LMFDB - Embedded newform 225.4.e.g.76.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			76.11
Character	$\chi$	$=$	225.76
Dual form			225.4.e.g.151.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23192 + 2.13376i) q^{2} +(4.97325 + 1.50557i) q^{3} +(0.964722 - 1.67095i) q^{4} +(2.91415 + 12.4665i) q^{6} +(9.62007 + 16.6624i) q^{7} +24.4647 q^{8} +(22.4665 + 14.9752i) q^{9} +O(q^{10})$	\(q+(1.23192 + 2.13376i) q^{2} +(4.97325 + 1.50557i) q^{3} +(0.964722 - 1.67095i) q^{4} +(2.91415 + 12.4665i) q^{6} +(9.62007 + 16.6624i) q^{7} +24.4647 q^{8} +(22.4665 + 14.9752i) q^{9} +(-19.9274 - 34.5153i) q^{11} +(7.31354 - 6.85759i) q^{12} +(-0.504548 + 0.873903i) q^{13} +(-23.7024 + 41.0538i) q^{14} +(22.4208 + 38.8340i) q^{16} +52.6170 q^{17} +(-4.27635 + 66.3864i) q^{18} -49.5371 q^{19} +(22.7565 + 97.3503i) q^{21} +(49.0982 - 85.0405i) q^{22} +(-13.7009 + 23.7307i) q^{23} +(121.669 + 36.8333i) q^{24} -2.48626 q^{26} +(89.1854 + 108.300i) q^{27} +37.1228 q^{28} +(127.477 + 220.796i) q^{29} +(84.3282 - 146.061i) q^{31} +(42.6170 - 73.8149i) q^{32} +(-47.1388 - 201.656i) q^{33} +(64.8202 + 112.272i) q^{34} +(46.6967 - 23.0935i) q^{36} -419.938 q^{37} +(-61.0260 - 105.700i) q^{38} +(-3.82497 + 3.58651i) q^{39} +(-199.285 + 345.172i) q^{41} +(-179.687 + 168.485i) q^{42} +(-179.414 - 310.754i) q^{43} -76.8977 q^{44} -67.5141 q^{46} +(-70.6510 - 122.371i) q^{47} +(53.0371 + 226.888i) q^{48} +(-13.5915 + 23.5411i) q^{49} +(261.678 + 79.2187i) q^{51} +(0.973497 + 1.68615i) q^{52} +290.878 q^{53} +(-121.217 + 323.718i) q^{54} +(235.352 + 407.641i) q^{56} +(-246.361 - 74.5817i) q^{57} +(-314.083 + 544.008i) q^{58} +(-14.3659 + 24.8825i) q^{59} +(-366.364 - 634.561i) q^{61} +415.544 q^{62} +(-33.3939 + 518.409i) q^{63} +568.737 q^{64} +(372.212 - 349.007i) q^{66} +(88.2730 - 152.893i) q^{67} +(50.7608 - 87.9203i) q^{68} +(-103.866 + 97.3911i) q^{69} -802.814 q^{71} +(549.635 + 366.363i) q^{72} +512.820 q^{73} +(-517.332 - 896.046i) q^{74} +(-47.7895 + 82.7739i) q^{76} +(383.406 - 664.079i) q^{77} +(-12.3648 - 3.74324i) q^{78} +(-306.174 - 530.309i) q^{79} +(280.488 + 672.880i) q^{81} -982.017 q^{82} +(-40.4081 - 69.9889i) q^{83} +(184.621 + 55.8910i) q^{84} +(442.049 - 765.651i) q^{86} +(301.549 + 1290.00i) q^{87} +(-487.518 - 844.405i) q^{88} +24.0097 q^{89} -19.4151 q^{91} +(26.4352 + 45.7871i) q^{92} +(639.290 - 599.435i) q^{93} +(174.073 - 301.504i) q^{94} +(323.079 - 302.937i) q^{96} +(-683.960 - 1184.65i) q^{97} -66.9747 q^{98} +(69.1736 - 1073.86i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) $ 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9	$ 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) $ 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9 + 90 * q^11 + 102 * q^14 - 146 * q^16 + 8 * q^19 + 30 * q^21 - 462 * q^24 - 936 * q^26 + 516 * q^29 - 38 * q^31 - 212 * q^34 + 864 * q^36 - 330 * q^39 + 576 * q^41 - 3288 * q^44 - 580 * q^46 + 4 * q^49 + 1260 * q^51 + 3726 * q^54 + 2430 * q^56 + 2202 * q^59 - 20 * q^61 - 644 * q^64 - 5052 * q^66 - 1452 * q^69 - 5904 * q^71 + 4080 * q^74 + 396 * q^76 + 218 * q^79 + 198 * q^81 - 4662 * q^84 + 6108 * q^86 - 8148 * q^89 - 1884 * q^91 + 1078 * q^94 + 11874 * q^96 + 1602 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.23192	+	2.13376i	0.435551	+	0.754397i	0.997340	−	0.0728836i	$-0.0232201\pi$
$2$	1.23192	+	2.13376i	0.435551	+	0.754397i	−0.561789	+	0.827280i	$0.689887\pi$
$3$	4.97325	+	1.50557i	0.957103	+	0.289747i
$3$	4.97325	+	1.50557i	0.957103	+	0.289747i
$4$	0.964722	−	1.67095i	0.120590	−	0.208869i
$5$		0			0
$5$		0			0
$6$	2.91415	+	12.4665i	0.198283	+	0.848235i
$7$	9.62007	+	16.6624i	0.519435	+	0.899688i	0.999745	+	0.0225888i	$0.00719086\pi$
$7$	9.62007	+	16.6624i	0.519435	+	0.899688i	−0.480310	+	0.877099i	$0.659476\pi$
$8$	24.4647			1.08120
$9$	22.4665	+	14.9752i	0.832093	+	0.554636i
$10$		0			0
$11$	−19.9274	−	34.5153i	−0.546213	−	0.946069i	−0.998529	−	0.0542113i	$-0.982736\pi$
$11$	−19.9274	−	34.5153i	−0.546213	−	0.946069i	0.452316	−	0.891858i	$-0.350598\pi$
$12$	7.31354	−	6.85759i	0.175936	−	0.164968i
$13$	−0.504548	+	0.873903i	−0.0107643	+	0.0186444i	−0.871357	−	0.490649i	$-0.836760\pi$
$13$	−0.504548	+	0.873903i	−0.0107643	+	0.0186444i	0.860593	+	0.509293i	$0.170093\pi$
$14$	−23.7024	+	41.0538i	−0.452481	+	0.783720i
$15$		0			0
$16$	22.4208	+	38.8340i	0.350326	+	0.606782i
$17$	52.6170			0.750676			0.375338	−	0.926888i	$-0.377527\pi$
$17$	52.6170			0.750676			0.375338	+	0.926888i	$0.377527\pi$
$18$	−4.27635	+	66.3864i	−0.0559970	+	0.869301i
$19$	−49.5371			−0.598136			−0.299068	−	0.954232i	$-0.596676\pi$
$19$	−49.5371			−0.598136			−0.299068	+	0.954232i	$0.596676\pi$
$20$		0			0
$21$	22.7565	+	97.3503i	0.236471	+	1.01160i
$22$	49.0982	−	85.0405i	0.475808	−	0.824123i
$23$	−13.7009	+	23.7307i	−0.124210	+	0.215139i	−0.921424	−	0.388559i	$-0.872973\pi$
$23$	−13.7009	+	23.7307i	−0.124210	+	0.215139i	0.797214	+	0.603697i	$0.206306\pi$
$24$	121.669	+	36.8333i	1.03482	+	0.313274i
$25$		0			0
$26$	−2.48626			−0.0187537
$27$	89.1854	+	108.300i	0.635694	+	0.771941i
$28$	37.1228			0.250555
$29$	127.477	+	220.796i	0.816269	+	1.41382i	0.908413	+	0.418074i	$0.137295\pi$
$29$	127.477	+	220.796i	0.816269	+	1.41382i	−0.0921441	+	0.995746i	$0.529372\pi$
$30$		0			0
$31$	84.3282	−	146.061i	0.488574	−	0.846234i	−0.511340	−	0.859379i	$-0.670851\pi$
$31$	84.3282	−	146.061i	0.488574	−	0.846234i	0.999914	+	0.0131441i	$0.00418403\pi$
$32$	42.6170	−	73.8149i	0.235428	−	0.407774i
$33$	−47.1388	−	201.656i	−0.248661	−	1.06375i
$34$	64.8202	+	112.272i	0.326958	+	0.566308i
$35$		0			0
$36$	46.6967	−	23.0935i	0.216188	−	0.106914i
$37$	−419.938			−1.86588			−0.932938	−	0.360038i	$-0.882764\pi$
$37$	−419.938			−1.86588			−0.932938	+	0.360038i	$0.882764\pi$
$38$	−61.0260	−	105.700i	−0.260519	−	0.451232i
$39$	−3.82497	+	3.58651i	−0.0157047	+	0.0147257i
$40$		0			0
$41$	−199.285	+	345.172i	−0.759100	+	1.31480i	0.184210	+	0.982887i	$0.441027\pi$
$41$	−199.285	+	345.172i	−0.759100	+	1.31480i	−0.943310	+	0.331913i	$0.892306\pi$
$42$	−179.687	+	168.485i	−0.660152	+	0.618996i
$43$	−179.414	−	310.754i	−0.636288	−	1.10208i	−0.986241	−	0.165316i	$-0.947136\pi$
$43$	−179.414	−	310.754i	−0.636288	−	1.10208i	0.349953	−	0.936767i	$-0.386198\pi$
$44$	−76.8977			−0.263472
$45$		0			0
$46$	−67.5141			−0.216400
$47$	−70.6510	−	122.371i	−0.219266	−	0.379780i	0.735318	−	0.677723i	$-0.237033\pi$
$47$	−70.6510	−	122.371i	−0.219266	−	0.379780i	−0.954584	+	0.297943i	$0.903700\pi$
$48$	53.0371	+	226.888i	0.159484	+	0.682259i
$49$	−13.5915	+	23.5411i	−0.0396253	+	0.0686330i
$50$		0			0
$51$	261.678	+	79.2187i	0.718475	+	0.217507i
$52$	0.973497	+	1.68615i	0.00259615	+	0.00449666i
$53$	290.878			0.753872			0.376936	−	0.926239i	$-0.376978\pi$
$53$	290.878			0.753872			0.376936	+	0.926239i	$0.376978\pi$
$54$	−121.217	+	323.718i	−0.305473	+	0.815785i
$55$		0			0
$56$	235.352	+	407.641i	0.561611	+	0.972738i
$57$	−246.361	−	74.5817i	−0.572478	−	0.173308i
$58$	−314.083	+	544.008i	−0.711054	+	1.23158i
$59$	−14.3659	+	24.8825i	−0.0316998	+	0.0549056i	−0.881440	−	0.472296i	$-0.843425\pi$
$59$	−14.3659	+	24.8825i	−0.0316998	+	0.0549056i	0.849740	+	0.527202i	$0.176759\pi$
$60$		0			0
$61$	−366.364	−	634.561i	−0.768985	−	1.33192i	−0.938114	−	0.346327i	$-0.887429\pi$
$61$	−366.364	−	634.561i	−0.768985	−	1.33192i	0.169129	−	0.985594i	$-0.445904\pi$
$62$	415.544			0.851195
$63$	−33.3939	+	518.409i	−0.0667815	+	1.03672i
$64$	568.737			1.11082
$65$		0			0
$66$	372.212	−	349.007i	0.694184	−	0.650907i
$67$	88.2730	−	152.893i	0.160959	−	0.278789i	−0.774254	−	0.632875i	$-0.781875\pi$
$67$	88.2730	−	152.893i	0.160959	−	0.278789i	0.935213	+	0.354086i	$0.115208\pi$
$68$	50.7608	−	87.9203i	0.0905243	−	0.156793i
$69$	−103.866	+	97.3911i	−0.181218	+	0.169920i
$70$		0			0
$71$	−802.814			−1.34192			−0.670961	−	0.741493i	$-0.734118\pi$
$71$	−802.814			−1.34192			−0.670961	+	0.741493i	$0.734118\pi$
$72$	549.635	+	366.363i	0.899655	+	0.599670i
$73$	512.820			0.822205			0.411103	−	0.911589i	$-0.365144\pi$
$73$	512.820			0.822205			0.411103	+	0.911589i	$0.365144\pi$
$74$	−517.332	−	896.046i	−0.812684	−	1.40761i
$75$		0			0
$76$	−47.7895	+	82.7739i	−0.0721294	+	0.124932i
$77$	383.406	−	664.079i	0.567444	−	0.982842i
$78$	−12.3648	−	3.74324i	−0.0179492	−	0.00543383i
$79$	−306.174	−	530.309i	−0.436041	−	0.755246i	0.561339	−	0.827586i	$-0.310286\pi$
$79$	−306.174	−	530.309i	−0.436041	−	0.755246i	−0.997380	+	0.0723406i	$0.976953\pi$
$80$		0			0
$81$	280.488	+	672.880i	0.384757	+	0.923018i
$82$	−982.017			−1.32251
$83$	−40.4081	−	69.9889i	−0.0534382	−	0.0925576i	0.838069	−	0.545564i	$-0.183685\pi$
$83$	−40.4081	−	69.9889i	−0.0534382	−	0.0925576i	−0.891507	+	0.453007i	$0.850351\pi$
$84$	184.621	+	55.8910i	0.239807	+	0.0725977i
$85$		0			0
$86$	442.049	−	765.651i	0.554272	−	0.960027i
$87$	301.549	+	1290.00i	0.371603	+	1.58968i
$88$	−487.518	−	844.405i	−0.590563	−	1.02289i
$89$	24.0097			0.0285957			0.0142979	−	0.999898i	$-0.495449\pi$
$89$	24.0097			0.0285957			0.0142979	+	0.999898i	$0.495449\pi$
$90$		0			0
$91$	−19.4151			−0.0223655
$92$	26.4352	+	45.7871i	0.0299572	+	0.0518873i
$93$	639.290	−	599.435i	0.712810	−	0.668371i
$94$	174.073	−	301.504i	0.191003	−	0.330827i
$95$		0			0
$96$	323.079	−	302.937i	0.343480	−	0.322067i
$97$	−683.960	−	1184.65i	−0.715934	−	1.24003i	−0.962598	−	0.270934i	$-0.912668\pi$
$97$	−683.960	−	1184.65i	−0.715934	−	1.24003i	0.246664	−	0.969101i	$-0.420666\pi$
$98$	−66.9747			−0.0690353
$99$	69.1736	−	1073.86i	0.0702243	−	1.09017i
$100$		0			0
$101$	−284.206	−	492.260i	−0.279996	−	0.484967i	0.691387	−	0.722484i	$-0.257000\pi$
$101$	−284.206	−	492.260i	−0.279996	−	0.484967i	−0.971383	+	0.237517i	$0.923666\pi$
$102$	153.334	+	655.948i	0.148846	+	0.636750i
$103$	−237.579	+	411.499i	−0.227276	+	0.393653i	−0.957000	−	0.290089i	$-0.906315\pi$
$103$	−237.579	+	411.499i	−0.227276	+	0.393653i	0.729724	+	0.683742i	$0.239648\pi$
$104$	−12.3436	+	21.3797i	−0.0116384	+	0.0201582i
$105$		0			0
$106$	358.340	+	620.664i	0.328350	+	0.568719i
$107$	1452.60			1.31242			0.656208	−	0.754580i	$-0.272159\pi$
$107$	1452.60			1.31242			0.656208	+	0.754580i	$0.272159\pi$
$108$	267.003	−	44.5444i	0.237893	−	0.0396879i
$109$	−1962.92			−1.72490			−0.862448	−	0.506146i	$-0.831070\pi$
$109$	−1962.92			−1.72490			−0.862448	+	0.506146i	$0.831070\pi$
$110$		0			0
$111$	−2088.46	−	632.247i	−1.78584	−	0.540633i
$112$	−431.380	+	747.172i	−0.363943	+	0.630367i
$113$	489.143	−	847.220i	0.407210	−	0.705308i	−0.587366	−	0.809321i	$-0.699835\pi$
$113$	489.143	−	847.220i	0.407210	−	0.705308i	0.994576	+	0.104013i	$0.0331685\pi$
$114$	−144.359	−	617.552i	−0.118600	−	0.507360i
$115$		0			0
$116$	491.918			0.393736
$117$	−24.4223	+	12.0778i	−0.0192978	+	0.00954356i
$118$	−70.7910			−0.0552275
$119$	506.179	+	876.728i	0.389928	+	0.675374i
$120$		0			0
$121$	−128.704	+	222.923i	−0.0966976	+	0.167485i
$122$	902.665	−	1563.46i	0.669864	−	1.16024i
$123$	−1510.78	+	1416.59i	−1.10750	+	1.03845i
$124$	−162.706	−	281.816i	−0.117834	−	0.204095i
$125$		0			0
$126$	−1147.30	+	567.387i	−0.811186	+	0.401165i
$127$	865.941			0.605038			0.302519	−	0.953143i	$-0.402172\pi$
$127$	865.941			0.605038			0.302519	+	0.953143i	$0.402172\pi$
$128$	359.705	+	623.028i	0.248389	+	0.430222i
$129$	−424.409	−	1815.58i	−0.289667	−	1.23917i
$130$		0			0
$131$	734.478	−	1272.15i	0.489860	−	0.848462i	−0.510072	−	0.860132i	$-0.670381\pi$
$131$	734.478	−	1272.15i	0.489860	−	0.848462i	0.999932	+	0.0116695i	$0.00371460\pi$
$132$	−382.432	−	115.775i	−0.252170	−	0.0763403i
$133$	−476.550	−	825.409i	−0.310693	−	0.538136i
$134$	434.983			0.280424
$135$		0			0
$136$	1287.26			0.811628
$137$	35.7677	+	61.9514i	0.0223054	+	0.0386341i	0.876963	−	0.480559i	$-0.159566\pi$
$137$	35.7677	+	61.9514i	0.0223054	+	0.0386341i	−0.854657	+	0.519193i	$0.826233\pi$
$138$	−335.765	−	101.647i	−0.207117	−	0.0627014i
$139$	−114.532	+	198.376i	−0.0698886	+	0.121051i	−0.898852	−	0.438252i	$-0.855598\pi$
$139$	−114.532	+	198.376i	−0.0698886	+	0.121051i	0.828964	+	0.559303i	$0.188931\pi$
$140$		0			0
$141$	−167.127	−	714.953i	−0.0998199	−	0.427020i
$142$	−989.006	−	1713.01i	−0.584476	−	1.01234i
$143$	40.2174			0.0235185
$144$	−77.8289	+	1208.22i	−0.0450399	+	0.699202i
$145$		0			0
$146$	631.755	+	1094.23i	0.358113	+	0.620269i
$147$	−103.037	+	96.6130i	−0.0578117	+	0.0542075i
$148$	−405.124	+	701.695i	−0.225006	+	0.389723i
$149$	417.572	−	723.256i	0.229589	−	0.397661i	−0.728097	−	0.685474i	$-0.759595\pi$
$149$	417.572	−	723.256i	0.229589	−	0.397661i	0.957686	+	0.287814i	$0.0929283\pi$
$150$		0			0
$151$	933.292	+	1616.51i	0.502982	+	0.871190i	0.999994	+	0.00344622i	$0.00109697\pi$
$151$	933.292	+	1616.51i	0.502982	+	0.871190i	−0.497013	+	0.867743i	$0.665570\pi$
$152$	−1211.91			−0.646702
$153$	1182.12	+	787.949i	0.624632	+	0.416352i
$154$	1889.31			0.988604
$155$		0			0
$156$	2.30283	+	9.85131i	0.00118189	+	0.00505600i
$157$	−1149.95	+	1991.78i	−0.584563	+	1.01249i	0.410367	+	0.911921i	$0.365401\pi$
$157$	−1149.95	+	1991.78i	−0.584563	+	1.01249i	−0.994930	+	0.100572i	$0.967933\pi$
$158$	754.367	−	1306.60i	0.379837	−	0.657896i
$159$	1446.61	+	437.938i	0.721533	+	0.218432i
$160$		0			0
$161$	−527.215			−0.258077
$162$	−1090.22	+	1427.43i	−0.528741	+	0.692281i
$163$	−44.9023			−0.0215768			−0.0107884	−	0.999942i	$-0.503434\pi$
$163$	−44.9023			−0.0215768			−0.0107884	+	0.999942i	$0.503434\pi$
$164$	384.510	+	665.990i	0.183080	+	0.317104i
$165$		0			0
$166$	99.5595	−	172.442i	0.0465501	−	0.0806272i
$167$	−588.281	+	1018.93i	−0.272590	+	0.472140i	−0.969524	−	0.244995i	$-0.921214\pi$
$167$	−588.281	+	1018.93i	−0.272590	+	0.472140i	0.696934	+	0.717135i	$0.254547\pi$
$168$	556.731	+	2381.64i	0.255671	+	1.09374i
$169$	1097.99	+	1901.78i	0.499768	+	0.865624i
$170$		0			0
$171$	−1112.93	−	741.827i	−0.497705	−	0.331748i
$172$	−692.339			−0.306921
$173$	534.045	+	924.994i	0.234698	+	0.406508i	0.959185	−	0.282780i	$-0.0912566\pi$
$173$	534.045	+	924.994i	0.234698	+	0.406508i	−0.724487	+	0.689288i	$0.757923\pi$
$174$	−2381.06	+	2232.61i	−1.03740	+	0.972724i
$175$		0			0
$176$	893.579	−	1547.72i	0.382705	−	0.662864i
$177$	−108.908	+	102.118i	−0.0462487	+	0.0433654i
$178$	29.5781	+	51.2308i	0.0124549	+	0.0215725i
$179$	−2779.66			−1.16068			−0.580339	−	0.814375i	$-0.697080\pi$
$179$	−2779.66			−1.16068			−0.580339	+	0.814375i	$0.697080\pi$
$180$		0			0
$181$	−3568.66			−1.46550			−0.732752	−	0.680496i	$-0.761764\pi$
$181$	−3568.66			−1.46550			−0.732752	+	0.680496i	$0.761764\pi$
$182$	−23.9180	−	41.4272i	−0.00974132	−	0.0168725i
$183$	−866.643	−	3707.42i	−0.350077	−	1.49760i
$184$	−335.189	+	580.564i	−0.134296	+	0.232607i
$185$		0			0
$186$	2066.60	+	625.631i	0.814682	+	0.246632i
$187$	−1048.52	−	1816.09i	−0.410029	−	0.710192i
$188$	−272.634			−0.105765
$189$	−946.579	+	2527.90i	−0.364304	+	0.972899i
$190$		0			0
$191$	1669.31	+	2891.33i	0.632392	+	1.09534i	0.987061	+	0.160344i	$0.0512603\pi$
$191$	1669.31	+	2891.33i	0.632392	+	1.09534i	−0.354669	+	0.934992i	$0.615406\pi$
$192$	2828.48	+	856.275i	1.06316	+	0.321856i
$193$	970.433	−	1680.84i	0.361934	−	0.626888i	−0.626345	−	0.779546i	$-0.715450\pi$
$193$	970.433	−	1680.84i	0.361934	−	0.626888i	0.988279	+	0.152658i	$0.0487832\pi$
$194$	1685.18	−	2918.81i	0.623652	−	1.08020i
$195$		0			0
$196$	26.2240	+	45.4213i	0.00955684	+	0.0165529i
$197$	1035.75			0.374588			0.187294	−	0.982304i	$-0.440028\pi$
$197$	1035.75			0.374588			0.187294	+	0.982304i	$0.440028\pi$
$198$	2376.56	−	1175.31i	0.853005	−	0.421847i
$199$	1565.53			0.557675			0.278838	−	0.960338i	$-0.410051\pi$
$199$	1565.53			0.557675			0.278838	+	0.960338i	$0.410051\pi$
$200$		0			0
$201$	669.196	−	627.476i	0.234833	−	0.220193i
$202$	700.242	−	1212.85i	0.243905	−	0.422456i
$203$	−2452.67	+	4248.14i	−0.847997	+	1.46877i
$204$	384.817	−	360.826i	0.132071	−	0.123838i
$205$		0			0
$206$	−1170.72			−0.395961
$207$	−663.184	+	327.972i	−0.222678	+	0.110124i
$208$	−45.2496			−0.0150841
$209$	987.147	+	1709.79i	0.326710	+	0.565878i
$210$		0			0
$211$	−1692.64	+	2931.73i	−0.552255	+	0.956534i	0.445856	+	0.895105i	$0.352899\pi$
$211$	−1692.64	+	2931.73i	−0.552255	+	0.956534i	−0.998111	+	0.0614294i	$0.980434\pi$
$212$	280.617	−	486.043i	0.0909096	−	0.157460i
$213$	−3992.60	−	1208.69i	−1.28436	−	0.388819i
$214$	1789.50	+	3099.50i	0.571624	+	0.990082i
$215$		0			0
$216$	2181.89	+	2649.53i	0.687310	+	0.834619i
$217$	3244.97			1.01513
$218$	−2418.17	−	4188.39i	−0.751280	−	1.30126i
$219$	2550.38	+	772.087i	0.786935	+	0.238232i
$220$		0			0
$221$	−26.5478	+	45.9821i	−0.00808054	+	0.0139959i
$222$	−1223.76	−	5235.14i	−0.369971	−	1.58270i
$223$	1182.77	+	2048.62i	0.355176	+	0.615183i	0.987148	−	0.159808i	$-0.0510875\pi$
$223$	1182.77	+	2048.62i	0.355176	+	0.615183i	−0.631972	+	0.774991i	$0.717754\pi$
$224$	1639.92			0.489158
$225$		0			0
$226$	2410.35			0.709443
$227$	−488.115	−	845.440i	−0.142720	−	0.247197i	0.785800	−	0.618480i	$-0.212251\pi$
$227$	−488.115	−	845.440i	−0.142720	−	0.247197i	−0.928520	+	0.371283i	$0.878918\pi$
$228$	−362.292	+	339.705i	−0.105234	+	0.0986733i
$229$	−797.640	+	1381.55i	−0.230173	+	0.398671i	−0.957859	−	0.287240i	$-0.907262\pi$
$229$	−797.640	+	1381.55i	−0.230173	+	0.398671i	0.727686	+	0.685910i	$0.240596\pi$
$230$		0			0
$231$	2906.60	−	2725.39i	0.827879	−	0.776266i
$232$	3118.67	+	5401.70i	0.882546	+	1.52862i
$233$	943.571			0.265302			0.132651	−	0.991163i	$-0.457651\pi$
$233$	943.571			0.265302			0.132651	+	0.991163i	$0.457651\pi$
$234$	−55.8576	−	37.2322i	−0.0156048	−	0.0104015i
$235$		0			0
$236$	27.7183	+	48.0095i	0.00764537	+	0.0132422i
$237$	−724.262	−	3098.33i	−0.198506	−	0.849190i
$238$	−1247.15	+	2160.13i	−0.339667	+	0.588320i
$239$	−1365.75	+	2365.54i	−0.369635	+	0.640227i	−0.989508	−	0.144475i	$-0.953851\pi$
$239$	−1365.75	+	2365.54i	−0.369635	+	0.640227i	0.619873	+	0.784702i	$0.287184\pi$
$240$		0			0
$241$	−1708.62	−	2959.41i	−0.456687	−	0.791006i	0.542096	−	0.840317i	$-0.317631\pi$
$241$	−1708.62	−	2959.41i	−0.456687	−	0.791006i	−0.998783	+	0.0493107i	$0.984298\pi$
$242$	−634.217			−0.168467
$243$	381.867	+	3768.70i	0.100810	+	0.994906i
$244$	−1413.76			−0.370928
$245$		0			0
$246$	−4883.82	−	1478.50i	−1.26578	−	0.383193i
$247$	24.9938	−	43.2906i	0.00643854	−	0.0111519i
$248$	2063.06	−	3573.32i	0.528244	−	0.914945i
$249$	−95.5865	−	408.910i	−0.0243275	−	0.104071i
$250$		0			0
$251$	−3164.50			−0.795782			−0.397891	−	0.917433i	$-0.630258\pi$
$251$	−3164.50			−0.795782			−0.397891	+	0.917433i	$0.630258\pi$
$252$	834.019	+	555.920i	0.208485	+	0.138967i
$253$	1092.10			0.271382
$254$	1066.77	+	1847.71i	0.263525	+	0.456439i
$255$		0			0
$256$	1388.69	−	2405.28i	0.339036	−	0.587227i
$257$	−2774.72	+	4805.95i	−0.673471	+	1.16649i	0.303442	+	0.952850i	$0.401864\pi$
$257$	−2774.72	+	4805.95i	−0.673471	+	1.16649i	−0.976913	+	0.213636i	$0.931469\pi$
$258$	3351.17	−	3142.24i	0.808661	−	0.758246i
$259$	−4039.83	−	6997.20i	−0.969201	−	1.67871i
$260$		0			0
$261$	−442.506	+	6869.50i	−0.104944	+	1.62916i
$262$	3619.29			0.853436
$263$	2068.82	+	3583.30i	0.485053	+	0.840136i	0.999853	−	0.0171742i	$-0.00546699\pi$
$263$	2068.82	+	3583.30i	0.485053	+	0.840136i	−0.514800	+	0.857311i	$0.672134\pi$
$264$	−1153.24	−	4933.43i	−0.268851	−	1.15012i
$265$		0			0
$266$	1174.15	−	2033.68i	0.270645	−	0.468771i
$267$	119.406	+	36.1483i	0.0273691	+	0.00828554i
$268$	−170.318	−	294.999i	−0.0388202	−	0.0672386i
$269$	−1026.74			−0.232719			−0.116359	−	0.993207i	$-0.537122\pi$
$269$	−1026.74			−0.232719			−0.116359	+	0.993207i	$0.537122\pi$
$270$		0			0
$271$	3400.66			0.762270			0.381135	−	0.924519i	$-0.375533\pi$
$271$	3400.66			0.762270			0.381135	+	0.924519i	$0.375533\pi$
$272$	1179.72	+	2043.33i	0.262981	+	0.455497i
$273$	−96.5564	−	29.2309i	−0.0214061	−	0.00648035i
$274$	−88.1261	+	152.639i	−0.0194303	+	0.0336542i
$275$		0			0
$276$	62.5331	+	267.511i	0.0136379	+	0.0583415i
$277$	1784.41	+	3090.68i	0.387056	+	0.670401i	0.992052	−	0.125828i	$-0.0401586\pi$
$277$	1784.41	+	3090.68i	0.387056	+	0.670401i	−0.604996	+	0.796228i	$0.706825\pi$
$278$	−564.381			−0.121760
$279$	4081.84	−	2018.64i	0.875891	−	0.433165i
$280$		0			0
$281$	3009.34	+	5212.33i	0.638869	+	1.10655i	0.985681	+	0.168618i	$0.0539306\pi$
$281$	3009.34	+	5212.33i	0.638869	+	1.10655i	−0.346813	+	0.937934i	$0.612736\pi$
$282$	1319.65	−	1237.38i	0.278666	−	0.261293i
$283$	2289.08	−	3964.81i	0.480819	−	0.832803i	−0.518939	−	0.854812i	$-0.673673\pi$
$283$	2289.08	−	3964.81i	0.480819	−	0.832803i	0.999758	+	0.0220082i	$0.00700601\pi$
$284$	−774.492	+	1341.46i	−0.161823	+	0.280285i
$285$		0			0
$286$	49.5448	+	85.8141i	0.0102435	+	0.0177423i
$287$	−7668.55			−1.57721
$288$	2062.85	−	1020.16i	0.422064	−	0.208728i
$289$	−2144.45			−0.436485
$290$		0			0
$291$	−1617.93	−	6921.34i	−0.325926	−	1.39428i
$292$	494.729	−	856.895i	0.0991500	−	0.171733i
$293$	−3239.87	+	5611.61i	−0.645990	+	1.11889i	0.338082	+	0.941117i	$0.390222\pi$
$293$	−3239.87	+	5611.61i	−0.645990	+	1.11889i	−0.984072	+	0.177771i	$0.943111\pi$
$294$	−333.082	−	100.835i	−0.0660739	−	0.0200028i
$295$		0			0
$296$	−10273.6			−2.01738
$297$	1960.78	−	5236.41i	0.383085	−	1.02305i
$298$	2057.67			0.399992
$299$	−13.8255	−	23.9466i	−0.00267409	−	0.00463166i
$300$		0			0
$301$	3451.95	−	5978.95i	0.661020	−	1.14492i
$302$	−2299.49	+	3982.83i	−0.438148	+	0.758895i
$303$	−672.298	−	2876.03i	−0.127467	−	0.545292i
$304$	−1110.66	−	1923.73i	−0.209543	−	0.362938i
$305$		0			0
$306$	−225.009	+	3493.05i	−0.0420356	+	0.652564i
$307$	708.452			0.131705			0.0658526	−	0.997829i	$-0.479023\pi$
$307$	708.452			0.131705			0.0658526	+	0.997829i	$0.479023\pi$
$308$	−739.761	−	1281.30i	−0.136857	−	0.237043i
$309$	−1801.08	+	1688.80i	−0.331586	+	0.310914i
$310$		0			0
$311$	3117.32	−	5399.35i	0.568382	−	0.984467i	−0.428344	−	0.903616i	$-0.640903\pi$
$311$	3117.32	−	5399.35i	0.568382	−	0.984467i	0.996726	−	0.0808511i	$-0.0257638\pi$
$312$	−93.5765	+	87.7427i	−0.0169799	+	0.0159213i
$313$	1315.71	+	2278.87i	0.237598	+	0.411532i	0.960024	−	0.279916i	$-0.0903066\pi$
$313$	1315.71	+	2278.87i	0.237598	+	0.411532i	−0.722427	+	0.691448i	$0.756973\pi$
$314$	−5666.63			−1.01843
$315$		0			0
$316$	−1181.49			−0.210329
$317$	251.267	+	435.207i	0.0445191	+	0.0771094i	0.887426	−	0.460950i	$-0.152491\pi$
$317$	251.267	+	435.207i	0.0445191	+	0.0771094i	−0.842907	+	0.538059i	$0.819158\pi$
$318$	847.663	+	3626.22i	0.149480	+	0.639461i
$319$	5080.56	−	8799.79i	0.891714	−	1.54449i
$320$		0			0
$321$	7224.17	+	2187.00i	1.25612	+	0.380269i
$322$	−649.490	−	1124.95i	−0.112406	−	0.194692i
$323$	−2606.49			−0.449007
$324$	1394.94	+	180.462i	0.239187	+	0.0309434i
$325$		0			0
$326$	−55.3162	−	95.8105i	−0.00939780	−	0.0162775i
$327$	−9762.10	−	2955.32i	−1.65090	−	0.499784i
$328$	−4875.44	+	8444.51i	−0.820736	+	1.42156i
$329$	1359.33	−	2354.44i	0.227789	−	0.394542i
$330$		0			0
$331$	−1543.57	−	2673.54i	−0.256321	−	0.443961i	0.708933	−	0.705276i	$-0.249177\pi$
$331$	−1543.57	−	2673.54i	−0.256321	−	0.443961i	−0.965253	+	0.261316i	$0.915844\pi$
$332$	−155.930			−0.0257765
$333$	−9434.54	−	6288.65i	−1.55258	−	1.03488i
$334$	−2898.87			−0.474908
$335$		0			0
$336$	−3270.28	+	3066.40i	−0.530978	+	0.497875i
$337$	2992.90	−	5183.86i	0.483780	−	0.837931i	−0.516047	−	0.856560i	$-0.672597\pi$
$337$	2992.90	−	5183.86i	0.483780	−	0.837931i	0.999826	+	0.0186295i	$0.00593028\pi$
$338$	−2705.28	+	4685.69i	−0.435349	+	0.754047i
$339$	3708.18	−	3477.00i	0.594103	−	0.557064i
$340$		0			0
$341$	−6721.77			−1.06746
$342$	211.838	−	3288.59i	0.0334938	−	0.519960i
$343$	6076.36			0.956539
$344$	−4389.30	−	7602.49i	−0.687951	−	1.19157i
$345$		0			0
$346$	−1315.81	+	2279.05i	−0.204446	+	0.354110i
$347$	−503.325	+	871.784i	−0.0778671	+	0.134870i	−0.902329	−	0.431047i	$-0.858144\pi$
$347$	−503.325	+	871.784i	−0.0778671	+	0.134870i	0.824462	+	0.565917i	$0.191478\pi$
$348$	2446.43	+	740.618i	0.376846	+	0.114084i
$349$	974.678	+	1688.19i	0.149494	+	0.258931i	0.931040	−	0.364916i	$-0.118902\pi$
$349$	974.678	+	1688.19i	0.149494	+	0.258931i	−0.781547	+	0.623847i	$0.785569\pi$
$350$		0			0
$351$	−139.642	+	23.2967i	−0.0212352	+	0.00354269i
$352$	−3396.99			−0.514376
$353$	−1295.87	−	2244.50i	−0.195388	−	0.338422i	0.751640	−	0.659574i	$-0.229263\pi$
$353$	−1295.87	−	2244.50i	−0.195388	−	0.338422i	−0.947028	+	0.321152i	$0.895930\pi$
$354$	−352.062	−	106.581i	−0.0528584	−	0.0160020i
$355$		0			0
$356$	23.1627	−	40.1189i	0.00344837	−	0.00597275i
$357$	1197.38	+	5122.28i	0.177513	+	0.759383i
$358$	−3424.33	−	5931.11i	−0.505534	−	0.875611i
$359$	−605.954			−0.0890837			−0.0445418	−	0.999008i	$-0.514183\pi$
$359$	−605.954			−0.0890837			−0.0445418	+	0.999008i	$0.514183\pi$
$360$		0			0
$361$	−4405.08			−0.642233
$362$	−4396.32	−	7614.64i	−0.638302	−	1.10557i
$363$	−975.706	+	914.877i	−0.141078	+	0.132283i
$364$	−18.7302	+	32.4417i	−0.00269706	+	0.00467145i
$365$		0			0
$366$	6843.09	−	6416.46i	0.977306	−	0.916377i
$367$	4880.13	+	8452.63i	0.694117	+	1.20225i	0.970478	+	0.241191i	$0.0775381\pi$
$367$	4880.13	+	8452.63i	0.694117	+	1.20225i	−0.276361	+	0.961054i	$0.589129\pi$
$368$	−1228.75			−0.174056
$369$	−9646.25	+	4770.48i	−1.36088	+	0.673011i
$370$		0			0
$371$	2798.27	+	4846.75i	0.391587	+	0.678249i
$372$	−384.887	−	1646.51i	−0.0536436	−	0.229482i
$373$	3911.81	−	6775.45i	0.543018	−	0.940535i	−0.455711	−	0.890128i	$-0.650615\pi$
$373$	3911.81	−	6775.45i	0.543018	−	0.940535i	0.998729	−	0.0504071i	$-0.0160519\pi$
$374$	2583.40	−	4474.58i	0.357178	−	0.618650i
$375$		0			0
$376$	−1728.45	−	2993.77i	−0.237069	−	0.410616i
$377$	−257.272			−0.0351464
$378$	−6560.05	+	1094.42i	−0.892625	+	0.148918i
$379$	2731.46			0.370200			0.185100	−	0.982720i	$-0.440739\pi$
$379$	2731.46			0.370200			0.185100	+	0.982720i	$0.440739\pi$
$380$		0			0
$381$	4306.54	+	1303.74i	0.579084	+	0.175308i
$382$	−4112.93	+	7123.80i	−0.550879	+	0.954150i
$383$	6299.93	−	10911.8i	0.840500	−	1.45579i	−0.0489732	−	0.998800i	$-0.515595\pi$
$383$	6299.93	−	10911.8i	0.840500	−	1.45579i	0.889473	−	0.456988i	$-0.151072\pi$
$384$	850.893	+	3640.04i	0.113078	+	0.483737i
$385$		0			0
$386$	4782.00			0.630563
$387$	622.795	−	9668.32i	0.0818048	−	1.26994i
$388$	−2639.33			−0.345339
$389$	2471.73	+	4281.16i	0.322163	+	0.558003i	0.980934	−	0.194340i	$-0.0622566\pi$
$389$	2471.73	+	4281.16i	0.322163	+	0.558003i	−0.658771	+	0.752344i	$0.728923\pi$
$390$		0			0
$391$	−720.902	+	1248.64i	−0.0932419	+	0.161500i
$392$	−332.511	+	575.925i	−0.0428427	+	0.0742057i
$393$	5568.06	−	5220.93i	0.714686	−	0.670130i
$394$	1275.96	+	2210.03i	0.163152	+	0.282588i
$395$		0			0
$396$	−1727.62	−	1151.56i	−0.219233	−	0.146131i
$397$	7067.06			0.893415			0.446707	−	0.894680i	$-0.352597\pi$
$397$	7067.06			0.893415			0.446707	+	0.894680i	$0.352597\pi$
$398$	1928.61	+	3340.46i	0.242896	+	0.420708i
$399$	−1127.29	−	4822.45i	−0.141442	−	0.605074i
$400$		0			0
$401$	458.792	−	794.651i	0.0571346	−	0.0989600i	−0.836043	−	0.548663i	$-0.815137\pi$
$401$	458.792	−	794.651i	0.0571346	−	0.0989600i	0.893178	+	0.449703i	$0.148470\pi$
$402$	2163.28	+	654.898i	0.268394	+	0.0812521i
$403$	85.0952	+	147.389i	0.0105183	+	0.0182183i
$404$	−1096.72			−0.135059
$405$		0			0
$406$	−12086.0			−1.47738
$407$	8368.28	+	14494.3i	1.01917	+	1.76525i
$408$	6401.86	+	1938.06i	0.776812	+	0.235167i
$409$	−7367.76	+	12761.3i	−0.890739	+	1.54281i	−0.0517481	+	0.998660i	$0.516479\pi$
$409$	−7367.76	+	12761.3i	−0.890739	+	1.54281i	−0.838991	+	0.544145i	$0.816854\pi$
$410$		0			0
$411$	84.6093	+	361.951i	0.0101544	+	0.0434397i
$412$	458.396	+	793.965i	0.0548144	+	0.0949414i
$413$	−552.805			−0.0658638
$414$	−1516.80	−	1011.04i	−0.180065	−	0.120023i
$415$		0			0
$416$	43.0047	+	74.4863i	0.00506846	+	0.00877883i
$417$	−868.268	+	814.137i	−0.101965	+	0.0956078i
$418$	−2432.18	+	4212.66i	−0.284598	+	0.492938i
$419$	4627.46	−	8014.99i	0.539537	−	0.934506i	−0.459392	−	0.888234i	$-0.651932\pi$
$419$	4627.46	−	8014.99i	0.539537	−	0.934506i	0.998929	−	0.0462722i	$-0.0147342\pi$
$420$		0			0
$421$	5100.98	+	8835.15i	0.590514	+	1.02280i	0.994163	+	0.107886i	$0.0344082\pi$
$421$	5100.98	+	8835.15i	0.590514	+	1.02280i	−0.403649	+	0.914914i	$0.632258\pi$
$422$	−8340.80			−0.962142
$423$	245.249	−	3807.26i	0.0281901	−	0.437625i
$424$	7116.24			0.815083
$425$		0			0
$426$	−2339.52	−	10008.2i	−0.266080	−	1.13827i
$427$	7048.89	−	12209.0i	0.798875	−	1.38369i
$428$	1401.36	−	2427.23i	0.158265	−	0.274122i
$429$	200.011	+	60.5501i	0.0225096	+	0.00681443i
$430$		0			0
$431$	8057.20			0.900468			0.450234	−	0.892911i	$-0.351341\pi$
$431$	8057.20			0.900468			0.450234	+	0.892911i	$0.351341\pi$
$432$	−2206.13	+	5891.61i	−0.245700	+	0.656158i
$433$	−4306.26			−0.477935			−0.238967	−	0.971028i	$-0.576809\pi$
$433$	−4306.26			−0.477935			−0.238967	+	0.971028i	$0.576809\pi$
$434$	3997.56	+	6923.98i	0.442141	+	0.765810i
$435$		0			0
$436$	−1893.67	+	3279.94i	−0.208006	+	0.360276i
$437$	678.704	−	1175.55i	0.0742948	−	0.128682i
$438$	1494.43	+	6393.05i	0.163029	+	0.697424i
$439$	2360.90	+	4089.19i	0.256673	+	0.444571i	0.965349	−	0.260964i	$-0.0840403\pi$
$439$	2360.90	+	4089.19i	0.256673	+	0.444571i	−0.708676	+	0.705535i	$0.750707\pi$
$440$		0			0
$441$	−657.885	+	325.352i	−0.0710382	+	0.0351314i
$442$	−130.820			−0.0140779
$443$	7677.19	+	13297.3i	0.823373	+	1.42612i	0.903157	+	0.429311i	$0.141244\pi$
$443$	7677.19	+	13297.3i	0.823373	+	1.42612i	−0.0797840	+	0.996812i	$0.525423\pi$
$444$	−3071.23	+	2879.76i	−0.328276	+	0.307810i
$445$		0			0
$446$	−2914.17	+	5047.50i	−0.309395	+	0.535888i
$447$	3165.60	−	2968.25i	0.334962	−	0.314079i
$448$	5471.29	+	9476.56i	0.576996	+	0.999387i
$449$	5448.64			0.572688			0.286344	−	0.958127i	$-0.407560\pi$
$449$	5448.64			0.572688			0.286344	+	0.958127i	$0.407560\pi$
$450$		0			0
$451$	15885.0			1.65852
$452$	−943.774	−	1634.66i	−0.0982111	−	0.170107i
$453$	2207.73	+	9444.45i	0.228980	+	0.979556i
$454$	1202.64	−	2083.04i	0.124323	−	0.215334i
$455$		0			0
$456$	−6027.13	−	1824.62i	−0.618961	−	0.187380i
$457$	−26.3653	−	45.6661i	−0.00269873	−	0.00467433i	0.864673	−	0.502335i	$-0.167526\pi$
$457$	−26.3653	−	45.6661i	−0.00269873	−	0.00467433i	−0.867372	+	0.497661i	$0.834192\pi$
$458$	−3930.53			−0.401008
$459$	4692.67	+	5698.44i	0.477201	+	0.579478i
$460$		0			0
$461$	1583.51	+	2742.72i	0.159982	+	0.277096i	0.934862	−	0.355012i	$-0.115523\pi$
$461$	1583.51	+	2742.72i	0.159982	+	0.277096i	−0.774880	+	0.632108i	$0.782190\pi$
$462$	9396.03	+	2844.49i	0.946196	+	0.286446i
$463$	6546.21	−	11338.4i	0.657081	−	1.13810i	−0.324287	−	0.945959i	$-0.605124\pi$
$463$	6546.21	−	11338.4i	0.657081	−	1.13810i	0.981368	−	0.192138i	$-0.0615422\pi$
$464$	−5716.26	+	9900.86i	−0.571920	+	0.990594i
$465$		0			0
$466$	1162.41	+	2013.35i	0.115553	+	0.200143i
$467$	13225.4			1.31049			0.655246	−	0.755416i	$-0.272565\pi$
$467$	13225.4			1.31049			0.655246	+	0.755416i	$0.272565\pi$
$468$	−3.37928	+	52.4601i	−0.000333776	+	0.00518156i
$469$	3396.77			0.334431
$470$		0			0
$471$	−8717.79	+	8174.29i	−0.852854	+	0.799684i
$472$	−351.458	+	608.743i	−0.0342736	+	0.0593637i
$473$	−7150.52	+	12385.1i	−0.695098	+	1.20394i
$474$	5718.84	−	5362.31i	0.554167	−	0.519618i
$475$		0			0
$476$	1953.29			0.188086
$477$	6535.02	+	4355.96i	0.627291	+	0.418125i
$478$	−6729.99			−0.643981
$479$	4279.30	+	7411.96i	0.408196	+	0.707017i	0.994688	−	0.102939i	$-0.0328246\pi$
$479$	4279.30	+	7411.96i	0.408196	+	0.707017i	−0.586491	+	0.809955i	$0.699491\pi$
$480$		0			0
$481$	211.879	−	366.985i	0.0200849	−	0.0347881i
$482$	4209.77	−	7291.54i	0.397822	−	0.689047i
$483$	−2621.98	−	793.761i	−0.247006	−	0.0747772i
$484$	248.328	+	430.117i	0.0233216	+	0.0403942i
$485$		0			0
$486$	−7571.05	+	5457.56i	−0.706646	+	0.509383i
$487$	−19531.3			−1.81735			−0.908674	−	0.417506i	$-0.862904\pi$
$487$	−19531.3			−1.81735			−0.908674	+	0.417506i	$0.862904\pi$
$488$	−8962.96	−	15524.3i	−0.831423	−	1.44007i
$489$	−223.310	−	67.6036i	−0.0206512	−	0.00625182i
$490$		0			0
$491$	9744.11	−	16877.3i	0.895612	−	1.55125i	0.0625676	−	0.998041i	$-0.480071\pi$
$491$	9744.11	−	16877.3i	0.895612	−	1.55125i	0.833045	−	0.553206i	$-0.186596\pi$
$492$	909.568	+	3891.04i	0.0833465	+	0.356548i
$493$	6707.43	+	11617.6i	0.612754	+	1.06132i
$494$	123.162			0.0112173
$495$		0			0
$496$	7562.83			0.684640
$497$	−7723.12	−	13376.8i	−0.697041	−	1.20731i
$498$	754.759	−	707.705i	0.0679148	−	0.0636807i
$499$	169.765	−	294.042i	0.0152299	−	0.0263790i	−0.858310	−	0.513132i	$-0.828485\pi$
$499$	169.765	−	294.042i	0.0152299	−	0.0263790i	0.873540	+	0.486753i	$0.161819\pi$
$500$		0			0
$501$	−4459.75	+	4181.71i	−0.397698	+	0.372904i
$502$	−3898.42	−	6752.26i	−0.346604	−	0.600335i
$503$	5550.25			0.491995			0.245998	−	0.969270i	$-0.420884\pi$
$503$	5550.25			0.491995			0.245998	+	0.969270i	$0.420884\pi$
$504$	−816.970	+	12682.7i	−0.0722039	+	1.12090i
$505$		0			0
$506$	1345.38	+	2330.27i	0.118201	+	0.204729i
$507$	2597.33	+	11111.1i	0.227517	+	0.973298i
$508$	835.393	−	1446.94i	0.0729617	−	0.126373i
$509$	−2824.49	+	4892.17i	−0.245960	+	0.426015i	−0.962401	−	0.271633i	$-0.912436\pi$
$509$	−2824.49	+	4892.17i	−0.245960	+	0.426015i	0.716441	+	0.697647i	$0.245770\pi$
$510$		0			0
$511$	4933.36	+	8544.83i	0.427082	+	0.739728i
$512$	12598.3			1.08745
$513$	−4417.99	−	5364.88i	−0.380232	−	0.461726i
$514$	−13673.0			−1.17332
$515$		0			0
$516$	−3443.18	−	1042.37i	−0.293755	−	0.0889294i
$517$	−2815.78	+	4877.08i	−0.239532	+	0.414882i
$518$	9953.54	−	17240.0i	0.844273	−	1.46232i
$519$	1263.30	+	5404.27i	0.106845	+	0.457074i
$520$		0			0
$521$	−11159.0			−0.938359			−0.469180	−	0.883103i	$-0.655450\pi$
$521$	−11159.0			−0.938359			−0.469180	+	0.883103i	$0.655450\pi$
$522$	−15203.0	+	7518.50i	−1.27474	+	0.630414i
$523$	−9476.61			−0.792320			−0.396160	−	0.918182i	$-0.629657\pi$
$523$	−9476.61			−0.792320			−0.396160	+	0.918182i	$0.629657\pi$
$524$	−1417.13	−	2454.55i	−0.118145	−	0.204633i
$525$		0			0
$526$	−5097.26	+	8828.72i	−0.422531	+	0.731845i
$527$	4437.10	−	7685.27i	0.366761	−	0.635248i
$528$	6774.21	−	6351.88i	0.558351	−	0.523542i
$529$	5708.07	+	9886.67i	0.469144	+	0.812580i
$530$		0			0
$531$	−695.373	+	343.891i	−0.0568298	+	0.0281047i
$532$	−1838.95			−0.149866
$533$	−201.098	−	348.312i	−0.0163424	−	0.0283059i
$534$	69.9678	+	299.316i	0.00567004	+	0.0242559i
$535$		0			0
$536$	2159.57	−	3740.48i	0.174028	−	0.301426i
$537$	−13823.9	−	4184.97i	−1.11089	−	0.336303i
$538$	−1264.86	−	2190.81i	−0.101361	−	0.175562i
$539$	1083.37			0.0865754
$540$		0			0
$541$	8285.40			0.658442			0.329221	−	0.944253i	$-0.393214\pi$
$541$	8285.40			0.658442			0.329221	+	0.944253i	$0.393214\pi$
$542$	4189.35	+	7256.17i	0.332008	+	0.575054i
$543$	−17747.8	−	5372.87i	−1.40264	−	0.424626i
$544$	2242.38	−	3883.92i	0.176730	−	0.306106i
$545$		0			0
$546$	−56.5787	−	242.038i	−0.00443469	−	0.0189712i
$547$	−3459.15	−	5991.42i	−0.270389	−	0.468327i	0.698573	−	0.715539i	$-0.253819\pi$
$547$	−3459.15	−	5991.42i	−0.270389	−	0.468327i	−0.968961	+	0.247212i	$0.920486\pi$
$548$	138.023			0.0107593
$549$	1271.75	−	19742.7i	0.0988651	−	1.53479i
$550$		0			0
$551$	−6314.82	−	10937.6i	−0.488240	−	0.845657i
$552$	−2541.06	+	2382.64i	−0.195932	+	0.183717i
$553$	5890.83	−	10203.2i	0.452990	−	0.784602i
$554$	−4396.51	+	7614.97i	−0.337165	+	0.583988i
$555$		0			0
$556$	220.984	+	382.755i	0.0168558	+	0.0291950i
$557$	−15622.7			−1.18843			−0.594216	−	0.804305i	$-0.702538\pi$
$557$	−15622.7			−1.18843			−0.594216	+	0.804305i	$0.702538\pi$
$558$	9335.82	+	6222.84i	0.708274	+	0.472104i
$559$	362.092			0.0273969
$560$		0			0
$561$	−2480.31	−	10610.5i	−0.186664	−	0.798532i
$562$	−7414.56	+	12842.4i	−0.556520	+	0.963921i
$563$	−4064.65	+	7040.18i	−0.304271	+	0.527013i	−0.977099	−	0.212786i	$-0.931746\pi$
$563$	−4064.65	+	7040.18i	−0.304271	+	0.527013i	0.672828	+	0.739799i	$0.265080\pi$
$564$	−1355.88	−	410.471i	−0.101228	−	0.0306453i
$565$		0			0
$566$	11279.9			0.837686
$567$	−8513.52	+	11146.8i	−0.630572	+	0.825609i
$568$	−19640.6			−1.45088
$569$	−4087.84	−	7080.34i	−0.301179	−	0.521658i	0.675224	−	0.737613i	$-0.264047\pi$
$569$	−4087.84	−	7080.34i	−0.301179	−	0.521658i	−0.976403	+	0.215955i	$0.930714\pi$
$570$		0			0
$571$	−3939.42	+	6823.27i	−0.288721	+	0.500079i	−0.973505	−	0.228667i	$-0.926563\pi$
$571$	−3939.42	+	6823.27i	−0.288721	+	0.500079i	0.684784	+	0.728746i	$0.259897\pi$
$572$	38.7986	−	67.2011i	0.00283610	−	0.00491227i
$573$	3948.79	+	16892.6i	0.287894	+	1.23158i
$574$	−9447.07	−	16362.8i	−0.686957	−	1.18984i
$575$		0			0
$576$	12777.5	+	8516.95i	0.924302	+	0.616099i
$577$	−16673.4			−1.20299			−0.601493	−	0.798878i	$-0.705427\pi$
$577$	−16673.4			−1.20299			−0.601493	+	0.798878i	$0.705427\pi$
$578$	−2641.80	−	4575.74i	−0.190112	−	0.329283i
$579$	7356.83	−	6898.18i	0.528047	−	0.495127i
$580$		0			0
$581$	777.458	−	1346.60i	0.0555153	−	0.0961553i
$582$	12775.3	−	11978.8i	0.909884	−	0.853159i
$583$	−5796.46	−	10039.8i	−0.411775	−	0.713215i
$584$	12546.0			0.888965
$585$		0			0
$586$	−15965.1			−1.12545
$587$	−1506.09	−	2608.63i	−0.105900	−	0.183424i	0.808206	−	0.588900i	$-0.200439\pi$
$587$	−1506.09	−	2608.63i	−0.105900	−	0.183424i	−0.914105	+	0.405477i	$0.867106\pi$
$588$	62.0335	+	265.374i	0.00435071	+	0.0186119i
$589$	−4177.37	+	7235.42i	−0.292234	+	0.506164i
$590$		0			0
$591$	5151.03	+	1559.39i	0.358519	+	0.108536i
$592$	−9415.37	−	16307.9i	−0.653664	−	1.13218i
$593$	7922.71			0.548645			0.274323	−	0.961638i	$-0.411546\pi$
$593$	7922.71			0.548645			0.274323	+	0.961638i	$0.411546\pi$
$594$	13588.8	−	2267.03i	0.938642	−	0.156595i
$595$		0			0
$596$	−805.682	−	1395.48i	−0.0553725	−	0.0959080i
$597$	7785.77	+	2357.02i	0.533753	+	0.161585i
$598$	34.0641	−	59.0007i	0.00232940	−	0.00403465i
$599$	11289.3	−	19553.6i	0.770061	−	1.33378i	−0.167468	−	0.985878i	$-0.553559\pi$
$599$	11289.3	−	19553.6i	0.770061	−	1.33378i	0.937529	−	0.347907i	$-0.113108\pi$
$600$		0			0
$601$	−5309.35	−	9196.07i	−0.360354	−	0.624152i	0.627665	−	0.778484i	$-0.284011\pi$
$601$	−5309.35	−	9196.07i	−0.360354	−	0.624152i	−0.988019	+	0.154332i	$0.950678\pi$
$602$	17010.2			1.15163
$603$	4272.79	−	2113.07i	0.288560	−	0.142705i
$604$	3601.47			0.242619
$605$		0			0
$606$	5308.52	−	4977.57i	0.355848	−	0.333663i
$607$	6795.28	−	11769.8i	0.454385	−	0.787018i	−0.544267	−	0.838912i	$-0.683192\pi$
$607$	6795.28	−	11769.8i	0.454385	−	0.787018i	0.998653	+	0.0518935i	$0.0165256\pi$
$608$	−2111.12	+	3656.58i	−0.140818	+	0.243904i
$609$	−18593.6	+	17434.4i	−1.23719	+	1.16006i
$610$		0			0
$611$	142.587			0.00944102
$612$	2457.04	−	1215.11i	0.162288	−	0.0802580i
$613$	−5457.57			−0.359591			−0.179796	−	0.983704i	$-0.557544\pi$
$613$	−5457.57			−0.359591			−0.179796	+	0.983704i	$0.557544\pi$
$614$	872.760	+	1511.66i	0.0573643	+	0.0993580i
$615$		0			0
$616$	9379.91	−	16246.5i	0.613518	−	1.06264i
$617$	2986.05	−	5171.99i	0.194836	−	0.337466i	−0.752011	−	0.659151i	$-0.770916\pi$
$617$	2986.05	−	5171.99i	0.194836	−	0.337466i	0.946847	+	0.321685i	$0.104249\pi$
$618$	−5822.28	−	1762.60i	−0.378975	−	0.114729i
$619$	419.816	+	727.143i	0.0272598	+	0.0472154i	0.879333	−	0.476206i	$-0.157989\pi$
$619$	419.816	+	727.143i	0.0272598	+	0.0472154i	−0.852074	+	0.523422i	$0.824655\pi$
$620$		0			0
$621$	−3791.97	+	632.617i	−0.245034	+	0.0408793i
$622$	15361.2			0.990238
$623$	230.975	+	400.060i	0.0148536	+	0.0257272i
$624$	−225.038	−	68.1265i	−0.0144370	−	0.00437058i
$625$		0			0
$626$	−3241.70	+	5614.79i	−0.206972	+	0.358486i
$627$	2335.12	+	9989.43i	0.148733	+	0.636267i
$628$	2218.77	+	3843.03i	0.140985	+	0.244194i
$629$	−22095.9			−1.40067
$630$		0			0
$631$	−13699.4			−0.864284			−0.432142	−	0.901806i	$-0.642242\pi$
$631$	−13699.4			−0.864284			−0.432142	+	0.901806i	$0.642242\pi$
$632$	−7490.44	−	12973.8i	−0.471446	−	0.816568i
$633$	−12831.8	+	12031.9i	−0.805718	+	0.755487i
$634$	−619.084	+	1072.29i	−0.0387807	+	0.0671702i
$635$		0			0
$636$	2127.35	−	1994.72i	0.132634	−	0.124365i
$637$	−13.7151	−	23.7552i	−0.000853080	−	0.00147758i
$638$	25035.5			1.55355
$639$	−18036.4	−	12022.3i	−1.11660	−	0.744279i
$640$		0			0
$641$	3969.68	+	6875.69i	0.244607	+	0.423671i	0.962021	−	0.272975i	$-0.0880078\pi$
$641$	3969.68	+	6875.69i	0.244607	+	0.423671i	−0.717414	+	0.696647i	$0.754674\pi$
$642$	4233.11	+	18108.8i	0.260230	+	1.11324i
$643$	−3817.98	+	6612.93i	−0.234162	+	0.405581i	−0.959029	−	0.283308i	$-0.908568\pi$
$643$	−3817.98	+	6612.93i	−0.234162	+	0.405581i	0.724867	+	0.688889i	$0.241901\pi$
$644$	−508.617	+	880.950i	−0.0311216	+	0.0539042i
$645$		0			0
$646$	−3211.00	−	5561.62i	−0.195565	−	0.338729i
$647$	22084.3			1.34192			0.670962	−	0.741491i	$-0.265881\pi$
$647$	22084.3			1.34192			0.670962	+	0.741491i	$0.265881\pi$
$648$	6862.04	+	16461.8i	0.415997	+	0.997963i
$649$	1145.10			0.0692593
$650$		0			0
$651$	16138.1	+	4885.54i	0.971583	+	0.294131i
$652$	−43.3182	+	75.0294i	−0.00260195	+	0.00450671i
$653$	3318.99	−	5748.65i	0.198900	−	0.344506i	−0.749272	−	0.662263i	$-0.769596\pi$
$653$	3318.99	−	5748.65i	0.198900	−	0.344506i	0.948172	+	0.317757i	$0.102930\pi$
$654$	−5720.24	−	24470.7i	−0.342017	−	1.46312i
$655$		0			0
$656$	−17872.6			−1.06373
$657$	11521.3	+	7679.57i	0.684151	+	0.456025i
$658$	6698.39			0.396855
$659$	−11906.1	−	20622.0i	−0.703789	−	1.21900i	−0.967127	−	0.254295i	$-0.918157\pi$
$659$	−11906.1	−	20622.0i	−0.703789	−	1.21900i	0.263338	−	0.964704i	$-0.415177\pi$
$660$		0			0
$661$	499.912	−	865.873i	0.0294165	−	0.0509509i	−0.850942	−	0.525259i	$-0.823968\pi$
$661$	499.912	−	865.873i	0.0294165	−	0.0509509i	0.880359	+	0.474308i	$0.157302\pi$
$662$	3803.12	−	6587.20i	0.223282	−	0.386735i
$663$	−201.258	+	188.711i	−0.0117892	+	0.0110542i
$664$	−988.571	−	1712.26i	−0.0577771	−	0.100073i
$665$		0			0
$666$	1795.80	−	27878.2i	0.104483	−	1.62201i
$667$	−6986.19			−0.405557
$668$	1135.06	+	1965.97i	0.0657435	+	0.113871i
$669$	2797.88	+	11969.1i	0.161692	+	0.691705i
$670$		0			0
$671$	−14601.4	+	25290.3i	−0.840059	+	1.45502i
$672$	8155.72	+	2469.01i	0.468175	+	0.141732i
$673$	5311.03	+	9198.98i	0.304198	+	0.526886i	0.977082	−	0.212861i	$-0.0682782\pi$
$673$	5311.03	+	9198.98i	0.304198	+	0.526886i	−0.672884	+	0.739748i	$0.734945\pi$
$674$	14748.1			0.842843
$675$		0			0
$676$	4237.02			0.241069
$677$	12453.9	+	21570.8i	0.707005	+	1.22457i	0.965963	+	0.258680i	$0.0832874\pi$
$677$	12453.9	+	21570.8i	0.707005	+	1.22457i	−0.258959	+	0.965888i	$0.583379\pi$
$678$	11987.3	+	3628.95i	0.679010	+	0.205559i
$679$	13159.5	−	22792.9i	0.743763	−	1.28823i
$680$		0			0
$681$	−1154.65	−	4939.48i	−0.0649725	−	0.277946i
$682$	−8280.72	−	14342.6i	−0.464934	−	0.805289i
$683$	−17115.6			−0.958874			−0.479437	−	0.877576i	$-0.659159\pi$
$683$	−17115.6			−0.958874			−0.479437	+	0.877576i	$0.659159\pi$
$684$	−2313.22	+	1143.98i	−0.129310	+	0.0639493i
$685$		0			0
$686$	7485.62	+	12965.5i	0.416622	+	0.721610i
$687$	−6046.89	+	5669.91i	−0.335813	+	0.314877i
$688$	8045.23	−	13934.7i	0.445816	−	0.772176i
$689$	−146.762	+	254.199i	−0.00811493	+	0.0140555i
$690$		0			0
$691$	−14449.9	−	25028.0i	−0.795514	−	1.37787i	−0.922512	−	0.385967i	$-0.873868\pi$
$691$	−14449.9	−	25028.0i	−0.795514	−	1.37787i	0.126999	−	0.991903i	$-0.459466\pi$
$692$	2060.82			0.113209
$693$	18558.5	−	9177.96i	1.01729	−	0.503091i
$694$	−2480.23			−0.135660
$695$		0			0
$696$	7377.30	+	31559.4i	0.401775	+	1.71876i
$697$	−10485.8	+	18161.9i	−0.569839	+	0.986989i
$698$	−2401.46	+	4159.45i	−0.130224	+	0.225555i
$699$	4692.62	+	1420.61i	0.253921	+	0.0768706i
$700$		0			0
$701$	576.680			0.0310712			0.0155356	−	0.999879i	$-0.495055\pi$
$701$	576.680			0.0310712			0.0155356	+	0.999879i	$0.495055\pi$
$702$	−221.738	−	269.263i	−0.0119216	−	0.0144767i
$703$	20802.5			1.11605
$704$	−11333.5	−	19630.2i	−0.606742	−	1.05091i
$705$		0			0
$706$	3192.82	−	5530.12i	0.170203	−	0.294800i
$707$	5468.17	−	9471.15i	0.290879	−	0.503818i
$708$	65.5683	+	280.495i	0.00348052	+	0.0148893i
$709$	−2858.78	−	4951.55i	−0.151430	−	0.262284i	0.780324	−	0.625376i	$-0.215054\pi$
$709$	−2858.78	−	4951.55i	−0.151430	−	0.262284i	−0.931753	+	0.363092i	$0.881721\pi$
$710$		0			0
$711$	1062.81	−	16499.2i	0.0560600	−	0.870279i
$712$	587.389			0.0309176
$713$	2310.75	+	4002.33i	0.121372	+	0.210222i
$714$	−9454.62	+	8865.18i	−0.495560	+	0.464665i
$715$		0			0
$716$	−2681.60	+	4644.66i	−0.139966	+	0.242429i
$717$	−10353.7	+	9708.22i	−0.539284	+	0.505663i
$718$	−746.490	−	1292.96i	−0.0388005	−	0.0672044i
$719$	−14799.9			−0.767655			−0.383827	−	0.923405i	$-0.625394\pi$
$719$	−14799.9			−0.767655			−0.383827	+	0.923405i	$0.625394\pi$
$720$		0			0
$721$	−9142.12			−0.472219
$722$	−5426.72	−	9399.36i	−0.279725	−	0.484498i
$723$	−4041.78	−	17290.3i	−0.207905	−	0.889398i
$724$	−3442.76	+	5963.04i	−0.176725	+	0.306098i
$725$		0			0
$726$	−3154.12	−	954.860i	−0.161240	−	0.0488129i
$727$	3205.20	+	5551.57i	0.163513	+	0.283214i	0.936126	−	0.351664i	$-0.114384\pi$
$727$	3205.20	+	5551.57i	0.163513	+	0.283214i	−0.772613	+	0.634877i	$0.781051\pi$
$728$	−474.985			−0.0241815
$729$	−3774.92	+	19317.6i	−0.191786	+	0.981437i
$730$		0			0
$731$	−9440.23	−	16351.0i	−0.477646	−	0.827308i
$732$	−7030.97	−	2128.51i	−0.355017	−	0.107476i
$733$	−8934.62	+	15475.2i	−0.450215	+	0.779796i	−0.998399	−	0.0565621i	$-0.981986\pi$
$733$	−8934.62	+	15475.2i	−0.450215	+	0.779796i	0.548184	+	0.836358i	$0.315319\pi$
$734$	−12023.9	+	20826.0i	−0.604647	+	1.04728i
$735$		0			0
$736$	1167.79	+	2022.66i	0.0584853	+	0.101299i
$737$	−7036.21			−0.351672
$738$	−22062.5	−	14705.9i	−1.10045	−	0.733511i
$739$	11099.7			0.552516			0.276258	−	0.961084i	$-0.410906\pi$
$739$	11099.7			0.552516			0.276258	+	0.961084i	$0.410906\pi$
$740$		0			0
$741$	189.478	−	177.665i	0.00939358	−	0.00880795i
$742$	−6894.52	+	11941.7i	−0.341113	+	0.590825i
$743$	5428.81	−	9402.97i	0.268053	−	0.464282i	−0.700306	−	0.713843i	$-0.746953\pi$
$743$	5428.81	−	9402.97i	0.268053	−	0.464282i	0.968359	+	0.249561i	$0.0802863\pi$
$744$	15640.0	−	14665.0i	0.770687	−	0.722639i
$745$		0			0
$746$	19276.2			0.946049
$747$	140.268	−	2177.53i	0.00687032	−	0.106655i
$748$	−4046.13			−0.197782
$749$	13974.1	+	24203.9i	0.681715	+	1.18076i
$750$		0			0
$751$	16117.0	−	27915.4i	0.783111	−	1.35639i	−0.147010	−	0.989135i	$-0.546965\pi$
$751$	16117.0	−	27915.4i	0.783111	−	1.35639i	0.930121	−	0.367253i	$-0.119702\pi$
$752$	3168.11	−	5487.33i	0.153629	−	0.266093i
$753$	−15737.8	−	4764.38i	−0.761645	−	0.230576i
$754$	−316.940	−	548.956i	−0.0153081	−	0.0265143i
$755$		0			0
$756$	3310.81	+	4020.41i	0.159276	+	0.193414i
$757$	9410.28			0.451813			0.225906	−	0.974149i	$-0.427466\pi$
$757$	9410.28			0.451813			0.225906	+	0.974149i	$0.427466\pi$
$758$	3364.96	+	5828.27i	0.161241	+	0.279278i
$759$	5431.27	+	1644.23i	0.259740	+	0.0786321i
$760$		0			0
$761$	−17383.6	+	30109.2i	−0.828060	+	1.43424i	0.0714983	+	0.997441i	$0.477222\pi$
$761$	−17383.6	+	30109.2i	−0.828060	+	1.43424i	−0.899558	+	0.436801i	$0.856111\pi$
$762$	2523.48	+	10795.2i	0.119969	+	0.513215i
$763$	−18883.4	−	32707.0i	−0.895971	−	1.55187i
$764$	6441.68			0.305042
$765$		0			0
$766$	31044.2			1.46432
$767$	−14.4966	−	25.1089i	−0.000682454	−	0.00118204i
$768$	10527.6	−	9871.30i	0.494640	−	0.463802i
$769$	14543.2	−	25189.6i	0.681980	−	1.18122i	−0.292396	−	0.956297i	$-0.594452\pi$
$769$	14543.2	−	25189.6i	0.681980	−	1.18122i	0.974376	−	0.224927i	$-0.0722143\pi$
$770$		0			0
$771$	−21035.1	+	19723.7i	−0.982568	+	0.921311i
$772$	−1872.40	−	3243.08i	−0.0872915	−	0.151193i
$773$	2942.77			0.136927			0.0684633	−	0.997654i	$-0.478190\pi$
$773$	2942.77			0.136927			0.0684633	+	0.997654i	$0.478190\pi$
$774$	21397.1	−	10581.7i	0.993672	−	0.491412i
$775$		0			0
$776$	−16732.9	−	28982.2i	−0.774065	−	1.34072i
$777$	−9556.33	−	40881.1i	−0.441225	−	1.88752i
$778$	−6089.97	+	10548.1i	−0.280637	+	0.486078i
$779$	9872.01	−	17098.8i	0.454045	−	0.786430i
$780$		0			0
$781$	15998.0	+	27709.4i	0.732975	+	1.26955i
$782$	−3552.39			−0.162446
$783$	−12543.2	+	33497.5i	−0.572488	+	1.52887i
$784$	−1218.93			−0.0555270
$785$		0			0
$786$	17999.6	+	5449.10i	0.816827	+	0.247281i
$787$	16914.6	−	29296.9i	0.766124	−	1.32697i	−0.173527	−	0.984829i	$-0.555516\pi$
$787$	16914.6	−	29296.9i	0.766124	−	1.32697i	0.939650	−	0.342136i	$-0.111150\pi$
$788$	999.207	−	1730.68i	0.0451717	−	0.0782397i
$789$	4893.85	+	20935.4i	0.220818	+	0.944640i
$790$		0			0
$791$	18822.4			0.846076
$792$	1692.31	−	26271.5i	0.0759262	−	1.17868i
$793$	739.392			0.0331105
$794$	8706.09	+	15079.4i	0.389128	+	0.673989i
$795$		0			0
$796$	1510.30	−	2615.92i	0.0672502	−	0.116481i
$797$	−11452.3	+	19836.0i	−0.508987	+	0.881591i	0.490959	+	0.871183i	$0.336647\pi$
$797$	−11452.3	+	19836.0i	−0.508987	+	0.881591i	−0.999946	+	0.0104085i	$0.996687\pi$
$798$	8901.20	−	8346.27i	0.394861	−	0.370244i
$799$	−3717.44	−	6438.80i	−0.164598	−	0.285092i
$800$		0			0
$801$	539.413	+	359.549i	0.0237943	+	0.0158602i
$802$	2260.79			0.0995402
$803$	−10219.2	−	17700.1i	−0.449099	−	0.777863i
$804$	−402.891	−	1723.53i	−0.0176727	−	0.0756023i
$805$		0			0
$806$	−209.662	+	363.145i	−0.00916256	+	0.0158700i
$807$	−5106.23	−	1545.83i	−0.222736	−	0.0674297i
$808$	−6953.01	−	12043.0i	−0.302730	−	0.524344i
$809$	−30665.7			−1.33269			−0.666347	−	0.745642i	$-0.732143\pi$
$809$	−30665.7			−1.33269			−0.666347	+	0.745642i	$0.732143\pi$
$810$		0			0
$811$	−35135.2			−1.52129			−0.760644	−	0.649169i	$-0.775117\pi$
$811$	−35135.2			−1.52129			−0.760644	+	0.649169i	$0.775117\pi$
$812$	4732.28	+	8196.56i	0.204520	+	0.354240i
$813$	16912.3	+	5119.93i	0.729571	+	0.220866i
$814$	−20618.2	+	35711.8i	−0.887798	+	1.53771i
$815$		0			0
$816$	2790.65	+	11938.2i	0.119721	+	0.512156i
$817$	8887.65	+	15393.9i	0.380587	+	0.659196i
$818$	−36306.1			−1.55185
$819$	−436.190	−	290.745i	−0.0186102	−	0.0124047i
$820$		0			0
$821$	−17218.5	−	29823.3i	−0.731948	−	1.26777i	−0.956050	−	0.293205i	$-0.905278\pi$
$821$	−17218.5	−	29823.3i	−0.731948	−	1.26777i	0.224102	−	0.974566i	$-0.428055\pi$
$822$	−668.083	+	626.432i	−0.0283480	+	0.0265807i
$823$	−21400.9	+	37067.4i	−0.906426	+	1.56998i	−0.0874340	+	0.996170i	$0.527867\pi$
$823$	−21400.9	+	37067.4i	−0.906426	+	1.56998i	−0.818992	+	0.573805i	$0.805467\pi$
$824$	−5812.30	+	10067.2i	−0.245729	+	0.425616i
$825$		0			0
$826$	−681.014	−	1179.55i	−0.0286871	−	0.0496875i
$827$	−23589.1			−0.991868			−0.495934	−	0.868360i	$-0.665174\pi$
$827$	−23589.1			−0.991868			−0.495934	+	0.868360i	$0.665174\pi$
$828$	−91.7638	+	1424.55i	−0.00385146	+	0.0597904i
$829$	−26766.2			−1.12139			−0.560693	−	0.828024i	$-0.689465\pi$
$829$	−26766.2			−1.12139			−0.560693	+	0.828024i	$0.689465\pi$
$830$		0			0
$831$	4221.06	+	18057.3i	0.176206	+	0.753791i
$832$	−286.955	+	497.021i	−0.0119572	+	0.0207105i
$833$	−715.142	+	1238.66i	−0.0297458	+	0.0515212i
$834$	−2806.81	−	849.717i	−0.116537	−	0.0352797i
$835$		0			0
$836$	3809.29			0.157592
$837$	23339.3	−	3893.71i	0.963826	−	0.160796i
$838$	22802.7			0.939985
$839$	15167.2	+	26270.3i	0.624110	+	1.08099i	0.988712	+	0.149827i	$0.0478716\pi$
$839$	15167.2	+	26270.3i	0.624110	+	1.08099i	−0.364602	+	0.931163i	$0.618795\pi$
$840$		0			0
$841$	−20306.0	+	35171.1i	−0.832590	+	1.44209i
$842$	−12568.0	+	21768.5i	−0.514398	+	0.890964i
$843$	7118.67	+	30453.0i	0.290842	+	1.24420i
$844$	3265.85	+	5656.61i	0.133193	+	0.230697i
$845$		0			0
$846$	8425.90	−	4166.96i	0.342421	−	0.169342i
$847$	−4952.58			−0.200912
$848$	6521.74	+	11296.0i	0.264101	+	0.457436i
$849$	17353.5	−	16271.6i	0.701496	−	0.657762i
$850$		0			0
$851$	5753.54	−	9965.43i	0.231761	−	0.401422i
$852$	−5871.41	+	5505.37i	−0.236093	+	0.221374i
$853$	−3266.89	−	5658.41i	−0.131133	−	0.227128i	0.792981	−	0.609247i	$-0.208528\pi$
$853$	−3266.89	−	5658.41i	−0.131133	−	0.227128i	−0.924113	+	0.382118i	$0.875195\pi$
$854$	34734.8			1.39180
$855$		0			0
$856$	35537.5			1.41898
$857$	−18776.5	−	32521.9i	−0.748417	−	1.29630i	−0.948581	−	0.316534i	$-0.897481\pi$
$857$	−18776.5	−	32521.9i	−0.748417	−	1.29630i	0.200164	−	0.979762i	$-0.435853\pi$
$858$	117.199	+	501.368i	0.00466331	+	0.0199492i
$859$	−18319.0	+	31729.4i	−0.727631	+	1.26029i	0.230251	+	0.973131i	$0.426045\pi$
$859$	−18319.0	+	31729.4i	−0.727631	+	1.26029i	−0.957882	+	0.287163i	$0.907288\pi$
$860$		0			0
$861$	−38137.6	−	11545.6i	−1.50956	−	0.456993i
$862$	9925.86	+	17192.1i	0.392200	+	0.679310i
$863$	14614.7			0.576467			0.288233	−	0.957560i	$-0.406932\pi$
$863$	14614.7			0.576467			0.288233	+	0.957560i	$0.406932\pi$
$864$	11795.0	−	1967.77i	0.464437	−	0.0774826i
$865$		0			0
$866$	−5304.99	−	9188.52i	−0.208165	−	0.360553i
$867$	−10664.9	−	3228.62i	−0.417761	−	0.126470i
$868$	3130.50	−	5422.18i	0.122415	−	0.212028i
$869$	−12202.5	+	21135.4i	−0.476343	+	0.825050i
$870$		0			0
$871$	89.0759	+	154.284i	0.00346524	+	0.00600197i
$872$	−48022.2			−1.86495
$873$	2374.21	−	36857.5i	0.0920446	−	1.42891i
$874$	3344.45			0.129437
$875$		0			0
$876$	3750.53	−	3516.71i	0.144656	−	0.135638i
$877$	−694.282	+	1202.53i	−0.0267323	+	0.0463017i	−0.879082	−	0.476670i	$-0.841844\pi$
$877$	−694.282	+	1202.53i	−0.0267323	+	0.0463017i	0.852350	+	0.522972i	$0.175177\pi$
$878$	−5816.90	+	10075.2i	−0.223589	+	0.387267i
$879$	−24561.4	+	23030.1i	−0.942474	+	0.883717i
$880$		0			0
$881$	23664.2			0.904957			0.452478	−	0.891775i	$-0.350540\pi$
$881$	23664.2			0.904957			0.452478	+	0.891775i	$0.350540\pi$
$882$	−1504.69	−	1002.96i	−0.0574438	−	0.0382895i
$883$	49607.6			1.89063			0.945317	−	0.326152i	$-0.105752\pi$
$883$	49607.6			1.89063			0.945317	+	0.326152i	$0.105752\pi$
$884$	51.2225	+	88.7200i	0.00194887	+	0.00337554i
$885$		0			0
$886$	−18915.4	+	32762.5i	−0.717242	+	1.24230i
$887$	−5738.51	+	9939.40i	−0.217227	+	0.376248i	−0.953959	−	0.299936i	$-0.903035\pi$
$887$	−5738.51	+	9939.40i	−0.217227	+	0.376248i	0.736732	+	0.676185i	$0.236368\pi$
$888$	−51093.4	−	15467.7i	−1.93084	−	0.584530i
$889$	8330.41	+	14428.7i	0.314278	+	0.544345i
$890$		0			0
$891$	17635.3	−	23089.9i	0.663079	−	0.868171i
$892$	4564.19			0.171323
$893$	3499.84	+	6061.91i	0.131151	+	0.227160i
$894$	10233.3	+	3097.97i	0.382833	+	0.115897i
$895$		0			0
$896$	−6920.78	+	11987.1i	−0.258044	+	0.446945i
$897$	−32.7047	−	139.908i	−0.00121737	−	0.00520778i
$898$	6712.31	+	11626.1i	0.249435	+	0.432034i
$899$	42999.4			1.59523
$900$		0			0
$901$	15305.1			0.565914
$902$	19569.1	+	33894.6i	0.722371	+	1.25118i
$903$	26169.2	−	24537.7i	0.964402	−	0.904278i
$904$	11966.7	−	20727.0i	0.440273	−	0.762576i
$905$		0			0
$906$	−17432.4	+	16345.6i	−0.639241	+	0.599389i
$907$	5866.89	+	10161.8i	0.214782	+	0.372013i	0.953205	−	0.302325i	$-0.0977627\pi$
$907$	5866.89	+	10161.8i	0.214782	+	0.372013i	−0.738423	+	0.674337i	$0.764429\pi$
$908$	−1883.58			−0.0688424
$909$	986.558	−	15315.4i	0.0359979	−	0.558834i
$910$		0			0
$911$	17506.7	+	30322.5i	0.636688	+	1.10278i	0.986155	+	0.165827i	$0.0530293\pi$
$911$	17506.7	+	30322.5i	0.636688	+	1.10278i	−0.349467	+	0.936949i	$0.613637\pi$
$912$	−2627.30	−	11239.4i	−0.0953933	−	0.408084i
$913$	−1610.46	+	2789.40i	−0.0583773	+	0.101112i
$914$	64.9602	−	112.514i	0.00235087	−	0.00407182i
$915$		0			0
$916$	1539.00	+	2665.63i	0.0555132	+	0.0961516i
$917$	28262.9			1.01780
$918$	−6378.07	+	17033.1i	−0.229311	+	0.612391i
$919$	16026.6			0.575264			0.287632	−	0.957741i	$-0.407132\pi$
$919$	16026.6			0.575264			0.287632	+	0.957741i	$0.407132\pi$
$920$		0			0
$921$	3523.31	+	1066.63i	0.126055	+	0.0381612i
$922$	−3901.54	+	6757.66i	−0.139360	+	0.241379i
$923$	405.058	−	701.581i	0.0144449	−	0.0250193i
$924$	−1749.93	−	7486.02i	−0.0623034	−	0.266528i
$925$		0			0
$926$	32257.8			1.14477
$927$	−11499.9	+	5687.16i	−0.407449	+	0.201500i
$928$	21730.7			0.768691
$929$	−12943.4	−	22418.6i	−0.457114	−	0.791745i	0.541693	−	0.840577i	$-0.317784\pi$
$929$	−12943.4	−	22418.6i	−0.457114	−	0.791745i	−0.998807	+	0.0488314i	$0.984450\pi$
$930$		0			0
$931$	673.282	−	1166.16i	0.0237013	−	0.0410519i
$932$	910.284	−	1576.66i	0.0319929	−	0.0554132i
$933$	23632.3	−	22159.0i	0.829247	−	0.777549i
$934$	16292.7	+	28219.8i	0.570786	+	0.988631i
$935$		0			0
$936$	−597.483	+	295.480i	−0.0208647	+	0.0103185i
$937$	6331.15			0.220736			0.110368	−	0.993891i	$-0.464797\pi$
$937$	6331.15			0.220736			0.110368	+	0.993891i	$0.464797\pi$
$938$	4184.56	+	7247.88i	0.145662	+	0.252294i
$939$	3112.34	+	13314.3i	0.108165	+	0.462721i
$940$		0			0
$941$	14377.4	−	24902.3i	0.498075	−	0.862691i	−0.501923	−	0.864912i	$-0.667374\pi$
$941$	14377.4	−	24902.3i	0.498075	−	0.862691i	0.999998	+	0.00222173i	$0.000707200\pi$
$942$	−28181.6	−	8531.52i	−0.974741	−	0.295087i
$943$	−5460.78	−	9458.35i	−0.188576	−	0.326624i
$944$	−1288.39			−0.0444210
$945$		0			0
$946$	−35235.6			−1.21100
$947$	14620.3	+	25323.2i	0.501687	+	0.868947i	0.999998	+	0.00194886i	$0.000620342\pi$
$947$	14620.3	+	25323.2i	0.501687	+	0.868947i	−0.498311	+	0.866998i	$0.666046\pi$
$948$	−5875.86	−	1778.82i	−0.201307	−	0.0609424i
$949$	−258.742	+	448.154i	−0.00885050	+	0.0153295i
$950$		0			0
$951$	594.379	+	2542.70i	0.0202672	+	0.0867010i
$952$	12383.5	+	21448.9i	0.421588	+	0.730212i
$953$	−28758.3			−0.977517			−0.488758	−	0.872419i	$-0.662550\pi$
$953$	−28758.3			−0.977517			−0.488758	+	0.872419i	$0.662550\pi$
$954$	−1243.90	+	19310.4i	−0.0422145	+	0.655341i
$955$		0			0
$956$	2635.13	+	4564.19i	0.0891489	+	0.154410i
$957$	38515.6	−	36114.4i	1.30098	−	1.21987i
$958$	−10543.5	+	18261.9i	−0.355581	+	0.615884i
$959$	−688.175	+	1191.95i	−0.0231724	+	0.0401358i
$960$		0			0
$961$	673.025	+	1165.71i	0.0225916	+	0.0391297i
$962$	1044.08			0.0349920
$963$	32634.9	+	21753.0i	1.09205	+	0.727914i
$964$	−6593.36			−0.220288
$965$		0			0
$966$	−1536.39	−	6572.51i	−0.0511722	−	0.218910i
$967$	22347.6	−	38707.1i	0.743174	−	1.28721i	−0.207869	−	0.978157i	$-0.566653\pi$
$967$	22347.6	−	38707.1i	0.743174	−	1.28721i	0.951043	−	0.309058i	$-0.100014\pi$
$968$	−3148.71	+	5453.73i	−0.104549	+	0.181084i
$969$	−12962.8	−	3924.26i	−0.429746	−	0.130099i
$970$		0			0
$971$	−30462.4			−1.00678			−0.503391	−	0.864059i	$-0.667914\pi$
$971$	−30462.4			−1.00678			−0.503391	+	0.864059i	$0.667914\pi$
$972$	6665.69	+	2997.67i	0.219961	+	0.0989200i
$973$	−4407.24			−0.145210
$974$	−24061.1	−	41675.1i	−0.791548	−	1.37100i
$975$		0			0
$976$	16428.4	−	28454.8i	0.538790	−	0.933212i
$977$	5904.00	−	10226.0i	0.193332	−	0.334861i	−0.753020	−	0.657997i	$-0.771404\pi$
$977$	5904.00	−	10226.0i	0.193332	−	0.334861i	0.946353	+	0.323136i	$0.104737\pi$
$978$	−130.852	−	559.773i	−0.00427831	−	0.0183022i
$979$	−478.451	−	828.701i	−0.0156194	−	0.0270535i
$980$		0			0
$981$	−44099.9	−	29395.1i	−1.43527	−	0.956690i
$982$	48016.1			1.56034
$983$	12351.5	+	21393.3i	0.400763	+	0.694142i	0.993818	−	0.111020i	$-0.0354117\pi$
$983$	12351.5	+	21393.3i	0.400763	+	0.694142i	−0.593055	+	0.805162i	$0.702078\pi$
$984$	−36960.6	+	34656.4i	−1.19742	+	1.12277i
$985$		0			0
$986$	−16526.1	+	28624.1i	−0.533771	+	0.924519i
$987$	10305.1	−	9662.63i	0.332335	−	0.311616i
$988$	−48.2242	−	83.5268i	−0.00155285	−	0.00268962i
$989$	9832.55			0.316134
$990$		0			0
$991$	14443.0			0.462965			0.231482	−	0.972839i	$-0.425642\pi$
$991$	14443.0			0.462965			0.231482	+	0.972839i	$0.425642\pi$
$992$	−7187.63	−	12449.3i	−0.230048	−	0.398455i
$993$	−3651.35	−	15620.1i	−0.116689	−	0.499184i
$994$	19028.6	−	32958.5i	0.607194	−	1.05169i
$995$		0			0
$996$	−775.482	−	234.765i	−0.0246708	−	0.00746867i
$997$	23834.7	+	41282.9i	0.757123	+	1.31138i	0.944312	+	0.329051i	$0.106729\pi$
$997$	23834.7	+	41282.9i	0.757123	+	1.31138i	−0.187189	+	0.982324i	$0.559938\pi$
$998$	836.551			0.0265336
$999$	−37452.4	−	45479.4i	−1.18613	−	1.44035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.g.76.11		32
5.2	odd	4		45.4.j.a.4.6	✓	32
5.3	odd	4		45.4.j.a.4.11	yes	32
5.4	even	2	inner	225.4.e.g.76.6		32
9.4	even	3		2025.4.a.bk.1.6		16
9.5	odd	6		2025.4.a.bl.1.11		16
9.7	even	3	inner	225.4.e.g.151.11		32
15.2	even	4		135.4.j.a.64.11		32
15.8	even	4		135.4.j.a.64.6		32
45.2	even	12		135.4.j.a.19.6		32
45.4	even	6		2025.4.a.bk.1.11		16
45.7	odd	12		45.4.j.a.34.11	yes	32
45.13	odd	12		405.4.b.e.244.11		16
45.14	odd	6		2025.4.a.bl.1.6		16
45.22	odd	12		405.4.b.e.244.6		16
45.23	even	12		405.4.b.f.244.6		16
45.32	even	12		405.4.b.f.244.11		16
45.34	even	6	inner	225.4.e.g.151.6		32
45.38	even	12		135.4.j.a.19.11		32
45.43	odd	12		45.4.j.a.34.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.j.a.4.6	✓	32	5.2	odd	4
45.4.j.a.4.11	yes	32	5.3	odd	4
45.4.j.a.34.6	yes	32	45.43	odd	12
45.4.j.a.34.11	yes	32	45.7	odd	12
135.4.j.a.19.6		32	45.2	even	12
135.4.j.a.19.11		32	45.38	even	12
135.4.j.a.64.6		32	15.8	even	4
135.4.j.a.64.11		32	15.2	even	4
225.4.e.g.76.6		32	5.4	even	2	inner
225.4.e.g.76.11		32	1.1	even	1	trivial
225.4.e.g.151.6		32	45.34	even	6	inner
225.4.e.g.151.11		32	9.7	even	3	inner
405.4.b.e.244.6		16	45.22	odd	12
405.4.b.e.244.11		16	45.13	odd	12
405.4.b.f.244.6		16	45.23	even	12
405.4.b.f.244.11		16	45.32	even	12
2025.4.a.bk.1.6		16	9.4	even	3
2025.4.a.bk.1.11		16	45.4	even	6
2025.4.a.bl.1.6		16	45.14	odd	6
2025.4.a.bl.1.11		16	9.5	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23192 + 2.13376i) q^{2} +(4.97325 + 1.50557i) q^{3} +(0.964722 - 1.67095i) q^{4} +(2.91415 + 12.4665i) q^{6} +(9.62007 + 16.6624i) q^{7} +24.4647 q^{8} +(22.4665 + 14.9752i) q^{9} +O(q^{10})\)	\(q+(1.23192 + 2.13376i) q^{2} +(4.97325 + 1.50557i) q^{3} +(0.964722 - 1.67095i) q^{4} +(2.91415 + 12.4665i) q^{6} +(9.62007 + 16.6624i) q^{7} +24.4647 q^{8} +(22.4665 + 14.9752i) q^{9} +(-19.9274 - 34.5153i) q^{11} +(7.31354 - 6.85759i) q^{12} +(-0.504548 + 0.873903i) q^{13} +(-23.7024 + 41.0538i) q^{14} +(22.4208 + 38.8340i) q^{16} +52.6170 q^{17} +(-4.27635 + 66.3864i) q^{18} -49.5371 q^{19} +(22.7565 + 97.3503i) q^{21} +(49.0982 - 85.0405i) q^{22} +(-13.7009 + 23.7307i) q^{23} +(121.669 + 36.8333i) q^{24} -2.48626 q^{26} +(89.1854 + 108.300i) q^{27} +37.1228 q^{28} +(127.477 + 220.796i) q^{29} +(84.3282 - 146.061i) q^{31} +(42.6170 - 73.8149i) q^{32} +(-47.1388 - 201.656i) q^{33} +(64.8202 + 112.272i) q^{34} +(46.6967 - 23.0935i) q^{36} -419.938 q^{37} +(-61.0260 - 105.700i) q^{38} +(-3.82497 + 3.58651i) q^{39} +(-199.285 + 345.172i) q^{41} +(-179.687 + 168.485i) q^{42} +(-179.414 - 310.754i) q^{43} -76.8977 q^{44} -67.5141 q^{46} +(-70.6510 - 122.371i) q^{47} +(53.0371 + 226.888i) q^{48} +(-13.5915 + 23.5411i) q^{49} +(261.678 + 79.2187i) q^{51} +(0.973497 + 1.68615i) q^{52} +290.878 q^{53} +(-121.217 + 323.718i) q^{54} +(235.352 + 407.641i) q^{56} +(-246.361 - 74.5817i) q^{57} +(-314.083 + 544.008i) q^{58} +(-14.3659 + 24.8825i) q^{59} +(-366.364 - 634.561i) q^{61} +415.544 q^{62} +(-33.3939 + 518.409i) q^{63} +568.737 q^{64} +(372.212 - 349.007i) q^{66} +(88.2730 - 152.893i) q^{67} +(50.7608 - 87.9203i) q^{68} +(-103.866 + 97.3911i) q^{69} -802.814 q^{71} +(549.635 + 366.363i) q^{72} +512.820 q^{73} +(-517.332 - 896.046i) q^{74} +(-47.7895 + 82.7739i) q^{76} +(383.406 - 664.079i) q^{77} +(-12.3648 - 3.74324i) q^{78} +(-306.174 - 530.309i) q^{79} +(280.488 + 672.880i) q^{81} -982.017 q^{82} +(-40.4081 - 69.9889i) q^{83} +(184.621 + 55.8910i) q^{84} +(442.049 - 765.651i) q^{86} +(301.549 + 1290.00i) q^{87} +(-487.518 - 844.405i) q^{88} +24.0097 q^{89} -19.4151 q^{91} +(26.4352 + 45.7871i) q^{92} +(639.290 - 599.435i) q^{93} +(174.073 - 301.504i) q^{94} +(323.079 - 302.937i) q^{96} +(-683.960 - 1184.65i) q^{97} -66.9747 q^{98} +(69.1736 - 1073.86i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) \) 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9	\( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) \) 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9 + 90 * q^11 + 102 * q^14 - 146 * q^16 + 8 * q^19 + 30 * q^21 - 462 * q^24 - 936 * q^26 + 516 * q^29 - 38 * q^31 - 212 * q^34 + 864 * q^36 - 330 * q^39 + 576 * q^41 - 3288 * q^44 - 580 * q^46 + 4 * q^49 + 1260 * q^51 + 3726 * q^54 + 2430 * q^56 + 2202 * q^59 - 20 * q^61 - 644 * q^64 - 5052 * q^66 - 1452 * q^69 - 5904 * q^71 + 4080 * q^74 + 396 * q^76 + 218 * q^79 + 198 * q^81 - 4662 * q^84 + 6108 * q^86 - 8148 * q^89 - 1884 * q^91 + 1078 * q^94 + 11874 * q^96 + 1602 * q^99

Introduction

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