LMFDB - Embedded newform 945.2.ce.a.937.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(118,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 6]))

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

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

chi := DirichletCharacter("945.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.ce (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			937.11
Character	$\chi$	$=$	945.937
Dual form			945.2.ce.a.118.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41025 + 0.377876i) q^{2} +(0.113968 - 0.0657996i) q^{4} +(-1.50611 + 1.65277i) q^{5} +(2.52369 - 0.794356i) q^{7} +(1.92889 - 1.92889i) q^{8} +O(q^{10})$	\(q+(-1.41025 + 0.377876i) q^{2} +(0.113968 - 0.0657996i) q^{4} +(-1.50611 + 1.65277i) q^{5} +(2.52369 - 0.794356i) q^{7} +(1.92889 - 1.92889i) q^{8} +(1.49945 - 2.89994i) q^{10} +(1.95430 - 3.38495i) q^{11} +(-0.0948685 + 0.354054i) q^{13} +(-3.25887 + 2.07388i) q^{14} +(-2.12294 + 3.67704i) q^{16} +(-1.41297 + 1.41297i) q^{17} -3.83464 q^{19} +(-0.0628967 + 0.287464i) q^{20} +(-1.47697 + 5.51212i) q^{22} +(-6.23526 - 1.67073i) q^{23} +(-0.463289 - 4.97849i) q^{25} -0.535154i q^{26} +(0.235352 - 0.256589i) q^{28} +(-3.97286 - 2.29373i) q^{29} +(1.80914 - 1.04451i) q^{31} +(0.192368 - 0.717928i) q^{32} +(1.45872 - 2.52657i) q^{34} +(-2.48805 + 5.36746i) q^{35} +(-0.0303530 - 0.0303530i) q^{37} +(5.40781 - 1.44902i) q^{38} +(0.282896 + 6.09313i) q^{40} +(9.89957 - 5.71552i) q^{41} +(-0.122307 - 0.456457i) q^{43} -0.514369i q^{44} +9.42462 q^{46} +(-3.03299 - 11.3193i) q^{47} +(5.73800 - 4.00941i) q^{49} +(2.53460 + 6.84586i) q^{50} +(0.0124846 + 0.0465932i) q^{52} +(8.71292 - 8.71292i) q^{53} +(2.65116 + 8.32811i) q^{55} +(3.33569 - 6.40015i) q^{56} +(6.46947 + 1.73349i) q^{58} +(4.90552 + 8.49662i) q^{59} +(5.75087 + 3.32027i) q^{61} +(-2.15664 + 2.15664i) q^{62} -7.40661i q^{64} +(-0.442288 - 0.690039i) q^{65} +(1.02256 - 3.81623i) q^{67} +(-0.0680608 + 0.254006i) q^{68} +(1.48055 - 8.50964i) q^{70} -2.12555 q^{71} +(-8.94714 - 8.94714i) q^{73} +(0.0542751 + 0.0313357i) q^{74} +(-0.437027 + 0.252318i) q^{76} +(2.24319 - 10.0950i) q^{77} +(3.15769 + 1.82309i) q^{79} +(-2.87992 - 9.04674i) q^{80} +(-11.8011 + 11.8011i) q^{82} +(-13.1782 + 3.53109i) q^{83} +(-0.207230 - 4.46340i) q^{85} +(0.344968 + 0.597502i) q^{86} +(-2.75957 - 10.2988i) q^{88} -1.00672 q^{89} +(0.0418267 + 0.968881i) q^{91} +(-0.820555 + 0.219867i) q^{92} +(8.55454 + 14.8169i) q^{94} +(5.77537 - 6.33777i) q^{95} +(-3.15650 - 11.7802i) q^{97} +(-6.57696 + 7.82253i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8}+O(q^{10}) $ 176 * q + 4 * q^2 - 2 * q^7 + 32 * q^8	$ 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8} + 12 q^{11} + 56 q^{16} + 12 q^{22} + 12 q^{23} - 4 q^{25} - 32 q^{28} - 48 q^{32} + 8 q^{35} - 16 q^{37} - 4 q^{43} - 80 q^{46} + 76 q^{50} - 64 q^{53} + 52 q^{56} - 44 q^{58} - 20 q^{65} - 4 q^{67} + 18 q^{70} + 64 q^{71} - 26 q^{77} - 4 q^{85} - 80 q^{86} - 60 q^{88} - 16 q^{91} + 68 q^{92} - 40 q^{95} + 120 q^{98}+O(q^{100}) $ 176 * q + 4 * q^2 - 2 * q^7 + 32 * q^8 + 12 * q^11 + 56 * q^16 + 12 * q^22 + 12 * q^23 - 4 * q^25 - 32 * q^28 - 48 * q^32 + 8 * q^35 - 16 * q^37 - 4 * q^43 - 80 * q^46 + 76 * q^50 - 64 * q^53 + 52 * q^56 - 44 * q^58 - 20 * q^65 - 4 * q^67 + 18 * q^70 + 64 * q^71 - 26 * q^77 - 4 * q^85 - 80 * q^86 - 60 * q^88 - 16 * q^91 + 68 * q^92 - 40 * q^95 + 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.41025	+	0.377876i	−0.997198	+	0.267198i	−0.720271	−	0.693692i	$-0.755983\pi$
$2$	−1.41025	+	0.377876i	−0.997198	+	0.267198i	−0.276927	+	0.960891i	$0.589316\pi$
$3$		0			0
$3$		0			0
$4$	0.113968	−	0.0657996i	0.0569841	−	0.0328998i
$5$	−1.50611	+	1.65277i	−0.673551	+	0.739141i
$5$	−1.50611	+	1.65277i	−0.673551	+	0.739141i
$6$		0			0
$7$	2.52369	−	0.794356i	0.953864	−	0.300238i
$7$	2.52369	−	0.794356i	0.953864	−	0.300238i
$8$	1.92889	−	1.92889i	0.681966	−	0.681966i
$9$		0			0
$10$	1.49945	−	2.89994i	0.474167	−	0.917042i
$11$	1.95430	−	3.38495i	0.589245	−	1.02060i	−0.405087	−	0.914278i	$-0.632759\pi$
$11$	1.95430	−	3.38495i	0.589245	−	1.02060i	0.994332	−	0.106324i	$-0.0339079\pi$
$12$		0			0
$13$	−0.0948685	+	0.354054i	−0.0263118	+	0.0981969i	−0.977833	−	0.209386i	$-0.932853\pi$
$13$	−0.0948685	+	0.354054i	−0.0263118	+	0.0981969i	0.951521	+	0.307583i	$0.0995202\pi$
$14$	−3.25887	+	2.07388i	−0.870968	+	0.554268i
$15$		0			0
$16$	−2.12294	+	3.67704i	−0.530735	+	0.919260i
$17$	−1.41297	+	1.41297i	−0.342696	+	0.342696i	−0.857380	−	0.514684i	$-0.827909\pi$
$17$	−1.41297	+	1.41297i	−0.342696	+	0.342696i	0.514684	+	0.857380i	$0.327909\pi$
$18$		0			0
$19$	−3.83464			−0.879727			−0.439863	−	0.898065i	$-0.644973\pi$
$19$	−3.83464			−0.879727			−0.439863	+	0.898065i	$0.644973\pi$
$20$	−0.0628967	+	0.287464i	−0.0140641	+	0.0642789i
$21$		0			0
$22$	−1.47697	+	5.51212i	−0.314891	+	1.17519i
$23$	−6.23526	−	1.67073i	−1.30014	−	0.348372i	−0.458638	−	0.888623i	$-0.651663\pi$
$23$	−6.23526	−	1.67073i	−1.30014	−	0.348372i	−0.841504	+	0.540251i	$0.818329\pi$
$24$		0			0
$25$	−0.463289	−	4.97849i	−0.0926578	−	0.995698i
$26$		−	0.535154i		−	0.104952i
$27$		0			0
$28$	0.235352	−	0.256589i	0.0444773	−	0.0484907i
$29$	−3.97286	−	2.29373i	−0.737741	−	0.425935i	0.0835066	−	0.996507i	$-0.473388\pi$
$29$	−3.97286	−	2.29373i	−0.737741	−	0.425935i	−0.821247	+	0.570572i	$0.806721\pi$
$30$		0			0
$31$	1.80914	−	1.04451i	0.324931	−	0.187599i	−0.328658	−	0.944449i	$-0.606596\pi$
$31$	1.80914	−	1.04451i	0.324931	−	0.187599i	0.653588	+	0.756850i	$0.273263\pi$
$32$	0.192368	−	0.717928i	0.0340062	−	0.126913i
$33$		0			0
$34$	1.45872	−	2.52657i	0.250168	−	0.433303i
$35$	−2.48805	+	5.36746i	−0.420558	+	0.907266i
$36$		0			0
$37$	−0.0303530	−	0.0303530i	−0.00499001	−	0.00499001i	0.704607	−	0.709597i	$-0.251123\pi$
$37$	−0.0303530	−	0.0303530i	−0.00499001	−	0.00499001i	−0.709597	+	0.704607i	$0.751123\pi$
$38$	5.40781	−	1.44902i	0.877262	−	0.235062i
$39$		0			0
$40$	0.282896	+	6.09313i	0.0447298	+	0.963408i
$41$	9.89957	−	5.71552i	1.54605	−	0.892614i	0.547616	−	0.836730i	$-0.315535\pi$
$41$	9.89957	−	5.71552i	1.54605	−	0.892614i	0.998437	−	0.0558847i	$-0.0177979\pi$
$42$		0			0
$43$	−0.122307	−	0.456457i	−0.0186517	−	0.0696090i	0.955973	−	0.293455i	$-0.0948052\pi$
$43$	−0.122307	−	0.456457i	−0.0186517	−	0.0696090i	−0.974624	+	0.223846i	$0.928139\pi$
$44$		−	0.514369i		−	0.0775441i
$45$		0			0
$46$	9.42462			1.38958
$47$	−3.03299	−	11.3193i	−0.442406	−	1.65108i	−0.722695	−	0.691167i	$-0.757097\pi$
$47$	−3.03299	−	11.3193i	−0.442406	−	1.65108i	0.280288	−	0.959916i	$-0.409570\pi$
$48$		0			0
$49$	5.73800	−	4.00941i	0.819714	−	0.572773i
$50$	2.53460	+	6.84586i	0.358447	+	0.968150i
$51$		0			0
$52$	0.0124846	+	0.0465932i	0.00173130	+	0.00646132i
$53$	8.71292	−	8.71292i	1.19681	−	1.19681i	0.221696	−	0.975116i	$-0.428841\pi$
$53$	8.71292	−	8.71292i	1.19681	−	1.19681i	0.975116	−	0.221696i	$-0.0711591\pi$
$54$		0			0
$55$	2.65116	+	8.32811i	0.357482	+	1.12296i
$56$	3.33569	−	6.40015i	0.445751	−	0.855256i
$57$		0			0
$58$	6.46947	+	1.73349i	0.849483	+	0.227618i
$59$	4.90552	+	8.49662i	0.638645	+	1.10617i	0.985730	+	0.168332i	$0.0538380\pi$
$59$	4.90552	+	8.49662i	0.638645	+	1.10617i	−0.347086	+	0.937833i	$0.612829\pi$
$60$		0			0
$61$	5.75087	+	3.32027i	0.736323	+	0.425116i	0.820731	−	0.571315i	$-0.193566\pi$
$61$	5.75087	+	3.32027i	0.736323	+	0.425116i	−0.0844077	+	0.996431i	$0.526900\pi$
$62$	−2.15664	+	2.15664i	−0.273894	+	0.273894i
$63$		0			0
$64$		−	7.40661i		−	0.925826i
$65$	−0.442288	−	0.690039i	−0.0548590	−	0.0855888i
$66$		0			0
$67$	1.02256	−	3.81623i	0.124925	−	0.466227i	−0.874912	−	0.484282i	$-0.839081\pi$
$67$	1.02256	−	3.81623i	0.124925	−	0.466227i	0.999837	+	0.0180555i	$0.00574754\pi$
$68$	−0.0680608	+	0.254006i	−0.00825359	+	0.0308028i
$69$		0			0
$70$	1.48055	−	8.50964i	0.176960	−	1.01710i
$71$	−2.12555			−0.252256			−0.126128	−	0.992014i	$-0.540255\pi$
$71$	−2.12555			−0.252256			−0.126128	+	0.992014i	$0.540255\pi$
$72$		0			0
$73$	−8.94714	−	8.94714i	−1.04718	−	1.04718i	−0.998830	−	0.0483534i	$-0.984603\pi$
$73$	−8.94714	−	8.94714i	−1.04718	−	1.04718i	−0.0483534	−	0.998830i	$-0.515397\pi$
$74$	0.0542751	+	0.0313357i	0.00630935	+	0.00364270i
$75$		0			0
$76$	−0.437027	+	0.252318i	−0.0501304	+	0.0289428i
$77$	2.24319	−	10.0950i	0.255635	−	1.15043i
$78$		0			0
$79$	3.15769	+	1.82309i	0.355268	+	0.205114i	0.667003	−	0.745055i	$-0.267577\pi$
$79$	3.15769	+	1.82309i	0.355268	+	0.205114i	−0.311735	+	0.950169i	$0.600910\pi$
$80$	−2.87992	−	9.04674i	−0.321985	−	1.01146i
$81$		0			0
$82$	−11.8011	+	11.8011i	−1.30322	+	1.30322i
$83$	−13.1782	+	3.53109i	−1.44649	+	0.387587i	−0.894803	−	0.446461i	$-0.852684\pi$
$83$	−13.1782	+	3.53109i	−1.44649	+	0.387587i	−0.551692	+	0.834048i	$0.686018\pi$
$84$		0			0
$85$	−0.207230	−	4.46340i	−0.0224772	−	0.484123i
$86$	0.344968	+	0.597502i	0.0371988	+	0.0644303i
$87$		0			0
$88$	−2.75957	−	10.2988i	−0.294171	−	1.09786i
$89$	−1.00672			−0.106712			−0.0533561	−	0.998576i	$-0.516992\pi$
$89$	−1.00672			−0.106712			−0.0533561	+	0.998576i	$0.516992\pi$
$90$		0			0
$91$	0.0418267	+	0.968881i	0.00438463	+	0.101566i
$92$	−0.820555	+	0.219867i	−0.0855488	+	0.0229227i
$93$		0			0
$94$	8.55454	+	14.8169i	0.882334	+	1.52825i
$95$	5.77537	−	6.33777i	0.592541	−	0.650242i
$96$		0			0
$97$	−3.15650	−	11.7802i	−0.320494	−	1.19610i	−0.918765	−	0.394806i	$-0.870812\pi$
$97$	−3.15650	−	11.7802i	−0.320494	−	1.19610i	0.598271	−	0.801294i	$-0.295855\pi$
$98$	−6.57696	+	7.82253i	−0.664373	+	0.790195i
$99$		0			0
$100$	−0.380383	−	0.536905i	−0.0380383	−	0.0536905i
$101$	5.32516	+	3.07448i	0.529873	+	0.305923i	0.740965	−	0.671544i	$-0.234368\pi$
$101$	5.32516	+	3.07448i	0.529873	+	0.305923i	−0.211091	+	0.977466i	$0.567702\pi$
$102$		0			0
$103$	−1.04524	+	3.90090i	−0.102991	+	0.384367i	−0.998109	−	0.0614609i	$-0.980424\pi$
$103$	−1.04524	+	3.90090i	−0.102991	+	0.384367i	0.895119	+	0.445828i	$0.147091\pi$
$104$	0.499941	+	0.865923i	0.0490232	+	0.0849108i
$105$		0			0
$106$	−8.99501	+	15.5798i	−0.873672	+	1.51324i
$107$	2.19807	+	2.19807i	0.212495	+	0.212495i	0.805327	−	0.592831i	$-0.201990\pi$
$107$	2.19807	+	2.19807i	0.212495	+	0.212495i	−0.592831	+	0.805327i	$0.701990\pi$
$108$		0			0
$109$		−	8.35559i		−	0.800320i	−0.916445	−	0.400160i	$-0.868955\pi$
$109$		−	8.35559i		−	0.800320i	0.916445	−	0.400160i	$-0.131045\pi$
$110$	−6.88579	−	10.7429i	−0.656534	−	1.02430i
$111$		0			0
$112$	−2.43676	+	10.9661i	−0.230252	+	1.03620i
$113$	12.9042	+	3.45767i	1.21393	+	0.325271i	0.808301	−	0.588769i	$-0.200387\pi$
$113$	12.9042	+	3.45767i	1.21393	+	0.325271i	0.405625	+	0.914040i	$0.367054\pi$
$114$		0			0
$115$	12.1523	−	7.78915i	1.13321	−	0.726342i
$116$	−0.603705			−0.0560526
$117$		0			0
$118$	−10.1287	−	10.1287i	−0.932421	−	0.932421i
$119$	−2.44349	+	4.68830i	−0.223995	+	0.429776i
$120$		0			0
$121$	−2.13861	−	3.70417i	−0.194419	−	0.336743i
$122$	−9.36482	−	2.50930i	−0.847851	−	0.227181i
$123$		0			0
$124$	0.137456	−	0.238081i	0.0123439	−	0.0213803i
$125$	8.92605	+	6.73243i	0.798371	+	0.602166i
$126$		0			0
$127$	−9.18444	−	9.18444i	−0.814987	−	0.814987i	0.170390	−	0.985377i	$-0.445497\pi$
$127$	−9.18444	−	9.18444i	−0.814987	−	0.814987i	−0.985377	+	0.170390i	$0.945497\pi$
$128$	3.18351	+	11.8810i	0.281386	+	1.05015i
$129$		0			0
$130$	0.884486	+	0.805998i	0.0775745	+	0.0706907i
$131$	9.99028	−	5.76789i	0.872855	−	0.503943i	0.00455882	−	0.999990i	$-0.498549\pi$
$131$	9.99028	−	5.76789i	0.872855	−	0.503943i	0.868296	+	0.496047i	$0.165216\pi$
$132$		0			0
$133$	−9.67743	+	3.04607i	−0.839140	+	0.264128i
$134$			5.76824i			0.498300i
$135$		0			0
$136$			5.45093i			0.467414i
$137$	5.08704	−	1.36307i	0.434615	−	0.116455i	−0.0348765	−	0.999392i	$-0.511104\pi$
$137$	5.08704	−	1.36307i	0.434615	−	0.116455i	0.469492	+	0.882937i	$0.344437\pi$
$138$		0			0
$139$	5.20435	+	9.01419i	0.441427	+	0.764574i	0.997796	−	0.0663616i	$-0.0211391\pi$
$139$	5.20435	+	9.01419i	0.441427	+	0.764574i	−0.556369	+	0.830936i	$0.687806\pi$
$140$	0.0696173	+	0.775432i	0.00588374	+	0.0655360i
$141$		0			0
$142$	2.99756	−	0.803193i	0.251549	−	0.0674025i
$143$	1.01305	+	1.01305i	0.0847159	+	0.0847159i
$144$		0			0
$145$	9.77455	−	3.11161i	0.811732	−	0.258405i
$146$	15.9986	+	9.23681i	1.32406	+	0.764444i
$147$		0			0
$148$	−0.00545649	−	0.00146206i	−0.000448521	−	0.000120181i
$149$	0.639215	−	0.369051i	0.0523665	−	0.0302338i	−0.473588	−	0.880746i	$-0.657041\pi$
$149$	0.639215	−	0.369051i	0.0523665	−	0.0302338i	0.525955	+	0.850513i	$0.323708\pi$
$150$		0			0
$151$	10.1772	−	17.6275i	0.828211	−	1.43450i	−0.0712291	−	0.997460i	$-0.522692\pi$
$151$	10.1772	−	17.6275i	0.828211	−	1.43450i	0.899440	−	0.437044i	$-0.143975\pi$
$152$	−7.39660	+	7.39660i	−0.599944	+	0.599944i
$153$		0			0
$154$	0.651182	+	15.0841i	0.0524737	+	1.21551i
$155$	−0.998426	+	4.56322i	−0.0801955	+	0.366527i
$156$		0			0
$157$	−9.23084	−	2.47340i	−0.736701	−	0.197399i	−0.129090	−	0.991633i	$-0.541206\pi$
$157$	−9.23084	−	2.47340i	−0.736701	−	0.197399i	−0.607612	+	0.794234i	$0.707872\pi$
$158$	−5.14204	−	1.37781i	−0.409079	−	0.109612i
$159$		0			0
$160$	0.896842	+	1.39922i	0.0709016	+	0.110618i
$161$	−17.0630	+	0.736612i	−1.34475	+	0.0580531i
$162$		0			0
$163$	−6.94454	+	6.94454i	−0.543938	+	0.543938i	−0.924681	−	0.380743i	$-0.875668\pi$
$163$	−6.94454	+	6.94454i	−0.543938	+	0.543938i	0.380743	+	0.924681i	$0.375668\pi$
$164$	0.752158	−	1.30278i	0.0587336	−	0.101730i
$165$		0			0
$166$	17.2503	−	9.95944i	1.33888	−	0.773003i
$167$	−17.6752	−	4.73607i	−1.36775	−	0.366488i	−0.501095	−	0.865393i	$-0.667069\pi$
$167$	−17.6752	−	4.73607i	−1.36775	−	0.366488i	−0.866657	+	0.498905i	$0.833736\pi$
$168$		0			0
$169$	11.1420	+	6.43282i	0.857075	+	0.494833i
$170$	1.97886	+	6.21620i	0.151771	+	0.476761i
$171$		0			0
$172$	−0.0439738	−	0.0439738i	−0.00335297	−	0.00335297i
$173$	14.8893	−	3.98957i	1.13201	−	0.303321i	0.356276	−	0.934381i	$-0.384046\pi$
$173$	14.8893	−	3.98957i	1.13201	−	0.303321i	0.775735	+	0.631059i	$0.217379\pi$
$174$		0			0
$175$	−5.12389	−	12.1961i	−0.387330	−	0.921941i
$176$	8.29774	+	14.3721i	0.625466	+	1.08334i
$177$		0			0
$178$	1.41973	−	0.380415i	0.106413	−	0.0285133i
$179$		−	2.84155i		−	0.212388i	−0.994345	−	0.106194i	$-0.966134\pi$
$179$		−	2.84155i		−	0.212388i	0.994345	−	0.106194i	$-0.0338664\pi$
$180$		0			0
$181$		−	20.2943i		−	1.50846i	−0.656609	−	0.754231i	$-0.728010\pi$
$181$		−	20.2943i		−	1.50846i	0.656609	−	0.754231i	$-0.271990\pi$
$182$	−0.425103	−	1.35056i	−0.0315107	−	0.100110i
$183$		0			0
$184$	−15.2498	+	8.80448i	−1.12423	+	0.649075i
$185$	0.0958814	−	0.00445165i	0.00704934	−	0.000327292i
$186$		0			0
$187$	2.02147	+	7.54421i	0.147824	+	0.551687i
$188$	−1.09047	−	1.09047i	−0.0795304	−	0.0795304i
$189$		0			0
$190$	−5.74984	+	11.1202i	−0.417137	+	0.806746i
$191$	−6.13621	+	10.6282i	−0.444000	+	0.769031i	−0.997982	−	0.0634977i	$-0.979774\pi$
$191$	−6.13621	+	10.6282i	−0.444000	+	0.769031i	0.553982	+	0.832529i	$0.313108\pi$
$192$		0			0
$193$	−7.81281	−	2.09344i	−0.562378	−	0.150689i	−0.0335796	−	0.999436i	$-0.510691\pi$
$193$	−7.81281	−	2.09344i	−0.562378	−	0.150689i	−0.528799	+	0.848747i	$0.677357\pi$
$194$	8.90292	+	15.4203i	0.639192	+	1.10711i
$195$		0			0
$196$	0.390131	−	0.834503i	0.0278665	−	0.0596074i
$197$	1.52429	+	1.52429i	0.108601	+	0.108601i	0.759319	−	0.650718i	$-0.225532\pi$
$197$	1.52429	+	1.52429i	0.108601	+	0.108601i	−0.650718	+	0.759319i	$0.725532\pi$
$198$		0			0
$199$	−11.3535			−0.804828			−0.402414	−	0.915458i	$-0.631829\pi$
$199$	−11.3535			−0.804828			−0.402414	+	0.915458i	$0.631829\pi$
$200$	−10.4966	−	8.70933i	−0.742222	−	0.615843i
$201$		0			0
$202$	−8.67159	−	2.32355i	−0.610131	−	0.163484i
$203$	−11.8483	−	2.63279i	−0.831586	−	0.184786i
$204$		0			0
$205$	−5.46337	+	24.9699i	−0.381578	+	1.74397i
$206$		−	5.89622i		−	0.410809i
$207$		0			0
$208$	−1.10047	−	1.10047i	−0.0763039	−	0.0763039i
$209$	−7.49405	+	12.9801i	−0.518374	+	0.897851i
$210$		0			0
$211$	−0.887630	−	1.53742i	−0.0611069	−	0.105840i	0.833854	−	0.551986i	$-0.186130\pi$
$211$	−0.887630	−	1.53742i	−0.0611069	−	0.105840i	−0.894960	+	0.446145i	$0.852796\pi$
$212$	0.419689	−	1.56630i	0.0288244	−	0.107574i
$213$		0			0
$214$	−3.93043	−	2.26923i	−0.268678	−	0.155122i
$215$	0.938625	+	0.485327i	0.0640137	+	0.0330990i
$216$		0			0
$217$	3.73599	−	4.07310i	0.253615	−	0.276500i
$218$	3.15737	+	11.7835i	0.213844	+	0.798078i
$219$		0			0
$220$	0.850133	+	0.774695i	0.0573160	+	0.0522299i
$221$	−0.366222	−	0.634314i	−0.0246347	−	0.0426686i
$222$		0			0
$223$	19.2534	−	5.15894i	1.28930	−	0.345468i	0.451908	−	0.892065i	$-0.350744\pi$
$223$	19.2534	−	5.15894i	1.28930	−	0.345468i	0.837396	+	0.546597i	$0.184077\pi$
$224$	−0.0848135	−	1.96464i	−0.00566684	−	0.131268i
$225$		0			0
$226$	−19.5048			−1.29744
$227$	−3.11388	−	11.6212i	−0.206676	−	0.771325i	−0.988932	−	0.148368i	$-0.952598\pi$
$227$	−3.11388	−	11.6212i	−0.206676	−	0.771325i	0.782256	−	0.622957i	$-0.214069\pi$
$228$		0			0
$229$	−4.78689	−	8.29114i	−0.316327	−	0.547894i	0.663392	−	0.748272i	$-0.269116\pi$
$229$	−4.78689	−	8.29114i	−0.316327	−	0.547894i	−0.979719	+	0.200378i	$0.935783\pi$
$230$	−14.1945	+	15.5767i	−0.935956	+	1.02710i
$231$		0			0
$232$	−12.0876	+	3.23885i	−0.793587	+	0.212641i
$233$	−6.37266	+	6.37266i	−0.417487	+	0.417487i	−0.884337	−	0.466850i	$-0.845389\pi$
$233$	−6.37266	+	6.37266i	−0.417487	+	0.417487i	0.466850	+	0.884337i	$0.345389\pi$
$234$		0			0
$235$	23.2761	+	12.0352i	1.51837	+	0.785088i
$236$	1.11815	+	0.645563i	0.0727852	+	0.0420226i
$237$		0			0
$238$	1.67435	−	7.53501i	0.108532	−	0.488422i
$239$	−5.05325	+	2.91749i	−0.326867	+	0.188717i	−0.654449	−	0.756106i	$-0.727100\pi$
$239$	−5.05325	+	2.91749i	−0.326867	+	0.188717i	0.327582	+	0.944823i	$0.393766\pi$
$240$		0			0
$241$	7.01801	+	4.05185i	0.452070	+	0.261003i	0.708704	−	0.705506i	$-0.249280\pi$
$241$	7.01801	+	4.05185i	0.452070	+	0.261003i	−0.256634	+	0.966509i	$0.582614\pi$
$242$	4.41569	+	4.41569i	0.283851	+	0.283851i
$243$		0			0
$244$	0.873888			0.0559450
$245$	−2.01540	+	15.5222i	−0.128759	+	0.991676i
$246$		0			0
$247$	0.363787	−	1.35767i	0.0231472	−	0.0863865i
$248$	1.47489	−	5.50437i	0.0936556	−	0.349528i
$249$		0			0
$250$	−15.1320	−	6.12147i	−0.957032	−	0.387156i
$251$		−	7.52743i		−	0.475127i	−0.971372	−	0.237564i	$-0.923651\pi$
$251$		−	7.52743i		−	0.475127i	0.971372	−	0.237564i	$-0.0763488\pi$
$252$		0			0
$253$	−17.8410	+	17.8410i	−1.12165	+	1.12165i
$254$	16.4229	+	9.48179i	1.03047	+	0.594940i
$255$		0			0
$256$	−1.57250	−	2.72365i	−0.0982814	−	0.170228i
$257$	−12.0491	−	3.22856i	−0.751604	−	0.201392i	−0.137375	−	0.990519i	$-0.543866\pi$
$257$	−12.0491	−	3.22856i	−0.751604	−	0.201392i	−0.614230	+	0.789127i	$0.710533\pi$
$258$		0			0
$259$	−0.100713	−	0.0524904i	−0.00625798	−	0.00326160i
$260$	−0.0958110	−	0.0495401i	−0.00594194	−	0.00307235i
$261$		0			0
$262$	−11.9093	+	11.9093i	−0.735756	+	0.735756i
$263$	−0.132720	−	0.495319i	−0.00818389	−	0.0305427i	0.961713	−	0.274058i	$-0.0883660\pi$
$263$	−0.132720	−	0.495319i	−0.00818389	−	0.0305427i	−0.969897	+	0.243515i	$0.921699\pi$
$264$		0			0
$265$	1.27786	+	27.5230i	0.0784983	+	1.69073i
$266$	12.4966	−	7.95259i	0.766214	−	0.487605i
$267$		0			0
$268$	−0.134567	−	0.502212i	−0.00822001	−	0.0306775i
$269$	5.16747			0.315066			0.157533	−	0.987514i	$-0.449646\pi$
$269$	5.16747			0.315066			0.157533	+	0.987514i	$0.449646\pi$
$270$		0			0
$271$			0.0214709i			0.00130426i	1.00000		0.000652132i	$0.000207580\pi$
$271$			0.0214709i			0.00130426i	−1.00000		0.000652132i	$0.999792\pi$
$272$	−2.19590	−	8.19520i	−0.133146	−	0.496907i
$273$		0			0
$274$	−6.65894	+	3.84454i	−0.402281	+	0.232257i
$275$	−17.7574	−	8.16127i	−1.07081	−	0.492143i
$276$		0			0
$277$	10.9849	−	2.94340i	0.660019	−	0.176851i	0.0867643	−	0.996229i	$-0.472347\pi$
$277$	10.9849	−	2.94340i	0.660019	−	0.176851i	0.573254	+	0.819377i	$0.305681\pi$
$278$	−10.7457	−	10.7457i	−0.644483	−	0.644483i
$279$		0			0
$280$	5.55406	+	15.1524i	0.331918	+	0.905531i
$281$	−6.07820	+	10.5278i	−0.362595	+	0.628033i	−0.988387	−	0.151957i	$-0.951443\pi$
$281$	−6.07820	+	10.5278i	−0.362595	+	0.628033i	0.625792	+	0.779990i	$0.284776\pi$
$282$		0			0
$283$	−6.87930	+	25.6739i	−0.408932	+	1.52615i	0.387756	+	0.921762i	$0.373250\pi$
$283$	−6.87930	+	25.6739i	−0.408932	+	1.52615i	−0.796687	+	0.604392i	$0.793416\pi$
$284$	−0.242245	+	0.139860i	−0.0143746	+	0.00829917i
$285$		0			0
$286$	−1.81147	−	1.04585i	−0.107115	−	0.0618426i
$287$	20.4433	−	22.2880i	1.20673	−	1.31562i
$288$		0			0
$289$			13.0070i			0.765119i
$290$	−12.6088	+	8.08172i	−0.740412	+	0.474575i
$291$		0			0
$292$	−1.60841	−	0.430971i	−0.0941249	−	0.0252207i
$293$	5.97252	−	22.2897i	0.348918	−	1.30218i	−0.539049	−	0.842274i	$-0.681216\pi$
$293$	5.97252	−	22.2897i	0.348918	−	1.30218i	0.887967	−	0.459907i	$-0.152117\pi$
$294$		0			0
$295$	−21.4312	−	4.68911i	−1.24777	−	0.273011i
$296$	−0.117095			−0.00680603
$297$		0			0
$298$	−0.761999	+	0.761999i	−0.0441414	+	0.0441414i
$299$	1.18306	−	2.04912i	0.0684181	−	0.118504i
$300$		0			0
$301$	−0.671255	−	1.05480i	−0.0386905	−	0.0607976i
$302$	−7.69146	+	28.7049i	−0.442594	+	1.65178i
$303$		0			0
$304$	8.14071	−	14.1001i	0.466902	−	0.808698i
$305$	−14.1491	+	4.50418i	−0.810172	+	0.257909i
$306$		0			0
$307$	−14.6287	+	14.6287i	−0.834902	+	0.834902i	−0.988183	−	0.153281i	$-0.951016\pi$
$307$	−14.6287	+	14.6287i	−0.834902	+	0.834902i	0.153281	+	0.988183i	$0.451016\pi$
$308$	−0.408593	−	1.29811i	−0.0232817	−	0.0739665i
$309$		0			0
$310$	−0.316299	−	6.81257i	−0.0179646	−	0.386928i
$311$	−12.9578	+	7.48121i	−0.734772	+	0.424221i	−0.820165	−	0.572127i	$-0.806119\pi$
$311$	−12.9578	+	7.48121i	−0.734772	+	0.424221i	0.0853935	+	0.996347i	$0.472785\pi$
$312$		0			0
$313$	−12.5111	+	3.35233i	−0.707167	+	0.189485i	−0.594439	−	0.804141i	$-0.702626\pi$
$313$	−12.5111	+	3.35233i	−0.707167	+	0.189485i	−0.112728	+	0.993626i	$0.535959\pi$
$314$	13.9524			0.787382
$315$		0			0
$316$	0.479835			0.0269929
$317$	−25.1441	+	6.73734i	−1.41223	+	0.378407i	−0.882722	−	0.469896i	$-0.844291\pi$
$317$	−25.1441	+	6.73734i	−1.41223	+	0.378407i	−0.529512	+	0.848303i	$0.677625\pi$
$318$		0			0
$319$	−15.5283	+	8.96529i	−0.869420	+	0.501960i
$320$	12.2414	+	11.1551i	0.684316	+	0.623591i
$321$		0			0
$322$	23.7848	−	7.48651i	1.32547	−	0.417207i
$323$	5.41823	−	5.41823i	0.301479	−	0.301479i
$324$		0			0
$325$	1.80661	+	0.308273i	0.100212	+	0.0170999i
$326$	7.16937	−	12.4177i	0.397075	−	0.687754i
$327$		0			0
$328$	8.07058	−	30.1198i	0.445623	−	1.66309i
$329$	−16.6458	−	26.1570i	−0.917714	−	1.44208i
$330$		0			0
$331$	3.19019	−	5.52557i	0.175349	−	0.303713i	−0.764933	−	0.644110i	$-0.777228\pi$
$331$	3.19019	−	5.52557i	0.175349	−	0.303713i	0.940282	+	0.340397i	$0.110561\pi$
$332$	−1.26955	+	1.26955i	−0.0696757	+	0.0696757i
$333$		0			0
$334$	26.7162			1.46184
$335$	4.76727	+	7.43769i	0.260464	+	0.406365i
$336$		0			0
$337$	−0.663023	+	2.47444i	−0.0361172	+	0.134791i	−0.981630	−	0.190793i	$-0.938894\pi$
$337$	−0.663023	+	2.47444i	−0.0361172	+	0.134791i	0.945513	+	0.325584i	$0.105561\pi$
$338$	−18.1438	−	4.86162i	−0.986892	−	0.264437i
$339$		0			0
$340$	−0.317307	−	0.495050i	−0.0172084	−	0.0268478i
$341$		−	8.16512i		−	0.442166i
$342$		0			0
$343$	11.2960	−	14.6765i	0.609927	−	0.792458i
$344$	−1.11637	−	0.644538i	−0.0601908	−	0.0347512i
$345$		0			0
$346$	−19.4901	+	11.2526i	−1.04779	+	0.604943i
$347$	2.12587	−	7.93384i	0.114122	−	0.425911i	−0.885097	−	0.465406i	$-0.845908\pi$
$347$	2.12587	−	7.93384i	0.114122	−	0.425911i	0.999220	+	0.0394952i	$0.0125750\pi$
$348$		0			0
$349$	−8.03047	+	13.9092i	−0.429861	+	0.744541i	−0.996861	−	0.0791769i	$-0.974771\pi$
$349$	−8.03047	+	13.9092i	−0.429861	+	0.744541i	0.567000	+	0.823718i	$0.308104\pi$
$350$	11.8346	+	15.2634i	0.632586	+	0.815864i
$351$		0			0
$352$	−2.05421	−	2.05421i	−0.109490	−	0.109490i
$353$	−6.06709	+	1.62567i	−0.322918	+	0.0865257i	−0.416637	−	0.909073i	$-0.636791\pi$
$353$	−6.06709	+	1.62567i	−0.322918	+	0.0865257i	0.0937184	+	0.995599i	$0.470125\pi$
$354$		0			0
$355$	3.20130	−	3.51304i	0.169907	−	0.186453i
$356$	−0.114734	+	0.0662417i	−0.00608089	+	0.00351080i
$357$		0			0
$358$	1.07375	+	4.00730i	0.0567496	+	0.211792i
$359$		−	29.1921i		−	1.54070i	−0.637620	−	0.770351i	$-0.720081\pi$
$359$		−	29.1921i		−	1.54070i	0.637620	−	0.770351i	$-0.279919\pi$
$360$		0			0
$361$	−4.29554			−0.226081
$362$	7.66872	+	28.6201i	0.403059	+	1.50424i
$363$		0			0
$364$	0.0685189	+	0.107669i	0.00359137	+	0.00564341i
$365$	28.2629	−	1.31221i	1.47935	−	0.0686843i
$366$		0			0
$367$	4.94689	+	18.4620i	0.258226	+	0.963711i	0.966267	+	0.257541i	$0.0829121\pi$
$367$	4.94689	+	18.4620i	0.258226	+	0.963711i	−0.708042	+	0.706170i	$0.750421\pi$
$368$	19.3804	−	19.3804i	1.01028	−	1.01028i
$369$		0			0
$370$	−0.133535	+	0.0425092i	−0.00694214	+	0.00220995i
$371$	15.0675	−	28.9098i	0.782267	−	1.50092i
$372$		0			0
$373$	36.1317	+	9.68146i	1.87083	+	0.501287i	0.999952	+	0.00978595i	$0.00311501\pi$
$373$	36.1317	+	9.68146i	1.87083	+	0.501287i	0.870877	+	0.491501i	$0.163552\pi$
$374$	−5.70155	−	9.87537i	−0.294820	−	0.510643i
$375$		0			0
$376$	−27.6839	−	15.9833i	−1.42769	−	0.824277i
$377$	1.18900	−	1.18900i	0.0612368	−	0.0612368i
$378$		0			0
$379$		−	21.0974i		−	1.08370i	−0.840474	−	0.541851i	$-0.817724\pi$
$379$		−	21.0974i		−	1.08370i	0.840474	−	0.541851i	$-0.182276\pi$
$380$	0.241186	−	1.10232i	0.0123726	−	0.0565479i
$381$		0			0
$382$	4.63745	−	17.3072i	0.237272	−	0.885513i
$383$	−1.05310	+	3.93021i	−0.0538107	+	0.200824i	−0.987598	−	0.157005i	$-0.949816\pi$
$383$	−1.05310	+	3.93021i	−0.0538107	+	0.200824i	0.933787	+	0.357829i	$0.116483\pi$
$384$		0			0
$385$	13.3062	+	18.9116i	0.678146	+	0.963824i
$386$	11.8091			0.601067
$387$		0			0
$388$	−1.13487	−	1.13487i	−0.0576145	−	0.0576145i
$389$	26.8857	+	15.5225i	1.36316	+	0.787021i	0.990043	−	0.140763i	$-0.0449554\pi$
$389$	26.8857	+	15.5225i	1.36316	+	0.787021i	0.373118	+	0.927784i	$0.378289\pi$
$390$		0			0
$391$	11.1709	−	6.44954i	0.564939	−	0.326167i
$392$	3.33425	−	18.8017i	0.168405	−	0.949629i
$393$		0			0
$394$	−2.72562	−	1.57364i	−0.137315	−	0.0792786i
$395$	−7.76898	+	2.47316i	−0.390900	+	0.124438i
$396$		0			0
$397$	4.43818	−	4.43818i	0.222746	−	0.222746i	−0.586908	−	0.809654i	$-0.699655\pi$
$397$	4.43818	−	4.43818i	0.222746	−	0.222746i	0.809654	+	0.586908i	$0.199655\pi$
$398$	16.0113	−	4.29021i	0.802573	−	0.215049i
$399$		0			0
$400$	19.2896	+	8.86550i	0.964482	+	0.443275i
$401$	19.1412	+	33.1535i	0.955866	+	1.65561i	0.732375	+	0.680902i	$0.238412\pi$
$401$	19.1412	+	33.1535i	0.955866	+	1.65561i	0.223491	+	0.974706i	$0.428255\pi$
$402$		0			0
$403$	0.198181	+	0.739623i	0.00987212	+	0.0368432i
$404$	0.809199			0.0402591
$405$		0			0
$406$	17.7039	−	0.764280i	0.878631	−	0.0379306i
$407$	−0.162063	+	0.0434245i	−0.00803314	+	0.00215247i
$408$		0			0
$409$	−15.0631	−	26.0901i	−0.744823	−	1.29007i	−0.950277	−	0.311404i	$-0.899201\pi$
$409$	−15.0631	−	26.0901i	−0.744823	−	1.29007i	0.205455	−	0.978667i	$-0.434133\pi$
$410$	−1.73078	−	37.2783i	−0.0854773	−	1.84104i
$411$		0			0
$412$	0.137553	+	0.513355i	0.00677676	+	0.0252912i
$413$	19.1294	+	17.5461i	0.941294	+	0.863386i
$414$		0			0
$415$	14.0117	−	27.0987i	0.687807	−	1.33022i
$416$	0.235936	+	0.136218i	0.0115677	+	0.00667862i
$417$		0			0
$418$	5.66364	−	21.1370i	0.277018	−	1.03384i
$419$	−5.18972	−	8.98886i	−0.253534	−	0.439134i	0.710962	−	0.703230i	$-0.248260\pi$
$419$	−5.18972	−	8.98886i	−0.253534	−	0.439134i	−0.964496	+	0.264096i	$0.914926\pi$
$420$		0			0
$421$	−9.30441	+	16.1157i	−0.453469	+	0.785432i	−0.998599	−	0.0529202i	$-0.983147\pi$
$421$	−9.30441	+	16.1157i	−0.453469	+	0.785432i	0.545130	+	0.838352i	$0.316480\pi$
$422$	1.83273	+	1.83273i	0.0892161	+	0.0892161i
$423$		0			0
$424$		−	33.6126i		−	1.63237i
$425$	7.68907	+	6.37985i	0.372975	+	0.309468i
$426$		0			0
$427$	17.1509	+	3.81107i	0.829989	+	0.184431i
$428$	0.395142	+	0.105878i	0.0190999	+	0.00511780i
$429$		0			0
$430$	−1.50709	−	0.329749i	−0.0726784	−	0.0159019i
$431$	−25.3205			−1.21964			−0.609822	−	0.792538i	$-0.708759\pi$
$431$	−25.3205			−1.21964			−0.609822	+	0.792538i	$0.708759\pi$
$432$		0			0
$433$	13.9170	+	13.9170i	0.668810	+	0.668810i	0.957441	−	0.288630i	$-0.0931999\pi$
$433$	13.9170	+	13.9170i	0.668810	+	0.668810i	−0.288630	+	0.957441i	$0.593200\pi$
$434$	−3.72955	+	7.15584i	−0.179024	+	0.343491i
$435$		0			0
$436$	−0.549794	−	0.952271i	−0.0263304	−	0.0456055i
$437$	23.9100	+	6.40666i	1.14377	+	0.306472i
$438$		0			0
$439$	14.7353	−	25.5223i	0.703278	−	1.21811i	−0.264031	−	0.964514i	$-0.585052\pi$
$439$	14.7353	−	25.5223i	0.703278	−	1.21811i	0.967309	−	0.253599i	$-0.0816144\pi$
$440$	21.1778	+	10.9502i	1.00961	+	0.522032i
$441$		0			0
$442$	0.756157	+	0.756157i	0.0359667	+	0.0359667i
$443$	−3.95131	−	14.7465i	−0.187732	−	0.700627i	−0.994029	−	0.109116i	$-0.965198\pi$
$443$	−3.95131	−	14.7465i	−0.187732	−	0.700627i	0.806297	−	0.591512i	$-0.201469\pi$
$444$		0			0
$445$	1.51623	−	1.66388i	0.0718761	−	0.0788753i
$446$	−25.2027	+	14.5508i	−1.19338	+	0.689000i
$447$		0			0
$448$	−5.88349	−	18.6920i	−0.277969	−	0.883112i
$449$		−	3.06142i		−	0.144478i	−0.997387	−	0.0722388i	$-0.976986\pi$
$449$		−	3.06142i		−	0.144478i	0.997387	−	0.0722388i	$-0.0230144\pi$
$450$		0			0
$451$		−	44.6795i		−	2.10387i
$452$	1.69818	−	0.455027i	0.0798758	−	0.0214027i
$453$		0			0
$454$	8.78272	+	15.2121i	0.412194	+	0.713940i
$455$	−1.66433	−	1.39011i	−0.0780251	−	0.0651693i
$456$		0			0
$457$	−4.44611	+	1.19133i	−0.207980	+	0.0557282i	−0.361305	−	0.932448i	$-0.617669\pi$
$457$	−4.44611	+	1.19133i	−0.207980	+	0.0557282i	0.153325	+	0.988176i	$0.451002\pi$
$458$	9.88374	+	9.88374i	0.461837	+	0.461837i
$459$		0			0
$460$	0.872454	−	1.68733i	0.0406784	−	0.0786722i
$461$	−31.5764	−	18.2307i	−1.47066	−	0.849087i	−0.471204	−	0.882024i	$-0.656180\pi$
$461$	−31.5764	−	18.2307i	−1.47066	−	0.849087i	−0.999457	+	0.0329376i	$0.989514\pi$
$462$		0			0
$463$	26.0444	+	6.97859i	1.21039	+	0.324323i	0.806914	−	0.590669i	$-0.201136\pi$
$463$	26.0444	+	6.97859i	1.21039	+	0.324323i	0.403474	+	0.914991i	$0.367803\pi$
$464$	16.8683	−	9.73890i	0.783090	−	0.452117i
$465$		0			0
$466$	6.57898	−	11.3951i	0.304765	−	0.527869i
$467$	−26.5122	+	26.5122i	−1.22684	+	1.22684i	−0.261688	+	0.965153i	$0.584279\pi$
$467$	−26.5122	+	26.5122i	−1.22684	+	1.22684i	−0.965153	+	0.261688i	$0.915721\pi$
$468$		0			0
$469$	−0.450836	−	10.4432i	−0.0208177	−	0.482224i
$470$	−37.3730	−	8.17715i	−1.72389	−	0.377184i
$471$		0			0
$472$	25.8513	+	6.92683i	1.18990	+	0.318833i
$473$	−1.78411	−	0.478051i	−0.0820335	−	0.0219808i
$474$		0			0
$475$	1.77655	+	19.0907i	0.0815135	+	0.875942i
$476$	0.0300074	+	0.695098i	0.00137539	+	0.0318597i
$477$		0			0
$478$	6.02390	−	6.02390i	0.275527	−	0.275527i
$479$	4.24052	−	7.34480i	0.193754	−	0.335592i	−0.752737	−	0.658321i	$-0.771267\pi$
$479$	4.24052	−	7.34480i	0.193754	−	0.335592i	0.946491	+	0.322729i	$0.104600\pi$
$480$		0			0
$481$	0.0136262	−	0.00786707i	0.000621299	−	0.000358707i
$482$	−11.4283	−	3.06219i	−0.520543	−	0.139479i
$483$		0			0
$484$	−0.487466	−	0.281439i	−0.0221575	−	0.0127927i
$485$	24.2240	+	12.5253i	1.09996	+	0.568744i
$486$		0			0
$487$	2.65490	+	2.65490i	0.120305	+	0.120305i	0.764696	−	0.644391i	$-0.222889\pi$
$487$	2.65490	+	2.65490i	0.120305	+	0.120305i	−0.644391	+	0.764696i	$0.722889\pi$
$488$	17.4972	−	4.68837i	0.792063	−	0.212233i
$489$		0			0
$490$	−3.02324	−	22.6518i	−0.136576	−	1.02330i
$491$	2.01799	+	3.49526i	0.0910707	+	0.157739i	0.907962	−	0.419053i	$-0.137638\pi$
$491$	2.01799	+	3.49526i	0.0910707	+	0.157739i	−0.816891	+	0.576792i	$0.804304\pi$
$492$		0			0
$493$	8.85450	−	2.37256i	0.398787	−	0.106855i
$494$			2.05212i			0.0923293i
$495$		0			0
$496$			8.86969i			0.398261i
$497$	−5.36422	+	1.68844i	−0.240618	+	0.0757370i
$498$		0			0
$499$	−6.03591	+	3.48484i	−0.270205	+	0.156003i	−0.628981	−	0.777421i	$-0.716528\pi$
$499$	−6.03591	+	3.48484i	−0.270205	+	0.156003i	0.358776	+	0.933424i	$0.383194\pi$
$500$	1.46028	+	0.179952i	0.0653056	+	0.00804769i
$501$		0			0
$502$	2.84443	+	10.6156i	0.126953	+	0.473796i
$503$	−12.3235	−	12.3235i	−0.549477	−	0.549477i	0.376812	−	0.926290i	$-0.377020\pi$
$503$	−12.3235	−	12.3235i	−0.549477	−	0.549477i	−0.926290	+	0.376812i	$0.877020\pi$
$504$		0			0
$505$	−13.1017	+	4.17076i	−0.583017	+	0.185597i
$506$	18.4186	−	31.9019i	0.818805	−	1.41821i
$507$		0			0
$508$	−1.65107	−	0.442402i	−0.0732542	−	0.0196284i
$509$	15.1933	+	26.3156i	0.673433	+	1.16642i	0.976924	+	0.213586i	$0.0685145\pi$
$509$	15.1933	+	26.3156i	0.673433	+	1.16642i	−0.303491	+	0.952834i	$0.598152\pi$
$510$		0			0
$511$	−29.6870	−	15.4726i	−1.31328	−	0.684466i
$512$	−14.1482	−	14.1482i	−0.625269	−	0.625269i
$513$		0			0
$514$	18.2123			0.803310
$515$	−4.87304	−	7.60272i	−0.214732	−	0.335016i
$516$		0			0
$517$	−44.2425	−	11.8547i	−1.94578	−	0.521371i
$518$	0.161865	+	0.0359678i	0.00711194	+	0.00158034i
$519$		0			0
$520$	−2.18413	−	0.477885i	−0.0957806	−	0.0209567i
$521$			41.4003i			1.81378i	0.421367	+	0.906890i	$0.361550\pi$
$521$			41.4003i			1.81378i	−0.421367	+	0.906890i	$0.638450\pi$
$522$		0			0
$523$	4.38267	+	4.38267i	0.191641	+	0.191641i	0.796405	−	0.604764i	$-0.206733\pi$
$523$	4.38267	+	4.38267i	0.191641	+	0.191641i	−0.604764	+	0.796405i	$0.706733\pi$
$524$	0.759049	−	1.31471i	0.0331592	−	0.0574335i
$525$		0			0
$526$	0.374338	+	0.648373i	0.0163219	+	0.0282704i
$527$	−1.08040	+	4.03211i	−0.0470630	+	0.175642i
$528$		0			0
$529$	16.1686	+	9.33493i	0.702981	+	0.405866i
$530$	−12.2024	−	38.3315i	−0.530038	−	1.66501i
$531$		0			0
$532$	−0.902489	+	0.983926i	−0.0391279	+	0.0426586i
$533$	1.08445	+	4.04721i	0.0469726	+	0.175304i
$534$		0			0
$535$	−6.94342	+	0.322375i	−0.300190	+	0.0139375i
$536$	−5.38869	−	9.33349i	−0.232756	−	0.403145i
$537$		0			0
$538$	−7.28744	+	1.95266i	−0.314184	+	0.0841853i
$539$	−2.35789	−	27.2585i	−0.101562	−	1.17411i
$540$		0			0
$541$	23.6955			1.01875			0.509374	−	0.860545i	$-0.329877\pi$
$541$	23.6955			1.01875			0.509374	+	0.860545i	$0.329877\pi$
$542$	−0.00811333	−	0.0302794i	−0.000348497	−	0.00130061i
$543$		0			0
$544$	0.742601	+	1.28622i	0.0318387	+	0.0551463i
$545$	13.8099	+	12.5844i	0.591549	+	0.539056i
$546$		0			0
$547$	−21.1492	+	5.66691i	−0.904275	+	0.242300i	−0.680851	−	0.732422i	$-0.738390\pi$
$547$	−21.1492	+	5.66691i	−0.904275	+	0.242300i	−0.223424	+	0.974721i	$0.571723\pi$
$548$	0.490072	−	0.490072i	0.0209348	−	0.0209348i
$549$		0			0
$550$	28.1263	+	4.79937i	1.19931	+	0.204646i
$551$	15.2345	+	8.79562i	0.649010	+	0.374706i
$552$		0			0
$553$	9.41722	+	2.09259i	0.400461	+	0.0889859i
$554$	−14.3792	+	8.30185i	−0.610915	+	0.352712i
$555$		0			0
$556$	1.18626	+	0.684888i	0.0503086	+	0.0290457i
$557$	22.0540	+	22.0540i	0.934458	+	0.934458i	0.997980	−	0.0635225i	$-0.0202335\pi$
$557$	22.0540	+	22.0540i	0.934458	+	0.934458i	−0.0635225	+	0.997980i	$0.520233\pi$
$558$		0			0
$559$	0.173214			0.00732615
$560$	−14.4544	−	20.5435i	−0.610808	−	0.868120i
$561$		0			0
$562$	4.59361	−	17.1436i	0.193770	−	0.723158i
$563$	0.997144	−	3.72139i	0.0420246	−	0.156838i	−0.941725	−	0.336384i	$-0.890796\pi$
$563$	0.997144	−	3.72139i	0.0420246	−	0.156838i	0.983750	+	0.179546i	$0.0574628\pi$
$564$		0			0
$565$	−25.1499	+	16.1201i	−1.05806	+	0.678176i
$566$		−	38.8061i		−	1.63114i
$567$		0			0
$568$	−4.09995	+	4.09995i	−0.172030	+	0.172030i
$569$	−10.4167	−	6.01410i	−0.436692	−	0.252124i	0.265502	−	0.964110i	$-0.414462\pi$
$569$	−10.4167	−	6.01410i	−0.436692	−	0.252124i	−0.702193	+	0.711986i	$0.747796\pi$
$570$		0			0
$571$	15.7271	+	27.2401i	0.658158	+	1.13996i	0.981092	+	0.193541i	$0.0619973\pi$
$571$	15.7271	+	27.2401i	0.658158	+	1.13996i	−0.322935	+	0.946421i	$0.604669\pi$
$572$	0.182115	+	0.0487975i	0.00761459	+	0.00204032i
$573$		0			0
$574$	−20.4081	+	39.1567i	−0.851816	+	1.63437i
$575$	−5.42900	+	31.8162i	−0.226405	+	1.32683i
$576$		0			0
$577$	22.5174	−	22.5174i	0.937411	−	0.937411i	−0.0607420	−	0.998153i	$-0.519347\pi$
$577$	22.5174	−	22.5174i	0.937411	−	0.937411i	0.998153	+	0.0607420i	$0.0193467\pi$
$578$	−4.91504	−	18.3432i	−0.204439	−	0.762976i
$579$		0			0
$580$	0.909245	−	0.997786i	0.0377543	−	0.0414308i
$581$	−30.4527	+	19.3795i	−1.26339	+	0.803999i
$582$		0			0
$583$	−12.4651	−	46.5205i	−0.516253	−	1.92668i
$584$	−34.5161			−1.42829
$585$		0			0
$586$			33.6910i			1.39176i
$587$	1.69351	+	6.32026i	0.0698986	+	0.260865i	0.992028	−	0.126016i	$-0.0402191\pi$
$587$	1.69351	+	6.32026i	0.0698986	+	0.260865i	−0.922130	+	0.386881i	$0.873552\pi$
$588$		0			0
$589$	−6.93739	+	4.00530i	−0.285850	+	0.165036i
$590$	31.9953	−	1.48550i	1.31722	−	0.0611571i
$591$		0			0
$592$	0.176047	−	0.0471716i	0.00723548	−	0.00193874i
$593$	−25.4392	−	25.4392i	−1.04466	−	1.04466i	−0.998955	−	0.0457067i	$-0.985446\pi$
$593$	−25.4392	−	25.4392i	−1.04466	−	1.04466i	−0.0457067	−	0.998955i	$-0.514554\pi$
$594$		0			0
$595$	−4.06851	−	11.0996i	−0.166793	−	0.455039i
$596$	0.0485668	−	0.0841201i	0.00198937	−	0.00344570i
$597$		0			0
$598$	−0.894100	+	3.33683i	−0.0365625	+	0.136453i
$599$	−38.3139	+	22.1205i	−1.56546	+	0.903820i	−0.568775	+	0.822493i	$0.692583\pi$
$599$	−38.3139	+	22.1205i	−1.56546	+	0.903820i	−0.996687	+	0.0813272i	$0.974084\pi$
$600$		0			0
$601$	15.6353	+	9.02705i	0.637778	+	0.368221i	0.783758	−	0.621066i	$-0.213300\pi$
$601$	15.6353	+	9.02705i	0.637778	+	0.368221i	−0.145980	+	0.989288i	$0.546634\pi$
$602$	1.34522	+	1.23388i	0.0548271	+	0.0502892i
$603$		0			0
$604$		−	2.67863i		−	0.108992i
$605$	9.34311	+	2.04426i	0.379851	+	0.0831109i
$606$		0			0
$607$	−37.3229	−	10.0006i	−1.51489	−	0.405913i	−0.596833	−	0.802365i	$-0.703575\pi$
$607$	−37.3229	−	10.0006i	−1.51489	−	0.405913i	−0.918055	+	0.396452i	$0.870241\pi$
$608$	−0.737663	+	2.75300i	−0.0299162	+	0.111649i
$609$		0			0
$610$	18.2517	−	11.6986i	0.738990	−	0.473663i
$611$	4.29536			0.173772
$612$		0			0
$613$	−23.5939	+	23.5939i	−0.952949	+	0.952949i	−0.998942	−	0.0459926i	$-0.985355\pi$
$613$	−23.5939	+	23.5939i	−0.952949	+	0.952949i	0.0459926	+	0.998942i	$0.485355\pi$
$614$	15.1023	−	26.1579i	0.609478	−	1.05565i
$615$		0			0
$616$	−15.1452	−	23.7990i	−0.610219	−	0.958889i
$617$	4.85497	−	18.1190i	0.195454	−	0.729444i	−0.796695	−	0.604382i	$-0.793420\pi$
$617$	4.85497	−	18.1190i	0.195454	−	0.729444i	0.992149	−	0.125062i	$-0.0399131\pi$
$618$		0			0
$619$	6.29505	−	10.9033i	0.253019	−	0.438243i	−0.711336	−	0.702852i	$-0.751910\pi$
$619$	6.29505	−	10.9033i	0.253019	−	0.438243i	0.964356	+	0.264609i	$0.0852430\pi$
$620$	0.186469	+	0.585758i	0.00748878	+	0.0235246i
$621$		0			0
$622$	15.4468	−	15.4468i	0.619362	−	0.619362i
$623$	−2.54065	+	0.799694i	−0.101789	+	0.0320391i
$624$		0			0
$625$	−24.5707	+	4.61296i	−0.982829	+	0.184518i
$626$	16.3770	−	9.45525i	0.654556	−	0.377908i
$627$		0			0
$628$	−1.21477	+	0.325497i	−0.0484746	+	0.0129887i
$629$	0.0857758			0.00342011
$630$		0			0
$631$	0.280570			0.0111693			0.00558466	−	0.999984i	$-0.498222\pi$
$631$	0.280570			0.0111693			0.00558466	+	0.999984i	$0.498222\pi$
$632$	9.60740	−	2.57430i	0.382162	−	0.102400i
$633$		0			0
$634$	32.9136	−	19.0027i	1.30717	−	0.754693i
$635$	29.0125	−	1.34701i	1.15133	−	0.0534546i
$636$		0			0
$637$	0.875195	+	2.41193i	0.0346765	+	0.0955641i
$638$	18.5111	−	18.5111i	0.732861	−	0.732861i
$639$		0			0
$640$	−24.4313	−	12.6325i	−0.965733	−	0.499343i
$641$	3.24741	−	5.62468i	0.128265	−	0.222162i	−0.794739	−	0.606951i	$-0.792393\pi$
$641$	3.24741	−	5.62468i	0.128265	−	0.222162i	0.923004	+	0.384789i	$0.125726\pi$
$642$		0			0
$643$	−3.51060	+	13.1017i	−0.138445	+	0.516683i	0.861515	+	0.507732i	$0.169516\pi$
$643$	−3.51060	+	13.1017i	−0.138445	+	0.516683i	−0.999960	+	0.00895086i	$0.997151\pi$
$644$	−1.89617	+	1.20669i	−0.0747196	+	0.0475502i
$645$		0			0
$646$	−5.59365	+	9.68849i	−0.220079	+	0.381188i
$647$	22.4871	−	22.4871i	0.884059	−	0.884059i	−0.109886	−	0.993944i	$-0.535048\pi$
$647$	22.4871	−	22.4871i	0.884059	−	0.884059i	0.993944	+	0.109886i	$0.0350484\pi$
$648$		0			0
$649$	38.3475			1.50527
$650$	−2.66426	+	0.247931i	−0.104501	+	0.00972465i
$651$		0			0
$652$	−0.334509	+	1.24840i	−0.0131004	+	0.0488913i
$653$	23.4308	+	6.27826i	0.916917	+	0.245687i	0.686267	−	0.727350i	$-0.259248\pi$
$653$	23.4308	+	6.27826i	0.916917	+	0.245687i	0.230650	+	0.973037i	$0.425915\pi$
$654$		0			0
$655$	−5.51343	+	25.1987i	−0.215428	+	0.984594i
$656$			48.5348i			1.89497i
$657$		0			0
$658$	33.3589	+	30.5979i	1.30047	+	1.19283i
$659$	15.5047	+	8.95163i	0.603977	+	0.348706i	0.770604	−	0.637314i	$-0.219954\pi$
$659$	15.5047	+	8.95163i	0.603977	+	0.348706i	−0.166628	+	0.986020i	$0.553288\pi$
$660$		0			0
$661$	−13.2369	+	7.64232i	−0.514855	+	0.297252i	−0.734827	−	0.678254i	$-0.762737\pi$
$661$	−13.2369	+	7.64232i	−0.514855	+	0.297252i	0.219972	+	0.975506i	$0.429403\pi$
$662$	−2.41099	+	8.99794i	−0.0937058	+	0.349715i
$663$		0			0
$664$	−18.6082	+	32.2304i	−0.722139	+	1.25078i
$665$	9.54079	−	20.5823i	0.369976	−	0.798146i
$666$		0			0
$667$	20.9396	+	20.9396i	0.810784	+	0.810784i
$668$	−2.32605	+	0.623262i	−0.0899974	+	0.0241147i
$669$		0			0
$670$	−9.53357	−	8.68758i	−0.368314	−	0.335631i
$671$	22.4779	−	12.9776i	0.867749	−	0.500995i
$672$		0			0
$673$	2.43720	+	9.09576i	0.0939472	+	0.350616i	0.996858	−	0.0792128i	$-0.0252407\pi$
$673$	2.43720	+	9.09576i	0.0939472	+	0.350616i	−0.902911	+	0.429829i	$0.858574\pi$
$674$		−	3.74012i		−	0.144064i
$675$		0			0
$676$	1.69311			0.0651195
$677$	−8.13234	−	30.3503i	−0.312551	−	1.16646i	−0.926248	−	0.376915i	$-0.876985\pi$
$677$	−8.13234	−	30.3503i	−0.312551	−	1.16646i	0.613697	−	0.789542i	$-0.289682\pi$
$678$		0			0
$679$	−17.3237	−	27.2222i	−0.664823	−	1.04469i
$680$	−9.00913	−	8.20968i	−0.345484	−	0.314827i
$681$		0			0
$682$	3.08540	+	11.5149i	0.118146	+	0.440927i
$683$	−23.8050	+	23.8050i	−0.910874	+	0.910874i	−0.996341	−	0.0854672i	$-0.972762\pi$
$683$	−23.8050	+	23.8050i	−0.910874	+	0.910874i	0.0854672	+	0.996341i	$0.472762\pi$
$684$		0			0
$685$	−5.40879	+	10.4606i	−0.206659	+	0.399680i
$686$	−10.3843	+	24.9661i	−0.396475	+	0.953209i
$687$		0			0
$688$	1.93806	+	0.519302i	0.0738879	+	0.0197982i
$689$	2.25826	+	3.91143i	0.0860330	+	0.149013i
$690$		0			0
$691$	31.6309	+	18.2621i	1.20330	+	0.694724i	0.961287	−	0.275549i	$-0.0888598\pi$
$691$	31.6309	+	18.2621i	1.20330	+	0.694724i	0.242011	+	0.970274i	$0.422193\pi$
$692$	1.43439	−	1.43439i	0.0545274	−	0.0545274i
$693$		0			0
$694$			11.9920i			0.455211i
$695$	−22.7367	−	4.97475i	−0.862451	−	0.188703i
$696$		0			0
$697$	−5.91194	+	22.0637i	−0.223931	+	0.835721i
$698$	6.06904	−	22.6500i	0.229716	−	0.857313i
$699$		0			0
$700$	−1.38646	−	1.05282i	−0.0524033	−	0.0397929i
$701$	−18.2879			−0.690725			−0.345363	−	0.938469i	$-0.612244\pi$
$701$	−18.2879			−0.690725			−0.345363	+	0.938469i	$0.612244\pi$
$702$		0			0
$703$	0.116393	+	0.116393i	0.00438984	+	0.00438984i
$704$	−25.0710	−	14.4748i	−0.944900	−	0.545538i
$705$		0			0
$706$	7.94182	−	4.58521i	0.298894	−	0.172567i
$707$	15.8813	+	3.52896i	0.597277	+	0.132720i
$708$		0			0
$709$	−7.14195	−	4.12341i	−0.268222	−	0.154858i	0.359858	−	0.933007i	$-0.382825\pi$
$709$	−7.14195	−	4.12341i	−0.268222	−	0.154858i	−0.628079	+	0.778149i	$0.716159\pi$
$710$	−3.18715	+	6.16396i	−0.119611	+	0.231329i
$711$		0			0
$712$	−1.94185	+	1.94185i	−0.0727740	+	0.0727740i
$713$	−13.0255	+	3.49018i	−0.487810	+	0.130708i
$714$		0			0
$715$	−3.20011	+	0.148577i	−0.119677	+	0.00555647i
$716$	−0.186973	−	0.323846i	−0.00698750	−	0.0121027i
$717$		0			0
$718$	11.0310	+	41.1682i	0.411673	+	1.53638i
$719$	25.4661			0.949724			0.474862	−	0.880060i	$-0.342498\pi$
$719$	25.4661			0.949724			0.474862	+	0.880060i	$0.342498\pi$
$720$		0			0
$721$	0.460838	+	10.6750i	0.0171625	+	0.397556i
$722$	6.05779	−	1.62318i	0.225448	−	0.0604085i
$723$		0			0
$724$	−1.33536	−	2.31290i	−0.0496281	−	0.0859584i
$725$	−9.57873	+	20.8415i	−0.355745	+	0.774033i
$726$		0			0
$727$	−5.30055	−	19.7819i	−0.196586	−	0.733671i	−0.991850	−	0.127407i	$-0.959334\pi$
$727$	−5.30055	−	19.7819i	−0.196586	−	0.733671i	0.795264	−	0.606263i	$-0.207332\pi$
$728$	1.94955	+	1.78819i	0.0722550	+	0.0662747i
$729$		0			0
$730$	−39.3619	+	12.5304i	−1.45685	+	0.463771i
$731$	0.817776	+	0.472143i	0.0302466	+	0.0174629i
$732$		0			0
$733$	5.56254	−	20.7597i	0.205457	−	0.766776i	−0.783853	−	0.620947i	$-0.786748\pi$
$733$	5.56254	−	20.7597i	0.205457	−	0.766776i	0.989310	−	0.145829i	$-0.0465850\pi$
$734$	−13.9527	−	24.1668i	−0.515004	−	0.892013i
$735$		0			0
$736$	−2.39893	+	4.15508i	−0.0884259	+	0.153158i
$737$	−10.9194	−	10.9194i	−0.402220	−	0.402220i
$738$		0			0
$739$			43.5443i			1.60180i	0.598796	+	0.800901i	$0.295646\pi$
$739$			43.5443i			1.60180i	−0.598796	+	0.800901i	$0.704354\pi$
$740$	0.0106345	−	0.00681630i	0.000390932	−	0.000250572i
$741$		0			0
$742$	−10.3247	+	46.4638i	−0.379030	+	1.70574i
$743$	−37.9631	−	10.1722i	−1.39273	−	0.373181i	−0.517002	−	0.855984i	$-0.672952\pi$
$743$	−37.9631	−	10.1722i	−1.39273	−	0.373181i	−0.875729	+	0.482803i	$0.839619\pi$
$744$		0			0
$745$	−0.352770	+	1.61230i	−0.0129245	+	0.0590703i
$746$	−54.6132			−1.99953
$747$		0			0
$748$	0.726789	+	0.726789i	0.0265740	+	0.0265740i
$749$	7.29329	+	3.80119i	0.266491	+	0.138892i
$750$		0			0
$751$	−12.6732	−	21.9506i	−0.462452	−	0.800990i	0.536631	−	0.843817i	$-0.319697\pi$
$751$	−12.6732	−	21.9506i	−0.462452	−	0.800990i	−0.999082	+	0.0428274i	$0.986363\pi$
$752$	48.0602	+	12.8777i	1.75258	+	0.469601i
$753$		0			0
$754$	−1.22750	+	2.12609i	−0.0447028	+	0.0774276i
$755$	13.8062	+	43.3695i	0.502457	+	1.57838i
$756$		0			0
$757$	−2.86625	−	2.86625i	−0.104176	−	0.104176i	0.653098	−	0.757273i	$-0.273469\pi$
$757$	−2.86625	−	2.86625i	−0.104176	−	0.104176i	−0.757273	+	0.653098i	$0.773469\pi$
$758$	7.97221	+	29.7527i	0.289564	+	1.08067i
$759$		0			0
$760$	−1.08481	−	23.3649i	−0.0393500	−	0.847536i
$761$	−13.3875	+	7.72926i	−0.485295	+	0.280185i	−0.722621	−	0.691245i	$-0.757063\pi$
$761$	−13.3875	+	7.72926i	−0.485295	+	0.280185i	0.237325	+	0.971430i	$0.423729\pi$
$762$		0			0
$763$	−6.63731	−	21.0869i	−0.240287	−	0.763397i
$764$			1.61504i			0.0584301i
$765$		0			0
$766$		−	5.94052i		−	0.214640i
$767$	−3.47364	+	0.930760i	−0.125426	+	0.0336078i
$768$		0			0
$769$	−7.41964	−	12.8512i	−0.267559	−	0.463426i	0.700672	−	0.713484i	$-0.252884\pi$
$769$	−7.41964	−	12.8512i	−0.267559	−	0.463426i	−0.968231	+	0.250058i	$0.919550\pi$
$770$	−25.9113	−	21.6420i	−0.933778	−	0.779924i
$771$		0			0
$772$	−1.02816	+	0.275494i	−0.0370043	+	0.00991526i
$773$	−6.14208	−	6.14208i	−0.220915	−	0.220915i	0.587969	−	0.808884i	$-0.299928\pi$
$773$	−6.14208	−	6.14208i	−0.220915	−	0.220915i	−0.808884	+	0.587969i	$0.799928\pi$
$774$		0			0
$775$	−6.03821	−	8.52286i	−0.216899	−	0.306150i
$776$	−28.8113	−	16.6342i	−1.03427	−	0.597134i
$777$		0			0
$778$	−43.7812	−	11.7311i	−1.56963	−	0.420582i
$779$	−37.9613	+	21.9170i	−1.36010	+	0.785257i
$780$		0			0
$781$	−4.15397	+	7.19488i	−0.148641	+	0.257453i
$782$	−13.3167	+	13.3167i	−0.476204	+	0.476204i
$783$		0			0
$784$	2.56136	+	29.6106i	0.0914770	+	1.05752i
$785$	17.9906	−	11.5312i	0.642111	−	0.411568i
$786$		0			0
$787$	45.4416	+	12.1760i	1.61982	+	0.434029i	0.950948	−	0.309352i	$-0.100112\pi$
$787$	45.4416	+	12.1760i	1.61982	+	0.434029i	0.668869	+	0.743380i	$0.266779\pi$
$788$	0.274017	+	0.0734228i	0.00976147	+	0.00261558i
$789$		0			0
$790$	10.0217	−	6.42349i	0.356555	−	0.228537i
$791$	35.3128	−	1.52446i	1.25558	−	0.0542035i
$792$		0			0
$793$	−1.72113	+	1.72113i	−0.0611191	+	0.0611191i
$794$	−4.58186	+	7.93602i	−0.162604	+	0.281639i
$795$		0			0
$796$	−1.29394	+	0.747055i	−0.0458624	+	0.0264787i
$797$	18.6147	+	4.98780i	0.659367	+	0.176677i	0.572960	−	0.819583i	$-0.305795\pi$
$797$	18.6147	+	4.98780i	0.659367	+	0.176677i	0.0864066	+	0.996260i	$0.472462\pi$
$798$		0			0
$799$	20.2793	+	11.7083i	0.717430	+	0.414208i
$800$	−3.66332	−	0.625096i	−0.129518	−	0.0221005i
$801$		0			0
$802$	−39.5218	−	39.5218i	−1.39556	−	1.39556i
$803$	−47.7711	+	12.8002i	−1.68581	+	0.451710i
$804$		0			0
$805$	24.4813	−	29.3106i	0.862851	−	1.03306i
$806$	−0.558971	−	0.968166i	−0.0196889	−	0.0341022i
$807$		0			0
$808$	16.2020	−	4.34132i	0.569985	−	0.152727i
$809$			27.6394i			0.971751i	0.874028	+	0.485876i	$0.161499\pi$
$809$			27.6394i			0.971751i	−0.874028	+	0.485876i	$0.838501\pi$
$810$		0			0
$811$		−	13.5840i		−	0.476997i	−0.971143	−	0.238499i	$-0.923345\pi$
$811$		−	13.5840i		−	0.476997i	0.971143	−	0.238499i	$-0.0766552\pi$
$812$	−1.52356	+	0.479557i	−0.0534666	+	0.0168292i
$813$		0			0
$814$	0.212140	−	0.122479i	0.00743550	−	0.00429289i
$815$	−1.01850	−	21.9369i	−0.0356766	−	0.768417i
$816$		0			0
$817$	0.469004	+	1.75035i	0.0164084	+	0.0612369i
$818$	31.1016	+	31.1016i	1.08744	+	1.08744i
$819$		0			0
$820$	1.02036	+	3.20526i	0.0356324	+	0.111933i
$821$	4.88248	−	8.45670i	0.170400	−	0.295141i	−0.768160	−	0.640258i	$-0.778827\pi$
$821$	4.88248	−	8.45670i	0.170400	−	0.295141i	0.938560	+	0.345117i	$0.112161\pi$
$822$		0			0
$823$	−41.1250	−	11.0194i	−1.43353	−	0.384113i	−0.543266	−	0.839561i	$-0.682812\pi$
$823$	−41.1250	−	11.0194i	−1.43353	−	0.384113i	−0.890262	+	0.455448i	$0.849479\pi$
$824$	5.50825	+	9.54058i	0.191889	+	0.332362i
$825$		0			0
$826$	−33.6074	−	17.5159i	−1.16935	−	0.609454i
$827$	35.2828	+	35.2828i	1.22690	+	1.22690i	0.965129	+	0.261774i	$0.0843075\pi$
$827$	35.2828	+	35.2828i	1.22690	+	1.22690i	0.261774	+	0.965129i	$0.415693\pi$
$828$		0			0
$829$	−30.6110			−1.06316			−0.531582	−	0.847007i	$-0.678402\pi$
$829$	−30.6110			−1.06316			−0.531582	+	0.847007i	$0.678402\pi$
$830$	−9.52007	+	43.5107i	−0.330446	+	1.51028i
$831$		0			0
$832$	2.62234	+	0.702654i	0.0909133	+	0.0243601i
$833$	−2.44243	+	13.7728i	−0.0846253	+	0.477199i
$834$		0			0
$835$	34.4484	−	22.0801i	1.19214	−	0.764112i
$836$			1.97242i			0.0682176i
$837$		0			0
$838$	10.7155	+	10.7155i	0.370160	+	0.370160i
$839$	8.60220	−	14.8995i	0.296981	−	0.514386i	−0.678463	−	0.734635i	$-0.737354\pi$
$839$	8.60220	−	14.8995i	0.296981	−	0.514386i	0.975444	+	0.220249i	$0.0706868\pi$
$840$		0			0
$841$	−3.97761	−	6.88943i	−0.137159	−	0.237567i
$842$	7.03182	−	26.2431i	0.242333	−	0.904397i
$843$		0			0
$844$	−0.202323	−	0.116811i	−0.00696425	−	0.00402081i
$845$	−27.4130	+	8.72660i	−0.943035	+	0.300204i
$846$		0			0
$847$	−8.33961	−	7.64936i	−0.286552	−	0.262835i
$848$	13.5407	+	50.5348i	0.464991	+	1.73537i
$849$		0			0
$850$	−13.2543	−	6.09167i	−0.454619	−	0.208943i
$851$	0.138547	+	0.239971i	0.00474934	+	0.00822610i
$852$		0			0
$853$	15.8076	−	4.23563i	0.541241	−	0.145025i	0.0221670	−	0.999754i	$-0.492943\pi$
$853$	15.8076	−	4.23563i	0.541241	−	0.145025i	0.519074	+	0.854729i	$0.326277\pi$
$854$	−25.6272	+	1.10633i	−0.876943	+	0.0378577i
$855$		0			0
$856$	8.47967			0.289829
$857$	0.927430	+	3.46122i	0.0316804	+	0.118233i	0.979955	−	0.199217i	$-0.0638400\pi$
$857$	0.927430	+	3.46122i	0.0316804	+	0.118233i	−0.948275	+	0.317450i	$0.897173\pi$
$858$		0			0
$859$	−8.69388	−	15.0582i	−0.296631	−	0.513781i	0.678732	−	0.734386i	$-0.262530\pi$
$859$	−8.69388	−	15.0582i	−0.296631	−	0.513781i	−0.975363	+	0.220606i	$0.929197\pi$
$860$	0.138908	−	0.00644931i	0.00473671	−	0.000219920i
$861$		0			0
$862$	35.7082	−	9.56800i	1.21623	−	0.325887i
$863$	4.87607	−	4.87607i	0.165984	−	0.165984i	−0.619228	−	0.785211i	$-0.712554\pi$
$863$	4.87607	−	4.87607i	0.165984	−	0.165984i	0.785211	+	0.619228i	$0.212554\pi$
$864$		0			0
$865$	−15.8310	+	30.6173i	−0.538270	+	1.04102i
$866$	−24.8854	−	14.3676i	−0.845642	−	0.488231i
$867$		0			0
$868$	0.157775	−	0.710031i	0.00535523	−	0.0241000i
$869$	12.3422	−	7.12576i	0.418680	−	0.241725i
$870$		0			0
$871$	1.25414	+	0.724080i	0.0424950	+	0.0245345i
$872$	−16.1170	−	16.1170i	−0.545791	−	0.545791i
$873$		0			0
$874$	−36.1400			−1.22245
$875$	27.8745	+	9.90007i	0.942331	+	0.334683i
$876$		0			0
$877$	−11.9166	+	44.4733i	−0.402394	+	1.50176i	0.406417	+	0.913688i	$0.366778\pi$
$877$	−11.9166	+	44.4733i	−0.402394	+	1.50176i	−0.808811	+	0.588068i	$0.799889\pi$
$878$	−11.1362	+	41.5610i	−0.375830	+	1.40262i
$879$		0			0
$880$	−36.2510	−	7.93167i	−1.22202	−	0.267377i
$881$		−	23.7070i		−	0.798708i	−0.916797	−	0.399354i	$-0.869234\pi$
$881$		−	23.7070i		−	0.798708i	0.916797	−	0.399354i	$-0.130766\pi$
$882$		0			0
$883$	10.8246	−	10.8246i	0.364276	−	0.364276i	−0.501109	−	0.865384i	$-0.667074\pi$
$883$	10.8246	−	10.8246i	0.364276	−	0.364276i	0.865384	+	0.501109i	$0.167074\pi$
$884$	−0.0834752	−	0.0481944i	−0.00280758	−	0.00162095i
$885$		0			0
$886$	11.1447	+	19.3032i	0.374413	+	0.648502i
$887$	3.90146	+	1.04539i	0.130998	+	0.0351009i	0.323722	−	0.946152i	$-0.395066\pi$
$887$	3.90146	+	1.04539i	0.130998	+	0.0351009i	−0.192724	+	0.981253i	$0.561732\pi$
$888$		0			0
$889$	−30.4744	−	15.8829i	−1.02208	−	0.532696i
$890$	−1.50952	+	2.91943i	−0.0505993	+	0.0978594i
$891$		0			0
$892$	1.85482	−	1.85482i	0.0621040	−	0.0621040i
$893$	11.6304	+	43.4053i	0.389197	+	1.45250i
$894$		0			0
$895$	4.69643	+	4.27968i	0.156984	+	0.143054i
$896$	17.4720	+	27.4552i	0.583698	+	0.917213i
$897$		0			0
$898$	1.15684	+	4.31738i	0.0386042	+	0.144073i
$899$	−9.58325			−0.319619
$900$		0			0
$901$			24.6222i			0.820284i
$902$	16.8833	+	63.0093i	0.562152	+	2.09798i
$903$		0			0
$904$	31.5603	−	18.2214i	1.04968	−	0.606033i
$905$	33.5418	+	30.5654i	1.11497	+	1.01603i
$906$		0			0
$907$	−21.2432	+	5.69211i	−0.705370	+	0.189003i	−0.593635	−	0.804735i	$-0.702308\pi$
$907$	−21.2432	+	5.69211i	−0.705370	+	0.189003i	−0.111735	+	0.993738i	$0.535641\pi$
$908$	−1.11955	−	1.11955i	−0.0371536	−	0.0371536i
$909$		0			0
$910$	2.87242	+	1.33149i	0.0952196	+	0.0441385i
$911$	4.61287	−	7.98972i	0.152831	−	0.264711i	−0.779436	−	0.626482i	$-0.784494\pi$
$911$	4.61287	−	7.98972i	0.152831	−	0.264711i	0.932267	+	0.361770i	$0.117828\pi$
$912$		0			0
$913$	−13.8016	+	51.5084i	−0.456767	+	1.70468i
$914$	5.81996	−	3.36016i	0.192507	−	0.111144i
$915$		0			0
$916$	−1.09111	−	0.629951i	−0.0360512	−	0.0208142i
$917$	20.6306	−	22.4922i	0.681282	−	0.742758i
$918$		0			0
$919$		−	29.1931i		−	0.962991i	−0.876449	−	0.481496i	$-0.840094\pi$
$919$		−	29.1931i		−	0.962991i	0.876449	−	0.481496i	$-0.159906\pi$
$920$	8.41606	−	38.4649i	0.277469	−	1.26815i
$921$		0			0
$922$	51.4196	+	13.7779i	1.69342	+	0.453749i
$923$	0.201648	−	0.752559i	0.00663731	−	0.0247708i
$924$		0			0
$925$	−0.137050	+	0.165174i	−0.00450618	+	0.00543090i
$926$	−39.3663			−1.29366
$927$		0			0
$928$	−2.41098	+	2.41098i	−0.0791444	+	0.0791444i
$929$	18.9546	−	32.8304i	0.621882	−	1.07713i	−0.367253	−	0.930121i	$-0.619702\pi$
$929$	18.9546	−	32.8304i	0.621882	−	1.07713i	0.989135	−	0.147010i	$-0.0469649\pi$
$930$		0			0
$931$	−22.0031	+	15.3747i	−0.721124	+	0.503884i
$932$	−0.306962	+	1.14560i	−0.0100549	+	0.0375253i
$933$		0			0
$934$	27.3706	−	47.4073i	0.895593	−	1.55121i
$935$	−15.5134	−	8.02137i	−0.507342	−	0.262327i
$936$		0			0
$937$	38.2007	−	38.2007i	1.24796	−	1.24796i	0.291343	−	0.956619i	$-0.405898\pi$
$937$	38.2007	−	38.2007i	1.24796	−	1.24796i	0.956619	−	0.291343i	$-0.0941022\pi$
$938$	4.58204	+	14.5572i	0.149609	+	0.475311i
$939$		0			0
$940$	3.44465	−	0.159931i	0.112352	−	0.00521636i
$941$	−24.9324	+	14.3947i	−0.812774	+	0.469255i	−0.847918	−	0.530127i	$-0.822144\pi$
$941$	−24.9324	+	14.3947i	−0.812774	+	0.469255i	0.0351445	+	0.999382i	$0.488811\pi$
$942$		0			0
$943$	−71.2755	+	19.0982i	−2.32105	+	0.621924i
$944$	−41.6565			−1.35580
$945$		0			0
$946$	2.69669			0.0876769
$947$	25.9839	−	6.96236i	0.844363	−	0.226246i	0.189393	−	0.981901i	$-0.439348\pi$
$947$	25.9839	−	6.96236i	0.844363	−	0.226246i	0.654970	+	0.755655i	$0.272681\pi$
$948$		0			0
$949$	4.01657	−	2.31897i	0.130384	−	0.0752770i
$950$	−9.71929	−	26.2514i	−0.315336	−	0.851708i
$951$		0			0
$952$	4.32998	+	13.7565i	0.140336	+	0.445849i
$953$	20.7929	−	20.7929i	0.673548	−	0.673548i	−0.284984	−	0.958532i	$-0.591988\pi$
$953$	20.7929	−	20.7929i	0.673548	−	0.673548i	0.958532	+	0.284984i	$0.0919884\pi$
$954$		0			0
$955$	−8.32422	−	26.1490i	−0.269365	−	0.846161i
$956$	−0.383940	+	0.665003i	−0.0124175	+	0.0215077i
$957$		0			0
$958$	−3.20478	+	11.9604i	−0.103542	+	0.386423i
$959$	11.7553	−	7.48088i	0.379600	−	0.241570i
$960$		0			0
$961$	−13.3180	+	23.0675i	−0.429613	+	0.744112i
$962$	−0.0162435	+	0.0162435i	−0.000523713	+	0.000523713i
$963$		0			0
$964$	1.06644			0.0343477
$965$	15.2269	−	9.75983i	0.490171	−	0.314180i
$966$		0			0
$967$	8.10188	−	30.2366i	0.260539	−	0.972345i	−0.704386	−	0.709817i	$-0.748777\pi$
$967$	8.10188	−	30.2366i	0.260539	−	0.972345i	0.964925	−	0.262527i	$-0.0845559\pi$
$968$	−11.2701	−	3.01981i	−0.362234	−	0.0970604i
$969$		0			0
$970$	−38.8949	−	8.51015i	−1.24884	−	0.273245i
$971$			0.191830i			0.00615612i	0.999995	+	0.00307806i	$0.000979779\pi$
$971$			0.191830i			0.00615612i	−0.999995	+	0.00307806i	$0.999020\pi$
$972$		0			0
$973$	20.2946	+	18.6149i	0.650616	+	0.596766i
$974$	−4.74729	−	2.74085i	−0.152113	−	0.0878225i
$975$		0			0
$976$	−24.4175	+	14.0974i	−0.781585	+	0.451248i
$977$	8.29492	−	30.9571i	0.265378	−	0.990404i	−0.696640	−	0.717420i	$-0.745323\pi$
$977$	8.29492	−	30.9571i	0.265378	−	0.990404i	0.962019	−	0.272984i	$-0.0880106\pi$
$978$		0			0
$979$	−1.96744	+	3.40770i	−0.0628795	+	0.108911i
$980$	0.791662	+	1.90165i	0.0252887	+	0.0607459i
$981$		0			0
$982$	−4.16665	−	4.16665i	−0.132963	−	0.132963i
$983$	25.7930	−	6.91122i	0.822670	−	0.220434i	0.177156	−	0.984183i	$-0.443310\pi$
$983$	25.7930	−	6.91122i	0.822670	−	0.220434i	0.645513	+	0.763749i	$0.276643\pi$
$984$		0			0
$985$	−4.81503	+	0.223556i	−0.153420	+	0.00712308i
$986$	−11.5905	+	6.69180i	−0.369118	+	0.213110i
$987$		0			0
$988$	−0.0478740	−	0.178668i	−0.00152307	−	0.00568419i
$989$			3.05047i			0.0969993i
$990$		0			0
$991$	−57.6436			−1.83111			−0.915554	−	0.402194i	$-0.868248\pi$
$991$	−57.6436			−1.83111			−0.915554	+	0.402194i	$0.868248\pi$
$992$	−0.401859	−	1.49976i	−0.0127591	−	0.0476174i
$993$		0			0
$994$	6.92688	−	4.40814i	0.219707	−	0.139818i
$995$	17.0996	−	18.7647i	0.542093	−	0.594881i
$996$		0			0
$997$	7.64061	+	28.5152i	0.241981	+	0.903084i	0.974877	+	0.222744i	$0.0715014\pi$
$997$	7.64061	+	28.5152i	0.241981	+	0.903084i	−0.732896	+	0.680340i	$0.761832\pi$
$998$	7.19532	−	7.19532i	0.227764	−	0.227764i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.ce.a.937.11		176
3.2	odd	2		315.2.cb.a.97.34	yes	176
5.3	odd	4	inner	945.2.ce.a.748.33		176
7.6	odd	2	inner	945.2.ce.a.937.12		176
9.4	even	3	inner	945.2.ce.a.307.34		176
9.5	odd	6		315.2.cb.a.202.11	yes	176
15.8	even	4		315.2.cb.a.223.12	yes	176
21.20	even	2		315.2.cb.a.97.33	yes	176
35.13	even	4	inner	945.2.ce.a.748.34		176
45.13	odd	12	inner	945.2.ce.a.118.12		176
45.23	even	12		315.2.cb.a.13.33	✓	176
63.13	odd	6	inner	945.2.ce.a.307.33		176
63.41	even	6		315.2.cb.a.202.12	yes	176
105.83	odd	4		315.2.cb.a.223.11	yes	176
315.13	even	12	inner	945.2.ce.a.118.11		176
315.293	odd	12		315.2.cb.a.13.34	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.cb.a.13.33	✓	176	45.23	even	12
315.2.cb.a.13.34	yes	176	315.293	odd	12
315.2.cb.a.97.33	yes	176	21.20	even	2
315.2.cb.a.97.34	yes	176	3.2	odd	2
315.2.cb.a.202.11	yes	176	9.5	odd	6
315.2.cb.a.202.12	yes	176	63.41	even	6
315.2.cb.a.223.11	yes	176	105.83	odd	4
315.2.cb.a.223.12	yes	176	15.8	even	4
945.2.ce.a.118.11		176	315.13	even	12	inner
945.2.ce.a.118.12		176	45.13	odd	12	inner
945.2.ce.a.307.33		176	63.13	odd	6	inner
945.2.ce.a.307.34		176	9.4	even	3	inner
945.2.ce.a.748.33		176	5.3	odd	4	inner
945.2.ce.a.748.34		176	35.13	even	4	inner
945.2.ce.a.937.11		176	1.1	even	1	trivial
945.2.ce.a.937.12		176	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.ce (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41025 + 0.377876i) q^{2} +(0.113968 - 0.0657996i) q^{4} +(-1.50611 + 1.65277i) q^{5} +(2.52369 - 0.794356i) q^{7} +(1.92889 - 1.92889i) q^{8} +O(q^{10})\)	\(q+(-1.41025 + 0.377876i) q^{2} +(0.113968 - 0.0657996i) q^{4} +(-1.50611 + 1.65277i) q^{5} +(2.52369 - 0.794356i) q^{7} +(1.92889 - 1.92889i) q^{8} +(1.49945 - 2.89994i) q^{10} +(1.95430 - 3.38495i) q^{11} +(-0.0948685 + 0.354054i) q^{13} +(-3.25887 + 2.07388i) q^{14} +(-2.12294 + 3.67704i) q^{16} +(-1.41297 + 1.41297i) q^{17} -3.83464 q^{19} +(-0.0628967 + 0.287464i) q^{20} +(-1.47697 + 5.51212i) q^{22} +(-6.23526 - 1.67073i) q^{23} +(-0.463289 - 4.97849i) q^{25} -0.535154i q^{26} +(0.235352 - 0.256589i) q^{28} +(-3.97286 - 2.29373i) q^{29} +(1.80914 - 1.04451i) q^{31} +(0.192368 - 0.717928i) q^{32} +(1.45872 - 2.52657i) q^{34} +(-2.48805 + 5.36746i) q^{35} +(-0.0303530 - 0.0303530i) q^{37} +(5.40781 - 1.44902i) q^{38} +(0.282896 + 6.09313i) q^{40} +(9.89957 - 5.71552i) q^{41} +(-0.122307 - 0.456457i) q^{43} -0.514369i q^{44} +9.42462 q^{46} +(-3.03299 - 11.3193i) q^{47} +(5.73800 - 4.00941i) q^{49} +(2.53460 + 6.84586i) q^{50} +(0.0124846 + 0.0465932i) q^{52} +(8.71292 - 8.71292i) q^{53} +(2.65116 + 8.32811i) q^{55} +(3.33569 - 6.40015i) q^{56} +(6.46947 + 1.73349i) q^{58} +(4.90552 + 8.49662i) q^{59} +(5.75087 + 3.32027i) q^{61} +(-2.15664 + 2.15664i) q^{62} -7.40661i q^{64} +(-0.442288 - 0.690039i) q^{65} +(1.02256 - 3.81623i) q^{67} +(-0.0680608 + 0.254006i) q^{68} +(1.48055 - 8.50964i) q^{70} -2.12555 q^{71} +(-8.94714 - 8.94714i) q^{73} +(0.0542751 + 0.0313357i) q^{74} +(-0.437027 + 0.252318i) q^{76} +(2.24319 - 10.0950i) q^{77} +(3.15769 + 1.82309i) q^{79} +(-2.87992 - 9.04674i) q^{80} +(-11.8011 + 11.8011i) q^{82} +(-13.1782 + 3.53109i) q^{83} +(-0.207230 - 4.46340i) q^{85} +(0.344968 + 0.597502i) q^{86} +(-2.75957 - 10.2988i) q^{88} -1.00672 q^{89} +(0.0418267 + 0.968881i) q^{91} +(-0.820555 + 0.219867i) q^{92} +(8.55454 + 14.8169i) q^{94} +(5.77537 - 6.33777i) q^{95} +(-3.15650 - 11.7802i) q^{97} +(-6.57696 + 7.82253i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8}+O(q^{10}) \) 176 * q + 4 * q^2 - 2 * q^7 + 32 * q^8	\( 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8} + 12 q^{11} + 56 q^{16} + 12 q^{22} + 12 q^{23} - 4 q^{25} - 32 q^{28} - 48 q^{32} + 8 q^{35} - 16 q^{37} - 4 q^{43} - 80 q^{46} + 76 q^{50} - 64 q^{53} + 52 q^{56} - 44 q^{58} - 20 q^{65} - 4 q^{67} + 18 q^{70} + 64 q^{71} - 26 q^{77} - 4 q^{85} - 80 q^{86} - 60 q^{88} - 16 q^{91} + 68 q^{92} - 40 q^{95} + 120 q^{98}+O(q^{100}) \) 176 * q + 4 * q^2 - 2 * q^7 + 32 * q^8 + 12 * q^11 + 56 * q^16 + 12 * q^22 + 12 * q^23 - 4 * q^25 - 32 * q^28 - 48 * q^32 + 8 * q^35 - 16 * q^37 - 4 * q^43 - 80 * q^46 + 76 * q^50 - 64 * q^53 + 52 * q^56 - 44 * q^58 - 20 * q^65 - 4 * q^67 + 18 * q^70 + 64 * q^71 - 26 * q^77 - 4 * q^85 - 80 * q^86 - 60 * q^88 - 16 * q^91 + 68 * q^92 - 40 * q^95 + 120 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more