LMFDB - Embedded newform 756.2.bi.c.307.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(307,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("756.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bi (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.9
Character	$\chi$	$=$	756.307
Dual form			756.2.bi.c.559.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02930 - 0.969818i) q^{2} +(0.118905 + 1.99646i) q^{4} +(-3.45303 - 1.99361i) q^{5} +(-2.03435 - 1.69157i) q^{7} +(1.81382 - 2.17027i) q^{8} +O(q^{10})$	\(q+(-1.02930 - 0.969818i) q^{2} +(0.118905 + 1.99646i) q^{4} +(-3.45303 - 1.99361i) q^{5} +(-2.03435 - 1.69157i) q^{7} +(1.81382 - 2.17027i) q^{8} +(1.62076 + 5.40083i) q^{10} +(1.72816 - 0.997755i) q^{11} +(-2.38515 - 1.37707i) q^{13} +(0.453437 + 3.71408i) q^{14} +(-3.97172 + 0.474777i) q^{16} +2.88632i q^{17} +0.0855521 q^{19} +(3.56959 - 7.13090i) q^{20} +(-2.74643 - 0.649017i) q^{22} +(-5.06735 - 2.92564i) q^{23} +(5.44896 + 9.43788i) q^{25} +(1.11952 + 3.73057i) q^{26} +(3.13526 - 4.26264i) q^{28} +(2.39499 + 4.14825i) q^{29} +(0.893108 - 1.54691i) q^{31} +(4.54853 + 3.36316i) q^{32} +(2.79921 - 2.97088i) q^{34} +(3.65236 + 9.89675i) q^{35} +6.22828 q^{37} +(-0.0880585 - 0.0829700i) q^{38} +(-10.5898 + 3.87797i) q^{40} +(3.94059 + 2.27510i) q^{41} +(-9.28817 + 5.36253i) q^{43} +(2.19747 + 3.33157i) q^{44} +(2.37847 + 7.92576i) q^{46} +(2.22398 + 3.85205i) q^{47} +(1.27718 + 6.88250i) q^{49} +(3.54443 - 14.9989i) q^{50} +(2.46565 - 4.92560i) q^{52} -2.30892 q^{53} -7.95654 q^{55} +(-7.36111 + 1.34689i) q^{56} +(1.55789 - 6.59248i) q^{58} +(-2.41588 + 4.18443i) q^{59} +(-7.08218 + 4.08890i) q^{61} +(-2.41949 + 0.726076i) q^{62} +(-1.42013 - 7.87294i) q^{64} +(5.49066 + 9.51011i) q^{65} +(1.76145 + 1.01697i) q^{67} +(-5.76243 + 0.343197i) q^{68} +(5.83869 - 13.7288i) q^{70} +3.57003i q^{71} +11.4000i q^{73} +(-6.41075 - 6.04030i) q^{74} +(0.0101725 + 0.170801i) q^{76} +(-5.20346 - 0.893522i) q^{77} +(11.4989 - 6.63892i) q^{79} +(14.6610 + 6.27865i) q^{80} +(-1.84960 - 6.16341i) q^{82} +(-8.56210 - 14.8300i) q^{83} +(5.75420 - 9.96656i) q^{85} +(14.7610 + 3.48820i) q^{86} +(0.969175 - 5.56032i) q^{88} +7.76882i q^{89} +(2.52283 + 6.83608i) q^{91} +(5.23839 - 10.4646i) q^{92} +(1.44665 - 6.12176i) q^{94} +(-0.295414 - 0.170557i) q^{95} +(4.07462 - 2.35248i) q^{97} +(5.36018 - 8.32277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.02930	−	0.969818i	−0.727823	−	0.685765i
$2$	−1.02930	−	0.969818i	−0.727823	−	0.685765i
$3$		0			0
$3$		0			0
$4$	0.118905	+	1.99646i	0.0594523	+	0.998231i
$5$	−3.45303	−	1.99361i	−1.54424	−	0.891570i	−0.998564	−	0.0535758i	$-0.982938\pi$
$5$	−3.45303	−	1.99361i	−1.54424	−	0.891570i	−0.545680	−	0.837994i	$-0.683729\pi$
$6$		0			0
$7$	−2.03435	−	1.69157i	−0.768913	−	0.639353i
$7$	−2.03435	−	1.69157i	−0.768913	−	0.639353i
$8$	1.81382	−	2.17027i	0.641281	−	0.767306i
$9$		0			0
$10$	1.62076	+	5.40083i	0.512529	+	1.70789i
$11$	1.72816	−	0.997755i	0.521061	−	0.300834i	−0.216308	−	0.976325i	$-0.569402\pi$
$11$	1.72816	−	0.997755i	0.521061	−	0.300834i	0.737368	+	0.675491i	$0.236068\pi$
$12$		0			0
$13$	−2.38515	−	1.37707i	−0.661521	−	0.381929i	0.131335	−	0.991338i	$-0.458074\pi$
$13$	−2.38515	−	1.37707i	−0.661521	−	0.381929i	−0.792856	+	0.609409i	$0.791407\pi$
$14$	0.453437	+	3.71408i	0.121186	+	0.992630i
$15$		0			0
$16$	−3.97172	+	0.474777i	−0.992931	+	0.118694i
$17$			2.88632i			0.700035i	0.936743	+	0.350018i	$0.113824\pi$
$17$			2.88632i			0.700035i	−0.936743	+	0.350018i	$0.886176\pi$
$18$		0			0
$19$	0.0855521			0.0196270			0.00981349	−	0.999952i	$-0.496876\pi$
$19$	0.0855521			0.0196270			0.00981349	+	0.999952i	$0.496876\pi$
$20$	3.56959	−	7.13090i	0.798184	−	1.59452i
$21$		0			0
$22$	−2.74643	−	0.649017i	−0.585542	−	0.138371i
$23$	−5.06735	−	2.92564i	−1.05662	−	0.610037i	−0.132122	−	0.991234i	$-0.542179\pi$
$23$	−5.06735	−	2.92564i	−1.05662	−	0.610037i	−0.924494	+	0.381196i	$0.875512\pi$
$24$		0			0
$25$	5.44896	+	9.43788i	1.08979	+	1.88758i
$26$	1.11952	+	3.73057i	0.219556	+	0.731625i
$27$		0			0
$28$	3.13526	−	4.26264i	0.592509	−	0.805564i
$29$	2.39499	+	4.14825i	0.444739	+	0.770310i	0.998034	−	0.0626752i	$-0.0199632\pi$
$29$	2.39499	+	4.14825i	0.444739	+	0.770310i	−0.553295	+	0.832985i	$0.686630\pi$
$30$		0			0
$31$	0.893108	−	1.54691i	0.160407	−	0.277833i	−0.774608	−	0.632442i	$-0.782053\pi$
$31$	0.893108	−	1.54691i	0.160407	−	0.277833i	0.935015	+	0.354609i	$0.115386\pi$
$32$	4.54853	+	3.36316i	0.804074	+	0.594529i
$33$		0			0
$34$	2.79921	−	2.97088i	0.480060	−	0.509502i
$35$	3.65236	+	9.89675i	0.617361	+	1.67286i
$36$		0			0
$37$	6.22828			1.02392			0.511961	−	0.859009i	$-0.328919\pi$
$37$	6.22828			1.02392			0.511961	+	0.859009i	$0.328919\pi$
$38$	−0.0880585	−	0.0829700i	−0.0142850	−	0.0134595i
$39$		0			0
$40$	−10.5898	+	3.87797i	−1.67440	+	0.613160i
$41$	3.94059	+	2.27510i	0.615417	+	0.355311i	0.775083	−	0.631860i	$-0.217708\pi$
$41$	3.94059	+	2.27510i	0.615417	+	0.355311i	−0.159666	+	0.987171i	$0.551042\pi$
$42$		0			0
$43$	−9.28817	+	5.36253i	−1.41643	+	0.817777i	−0.995983	−	0.0895388i	$-0.971461\pi$
$43$	−9.28817	+	5.36253i	−1.41643	+	0.817777i	−0.420449	+	0.907316i	$0.638127\pi$
$44$	2.19747	+	3.33157i	0.331281	+	0.502254i
$45$		0			0
$46$	2.37847	+	7.92576i	0.350687	+	1.16859i
$47$	2.22398	+	3.85205i	0.324401	+	0.561879i	0.981391	−	0.192020i	$-0.0615039\pi$
$47$	2.22398	+	3.85205i	0.324401	+	0.561879i	−0.656990	+	0.753899i	$0.728171\pi$
$48$		0			0
$49$	1.27718	+	6.88250i	0.182454	+	0.983214i
$50$	3.54443	−	14.9989i	0.501258	−	2.12116i
$51$		0			0
$52$	2.46565	−	4.92560i	0.341925	−	0.683057i
$53$	−2.30892			−0.317154			−0.158577	−	0.987347i	$-0.550691\pi$
$53$	−2.30892			−0.317154			−0.158577	+	0.987347i	$0.550691\pi$
$54$		0			0
$55$	−7.95654			−1.07286
$56$	−7.36111	+	1.34689i	−0.983669	+	0.179986i
$57$		0			0
$58$	1.55789	−	6.59248i	0.204561	−	0.865635i
$59$	−2.41588	+	4.18443i	−0.314521	+	0.544767i	−0.979336	−	0.202242i	$-0.935177\pi$
$59$	−2.41588	+	4.18443i	−0.314521	+	0.544767i	0.664814	+	0.747009i	$0.268511\pi$
$60$		0			0
$61$	−7.08218	+	4.08890i	−0.906780	+	0.523530i	−0.879394	−	0.476095i	$-0.842052\pi$
$61$	−7.08218	+	4.08890i	−0.906780	+	0.523530i	−0.0273862	+	0.999625i	$0.508718\pi$
$62$	−2.41949	+	0.726076i	−0.307276	+	0.0922117i
$63$		0			0
$64$	−1.42013	−	7.87294i	−0.177516	−	0.984118i
$65$	5.49066	+	9.51011i	0.681033	+	1.17958i
$66$		0			0
$67$	1.76145	+	1.01697i	0.215195	+	0.124243i	0.603724	−	0.797194i	$-0.293683\pi$
$67$	1.76145	+	1.01697i	0.215195	+	0.124243i	−0.388528	+	0.921437i	$0.627016\pi$
$68$	−5.76243	+	0.343197i	−0.698797	+	0.0416187i
$69$		0			0
$70$	5.83869	−	13.7288i	0.697857	−	1.64091i
$71$			3.57003i			0.423685i	0.977304	+	0.211842i	$0.0679464\pi$
$71$			3.57003i			0.423685i	−0.977304	+	0.211842i	$0.932054\pi$
$72$		0			0
$73$			11.4000i			1.33426i	0.744940	+	0.667132i	$0.232478\pi$
$73$			11.4000i			1.33426i	−0.744940	+	0.667132i	$0.767522\pi$
$74$	−6.41075	−	6.04030i	−0.745234	−	0.702170i
$75$		0			0
$76$	0.0101725	+	0.170801i	0.00116687	+	0.0195923i
$77$	−5.20346	−	0.893522i	−0.592990	−	0.101826i
$78$		0			0
$79$	11.4989	−	6.63892i	1.29373	−	0.746936i	0.314418	−	0.949285i	$-0.398191\pi$
$79$	11.4989	−	6.63892i	1.29373	−	0.746936i	0.979314	+	0.202348i	$0.0648573\pi$
$80$	14.6610	+	6.27865i	1.63915	+	0.701974i
$81$		0			0
$82$	−1.84960	−	6.16341i	−0.204255	−	0.680635i
$83$	−8.56210	−	14.8300i	−0.939812	−	1.62780i	−0.765820	−	0.643056i	$-0.777666\pi$
$83$	−8.56210	−	14.8300i	−0.939812	−	1.62780i	−0.173993	−	0.984747i	$-0.555667\pi$
$84$		0			0
$85$	5.75420	−	9.96656i	0.624130	−	1.08103i
$86$	14.7610	+	3.48820i	1.59172	+	0.376143i
$87$		0			0
$88$	0.969175	−	5.56032i	0.103314	−	0.592732i
$89$			7.76882i			0.823493i	0.911298	+	0.411746i	$0.135081\pi$
$89$			7.76882i			0.823493i	−0.911298	+	0.411746i	$0.864919\pi$
$90$		0			0
$91$	2.52283	+	6.83608i	0.264464	+	0.716616i
$92$	5.23839	−	10.4646i	0.546140	−	1.09101i
$93$		0			0
$94$	1.44665	−	6.12176i	0.149211	−	0.631411i
$95$	−0.295414	−	0.170557i	−0.0303089	−	0.0174988i
$96$		0			0
$97$	4.07462	−	2.35248i	0.413715	−	0.238859i	−0.278670	−	0.960387i	$-0.589893\pi$
$97$	4.07462	−	2.35248i	0.413715	−	0.238859i	0.692385	+	0.721528i	$0.256560\pi$
$98$	5.36018	−	8.32277i	0.541460	−	0.840727i
$99$		0			0
$100$	−18.1945	+	12.0009i	−1.81945	+	1.20009i
$101$	2.46857	−	1.42523i	0.245631	−	0.141815i	−0.372131	−	0.928180i	$-0.621373\pi$
$101$	2.46857	−	1.42523i	0.245631	−	0.141815i	0.617762	+	0.786365i	$0.288039\pi$
$102$		0			0
$103$	−1.02846	+	1.78135i	−0.101337	+	0.175521i	−0.912236	−	0.409665i	$-0.865645\pi$
$103$	−1.02846	+	1.78135i	−0.101337	+	0.175521i	0.810899	+	0.585187i	$0.198979\pi$
$104$	−7.31483	+	2.67867i	−0.717278	+	0.262665i
$105$		0			0
$106$	2.37656	+	2.23923i	0.230832	+	0.217493i
$107$		−	15.5534i		−	1.50361i	−0.659387	−	0.751803i	$-0.729184\pi$
$107$		−	15.5534i		−	1.50361i	0.659387	−	0.751803i	$-0.270816\pi$
$108$		0			0
$109$	1.28192			0.122786			0.0613930	−	0.998114i	$-0.480446\pi$
$109$	1.28192			0.122786			0.0613930	+	0.998114i	$0.480446\pi$
$110$	8.18964	+	7.71640i	0.780852	+	0.735730i
$111$		0			0
$112$	8.88300	+	5.75258i	0.839365	+	0.543568i
$113$	−7.39267	+	12.8045i	−0.695444	+	1.20454i	0.274586	+	0.961562i	$0.411459\pi$
$113$	−7.39267	+	12.8045i	−0.695444	+	1.20454i	−0.970031	+	0.242982i	$0.921874\pi$
$114$		0			0
$115$	11.6652	+	20.2046i	1.08778	+	1.88409i
$116$	−7.99704	+	5.27475i	−0.742507	+	0.489749i
$117$		0			0
$118$	6.54480	−	1.96406i	0.602498	−	0.180806i
$119$	4.88241	−	5.87179i	0.447570	−	0.538266i
$120$		0			0
$121$	−3.50897	+	6.07771i	−0.318997	+	0.552519i
$122$	11.2552	+	2.65974i	1.01899	+	0.240801i
$123$		0			0
$124$	3.19454	+	1.59912i	0.286878	+	0.143605i
$125$		−	23.5163i		−	2.10336i
$126$		0			0
$127$			0.327377i			0.0290500i	0.999895	+	0.0145250i	$0.00462361\pi$
$127$			0.327377i			0.0290500i	−0.999895	+	0.0145250i	$0.995376\pi$
$128$	−6.17359	+	9.48087i	−0.545673	+	0.837998i
$129$		0			0
$130$	3.57155	−	15.1137i	0.313246	−	1.32556i
$131$	1.15307	−	1.99717i	0.100744	−	0.174494i	−0.811247	−	0.584703i	$-0.801211\pi$
$131$	1.15307	−	1.99717i	0.100744	−	0.174494i	0.911991	+	0.410209i	$0.134544\pi$
$132$		0			0
$133$	−0.174043	−	0.144717i	−0.0150914	−	0.0125486i
$134$	−0.826776	−	2.75506i	−0.0714226	−	0.238001i
$135$		0			0
$136$	6.26409	+	5.23526i	0.537141	+	0.448920i
$137$	−6.07413	−	10.5207i	−0.518948	−	0.898844i	−0.999758	−	0.0220190i	$-0.992991\pi$
$137$	−6.07413	−	10.5207i	−0.518948	−	0.898844i	0.480810	−	0.876825i	$-0.340343\pi$
$138$		0			0
$139$	4.45697	−	7.71970i	0.378035	−	0.654776i	−0.612741	−	0.790284i	$-0.709933\pi$
$139$	4.45697	−	7.71970i	0.378035	−	0.654776i	0.990776	+	0.135507i	$0.0432665\pi$
$140$	−19.3242	+	8.46856i	−1.63319	+	0.715724i
$141$		0			0
$142$	3.46228	−	3.67462i	0.290548	−	0.308368i
$143$	−5.49590			−0.459590
$144$		0			0
$145$		−	19.0987i		−	1.58606i
$146$	11.0559	−	11.7339i	0.914992	−	0.971108i
$147$		0			0
$148$	0.740571	+	12.4345i	0.0608746	+	1.02211i
$149$	1.02048	−	1.76752i	0.0836008	−	0.144801i	−0.821193	−	0.570650i	$-0.806691\pi$
$149$	1.02048	−	1.76752i	0.0836008	−	0.144801i	0.904794	+	0.425849i	$0.140025\pi$
$150$		0			0
$151$	−9.32355	+	5.38296i	−0.758740	+	0.438059i	−0.828843	−	0.559481i	$-0.811000\pi$
$151$	−9.32355	+	5.38296i	−0.758740	+	0.438059i	0.0701032	+	0.997540i	$0.477667\pi$
$152$	0.155176	−	0.185671i	0.0125864	−	0.0150599i
$153$		0			0
$154$	4.48936	+	5.96612i	0.361763	+	0.480763i
$155$	−6.16786	+	3.56102i	−0.495415	+	0.286028i
$156$		0			0
$157$	−6.83827	−	3.94808i	−0.545753	−	0.315091i	0.201654	−	0.979457i	$-0.435368\pi$
$157$	−6.83827	−	3.94808i	−0.545753	−	0.315091i	−0.747407	+	0.664366i	$0.768702\pi$
$158$	−18.2744	−	4.31847i	−1.45383	−	0.343559i
$159$		0			0
$160$	−9.00139	−	20.6811i	−0.711623	−	1.63499i
$161$	5.35986	+	14.5236i	0.422416	+	1.14462i
$162$		0			0
$163$		−	13.3844i		−	1.04835i	−0.851611	−	0.524175i	$-0.824374\pi$
$163$		−	13.3844i		−	1.04835i	0.851611	−	0.524175i	$-0.175626\pi$
$164$	−4.07360	+	8.13776i	−0.318095	+	0.635452i
$165$		0			0
$166$	−5.56945	+	23.5681i	−0.432273	+	1.82924i
$167$	−6.33117	+	10.9659i	−0.489921	+	0.848568i	−0.999933	−	0.0115994i	$-0.996308\pi$
$167$	−6.33117	+	10.9659i	−0.489921	+	0.848568i	0.510012	+	0.860167i	$0.329641\pi$
$168$		0			0
$169$	−2.70738	−	4.68932i	−0.208260	−	0.360717i
$170$	−15.5885	+	4.67803i	−1.19559	+	0.358788i
$171$		0			0
$172$	−11.8105	−	17.9058i	−0.900541	−	1.36531i
$173$	−6.59908	+	3.80998i	−0.501719	+	0.289668i	−0.729423	−	0.684063i	$-0.760211\pi$
$173$	−6.59908	+	3.80998i	−0.501719	+	0.289668i	0.227704	+	0.973730i	$0.426878\pi$
$174$		0			0
$175$	4.87973	−	28.4173i	0.368873	−	2.14814i
$176$	−6.39007	+	4.78330i	−0.481670	+	0.360555i
$177$		0			0
$178$	7.53434	−	7.99642i	0.564723	−	0.599357i
$179$		−	8.19202i		−	0.612300i	−0.951983	−	0.306150i	$-0.900959\pi$
$179$		−	8.19202i		−	0.612300i	0.951983	−	0.306150i	$-0.0990410\pi$
$180$		0			0
$181$		−	3.68997i		−	0.274274i	−0.990552	−	0.137137i	$-0.956210\pi$
$181$		−	3.68997i		−	0.274274i	0.990552	−	0.137137i	$-0.0437900\pi$
$182$	4.03302	−	9.48304i	0.298947	−	0.702930i
$183$		0			0
$184$	−15.5407	+	5.69094i	−1.14567	+	0.419542i
$185$	−21.5065	−	12.4168i	−1.58119	−	0.912898i
$186$		0			0
$187$	2.87984	+	4.98803i	0.210595	+	0.364761i
$188$	−7.42603	+	4.89812i	−0.541599	+	0.357232i
$189$		0			0
$190$	0.138659	+	0.462052i	0.0100594	+	0.0335208i
$191$	−8.72331	+	5.03641i	−0.631197	+	0.364422i	−0.781215	−	0.624262i	$-0.785400\pi$
$191$	−8.72331	+	5.03641i	−0.631197	+	0.364422i	0.150019	+	0.988683i	$0.452067\pi$
$192$		0			0
$193$	−5.87003	+	10.1672i	−0.422534	+	0.731851i	−0.996187	−	0.0872481i	$-0.972193\pi$
$193$	−5.87003	+	10.1672i	−0.422534	+	0.731851i	0.573652	+	0.819099i	$0.305526\pi$
$194$	−6.47548	−	1.53024i	−0.464912	−	0.109865i
$195$		0			0
$196$	−13.5888	+	3.36820i	−0.970628	+	0.240586i
$197$	−20.3333			−1.44869			−0.724343	−	0.689440i	$-0.757857\pi$
$197$	−20.3333			−1.44869			−0.724343	+	0.689440i	$0.757857\pi$
$198$		0			0
$199$	−22.7777			−1.61467			−0.807335	−	0.590093i	$-0.799091\pi$
$199$	−22.7777			−1.61467			−0.807335	+	0.590093i	$0.799091\pi$
$200$	30.3662	+	5.29288i	2.14721	+	0.374263i
$201$		0			0
$202$	−3.92310	−	0.927078i	−0.276028	−	0.0652290i
$203$	2.14479	−	12.4903i	0.150535	−	0.876646i
$204$		0			0
$205$	−9.07133	−	15.7120i	−0.633569	−	1.09737i
$206$	2.78618	−	0.836115i	0.194122	−	0.0582549i
$207$		0			0
$208$	10.1269	+	4.33691i	0.702177	+	0.300711i
$209$	0.147848	−	0.0853600i	0.0102269	−	0.00590447i
$210$		0			0
$211$	20.1250	+	11.6191i	1.38546	+	0.799895i	0.992799	−	0.119789i	$-0.0382218\pi$
$211$	20.1250	+	11.6191i	1.38546	+	0.799895i	0.392659	+	0.919684i	$0.371555\pi$
$212$	−0.274541	−	4.60967i	−0.0188556	−	0.316593i
$213$		0			0
$214$	−15.0840	+	16.0091i	−1.03112	+	1.09436i
$215$	42.7631			2.91642
$216$		0			0
$217$	−4.43360	+	1.63620i	−0.300972	+	0.111073i
$218$	−1.31948	−	1.24323i	−0.0893665	−	0.0842024i
$219$		0			0
$220$	−0.946069	−	15.8849i	−0.0637840	−	1.07096i
$221$	3.97465	−	6.88430i	0.267364	−	0.463088i
$222$		0			0
$223$	4.17435	+	7.23018i	0.279535	+	0.484169i	0.971269	−	0.237984i	$-0.0764864\pi$
$223$	4.17435	+	7.23018i	0.279535	+	0.484169i	−0.691734	+	0.722152i	$0.743153\pi$
$224$	−3.56429	−	14.5360i	−0.238149	−	0.971229i
$225$		0			0
$226$	20.0273	−	6.01007i	1.33220	−	0.399784i
$227$	3.33734	+	5.78045i	0.221507	+	0.383662i	0.955266	−	0.295748i	$-0.0955690\pi$
$227$	3.33734	+	5.78045i	0.221507	+	0.383662i	−0.733759	+	0.679410i	$0.762236\pi$
$228$		0			0
$229$	8.63009	+	4.98258i	0.570292	+	0.329258i	0.757266	−	0.653107i	$-0.226535\pi$
$229$	8.63009	+	4.98258i	0.570292	+	0.329258i	−0.186974	+	0.982365i	$0.559868\pi$
$230$	7.58792	−	32.1097i	0.500333	−	2.11725i
$231$		0			0
$232$	13.3469	+	2.32639i	0.876266	+	0.152735i
$233$	−3.55156			−0.232670			−0.116335	−	0.993210i	$-0.537115\pi$
$233$	−3.55156			−0.232670			−0.116335	+	0.993210i	$0.537115\pi$
$234$		0			0
$235$		−	17.7350i		−	1.15690i
$236$	−8.64133	−	4.32567i	−0.562502	−	0.281577i
$237$		0			0
$238$	−10.7200	+	1.30876i	−0.694876	+	0.0848346i
$239$	5.01808	+	2.89719i	0.324592	+	0.187403i	0.653438	−	0.756980i	$-0.273326\pi$
$239$	5.01808	+	2.89719i	0.324592	+	0.187403i	−0.328845	+	0.944384i	$0.606659\pi$
$240$		0			0
$241$	−2.63364	+	1.52053i	−0.169648	+	0.0979461i	−0.582420	−	0.812888i	$-0.697894\pi$
$241$	−2.63364	+	1.52053i	−0.169648	+	0.0979461i	0.412772	+	0.910834i	$0.364561\pi$
$242$	9.50605	−	2.85271i	0.611072	−	0.183379i
$243$		0			0
$244$	−9.00543	−	13.6531i	−0.576514	−	0.874051i
$245$	9.31087	−	26.3117i	0.594850	−	1.68099i
$246$		0			0
$247$	−0.204054	−	0.117811i	−0.0129837	−	0.00749612i
$248$	−1.73727	−	4.74409i	−0.110317	−	0.301250i
$249$		0			0
$250$	−22.8066	+	24.2053i	−1.44241	+	1.53088i
$251$	−15.9355			−1.00584			−0.502920	−	0.864333i	$-0.667741\pi$
$251$	−15.9355			−1.00584			−0.502920	+	0.864333i	$0.667741\pi$
$252$		0			0
$253$	−11.6763			−0.734081
$254$	0.317496	−	0.336968i	0.0199215	−	0.0211432i
$255$		0			0
$256$	15.5492	−	3.77137i	0.971823	−	0.235711i
$257$	17.9529	+	10.3651i	1.11987	+	0.646559i	0.941369	−	0.337380i	$-0.109541\pi$
$257$	17.9529	+	10.3651i	1.11987	+	0.646559i	0.178505	+	0.983939i	$0.442874\pi$
$258$		0			0
$259$	−12.6705	−	10.5356i	−0.787307	−	0.654648i
$260$	−18.3337	+	12.0927i	−1.13701	+	0.749957i
$261$		0			0
$262$	−3.12375	+	0.937417i	−0.192986	+	0.0579138i
$263$	−1.29122	+	0.745488i	−0.0796202	+	0.0459687i	−0.539282	−	0.842126i	$-0.681304\pi$
$263$	−1.29122	+	0.745488i	−0.0796202	+	0.0459687i	0.459661	+	0.888094i	$0.347971\pi$
$264$		0			0
$265$	7.97277	+	4.60308i	0.489763	+	0.282765i
$266$	0.0387925	+	0.317747i	0.00237852	+	0.0194823i
$267$		0			0
$268$	−1.82091	+	3.63759i	−0.111230	+	0.222201i
$269$			18.2450i			1.11242i	0.831043	+	0.556209i	$0.187745\pi$
$269$			18.2450i			1.11242i	−0.831043	+	0.556209i	$0.812255\pi$
$270$		0			0
$271$	−15.4908			−0.940998			−0.470499	−	0.882400i	$-0.655926\pi$
$271$	−15.4908			−0.940998			−0.470499	+	0.882400i	$0.655926\pi$
$272$	−1.37036	−	11.4637i	−0.0830902	−	0.695087i
$273$		0			0
$274$	−3.95108	+	16.7197i	−0.238694	+	1.01008i
$275$	18.8334	+	10.8735i	1.13570	+	0.655694i
$276$		0			0
$277$	−9.29870	−	16.1058i	−0.558705	−	0.967705i	−0.997605	−	0.0691691i	$-0.977965\pi$
$277$	−9.29870	−	16.1058i	−0.558705	−	0.967705i	0.438900	−	0.898536i	$-0.355368\pi$
$278$	−12.0743	+	3.62341i	−0.724165	+	0.217318i
$279$		0			0
$280$	28.1033	+	10.0243i	1.67949	+	0.599067i
$281$	9.87259	+	17.0998i	0.588950	+	1.02009i	0.994370	+	0.105960i	$0.0337917\pi$
$281$	9.87259	+	17.0998i	0.588950	+	1.02009i	−0.405421	+	0.914130i	$0.632875\pi$
$282$		0			0
$283$	−8.53005	+	14.7745i	−0.507059	+	0.878252i	0.492908	+	0.870082i	$0.335934\pi$
$283$	−8.53005	+	14.7745i	−0.507059	+	0.878252i	−0.999967	+	0.00817031i	$0.997399\pi$
$284$	−7.12743	+	0.424493i	−0.422935	+	0.0251890i
$285$		0			0
$286$	5.65691	+	5.33002i	0.334500	+	0.315171i
$287$	−4.16806	−	11.2941i	−0.246033	−	0.666672i
$288$		0			0
$289$	8.66916			0.509950
$290$	−18.5223	+	19.6582i	−1.08767	+	1.15437i
$291$		0			0
$292$	−22.7596	+	1.35551i	−1.33190	+	0.0793251i
$293$	22.2955	+	12.8723i	1.30252	+	0.752009i	0.980835	−	0.194838i	$-0.0624181\pi$
$293$	22.2955	+	12.8723i	1.30252	+	0.752009i	0.321683	+	0.946847i	$0.395751\pi$
$294$		0			0
$295$	16.6843	−	9.63266i	0.971395	−	0.560835i
$296$	11.2970	−	13.5170i	0.656622	−	0.785662i
$297$		0			0
$298$	−2.76455	+	0.829624i	−0.160146	+	0.0480588i
$299$	8.05759	+	13.9562i	0.465982	+	0.807105i
$300$		0			0
$301$	27.9665	+	4.80232i	1.61196	+	0.276801i
$302$	14.8172	+	3.50149i	0.852634	+	0.201488i
$303$		0			0
$304$	−0.339789	+	0.0406182i	−0.0194882	+	0.00232961i
$305$	32.6067			1.86705
$306$		0			0
$307$	−7.34083			−0.418963			−0.209482	−	0.977813i	$-0.567178\pi$
$307$	−7.34083			−0.418963			−0.209482	+	0.977813i	$0.567178\pi$
$308$	1.16517	−	10.4948i	0.0663916	−	0.597995i
$309$		0			0
$310$	9.80210	+	2.31636i	0.556722	+	0.131561i
$311$	−14.2106	+	24.6135i	−0.805809	+	1.39570i	0.109935	+	0.993939i	$0.464936\pi$
$311$	−14.2106	+	24.6135i	−0.805809	+	1.39570i	−0.915744	+	0.401763i	$0.868398\pi$
$312$		0			0
$313$	−12.8704	+	7.43074i	−0.727479	+	0.420010i	−0.817499	−	0.575930i	$-0.804640\pi$
$313$	−12.8704	+	7.43074i	−0.727479	+	0.420010i	0.0900203	+	0.995940i	$0.471307\pi$
$314$	3.20969	+	10.6956i	0.181133	+	0.603589i
$315$		0			0
$316$	14.6216	+	22.1678i	0.822530	+	1.24704i
$317$	−10.7056	−	18.5426i	−0.601284	−	1.04145i	−0.992627	−	0.121209i	$-0.961323\pi$
$317$	−10.7056	−	18.5426i	−0.601284	−	1.04145i	0.391343	−	0.920245i	$-0.372010\pi$
$318$		0			0
$319$	8.27787	+	4.77923i	0.463472	+	0.267585i
$320$	−10.7918	+	30.0167i	−0.603281	+	1.67799i
$321$		0			0
$322$	8.56832	−	20.1471i	0.477494	−	1.12276i
$323$			0.246931i			0.0137396i
$324$		0			0
$325$		−	30.0143i		−	1.66489i
$326$	−12.9805	+	13.7765i	−0.718921	+	0.763013i
$327$		0			0
$328$	12.0851	−	4.42552i	0.667288	−	0.244359i
$329$	1.99165	−	11.5984i	0.109803	−	0.639443i
$330$		0			0
$331$	−14.7097	+	8.49262i	−0.808515	+	0.466797i	−0.846440	−	0.532484i	$-0.821259\pi$
$331$	−14.7097	+	8.49262i	−0.808515	+	0.466797i	0.0379246	+	0.999281i	$0.487925\pi$
$332$	28.5894	−	18.8573i	1.56905	−	1.03493i
$333$		0			0
$334$	17.1516	−	5.14710i	0.938494	−	0.281637i
$335$	−4.05490	−	7.02329i	−0.221543	−	0.383723i
$336$		0			0
$337$	4.90546	−	8.49651i	0.267217	−	0.462834i	−0.700925	−	0.713235i	$-0.747229\pi$
$337$	4.90546	−	8.49651i	0.267217	−	0.462834i	0.968142	+	0.250401i	$0.0805625\pi$
$338$	−1.76109	+	7.45237i	−0.0957907	+	0.405355i
$339$		0			0
$340$	20.5821	+	10.3030i	1.11622	+	0.558757i
$341$		−	3.56441i		−	0.193024i
$342$		0			0
$343$	9.04400	−	16.1619i	0.488330	−	0.872659i
$344$	−5.20892	+	29.8845i	−0.280846	+	1.61126i
$345$		0			0
$346$	10.4874	+	2.47831i	0.563807	+	0.133235i
$347$	3.21012	+	1.85336i	0.172328	+	0.0994937i	0.583683	−	0.811982i	$-0.301611\pi$
$347$	3.21012	+	1.85336i	0.172328	+	0.0994937i	−0.411355	+	0.911475i	$0.634944\pi$
$348$		0			0
$349$	4.31419	−	2.49080i	0.230933	−	0.133329i	−0.380069	−	0.924958i	$-0.624100\pi$
$349$	4.31419	−	2.49080i	0.230933	−	0.133329i	0.611003	+	0.791629i	$0.290767\pi$
$350$	−32.5823	+	24.5174i	−1.74160	+	1.31051i
$351$		0			0
$352$	11.2162	+	1.27377i	0.597826	+	0.0678923i
$353$	10.4059	−	6.00788i	0.553853	−	0.319767i	−0.196822	−	0.980439i	$-0.563062\pi$
$353$	10.4059	−	6.00788i	0.553853	−	0.319767i	0.750674	+	0.660672i	$0.229729\pi$
$354$		0			0
$355$	7.11725	−	12.3274i	0.377744	−	0.654273i
$356$	−15.5101	+	0.923748i	−0.822036	+	0.0489586i
$357$		0			0
$358$	−7.94477	+	8.43202i	−0.419894	+	0.445646i
$359$			27.6368i			1.45861i	0.684187	+	0.729307i	$0.260157\pi$
$359$			27.6368i			1.45861i	−0.684187	+	0.729307i	$0.739843\pi$
$360$		0			0
$361$	−18.9927			−0.999615
$362$	−3.57860	+	3.79808i	−0.188087	+	0.199623i
$363$		0			0
$364$	−13.3480	+	5.84957i	−0.699626	+	0.306601i
$365$	22.7271	−	39.3644i	1.18959	−	2.06043i
$366$		0			0
$367$	14.7663	+	25.5760i	0.770796	+	1.33506i	0.937127	+	0.348988i	$0.113475\pi$
$367$	14.7663	+	25.5760i	0.770796	+	1.33506i	−0.166331	+	0.986070i	$0.553192\pi$
$368$	21.5151	+	9.21395i	1.12155	+	0.480311i
$369$		0			0
$370$	10.0945	+	33.6379i	0.524790	+	1.74875i
$371$	4.69715	+	3.90570i	0.243864	+	0.202774i
$372$		0			0
$373$	−6.89959	+	11.9504i	−0.357247	+	0.618770i	−0.987500	−	0.157620i	$-0.949618\pi$
$373$	−6.89959	+	11.9504i	−0.357247	+	0.618770i	0.630253	+	0.776390i	$0.282951\pi$
$374$	1.87327	−	7.92709i	0.0968646	−	0.409900i
$375$		0			0
$376$	12.3939	+	2.16028i	0.639165	+	0.111408i
$377$		−	13.1922i		−	0.679435i
$378$		0			0
$379$		−	16.1019i		−	0.827099i	−0.910482	−	0.413549i	$-0.864289\pi$
$379$		−	16.1019i		−	0.827099i	0.910482	−	0.413549i	$-0.135711\pi$
$380$	0.305385	−	0.610063i	0.0156659	−	0.0312956i
$381$		0			0
$382$	13.8633	+	3.27607i	0.709307	+	0.167618i
$383$	8.61022	−	14.9133i	0.439962	−	0.762036i	−0.557724	−	0.830026i	$-0.688325\pi$
$383$	8.61022	−	14.9133i	0.439962	−	0.762036i	0.997686	+	0.0679904i	$0.0216587\pi$
$384$		0			0
$385$	16.1864	+	13.4590i	0.824935	+	0.685936i
$386$	15.9023	−	4.77220i	0.809408	−	0.242898i
$387$		0			0
$388$	5.18114	+	7.85511i	0.263032	+	0.398783i
$389$	−2.16557	−	3.75088i	−0.109799	−	0.190177i	0.805890	−	0.592066i	$-0.201687\pi$
$389$	−2.16557	−	3.75088i	−0.109799	−	0.190177i	−0.915689	+	0.401888i	$0.868354\pi$
$390$		0			0
$391$	8.44432	−	14.6260i	0.427048	−	0.739668i
$392$	17.2534	+	9.71178i	0.871431	+	0.490519i
$393$		0			0
$394$	20.9290	+	19.7196i	1.05439	+	0.993458i
$395$	−52.9416			−2.66378
$396$		0			0
$397$			28.5958i			1.43518i	0.696466	+	0.717590i	$0.254755\pi$
$397$			28.5958i			1.43518i	−0.696466	+	0.717590i	$0.745245\pi$
$398$	23.4450	+	22.0903i	1.17519	+	1.10728i
$399$		0			0
$400$	−26.1227	−	34.8976i	−1.30613	−	1.74488i
$401$	6.03293	−	10.4493i	0.301270	−	0.521815i	−0.675154	−	0.737677i	$-0.735923\pi$
$401$	6.03293	−	10.4493i	0.301270	−	0.521815i	0.976424	+	0.215862i	$0.0692561\pi$
$402$		0			0
$403$	−4.26039	+	2.45974i	−0.212225	+	0.122528i
$404$	3.13894	+	4.75893i	0.156168	+	0.236766i
$405$		0			0
$406$	−14.3209	+	10.7762i	−0.710736	+	0.534812i
$407$	10.7635	−	6.21430i	0.533526	−	0.308031i
$408$		0			0
$409$	−19.8538	−	11.4626i	−0.981705	−	0.566788i	−0.0789208	−	0.996881i	$-0.525147\pi$
$409$	−19.8538	−	11.4626i	−0.981705	−	0.566788i	−0.902785	+	0.430093i	$0.858481\pi$
$410$	−5.90070	+	24.9699i	−0.291415	+	1.23317i
$411$		0			0
$412$	−3.67868	−	1.84147i	−0.181236	−	0.0907229i
$413$	11.9930	−	4.42598i	0.590138	−	0.217788i
$414$		0			0
$415$			68.2779i			3.35163i
$416$	−6.21762	−	14.2853i	−0.304844	−	0.700393i
$417$		0			0
$418$	−0.234963	−	0.0555248i	−0.0114924	−	0.00271581i
$419$	5.84657	−	10.1266i	0.285624	−	0.494715i	−0.687136	−	0.726528i	$-0.741133\pi$
$419$	5.84657	−	10.1266i	0.285624	−	0.494715i	0.972760	+	0.231813i	$0.0744659\pi$
$420$		0			0
$421$	5.56174	+	9.63321i	0.271063	+	0.469494i	0.969134	−	0.246534i	$-0.0792916\pi$
$421$	5.56174	+	9.63321i	0.271063	+	0.469494i	−0.698072	+	0.716028i	$0.745958\pi$
$422$	−9.44609	−	31.4771i	−0.459828	−	1.53228i
$423$		0			0
$424$	−4.18795	+	5.01097i	−0.203385	+	0.243354i
$425$	−27.2407	+	15.7274i	−1.32137	+	0.762893i
$426$		0			0
$427$	21.3243	+	3.66174i	1.03196	+	0.177204i
$428$	31.0518	−	1.84937i	1.50095	−	0.0893929i
$429$		0			0
$430$	−44.0160	−	41.4725i	−2.12264	−	1.99998i
$431$			33.5046i			1.61386i	0.590647	+	0.806930i	$0.298873\pi$
$431$			33.5046i			1.61386i	−0.590647	+	0.806930i	$0.701127\pi$
$432$		0			0
$433$		−	6.77529i		−	0.325600i	−0.986659	−	0.162800i	$-0.947948\pi$
$433$		−	6.77529i		−	0.325600i	0.986659	−	0.162800i	$-0.0520525\pi$
$434$	6.15031	+	2.61565i	0.295224	+	0.125555i
$435$		0			0
$436$	0.152427	+	2.55931i	0.00729992	+	0.122569i
$437$	−0.433522	−	0.250294i	−0.0207382	−	0.0119732i
$438$		0			0
$439$	−0.0179749	−	0.0311334i	−0.000857895	−	0.00148592i	0.865596	−	0.500743i	$-0.166940\pi$
$439$	−0.0179749	−	0.0311334i	−0.000857895	−	0.00148592i	−0.866454	+	0.499257i	$0.833606\pi$
$440$	−14.4317	+	17.2678i	−0.688005	+	0.823211i
$441$		0			0
$442$	−10.7676	+	3.23130i	−0.512163	+	0.153697i
$443$	13.0209	−	7.51761i	0.618641	−	0.357172i	−0.157699	−	0.987487i	$-0.550408\pi$
$443$	13.0209	−	7.51761i	0.618641	−	0.357172i	0.776340	+	0.630315i	$0.217074\pi$
$444$		0			0
$445$	15.4880	−	26.8260i	0.734201	−	1.27167i
$446$	2.71532	−	11.4904i	0.128574	−	0.544084i
$447$		0			0
$448$	−10.4286	+	18.4186i	−0.492704	+	0.870197i
$449$	22.0365			1.03997			0.519983	−	0.854177i	$-0.325938\pi$
$449$	22.0365			1.03997			0.519983	+	0.854177i	$0.325938\pi$
$450$		0			0
$451$	9.07998			0.427559
$452$	−26.4427	−	13.2367i	−1.24376	−	0.622601i
$453$		0			0
$454$	2.17087	−	9.18642i	0.101884	−	0.431140i
$455$	4.91707	−	28.6348i	0.230516	−	1.34242i
$456$		0			0
$457$	−8.88558	−	15.3903i	−0.415650	−	0.719927i	0.579846	−	0.814726i	$-0.303113\pi$
$457$	−8.88558	−	15.3903i	−0.415650	−	0.719927i	−0.995496	+	0.0947989i	$0.969779\pi$
$458$	−4.05072	−	13.4982i	−0.189278	−	0.630728i
$459$		0			0
$460$	−38.9508	+	25.6915i	−1.81609	+	1.19787i
$461$	−29.7074	+	17.1515i	−1.38361	+	0.798827i	−0.992585	−	0.121553i	$-0.961213\pi$
$461$	−29.7074	+	17.1515i	−1.38361	+	0.798827i	−0.391025	+	0.920380i	$0.627879\pi$
$462$		0			0
$463$	−30.4583	−	17.5851i	−1.41552	−	0.817248i	−0.419615	−	0.907702i	$-0.637835\pi$
$463$	−30.4583	−	17.5851i	−1.41552	−	0.817248i	−0.995901	+	0.0904537i	$0.971168\pi$
$464$	−11.4817	−	15.3386i	−0.533026	−	0.712077i
$465$		0			0
$466$	3.65561	+	3.44437i	0.169343	+	0.159557i
$467$	2.10775			0.0975348			0.0487674	−	0.998810i	$-0.484471\pi$
$467$	2.10775			0.0975348			0.0487674	+	0.998810i	$0.484471\pi$
$468$		0			0
$469$	−1.86313	−	5.04850i	−0.0860313	−	0.233118i
$470$	−17.1997	+	18.2546i	−0.793365	+	0.842021i
$471$		0			0
$472$	4.69937	+	12.8329i	0.216306	+	0.590683i
$473$	−10.7010	+	18.5346i	−0.492031	+	0.852223i
$474$		0			0
$475$	0.466170	+	0.807430i	0.0213893	+	0.0370474i
$476$	12.3034	+	9.04937i	0.563923	+	0.414777i
$477$		0			0
$478$	−2.35534	−	7.84869i	−0.107731	−	0.358991i
$479$	0.601718	+	1.04221i	0.0274932	+	0.0476196i	0.879445	−	0.476001i	$-0.157914\pi$
$479$	0.601718	+	1.04221i	0.0274932	+	0.0476196i	−0.851951	+	0.523621i	$0.824581\pi$
$480$		0			0
$481$	−14.8554	−	8.57675i	−0.677346	−	0.391066i
$482$	4.18544	+	0.989073i	0.190641	+	0.0450510i
$483$		0			0
$484$	−12.5512	−	6.28286i	−0.570507	−	0.285584i
$485$	−18.7597			−0.851836
$486$		0			0
$487$		−	4.23920i		−	0.192097i	−0.995377	−	0.0960483i	$-0.969380\pi$
$487$		−	4.23920i		−	0.192097i	0.995377	−	0.0960483i	$-0.0306203\pi$
$488$	−3.97177	+	22.7867i	−0.179794	+	1.03151i
$489$		0			0
$490$	−35.1012	+	18.0527i	−1.58571	+	0.815538i
$491$	−14.4458	−	8.34027i	−0.651928	−	0.376391i	0.137266	−	0.990534i	$-0.456168\pi$
$491$	−14.4458	−	8.34027i	−0.651928	−	0.376391i	−0.789195	+	0.614143i	$0.789502\pi$
$492$		0			0
$493$	−11.9732	+	6.91271i	−0.539244	+	0.311333i
$494$	0.0957774	+	0.319158i	0.00430923	+	0.0143596i
$495$		0			0
$496$	−2.81274	+	6.56792i	−0.126296	+	0.294908i
$497$	6.03896	−	7.26270i	0.270884	−	0.325777i
$498$		0			0
$499$	−26.1648	−	15.1063i	−1.17130	−	0.676249i	−0.217312	−	0.976102i	$-0.569729\pi$
$499$	−26.1648	−	15.1063i	−1.17130	−	0.676249i	−0.953985	+	0.299853i	$0.903062\pi$
$500$	46.9494	−	2.79620i	2.09964	−	0.125050i
$501$		0			0
$502$	16.4024	+	15.4545i	0.732073	+	0.689770i
$503$	−9.33949			−0.416427			−0.208214	−	0.978083i	$-0.566765\pi$
$503$	−9.33949			−0.416427			−0.208214	+	0.978083i	$0.566765\pi$
$504$		0			0
$505$	−11.3654			−0.505753
$506$	12.0184	+	11.3239i	0.534281	+	0.503407i
$507$		0			0
$508$	−0.653595	+	0.0389266i	−0.0289986	+	0.00172709i
$509$	9.96494	+	5.75326i	0.441688	+	0.255009i	0.704313	−	0.709889i	$-0.251255\pi$
$509$	9.96494	+	5.75326i	0.441688	+	0.255009i	−0.262625	+	0.964898i	$0.584588\pi$
$510$		0			0
$511$	19.2838	−	23.1915i	0.853066	−	1.02593i
$512$	−19.6623	−	11.1980i	−0.868957	−	0.494887i
$513$		0			0
$514$	−8.42661	−	28.0799i	−0.371682	−	1.23855i
$515$	7.10263	−	4.10070i	0.312979	−	0.180699i
$516$		0			0
$517$	7.68680	+	4.43798i	0.338065	+	0.195182i
$518$	2.82413	+	23.1323i	0.124085	+	1.01638i
$519$		0			0
$520$	30.5986	+	5.33339i	1.34184	+	0.233885i
$521$		−	28.7291i		−	1.25865i	−0.777144	−	0.629323i	$-0.783332\pi$
$521$		−	28.7291i		−	1.25865i	0.777144	−	0.629323i	$-0.216668\pi$
$522$		0			0
$523$	20.1932			0.882986			0.441493	−	0.897265i	$-0.354449\pi$
$523$	20.1932			0.882986			0.441493	+	0.897265i	$0.354449\pi$
$524$	4.12439	+	2.06458i	0.180175	+	0.0901918i
$525$		0			0
$526$	2.05204	+	0.484923i	0.0894732	+	0.0211437i
$527$	4.46487	+	2.57779i	0.194493	+	0.112291i
$528$		0			0
$529$	5.61870	+	9.73187i	0.244291	+	0.423125i
$530$	−3.74220	−	12.4701i	−0.162551	−	0.541665i
$531$		0			0
$532$	0.268228	−	0.364678i	0.0116292	−	0.0158108i
$533$	−6.26593	−	10.8529i	−0.271408	−	0.470092i
$534$		0			0
$535$	−31.0075	+	53.7065i	−1.34057	+	2.32193i
$536$	5.40206	−	1.97822i	0.233333	−	0.0854459i
$537$		0			0
$538$	17.6943	−	18.7795i	0.762857	−	0.809643i
$539$	9.07422	+	10.6198i	0.390855	+	0.457426i
$540$		0			0
$541$	31.7977			1.36709			0.683545	−	0.729908i	$-0.260437\pi$
$541$	31.7977			1.36709			0.683545	+	0.729908i	$0.260437\pi$
$542$	15.9446	+	15.0232i	0.684880	+	0.645304i
$543$		0			0
$544$	−9.70717	+	13.1285i	−0.416191	+	0.562880i
$545$	−4.42653	−	2.55566i	−0.189612	−	0.109472i
$546$		0			0
$547$	−6.72258	+	3.88128i	−0.287437	+	0.165952i	−0.636785	−	0.771041i	$-0.719736\pi$
$547$	−6.72258	+	3.88128i	−0.287437	+	0.165952i	0.349349	+	0.936993i	$0.386403\pi$
$548$	20.2819	−	13.3777i	0.866401	−	0.571468i
$549$		0			0
$550$	−8.83986	−	29.4570i	−0.376933	−	1.25605i
$551$	0.204896	+	0.354891i	0.00872888	+	0.0151189i
$552$		0			0
$553$	−34.6231	−	5.94537i	−1.47232	−	0.252823i
$554$	−6.04860	+	25.5957i	−0.256980	+	1.08746i
$555$		0			0
$556$	15.9420	+	7.98026i	0.676093	+	0.338439i
$557$	−28.2834			−1.19841			−0.599203	−	0.800597i	$-0.704516\pi$
$557$	−28.2834			−1.19841			−0.599203	+	0.800597i	$0.704516\pi$
$558$		0			0
$559$	29.5382			1.24933
$560$	−19.2049	−	37.5731i	−0.811555	−	1.58775i
$561$		0			0
$562$	6.42190	−	27.1754i	0.270892	−	1.14633i
$563$	12.2242	−	21.1729i	0.515187	−	0.892331i	−0.484657	−	0.874704i	$-0.661056\pi$
$563$	12.2242	−	21.1729i	0.515187	−	0.892331i	0.999845	−	0.0176266i	$-0.00561102\pi$
$564$		0			0
$565$	51.0543	−	29.4762i	2.14787	−	1.24007i
$566$	23.1085	−	6.93473i	0.971324	−	0.291488i
$567$		0			0
$568$	7.74793	+	6.47539i	0.325096	+	0.271701i
$569$	12.6476	+	21.9063i	0.530215	+	0.918360i	0.999379	+	0.0352483i	$0.0112222\pi$
$569$	12.6476	+	21.9063i	0.530215	+	0.918360i	−0.469163	+	0.883111i	$0.655444\pi$
$570$		0			0
$571$	15.5735	+	8.99137i	0.651731	+	0.376277i	0.789119	−	0.614240i	$-0.210537\pi$
$571$	15.5735	+	8.99137i	0.651731	+	0.376277i	−0.137388	+	0.990517i	$0.543871\pi$
$572$	−0.653488	−	10.9724i	−0.0273237	−	0.458777i
$573$		0			0
$574$	−6.66310	+	15.6673i	−0.278112	+	0.653940i
$575$		−	63.7667i		−	2.65926i
$576$		0			0
$577$			13.5843i			0.565523i	0.959190	+	0.282762i	$0.0912505\pi$
$577$			13.5843i			0.565523i	−0.959190	+	0.282762i	$0.908749\pi$
$578$	−8.92314	−	8.40751i	−0.371154	−	0.349706i
$579$		0			0
$580$	38.1299	−	2.27093i	1.58326	−	0.0942951i
$581$	−7.66764	+	44.6528i	−0.318107	+	1.85251i
$582$		0			0
$583$	−3.99018	+	2.30373i	−0.165257	+	0.0954109i
$584$	24.7410	+	20.6774i	1.02379	+	0.855638i
$585$		0			0
$586$	−10.4649	−	34.8721i	−0.432301	−	1.44055i
$587$	23.6479	+	40.9593i	0.976052	+	1.69057i	0.676418	+	0.736518i	$0.263531\pi$
$587$	23.6479	+	40.9593i	0.976052	+	1.69057i	0.299634	+	0.954054i	$0.403135\pi$
$588$		0			0
$589$	0.0764072	−	0.132341i	0.00314830	−	0.00545302i
$590$	−26.5150	−	6.26583i	−1.09160	−	0.257960i
$591$		0			0
$592$	−24.7370	+	2.95704i	−1.01668	+	0.121534i
$593$		−	0.875544i		−	0.0359543i	−0.999838	−	0.0179772i	$-0.994277\pi$
$593$		−	0.875544i		−	0.0359543i	0.999838	−	0.0179772i	$-0.00572261\pi$
$594$		0			0
$595$	−28.5652	+	10.5419i	−1.17106	+	0.432175i
$596$	3.65013	+	1.82718i	0.149515	+	0.0748442i
$597$		0			0
$598$	5.24128	−	22.1794i	0.214332	−	0.906984i
$599$	−12.3931	−	7.15518i	−0.506370	−	0.292353i	0.224970	−	0.974366i	$-0.427771\pi$
$599$	−12.3931	−	7.15518i	−0.506370	−	0.292353i	−0.731340	+	0.682013i	$0.761105\pi$
$600$		0			0
$601$	−30.3634	+	17.5303i	−1.23855	+	0.715076i	−0.968797	−	0.247854i	$-0.920275\pi$
$601$	−30.3634	+	17.5303i	−1.23855	+	0.715076i	−0.269751	+	0.962930i	$0.586941\pi$
$602$	−24.1285	−	32.0654i	−0.983402	−	1.30689i
$603$		0			0
$604$	−11.8555	−	17.9741i	−0.482393	−	0.731354i
$605$	24.2332	−	13.9910i	0.985219	−	0.568816i
$606$		0			0
$607$	18.7611	−	32.4951i	0.761489	−	1.31894i	−0.180594	−	0.983558i	$-0.557802\pi$
$607$	18.7611	−	32.4951i	0.761489	−	1.31894i	0.942083	−	0.335380i	$-0.108865\pi$
$608$	0.389136	+	0.287726i	0.0157816	+	0.0116688i
$609$		0			0
$610$	−33.5619	−	31.6225i	−1.35888	−	1.28036i
$611$		−	12.2503i		−	0.495593i
$612$		0			0
$613$	−0.149504			−0.00603840			−0.00301920	−	0.999995i	$-0.500961\pi$
$613$	−0.149504			−0.00603840			−0.00301920	+	0.999995i	$0.500961\pi$
$614$	7.55589	+	7.11927i	0.304931	+	0.287310i
$615$		0			0
$616$	−11.3773	+	9.67223i	−0.458405	+	0.389705i
$617$	3.41249	−	5.91061i	0.137382	−	0.237952i	−0.789123	−	0.614235i	$-0.789465\pi$
$617$	3.41249	−	5.91061i	0.137382	−	0.237952i	0.926505	+	0.376283i	$0.122798\pi$
$618$		0			0
$619$	−10.1762	−	17.6257i	−0.409016	−	0.708436i	0.585764	−	0.810482i	$-0.300795\pi$
$619$	−10.1762	−	17.6257i	−0.409016	−	0.708436i	−0.994780	+	0.102045i	$0.967461\pi$
$620$	−7.84282	−	11.8905i	−0.314975	−	0.477533i
$621$		0			0
$622$	38.4975	−	11.5529i	1.54361	−	0.463228i
$623$	13.1415	−	15.8045i	0.526503	−	0.633194i
$624$		0			0
$625$	−19.6376	+	34.0133i	−0.785503	+	1.36053i
$626$	20.4539	+	4.83353i	0.817504	+	0.193187i
$627$		0			0
$628$	7.06908	−	14.1218i	0.282087	−	0.563521i
$629$			17.9768i			0.716782i
$630$		0			0
$631$		−	21.2923i		−	0.847634i	−0.905748	−	0.423817i	$-0.860690\pi$
$631$		−	21.2923i		−	0.847634i	0.905748	−	0.423817i	$-0.139310\pi$
$632$	6.44875	−	36.9976i	0.256517	−	1.47168i
$633$		0			0
$634$	−6.96372	+	29.4682i	−0.276565	+	1.17033i
$635$	0.652661	−	1.13044i	0.0259001	−	0.0448603i
$636$		0			0
$637$	6.43139	−	18.1745i	0.254821	−	0.720102i
$638$	−3.88540	−	12.9473i	−0.153824	−	0.512587i
$639$		0			0
$640$	40.2188	−	20.4300i	1.58979	−	0.807568i
$641$	3.95191	+	6.84490i	0.156091	+	0.270357i	0.933456	−	0.358693i	$-0.116777\pi$
$641$	3.95191	+	6.84490i	0.156091	+	0.270357i	−0.777365	+	0.629050i	$0.783444\pi$
$642$		0			0
$643$	−20.3837	+	35.3055i	−0.803853	+	1.39231i	0.113209	+	0.993571i	$0.463887\pi$
$643$	−20.3837	+	35.3055i	−0.803853	+	1.39231i	−0.917062	+	0.398744i	$0.869446\pi$
$644$	−28.3584	+	12.4277i	−1.11748	+	0.489719i
$645$		0			0
$646$	0.239478	−	0.254165i	0.00942213	−	0.00999999i
$647$	−17.8067			−0.700054			−0.350027	−	0.936740i	$-0.613828\pi$
$647$	−17.8067			−0.700054			−0.350027	+	0.936740i	$0.613828\pi$
$648$		0			0
$649$			9.64184i			0.378475i
$650$	−29.1084	+	30.8936i	−1.14173	+	1.21175i
$651$		0			0
$652$	26.7215	−	1.59147i	1.04649	−	0.0623268i
$653$	−6.78123	+	11.7454i	−0.265370	+	0.459635i	−0.967661	−	0.252256i	$-0.918827\pi$
$653$	−6.78123	+	11.7454i	−0.265370	+	0.459635i	0.702290	+	0.711891i	$0.252161\pi$
$654$		0			0
$655$	−7.96317	+	4.59754i	−0.311147	+	0.179641i
$656$	−16.7311	−	7.16517i	−0.653240	−	0.279753i
$657$		0			0
$658$	−13.2984	+	10.0067i	−0.518425	+	0.390102i
$659$	−37.2494	+	21.5060i	−1.45103	+	0.837754i	−0.998540	−	0.0540142i	$-0.982798\pi$
$659$	−37.2494	+	21.5060i	−1.45103	+	0.837754i	−0.452492	+	0.891768i	$0.649465\pi$
$660$		0			0
$661$	37.6797	+	21.7544i	1.46557	+	0.846148i	0.999260	−	0.0384716i	$-0.0122489\pi$
$661$	37.6797	+	21.7544i	1.46557	+	0.846148i	0.466312	+	0.884620i	$0.345582\pi$
$662$	23.3769	+	5.52426i	0.908569	+	0.214706i
$663$		0			0
$664$	−47.7151	−	8.31684i	−1.85171	−	0.322756i
$665$	0.312467	+	0.846688i	0.0121169	+	0.0328331i
$666$		0			0
$667$		−	28.0275i		−	1.08523i
$668$	−22.6458	−	11.3361i	−0.876194	−	0.438605i
$669$		0			0
$670$	−2.63762	+	11.1616i	−0.101900	+	0.431209i
$671$	−8.15943	+	14.1326i	−0.314991	+	0.545581i
$672$		0			0
$673$	21.6667	+	37.5278i	0.835189	+	1.44659i	0.893877	+	0.448313i	$0.147975\pi$
$673$	21.6667	+	37.5278i	0.835189	+	1.44659i	−0.0586878	+	0.998276i	$0.518692\pi$
$674$	−13.2892	+	3.98802i	−0.511882	+	0.153613i
$675$		0			0
$676$	9.04013	−	5.96276i	0.347697	−	0.229337i
$677$	18.0239	−	10.4061i	0.692714	−	0.399939i	−0.111914	−	0.993718i	$-0.535698\pi$
$677$	18.0239	−	10.4061i	0.692714	−	0.399939i	0.804628	+	0.593779i	$0.202365\pi$
$678$		0			0
$679$	−12.2686	−	2.10673i	−0.470826	−	0.0808488i
$680$	−11.1931	−	30.5657i	−0.429234	−	1.17214i
$681$		0			0
$682$	−3.45683	+	3.66884i	−0.132369	+	0.140487i
$683$			10.0088i			0.382976i	0.981495	+	0.191488i	$0.0613313\pi$
$683$			10.0088i			0.382976i	−0.981495	+	0.191488i	$0.938669\pi$
$684$		0			0
$685$			48.4378i			1.85071i
$686$	−24.9830	+	7.86433i	−0.953857	+	0.300262i
$687$		0			0
$688$	34.3440	−	25.7083i	1.30935	−	0.980119i
$689$	5.50711	+	3.17953i	0.209804	+	0.121130i
$690$		0			0
$691$	−17.4952	−	30.3025i	−0.665548	−	1.15276i	−0.979136	−	0.203204i	$-0.934864\pi$
$691$	−17.4952	−	30.3025i	−0.665548	−	1.15276i	0.313588	−	0.949559i	$-0.398469\pi$
$692$	−8.39115	−	12.7218i	−0.318984	−	0.483610i
$693$		0			0
$694$	−1.50674	−	5.02089i	−0.0571950	−	0.190590i
$695$	−30.7801	+	17.7709i	−1.16756	+	0.674089i
$696$		0			0
$697$	−6.56667	+	11.3738i	−0.248730	+	0.430814i
$698$	−6.85620	−	1.62021i	−0.259511	−	0.0613258i
$699$		0			0
$700$	57.3142	+	6.36324i	2.16627	+	0.240508i
$701$	−30.2491			−1.14249			−0.571246	−	0.820779i	$-0.693540\pi$
$701$	−30.2491			−1.14249			−0.571246	+	0.820779i	$0.693540\pi$
$702$		0			0
$703$	0.532842			0.0200965
$704$	−10.3095	−	12.1888i	−0.388553	−	0.459382i
$705$		0			0
$706$	−16.5374	−	3.90799i	−0.622392	−	0.147079i
$707$	−7.43280	−	1.27634i	−0.279539	−	0.0480016i
$708$		0			0
$709$	−19.3696	−	33.5492i	−0.727441	−	1.25997i	−0.957961	−	0.286897i	$-0.907376\pi$
$709$	−19.3696	−	33.5492i	−0.727441	−	1.25997i	0.230520	−	0.973068i	$-0.425957\pi$
$710$	−19.2811	+	5.78616i	−0.723608	+	0.217151i
$711$		0			0
$712$	16.8604	+	14.0912i	0.631871	+	0.528091i
$713$	−9.05138	+	5.22582i	−0.338977	+	0.195708i
$714$		0			0
$715$	18.9775	+	10.9567i	0.709719	+	0.409756i
$716$	16.3551	−	0.974070i	0.611217	−	0.0364027i
$717$		0			0
$718$	26.8027	−	28.4465i	1.00027	−	1.06161i
$719$	−12.3006			−0.458734			−0.229367	−	0.973340i	$-0.573666\pi$
$719$	−12.3006			−0.458734			−0.229367	+	0.973340i	$0.573666\pi$
$720$		0			0
$721$	5.10553	−	1.88417i	0.190140	−	0.0701703i
$722$	19.5491	+	18.4195i	0.727543	+	0.685501i
$723$		0			0
$724$	7.36689	−	0.438755i	0.273788	−	0.0163062i
$725$	−26.1004	+	45.2073i	−0.969346	+	1.67896i
$726$		0			0
$727$	−10.0761	−	17.4523i	−0.373701	−	0.647269i	0.616431	−	0.787409i	$-0.288578\pi$
$727$	−10.0761	−	17.4523i	−0.373701	−	0.647269i	−0.990132	+	0.140140i	$0.955245\pi$
$728$	19.4121	+	6.92419i	0.719460	+	0.256628i
$729$		0			0
$730$	−61.5692	+	18.4766i	−2.27878	+	0.683848i
$731$	−15.4780	−	26.8086i	−0.572473	−	0.991553i
$732$		0			0
$733$	−25.3422	−	14.6313i	−0.936034	−	0.540419i	−0.0473190	−	0.998880i	$-0.515068\pi$
$733$	−25.3422	−	14.6313i	−0.936034	−	0.540419i	−0.888715	+	0.458460i	$0.848401\pi$
$734$	9.60517	−	40.6460i	0.354533	−	1.50027i
$735$		0			0
$736$	−13.2096	−	30.3497i	−0.486913	−	1.11870i
$737$	4.05876			0.149506
$738$		0			0
$739$			11.9818i			0.440757i	0.975414	+	0.220378i	$0.0707292\pi$
$739$			11.9818i			0.440757i	−0.975414	+	0.220378i	$0.929271\pi$
$740$	22.2324	−	44.4132i	0.817278	−	1.63266i
$741$		0			0
$742$	−1.04695	−	8.57550i	−0.0384347	−	0.314817i
$743$	30.9885	+	17.8912i	1.13686	+	0.656365i	0.945651	−	0.325184i	$-0.105426\pi$
$743$	30.9885	+	17.8912i	1.13686	+	0.656365i	0.191207	+	0.981550i	$0.438760\pi$
$744$		0			0
$745$	−7.04749	+	4.06887i	−0.258200	+	0.149072i
$746$	18.6915	−	5.60920i	0.684343	−	0.205367i
$747$		0			0
$748$	−9.61599	+	6.34259i	−0.351595	+	0.231908i
$749$	−26.3097	+	31.6412i	−0.961336	+	1.15614i
$750$		0			0
$751$	−5.11442	−	2.95281i	−0.186628	−	0.107750i	0.403775	−	0.914858i	$-0.367698\pi$
$751$	−5.11442	−	2.95281i	−0.186628	−	0.107750i	−0.590403	+	0.807109i	$0.701031\pi$
$752$	−10.6619	−	14.2434i	−0.388800	−	0.519402i
$753$		0			0
$754$	−12.7941	+	13.5787i	−0.465933	+	0.494508i
$755$	42.9261			1.56224
$756$		0			0
$757$	−14.4509			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$757$	−14.4509			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$758$	−15.6159	+	16.5736i	−0.567196	+	0.601982i
$759$		0			0
$760$	−0.905983	+	0.331768i	−0.0328635	+	0.0120345i
$761$	−24.8767	−	14.3626i	−0.901781	−	0.520643i	−0.0240032	−	0.999712i	$-0.507641\pi$
$761$	−24.8767	−	14.3626i	−0.901781	−	0.520643i	−0.877777	+	0.479069i	$0.840975\pi$
$762$		0			0
$763$	−2.60789	−	2.16846i	−0.0944118	−	0.0785037i
$764$	−11.0922	−	16.8169i	−0.401303	−	0.608415i
$765$		0			0
$766$	−23.3257	+	6.99990i	−0.842792	+	0.252917i
$767$	11.5245	−	6.65366i	0.416125	−	0.240250i
$768$		0			0
$769$	5.21450	+	3.01059i	0.188040	+	0.108565i	0.591065	−	0.806624i	$-0.298708\pi$
$769$	5.21450	+	3.01059i	0.188040	+	0.108565i	−0.403025	+	0.915189i	$0.632041\pi$
$770$	−3.60779	−	29.5512i	−0.130016	−	1.06495i
$771$		0			0
$772$	−20.9964	−	10.5104i	−0.755677	−	0.378277i
$773$		−	32.8018i		−	1.17980i	−0.807476	−	0.589900i	$-0.799167\pi$
$773$		−	32.8018i		−	1.17980i	0.807476	−	0.589900i	$-0.200833\pi$
$774$		0			0
$775$	19.4660			0.699241
$776$	2.28510	−	13.1100i	0.0820303	−	0.470622i
$777$		0			0
$778$	−1.40866	+	5.96099i	−0.0505028	+	0.213712i
$779$	0.337126	+	0.194640i	0.0120788	+	0.00697369i
$780$		0			0
$781$	3.56202	+	6.16959i	0.127459	+	0.220765i
$782$	−22.8763	+	6.86503i	−0.818054	+	0.245493i
$783$		0			0
$784$	−8.34026	−	26.7290i	−0.297867	−	0.954608i
$785$	15.7418	+	27.2657i	0.561851	+	0.973154i
$786$		0			0
$787$	0.916080	−	1.58670i	0.0326547	−	0.0565597i	−0.849236	−	0.528013i	$-0.822937\pi$
$787$	0.916080	−	1.58670i	0.0326547	−	0.0565597i	0.881891	+	0.471454i	$0.156270\pi$
$788$	−2.41772	−	40.5946i	−0.0861277	−	1.44612i
$789$		0			0
$790$	54.4927	+	51.3438i	1.93876	+	1.82673i
$791$	36.6990	−	13.5436i	1.30487	−	0.481556i
$792$		0			0
$793$	22.5227			0.799805
$794$	27.7327	−	29.4335i	0.984197	−	1.04456i
$795$		0			0
$796$	−2.70838	−	45.4749i	−0.0959959	−	1.61181i
$797$	−24.2935	−	14.0259i	−0.860520	−	0.496822i	0.00366627	−	0.999993i	$-0.498833\pi$
$797$	−24.2935	−	14.0259i	−0.860520	−	0.496822i	−0.864186	+	0.503172i	$0.832166\pi$
$798$		0			0
$799$	−11.1182	+	6.41912i	−0.393335	+	0.227092i
$800$	−6.95636	+	61.2542i	−0.245944	+	2.16566i
$801$		0			0
$802$	−16.3436	+	4.90463i	−0.577114	+	0.173188i
$803$	11.3744	+	19.7010i	0.401392	+	0.695232i
$804$		0			0
$805$	10.4465	−	60.8358i	0.368192	−	2.14418i
$806$	6.77070	+	1.60000i	0.238488	+	0.0563577i
$807$		0			0
$808$	1.38440	−	7.94255i	0.0487031	−	0.279418i
$809$	21.3196			0.749557			0.374779	−	0.927114i	$-0.377719\pi$
$809$	21.3196			0.749557			0.374779	+	0.927114i	$0.377719\pi$
$810$		0			0
$811$	7.69767			0.270302			0.135151	−	0.990825i	$-0.456848\pi$
$811$	7.69767			0.270302			0.135151	+	0.990825i	$0.456848\pi$
$812$	25.1914	+	2.79685i	0.884045	+	0.0981500i
$813$		0			0
$814$	−17.1056	−	4.04226i	−0.599549	−	0.141681i
$815$	−26.6833	+	46.2169i	−0.934676	+	1.61891i
$816$		0			0
$817$	−0.794622	+	0.458775i	−0.0278003	+	0.0160505i
$818$	9.31880	+	31.0529i	0.325824	+	1.08574i
$819$		0			0
$820$	30.2898	−	19.9788i	1.05777	−	0.697690i
$821$	−9.17336	−	15.8887i	−0.320152	−	0.554520i	0.660367	−	0.750943i	$-0.270401\pi$
$821$	−9.17336	−	15.8887i	−0.320152	−	0.554520i	−0.980519	+	0.196423i	$0.937067\pi$
$822$		0			0
$823$	10.2067	+	5.89282i	0.355782	+	0.205411i	0.667229	−	0.744853i	$-0.267480\pi$
$823$	10.2067	+	5.89282i	0.355782	+	0.205411i	−0.311447	+	0.950264i	$0.600814\pi$
$824$	2.00056	+	5.46308i	0.0696929	+	0.190315i
$825$		0			0
$826$	−16.6368	−	7.07541i	−0.578868	−	0.246185i
$827$			6.80800i			0.236737i	0.992970	+	0.118369i	$0.0377665\pi$
$827$			6.80800i			0.236737i	−0.992970	+	0.118369i	$0.962234\pi$
$828$		0			0
$829$		−	6.20652i		−	0.215561i	−0.994175	−	0.107781i	$-0.965626\pi$
$829$		−	6.20652i		−	0.215561i	0.994175	−	0.107781i	$-0.0343744\pi$
$830$	66.2172	−	70.2783i	2.29843	−	2.43939i
$831$		0			0
$832$	−7.45434	+	20.7337i	−0.258433	+	0.718813i
$833$	−19.8651	+	3.68635i	−0.688285	+	0.127725i
$834$		0			0
$835$	43.7235	−	25.2438i	1.51311	−	0.873597i
$836$	0.187998	+	0.285023i	0.00650204	+	0.00985773i
$837$		0			0
$838$	−15.8388	+	4.75313i	−0.547142	+	0.164194i
$839$	−19.9867	−	34.6180i	−0.690017	−	1.19514i	−0.971832	−	0.235676i	$-0.924270\pi$
$839$	−19.9867	−	34.6180i	−0.690017	−	1.19514i	0.281815	−	0.959469i	$-0.409064\pi$
$840$		0			0
$841$	3.02804	−	5.24471i	0.104415	−	0.180852i
$842$	3.61779	−	15.3093i	0.124677	−	0.527594i
$843$		0			0
$844$	−20.8042	+	41.5603i	−0.716111	+	1.43056i
$845$			21.5898i			0.742713i
$846$		0			0
$847$	17.4194	−	6.42854i	0.598536	−	0.220887i
$848$	9.17038	−	1.09622i	0.314912	−	0.0376444i
$849$		0			0
$850$	43.2916	+	10.2304i	1.48489	+	0.350898i
$851$	−31.5609	−	18.2217i	−1.08189	−	0.624631i
$852$		0			0
$853$	25.2532	−	14.5799i	0.864652	−	0.499207i	−0.000915480	−	1.00000i	$-0.500291\pi$
$853$	25.2532	−	14.5799i	0.864652	−	0.499207i	0.865567	+	0.500793i	$0.166958\pi$
$854$	−18.3978	−	24.4497i	−0.629560	−	0.836652i
$855$		0			0
$856$	−33.7551	−	28.2111i	−1.15373	−	0.964235i
$857$	−30.8516	+	17.8122i	−1.05387	+	0.608452i	−0.923730	−	0.383044i	$-0.874876\pi$
$857$	−30.8516	+	17.8122i	−1.05387	+	0.608452i	−0.130139	+	0.991496i	$0.541542\pi$
$858$		0			0
$859$	−0.414494	+	0.717924i	−0.0141423	+	0.0244953i	−0.873010	−	0.487702i	$-0.837835\pi$
$859$	−0.414494	+	0.717924i	−0.0141423	+	0.0244953i	0.858868	+	0.512198i	$0.171168\pi$
$860$	5.08474	+	85.3750i	0.173388	+	2.91126i
$861$		0			0
$862$	32.4934	−	34.4862i	1.10673	−	1.17460i
$863$			7.37519i			0.251054i	0.992090	+	0.125527i	$0.0400622\pi$
$863$			7.37519i			0.251054i	−0.992090	+	0.125527i	$0.959938\pi$
$864$		0			0
$865$	30.3825			1.03304
$866$	−6.57080	+	6.97379i	−0.223285	+	0.236979i
$867$		0			0
$868$	−3.79379	−	8.65696i	−0.128770	−	0.293836i
$869$	13.2480	−	22.9462i	0.449408	−	0.778398i
$870$		0			0
$871$	−2.80088	−	4.85127i	−0.0949042	−	0.164379i
$872$	2.32518	−	2.78212i	0.0787404	−	0.0942145i
$873$		0			0
$874$	0.203483	+	0.678065i	0.00688292	+	0.0229359i
$875$	−39.7795	+	47.8405i	−1.34479	+	1.61730i
$876$		0			0
$877$	−10.0813	+	17.4613i	−0.340420	+	0.589625i	−0.984511	−	0.175324i	$-0.943903\pi$
$877$	−10.0813	+	17.4613i	−0.340420	+	0.589625i	0.644091	+	0.764949i	$0.277236\pi$
$878$	−0.0116923	+	0.0494779i	−0.000394595	+	0.00166980i
$879$		0			0
$880$	31.6012	−	3.77758i	1.06528	−	0.127342i
$881$			15.9543i			0.537513i	0.963208	+	0.268756i	$0.0866126\pi$
$881$			15.9543i			0.537513i	−0.963208	+	0.268756i	$0.913387\pi$
$882$		0			0
$883$			53.4055i			1.79724i	0.438731	+	0.898619i	$0.355428\pi$
$883$			53.4055i			1.79724i	−0.438731	+	0.898619i	$0.644572\pi$
$884$	14.2169	+	7.11667i	0.478164	+	0.239359i
$885$		0			0
$886$	−20.6931	−	4.89004i	−0.695197	−	0.164284i
$887$	18.7836	−	32.5342i	0.630692	−	1.09239i	−0.356719	−	0.934212i	$-0.616105\pi$
$887$	18.7836	−	32.5342i	0.630692	−	1.09239i	0.987411	−	0.158178i	$-0.0505621\pi$
$888$		0			0
$889$	0.553781	−	0.666000i	0.0185732	−	0.0223369i
$890$	−41.9581	+	12.5914i	−1.40644	+	0.422064i
$891$		0			0
$892$	−13.9384	+	9.19362i	−0.466693	+	0.307825i
$893$	0.190266	+	0.329551i	0.00636702	+	0.0110280i
$894$		0			0
$895$	−16.3317	+	28.2873i	−0.545908	+	0.945541i
$896$	28.5968	−	8.84437i	0.955352	−	0.295470i
$897$		0			0
$898$	−22.6821	−	21.3714i	−0.756911	−	0.713172i
$899$	8.55594			0.285357
$900$		0			0
$901$		−	6.66427i		−	0.222019i
$902$	−9.34599	−	8.80593i	−0.311187	−	0.293205i
$903$		0			0
$904$	14.3802	+	39.2691i	0.478279	+	1.30607i
$905$	−7.35637	+	12.7416i	−0.244534	+	0.423545i
$906$		0			0
$907$	24.9768	−	14.4203i	0.829340	−	0.478819i	−0.0242869	−	0.999705i	$-0.507732\pi$
$907$	24.9768	−	14.4203i	0.829340	−	0.478819i	0.853627	+	0.520886i	$0.174398\pi$
$908$	−11.1436	+	7.35020i	−0.369814	+	0.243925i
$909$		0			0
$910$	−32.8316	+	24.7050i	−1.08836	+	0.818963i
$911$	−3.53596	+	2.04149i	−0.117152	+	0.0676376i	−0.557431	−	0.830223i	$-0.688213\pi$
$911$	−3.53596	+	2.04149i	−0.117152	+	0.0676376i	0.440279	+	0.897861i	$0.354879\pi$
$912$		0			0
$913$	−29.5934	−	17.0857i	−0.979398	−	0.565456i
$914$	−5.77987	+	24.4586i	−0.191181	+	0.809018i
$915$		0			0
$916$	−8.92138	+	17.8221i	−0.294771	+	0.588859i
$917$	−5.72411	+	2.11246i	−0.189027	+	0.0697595i
$918$		0			0
$919$		−	0.244050i		−	0.00805047i	−0.999992	−	0.00402523i	$-0.998719\pi$
$919$		−	0.244050i		−	0.00805047i	0.999992	−	0.00402523i	$-0.00128128\pi$
$920$	65.0080	+	11.3310i	2.14325	+	0.373573i
$921$		0			0
$922$	47.2116	+	11.1567i	1.55483	+	0.367426i
$923$	4.91617	−	8.51505i	0.161818	−	0.280276i
$924$		0			0
$925$	33.9376	+	58.7817i	1.11586	+	1.93273i
$926$	14.2963	+	47.6393i	0.469804	+	1.56552i
$927$		0			0
$928$	−3.05754	+	26.9232i	−0.100369	+	0.883796i
$929$	18.5771	−	10.7255i	0.609496	−	0.351893i	−0.163272	−	0.986581i	$-0.552205\pi$
$929$	18.5771	−	10.7255i	0.609496	−	0.351893i	0.772768	+	0.634688i	$0.218871\pi$
$930$		0			0
$931$	0.109265	+	0.588812i	0.00358103	+	0.0192975i
$932$	−0.422297	−	7.09055i	−0.0138328	−	0.232259i
$933$		0			0
$934$	−2.16950	−	2.04413i	−0.0709881	−	0.0668860i
$935$		−	22.9651i		−	0.751040i
$936$		0			0
$937$		−	57.2133i		−	1.86908i	−0.355863	−	0.934538i	$-0.615813\pi$
$937$		−	57.2133i		−	1.86908i	0.355863	−	0.934538i	$-0.384187\pi$
$938$	−2.97842	+	7.00330i	−0.0972487	+	0.228666i
$939$		0			0
$940$	35.4073	−	2.10877i	1.15486	−	0.0687806i
$941$	−8.14635	−	4.70330i	−0.265564	−	0.153323i	0.361306	−	0.932447i	$-0.382331\pi$
$941$	−8.14635	−	4.70330i	−0.265564	−	0.153323i	−0.626870	+	0.779124i	$0.715664\pi$
$942$		0			0
$943$	−13.3122	−	23.0575i	−0.433506	−	0.750855i
$944$	7.60855	−	17.7664i	0.247637	−	0.578248i
$945$		0			0
$946$	28.9897	−	8.69964i	0.942537	−	0.282850i
$947$	33.4447	−	19.3093i	1.08681	−	0.627469i	0.154083	−	0.988058i	$-0.450758\pi$
$947$	33.4447	−	19.3093i	1.08681	−	0.627469i	0.932725	+	0.360589i	$0.117424\pi$
$948$		0			0
$949$	15.6985	−	27.1906i	0.509594	−	0.882643i
$950$	0.303233	−	1.28319i	0.00983818	−	0.0416320i
$951$		0			0
$952$	−3.88756	−	21.2465i	−0.125997	−	0.688603i
$953$	−52.7991			−1.71033			−0.855166	−	0.518355i	$-0.826545\pi$
$953$	−52.7991			−1.71033			−0.855166	+	0.518355i	$0.826545\pi$
$954$		0			0
$955$	40.1625			1.29963
$956$	−5.18745	+	10.3629i	−0.167774	+	0.335160i
$957$		0			0
$958$	0.391404	−	1.65630i	0.0126457	−	0.0535125i
$959$	−5.43958	+	31.6776i	−0.175653	+	1.02292i
$960$		0			0
$961$	13.9047	+	24.0837i	0.448539	+	0.776893i
$962$	6.97269	+	23.2350i	0.224809	+	0.749127i
$963$		0			0
$964$	−3.34884	−	5.07716i	−0.107859	−	0.163524i
$965$	40.5388	−	23.4051i	1.30499	−	0.753437i
$966$		0			0
$967$	9.22794	+	5.32776i	0.296751	+	0.171329i	0.640982	−	0.767556i	$-0.278527\pi$
$967$	9.22794	+	5.32776i	0.296751	+	0.171329i	−0.344232	+	0.938885i	$0.611861\pi$
$968$	6.82564	+	18.6393i	0.219384	+	0.599089i
$969$		0			0
$970$	19.3093	+	18.1935i	0.619986	+	0.584159i
$971$	−9.00425			−0.288960			−0.144480	−	0.989508i	$-0.546151\pi$
$971$	−9.00425			−0.288960			−0.144480	+	0.989508i	$0.546151\pi$
$972$		0			0
$973$	−22.1255	+	8.16531i	−0.709310	+	0.261768i
$974$	−4.11126	+	4.36340i	−0.131733	+	0.139812i
$975$		0			0
$976$	26.1871	−	19.6024i	0.838230	−	0.627458i
$977$	4.49955	−	7.79345i	0.143953	−	0.249334i	−0.785029	−	0.619459i	$-0.787352\pi$
$977$	4.49955	−	7.79345i	0.143953	−	0.249334i	0.928982	+	0.370125i	$0.120685\pi$
$978$		0			0
$979$	7.75137	+	13.4258i	0.247735	+	0.429090i
$980$	53.6374	+	15.4602i	1.71339	+	0.493859i
$981$		0			0
$982$	6.78044	+	22.5944i	0.216373	+	0.721016i
$983$	−2.02127	−	3.50095i	−0.0644686	−	0.111663i	0.831990	−	0.554791i	$-0.187202\pi$
$983$	−2.02127	−	3.50095i	−0.0644686	−	0.111663i	−0.896458	+	0.443128i	$0.853869\pi$
$984$		0			0
$985$	70.2115	+	40.5366i	2.23712	+	1.29160i
$986$	19.0280	+	4.49656i	0.605975	+	0.143200i
$987$		0			0
$988$	0.210942	−	0.421395i	0.00671095	−	0.0134064i
$989$	62.7552			1.99550
$990$		0			0
$991$			27.3007i			0.867235i	0.901097	+	0.433617i	$0.142763\pi$
$991$			27.3007i			0.867235i	−0.901097	+	0.433617i	$0.857237\pi$
$992$	9.26483	−	4.03249i	0.294159	−	0.128032i
$993$		0			0
$994$	−13.2594	+	1.61879i	−0.420562	+	0.0513447i
$995$	78.6523	+	45.4099i	2.49344	+	1.43959i
$996$		0			0
$997$	−28.4727	+	16.4387i	−0.901740	+	0.520620i	−0.877764	−	0.479093i	$-0.840966\pi$
$997$	−28.4727	+	16.4387i	−0.901740	+	0.520620i	−0.0239754	+	0.999713i	$0.507632\pi$
$998$	12.2810	+	40.9239i	0.388749	+	1.29542i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bi.c.307.9		80
3.2	odd	2		252.2.bi.c.139.32	yes	80
4.3	odd	2	inner	756.2.bi.c.307.15		80
7.6	odd	2	inner	756.2.bi.c.307.10		80
9.2	odd	6		252.2.bi.c.223.26	yes	80
9.7	even	3	inner	756.2.bi.c.559.16		80
12.11	even	2		252.2.bi.c.139.25	✓	80
21.20	even	2		252.2.bi.c.139.31	yes	80
28.27	even	2	inner	756.2.bi.c.307.16		80
36.7	odd	6	inner	756.2.bi.c.559.10		80
36.11	even	6		252.2.bi.c.223.31	yes	80
63.20	even	6		252.2.bi.c.223.25	yes	80
63.34	odd	6	inner	756.2.bi.c.559.15		80
84.83	odd	2		252.2.bi.c.139.26	yes	80
252.83	odd	6		252.2.bi.c.223.32	yes	80
252.223	even	6	inner	756.2.bi.c.559.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.25	✓	80	12.11	even	2
252.2.bi.c.139.26	yes	80	84.83	odd	2
252.2.bi.c.139.31	yes	80	21.20	even	2
252.2.bi.c.139.32	yes	80	3.2	odd	2
252.2.bi.c.223.25	yes	80	63.20	even	6
252.2.bi.c.223.26	yes	80	9.2	odd	6
252.2.bi.c.223.31	yes	80	36.11	even	6
252.2.bi.c.223.32	yes	80	252.83	odd	6
756.2.bi.c.307.9		80	1.1	even	1	trivial
756.2.bi.c.307.10		80	7.6	odd	2	inner
756.2.bi.c.307.15		80	4.3	odd	2	inner
756.2.bi.c.307.16		80	28.27	even	2	inner
756.2.bi.c.559.9		80	252.223	even	6	inner
756.2.bi.c.559.10		80	36.7	odd	6	inner
756.2.bi.c.559.15		80	63.34	odd	6	inner
756.2.bi.c.559.16		80	9.7	even	3	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02930 - 0.969818i) q^{2} +(0.118905 + 1.99646i) q^{4} +(-3.45303 - 1.99361i) q^{5} +(-2.03435 - 1.69157i) q^{7} +(1.81382 - 2.17027i) q^{8} +O(q^{10})\)	\(q+(-1.02930 - 0.969818i) q^{2} +(0.118905 + 1.99646i) q^{4} +(-3.45303 - 1.99361i) q^{5} +(-2.03435 - 1.69157i) q^{7} +(1.81382 - 2.17027i) q^{8} +(1.62076 + 5.40083i) q^{10} +(1.72816 - 0.997755i) q^{11} +(-2.38515 - 1.37707i) q^{13} +(0.453437 + 3.71408i) q^{14} +(-3.97172 + 0.474777i) q^{16} +2.88632i q^{17} +0.0855521 q^{19} +(3.56959 - 7.13090i) q^{20} +(-2.74643 - 0.649017i) q^{22} +(-5.06735 - 2.92564i) q^{23} +(5.44896 + 9.43788i) q^{25} +(1.11952 + 3.73057i) q^{26} +(3.13526 - 4.26264i) q^{28} +(2.39499 + 4.14825i) q^{29} +(0.893108 - 1.54691i) q^{31} +(4.54853 + 3.36316i) q^{32} +(2.79921 - 2.97088i) q^{34} +(3.65236 + 9.89675i) q^{35} +6.22828 q^{37} +(-0.0880585 - 0.0829700i) q^{38} +(-10.5898 + 3.87797i) q^{40} +(3.94059 + 2.27510i) q^{41} +(-9.28817 + 5.36253i) q^{43} +(2.19747 + 3.33157i) q^{44} +(2.37847 + 7.92576i) q^{46} +(2.22398 + 3.85205i) q^{47} +(1.27718 + 6.88250i) q^{49} +(3.54443 - 14.9989i) q^{50} +(2.46565 - 4.92560i) q^{52} -2.30892 q^{53} -7.95654 q^{55} +(-7.36111 + 1.34689i) q^{56} +(1.55789 - 6.59248i) q^{58} +(-2.41588 + 4.18443i) q^{59} +(-7.08218 + 4.08890i) q^{61} +(-2.41949 + 0.726076i) q^{62} +(-1.42013 - 7.87294i) q^{64} +(5.49066 + 9.51011i) q^{65} +(1.76145 + 1.01697i) q^{67} +(-5.76243 + 0.343197i) q^{68} +(5.83869 - 13.7288i) q^{70} +3.57003i q^{71} +11.4000i q^{73} +(-6.41075 - 6.04030i) q^{74} +(0.0101725 + 0.170801i) q^{76} +(-5.20346 - 0.893522i) q^{77} +(11.4989 - 6.63892i) q^{79} +(14.6610 + 6.27865i) q^{80} +(-1.84960 - 6.16341i) q^{82} +(-8.56210 - 14.8300i) q^{83} +(5.75420 - 9.96656i) q^{85} +(14.7610 + 3.48820i) q^{86} +(0.969175 - 5.56032i) q^{88} +7.76882i q^{89} +(2.52283 + 6.83608i) q^{91} +(5.23839 - 10.4646i) q^{92} +(1.44665 - 6.12176i) q^{94} +(-0.295414 - 0.170557i) q^{95} +(4.07462 - 2.35248i) q^{97} +(5.36018 - 8.32277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8}+O(q^{10}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56} - 14 q^{58} - 8 q^{64} + 40 q^{65} - 22 q^{70} - 64 q^{74} + 12 q^{77} + 40 q^{85} + 52 q^{86} + 6 q^{88} - 30 q^{92} - 20 q^{98}+O(q^{100}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

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