LMFDB - Embedded newform 324.3.j.a.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	324.19
Dual form			324.3.j.a.307.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.747520 - 1.85505i) q^{2} +(-2.88243 + 2.77337i) q^{4} +(-0.463207 - 2.62698i) q^{5} +(-4.34885 + 5.18275i) q^{7} +(7.29942 + 3.27390i) q^{8} +O(q^{10})$	\(q+(-0.747520 - 1.85505i) q^{2} +(-2.88243 + 2.77337i) q^{4} +(-0.463207 - 2.62698i) q^{5} +(-4.34885 + 5.18275i) q^{7} +(7.29942 + 3.27390i) q^{8} +(-4.52692 + 2.82299i) q^{10} +(18.5390 + 3.26893i) q^{11} +(-4.76031 - 1.73261i) q^{13} +(12.8651 + 4.19312i) q^{14} +(0.616783 - 15.9881i) q^{16} +(-7.37511 - 12.7741i) q^{17} +(28.7994 + 16.6273i) q^{19} +(8.62076 + 6.28743i) q^{20} +(-7.79427 - 36.8345i) q^{22} +(-11.3558 - 13.5334i) q^{23} +(16.8059 - 6.11683i) q^{25} +(0.344344 + 10.1258i) q^{26} +(-1.83848 - 26.9999i) q^{28} +(38.2238 - 13.9123i) q^{29} +(-4.43128 - 5.28100i) q^{31} +(-30.1198 + 10.8073i) q^{32} +(-18.1835 + 23.2301i) q^{34} +(15.6294 + 9.02364i) q^{35} +(-4.65176 - 8.05708i) q^{37} +(9.31644 - 65.8536i) q^{38} +(5.21932 - 20.6919i) q^{40} +(20.9136 + 7.61194i) q^{41} +(42.0191 + 7.40910i) q^{43} +(-62.5034 + 41.9933i) q^{44} +(-16.6164 + 31.1821i) q^{46} +(35.0594 - 41.7822i) q^{47} +(0.560291 + 3.17757i) q^{49} +(-23.9097 - 26.6033i) q^{50} +(18.5264 - 8.20799i) q^{52} -25.6875 q^{53} -50.2159i q^{55} +(-48.7119 + 23.5934i) q^{56} +(-54.3811 - 60.5073i) q^{58} +(15.3255 - 2.70230i) q^{59} +(-48.6391 - 40.8131i) q^{61} +(-6.48405 + 12.1679i) q^{62} +(42.5632 + 47.7951i) q^{64} +(-2.34652 + 13.3078i) q^{65} +(-11.8552 + 32.5718i) q^{67} +(56.6855 + 16.3664i) q^{68} +(5.05602 - 35.7387i) q^{70} +(23.7276 - 13.6991i) q^{71} +(18.2594 - 31.6262i) q^{73} +(-11.4690 + 14.6521i) q^{74} +(-129.126 + 31.9444i) q^{76} +(-97.5656 + 81.8672i) q^{77} +(43.9448 + 120.737i) q^{79} +(-42.2861 + 5.78553i) q^{80} +(-1.51282 - 44.4859i) q^{82} +(-0.482480 - 1.32560i) q^{83} +(-30.1410 + 25.2913i) q^{85} +(-17.6658 - 83.4860i) q^{86} +(124.622 + 84.5563i) q^{88} +(34.1806 - 59.2025i) q^{89} +(29.6815 - 17.1366i) q^{91} +(70.2655 + 7.51495i) q^{92} +(-103.716 - 33.8040i) q^{94} +(30.3396 - 83.3573i) q^{95} +(-19.7333 + 111.913i) q^{97} +(5.47572 - 3.41466i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.747520	−	1.85505i	−0.373760	−	0.927525i
$2$	−0.747520	−	1.85505i	−0.373760	−	0.927525i
$3$		0			0
$3$		0			0
$4$	−2.88243	+	2.77337i	−0.720607	+	0.693344i
$5$	−0.463207	−	2.62698i	−0.0926415	−	0.525396i	−0.995445	−	0.0953418i	$-0.969606\pi$
$5$	−0.463207	−	2.62698i	−0.0926415	−	0.525396i	0.902803	−	0.430054i	$-0.141506\pi$
$6$		0			0
$7$	−4.34885	+	5.18275i	−0.621264	+	0.740393i	−0.981287	−	0.192550i	$-0.938324\pi$
$7$	−4.34885	+	5.18275i	−0.621264	+	0.740393i	0.360023	+	0.932943i	$0.382769\pi$
$8$	7.29942	+	3.27390i	0.912428	+	0.409237i
$9$		0			0
$10$	−4.52692	+	2.82299i	−0.452692	+	0.282299i
$11$	18.5390	+	3.26893i	1.68537	+	0.297176i	0.932547	−	0.361049i	$-0.117581\pi$
$11$	18.5390	+	3.26893i	1.68537	+	0.297176i	0.752821	+	0.658225i	$0.228693\pi$
$12$		0			0
$13$	−4.76031	−	1.73261i	−0.366177	−	0.133278i	0.152377	−	0.988322i	$-0.451307\pi$
$13$	−4.76031	−	1.73261i	−0.366177	−	0.133278i	−0.518554	+	0.855045i	$0.673530\pi$
$14$	12.8651	+	4.19312i	0.918937	+	0.299509i
$15$		0			0
$16$	0.616783	−	15.9881i	0.0385490	−	0.999257i
$17$	−7.37511	−	12.7741i	−0.433830	−	0.751416i	0.563369	−	0.826205i	$-0.309505\pi$
$17$	−7.37511	−	12.7741i	−0.433830	−	0.751416i	−0.997199	+	0.0747894i	$0.976172\pi$
$18$		0			0
$19$	28.7994	+	16.6273i	1.51576	+	0.875123i	0.999829	+	0.0184912i	$0.00588628\pi$
$19$	28.7994	+	16.6273i	1.51576	+	0.875123i	0.515928	+	0.856632i	$0.327447\pi$
$20$	8.62076	+	6.28743i	0.431038	+	0.314372i
$21$		0			0
$22$	−7.79427	−	36.8345i	−0.354285	−	1.67429i
$23$	−11.3558	−	13.5334i	−0.493732	−	0.588407i	0.460430	−	0.887696i	$-0.347695\pi$
$23$	−11.3558	−	13.5334i	−0.493732	−	0.588407i	−0.954163	+	0.299289i	$0.903251\pi$
$24$		0			0
$25$	16.8059	−	6.11683i	0.672234	−	0.244673i
$26$	0.344344	+	10.1258i	0.0132440	+	0.389453i
$27$		0			0
$28$	−1.83848	−	26.9999i	−0.0656600	−	0.964282i
$29$	38.2238	−	13.9123i	1.31806	−	0.479735i	0.415224	−	0.909719i	$-0.363703\pi$
$29$	38.2238	−	13.9123i	1.31806	−	0.479735i	0.902836	+	0.429984i	$0.141481\pi$
$30$		0			0
$31$	−4.43128	−	5.28100i	−0.142945	−	0.170355i	0.689822	−	0.723979i	$-0.257689\pi$
$31$	−4.43128	−	5.28100i	−0.142945	−	0.170355i	−0.832767	+	0.553624i	$0.813244\pi$
$32$	−30.1198	+	10.8073i	−0.941244	+	0.337727i
$33$		0			0
$34$	−18.1835	+	23.2301i	−0.534809	+	0.683238i
$35$	15.6294	+	9.02364i	0.446555	+	0.257818i
$36$		0			0
$37$	−4.65176	−	8.05708i	−0.125723	−	0.217759i	0.796292	−	0.604912i	$-0.206792\pi$
$37$	−4.65176	−	8.05708i	−0.125723	−	0.217759i	−0.922015	+	0.387153i	$0.873458\pi$
$38$	9.31644	−	65.8536i	0.245169	−	1.73299i
$39$		0			0
$40$	5.21932	−	20.6919i	0.130483	−	0.517298i
$41$	20.9136	+	7.61194i	0.510089	+	0.185657i	0.584226	−	0.811591i	$-0.301398\pi$
$41$	20.9136	+	7.61194i	0.510089	+	0.185657i	−0.0741374	+	0.997248i	$0.523620\pi$
$42$		0			0
$43$	42.0191	+	7.40910i	0.977188	+	0.172305i	0.639363	−	0.768905i	$-0.279198\pi$
$43$	42.0191	+	7.40910i	0.977188	+	0.172305i	0.337824	+	0.941209i	$0.390309\pi$
$44$	−62.5034	+	41.9933i	−1.42053	+	0.954392i
$45$		0			0
$46$	−16.6164	+	31.1821i	−0.361225	+	0.677872i
$47$	35.0594	−	41.7822i	0.745945	−	0.888982i	−0.250928	−	0.968006i	$-0.580736\pi$
$47$	35.0594	−	41.7822i	0.745945	−	0.888982i	0.996873	+	0.0790235i	$0.0251802\pi$
$48$		0			0
$49$	0.560291	+	3.17757i	0.0114345	+	0.0648483i
$50$	−23.9097	−	26.6033i	−0.478195	−	0.532065i
$51$		0			0
$52$	18.5264	−	8.20799i	0.356277	−	0.157846i
$53$	−25.6875			−0.484670			−0.242335	−	0.970193i	$-0.577913\pi$
$53$	−25.6875			−0.484670			−0.242335	+	0.970193i	$0.577913\pi$
$54$		0			0
$55$		−	50.2159i		−	0.913016i
$56$	−48.7119	+	23.5934i	−0.869855	+	0.421311i
$57$		0			0
$58$	−54.3811	−	60.5073i	−0.937605	−	1.04323i
$59$	15.3255	−	2.70230i	0.259755	−	0.0458018i	−0.0422541	−	0.999107i	$-0.513454\pi$
$59$	15.3255	−	2.70230i	0.259755	−	0.0458018i	0.302009	+	0.953305i	$0.402343\pi$
$60$		0			0
$61$	−48.6391	−	40.8131i	−0.797363	−	0.669067i	0.150193	−	0.988657i	$-0.452010\pi$
$61$	−48.6391	−	40.8131i	−0.797363	−	0.669067i	−0.947556	+	0.319590i	$0.896455\pi$
$62$	−6.48405	+	12.1679i	−0.104581	+	0.196257i
$63$		0			0
$64$	42.5632	+	47.7951i	0.665050	+	0.746799i
$65$	−2.34652	+	13.3078i	−0.0361003	+	0.204735i
$66$		0			0
$67$	−11.8552	+	32.5718i	−0.176943	+	0.486147i	−0.996182	−	0.0873060i	$-0.972174\pi$
$67$	−11.8552	+	32.5718i	−0.176943	+	0.486147i	0.819239	+	0.573453i	$0.194396\pi$
$68$	56.6855	+	16.3664i	0.833611	+	0.240682i
$69$		0			0
$70$	5.05602	−	35.7387i	0.0722289	−	0.510553i
$71$	23.7276	−	13.6991i	0.334192	−	0.192946i	−0.323509	−	0.946225i	$-0.604863\pi$
$71$	23.7276	−	13.6991i	0.334192	−	0.192946i	0.657701	+	0.753279i	$0.271529\pi$
$72$		0			0
$73$	18.2594	−	31.6262i	0.250129	−	0.433235i	−0.713432	−	0.700724i	$-0.752860\pi$
$73$	18.2594	−	31.6262i	0.250129	−	0.433235i	0.963561	+	0.267489i	$0.0861938\pi$
$74$	−11.4690	+	14.6521i	−0.154987	+	0.198001i
$75$		0			0
$76$	−129.126	+	31.9444i	−1.69903	+	0.420321i
$77$	−97.5656	+	81.8672i	−1.26709	+	1.06321i
$78$		0			0
$79$	43.9448	+	120.737i	0.556263	+	1.52832i	0.825015	+	0.565111i	$0.191167\pi$
$79$	43.9448	+	120.737i	0.556263	+	1.52832i	−0.268752	+	0.963209i	$0.586611\pi$
$80$	−42.2861	+	5.78553i	−0.528577	+	0.0723192i
$81$		0			0
$82$	−1.51282	−	44.4859i	−0.0184490	−	0.542511i
$83$	−0.482480	−	1.32560i	−0.00581301	−	0.0159711i	0.936752	−	0.349993i	$-0.113816\pi$
$83$	−0.482480	−	1.32560i	−0.00581301	−	0.0159711i	−0.942565	+	0.334022i	$0.891594\pi$
$84$		0			0
$85$	−30.1410	+	25.2913i	−0.354600	+	0.297545i
$86$	−17.6658	−	83.4860i	−0.205417	−	0.970767i
$87$		0			0
$88$	124.622	+	84.5563i	1.41616	+	0.960867i
$89$	34.1806	−	59.2025i	0.384052	−	0.665197i	−0.607585	−	0.794254i	$-0.707862\pi$
$89$	34.1806	−	59.2025i	0.384052	−	0.665197i	0.991637	+	0.129057i	$0.0411951\pi$
$90$		0			0
$91$	29.6815	−	17.1366i	0.326171	−	0.188315i
$92$	70.2655	+	7.51495i	0.763756	+	0.0816842i
$93$		0			0
$94$	−103.716	−	33.8040i	−1.10336	−	0.359617i
$95$	30.3396	−	83.3573i	0.319364	−	0.877446i
$96$		0			0
$97$	−19.7333	+	111.913i	−0.203436	+	1.15375i	0.696445	+	0.717610i	$0.254764\pi$
$97$	−19.7333	+	111.913i	−0.203436	+	1.15375i	−0.899881	+	0.436135i	$0.856347\pi$
$98$	5.47572	−	3.41466i	0.0558747	−	0.0348435i
$99$		0			0
$100$	−31.4774	+	64.2403i	−0.314774	+	0.642403i
$101$	129.982	+	109.068i	1.28695	+	1.07988i	0.992245	+	0.124296i	$0.0396674\pi$
$101$	129.982	+	109.068i	1.28695	+	1.07988i	0.294710	+	0.955587i	$0.404777\pi$
$102$		0			0
$103$	13.3003	−	2.34520i	0.129129	−	0.0227689i	−0.108710	−	0.994073i	$-0.534672\pi$
$103$	13.3003	−	2.34520i	0.129129	−	0.0227689i	0.237839	+	0.971305i	$0.423561\pi$
$104$	−29.0751	−	28.2318i	−0.279568	−	0.271460i
$105$		0			0
$106$	19.2019	+	47.6517i	0.181150	+	0.449544i
$107$			161.176i			1.50632i	0.657838	+	0.753159i	$0.271471\pi$
$107$			161.176i			1.50632i	−0.657838	+	0.753159i	$0.728529\pi$
$108$		0			0
$109$	67.0064			0.614738			0.307369	−	0.951590i	$-0.400551\pi$
$109$	67.0064			0.614738			0.307369	+	0.951590i	$0.400551\pi$
$110$	−93.1530	+	37.5374i	−0.846846	+	0.341249i
$111$		0			0
$112$	80.1801	+	72.7265i	0.715894	+	0.649343i
$113$	2.48868	+	14.1140i	0.0220237	+	0.124903i	0.993837	−	0.110847i	$-0.0353564\pi$
$113$	2.48868	+	14.1140i	0.0220237	+	0.124903i	−0.971814	+	0.235750i	$0.924245\pi$
$114$		0			0
$115$	−30.2918	+	36.1003i	−0.263407	+	0.313916i
$116$	−71.5932	+	146.110i	−0.617183	+	1.25957i
$117$		0			0
$118$	−16.4690	−	26.4096i	−0.139568	−	0.223810i
$119$	98.2781	+	17.3291i	0.825866	+	0.145623i
$120$		0			0
$121$	219.307	+	79.8214i	1.81246	+	0.659681i
$122$	−39.3516	+	120.737i	−0.322554	+	0.989645i
$123$		0			0
$124$	27.4190	+	2.93249i	0.221121	+	0.0236491i
$125$	−57.1972	−	99.0685i	−0.457578	−	0.792548i
$126$		0			0
$127$	123.798	+	71.4751i	0.974791	+	0.562796i	0.900693	−	0.434455i	$-0.143059\pi$
$127$	123.798	+	71.4751i	0.974791	+	0.562796i	0.0740975	+	0.997251i	$0.476392\pi$
$128$	56.8456	−	114.685i	0.444106	−	0.895974i
$129$		0			0
$130$	26.4407	−	5.59492i	0.203390	−	0.0430378i
$131$	−50.1592	−	59.7775i	−0.382895	−	0.456316i	0.539831	−	0.841774i	$-0.318488\pi$
$131$	−50.1592	−	59.7775i	−0.382895	−	0.456316i	−0.922726	+	0.385457i	$0.874044\pi$
$132$		0			0
$133$	−211.420	+	76.9504i	−1.58962	+	0.578575i
$134$	69.2844	−	2.35613i	0.517048	−	0.0175831i
$135$		0			0
$136$	−12.0131	−	117.389i	−0.0883314	−	0.863152i
$137$	−206.641	+	75.2110i	−1.50833	+	0.548985i	−0.958201	−	0.286097i	$-0.907642\pi$
$137$	−206.641	+	75.2110i	−1.50833	+	0.548985i	−0.550125	+	0.835083i	$0.685420\pi$
$138$		0			0
$139$	−127.475	−	151.919i	−0.917089	−	1.09294i	−0.995380	−	0.0960135i	$-0.969391\pi$
$139$	−127.475	−	151.919i	−0.917089	−	1.09294i	0.0782911	−	0.996931i	$-0.475054\pi$
$140$	−70.0766	+	17.3362i	−0.500547	+	0.123830i
$141$		0			0
$142$	−43.1495	−	33.7756i	−0.303870	−	0.237856i
$143$	−82.5878	−	47.6821i	−0.577537	−	0.333441i
$144$		0			0
$145$	−54.2529	−	93.9688i	−0.374158	−	0.648060i
$146$	−72.3174	−	10.2309i	−0.495325	−	0.0700746i
$147$		0			0
$148$	35.7537	+	10.3229i	0.241579	+	0.0697492i
$149$	−207.161	−	75.4005i	−1.39034	−	0.506044i	−0.465046	−	0.885286i	$-0.653962\pi$
$149$	−207.161	−	75.4005i	−1.39034	−	0.506044i	−0.925297	+	0.379243i	$0.876184\pi$
$150$		0			0
$151$	−103.590	−	18.2656i	−0.686023	−	0.120964i	−0.180237	−	0.983623i	$-0.557686\pi$
$151$	−103.590	−	18.2656i	−0.686023	−	0.120964i	−0.505786	+	0.862659i	$0.668798\pi$
$152$	155.783	+	215.656i	1.02489	+	1.41879i
$153$		0			0
$154$	224.800	+	119.792i	1.45974	+	0.777868i
$155$	−11.8205	+	14.0871i	−0.0762611	+	0.0908845i
$156$		0			0
$157$	46.2911	+	262.530i	0.294848	+	1.67216i	0.667820	+	0.744322i	$0.267227\pi$
$157$	46.2911	+	262.530i	0.294848	+	1.67216i	−0.372973	+	0.927842i	$0.621662\pi$
$158$	191.124	−	171.773i	1.20965	−	1.08717i
$159$		0			0
$160$	42.3422	+	74.1181i	0.264639	+	0.463238i
$161$	119.525			0.742391
$162$		0			0
$163$		−	179.334i		−	1.10021i	−0.835096	−	0.550104i	$-0.814588\pi$
$163$		−	179.334i		−	1.10021i	0.835096	−	0.550104i	$-0.185412\pi$
$164$	−81.3928	+	36.0605i	−0.496298	+	0.219881i
$165$		0			0
$166$	−2.09840	+	1.88594i	−0.0126409	+	0.0113611i
$167$	−190.029	+	33.5073i	−1.13790	+	0.200642i	−0.710687	−	0.703508i	$-0.751616\pi$
$167$	−190.029	+	33.5073i	−1.13790	+	0.200642i	−0.427213	+	0.904151i	$0.640505\pi$
$168$		0			0
$169$	−109.803	−	92.1356i	−0.649721	−	0.545181i
$170$	69.4477	+	37.0074i	0.408516	+	0.217690i
$171$		0			0
$172$	−141.665	+	95.1784i	−0.823635	+	0.553363i
$173$	43.0667	−	244.244i	0.248941	−	1.41181i	−0.562219	−	0.826988i	$-0.690052\pi$
$173$	43.0667	−	244.244i	0.248941	−	1.41181i	0.811160	−	0.584825i	$-0.198837\pi$
$174$		0			0
$175$	−41.3841	+	113.702i	−0.236480	+	0.649724i
$176$	63.6986	−	294.388i	0.361924	−	1.67266i
$177$		0			0
$178$	−135.374	−	19.1517i	−0.760530	−	0.107594i
$179$	−24.5003	+	14.1453i	−0.136873	+	0.0790238i	−0.566873	−	0.823805i	$-0.691847\pi$
$179$	−24.5003	+	14.1453i	−0.136873	+	0.0790238i	0.430000	+	0.902829i	$0.358514\pi$
$180$		0			0
$181$	134.243	−	232.516i	0.741676	−	1.28462i	−0.210056	−	0.977689i	$-0.567365\pi$
$181$	134.243	−	232.516i	0.741676	−	1.28462i	0.951732	−	0.306931i	$-0.0993019\pi$
$182$	−53.9769	−	42.2508i	−0.296576	−	0.232147i
$183$		0			0
$184$	−38.5843	−	135.964i	−0.209697	−	0.738933i
$185$	−19.0111	+	15.9522i	−0.102762	+	0.0862280i
$186$		0			0
$187$	−94.9700	−	260.928i	−0.507861	−	1.39534i
$188$	14.8214	+	217.667i	0.0788373	+	1.15780i
$189$		0			0
$190$	−177.312	+	6.02978i	−0.933219	+	0.0317357i
$191$	−10.7627	−	29.5704i	−0.0563494	−	0.154819i	0.908324	−	0.418267i	$-0.137362\pi$
$191$	−10.7627	−	29.5704i	−0.0563494	−	0.154819i	−0.964674	+	0.263448i	$0.915140\pi$
$192$		0			0
$193$	178.497	−	149.777i	0.924855	−	0.776045i	−0.0500319	−	0.998748i	$-0.515932\pi$
$193$	178.497	−	149.777i	0.924855	−	0.776045i	0.974886	+	0.222703i	$0.0714879\pi$
$194$	222.356	−	47.0511i	1.14616	−	0.242531i
$195$		0			0
$196$	−10.4276	−	7.60521i	−0.0532020	−	0.0388021i
$197$	126.054	−	218.332i	0.639867	−	1.10828i	−0.345595	−	0.938384i	$-0.612323\pi$
$197$	126.054	−	218.332i	0.639867	−	1.10828i	0.985462	−	0.169898i	$-0.0543439\pi$
$198$		0			0
$199$	−258.347	+	149.157i	−1.29823	+	0.749531i	−0.980098	−	0.198517i	$-0.936388\pi$
$199$	−258.347	+	149.157i	−1.29823	+	0.749531i	−0.318128	+	0.948048i	$0.603054\pi$
$200$	142.699	+	10.3713i	0.713495	+	0.0518566i
$201$		0			0
$202$	105.163	−	322.655i	0.520607	−	1.59730i
$203$	−94.1252	+	258.607i	−0.463671	+	1.27393i
$204$		0			0
$205$	10.3091	−	58.4656i	0.0502881	−	0.285198i
$206$	−14.2927	−	22.9196i	−0.0693820	−	0.111260i
$207$		0			0
$208$	−30.6372	+	75.0397i	−0.147294	+	0.360768i
$209$	479.560	+	402.398i	2.29454	+	1.92535i
$210$		0			0
$211$	79.4973	−	14.0175i	0.376764	−	0.0664337i	0.0179406	−	0.999839i	$-0.494289\pi$
$211$	79.4973	−	14.0175i	0.376764	−	0.0664337i	0.358824	+	0.933405i	$0.383178\pi$
$212$	74.0424	−	71.2411i	0.349257	−	0.336043i
$213$		0			0
$214$	298.990	−	120.482i	1.39715	−	0.563001i
$215$		−	113.815i		−	0.529373i
$216$		0			0
$217$	46.6411			0.214936
$218$	−50.0886	−	124.300i	−0.229764	−	0.570185i
$219$		0			0
$220$	139.267	+	144.744i	0.633034	+	0.657926i
$221$	12.9753	+	73.5867i	0.0587119	+	0.332971i
$222$		0			0
$223$	86.4593	−	103.038i	0.387710	−	0.462055i	−0.536522	−	0.843886i	$-0.680262\pi$
$223$	86.4593	−	103.038i	0.387710	−	0.462055i	0.924232	+	0.381832i	$0.124707\pi$
$224$	74.9751	−	203.103i	0.334710	−	0.906709i
$225$		0			0
$226$	24.3219	−	15.1671i	0.107619	−	0.0671112i
$227$	−301.128	−	53.0971i	−1.32656	−	0.233908i	−0.534922	−	0.844902i	$-0.679659\pi$
$227$	−301.128	−	53.0971i	−1.32656	−	0.233908i	−0.791635	+	0.610994i	$0.790770\pi$
$228$		0			0
$229$	−208.128	−	75.7525i	−0.908858	−	0.330797i	−0.155061	−	0.987905i	$-0.549557\pi$
$229$	−208.128	−	75.7525i	−0.908858	−	0.330797i	−0.753797	+	0.657108i	$0.771780\pi$
$230$	89.6117	+	29.2071i	0.389616	+	0.126987i
$231$		0			0
$232$	324.559	+	23.5888i	1.39896	+	0.101676i
$233$	−42.1249	−	72.9625i	−0.180794	−	0.313144i	0.761357	−	0.648332i	$-0.224533\pi$
$233$	−42.1249	−	72.9625i	−0.180794	−	0.313144i	−0.942151	+	0.335189i	$0.891200\pi$
$234$		0			0
$235$	−126.001	−	72.7465i	−0.536173	−	0.309560i
$236$	−36.6802	+	50.2926i	−0.155425	+	0.213104i
$237$		0			0
$238$	−41.3185	−	195.265i	−0.173607	−	0.820440i
$239$	80.0260	+	95.3713i	0.334837	+	0.399043i	0.907023	−	0.421081i	$-0.138349\pi$
$239$	80.0260	+	95.3713i	0.334837	+	0.399043i	−0.572186	+	0.820124i	$0.693905\pi$
$240$		0			0
$241$	−142.642	+	51.9174i	−0.591876	+	0.215425i	−0.620554	−	0.784164i	$-0.713092\pi$
$241$	−142.642	+	51.9174i	−0.591876	+	0.215425i	0.0286786	+	0.999589i	$0.490870\pi$
$242$	−15.8639	−	466.495i	−0.0655535	−	1.92766i
$243$		0			0
$244$	253.389	−	17.2538i	1.03848	−	0.0707123i
$245$	8.08788	−	2.94375i	0.0330117	−	0.0120153i
$246$		0			0
$247$	−108.285	−	129.049i	−0.438402	−	0.522467i
$248$	−15.0564	−	53.0558i	−0.0607112	−	0.213935i
$249$		0			0
$250$	−141.021	+	180.159i	−0.564084	+	0.720637i
$251$	18.3430	+	10.5903i	0.0730796	+	0.0421925i	0.536095	−	0.844158i	$-0.319899\pi$
$251$	18.3430	+	10.5903i	0.0730796	+	0.0421925i	−0.463015	+	0.886350i	$0.653232\pi$
$252$		0			0
$253$	−166.287	−	288.017i	−0.657260	−	1.13841i
$254$	40.0481	−	283.081i	0.157670	−	1.11449i
$255$		0			0
$256$	−255.239	−	19.7224i	−0.997028	−	0.0770406i
$257$	−36.6814	−	13.3509i	−0.142729	−	0.0519491i	0.269668	−	0.962953i	$-0.413086\pi$
$257$	−36.6814	−	13.3509i	−0.142729	−	0.0519491i	−0.412397	+	0.911004i	$0.635308\pi$
$258$		0			0
$259$	61.9877	+	10.9301i	0.239335	+	0.0422011i
$260$	−30.1438	−	44.8665i	−0.115938	−	0.172564i
$261$		0			0
$262$	−73.3952	+	137.733i	−0.280134	+	0.525698i
$263$	−247.344	+	294.773i	−0.940472	+	1.12081i	0.0520376	+	0.998645i	$0.483428\pi$
$263$	−247.344	+	294.773i	−0.940472	+	1.12081i	−0.992510	+	0.122166i	$0.961016\pi$
$264$		0			0
$265$	11.8987	+	67.4806i	0.0449006	+	0.254644i
$266$	300.787	+	334.672i	1.13078	+	1.25817i
$267$		0			0
$268$	−56.1622	−	126.765i	−0.209561	−	0.473003i
$269$	−128.494			−0.477672			−0.238836	−	0.971060i	$-0.576766\pi$
$269$	−128.494			−0.477672			−0.238836	+	0.971060i	$0.576766\pi$
$270$		0			0
$271$			173.624i			0.640678i	0.947303	+	0.320339i	$0.103797\pi$
$271$			173.624i			0.640678i	−0.947303	+	0.320339i	$0.896203\pi$
$272$	−208.782	+	110.035i	−0.767581	+	0.404541i
$273$		0			0
$274$	293.988	+	327.107i	1.07295	+	1.19382i
$275$	331.560	−	58.4630i	1.20567	−	0.212593i
$276$		0			0
$277$	123.403	+	103.547i	0.445498	+	0.373818i	0.837762	−	0.546035i	$-0.183864\pi$
$277$	123.403	+	103.547i	0.445498	+	0.373818i	−0.392264	+	0.919853i	$0.628308\pi$
$278$	−186.528	+	350.036i	−0.670962	+	1.25912i
$279$		0			0
$280$	84.5432	+	117.036i	0.301940	+	0.417987i
$281$	14.1148	−	80.0493i	0.0502308	−	0.284873i	−0.949337	−	0.314259i	$-0.898244\pi$
$281$	14.1148	−	80.0493i	0.0502308	−	0.284873i	0.999568	+	0.0293859i	$0.00935517\pi$
$282$		0			0
$283$	−109.608	+	301.145i	−0.387306	+	1.06412i	0.580903	+	0.813973i	$0.302700\pi$
$283$	−109.608	+	301.145i	−0.387306	+	1.06412i	−0.968209	+	0.250142i	$0.919523\pi$
$284$	−30.4003	+	105.292i	−0.107043	+	0.370748i
$285$		0			0
$286$	−26.7167	+	188.848i	−0.0934149	+	0.660307i
$287$	−130.401	+	75.2871i	−0.454359	+	0.262324i
$288$		0			0
$289$	35.7154	−	61.8609i	0.123583	−	0.214052i
$290$	−133.762	+	170.885i	−0.461247	+	0.589260i
$291$		0			0
$292$	35.0799	+	141.800i	0.120137	+	0.485618i
$293$	38.6454	−	32.4274i	0.131896	−	0.110674i	−0.574453	−	0.818537i	$-0.694785\pi$
$293$	38.6454	−	32.4274i	0.131896	−	0.110674i	0.706349	+	0.707864i	$0.250341\pi$
$294$		0			0
$295$	−14.1978	−	39.0081i	−0.0481281	−	0.132231i
$296$	−7.57709	−	74.0414i	−0.0255983	−	0.250140i
$297$		0			0
$298$	14.9853	+	440.658i	0.0502863	+	1.47872i
$299$	30.6093	+	84.0982i	0.102372	+	0.281265i
$300$		0			0
$301$	−221.134	+	185.553i	−0.734665	+	0.616457i
$302$	43.5515	+	205.818i	0.144210	+	0.681516i
$303$		0			0
$304$	283.603	−	450.192i	0.932903	−	1.48090i
$305$	−84.6851	+	146.679i	−0.277656	+	0.480915i
$306$		0			0
$307$	109.109	−	62.9942i	0.355404	−	0.205193i	−0.311659	−	0.950194i	$-0.600885\pi$
$307$	109.109	−	62.9942i	0.355404	−	0.205193i	0.667063	+	0.745001i	$0.267551\pi$
$308$	54.1772	−	506.562i	0.175900	−	1.64468i
$309$		0			0
$310$	34.9683	+	11.3972i	0.112801	+	0.0367652i
$311$	78.4332	−	215.493i	0.252197	−	0.692905i	−0.747396	−	0.664378i	$-0.768696\pi$
$311$	78.4332	−	215.493i	0.252197	−	0.692905i	0.999593	−	0.0285262i	$-0.00908142\pi$
$312$		0			0
$313$	51.3526	−	291.235i	0.164066	−	0.930463i	−0.785957	−	0.618281i	$-0.787829\pi$
$313$	51.3526	−	291.235i	0.164066	−	0.930463i	0.950023	−	0.312181i	$-0.101060\pi$
$314$	452.403	−	282.119i	1.44077	−	0.898467i
$315$		0			0
$316$	−461.517	−	226.141i	−1.46050	−	0.715637i
$317$	−144.559	−	121.299i	−0.456021	−	0.382647i	0.385643	−	0.922648i	$-0.373980\pi$
$317$	−144.559	−	121.299i	−0.456021	−	0.382647i	−0.841665	+	0.540001i	$0.818424\pi$
$318$		0			0
$319$	754.110	−	132.970i	2.36398	−	0.416834i
$320$	105.841	−	133.952i	0.330754	−	0.418599i
$321$		0			0
$322$	−89.3473	−	221.725i	−0.277476	−	0.688587i
$323$		−	490.514i		−	1.51862i
$324$		0			0
$325$	−90.5991			−0.278766
$326$	−332.674	+	134.056i	−1.02047	+	0.411214i
$327$		0			0
$328$	127.737	+	124.032i	0.389441	+	0.378146i
$329$	64.0787	+	363.408i	0.194768	+	1.10459i
$330$		0			0
$331$	−114.150	+	136.038i	−0.344863	+	0.410992i	−0.910399	−	0.413732i	$-0.864225\pi$
$331$	−114.150	+	136.038i	−0.344863	+	0.410992i	0.565536	+	0.824724i	$0.308670\pi$
$332$	5.06710	+	2.48286i	0.0152624	+	0.00747848i
$333$		0			0
$334$	204.208	+	327.467i	0.611402	+	0.980439i
$335$	91.0570	+	16.0558i	0.271812	+	0.0479278i
$336$		0			0
$337$	337.952	+	123.004i	1.00282	+	0.364998i	0.790673	−	0.612238i	$-0.209731\pi$
$337$	337.952	+	123.004i	1.00282	+	0.364998i	0.212151	+	0.977237i	$0.431953\pi$
$338$	−88.8364	+	272.563i	−0.262829	+	0.806400i
$339$		0			0
$340$	16.7370	−	156.493i	0.0492265	−	0.460273i
$341$	−64.8885	−	112.390i	−0.190289	−	0.329590i
$342$		0			0
$343$	−306.005	−	176.672i	−0.892144	−	0.515079i
$344$	282.458	+	191.648i	0.821100	+	0.557117i
$345$		0			0
$346$	−485.278	+	102.686i	−1.40254	+	0.296780i
$347$	178.381	+	212.586i	0.514065	+	0.612639i	0.959167	−	0.282841i	$-0.0912770\pi$
$347$	178.381	+	212.586i	0.514065	+	0.612639i	−0.445102	+	0.895480i	$0.646833\pi$
$348$		0			0
$349$	49.7907	−	18.1223i	0.142667	−	0.0519265i	−0.269700	−	0.962944i	$-0.586924\pi$
$349$	49.7907	−	18.1223i	0.142667	−	0.0519265i	0.412367	+	0.911018i	$0.364702\pi$
$350$	241.858	−	8.22479i	0.691023	−	0.0234994i
$351$		0			0
$352$	−593.721	+	101.897i	−1.68671	+	0.289479i
$353$	128.371	−	46.7231i	0.363657	−	0.132360i	−0.153728	−	0.988113i	$-0.549128\pi$
$353$	128.371	−	46.7231i	0.363657	−	0.132360i	0.517385	+	0.855753i	$0.326906\pi$
$354$		0			0
$355$	−46.9782	−	55.9864i	−0.132333	−	0.157708i
$356$	65.6677	+	265.443i	0.184460	+	0.745625i
$357$		0			0
$358$	44.5546	+	34.8755i	0.124454	+	0.0974175i
$359$	166.650	+	96.2154i	0.464206	+	0.268009i	0.713811	−	0.700338i	$-0.246968\pi$
$359$	166.650	+	96.2154i	0.464206	+	0.268009i	−0.249605	+	0.968348i	$0.580301\pi$
$360$		0			0
$361$	372.437	+	645.079i	1.03168	+	1.78692i
$362$	−531.679	−	75.2177i	−1.46873	−	0.207784i
$363$		0			0
$364$	−38.0286	+	131.713i	−0.104474	+	0.361849i
$365$	−91.5392	−	33.3176i	−0.250792	−	0.0912810i
$366$		0			0
$367$	−239.898	−	42.3005i	−0.653673	−	0.115260i	−0.163030	−	0.986621i	$-0.552127\pi$
$367$	−239.898	−	42.3005i	−0.653673	−	0.115260i	−0.490642	+	0.871361i	$0.663238\pi$
$368$	−223.377	+	173.211i	−0.607003	+	0.470683i
$369$		0			0
$370$	43.8032	+	23.3419i	0.118387	+	0.0630863i
$371$	111.711	−	133.132i	0.301108	−	0.358847i
$372$		0			0
$373$	−68.4605	−	388.259i	−0.183540	−	1.04091i	−0.927817	−	0.373037i	$-0.878317\pi$
$373$	−68.4605	−	388.259i	−0.183540	−	1.04091i	0.744276	−	0.667872i	$-0.232795\pi$
$374$	−413.042	+	371.223i	−1.10439	+	0.992574i
$375$		0			0
$376$	392.704	−	190.205i	1.04443	−	0.505864i
$377$	−206.061			−0.546582
$378$		0			0
$379$			353.110i			0.931690i	0.884866	+	0.465845i	$0.154249\pi$
$379$			353.110i			0.931690i	−0.884866	+	0.465845i	$0.845751\pi$
$380$	143.729	+	324.415i	0.378235	+	0.853722i
$381$		0			0
$382$	−46.8092	+	42.0699i	−0.122537	+	0.110131i
$383$	−45.9409	+	8.10062i	−0.119950	+	0.0211504i	−0.233301	−	0.972405i	$-0.574953\pi$
$383$	−45.9409	+	8.10062i	−0.119950	+	0.0211504i	0.113351	+	0.993555i	$0.463842\pi$
$384$		0			0
$385$	260.257	+	218.381i	0.675991	+	0.567224i
$386$	−411.273	−	219.160i	−1.06548	−	0.567772i
$387$		0			0
$388$	−253.498	−	377.310i	−0.653345	−	0.972449i
$389$	28.7035	−	162.786i	0.0737880	−	0.418472i	−0.925430	−	0.378920i	$-0.876296\pi$
$389$	28.7035	−	162.786i	0.0737880	−	0.418472i	0.999217	−	0.0395526i	$-0.0125933\pi$
$390$		0			0
$391$	−89.1256	+	244.870i	−0.227943	+	0.626267i
$392$	−6.31323	+	25.0287i	−0.0161052	+	0.0638488i
$393$		0			0
$394$	−499.244	−	70.6290i	−1.26712	−	0.179261i
$395$	296.819	−	171.368i	0.751440	−	0.433844i
$396$		0			0
$397$	−330.658	+	572.717i	−0.832892	+	1.44261i	0.0628427	+	0.998023i	$0.479983\pi$
$397$	−330.658	+	572.717i	−0.832892	+	1.44261i	−0.895735	+	0.444588i	$0.853350\pi$
$398$	469.813	+	367.749i	1.18043	+	0.923993i
$399$		0			0
$400$	−87.4310	−	272.467i	−0.218577	−	0.681166i
$401$	−322.430	+	270.551i	−0.804065	+	0.674690i	−0.949183	−	0.314724i	$-0.898088\pi$
$401$	−322.430	+	270.551i	−0.804065	+	0.674690i	0.145119	+	0.989414i	$0.453644\pi$
$402$		0			0
$403$	11.9444	+	32.8169i	0.0296386	+	0.0814314i
$404$	−677.152	+	46.1087i	−1.67612	+	0.114131i
$405$		0			0
$406$	550.089	−	18.7067i	1.35490	−	0.0460757i
$407$	−59.9011	−	164.577i	−0.147177	−	0.404366i
$408$		0			0
$409$	−298.130	+	250.161i	−0.728925	+	0.611640i	−0.929838	−	0.367969i	$-0.880053\pi$
$409$	−298.130	+	250.161i	−0.728925	+	0.611640i	0.200914	+	0.979609i	$0.435609\pi$
$410$	−116.163	+	24.5804i	−0.283324	+	0.0599521i
$411$		0			0
$412$	−31.8330	+	43.6466i	−0.0772646	+	0.105938i
$413$	−52.6430	+	91.1803i	−0.127465	+	0.220776i
$414$		0			0
$415$	−3.25884	+	1.88149i	−0.00785263	+	0.00453372i
$416$	162.104	+	0.739996i	0.389674	+	0.00177884i
$417$		0			0
$418$	387.989	−	1190.41i	0.928203	−	2.84787i
$419$	1.34000	−	3.68161i	0.00319809	−	0.00878667i	−0.938083	−	0.346410i	$-0.887401\pi$
$419$	1.34000	−	3.68161i	0.00319809	−	0.00878667i	0.941281	+	0.337623i	$0.109623\pi$
$420$		0			0
$421$	−74.4542	+	422.251i	−0.176851	+	1.00297i	0.759135	+	0.650933i	$0.225622\pi$
$421$	−74.4542	+	422.251i	−0.176851	+	1.00297i	−0.935986	+	0.352038i	$0.885489\pi$
$422$	−85.4290	−	136.993i	−0.202438	−	0.324628i
$423$		0			0
$424$	−187.504	−	84.0983i	−0.442227	−	0.198345i
$425$	−202.082	−	169.567i	−0.475487	−	0.398981i
$426$		0			0
$427$	423.048	−	74.5948i	0.990746	−	0.174695i
$428$	−447.002	−	464.578i	−1.04440	−	1.08546i
$429$		0			0
$430$	−211.133	+	85.0791i	−0.491007	+	0.197858i
$431$			112.825i			0.261775i	0.991397	+	0.130887i	$0.0417826\pi$
$431$			112.825i			0.261775i	−0.991397	+	0.130887i	$0.958217\pi$
$432$		0			0
$433$	164.343			0.379546			0.189773	−	0.981828i	$-0.439225\pi$
$433$	164.343			0.379546			0.189773	+	0.981828i	$0.439225\pi$
$434$	−34.8651	−	86.5216i	−0.0803344	−	0.199359i
$435$		0			0
$436$	−193.141	+	185.834i	−0.442984	+	0.426224i
$437$	−102.018	−	578.570i	−0.233450	−	1.32396i
$438$		0			0
$439$	424.795	−	506.251i	0.967642	−	1.15319i	−0.0205222	−	0.999789i	$-0.506533\pi$
$439$	424.795	−	506.251i	0.967642	−	1.15319i	0.988164	−	0.153401i	$-0.0490227\pi$
$440$	164.402	−	366.547i	0.373640	−	0.833062i
$441$		0			0
$442$	126.808	−	79.0774i	0.286895	−	0.178908i
$443$	−230.174	−	40.5858i	−0.519580	−	0.0916159i	−0.0922926	−	0.995732i	$-0.529420\pi$
$443$	−230.174	−	40.5858i	−0.519580	−	0.0916159i	−0.427287	+	0.904116i	$0.640531\pi$
$444$		0			0
$445$	−171.357	−	62.3687i	−0.385071	−	0.140154i
$446$	−255.771	−	83.3633i	−0.573478	−	0.186913i
$447$		0			0
$448$	−432.811	+	12.7408i	−0.966097	+	0.0284392i
$449$	122.709	+	212.538i	0.273294	+	0.473360i	0.969703	−	0.244285i	$-0.0785534\pi$
$449$	122.709	+	212.538i	0.273294	+	0.473360i	−0.696409	+	0.717645i	$0.745220\pi$
$450$		0			0
$451$	362.836	+	209.483i	0.804514	+	0.464487i
$452$	−46.3169	−	33.7806i	−0.102471	−	0.0747358i
$453$		0			0
$454$	126.602	+	598.300i	0.278858	+	1.31784i
$455$	−58.7663	−	70.0350i	−0.129157	−	0.153923i
$456$		0			0
$457$	429.197	−	156.215i	0.939162	−	0.341827i	0.173327	−	0.984864i	$-0.444548\pi$
$457$	429.197	−	156.215i	0.939162	−	0.341827i	0.765835	+	0.643037i	$0.222326\pi$
$458$	15.0553	+	442.715i	0.0328718	+	0.966627i
$459$		0			0
$460$	−12.8059	−	188.067i	−0.0278389	−	0.408841i
$461$	−613.064	+	223.137i	−1.32986	+	0.484029i	−0.906604	−	0.421982i	$-0.861334\pi$
$461$	−613.064	+	223.137i	−1.32986	+	0.484029i	−0.423254	+	0.906011i	$0.639112\pi$
$462$		0			0
$463$	−153.827	−	183.324i	−0.332240	−	0.395948i	0.573901	−	0.818925i	$-0.305430\pi$
$463$	−153.827	−	183.324i	−0.332240	−	0.395948i	−0.906140	+	0.422977i	$0.860985\pi$
$464$	−198.856	−	619.707i	−0.428568	−	1.33557i
$465$		0			0
$466$	−103.860	+	132.685i	−0.222875	+	0.284731i
$467$	81.5519	+	47.0840i	0.174629	+	0.100822i	0.584767	−	0.811201i	$-0.301186\pi$
$467$	81.5519	+	47.0840i	0.174629	+	0.100822i	−0.410138	+	0.912024i	$0.634519\pi$
$468$		0			0
$469$	−117.255	−	203.092i	−0.250012	−	0.433033i
$470$	−40.7605	+	288.117i	−0.0867245	+	0.613015i
$471$		0			0
$472$	120.715	+	30.4489i	0.255751	+	0.0645105i
$473$	754.774	+	274.715i	1.59572	+	0.580793i
$474$		0			0
$475$	585.705	+	103.276i	1.23306	+	0.217422i
$476$	−331.340	+	222.612i	−0.696092	+	0.467673i
$477$		0			0
$478$	117.098	−	219.744i	0.244974	−	0.459716i
$479$	220.464	−	262.739i	0.460260	−	0.548516i	−0.485137	−	0.874438i	$-0.661230\pi$
$479$	220.464	−	262.739i	0.460260	−	0.548516i	0.945397	+	0.325922i	$0.105675\pi$
$480$		0			0
$481$	8.18402	+	46.4139i	0.0170146	+	0.0964945i
$482$	202.937	+	225.799i	0.421032	+	0.468462i
$483$		0			0
$484$	−853.513	+	378.142i	−1.76346	+	0.781286i
$485$	303.135			0.625020
$486$		0			0
$487$			446.412i			0.916656i	0.888783	+	0.458328i	$0.151552\pi$
$487$			446.412i			0.916656i	−0.888783	+	0.458328i	$0.848448\pi$
$488$	−221.420	−	457.152i	−0.453729	−	0.936786i
$489$		0			0
$490$	−11.5066	−	12.8029i	−0.0234830	−	0.0261284i
$491$	−5.90542	+	1.04128i	−0.0120273	+	0.00212074i	−0.179659	−	0.983729i	$-0.557499\pi$
$491$	−5.90542	+	1.04128i	−0.0120273	+	0.00212074i	0.167631	+	0.985850i	$0.446388\pi$
$492$		0			0
$493$	−459.621	−	385.668i	−0.932295	−	0.782288i
$494$	−158.448	+	297.342i	−0.320744	+	0.601906i
$495$		0			0
$496$	−87.1663	+	67.5906i	−0.175739	+	0.136271i
$497$	−32.1885	+	182.550i	−0.0647655	+	0.367304i
$498$		0			0
$499$	−274.772	+	754.929i	−0.550645	+	1.51288i	0.282188	+	0.959359i	$0.408940\pi$
$499$	−274.772	+	754.929i	−0.550645	+	1.51288i	−0.832833	+	0.553525i	$0.813282\pi$
$500$	439.621	+	126.928i	0.879242	+	0.253857i
$501$		0			0
$502$	5.93385	−	41.9436i	0.0118204	−	0.0835531i
$503$	127.666	−	73.7082i	0.253810	−	0.146537i	−0.367698	−	0.929945i	$-0.619854\pi$
$503$	127.666	−	73.7082i	0.253810	−	0.146537i	0.621508	+	0.783408i	$0.286521\pi$
$504$		0			0
$505$	226.311	−	391.982i	0.448141	−	0.776203i
$506$	−409.984	+	523.769i	−0.810245	+	1.03512i
$507$		0			0
$508$	−555.067	+	137.318i	−1.09265	+	0.270311i
$509$	519.941	−	436.282i	1.02149	−	0.857136i	0.0316799	−	0.999498i	$-0.489914\pi$
$509$	519.941	−	436.282i	1.02149	−	0.857136i	0.989815	+	0.142362i	$0.0454698\pi$
$510$		0			0
$511$	84.5035	+	232.171i	0.165369	+	0.454347i
$512$	154.210	+	488.225i	0.301192	+	0.953564i
$513$		0			0
$514$	2.65340	+	78.0259i	0.00516226	+	0.151801i
$515$	−12.3216	−	33.8533i	−0.0239254	−	0.0657345i
$516$		0			0
$517$	786.551	−	659.995i	1.52138	−	1.27659i
$518$	−26.0611	−	123.161i	−0.0503110	−	0.237762i
$519$		0			0
$520$	−60.6966	+	89.4569i	−0.116724	+	0.172033i
$521$	−107.426	+	186.067i	−0.206192	+	0.357135i	−0.950512	−	0.310688i	$-0.899441\pi$
$521$	−107.426	+	186.067i	−0.206192	+	0.357135i	0.744320	+	0.667823i	$0.232774\pi$
$522$		0			0
$523$	535.275	−	309.041i	1.02347	−	0.590901i	0.108363	−	0.994111i	$-0.465439\pi$
$523$	535.275	−	309.041i	1.02347	−	0.590901i	0.915107	+	0.403210i	$0.132106\pi$
$524$	310.366	+	33.1938i	0.592301	+	0.0633470i
$525$		0			0
$526$	731.714	+	238.487i	1.39109	+	0.453398i
$527$	−34.7786	+	95.5535i	−0.0659936	+	0.181316i
$528$		0			0
$529$	37.6630	−	213.598i	0.0711966	−	0.403776i
$530$	116.285	−	72.5157i	0.219407	−	0.136822i
$531$		0			0
$532$	395.989	−	808.150i	0.744341	−	1.51908i
$533$	−86.3668	−	72.4704i	−0.162039	−	0.135967i
$534$		0			0
$535$	423.406	−	74.6579i	0.791414	−	0.139548i
$536$	−193.173	+	198.943i	−0.360397	+	0.371162i
$537$		0			0
$538$	96.0517	+	238.363i	0.178535	+	0.443053i
$539$			60.7406i			0.112691i
$540$		0			0
$541$	−647.938			−1.19767			−0.598834	−	0.800873i	$-0.704369\pi$
$541$	−647.938			−1.19767			−0.598834	+	0.800873i	$0.704369\pi$
$542$	322.081	−	129.787i	0.594245	−	0.239460i
$543$		0			0
$544$	360.190	+	305.048i	0.662114	+	0.560750i
$545$	−31.0379	−	176.024i	−0.0569502	−	0.322981i
$546$		0			0
$547$	−431.014	+	513.662i	−0.787960	+	0.939054i	−0.999264	−	0.0383666i	$-0.987785\pi$
$547$	−431.014	+	513.662i	−0.787960	+	0.939054i	0.211304	+	0.977420i	$0.432229\pi$
$548$	387.038	−	789.882i	0.706274	−	1.44139i
$549$		0			0
$550$	−356.299	−	571.358i	−0.647817	−	1.03883i
$551$	1332.15	+	234.893i	2.41769	+	0.426304i
$552$		0			0
$553$	−816.861	−	297.313i	−1.47714	−	0.537637i
$554$	99.8396	−	306.323i	0.180216	−	0.552929i
$555$		0			0
$556$	788.767	+	84.3593i	1.41865	+	0.151725i
$557$	334.348	+	579.107i	0.600265	+	1.03969i	0.992781	+	0.119944i	$0.0382716\pi$
$557$	334.348	+	579.107i	0.600265	+	1.03969i	−0.392515	+	0.919745i	$0.628395\pi$
$558$		0			0
$559$	−187.187	−	108.072i	−0.334860	−	0.193331i
$560$	153.911	−	244.319i	0.274841	−	0.436284i
$561$		0			0
$562$	−159.047	+	33.6547i	−0.283001	+	0.0598837i
$563$	−30.5238	−	36.3768i	−0.0542163	−	0.0646125i	0.738255	−	0.674522i	$-0.235650\pi$
$563$	−30.5238	−	36.3768i	−0.0542163	−	0.0646125i	−0.792471	+	0.609910i	$0.791206\pi$
$564$		0			0
$565$	35.9245	−	13.0754i	0.0635831	−	0.0231424i
$566$	640.573	−	21.7838i	1.13175	−	0.0384872i
$567$		0			0
$568$	218.048	−	22.3141i	0.383887	−	0.0392853i
$569$	−114.639	+	41.7252i	−0.201475	+	0.0733307i	−0.440786	−	0.897612i	$-0.645300\pi$
$569$	−114.639	+	41.7252i	−0.201475	+	0.0733307i	0.239312	+	0.970943i	$0.423078\pi$
$570$		0			0
$571$	−604.450	−	720.356i	−1.05858	−	1.26157i	−0.963958	−	0.266056i	$-0.914280\pi$
$571$	−604.450	−	720.356i	−1.05858	−	1.26157i	−0.0946241	−	0.995513i	$-0.530165\pi$
$572$	370.294	−	91.6067i	0.647366	−	0.160152i
$573$		0			0
$574$	237.139	+	185.622i	0.413134	+	0.323383i
$575$	−273.626	−	157.978i	−0.475871	−	0.274744i
$576$		0			0
$577$	−71.2440	−	123.398i	−0.123473	−	0.213862i	0.797662	−	0.603105i	$-0.206070\pi$
$577$	−71.2440	−	123.398i	−0.123473	−	0.213862i	−0.921135	+	0.389243i	$0.872737\pi$
$578$	−141.453	−	20.0117i	−0.244729	−	0.0346222i
$579$		0			0
$580$	416.991	+	120.395i	0.718949	+	0.207577i
$581$	8.96850	+	3.26427i	0.0154363	+	0.00561836i
$582$		0			0
$583$	−476.222	−	83.9708i	−0.816848	−	0.144032i
$584$	236.824	−	171.074i	0.405520	−	0.292934i
$585$		0			0
$586$	−89.0426	−	47.4491i	−0.151950	−	0.0809712i
$587$	109.295	−	130.253i	0.186192	−	0.221895i	−0.664871	−	0.746958i	$-0.731514\pi$
$587$	109.295	−	130.253i	0.186192	−	0.221895i	0.851064	+	0.525063i	$0.175958\pi$
$588$		0			0
$589$	−39.8093	−	225.770i	−0.0675880	−	0.383311i
$590$	−61.7489	+	55.4970i	−0.104659	+	0.0940627i
$591$		0			0
$592$	−131.687	+	69.4033i	−0.222444	+	0.117235i
$593$	669.024			1.12820			0.564101	−	0.825706i	$-0.309223\pi$
$593$	669.024			1.12820			0.564101	+	0.825706i	$0.309223\pi$
$594$		0			0
$595$		−	266.202i		−	0.447398i
$596$	806.241	−	357.199i	1.35275	−	0.599327i
$597$		0			0
$598$	133.125	−	119.647i	0.222618	−	0.200078i
$599$	483.540	−	85.2611i	0.807245	−	0.142339i	0.245229	−	0.969465i	$-0.421137\pi$
$599$	483.540	−	85.2611i	0.807245	−	0.142339i	0.562016	+	0.827126i	$0.310026\pi$
$600$		0			0
$601$	231.159	+	193.966i	0.384624	+	0.322738i	0.814515	−	0.580143i	$-0.197003\pi$
$601$	231.159	+	193.966i	0.384624	+	0.322738i	−0.429890	+	0.902881i	$0.641448\pi$
$602$	509.513	+	271.510i	0.846368	+	0.451013i
$603$		0			0
$604$	349.247	−	234.643i	0.578223	−	0.388482i
$605$	108.104	−	613.090i	0.178685	−	1.01337i
$606$		0			0
$607$	−66.6834	+	183.211i	−0.109857	+	0.301830i	−0.982424	−	0.186665i	$-0.940232\pi$
$607$	−66.6834	+	183.211i	−0.109857	+	0.301830i	0.872566	+	0.488496i	$0.162454\pi$
$608$	−1047.13	−	189.570i	−1.72225	−	0.311792i
$609$		0			0
$610$	335.401	+	47.4498i	0.549837	+	0.0777866i
$611$	−239.286	+	138.152i	−0.391630	+	0.226107i
$612$		0			0
$613$	−296.011	+	512.707i	−0.482890	+	0.836389i	−0.999807	−	0.0196459i	$-0.993746\pi$
$613$	−296.011	+	512.707i	−0.482890	+	0.836389i	0.516917	+	0.856035i	$0.327079\pi$
$614$	−198.419	−	155.314i	−0.323158	−	0.252954i
$615$		0			0
$616$	−980.197	+	278.164i	−1.59123	+	0.451565i
$617$	272.885	−	228.978i	0.442277	−	0.371114i	−0.394284	−	0.918989i	$-0.629007\pi$
$617$	272.885	−	228.978i	0.442277	−	0.371114i	0.836561	+	0.547874i	$0.184563\pi$
$618$		0			0
$619$	190.318	+	522.895i	0.307461	+	0.844741i	0.993150	+	0.116847i	$0.0372787\pi$
$619$	190.318	+	522.895i	0.307461	+	0.844741i	−0.685689	+	0.727894i	$0.740499\pi$
$620$	−4.99712	−	73.3876i	−0.00805987	−	0.118367i
$621$		0			0
$622$	−458.381	+	15.5880i	−0.736948	+	0.0250612i
$623$	158.186	+	434.612i	0.253910	+	0.697612i
$624$		0			0
$625$	108.750	−	91.2519i	0.174000	−	0.146003i
$626$	−578.643	+	122.442i	−0.924349	+	0.195595i
$627$		0			0
$628$	−861.524	−	628.341i	−1.37185	−	1.00054i
$629$	−68.6145	+	118.844i	−0.109085	+	0.188941i
$630$		0			0
$631$	716.677	−	413.773i	1.13578	−	0.655742i	0.190397	−	0.981707i	$-0.439022\pi$
$631$	716.677	−	413.773i	1.13578	−	0.655742i	0.945382	+	0.325965i	$0.105689\pi$
$632$	−74.5100	+	1025.18i	−0.117896	+	1.62213i
$633$		0			0
$634$	−116.956	+	358.837i	−0.184473	+	0.565989i
$635$	130.419	−	358.324i	0.205385	−	0.564289i
$636$		0			0
$637$	2.83833	−	16.0970i	0.00445578	−	0.0252700i
$638$	−810.379	−	1299.52i	−1.27019	−	2.03686i
$639$		0			0
$640$	−327.606	−	96.2094i	−0.511884	−	0.150327i
$641$	−18.1457	−	15.2260i	−0.0283084	−	0.0237536i	0.628524	−	0.777790i	$-0.283660\pi$
$641$	−18.1457	−	15.2260i	−0.0283084	−	0.0237536i	−0.656832	+	0.754037i	$0.728104\pi$
$642$		0			0
$643$	−511.335	+	90.1621i	−0.795233	+	0.140221i	−0.556482	−	0.830860i	$-0.687849\pi$
$643$	−511.335	+	90.1621i	−0.795233	+	0.140221i	−0.238751	+	0.971081i	$0.576738\pi$
$644$	−344.522	+	331.488i	−0.534972	+	0.514732i
$645$		0			0
$646$	−909.928	+	366.669i	−1.40856	+	0.567599i
$647$			728.461i			1.12591i	0.826489	+	0.562953i	$0.190335\pi$
$647$			728.461i			1.12591i	−0.826489	+	0.562953i	$0.809665\pi$
$648$		0			0
$649$	292.954			0.451393
$650$	67.7246	+	168.066i	0.104192	+	0.258563i
$651$		0			0
$652$	497.360	+	516.917i	0.762822	+	0.792818i
$653$	−101.708	−	576.816i	−0.155755	−	0.883332i	−0.958092	−	0.286460i	$-0.907521\pi$
$653$	−101.708	−	576.816i	−0.155755	−	0.883332i	0.802337	−	0.596871i	$-0.203590\pi$
$654$		0			0
$655$	−133.800	+	159.457i	−0.204275	+	0.243445i
$656$	134.600	−	329.675i	0.205183	−	0.502553i
$657$		0			0
$658$	626.241	−	390.524i	0.951734	−	0.593502i
$659$	−1165.69	−	205.543i	−1.76888	−	0.311901i	−0.808064	−	0.589095i	$-0.799485\pi$
$659$	−1165.69	−	205.543i	−1.76888	−	0.311901i	−0.960814	+	0.277194i	$0.910596\pi$
$660$		0			0
$661$	−112.165	−	40.8248i	−0.169690	−	0.0617622i	0.255778	−	0.966736i	$-0.417668\pi$
$661$	−112.165	−	40.8248i	−0.169690	−	0.0617622i	−0.425468	+	0.904973i	$0.639891\pi$
$662$	337.687	+	110.062i	0.510102	+	0.166257i
$663$		0			0
$664$	0.818062	−	11.2557i	0.00123202	−	0.0169514i
$665$	300.078	+	519.751i	0.451246	+	0.781580i
$666$		0			0
$667$	−622.344	−	359.310i	−0.933049	−	0.538696i
$668$	454.818	−	623.605i	0.680865	−	0.933540i
$669$		0			0
$670$	−38.2826	−	180.917i	−0.0571382	−	0.270026i
$671$	−768.308	−	915.634i	−1.14502	−	1.36458i
$672$		0			0
$673$	989.622	−	360.193i	1.47046	−	0.535205i	0.522237	−	0.852800i	$-0.325098\pi$
$673$	989.622	−	360.193i	1.47046	−	0.535205i	0.948226	+	0.317595i	$0.102875\pi$
$674$	−24.4463	−	718.866i	−0.0362704	−	1.06657i
$675$		0			0
$676$	572.026	−	38.9505i	0.846192	−	0.0576190i
$677$	−529.374	+	192.676i	−0.781940	+	0.284603i	−0.701982	−	0.712195i	$-0.747701\pi$
$677$	−529.374	+	192.676i	−0.781940	+	0.284603i	−0.0799588	+	0.996798i	$0.525479\pi$
$678$		0			0
$679$	−494.202	−	588.967i	−0.727838	−	0.867404i
$680$	−302.813	+	85.9334i	−0.445314	+	0.126373i
$681$		0			0
$682$	−159.984	+	204.386i	−0.234581	+	0.299685i
$683$	226.467	+	130.751i	0.331577	+	0.191436i	0.656541	−	0.754290i	$-0.272019\pi$
$683$	226.467	+	130.751i	0.331577	+	0.191436i	−0.324964	+	0.945726i	$0.605352\pi$
$684$		0			0
$685$	293.295	+	508.002i	0.428168	+	0.741609i
$686$	−98.9910	+	699.721i	−0.144302	+	1.02000i
$687$		0			0
$688$	144.374	−	667.236i	0.209846	−	0.969819i
$689$	122.280	+	44.5065i	0.177475	+	0.0645957i
$690$		0			0
$691$	720.416	+	127.029i	1.04257	+	0.183833i	0.668611	−	0.743612i	$-0.266889\pi$
$691$	720.416	+	127.029i	1.04257	+	0.183833i	0.373959	+	0.927445i	$0.378000\pi$
$692$	553.242	+	823.455i	0.799483	+	1.18996i
$693$		0			0
$694$	261.014	−	489.817i	0.376101	−	0.705788i
$695$	−340.041	+	405.245i	−0.489268	+	0.583087i
$696$		0			0
$697$	−57.0050	−	323.291i	−0.0817862	−	0.463832i
$698$	−70.8374	−	78.8175i	−0.101486	−	0.112919i
$699$		0			0
$700$	−196.051	−	442.511i	−0.280073	−	0.632158i
$701$	−980.935			−1.39934			−0.699668	−	0.714468i	$-0.746669\pi$
$701$	−980.935			−1.39934			−0.699668	+	0.714468i	$0.746669\pi$
$702$		0			0
$703$		−	309.385i		−	0.440093i
$704$	632.842	+	1025.21i	0.898923	+	1.45627i
$705$		0			0
$706$	−182.634	−	203.208i	−0.258688	−	0.287830i
$707$	−1130.55	+	199.346i	−1.59908	+	0.281960i
$708$		0			0
$709$	−36.9636	−	31.0162i	−0.0521349	−	0.0437464i	0.616348	−	0.787474i	$-0.288612\pi$
$709$	−36.9636	−	31.0162i	−0.0521349	−	0.0437464i	−0.668483	+	0.743728i	$0.733056\pi$
$710$	−68.7405	+	128.998i	−0.0968177	+	0.181687i
$711$		0			0
$712$	443.322	−	320.241i	0.622643	−	0.449776i
$713$	−21.1487	+	119.940i	−0.0296616	+	0.168219i
$714$		0			0
$715$	−87.0046	+	239.043i	−0.121685	+	0.334326i
$716$	31.3903	−	108.721i	0.0438412	−	0.151845i
$717$		0			0
$718$	53.9103	−	381.067i	0.0750840	−	0.530734i
$719$	−1170.39	+	675.725i	−1.62780	+	0.939813i	−0.643057	+	0.765818i	$0.722334\pi$
$719$	−1170.39	+	675.725i	−1.62780	+	0.939813i	−0.984747	+	0.173994i	$0.944333\pi$
$720$		0			0
$721$	−45.6863	+	79.1311i	−0.0633652	+	0.109752i
$722$	918.251	−	1173.10i	1.27182	−	1.62479i
$723$		0			0
$724$	257.908	+	1042.52i	0.356226	+	1.43994i
$725$	557.284	−	467.617i	0.768667	−	0.644988i
$726$		0			0
$727$	−264.383	−	726.385i	−0.363662	−	0.999154i	−0.977724	−	0.209896i	$-0.932687\pi$
$727$	−264.383	−	726.385i	−0.363662	−	0.999154i	0.614061	−	0.789258i	$-0.289535\pi$
$728$	272.762	−	27.9133i	0.374673	−	0.0383424i
$729$		0			0
$730$	6.62163	+	194.716i	0.00907073	+	0.266734i
$731$	−215.251	−	591.397i	−0.294461	−	0.809025i
$732$		0			0
$733$	−1060.19	+	889.603i	−1.44637	+	1.21365i	−0.511190	+	0.859468i	$0.670795\pi$
$733$	−1060.19	+	889.603i	−1.44637	+	1.21365i	−0.935178	+	0.354179i	$0.884760\pi$
$734$	100.859	+	476.643i	0.137410	+	0.649378i
$735$		0			0
$736$	488.295	+	284.897i	0.663444	+	0.387088i
$737$	−326.259	+	565.097i	−0.442685	+	0.766753i
$738$		0			0
$739$	−295.927	+	170.854i	−0.400442	+	0.231196i	−0.686675	−	0.726965i	$-0.740930\pi$
$739$	−295.927	+	170.854i	−0.400442	+	0.231196i	0.286232	+	0.958160i	$0.407597\pi$
$740$	10.5567	−	98.7058i	0.0142658	−	0.133386i
$741$		0			0
$742$	−330.473	−	107.711i	−0.445382	−	0.145163i
$743$	−191.604	+	526.428i	−0.257879	+	0.708517i	0.741419	+	0.671043i	$0.234153\pi$
$743$	−191.604	+	526.428i	−0.257879	+	0.708517i	−0.999298	+	0.0374741i	$0.988069\pi$
$744$		0			0
$745$	−102.117	+	579.134i	−0.137070	+	0.777361i
$746$	−669.064	+	417.229i	−0.896869	+	0.559288i
$747$		0			0
$748$	997.395	+	488.718i	1.33342	+	0.653367i
$749$	−835.336	−	700.930i	−1.11527	−	0.935821i
$750$		0			0
$751$	732.986	−	129.245i	0.976013	−	0.172097i	0.337178	−	0.941441i	$-0.390528\pi$
$751$	732.986	−	129.245i	0.976013	−	0.172097i	0.638835	+	0.769344i	$0.279417\pi$
$752$	−646.394	−	586.304i	−0.859566	−	0.779660i
$753$		0			0
$754$	154.035	+	382.254i	0.204290	+	0.506969i
$755$			280.588i			0.371640i
$756$		0			0
$757$	−34.0389			−0.0449655			−0.0224828	−	0.999747i	$-0.507157\pi$
$757$	−34.0389			−0.0449655			−0.0224828	+	0.999747i	$0.507157\pi$
$758$	655.038	−	263.957i	0.864166	−	0.348228i
$759$		0			0
$760$	494.365	−	509.132i	0.650480	−	0.669910i
$761$	−27.3928	−	155.352i	−0.0359958	−	0.204142i	0.961506	−	0.274784i	$-0.0886063\pi$
$761$	−27.3928	−	155.352i	−0.0359958	−	0.204142i	−0.997502	+	0.0706419i	$0.977495\pi$
$762$		0			0
$763$	−291.401	+	347.278i	−0.381914	+	0.455148i
$764$	113.033	+	55.3854i	0.147948	+	0.0724940i
$765$		0			0
$766$	49.3688	+	79.1673i	0.0644501	+	0.103352i
$767$	−77.6362	−	13.6894i	−0.101221	−	0.0178479i
$768$		0			0
$769$	271.545	+	98.8342i	0.353114	+	0.128523i	0.512486	−	0.858696i	$-0.328725\pi$
$769$	271.545	+	98.8342i	0.353114	+	0.128523i	−0.159372	+	0.987219i	$0.550947\pi$
$770$	210.561	−	646.034i	0.273456	−	0.839005i
$771$		0			0
$772$	−99.1176	+	926.759i	−0.128391	+	1.20047i
$773$	−514.374	−	890.922i	−0.665426	−	1.15255i	−0.979170	−	0.203043i	$-0.934917\pi$
$773$	−514.374	−	890.922i	−0.665426	−	1.15255i	0.313744	−	0.949508i	$-0.398417\pi$
$774$		0			0
$775$	−106.774	−	61.6463i	−0.137774	−	0.0795436i
$776$	−510.435	+	752.298i	−0.657777	+	0.969456i
$777$		0			0
$778$	−323.432	+	68.4391i	−0.415723	+	0.0879680i
$779$	475.734	+	566.957i	0.610698	+	0.727801i
$780$		0			0
$781$	484.669	−	176.405i	0.620575	−	0.225871i
$782$	520.870	−	17.7131i	0.666075	−	0.0226510i
$783$		0			0
$784$	51.1489	−	6.99812i	0.0652409	−	0.00892617i
$785$	668.218	−	243.212i	0.851233	−	0.309824i
$786$		0			0
$787$	−541.136	−	644.900i	−0.687593	−	0.819441i	0.303469	−	0.952841i	$-0.401855\pi$
$787$	−541.136	−	644.900i	−0.687593	−	0.819441i	−0.991062	+	0.133400i	$0.957411\pi$
$788$	242.174	+	978.920i	0.307328	+	1.24228i
$789$		0			0
$790$	−539.775	−	422.513i	−0.683260	−	0.534826i
$791$	−83.9724	−	48.4815i	−0.106160	−	0.0612914i
$792$		0			0
$793$	160.824	+	278.555i	0.202805	+	0.351268i
$794$	1309.59	+	185.271i	1.64936	+	0.233338i
$795$		0			0
$796$	330.999	−	1146.43i	0.415828	−	1.44023i
$797$	−50.5238	−	18.3892i	−0.0633925	−	0.0230730i	0.310129	−	0.950694i	$-0.399628\pi$
$797$	−50.5238	−	18.3892i	−0.0633925	−	0.0230730i	−0.373522	+	0.927621i	$0.621850\pi$
$798$		0			0
$799$	−792.295	−	139.703i	−0.991609	−	0.174847i
$800$	−440.083	+	365.863i	−0.550104	+	0.457329i
$801$		0			0
$802$	742.908	+	395.882i	0.926320	+	0.493618i
$803$	441.896	−	526.631i	0.550306	−	0.655829i
$804$		0			0
$805$	−55.3648	−	313.990i	−0.0687762	−	0.390049i
$806$	51.9483	−	46.6887i	0.0644520	−	0.0579264i
$807$		0			0
$808$	591.719	+	1221.68i	0.732325	+	1.51199i
$809$	−491.114			−0.607063			−0.303531	−	0.952821i	$-0.598166\pi$
$809$	−491.114			−0.607063			−0.303531	+	0.952821i	$0.598166\pi$
$810$		0			0
$811$		−	1304.91i		−	1.60901i	−0.593943	−	0.804507i	$-0.702430\pi$
$811$		−	1304.91i		−	1.60901i	0.593943	−	0.804507i	$-0.297570\pi$
$812$	−445.905	−	1006.46i	−0.549144	−	1.23948i
$813$		0			0
$814$	−260.521	+	234.144i	−0.320051	+	0.287646i
$815$	−471.107	+	83.0688i	−0.578045	+	0.101925i
$816$		0			0
$817$	1086.93	+	912.043i	1.33039	+	1.11633i
$818$	686.920	+	366.046i	0.839755	+	0.447490i
$819$		0			0
$820$	132.432	+	197.114i	0.161502	+	0.240383i
$821$	−227.261	+	1288.86i	−0.276810	+	1.56987i	0.456341	+	0.889805i	$0.349160\pi$
$821$	−227.261	+	1288.86i	−0.276810	+	1.56987i	−0.733152	+	0.680065i	$0.761951\pi$
$822$		0			0
$823$	−45.6295	+	125.366i	−0.0554428	+	0.152328i	−0.964322	−	0.264731i	$-0.914717\pi$
$823$	−45.6295	+	125.366i	−0.0554428	+	0.152328i	0.908879	+	0.417059i	$0.136939\pi$
$824$	104.762	+	26.4252i	0.127139	+	0.0320694i
$825$		0			0
$826$	208.496	+	29.4963i	0.252416	+	0.0357098i
$827$	1078.20	−	622.498i	1.30375	−	0.752718i	0.322701	−	0.946501i	$-0.395409\pi$
$827$	1078.20	−	622.498i	1.30375	−	0.752718i	0.981044	+	0.193783i	$0.0620757\pi$
$828$		0			0
$829$	−494.673	+	856.798i	−0.596710	+	1.03353i	0.396593	+	0.917995i	$0.370193\pi$
$829$	−494.673	+	856.798i	−0.596710	+	1.03353i	−0.993303	+	0.115538i	$0.963141\pi$
$830$	5.92631	+	4.63886i	0.00714014	+	0.00558899i
$831$		0			0
$832$	−119.803	−	301.265i	−0.143995	−	0.362097i
$833$	36.4583	−	30.5921i	0.0437674	−	0.0367252i
$834$		0			0
$835$	176.046	+	483.682i	0.210833	+	0.579260i
$836$	−2498.30	+	170.114i	−2.98839	+	0.203486i
$837$		0			0
$838$	−7.83126	+	0.266315i	−0.00934518	+	0.000317799i
$839$	−11.0695	−	30.4133i	−0.0131937	−	0.0362495i	0.932921	−	0.360081i	$-0.117251\pi$
$839$	−11.0695	−	30.4133i	−0.0131937	−	0.0362495i	−0.946115	+	0.323832i	$0.895029\pi$
$840$		0			0
$841$	623.260	−	522.977i	0.741094	−	0.621852i
$842$	838.952	−	177.524i	0.996381	−	0.210837i
$843$		0			0
$844$	−190.269	+	260.880i	−0.225438	+	0.309100i
$845$	−191.177	+	331.128i	−0.226245	+	0.391867i
$846$		0			0
$847$	−1367.43	+	789.486i	−1.61444	+	0.932096i
$848$	−15.8436	+	410.695i	−0.0186835	+	0.484310i
$849$		0			0
$850$	−163.495	+	501.627i	−0.192347	+	0.590149i
$851$	−56.2148	+	154.449i	−0.0660574	+	0.181491i
$852$		0			0
$853$	156.148	−	885.558i	0.183057	−	1.03817i	−0.745369	−	0.666652i	$-0.767727\pi$
$853$	156.148	−	885.558i	0.183057	−	1.03817i	0.928426	−	0.371517i	$-0.121162\pi$
$854$	−454.614	−	729.015i	−0.532335	−	0.853648i
$855$		0			0
$856$	−527.674	+	1176.49i	−0.616442	+	1.37441i
$857$	−936.816	−	786.082i	−1.09313	−	0.917249i	−0.0961902	−	0.995363i	$-0.530666\pi$
$857$	−936.816	−	786.082i	−1.09313	−	0.917249i	−0.996944	+	0.0781141i	$0.975110\pi$
$858$		0			0
$859$	−256.657	+	45.2555i	−0.298785	+	0.0526839i	−0.321031	−	0.947069i	$-0.604029\pi$
$859$	−256.657	+	45.2555i	−0.298785	+	0.0526839i	0.0222459	+	0.999753i	$0.492918\pi$
$860$	315.652	+	328.064i	0.367037	+	0.381470i
$861$		0			0
$862$	209.296	−	84.3389i	0.242803	−	0.0978410i
$863$			545.581i			0.632191i	0.948727	+	0.316095i	$0.102372\pi$
$863$			545.581i			0.632191i	−0.948727	+	0.316095i	$0.897628\pi$
$864$		0			0
$865$	−661.572			−0.764823
$866$	−122.850	−	304.865i	−0.141859	−	0.352038i
$867$		0			0
$868$	−134.440	+	129.353i	−0.154884	+	0.149024i
$869$	420.012	+	2382.01i	0.483328	+	2.74109i
$870$		0			0
$871$	112.869	−	134.512i	0.129585	−	0.154433i
$872$	489.108	+	219.372i	0.560904	+	0.251574i
$873$		0			0
$874$	−997.017	+	621.740i	−1.14075	+	0.711374i
$875$	762.189	+	134.395i	0.871074	+	0.153594i
$876$		0			0
$877$	−555.246	−	202.093i	−0.633119	−	0.230437i	0.00546906	−	0.999985i	$-0.498259\pi$
$877$	−555.246	−	202.093i	−0.633119	−	0.230437i	−0.638588	+	0.769548i	$0.720481\pi$
$878$	−1256.66	−	409.583i	−1.43128	−	0.466496i
$879$		0			0
$880$	−802.857	−	30.9723i	−0.912338	−	0.0351958i
$881$	515.317	+	892.555i	0.584922	+	1.01312i	0.994885	+	0.101013i	$0.0322084\pi$
$881$	515.317	+	892.555i	0.584922	+	1.01312i	−0.409963	+	0.912102i	$0.634458\pi$
$882$		0			0
$883$	1233.98	+	712.438i	1.39748	+	0.806838i	0.994129	−	0.108205i	$-0.0345104\pi$
$883$	1233.98	+	712.438i	1.39748	+	0.806838i	0.403356	+	0.915043i	$0.367844\pi$
$884$	−241.484	−	176.123i	−0.273172	−	0.199234i
$885$		0			0
$886$	96.7707	+	457.323i	0.109222	+	0.516166i
$887$	−116.721	−	139.102i	−0.131590	−	0.156823i	0.696226	−	0.717823i	$-0.254861\pi$
$887$	−116.721	−	139.102i	−0.131590	−	0.156823i	−0.827816	+	0.561000i	$0.810417\pi$
$888$		0			0
$889$	−908.818	+	330.783i	−1.02229	+	0.372084i
$890$	12.3953	+	364.497i	0.0139274	+	0.409547i
$891$		0			0
$892$	36.5508	+	536.784i	0.0409762	+	0.601776i
$893$	1704.42	−	620.356i	1.90864	−	0.694688i
$894$		0			0
$895$	48.5080	+	57.8096i	0.0541989	+	0.0645918i
$896$	347.170	+	793.363i	0.387466	+	0.885450i
$897$		0			0
$898$	302.542	−	386.508i	0.336907	−	0.430410i
$899$	−242.851	−	140.210i	−0.270135	−	0.155962i
$900$		0			0
$901$	189.448	+	328.134i	0.210265	+	0.364189i
$902$	117.375	−	829.672i	0.130128	−	0.919814i
$903$		0			0
$904$	−28.0419	+	111.172i	−0.0310198	+	0.122978i
$905$	−672.998	−	244.951i	−0.743644	−	0.270664i
$906$		0			0
$907$	−576.345	−	101.625i	−0.635441	−	0.112045i	−0.153358	−	0.988171i	$-0.549009\pi$
$907$	−576.345	−	101.625i	−0.635441	−	0.112045i	−0.482083	+	0.876125i	$0.660120\pi$
$908$	1015.24	−	682.094i	1.11810	−	0.751204i
$909$		0			0
$910$	−85.9895	+	161.367i	−0.0944939	+	0.177326i
$911$	88.0696	−	104.957i	0.0966735	−	0.115211i	−0.715539	−	0.698573i	$-0.753819\pi$
$911$	88.0696	−	104.957i	0.0966735	−	0.115211i	0.812212	+	0.583362i	$0.198263\pi$
$912$		0			0
$913$	−4.61141	−	26.1526i	−0.00505083	−	0.0286447i
$914$	−610.620	−	679.409i	−0.668075	−	0.743336i
$915$		0			0
$916$	810.005	−	358.867i	0.884285	−	0.391776i
$917$	527.947			0.575733
$918$		0			0
$919$			654.910i			0.712633i	0.934365	+	0.356316i	$0.115967\pi$
$919$			654.910i			0.712633i	−0.934365	+	0.356316i	$0.884033\pi$
$920$	−339.301	+	164.339i	−0.368806	+	0.178630i
$921$		0			0
$922$	872.209	+	970.466i	0.945997	+	1.05257i
$923$	−136.686	+	24.1014i	−0.148089	+	0.0261121i
$924$		0			0
$925$	−127.461	−	106.952i	−0.137795	−	0.115624i
$926$	−225.086	+	422.395i	−0.243074	+	0.456150i
$927$		0			0
$928$	−1000.94	+	832.130i	−1.07860	+	0.896692i
$929$	−78.7080	+	446.375i	−0.0847234	+	0.480490i	0.912693	+	0.408647i	$0.133999\pi$
$929$	−78.7080	+	446.375i	−0.0847234	+	0.480490i	−0.997416	+	0.0718432i	$0.977112\pi$
$930$		0			0
$931$	−36.6984	+	100.828i	−0.0394183	+	0.108301i
$932$	323.774	+	93.4809i	0.347397	+	0.100301i
$933$		0			0
$934$	26.3816	−	186.479i	0.0282458	−	0.199657i
$935$	−641.461	+	370.348i	−0.686055	+	0.396094i
$936$		0			0
$937$	−245.002	+	424.356i	−0.261475	+	0.452888i	−0.966634	−	0.256161i	$-0.917542\pi$
$937$	−245.002	+	424.356i	−0.261475	+	0.452888i	0.705159	+	0.709049i	$0.250875\pi$
$938$	−289.096	+	369.331i	−0.308205	+	0.393743i
$939$		0			0
$940$	564.941	−	139.760i	0.601001	−	0.148681i
$941$	−251.005	+	210.618i	−0.266743	+	0.223824i	−0.766342	−	0.642433i	$-0.777925\pi$
$941$	−251.005	+	210.618i	−0.266743	+	0.223824i	0.499599	+	0.866257i	$0.333481\pi$
$942$		0			0
$943$	−134.477	−	369.472i	−0.142605	−	0.391805i
$944$	−33.7522	−	246.693i	−0.0357544	−	0.261327i
$945$		0			0
$946$	−54.5977	−	1605.50i	−0.0577143	−	1.69714i
$947$	422.437	+	1160.64i	0.446079	+	1.22559i	0.935432	+	0.353507i	$0.115011\pi$
$947$	422.437	+	1160.64i	0.446079	+	1.22559i	−0.489353	+	0.872086i	$0.662767\pi$
$948$		0			0
$949$	−141.716	+	118.914i	−0.149332	+	0.125304i
$950$	−246.245	−	1163.71i	−0.259205	−	1.22496i
$951$		0			0
$952$	660.640	+	448.245i	0.693950	+	0.470845i
$953$	−25.7103	+	44.5315i	−0.0269782	+	0.0467277i	−0.879199	−	0.476454i	$-0.841922\pi$
$953$	−25.7103	+	44.5315i	−0.0269782	+	0.0467277i	0.852221	+	0.523182i	$0.175255\pi$
$954$		0			0
$955$	−72.6954	+	41.9707i	−0.0761209	+	0.0439484i
$956$	−495.170	−	52.9587i	−0.517960	−	0.0553962i
$957$		0			0
$958$	−652.196	−	212.570i	−0.680789	−	0.221889i
$959$	508.848	−	1398.05i	0.530603	−	1.45782i
$960$		0			0
$961$	158.623	−	899.597i	0.165061	−	0.936105i
$962$	79.9824	−	49.8771i	0.0831417	−	0.0518472i
$963$		0			0
$964$	267.169	−	545.248i	0.277146	−	0.565610i
$965$	−476.141	−	399.530i	−0.493411	−	0.414021i
$966$		0			0
$967$	74.2039	−	13.0841i	0.0767362	−	0.0135307i	−0.135148	−	0.990825i	$-0.543151\pi$
$967$	74.2039	−	13.0841i	0.0767362	−	0.0135307i	0.211884	+	0.977295i	$0.432040\pi$
$968$	1339.49	+	1300.64i	1.38377	+	1.34364i
$969$		0			0
$970$	−226.599	−	562.330i	−0.233607	−	0.579722i
$971$		−	1155.37i		−	1.18988i	−0.803770	−	0.594940i	$-0.797176\pi$
$971$		−	1155.37i		−	1.18988i	0.803770	−	0.594940i	$-0.202824\pi$
$972$		0			0
$973$	1341.73			1.37896
$974$	828.116	−	333.702i	0.850222	−	0.342609i
$975$		0			0
$976$	−682.524	+	752.475i	−0.699307	+	0.770978i
$977$	−117.331	−	665.415i	−0.120093	−	0.681080i	−0.984102	−	0.177604i	$-0.943165\pi$
$977$	−117.331	−	665.415i	−0.120093	−	0.681080i	0.864009	−	0.503476i	$-0.167946\pi$
$978$		0			0
$979$	827.205	−	985.824i	0.844949	−	1.00697i
$980$	−15.1486	+	30.9158i	−0.0154578	+	0.0315468i
$981$		0			0
$982$	6.34605	+	10.1765i	0.00646237	+	0.0103630i
$983$	−355.871	−	62.7497i	−0.362026	−	0.0638349i	−0.0103231	−	0.999947i	$-0.503286\pi$
$983$	−355.871	−	62.7497i	−0.362026	−	0.0638349i	−0.351702	+	0.936112i	$0.614397\pi$
$984$		0			0
$985$	−631.942	−	230.008i	−0.641565	−	0.233511i
$986$	−371.858	+	1140.92i	−0.377138	+	1.15712i
$987$		0			0
$988$	670.027	+	71.6598i	0.678165	+	0.0725302i
$989$	−376.892	−	652.796i	−0.381084	−	0.660057i
$990$		0			0
$991$	1393.22	+	804.374i	1.40587	+	0.811679i	0.994987	−	0.100009i	$-0.0318873\pi$
$991$	1393.22	+	804.374i	1.40587	+	0.811679i	0.410883	+	0.911688i	$0.365221\pi$
$992$	190.543	+	111.173i	0.192079	+	0.112069i
$993$		0			0
$994$	362.701	−	76.7484i	0.364890	−	0.0772117i
$995$	511.500	+	609.582i	0.514070	+	0.612645i
$996$		0			0
$997$	−833.657	+	303.426i	−0.836165	+	0.304339i	−0.724387	−	0.689394i	$-0.757877\pi$
$997$	−833.657	+	303.426i	−0.836165	+	0.304339i	−0.111779	+	0.993733i	$0.535655\pi$
$998$	1605.83	−	54.6090i	1.60905	−	0.0547184i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.19.12		204
3.2	odd	2		108.3.j.a.7.23	yes	204
4.3	odd	2	inner	324.3.j.a.19.20		204
12.11	even	2		108.3.j.a.7.15	✓	204
27.4	even	9	inner	324.3.j.a.307.20		204
27.23	odd	18		108.3.j.a.31.15	yes	204
108.23	even	18		108.3.j.a.31.23	yes	204
108.31	odd	18	inner	324.3.j.a.307.12		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.15	✓	204	12.11	even	2
108.3.j.a.7.23	yes	204	3.2	odd	2
108.3.j.a.31.15	yes	204	27.23	odd	18
108.3.j.a.31.23	yes	204	108.23	even	18
324.3.j.a.19.12		204	1.1	even	1	trivial
324.3.j.a.19.20		204	4.3	odd	2	inner
324.3.j.a.307.12		204	108.31	odd	18	inner
324.3.j.a.307.20		204	27.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.747520 - 1.85505i) q^{2} +(-2.88243 + 2.77337i) q^{4} +(-0.463207 - 2.62698i) q^{5} +(-4.34885 + 5.18275i) q^{7} +(7.29942 + 3.27390i) q^{8} +O(q^{10})\)	\(q+(-0.747520 - 1.85505i) q^{2} +(-2.88243 + 2.77337i) q^{4} +(-0.463207 - 2.62698i) q^{5} +(-4.34885 + 5.18275i) q^{7} +(7.29942 + 3.27390i) q^{8} +(-4.52692 + 2.82299i) q^{10} +(18.5390 + 3.26893i) q^{11} +(-4.76031 - 1.73261i) q^{13} +(12.8651 + 4.19312i) q^{14} +(0.616783 - 15.9881i) q^{16} +(-7.37511 - 12.7741i) q^{17} +(28.7994 + 16.6273i) q^{19} +(8.62076 + 6.28743i) q^{20} +(-7.79427 - 36.8345i) q^{22} +(-11.3558 - 13.5334i) q^{23} +(16.8059 - 6.11683i) q^{25} +(0.344344 + 10.1258i) q^{26} +(-1.83848 - 26.9999i) q^{28} +(38.2238 - 13.9123i) q^{29} +(-4.43128 - 5.28100i) q^{31} +(-30.1198 + 10.8073i) q^{32} +(-18.1835 + 23.2301i) q^{34} +(15.6294 + 9.02364i) q^{35} +(-4.65176 - 8.05708i) q^{37} +(9.31644 - 65.8536i) q^{38} +(5.21932 - 20.6919i) q^{40} +(20.9136 + 7.61194i) q^{41} +(42.0191 + 7.40910i) q^{43} +(-62.5034 + 41.9933i) q^{44} +(-16.6164 + 31.1821i) q^{46} +(35.0594 - 41.7822i) q^{47} +(0.560291 + 3.17757i) q^{49} +(-23.9097 - 26.6033i) q^{50} +(18.5264 - 8.20799i) q^{52} -25.6875 q^{53} -50.2159i q^{55} +(-48.7119 + 23.5934i) q^{56} +(-54.3811 - 60.5073i) q^{58} +(15.3255 - 2.70230i) q^{59} +(-48.6391 - 40.8131i) q^{61} +(-6.48405 + 12.1679i) q^{62} +(42.5632 + 47.7951i) q^{64} +(-2.34652 + 13.3078i) q^{65} +(-11.8552 + 32.5718i) q^{67} +(56.6855 + 16.3664i) q^{68} +(5.05602 - 35.7387i) q^{70} +(23.7276 - 13.6991i) q^{71} +(18.2594 - 31.6262i) q^{73} +(-11.4690 + 14.6521i) q^{74} +(-129.126 + 31.9444i) q^{76} +(-97.5656 + 81.8672i) q^{77} +(43.9448 + 120.737i) q^{79} +(-42.2861 + 5.78553i) q^{80} +(-1.51282 - 44.4859i) q^{82} +(-0.482480 - 1.32560i) q^{83} +(-30.1410 + 25.2913i) q^{85} +(-17.6658 - 83.4860i) q^{86} +(124.622 + 84.5563i) q^{88} +(34.1806 - 59.2025i) q^{89} +(29.6815 - 17.1366i) q^{91} +(70.2655 + 7.51495i) q^{92} +(-103.716 - 33.8040i) q^{94} +(30.3396 - 83.3573i) q^{95} +(-19.7333 + 111.913i) q^{97} +(5.47572 - 3.41466i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more