LMFDB - Embedded newform 360.2.w.e.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.5
Character	$\chi$	$=$	360.307
Dual form			360.2.w.e.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.624608 + 1.26880i) q^{2} +(-1.21973 - 1.58501i) q^{4} +(-2.11218 + 0.733965i) q^{5} +(1.93078 - 1.93078i) q^{7} +(2.77292 - 0.557590i) q^{8} +O(q^{10})$	\(q+(-0.624608 + 1.26880i) q^{2} +(-1.21973 - 1.58501i) q^{4} +(-2.11218 + 0.733965i) q^{5} +(1.93078 - 1.93078i) q^{7} +(2.77292 - 0.557590i) q^{8} +(0.388025 - 3.13838i) q^{10} +4.20687 q^{11} +(2.27101 + 2.27101i) q^{13} +(1.24380 + 3.65576i) q^{14} +(-1.02452 + 3.86657i) q^{16} +(-1.69849 - 1.69849i) q^{17} +7.77148i q^{19} +(3.73963 + 2.45259i) q^{20} +(-2.62765 + 5.33770i) q^{22} +(0.437531 + 0.437531i) q^{23} +(3.92259 - 3.10053i) q^{25} +(-4.29995 + 1.46298i) q^{26} +(-5.41533 - 0.705274i) q^{28} +8.36777 q^{29} -1.26260i q^{31} +(-4.26600 - 3.71500i) q^{32} +(3.21595 - 1.09416i) q^{34} +(-2.66102 + 5.49527i) q^{35} +(2.88977 - 2.88977i) q^{37} +(-9.86049 - 4.85413i) q^{38} +(-5.44765 + 3.21296i) q^{40} +5.94942 q^{41} +(-0.177936 + 0.177936i) q^{43} +(-5.13125 - 6.66794i) q^{44} +(-0.828427 + 0.281856i) q^{46} +(-0.719388 + 0.719388i) q^{47} -0.455798i q^{49} +(1.48388 + 6.91362i) q^{50} +(0.829554 - 6.36959i) q^{52} +(-3.32260 - 3.32260i) q^{53} +(-8.88566 + 3.08770i) q^{55} +(4.27731 - 6.43047i) q^{56} +(-5.22657 + 10.6171i) q^{58} +7.13953i q^{59} -8.69395i q^{61} +(1.60199 + 0.788631i) q^{62} +(7.37819 - 3.09231i) q^{64} +(-6.46361 - 3.12993i) q^{65} +(-3.94942 - 3.94942i) q^{67} +(-0.620426 + 4.76384i) q^{68} +(-5.31032 - 6.80870i) q^{70} +2.11259i q^{71} +(-2.82206 + 2.82206i) q^{73} +(1.86158 + 5.47153i) q^{74} +(12.3179 - 9.47911i) q^{76} +(8.12253 - 8.12253i) q^{77} +12.6472 q^{79} +(-0.673966 - 8.91884i) q^{80} +(-3.71605 + 7.54865i) q^{82} +(-7.63831 + 7.63831i) q^{83} +(4.83416 + 2.34089i) q^{85} +(-0.114626 - 0.336906i) q^{86} +(11.6653 - 2.34571i) q^{88} -11.6063i q^{89} +8.76962 q^{91} +(0.159821 - 1.22716i) q^{92} +(-0.463427 - 1.36210i) q^{94} +(-5.70399 - 16.4147i) q^{95} +(-6.58532 - 6.58532i) q^{97} +(0.578319 + 0.284695i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.624608	+	1.26880i	−0.441664	+	0.897180i
$2$	−0.624608	+	1.26880i	−0.441664	+	0.897180i
$3$		0			0
$3$		0			0
$4$	−1.21973	−	1.58501i	−0.609865	−	0.792505i
$5$	−2.11218	+	0.733965i	−0.944595	+	0.328239i
$5$	−2.11218	+	0.733965i	−0.944595	+	0.328239i
$6$		0			0
$7$	1.93078	−	1.93078i	0.729765	−	0.729765i	−0.240808	−	0.970573i	$-0.577412\pi$
$7$	1.93078	−	1.93078i	0.729765	−	0.729765i	0.970573	+	0.240808i	$0.0774123\pi$
$8$	2.77292	−	0.557590i	0.980376	−	0.197138i
$9$		0			0
$10$	0.388025	−	3.13838i	0.122704	−	0.992443i
$11$	4.20687			1.26842			0.634210	−	0.773161i	$-0.281326\pi$
$11$	4.20687			1.26842			0.634210	+	0.773161i	$0.281326\pi$
$12$		0			0
$13$	2.27101	+	2.27101i	0.629864	+	0.629864i	0.948034	−	0.318170i	$-0.103068\pi$
$13$	2.27101	+	2.27101i	0.629864	+	0.629864i	−0.318170	+	0.948034i	$0.603068\pi$
$14$	1.24380	+	3.65576i	0.332420	+	0.977042i
$15$		0			0
$16$	−1.02452	+	3.86657i	−0.256129	+	0.966643i
$17$	−1.69849	−	1.69849i	−0.411945	−	0.411945i	0.470470	−	0.882416i	$-0.344084\pi$
$17$	−1.69849	−	1.69849i	−0.411945	−	0.411945i	−0.882416	+	0.470470i	$0.844084\pi$
$18$		0			0
$19$			7.77148i			1.78290i	0.453119	+	0.891450i	$0.350311\pi$
$19$			7.77148i			1.78290i	−0.453119	+	0.891450i	$0.649689\pi$
$20$	3.73963	+	2.45259i	0.836206	+	0.548415i
$21$		0			0
$22$	−2.62765	+	5.33770i	−0.560216	+	1.13800i
$23$	0.437531	+	0.437531i	0.0912316	+	0.0912316i	0.751250	−	0.660018i	$-0.229451\pi$
$23$	0.437531	+	0.437531i	0.0912316	+	0.0912316i	−0.660018	+	0.751250i	$0.729451\pi$
$24$		0			0
$25$	3.92259	−	3.10053i	0.784518	−	0.620106i
$26$	−4.29995	+	1.46298i	−0.843290	+	0.286913i
$27$		0			0
$28$	−5.41533	−	0.705274i	−1.02340	−	0.133284i
$29$	8.36777			1.55386			0.776928	−	0.629590i	$-0.216777\pi$
$29$	8.36777			1.55386			0.776928	+	0.629590i	$0.216777\pi$
$30$		0			0
$31$		−	1.26260i		−	0.226770i	−0.993551	−	0.113385i	$-0.963831\pi$
$31$		−	1.26260i		−	0.226770i	0.993551	−	0.113385i	$-0.0361693\pi$
$32$	−4.26600	−	3.71500i	−0.754130	−	0.656725i
$33$		0			0
$34$	3.21595	−	1.09416i	0.551531	−	0.187648i
$35$	−2.66102	+	5.49527i	−0.449795	+	0.928870i
$36$		0			0
$37$	2.88977	−	2.88977i	0.475075	−	0.475075i	−0.428477	−	0.903553i	$-0.640950\pi$
$37$	2.88977	−	2.88977i	0.475075	−	0.475075i	0.903553	+	0.428477i	$0.140950\pi$
$38$	−9.86049	−	4.85413i	−1.59958	−	0.787443i
$39$		0			0
$40$	−5.44765	+	3.21296i	−0.861350	+	0.508013i
$41$	5.94942			0.929143			0.464571	−	0.885536i	$-0.346208\pi$
$41$	5.94942			0.929143			0.464571	+	0.885536i	$0.346208\pi$
$42$		0			0
$43$	−0.177936	+	0.177936i	−0.0271350	+	0.0271350i	−0.720544	−	0.693409i	$-0.756108\pi$
$43$	−0.177936	+	0.177936i	−0.0271350	+	0.0271350i	0.693409	+	0.720544i	$0.256108\pi$
$44$	−5.13125	−	6.66794i	−0.773565	−	1.00523i
$45$		0			0
$46$	−0.828427	+	0.281856i	−0.122145	+	0.0415574i
$47$	−0.719388	+	0.719388i	−0.104933	+	0.104933i	−0.757624	−	0.652691i	$-0.773640\pi$
$47$	−0.719388	+	0.719388i	−0.104933	+	0.104933i	0.652691	+	0.757624i	$0.273640\pi$
$48$		0			0
$49$		−	0.455798i		−	0.0651141i
$50$	1.48388	+	6.91362i	0.209853	+	0.977733i
$51$		0			0
$52$	0.829554	−	6.36959i	0.115038	−	0.883303i
$53$	−3.32260	−	3.32260i	−0.456394	−	0.456394i	0.441076	−	0.897470i	$-0.354597\pi$
$53$	−3.32260	−	3.32260i	−0.456394	−	0.456394i	−0.897470	+	0.441076i	$0.854597\pi$
$54$		0			0
$55$	−8.88566	+	3.08770i	−1.19814	+	0.416345i
$56$	4.27731	−	6.43047i	0.571580	−	0.859308i
$57$		0			0
$58$	−5.22657	+	10.6171i	−0.686282	+	1.39409i
$59$			7.13953i			0.929488i	0.885445	+	0.464744i	$0.153854\pi$
$59$			7.13953i			0.929488i	−0.885445	+	0.464744i	$0.846146\pi$
$60$		0			0
$61$		−	8.69395i		−	1.11315i	−0.830799	−	0.556573i	$-0.812116\pi$
$61$		−	8.69395i		−	1.11315i	0.830799	−	0.556573i	$-0.187884\pi$
$62$	1.60199	+	0.788631i	0.203454	+	0.100156i
$63$		0			0
$64$	7.37819	−	3.09231i	0.922273	−	0.386538i
$65$	−6.46361	−	3.12993i	−0.801712	−	0.388220i
$66$		0			0
$67$	−3.94942	−	3.94942i	−0.482498	−	0.482498i	0.423431	−	0.905929i	$-0.360826\pi$
$67$	−3.94942	−	3.94942i	−0.482498	−	0.482498i	−0.905929	+	0.423431i	$0.860826\pi$
$68$	−0.620426	+	4.76384i	−0.0752377	+	0.577700i
$69$		0			0
$70$	−5.31032	−	6.80870i	−0.634705	−	0.813796i
$71$			2.11259i			0.250718i	0.992111	+	0.125359i	$0.0400083\pi$
$71$			2.11259i			0.250718i	−0.992111	+	0.125359i	$0.959992\pi$
$72$		0			0
$73$	−2.82206	+	2.82206i	−0.330298	+	0.330298i	−0.852699	−	0.522402i	$-0.825036\pi$
$73$	−2.82206	+	2.82206i	−0.330298	+	0.330298i	0.522402	+	0.852699i	$0.325036\pi$
$74$	1.86158	+	5.47153i	0.216404	+	0.636052i
$75$		0			0
$76$	12.3179	−	9.47911i	1.41296	−	1.08733i
$77$	8.12253	−	8.12253i	0.925648	−	0.925648i
$78$		0			0
$79$	12.6472			1.42292			0.711459	−	0.702728i	$-0.248035\pi$
$79$	12.6472			1.42292			0.711459	+	0.702728i	$0.248035\pi$
$80$	−0.673966	−	8.91884i	−0.0753517	−	0.997157i
$81$		0			0
$82$	−3.71605	+	7.54865i	−0.410369	+	0.833609i
$83$	−7.63831	+	7.63831i	−0.838414	+	0.838414i	−0.988650	−	0.150237i	$-0.951996\pi$
$83$	−7.63831	+	7.63831i	−0.838414	+	0.838414i	0.150237	+	0.988650i	$0.451996\pi$
$84$		0			0
$85$	4.83416	+	2.34089i	0.524338	+	0.253905i
$86$	−0.114626	−	0.336906i	−0.0123604	−	0.0363295i
$87$		0			0
$88$	11.6653	−	2.34571i	1.24353	−	0.250053i
$89$		−	11.6063i		−	1.23026i	−0.788425	−	0.615131i	$-0.789103\pi$
$89$		−	11.6063i		−	1.23026i	0.788425	−	0.615131i	$-0.210897\pi$
$90$		0			0
$91$	8.76962			0.919306
$92$	0.159821	−	1.22716i	0.0166625	−	0.127940i
$93$		0			0
$94$	−0.463427	−	1.36210i	−0.0477989	−	0.140490i
$95$	−5.70399	−	16.4147i	−0.585217	−	1.68412i
$96$		0			0
$97$	−6.58532	−	6.58532i	−0.668638	−	0.668638i	0.288763	−	0.957401i	$-0.406756\pi$
$97$	−6.58532	−	6.58532i	−0.668638	−	0.668638i	−0.957401	+	0.288763i	$0.906756\pi$
$98$	0.578319	+	0.284695i	0.0584191	+	0.0287586i
$99$		0			0
$100$	−9.69887	−	2.43554i	−0.969887	−	0.243554i
$101$			7.79553i			0.775684i	0.921726	+	0.387842i	$0.126779\pi$
$101$			7.79553i			0.775684i	−0.921726	+	0.387842i	$0.873221\pi$
$102$		0			0
$103$	−6.64232	−	6.64232i	−0.654487	−	0.654487i	0.299583	−	0.954070i	$-0.403152\pi$
$103$	−6.64232	−	6.64232i	−0.654487	−	0.654487i	−0.954070	+	0.299583i	$0.903152\pi$
$104$	7.56362	+	5.03104i	0.741674	+	0.493334i
$105$		0			0
$106$	6.29105	−	2.14041i	0.611041	−	0.207895i
$107$	−3.95523	−	3.95523i	−0.382367	−	0.382367i	0.489587	−	0.871954i	$-0.337147\pi$
$107$	−3.95523	−	3.95523i	−0.382367	−	0.382367i	−0.871954	+	0.489587i	$0.837147\pi$
$108$		0			0
$109$	−20.3970			−1.95368			−0.976839	−	0.213976i	$-0.931359\pi$
$109$	−20.3970			−1.95368			−0.976839	+	0.213976i	$0.931359\pi$
$110$	1.63237	−	13.2028i	0.155641	−	1.25883i
$111$		0			0
$112$	5.48737	+	9.44360i	0.518508	+	0.892336i
$113$	11.2920	−	11.2920i	1.06227	−	1.06227i	0.0643374	−	0.997928i	$-0.479507\pi$
$113$	11.2920	−	11.2920i	1.06227	−	1.06227i	0.997928	−	0.0643374i	$-0.0204934\pi$
$114$		0			0
$115$	−1.24528	−	0.603011i	−0.116123	−	0.0562311i
$116$	−10.2064	−	13.2630i	−0.947642	−	1.23144i
$117$		0			0
$118$	−9.05867	−	4.45941i	−0.833918	−	0.410522i
$119$	−6.55883			−0.601247
$120$		0			0
$121$	6.69778			0.608889
$122$	11.0309	+	5.43031i	0.998692	+	0.491637i
$123$		0			0
$124$	−2.00124	+	1.54003i	−0.179716	+	0.138299i
$125$	−6.00953	+	9.42791i	−0.537509	+	0.843258i
$126$		0			0
$127$	−2.31832	+	2.31832i	−0.205717	+	0.205717i	−0.802444	−	0.596727i	$-0.796468\pi$
$127$	−2.31832	+	2.31832i	−0.205717	+	0.205717i	0.596727	+	0.802444i	$0.296468\pi$
$128$	−0.684942	+	11.2930i	−0.0605409	+	0.998166i
$129$		0			0
$130$	8.00849	−	6.24608i	0.702391	−	0.547817i
$131$	1.12681			0.0984495			0.0492247	−	0.998788i	$-0.484325\pi$
$131$	1.12681			0.0984495			0.0492247	+	0.998788i	$0.484325\pi$
$132$		0			0
$133$	15.0050	+	15.0050i	1.30110	+	1.30110i
$134$	7.47787	−	2.54420i	0.645990	−	0.219786i
$135$		0			0
$136$	−5.65685	−	3.76273i	−0.485071	−	0.322651i
$137$	−1.99106	−	1.99106i	−0.170107	−	0.170107i	0.616919	−	0.787027i	$-0.288381\pi$
$137$	−1.99106	−	1.99106i	−0.170107	−	0.170107i	−0.787027	+	0.616919i	$0.788381\pi$
$138$		0			0
$139$			5.79584i			0.491597i	0.969321	+	0.245798i	$0.0790501\pi$
$139$			5.79584i			0.491597i	−0.969321	+	0.245798i	$0.920950\pi$
$140$	11.9558	−	2.48499i	1.01045	−	0.210020i
$141$		0			0
$142$	−2.68046	−	1.31954i	−0.224939	−	0.110733i
$143$	9.55384	+	9.55384i	0.798932	+	0.798932i
$144$		0			0
$145$	−17.6742	+	6.14164i	−1.46776	+	0.510036i
$146$	−1.81796	−	5.34333i	−0.150456	−	0.442217i
$147$		0			0
$148$	−8.10506	−	1.05558i	−0.666231	−	0.0867678i
$149$	−20.7586			−1.70061			−0.850307	−	0.526287i	$-0.823584\pi$
$149$	−20.7586			−1.70061			−0.850307	+	0.526287i	$0.823584\pi$
$150$		0			0
$151$			23.2591i			1.89280i	0.322998	+	0.946400i	$0.395309\pi$
$151$			23.2591i			1.89280i	−0.322998	+	0.946400i	$0.604691\pi$
$152$	4.33330	+	21.5497i	0.351477	+	1.74791i
$153$		0			0
$154$	5.23251	+	15.3793i	0.421648	+	1.23930i
$155$	0.926705	+	2.66684i	0.0744347	+	0.214206i
$156$		0			0
$157$	−5.15182	+	5.15182i	−0.411160	+	0.411160i	−0.882142	−	0.470983i	$-0.843899\pi$
$157$	−5.15182	+	5.15182i	−0.411160	+	0.411160i	0.470983	+	0.882142i	$0.343899\pi$
$158$	−7.89952	+	16.0468i	−0.628452	+	1.27661i
$159$		0			0
$160$	11.7372	+	4.71565i	0.927910	+	0.372805i
$161$	1.68955			0.133155
$162$		0			0
$163$	6.96741	−	6.96741i	0.545730	−	0.545730i	−0.379473	−	0.925203i	$-0.623895\pi$
$163$	6.96741	−	6.96741i	0.545730	−	0.545730i	0.925203	+	0.379473i	$0.123895\pi$
$164$	−7.25668	−	9.42989i	−0.566652	−	0.736350i
$165$		0			0
$166$	−4.92058	−	14.4625i	−0.381911	−	1.12251i
$167$	−9.40668	+	9.40668i	−0.727911	+	0.727911i	−0.970203	−	0.242292i	$-0.922101\pi$
$167$	−9.40668	+	9.40668i	−0.727911	+	0.727911i	0.242292	+	0.970203i	$0.422101\pi$
$168$		0			0
$169$		−	2.68505i		−	0.206542i
$170$	−5.98958	+	4.67146i	−0.459380	+	0.358285i
$171$		0			0
$172$	0.499065	+	0.0649965i	0.0380533	+	0.00495594i
$173$	12.1330	+	12.1330i	0.922452	+	0.922452i	0.997202	−	0.0747507i	$-0.0238161\pi$
$173$	12.1330	+	12.1330i	0.922452	+	0.922452i	−0.0747507	+	0.997202i	$0.523816\pi$
$174$		0			0
$175$	1.58722	−	13.5601i	0.119983	−	1.02505i
$176$	−4.31001	+	16.2662i	−0.324879	+	1.22611i
$177$		0			0
$178$	14.7261	+	7.24937i	1.10377	+	0.543363i
$179$		−	1.21634i		−	0.0909135i	−0.998966	−	0.0454568i	$-0.985526\pi$
$179$		−	1.21634i		−	0.0909135i	0.998966	−	0.0454568i	$-0.0144743\pi$
$180$		0			0
$181$		−	5.53431i		−	0.411362i	−0.978619	−	0.205681i	$-0.934059\pi$
$181$		−	5.53431i		−	0.411362i	0.978619	−	0.205681i	$-0.0659409\pi$
$182$	−5.47757	+	11.1269i	−0.406025	+	0.824783i
$183$		0			0
$184$	1.45720	+	0.969277i	0.107426	+	0.0714560i
$185$	−3.98272	+	8.22470i	−0.292815	+	0.604692i
$186$		0			0
$187$	−7.14535	−	7.14535i	−0.522520	−	0.522520i
$188$	2.01770	+	0.262778i	0.147156	+	0.0191650i
$189$		0			0
$190$	24.3899	+	3.01553i	1.76943	+	0.218769i
$191$			6.77019i			0.489874i	0.969539	+	0.244937i	$0.0787673\pi$
$191$			6.77019i			0.489874i	−0.969539	+	0.244937i	$0.921233\pi$
$192$		0			0
$193$	4.76325	−	4.76325i	0.342867	−	0.342867i	−0.514577	−	0.857444i	$-0.672051\pi$
$193$	4.76325	−	4.76325i	0.342867	−	0.342867i	0.857444	+	0.514577i	$0.172051\pi$
$194$	12.4687	−	4.24224i	0.895202	−	0.304575i
$195$		0			0
$196$	−0.722445	+	0.555951i	−0.0516032	+	0.0397108i
$197$	8.95104	−	8.95104i	0.637735	−	0.637735i	−0.312261	−	0.949996i	$-0.601086\pi$
$197$	8.95104	−	8.95104i	0.637735	−	0.637735i	0.949996	+	0.312261i	$0.101086\pi$
$198$		0			0
$199$	2.11669			0.150048			0.0750241	−	0.997182i	$-0.476097\pi$
$199$	2.11669			0.150048			0.0750241	+	0.997182i	$0.476097\pi$
$200$	9.14822	−	10.7847i	0.646877	−	0.762595i
$201$		0			0
$202$	−9.89101	−	4.86915i	−0.695929	−	0.342592i
$203$	16.1563	−	16.1563i	1.13395	−	1.13395i
$204$		0			0
$205$	−12.5662	+	4.36666i	−0.877663	+	0.304981i
$206$	12.5766	−	4.27896i	0.876256	−	0.298129i
$207$		0			0
$208$	−11.1077	+	6.45433i	−0.770180	+	0.447527i
$209$			32.6936i			2.26147i
$210$		0			0
$211$	−19.4527			−1.33918			−0.669589	−	0.742732i	$-0.733530\pi$
$211$	−19.4527			−1.33918			−0.669589	+	0.742732i	$0.733530\pi$
$212$	−1.21368	+	9.31903i	−0.0833559	+	0.640034i
$213$		0			0
$214$	7.48889	−	2.54795i	0.511930	−	0.174174i
$215$	0.245234	−	0.506431i	0.0167248	−	0.0345383i
$216$		0			0
$217$	−2.43780	−	2.43780i	−0.165489	−	0.165489i
$218$	12.7401	−	25.8798i	0.862870	−	1.75280i
$219$		0			0
$220$	15.7321	+	10.3177i	1.06066	+	0.695620i
$221$		−	7.71459i		−	0.518939i
$222$		0			0
$223$	−8.70623	−	8.70623i	−0.583012	−	0.583012i	0.352717	−	0.935730i	$-0.385258\pi$
$223$	−8.70623	−	8.70623i	−0.583012	−	0.583012i	−0.935730	+	0.352717i	$0.885258\pi$
$224$	−15.4095	+	1.06386i	−1.02959	+	0.0710822i
$225$		0			0
$226$	7.27430	+	21.3805i	0.483879	+	1.42221i
$227$	−12.1115	−	12.1115i	−0.803870	−	0.803870i	0.179828	−	0.983698i	$-0.442446\pi$
$227$	−12.1115	−	12.1115i	−0.803870	−	0.803870i	−0.983698	+	0.179828i	$0.942446\pi$
$228$		0			0
$229$	−7.68924			−0.508119			−0.254060	−	0.967189i	$-0.581766\pi$
$229$	−7.68924			−0.508119			−0.254060	+	0.967189i	$0.581766\pi$
$230$	1.54291	−	1.20337i	0.101737	−	0.0793477i
$231$		0			0
$232$	23.2032	−	4.66578i	1.52336	−	0.306323i
$233$	−11.9078	+	11.9078i	−0.780104	+	0.780104i	−0.979848	−	0.199744i	$-0.935989\pi$
$233$	−11.9078	+	11.9078i	−0.780104	+	0.780104i	0.199744	+	0.979848i	$0.435989\pi$
$234$		0			0
$235$	0.991470	−	2.04748i	0.0646763	−	0.133563i
$236$	11.3162	−	8.70830i	0.736624	−	0.566862i
$237$		0			0
$238$	4.09669	−	8.32187i	0.265549	−	0.539427i
$239$	11.8704			0.767834			0.383917	−	0.923368i	$-0.374575\pi$
$239$	11.8704			0.767834			0.383917	+	0.923368i	$0.374575\pi$
$240$		0			0
$241$	23.6379			1.52265			0.761326	−	0.648369i	$-0.224549\pi$
$241$	23.6379			1.52265			0.761326	+	0.648369i	$0.224549\pi$
$242$	−4.18348	+	8.49817i	−0.268924	+	0.546283i
$243$		0			0
$244$	−13.7800	+	10.6043i	−0.882174	+	0.678869i
$245$	0.334540	+	0.962727i	0.0213730	+	0.0615064i
$246$		0			0
$247$	−17.6491	+	17.6491i	−1.12298	+	1.12298i
$248$	−0.704014	−	3.50109i	−0.0447049	−	0.222320i
$249$		0			0
$250$	−8.20857	−	13.5137i	−0.519156	−	0.854680i
$251$	4.56274			0.287998			0.143999	−	0.989578i	$-0.454004\pi$
$251$	4.56274			0.287998			0.143999	+	0.989578i	$0.454004\pi$
$252$		0			0
$253$	1.84064	+	1.84064i	0.115720	+	0.115720i
$254$	−1.49345	−	4.38953i	−0.0937075	−	0.275423i
$255$		0			0
$256$	−13.9007	−	7.92273i	−0.868796	−	0.495170i
$257$	−11.7447	−	11.7447i	−0.732616	−	0.732616i	0.238521	−	0.971137i	$-0.423337\pi$
$257$	−11.7447	−	11.7447i	−0.732616	−	0.732616i	−0.971137	+	0.238521i	$0.923337\pi$
$258$		0			0
$259$		−	11.1590i		−	0.693387i
$260$	2.92289	+	14.0626i	0.181270	+	0.872123i
$261$		0			0
$262$	−0.703812	+	1.42970i	−0.0434816	+	0.0883269i
$263$	5.06680	+	5.06680i	0.312432	+	0.312432i	0.845851	−	0.533419i	$-0.179093\pi$
$263$	5.06680	+	5.06680i	0.312432	+	0.312432i	−0.533419	+	0.845851i	$0.679093\pi$
$264$		0			0
$265$	9.45659	+	4.57925i	0.580914	+	0.281301i
$266$	−28.4106	+	9.66617i	−1.74197	+	0.592671i
$267$		0			0
$268$	−1.44264	+	11.0771i	−0.0881234	+	0.676641i
$269$	−7.23542			−0.441151			−0.220576	−	0.975370i	$-0.570794\pi$
$269$	−7.23542			−0.441151			−0.220576	+	0.975370i	$0.570794\pi$
$270$		0			0
$271$		−	0.777901i		−	0.0472541i	−0.999721	−	0.0236271i	$-0.992479\pi$
$271$		−	0.777901i		−	0.0472541i	0.999721	−	0.0236271i	$-0.00752143\pi$
$272$	8.30748	−	4.82721i	0.503715	−	0.292693i
$273$		0			0
$274$	3.76989	−	1.28263i	0.227747	−	0.0774866i
$275$	16.5018	−	13.0435i	0.995099	−	0.786554i
$276$		0			0
$277$	16.9790	−	16.9790i	1.02017	−	1.02017i	0.0203754	−	0.999792i	$-0.493514\pi$
$277$	16.9790	−	16.9790i	1.02017	−	1.02017i	0.999792	−	0.0203754i	$-0.00648613\pi$
$278$	−7.35379	−	3.62013i	−0.441051	−	0.217121i
$279$		0			0
$280$	−4.31470	+	16.7217i	−0.257853	+	0.999313i
$281$	0.308585			0.0184087			0.00920433	−	0.999958i	$-0.497070\pi$
$281$	0.308585			0.0184087			0.00920433	+	0.999958i	$0.497070\pi$
$282$		0			0
$283$	−4.46433	+	4.46433i	−0.265377	+	0.265377i	−0.827234	−	0.561857i	$-0.810087\pi$
$283$	−4.46433	+	4.46433i	−0.265377	+	0.265377i	0.561857	+	0.827234i	$0.310087\pi$
$284$	3.34847	−	2.57679i	0.198695	−	0.152904i
$285$		0			0
$286$	−18.0894	+	6.15455i	−1.06965	+	0.363926i
$287$	11.4870	−	11.4870i	0.678056	−	0.678056i
$288$		0			0
$289$		−	11.2302i		−	0.660602i
$290$	3.24690	−	26.2612i	0.190665	−	1.54211i
$291$		0			0
$292$	7.91516	+	1.03084i	0.463200	+	0.0603256i
$293$	−12.2194	−	12.2194i	−0.713864	−	0.713864i	0.253477	−	0.967341i	$-0.418426\pi$
$293$	−12.2194	−	12.2194i	−0.713864	−	0.713864i	−0.967341	+	0.253477i	$0.918426\pi$
$294$		0			0
$295$	−5.24016	−	15.0800i	−0.305094	−	0.877989i
$296$	6.40180	−	9.62441i	0.372097	−	0.559408i
$297$		0			0
$298$	12.9660	−	26.3387i	0.751101	−	1.52576i
$299$			1.98727i			0.114927i
$300$		0			0
$301$			0.687110i			0.0396043i
$302$	−29.5113	−	14.5278i	−1.69818	−	0.835982i
$303$		0			0
$304$	−30.0490	−	7.96200i	−1.72343	−	0.456652i
$305$	6.38105	+	18.3632i	0.365378	+	1.05147i
$306$		0			0
$307$	21.3452	+	21.3452i	1.21823	+	1.21823i	0.968250	+	0.249983i	$0.0804249\pi$
$307$	21.3452	+	21.3452i	1.21823	+	1.21823i	0.249983	+	0.968250i	$0.419575\pi$
$308$	−22.7816	−	2.96700i	−1.29810	−	0.169060i
$309$		0			0
$310$	−3.96252	−	0.489921i	−0.225056	−	0.0278256i
$311$		−	7.87420i		−	0.446505i	−0.974761	−	0.223253i	$-0.928333\pi$
$311$		−	7.87420i		−	0.446505i	0.974761	−	0.223253i	$-0.0716675\pi$
$312$		0			0
$313$	−6.46103	+	6.46103i	−0.365199	+	0.365199i	−0.865723	−	0.500524i	$-0.833141\pi$
$313$	−6.46103	+	6.46103i	−0.365199	+	0.365199i	0.500524	+	0.865723i	$0.333141\pi$
$314$	−3.31878	−	9.75451i	−0.187290	−	0.550479i
$315$		0			0
$316$	−15.4261	−	20.0459i	−0.867788	−	1.12767i
$317$	−3.64026	+	3.64026i	−0.204457	+	0.204457i	−0.801907	−	0.597449i	$-0.796181\pi$
$317$	−3.64026	+	3.64026i	−0.204457	+	0.204457i	0.597449	+	0.801907i	$0.296181\pi$
$318$		0			0
$319$	35.2021			1.97094
$320$	−13.3144	+	11.9468i	−0.744298	+	0.667848i
$321$		0			0
$322$	−1.05531	+	2.14371i	−0.0588099	+	0.119464i
$323$	13.1998	−	13.1998i	0.734457	−	0.734457i
$324$		0			0
$325$	15.9496	+	1.86691i	0.884722	+	0.103558i
$326$	4.48839	+	13.1922i	0.248589	+	0.730648i
$327$		0			0
$328$	16.4973	−	3.31733i	0.910909	−	0.183169i
$329$			2.77795i			0.153154i
$330$		0			0
$331$	−0.127352			−0.00699991			−0.00349996	−	0.999994i	$-0.501114\pi$
$331$	−0.127352			−0.00699991			−0.00349996	+	0.999994i	$0.501114\pi$
$332$	21.4235	+	2.79012i	1.17577	+	0.153128i
$333$		0			0
$334$	−6.05976	−	17.8107i	−0.331575	−	0.974560i
$335$	11.2406	+	5.44314i	0.614140	+	0.297390i
$336$		0			0
$337$	23.8335	+	23.8335i	1.29830	+	1.29830i	0.929517	+	0.368779i	$0.120224\pi$
$337$	23.8335	+	23.8335i	1.29830	+	1.29830i	0.368779	+	0.929517i	$0.379776\pi$
$338$	3.40680	+	1.67710i	0.185306	+	0.0912224i
$339$		0			0
$340$	−2.18604	−	10.5174i	−0.118554	−	0.570388i
$341$		−	5.31160i		−	0.287639i
$342$		0			0
$343$	12.6354	+	12.6354i	0.682247	+	0.682247i
$344$	−0.394187	+	0.592618i	−0.0212532	+	0.0319518i
$345$		0			0
$346$	−22.9727	+	7.81601i	−1.23502	+	0.420191i
$347$	−10.2254	−	10.2254i	−0.548929	−	0.548929i	0.377202	−	0.926131i	$-0.376886\pi$
$347$	−10.2254	−	10.2254i	−0.548929	−	0.548929i	−0.926131	+	0.377202i	$0.876886\pi$
$348$		0			0
$349$	0.105474			0.00564588			0.00282294	−	0.999996i	$-0.499101\pi$
$349$	0.105474			0.00564588			0.00282294	+	0.999996i	$0.499101\pi$
$350$	16.2137	+	10.4836i	0.866659	+	0.560372i
$351$		0			0
$352$	−17.9465	−	15.6285i	−0.956553	−	0.833004i
$353$	2.15119	−	2.15119i	0.114496	−	0.114496i	−0.647537	−	0.762034i	$-0.724201\pi$
$353$	2.15119	−	2.15119i	0.114496	−	0.114496i	0.762034	+	0.647537i	$0.224201\pi$
$354$		0			0
$355$	−1.55056	−	4.46216i	−0.0822954	−	0.236827i
$356$	−18.3961	+	14.1565i	−0.974989	+	0.750294i
$357$		0			0
$358$	1.54330	+	0.759735i	0.0815658	+	0.0401533i
$359$	−6.98848			−0.368838			−0.184419	−	0.982848i	$-0.559040\pi$
$359$	−6.98848			−0.368838			−0.184419	+	0.982848i	$0.559040\pi$
$360$		0			0
$361$	−41.3959			−2.17873
$362$	7.02195	+	3.45677i	0.369066	+	0.181684i
$363$		0			0
$364$	−10.6966	−	13.8999i	−0.560653	−	0.728555i
$365$	3.88941	−	8.03200i	0.203581	−	0.420414i
$366$		0			0
$367$	21.8147	−	21.8147i	1.13872	−	1.13872i	0.150037	−	0.988680i	$-0.452061\pi$
$367$	21.8147	−	21.8147i	1.13872	−	1.13872i	0.988680	−	0.150037i	$-0.0479394\pi$
$368$	−2.14000	+	1.24349i	−0.111555	+	0.0648213i
$369$		0			0
$370$	−7.94790	−	10.1905i	−0.413191	−	0.529779i
$371$	−12.8304			−0.666121
$372$		0			0
$373$	−18.7431	−	18.7431i	−0.970481	−	0.970481i	0.0290952	−	0.999577i	$-0.490737\pi$
$373$	−18.7431	−	18.7431i	−0.970481	−	0.970481i	−0.999577	+	0.0290952i	$0.990737\pi$
$374$	13.5291	−	4.60301i	0.699573	−	0.238016i
$375$		0			0
$376$	−1.59368	+	2.39593i	−0.0821879	+	0.123561i
$377$	19.0033	+	19.0033i	0.978718	+	0.978718i
$378$		0			0
$379$		−	8.78967i		−	0.451495i	−0.974186	−	0.225748i	$-0.927518\pi$
$379$		−	8.78967i		−	0.451495i	0.974186	−	0.225748i	$-0.0724825\pi$
$380$	−19.0602	+	29.0625i	−0.977768	+	1.49087i
$381$		0			0
$382$	−8.59005	−	4.22871i	−0.439505	−	0.216360i
$383$	−19.6476	−	19.6476i	−1.00395	−	1.00395i	−0.999992	−	0.00395500i	$-0.998741\pi$
$383$	−19.6476	−	19.6476i	−1.00395	−	1.00395i	−0.00395500	−	0.999992i	$-0.501259\pi$
$384$		0			0
$385$	−11.1946	+	23.1179i	−0.570529	+	1.17820i
$386$	3.06847	+	9.01880i	0.156181	+	0.459045i
$387$		0			0
$388$	−2.40549	+	18.4701i	−0.122120	+	0.937678i
$389$	−8.74845			−0.443564			−0.221782	−	0.975096i	$-0.571187\pi$
$389$	−8.74845			−0.443564			−0.221782	+	0.975096i	$0.571187\pi$
$390$		0			0
$391$		−	1.48629i		−	0.0751649i
$392$	−0.254149	−	1.26389i	−0.0128364	−	0.0638362i
$393$		0			0
$394$	5.76623	+	16.9480i	0.290499	+	0.853829i
$395$	−26.7131	+	9.28258i	−1.34408	+	0.467057i
$396$		0			0
$397$	19.4491	−	19.4491i	0.976124	−	0.976124i	−0.0235978	−	0.999722i	$-0.507512\pi$
$397$	19.4491	−	19.4491i	0.976124	−	0.976124i	0.999722	+	0.0235978i	$0.00751210\pi$
$398$	−1.32210	+	2.68567i	−0.0662710	+	0.134620i
$399$		0			0
$400$	7.96965	+	18.3435i	0.398483	+	0.917176i
$401$	−6.57788			−0.328484			−0.164242	−	0.986420i	$-0.552518\pi$
$401$	−6.57788			−0.328484			−0.164242	+	0.986420i	$0.552518\pi$
$402$		0			0
$403$	2.86738	−	2.86738i	0.142834	−	0.142834i
$404$	12.3560	−	9.50845i	0.614734	−	0.473063i
$405$		0			0
$406$	10.4078	+	30.5905i	0.516532	+	1.51818i
$407$	12.1569	−	12.1569i	0.602595	−	0.602595i
$408$		0			0
$409$			12.7208i			0.629002i	0.949257	+	0.314501i	$0.101837\pi$
$409$			12.7208i			0.629002i	−0.949257	+	0.314501i	$0.898163\pi$
$410$	2.30852	−	18.6715i	0.114010	−	0.922121i
$411$		0			0
$412$	−2.42631	+	18.6300i	−0.119536	+	0.917833i
$413$	13.7848	+	13.7848i	0.678308	+	0.678308i
$414$		0			0
$415$	10.5272	−	21.7397i	0.516761	−	1.06716i
$416$	−1.25133	−	18.1249i	−0.0613514	−	0.888647i
$417$		0			0
$418$	−41.4818	−	20.4207i	−2.02894	−	0.998809i
$419$		−	10.7345i		−	0.524415i	−0.965011	−	0.262208i	$-0.915549\pi$
$419$		−	10.7345i		−	0.524415i	0.965011	−	0.262208i	$-0.0844505\pi$
$420$		0			0
$421$			18.1886i			0.886460i	0.896408	+	0.443230i	$0.146167\pi$
$421$			18.1886i			0.886460i	−0.896408	+	0.443230i	$0.853833\pi$
$422$	12.1503	−	24.6817i	0.591468	−	1.20148i
$423$		0			0
$424$	−11.0660	−	7.36066i	−0.537410	−	0.357465i
$425$	−11.9287	−	1.39627i	−0.578628	−	0.0677291i
$426$		0			0
$427$	−16.7861	−	16.7861i	−0.812335	−	0.812335i
$428$	−1.44477	+	11.0934i	−0.0698355	+	0.536220i
$429$		0			0
$430$	0.489388	+	0.627475i	0.0236004	+	0.0302595i
$431$			8.54802i			0.411744i	0.978579	+	0.205872i	$0.0660030\pi$
$431$			8.54802i			0.411744i	−0.978579	+	0.205872i	$0.933997\pi$
$432$		0			0
$433$	−6.46852	+	6.46852i	−0.310857	+	0.310857i	−0.845242	−	0.534384i	$-0.820544\pi$
$433$	−6.46852	+	6.46852i	−0.310857	+	0.310857i	0.534384	+	0.845242i	$0.320544\pi$
$434$	4.61576	−	1.57042i	0.221564	−	0.0753828i
$435$		0			0
$436$	24.8788	+	32.3294i	1.19148	+	1.54830i
$437$	−3.40027	+	3.40027i	−0.162657	+	0.162657i
$438$		0			0
$439$	−17.8508			−0.851974			−0.425987	−	0.904729i	$-0.640073\pi$
$439$	−17.8508			−0.851974			−0.425987	+	0.904729i	$0.640073\pi$
$440$	−22.9176	+	13.5165i	−1.09255	+	0.644373i
$441$		0			0
$442$	9.78830	+	4.81859i	0.465582	+	0.229197i
$443$	−4.61480	+	4.61480i	−0.219256	+	0.219256i	−0.808185	−	0.588929i	$-0.799550\pi$
$443$	−4.61480	+	4.61480i	−0.219256	+	0.219256i	0.588929	+	0.808185i	$0.299550\pi$
$444$		0			0
$445$	8.51859	+	24.5145i	0.403820	+	1.16210i
$446$	16.4845	−	5.60853i	0.780563	−	0.265571i
$447$		0			0
$448$	8.27508	−	20.2162i	0.390961	−	0.955125i
$449$		−	16.6186i		−	0.784282i	−0.919905	−	0.392141i	$-0.871735\pi$
$449$		−	16.6186i		−	0.784282i	0.919905	−	0.392141i	$-0.128265\pi$
$450$		0			0
$451$	25.0284			1.17854
$452$	−31.6712	−	4.12476i	−1.48969	−	0.194012i
$453$		0			0
$454$	22.9321	−	7.80220i	1.07626	−	0.366176i
$455$	−18.5230	+	6.43659i	−0.868371	+	0.301752i
$456$		0			0
$457$	7.48912	+	7.48912i	0.350326	+	0.350326i	0.860231	−	0.509905i	$-0.170319\pi$
$457$	7.48912	+	7.48912i	0.350326	+	0.350326i	−0.509905	+	0.860231i	$0.670319\pi$
$458$	4.80276	−	9.75614i	0.224418	−	0.455875i
$459$		0			0
$460$	0.563122	+	2.70929i	0.0262557	+	0.126321i
$461$		−	18.8340i		−	0.877187i	−0.898686	−	0.438593i	$-0.855477\pi$
$461$		−	18.8340i		−	0.877187i	0.898686	−	0.438593i	$-0.144523\pi$
$462$		0			0
$463$	0.590827	+	0.590827i	0.0274581	+	0.0274581i	0.720703	−	0.693244i	$-0.243819\pi$
$463$	0.590827	+	0.590827i	0.0274581	+	0.0274581i	−0.693244	+	0.720703i	$0.743819\pi$
$464$	−8.57291	+	32.3546i	−0.397987	+	1.50202i
$465$		0			0
$466$	−7.67095	−	22.5463i	−0.355350	−	1.04444i
$467$	26.2940	+	26.2940i	1.21674	+	1.21674i	0.968766	+	0.247977i	$0.0797657\pi$
$467$	26.2940	+	26.2940i	1.21674	+	1.21674i	0.247977	+	0.968766i	$0.420234\pi$
$468$		0			0
$469$	−15.2509			−0.704220
$470$	1.97857	+	2.53685i	0.0912647	+	0.117016i
$471$		0			0
$472$	3.98093	+	19.7974i	0.183237	+	0.911247i
$473$	−0.748554	+	0.748554i	−0.0344186	+	0.0344186i
$474$		0			0
$475$	24.0957	+	30.4843i	1.10559	+	1.39872i
$476$	8.00000	+	10.3958i	0.366679	+	0.476491i
$477$		0			0
$478$	−7.41436	+	15.0613i	−0.339125	+	0.688886i
$479$	40.8184			1.86504			0.932520	−	0.361117i	$-0.117605\pi$
$479$	40.8184			1.86504			0.932520	+	0.361117i	$0.117605\pi$
$480$		0			0
$481$	13.1254			0.598466
$482$	−14.7644	+	29.9919i	−0.672501	+	1.36609i
$483$		0			0
$484$	−8.16948	−	10.6160i	−0.371340	−	0.482548i
$485$	18.7428	+	9.07597i	0.851065	+	0.412119i
$486$		0			0
$487$	−28.6832	+	28.6832i	−1.29976	+	1.29976i	−0.371212	+	0.928548i	$0.621058\pi$
$487$	−28.6832	+	28.6832i	−1.29976	+	1.29976i	−0.928548	+	0.371212i	$0.878942\pi$
$488$	−4.84765	−	24.1076i	−0.219443	−	1.09130i
$489$		0			0
$490$	−1.43047	−	0.176861i	−0.0646220	−	0.00798977i
$491$	−8.05656			−0.363587			−0.181794	−	0.983337i	$-0.558190\pi$
$491$	−8.05656			−0.363587			−0.181794	+	0.983337i	$0.558190\pi$
$492$		0			0
$493$	−14.2126	−	14.2126i	−0.640103	−	0.640103i
$494$	−11.3695	−	33.4170i	−0.511537	−	1.50350i
$495$		0			0
$496$	4.88194	+	1.29356i	0.219205	+	0.0580823i
$497$	4.07894	+	4.07894i	0.182965	+	0.182965i
$498$		0			0
$499$			0.908603i			0.0406747i	0.999793	+	0.0203373i	$0.00647402\pi$
$499$			0.908603i			0.0406747i	−0.999793	+	0.0203373i	$0.993526\pi$
$500$	22.2733	−	1.97433i	0.996094	−	0.0882949i
$501$		0			0
$502$	−2.84993	+	5.78923i	−0.127198	+	0.258386i
$503$	−19.9003	−	19.9003i	−0.887311	−	0.887311i	0.106953	−	0.994264i	$-0.465891\pi$
$503$	−19.9003	−	19.9003i	−0.887311	−	0.887311i	−0.994264	+	0.106953i	$0.965891\pi$
$504$		0			0
$505$	−5.72165	−	16.4656i	−0.254610	−	0.732707i
$506$	−3.48509	+	1.18573i	−0.154931	+	0.0527123i
$507$		0			0
$508$	6.50227	+	0.846835i	0.288492	+	0.0375722i
$509$	3.39092			0.150300			0.0751501	−	0.997172i	$-0.476056\pi$
$509$	3.39092			0.150300			0.0751501	+	0.997172i	$0.476056\pi$
$510$		0			0
$511$			10.8976i			0.482079i
$512$	18.7349	−	12.6887i	0.827973	−	0.560768i
$513$		0			0
$514$	22.2376	−	7.56592i	0.980860	−	0.333718i
$515$	18.9050	+	9.15453i	0.833053	+	0.403397i
$516$		0			0
$517$	−3.02637	+	3.02637i	−0.133100	+	0.133100i
$518$	14.1586	+	6.97000i	0.622093	+	0.306244i
$519$		0			0
$520$	−19.6683	−	5.07502i	−0.862512	−	0.222554i
$521$	16.1766			0.708709			0.354355	−	0.935111i	$-0.384701\pi$
$521$	16.1766			0.708709			0.354355	+	0.935111i	$0.384701\pi$
$522$		0			0
$523$	24.2781	−	24.2781i	1.06161	−	1.06161i	0.0636352	−	0.997973i	$-0.479731\pi$
$523$	24.2781	−	24.2781i	1.06161	−	1.06161i	0.997973	−	0.0636352i	$-0.0202694\pi$
$524$	−1.37440	−	1.78600i	−0.0600409	−	0.0780217i
$525$		0			0
$526$	−9.59354	+	3.26402i	−0.418298	+	0.142318i
$527$	−2.14452	+	2.14452i	−0.0934168	+	0.0934168i
$528$		0			0
$529$		−	22.6171i		−	0.983354i
$530$	−11.7168	+	9.13833i	−0.508947	+	0.396944i
$531$		0			0
$532$	5.48102	−	42.0851i	0.237633	−	1.82462i
$533$	13.5112	+	13.5112i	0.585234	+	0.585234i
$534$		0			0
$535$	11.2572	+	5.45115i	0.486689	+	0.235674i
$536$	−13.1536	−	8.74927i	−0.568148	−	0.377911i
$537$		0			0
$538$	4.51930	−	9.18033i	0.194841	−	0.395792i
$539$		−	1.91749i		−	0.0825920i
$540$		0			0
$541$		−	19.9175i		−	0.856320i	−0.903703	−	0.428160i	$-0.859162\pi$
$541$		−	19.9175i		−	0.856320i	0.903703	−	0.428160i	$-0.140838\pi$
$542$	0.987004	+	0.485883i	0.0423955	+	0.0208705i
$543$		0			0
$544$	0.935873	+	13.5557i	0.0401252	+	0.581195i
$545$	43.0821	−	14.9707i	1.84543	−	0.641273i
$546$		0			0
$547$	−21.4356	−	21.4356i	−0.916521	−	0.916521i	0.0802534	−	0.996774i	$-0.474427\pi$
$547$	−21.4356	−	21.4356i	−0.916521	−	0.916521i	−0.996774	+	0.0802534i	$0.974427\pi$
$548$	−0.727293	+	5.58440i	−0.0310684	+	0.238554i
$549$		0			0
$550$	6.24251	+	29.0847i	0.266181	+	1.24018i
$551$			65.0299i			2.77037i
$552$		0			0
$553$	24.4189	−	24.4189i	1.03840	−	1.03840i
$554$	10.9378	+	32.1482i	0.464703	+	1.36585i
$555$		0			0
$556$	9.18647	−	7.06936i	0.389593	−	0.299808i
$557$	−4.86295	+	4.86295i	−0.206050	+	0.206050i	−0.802586	−	0.596536i	$-0.796543\pi$
$557$	−4.86295	+	4.86295i	−0.206050	+	0.206050i	0.596536	+	0.802586i	$0.296543\pi$
$558$		0			0
$559$	−0.808188			−0.0341827
$560$	−18.5216	−	15.9190i	−0.782679	−	0.672701i
$561$		0			0
$562$	−0.192745	+	0.391535i	−0.00813045	+	0.0165159i
$563$	−15.7349	+	15.7349i	−0.663145	+	0.663145i	−0.956120	−	0.292975i	$-0.905355\pi$
$563$	−15.7349	+	15.7349i	−0.663145	+	0.663145i	0.292975	+	0.956120i	$0.405355\pi$
$564$		0			0
$565$	−15.5628	+	32.1388i	−0.654734	+	1.35209i
$566$	−2.87591	−	8.45282i	−0.120883	−	0.355298i
$567$		0			0
$568$	1.17796	+	5.85804i	0.0494260	+	0.245798i
$569$		−	39.1445i		−	1.64102i	−0.571631	−	0.820511i	$-0.693689\pi$
$569$		−	39.1445i		−	1.64102i	0.571631	−	0.820511i	$-0.306311\pi$
$570$		0			0
$571$	−28.1211			−1.17683			−0.588417	−	0.808558i	$-0.700248\pi$
$571$	−28.1211			−1.17683			−0.588417	+	0.808558i	$0.700248\pi$
$572$	3.48983	−	26.7960i	0.145917	−	1.12040i
$573$		0			0
$574$	7.39989	+	21.7496i	0.308865	+	0.907812i
$575$	3.07283	+	0.359679i	0.128146	+	0.0149996i
$576$		0			0
$577$	−6.32515	−	6.32515i	−0.263319	−	0.263319i	0.563082	−	0.826401i	$-0.309616\pi$
$577$	−6.32515	−	6.32515i	−0.263319	−	0.263319i	−0.826401	+	0.563082i	$0.809616\pi$
$578$	14.2490	+	7.01449i	0.592679	+	0.291764i
$579$		0			0
$580$	31.2923	+	20.5227i	1.29934	+	0.852157i
$581$			29.4957i			1.22369i
$582$		0			0
$583$	−13.9778	−	13.9778i	−0.578899	−	0.578899i
$584$	−6.25181	+	9.39892i	−0.258702	+	0.388930i
$585$		0			0
$586$	23.1363	−	7.87169i	0.955754	−	0.325177i
$587$	2.39334	+	2.39334i	0.0987836	+	0.0987836i	0.754771	−	0.655988i	$-0.227748\pi$
$587$	2.39334	+	2.39334i	0.0987836	+	0.0987836i	−0.655988	+	0.754771i	$0.727748\pi$
$588$		0			0
$589$	9.81228			0.404308
$590$	22.4066	+	2.77032i	0.922464	+	0.114052i
$591$		0			0
$592$	8.21288	+	14.1341i	0.337547	+	0.580909i
$593$	−19.0151	+	19.0151i	−0.780857	+	0.780857i	−0.979975	−	0.199119i	$-0.936192\pi$
$593$	−19.0151	+	19.0151i	−0.780857	+	0.780857i	0.199119	+	0.979975i	$0.436192\pi$
$594$		0			0
$595$	13.8534	−	4.81395i	0.567934	−	0.197353i
$596$	25.3199	+	32.9027i	1.03715	+	1.34775i
$597$		0			0
$598$	−2.52146	−	1.24127i	−0.103110	−	0.0507592i
$599$	18.5779			0.759073			0.379536	−	0.925177i	$-0.376084\pi$
$599$	18.5779			0.759073			0.379536	+	0.925177i	$0.376084\pi$
$600$		0			0
$601$	−14.0090			−0.571441			−0.285720	−	0.958313i	$-0.592233\pi$
$601$	−14.0090			−0.571441			−0.285720	+	0.958313i	$0.592233\pi$
$602$	−0.871808	−	0.429174i	−0.0355322	−	0.0174918i
$603$		0			0
$604$	36.8659	−	28.3698i	1.50005	−	1.15435i
$605$	−14.1469	+	4.91593i	−0.575153	+	0.199861i
$606$		0			0
$607$	0.0307136	−	0.0307136i	0.00124663	−	0.00124663i	−0.706483	−	0.707730i	$-0.749719\pi$
$607$	0.0307136	−	0.0307136i	0.00124663	−	0.00124663i	0.707730	+	0.706483i	$0.249719\pi$
$608$	28.8711	−	33.1531i	1.17088	−	1.34454i
$609$		0			0
$610$	−27.2849	−	3.37347i	−1.10473	−	0.136588i
$611$	−3.26747			−0.132188
$612$		0			0
$613$	4.42985	+	4.42985i	0.178920	+	0.178920i	0.790885	−	0.611965i	$-0.209621\pi$
$613$	4.42985	+	4.42985i	0.178920	+	0.178920i	−0.611965	+	0.790885i	$0.709621\pi$
$614$	−40.4152	+	13.7505i	−1.63102	+	0.554925i
$615$		0			0
$616$	17.9941	−	27.0522i	0.725003	−	1.08996i
$617$	14.8477	+	14.8477i	0.597747	+	0.597747i	0.939712	−	0.341966i	$-0.111093\pi$
$617$	14.8477	+	14.8477i	0.597747	+	0.597747i	−0.341966	+	0.939712i	$0.611093\pi$
$618$		0			0
$619$			21.2082i			0.852431i	0.904622	+	0.426215i	$0.140153\pi$
$619$			21.2082i			0.852431i	−0.904622	+	0.426215i	$0.859847\pi$
$620$	3.09664	−	4.72166i	0.124364	−	0.189626i
$621$		0			0
$622$	9.99083	+	4.91829i	0.400596	+	0.197205i
$623$	−22.4091	−	22.4091i	−0.897802	−	0.897802i
$624$		0			0
$625$	5.77345	−	24.3242i	0.230938	−	0.972968i
$626$	−4.16218	−	12.2334i	−0.166354	−	0.488945i
$627$		0			0
$628$	14.4495	+	1.88186i	0.576598	+	0.0750942i
$629$	−9.81652			−0.391410
$630$		0			0
$631$			14.4286i			0.574393i	0.957872	+	0.287197i	$0.0927233\pi$
$631$			14.4286i			0.574393i	−0.957872	+	0.287197i	$0.907277\pi$
$632$	35.0696	−	7.05193i	1.39499	−	0.280511i
$633$		0			0
$634$	−2.34504	−	6.89251i	−0.0931336	−	0.273737i
$635$	3.19513	−	6.59826i	0.126795	−	0.261844i
$636$		0			0
$637$	1.03512	−	1.03512i	0.0410130	−	0.0410130i
$638$	−21.9875	+	44.6646i	−0.870494	+	1.76829i
$639$		0			0
$640$	−6.84191	−	24.3555i	−0.270450	−	0.962734i
$641$	−25.6394			−1.01269			−0.506347	−	0.862330i	$-0.669004\pi$
$641$	−25.6394			−1.01269			−0.506347	+	0.862330i	$0.669004\pi$
$642$		0			0
$643$	−19.1519	+	19.1519i	−0.755277	+	0.755277i	−0.975459	−	0.220181i	$-0.929335\pi$
$643$	−19.1519	+	19.1519i	−0.755277	+	0.755277i	0.220181	+	0.975459i	$0.429335\pi$
$644$	−2.06080	−	2.67796i	−0.0812067	−	0.105526i
$645$		0			0
$646$	8.50328	+	24.9927i	0.334557	+	0.983324i
$647$	−28.0162	+	28.0162i	−1.10143	+	1.10143i	−0.107193	+	0.994238i	$0.534186\pi$
$647$	−28.0162	+	28.0162i	−1.10143	+	1.10143i	−0.994238	+	0.107193i	$0.965814\pi$
$648$		0			0
$649$			30.0351i			1.17898i
$650$	−12.3310	+	19.0708i	−0.483660	+	0.748018i
$651$		0			0
$652$	−19.5418	−	2.54506i	−0.765315	−	0.0996721i
$653$	−20.1570	−	20.1570i	−0.788804	−	0.788804i	0.192494	−	0.981298i	$-0.438342\pi$
$653$	−20.1570	−	20.1570i	−0.788804	−	0.788804i	−0.981298	+	0.192494i	$0.938342\pi$
$654$		0			0
$655$	−2.38001	+	0.827036i	−0.0929949	+	0.0323150i
$656$	−6.09527	+	23.0038i	−0.237980	+	0.898149i
$657$		0			0
$658$	−3.52468	−	1.73513i	−0.137406	−	0.0676425i
$659$		−	4.21893i		−	0.164346i	−0.996618	−	0.0821732i	$-0.973814\pi$
$659$		−	4.21893i		−	0.164346i	0.996618	−	0.0821732i	$-0.0261861\pi$
$660$		0			0
$661$		−	24.1292i		−	0.938516i	−0.883061	−	0.469258i	$-0.844521\pi$
$661$		−	24.1292i		−	0.938516i	0.883061	−	0.469258i	$-0.155479\pi$
$662$	0.0795452	−	0.161585i	0.00309161	−	0.00628019i
$663$		0			0
$664$	−16.9214	+	25.4395i	−0.656677	+	0.987243i
$665$	−42.7064	−	20.6801i	−1.65608	−	0.801939i
$666$		0			0
$667$	3.66116	+	3.66116i	0.141761	+	0.141761i
$668$	26.3833	+	3.43607i	1.02080	+	0.132946i
$669$		0			0
$670$	−13.9272	+	10.8623i	−0.538056	+	0.419647i
$671$		−	36.5743i		−	1.41194i
$672$		0			0
$673$	−11.3369	+	11.3369i	−0.437007	+	0.437007i	−0.891003	−	0.453997i	$-0.849998\pi$
$673$	−11.3369	+	11.3369i	−0.437007	+	0.437007i	0.453997	+	0.891003i	$0.349998\pi$
$674$	−45.1267	+	15.3535i	−1.73822	+	0.591395i
$675$		0			0
$676$	−4.25583	+	3.27504i	−0.163686	+	0.125963i
$677$	−3.51914	+	3.51914i	−0.135251	+	0.135251i	−0.771491	−	0.636240i	$-0.780489\pi$
$677$	−3.51914	+	3.51914i	−0.135251	+	0.135251i	0.636240	+	0.771491i	$0.280489\pi$
$678$		0			0
$679$	−25.4296			−0.975897
$680$	14.7100	+	3.79562i	0.564102	+	0.145555i
$681$		0			0
$682$	6.73939	+	3.31767i	0.258064	+	0.127040i
$683$	−2.23616	+	2.23616i	−0.0855643	+	0.0855643i	−0.748594	−	0.663029i	$-0.769271\pi$
$683$	−2.23616	+	2.23616i	−0.0855643	+	0.0855643i	0.663029	+	0.748594i	$0.269271\pi$
$684$		0			0
$685$	5.66683	+	2.74410i	0.216518	+	0.104847i
$686$	−23.9240	+	8.13968i	−0.913423	+	0.310774i
$687$		0			0
$688$	−0.505704	−	0.870301i	−0.0192798	−	0.0331799i
$689$		−	15.0913i		−	0.574933i
$690$		0			0
$691$	−25.5922			−0.973573			−0.486786	−	0.873521i	$-0.661831\pi$
$691$	−25.5922			−0.973573			−0.486786	+	0.873521i	$0.661831\pi$
$692$	4.43193	−	34.0298i	0.168477	−	1.29362i
$693$		0			0
$694$	19.3609	−	6.58718i	0.734931	−	0.250046i
$695$	−4.25394	−	12.2418i	−0.161361	−	0.464360i
$696$		0			0
$697$	−10.1050	−	10.1050i	−0.382756	−	0.382756i
$698$	−0.0658798	+	0.133826i	−0.00249359	+	0.00506538i
$699$		0			0
$700$	−23.4288	+	14.0239i	−0.885527	+	0.530053i
$701$		−	26.7541i		−	1.01049i	−0.862976	−	0.505245i	$-0.831402\pi$
$701$		−	26.7541i		−	1.01049i	0.862976	−	0.505245i	$-0.168598\pi$
$702$		0			0
$703$	22.4578	+	22.4578i	0.847012	+	0.847012i
$704$	31.0391	−	13.0089i	1.16983	−	0.490293i
$705$		0			0
$706$	1.38579	+	4.07309i	0.0521549	+	0.153293i
$707$	15.0514	+	15.0514i	0.566067	+	0.566067i
$708$		0			0
$709$	−9.84383			−0.369693			−0.184846	−	0.982767i	$-0.559179\pi$
$709$	−9.84383			−0.369693			−0.184846	+	0.982767i	$0.559179\pi$
$710$	6.63011	+	0.819737i	0.248823	+	0.0307642i
$711$		0			0
$712$	−6.47154	−	32.1833i	−0.242531	−	1.20612i
$713$	0.552428	−	0.552428i	0.0206886	−	0.0206886i
$714$		0			0
$715$	−27.1916	−	13.1672i	−1.01691	−	0.492426i
$716$	−1.92791	+	1.48361i	−0.0720494	+	0.0554450i
$717$		0			0
$718$	4.36506	−	8.86702i	0.162903	−	0.330914i
$719$	−14.3100			−0.533671			−0.266836	−	0.963742i	$-0.585978\pi$
$719$	−14.3100			−0.533671			−0.266836	+	0.963742i	$0.585978\pi$
$720$		0			0
$721$	−25.6497			−0.955243
$722$	25.8562	−	52.5233i	0.962268	−	1.95472i
$723$		0			0
$724$	−8.77193	+	6.75036i	−0.326006	+	0.250875i
$725$	32.8233	−	25.9445i	1.21903	−	0.963554i
$726$		0			0
$727$	−30.2169	+	30.2169i	−1.12068	+	1.12068i	−0.129043	+	0.991639i	$0.541190\pi$
$727$	−30.2169	+	30.2169i	−1.12068	+	1.12068i	−0.991639	+	0.129043i	$0.958810\pi$
$728$	24.3175	−	4.88985i	0.901265	−	0.181230i
$729$		0			0
$730$	7.76168	+	9.95174i	0.287273	+	0.368331i
$731$	0.604447			0.0223563
$732$		0			0
$733$	34.2747	+	34.2747i	1.26596	+	1.26596i	0.948154	+	0.317810i	$0.102947\pi$
$733$	34.2747	+	34.2747i	1.26596	+	1.26596i	0.317810	+	0.948154i	$0.397053\pi$
$734$	14.0530	+	41.3042i	0.518704	+	1.52457i
$735$		0			0
$736$	−0.241080	−	3.49194i	−0.00888634	−	0.128715i
$737$	−16.6147	−	16.6147i	−0.612010	−	0.612010i
$738$		0			0
$739$			35.7420i			1.31479i	0.753546	+	0.657395i	$0.228342\pi$
$739$			35.7420i			1.31479i	−0.753546	+	0.657395i	$0.771658\pi$
$740$	17.8941	−	3.71926i	0.657799	−	0.136723i
$741$		0			0
$742$	8.01397	−	16.2793i	0.294202	−	0.597631i
$743$	15.4626	+	15.4626i	0.567267	+	0.567267i	0.931362	−	0.364095i	$-0.118621\pi$
$743$	15.4626	+	15.4626i	0.567267	+	0.567267i	−0.364095	+	0.931362i	$0.618621\pi$
$744$		0			0
$745$	43.8459	−	15.2361i	1.60639	−	0.558208i
$746$	35.4884	−	12.0743i	1.29932	−	0.442070i
$747$		0			0
$748$	−2.61005	+	20.0409i	−0.0954330	+	0.732766i
$749$	−15.2733			−0.558076
$750$		0			0
$751$		−	47.6026i		−	1.73704i	−0.495652	−	0.868521i	$-0.665071\pi$
$751$		−	47.6026i		−	1.73704i	0.495652	−	0.868521i	$-0.334929\pi$
$752$	−2.04454	−	3.51859i	−0.0745567	−	0.128310i
$753$		0			0
$754$	−35.9810	+	12.2418i	−1.31035	+	0.445822i
$755$	−17.0714	−	49.1274i	−0.621290	−	1.78793i
$756$		0			0
$757$	−13.1759	+	13.1759i	−0.478885	+	0.478885i	−0.904775	−	0.425890i	$-0.859961\pi$
$757$	−13.1759	+	13.1759i	−0.478885	+	0.478885i	0.425890	+	0.904775i	$0.359961\pi$
$758$	11.1524	+	5.49010i	0.405073	+	0.199409i
$759$		0			0
$760$	−24.9694	−	42.3363i	−0.905736	−	1.53570i
$761$	−13.4188			−0.486432			−0.243216	−	0.969972i	$-0.578202\pi$
$761$	−13.4188			−0.486432			−0.243216	+	0.969972i	$0.578202\pi$
$762$		0			0
$763$	−39.3820	+	39.3820i	−1.42573	+	1.42573i
$764$	10.7308	−	8.25781i	0.388228	−	0.298757i
$765$		0			0
$766$	37.2011	−	12.6569i	1.34413	−	0.457314i
$767$	−16.2139	+	16.2139i	−0.585451	+	0.585451i
$768$		0			0
$769$		−	36.8980i		−	1.33058i	−0.746587	−	0.665288i	$-0.768309\pi$
$769$		−	36.8980i		−	1.33058i	0.746587	−	0.665288i	$-0.231691\pi$
$770$	−22.3399	−	28.6433i	−0.805073	−	1.03223i
$771$		0			0
$772$	−13.3597	−	1.73992i	−0.480826	−	0.0626212i
$773$	19.3598	+	19.3598i	0.696323	+	0.696323i	0.963616	−	0.267292i	$-0.0861289\pi$
$773$	19.3598	+	19.3598i	0.696323	+	0.696323i	−0.267292	+	0.963616i	$0.586129\pi$
$774$		0			0
$775$	−3.91473	−	4.95267i	−0.140621	−	0.177905i
$776$	−21.9325	−	14.5887i	−0.787330	−	0.523703i
$777$		0			0
$778$	5.46435	−	11.1001i	0.195906	−	0.397957i
$779$			46.2358i			1.65657i
$780$		0			0
$781$			8.88739i			0.318016i
$782$	1.88581	+	0.928347i	0.0674364	+	0.0331976i
$783$		0			0
$784$	1.76238	+	0.466973i	0.0629420	+	0.0166776i
$785$	7.10030	−	14.6628i	0.253421	−	0.523338i
$786$		0			0
$787$	12.9107	+	12.9107i	0.460215	+	0.460215i	0.898726	−	0.438511i	$-0.144494\pi$
$787$	12.9107	+	12.9107i	0.460215	+	0.460215i	−0.438511	+	0.898726i	$0.644494\pi$
$788$	−25.1054	−	3.26964i	−0.894341	−	0.116476i
$789$		0			0
$790$	4.90742	−	39.6916i	0.174598	−	1.41217i
$791$		−	43.6048i		−	1.55041i
$792$		0			0
$793$	19.7440	−	19.7440i	0.701131	−	0.701131i
$794$	12.5291	+	36.8252i	0.444640	+	1.30688i
$795$		0			0
$796$	−2.58179	−	3.35498i	−0.0915092	−	0.118914i
$797$	−22.7573	+	22.7573i	−0.806106	+	0.806106i	−0.984042	−	0.177936i	$-0.943058\pi$
$797$	−22.7573	+	22.7573i	−0.806106	+	0.806106i	0.177936	+	0.984042i	$0.443058\pi$
$798$		0			0
$799$	2.44375			0.0864537
$800$	−28.2522	−	1.34557i	−0.998868	−	0.0475731i
$801$		0			0
$802$	4.10860	−	8.34605i	0.145080	−	0.294709i
$803$	−11.8721	+	11.8721i	−0.418956	+	0.418956i
$804$		0			0
$805$	−3.56863	+	1.24007i	−0.125778	+	0.0437067i
$806$	1.84716	+	5.42913i	0.0650633	+	0.191233i
$807$		0			0
$808$	4.34671	+	21.6164i	0.152917	+	0.760462i
$809$		−	28.1842i		−	0.990902i	−0.868636	−	0.495451i	$-0.835003\pi$
$809$		−	28.1842i		−	0.990902i	0.868636	−	0.495451i	$-0.164997\pi$
$810$		0			0
$811$	12.5892			0.442067			0.221033	−	0.975266i	$-0.429057\pi$
$811$	12.5892			0.442067			0.221033	+	0.975266i	$0.429057\pi$
$812$	−45.3142	−	5.90157i	−1.59022	−	0.207105i
$813$		0			0
$814$	7.83143	+	23.0180i	0.274492	+	0.806781i
$815$	−9.60258	+	19.8303i	−0.336364	+	0.694623i
$816$		0			0
$817$	−1.38283	−	1.38283i	−0.0483790	−	0.0483790i
$818$	−16.1402	−	7.94550i	−0.564329	−	0.277808i
$819$		0			0
$820$	22.2486	+	14.5914i	0.776955	+	0.509556i
$821$		−	47.0644i		−	1.64256i	−0.570527	−	0.821279i	$-0.693261\pi$
$821$		−	47.0644i		−	1.64256i	0.570527	−	0.821279i	$-0.306739\pi$
$822$		0			0
$823$	−7.05493	−	7.05493i	−0.245919	−	0.245919i	0.573374	−	0.819294i	$-0.305634\pi$
$823$	−7.05493	−	7.05493i	−0.245919	−	0.245919i	−0.819294	+	0.573374i	$0.805634\pi$
$824$	−22.1223	−	14.7149i	−0.770667	−	0.512619i
$825$		0			0
$826$	−26.1004	+	8.88015i	−0.908149	+	0.308980i
$827$	3.50851	+	3.50851i	0.122003	+	0.122003i	0.765472	−	0.643469i	$-0.222506\pi$
$827$	3.50851	+	3.50851i	0.122003	+	0.122003i	−0.643469	+	0.765472i	$0.722506\pi$
$828$		0			0
$829$	29.6726			1.03057			0.515286	−	0.857019i	$-0.327686\pi$
$829$	29.6726			1.03057			0.515286	+	0.857019i	$0.327686\pi$
$830$	21.0081	+	26.9358i	0.729201	+	0.934955i
$831$		0			0
$832$	23.7786	+	9.73327i	0.824373	+	0.337440i
$833$	−0.774171	+	0.774171i	−0.0268234	+	0.0268234i
$834$		0			0
$835$	12.9644	−	26.7728i	0.448652	−	0.926510i
$836$	51.8197	−	39.8774i	1.79222	−	1.37919i
$837$		0			0
$838$	13.6200	+	6.70486i	0.470495	+	0.231616i
$839$	−3.80747			−0.131448			−0.0657242	−	0.997838i	$-0.520936\pi$
$839$	−3.80747			−0.131448			−0.0657242	+	0.997838i	$0.520936\pi$
$840$		0			0
$841$	41.0195			1.41447
$842$	−23.0778	−	11.3608i	−0.795314	−	0.391518i
$843$		0			0
$844$	23.7270	+	30.8327i	0.816718	+	1.06131i
$845$	1.97073	+	5.67130i	0.0677952	+	0.195099i
$846$		0			0
$847$	12.9319	−	12.9319i	0.444346	−	0.444346i
$848$	16.2511	−	9.44301i	0.558066	−	0.324274i
$849$		0			0
$850$	9.22237	−	14.2631i	0.316325	−	0.489220i
$851$	2.52873			0.0866837
$852$		0			0
$853$	−37.7460	−	37.7460i	−1.29240	−	1.29240i	−0.933300	−	0.359097i	$-0.883085\pi$
$853$	−37.7460	−	37.7460i	−1.29240	−	1.29240i	−0.359097	−	0.933300i	$-0.616915\pi$
$854$	31.7830	−	10.8135i	1.08759	−	0.370031i
$855$		0			0
$856$	−13.1729	−	8.76215i	−0.450242	−	0.299484i
$857$	5.56897	+	5.56897i	0.190233	+	0.190233i	0.795797	−	0.605564i	$-0.207052\pi$
$857$	5.56897	+	5.56897i	0.190233	+	0.190233i	−0.605564	+	0.795797i	$0.707052\pi$
$858$		0			0
$859$		−	19.7536i		−	0.673985i	−0.941507	−	0.336993i	$-0.890590\pi$
$859$		−	19.7536i		−	0.673985i	0.941507	−	0.336993i	$-0.109410\pi$
$860$	−1.10182	+	0.229012i	−0.0375717	+	0.00780923i
$861$		0			0
$862$	−10.8458	−	5.33916i	−0.369408	−	0.181852i
$863$	25.6303	+	25.6303i	0.872465	+	0.872465i	0.992741	−	0.120275i	$-0.0383777\pi$
$863$	25.6303	+	25.6303i	0.872465	+	0.872465i	−0.120275	+	0.992741i	$0.538378\pi$
$864$		0			0
$865$	−34.5321	−	16.7218i	−1.17413	−	0.568558i
$866$	−4.16700	−	12.2476i	−0.141601	−	0.416190i
$867$		0			0
$868$	−0.890480	+	6.83740i	−0.0302249	+	0.232077i
$869$	53.2050			1.80486
$870$		0			0
$871$		−	17.9383i		−	0.607816i
$872$	−56.5593	+	11.3732i	−1.91534	+	0.385144i
$873$		0			0
$874$	−2.19044	−	6.43810i	−0.0740928	−	0.217772i
$875$	6.60012	+	29.8063i	0.223125	+	1.00764i
$876$		0			0
$877$	−4.44061	+	4.44061i	−0.149949	+	0.149949i	−0.778095	−	0.628147i	$-0.783814\pi$
$877$	−4.44061	+	4.44061i	−0.149949	+	0.149949i	0.628147	+	0.778095i	$0.283814\pi$
$878$	11.1498	−	22.6492i	0.376287	−	0.764375i
$879$		0			0
$880$	−2.83529	−	37.5204i	−0.0955776	−	1.26481i
$881$	17.9007			0.603090			0.301545	−	0.953452i	$-0.402498\pi$
$881$	17.9007			0.603090			0.301545	+	0.953452i	$0.402498\pi$
$882$		0			0
$883$	10.7065	−	10.7065i	0.360302	−	0.360302i	−0.503622	−	0.863924i	$-0.667999\pi$
$883$	10.7065	−	10.7065i	0.360302	−	0.360302i	0.863924	+	0.503622i	$0.167999\pi$
$884$	−12.2277	+	9.40971i	−0.411262	+	0.316483i
$885$		0			0
$886$	−2.97284	−	8.73772i	−0.0998745	−	0.293549i
$887$	−9.62314	+	9.62314i	−0.323113	+	0.323113i	−0.849960	−	0.526847i	$-0.823374\pi$
$887$	−9.62314	+	9.62314i	−0.323113	+	0.323113i	0.526847	+	0.849960i	$0.323374\pi$
$888$		0			0
$889$			8.95230i			0.300251i
$890$	−36.4249	−	4.50352i	−1.22097	−	0.150958i
$891$		0			0
$892$	−3.18021	+	24.4187i	−0.106481	+	0.817599i
$893$	−5.59071	−	5.59071i	−0.187086	−	0.187086i
$894$		0			0
$895$	0.892751	+	2.56913i	0.0298414	+	0.0858764i
$896$	20.4817	+	23.1266i	0.684246	+	0.772607i
$897$		0			0
$898$	21.0858	+	10.3801i	0.703642	+	0.346389i
$899$		−	10.5652i		−	0.352368i
$900$		0			0
$901$			11.2868i			0.376019i
$902$	−15.6330	+	31.7562i	−0.520520	+	1.05737i
$903$		0			0
$904$	25.0156	−	37.6083i	0.832007	−	1.25083i
$905$	4.06199	+	11.6894i	0.135025	+	0.388570i
$906$		0			0
$907$	24.0535	+	24.0535i	0.798684	+	0.798684i	0.982888	−	0.184204i	$-0.0589706\pi$
$907$	24.0535	+	24.0535i	0.798684	+	0.798684i	−0.184204	+	0.982888i	$0.558971\pi$
$908$	−4.42410	+	33.9697i	−0.146819	+	1.12732i
$909$		0			0
$910$	3.40283	−	27.5224i	0.112803	−	0.912359i
$911$		−	42.2124i		−	1.39856i	−0.714848	−	0.699280i	$-0.753504\pi$
$911$		−	42.2124i		−	1.39856i	0.714848	−	0.699280i	$-0.246496\pi$
$912$		0			0
$913$	−32.1334	+	32.1334i	−1.06346	+	1.06346i
$914$	−14.1800	+	4.82447i	−0.469032	+	0.159579i
$915$		0			0
$916$	9.37880	+	12.1875i	0.309884	+	0.402687i
$917$	2.17561	−	2.17561i	0.0718450	−	0.0718450i
$918$		0			0
$919$	7.62336			0.251471			0.125736	−	0.992064i	$-0.459871\pi$
$919$	7.62336			0.251471			0.125736	+	0.992064i	$0.459871\pi$
$920$	−3.78929	−	0.977750i	−0.124929	−	0.0322355i
$921$		0			0
$922$	23.8967	+	11.7639i	0.786995	+	0.387422i
$923$	−4.79770	+	4.79770i	−0.157918	+	0.157918i
$924$		0			0
$925$	2.37558	−	20.2952i	0.0781084	−	0.667302i
$926$	−1.11868	+	0.380609i	−0.0367621	+	0.0125076i
$927$		0			0
$928$	−35.6969	−	31.0863i	−1.17181	−	1.02046i
$929$			36.8505i			1.20902i	0.796596	+	0.604512i	$0.206632\pi$
$929$			36.8505i			1.20902i	−0.796596	+	0.604512i	$0.793368\pi$
$930$		0			0
$931$	3.54223			0.116092
$932$	33.3982	+	4.34967i	1.09400	+	0.142478i
$933$		0			0
$934$	−49.7854	+	16.9385i	−1.62903	+	0.554246i
$935$	20.3367	+	9.84782i	0.665081	+	0.322058i
$936$		0			0
$937$	−26.1716	−	26.1716i	−0.854990	−	0.854990i	0.135753	−	0.990743i	$-0.456655\pi$
$937$	−26.1716	−	26.1716i	−0.854990	−	0.854990i	−0.990743	+	0.135753i	$0.956655\pi$
$938$	9.52582	−	19.3504i	0.311029	−	0.631813i
$939$		0			0
$940$	−4.45460	+	0.925883i	−0.145293	+	0.0301990i
$941$			49.5596i			1.61560i	0.589459	+	0.807798i	$0.299341\pi$
$941$			49.5596i			1.61560i	−0.589459	+	0.807798i	$0.700659\pi$
$942$		0			0
$943$	2.60306	+	2.60306i	0.0847672	+	0.0847672i
$944$	−27.6055	−	7.31456i	−0.898483	−	0.238069i
$945$		0			0
$946$	−0.482216	−	1.41732i	−0.0156782	−	0.0460811i
$947$	28.2113	+	28.2113i	0.916743	+	0.916743i	0.996791	−	0.0800484i	$-0.0255075\pi$
$947$	28.2113	+	28.2113i	0.916743	+	0.916743i	−0.0800484	+	0.996791i	$0.525507\pi$
$948$		0			0
$949$	−12.8179			−0.416085
$950$	−53.7290	+	11.5320i	−1.74320	+	0.374146i
$951$		0			0
$952$	−18.1871	+	3.65713i	−0.589448	+	0.118528i
$953$	20.7731	−	20.7731i	0.672907	−	0.672907i	−0.285478	−	0.958385i	$-0.592152\pi$
$953$	20.7731	−	20.7731i	0.672907	−	0.672907i	0.958385	+	0.285478i	$0.0921523\pi$
$954$		0			0
$955$	−4.96908	−	14.2999i	−0.160796	−	0.462732i
$956$	−14.4787	−	18.8148i	−0.468275	−	0.608513i
$957$		0			0
$958$	−25.4955	+	51.7906i	−0.823722	+	1.67328i
$959$	−7.68857			−0.248277
$960$		0			0
$961$	29.4058			0.948575
$962$	−8.19821	+	16.6535i	−0.264321	+	0.536932i
$963$		0			0
$964$	−28.8319	−	37.4663i	−0.928613	−	1.20671i
$965$	−6.56478	+	13.5569i	−0.211328	+	0.436412i
$966$		0			0
$967$	30.8527	−	30.8527i	0.992155	−	0.992155i	−0.00781439	−	0.999969i	$-0.502487\pi$
$967$	30.8527	−	30.8527i	0.992155	−	0.992155i	0.999969	+	0.00781439i	$0.00248742\pi$
$968$	18.5724	−	3.73461i	0.596940	−	0.120035i
$969$		0			0
$970$	−23.2225	+	18.1120i	−0.745630	+	0.581540i
$971$	8.20145			0.263197			0.131598	−	0.991303i	$-0.457989\pi$
$971$	8.20145			0.263197			0.131598	+	0.991303i	$0.457989\pi$
$972$		0			0
$973$	11.1905	+	11.1905i	0.358750	+	0.358750i
$974$	−18.4776	−	54.3091i	−0.592061	−	1.74018i
$975$		0			0
$976$	33.6158	+	8.90709i	1.07601	+	0.285109i
$977$	−21.2688	−	21.2688i	−0.680448	−	0.680448i	0.279653	−	0.960101i	$-0.409781\pi$
$977$	−21.2688	−	21.2688i	−0.680448	−	0.680448i	−0.960101	+	0.279653i	$0.909781\pi$
$978$		0			0
$979$		−	48.8261i		−	1.56049i
$980$	1.11788	−	1.70452i	0.0357095	−	0.0544488i
$981$		0			0
$982$	5.03219	−	10.2222i	0.160584	−	0.326203i
$983$	−16.5320	−	16.5320i	−0.527288	−	0.527288i	0.392475	−	0.919763i	$-0.371619\pi$
$983$	−16.5320	−	16.5320i	−0.527288	−	0.527288i	−0.919763	+	0.392475i	$0.871619\pi$
$984$		0			0
$985$	−12.3364	+	25.4759i	−0.393072	+	0.811731i
$986$	26.9103	−	9.15571i	0.856999	−	0.291577i
$987$		0			0
$988$	49.5011	+	6.44686i	1.57484	+	0.205102i
$989$	−0.155705			−0.00495114
$990$		0			0
$991$			7.20959i			0.229020i	0.993422	+	0.114510i	$0.0365298\pi$
$991$			7.20959i			0.229020i	−0.993422	+	0.114510i	$0.963470\pi$
$992$	−4.69057	+	5.38626i	−0.148926	+	0.171014i
$993$		0			0
$994$	−7.72311	+	2.62764i	−0.244962	+	0.0833436i
$995$	−4.47083	+	1.55358i	−0.141735	+	0.0492517i
$996$		0			0
$997$	−4.15041	+	4.15041i	−0.131445	+	0.131445i	−0.769768	−	0.638323i	$-0.779628\pi$
$997$	−4.15041	+	4.15041i	−0.131445	+	0.131445i	0.638323	+	0.769768i	$0.279628\pi$
$998$	−1.15284	−	0.567520i	−0.0364925	−	0.0179645i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.e.307.5		24
3.2	odd	2		120.2.v.a.67.8	yes	24
4.3	odd	2		1440.2.bi.e.847.2		24
5.3	odd	4	inner	360.2.w.e.163.11		24
8.3	odd	2	inner	360.2.w.e.307.11		24
8.5	even	2		1440.2.bi.e.847.11		24
12.11	even	2		480.2.bh.a.367.12		24
15.2	even	4		600.2.v.b.43.11		24
15.8	even	4		120.2.v.a.43.2	✓	24
15.14	odd	2		600.2.v.b.307.5		24
20.3	even	4		1440.2.bi.e.1423.11		24
24.5	odd	2		480.2.bh.a.367.7		24
24.11	even	2		120.2.v.a.67.2	yes	24
40.3	even	4	inner	360.2.w.e.163.5		24
40.13	odd	4		1440.2.bi.e.1423.2		24
60.23	odd	4		480.2.bh.a.463.7		24
60.47	odd	4		2400.2.bh.b.943.3		24
60.59	even	2		2400.2.bh.b.1807.4		24
120.29	odd	2		2400.2.bh.b.1807.3		24
120.53	even	4		480.2.bh.a.463.12		24
120.59	even	2		600.2.v.b.307.11		24
120.77	even	4		2400.2.bh.b.943.4		24
120.83	odd	4		120.2.v.a.43.8	yes	24
120.107	odd	4		600.2.v.b.43.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.2	✓	24	15.8	even	4
120.2.v.a.43.8	yes	24	120.83	odd	4
120.2.v.a.67.2	yes	24	24.11	even	2
120.2.v.a.67.8	yes	24	3.2	odd	2
360.2.w.e.163.5		24	40.3	even	4	inner
360.2.w.e.163.11		24	5.3	odd	4	inner
360.2.w.e.307.5		24	1.1	even	1	trivial
360.2.w.e.307.11		24	8.3	odd	2	inner
480.2.bh.a.367.7		24	24.5	odd	2
480.2.bh.a.367.12		24	12.11	even	2
480.2.bh.a.463.7		24	60.23	odd	4
480.2.bh.a.463.12		24	120.53	even	4
600.2.v.b.43.5		24	120.107	odd	4
600.2.v.b.43.11		24	15.2	even	4
600.2.v.b.307.5		24	15.14	odd	2
600.2.v.b.307.11		24	120.59	even	2
1440.2.bi.e.847.2		24	4.3	odd	2
1440.2.bi.e.847.11		24	8.5	even	2
1440.2.bi.e.1423.2		24	40.13	odd	4
1440.2.bi.e.1423.11		24	20.3	even	4
2400.2.bh.b.943.3		24	60.47	odd	4
2400.2.bh.b.943.4		24	120.77	even	4
2400.2.bh.b.1807.3		24	120.29	odd	2
2400.2.bh.b.1807.4		24	60.59	even	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.624608 + 1.26880i) q^{2} +(-1.21973 - 1.58501i) q^{4} +(-2.11218 + 0.733965i) q^{5} +(1.93078 - 1.93078i) q^{7} +(2.77292 - 0.557590i) q^{8} +O(q^{10})\)	\(q+(-0.624608 + 1.26880i) q^{2} +(-1.21973 - 1.58501i) q^{4} +(-2.11218 + 0.733965i) q^{5} +(1.93078 - 1.93078i) q^{7} +(2.77292 - 0.557590i) q^{8} +(0.388025 - 3.13838i) q^{10} +4.20687 q^{11} +(2.27101 + 2.27101i) q^{13} +(1.24380 + 3.65576i) q^{14} +(-1.02452 + 3.86657i) q^{16} +(-1.69849 - 1.69849i) q^{17} +7.77148i q^{19} +(3.73963 + 2.45259i) q^{20} +(-2.62765 + 5.33770i) q^{22} +(0.437531 + 0.437531i) q^{23} +(3.92259 - 3.10053i) q^{25} +(-4.29995 + 1.46298i) q^{26} +(-5.41533 - 0.705274i) q^{28} +8.36777 q^{29} -1.26260i q^{31} +(-4.26600 - 3.71500i) q^{32} +(3.21595 - 1.09416i) q^{34} +(-2.66102 + 5.49527i) q^{35} +(2.88977 - 2.88977i) q^{37} +(-9.86049 - 4.85413i) q^{38} +(-5.44765 + 3.21296i) q^{40} +5.94942 q^{41} +(-0.177936 + 0.177936i) q^{43} +(-5.13125 - 6.66794i) q^{44} +(-0.828427 + 0.281856i) q^{46} +(-0.719388 + 0.719388i) q^{47} -0.455798i q^{49} +(1.48388 + 6.91362i) q^{50} +(0.829554 - 6.36959i) q^{52} +(-3.32260 - 3.32260i) q^{53} +(-8.88566 + 3.08770i) q^{55} +(4.27731 - 6.43047i) q^{56} +(-5.22657 + 10.6171i) q^{58} +7.13953i q^{59} -8.69395i q^{61} +(1.60199 + 0.788631i) q^{62} +(7.37819 - 3.09231i) q^{64} +(-6.46361 - 3.12993i) q^{65} +(-3.94942 - 3.94942i) q^{67} +(-0.620426 + 4.76384i) q^{68} +(-5.31032 - 6.80870i) q^{70} +2.11259i q^{71} +(-2.82206 + 2.82206i) q^{73} +(1.86158 + 5.47153i) q^{74} +(12.3179 - 9.47911i) q^{76} +(8.12253 - 8.12253i) q^{77} +12.6472 q^{79} +(-0.673966 - 8.91884i) q^{80} +(-3.71605 + 7.54865i) q^{82} +(-7.63831 + 7.63831i) q^{83} +(4.83416 + 2.34089i) q^{85} +(-0.114626 - 0.336906i) q^{86} +(11.6653 - 2.34571i) q^{88} -11.6063i q^{89} +8.76962 q^{91} +(0.159821 - 1.22716i) q^{92} +(-0.463427 - 1.36210i) q^{94} +(-5.70399 - 16.4147i) q^{95} +(-6.58532 - 6.58532i) q^{97} +(0.578319 + 0.284695i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

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