i	−0.507429	+	0.0753972i
$995$	−594.781	−	594.781i	−0.597770	−	0.597770i
$996$	349.629	+	349.629i	0.351033	+	0.351033i
$997$	254.766	−	254.766i	0.255532	−	0.255532i	−0.567702	−	0.823234i	$-0.692167\pi$
$997$	254.766	−	254.766i	0.255532	−	0.255532i	0.823234	+	0.567702i	$0.192167\pi$
$998$	629.149	−	629.149i	0.630410	−	0.630410i
$999$	145.950	+	145.950i	0.146096	+	0.146096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.16	yes	108
7.6	odd	2	inner	287.3.g.a.132.15	✓	108
41.32	even	4	inner	287.3.g.a.237.39	yes	108
287.237	odd	4	inner	287.3.g.a.237.40	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.15	✓	108	7.6	odd	2	inner
287.3.g.a.132.16	yes	108	1.1	even	1	trivial
287.3.g.a.237.39	yes	108	41.32	even	4	inner
287.3.g.a.237.40	yes	108	287.237	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73155i q^{2} +(2.85212 - 2.85212i) q^{3} +1.00173 q^{4} -4.47811 q^{5} +(-4.93859 - 4.93859i) q^{6} +(5.62348 + 4.16852i) q^{7} -8.66075i q^{8} -7.26914i q^{9} +O(q^{10})\)	\(q-1.73155i q^{2} +(2.85212 - 2.85212i) q^{3} +1.00173 q^{4} -4.47811 q^{5} +(-4.93859 - 4.93859i) q^{6} +(5.62348 + 4.16852i) q^{7} -8.66075i q^{8} -7.26914i q^{9} +7.75408i q^{10} +(-4.70640 - 4.70640i) q^{11} +(2.85705 - 2.85705i) q^{12} +(10.0575 - 10.0575i) q^{13} +(7.21800 - 9.73734i) q^{14} +(-12.7721 + 12.7721i) q^{15} -10.9896 q^{16} +(-19.3478 - 19.3478i) q^{17} -12.5869 q^{18} +(-10.5848 - 10.5848i) q^{19} -4.48586 q^{20} +(27.9279 - 4.14972i) q^{21} +(-8.14938 + 8.14938i) q^{22} +20.4618 q^{23} +(-24.7015 - 24.7015i) q^{24} -4.94651 q^{25} +(-17.4150 - 17.4150i) q^{26} +(4.93661 + 4.93661i) q^{27} +(5.63320 + 4.17573i) q^{28} +(32.3802 + 32.3802i) q^{29} +(22.1156 + 22.1156i) q^{30} +50.2490i q^{31} -15.6139i q^{32} -26.8464 q^{33} +(-33.5018 + 33.5018i) q^{34} +(-25.1826 - 18.6671i) q^{35} -7.28172i q^{36} +29.5649 q^{37} +(-18.3280 + 18.3280i) q^{38} -57.3701i q^{39} +38.7838i q^{40} +(22.5580 - 34.2365i) q^{41} +(-7.18545 - 48.3586i) q^{42} +74.9758i q^{43} +(-4.71454 - 4.71454i) q^{44} +32.5520i q^{45} -35.4307i q^{46} +(-8.59188 - 8.59188i) q^{47} +(-31.3437 + 31.3437i) q^{48} +(14.2470 + 46.8831i) q^{49} +8.56513i q^{50} -110.365 q^{51} +(10.0749 - 10.0749i) q^{52} +(16.4924 + 16.4924i) q^{53} +(8.54799 - 8.54799i) q^{54} +(21.0758 + 21.0758i) q^{55} +(36.1025 - 48.7035i) q^{56} -60.3779 q^{57} +(56.0680 - 56.0680i) q^{58} -3.81468i q^{59} +(-12.7942 + 12.7942i) q^{60} -4.31241 q^{61} +87.0088 q^{62} +(30.3015 - 40.8779i) q^{63} -70.9948 q^{64} +(-45.0384 + 45.0384i) q^{65} +46.4860i q^{66} +(80.1024 - 80.1024i) q^{67} +(-19.3813 - 19.3813i) q^{68} +(58.3595 - 58.3595i) q^{69} +(-32.3230 + 43.6049i) q^{70} +(-29.7478 - 29.7478i) q^{71} -62.9563 q^{72} +5.88004 q^{73} -51.1932i q^{74} +(-14.1080 + 14.1080i) q^{75} +(-10.6031 - 10.6031i) q^{76} +(-6.84763 - 46.0851i) q^{77} -99.3393 q^{78} +(-89.2277 - 89.2277i) q^{79} +49.2128 q^{80} +93.5818 q^{81} +(-59.2822 - 39.0604i) q^{82} +122.374i q^{83} +(27.9762 - 4.15689i) q^{84} +(86.6417 + 86.6417i) q^{85} +129.825 q^{86} +184.704 q^{87} +(-40.7610 + 40.7610i) q^{88} +(-39.5686 + 39.5686i) q^{89} +56.3655 q^{90} +(98.4826 - 14.6332i) q^{91} +20.4972 q^{92} +(143.316 + 143.316i) q^{93} +(-14.8773 + 14.8773i) q^{94} +(47.3997 + 47.3997i) q^{95} +(-44.5327 - 44.5327i) q^{96} +(70.3650 + 70.3650i) q^{97} +(81.1805 - 24.6693i) q^{98} +(-34.2115 + 34.2115i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more