LMFDB - Embedded newform 360.2.w.e.307.2

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			307.2
Character	$\chi$	$=$	360.307
Dual form			360.2.w.e.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25738 - 0.647304i) q^{2} +(1.16200 + 1.62781i) q^{4} +(-1.28903 + 1.82713i) q^{5} +(-1.45533 + 1.45533i) q^{7} +(-0.407381 - 2.79894i) q^{8} +O(q^{10})$	\(q+(-1.25738 - 0.647304i) q^{2} +(1.16200 + 1.62781i) q^{4} +(-1.28903 + 1.82713i) q^{5} +(-1.45533 + 1.45533i) q^{7} +(-0.407381 - 2.79894i) q^{8} +(2.80350 - 1.46300i) q^{10} -0.725670 q^{11} +(-4.57738 - 4.57738i) q^{13} +(2.77193 - 0.887857i) q^{14} +(-1.29953 + 3.78302i) q^{16} +(-2.36535 - 2.36535i) q^{17} -6.41350i q^{19} +(-4.47207 + 0.0248209i) q^{20} +(0.912441 + 0.469729i) q^{22} +(1.35791 + 1.35791i) q^{23} +(-1.67680 - 4.71045i) q^{25} +(2.79254 + 8.71844i) q^{26} +(-4.06008 - 0.677911i) q^{28} -2.91898 q^{29} +5.71240i q^{31} +(4.08276 - 3.91549i) q^{32} +(1.44304 + 4.50523i) q^{34} +(-0.783110 - 4.53503i) q^{35} +(-2.65700 + 2.65700i) q^{37} +(-4.15148 + 8.06419i) q^{38} +(5.63914 + 2.86358i) q^{40} -1.02625 q^{41} +(-7.38725 + 7.38725i) q^{43} +(-0.843226 - 1.18125i) q^{44} +(-0.828427 - 2.58639i) q^{46} +(1.22848 - 1.22848i) q^{47} +2.76404i q^{49} +(-0.940718 + 7.00821i) q^{50} +(2.13220 - 12.7700i) q^{52} +(-9.48969 - 9.48969i) q^{53} +(0.935410 - 1.32589i) q^{55} +(4.66624 + 3.48050i) q^{56} +(3.67027 + 1.88947i) q^{58} +6.43011i q^{59} -1.18105i q^{61} +(3.69766 - 7.18265i) q^{62} +(-7.66808 + 2.28046i) q^{64} +(14.2638 - 2.46308i) q^{65} +(3.02625 + 3.02625i) q^{67} +(1.10181 - 6.59886i) q^{68} +(-1.95088 + 6.20916i) q^{70} +6.55658i q^{71} +(4.38725 - 4.38725i) q^{73} +(5.06073 - 1.62097i) q^{74} +(10.4400 - 7.45247i) q^{76} +(1.05609 - 1.05609i) q^{77} +6.75224 q^{79} +(-5.23693 - 7.25083i) q^{80} +(1.29039 + 0.664297i) q^{82} +(-1.37207 + 1.37207i) q^{83} +(7.37079 - 1.27279i) q^{85} +(14.0704 - 4.50677i) q^{86} +(0.295624 + 2.03110i) q^{88} -4.63060i q^{89} +13.3232 q^{91} +(-0.632534 + 3.78831i) q^{92} +(-2.33986 + 0.749462i) q^{94} +(11.7183 + 8.26720i) q^{95} +(3.27977 + 3.27977i) q^{97} +(1.78918 - 3.47545i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.25738	−	0.647304i	−0.889100	−	0.457713i
$2$	−1.25738	−	0.647304i	−0.889100	−	0.457713i
$3$		0			0
$3$		0			0
$4$	1.16200	+	1.62781i	0.580998	+	0.813905i
$5$	−1.28903	+	1.82713i	−0.576472	+	0.817117i
$5$	−1.28903	+	1.82713i	−0.576472	+	0.817117i
$6$		0			0
$7$	−1.45533	+	1.45533i	−0.550062	+	0.550062i	−0.926459	−	0.376397i	$-0.877163\pi$
$7$	−1.45533	+	1.45533i	−0.550062	+	0.550062i	0.376397	+	0.926459i	$0.377163\pi$
$8$	−0.407381	−	2.79894i	−0.144031	−	0.989573i
$9$		0			0
$10$	2.80350	−	1.46300i	0.886546	−	0.462640i
$11$	−0.725670			−0.218798			−0.109399	−	0.993998i	$-0.534893\pi$
$11$	−0.725670			−0.218798			−0.109399	+	0.993998i	$0.534893\pi$
$12$		0			0
$13$	−4.57738	−	4.57738i	−1.26954	−	1.26954i	−0.946328	−	0.323208i	$-0.895239\pi$
$13$	−4.57738	−	4.57738i	−1.26954	−	1.26954i	−0.323208	−	0.946328i	$-0.604761\pi$
$14$	2.77193	−	0.887857i	0.740831	−	0.237290i
$15$		0			0
$16$	−1.29953	+	3.78302i	−0.324882	+	0.945754i
$17$	−2.36535	−	2.36535i	−0.573681	−	0.573681i	0.359474	−	0.933155i	$-0.382956\pi$
$17$	−2.36535	−	2.36535i	−0.573681	−	0.573681i	−0.933155	+	0.359474i	$0.882956\pi$
$18$		0			0
$19$		−	6.41350i		−	1.47136i	−0.677330	−	0.735679i	$-0.736863\pi$
$19$		−	6.41350i		−	1.47136i	0.677330	−	0.735679i	$-0.263137\pi$
$20$	−4.47207	+	0.0248209i	−0.999985	+	0.00555013i
$21$		0			0
$22$	0.912441	+	0.469729i	0.194533	+	0.100146i
$23$	1.35791	+	1.35791i	0.283144	+	0.283144i	0.834362	−	0.551217i	$-0.185836\pi$
$23$	1.35791	+	1.35791i	0.283144	+	0.283144i	−0.551217	+	0.834362i	$0.685836\pi$
$24$		0			0
$25$	−1.67680	−	4.71045i	−0.335360	−	0.942090i
$26$	2.79254	+	8.71844i	0.547662	+	1.70983i
$27$		0			0
$28$	−4.06008	−	0.677911i	−0.767283	−	0.128113i
$29$	−2.91898			−0.542042			−0.271021	−	0.962573i	$-0.587361\pi$
$29$	−2.91898			−0.542042			−0.271021	+	0.962573i	$0.587361\pi$
$30$		0			0
$31$			5.71240i			1.02598i	0.858395	+	0.512989i	$0.171462\pi$
$31$			5.71240i			1.02598i	−0.858395	+	0.512989i	$0.828538\pi$
$32$	4.08276	−	3.91549i	0.721737	−	0.692168i
$33$		0			0
$34$	1.44304	+	4.50523i	0.247479	+	0.772640i
$35$	−0.783110	−	4.53503i	−0.132370	−	0.766560i
$36$		0			0
$37$	−2.65700	+	2.65700i	−0.436808	+	0.436808i	−0.890936	−	0.454128i	$-0.849951\pi$
$37$	−2.65700	+	2.65700i	−0.436808	+	0.436808i	0.454128	+	0.890936i	$0.349951\pi$
$38$	−4.15148	+	8.06419i	−0.673460	+	1.30819i
$39$		0			0
$40$	5.63914	+	2.86358i	0.891627	+	0.452771i
$41$	−1.02625			−0.160274			−0.0801368	−	0.996784i	$-0.525536\pi$
$41$	−1.02625			−0.160274			−0.0801368	+	0.996784i	$0.525536\pi$
$42$		0			0
$43$	−7.38725	+	7.38725i	−1.12655	+	1.12655i	−0.135810	+	0.990735i	$0.543364\pi$
$43$	−7.38725	+	7.38725i	−1.12655	+	1.12655i	−0.990735	+	0.135810i	$0.956636\pi$
$44$	−0.843226	−	1.18125i	−0.127121	−	0.178081i
$45$		0			0
$46$	−0.828427	−	2.58639i	−0.122145	−	0.381342i
$47$	1.22848	−	1.22848i	0.179192	−	0.179192i	−0.611812	−	0.791004i	$-0.709559\pi$
$47$	1.22848	−	1.22848i	0.179192	−	0.179192i	0.791004	+	0.611812i	$0.209559\pi$
$48$		0			0
$49$			2.76404i			0.394864i
$50$	−0.940718	+	7.00821i	−0.133038	+	0.991111i
$51$		0			0
$52$	2.13220	−	12.7700i	0.295684	−	1.77088i
$53$	−9.48969	−	9.48969i	−1.30351	−	1.30351i	−0.926010	−	0.377500i	$-0.876784\pi$
$53$	−9.48969	−	9.48969i	−1.30351	−	1.30351i	−0.377500	−	0.926010i	$-0.623216\pi$
$54$		0			0
$55$	0.935410	−	1.32589i	0.126131	−	0.178783i
$56$	4.66624	+	3.48050i	0.623553	+	0.465101i
$57$		0			0
$58$	3.67027	+	1.88947i	0.481929	+	0.248099i
$59$			6.43011i			0.837129i	0.908187	+	0.418564i	$0.137467\pi$
$59$			6.43011i			0.837129i	−0.908187	+	0.418564i	$0.862533\pi$
$60$		0			0
$61$		−	1.18105i		−	0.151218i	−0.997138	−	0.0756089i	$-0.975910\pi$
$61$		−	1.18105i		−	0.151218i	0.997138	−	0.0756089i	$-0.0240901\pi$
$62$	3.69766	−	7.18265i	0.469603	−	0.912197i
$63$		0			0
$64$	−7.66808	+	2.28046i	−0.958510	+	0.285058i
$65$	14.2638	−	2.46308i	1.76921	−	0.305508i
$66$		0			0
$67$	3.02625	+	3.02625i	0.369716	+	0.369716i	0.867373	−	0.497658i	$-0.165806\pi$
$67$	3.02625	+	3.02625i	0.369716	+	0.369716i	−0.497658	+	0.867373i	$0.665806\pi$
$68$	1.10181	−	6.59886i	0.133614	−	0.800229i
$69$		0			0
$70$	−1.95088	+	6.20916i	−0.233174	+	0.742136i
$71$			6.55658i			0.778123i	0.921212	+	0.389062i	$0.127201\pi$
$71$			6.55658i			0.778123i	−0.921212	+	0.389062i	$0.872799\pi$
$72$		0			0
$73$	4.38725	−	4.38725i	0.513489	−	0.513489i	−0.402105	−	0.915594i	$-0.631721\pi$
$73$	4.38725	−	4.38725i	0.513489	−	0.513489i	0.915594	+	0.402105i	$0.131721\pi$
$74$	5.06073	−	1.62097i	0.588298	−	0.188433i
$75$		0			0
$76$	10.4400	−	7.45247i	1.19755	−	0.854857i
$77$	1.05609	−	1.05609i	0.120352	−	0.120352i
$78$		0			0
$79$	6.75224			0.759686			0.379843	−	0.925051i	$-0.375978\pi$
$79$	6.75224			0.759686			0.379843	+	0.925051i	$0.375978\pi$
$80$	−5.23693	−	7.25083i	−0.585506	−	0.810668i
$81$		0			0
$82$	1.29039	+	0.664297i	0.142499	+	0.0733593i
$83$	−1.37207	+	1.37207i	−0.150604	+	0.150604i	−0.778388	−	0.627784i	$-0.783962\pi$
$83$	−1.37207	+	1.37207i	−0.150604	+	0.150604i	0.627784	+	0.778388i	$0.283962\pi$
$84$		0			0
$85$	7.37079	−	1.27279i	0.799475	−	0.138053i
$86$	14.0704	−	4.50677i	1.51725	−	0.485977i
$87$		0			0
$88$	0.295624	+	2.03110i	0.0315136	+	0.216516i
$89$		−	4.63060i		−	0.490843i	−0.969416	−	0.245421i	$-0.921074\pi$
$89$		−	4.63060i		−	0.490843i	0.969416	−	0.245421i	$-0.0789263\pi$
$90$		0			0
$91$	13.3232			1.39665
$92$	−0.632534	+	3.78831i	−0.0659463	+	0.394959i
$93$		0			0
$94$	−2.33986	+	0.749462i	−0.241338	+	0.0773011i
$95$	11.7183	+	8.26720i	1.20227	+	0.848197i
$96$		0			0
$97$	3.27977	+	3.27977i	0.333010	+	0.333010i	0.853728	−	0.520719i	$-0.174336\pi$
$97$	3.27977	+	3.27977i	0.333010	+	0.333010i	−0.520719	+	0.853728i	$0.674336\pi$
$98$	1.78918	−	3.47545i	0.180734	−	0.351073i
$99$		0			0
$100$	5.71928	−	8.20304i	0.571928	−	0.820304i
$101$		−	13.5791i		−	1.35117i	−0.737284	−	0.675583i	$-0.763892\pi$
$101$		−	13.5791i		−	1.35117i	0.737284	−	0.675583i	$-0.236108\pi$
$102$		0			0
$103$	−7.90300	−	7.90300i	−0.778706	−	0.778706i	0.200905	−	0.979611i	$-0.435612\pi$
$103$	−7.90300	−	7.90300i	−0.778706	−	0.778706i	−0.979611	+	0.200905i	$0.935612\pi$
$104$	−10.9470	+	14.6765i	−1.07345	+	1.43915i
$105$		0			0
$106$	5.78941	+	18.0748i	0.562318	+	1.75558i
$107$	11.1728	+	11.1728i	1.08012	+	1.08012i	0.996498	+	0.0836196i	$0.0266481\pi$
$107$	11.1728	+	11.1728i	1.08012	+	1.08012i	0.0836196	+	0.996498i	$0.473352\pi$
$108$		0			0
$109$	−12.4480			−1.19230			−0.596150	−	0.802873i	$-0.703304\pi$
$109$	−12.4480			−1.19230			−0.596150	+	0.802873i	$0.703304\pi$
$110$	−2.03442	+	1.06165i	−0.193974	+	0.101225i
$111$		0			0
$112$	−3.61429	−	7.39677i	−0.341518	−	0.698929i
$113$	−9.43541	+	9.43541i	−0.887609	+	0.887609i	−0.994293	−	0.106684i	$-0.965977\pi$
$113$	−9.43541	+	9.43541i	−0.887609	+	0.887609i	0.106684	+	0.994293i	$0.465977\pi$
$114$		0			0
$115$	−4.23147	+	0.730691i	−0.394587	+	0.0681373i
$116$	−3.39185	−	4.75155i	−0.314925	−	0.441171i
$117$		0			0
$118$	4.16223	−	8.08507i	0.383165	−	0.744291i
$119$	6.88470			0.631120
$120$		0			0
$121$	−10.4734			−0.952128
$122$	−0.764497	+	1.48502i	−0.0692143	+	0.134448i
$123$		0			0
$124$	−9.29870	+	6.63779i	−0.835048	+	0.596091i
$125$	10.7680	+	3.00818i	0.963124	+	0.269060i
$126$		0			0
$127$	9.88355	−	9.88355i	0.877024	−	0.877024i	−0.116202	−	0.993226i	$-0.537072\pi$
$127$	9.88355	−	9.88355i	0.877024	−	0.877024i	0.993226	+	0.116202i	$0.0370720\pi$
$128$	11.1178	+	2.09617i	0.982686	+	0.185277i
$129$		0			0
$130$	−19.5294	−	6.13601i	−1.71284	−	0.538164i
$131$	−14.0012			−1.22329			−0.611647	−	0.791131i	$-0.709493\pi$
$131$	−14.0012			−1.22329			−0.611647	+	0.791131i	$0.709493\pi$
$132$		0			0
$133$	9.33375	+	9.33375i	0.809338	+	0.809338i
$134$	−1.84624	−	5.76404i	−0.159491	−	0.497938i
$135$		0			0
$136$	−5.65685	+	7.58405i	−0.485071	+	0.650327i
$137$	4.31776	+	4.31776i	0.368891	+	0.368891i	0.867073	−	0.498182i	$-0.165999\pi$
$137$	4.31776	+	4.31776i	0.368891	+	0.368891i	−0.498182	+	0.867073i	$0.665999\pi$
$138$		0			0
$139$		−	10.2753i		−	0.871538i	−0.900058	−	0.435769i	$-0.856476\pi$
$139$		−	10.2753i		−	0.871538i	0.900058	−	0.435769i	$-0.143524\pi$
$140$	6.47220	−	6.54444i	0.547001	−	0.553106i
$141$		0			0
$142$	4.24410	−	8.24410i	0.356157	−	0.691829i
$143$	3.32166	+	3.32166i	0.277772	+	0.277772i
$144$		0			0
$145$	3.76266	−	5.33336i	0.312472	−	0.442912i
$146$	−8.35631	+	2.67655i	−0.691574	+	0.221513i
$147$		0			0
$148$	−7.41251	−	1.23767i	−0.609305	−	0.101736i
$149$	−3.03780			−0.248867			−0.124433	−	0.992228i	$-0.539711\pi$
$149$	−3.03780			−0.248867			−0.124433	+	0.992228i	$0.539711\pi$
$150$		0			0
$151$			5.52994i			0.450020i	0.974356	+	0.225010i	$0.0722415\pi$
$151$			5.52994i			0.450020i	−0.974356	+	0.225010i	$0.927758\pi$
$152$	−17.9510	+	2.61274i	−1.45602	+	0.211921i
$153$		0			0
$154$	−2.01151	+	0.644291i	−0.162092	+	0.0519185i
$155$	−10.4373	−	7.36346i	−0.838344	−	0.591447i
$156$		0			0
$157$	4.36202	−	4.36202i	0.348127	−	0.348127i	−0.511284	−	0.859412i	$-0.670830\pi$
$157$	4.36202	−	4.36202i	0.348127	−	0.348127i	0.859412	+	0.511284i	$0.170830\pi$
$158$	−8.49011	−	4.37075i	−0.675437	−	0.347718i
$159$		0			0
$160$	1.89131	+	12.5069i	0.149521	+	0.988759i
$161$	−3.95241			−0.311494
$162$		0			0
$163$	−9.10371	+	9.10371i	−0.713058	+	0.713058i	−0.967174	−	0.254116i	$-0.918215\pi$
$163$	−9.10371	+	9.10371i	−0.713058	+	0.713058i	0.254116	+	0.967174i	$0.418215\pi$
$164$	−1.19250	−	1.67054i	−0.0931187	−	0.130448i
$165$		0			0
$166$	2.61335	−	0.837062i	0.202835	−	0.0649686i
$167$	−15.2102	+	15.2102i	−1.17700	+	1.17700i	−0.196497	+	0.980504i	$0.562957\pi$
$167$	−15.2102	+	15.2102i	−1.17700	+	1.17700i	−0.980504	+	0.196497i	$0.937043\pi$
$168$		0			0
$169$			28.9048i			2.22344i
$170$	−10.0918	−	3.17076i	−0.774002	−	0.243187i
$171$		0			0
$172$	−20.6090	−	3.44108i	−1.57142	−	0.262380i
$173$	5.23564	+	5.23564i	0.398058	+	0.398058i	0.877548	−	0.479489i	$-0.159178\pi$
$173$	5.23564	+	5.23564i	0.398058	+	0.398058i	−0.479489	+	0.877548i	$0.659178\pi$
$174$		0			0
$175$	9.29554	+	4.41495i	0.702677	+	0.333739i
$176$	0.943030	−	2.74522i	0.0710835	−	0.206929i
$177$		0			0
$178$	−2.99741	+	5.82241i	−0.224665	+	0.436408i
$179$		−	16.3444i		−	1.22164i	−0.791771	−	0.610819i	$-0.790840\pi$
$179$		−	16.3444i		−	1.22164i	0.791771	−	0.610819i	$-0.209160\pi$
$180$		0			0
$181$			1.33892i			0.0995215i	0.998761	+	0.0497608i	$0.0158459\pi$
$181$			1.33892i			0.0995215i	−0.998761	+	0.0497608i	$0.984154\pi$
$182$	−16.7522	−	8.62413i	−1.24176	−	0.639263i
$183$		0			0
$184$	3.24752	−	4.35390i	0.239411	−	0.320974i
$185$	−1.42973	−	8.27963i	−0.105116	−	0.608731i
$186$		0			0
$187$	1.71646	+	1.71646i	0.125520	+	0.125520i
$188$	3.42722	+	0.572242i	0.249955	+	0.0417350i
$189$		0			0
$190$	−9.38294	−	17.9803i	−0.680710	−	1.30443i
$191$		−	18.5684i		−	1.34356i	−0.740750	−	0.671780i	$-0.765530\pi$
$191$		−	18.5684i		−	1.34356i	0.740750	−	0.671780i	$-0.234470\pi$
$192$		0			0
$193$	2.10748	−	2.10748i	0.151700	−	0.151700i	−0.627177	−	0.778877i	$-0.715790\pi$
$193$	2.10748	−	2.10748i	0.151700	−	0.151700i	0.778877	+	0.627177i	$0.215790\pi$
$194$	−2.00090	−	6.24691i	−0.143656	−	0.448502i
$195$		0			0
$196$	−4.49934	+	3.21181i	−0.321381	+	0.229415i
$197$	−8.63291	+	8.63291i	−0.615069	+	0.615069i	−0.944263	−	0.329193i	$-0.893223\pi$
$197$	−8.63291	+	8.63291i	−0.615069	+	0.615069i	0.329193	+	0.944263i	$0.393223\pi$
$198$		0			0
$199$	2.36127			0.167386			0.0836932	−	0.996492i	$-0.473328\pi$
$199$	2.36127			0.167386			0.0836932	+	0.996492i	$0.473328\pi$
$200$	−12.5011	+	6.61221i	−0.883965	+	0.467554i
$201$		0			0
$202$	−8.78977	+	17.0740i	−0.618446	+	1.20132i
$203$	4.24808	−	4.24808i	0.298157	−	0.298157i
$204$		0			0
$205$	1.32287	−	1.87510i	0.0923932	−	0.130962i
$206$	4.82142	+	15.0527i	0.335924	+	1.04877i
$207$		0			0
$208$	23.2647	−	11.3679i	1.61312	−	0.788219i
$209$			4.65409i			0.321930i
$210$		0			0
$211$	−3.38157			−0.232797			−0.116398	−	0.993203i	$-0.537135\pi$
$211$	−3.38157			−0.232797			−0.116398	+	0.993203i	$0.537135\pi$
$212$	4.42043	−	26.4744i	0.303596	−	1.81827i
$213$		0			0
$214$	−6.81625	−	21.2807i	−0.465949	−	1.45472i
$215$	−3.97507	−	23.0199i	−0.271098	−	1.56994i
$216$		0			0
$217$	−8.31341	−	8.31341i	−0.564351	−	0.564351i
$218$	15.6518	+	8.05762i	1.06007	+	0.545731i
$219$		0			0
$220$	3.24524	−	0.0180118i	0.218794	−	0.00121436i
$221$			21.6542i			1.45662i
$222$		0			0
$223$	9.32012	+	9.32012i	0.624122	+	0.624122i	0.946583	−	0.322461i	$-0.104510\pi$
$223$	9.32012	+	9.32012i	0.624122	+	0.624122i	−0.322461	+	0.946583i	$0.604510\pi$
$224$	−0.243432	+	11.6401i	−0.0162650	+	0.777735i
$225$		0			0
$226$	17.9714	−	5.75630i	1.19544	−	0.382903i
$227$	14.9247	+	14.9247i	0.990590	+	0.990590i	0.999956	−	0.00936616i	$-0.00298138\pi$
$227$	14.9247	+	14.9247i	0.990590	+	0.990590i	−0.00936616	+	0.999956i	$0.502981\pi$
$228$		0			0
$229$	13.5299			0.894082			0.447041	−	0.894514i	$-0.352478\pi$
$229$	13.5299			0.894082			0.447041	+	0.894514i	$0.352478\pi$
$230$	5.79354	+	1.82029i	0.382015	+	0.120027i
$231$		0			0
$232$	1.18914	+	8.17005i	0.0780707	+	0.536390i
$233$	−4.26526	+	4.26526i	−0.279426	+	0.279426i	−0.832880	−	0.553454i	$-0.813310\pi$
$233$	−4.26526	+	4.26526i	−0.279426	+	0.279426i	0.553454	+	0.832880i	$0.313310\pi$
$234$		0			0
$235$	0.661043	+	3.82813i	0.0431217	+	0.249720i
$236$	−10.4670	+	7.47176i	−0.681343	+	0.486370i
$237$		0			0
$238$	−8.65667	−	4.45649i	−0.561129	−	0.288872i
$239$	−2.73939			−0.177196			−0.0885981	−	0.996067i	$-0.528239\pi$
$239$	−2.73939			−0.177196			−0.0885981	+	0.996067i	$0.528239\pi$
$240$		0			0
$241$	−16.4833			−1.06178			−0.530890	−	0.847440i	$-0.678142\pi$
$241$	−16.4833			−1.06178			−0.530890	+	0.847440i	$0.678142\pi$
$242$	13.1690	+	6.77947i	0.846537	+	0.435801i
$243$		0			0
$244$	1.92252	−	1.37237i	0.123077	−	0.0878573i
$245$	−5.05027	−	3.56294i	−0.322650	−	0.227628i
$246$		0			0
$247$	−29.3570	+	29.3570i	−1.86794	+	1.86794i
$248$	15.9886	−	2.32712i	1.01528	−	0.147772i
$249$		0			0
$250$	−11.5923	−	10.7526i	−0.733161	−	0.680055i
$251$	14.0488			0.886754			0.443377	−	0.896335i	$-0.353780\pi$
$251$	14.0488			0.886754			0.443377	+	0.896335i	$0.353780\pi$
$252$		0			0
$253$	−0.985396	−	0.985396i	−0.0619513	−	0.0619513i
$254$	−18.8250	+	6.02970i	−1.18119	+	0.378337i
$255$		0			0
$256$	−12.6224	−	9.83229i	−0.788903	−	0.614518i
$257$	−4.43264	−	4.43264i	−0.276501	−	0.276501i	0.555210	−	0.831710i	$-0.312638\pi$
$257$	−4.43264	−	4.43264i	−0.276501	−	0.276501i	−0.831710	+	0.555210i	$0.812638\pi$
$258$		0			0
$259$		−	7.73360i		−	0.480543i
$260$	20.5840	+	20.3567i	1.27656	+	1.26247i
$261$		0			0
$262$	17.6049	+	9.06306i	1.08763	+	0.559918i
$263$	−19.3432	−	19.3432i	−1.19275	−	1.19275i	−0.976292	−	0.216458i	$-0.930549\pi$
$263$	−19.3432	−	19.3432i	−1.19275	−	1.19275i	−0.216458	−	0.976292i	$-0.569451\pi$
$264$		0			0
$265$	29.5714	−	5.10639i	1.81656	−	0.313683i
$266$	−5.69428	−	17.7778i	−0.349138	−	1.09003i
$267$		0			0
$268$	−1.40967	+	8.44266i	−0.0861093	+	0.515717i
$269$	24.0508			1.46640			0.733201	−	0.680012i	$-0.238026\pi$
$269$	24.0508			1.46640			0.733201	+	0.680012i	$0.238026\pi$
$270$		0			0
$271$		−	24.3905i		−	1.48162i	−0.671716	−	0.740809i	$-0.734442\pi$
$271$		−	24.3905i		−	1.48162i	0.671716	−	0.740809i	$-0.265558\pi$
$272$	12.0220	−	5.87431i	0.728940	−	0.356182i
$273$		0			0
$274$	−2.63415	−	8.22396i	−0.159135	−	0.496827i
$275$	1.21680	+	3.41823i	0.0733761	+	0.206127i
$276$		0			0
$277$	6.76755	−	6.76755i	0.406623	−	0.406623i	−0.473936	−	0.880559i	$-0.657167\pi$
$277$	6.76755	−	6.76755i	0.406623	−	0.406623i	0.880559	+	0.473936i	$0.157167\pi$
$278$	−6.65123	+	12.9199i	−0.398914	+	0.774885i
$279$		0			0
$280$	−12.3742	+	4.03936i	−0.739502	+	0.241398i
$281$	−4.79740			−0.286189			−0.143094	−	0.989709i	$-0.545705\pi$
$281$	−4.79740			−0.286189			−0.143094	+	0.989709i	$0.545705\pi$
$282$		0			0
$283$	−1.57491	+	1.57491i	−0.0936188	+	0.0936188i	−0.752365	−	0.658746i	$-0.771087\pi$
$283$	−1.57491	+	1.57491i	−0.0936188	+	0.0936188i	0.658746	+	0.752365i	$0.271087\pi$
$284$	−10.6729	+	7.61872i	−0.633318	+	0.452088i
$285$		0			0
$286$	−2.02646	−	6.32671i	−0.119827	−	0.374106i
$287$	1.49353	−	1.49353i	0.0881604	−	0.0881604i
$288$		0			0
$289$		−	5.81028i		−	0.341781i
$290$	−8.18339	+	4.27047i	−0.480545	+	0.250770i
$291$		0			0
$292$	12.2396	+	2.04364i	0.716267	+	0.119595i
$293$	16.8458	+	16.8458i	0.984141	+	0.984141i	0.999876	−	0.0157353i	$-0.00500890\pi$
$293$	16.8458	+	16.8458i	0.984141	+	0.984141i	−0.0157353	+	0.999876i	$0.505009\pi$
$294$		0			0
$295$	−11.7486	−	8.28861i	−0.684032	−	0.482581i
$296$	8.51918	+	6.35436i	0.495167	+	0.369340i
$297$		0			0
$298$	3.81967	+	1.96638i	0.221267	+	0.113909i
$299$		−	12.4314i		−	0.718924i
$300$		0			0
$301$		−	21.5017i		−	1.23934i
$302$	3.57955	−	6.95323i	0.205980	−	0.400113i
$303$		0			0
$304$	24.2624	+	8.33454i	1.39154	+	0.478019i
$305$	2.15793	+	1.52241i	0.123563	+	0.0871728i
$306$		0			0
$307$	13.5999	+	13.5999i	0.776185	+	0.776185i	0.979180	−	0.202994i	$-0.0650673\pi$
$307$	13.5999	+	13.5999i	0.776185	+	0.776185i	−0.202994	+	0.979180i	$0.565067\pi$
$308$	2.94628	+	0.491940i	0.167880	+	0.0280309i
$309$		0			0
$310$	8.35723	+	16.0147i	0.474659	+	0.909576i
$311$		−	6.98730i		−	0.396213i	−0.980180	−	0.198107i	$-0.936521\pi$
$311$		−	6.98730i		−	0.396213i	0.980180	−	0.198107i	$-0.0634792\pi$
$312$		0			0
$313$	13.3659	−	13.3659i	0.755486	−	0.755486i	−0.220011	−	0.975497i	$-0.570609\pi$
$313$	13.3659	−	13.3659i	0.755486	−	0.755486i	0.975497	+	0.220011i	$0.0706093\pi$
$314$	−8.30826	+	2.66115i	−0.468862	+	0.150178i
$315$		0			0
$316$	7.84607	+	10.9914i	0.441376	+	0.618312i
$317$	2.24312	−	2.24312i	0.125986	−	0.125986i	−0.641302	−	0.767288i	$-0.721605\pi$
$317$	2.24312	−	2.24312i	0.125986	−	0.125986i	0.767288	+	0.641302i	$0.221605\pi$
$318$		0			0
$319$	2.11822			0.118597
$320$	5.71769	−	16.9502i	0.319628	−	0.947543i
$321$		0			0
$322$	4.96968	+	2.55841i	0.276949	+	0.142575i
$323$	−15.1702	+	15.1702i	−0.844090	+	0.844090i
$324$		0			0
$325$	−13.8861	+	29.2369i	−0.770265	+	1.62177i
$326$	17.3397	−	5.55394i	0.960355	−	0.307604i
$327$		0			0
$328$	0.418075	+	2.87241i	0.0230843	+	0.158603i
$329$			3.57567i			0.197133i
$330$		0			0
$331$	−0.360999			−0.0198423			−0.00992116	−	0.999951i	$-0.503158\pi$
$331$	−0.360999			−0.0198423			−0.00992116	+	0.999951i	$0.503158\pi$
$332$	−3.82780	−	0.639127i	−0.210078	−	0.0350767i
$333$		0			0
$334$	28.9706	−	9.27935i	1.58520	−	0.507744i
$335$	−9.43028	+	1.62842i	−0.515231	+	0.0889702i
$336$		0			0
$337$	−0.546946	−	0.546946i	−0.0297941	−	0.0297941i	0.692053	−	0.721847i	$-0.256707\pi$
$337$	−0.546946	−	0.546946i	−0.0297941	−	0.0297941i	−0.721847	+	0.692053i	$0.756707\pi$
$338$	18.7102	−	36.3442i	1.01770	−	1.97686i
$339$		0			0
$340$	10.6367	+	10.5193i	0.576856	+	0.570488i
$341$		−	4.14532i		−	0.224482i
$342$		0			0
$343$	−14.2099	−	14.2099i	−0.767261	−	0.767261i
$344$	23.6859	+	17.6670i	1.27706	+	0.952542i
$345$		0			0
$346$	−3.19413	−	9.97223i	−0.171717	−	0.536110i
$347$	−11.5591	−	11.5591i	−0.620526	−	0.620526i	0.325140	−	0.945666i	$-0.394589\pi$
$347$	−11.5591	−	11.5591i	−0.620526	−	0.620526i	−0.945666	+	0.325140i	$0.894589\pi$
$348$		0			0
$349$	−10.5842			−0.566562			−0.283281	−	0.959037i	$-0.591423\pi$
$349$	−10.5842			−0.566562			−0.283281	+	0.959037i	$0.591423\pi$
$350$	−8.83019	−	11.5683i	−0.471994	−	0.618351i
$351$		0			0
$352$	−2.96274	+	2.84135i	−0.157914	+	0.151445i
$353$	16.2334	−	16.2334i	0.864016	−	0.864016i	−0.127785	−	0.991802i	$-0.540787\pi$
$353$	16.2334	−	16.2334i	0.864016	−	0.864016i	0.991802	+	0.127785i	$0.0407869\pi$
$354$		0			0
$355$	−11.9797	−	8.45163i	−0.635818	−	0.448566i
$356$	7.53774	−	5.38074i	0.399499	−	0.285179i
$357$		0			0
$358$	−10.5798	+	20.5511i	−0.559159	+	1.08616i
$359$	−6.79961			−0.358869			−0.179435	−	0.983770i	$-0.557427\pi$
$359$	−6.79961			−0.358869			−0.179435	+	0.983770i	$0.557427\pi$
$360$		0			0
$361$	−22.1330			−1.16490
$362$	0.866691	−	1.68353i	0.0455523	−	0.0884846i
$363$		0			0
$364$	15.4815	+	21.6876i	0.811449	+	1.13674i
$365$	2.36078	+	13.6714i	0.123569	+	0.715592i
$366$		0			0
$367$	3.23043	−	3.23043i	0.168627	−	0.168627i	−0.617748	−	0.786376i	$-0.711955\pi$
$367$	3.23043	−	3.23043i	0.168627	−	0.168627i	0.786376	+	0.617748i	$0.211955\pi$
$368$	−6.90166	+	3.37236i	−0.359774	+	0.175796i
$369$		0			0
$370$	−3.56173	+	11.3361i	−0.185165	+	0.589335i
$371$	27.6212			1.43402
$372$		0			0
$373$	2.12448	+	2.12448i	0.110001	+	0.110001i	0.759965	−	0.649964i	$-0.225216\pi$
$373$	2.12448	+	2.12448i	0.110001	+	0.110001i	−0.649964	+	0.759965i	$0.725216\pi$
$374$	−1.04717	−	3.26931i	−0.0541477	−	0.169052i
$375$		0			0
$376$	−3.93889	−	2.93797i	−0.203133	−	0.151514i
$377$	13.3613	+	13.3613i	0.688142	+	0.688142i
$378$		0			0
$379$		−	19.0820i		−	0.980175i	−0.871673	−	0.490087i	$-0.836965\pi$
$379$		−	19.0820i		−	0.980175i	0.871673	−	0.490087i	$-0.163035\pi$
$380$	0.159189	+	28.6816i	0.00816623	+	1.47134i
$381$		0			0
$382$	−12.0194	+	23.3475i	−0.614965	+	1.19456i
$383$	2.96986	+	2.96986i	0.151753	+	0.151753i	0.778900	−	0.627148i	$-0.215778\pi$
$383$	2.96986	+	2.96986i	0.151753	+	0.151753i	−0.627148	+	0.778900i	$0.715778\pi$
$384$		0			0
$385$	0.568279	+	3.29094i	0.0289622	+	0.167722i
$386$	−4.01409	+	1.28572i	−0.204312	+	0.0654415i
$387$		0			0
$388$	−1.52776	+	9.14991i	−0.0775603	+	0.464516i
$389$	0.831983			0.0421832			0.0210916	−	0.999778i	$-0.493286\pi$
$389$	0.831983			0.0421832			0.0210916	+	0.999778i	$0.493286\pi$
$390$		0			0
$391$		−	6.42387i		−	0.324869i
$392$	7.73638	−	1.12602i	0.390746	−	0.0568725i
$393$		0			0
$394$	16.4429	−	5.26671i	0.828383	−	0.265333i
$395$	−8.70384	+	12.3372i	−0.437938	+	0.620752i
$396$		0			0
$397$	−11.7504	+	11.7504i	−0.589736	+	0.589736i	−0.937560	−	0.347824i	$-0.886921\pi$
$397$	−11.7504	+	11.7504i	−0.589736	+	0.589736i	0.347824	+	0.937560i	$0.386921\pi$
$398$	−2.96901	−	1.52846i	−0.148823	−	0.0766149i
$399$		0			0
$400$	19.9988	−	0.222002i	0.999938	−	0.0111001i
$401$	−27.1058			−1.35360			−0.676799	−	0.736168i	$-0.736633\pi$
$401$	−27.1058			−1.35360			−0.676799	+	0.736168i	$0.736633\pi$
$402$		0			0
$403$	26.1478	−	26.1478i	1.30252	−	1.30252i
$404$	22.1041	−	15.7788i	1.09972	−	0.785025i
$405$		0			0
$406$	−8.09123	+	2.59164i	−0.401561	+	0.128621i
$407$	1.92810	−	1.92810i	0.0955725	−	0.0955725i
$408$		0			0
$409$			13.2732i			0.656319i	0.944622	+	0.328159i	$0.106428\pi$
$409$			13.2732i			0.656319i	−0.944622	+	0.328159i	$0.893572\pi$
$410$	−2.87710	+	1.50140i	−0.142090	+	0.0741491i
$411$		0			0
$412$	3.68133	−	22.0478i	0.181366	−	1.08622i
$413$	−9.35791	−	9.35791i	−0.460473	−	0.460473i
$414$		0			0
$415$	−0.738307	−	4.27558i	−0.0362421	−	0.209880i
$416$	−36.6110	−	0.765655i	−1.79500	−	0.0375393i
$417$		0			0
$418$	3.01261	−	5.85194i	0.147351	−	0.286228i
$419$		−	24.3069i		−	1.18747i	−0.804662	−	0.593734i	$-0.797653\pi$
$419$		−	24.3069i		−	1.18747i	0.804662	−	0.593734i	$-0.202347\pi$
$420$		0			0
$421$			1.60486i			0.0782162i	0.999235	+	0.0391081i	$0.0124517\pi$
$421$			1.60486i			0.0782162i	−0.999235	+	0.0391081i	$0.987548\pi$
$422$	4.25191	+	2.18890i	0.206980	+	0.106554i
$423$		0			0
$424$	−22.6951	+	30.4270i	−1.10217	+	1.47766i
$425$	−7.17563	+	15.1081i	−0.348069	+	0.732848i
$426$		0			0
$427$	1.71881	+	1.71881i	0.0831792	+	0.0831792i
$428$	−5.20445	+	31.1700i	−0.251567	+	1.50666i
$429$		0			0
$430$	−9.90267	+	31.5177i	−0.477549	+	1.51992i
$431$			16.0008i			0.770733i	0.922764	+	0.385367i	$0.125925\pi$
$431$			16.0008i			0.770733i	−0.922764	+	0.385367i	$0.874075\pi$
$432$		0			0
$433$	−17.6673	+	17.6673i	−0.849037	+	0.849037i	−0.990013	−	0.140976i	$-0.954976\pi$
$433$	−17.6673	+	17.6673i	−0.849037	+	0.849037i	0.140976	+	0.990013i	$0.454976\pi$
$434$	5.07180	+	15.8344i	0.243454	+	0.760076i
$435$		0			0
$436$	−14.4645	−	20.2629i	−0.692724	−	0.970419i
$437$	8.70898	−	8.70898i	0.416607	−	0.416607i
$438$		0			0
$439$	−34.5085			−1.64700			−0.823500	−	0.567316i	$-0.807982\pi$
$439$	−34.5085			−1.64700			−0.823500	+	0.567316i	$0.807982\pi$
$440$	−4.09216	−	2.07801i	−0.195086	−	0.0990653i
$441$		0			0
$442$	14.0168	−	27.2275i	0.666712	−	1.29508i
$443$	2.03044	−	2.03044i	0.0964691	−	0.0964691i	−0.657225	−	0.753694i	$-0.728270\pi$
$443$	2.03044	−	2.03044i	0.0964691	−	0.0964691i	0.753694	+	0.657225i	$0.228270\pi$
$444$		0			0
$445$	8.46071	+	5.96899i	0.401076	+	0.282957i
$446$	−5.68596	−	17.7519i	−0.269238	−	0.840575i
$447$		0			0
$448$	7.84075	−	14.4784i	0.370440	−	0.684040i
$449$			19.7303i			0.931129i	0.885014	+	0.465565i	$0.154149\pi$
$449$			19.7303i			0.931129i	−0.885014	+	0.465565i	$0.845851\pi$
$450$		0			0
$451$	0.744720			0.0350675
$452$	−26.3230	−	4.39514i	−1.23813	−	0.206730i
$453$		0			0
$454$	−9.10520	−	28.4269i	−0.427328	−	1.33414i
$455$	−17.1740	+	24.3431i	−0.805128	+	1.14122i
$456$		0			0
$457$	−22.2146	−	22.2146i	−1.03915	−	1.03915i	−0.999202	−	0.0399513i	$-0.987280\pi$
$457$	−22.2146	−	22.2146i	−1.03915	−	1.03915i	−0.0399513	−	0.999202i	$-0.512720\pi$
$458$	−17.0122	−	8.75796i	−0.794928	−	0.409233i
$459$		0			0
$460$	−6.10638	−	6.03897i	−0.284712	−	0.281569i
$461$		−	20.6988i		−	0.964039i	−0.876161	−	0.482019i	$-0.839904\pi$
$461$		−	20.6988i		−	0.964039i	0.876161	−	0.482019i	$-0.160096\pi$
$462$		0			0
$463$	5.67502	+	5.67502i	0.263741	+	0.263741i	0.826572	−	0.562831i	$-0.190288\pi$
$463$	5.67502	+	5.67502i	0.263741	+	0.263741i	−0.562831	+	0.826572i	$0.690288\pi$
$464$	3.79331	−	11.0426i	0.176100	−	0.512638i
$465$		0			0
$466$	8.12395	−	2.60212i	0.376335	−	0.120541i
$467$	−3.78863	−	3.78863i	−0.175317	−	0.175317i	0.613994	−	0.789311i	$-0.289562\pi$
$467$	−3.78863	−	3.78863i	−0.175317	−	0.175317i	−0.789311	+	0.613994i	$0.789562\pi$
$468$		0			0
$469$	−8.80837			−0.406733
$470$	1.64678	−	5.24130i	0.0759605	−	0.241763i
$471$		0			0
$472$	17.9975	−	2.61950i	0.828400	−	0.120572i
$473$	5.36071	−	5.36071i	0.246485	−	0.246485i
$474$		0			0
$475$	−30.2105	+	10.7542i	−1.38615	+	0.493435i
$476$	8.00000	+	11.2070i	0.366679	+	0.513672i
$477$		0			0
$478$	3.44444	+	1.77321i	0.157545	+	0.0811050i
$479$	11.8931			0.543409			0.271705	−	0.962381i	$-0.412413\pi$
$479$	11.8931			0.543409			0.271705	+	0.962381i	$0.412413\pi$
$480$		0			0
$481$	24.3242			1.10909
$482$	20.7257	+	10.6697i	0.944030	+	0.485991i
$483$		0			0
$484$	−12.1701	−	17.0487i	−0.553184	−	0.774941i
$485$	−10.2203	+	1.76484i	−0.464079	+	0.0801372i
$486$		0			0
$487$	22.1137	−	22.1137i	1.00207	−	1.00207i	0.00207135	−	0.999998i	$-0.499341\pi$
$487$	22.1137	−	22.1137i	1.00207	−	1.00207i	0.999998	−	0.00207135i	$-0.000659332\pi$
$488$	−3.30568	+	0.481137i	−0.149641	+	0.0217800i
$489$		0			0
$490$	4.04379	+	7.74901i	0.182680	+	0.350065i
$491$	−17.8731			−0.806600			−0.403300	−	0.915068i	$-0.632137\pi$
$491$	−17.8731			−0.806600			−0.403300	+	0.915068i	$0.632137\pi$
$492$		0			0
$493$	6.90441	+	6.90441i	0.310959	+	0.310959i
$494$	55.9158	−	17.9100i	2.51577	−	0.805807i
$495$		0			0
$496$	−21.6101	−	7.42344i	−0.970323	−	0.333322i
$497$	−9.54197	−	9.54197i	−0.428016	−	0.428016i
$498$		0			0
$499$		−	10.6090i		−	0.474923i	−0.971397	−	0.237461i	$-0.923685\pi$
$499$		−	10.6090i		−	0.474923i	0.971397	−	0.237461i	$-0.0763153\pi$
$500$	7.61569	+	21.0238i	0.340584	+	0.940214i
$501$		0			0
$502$	−17.6647	−	9.09386i	−0.788414	−	0.405879i
$503$	−8.19221	−	8.19221i	−0.365273	−	0.365273i	0.500477	−	0.865750i	$-0.333158\pi$
$503$	−8.19221	−	8.19221i	−0.365273	−	0.365273i	−0.865750	+	0.500477i	$0.833158\pi$
$504$		0			0
$505$	24.8107	+	17.5038i	1.10406	+	0.778909i
$506$	0.601165	+	1.87687i	0.0267250	+	0.0834369i
$507$		0			0
$508$	27.5732	+	4.60389i	1.22336	+	0.204265i
$509$	−35.0769			−1.55476			−0.777379	−	0.629033i	$-0.783451\pi$
$509$	−35.0769			−1.55476			−0.777379	+	0.629033i	$0.783451\pi$
$510$		0			0
$511$			12.7698i			0.564902i
$512$	9.50670	+	20.5335i	0.420141	+	0.907459i
$513$		0			0
$514$	2.70424	+	8.44277i	0.119279	+	0.372395i
$515$	24.6270	−	4.25260i	1.08520	−	0.187392i
$516$		0			0
$517$	−0.891469	+	0.891469i	−0.0392068	+	0.0392068i
$518$	−5.00599	+	9.72406i	−0.219951	+	0.427251i
$519$		0			0
$520$	−12.7048	−	38.9201i	−0.557143	−	1.70676i
$521$	13.5092			0.591848			0.295924	−	0.955211i	$-0.404372\pi$
$521$	13.5092			0.591848			0.295924	+	0.955211i	$0.404372\pi$
$522$		0			0
$523$	3.12911	−	3.12911i	0.136827	−	0.136827i	−0.635376	−	0.772203i	$-0.719155\pi$
$523$	3.12911	−	3.12911i	0.136827	−	0.136827i	0.772203	+	0.635376i	$0.219155\pi$
$524$	−16.2694	−	22.7914i	−0.710732	−	0.995646i
$525$		0			0
$526$	11.8008	+	36.8425i	0.514537	+	1.60641i
$527$	13.5118	−	13.5118i	0.588583	−	0.588583i
$528$		0			0
$529$		−	19.3121i		−	0.839659i
$530$	−40.4878	−	12.7210i	−1.75868	−	0.552565i
$531$		0			0
$532$	−4.34779	+	26.0393i	−0.188500	+	1.12895i
$533$	4.69754	+	4.69754i	0.203473	+	0.203473i
$534$		0			0
$535$	−34.8163	+	6.01208i	−1.50524	+	0.259925i
$536$	7.23745	−	9.70312i	0.312610	−	0.419111i
$537$		0			0
$538$	−30.2409	−	15.5681i	−1.30378	−	0.671191i
$539$		−	2.00578i		−	0.0863952i
$540$		0			0
$541$			39.9149i			1.71608i	0.513585	+	0.858038i	$0.328317\pi$
$541$			39.9149i			1.71608i	−0.513585	+	0.858038i	$0.671683\pi$
$542$	−15.7881	+	30.6681i	−0.678155	+	1.31731i
$543$		0			0
$544$	−18.9186	−	0.395650i	−0.811130	−	0.0169633i
$545$	16.0458	−	22.7441i	0.687327	−	0.974249i
$546$		0			0
$547$	24.0087	+	24.0087i	1.02654	+	1.02654i	0.999638	+	0.0269017i	$0.00856410\pi$
$547$	24.0087	+	24.0087i	1.02654	+	1.02654i	0.0269017	+	0.999638i	$0.491436\pi$
$548$	−2.01127	+	12.0457i	−0.0859173	+	0.514567i
$549$		0			0
$550$	0.682651	−	5.08565i	0.0291083	−	0.216853i
$551$			18.7209i			0.797538i
$552$		0			0
$553$	−9.82671	+	9.82671i	−0.417874	+	0.417874i
$554$	−12.8900	+	4.12871i	−0.547645	+	0.175412i
$555$		0			0
$556$	16.7262	−	11.9398i	0.709349	−	0.506362i
$557$	−5.38621	+	5.38621i	−0.228221	+	0.228221i	−0.811949	−	0.583728i	$-0.801593\pi$
$557$	−5.38621	+	5.38621i	−0.228221	+	0.228221i	0.583728	+	0.811949i	$0.301593\pi$
$558$		0			0
$559$	67.6285			2.86038
$560$	18.1738	+	2.93089i	0.767982	+	0.123853i
$561$		0			0
$562$	6.03214	+	3.10537i	0.254451	+	0.130992i
$563$	−11.0962	+	11.0962i	−0.467648	+	0.467648i	−0.901152	−	0.433504i	$-0.857277\pi$
$563$	−11.0962	+	11.0962i	−0.467648	+	0.467648i	0.433504	+	0.901152i	$0.357277\pi$
$564$		0			0
$565$	−5.07718	−	29.4022i	−0.213599	−	1.23696i
$566$	2.99971	−	0.960813i	0.126087	−	0.0403860i
$567$		0			0
$568$	18.3515	−	2.67103i	0.770010	−	0.112074i
$569$		−	13.7723i		−	0.577366i	−0.957425	−	0.288683i	$-0.906783\pi$
$569$		−	13.7723i		−	0.577366i	0.957425	−	0.288683i	$-0.0932173\pi$
$570$		0			0
$571$	−2.65223			−0.110992			−0.0554962	−	0.998459i	$-0.517674\pi$
$571$	−2.65223			−0.110992			−0.0554962	+	0.998459i	$0.517674\pi$
$572$	−1.54728	+	9.26680i	−0.0646949	+	0.387464i
$573$		0			0
$574$	−2.84470	+	0.911165i	−0.118736	+	0.0380313i
$575$	4.11943	−	8.67333i	0.171792	−	0.361703i
$576$		0			0
$577$	−15.4206	−	15.4206i	−0.641968	−	0.641968i	0.309071	−	0.951039i	$-0.399982\pi$
$577$	−15.4206	−	15.4206i	−0.641968	−	0.641968i	−0.951039	+	0.309071i	$0.899982\pi$
$578$	−3.76101	+	7.30571i	−0.156438	+	0.303878i
$579$		0			0
$580$	13.0539	−	0.0724519i	0.542034	−	0.00300840i
$581$		−	3.99361i		−	0.165683i
$582$		0			0
$583$	6.88638	+	6.88638i	0.285205	+	0.285205i
$584$	−14.0669	−	10.4924i	−0.582093	−	0.434177i
$585$		0			0
$586$	−10.2772	−	32.0858i	−0.424546	−	1.32545i
$587$	−24.4859	−	24.4859i	−1.01064	−	1.01064i	−0.999943	−	0.0107002i	$-0.996594\pi$
$587$	−24.4859	−	24.4859i	−1.01064	−	1.01064i	−0.0107002	−	0.999943i	$-0.503406\pi$
$588$		0			0
$589$	36.6365			1.50958
$590$	9.40723	+	18.0268i	0.387290	+	0.742153i
$591$		0			0
$592$	−6.59862	−	13.5043i	−0.271202	−	0.555024i
$593$	29.7519	−	29.7519i	1.22176	−	1.22176i	0.254759	−	0.967005i	$-0.418004\pi$
$593$	29.7519	−	29.7519i	1.22176	−	1.22176i	0.967005	−	0.254759i	$-0.0819961\pi$
$594$		0			0
$595$	−8.87459	+	12.5792i	−0.363823	+	0.515699i
$596$	−3.52992	−	4.94497i	−0.144591	−	0.202554i
$597$		0			0
$598$	−8.04686	+	15.6309i	−0.329061	+	0.639195i
$599$	−2.67797			−0.109419			−0.0547094	−	0.998502i	$-0.517423\pi$
$599$	−2.67797			−0.109419			−0.0547094	+	0.998502i	$0.517423\pi$
$600$		0			0
$601$	14.2758			0.582321			0.291161	−	0.956674i	$-0.405959\pi$
$601$	14.2758			0.582321			0.291161	+	0.956674i	$0.405959\pi$
$602$	−13.9182	+	27.0358i	−0.567262	+	1.10190i
$603$		0			0
$604$	−9.00170	+	6.42577i	−0.366274	+	0.261461i
$605$	13.5005	−	19.1363i	0.548875	−	0.778000i
$606$		0			0
$607$	−4.79670	+	4.79670i	−0.194692	+	0.194692i	−0.797720	−	0.603028i	$-0.793961\pi$
$607$	−4.79670	+	4.79670i	−0.194692	+	0.194692i	0.603028	+	0.797720i	$0.293961\pi$
$608$	−25.1120	−	26.1848i	−1.01843	−	1.06193i
$609$		0			0
$610$	−1.72787	−	3.31108i	−0.0699595	−	0.134062i
$611$	−11.2464			−0.454981
$612$		0			0
$613$	−8.18940	−	8.18940i	−0.330767	−	0.330767i	0.522111	−	0.852878i	$-0.325145\pi$
$613$	−8.18940	−	8.18940i	−0.330767	−	0.330767i	−0.852878	+	0.522111i	$0.825145\pi$
$614$	−8.29692	−	25.9034i	−0.334837	−	1.04538i
$615$		0			0
$616$	−3.38615	−	2.52569i	−0.136432	−	0.101763i
$617$	−19.8311	−	19.8311i	−0.798368	−	0.798368i	0.184470	−	0.982838i	$-0.440943\pi$
$617$	−19.8311	−	19.8311i	−0.798368	−	0.798368i	−0.982838	+	0.184470i	$0.940943\pi$
$618$		0			0
$619$			14.8818i			0.598149i	0.954230	+	0.299075i	$0.0966780\pi$
$619$			14.8818i			0.598149i	−0.954230	+	0.299075i	$0.903322\pi$
$620$	−0.141787	−	25.5462i	−0.00569431	−	1.02596i
$621$		0			0
$622$	−4.52290	+	8.78567i	−0.181352	+	0.352273i
$623$	6.73904	+	6.73904i	0.269994	+	0.269994i
$624$		0			0
$625$	−19.3767	+	15.7970i	−0.775067	+	0.631879i
$626$	−25.4578	+	8.15420i	−1.01750	+	0.325907i
$627$		0			0
$628$	12.1692	+	2.03189i	0.485604	+	0.0810812i
$629$	12.5694			0.501176
$630$		0			0
$631$			25.6770i			1.02218i	0.859526	+	0.511092i	$0.170759\pi$
$631$			25.6770i			1.02218i	−0.859526	+	0.511092i	$0.829241\pi$
$632$	−2.75073	−	18.8991i	−0.109418	−	0.751765i
$633$		0			0
$634$	−4.27243	+	1.36847i	−0.169680	+	0.0543489i
$635$	5.31833	+	30.7987i	0.211051	+	1.22221i
$636$		0			0
$637$	12.6521	−	12.6521i	0.501293	−	0.501293i
$638$	−2.66340	−	1.37113i	−0.105445	−	0.0542836i
$639$		0			0
$640$	−18.1612	+	17.6117i	−0.717884	+	0.696163i
$641$	−21.1942			−0.837122			−0.418561	−	0.908189i	$-0.637465\pi$
$641$	−21.1942			−0.837122			−0.418561	+	0.908189i	$0.637465\pi$
$642$		0			0
$643$	−21.5857	+	21.5857i	−0.851256	+	0.851256i	−0.990288	−	0.139032i	$-0.955601\pi$
$643$	−21.5857	+	21.5857i	−0.851256	+	0.851256i	0.139032	+	0.990288i	$0.455601\pi$
$644$	−4.59269	−	6.43378i	−0.180977	−	0.253526i
$645$		0			0
$646$	28.8943	−	9.25491i	1.13683	−	0.364130i
$647$	−4.64626	+	4.64626i	−0.182663	+	0.182663i	−0.792515	−	0.609852i	$-0.791229\pi$
$647$	−4.64626	+	4.64626i	−0.182663	+	0.182663i	0.609852	+	0.792515i	$0.291229\pi$
$648$		0			0
$649$		−	4.66614i		−	0.183162i
$650$	36.3853	−	27.7732i	1.42715	−	1.08936i
$651$		0			0
$652$	−25.3976	−	4.24063i	−0.994646	−	0.166076i
$653$	−5.98212	−	5.98212i	−0.234098	−	0.234098i	0.580303	−	0.814401i	$-0.302934\pi$
$653$	−5.98212	−	5.98212i	−0.234098	−	0.234098i	−0.814401	+	0.580303i	$0.802934\pi$
$654$		0			0
$655$	18.0480	−	25.5821i	0.705195	−	0.999575i
$656$	1.33365	−	3.88233i	0.0520701	−	0.151580i
$657$		0			0
$658$	2.31455	−	4.49597i	0.0902304	−	0.175271i
$659$			41.9465i			1.63400i	0.576635	+	0.817002i	$0.304365\pi$
$659$			41.9465i			1.63400i	−0.576635	+	0.817002i	$0.695635\pi$
$660$		0			0
$661$		−	49.8515i		−	1.93900i	−0.245095	−	0.969499i	$-0.578819\pi$
$661$		−	49.8515i		−	1.93900i	0.245095	−	0.969499i	$-0.421181\pi$
$662$	0.453913	+	0.233676i	0.0176418	+	0.00908208i
$663$		0			0
$664$	4.39928	+	3.28137i	0.170725	+	0.127342i
$665$	−29.0854	+	5.02248i	−1.12789	+	0.194763i
$666$		0			0
$667$	−3.96373	−	3.96373i	−0.153476	−	0.153476i
$668$	−42.4335	−	7.08512i	−1.64180	−	0.274132i
$669$		0			0
$670$	12.9115	+	4.05671i	0.498815	+	0.156725i
$671$			0.857052i			0.0330861i
$672$		0			0
$673$	14.3656	−	14.3656i	0.553754	−	0.553754i	−0.373768	−	0.927522i	$-0.621934\pi$
$673$	14.3656	−	14.3656i	0.553754	−	0.553754i	0.927522	+	0.373768i	$0.121934\pi$
$674$	0.333678	+	1.04176i	0.0128528	+	0.0401270i
$675$		0			0
$676$	−47.0515	+	33.5872i	−1.80967	+	1.29182i
$677$	−1.59459	+	1.59459i	−0.0612852	+	0.0612852i	−0.737085	−	0.675800i	$-0.763798\pi$
$677$	−1.59459	+	1.59459i	−0.0612852	+	0.0612852i	0.675800	+	0.737085i	$0.263798\pi$
$678$		0			0
$679$	−9.54627			−0.366352
$680$	−6.56518	−	20.1119i	−0.251763	−	0.771255i
$681$		0			0
$682$	−2.68328	+	5.21223i	−0.102748	+	0.199587i
$683$	3.56279	−	3.56279i	0.136326	−	0.136326i	−0.635651	−	0.771977i	$-0.719268\pi$
$683$	3.56279	−	3.56279i	0.136326	−	0.136326i	0.771977	+	0.635651i	$0.219268\pi$
$684$		0			0
$685$	−13.4548	+	2.32338i	−0.514083	+	0.0887719i
$686$	8.66908	+	27.0653i	0.330987	+	1.03336i
$687$		0			0
$688$	−18.3461	−	37.5461i	−0.699440	−	1.43143i
$689$			86.8758i			3.30970i
$690$		0			0
$691$	5.67883			0.216033			0.108016	−	0.994149i	$-0.465550\pi$
$691$	5.67883			0.216033			0.108016	+	0.994149i	$0.465550\pi$
$692$	−2.43883	+	14.6064i	−0.0927105	+	0.555253i
$693$		0			0
$694$	7.05192	+	22.0164i	0.267687	+	0.835732i
$695$	18.7743	+	13.2452i	0.712149	+	0.502417i
$696$		0			0
$697$	2.42744	+	2.42744i	0.0919459	+	0.0919459i
$698$	13.3084	+	6.85122i	0.503730	+	0.259323i
$699$		0			0
$700$	3.61468	+	20.2615i	0.136622	+	0.765814i
$701$			14.1700i			0.535194i	0.963531	+	0.267597i	$0.0862296\pi$
$701$			14.1700i			0.535194i	−0.963531	+	0.267597i	$0.913770\pi$
$702$		0			0
$703$	17.0407	+	17.0407i	0.642701	+	0.642701i
$704$	5.56450	−	1.65486i	0.209720	−	0.0623700i
$705$		0			0
$706$	−30.9194	+	9.90357i	−1.16367	+	0.372726i
$707$	19.7620	+	19.7620i	0.743225	+	0.743225i
$708$		0			0
$709$	−14.5473			−0.546337			−0.273168	−	0.961966i	$-0.588072\pi$
$709$	−14.5473			−0.546337			−0.273168	+	0.961966i	$0.588072\pi$
$710$	9.59226	+	18.3814i	0.359991	+	0.689842i
$711$		0			0
$712$	−12.9608	+	1.88642i	−0.485725	+	0.0706965i
$713$	−7.75694	+	7.75694i	−0.290500	+	0.290500i
$714$		0			0
$715$	−10.3508	+	1.78738i	−0.387099	+	0.0668444i
$716$	26.6056	−	18.9921i	0.994297	−	0.709769i
$717$		0			0
$718$	8.54967	+	4.40141i	0.319071	+	0.164259i
$719$	41.3534			1.54222			0.771110	−	0.636702i	$-0.219702\pi$
$719$	41.3534			1.54222			0.771110	+	0.636702i	$0.219702\pi$
$720$		0			0
$721$	23.0029			0.856673
$722$	27.8296	+	14.3268i	1.03571	+	0.533188i
$723$		0			0
$724$	−2.17952	+	1.55583i	−0.0810010	+	0.0578218i
$725$	4.89456	+	13.7497i	0.181779	+	0.510652i
$726$		0			0
$727$	−17.1262	+	17.1262i	−0.635177	+	0.635177i	−0.949362	−	0.314185i	$-0.898269\pi$
$727$	−17.1262	+	17.1262i	−0.635177	+	0.635177i	0.314185	+	0.949362i	$0.398269\pi$
$728$	−5.42760	−	37.2907i	−0.201160	−	1.38208i
$729$		0			0
$730$	5.88114	−	18.7182i	0.217671	−	0.692792i
$731$	34.9468			1.29255
$732$		0			0
$733$	−10.8014	−	10.8014i	−0.398958	−	0.398958i	0.478907	−	0.877865i	$-0.341033\pi$
$733$	−10.8014	−	10.8014i	−0.398958	−	0.398958i	−0.877865	+	0.478907i	$0.841033\pi$
$734$	−6.15295	+	1.97080i	−0.227109	+	0.0727437i
$735$		0			0
$736$	10.8609	+	0.227137i	0.400339	+	0.00837239i
$737$	−2.19606	−	2.19606i	−0.0808929	−	0.0808929i
$738$		0			0
$739$			28.4640i			1.04707i	0.852006	+	0.523533i	$0.175386\pi$
$739$			28.4640i			1.04707i	−0.852006	+	0.523533i	$0.824614\pi$
$740$	11.8163	−	11.9482i	0.434377	−	0.439225i
$741$		0			0
$742$	−34.7303	−	17.8793i	−1.27499	−	0.656370i
$743$	37.4663	+	37.4663i	1.37451	+	1.37451i	0.853634	+	0.520873i	$0.174393\pi$
$743$	37.4663	+	37.4663i	1.37451	+	1.37451i	0.520873	+	0.853634i	$0.325607\pi$
$744$		0			0
$745$	3.91582	−	5.55046i	0.143465	−	0.203353i
$746$	−1.29609	−	4.04645i	−0.0474531	−	0.148151i
$747$		0			0
$748$	−0.799550	+	4.78859i	−0.0292345	+	0.175088i
$749$	−32.5202			−1.18826
$750$		0			0
$751$			33.7409i			1.23122i	0.788050	+	0.615611i	$0.211091\pi$
$751$			33.7409i			1.23122i	−0.788050	+	0.615611i	$0.788909\pi$
$752$	3.05091	+	6.24380i	0.111255	+	0.227688i
$753$		0			0
$754$	−8.15138	−	25.4490i	−0.296856	−	0.926798i
$755$	−10.1039	−	7.12826i	−0.367719	−	0.259424i
$756$		0			0
$757$	3.61554	−	3.61554i	0.131409	−	0.131409i	−0.638343	−	0.769752i	$-0.720380\pi$
$757$	3.61554	−	3.61554i	0.131409	−	0.131409i	0.769752	+	0.638343i	$0.220380\pi$
$758$	−12.3518	+	23.9932i	−0.448638	+	0.871473i
$759$		0			0
$760$	18.3656	−	36.1667i	0.666189	−	1.31190i
$761$	53.5331			1.94057			0.970286	−	0.241959i	$-0.0777901\pi$
$761$	53.5331			1.94057			0.970286	+	0.241959i	$0.0777901\pi$
$762$		0			0
$763$	18.1159	−	18.1159i	0.655839	−	0.655839i
$764$	30.2258	−	21.5764i	1.09353	−	0.780606i
$765$		0			0
$766$	−1.81184	−	5.65664i	−0.0654643	−	0.204383i
$767$	29.4330	−	29.4330i	1.06277	−	1.06277i
$768$		0			0
$769$			0.470664i			0.0169726i	0.999964	+	0.00848630i	$0.00270130\pi$
$769$			0.470664i			0.0169726i	−0.999964	+	0.00848630i	$0.997299\pi$
$770$	1.41569	−	4.50580i	0.0510180	−	0.162378i
$771$		0			0
$772$	5.87947	+	0.981695i	0.211607	+	0.0353320i
$773$	13.2975	+	13.2975i	0.478279	+	0.478279i	0.904581	−	0.426302i	$-0.140184\pi$
$773$	13.2975	+	13.2975i	0.478279	+	0.478279i	−0.426302	+	0.904581i	$0.640184\pi$
$774$		0			0
$775$	26.9080	−	9.57857i	0.966563	−	0.344072i
$776$	7.84374	−	10.5160i	0.281574	−	0.377501i
$777$		0			0
$778$	−1.04612	−	0.538546i	−0.0375051	−	0.0193078i
$779$			6.58187i			0.235820i
$780$		0			0
$781$		−	4.75791i		−	0.170252i
$782$	−4.15819	+	8.07722i	−0.148697	+	0.288841i
$783$		0			0
$784$	−10.4564	−	3.59196i	−0.373444	−	0.128284i
$785$	2.34720	+	13.5928i	0.0837751	+	0.485146i
$786$		0			0
$787$	−13.2592	−	13.2592i	−0.472639	−	0.472639i	0.430128	−	0.902768i	$-0.358468\pi$
$787$	−13.2592	−	13.2592i	−0.472639	−	0.472639i	−0.902768	+	0.430128i	$0.858468\pi$
$788$	−24.0841	−	4.02133i	−0.857962	−	0.143254i
$789$		0			0
$790$	18.9299	−	9.87850i	0.673497	−	0.351461i
$791$		−	27.4632i		−	0.976480i
$792$		0			0
$793$	−5.40611	+	5.40611i	−0.191977	+	0.191977i
$794$	22.3808	−	7.16862i	0.794265	−	0.254405i
$795$		0			0
$796$	2.74379	+	3.84371i	0.0972511	+	0.136237i
$797$	17.1774	−	17.1774i	0.608453	−	0.608453i	−0.334089	−	0.942542i	$-0.608428\pi$
$797$	17.1774	−	17.1774i	0.608453	−	0.608453i	0.942542	+	0.334089i	$0.108428\pi$
$798$		0			0
$799$	−5.81155			−0.205598
$800$	−25.2897	−	12.6661i	−0.894126	−	0.447815i
$801$		0			0
$802$	34.0822	+	17.5457i	1.20348	+	0.619559i
$803$	−3.18370	+	3.18370i	−0.112350	+	0.112350i
$804$		0			0
$805$	5.09478	−	7.22157i	0.179567	−	0.254527i
$806$	−49.8033	+	15.9521i	−1.75424	+	0.561889i
$807$		0			0
$808$	−38.0069	+	5.53184i	−1.33708	+	0.194610i
$809$		−	41.7364i		−	1.46737i	−0.679488	−	0.733686i	$-0.737798\pi$
$809$		−	41.7364i		−	1.46737i	0.679488	−	0.733686i	$-0.262202\pi$
$810$		0			0
$811$	34.4392			1.20932			0.604661	−	0.796483i	$-0.293308\pi$
$811$	34.4392			1.20932			0.604661	+	0.796483i	$0.293308\pi$
$812$	11.8513	+	1.97881i	0.415900	+	0.0694427i
$813$		0			0
$814$	−3.67242	+	1.17629i	−0.128718	+	0.0412288i
$815$	−4.89870	−	28.3686i	−0.171594	−	0.993709i
$816$		0			0
$817$	47.3782	+	47.3782i	1.65755	+	1.65755i
$818$	8.59181	−	16.6895i	0.300405	−	0.583533i
$819$		0			0
$820$	4.58947	−	0.0254725i	0.160271	−	0.000889539i
$821$			12.0902i			0.421952i	0.977491	+	0.210976i	$0.0676642\pi$
$821$			12.0902i			0.421952i	−0.977491	+	0.210976i	$0.932336\pi$
$822$		0			0
$823$	10.0784	+	10.0784i	0.351310	+	0.351310i	0.860597	−	0.509287i	$-0.170091\pi$
$823$	10.0784	+	10.0784i	0.351310	+	0.351310i	−0.509287	+	0.860597i	$0.670091\pi$
$824$	−18.9005	+	25.3395i	−0.658429	+	0.882744i
$825$		0			0
$826$	5.70902	+	17.8238i	0.198642	+	0.620171i
$827$	−22.1941	−	22.1941i	−0.771763	−	0.771763i	0.206652	−	0.978415i	$-0.433743\pi$
$827$	−22.1941	−	22.1941i	−0.771763	−	0.771763i	−0.978415	+	0.206652i	$0.933743\pi$
$828$		0			0
$829$	2.71154			0.0941755			0.0470878	−	0.998891i	$-0.485006\pi$
$829$	2.71154			0.0941755			0.0470878	+	0.998891i	$0.485006\pi$
$830$	−1.83927	+	5.85392i	−0.0638418	+	0.203193i
$831$		0			0
$832$	45.5382	+	24.6612i	1.57875	+	0.854972i
$833$	6.53792	−	6.53792i	0.226526	−	0.226526i
$834$		0			0
$835$	−8.18460	−	47.3974i	−0.283240	−	1.64026i
$836$	−7.57597	+	5.40803i	−0.262020	+	0.187041i
$837$		0			0
$838$	−15.7339	+	30.5629i	−0.543519	+	1.05578i
$839$	−53.2192			−1.83733			−0.918666	−	0.395036i	$-0.870732\pi$
$839$	−53.2192			−1.83733			−0.918666	+	0.395036i	$0.870732\pi$
$840$		0			0
$841$	−20.4795			−0.706191
$842$	1.03883	−	2.01792i	0.0358005	−	0.0695420i
$843$		0			0
$844$	−3.92937	−	5.50455i	−0.135255	−	0.189475i
$845$	−52.8127	−	37.2591i	−1.81681	−	1.28175i
$846$		0			0
$847$	15.2422	−	15.2422i	0.523729	−	0.523729i
$848$	48.2318	−	23.5675i	1.65629	−	0.809313i
$849$		0			0
$850$	18.8020	−	14.3517i	0.644902	−	0.492260i
$851$	−7.21594			−0.247359
$852$		0			0
$853$	−18.5528	−	18.5528i	−0.635236	−	0.635236i	0.314141	−	0.949376i	$-0.398284\pi$
$853$	−18.5528	−	18.5528i	−0.635236	−	0.635236i	−0.949376	+	0.314141i	$0.898284\pi$
$854$	−1.04860	−	3.27379i	−0.0358825	−	0.112027i
$855$		0			0
$856$	26.7204	−	35.8236i	0.913285	−	1.22443i
$857$	12.8811	+	12.8811i	0.440009	+	0.440009i	0.892015	−	0.452006i	$-0.149291\pi$
$857$	12.8811	+	12.8811i	0.440009	+	0.440009i	−0.452006	+	0.892015i	$0.649291\pi$
$858$		0			0
$859$			3.82914i			0.130648i	0.997864	+	0.0653242i	$0.0208082\pi$
$859$			3.82914i			0.130648i	−0.997864	+	0.0653242i	$0.979192\pi$
$860$	32.8529	−	33.2196i	1.12028	−	1.13278i
$861$		0			0
$862$	10.3574	−	20.1191i	0.352774	−	0.685259i
$863$	16.5089	+	16.5089i	0.561970	+	0.561970i	0.929867	−	0.367897i	$-0.119922\pi$
$863$	16.5089	+	16.5089i	0.561970	+	0.561970i	−0.367897	+	0.929867i	$0.619922\pi$
$864$		0			0
$865$	−16.3151	+	2.81729i	−0.554730	+	0.0957908i
$866$	33.6506	−	10.7784i	1.14349	−	0.366264i
$867$		0			0
$868$	3.87250	−	23.1928i	0.131441	−	0.787215i
$869$	−4.89989			−0.166218
$870$		0			0
$871$		−	27.7046i		−	0.938734i
$872$	5.07107	+	34.8411i	0.171728	+	1.17987i
$873$		0			0
$874$	−16.5878	+	5.31312i	−0.561092	+	0.179719i
$875$	−20.0489	+	11.2932i	−0.677777	+	0.381778i
$876$		0			0
$877$	27.6423	−	27.6423i	0.933416	−	0.933416i	−0.0645020	−	0.997918i	$-0.520546\pi$
$877$	27.6423	−	27.6423i	0.933416	−	0.933416i	0.997918	+	0.0645020i	$0.0205459\pi$
$878$	43.3902	+	22.3375i	1.46435	+	0.753853i
$879$		0			0
$880$	3.80028	+	5.26171i	0.128107	+	0.177372i
$881$	14.6973			0.495165			0.247582	−	0.968867i	$-0.420364\pi$
$881$	14.6973			0.495165			0.247582	+	0.968867i	$0.420364\pi$
$882$		0			0
$883$	−31.5345	+	31.5345i	−1.06122	+	1.06122i	−0.0632202	+	0.998000i	$0.520137\pi$
$883$	−31.5345	+	31.5345i	−1.06122	+	1.06122i	−0.998000	+	0.0632202i	$0.979863\pi$
$884$	−35.2489	+	25.1620i	−1.18555	+	0.846291i
$885$		0			0
$886$	−3.86734	+	1.23872i	−0.129926	+	0.0416156i
$887$	18.5981	−	18.5981i	0.624464	−	0.624464i	−0.322206	−	0.946670i	$-0.604424\pi$
$887$	18.5981	−	18.5981i	0.624464	−	0.624464i	0.946670	+	0.322206i	$0.104424\pi$
$888$		0			0
$889$			28.7676i			0.964835i
$890$	−6.77456	−	12.9819i	−0.227084	−	0.435155i
$891$		0			0
$892$	−4.34144	+	26.0013i	−0.145362	+	0.870589i
$893$	−7.87885	−	7.87885i	−0.263656	−	0.263656i
$894$		0			0
$895$	29.8633	+	21.0684i	0.998221	+	0.704240i
$896$	−19.2307	+	13.1295i	−0.642452	+	0.438624i
$897$		0			0
$898$	12.7715	−	24.8084i	0.426190	−	0.827867i
$899$		−	16.6744i		−	0.556123i
$900$		0			0
$901$			44.8928i			1.49560i
$902$	−0.936394	−	0.482060i	−0.0311785	−	0.0160508i
$903$		0			0
$904$	30.2529	+	22.5653i	1.00620	+	0.750511i
$905$	−2.44639	−	1.72591i	−0.0813207	−	0.0573713i
$906$		0			0
$907$	−15.1848	−	15.1848i	−0.504203	−	0.504203i	0.408538	−	0.912741i	$-0.366039\pi$
$907$	−15.1848	−	15.1848i	−0.504203	−	0.504203i	−0.912741	+	0.408538i	$0.866039\pi$
$908$	−6.95215	+	41.6371i	−0.230715	+	1.38178i
$909$		0			0
$910$	37.3516	−	19.4917i	1.23819	−	0.646145i
$911$			51.3671i			1.70187i	0.525272	+	0.850934i	$0.323964\pi$
$911$			51.3671i			1.70187i	−0.525272	+	0.850934i	$0.676036\pi$
$912$		0			0
$913$	0.995667	−	0.995667i	0.0329518	−	0.0329518i
$914$	13.5525	+	42.3116i	0.448277	+	1.39954i
$915$		0			0
$916$	15.7217	+	22.0241i	0.519460	+	0.727697i
$917$	20.3764	−	20.3764i	0.672888	−	0.672888i
$918$		0			0
$919$	−31.4287			−1.03674			−0.518369	−	0.855157i	$-0.673461\pi$
$919$	−31.4287			−1.03674			−0.518369	+	0.855157i	$0.673461\pi$
$920$	3.76898	+	11.5460i	0.124260	+	0.380659i
$921$		0			0
$922$	−13.3984	+	26.0262i	−0.441253	+	0.857127i
$923$	30.0120	−	30.0120i	0.987855	−	0.987855i
$924$		0			0
$925$	16.9709	+	8.06040i	0.558000	+	0.265024i
$926$	−3.46218	−	10.8091i	−0.113774	−	0.355209i
$927$		0			0
$928$	−11.9175	+	11.4293i	−0.391212	+	0.375184i
$929$		−	17.2221i		−	0.565038i	−0.959262	−	0.282519i	$-0.908830\pi$
$929$		−	17.2221i		−	0.565038i	0.959262	−	0.282519i	$-0.0911700\pi$
$930$		0			0
$931$	17.7272			0.580986
$932$	−11.8992	−	1.98681i	−0.389773	−	0.0650803i
$933$		0			0
$934$	2.31135	+	7.21614i	0.0756295	+	0.236119i
$935$	−5.34876	+	0.923625i	−0.174923	+	0.0302058i
$936$		0			0
$937$	−29.3915	−	29.3915i	−0.960177	−	0.960177i	0.0390597	−	0.999237i	$-0.487564\pi$
$937$	−29.3915	−	29.3915i	−0.960177	−	0.960177i	−0.999237	+	0.0390597i	$0.987564\pi$
$938$	11.0755	+	5.70169i	0.361626	+	0.186167i
$939$		0			0
$940$	−5.46334	+	5.52433i	−0.178195	+	0.180184i
$941$		−	40.1614i		−	1.30922i	−0.755966	−	0.654611i	$-0.772832\pi$
$941$		−	40.1614i		−	1.30922i	0.755966	−	0.654611i	$-0.227168\pi$
$942$		0			0
$943$	−1.39356	−	1.39356i	−0.0453806	−	0.0453806i
$944$	−24.3252	−	8.35612i	−0.791718	−	0.271968i
$945$		0			0
$946$	−10.2104	+	3.27043i	−0.331970	+	0.106331i
$947$	−20.5497	−	20.5497i	−0.667777	−	0.667777i	0.289424	−	0.957201i	$-0.406536\pi$
$947$	−20.5497	−	20.5497i	−0.667777	−	0.667777i	−0.957201	+	0.289424i	$0.906536\pi$
$948$		0			0
$949$	−40.1642			−1.30379
$950$	44.9472	+	6.03330i	1.45828	+	0.195746i
$951$		0			0
$952$	−2.80470	−	19.2698i	−0.0909007	−	0.624539i
$953$	−14.0425	+	14.0425i	−0.454882	+	0.454882i	−0.896971	−	0.442089i	$-0.854238\pi$
$953$	−14.0425	+	14.0425i	−0.454882	+	0.454882i	0.442089	+	0.896971i	$0.354238\pi$
$954$		0			0
$955$	33.9268	+	23.9352i	1.09785	+	0.774525i
$956$	−3.18316	−	4.45920i	−0.102951	−	0.144221i
$957$		0			0
$958$	−14.9541	−	7.69844i	−0.483145	−	0.248725i
$959$	−12.5675			−0.405826
$960$		0			0
$961$	−1.63154			−0.0526302
$962$	−30.5847	−	15.7451i	−0.986089	−	0.507643i
$963$		0			0
$964$	−19.1535	−	26.8316i	−0.616893	−	0.864189i
$965$	1.13404	+	6.56726i	0.0365059	+	0.211408i
$966$		0			0
$967$	−0.168063	+	0.168063i	−0.00540454	+	0.00540454i	−0.709804	−	0.704399i	$-0.751216\pi$
$967$	−0.168063	+	0.168063i	−0.00540454	+	0.00540454i	0.704399	+	0.709804i	$0.251216\pi$
$968$	4.26666	+	29.3144i	0.137136	+	0.942200i
$969$		0			0
$970$	13.9931	+	4.39655i	0.449292	+	0.141165i
$971$	45.2762			1.45298			0.726492	−	0.687175i	$-0.241149\pi$
$971$	45.2762			1.45298			0.726492	+	0.687175i	$0.241149\pi$
$972$		0			0
$973$	14.9539	+	14.9539i	0.479400	+	0.479400i
$974$	−42.1196	+	13.4910i	−1.34960	+	0.432280i
$975$		0			0
$976$	4.46793	+	1.53481i	0.143015	+	0.0491280i
$977$	−33.1509	−	33.1509i	−1.06059	−	1.06059i	−0.998042	−	0.0625482i	$-0.980077\pi$
$977$	−33.1509	−	33.1509i	−1.06059	−	1.06059i	−0.0625482	−	0.998042i	$-0.519923\pi$
$978$		0			0
$979$			3.36029i			0.107395i
$980$	−0.0686062	−	12.3610i	−0.00219154	−	0.394857i
$981$		0			0
$982$	22.4732	+	11.5693i	0.717149	+	0.369191i
$983$	3.16720	+	3.16720i	0.101018	+	0.101018i	0.755809	−	0.654792i	$-0.227244\pi$
$983$	3.16720	+	3.16720i	0.101018	+	0.101018i	−0.654792	+	0.755809i	$0.727244\pi$
$984$		0			0
$985$	−4.64536	−	26.9015i	−0.148013	−	0.857154i
$986$	−4.21220	−	13.1507i	−0.134144	−	0.418803i
$987$		0			0
$988$	−81.9004	−	13.6749i	−2.60560	−	0.435057i
$989$	−20.0625			−0.637950
$990$		0			0
$991$		−	28.3462i		−	0.900447i	−0.892916	−	0.450224i	$-0.851344\pi$
$991$		−	28.3462i		−	0.900447i	0.892916	−	0.450224i	$-0.148656\pi$
$992$	22.3669	+	23.3224i	0.710148	+	0.740486i
$993$		0			0
$994$	5.82131	+	18.1744i	0.184641	+	0.576457i
$995$	−3.04375	+	4.31435i	−0.0964935	+	0.136774i
$996$		0			0
$997$	−28.3453	+	28.3453i	−0.897705	+	0.897705i	−0.995233	−	0.0975279i	$-0.968906\pi$
$997$	−28.3453	+	28.3453i	−0.897705	+	0.897705i	0.0975279	+	0.995233i	$0.468906\pi$
$998$	−6.86723	+	13.3395i	−0.217378	+	0.422254i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.e.307.2		24
3.2	odd	2		120.2.v.a.67.11	yes	24
4.3	odd	2		1440.2.bi.e.847.4		24
5.3	odd	4	inner	360.2.w.e.163.4		24
8.3	odd	2	inner	360.2.w.e.307.4		24
8.5	even	2		1440.2.bi.e.847.9		24
12.11	even	2		480.2.bh.a.367.10		24
15.2	even	4		600.2.v.b.43.4		24
15.8	even	4		120.2.v.a.43.9	✓	24
15.14	odd	2		600.2.v.b.307.2		24
20.3	even	4		1440.2.bi.e.1423.9		24
24.5	odd	2		480.2.bh.a.367.9		24
24.11	even	2		120.2.v.a.67.9	yes	24
40.3	even	4	inner	360.2.w.e.163.2		24
40.13	odd	4		1440.2.bi.e.1423.4		24
60.23	odd	4		480.2.bh.a.463.9		24
60.47	odd	4		2400.2.bh.b.943.2		24
60.59	even	2		2400.2.bh.b.1807.1		24
120.29	odd	2		2400.2.bh.b.1807.2		24
120.53	even	4		480.2.bh.a.463.10		24
120.59	even	2		600.2.v.b.307.4		24
120.77	even	4		2400.2.bh.b.943.1		24
120.83	odd	4		120.2.v.a.43.11	yes	24
120.107	odd	4		600.2.v.b.43.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.9	✓	24	15.8	even	4
120.2.v.a.43.11	yes	24	120.83	odd	4
120.2.v.a.67.9	yes	24	24.11	even	2
120.2.v.a.67.11	yes	24	3.2	odd	2
360.2.w.e.163.2		24	40.3	even	4	inner
360.2.w.e.163.4		24	5.3	odd	4	inner
360.2.w.e.307.2		24	1.1	even	1	trivial
360.2.w.e.307.4		24	8.3	odd	2	inner
480.2.bh.a.367.9		24	24.5	odd	2
480.2.bh.a.367.10		24	12.11	even	2
480.2.bh.a.463.9		24	60.23	odd	4
480.2.bh.a.463.10		24	120.53	even	4
600.2.v.b.43.2		24	120.107	odd	4
600.2.v.b.43.4		24	15.2	even	4
600.2.v.b.307.2		24	15.14	odd	2
600.2.v.b.307.4		24	120.59	even	2
1440.2.bi.e.847.4		24	4.3	odd	2
1440.2.bi.e.847.9		24	8.5	even	2
1440.2.bi.e.1423.4		24	40.13	odd	4
1440.2.bi.e.1423.9		24	20.3	even	4
2400.2.bh.b.943.1		24	120.77	even	4
2400.2.bh.b.943.2		24	60.47	odd	4
2400.2.bh.b.1807.1		24	60.59	even	2
2400.2.bh.b.1807.2		24	120.29	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.25738 - 0.647304i) q^{2} +(1.16200 + 1.62781i) q^{4} +(-1.28903 + 1.82713i) q^{5} +(-1.45533 + 1.45533i) q^{7} +(-0.407381 - 2.79894i) q^{8} +O(q^{10})\)	\(q+(-1.25738 - 0.647304i) q^{2} +(1.16200 + 1.62781i) q^{4} +(-1.28903 + 1.82713i) q^{5} +(-1.45533 + 1.45533i) q^{7} +(-0.407381 - 2.79894i) q^{8} +(2.80350 - 1.46300i) q^{10} -0.725670 q^{11} +(-4.57738 - 4.57738i) q^{13} +(2.77193 - 0.887857i) q^{14} +(-1.29953 + 3.78302i) q^{16} +(-2.36535 - 2.36535i) q^{17} -6.41350i q^{19} +(-4.47207 + 0.0248209i) q^{20} +(0.912441 + 0.469729i) q^{22} +(1.35791 + 1.35791i) q^{23} +(-1.67680 - 4.71045i) q^{25} +(2.79254 + 8.71844i) q^{26} +(-4.06008 - 0.677911i) q^{28} -2.91898 q^{29} +5.71240i q^{31} +(4.08276 - 3.91549i) q^{32} +(1.44304 + 4.50523i) q^{34} +(-0.783110 - 4.53503i) q^{35} +(-2.65700 + 2.65700i) q^{37} +(-4.15148 + 8.06419i) q^{38} +(5.63914 + 2.86358i) q^{40} -1.02625 q^{41} +(-7.38725 + 7.38725i) q^{43} +(-0.843226 - 1.18125i) q^{44} +(-0.828427 - 2.58639i) q^{46} +(1.22848 - 1.22848i) q^{47} +2.76404i q^{49} +(-0.940718 + 7.00821i) q^{50} +(2.13220 - 12.7700i) q^{52} +(-9.48969 - 9.48969i) q^{53} +(0.935410 - 1.32589i) q^{55} +(4.66624 + 3.48050i) q^{56} +(3.67027 + 1.88947i) q^{58} +6.43011i q^{59} -1.18105i q^{61} +(3.69766 - 7.18265i) q^{62} +(-7.66808 + 2.28046i) q^{64} +(14.2638 - 2.46308i) q^{65} +(3.02625 + 3.02625i) q^{67} +(1.10181 - 6.59886i) q^{68} +(-1.95088 + 6.20916i) q^{70} +6.55658i q^{71} +(4.38725 - 4.38725i) q^{73} +(5.06073 - 1.62097i) q^{74} +(10.4400 - 7.45247i) q^{76} +(1.05609 - 1.05609i) q^{77} +6.75224 q^{79} +(-5.23693 - 7.25083i) q^{80} +(1.29039 + 0.664297i) q^{82} +(-1.37207 + 1.37207i) q^{83} +(7.37079 - 1.27279i) q^{85} +(14.0704 - 4.50677i) q^{86} +(0.295624 + 2.03110i) q^{88} -4.63060i q^{89} +13.3232 q^{91} +(-0.632534 + 3.78831i) q^{92} +(-2.33986 + 0.749462i) q^{94} +(11.7183 + 8.26720i) q^{95} +(3.27977 + 3.27977i) q^{97} +(1.78918 - 3.47545i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 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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