LMFDB - Embedded newform 945.2.ce.a.307.34

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			307.34
Character	$\chi$	$=$	945.307
Dual form			945.2.ce.a.748.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.377876 - 1.41025i) q^{2} +(-0.113968 - 0.0657996i) q^{4} +(2.18439 + 0.477942i) q^{5} +(-0.573911 + 2.58276i) q^{7} +(1.92889 - 1.92889i) q^{8} +O(q^{10})$	\(q+(0.377876 - 1.41025i) q^{2} +(-0.113968 - 0.0657996i) q^{4} +(2.18439 + 0.477942i) q^{5} +(-0.573911 + 2.58276i) q^{7} +(1.92889 - 1.92889i) q^{8} +(1.49945 - 2.89994i) q^{10} +(1.95430 + 3.38495i) q^{11} +(0.354054 - 0.0948685i) q^{13} +(3.42547 + 1.78532i) q^{14} +(-2.12294 - 3.67704i) q^{16} +(-1.41297 + 1.41297i) q^{17} -3.83464 q^{19} +(-0.217503 - 0.198202i) q^{20} +(5.51212 - 1.47697i) q^{22} +(1.67073 + 6.23526i) q^{23} +(4.54314 + 2.08803i) q^{25} -0.535154i q^{26} +(0.235352 - 0.256589i) q^{28} +(3.97286 - 2.29373i) q^{29} +(-1.80914 - 1.04451i) q^{31} +(-0.717928 + 0.192368i) q^{32} +(1.45872 + 2.52657i) q^{34} +(-2.48805 + 5.36746i) q^{35} +(-0.0303530 - 0.0303530i) q^{37} +(-1.44902 + 5.40781i) q^{38} +(5.13535 - 3.29156i) q^{40} +(-9.89957 - 5.71552i) q^{41} +(0.456457 + 0.122307i) q^{43} -0.514369i q^{44} +9.42462 q^{46} +(11.3193 + 3.03299i) q^{47} +(-6.34125 - 2.96454i) q^{49} +(4.66138 - 5.61796i) q^{50} +(-0.0465932 - 0.0124846i) q^{52} +(8.71292 - 8.71292i) q^{53} +(2.65116 + 8.32811i) q^{55} +(3.87484 + 6.08887i) q^{56} +(-1.73349 - 6.46947i) q^{58} +(4.90552 - 8.49662i) q^{59} +(-5.75087 + 3.32027i) q^{61} +(-2.15664 + 2.15664i) q^{62} -7.40661i q^{64} +(0.818735 - 0.0380128i) q^{65} +(-3.81623 + 1.02256i) q^{67} +(0.254006 - 0.0680608i) q^{68} +(6.62929 + 5.53701i) q^{70} -2.12555 q^{71} +(-8.94714 - 8.94714i) q^{73} +(-0.0542751 + 0.0313357i) q^{74} +(0.437027 + 0.252318i) q^{76} +(-9.86410 + 3.10483i) q^{77} +(-3.15769 + 1.82309i) q^{79} +(-2.87992 - 9.04674i) q^{80} +(-11.8011 + 11.8011i) q^{82} +(3.53109 - 13.1782i) q^{83} +(-3.76180 + 2.41116i) q^{85} +(0.344968 - 0.597502i) q^{86} +(10.2988 + 2.75957i) q^{88} -1.00672 q^{89} +(0.0418267 + 0.968881i) q^{91} +(0.219867 - 0.820555i) q^{92} +(8.55454 - 14.8169i) q^{94} +(-8.37636 - 1.83273i) q^{95} +(11.7802 + 3.15650i) q^{97} +(-6.57696 + 7.82253i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.377876	−	1.41025i	0.267198	−	0.997198i	−0.693692	−	0.720271i	$-0.744017\pi$
$2$	0.377876	−	1.41025i	0.267198	−	0.997198i	0.960891	−	0.276927i	$-0.0893160\pi$
$3$		0			0
$3$		0			0
$4$	−0.113968	−	0.0657996i	−0.0569841	−	0.0328998i
$5$	2.18439	+	0.477942i	0.976890	+	0.213742i
$5$	2.18439	+	0.477942i	0.976890	+	0.213742i
$6$		0			0
$7$	−0.573911	+	2.58276i	−0.216918	+	0.976190i
$7$	−0.573911	+	2.58276i	−0.216918	+	0.976190i
$8$	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	0.994332	+	0.106324i	$0.0339079\pi$
$11$	1.95430	+	3.38495i	0.589245	+	1.02060i	−0.405087	+	0.914278i	$0.632759\pi$
$12$		0			0
$13$	0.354054	−	0.0948685i	0.0981969	−	0.0263118i	−0.209386	−	0.977833i	$-0.567147\pi$
$13$	0.354054	−	0.0948685i	0.0981969	−	0.0263118i	0.307583	+	0.951521i	$0.400480\pi$
$14$	3.42547	+	1.78532i	0.915495	+	0.477147i
$15$		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	$0.644973\pi$
$20$	−0.217503	−	0.198202i	−0.0486351	−	0.0443194i
$21$		0			0
$22$	5.51212	−	1.47697i	1.17519	−	0.314891i
$23$	1.67073	+	6.23526i	0.348372	+	1.30014i	0.888623	+	0.458638i	$0.151663\pi$
$23$	1.67073	+	6.23526i	0.348372	+	1.30014i	−0.540251	+	0.841504i	$0.681671\pi$
$24$		0			0
$25$	4.54314	+	2.08803i	0.908629	+	0.417605i
$26$		−	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	$-0.526612\pi$
$29$	3.97286	−	2.29373i	0.737741	−	0.425935i	0.821247	+	0.570572i	$0.193279\pi$
$30$		0			0
$31$	−1.80914	−	1.04451i	−0.324931	−	0.187599i	0.328658	−	0.944449i	$-0.393404\pi$
$31$	−1.80914	−	1.04451i	−0.324931	−	0.187599i	−0.653588	+	0.756850i	$0.726737\pi$
$32$	−0.717928	+	0.192368i	−0.126913	+	0.0340062i
$33$		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	$0.751123\pi$
$38$	−1.44902	+	5.40781i	−0.235062	+	0.877262i
$39$		0			0
$40$	5.13535	−	3.29156i	0.811971	−	0.520441i
$41$	−9.89957	−	5.71552i	−1.54605	−	0.892614i	−0.998437	−	0.0558847i	$-0.982202\pi$
$41$	−9.89957	−	5.71552i	−1.54605	−	0.892614i	−0.547616	−	0.836730i	$-0.684465\pi$
$42$		0			0
$43$	0.456457	+	0.122307i	0.0696090	+	0.0186517i	0.293455	−	0.955973i	$-0.405195\pi$
$43$	0.456457	+	0.122307i	0.0696090	+	0.0186517i	−0.223846	+	0.974624i	$0.571861\pi$
$44$		−	0.514369i		−	0.0775441i
$45$		0			0
$46$	9.42462			1.38958
$47$	11.3193	+	3.03299i	1.65108	+	0.442406i	0.959916	−	0.280288i	$-0.0904301\pi$
$47$	11.3193	+	3.03299i	1.65108	+	0.442406i	0.691167	+	0.722695i	$0.257097\pi$
$48$		0			0
$49$	−6.34125	−	2.96454i	−0.905893	−	0.423506i
$50$	4.66138	−	5.61796i	0.659219	−	0.794500i
$51$		0			0
$52$	−0.0465932	−	0.0124846i	−0.00646132	−	0.00173130i
$53$	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
$56$	3.87484	+	6.08887i	0.517798	+	0.813659i
$57$		0			0
$58$	−1.73349	−	6.46947i	−0.227618	−	0.849483i
$59$	4.90552	−	8.49662i	0.638645	−	1.10617i	−0.347086	−	0.937833i	$-0.612829\pi$
$59$	4.90552	−	8.49662i	0.638645	−	1.10617i	0.985730	−	0.168332i	$-0.0538380\pi$
$60$		0			0
$61$	−5.75087	+	3.32027i	−0.736323	+	0.425116i	−0.820731	−	0.571315i	$-0.806434\pi$
$61$	−5.75087	+	3.32027i	−0.736323	+	0.425116i	0.0844077	+	0.996431i	$0.473100\pi$
$62$	−2.15664	+	2.15664i	−0.273894	+	0.273894i
$63$		0			0
$64$		−	7.40661i		−	0.925826i
$65$	0.818735	−	0.0380128i	0.101552	−	0.00471491i
$66$		0			0
$67$	−3.81623	+	1.02256i	−0.466227	+	0.124925i	−0.484282	−	0.874912i	$-0.660919\pi$
$67$	−3.81623	+	1.02256i	−0.466227	+	0.124925i	0.0180555	+	0.999837i	$0.494252\pi$
$68$	0.254006	−	0.0680608i	0.0308028	−	0.00825359i
$69$		0			0
$70$	6.62929	+	5.53701i	0.792351	+	0.661800i
$71$	−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
$77$	−9.86410	+	3.10483i	−1.12412	+	0.353828i
$78$		0			0
$79$	−3.15769	+	1.82309i	−0.355268	+	0.205114i	−0.667003	−	0.745055i	$-0.732423\pi$
$79$	−3.15769	+	1.82309i	−0.355268	+	0.205114i	0.311735	+	0.950169i	$0.399090\pi$
$80$	−2.87992	−	9.04674i	−0.321985	−	1.01146i
$81$		0			0
$82$	−11.8011	+	11.8011i	−1.30322	+	1.30322i
$83$	3.53109	−	13.1782i	0.387587	−	1.44649i	−0.446461	−	0.894803i	$-0.647316\pi$
$83$	3.53109	−	13.1782i	0.387587	−	1.44649i	0.834048	−	0.551692i	$-0.186018\pi$
$84$		0			0
$85$	−3.76180	+	2.41116i	−0.408024	+	0.261528i
$86$	0.344968	−	0.597502i	0.0371988	−	0.0644303i
$87$		0			0
$88$	10.2988	+	2.75957i	1.09786	+	0.294171i
$89$	−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
$92$	0.219867	−	0.820555i	0.0229227	−	0.0855488i
$93$		0			0
$94$	8.55454	−	14.8169i	0.882334	−	1.52825i
$95$	−8.37636	−	1.83273i	−0.859396	−	0.188035i
$96$		0			0
$97$	11.7802	+	3.15650i	1.19610	+	0.320494i	0.801294	−	0.598271i	$-0.204145\pi$
$97$	11.7802	+	3.15650i	1.19610	+	0.320494i	0.394806	+	0.918765i	$0.370812\pi$
$98$	−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	$-0.765632\pi$
$101$	−5.32516	+	3.07448i	−0.529873	+	0.305923i	0.211091	+	0.977466i	$0.432298\pi$
$102$		0			0
$103$	3.90090	−	1.04524i	0.384367	−	0.102991i	−0.0614609	−	0.998109i	$-0.519576\pi$
$103$	3.90090	−	1.04524i	0.384367	−	0.102991i	0.445828	+	0.895119i	$0.352909\pi$
$104$	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	$-0.131045\pi$
$110$	12.7465	−	0.591806i	1.21533	−	0.0564265i
$111$		0			0
$112$	10.7153	−	3.37274i	1.01250	−	0.318694i
$113$	−3.45767	−	12.9042i	−0.325271	−	1.21393i	−0.914040	−	0.405625i	$-0.867054\pi$
$113$	−3.45767	−	12.9042i	−0.325271	−	1.21393i	0.588769	−	0.808301i	$-0.299613\pi$
$114$		0			0
$115$	0.669446	+	14.4188i	0.0624261	+	1.34456i
$116$	−0.603705			−0.0560526
$117$		0			0
$118$	−10.1287	−	10.1287i	−0.932421	−	0.932421i
$119$	−2.83844	−	4.46028i	−0.260199	−	0.408873i
$120$		0			0
$121$	−2.13861	+	3.70417i	−0.194419	+	0.336743i
$122$	2.50930	+	9.36482i	0.227181	+	0.847851i
$123$		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	$0.945497\pi$
$128$	−11.8810	−	3.18351i	−1.05015	−	0.281386i
$129$		0			0
$130$	0.255772	−	1.16899i	0.0224327	−	0.102527i
$131$	−9.99028	−	5.76789i	−0.872855	−	0.503943i	−0.00455882	−	0.999990i	$-0.501451\pi$
$131$	−9.99028	−	5.76789i	−0.872855	−	0.503943i	−0.868296	+	0.496047i	$0.834784\pi$
$132$		0			0
$133$	2.20074	−	9.90394i	0.190828	−	0.858780i
$134$			5.76824i			0.498300i
$135$		0			0
$136$			5.45093i			0.467414i
$137$	−1.36307	+	5.08704i	−0.116455	+	0.434615i	−0.999392	−	0.0348765i	$-0.988896\pi$
$137$	−1.36307	+	5.08704i	−0.116455	+	0.434615i	0.882937	+	0.469492i	$0.155563\pi$
$138$		0			0
$139$	5.20435	−	9.01419i	0.441427	−	0.764574i	−0.556369	−	0.830936i	$-0.687806\pi$
$139$	5.20435	−	9.01419i	0.441427	−	0.764574i	0.997796	+	0.0663616i	$0.0211391\pi$
$140$	0.636735	−	0.448006i	0.0538139	−	0.0378635i
$141$		0			0
$142$	−0.803193	+	2.99756i	−0.0674025	+	0.251549i
$143$	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
$148$	0.00146206	+	0.00545649i	0.000120181	+	0.000448521i
$149$	−0.639215	−	0.369051i	−0.0523665	−	0.0302338i	0.473588	−	0.880746i	$-0.342959\pi$
$149$	−0.639215	−	0.369051i	−0.0523665	−	0.0302338i	−0.525955	+	0.850513i	$0.676292\pi$
$150$		0			0
$151$	10.1772	+	17.6275i	0.828211	+	1.43450i	0.899440	+	0.437044i	$0.143975\pi$
$151$	10.1772	+	17.6275i	0.828211	+	1.43450i	−0.0712291	+	0.997460i	$0.522692\pi$
$152$	−7.39660	+	7.39660i	−0.599944	+	0.599944i
$153$		0			0
$154$	0.651182	+	15.0841i	0.0524737	+	1.21551i
$155$	−3.45265	−	3.14627i	−0.277324	−	0.252715i
$156$		0			0
$157$	2.47340	+	9.23084i	0.197399	+	0.736701i	0.991633	+	0.129090i	$0.0412056\pi$
$157$	2.47340	+	9.23084i	0.197399	+	0.736701i	−0.794234	+	0.607612i	$0.792128\pi$
$158$	1.37781	+	5.14204i	0.109612	+	0.409079i
$159$		0			0
$160$	−1.66018	+	0.0770800i	−0.131249	+	0.00609371i
$161$	−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
$167$	4.73607	+	17.6752i	0.366488	+	1.36775i	0.865393	+	0.501095i	$0.167069\pi$
$167$	4.73607	+	17.6752i	0.366488	+	1.36775i	−0.498905	+	0.866657i	$0.666264\pi$
$168$		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
$173$	−3.98957	+	14.8893i	−0.303321	+	1.13201i	0.631059	+	0.775735i	$0.282621\pi$
$173$	−3.98957	+	14.8893i	−0.303321	+	1.13201i	−0.934381	+	0.356276i	$0.884046\pi$
$174$		0			0
$175$	−8.00022	+	10.5355i	−0.604760	+	0.796408i
$176$	8.29774	−	14.3721i	0.625466	−	1.08334i
$177$		0			0
$178$	−0.380415	+	1.41973i	−0.0285133	+	0.106413i
$179$		−	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	$-0.271990\pi$
$182$	1.38217	+	0.307131i	0.102453	+	0.0227660i
$183$		0			0
$184$	15.2498	+	8.80448i	1.12423	+	0.649075i
$185$	−0.0517959	−	0.0808099i	−0.00380811	−	0.00594126i
$186$		0			0
$187$	−7.54421	−	2.02147i	−0.551687	−	0.147824i
$188$	−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	0.553982	−	0.832529i	$-0.313108\pi$
$191$	−6.13621	−	10.6282i	−0.444000	−	0.769031i	−0.997982	+	0.0634977i	$0.979774\pi$
$192$		0			0
$193$	2.09344	+	7.81281i	0.150689	+	0.562378i	0.999436	+	0.0335796i	$0.0106907\pi$
$193$	2.09344	+	7.81281i	0.150689	+	0.562378i	−0.848747	+	0.528799i	$0.822643\pi$
$194$	8.90292	−	15.4203i	0.639192	−	1.10711i
$195$		0			0
$196$	0.527635	+	0.755115i	0.0376882	+	0.0539368i
$197$	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	$0.631829\pi$
$200$	12.7908	−	4.73566i	0.904447	−	0.334861i
$201$		0			0
$202$	2.32355	+	8.67159i	0.163484	+	0.610131i
$203$	3.64408	+	11.5773i	0.255764	+	0.812568i
$204$		0			0
$205$	−18.8929	−	17.2164i	−1.31954	−	1.20244i
$206$		−	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	−0.894960	−	0.446145i	$-0.852796\pi$
$211$	−0.887630	+	1.53742i	−0.0611069	+	0.105840i	0.833854	+	0.551986i	$0.186130\pi$
$212$	−1.56630	+	0.419689i	−0.107574	+	0.0288244i
$213$		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
$218$	−11.7835	−	3.15737i	−0.798078	−	0.213844i
$219$		0			0
$220$	0.245839	−	1.12358i	0.0165744	−	0.0757521i
$221$	−0.366222	+	0.634314i	−0.0246347	+	0.0426686i
$222$		0			0
$223$	−5.15894	+	19.2534i	−0.345468	+	1.28930i	0.546597	+	0.837396i	$0.315923\pi$
$223$	−5.15894	+	19.2534i	−0.345468	+	1.28930i	−0.892065	+	0.451908i	$0.850744\pi$
$224$	−0.0848135	−	1.96464i	−0.00566684	−	0.131268i
$225$		0			0
$226$	−19.5048			−1.29744
$227$	11.6212	+	3.11388i	0.771325	+	0.206676i	0.622957	−	0.782256i	$-0.285931\pi$
$227$	11.6212	+	3.11388i	0.771325	+	0.206676i	0.148368	+	0.988932i	$0.452598\pi$
$228$		0			0
$229$	−4.78689	+	8.29114i	−0.316327	+	0.547894i	−0.979719	−	0.200378i	$-0.935783\pi$
$229$	−4.78689	+	8.29114i	−0.316327	+	0.547894i	0.663392	+	0.748272i	$0.269116\pi$
$230$	20.5871	+	4.50442i	1.35747	+	0.297013i
$231$		0			0
$232$	3.23885	−	12.0876i	0.212641	−	0.793587i
$233$	−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
$238$	−7.36269	+	2.31748i	−0.477252	+	0.150220i
$239$	5.05325	+	2.91749i	0.326867	+	0.188717i	0.654449	−	0.756106i	$-0.272900\pi$
$239$	5.05325	+	2.91749i	0.326867	+	0.188717i	−0.327582	+	0.944823i	$0.606234\pi$
$240$		0			0
$241$	−7.01801	+	4.05185i	−0.452070	+	0.261003i	−0.708704	−	0.705506i	$-0.750720\pi$
$241$	−7.01801	+	4.05185i	−0.452070	+	0.261003i	0.256634	+	0.966509i	$0.417386\pi$
$242$	4.41569	+	4.41569i	0.283851	+	0.283851i
$243$		0			0
$244$	0.873888			0.0559450
$245$	−12.4349	−	9.50648i	−0.794437	−	0.607346i
$246$		0			0
$247$	−1.35767	+	0.363787i	−0.0863865	+	0.0231472i
$248$	−5.50437	+	1.47489i	−0.349528	+	0.0936556i
$249$		0			0
$250$	12.8674	−	10.0440i	0.813803	−	0.635236i
$251$		−	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
$257$	3.22856	+	12.0491i	0.201392	+	0.751604i	0.990519	+	0.137375i	$0.0438665\pi$
$257$	3.22856	+	12.0491i	0.201392	+	0.751604i	−0.789127	+	0.614230i	$0.789467\pi$
$258$		0			0
$259$	0.0958144	−	0.0609745i	0.00595362	−	0.00378877i
$260$	−0.0958110	−	0.0495401i	−0.00594194	−	0.00307235i
$261$		0			0
$262$	−11.9093	+	11.9093i	−0.735756	+	0.735756i
$263$	0.495319	+	0.132720i	0.0305427	+	0.00818389i	0.274058	−	0.961713i	$-0.411634\pi$
$263$	0.495319	+	0.132720i	0.0305427	+	0.00818389i	−0.243515	+	0.969897i	$0.578301\pi$
$264$		0			0
$265$	23.1967	−	14.8682i	1.42496	−	0.913344i
$266$	−13.1354	−	6.84606i	−0.805385	−	0.419759i
$267$		0			0
$268$	0.502212	+	0.134567i	0.0306775	+	0.00822001i
$269$	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	$0.999792\pi$
$272$	8.19520	+	2.19590i	0.496907	+	0.133146i
$273$		0			0
$274$	6.65894	+	3.84454i	0.402281	+	0.232257i
$275$	1.81081	+	19.4590i	0.109196	+	1.17342i
$276$		0			0
$277$	−2.94340	+	10.9849i	−0.176851	+	0.660019i	0.819377	+	0.573254i	$0.194319\pi$
$277$	−2.94340	+	10.9849i	−0.176851	+	0.660019i	−0.996229	+	0.0867643i	$0.972347\pi$
$278$	−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	0.625792	−	0.779990i	$-0.284776\pi$
$281$	−6.07820	−	10.5278i	−0.362595	−	0.628033i	−0.988387	+	0.151957i	$0.951443\pi$
$282$		0			0
$283$	25.6739	−	6.87930i	1.52615	−	0.408932i	0.604392	−	0.796687i	$-0.293416\pi$
$283$	25.6739	−	6.87930i	1.52615	−	0.408932i	0.921762	+	0.387756i	$0.126750\pi$
$284$	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
$290$	−0.694591	−	14.9604i	−0.0407878	−	0.878503i
$291$		0			0
$292$	0.430971	+	1.60841i	0.0252207	+	0.0941249i
$293$	−22.2897	+	5.97252i	−1.30218	+	0.348918i	−0.842274	−	0.539049i	$-0.818784\pi$
$293$	−22.2897	+	5.97252i	−1.30218	+	0.348918i	−0.459907	+	0.887967i	$0.652117\pi$
$294$		0			0
$295$	14.7765	−	16.2154i	0.860320	−	0.944097i
$296$	−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
$301$	−0.577855	+	1.10872i	−0.0333070	+	0.0639057i
$302$	28.7049	−	7.69146i	1.65178	−	0.442594i
$303$		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	$0.451016\pi$
$308$	1.32849	+	0.295202i	0.0756978	+	0.0168207i
$309$		0			0
$310$	−5.74171	+	3.68021i	−0.326107	+	0.209022i
$311$	12.9578	+	7.48121i	0.734772	+	0.424221i	0.820165	−	0.572127i	$-0.193881\pi$
$311$	12.9578	+	7.48121i	0.734772	+	0.424221i	−0.0853935	+	0.996347i	$0.527215\pi$
$312$		0			0
$313$	3.35233	−	12.5111i	0.189485	−	0.707167i	−0.804141	−	0.594439i	$-0.797374\pi$
$313$	3.35233	−	12.5111i	0.189485	−	0.707167i	0.993626	−	0.112728i	$-0.0359590\pi$
$314$	13.9524			0.787382
$315$		0			0
$316$	0.479835			0.0269929
$317$	6.73734	−	25.1441i	0.378407	−	1.41223i	−0.469896	−	0.882722i	$-0.655709\pi$
$317$	6.73734	−	25.1441i	0.378407	−	1.41223i	0.848303	−	0.529512i	$-0.177625\pi$
$318$		0			0
$319$	15.5283	+	8.96529i	0.869420	+	0.501960i
$320$	3.53993	−	16.1789i	0.197888	−	0.904430i
$321$		0			0
$322$	−5.40889	+	24.3415i	−0.301426	+	1.35650i
$323$	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
$328$	−30.1198	+	8.07058i	−1.66309	+	0.445623i
$329$	−14.3297	+	27.4942i	−0.790022	+	1.51580i
$330$		0			0
$331$	3.19019	+	5.52557i	0.175349	+	0.303713i	0.940282	−	0.340397i	$-0.110561\pi$
$331$	3.19019	+	5.52557i	0.175349	+	0.303713i	−0.764933	+	0.644110i	$0.777228\pi$
$332$	−1.26955	+	1.26955i	−0.0696757	+	0.0696757i
$333$		0			0
$334$	26.7162			1.46184
$335$	−8.82486	+	0.409727i	−0.482154	+	0.0223858i
$336$		0			0
$337$	2.47444	−	0.663023i	0.134791	−	0.0361172i	−0.190793	−	0.981630i	$-0.561106\pi$
$337$	2.47444	−	0.663023i	0.134791	−	0.0361172i	0.325584	+	0.945513i	$0.394439\pi$
$338$	4.86162	+	18.1438i	0.264437	+	0.986892i
$339$		0			0
$340$	0.587379	−	0.0272713i	0.0318551	−	0.00147899i
$341$		−	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
$347$	−7.93384	+	2.12587i	−0.425911	+	0.114122i	−0.465406	−	0.885097i	$-0.654092\pi$
$347$	−7.93384	+	2.12587i	−0.425911	+	0.114122i	0.0394952	+	0.999220i	$0.487425\pi$
$348$		0			0
$349$	−8.03047	−	13.9092i	−0.429861	−	0.744541i	0.567000	−	0.823718i	$-0.308104\pi$
$349$	−8.03047	−	13.9092i	−0.429861	−	0.744541i	−0.996861	+	0.0791769i	$0.974771\pi$
$350$	11.8346	+	15.2634i	0.632586	+	0.815864i
$351$		0			0
$352$	−2.05421	−	2.05421i	−0.109490	−	0.109490i
$353$	1.62567	−	6.06709i	0.0865257	−	0.322918i	−0.909073	−	0.416637i	$-0.863209\pi$
$353$	1.62567	−	6.06709i	0.0865257	−	0.322918i	0.995599	+	0.0937184i	$0.0298753\pi$
$354$		0			0
$355$	−4.64303	−	1.01589i	−0.246427	−	0.0539178i
$356$	0.114734	+	0.0662417i	0.00608089	+	0.00351080i
$357$		0			0
$358$	−4.00730	−	1.07375i	−0.211792	−	0.0567496i
$359$		−	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
$362$	−28.6201	−	7.66872i	−1.50424	−	0.403059i
$363$		0			0
$364$	0.0589851	−	0.113174i	0.00309166	−	0.00593192i
$365$	−15.2679	−	23.8203i	−0.799156	−	1.24681i
$366$		0			0
$367$	−18.4620	−	4.94689i	−0.963711	−	0.258226i	−0.257541	−	0.966267i	$-0.582912\pi$
$367$	−18.4620	−	4.94689i	−0.963711	−	0.258226i	−0.706170	+	0.708042i	$0.749579\pi$
$368$	19.3804	−	19.3804i	1.01028	−	1.01028i
$369$		0			0
$370$	−0.133535	+	0.0425092i	−0.00694214	+	0.00220995i
$371$	17.5029	+	27.5038i	0.908705	+	1.42793i
$372$		0			0
$373$	−9.68146	−	36.1317i	−0.501287	−	1.87083i	−0.491501	−	0.870877i	$-0.663552\pi$
$373$	−9.68146	−	36.1317i	−0.501287	−	1.87083i	−0.00978595	−	0.999952i	$-0.503115\pi$
$374$	−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	$-0.182276\pi$
$380$	0.834045	+	0.760034i	0.0427856	+	0.0389889i
$381$		0			0
$382$	−17.3072	+	4.63745i	−0.885513	+	0.237272i
$383$	3.93021	−	1.05310i	0.200824	−	0.0538107i	−0.157005	−	0.987598i	$-0.550184\pi$
$383$	3.93021	−	1.05310i	0.200824	−	0.0538107i	0.357829	+	0.933787i	$0.383517\pi$
$384$		0			0
$385$	−23.0310	+	2.06769i	−1.17377	+	0.105379i
$386$	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	$-0.955045\pi$
$389$	−26.8857	+	15.5225i	−1.36316	+	0.787021i	−0.373118	+	0.927784i	$0.621711\pi$
$390$		0			0
$391$	−11.1709	−	6.44954i	−0.564939	−	0.326167i
$392$	−17.9499	+	6.51331i	−0.906605	+	0.328972i
$393$		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	$0.199655\pi$
$398$	−4.29021	+	16.0113i	−0.215049	+	0.802573i
$399$		0			0
$400$	−1.96707	−	21.1381i	−0.0983534	−	1.05690i
$401$	19.1412	−	33.1535i	0.955866	−	1.65561i	0.223491	−	0.974706i	$-0.428255\pi$
$401$	19.1412	−	33.1535i	0.955866	−	1.65561i	0.732375	−	0.680902i	$-0.238412\pi$
$402$		0			0
$403$	−0.739623	−	0.198181i	−0.0368432	−	0.00987212i
$404$	0.809199			0.0402591
$405$		0			0
$406$	17.7039	−	0.764280i	0.878631	−	0.0379306i
$407$	0.0434245	−	0.162063i	0.00215247	−	0.00803314i
$408$		0			0
$409$	−15.0631	+	26.0901i	−0.744823	+	1.29007i	0.205455	+	0.978667i	$0.434133\pi$
$409$	−15.0631	+	26.0901i	−0.744823	+	1.29007i	−0.950277	+	0.311404i	$0.899201\pi$
$410$	−31.4186	+	20.1380i	−1.55165	+	0.994547i
$411$		0			0
$412$	−0.513355	−	0.137553i	−0.0252912	−	0.00677676i
$413$	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
$418$	−21.1370	+	5.66364i	−1.03384	+	0.277018i
$419$	−5.18972	+	8.98886i	−0.253534	+	0.439134i	−0.964496	−	0.264096i	$-0.914926\pi$
$419$	−5.18972	+	8.98886i	−0.253534	+	0.439134i	0.710962	+	0.703230i	$0.248260\pi$
$420$		0			0
$421$	−9.30441	−	16.1157i	−0.453469	−	0.785432i	0.545130	−	0.838352i	$-0.316480\pi$
$421$	−9.30441	−	16.1157i	−0.453469	−	0.785432i	−0.998599	+	0.0529202i	$0.983147\pi$
$422$	1.83273	+	1.83273i	0.0892161	+	0.0892161i
$423$		0			0
$424$		−	33.6126i		−	1.63237i
$425$	−9.36964	+	3.46901i	−0.454495	+	0.168272i
$426$		0			0
$427$	−5.27495	−	16.7586i	−0.255273	−	0.811007i
$428$	−0.105878	−	0.395142i	−0.00511780	−	0.0190999i
$429$		0			0
$430$	1.03912	−	1.14030i	0.0501106	−	0.0549904i
$431$	−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	$0.593200\pi$
$434$	−4.33236	−	6.80781i	−0.207960	−	0.326785i
$435$		0			0
$436$	−0.549794	+	0.952271i	−0.0263304	+	0.0456055i
$437$	−6.40666	−	23.9100i	−0.306472	−	1.14377i
$438$		0			0
$439$	14.7353	+	25.5223i	0.703278	+	1.21811i	0.967309	+	0.253599i	$0.0816144\pi$
$439$	14.7353	+	25.5223i	0.703278	+	1.21811i	−0.264031	+	0.964514i	$0.585052\pi$
$440$	21.1778	+	10.9502i	1.00961	+	0.522032i
$441$		0			0
$442$	0.756157	+	0.756157i	0.0359667	+	0.0359667i
$443$	14.7465	+	3.95131i	0.700627	+	0.187732i	0.591512	−	0.806297i	$-0.298531\pi$
$443$	14.7465	+	3.95131i	0.700627	+	0.187732i	0.109116	+	0.994029i	$0.465198\pi$
$444$		0			0
$445$	−2.19907	−	0.481154i	−0.104246	−	0.0228089i
$446$	25.2027	+	14.5508i	1.19338	+	0.689000i
$447$		0			0
$448$	19.1295	+	4.25073i	0.903782	+	0.200828i
$449$		−	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
$452$	−0.455027	+	1.69818i	−0.0214027	+	0.0798758i
$453$		0			0
$454$	8.78272	−	15.2121i	0.412194	−	0.713940i
$455$	−0.371703	+	2.13641i	−0.0174257	+	0.100156i
$456$		0			0
$457$	1.19133	−	4.44611i	0.0557282	−	0.207980i	−0.932448	−	0.361305i	$-0.882331\pi$
$457$	1.19133	−	4.44611i	0.0557282	−	0.207980i	0.988176	+	0.153325i	$0.0489980\pi$
$458$	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	$-0.343820\pi$
$461$	31.5764	−	18.2307i	1.47066	−	0.849087i	0.999457	+	0.0329376i	$0.0104863\pi$
$462$		0			0
$463$	−6.97859	−	26.0444i	−0.324323	−	1.21039i	−0.914991	−	0.403474i	$-0.867803\pi$
$463$	−6.97859	−	26.0444i	−0.324323	−	1.21039i	0.590669	−	0.806914i	$-0.298864\pi$
$464$	−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
$470$	25.7681	−	28.2774i	1.18859	−	1.30434i
$471$		0			0
$472$	−6.92683	−	25.8513i	−0.318833	−	1.18990i
$473$	0.478051	+	1.78411i	0.0219808	+	0.0820335i
$474$		0			0
$475$	−17.4213	−	8.00682i	−0.799345	−	0.367378i
$476$	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	0.946491	−	0.322729i	$-0.104600\pi$
$479$	4.24052	+	7.34480i	0.193754	+	0.335592i	−0.752737	+	0.658321i	$0.771267\pi$
$480$		0			0
$481$	−0.0136262	−	0.00786707i	−0.000621299	−	0.000358707i
$482$	3.06219	+	11.4283i	0.139479	+	0.520543i
$483$		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	$0.722889\pi$
$488$	−4.68837	+	17.4972i	−0.212233	+	0.792063i
$489$		0			0
$490$	−18.1054	+	13.9441i	−0.817917	+	0.629929i
$491$	2.01799	−	3.49526i	0.0910707	−	0.157739i	−0.816891	−	0.576792i	$-0.804304\pi$
$491$	2.01799	−	3.49526i	0.0910707	−	0.157739i	0.907962	+	0.419053i	$0.137638\pi$
$492$		0			0
$493$	−2.37256	+	8.85450i	−0.106855	+	0.398787i
$494$			2.05212i			0.0923293i
$495$		0			0
$496$			8.86969i			0.398261i
$497$	1.21988	−	5.48977i	0.0547189	−	0.246250i
$498$		0			0
$499$	6.03591	+	3.48484i	0.270205	+	0.156003i	0.628981	−	0.777421i	$-0.283472\pi$
$499$	6.03591	+	3.48484i	0.270205	+	0.156003i	−0.358776	+	0.933424i	$0.616806\pi$
$500$	−0.574296	−	1.35461i	−0.0256833	−	0.0605801i
$501$		0			0
$502$	−10.6156	−	2.84443i	−0.473796	−	0.126953i
$503$	−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
$508$	0.442402	+	1.65107i	0.0196284	+	0.0732542i
$509$	15.1933	−	26.3156i	0.673433	−	1.16642i	−0.303491	−	0.952834i	$-0.598152\pi$
$509$	15.1933	−	26.3156i	0.673433	−	1.16642i	0.976924	−	0.213586i	$-0.0685145\pi$
$510$		0			0
$511$	28.2431	−	17.9734i	1.24940	−	0.795097i
$512$	−14.1482	−	14.1482i	−0.625269	−	0.625269i
$513$		0			0
$514$	18.2123			0.803310
$515$	9.02067	−	0.418818i	0.397498	−	0.0184553i
$516$		0			0
$517$	11.8547	+	44.2425i	0.521371	+	1.94578i
$518$	−0.0497835	−	0.158163i	−0.00218736	−	0.00694929i
$519$		0			0
$520$	1.50593	−	1.65257i	0.0660393	−	0.0724701i
$521$			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
$527$	4.03211	−	1.08040i	0.175642	−	0.0470630i
$528$		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
$533$	−4.04721	−	1.08445i	−0.175304	−	0.0469726i
$534$		0			0
$535$	3.75090	+	5.85200i	0.162165	+	0.253004i
$536$	−5.38869	+	9.33349i	−0.232756	+	0.403145i
$537$		0			0
$538$	1.95266	−	7.28744i	0.0841853	−	0.314184i
$539$	−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	$0.329877\pi$
$542$	0.0302794	+	0.00811333i	0.00130061	+	0.000348497i
$543$		0			0
$544$	0.742601	−	1.28622i	0.0318387	−	0.0551463i
$545$	3.99348	−	18.2519i	0.171062	−	0.781825i
$546$		0			0
$547$	5.66691	−	21.1492i	0.242300	−	0.904275i	−0.732422	−	0.680851i	$-0.761610\pi$
$547$	5.66691	−	21.1492i	0.242300	−	0.904275i	0.974721	−	0.223424i	$-0.0717233\pi$
$548$	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
$553$	−2.89637	−	9.20184i	−0.123166	−	0.391302i
$554$	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
$560$	25.0183	−	2.24612i	1.05722	−	0.0949157i
$561$		0			0
$562$	−17.1436	+	4.59361i	−0.723158	+	0.193770i
$563$	−3.72139	+	0.997144i	−0.156838	+	0.0420246i	−0.336384	−	0.941725i	$-0.609204\pi$
$563$	−3.72139	+	0.997144i	−0.156838	+	0.0420246i	0.179546	+	0.983750i	$0.442537\pi$
$564$		0			0
$565$	−1.38545	−	29.8404i	−0.0582865	−	1.25540i
$566$		−	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	$-0.585538\pi$
$569$	10.4167	−	6.01410i	0.436692	−	0.252124i	0.702193	+	0.711986i	$0.252204\pi$
$570$		0			0
$571$	15.7271	−	27.2401i	0.658158	−	1.13996i	−0.322935	−	0.946421i	$-0.604669\pi$
$571$	15.7271	−	27.2401i	0.658158	−	1.13996i	0.981092	−	0.193541i	$-0.0619973\pi$
$572$	−0.0487975	−	0.182115i	−0.00204032	−	0.00761459i
$573$		0			0
$574$	−23.7066	−	37.2522i	−0.989496	−	1.55488i
$575$	−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	$0.0193467\pi$
$578$	18.3432	+	4.91504i	0.762976	+	0.204439i
$579$		0			0
$580$	−1.31873	−	0.288536i	−0.0547573	−	0.0119808i
$581$	32.0095	+	16.6830i	1.32798	+	0.692129i
$582$		0			0
$583$	46.5205	+	12.4651i	1.92668	+	0.516253i
$584$	−34.5161			−1.42829
$585$		0			0
$586$			33.6910i			1.39176i
$587$	−6.32026	−	1.69351i	−0.260865	−	0.0698986i	0.126016	−	0.992028i	$-0.459781\pi$
$587$	−6.32026	−	1.69351i	−0.260865	−	0.0698986i	−0.386881	+	0.922130i	$0.626448\pi$
$588$		0			0
$589$	6.93739	+	4.00530i	0.285850	+	0.165036i
$590$	−17.2841	−	26.9660i	−0.711575	−	1.11017i
$591$		0			0
$592$	−0.0471716	+	0.176047i	−0.00193874	+	0.00723548i
$593$	−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
$598$	3.33683	−	0.894100i	0.136453	−	0.0365625i
$599$	38.3139	+	22.1205i	1.56546	+	0.903820i	0.996687	+	0.0813272i	$0.0259159\pi$
$599$	38.3139	+	22.1205i	1.56546	+	0.903820i	0.568775	+	0.822493i	$0.307417\pi$
$600$		0			0
$601$	−15.6353	+	9.02705i	−0.637778	+	0.368221i	−0.783758	−	0.621066i	$-0.786700\pi$
$601$	−15.6353	+	9.02705i	−0.637778	+	0.368221i	0.145980	+	0.989288i	$0.453366\pi$
$602$	1.34522	+	1.23388i	0.0548271	+	0.0502892i
$603$		0			0
$604$		−	2.67863i		−	0.108992i
$605$	−6.44193	+	7.06924i	−0.261902	+	0.287405i
$606$		0			0
$607$	10.0006	+	37.3229i	0.405913	+	1.51489i	0.802365	+	0.596833i	$0.203575\pi$
$607$	10.0006	+	37.3229i	0.405913	+	1.51489i	−0.396452	+	0.918055i	$0.629759\pi$
$608$	2.75300	−	0.737663i	0.111649	−	0.0299162i
$609$		0			0
$610$	1.00545	+	21.6557i	0.0407094	+	0.876815i
$611$	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
$616$	−13.0379	+	25.0157i	−0.525312	+	1.00791i
$617$	−18.1190	+	4.85497i	−0.729444	+	0.195454i	−0.604382	−	0.796695i	$-0.706580\pi$
$617$	−18.1190	+	4.85497i	−0.729444	+	0.195454i	−0.125062	+	0.992149i	$0.539913\pi$
$618$		0			0
$619$	6.29505	+	10.9033i	0.253019	+	0.438243i	0.964356	−	0.264609i	$-0.0852430\pi$
$619$	6.29505	+	10.9033i	0.253019	+	0.438243i	−0.711336	+	0.702852i	$0.751910\pi$
$620$	0.186469	+	0.585758i	0.00748878	+	0.0235246i
$621$		0			0
$622$	15.4468	−	15.4468i	0.619362	−	0.619362i
$623$	0.577768	−	2.60011i	0.0231478	−	0.104171i
$624$		0			0
$625$	16.2803	+	18.9724i	0.651212	+	0.758896i
$626$	−16.3770	−	9.45525i	−0.654556	−	0.377908i
$627$		0			0
$628$	0.325497	−	1.21477i	0.0129887	−	0.0484746i
$629$	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	$0.498222\pi$
$632$	−2.57430	+	9.60740i	−0.102400	+	0.382162i
$633$		0			0
$634$	−32.9136	−	19.0027i	−1.30717	−	0.754693i
$635$	−15.6728	−	24.4520i	−0.621956	−	0.970350i
$636$		0			0
$637$	−2.52639	−	0.448023i	−0.100099	−	0.0177513i
$638$	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	0.923004	−	0.384789i	$-0.125726\pi$
$641$	3.24741	+	5.62468i	0.128265	+	0.222162i	−0.794739	+	0.606951i	$0.792393\pi$
$642$		0			0
$643$	13.1017	−	3.51060i	0.516683	−	0.138445i	0.00895086	−	0.999960i	$-0.497151\pi$
$643$	13.1017	−	3.51060i	0.516683	−	0.138445i	0.507732	+	0.861515i	$0.330484\pi$
$644$	1.99311	+	1.03879i	0.0785395	+	0.0409340i
$645$		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
$650$	1.11741	−	2.43128i	0.0438286	−	0.0953627i
$651$		0			0
$652$	1.24840	−	0.334509i	0.0488913	−	0.0131004i
$653$	−6.27826	−	23.4308i	−0.245687	−	0.916917i	−0.973037	−	0.230650i	$-0.925915\pi$
$653$	−6.27826	−	23.4308i	−0.245687	−	0.916917i	0.727350	−	0.686267i	$-0.240752\pi$
$654$		0			0
$655$	−19.0660	−	17.3741i	−0.744969	−	0.678863i
$656$			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	$-0.780046\pi$
$659$	−15.5047	+	8.95163i	−0.603977	+	0.348706i	0.166628	+	0.986020i	$0.446712\pi$
$660$		0			0
$661$	13.2369	+	7.64232i	0.514855	+	0.297252i	0.734827	−	0.678254i	$-0.237263\pi$
$661$	13.2369	+	7.64232i	0.514855	+	0.297252i	−0.219972	+	0.975506i	$0.570597\pi$
$662$	8.99794	−	2.41099i	0.349715	−	0.0937058i
$663$		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
$668$	0.623262	−	2.32605i	0.0241147	−	0.0899974i
$669$		0			0
$670$	−2.75688	+	12.6001i	−0.106508	+	0.486784i
$671$	−22.4779	−	12.9776i	−0.867749	−	0.500995i
$672$		0			0
$673$	−9.09576	−	2.43720i	−0.350616	−	0.0939472i	0.0792128	−	0.996858i	$-0.474759\pi$
$673$	−9.09576	−	2.43720i	−0.350616	−	0.0939472i	−0.429829	+	0.902911i	$0.641426\pi$
$674$		−	3.74012i		−	0.144064i
$675$		0			0
$676$	1.69311			0.0651195
$677$	30.3503	+	8.13234i	1.16646	+	0.312551i	0.789542	−	0.613697i	$-0.210318\pi$
$677$	30.3503	+	8.13234i	1.16646	+	0.312551i	0.376915	+	0.926248i	$0.376985\pi$
$678$		0			0
$679$	−14.9133	+	28.6139i	−0.572319	+	1.09810i
$680$	−2.60523	+	11.9070i	−0.0999060	+	0.456612i
$681$		0			0
$682$	−11.5149	−	3.08540i	−0.440927	−	0.118146i
$683$	−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
$686$	−16.4291	−	21.4761i	−0.627266	−	0.819962i
$687$		0			0
$688$	−0.519302	−	1.93806i	−0.0197982	−	0.0738879i
$689$	2.25826	−	3.91143i	0.0860330	−	0.149013i
$690$		0			0
$691$	−31.6309	+	18.2621i	−1.20330	+	0.694724i	−0.961287	−	0.275549i	$-0.911140\pi$
$691$	−31.6309	+	18.2621i	−1.20330	+	0.694724i	−0.242011	+	0.970274i	$0.577807\pi$
$692$	1.43439	−	1.43439i	0.0545274	−	0.0545274i
$693$		0			0
$694$			11.9920i			0.455211i
$695$	15.6766	−	17.2032i	0.594647	−	0.652553i
$696$		0			0
$697$	22.0637	−	5.91194i	0.835721	−	0.223931i
$698$	−22.6500	+	6.06904i	−0.857313	+	0.229716i
$699$		0			0
$700$	1.60500	−	0.674300i	0.0606633	−	0.0254861i
$701$	−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
$707$	−4.88447	−	15.5181i	−0.183699	−	0.583617i
$708$		0			0
$709$	7.14195	−	4.12341i	0.268222	−	0.154858i	−0.359858	−	0.933007i	$-0.617175\pi$
$709$	7.14195	−	4.12341i	0.268222	−	0.154858i	0.628079	+	0.778149i	$0.283841\pi$
$710$	−3.18715	+	6.16396i	−0.119611	+	0.231329i
$711$		0			0
$712$	−1.94185	+	1.94185i	−0.0727740	+	0.0727740i
$713$	3.49018	−	13.0255i	0.130708	−	0.487810i
$714$		0			0
$715$	1.72873	+	2.69709i	0.0646508	+	0.100865i
$716$	−0.186973	+	0.323846i	−0.00698750	+	0.0121027i
$717$		0			0
$718$	−41.1682	−	11.0310i	−1.53638	−	0.411673i
$719$	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
$722$	−1.62318	+	6.05779i	−0.0604085	+	0.225448i
$723$		0			0
$724$	−1.33536	+	2.31290i	−0.0496281	+	0.0859584i
$725$	22.8386	−	2.12532i	0.848205	−	0.0789323i
$726$		0			0
$727$	19.7819	+	5.30055i	0.733671	+	0.196586i	0.606263	−	0.795264i	$-0.292668\pi$
$727$	19.7819	+	5.30055i	0.733671	+	0.196586i	0.127407	+	0.991850i	$0.459334\pi$
$728$	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
$733$	−20.7597	+	5.56254i	−0.766776	+	0.205457i	−0.620947	−	0.783853i	$-0.713252\pi$
$733$	−20.7597	+	5.56254i	−0.766776	+	0.205457i	−0.145829	+	0.989310i	$0.546585\pi$
$734$	−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	$0.704354\pi$
$740$	0.000585834		0.0126179i	2.15357e−5		0.000463844i
$741$		0			0
$742$	45.4012	−	14.2905i	1.66673	−	0.524620i
$743$	10.1722	+	37.9631i	0.373181	+	1.39273i	0.855984	+	0.517002i	$0.172952\pi$
$743$	10.1722	+	37.9631i	0.373181	+	1.39273i	−0.482803	+	0.875729i	$0.660381\pi$
$744$		0			0
$745$	−1.21991	−	1.11166i	−0.0446941	−	0.0407281i
$746$	−54.6132			−1.99953
$747$		0			0
$748$	0.726789	+	0.726789i	0.0265740	+	0.0265740i
$749$	−6.93857	+	4.41558i	−0.253530	+	0.161342i
$750$		0			0
$751$	−12.6732	+	21.9506i	−0.462452	+	0.800990i	−0.999082	−	0.0428274i	$-0.986363\pi$
$751$	−12.6732	+	21.9506i	−0.462452	+	0.800990i	0.536631	+	0.843817i	$0.319697\pi$
$752$	−12.8777	−	48.0602i	−0.469601	−	1.75258i
$753$		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	$0.773469\pi$
$758$	−29.7527	−	7.97221i	−1.08067	−	0.289564i
$759$		0			0
$760$	−19.6922	+	12.6219i	−0.714312	+	0.457846i
$761$	13.3875	+	7.72926i	0.485295	+	0.280185i	0.722621	−	0.691245i	$-0.242937\pi$
$761$	13.3875	+	7.72926i	0.485295	+	0.280185i	−0.237325	+	0.971430i	$0.576271\pi$
$762$		0			0
$763$	21.5804	+	4.79536i	0.781264	+	0.173604i
$764$			1.61504i			0.0584301i
$765$		0			0
$766$		−	5.94052i		−	0.214640i
$767$	0.930760	−	3.47364i	0.0336078	−	0.125426i
$768$		0			0
$769$	−7.41964	+	12.8512i	−0.267559	+	0.463426i	−0.968231	−	0.250058i	$-0.919550\pi$
$769$	−7.41964	+	12.8512i	−0.267559	+	0.463426i	0.700672	+	0.713484i	$0.252884\pi$
$770$	−5.78689	+	33.2608i	−0.208545	+	1.19864i
$771$		0			0
$772$	0.275494	−	1.02816i	0.00991526	−	0.0370043i
$773$	−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
$778$	11.7311	+	43.7812i	0.420582	+	1.56963i
$779$	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
$785$	0.991064	+	21.3459i	0.0353726	+	0.761869i
$786$		0			0
$787$	−12.1760	−	45.4416i	−0.434029	−	1.61982i	−0.743380	−	0.668869i	$-0.766779\pi$
$787$	−12.1760	−	45.4416i	−0.434029	−	1.61982i	0.309352	−	0.950948i	$-0.399888\pi$
$788$	−0.0734228	−	0.274017i	−0.00261558	−	0.00976147i
$789$		0			0
$790$	0.552073	+	11.8908i	0.0196419	+	0.423054i
$791$	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
$797$	−4.98780	−	18.6147i	−0.176677	−	0.659367i	−0.996260	−	0.0864066i	$-0.972462\pi$
$797$	−4.98780	−	18.6147i	−0.176677	−	0.659367i	0.819583	−	0.572960i	$-0.194205\pi$
$798$		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
$803$	12.8002	−	47.7711i	0.451710	−	1.68581i
$804$		0			0
$805$	−37.6244	−	6.54608i	−1.32609	−	0.230719i
$806$	−0.558971	+	0.968166i	−0.0196889	+	0.0341022i
$807$		0			0
$808$	−4.34132	+	16.2020i	−0.152727	+	0.569985i
$809$			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	$-0.0766552\pi$
$812$	0.346473	−	1.55922i	0.0121588	−	0.0547180i
$813$		0			0
$814$	−0.212140	−	0.122479i	−0.00743550	−	0.00429289i
$815$	−18.4887	+	11.8505i	−0.647630	+	0.415105i
$816$		0			0
$817$	−1.75035	−	0.469004i	−0.0612369	−	0.0164084i
$818$	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	0.938560	−	0.345117i	$-0.112161\pi$
$821$	4.88248	+	8.45670i	0.170400	+	0.295141i	−0.768160	+	0.640258i	$0.778827\pi$
$822$		0			0
$823$	11.0194	+	41.1250i	0.384113	+	1.43353i	0.839561	+	0.543266i	$0.182812\pi$
$823$	11.0194	+	41.1250i	0.384113	+	1.43353i	−0.455448	+	0.890262i	$0.650521\pi$
$824$	5.50825	−	9.54058i	0.191889	−	0.332362i
$825$		0			0
$826$	31.9729	−	20.3470i	1.11248	−	0.707961i
$827$	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	$0.678402\pi$
$830$	−32.9213	−	30.0000i	−1.14272	−	1.04131i
$831$		0			0
$832$	−0.702654	−	2.62234i	−0.0243601	−	0.0909133i
$833$	13.1488	−	4.77119i	0.455579	−	0.165312i
$834$		0			0
$835$	1.89769	+	40.8732i	0.0656724	+	1.41448i
$836$			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	0.975444	−	0.220249i	$-0.0706868\pi$
$839$	8.60220	+	14.8995i	0.296981	+	0.514386i	−0.678463	+	0.734635i	$0.737354\pi$
$840$		0			0
$841$	−3.97761	+	6.88943i	−0.137159	+	0.237567i
$842$	−26.2431	+	7.03182i	−0.904397	+	0.242333i
$843$		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
$848$	−50.5348	−	13.5407i	−1.73537	−	0.464991i
$849$		0			0
$850$	1.35161	+	14.5244i	0.0463600	+	0.498183i
$851$	0.138547	−	0.239971i	0.00474934	−	0.00822610i
$852$		0			0
$853$	−4.23563	+	15.8076i	−0.145025	+	0.541241i	0.854729	+	0.519074i	$0.173723\pi$
$853$	−4.23563	+	15.8076i	−0.145025	+	0.541241i	−0.999754	+	0.0221670i	$0.992943\pi$
$854$	−25.6272	+	1.10633i	−0.876943	+	0.0378577i
$855$		0			0
$856$	8.47967			0.289829
$857$	−3.46122	−	0.927430i	−0.118233	−	0.0316804i	0.199217	−	0.979955i	$-0.436160\pi$
$857$	−3.46122	−	0.927430i	−0.118233	−	0.0316804i	−0.317450	+	0.948275i	$0.602827\pi$
$858$		0			0
$859$	−8.69388	+	15.0582i	−0.296631	+	0.513781i	−0.975363	−	0.220606i	$-0.929197\pi$
$859$	−8.69388	+	15.0582i	−0.296631	+	0.513781i	0.678732	+	0.734386i	$0.262530\pi$
$860$	−0.0750391	−	0.117073i	−0.00255881	−	0.00399215i
$861$		0			0
$862$	−9.56800	+	35.7082i	−0.325887	+	1.21623i
$863$	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
$868$	−0.693792	+	0.218378i	−0.0235488	+	0.00741224i
$869$	−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
$875$	−22.5110	+	19.1900i	−0.761010	+	0.648741i
$876$		0			0
$877$	44.4733	−	11.9166i	1.50176	−	0.402394i	0.588068	−	0.808811i	$-0.299889\pi$
$877$	44.4733	−	11.9166i	1.50176	−	0.402394i	0.913688	+	0.406417i	$0.133222\pi$
$878$	41.5610	−	11.1362i	1.40262	−	0.375830i
$879$		0			0
$880$	24.9945	−	27.4285i	0.842566	−	0.924614i
$881$		−	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
$887$	−1.04539	−	3.90146i	−0.0351009	−	0.130998i	0.946152	−	0.323722i	$-0.104934\pi$
$887$	−1.04539	−	3.90146i	−0.0351009	−	0.130998i	−0.981253	+	0.192724i	$0.938268\pi$
$888$		0			0
$889$	28.9922	−	18.4501i	0.972367	−	0.618797i
$890$	−1.50952	+	2.91943i	−0.0505993	+	0.0978594i
$891$		0			0
$892$	1.85482	−	1.85482i	0.0621040	−	0.0621040i
$893$	−43.4053	−	11.6304i	−1.45250	−	0.389197i
$894$		0			0
$895$	1.35810	−	6.20706i	0.0453961	−	0.207479i
$896$	15.0409	−	28.8588i	0.502481	−	0.964104i
$897$		0			0
$898$	−4.31738	−	1.15684i	−0.144073	−	0.0386042i
$899$	−9.58325			−0.319619
$900$		0			0
$901$			24.6222i			0.820284i
$902$	−63.0093	−	16.8833i	−2.09798	−	0.562152i
$903$		0			0
$904$	−31.5603	−	18.2214i	−1.04968	−	0.606033i
$905$	9.69949	−	44.3307i	0.322422	−	1.47360i
$906$		0			0
$907$	5.69211	−	21.2432i	0.189003	−	0.705370i	−0.804735	−	0.593635i	$-0.797692\pi$
$907$	5.69211	−	21.2432i	0.189003	−	0.705370i	0.993738	−	0.111735i	$-0.0356409\pi$
$908$	−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	0.932267	−	0.361770i	$-0.117828\pi$
$911$	4.61287	+	7.98972i	0.152831	+	0.264711i	−0.779436	+	0.626482i	$0.784494\pi$
$912$		0			0
$913$	51.5084	−	13.8016i	1.70468	−	0.456767i
$914$	−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	$-0.159906\pi$
$920$	29.1035	+	26.5210i	0.959516	+	0.874370i
$921$		0			0
$922$	−13.7779	−	51.4196i	−0.453749	−	1.69342i
$923$	−0.752559	+	0.201648i	−0.0247708	+	0.00663731i
$924$		0			0
$925$	−0.0745203	−	0.201276i	−0.00245021	−	0.00661791i
$926$	−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	0.989135	+	0.147010i	$0.0469649\pi$
$929$	18.9546	+	32.8304i	0.621882	+	1.07713i	−0.367253	+	0.930121i	$0.619702\pi$
$930$		0			0
$931$	24.3164	+	11.3680i	0.796938	+	0.372570i
$932$	1.14560	−	0.306962i	0.0375253	−	0.0100549i
$933$		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	$-0.0941022\pi$
$938$	−14.8980	−	3.31046i	−0.486436	−	0.108090i
$939$		0			0
$940$	−1.86083	−	2.90319i	−0.0606935	−	0.0946915i
$941$	24.9324	+	14.3947i	0.812774	+	0.469255i	0.847918	−	0.530127i	$-0.177856\pi$
$941$	24.9324	+	14.3947i	0.812774	+	0.469255i	−0.0351445	+	0.999382i	$0.511189\pi$
$942$		0			0
$943$	19.0982	−	71.2755i	0.621924	−	2.32105i
$944$	−41.6565			−1.35580
$945$		0			0
$946$	2.69669			0.0876769
$947$	−6.96236	+	25.9839i	−0.226246	+	0.844363i	0.755655	+	0.654970i	$0.227319\pi$
$947$	−6.96236	+	25.9839i	−0.226246	+	0.844363i	−0.981901	+	0.189393i	$0.939348\pi$
$948$		0			0
$949$	−4.01657	−	2.31897i	−0.130384	−	0.0752770i
$950$	−17.8747	+	21.5429i	−0.579933	+	0.698942i
$951$		0			0
$952$	−14.0784	−	3.12835i	−0.456284	−	0.101390i
$953$	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
$958$	11.9604	−	3.20478i	0.386423	−	0.103542i
$959$	−12.3563	−	6.43998i	−0.399006	−	0.207958i
$960$		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
$965$	0.838818	+	18.0668i	0.0270025	+	0.581591i
$966$		0			0
$967$	−30.2366	+	8.10188i	−0.972345	+	0.260539i	−0.709817	−	0.704386i	$-0.751223\pi$
$967$	−30.2366	+	8.10188i	−0.972345	+	0.260539i	−0.262527	+	0.964925i	$0.584556\pi$
$968$	3.01981	+	11.2701i	0.0970604	+	0.362234i
$969$		0			0
$970$	26.8175	−	29.4289i	0.861057	−	0.944906i
$971$			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
$977$	−30.9571	+	8.29492i	−0.990404	+	0.265378i	−0.717420	−	0.696640i	$-0.754677\pi$
$977$	−30.9571	+	8.29492i	−0.990404	+	0.265378i	−0.272984	+	0.962019i	$0.588011\pi$
$978$		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
$983$	−6.91122	+	25.7930i	−0.220434	+	0.822670i	0.763749	+	0.645513i	$0.223357\pi$
$983$	−6.91122	+	25.7930i	−0.220434	+	0.822670i	−0.984183	+	0.177156i	$0.943310\pi$
$984$		0			0
$985$	2.60112	+	4.05816i	0.0828786	+	0.129304i
$986$	11.5905	+	6.69180i	0.369118	+	0.213110i
$987$		0			0
$988$	0.178668	+	0.0478740i	0.00568419	+	0.00152307i
$989$			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	$0.868248\pi$
$992$	1.49976	+	0.401859i	0.0476174	+	0.0127591i
$993$		0			0
$994$	−7.28100	−	3.79478i	−0.230939	−	0.120363i
$995$	−24.8005	−	5.42631i	−0.786228	−	0.172026i
$996$		0			0
$997$	−28.5152	−	7.64061i	−0.903084	−	0.241981i	−0.222744	−	0.974877i	$-0.571501\pi$
$997$	−28.5152	−	7.64061i	−0.903084	−	0.241981i	−0.680340	+	0.732896i	$0.738168\pi$
$998$	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.307.34		176
3.2	odd	2		315.2.cb.a.202.11	yes	176
5.3	odd	4	inner	945.2.ce.a.118.12		176
7.6	odd	2	inner	945.2.ce.a.307.33		176
9.2	odd	6		315.2.cb.a.97.34	yes	176
9.7	even	3	inner	945.2.ce.a.937.11		176
15.8	even	4		315.2.cb.a.13.33	✓	176
21.20	even	2		315.2.cb.a.202.12	yes	176
35.13	even	4	inner	945.2.ce.a.118.11		176
45.38	even	12		315.2.cb.a.223.12	yes	176
45.43	odd	12	inner	945.2.ce.a.748.33		176
63.20	even	6		315.2.cb.a.97.33	yes	176
63.34	odd	6	inner	945.2.ce.a.937.12		176
105.83	odd	4		315.2.cb.a.13.34	yes	176
315.83	odd	12		315.2.cb.a.223.11	yes	176
315.223	even	12	inner	945.2.ce.a.748.34		176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.cb.a.13.33	✓	176	15.8	even	4
315.2.cb.a.13.34	yes	176	105.83	odd	4
315.2.cb.a.97.33	yes	176	63.20	even	6
315.2.cb.a.97.34	yes	176	9.2	odd	6
315.2.cb.a.202.11	yes	176	3.2	odd	2
315.2.cb.a.202.12	yes	176	21.20	even	2
315.2.cb.a.223.11	yes	176	315.83	odd	12
315.2.cb.a.223.12	yes	176	45.38	even	12
945.2.ce.a.118.11		176	35.13	even	4	inner
945.2.ce.a.118.12		176	5.3	odd	4	inner
945.2.ce.a.307.33		176	7.6	odd	2	inner
945.2.ce.a.307.34		176	1.1	even	1	trivial
945.2.ce.a.748.33		176	45.43	odd	12	inner
945.2.ce.a.748.34		176	315.223	even	12	inner
945.2.ce.a.937.11		176	9.7	even	3	inner
945.2.ce.a.937.12		176	63.34	odd	6	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)

\(f(q)\)	\(=\)	\(q+(0.377876 - 1.41025i) q^{2} +(-0.113968 - 0.0657996i) q^{4} +(2.18439 + 0.477942i) q^{5} +(-0.573911 + 2.58276i) q^{7} +(1.92889 - 1.92889i) q^{8} +O(q^{10})\)	\(q+(0.377876 - 1.41025i) q^{2} +(-0.113968 - 0.0657996i) q^{4} +(2.18439 + 0.477942i) q^{5} +(-0.573911 + 2.58276i) q^{7} +(1.92889 - 1.92889i) q^{8} +(1.49945 - 2.89994i) q^{10} +(1.95430 + 3.38495i) q^{11} +(0.354054 - 0.0948685i) q^{13} +(3.42547 + 1.78532i) q^{14} +(-2.12294 - 3.67704i) q^{16} +(-1.41297 + 1.41297i) q^{17} -3.83464 q^{19} +(-0.217503 - 0.198202i) q^{20} +(5.51212 - 1.47697i) q^{22} +(1.67073 + 6.23526i) q^{23} +(4.54314 + 2.08803i) q^{25} -0.535154i q^{26} +(0.235352 - 0.256589i) q^{28} +(3.97286 - 2.29373i) q^{29} +(-1.80914 - 1.04451i) q^{31} +(-0.717928 + 0.192368i) q^{32} +(1.45872 + 2.52657i) q^{34} +(-2.48805 + 5.36746i) q^{35} +(-0.0303530 - 0.0303530i) q^{37} +(-1.44902 + 5.40781i) q^{38} +(5.13535 - 3.29156i) q^{40} +(-9.89957 - 5.71552i) q^{41} +(0.456457 + 0.122307i) q^{43} -0.514369i q^{44} +9.42462 q^{46} +(11.3193 + 3.03299i) q^{47} +(-6.34125 - 2.96454i) q^{49} +(4.66138 - 5.61796i) q^{50} +(-0.0465932 - 0.0124846i) q^{52} +(8.71292 - 8.71292i) q^{53} +(2.65116 + 8.32811i) q^{55} +(3.87484 + 6.08887i) q^{56} +(-1.73349 - 6.46947i) q^{58} +(4.90552 - 8.49662i) q^{59} +(-5.75087 + 3.32027i) q^{61} +(-2.15664 + 2.15664i) q^{62} -7.40661i q^{64} +(0.818735 - 0.0380128i) q^{65} +(-3.81623 + 1.02256i) q^{67} +(0.254006 - 0.0680608i) q^{68} +(6.62929 + 5.53701i) q^{70} -2.12555 q^{71} +(-8.94714 - 8.94714i) q^{73} +(-0.0542751 + 0.0313357i) q^{74} +(0.437027 + 0.252318i) q^{76} +(-9.86410 + 3.10483i) q^{77} +(-3.15769 + 1.82309i) q^{79} +(-2.87992 - 9.04674i) q^{80} +(-11.8011 + 11.8011i) q^{82} +(3.53109 - 13.1782i) q^{83} +(-3.76180 + 2.41116i) q^{85} +(0.344968 - 0.597502i) q^{86} +(10.2988 + 2.75957i) q^{88} -1.00672 q^{89} +(0.0418267 + 0.968881i) q^{91} +(0.219867 - 0.820555i) q^{92} +(8.55454 - 14.8169i) q^{94} +(-8.37636 - 1.83273i) q^{95} +(11.7802 + 3.15650i) q^{97} +(-6.57696 + 7.82253i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{2} - 2 q^{7} + 32 q^{8}+O(q^{10}) \) 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