LMFDB - Embedded newform 287.3.g.a.132.15

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			132.15
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73155i q^{2} +(-2.85212 + 2.85212i) q^{3} +1.00173 q^{4} +4.47811 q^{5} +(4.93859 + 4.93859i) q^{6} +(4.16852 + 5.62348i) q^{7} -8.66075i q^{8} -7.26914i q^{9} +O(q^{10})$	\(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} +(4.16852 + 5.62348i) 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} +(9.73734 - 7.21800i) 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} +(4.17573 + 5.63320i) 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} +(18.6671 + 25.1826i) 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} +(48.7035 - 36.1025i) 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} +(40.8779 - 30.3015i) 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} +(43.6049 - 32.3230i) 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	−0.998841	−	0.0481351i	$-0.984672\pi$
$3$	−2.85212	+	2.85212i	−0.950706	+	0.950706i	0.0481351	+	0.998841i	$0.484672\pi$
$4$	1.00173			0.250432
$5$	4.47811			0.895623			0.447811	−	0.894128i	$-0.352204\pi$
$5$	4.47811			0.895623			0.447811	+	0.894128i	$0.352204\pi$
$6$	4.93859	+	4.93859i	0.823098	+	0.823098i
$7$	4.16852	+	5.62348i	0.595502	+	0.803354i
$7$	4.16852	+	5.62348i	0.595502	+	0.803354i
$8$		−	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	−0.978743	−	0.205092i	$-0.934251\pi$
$13$	−10.0575	+	10.0575i	−0.773651	+	0.773651i	0.205092	+	0.978743i	$0.434251\pi$
$14$	9.73734	−	7.21800i	0.695524	−	0.515571i
$15$	−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	$0.0477079\pi$
$17$	19.3478	+	19.3478i	1.13811	+	1.13811i	0.149318	+	0.988789i	$0.452292\pi$
$18$	−12.5869			−0.699272
$19$	10.5848	+	10.5848i	0.557092	+	0.557092i	0.928479	−	0.371386i	$-0.121117\pi$
$19$	10.5848	+	10.5848i	0.557092	+	0.557092i	−0.371386	+	0.928479i	$0.621117\pi$
$20$	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
$28$	4.17573	+	5.63320i	0.149133	+	0.201186i
$29$	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	$-0.699213\pi$
$31$		−	50.2490i		−	1.62094i	0.585782	−	0.810468i	$-0.300787\pi$
$32$		−	15.6139i		−	0.487935i
$33$	26.8464			0.813528
$34$	33.5018	−	33.5018i	0.985346	−	0.985346i
$35$	18.6671	+	25.1826i	0.533345	+	0.719502i
$36$		−	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	0.792577	−	0.609771i	$-0.208739\pi$
$47$	8.59188	+	8.59188i	0.182806	+	0.182806i	−0.609771	+	0.792577i	$0.708739\pi$
$48$	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
$56$	48.7035	−	36.1025i	0.869706	−	0.644687i
$57$	−60.3779			−1.05926
$58$	56.0680	−	56.0680i	0.966690	−	0.966690i
$59$			3.81468i			0.0646556i	0.999477	+	0.0323278i	$0.0102920\pi$
$59$			3.81468i			0.0646556i	−0.999477	+	0.0323278i	$0.989708\pi$
$60$	−12.7942	+	12.7942i	−0.213237	+	0.213237i
$61$	4.31241			0.0706952			0.0353476	−	0.999375i	$-0.488746\pi$
$61$	4.31241			0.0706952			0.0353476	+	0.999375i	$0.488746\pi$
$62$	−87.0088			−1.40337
$63$	40.8779	−	30.3015i	0.648855	−	0.480977i
$64$	−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
$70$	43.6049	−	32.3230i	0.622927	−	0.461757i
$71$	−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	$-0.512823\pi$
$73$	−5.88004			−0.0805484			−0.0402742	+	0.999189i	$0.512823\pi$
$74$		−	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	$-0.736150\pi$
$83$		−	122.374i		−	1.47439i	0.675681	−	0.737194i	$-0.263850\pi$
$84$	−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	−0.448961	−	0.893552i	$-0.648206\pi$
$89$	39.5686	−	39.5686i	0.444591	−	0.444591i	0.893552	+	0.448961i	$0.148206\pi$
$90$	−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	0.244290	−	0.969702i	$-0.421445\pi$
$97$	−70.3650	−	70.3650i	−0.725413	−	0.725413i	−0.969702	+	0.244290i	$0.921445\pi$
$98$	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	0.302623	−	0.953110i	$-0.402138\pi$
$101$	−65.6992	−	65.6992i	−0.650487	−	0.650487i	−0.953110	+	0.302623i	$0.902138\pi$
$102$			191.102i			1.87355i
$103$	−117.150			−1.13738			−0.568690	−	0.822552i	$-0.692550\pi$
$103$	−117.150			−1.13738			−0.568690	+	0.822552i	$0.692550\pi$
$104$	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
$112$	−45.8104	−	61.7999i	−0.409021	−	0.551784i
$113$	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
$126$	−52.4687	−	70.7821i	−0.416418	−	0.561763i
$127$	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	$-0.409688\pi$
$131$	73.3426			0.559867			0.279934	+	0.960019i	$0.409688\pi$
$132$	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	$-0.918370\pi$
$139$		−	70.5142i		−	0.507296i	0.967297	−	0.253648i	$-0.0816305\pi$
$140$	18.6994	+	25.2261i	0.133567	+	0.180187i
$141$	−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
$147$	−93.0821	−	174.350i	−0.633211	−	1.18605i
$148$	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	−0.136801	−	0.990599i	$-0.543682\pi$
$157$	134.046	−	134.046i	0.853798	−	0.853798i	0.990599	+	0.136801i	$0.0436820\pi$
$158$	−154.502	+	154.502i	−0.977863	+	0.977863i
$159$	−94.0763			−0.591675
$160$		−	69.9209i		−	0.437005i
$161$	85.2954	+	115.067i	0.529785	+	0.714699i
$162$		−	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	−0.689111	−	0.724656i	$-0.741999\pi$
$167$	5.93594	−	5.93594i	0.0355446	−	0.0355446i	0.724656	+	0.689111i	$0.241999\pi$
$168$	−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	$-0.305163\pi$
$173$	198.807			1.14917			0.574587	+	0.818443i	$0.305163\pi$
$174$			319.825i			1.83808i
$175$	−20.6196	−	27.8166i	−0.117826	−	0.158952i
$176$	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	0.987513	−	0.157535i	$-0.0503546\pi$
$181$	150.226	+	150.226i	0.829979	+	0.829979i	−0.157535	+	0.987513i	$0.550355\pi$
$182$	−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	0.289686	−	0.957122i	$-0.406449\pi$
$199$	−132.820	−	132.820i	−0.667435	−	0.667435i	−0.957122	+	0.289686i	$0.906449\pi$
$200$			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
$217$	282.574	−	209.464i	1.30219	−	0.965271i
$218$	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	$-0.837318\pi$
$223$		−	218.148i		−	0.978243i	0.872216	−	0.489121i	$-0.162682\pi$
$224$	87.8045	−	65.0869i	0.391984	−	0.290566i
$225$			35.9569i			0.159808i
$226$		−	40.1658i		−	0.177725i
$227$	122.660	+	122.660i	0.540353	+	0.540353i	0.923632	−	0.383280i	$-0.125205\pi$
$227$	122.660	+	122.660i	0.540353	+	0.540353i	−0.383280	+	0.923632i	$0.625205\pi$
$228$	−60.4824			−0.265273
$229$	−36.8056	−	36.8056i	−0.160723	−	0.160723i	0.622164	−	0.782887i	$-0.286254\pi$
$229$	−36.8056	−	36.8056i	−0.160723	−	0.160723i	−0.782887	+	0.622164i	$0.786254\pi$
$230$		−	158.663i		−	0.689837i
$231$	111.910	+	150.970i	0.484458	+	0.653551i
$232$	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	$-0.699520\pi$
$241$	−282.725			−1.17313			−0.586565	+	0.809902i	$0.699520\pi$
$242$	−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	$-0.328726\pi$
$251$	257.266			1.02497			0.512483	+	0.858698i	$0.328726\pi$
$252$	40.9486	−	30.3539i	0.162494	−	0.120452i
$253$	−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	−0.631208	−	0.775614i	$-0.717440\pi$
$257$	37.1124	−	37.1124i	0.144406	−	0.144406i	0.775614	+	0.631208i	$0.217440\pi$
$258$	−370.275	+	370.275i	−1.43517	+	1.43517i
$259$	123.242	+	166.258i	0.475837	+	0.641921i
$260$	−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	$0.0991101\pi$
$269$			164.820i			0.612714i	−0.951917	+	0.306357i	$0.900890\pi$
$270$	−38.2788	+	38.2788i	−0.141774	+	0.141774i
$271$		−	310.635i		−	1.14626i	−0.819466	−	0.573128i	$-0.805730\pi$
$271$		−	310.635i		−	1.14626i	0.819466	−	0.573128i	$-0.194270\pi$
$272$	−212.625	−	212.625i	−0.781710	−	0.781710i
$273$	322.619	−	239.148i	1.18176	−	0.876001i
$274$	−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
$280$	218.100	−	161.671i	0.778928	−	0.577396i
$281$	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	$0.191046\pi$
$283$			319.675i			1.12959i	−0.825230	+	0.564797i	$0.808954\pi$
$284$	−29.7993	−	29.7993i	−0.104927	−	0.104927i
$285$	−270.379			−0.948699
$286$		−	163.924i		−	0.573161i
$287$	−286.561	+	15.8609i	−0.998472	+	0.0552643i
$288$	−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	$0.0206609\pi$
$293$	311.388	+	311.388i	1.06276	+	1.06276i	0.0648625	+	0.997894i	$0.479339\pi$
$294$	−301.896	+	161.176i	−1.02686	+	0.548219i
$295$			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
$301$	−421.625	+	312.538i	−1.40075	+	1.03833i
$302$	−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	$-0.499007\pi$
$307$	1.91460			0.00623650			0.00311825	+	0.999995i	$0.499007\pi$
$308$	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	$-0.989060\pi$
$311$	−321.503	−	321.503i	−1.03377	−	1.03377i	−0.0343624	−	0.999409i	$-0.510940\pi$
$312$	−496.868			−1.59253
$313$	277.304	+	277.304i	0.885956	+	0.885956i	0.994132	−	0.108176i	$-0.0345011\pi$
$313$	277.304	+	277.304i	0.885956	+	0.885956i	−0.108176	+	0.994132i	$0.534501\pi$
$314$	−232.108	−	232.108i	−0.739197	−	0.739197i
$315$	183.056	−	135.694i	0.581129	−	0.430774i
$316$	−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
$322$	199.244	−	147.693i	0.618769	−	0.458675i
$323$			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
$343$	−323.035	+	115.315i	−0.941792	+	0.336197i
$344$	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	$-0.701308\pi$
$349$	−412.592			−1.18221			−0.591106	+	0.806594i	$0.701308\pi$
$350$	−48.1658	+	35.7039i	−0.137617	+	0.102011i
$351$	99.2994			0.282904
$352$	−73.4854	+	73.4854i	−0.208765	+	0.208765i
$353$		−	496.470i		−	1.40643i	−0.710977	−	0.703216i	$-0.751747\pi$
$353$		−	496.470i		−	1.40643i	0.710977	−	0.703216i	$-0.248253\pi$
$354$	−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
$357$	−460.056	−	620.632i	−1.28867	−	1.73847i
$358$	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	$-0.210268\pi$
$367$	579.594			1.57928			0.789638	+	0.613573i	$0.210268\pi$
$368$	−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	0.929558	−	0.368676i	$-0.120189\pi$
$383$	214.818	+	214.818i	0.560882	+	0.560882i	−0.368676	+	0.929558i	$0.620189\pi$
$384$	−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	−0.509186	−	0.860656i	$-0.670054\pi$
$397$	139.534	−	139.534i	0.351470	−	0.351470i	0.860656	+	0.509186i	$0.170054\pi$
$398$	−229.984	+	229.984i	−0.577849	+	0.577849i
$399$	−251.686	−	339.534i	−0.630793	−	0.850962i
$400$	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	$0.190622\pi$
$409$			461.105i			1.12740i	−0.825981	+	0.563699i	$0.809378\pi$
$410$	265.472	+	174.917i	0.647494	+	0.426626i
$411$			74.1143i			0.180327i
$412$	−117.353			−0.284837
$413$	−21.4518	+	15.9016i	−0.0519413	+	0.0385025i
$414$	−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	$-0.392247\pi$
$419$	278.288			0.664173			0.332086	+	0.943249i	$0.392247\pi$
$420$	−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
$427$	17.9763	+	24.2507i	0.0420991	+	0.0567932i
$428$	−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	$-0.915057\pi$
$433$		−	228.364i		−	0.527399i	0.964605	−	0.263699i	$-0.0849427\pi$
$434$	−362.698	−	489.292i	−0.835709	−	1.12740i
$435$	−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	−0.987240	−	0.159238i	$-0.949096\pi$
$439$	−363.493	+	363.493i	−0.828003	+	0.828003i	0.159238	+	0.987240i	$0.449096\pi$
$440$	−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
$448$	−295.943	−	399.237i	−0.660587	−	0.891155i
$449$			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	$0.0193426\pi$
$461$			55.9924i			0.121459i	−0.998154	+	0.0607293i	$0.980657\pi$
$462$	261.413	−	193.778i	0.565829	−	0.419432i
$463$	−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	$0.0213533\pi$
$467$			62.6089i			0.134066i	−0.997751	+	0.0670331i	$0.978647\pi$
$468$	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	−0.930453	−	0.366412i	$-0.880586\pi$
$479$	−270.176	+	270.176i	−0.564041	+	0.564041i	0.366412	+	0.930453i	$0.380586\pi$
$480$	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	−0.267421	−	0.963580i	$-0.586171\pi$
$503$	350.168	−	350.168i	0.696159	−	0.696159i	0.963580	+	0.267421i	$0.0861714\pi$
$504$	−262.434	−	354.033i	−0.520703	−	0.702446i
$505$	−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	0.551653	−	0.834074i	$-0.313997\pi$
$509$	−143.752	−	143.752i	−0.282421	−	0.282421i	−0.834074	+	0.551653i	$0.813997\pi$
$510$			855.776i			1.67799i
$511$	−24.5110	−	33.0662i	−0.0479668	−	0.0647089i
$512$			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
$518$	287.884	−	213.400i	0.555760	−	0.411968i
$519$	−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	−0.00468391	−	0.999989i	$-0.501491\pi$
$521$	518.554	−	518.554i	0.995305	−	0.995305i	0.999989	+	0.00468391i	$0.00149094\pi$
$522$	−407.567	−	407.567i	−0.780779	−	0.780779i
$523$		−	82.1864i		−	0.157144i	−0.996908	−	0.0785721i	$-0.974964\pi$
$523$		−	82.1864i		−	0.157144i	0.996908	−	0.0785721i	$-0.0250361\pi$
$524$	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
$539$	287.703	−	153.599i	0.533771	−	0.284970i
$540$	−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
$546$	−414.097	−	558.632i	−0.758420	−	1.02314i
$547$	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
$560$	−205.144	−	276.747i	−0.366329	−	0.494191i
$561$	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	−0.317393	−	0.948294i	$-0.602807\pi$
$563$	355.197	−	355.197i	0.630901	−	0.630901i	0.948294	+	0.317393i	$0.102807\pi$
$564$	−49.0948			−0.0870476
$565$	103.876			0.183852
$566$	553.534			0.977975
$567$	390.097	+	526.255i	0.688002	+	0.928140i
$568$	−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
$574$	27.4639	+	496.196i	0.0478465	+	0.864453i
$575$	−101.214			−0.176025
$576$			516.071i			0.895957i
$577$	−220.514	+	220.514i	−0.382173	+	0.382173i	−0.871885	−	0.489711i	$-0.837102\pi$
$577$	−220.514	+	220.514i	−0.382173	+	0.382173i	0.489711	+	0.871885i	$0.337102\pi$
$578$	795.954			1.37708
$579$	660.259			1.14034
$580$	145.253	+	145.253i	0.250436	+	0.250436i
$581$	688.168	−	510.119i	1.18445	−	0.878001i
$582$		−	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	−0.658012	−	0.753007i	$-0.728603\pi$
$587$	55.7618	−	55.7618i	0.0949946	−	0.0949946i	0.753007	+	0.658012i	$0.228603\pi$
$588$	−93.2431	−	174.652i	−0.158577	−	0.297027i
$589$	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	0.852931	−	0.522023i	$-0.174823\pi$
$593$	196.228	+	196.228i	0.330908	+	0.330908i	−0.522023	+	0.852931i	$0.674823\pi$
$594$	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	$0.0252932\pi$
$601$	646.809	+	646.809i	1.07622	+	1.07622i	0.0793774	+	0.996845i	$0.474707\pi$
$602$	541.175	+	730.065i	0.898963	+	1.21273i
$603$	−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	$-0.760022\pi$
$607$	−885.026			−1.45803			−0.729016	+	0.684496i	$0.760022\pi$
$608$	165.270	−	165.270i	0.271825	−	0.271825i
$609$	−769.943	−	1038.68i	−1.26427	−	1.70555i
$610$		−	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	$-0.848430\pi$
$619$		−	567.474i		−	0.916760i	0.888756	−	0.458380i	$-0.151570\pi$
$620$		−	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
$630$	−234.961	−	316.970i	−0.372953	−	0.503127i
$631$	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
$637$	−328.237	−	614.813i	−0.515285	−	0.965170i
$638$	−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	−0.992961	−	0.118445i	$-0.962209\pi$
$643$	−562.313	+	562.313i	−0.874515	+	0.874515i	0.118445	+	0.992961i	$0.462209\pi$
$644$	85.4429	+	115.266i	0.132675	+	0.178984i
$645$	−957.599	−	957.599i	−1.48465	−	1.48465i
$646$	709.216			1.09786
$647$	−738.567			−1.14153			−0.570763	−	0.821115i	$-0.693352\pi$
$647$	−738.567			−1.14153			−0.570763	+	0.821115i	$0.693352\pi$
$648$		−	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	$-0.442565\pi$
$661$	237.247			0.358922			0.179461	+	0.983765i	$0.442565\pi$
$662$	−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	$-0.179760\pi$
$677$	1143.77			1.68946			0.844732	+	0.535190i	$0.179760\pi$
$678$	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
$686$	199.675	+	559.351i	0.291071	+	0.815380i
$687$	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	0.503439	−	0.864031i	$-0.332068\pi$
$691$	−249.169	−	249.169i	−0.360593	−	0.360593i	−0.864031	+	0.503439i	$0.832068\pi$
$692$	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
$700$	−20.6553	−	27.8647i	−0.0295075	−	0.0398067i
$701$	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
$714$	−1074.66	+	796.611i	−1.50512	+	1.11570i
$715$	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	0.100212	−	0.994966i	$-0.468048\pi$
$719$	−643.328	−	643.328i	−0.894754	−	0.894754i	−0.994966	+	0.100212i	$0.968048\pi$
$720$			357.735i			0.496854i
$721$	−488.342	−	658.791i	−0.677312	−	0.913719i
$722$	−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	$0.610076\pi$
$727$	−930.388	+	930.388i	−1.27976	+	1.27976i	−0.940799	+	0.338964i	$0.889924\pi$
$728$	−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	$-0.394590\pi$
$733$	476.649			0.650272			0.325136	+	0.945667i	$0.394590\pi$
$734$		−	1003.60i		−	1.36730i
$735$	−416.832	−	780.759i	−0.567118	−	1.06226i
$736$		−	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
$749$	−521.600	−	703.657i	−0.696395	−	0.939462i
$750$	−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	$-0.964493\pi$
$761$		−	169.426i		−	0.222637i	0.993785	−	0.111318i	$-0.0355073\pi$
$762$	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	$-0.994937\pi$
$769$		−	24.4605i		−	0.0318082i	0.999874	−	0.0159041i	$-0.00506265\pi$
$770$	−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	0.791994	−	0.610529i	$-0.209043\pi$
$773$	140.273	+	140.273i	0.181466	+	0.181466i	−0.610529	+	0.791994i	$0.709043\pi$
$774$		−	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	$-0.292614\pi$
$787$	954.470			1.21280			0.606398	+	0.795162i	$0.292614\pi$
$788$		−	255.176i		−	0.323828i
$789$		−	922.227i		−	1.16886i
$790$	−691.879	+	691.879i	−0.875796	+	0.875796i
$791$	96.6946	+	130.444i	0.122243	+	0.164911i
$792$	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	$0.140236\pi$
$797$			679.761i			0.852900i	−0.904511	+	0.426450i	$0.859764\pi$
$798$	−587.920	+	435.808i	−0.736742	+	0.546125i
$799$			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
$805$	381.962	+	515.281i	0.474487	+	0.640100i
$806$	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	$-0.743324\pi$
$811$	−1122.62			−1.38425			−0.692123	+	0.721780i	$0.743324\pi$
$812$	−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
$826$	27.5344	+	37.1448i	0.0333346	+	0.0449695i
$827$	−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	$-0.0725185\pi$
$829$	1615.16			1.94832			0.974160	+	0.225858i	$0.0725185\pi$
$830$	−948.900			−1.14325
$831$	330.135	−	330.135i	0.397275	−	0.397275i
$832$	714.027	−	714.027i	0.858206	−	0.858206i
$833$	−1182.73	+	631.438i	−1.41985	+	0.758029i
$834$	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	0.906665	−	0.421851i	$-0.138620\pi$
$839$	406.759	+	406.759i	0.484814	+	0.484814i	−0.421851	+	0.906665i	$0.638620\pi$
$840$	−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
$847$	431.318	−	319.723i	0.509230	−	0.377477i
$848$	−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	$-0.653500\pi$
$853$	−791.176			−0.927521			−0.463761	+	0.885961i	$0.653500\pi$
$854$	41.9914	−	31.1270i	0.0491702	−	0.0364484i
$855$	344.555	−	344.555i	0.402989	−	0.402989i
$856$			1083.71i			1.26601i
$857$		−	1152.87i		−	1.34524i	−0.739989	−	0.672619i	$-0.765169\pi$
$857$		−	1152.87i		−	1.34524i	0.739989	−	0.672619i	$-0.234831\pi$
$858$	467.531	+	467.531i	0.544908	+	0.544908i
$859$	−1060.95			−1.23510			−0.617550	−	0.786532i	$-0.711875\pi$
$859$	−1060.95			−1.23510			−0.617550	+	0.786532i	$0.711875\pi$
$860$			336.331i			0.391082i
$861$	772.070	−	862.544i	0.896713	−	1.00179i
$862$	−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
$868$	283.063	−	209.826i	0.326109	−	0.241735i
$869$			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
$875$	−559.014	−	754.130i	−0.638873	−	0.861862i
$876$	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	$-0.326280\pi$
$881$	914.596			1.03813			0.519067	+	0.854734i	$0.326280\pi$
$882$	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	0.996232	−	0.0867333i	$-0.0276428\pi$
$887$	806.725	+	806.725i	0.909498	+	0.909498i	−0.0867333	+	0.996232i	$0.527643\pi$
$888$	730.297	+	730.297i	0.822407	+	0.822407i
$889$	805.843	+	1087.11i	0.906460	+	1.22285i
$890$	−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
$896$	−340.082	+	252.093i	−0.379556	+	0.281354i
$897$		−	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
$917$	305.730	+	412.440i	0.333402	+	0.449771i
$918$	−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
$924$	112.103	+	151.231i	0.121324	+	0.163670i
$925$	−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	0.318317	−	0.947984i	$-0.396882\pi$
$929$	−584.961	−	584.961i	−0.629668	−	0.629668i	−0.947984	+	0.318317i	$0.896882\pi$
$930$	1111.29	−	1111.29i	1.19493	−	1.19493i
$931$	−647.047	+	345.446i	−0.695002	+	0.371048i
$932$	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	0.954355	−	0.298676i	$-0.0965449\pi$
$937$	614.371	+	614.371i	0.655679	+	0.655679i	−0.298676	+	0.954355i	$0.596545\pi$
$938$	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	$-0.308095\pi$
$941$	1067.14			1.13405			0.567023	+	0.823702i	$0.308095\pi$
$942$	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	−0.456557	−	0.889694i	$-0.650917\pi$
$971$	420.577	−	420.577i	0.433138	−	0.433138i	0.889694	+	0.456557i	$0.150917\pi$
$972$	−222.862	+	222.862i	−0.229282	+	0.229282i
$973$	396.535	−	293.939i	0.407538	−	0.302096i
$974$	−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	$-0.717915\pi$
$983$		−	1523.00i		−	1.54934i	0.632364	−	0.774672i	$-0.282085\pi$
$984$	−1402.91	+	288.475i	−1.42572	+	0.293166i
$985$		−	1140.74i		−	1.15811i
$986$	2169.59			2.20039
$987$	−204.299	−	275.607i	−0.206990	−	0.279237i
$988$	−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	−0.823234	−	0.567702i	$-0.807833\pi$
$997$	−254.766	+	254.766i	−0.255532	+	0.255532i	0.567702	+	0.823234i	$0.307833\pi$
$998$	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.132.15	✓	108
7.6	odd	2	inner	287.3.g.a.132.16	yes	108
41.32	even	4	inner	287.3.g.a.237.40	yes	108
287.237	odd	4	inner	287.3.g.a.237.39	yes	108

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

\(f(q)\)	\(=\)	\(q-1.73155i q^{2} +(-2.85212 + 2.85212i) q^{3} +1.00173 q^{4} +4.47811 q^{5} +(4.93859 + 4.93859i) q^{6} +(4.16852 + 5.62348i) q^{7} -8.66075i q^{8} -7.26914i q^{9} +O(q^{10})\)	\(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} +(4.16852 + 5.62348i) 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} +(9.73734 - 7.21800i) 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} +(4.17573 + 5.63320i) 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} +(18.6671 + 25.1826i) 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} +(48.7035 - 36.1025i) 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} +(40.8779 - 30.3015i) 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} +(43.6049 - 32.3230i) 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

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Database

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