LMFDB - Embedded newform 250.4.e.c.99.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,4,Mod(49,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("250.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	250.e (of order $10$, degree $4$, not 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:	$14.7504775014$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			99.7
Character	$\chi$	$=$	250.99
Dual form			250.4.e.c.149.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.90211 - 0.618034i) q^{2} +(2.58496 + 3.55790i) q^{3} +(3.23607 - 2.35114i) q^{4} +(7.11579 + 5.16993i) q^{6} -32.4633i q^{7} +(4.70228 - 6.47214i) q^{8} +(2.36687 - 7.28447i) q^{9} +(-13.6751 - 42.0875i) q^{11} +(16.7302 + 5.43598i) q^{12} +(-18.8504 - 6.12486i) q^{13} +(-20.0634 - 61.7488i) q^{14} +(4.94427 - 15.2169i) q^{16} +(-48.4207 + 66.6454i) q^{17} -15.3187i q^{18} +(8.36319 + 6.07621i) q^{19} +(115.501 - 83.9163i) q^{21} +(-52.0231 - 71.6036i) q^{22} +(184.908 - 60.0803i) q^{23} +35.1824 q^{24} -39.6409 q^{26} +(144.965 - 47.1019i) q^{27} +(-76.3257 - 105.053i) q^{28} +(-159.317 + 115.751i) q^{29} +(68.1740 + 49.5313i) q^{31} -32.0000i q^{32} +(114.394 - 157.449i) q^{33} +(-50.9126 + 156.693i) q^{34} +(-9.46747 - 29.1379i) q^{36} +(218.389 + 70.9588i) q^{37} +(19.6630 + 6.38891i) q^{38} +(-26.9359 - 82.9003i) q^{39} +(-6.39296 + 19.6755i) q^{41} +(167.833 - 231.002i) q^{42} -36.8678i q^{43} +(-143.207 - 104.046i) q^{44} +(314.584 - 228.559i) q^{46} +(249.612 + 343.561i) q^{47} +(66.9209 - 21.7439i) q^{48} -710.864 q^{49} -362.283 q^{51} +(-75.4016 + 24.4995i) q^{52} +(3.07504 + 4.23242i) q^{53} +(246.629 - 179.186i) q^{54} +(-210.107 - 152.651i) q^{56} +45.4621i q^{57} +(-231.502 + 318.635i) q^{58} +(-16.0299 + 49.3350i) q^{59} +(-38.3804 - 118.123i) q^{61} +(160.287 + 52.0803i) q^{62} +(-236.478 - 76.8363i) q^{63} +(-19.7771 - 60.8676i) q^{64} +(120.280 - 370.185i) q^{66} +(457.984 - 630.360i) q^{67} +329.513i q^{68} +(691.740 + 502.578i) q^{69} +(-496.268 + 360.560i) q^{71} +(-36.0164 - 49.5723i) q^{72} +(863.608 - 280.603i) q^{73} +459.255 q^{74} +41.3499 q^{76} +(-1366.30 + 443.937i) q^{77} +(-102.470 - 141.038i) q^{78} +(-500.100 + 363.344i) q^{79} +(375.005 + 272.457i) q^{81} +41.3761i q^{82} +(-265.719 + 365.730i) q^{83} +(176.470 - 543.118i) q^{84} +(-22.7855 - 70.1266i) q^{86} +(-823.659 - 267.623i) q^{87} +(-336.700 - 109.401i) q^{88} +(-266.987 - 821.703i) q^{89} +(-198.833 + 611.945i) q^{91} +(457.118 - 629.169i) q^{92} +370.592i q^{93} +(687.123 + 499.224i) q^{94} +(113.853 - 82.7188i) q^{96} +(384.094 + 528.660i) q^{97} +(-1352.14 + 439.338i) q^{98} -338.953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 28 q^{6} + 166 q^{9} + 304 q^{11} - 104 q^{14} - 128 q^{16} + 40 q^{19} + 514 q^{21} + 128 q^{24} - 1432 q^{26} - 210 q^{29} + 354 q^{31} - 684 q^{34} - 664 q^{36} + 292 q^{39} + 924 q^{41}+ \cdots + 3572 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 28 * q^6 + 166 * q^9 + 304 * q^11 - 104 * q^14 - 128 * q^16 + 40 * q^19 + 514 * q^21 + 128 * q^24 - 1432 * q^26 - 210 * q^29 + 354 * q^31 - 684 * q^34 - 664 * q^36 + 292 * q^39 + 924 * q^41 + 904 * q^44 + 2248 * q^46 - 3396 * q^49 - 7216 * q^51 - 780 * q^54 + 16 * q^56 - 2550 * q^59 + 504 * q^61 + 512 * q^64 + 1996 * q^66 + 10982 * q^69 + 7424 * q^71 + 2296 * q^74 - 400 * q^76 - 3500 * q^79 + 8212 * q^81 + 1224 * q^84 + 2148 * q^86 - 11320 * q^89 - 986 * q^91 + 4456 * q^94 + 448 * q^96 + 3572 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	1.90211	−	0.618034i	0.672499	−	0.218508i
$2$	1.90211	−	0.618034i	0.672499	−	0.218508i
$3$	2.58496	+	3.55790i	0.497476	+	0.684717i	0.981745	−	0.190202i	$-0.0609143\pi$
$3$	2.58496	+	3.55790i	0.497476	+	0.684717i	−0.484269	+	0.874919i	$0.660914\pi$
$4$	3.23607	−	2.35114i	0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	7.11579	+	5.16993i	0.484168	+	0.351769i
$7$		−	32.4633i		−	1.75285i	−0.481537	−	0.876426i	$-0.659921\pi$
$7$		−	32.4633i		−	1.75285i	0.481537	−	0.876426i	$-0.340079\pi$
$8$	4.70228	−	6.47214i	0.207813	−	0.286031i
$9$	2.36687	−	7.28447i	0.0876618	−	0.269795i
$10$		0			0
$11$	−13.6751	−	42.0875i	−0.374835	−	1.15362i	−0.943590	−	0.331117i	$-0.892575\pi$
$11$	−13.6751	−	42.0875i	−0.374835	−	1.15362i	0.568754	−	0.822507i	$-0.307425\pi$
$12$	16.7302	+	5.43598i	0.402467	+	0.130769i
$13$	−18.8504	−	6.12486i	−0.402166	−	0.130672i	0.100948	−	0.994892i	$-0.467812\pi$
$13$	−18.8504	−	6.12486i	−0.402166	−	0.130672i	−0.503114	+	0.864220i	$0.667812\pi$
$14$	−20.0634	−	61.7488i	−0.383012	−	1.17879i
$15$		0			0
$16$	4.94427	−	15.2169i	0.0772542	−	0.237764i
$17$	−48.4207	+	66.6454i	−0.690809	+	0.950817i	−1.00000		0.000182954i	$-0.999942\pi$
$17$	−48.4207	+	66.6454i	−0.690809	+	0.950817i	0.309191	+	0.951000i	$0.399942\pi$
$18$		−	15.3187i		−	0.200592i
$19$	8.36319	+	6.07621i	0.100981	+	0.0733673i	0.637130	−	0.770756i	$-0.280121\pi$
$19$	8.36319	+	6.07621i	0.100981	+	0.0733673i	−0.536149	+	0.844124i	$0.680121\pi$
$20$		0			0
$21$	115.501	−	83.9163i	1.20021	−	0.872002i
$22$	−52.0231	−	71.6036i	−0.504152	−	0.693906i
$23$	184.908	−	60.0803i	1.67635	−	0.544678i	0.692151	−	0.721753i	$-0.256663\pi$
$23$	184.908	−	60.0803i	1.67635	−	0.544678i	0.984197	+	0.177075i	$0.0566634\pi$
$24$	35.1824			0.299232
$25$		0			0
$26$	−39.6409			−0.299009
$27$	144.965	−	47.1019i	1.03328	−	0.335732i
$28$	−76.3257	−	105.053i	−0.515150	−	0.709043i
$29$	−159.317	+	115.751i	−1.02016	+	0.741186i	−0.966315	−	0.257363i	$-0.917146\pi$
$29$	−159.317	+	115.751i	−1.02016	+	0.741186i	−0.0538405	+	0.998550i	$0.517146\pi$
$30$		0			0
$31$	68.1740	+	49.5313i	0.394981	+	0.286970i	0.767493	−	0.641057i	$-0.221504\pi$
$31$	68.1740	+	49.5313i	0.394981	+	0.286970i	−0.372513	+	0.928027i	$0.621504\pi$
$32$		−	32.0000i		−	0.176777i
$33$	114.394	−	157.449i	0.603435	−	0.830557i
$34$	−50.9126	+	156.693i	−0.256807	+	0.790370i
$35$		0			0
$36$	−9.46747	−	29.1379i	−0.0438309	−	0.134898i
$37$	218.389	+	70.9588i	0.970348	+	0.315285i	0.750956	−	0.660352i	$-0.229593\pi$
$37$	218.389	+	70.9588i	0.970348	+	0.315285i	0.219391	+	0.975637i	$0.429593\pi$
$38$	19.6630	+	6.38891i	0.0839412	+	0.0272741i
$39$	−26.9359	−	82.9003i	−0.110595	−	0.340376i
$40$		0			0
$41$	−6.39296	+	19.6755i	−0.0243515	+	0.0749463i	−0.962494	−	0.271304i	$-0.912545\pi$
$41$	−6.39296	+	19.6755i	−0.0243515	+	0.0749463i	0.938142	+	0.346250i	$0.112545\pi$
$42$	167.833	−	231.002i	0.616599	−	0.848675i
$43$		−	36.8678i		−	0.130751i	−0.997861	−	0.0653753i	$-0.979176\pi$
$43$		−	36.8678i		−	0.130751i	0.997861	−	0.0653753i	$-0.0208245\pi$
$44$	−143.207	−	104.046i	−0.490666	−	0.356490i
$45$		0			0
$46$	314.584	−	228.559i	1.00832	−	0.732591i
$47$	249.612	+	343.561i	0.774673	+	1.06625i	0.995850	+	0.0910123i	$0.0290102\pi$
$47$	249.612	+	343.561i	0.774673	+	1.06625i	−0.221177	+	0.975234i	$0.570990\pi$
$48$	66.9209	−	21.7439i	0.201233	−	0.0653847i
$49$	−710.864			−2.07249
$50$		0			0
$51$	−362.283			−0.994702
$52$	−75.4016	+	24.4995i	−0.201083	+	0.0653358i
$53$	3.07504	+	4.23242i	0.00796960	+	0.0109692i	0.812983	−	0.582287i	$-0.197842\pi$
$53$	3.07504	+	4.23242i	0.00796960	+	0.0109692i	−0.805014	+	0.593256i	$0.797842\pi$
$54$	246.629	−	179.186i	0.621517	−	0.451558i
$55$		0			0
$56$	−210.107	−	152.651i	−0.501369	−	0.364266i
$57$			45.4621i			0.105642i
$58$	−231.502	+	318.635i	−0.524098	+	0.721359i
$59$	−16.0299	+	49.3350i	−0.0353715	+	0.108862i	−0.967183	−	0.254079i	$-0.918228\pi$
$59$	−16.0299	+	49.3350i	−0.0353715	+	0.108862i	0.931812	+	0.362942i	$0.118228\pi$
$60$		0			0
$61$	−38.3804	−	118.123i	−0.0805592	−	0.247936i	0.902663	−	0.430348i	$-0.141609\pi$
$61$	−38.3804	−	118.123i	−0.0805592	−	0.247936i	−0.983222	+	0.182413i	$0.941609\pi$
$62$	160.287	+	52.0803i	0.328329	+	0.106681i
$63$	−236.478	−	76.8363i	−0.472911	−	0.153658i
$64$	−19.7771	−	60.8676i	−0.0386271	−	0.118882i
$65$		0			0
$66$	120.280	−	370.185i	0.224326	−	0.690404i
$67$	457.984	−	630.360i	0.835098	−	1.14941i	−0.151854	−	0.988403i	$-0.548524\pi$
$67$	457.984	−	630.360i	0.835098	−	1.14941i	0.986953	−	0.161011i	$-0.0514756\pi$
$68$			329.513i			0.587637i
$69$	691.740	+	502.578i	1.20689	+	0.876860i
$70$		0			0
$71$	−496.268	+	360.560i	−0.829523	+	0.602684i	−0.919424	−	0.393267i	$-0.871345\pi$
$71$	−496.268	+	360.560i	−0.829523	+	0.602684i	0.0899013	+	0.995951i	$0.471345\pi$
$72$	−36.0164	−	49.5723i	−0.0589524	−	0.0811411i
$73$	863.608	−	280.603i	1.38463	−	0.449892i	0.480439	−	0.877028i	$-0.340477\pi$
$73$	863.608	−	280.603i	1.38463	−	0.449892i	0.904187	+	0.427136i	$0.140477\pi$
$74$	459.255			0.721450
$75$		0			0
$76$	41.3499			0.0624099
$77$	−1366.30	+	443.937i	−2.02213	+	0.657031i
$78$	−102.470	−	141.038i	−0.148750	−	0.204737i
$79$	−500.100	+	363.344i	−0.712224	+	0.517461i	−0.883890	−	0.467694i	$-0.845085\pi$
$79$	−500.100	+	363.344i	−0.712224	+	0.517461i	0.171667	+	0.985155i	$0.445085\pi$
$80$		0			0
$81$	375.005	+	272.457i	0.514411	+	0.373741i
$82$			41.3761i			0.0557223i
$83$	−265.719	+	365.730i	−0.351403	+	0.483664i	−0.947728	−	0.319078i	$-0.896627\pi$
$83$	−265.719	+	365.730i	−0.351403	+	0.483664i	0.596326	+	0.802743i	$0.296627\pi$
$84$	176.470	−	543.118i	0.229219	−	0.705465i
$85$		0			0
$86$	−22.7855	−	70.1266i	−0.0285701	−	0.0879296i
$87$	−823.659	−	267.623i	−1.01501	−	0.329795i
$88$	−336.700	−	109.401i	−0.407868	−	0.132524i
$89$	−266.987	−	821.703i	−0.317984	−	0.978656i	−0.974509	−	0.224350i	$-0.927974\pi$
$89$	−266.987	−	821.703i	−0.317984	−	0.978656i	0.656524	−	0.754305i	$-0.272026\pi$
$90$		0			0
$91$	−198.833	+	611.945i	−0.229048	+	0.704937i
$92$	457.118	−	629.169i	0.518020	−	0.712993i
$93$			370.592i			0.413211i
$94$	687.123	+	499.224i	0.753950	+	0.547777i
$95$		0			0
$96$	113.853	−	82.7188i	0.121042	−	0.0879422i
$97$	384.094	+	528.660i	0.402050	+	0.553374i	0.961257	−	0.275654i	$-0.0888944\pi$
$97$	384.094	+	528.660i	0.402050	+	0.553374i	−0.559207	+	0.829028i	$0.688894\pi$
$98$	−1352.14	+	439.338i	−1.39375	+	0.452856i
$99$	−338.953			−0.344101
$100$		0			0
$101$	684.563			0.674421			0.337211	−	0.941429i	$-0.390517\pi$
$101$	684.563			0.674421			0.337211	+	0.941429i	$0.390517\pi$
$102$	−689.104	+	223.903i	−0.668936	+	0.217350i
$103$	−2.26783	−	3.12140i	−0.00216948	−	0.00298603i	0.807931	−	0.589277i	$-0.200587\pi$
$103$	−2.26783	−	3.12140i	−0.00216948	−	0.00298603i	−0.810100	+	0.586291i	$0.800587\pi$
$104$	−128.281	+	93.2015i	−0.120952	+	0.0878765i
$105$		0			0
$106$	8.46485	+	6.15007i	0.00775640	+	0.00563536i
$107$			1045.89i			0.944951i	0.881344	+	0.472476i	$0.156640\pi$
$107$			1045.89i			0.944951i	−0.881344	+	0.472476i	$0.843360\pi$
$108$	358.372	−	493.257i	0.319300	−	0.439479i
$109$	356.163	−	1096.16i	0.312974	−	0.963236i	−0.663606	−	0.748082i	$-0.730975\pi$
$109$	356.163	−	1096.16i	0.312974	−	0.963236i	0.976580	−	0.215153i	$-0.0690252\pi$
$110$		0			0
$111$	312.063	+	960.430i	0.266844	+	0.821261i
$112$	−493.990	−	160.507i	−0.416765	−	0.135415i
$113$	129.218	+	41.9853i	0.107573	+	0.0349526i	0.362309	−	0.932058i	$-0.381989\pi$
$113$	129.218	+	41.9853i	0.107573	+	0.0349526i	−0.254736	+	0.967011i	$0.581989\pi$
$114$	28.0971	+	86.4741i	0.0230837	+	0.0710442i
$115$		0			0
$116$	−243.415	+	749.155i	−0.194832	+	0.599632i
$117$	−89.2328	+	122.818i	−0.0705092	+	0.0970476i
$118$			103.748i			0.0809387i
$119$	2163.53	+	1571.90i	1.66664	+	1.21089i
$120$		0			0
$121$	−507.551	+	368.758i	−0.381331	+	0.277053i
$122$	−146.008	−	200.963i	−0.108352	−	0.149134i
$123$	−86.5290	+	28.1150i	−0.0634314	+	0.0206101i
$124$	337.071			0.244112
$125$		0			0
$126$	−497.295			−0.351608
$127$	−1556.36	+	505.692i	−1.08744	+	0.353330i	−0.797256	−	0.603641i	$-0.793716\pi$
$127$	−1556.36	+	505.692i	−1.08744	+	0.353330i	−0.290182	+	0.956971i	$0.593716\pi$
$128$	−75.2365	−	103.554i	−0.0519534	−	0.0715077i
$129$	131.172	−	95.3018i	0.0895273	−	0.0650454i
$130$		0			0
$131$	874.934	+	635.677i	0.583537	+	0.423964i	0.839997	−	0.542590i	$-0.182556\pi$
$131$	874.934	+	635.677i	0.583537	+	0.423964i	−0.256461	+	0.966555i	$0.582556\pi$
$132$		−	778.471i		−	0.513312i
$133$	197.254	−	271.496i	0.128602	−	0.177005i
$134$	481.552	−	1482.07i	0.310446	−	0.955455i
$135$		0			0
$136$	203.650	+	626.771i	0.128403	+	0.395185i
$137$	2204.47	+	716.275i	1.37475	+	0.446683i	0.900939	−	0.433945i	$-0.142879\pi$
$137$	2204.47	+	716.275i	1.37475	+	0.446683i	0.473809	+	0.880628i	$0.342879\pi$
$138$	1626.38	+	528.442i	1.00324	+	0.325971i
$139$	327.762	+	1008.75i	0.200003	+	0.615546i	0.999882	+	0.0153844i	$0.00489720\pi$
$139$	327.762	+	1008.75i	0.200003	+	0.615546i	−0.799879	+	0.600162i	$0.795103\pi$
$140$		0			0
$141$	−577.118	+	1776.19i	−0.344696	+	1.06086i
$142$	−721.119	+	992.535i	−0.426162	+	0.586561i
$143$			877.124i			0.512929i
$144$	−99.1447	−	72.0328i	−0.0573754	−	0.0416857i
$145$		0			0
$146$	1469.26	−	1067.48i	0.832854	−	0.605104i
$147$	−1837.56	−	2529.18i	−1.03101	−	1.41907i
$148$	873.554	−	283.835i	0.485174	−	0.157643i
$149$	1830.45			1.00642			0.503209	−	0.864165i	$-0.332152\pi$
$149$	1830.45			1.00642			0.503209	+	0.864165i	$0.332152\pi$
$150$		0			0
$151$	−1585.52			−0.854491			−0.427246	−	0.904136i	$-0.640516\pi$
$151$	−1585.52			−0.854491			−0.427246	+	0.904136i	$0.640516\pi$
$152$	78.6521	−	25.5556i	0.0419706	−	0.0136371i
$153$	370.871	+	510.460i	0.195968	+	0.269727i
$154$	−2324.49	+	1688.84i	−1.21631	+	0.883704i
$155$		0			0
$156$	−282.077	−	204.941i	−0.144771	−	0.105182i
$157$			1535.51i			0.780554i	0.920698	+	0.390277i	$0.127621\pi$
$157$			1535.51i			0.780554i	−0.920698	+	0.390277i	$0.872379\pi$
$158$	−726.688	+	1000.20i	−0.365900	+	0.503618i
$159$	−7.10967	+	21.8813i	−0.00354612	+	0.0109138i
$160$		0			0
$161$	−1950.40	−	6002.72i	−0.954741	−	2.93839i
$162$	881.690	+	286.479i	0.427606	+	0.138938i
$163$	−1593.69	−	517.820i	−0.765811	−	0.248827i	−0.100040	−	0.994983i	$-0.531897\pi$
$163$	−1593.69	−	517.820i	−0.765811	−	0.248827i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	25.5719	+	78.7021i	0.0121758	+	0.0374732i
$165$		0			0
$166$	−279.393	+	859.884i	−0.130633	+	0.402048i
$167$	1209.69	−	1664.99i	0.560530	−	0.771503i	−0.430864	−	0.902417i	$-0.641791\pi$
$167$	1209.69	−	1664.99i	0.560530	−	0.771503i	0.991394	+	0.130914i	$0.0417911\pi$
$168$		−	1142.14i		−	0.524510i
$169$	−1459.59	−	1060.45i	−0.664355	−	0.482682i
$170$		0			0
$171$	64.0566	−	46.5398i	0.0286464	−	0.0208128i
$172$	−86.6813	−	119.307i	−0.0384267	−	0.0528898i
$173$	−4099.10	+	1331.88i	−1.80144	+	0.585323i	−0.999920	−	0.0126483i	$-0.995974\pi$
$173$	−4099.10	+	1331.88i	−1.80144	+	0.585323i	−0.801518	+	0.597971i	$0.795974\pi$
$174$	−1732.09			−0.754653
$175$		0			0
$176$	−708.055			−0.303248
$177$	−216.966	+	70.4964i	−0.0921364	+	0.0299369i
$178$	−1015.68	−	1397.96i	−0.427688	−	0.588662i
$179$	−2202.60	+	1600.28i	−0.919719	+	0.668215i	−0.943454	−	0.331503i	$-0.892444\pi$
$179$	−2202.60	+	1600.28i	−0.919719	+	0.668215i	0.0237350	+	0.999718i	$0.492444\pi$
$180$		0			0
$181$	1056.07	+	767.281i	0.433686	+	0.315091i	0.783121	−	0.621869i	$-0.213626\pi$
$181$	1056.07	+	767.281i	0.433686	+	0.315091i	−0.349435	+	0.936961i	$0.613626\pi$
$182$			1286.87i			0.524118i
$183$	321.057	−	441.897i	0.129690	−	0.178502i
$184$	480.642	−	1479.26i	0.192573	−	0.592679i
$185$		0			0
$186$	229.039	+	704.909i	0.0902900	+	0.277884i
$187$	3467.10	+	1126.53i	1.35583	+	0.440534i
$188$	1615.52	+	524.915i	0.626724	+	0.203635i
$189$	−1529.08	−	4706.03i	−0.588488	−	1.81118i
$190$		0			0
$191$	1225.39	−	3771.37i	0.464221	−	1.42872i	−0.395739	−	0.918363i	$-0.629511\pi$
$191$	1225.39	−	3771.37i	0.464221	−	1.42872i	0.859960	−	0.510362i	$-0.170489\pi$
$192$	165.438	−	227.705i	0.0621845	−	0.0855897i
$193$		−	1941.18i		−	0.723986i	−0.932181	−	0.361993i	$-0.882096\pi$
$193$		−	1941.18i		−	0.723986i	0.932181	−	0.361993i	$-0.117904\pi$
$194$	1057.32	+	768.188i	0.391295	+	0.284292i
$195$		0			0
$196$	−2300.40	+	1671.34i	−0.838340	+	0.609089i
$197$	−1186.45	−	1633.01i	−0.429092	−	0.590595i	0.538652	−	0.842528i	$-0.318934\pi$
$197$	−1186.45	−	1633.01i	−0.429092	−	0.590595i	−0.967745	+	0.251933i	$0.918934\pi$
$198$	−644.726	+	209.484i	−0.231408	+	0.0751889i
$199$	−985.509			−0.351060			−0.175530	−	0.984474i	$-0.556164\pi$
$199$	−985.509			−0.351060			−0.175530	+	0.984474i	$0.556164\pi$
$200$		0			0
$201$	3426.63			1.20247
$202$	1302.12	−	423.083i	0.453547	−	0.147366i
$203$	3757.65	+	5171.96i	1.29919	+	1.78818i
$204$	−1172.37	+	851.779i	−0.402365	+	0.292336i
$205$		0			0
$206$	−6.24281	−	4.53567i	−0.00211144	−	0.00153405i
$207$		−	1489.16i		−	0.500018i
$208$	−186.403	+	256.562i	−0.0621381	+	0.0855257i
$209$	141.366	−	435.079i	0.0467869	−	0.143995i
$210$		0			0
$211$	1338.94	+	4120.84i	0.436856	+	1.34450i	0.891173	+	0.453664i	$0.149884\pi$
$211$	1338.94	+	4120.84i	0.436856	+	1.34450i	−0.454317	+	0.890840i	$0.650116\pi$
$212$	19.9021	+	6.46657i	0.00644754	+	0.00209493i
$213$	−2565.67	−	833.636i	−0.825336	−	0.268168i
$214$	646.394	+	1989.40i	0.206479	+	0.635478i
$215$		0			0
$216$	376.815	−	1159.72i	0.118699	−	0.365318i
$217$	1607.95	−	2213.15i	0.503017	−	0.692343i
$218$		−	2305.13i		−	0.716162i
$219$	3230.75	+	2347.28i	0.996868	+	0.724267i
$220$		0			0
$221$	1320.94	−	959.722i	0.402065	−	0.292117i
$222$	1187.16	+	1633.98i	0.358904	+	0.493989i
$223$	4943.88	−	1606.36i	1.48460	−	0.482377i	0.549119	−	0.835744i	$-0.314963\pi$
$223$	4943.88	−	1606.36i	1.48460	−	0.482377i	0.935485	+	0.353367i	$0.114963\pi$
$224$	−1038.82			−0.309863
$225$		0			0
$226$	271.735			0.0799802
$227$	3561.42	−	1157.17i	1.04132	−	0.338345i	0.262064	−	0.965051i	$-0.415597\pi$
$227$	3561.42	−	1157.17i	1.04132	−	0.338345i	0.779256	+	0.626705i	$0.215597\pi$
$228$	106.888	+	147.119i	0.0310475	+	0.0427332i
$229$	−3401.89	+	2471.62i	−0.981673	+	0.713227i	−0.958082	−	0.286494i	$-0.907510\pi$
$229$	−3401.89	+	2471.62i	−0.981673	+	0.713227i	−0.0235912	+	0.999722i	$0.507510\pi$
$230$		0			0
$231$	−5111.31	−	3713.59i	−1.45584	−	1.05773i
$232$			1575.42i			0.445824i
$233$	3653.09	−	5028.05i	1.02713	−	1.41373i	0.120055	−	0.992767i	$-0.461693\pi$
$233$	3653.09	−	5028.05i	1.02713	−	1.41373i	0.907079	−	0.420961i	$-0.138307\pi$
$234$	−93.8249	+	288.763i	−0.0262116	+	0.0806712i
$235$		0			0
$236$	64.1197	+	197.340i	0.0176857	+	0.0544311i
$237$	−2585.48	−	840.073i	−0.708629	−	0.230247i
$238$	5086.76	+	1652.79i	1.38540	+	0.450144i
$239$	−262.864	−	809.011i	−0.0711432	−	0.218956i	0.909163	−	0.416441i	$-0.136723\pi$
$239$	−262.864	−	809.011i	−0.0711432	−	0.218956i	−0.980306	+	0.197485i	$0.936723\pi$
$240$		0			0
$241$	1457.32	−	4485.16i	0.389518	−	1.19881i	−0.543631	−	0.839325i	$-0.682951\pi$
$241$	1457.32	−	4485.16i	0.389518	−	1.19881i	0.933149	−	0.359490i	$-0.117049\pi$
$242$	−737.515	+	1015.10i	−0.195906	+	0.269642i
$243$		−	2076.95i		−	0.548298i
$244$	−401.925	−	292.016i	−0.105453	−	0.0766164i
$245$		0			0
$246$	−147.212	+	106.956i	−0.0381540	+	0.0277205i
$247$	−120.433	−	165.762i	−0.0310243	−	0.0427012i
$248$	641.146	−	208.321i	0.164165	−	0.0533403i
$249$	−1988.10			−0.505988
$250$		0			0
$251$	619.865			0.155879			0.0779393	−	0.996958i	$-0.475166\pi$
$251$	619.865			0.155879			0.0779393	+	0.996958i	$0.475166\pi$
$252$	−945.911	+	307.345i	−0.236456	+	0.0768291i
$253$	−5057.26	−	6960.72i	−1.25671	−	1.72971i
$254$	−2647.84	+	1923.77i	−0.654095	+	0.475228i
$255$		0			0
$256$	−207.108	−	150.473i	−0.0505636	−	0.0367366i
$257$			3006.52i			0.729733i	0.931060	+	0.364867i	$0.118885\pi$
$257$			3006.52i			0.729733i	−0.931060	+	0.364867i	$0.881115\pi$
$258$	190.604	−	262.343i	0.0459940	−	0.0633053i
$259$	2303.55	−	7089.61i	0.552648	−	1.70088i
$260$		0			0
$261$	466.101	+	1434.51i	0.110540	+	0.340207i
$262$	2057.09	+	668.390i	0.485067	+	0.157608i
$263$	458.796	+	149.072i	0.107569	+	0.0349512i	0.362307	−	0.932059i	$-0.381989\pi$
$263$	458.796	+	149.072i	0.107569	+	0.0349512i	−0.254738	+	0.967010i	$0.581989\pi$
$264$	−481.122	−	1480.74i	−0.112163	−	0.345202i
$265$		0			0
$266$	207.405	−	638.326i	0.0478075	−	0.147136i
$267$	2233.38	−	3073.99i	0.511913	−	0.704587i
$268$		−	3116.67i		−	0.710377i
$269$	4209.63	+	3058.48i	0.954148	+	0.693229i	0.951784	−	0.306768i	$-0.0992476\pi$
$269$	4209.63	+	3058.48i	0.954148	+	0.693229i	0.00236368	+	0.999997i	$0.499248\pi$
$270$		0			0
$271$	1750.36	−	1271.71i	0.392351	−	0.285059i	−0.374067	−	0.927402i	$-0.622037\pi$
$271$	1750.36	−	1271.71i	0.392351	−	0.285059i	0.766418	+	0.642342i	$0.222037\pi$
$272$	774.732	+	1066.33i	0.172702	+	0.237704i
$273$	−2691.21	+	874.428i	−0.596629	+	0.193856i
$274$	4635.83			1.02212
$275$		0			0
$276$	3420.15			0.745902
$277$	−4746.99	+	1542.39i	−1.02967	+	0.334561i	−0.774660	−	0.632377i	$-0.782079\pi$
$277$	−4746.99	+	1542.39i	−1.02967	+	0.334561i	−0.255011	+	0.966938i	$0.582079\pi$
$278$	1246.88	+	1716.19i	0.269004	+	0.370252i
$279$	522.168	−	379.377i	0.112048	−	0.0814076i
$280$		0			0
$281$	−355.968	−	258.626i	−0.0755704	−	0.0549051i	0.549359	−	0.835587i	$-0.314872\pi$
$281$	−355.968	−	258.626i	−0.0755704	−	0.0549051i	−0.624929	+	0.780682i	$0.714872\pi$
$282$			3735.19i			0.788748i
$283$	−2136.86	+	2941.14i	−0.448845	+	0.617783i	−0.972149	−	0.234364i	$-0.924699\pi$
$283$	−2136.86	+	2941.14i	−0.448845	+	0.617783i	0.523304	+	0.852146i	$0.324699\pi$
$284$	−758.229	+	2333.59i	−0.158425	+	0.487581i
$285$		0			0
$286$	542.093	+	1668.39i	0.112079	+	0.344944i
$287$	638.732	+	207.537i	0.131370	+	0.0426846i
$288$	−233.103	−	75.7398i	−0.0476935	−	0.0154966i
$289$	−578.844	−	1781.50i	−0.117819	−	0.362609i
$290$		0			0
$291$	−888.049	+	2733.13i	−0.178895	+	0.550581i
$292$	2134.96	−	2938.52i	0.427873	−	0.588917i
$293$			7040.42i			1.40377i	0.712288	+	0.701887i	$0.247659\pi$
$293$			7040.42i			1.40377i	−0.712288	+	0.701887i	$0.752341\pi$
$294$	−5058.36	−	3675.11i	−1.00343	−	0.729037i
$295$		0			0
$296$	1486.18	−	1079.77i	0.291833	−	0.212029i
$297$	−3964.80	−	5457.09i	−0.774617	−	1.06617i
$298$	3481.72	−	1131.28i	0.676815	−	0.219911i
$299$	−3853.57			−0.745344
$300$		0			0
$301$	−1196.85			−0.229187
$302$	−3015.85	+	979.908i	−0.574644	+	0.186713i
$303$	1769.57	+	2435.60i	0.335509	+	0.461788i
$304$	133.811	−	97.2194i	0.0252454	−	0.0183418i
$305$		0			0
$306$	1020.92	+	741.742i	0.190726	+	0.138571i
$307$		−	3985.50i		−	0.740927i	−0.928847	−	0.370463i	$-0.879199\pi$
$307$		−	3985.50i		−	0.740927i	0.928847	−	0.370463i	$-0.120801\pi$
$308$	−3377.68	+	4648.97i	−0.624873	+	0.860064i
$309$	5.24337	−	16.1374i	0.000965323	−	0.00297096i
$310$		0			0
$311$	1984.51	+	6107.70i	0.361837	+	1.11362i	0.951938	+	0.306290i	$0.0990878\pi$
$311$	1984.51	+	6107.70i	0.361837	+	1.11362i	−0.590101	+	0.807329i	$0.700912\pi$
$312$	−663.202	−	215.487i	−0.120341	−	0.0391012i
$313$	−6592.67	−	2142.09i	−1.19054	−	0.386831i	−0.354269	−	0.935143i	$-0.615270\pi$
$313$	−6592.67	−	2142.09i	−1.19054	−	0.386831i	−0.836273	+	0.548313i	$0.815270\pi$
$314$	948.996	+	2920.71i	0.170557	+	0.524921i
$315$		0			0
$316$	−764.085	+	2351.61i	−0.136023	+	0.418634i
$317$	−3884.35	+	5346.35i	−0.688223	+	0.947258i	−0.999996	−	0.00289895i	$-0.999077\pi$
$317$	−3884.35	+	5346.35i	−0.688223	+	0.947258i	0.311773	+	0.950157i	$0.399077\pi$
$318$			46.0148i			0.00811440i
$319$	7050.35	+	5122.38i	1.23744	+	0.899053i
$320$		0			0
$321$	−3721.16	+	2703.58i	−0.647024	+	0.470091i
$322$	−7419.77	−	10212.4i	−1.28412	−	1.76744i
$323$	−809.903	+	263.154i	−0.139518	+	0.0453321i
$324$	1854.13			0.317923
$325$		0			0
$326$	−3351.40			−0.569378
$327$	4820.68	−	1566.33i	0.815241	−	0.264888i
$328$	97.2811	+	133.896i	0.0163764	+	0.0225401i
$329$	11153.1	−	8103.22i	1.86897	−	1.35789i
$330$		0			0
$331$	3033.15	+	2203.71i	0.503676	+	0.365942i	0.810420	−	0.585850i	$-0.199239\pi$
$331$	3033.15	+	2203.71i	0.503676	+	0.365942i	−0.306743	+	0.951792i	$0.599239\pi$
$332$			1808.27i			0.298921i
$333$	1033.79	−	1422.90i	0.170125	−	0.234157i
$334$	1271.94	−	3914.63i	0.208376	−	0.641315i
$335$		0			0
$336$	−705.879	−	2172.47i	−0.114610	−	0.352732i
$337$	−300.782	−	97.7299i	−0.0486191	−	0.0157973i	0.284606	−	0.958644i	$-0.408137\pi$
$337$	−300.782	−	97.7299i	−0.0486191	−	0.0157973i	−0.333226	+	0.942847i	$0.608137\pi$
$338$	−3431.70	−	1115.03i	−0.552247	−	0.179436i
$339$	184.643	+	568.273i	0.0295824	+	0.0910453i
$340$		0			0
$341$	1152.37	−	3546.62i	0.183003	−	0.563226i
$342$	93.0796	−	128.113i	0.0147169	−	0.0202560i
$343$			11942.1i			1.87992i
$344$	−238.613	−	173.363i	−0.0373987	−	0.0271718i
$345$		0			0
$346$	−6973.80	+	5066.77i	−1.08357	+	0.787257i
$347$	3486.20	+	4798.35i	0.539335	+	0.742331i	0.988517	−	0.151109i	$-0.0482845\pi$
$347$	3486.20	+	4798.35i	0.539335	+	0.742331i	−0.449182	+	0.893440i	$0.648285\pi$
$348$	−3294.64	+	1070.49i	−0.507503	+	0.164898i
$349$	−8313.16			−1.27505			−0.637526	−	0.770429i	$-0.720042\pi$
$349$	−8313.16			−1.27505			−0.637526	+	0.770429i	$0.720042\pi$
$350$		0			0
$351$	−3021.13			−0.459419
$352$	−1346.80	+	437.602i	−0.203934	+	0.0662621i
$353$	2118.46	+	2915.82i	0.319418	+	0.439641i	0.938289	−	0.345851i	$-0.112410\pi$
$353$	2118.46	+	2915.82i	0.319418	+	0.439641i	−0.618872	+	0.785492i	$0.712410\pi$
$354$	−369.124	+	268.184i	−0.0554201	+	0.0402651i
$355$		0			0
$356$	−2795.93	−	2031.36i	−0.416247	−	0.302421i
$357$			11760.9i			1.74357i
$358$	−3200.56	+	4405.19i	−0.472499	+	0.650340i
$359$	−2483.37	+	7643.04i	−0.365090	+	1.12363i	0.584834	+	0.811153i	$0.301160\pi$
$359$	−2483.37	+	7643.04i	−0.365090	+	1.12363i	−0.949924	+	0.312480i	$0.898840\pi$
$360$		0			0
$361$	−2086.53	−	6421.66i	−0.304203	−	0.936239i
$362$	2482.97	+	806.767i	0.360503	+	0.117135i
$363$	−2624.00	−	852.590i	−0.379406	−	0.123277i
$364$	795.332	+	2447.78i	0.114524	+	0.352469i
$365$		0			0
$366$	337.579	−	1038.96i	0.0482119	−	0.148381i
$367$	−7641.29	+	10517.3i	−1.08684	+	1.49591i	−0.235090	+	0.971974i	$0.575538\pi$
$367$	−7641.29	+	10517.3i	−1.08684	+	1.49591i	−0.851755	+	0.523940i	$0.824462\pi$
$368$		−	3110.78i		−	0.440654i
$369$	128.194	+	93.1387i	0.0180855	+	0.0131399i
$370$		0			0
$371$	137.398	−	99.8257i	0.0192274	−	0.0139695i
$372$	871.315	+	1199.26i	0.121440	+	0.167147i
$373$	6641.04	−	2157.81i	0.921877	−	0.299536i	0.190641	−	0.981660i	$-0.438944\pi$
$373$	6641.04	−	2157.81i	0.921877	−	0.299536i	0.731237	+	0.682124i	$0.238944\pi$
$374$	7291.05			1.00805
$375$		0			0
$376$	3397.32			0.465967
$377$	3712.15	−	1206.15i	0.507124	−	0.164774i
$378$	−5816.97	−	8006.37i	−0.791515	−	1.08943i
$379$	−741.524	+	538.749i	−0.100500	+	0.0730176i	−0.636900	−	0.770946i	$-0.719784\pi$
$379$	−741.524	+	538.749i	−0.100500	+	0.0730176i	0.536400	+	0.843964i	$0.319784\pi$
$380$		0			0
$381$	−5822.33	−	4230.17i	−0.782906	−	0.568814i
$382$		−	7930.90i		−	1.06225i
$383$	329.322	−	453.273i	0.0439362	−	0.0604730i	−0.786484	−	0.617611i	$-0.788101\pi$
$383$	329.322	−	453.273i	0.0439362	−	0.0604730i	0.830420	+	0.557138i	$0.188101\pi$
$384$	173.951	−	535.367i	0.0231170	−	0.0711467i
$385$		0			0
$386$	−1199.72	−	3692.35i	−0.158197	−	0.486880i
$387$	−268.562	−	87.2611i	−0.0352759	−	0.0114618i
$388$	2485.91	+	807.721i	0.325265	+	0.105685i
$389$	917.355	+	2823.33i	0.119567	+	0.367991i	0.992872	−	0.119183i	$-0.0380277\pi$
$389$	917.355	+	2823.33i	0.119567	+	0.367991i	−0.873305	+	0.487174i	$0.838028\pi$
$390$		0			0
$391$	−4949.31	+	15232.4i	−0.640147	+	1.97017i
$392$	−3342.68	+	4600.81i	−0.430691	+	0.592796i
$393$			4756.12i			0.610470i
$394$	−3266.02	−	2372.90i	−0.417613	−	0.303414i
$395$		0			0
$396$	−1096.87	+	796.925i	−0.139192	+	0.101129i
$397$	−3716.55	−	5115.40i	−0.469845	−	0.646686i	0.506669	−	0.862141i	$-0.330877\pi$
$397$	−3716.55	−	5115.40i	−0.469845	−	0.646686i	−0.976514	+	0.215455i	$0.930877\pi$
$398$	−1874.55	+	609.078i	−0.236087	+	0.0767094i
$399$	1475.85			0.185175
$400$		0			0
$401$	−3008.68			−0.374679			−0.187339	−	0.982295i	$-0.559986\pi$
$401$	−3008.68			−0.374679			−0.187339	+	0.982295i	$0.559986\pi$
$402$	6517.83	−	2117.77i	0.808656	−	0.262748i
$403$	−981.734	−	1351.24i	−0.121349	−	0.167023i
$404$	2215.29	−	1609.50i	0.272809	−	0.198207i
$405$		0			0
$406$	10343.9	+	7515.30i	1.26443	+	0.918666i
$407$		−	10161.8i		−	1.23760i
$408$	−1703.56	+	2344.75i	−0.206712	+	0.284515i
$409$	−3472.20	+	10686.3i	−0.419778	+	1.29194i	0.488129	+	0.872771i	$0.337680\pi$
$409$	−3472.20	+	10686.3i	−0.419778	+	1.29194i	−0.907907	+	0.419172i	$0.862320\pi$
$410$		0			0
$411$	3150.04	+	9694.82i	0.378053	+	1.16353i
$412$	−14.6777	−	4.76908i	−0.00175514	−	0.000570281i
$413$	1601.58	+	520.384i	0.190819	+	0.0620010i
$414$	−920.352	−	2832.55i	−0.109258	−	0.336262i
$415$		0			0
$416$	−195.996	+	603.212i	−0.0230997	+	0.0710936i
$417$	−2741.77	+	3773.72i	−0.321978	+	0.443165i
$418$		−	914.937i		−	0.107060i
$419$	3609.66	+	2622.57i	0.420867	+	0.305778i	0.777987	−	0.628281i	$-0.216241\pi$
$419$	3609.66	+	2622.57i	0.420867	+	0.305778i	−0.357119	+	0.934059i	$0.616241\pi$
$420$		0			0
$421$	4617.41	−	3354.74i	0.534534	−	0.388361i	−0.287517	−	0.957775i	$-0.592830\pi$
$421$	4617.41	−	3354.74i	0.534534	−	0.388361i	0.822051	+	0.569414i	$0.192830\pi$
$422$	5093.64	+	7010.80i	0.587570	+	0.808721i
$423$	3093.46	−	1005.13i	0.355577	−	0.115534i
$424$	41.8525			0.00479372
$425$		0			0
$426$	−5395.40			−0.613634
$427$	−3834.65	+	1245.95i	−0.434595	+	0.141208i
$428$	2459.03	+	3384.56i	0.277714	+	0.382241i
$429$	−3120.72	+	2267.33i	−0.351211	+	0.255170i
$430$		0			0
$431$	6487.97	+	4713.79i	0.725092	+	0.526810i	0.888007	−	0.459830i	$-0.152090\pi$
$431$	6487.97	+	4713.79i	0.725092	+	0.526810i	−0.162915	+	0.986640i	$0.552090\pi$
$432$		−	2438.80i		−	0.271613i
$433$	3399.31	−	4678.75i	0.377276	−	0.519276i	−0.577584	−	0.816331i	$-0.696005\pi$
$433$	3399.31	−	4678.75i	0.377276	−	0.519276i	0.954860	+	0.297055i	$0.0960046\pi$
$434$	1690.70	−	5203.43i	0.186995	−	0.575513i
$435$		0			0
$436$	−1424.65	−	4384.62i	−0.156487	−	0.481618i
$437$	1911.48	+	621.078i	0.209242	+	0.0679867i
$438$	7595.95	+	2468.08i	0.828650	+	0.269245i
$439$	−3630.68	−	11174.1i	−0.394721	−	1.21483i	−0.929178	−	0.369632i	$-0.879484\pi$
$439$	−3630.68	−	11174.1i	−0.394721	−	1.21483i	0.534457	−	0.845196i	$-0.320516\pi$
$440$		0			0
$441$	−1682.52	+	5178.27i	−0.181678	+	0.559148i
$442$	1919.44	−	2641.89i	0.206558	−	0.284303i
$443$			3568.50i			0.382719i	0.981520	+	0.191360i	$0.0612897\pi$
$443$			3568.50i			0.382719i	−0.981520	+	0.191360i	$0.938710\pi$
$444$	3267.96	+	2374.31i	0.349303	+	0.253784i
$445$		0			0
$446$	8411.03	−	6110.97i	0.892990	−	0.648795i
$447$	4731.65	+	6512.55i	0.500669	+	0.689112i
$448$	−1975.96	+	642.029i	−0.208383	+	0.0677076i
$449$	14369.1			1.51029			0.755145	−	0.655558i	$-0.227566\pi$
$449$	14369.1			1.51029			0.755145	+	0.655558i	$0.227566\pi$
$450$		0			0
$451$	915.518			0.0955878
$452$	516.870	−	167.941i	0.0537866	−	0.0174763i
$453$	−4098.52	−	5641.13i	−0.425089	−	0.585085i
$454$	6059.05	−	4402.15i	0.626355	−	0.455073i
$455$		0			0
$456$	294.237	+	213.776i	0.0302169	+	0.0219539i
$457$			402.073i			0.0411558i	0.999788	+	0.0205779i	$0.00655061\pi$
$457$			402.073i			0.0411558i	−0.999788	+	0.0205779i	$0.993449\pi$
$458$	−4943.23	+	6803.78i	−0.504328	+	0.694148i
$459$	−3880.17	+	11941.9i	−0.394577	+	1.21438i
$460$		0			0
$461$	2232.00	+	6869.38i	0.225498	+	0.694010i	0.998241	+	0.0592914i	$0.0188841\pi$
$461$	2232.00	+	6869.38i	0.225498	+	0.694010i	−0.772743	+	0.634719i	$0.781116\pi$
$462$	−12017.4	−	3904.70i	−1.21018	−	0.393210i
$463$	−3116.67	−	1012.67i	−0.312838	−	0.101647i	0.148390	−	0.988929i	$-0.452591\pi$
$463$	−3116.67	−	1012.67i	−0.312838	−	0.101647i	−0.461228	+	0.887282i	$0.652591\pi$
$464$	973.661	+	2996.62i	0.0974162	+	0.299816i
$465$		0			0
$466$	3841.09	−	11821.7i	0.381835	−	1.17517i
$467$	3399.75	−	4679.36i	0.336877	−	0.463672i	−0.606649	−	0.794970i	$-0.707487\pi$
$467$	3399.75	−	4679.36i	0.336877	−	0.463672i	0.943526	+	0.331298i	$0.107487\pi$
$468$			607.248i			0.0599787i
$469$	−20463.6	−	14867.6i	−2.01475	−	1.46380i
$470$		0			0
$471$	−5463.18	+	3969.23i	−0.534459	+	0.388307i
$472$	243.926	+	335.735i	0.0237873	+	0.0327404i
$473$	−1551.67	+	504.169i	−0.150837	+	0.0490100i
$474$	−5437.07			−0.526863
$475$		0			0
$476$	10697.1			1.03004
$477$	38.1092	−	12.3824i	0.00365807	−	0.00118858i
$478$	−999.992	−	1376.37i	−0.0956874	−	0.131702i
$479$	1896.17	−	1377.64i	0.180873	−	0.131412i	−0.493665	−	0.869652i	$-0.664343\pi$
$479$	1896.17	−	1377.64i	0.180873	−	0.131412i	0.674538	+	0.738241i	$0.264343\pi$
$480$		0			0
$481$	−3682.10	−	2675.20i	−0.349042	−	0.253594i
$482$		−	9431.94i		−	0.891314i
$483$	16315.3	−	22456.1i	1.53701	−	2.11551i
$484$	−775.469	+	2386.65i	−0.0728277	+	0.224141i
$485$		0			0
$486$	−1283.63	−	3950.60i	−0.119808	−	0.368730i
$487$	−11188.2	−	3635.26i	−1.04104	−	0.338253i	−0.261892	−	0.965097i	$-0.584346\pi$
$487$	−11188.2	−	3635.26i	−1.04104	−	0.338253i	−0.779145	+	0.626844i	$0.784346\pi$
$488$	−944.983	−	307.044i	−0.0876585	−	0.0284820i
$489$	−2277.27	−	7008.72i	−0.210597	−	0.648150i
$490$		0			0
$491$	3398.57	−	10459.7i	0.312374	−	0.961387i	−0.664448	−	0.747334i	$-0.731333\pi$
$491$	3398.57	−	10459.7i	0.312374	−	0.961387i	0.976822	−	0.214053i	$-0.0686666\pi$
$492$	−213.912	+	294.424i	−0.0196014	+	0.0269790i
$493$		−	16222.5i		−	1.48200i
$494$	−331.525	−	240.867i	−0.0301943	−	0.0219375i
$495$		0			0
$496$	1090.78	−	792.501i	0.0987452	−	0.0717426i
$497$	11704.9	+	16110.5i	1.05642	+	1.45403i
$498$	−3781.60	+	1228.72i	−0.340276	+	0.110562i
$499$	−12608.1			−1.13109			−0.565545	−	0.824717i	$-0.691334\pi$
$499$	−12608.1			−1.13109			−0.565545	+	0.824717i	$0.691334\pi$
$500$		0			0
$501$	9050.87			0.807112
$502$	1179.05	−	383.098i	0.104828	−	0.0340607i
$503$	1904.41	+	2621.20i	0.168814	+	0.232353i	0.885039	−	0.465517i	$-0.154131\pi$
$503$	1904.41	+	2621.20i	0.168814	+	0.232353i	−0.716225	+	0.697870i	$0.754131\pi$
$504$	−1609.28	+	1169.21i	−0.142228	+	0.103335i
$505$		0			0
$506$	−13921.4	−	10114.5i	−1.22309	−	0.888627i
$507$		−	7934.29i		−	0.695018i
$508$	−3847.53	+	5295.68i	−0.336037	+	0.462515i
$509$	−1458.15	+	4487.74i	−0.126977	+	0.390797i	−0.994256	−	0.107026i	$-0.965867\pi$
$509$	−1458.15	+	4487.74i	−0.126977	+	0.390797i	0.867279	+	0.497823i	$0.165867\pi$
$510$		0			0
$511$	−9109.30	−	28035.6i	−0.788595	−	2.42704i
$512$	−486.941	−	158.217i	−0.0420312	−	0.0136568i
$513$	1498.57	+	486.914i	0.128973	+	0.0419060i
$514$	1858.13	+	5718.74i	0.159453	+	0.490744i
$515$		0			0
$516$	200.412	−	616.806i	0.0170982	−	0.0526228i
$517$	11046.2	−	15203.8i	0.939673	−	1.29335i
$518$		−	14908.9i		−	1.26459i
$519$	−15334.7	−	11141.3i	−1.29695	−	0.942292i
$520$		0			0
$521$	7016.16	−	5097.54i	0.589987	−	0.428651i	−0.252324	−	0.967643i	$-0.581195\pi$
$521$	7016.16	−	5097.54i	0.589987	−	0.428651i	0.842311	+	0.538992i	$0.181195\pi$
$522$	1773.15	+	2440.53i	0.148676	+	0.204635i
$523$	−4454.00	+	1447.19i	−0.372390	+	0.120997i	−0.489232	−	0.872154i	$-0.662723\pi$
$523$	−4454.00	+	1447.19i	−0.372390	+	0.120997i	0.116842	+	0.993150i	$0.462723\pi$
$524$	4325.91			0.360646
$525$		0			0
$526$	964.814			0.0799769
$527$	−6602.07	+	2145.14i	−0.545713	+	0.177313i
$528$	−1830.30	−	2519.19i	−0.150859	−	0.207639i
$529$	20738.1	−	15067.1i	1.70445	−	1.23836i
$530$		0			0
$531$	321.439	+	233.539i	0.0262698	+	0.0190861i
$532$		−	1342.35i		−	0.109395i
$533$	241.020	−	331.735i	0.0195867	−	0.0269588i
$534$	2348.32	−	7227.37i	0.190303	−	0.585691i
$535$		0			0
$536$	−1926.21	−	5928.26i	−0.155223	−	0.477728i
$537$	−11387.3	−	3699.94i	−0.915077	−	0.297327i
$538$	9897.44	+	3215.87i	0.793139	+	0.257707i
$539$	9721.11	+	29918.5i	0.776842	+	2.39087i
$540$		0			0
$541$	1143.80	−	3520.25i	0.0908980	−	0.279755i	−0.895265	−	0.445534i	$-0.853014\pi$
$541$	1143.80	−	3520.25i	0.0908980	−	0.279755i	0.986163	+	0.165779i	$0.0530138\pi$
$542$	2543.43	−	3500.73i	0.201567	−	0.277434i
$543$			5740.78i			0.453703i
$544$	2132.65	+	1549.46i	0.168082	+	0.122119i
$545$		0			0
$546$	−4578.57	+	3326.52i	−0.358873	+	0.260736i
$547$	11392.7	+	15680.7i	0.890524	+	1.22570i	0.973393	+	0.229141i	$0.0735917\pi$
$547$	11392.7	+	15680.7i	0.890524	+	1.22570i	−0.0828689	+	0.996560i	$0.526408\pi$
$548$	8817.88	−	2865.10i	0.687374	−	0.223341i
$549$	−951.304			−0.0739539
$550$		0			0
$551$	−2035.73			−0.157396
$552$	6505.51	−	2113.77i	0.501618	−	0.162985i
$553$	11795.3	+	16234.9i	0.907032	+	1.24842i
$554$	−8076.06	+	5867.60i	−0.619348	+	0.449983i
$555$		0			0
$556$	3432.37	+	2493.76i	0.261807	+	0.190214i
$557$			4428.74i			0.336897i	0.985710	+	0.168448i	$0.0538757\pi$
$557$			4428.74i			0.336897i	−0.985710	+	0.168448i	$0.946124\pi$
$558$	758.755	−	1044.34i	0.0575639	−	0.0792299i
$559$	−225.810	+	694.972i	−0.0170854	+	0.0525835i
$560$		0			0
$561$	4954.25	+	15247.6i	0.372849	+	1.14751i
$562$	−836.932	−	271.936i	−0.0628182	−	0.0204109i
$563$	10531.5	+	3421.90i	0.788367	+	0.256156i	0.675409	−	0.737444i	$-0.263967\pi$
$563$	10531.5	+	3421.90i	0.788367	+	0.256156i	0.112959	+	0.993600i	$0.463967\pi$
$564$	2308.47	+	7104.74i	0.172348	+	0.530432i
$565$		0			0
$566$	−2246.83	+	6915.03i	−0.166857	+	0.513534i
$567$	8844.85	−	12173.9i	0.655113	−	0.901685i
$568$			4907.36i			0.362515i
$569$	−21829.5	−	15860.1i	−1.60833	−	1.16852i	−0.868432	−	0.495809i	$-0.834872\pi$
$569$	−21829.5	−	15860.1i	−1.60833	−	1.16852i	−0.739903	−	0.672714i	$-0.765128\pi$
$570$		0			0
$571$	−10821.3	+	7862.17i	−0.793099	+	0.576220i	−0.908881	−	0.417055i	$-0.863062\pi$
$571$	−10821.3	+	7862.17i	−0.793099	+	0.576220i	0.115783	+	0.993275i	$0.463062\pi$
$572$	2062.24	+	2838.43i	0.150746	+	0.207484i
$573$	16585.7	−	5389.03i	1.20921	−	0.392897i
$574$	1343.20			0.0976730
$575$		0			0
$576$	−490.198			−0.0354599
$577$	9915.34	−	3221.69i	0.715391	−	0.232445i	0.0713674	−	0.997450i	$-0.477264\pi$
$577$	9915.34	−	3221.69i	0.715391	−	0.232445i	0.644024	+	0.765005i	$0.277264\pi$
$578$	−2202.05	−	3030.87i	−0.158466	−	0.218110i
$579$	6906.52	−	5017.88i	0.495726	−	0.360166i
$580$		0			0
$581$	11872.8	+	8626.10i	0.847792	+	0.615957i
$582$			5747.57i			0.409355i
$583$	136.081	−	187.299i	0.00966706	−	0.0133056i
$584$	2244.83	−	6908.87i	0.159061	−	0.489539i
$585$		0			0
$586$	4351.22	+	13391.7i	0.306736	+	0.944036i
$587$	12717.0	+	4132.00i	0.894184	+	0.290538i	0.719835	−	0.694146i	$-0.244218\pi$
$587$	12717.0	+	4132.00i	0.894184	+	0.290538i	0.174350	+	0.984684i	$0.444218\pi$
$588$	−11892.9	−	3864.24i	−0.834108	−	0.271018i
$589$	269.189	+	828.479i	0.0188315	+	0.0579573i
$590$		0			0
$591$	2743.15	−	8442.54i	0.190927	−	0.587614i
$592$	2159.55	−	2972.36i	0.149927	−	0.206357i
$593$		−	2768.13i		−	0.191693i	−0.995396	−	0.0958463i	$-0.969444\pi$
$593$		−	2768.13i		−	0.191693i	0.995396	−	0.0958463i	$-0.0305557\pi$
$594$	−10914.2	−	7929.61i	−0.753895	−	0.547737i
$595$		0			0
$596$	5923.46	−	4303.65i	0.407105	−	0.295779i
$597$	−2547.50	−	3506.34i	−0.174644	−	0.240377i
$598$	−7329.93	+	2381.64i	−0.501243	+	0.162864i
$599$	−4098.71			−0.279580			−0.139790	−	0.990181i	$-0.544643\pi$
$599$	−4098.71			−0.279580			−0.139790	+	0.990181i	$0.544643\pi$
$600$		0			0
$601$	−17523.5			−1.18935			−0.594673	−	0.803968i	$-0.702718\pi$
$601$	−17523.5			−1.18935			−0.594673	+	0.803968i	$0.702718\pi$
$602$	−2276.54	+	739.693i	−0.154128	+	0.0500791i
$603$	−3507.85	−	4828.15i	−0.236900	−	0.326065i
$604$	−5130.87	+	3727.79i	−0.345649	+	0.251129i
$605$		0			0
$606$	4871.21	+	3539.14i	0.326533	+	0.237240i
$607$		−	14982.0i		−	1.00182i	−0.865501	−	0.500908i	$-0.833000\pi$
$607$		−	14982.0i		−	1.00182i	0.865501	−	0.500908i	$-0.167000\pi$
$608$	194.439	−	267.622i	0.0129696	−	0.0178512i
$609$	−8687.92	+	26738.7i	−0.578083	+	1.77916i
$610$		0			0
$611$	−2601.02	−	8005.10i	−0.172219	−	0.530036i
$612$	2400.33	+	779.914i	0.158542	+	0.0515133i
$613$	−28387.1	−	9223.52i	−1.87038	−	0.607723i	−0.991400	−	0.130864i	$-0.958225\pi$
$613$	−28387.1	−	9223.52i	−1.87038	−	0.607723i	−0.878980	−	0.476859i	$-0.841775\pi$
$614$	−2463.17	−	7580.87i	−0.161898	−	0.498272i
$615$		0			0
$616$	−3551.50	+	10930.4i	−0.232295	+	0.714932i
$617$	−11272.8	+	15515.7i	−0.735538	+	1.01238i	0.263325	+	0.964707i	$0.415181\pi$
$617$	−11272.8	+	15515.7i	−0.735538	+	1.01238i	−0.998863	+	0.0476742i	$0.984819\pi$
$618$		−	33.9358i		−	0.00220890i
$619$	12120.6	+	8806.12i	0.787023	+	0.571806i	0.907079	−	0.420961i	$-0.138307\pi$
$619$	12120.6	+	8806.12i	0.787023	+	0.571806i	−0.120055	+	0.992767i	$0.538307\pi$
$620$		0			0
$621$	23975.3	−	17419.0i	1.54927	−	1.12561i
$622$	7549.53	+	10391.0i	0.486670	+	0.669843i
$623$	−26675.2	+	8667.29i	−1.71544	+	0.557380i
$624$	−1394.66			−0.0894731
$625$		0			0
$626$	−13863.9			−0.885164
$627$	1913.39	−	621.698i	0.121871	−	0.0395984i
$628$	3610.20	+	4969.01i	0.229399	+	0.315741i
$629$	−15303.6	+	11118.7i	−0.970103	+	0.704821i
$630$		0			0
$631$	−15151.7	−	11008.3i	−0.955908	−	0.694508i	−0.00371118	−	0.999993i	$-0.501181\pi$
$631$	−15151.7	−	11008.3i	−0.955908	−	0.694508i	−0.952197	+	0.305485i	$0.901181\pi$
$632$			4945.26i			0.311253i
$633$	−11200.4	+	15416.0i	−0.703280	+	0.967982i
$634$	−4084.24	+	12570.0i	−0.255846	+	0.787412i
$635$		0			0
$636$	28.4387	+	87.5253i	0.00177306	+	0.00545692i
$637$	13400.1	+	4353.94i	0.833485	+	0.270816i
$638$	16576.4	+	5385.98i	1.02863	+	0.334221i
$639$	1451.89	+	4468.44i	0.0898837	+	0.276634i
$640$		0			0
$641$	−5889.14	+	18124.9i	−0.362881	+	1.11683i	0.588416	+	0.808558i	$0.299752\pi$
$641$	−5889.14	+	18124.9i	−0.362881	+	1.11683i	−0.951297	+	0.308275i	$0.900248\pi$
$642$	−5407.16	+	7442.32i	−0.332404	+	0.457515i
$643$		−	10953.1i		−	0.671768i	−0.941903	−	0.335884i	$-0.890965\pi$
$643$		−	10953.1i		−	0.671768i	0.941903	−	0.335884i	$-0.109035\pi$
$644$	−20424.9	−	14839.5i	−1.24977	−	0.908012i
$645$		0			0
$646$	−1377.89	+	1001.10i	−0.0839201	+	0.0609715i
$647$	−6308.42	−	8682.80i	−0.383323	−	0.527598i	0.573138	−	0.819459i	$-0.305726\pi$
$647$	−6308.42	−	8682.80i	−0.383323	−	0.527598i	−0.956461	+	0.291860i	$0.905726\pi$
$648$	3526.76	−	1145.91i	0.213803	−	0.0694688i
$649$	2295.60			0.138845
$650$		0			0
$651$	12030.6			0.724298
$652$	−6374.75	+	2071.28i	−0.382906	+	0.124414i
$653$	4644.00	+	6391.92i	0.278306	+	0.383055i	0.925172	−	0.379548i	$-0.123921\pi$
$653$	4644.00	+	6391.92i	0.278306	+	0.383055i	−0.646866	+	0.762604i	$0.723921\pi$
$654$	8201.42	−	5958.68i	0.490368	−	0.356274i
$655$		0			0
$656$	267.792	+	194.562i	0.0159383	+	0.0115798i
$657$		−	6955.08i		−	0.413004i
$658$	16206.4	−	22306.2i	0.960171	−	1.32156i
$659$	4537.13	−	13963.8i	0.268196	−	0.825423i	−0.722743	−	0.691116i	$-0.757119\pi$
$659$	4537.13	−	13963.8i	0.268196	−	0.825423i	0.990940	−	0.134307i	$-0.0428808\pi$
$660$		0			0
$661$	−3412.01	−	10501.1i	−0.200774	−	0.617919i	−0.999860	−	0.0167028i	$-0.994683\pi$
$661$	−3412.01	−	10501.1i	−0.200774	−	0.617919i	0.799086	−	0.601216i	$-0.205317\pi$
$662$	7131.36	+	2317.12i	0.418683	+	0.136038i
$663$	6829.18	+	2218.94i	0.400035	+	0.129979i
$664$	1117.57	+	3439.54i	0.0653166	+	0.201024i
$665$		0			0
$666$	1087.00	−	3345.43i	0.0632436	−	0.194644i
$667$	−22504.7	+	30975.1i	−1.30643	+	1.79814i
$668$		−	8232.18i		−	0.476815i
$669$	18495.0	+	13437.4i	1.06885	+	0.776563i
$670$		0			0
$671$	−4446.64	+	3230.68i	−0.255828	+	0.185870i
$672$	−2685.32	−	3696.03i	−0.154150	−	0.212169i
$673$	−13104.2	+	4257.81i	−0.750564	+	0.243873i	−0.659224	−	0.751947i	$-0.729115\pi$
$673$	−13104.2	+	4257.81i	−0.750564	+	0.243873i	−0.0913399	+	0.995820i	$0.529115\pi$
$674$	−632.521			−0.0361481
$675$		0			0
$676$	−7216.60			−0.410594
$677$	6144.11	−	1996.34i	0.348799	−	0.113332i	−0.129377	−	0.991595i	$-0.541298\pi$
$677$	6144.11	−	1996.34i	0.348799	−	0.113332i	0.478177	+	0.878264i	$0.341298\pi$
$678$	702.424	+	966.804i	0.0397882	+	0.0547638i
$679$	17162.0	−	12468.9i	0.969983	−	0.704734i
$680$		0			0
$681$	13323.2	+	9679.90i	0.749703	+	0.544691i
$682$		−	7458.27i		−	0.418756i
$683$	−6638.66	+	9137.33i	−0.371920	+	0.511904i	−0.953421	−	0.301641i	$-0.902465\pi$
$683$	−6638.66	+	9137.33i	−0.371920	+	0.511904i	0.581501	+	0.813545i	$0.302465\pi$
$684$	97.8697	−	301.212i	0.00547097	−	0.0168379i
$685$		0			0
$686$	7380.60	+	22715.2i	0.410777	+	1.26424i
$687$	−17587.5	−	5714.53i	−0.976718	−	0.317355i
$688$	−561.013	−	182.284i	−0.0310878	−	0.0101010i
$689$	−32.0426	−	98.6170i	−0.00177174	−	0.00545284i
$690$		0			0
$691$	828.470	−	2549.77i	0.0456100	−	0.140373i	−0.925658	−	0.378361i	$-0.876488\pi$
$691$	828.470	−	2549.77i	0.0456100	−	0.140373i	0.971268	+	0.237988i	$0.0764878\pi$
$692$	−10133.5	+	13947.6i	−0.556675	+	0.766197i
$693$			11003.5i			0.603158i
$694$	9596.70	+	6972.41i	0.524907	+	0.381367i
$695$		0			0
$696$	−5605.17	+	4072.39i	−0.305264	+	0.221787i
$697$	−1001.73	−	1378.76i	−0.0544380	−	0.0749275i
$698$	−15812.6	+	5137.82i	−0.857471	+	0.278609i
$699$	27332.4			1.47898
$700$		0			0
$701$	−34520.6			−1.85995			−0.929976	−	0.367620i	$-0.880173\pi$
$701$	−34520.6			−1.85995			−0.929976	+	0.367620i	$0.880173\pi$
$702$	−5746.54	+	1867.16i	−0.308959	+	0.100387i
$703$	1395.26	+	1920.42i	0.0748555	+	0.103030i
$704$	−2291.31	+	1664.74i	−0.122666	+	0.0891224i
$705$		0			0
$706$	5831.63	+	4236.93i	0.310873	+	0.225862i
$707$		−	22223.1i		−	1.18216i
$708$	−536.369	+	738.248i	−0.0284717	+	0.0391879i
$709$	6361.25	−	19577.9i	0.336956	−	1.03704i	−0.628794	−	0.777572i	$-0.716451\pi$
$709$	6361.25	−	19577.9i	0.336956	−	1.03704i	0.965751	−	0.259472i	$-0.0835487\pi$
$710$		0			0
$711$	1463.10	+	4502.95i	0.0771736	+	0.237516i
$712$	−6573.62	−	2135.90i	−0.346007	−	0.112424i
$713$	15581.8	+	5062.82i	0.818432	+	0.265925i
$714$	7268.64	+	22370.6i	0.380983	+	1.17255i
$715$		0			0
$716$	−3365.27	+	10357.2i	−0.175651	+	0.540597i
$717$	2198.88	−	3026.50i	0.114531	−	0.157639i
$718$			16072.7i			0.835417i
$719$	−8049.33	−	5848.18i	−0.417510	−	0.303339i	0.359125	−	0.933289i	$-0.383075\pi$
$719$	−8049.33	−	5848.18i	−0.417510	−	0.303339i	−0.776635	+	0.629951i	$0.783075\pi$
$720$		0			0
$721$	−101.331	+	73.6213i	−0.00523407	+	0.00380277i
$722$	−7937.61	−	10925.2i	−0.409151	−	0.563149i
$723$	19724.8	−	6408.98i	1.01463	−	0.329672i
$724$	5221.50			0.268033
$725$		0			0
$726$	−5518.08			−0.282087
$727$	−9111.21	+	2960.41i	−0.464809	+	0.151026i	−0.532053	−	0.846711i	$-0.678579\pi$
$727$	−9111.21	+	2960.41i	−0.464809	+	0.151026i	0.0672442	+	0.997737i	$0.478579\pi$
$728$	3025.62	+	4164.41i	0.154034	+	0.212010i
$729$	17514.7	−	12725.2i	0.889840	−	0.646506i
$730$		0			0
$731$	2457.07	+	1785.16i	0.124320	+	0.0903238i
$732$		−	2184.86i		−	0.110321i
$733$	−18669.8	+	25696.8i	−0.940772	+	1.29486i	0.0147351	+	0.999891i	$0.495310\pi$
$733$	−18669.8	+	25696.8i	−0.940772	+	1.29486i	−0.955507	+	0.294970i	$0.904690\pi$
$734$	−8034.53	+	24727.7i	−0.404032	+	1.24348i
$735$		0			0
$736$	−1922.57	−	5917.06i	−0.0962865	−	0.296339i
$737$	−32793.3	−	10655.2i	−1.63902	−	0.532549i
$738$	301.403	+	97.9319i	0.0150336	+	0.00488472i
$739$	−4249.28	−	13077.9i	−0.211519	−	0.650987i	−0.999382	−	0.0351378i	$-0.988813\pi$
$739$	−4249.28	−	13077.9i	−0.211519	−	0.650987i	0.787864	−	0.615849i	$-0.211187\pi$
$740$		0			0
$741$	278.449	−	856.979i	0.0138044	−	0.0424857i
$742$	199.651	−	274.797i	0.00987795	−	0.0135958i
$743$		−	6312.16i		−	0.311670i	−0.987783	−	0.155835i	$-0.950193\pi$
$743$		−	6312.16i		−	0.311670i	0.987783	−	0.155835i	$-0.0498068\pi$
$744$	2398.52	+	1742.63i	0.118191	+	0.0858708i
$745$		0			0
$746$	11298.4	−	8208.78i	0.554510	−	0.402875i
$747$	2035.23	+	2801.26i	0.0996857	+	0.137206i
$748$	13868.4	−	4506.11i	0.677913	−	0.220267i
$749$	33952.9			1.65636
$750$		0			0
$751$	40114.6			1.94914			0.974569	−	0.224087i	$-0.0719400\pi$
$751$	40114.6			1.94914			0.974569	+	0.224087i	$0.0719400\pi$
$752$	6462.09	−	2099.66i	0.313362	−	0.101817i
$753$	1602.33	+	2205.42i	0.0775459	+	0.106733i
$754$	6315.49	−	4588.47i	0.305035	−	0.221621i
$755$		0			0
$756$	−16012.7	−	11633.9i	−0.770341	−	0.559686i
$757$			8151.37i			0.391369i	0.980667	+	0.195685i	$0.0626929\pi$
$757$			8151.37i			0.391369i	−0.980667	+	0.195685i	$0.937307\pi$
$758$	−1077.50	+	1483.05i	−0.0516312	+	0.0710643i
$759$	11692.7	−	35986.4i	0.559181	−	1.72098i
$760$		0			0
$761$	−1730.96	−	5327.36i	−0.0824538	−	0.253767i	0.901328	−	0.433138i	$-0.142594\pi$
$761$	−1730.96	−	5327.36i	−0.0824538	−	0.253767i	−0.983781	+	0.179371i	$0.942594\pi$
$762$	−13689.1	−	4447.87i	−0.650793	−	0.211456i
$763$	−35584.8	−	11562.2i	−1.68841	−	0.548597i
$764$	−4901.56	−	15085.5i	−0.232110	−	0.714362i
$765$		0			0
$766$	346.270	−	1065.71i	0.0163332	−	0.0502684i
$767$	604.341	−	831.804i	0.0284504	−	0.0391587i
$768$		−	1125.84i		−	0.0528973i
$769$	2973.61	+	2160.45i	0.139442	+	0.101311i	0.655320	−	0.755352i	$-0.272534\pi$
$769$	2973.61	+	2160.45i	0.139442	+	0.101311i	−0.515877	+	0.856662i	$0.672534\pi$
$770$		0			0
$771$	−10696.9	+	7771.73i	−0.499661	+	0.363025i
$772$	−4563.99	−	6281.80i	−0.212774	−	0.292859i
$773$	6444.75	−	2094.03i	0.299873	−	0.0974345i	−0.155216	−	0.987881i	$-0.549607\pi$
$773$	6444.75	−	2094.03i	0.299873	−	0.0974345i	0.455089	+	0.890446i	$0.349607\pi$
$774$	−564.766			−0.0262275
$775$		0			0
$776$	5227.68			0.241833
$777$	31178.7	−	10130.6i	1.43955	−	0.467738i
$778$	3489.83	+	4803.33i	0.160818	+	0.221347i
$779$	−173.018	+	125.705i	−0.00795766	+	0.00578158i
$780$		0			0
$781$	21961.6	+	15956.0i	1.00621	+	0.731051i
$782$			32032.6i			1.46481i
$783$	−17643.3	+	24283.9i	−0.805263	+	1.10835i
$784$	−3514.70	+	10817.1i	−0.160109	+	0.492764i
$785$		0			0
$786$	2939.45	+	9046.69i	0.133393	+	0.410540i
$787$	−4951.65	−	1608.89i	−0.224278	−	0.0728725i	0.194722	−	0.980858i	$-0.437619\pi$
$787$	−4951.65	−	1608.89i	−0.224278	−	0.0728725i	−0.419001	+	0.907986i	$0.637619\pi$
$788$	−7678.87	−	2495.02i	−0.347143	−	0.112794i
$789$	655.588	+	2017.69i	0.0295812	+	0.0910416i
$790$		0			0
$791$	1362.98	−	4194.82i	0.0612668	−	0.188560i
$792$	−1593.85	+	2193.75i	−0.0715089	+	0.0984235i
$793$			2461.74i			0.110238i
$794$	−10230.8	−	7433.11i	−0.457276	−	0.332231i
$795$		0			0
$796$	−3189.17	+	2317.07i	−0.142007	+	0.103174i
$797$	−19082.9	−	26265.4i	−0.848121	−	1.16734i	−0.984274	−	0.176650i	$-0.943474\pi$
$797$	−19082.9	−	26265.4i	−0.848121	−	1.16734i	0.136153	−	0.990688i	$-0.456526\pi$
$798$	2807.23	−	912.125i	0.124530	−	0.0404623i
$799$	−34983.2			−1.54896
$800$		0			0
$801$	−6617.60			−0.291912
$802$	−5722.85	+	1859.47i	−0.251971	+	0.0818703i
$803$	−23619.8	−	32509.9i	−1.03801	−	1.42870i
$804$	11088.8	−	8056.48i	0.486408	−	0.353396i
$805$		0			0
$806$	−2702.48	−	1963.47i	−0.118103	−	0.0858067i
$807$			22883.5i			0.998187i
$808$	3219.01	−	4430.58i	0.140154	−	0.192905i
$809$	−4880.74	+	15021.4i	−0.212111	+	0.652811i	0.787235	+	0.616653i	$0.211512\pi$
$809$	−4880.74	+	15021.4i	−0.212111	+	0.652811i	−0.999346	+	0.0361575i	$0.988488\pi$
$810$		0			0
$811$	1468.40	+	4519.27i	0.0635789	+	0.195676i	0.977800	−	0.209540i	$-0.0671965\pi$
$811$	1468.40	+	4519.27i	0.0635789	+	0.195676i	−0.914221	+	0.405215i	$0.867197\pi$
$812$	24320.0	+	7902.06i	1.05107	+	0.341512i
$813$	9049.25	+	2940.28i	0.390370	+	0.126839i
$814$	−6280.34	−	19328.9i	−0.270425	−	0.832282i
$815$		0			0
$816$	−1791.23	+	5512.83i	−0.0768450	+	0.236504i
$817$	224.016	−	308.332i	0.00959282	−	0.0132034i
$818$			22472.5i			0.960555i
$819$	3987.09	+	2896.79i	0.170110	+	0.123592i
$820$		0			0
$821$	−33068.5	+	24025.6i	−1.40572	+	1.02132i	−0.411794	+	0.911277i	$0.635098\pi$
$821$	−33068.5	+	24025.6i	−1.40572	+	1.02132i	−0.993927	+	0.110039i	$0.964902\pi$
$822$	11983.5	+	16493.8i	0.508480	+	0.699863i
$823$	−14439.2	+	4691.60i	−0.611568	+	0.198710i	−0.598393	−	0.801203i	$-0.704194\pi$
$823$	−14439.2	+	4691.60i	−0.611568	+	0.198710i	−0.0131750	+	0.999913i	$0.504194\pi$
$824$	−30.8661			−0.00130494
$825$		0			0
$826$	3367.99			0.141874
$827$	−15044.7	+	4888.31i	−0.632593	+	0.205542i	−0.607723	−	0.794149i	$-0.707917\pi$
$827$	−15044.7	+	4888.31i	−0.632593	+	0.205542i	−0.0248693	+	0.999691i	$0.507917\pi$
$828$	−3501.23	−	4819.02i	−0.146952	−	0.202262i
$829$	1.67554	−	1.21735i	7.01976e−5	−	5.10015e-5i	−0.587750	−	0.809042i	$-0.699986\pi$
$829$	1.67554	−	1.21735i	7.01976e−5	−	5.10015e-5i	0.587820	+	0.808991i	$0.299986\pi$
$830$		0			0
$831$	−17758.5	−	12902.3i	−0.741317	−	0.538598i
$832$			1268.51i			0.0528578i
$833$	34420.6	−	47375.8i	1.43169	−	1.97056i
$834$	−2882.87	+	8872.55i	−0.119695	+	0.368383i
$835$		0			0
$836$	−565.462	−	1740.31i	−0.0233935	−	0.0719976i
$837$	12215.8	+	3969.17i	0.504470	+	0.163912i
$838$	8486.82	+	2757.53i	0.349848	+	0.113672i
$839$	−5938.00	−	18275.3i	−0.244341	−	0.752005i	−0.995744	−	0.0921615i	$-0.970622\pi$
$839$	−5938.00	−	18275.3i	−0.244341	−	0.752005i	0.751403	−	0.659844i	$-0.229378\pi$
$840$		0			0
$841$	4447.16	−	13686.9i	0.182343	−	0.561193i
$842$	6709.49	−	9234.81i	0.274613	−	0.377972i
$843$		−	1935.04i		−	0.0790584i
$844$	14021.6	+	10187.3i	0.571852	+	0.415475i
$845$		0			0
$846$	5262.91	−	3823.73i	0.213880	−	0.155393i
$847$	11971.1	+	16476.8i	0.485633	+	0.668416i
$848$	79.6082	−	25.8663i	0.00322377	−	0.00104747i
$849$	−15988.0			−0.646296
$850$		0			0
$851$	44645.0			1.79837
$852$	−10262.7	+	3334.54i	−0.412668	+	0.134084i
$853$	14792.5	+	20360.1i	0.593769	+	0.817253i	0.995120	−	0.0986714i	$-0.0314593\pi$
$853$	14792.5	+	20360.1i	0.593769	+	0.817253i	−0.401351	+	0.915924i	$0.631459\pi$
$854$	−6523.90	+	4739.89i	−0.261409	+	0.189925i
$855$		0			0
$856$	6769.13	+	4918.06i	0.270285	+	0.196374i
$857$		−	32539.4i		−	1.29699i	−0.761217	−	0.648497i	$-0.775398\pi$
$857$		−	32539.4i		−	1.29699i	0.761217	−	0.648497i	$-0.224602\pi$
$858$	−4534.67	+	6241.43i	−0.180432	+	0.248344i
$859$	−14076.7	+	43323.7i	−0.559129	+	1.72082i	0.125654	+	0.992074i	$0.459897\pi$
$859$	−14076.7	+	43323.7i	−0.559129	+	1.72082i	−0.684783	+	0.728747i	$0.740103\pi$
$860$		0			0
$861$	912.704	+	2809.02i	0.0361265	+	0.111186i
$862$	15254.1	+	4956.37i	0.602735	+	0.195841i
$863$	3800.08	+	1234.72i	0.149892	+	0.0487027i	0.383002	−	0.923748i	$-0.374890\pi$
$863$	3800.08	+	1234.72i	0.149892	+	0.0487027i	−0.233110	+	0.972450i	$0.574890\pi$
$864$	−1507.26	−	4638.87i	−0.0593496	−	0.182659i
$865$		0			0
$866$	3574.25	−	11000.4i	0.140252	−	0.431650i
$867$	4842.10	−	6664.58i	0.189673	−	0.261062i
$868$		−	10942.4i		−	0.427891i
$869$	22131.2	+	16079.2i	0.863922	+	0.627676i
$870$		0			0
$871$	−12494.0	+	9077.45i	−0.486044	+	0.353132i
$872$	−5419.69	−	7459.57i	−0.210475	−	0.289694i
$873$	4760.11	−	1546.65i	0.184542	−	0.0599614i
$874$	4019.70			0.155570
$875$		0			0
$876$	15973.7			0.616098
$877$	−2331.16	+	757.438i	−0.0897577	+	0.0291641i	−0.353552	−	0.935415i	$-0.615026\pi$
$877$	−2331.16	+	757.438i	−0.0897577	+	0.0291641i	0.263794	+	0.964579i	$0.415026\pi$
$878$	−13811.9	−	19010.5i	−0.530899	−	0.730720i
$879$	−25049.1	+	18199.2i	−0.961189	+	0.698345i
$880$		0			0
$881$	−28818.0	−	20937.5i	−1.10205	−	0.800684i	−0.120654	−	0.992695i	$-0.538499\pi$
$881$	−28818.0	−	20937.5i	−1.10205	−	0.800684i	−0.981393	+	0.192011i	$0.938499\pi$
$882$			10889.5i			0.415724i
$883$	12345.8	−	16992.6i	0.470521	−	0.647617i	−0.506128	−	0.862459i	$-0.668924\pi$
$883$	12345.8	−	16992.6i	0.470521	−	0.647617i	0.976649	+	0.214842i	$0.0689236\pi$
$884$	2018.22	−	6211.45i	0.0767875	−	0.236328i
$885$		0			0
$886$	2205.45	+	6787.69i	0.0836272	+	0.257378i
$887$	−11581.2	−	3762.96i	−0.438398	−	0.142444i	0.0814984	−	0.996673i	$-0.474029\pi$
$887$	−11581.2	−	3762.96i	−0.438398	−	0.142444i	−0.519896	+	0.854229i	$0.674029\pi$
$888$	7683.44	+	2496.50i	0.290360	+	0.0943435i
$889$	16416.4	+	50524.5i	0.619335	+	1.90612i
$890$		0			0
$891$	6338.83	−	19508.9i	0.238338	−	0.733528i
$892$	12221.9	−	16822.1i	0.458768	−	0.631440i
$893$			4389.96i			0.164507i
$894$	13025.1	+	9463.29i	0.487276	+	0.354027i
$895$		0			0
$896$	−3361.71	+	2442.42i	−0.125342	+	0.0910666i
$897$	−9961.34	−	13710.6i	−0.370791	−	0.510350i
$898$	27331.7	−	8880.60i	1.01567	−	0.330011i
$899$	−16594.6			−0.615640
$900$		0			0
$901$	−430.967			−0.0159352
$902$	1741.42	−	565.821i	0.0642826	−	0.0208867i
$903$	−3093.81	−	4258.26i	−0.114015	−	0.156928i
$904$	879.352	−	638.887i	0.0323527	−	0.0235056i
$905$		0			0
$906$	−11282.3	−	8197.04i	−0.413718	−	0.300583i
$907$			33352.4i			1.22100i	0.792015	+	0.610501i	$0.209032\pi$
$907$			33352.4i			1.22100i	−0.792015	+	0.610501i	$0.790968\pi$
$908$	8804.31	−	12118.1i	0.321786	−	0.442900i
$909$	1620.27	−	4986.68i	0.0591210	−	0.181956i
$910$		0			0
$911$	5604.85	+	17249.9i	0.203839	+	0.627350i	0.999759	+	0.0219494i	$0.00698727\pi$
$911$	5604.85	+	17249.9i	0.203839	+	0.627350i	−0.795921	+	0.605401i	$0.793013\pi$
$912$	691.793	+	224.777i	0.0251179	+	0.00816131i
$913$	19026.4	+	6182.06i	0.689685	+	0.224092i
$914$	248.495	+	764.789i	0.00899287	+	0.0276772i
$915$		0			0
$916$	−5197.62	+	15996.6i	−0.187483	+	0.577013i
$917$	20636.1	−	28403.2i	0.743147	−	1.02285i
$918$			25113.0i			0.902889i
$919$	−25633.4	−	18623.8i	−0.920096	−	0.668489i	0.0234522	−	0.999725i	$-0.492534\pi$
$919$	−25633.4	−	18623.8i	−0.920096	−	0.668489i	−0.943548	+	0.331236i	$0.892534\pi$
$920$		0			0
$921$	14180.0	−	10302.4i	0.507325	−	0.368593i
$922$	8491.02	+	11686.9i	0.303294	+	0.417448i
$923$	11563.2	−	3757.12i	0.412360	−	0.133984i
$924$	−25271.7			−0.899761
$925$		0			0
$926$	−6554.13			−0.232594
$927$	−28.1054	+	9.13201i	−0.000995797	+	0.000323554i
$928$	3704.03	+	5098.16i	0.131024	+	0.180340i
$929$	−22563.0	+	16393.0i	−0.796844	+	0.578941i	−0.909987	−	0.414638i	$-0.863908\pi$
$929$	−22563.0	+	16393.0i	−0.796844	+	0.578941i	0.113143	+	0.993579i	$0.463908\pi$
$930$		0			0
$931$	−5945.09	−	4319.36i	−0.209283	−	0.152053i
$932$		−	24860.1i		−	0.873732i
$933$	−16600.7	+	22848.8i	−0.582509	+	0.801755i
$934$	3574.71	−	11001.8i	0.125234	−	0.385429i
$935$		0			0
$936$	375.300	+	1155.05i	0.0131058	+	0.0403356i
$937$	38777.9	+	12599.7i	1.35200	+	0.439290i	0.893363	−	0.449336i	$-0.148339\pi$
$937$	38777.9	+	12599.7i	1.35200	+	0.439290i	0.458633	+	0.888626i	$0.348339\pi$
$938$	−48112.7	−	15632.8i	−1.67477	−	0.544166i
$939$	−9420.48	−	28993.3i	−0.327397	−	1.00762i
$940$		0			0
$941$	−7635.56	+	23499.8i	−0.264519	+	0.814105i	0.727285	+	0.686335i	$0.240782\pi$
$941$	−7635.56	+	23499.8i	−0.264519	+	0.814105i	−0.991804	+	0.127769i	$0.959218\pi$
$942$	−7938.46	+	10926.4i	−0.274574	+	0.377919i
$943$			4022.25i			0.138900i
$944$	671.470	+	487.852i	0.0231509	+	0.0168201i
$945$		0			0
$946$	−2639.86	+	1917.97i	−0.0907287	+	0.0659183i
$947$	19473.6	+	26803.1i	0.668223	+	0.919730i	0.999718	−	0.0237270i	$-0.00755325\pi$
$947$	19473.6	+	26803.1i	0.668223	+	0.919730i	−0.331496	+	0.943457i	$0.607553\pi$
$948$	−10341.9	+	3360.29i	−0.354314	+	0.115124i
$949$	−17998.0			−0.615638
$950$		0			0
$951$	−29062.6			−0.990978
$952$	20347.0	−	6611.15i	0.692701	−	0.225072i
$953$	−18998.2	−	26148.8i	−0.645763	−	0.888816i	0.353144	−	0.935569i	$-0.385113\pi$
$953$	−18998.2	−	26148.8i	−0.645763	−	0.888816i	−0.998906	+	0.0467529i	$0.985113\pi$
$954$	64.8352	−	47.1055i	0.00220033	−	0.00159864i
$955$		0			0
$956$	−2752.74	−	1999.98i	−0.0931277	−	0.0676612i
$957$			38325.5i			1.29455i
$958$	2755.29	−	3792.33i	0.0929221	−	0.127896i
$959$	23252.6	−	71564.3i	0.782969	−	2.40973i
$960$		0			0
$961$	−7011.58	−	21579.4i	−0.235359	−	0.724361i
$962$	−8657.13	−	2812.87i	−0.290143	−	0.0942730i
$963$	7618.74	+	2475.48i	0.254943	+	0.0828361i
$964$	−5829.26	−	17940.6i	−0.194759	−	0.599407i
$965$		0			0
$966$	17155.0	−	52797.6i	0.571379	−	1.75852i
$967$	−7523.54	+	10355.3i	−0.250197	+	0.344367i	−0.915580	−	0.402135i	$-0.868268\pi$
$967$	−7523.54	+	10355.3i	−0.250197	+	0.344367i	0.665383	+	0.746502i	$0.268268\pi$
$968$			5018.94i			0.166648i
$969$	−3029.84	−	2201.31i	−0.100446	−	0.0729786i
$970$		0			0
$971$	30611.3	−	22240.4i	1.01170	−	0.735046i	0.0471385	−	0.998888i	$-0.484990\pi$
$971$	30611.3	−	22240.4i	1.01170	−	0.735046i	0.964566	+	0.263842i	$0.0849898\pi$
$972$	−4883.20	−	6721.15i	−0.161141	−	0.221791i
$973$	32747.3	−	10640.2i	1.07896	−	0.350576i
$974$	−23527.9			−0.774006
$975$		0			0
$976$	−1987.23			−0.0651738
$977$	28089.5	−	9126.82i	0.919817	−	0.298867i	0.189425	−	0.981895i	$-0.439337\pi$
$977$	28089.5	−	9126.82i	0.919817	−	0.298867i	0.730392	+	0.683028i	$0.239337\pi$
$978$	−8663.25	−	11923.9i	−0.283252	−	0.389863i
$979$	−30932.4	+	22473.7i	−1.00981	+	0.733669i
$980$		0			0
$981$	−7141.93	−	5188.91i	−0.232441	−	0.168878i
$982$		−	21996.0i		−	0.714788i
$983$	−624.445	+	859.475i	−0.0202611	+	0.0278871i	−0.819027	−	0.573754i	$-0.805486\pi$
$983$	−624.445	+	859.475i	−0.0202611	+	0.0278871i	0.798766	+	0.601641i	$0.205486\pi$
$984$	−224.920	+	692.232i	−0.00728677	+	0.0224264i
$985$		0			0
$986$	−10026.1	−	30857.1i	−0.323829	−	0.996642i
$987$	57660.8	+	18735.1i	1.85954	+	0.604200i
$988$	−779.461	−	253.262i	−0.0250992	−	0.00815521i
$989$	−2215.03	−	6817.15i	−0.0712171	−	0.219184i
$990$		0			0
$991$	15803.1	−	48637.0i	0.506561	−	1.55904i	−0.291568	−	0.956550i	$-0.594177\pi$
$991$	15803.1	−	48637.0i	0.506561	−	1.55904i	0.798130	−	0.602486i	$-0.205823\pi$
$992$	1585.00	−	2181.57i	0.0507297	−	0.0698234i
$993$			16488.1i			0.526924i
$994$	32220.9	+	23409.9i	1.02816	+	0.746998i
$995$		0			0
$996$	−6433.64	+	4674.31i	−0.204676	+	0.148706i
$997$	−27686.5	−	38107.1i	−0.879477	−	1.21050i	−0.976565	−	0.215221i	$-0.930953\pi$
$997$	−27686.5	−	38107.1i	−0.879477	−	1.21050i	0.0970879	−	0.995276i	$-0.469047\pi$
$998$	−23982.0	+	7792.21i	−0.760657	+	0.247152i
$999$	35000.9			1.10849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.e.c.99.7		32
5.2	odd	4		50.4.d.b.31.3	yes	16
5.3	odd	4		250.4.d.b.151.2		16
5.4	even	2	inner	250.4.e.c.99.2		32
25.2	odd	20		1250.4.a.j.1.3		8
25.3	odd	20		250.4.d.b.101.2		16
25.4	even	10	inner	250.4.e.c.149.7		32
25.21	even	5	inner	250.4.e.c.149.2		32
25.22	odd	20		50.4.d.b.21.3	✓	16
25.23	odd	20		1250.4.a.g.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.d.b.21.3	✓	16	25.22	odd	20
50.4.d.b.31.3	yes	16	5.2	odd	4
250.4.d.b.101.2		16	25.3	odd	20
250.4.d.b.151.2		16	5.3	odd	4
250.4.e.c.99.2		32	5.4	even	2	inner
250.4.e.c.99.7		32	1.1	even	1	trivial
250.4.e.c.149.2		32	25.21	even	5	inner
250.4.e.c.149.7		32	25.4	even	10	inner
1250.4.a.g.1.6		8	25.23	odd	20
1250.4.a.j.1.3		8	25.2	odd	20

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	250.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.90211 - 0.618034i) q^{2} +(2.58496 + 3.55790i) q^{3} +(3.23607 - 2.35114i) q^{4} +(7.11579 + 5.16993i) q^{6} -32.4633i q^{7} +(4.70228 - 6.47214i) q^{8} +(2.36687 - 7.28447i) q^{9} +(-13.6751 - 42.0875i) q^{11} +(16.7302 + 5.43598i) q^{12} +(-18.8504 - 6.12486i) q^{13} +(-20.0634 - 61.7488i) q^{14} +(4.94427 - 15.2169i) q^{16} +(-48.4207 + 66.6454i) q^{17} -15.3187i q^{18} +(8.36319 + 6.07621i) q^{19} +(115.501 - 83.9163i) q^{21} +(-52.0231 - 71.6036i) q^{22} +(184.908 - 60.0803i) q^{23} +35.1824 q^{24} -39.6409 q^{26} +(144.965 - 47.1019i) q^{27} +(-76.3257 - 105.053i) q^{28} +(-159.317 + 115.751i) q^{29} +(68.1740 + 49.5313i) q^{31} -32.0000i q^{32} +(114.394 - 157.449i) q^{33} +(-50.9126 + 156.693i) q^{34} +(-9.46747 - 29.1379i) q^{36} +(218.389 + 70.9588i) q^{37} +(19.6630 + 6.38891i) q^{38} +(-26.9359 - 82.9003i) q^{39} +(-6.39296 + 19.6755i) q^{41} +(167.833 - 231.002i) q^{42} -36.8678i q^{43} +(-143.207 - 104.046i) q^{44} +(314.584 - 228.559i) q^{46} +(249.612 + 343.561i) q^{47} +(66.9209 - 21.7439i) q^{48} -710.864 q^{49} -362.283 q^{51} +(-75.4016 + 24.4995i) q^{52} +(3.07504 + 4.23242i) q^{53} +(246.629 - 179.186i) q^{54} +(-210.107 - 152.651i) q^{56} +45.4621i q^{57} +(-231.502 + 318.635i) q^{58} +(-16.0299 + 49.3350i) q^{59} +(-38.3804 - 118.123i) q^{61} +(160.287 + 52.0803i) q^{62} +(-236.478 - 76.8363i) q^{63} +(-19.7771 - 60.8676i) q^{64} +(120.280 - 370.185i) q^{66} +(457.984 - 630.360i) q^{67} +329.513i q^{68} +(691.740 + 502.578i) q^{69} +(-496.268 + 360.560i) q^{71} +(-36.0164 - 49.5723i) q^{72} +(863.608 - 280.603i) q^{73} +459.255 q^{74} +41.3499 q^{76} +(-1366.30 + 443.937i) q^{77} +(-102.470 - 141.038i) q^{78} +(-500.100 + 363.344i) q^{79} +(375.005 + 272.457i) q^{81} +41.3761i q^{82} +(-265.719 + 365.730i) q^{83} +(176.470 - 543.118i) q^{84} +(-22.7855 - 70.1266i) q^{86} +(-823.659 - 267.623i) q^{87} +(-336.700 - 109.401i) q^{88} +(-266.987 - 821.703i) q^{89} +(-198.833 + 611.945i) q^{91} +(457.118 - 629.169i) q^{92} +370.592i q^{93} +(687.123 + 499.224i) q^{94} +(113.853 - 82.7188i) q^{96} +(384.094 + 528.660i) q^{97} +(-1352.14 + 439.338i) q^{98} -338.953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 28 q^{6} + 166 q^{9} + 304 q^{11} - 104 q^{14} - 128 q^{16} + 40 q^{19} + 514 q^{21} + 128 q^{24} - 1432 q^{26} - 210 q^{29} + 354 q^{31} - 684 q^{34} - 664 q^{36} + 292 q^{39} + 924 q^{41}+ \cdots + 3572 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 28 * q^6 + 166 * q^9 + 304 * q^11 - 104 * q^14 - 128 * q^16 + 40 * q^19 + 514 * q^21 + 128 * q^24 - 1432 * q^26 - 210 * q^29 + 354 * q^31 - 684 * q^34 - 664 * q^36 + 292 * q^39 + 924 * q^41 + 904 * q^44 + 2248 * q^46 - 3396 * q^49 - 7216 * q^51 - 780 * q^54 + 16 * q^56 - 2550 * q^59 + 504 * q^61 + 512 * q^64 + 1996 * q^66 + 10982 * q^69 + 7424 * q^71 + 2296 * q^74 - 400 * q^76 - 3500 * q^79 + 8212 * q^81 + 1224 * q^84 + 2148 * q^86 - 11320 * q^89 - 986 * q^91 + 4456 * q^94 + 448 * q^96 + 3572 * q^99

Introduction

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