LMFDB - Embedded newform 756.2.bi.c.307.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(307,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [80,6,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			307.16
Character	$\chi$	$=$	756.307
Dual form			756.2.bi.c.559.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.325239 - 1.37631i) q^{2} +(-1.78844 + 0.895257i) q^{4} +(3.45303 + 1.99361i) q^{5} +(-0.447766 - 2.60759i) q^{7} +(1.81382 + 2.17027i) q^{8} +(1.62076 - 5.40083i) q^{10} +(-1.72816 + 0.997755i) q^{11} +(2.38515 + 1.37707i) q^{13} +(-3.44321 + 1.46435i) q^{14} +(2.39703 - 3.20222i) q^{16} -2.88632i q^{17} +0.0855521 q^{19} +(-7.96033 - 0.474099i) q^{20} +(1.93528 + 2.05397i) q^{22} +(5.06735 + 2.92564i) q^{23} +(5.44896 + 9.43788i) q^{25} +(1.11952 - 3.73057i) q^{26} +(3.13526 + 4.26264i) q^{28} +(2.39499 + 4.14825i) q^{29} +(0.893108 - 1.54691i) q^{31} +(-5.18685 - 2.25756i) q^{32} +(-3.97246 + 0.938743i) q^{34} +(3.65236 - 9.89675i) q^{35} +6.22828 q^{37} +(-0.0278249 - 0.117746i) q^{38} +(1.93650 + 11.1101i) q^{40} +(-3.94059 - 2.27510i) q^{41} +(9.28817 - 5.36253i) q^{43} +(2.19747 - 3.33157i) q^{44} +(2.37847 - 7.92576i) q^{46} +(2.22398 + 3.85205i) q^{47} +(-6.59901 + 2.33518i) q^{49} +(11.2172 - 10.5690i) q^{50} +(-5.49852 - 0.327479i) q^{52} -2.30892 q^{53} -7.95654 q^{55} +(4.84700 - 5.70146i) q^{56} +(4.93031 - 4.64541i) q^{58} +(-2.41588 + 4.18443i) q^{59} +(7.08218 - 4.08890i) q^{61} +(-2.41949 - 0.726076i) q^{62} +(-1.42013 + 7.87294i) q^{64} +(5.49066 + 9.51011i) q^{65} +(-1.76145 - 1.01697i) q^{67} +(2.58400 + 5.16201i) q^{68} +(-14.8089 - 1.80795i) q^{70} -3.57003i q^{71} -11.4000i q^{73} +(-2.02568 - 8.57202i) q^{74} +(-0.153005 + 0.0765911i) q^{76} +(3.37555 + 4.05957i) q^{77} +(-11.4989 + 6.63892i) q^{79} +(14.6610 - 6.27865i) q^{80} +(-1.84960 + 6.16341i) q^{82} +(-8.56210 - 14.8300i) q^{83} +(5.75420 - 9.96656i) q^{85} +(-10.4014 - 11.0393i) q^{86} +(-5.29997 - 1.94083i) q^{88} -7.76882i q^{89} +(2.52283 - 6.83608i) q^{91} +(-11.6818 - 0.695744i) q^{92} +(4.57827 - 4.31372i) q^{94} +(0.295414 + 0.170557i) q^{95} +(-4.07462 + 2.35248i) q^{97} +(5.36018 + 8.32277i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 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}+ \cdots - 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

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 $

$2$	−0.325239	−	1.37631i	−0.229979	−	0.973196i
$2$	−0.325239	−	1.37631i	−0.229979	−	0.973196i
$3$		0			0
$3$		0			0
$4$	−1.78844	+	0.895257i	−0.894220	+	0.447628i
$5$	3.45303	+	1.99361i	1.54424	+	0.891570i	0.998564	+	0.0535758i	$0.0170619\pi$
$5$	3.45303	+	1.99361i	1.54424	+	0.891570i	0.545680	+	0.837994i	$0.316271\pi$
$6$		0			0
$7$	−0.447766	−	2.60759i	−0.169240	−	0.985575i
$7$	−0.447766	−	2.60759i	−0.169240	−	0.985575i
$8$	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	−0.737368	−	0.675491i	$-0.763932\pi$
$11$	−1.72816	+	0.997755i	−0.521061	+	0.300834i	0.216308	+	0.976325i	$0.430598\pi$
$12$		0			0
$13$	2.38515	+	1.37707i	0.661521	+	0.381929i	0.792856	−	0.609409i	$-0.208593\pi$
$13$	2.38515	+	1.37707i	0.661521	+	0.381929i	−0.131335	+	0.991338i	$0.541926\pi$
$14$	−3.44321	+	1.46435i	−0.920236	+	0.391365i
$15$		0			0
$16$	2.39703	−	3.20222i	0.599258	−	0.800556i
$17$		−	2.88632i		−	0.700035i	−0.936743	−	0.350018i	$-0.886176\pi$
$17$		−	2.88632i		−	0.700035i	0.936743	−	0.350018i	$-0.113824\pi$
$18$		0			0
$19$	0.0855521			0.0196270			0.00981349	−	0.999952i	$-0.496876\pi$
$19$	0.0855521			0.0196270			0.00981349	+	0.999952i	$0.496876\pi$
$20$	−7.96033	−	0.474099i	−1.77998	−	0.106012i
$21$		0			0
$22$	1.93528	+	2.05397i	0.412604	+	0.437908i
$23$	5.06735	+	2.92564i	1.05662	+	0.610037i	0.924494	−	0.381196i	$-0.124488\pi$
$23$	5.06735	+	2.92564i	1.05662	+	0.610037i	0.132122	+	0.991234i	$0.457821\pi$
$24$		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	$0.115386\pi$
$32$	−5.18685	−	2.25756i	−0.916914	−	0.399084i
$33$		0			0
$34$	−3.97246	+	0.938743i	−0.681271	+	0.160993i
$35$	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	$0.328919\pi$
$38$	−0.0278249	−	0.117746i	−0.00451379	−	0.0191009i
$39$		0			0
$40$	1.93650	+	11.1101i	0.306188	+	1.75665i
$41$	−3.94059	−	2.27510i	−0.615417	−	0.355311i	0.159666	−	0.987171i	$-0.448958\pi$
$41$	−3.94059	−	2.27510i	−0.615417	−	0.355311i	−0.775083	+	0.631860i	$0.782292\pi$
$42$		0			0
$43$	9.28817	−	5.36253i	1.41643	−	0.817777i	0.420449	−	0.907316i	$-0.361873\pi$
$43$	9.28817	−	5.36253i	1.41643	−	0.817777i	0.995983	+	0.0895388i	$0.0285393\pi$
$44$	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
$49$	−6.59901	+	2.33518i	−0.942716	+	0.333597i
$50$	11.2172	−	10.5690i	1.58635	−	1.49468i
$51$		0			0
$52$	−5.49852	−	0.327479i	−0.762508	−	0.0454132i
$53$	−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
$56$	4.84700	−	5.70146i	0.647707	−	0.761890i
$57$		0			0
$58$	4.93031	−	4.64541i	0.647382	−	0.609973i
$59$	−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	0.0273862	−	0.999625i	$-0.491282\pi$
$61$	7.08218	−	4.08890i	0.906780	−	0.523530i	0.879394	+	0.476095i	$0.157948\pi$
$62$	−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	0.388528	−	0.921437i	$-0.372984\pi$
$67$	−1.76145	−	1.01697i	−0.215195	−	0.124243i	−0.603724	+	0.797194i	$0.706317\pi$
$68$	2.58400	+	5.16201i	0.313356	+	0.625985i
$69$		0			0
$70$	−14.8089	−	1.80795i	−1.77000	−	0.216092i
$71$		−	3.57003i		−	0.423685i	−0.977304	−	0.211842i	$-0.932054\pi$
$71$		−	3.57003i		−	0.423685i	0.977304	−	0.211842i	$-0.0679464\pi$
$72$		0			0
$73$		−	11.4000i		−	1.33426i	−0.744940	−	0.667132i	$-0.767522\pi$
$73$		−	11.4000i		−	1.33426i	0.744940	−	0.667132i	$-0.232478\pi$
$74$	−2.02568	−	8.57202i	−0.235480	−	0.996477i
$75$		0			0
$76$	−0.153005	+	0.0765911i	−0.0175508	+	0.00878560i
$77$	3.37555	+	4.05957i	0.384679	+	0.462631i
$78$		0			0
$79$	−11.4989	+	6.63892i	−1.29373	+	0.746936i	−0.979314	−	0.202348i	$-0.935143\pi$
$79$	−11.4989	+	6.63892i	−1.29373	+	0.746936i	−0.314418	+	0.949285i	$0.601809\pi$
$80$	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
$86$	−10.4014	−	11.0393i	−1.12161	−	1.19039i
$87$		0			0
$88$	−5.29997	−	1.94083i	−0.564978	−	0.206893i
$89$		−	7.76882i		−	0.823493i	−0.911298	−	0.411746i	$-0.864919\pi$
$89$		−	7.76882i		−	0.823493i	0.911298	−	0.411746i	$-0.135081\pi$
$90$		0			0
$91$	2.52283	−	6.83608i	0.264464	−	0.716616i
$92$	−11.6818	−	0.695744i	−1.21792	−	0.0725363i
$93$		0			0
$94$	4.57827	−	4.31372i	0.472213	−	0.444926i
$95$	0.295414	+	0.170557i	0.0303089	+	0.0174988i
$96$		0			0
$97$	−4.07462	+	2.35248i	−0.413715	+	0.238859i	−0.692385	−	0.721528i	$-0.743440\pi$
$97$	−4.07462	+	2.35248i	−0.413715	+	0.238859i	0.278670	+	0.960387i	$0.410107\pi$
$98$	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	−0.617762	−	0.786365i	$-0.711961\pi$
$101$	−2.46857	+	1.42523i	−0.245631	+	0.141815i	0.372131	+	0.928180i	$0.378627\pi$
$102$		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	$0.198979\pi$
$104$	1.33762	+	7.67416i	0.131164	+	0.752513i
$105$		0			0
$106$	0.750949	+	3.17778i	0.0729387	+	0.308653i
$107$			15.5534i			1.50361i	0.659387	+	0.751803i	$0.270816\pi$
$107$			15.5534i			1.50361i	−0.659387	+	0.751803i	$0.729184\pi$
$108$		0			0
$109$	1.28192			0.122786			0.0613930	−	0.998114i	$-0.480446\pi$
$109$	1.28192			0.122786			0.0613930	+	0.998114i	$0.480446\pi$
$110$	2.58778	+	10.9506i	0.246735	+	1.04410i
$111$		0			0
$112$	−9.42339	−	4.81662i	−0.890426	−	0.455127i
$113$	−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
$119$	−7.52633	+	1.29240i	−0.689937	+	0.118474i
$120$		0			0
$121$	−3.50897	+	6.07771i	−0.318997	+	0.552519i
$122$	−7.93097	−	8.41738i	−0.718037	−	0.762074i
$123$		0			0
$124$	−0.212389	+	3.56611i	−0.0190731	+	0.320246i
$125$			23.5163i			2.10336i
$126$		0			0
$127$		−	0.327377i		−	0.0290500i	−0.999895	−	0.0145250i	$-0.995376\pi$
$127$		−	0.327377i		−	0.0290500i	0.999895	−	0.0145250i	$-0.00462361\pi$
$128$	11.2975	−	0.606051i	0.998564	−	0.0535678i
$129$		0			0
$130$	11.3030	−	10.6499i	0.991343	−	0.934058i
$131$	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
$133$	−0.0383073	−	0.223084i	−0.00332167	−	0.0193439i
$134$	−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	$0.0432665\pi$
$140$	2.32812	+	20.9695i	0.196762	+	1.77225i
$141$		0			0
$142$	−4.91346	+	1.16111i	−0.412328	+	0.0974384i
$143$	−5.49590			−0.459590
$144$		0			0
$145$			19.0987i			1.58606i
$146$	−15.6898	+	3.70771i	−1.29850	+	0.306852i
$147$		0			0
$148$	−11.1389	+	5.57591i	−0.915612	+	0.458337i
$149$	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	−0.0701032	−	0.997540i	$-0.522333\pi$
$151$	9.32355	−	5.38296i	0.758740	−	0.438059i	0.828843	+	0.559481i	$0.189000\pi$
$152$	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	0.747407	−	0.664366i	$-0.231298\pi$
$157$	6.83827	+	3.94808i	0.545753	+	0.315091i	−0.201654	+	0.979457i	$0.564632\pi$
$158$	12.8771	+	13.6668i	1.02445	+	1.08727i
$159$		0			0
$160$	−13.4097	−	18.1360i	−1.06013	−	1.43378i
$161$	5.35986	−	14.5236i	0.422416	−	1.14462i
$162$		0			0
$163$			13.3844i			1.04835i	0.851611	+	0.524175i	$0.175626\pi$
$163$			13.3844i			1.04835i	−0.851611	+	0.524175i	$0.824374\pi$
$164$	9.08431	+	0.541040i	0.709365	+	0.0422481i
$165$		0			0
$166$	−17.6259	+	16.6074i	−1.36803	+	1.28898i
$167$	−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	−0.227704	−	0.973730i	$-0.573122\pi$
$173$	6.59908	−	3.80998i	0.501719	−	0.289668i	0.729423	+	0.684063i	$0.239789\pi$
$174$		0			0
$175$	22.1702	−	18.4346i	1.67591	−	1.39353i
$176$	−0.947423	+	7.92561i	−0.0714147	+	0.597416i
$177$		0			0
$178$	−10.6923	+	2.52672i	−0.801420	+	0.189386i
$179$			8.19202i			0.612300i	0.951983	+	0.306150i	$0.0990410\pi$
$179$			8.19202i			0.612300i	−0.951983	+	0.306150i	$0.900959\pi$
$180$		0			0
$181$			3.68997i			0.274274i	0.990552	+	0.137137i	$0.0437900\pi$
$181$			3.68997i			0.274274i	−0.990552	+	0.137137i	$0.956210\pi$
$182$	−10.2291	−	1.24883i	−0.758229	−	0.0925691i
$183$		0			0
$184$	2.84183	+	16.3041i	0.209503	+	1.20195i
$185$	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	−0.150019	−	0.988683i	$-0.547933\pi$
$191$	8.72331	−	5.03641i	0.631197	−	0.364422i	0.781215	+	0.624262i	$0.214600\pi$
$192$		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	$0.305526\pi$
$194$	4.56296	+	4.84281i	0.327602	+	0.347693i
$195$		0			0
$196$	9.71135	−	10.0841i	0.693668	−	0.720295i
$197$	−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	$0.799091\pi$
$200$	−10.5993	+	28.9443i	−0.749484	+	2.04667i
$201$		0			0
$202$	2.76442	+	2.93396i	0.194504	+	0.206433i
$203$	9.74451	−	8.10259i	0.683931	−	0.568690i
$204$		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	−0.392659	−	0.919684i	$-0.628445\pi$
$211$	−20.1250	−	11.6191i	−1.38546	−	0.799895i	−0.992799	+	0.119789i	$0.961778\pi$
$212$	4.12936	−	2.06707i	0.283605	−	0.141967i
$213$		0			0
$214$	21.4063	−	5.05858i	1.46330	−	0.345797i
$215$	42.7631			2.91642
$216$		0			0
$217$	−4.43360	−	1.63620i	−0.300972	−	0.111073i
$218$	−0.416932	−	1.76432i	−0.0282382	−	0.119495i
$219$		0			0
$220$	14.2298	−	7.12314i	0.959372	−	0.480242i
$221$	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	0.186974	−	0.982365i	$-0.440132\pi$
$229$	−8.63009	−	4.98258i	−0.570292	−	0.329258i	−0.757266	+	0.653107i	$0.773465\pi$
$230$	24.0138	−	22.6262i	1.58342	−	1.49193i
$231$		0			0
$232$	−4.65873	+	12.7219i	−0.305861	+	0.835236i
$233$	−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
$236$	0.574520	−	9.64644i	0.0373981	−	0.627930i
$237$		0			0
$238$	4.22659	+	9.93820i	0.273969	+	0.644198i
$239$	−5.01808	−	2.89719i	−0.324592	−	0.187403i	0.328845	−	0.944384i	$-0.393341\pi$
$239$	−5.01808	−	2.89719i	−0.324592	−	0.187403i	−0.653438	+	0.756980i	$0.726674\pi$
$240$		0			0
$241$	2.63364	−	1.52053i	0.169648	−	0.0979461i	−0.412772	−	0.910834i	$-0.635439\pi$
$241$	2.63364	−	1.52053i	0.169648	−	0.0979461i	0.582420	+	0.812888i	$0.302106\pi$
$242$	9.50605	+	2.85271i	0.611072	+	0.183379i
$243$		0			0
$244$	−9.00543	+	13.6531i	−0.576514	+	0.874051i
$245$	−27.4420	−	5.09240i	−1.75321	−	0.325342i
$246$		0			0
$247$	0.204054	+	0.117811i	0.0129837	+	0.00749612i
$248$	4.97714	−	0.867525i	0.316049	−	0.0550879i
$249$		0			0
$250$	32.3657	−	7.64842i	2.04698	−	0.483729i
$251$	−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
$254$	−0.450571	+	0.106476i	−0.0282713	+	0.00668087i
$255$		0			0
$256$	−4.50849	−	15.3517i	−0.281780	−	0.959479i
$257$	−17.9529	−	10.3651i	−1.11987	−	0.646559i	−0.178505	−	0.983939i	$-0.557126\pi$
$257$	−17.9529	−	10.3651i	−1.11987	−	0.646559i	−0.941369	+	0.337380i	$0.890459\pi$
$258$		0			0
$259$	−2.78881	−	16.2408i	−0.173288	−	1.00915i
$260$	−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	−0.459661	−	0.888094i	$-0.652029\pi$
$263$	1.29122	−	0.745488i	0.0796202	−	0.0459687i	0.539282	+	0.842126i	$0.318696\pi$
$264$		0			0
$265$	−7.97277	−	4.60308i	−0.489763	−	0.282765i
$266$	−0.294573	+	0.125278i	−0.0180615	+	0.00768131i
$267$		0			0
$268$	4.06070	+	0.241846i	0.248047	+	0.0147731i
$269$		−	18.2450i		−	1.11242i	−0.831043	−	0.556209i	$-0.812255\pi$
$269$		−	18.2450i		−	1.11242i	0.831043	−	0.556209i	$-0.187745\pi$
$270$		0			0
$271$	−15.4908			−0.940998			−0.470499	−	0.882400i	$-0.655926\pi$
$271$	−15.4908			−0.940998			−0.470499	+	0.882400i	$0.655926\pi$
$272$	−9.24264	−	6.91860i	−0.560418	−	0.419502i
$273$		0			0
$274$	−12.5042	+	11.7816i	−0.755404	+	0.711753i
$275$	−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	$0.997399\pi$
$284$	3.19609	+	6.38479i	0.189653	+	0.378867i
$285$		0			0
$286$	1.78748	+	7.56404i	0.105696	+	0.447271i
$287$	−4.16806	+	11.2941i	−0.246033	+	0.666672i
$288$		0			0
$289$	8.66916			0.509950
$290$	26.2857	−	6.21164i	1.54355	−	0.364760i
$291$		0			0
$292$	10.2059	+	20.3881i	0.597254	+	1.19312i
$293$	−22.2955	−	12.8723i	−1.30252	−	0.752009i	−0.321683	−	0.946847i	$-0.604249\pi$
$293$	−22.2955	−	12.8723i	−1.30252	−	0.752009i	−0.980835	+	0.194838i	$0.937582\pi$
$294$		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
$301$	−18.1422	−	21.8185i	−1.04570	−	1.25760i
$302$	−10.4410	−	11.0813i	−0.600811	−	0.637658i
$303$		0			0
$304$	0.205071	−	0.273957i	0.0117616	−	0.0157125i
$305$	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	$0.567178\pi$
$308$	−9.67132	−	4.23832i	−0.551074	−	0.241501i
$309$		0			0
$310$	−6.90708	−	7.33069i	−0.392296	−	0.416355i
$311$	−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	−0.0900203	−	0.995940i	$-0.528693\pi$
$313$	12.8704	−	7.43074i	0.727479	−	0.420010i	0.817499	+	0.575930i	$0.195360\pi$
$314$	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
$320$	−20.5993	+	24.3543i	−1.15154	+	1.36145i
$321$		0			0
$322$	−21.7321	−	2.65318i	−1.21108	−	0.147856i
$323$		−	0.246931i		−	0.0137396i
$324$		0			0
$325$			30.0143i			1.66489i
$326$	18.4211	−	4.35314i	1.02025	−	0.241098i
$327$		0			0
$328$	−2.20993	−	12.6788i	−0.122023	−	0.700067i
$329$	9.04872	−	7.52404i	0.498872	−	0.414814i
$330$		0			0
$331$	14.7097	−	8.49262i	0.808515	−	0.466797i	−0.0379246	−	0.999281i	$-0.512075\pi$
$331$	14.7097	−	8.49262i	0.808515	−	0.466797i	0.846440	+	0.532484i	$0.178741\pi$
$332$	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	$0.0805625\pi$
$338$	−5.57340	+	5.25133i	−0.303153	+	0.285635i
$339$		0			0
$340$	−1.36840	+	22.9761i	−0.0742120	+	1.24605i
$341$			3.56441i			0.193024i
$342$		0			0
$343$	9.04400	+	16.1619i	0.488330	+	0.872659i
$344$	28.4852	+	10.4312i	1.53582	+	0.562411i
$345$		0			0
$346$	−7.38998	−	7.84321i	−0.397288	−	0.421653i
$347$	−3.21012	−	1.85336i	−0.172328	−	0.0994937i	0.411355	−	0.911475i	$-0.365056\pi$
$347$	−3.21012	−	1.85336i	−0.172328	−	0.0994937i	−0.583683	+	0.811982i	$0.698389\pi$
$348$		0			0
$349$	−4.31419	+	2.49080i	−0.230933	+	0.133329i	−0.611003	−	0.791629i	$-0.709233\pi$
$349$	−4.31419	+	2.49080i	−0.230933	+	0.133329i	0.380069	+	0.924958i	$0.375900\pi$
$350$	−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	−0.750674	−	0.660672i	$-0.770271\pi$
$353$	−10.4059	+	6.00788i	−0.553853	+	0.319767i	0.196822	+	0.980439i	$0.436938\pi$
$354$		0			0
$355$	7.11725	−	12.3274i	0.377744	−	0.654273i
$356$	6.95508	+	13.8941i	0.368619	+	0.736384i
$357$		0			0
$358$	11.2747	−	2.66436i	0.595888	−	0.140816i
$359$		−	27.6368i		−	1.45861i	−0.684187	−	0.729307i	$-0.739843\pi$
$359$		−	27.6368i		−	1.45861i	0.684187	−	0.729307i	$-0.260157\pi$
$360$		0			0
$361$	−18.9927			−0.999615
$362$	5.07853	−	1.20012i	0.266922	−	0.0630770i
$363$		0			0
$364$	1.60812	+	14.4845i	0.0842885	+	0.759194i
$365$	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
$371$	1.03386	+	6.02070i	0.0536751	+	0.312579i
$372$		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	$0.282951\pi$
$374$	5.92842	−	5.58584i	0.306551	−	0.288837i
$375$		0			0
$376$	−4.32608	+	11.8136i	−0.223101	+	0.609237i
$377$			13.1922i			0.679435i
$378$		0			0
$379$			16.1019i			0.827099i	0.910482	+	0.413549i	$0.135711\pi$
$379$			16.1019i			0.827099i	−0.910482	+	0.413549i	$0.864289\pi$
$380$	−0.681023	−	0.0405602i	−0.0349357	−	0.00208069i
$381$		0			0
$382$	−9.76880	−	10.3679i	−0.499815	−	0.530469i
$383$	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
$385$	3.56267	+	20.7474i	0.181571	+	1.05738i
$386$	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
$392$	−17.0374	−	10.0860i	−0.860517	−	0.509422i
$393$		0			0
$394$	6.61317	+	27.9848i	0.333167	+	1.40985i
$395$	−52.9416			−2.66378
$396$		0			0
$397$		−	28.5958i		−	1.43518i	−0.696466	−	0.717590i	$-0.745245\pi$
$397$		−	28.5958i		−	1.43518i	0.696466	−	0.717590i	$-0.254755\pi$
$398$	7.40820	+	31.3491i	0.371340	+	1.57139i
$399$		0			0
$400$	43.2835	+	5.17409i	2.16418	+	0.258704i
$401$	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	0.902785	−	0.430093i	$-0.141519\pi$
$409$	19.8538	+	11.4626i	0.981705	+	0.566788i	0.0789208	+	0.996881i	$0.474853\pi$
$410$	−18.6742	+	17.5951i	−0.922252	+	0.868959i
$411$		0			0
$412$	0.244578	−	4.10657i	0.0120495	−	0.202316i
$413$	11.9930	+	4.42598i	0.590138	+	0.217788i
$414$		0			0
$415$		−	68.2779i		−	3.35163i
$416$	−9.26259	−	12.5273i	−0.454136	−	0.614199i
$417$		0			0
$418$	0.165567	+	0.175722i	0.00809817	+	0.00859482i
$419$	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
$427$	−13.8333	−	16.6365i	−0.669441	−	0.805097i
$428$	−13.9243	−	27.8164i	−0.673057	−	1.34455i
$429$		0			0
$430$	−13.9082	−	58.8552i	−0.670715	−	2.83825i
$431$		−	33.5046i		−	1.61386i	−0.590647	−	0.806930i	$-0.701127\pi$
$431$		−	33.5046i		−	1.61386i	0.590647	−	0.806930i	$-0.298873\pi$
$432$		0			0
$433$			6.77529i			0.325600i	0.986659	+	0.162800i	$0.0520525\pi$
$433$			6.77529i			0.325600i	−0.986659	+	0.162800i	$0.947948\pi$
$434$	−0.809937	+	6.63415i	−0.0388782	+	0.318449i
$435$		0			0
$436$	−2.29264	+	1.14765i	−0.109798	+	0.0549625i
$437$	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	−0.776340	−	0.630315i	$-0.782926\pi$
$443$	−13.0209	+	7.51761i	−0.618641	+	0.357172i	0.157699	+	0.987487i	$0.449592\pi$
$444$		0			0
$445$	15.4880	−	26.8260i	0.734201	−	1.27167i
$446$	8.59328	−	8.09671i	0.406904	−	0.383390i
$447$		0			0
$448$	21.1653	+	0.177875i	0.999965	+	0.00840381i
$449$	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
$452$	1.75805	−	29.5184i	0.0826916	−	1.38843i
$453$		0			0
$454$	6.87024	−	6.47323i	0.322436	−	0.303804i
$455$	22.3399	−	18.5757i	1.04731	−	0.870842i
$456$		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	0.391025	−	0.920380i	$-0.372121\pi$
$461$	29.7074	−	17.1515i	1.38361	−	0.798827i	0.992585	+	0.121553i	$0.0387874\pi$
$462$		0			0
$463$	30.4583	+	17.5851i	1.41552	+	0.817248i	0.995901	−	0.0904537i	$-0.0288317\pi$
$463$	30.4583	+	17.5851i	1.41552	+	0.817248i	0.419615	+	0.907702i	$0.362165\pi$
$464$	19.0245	+	2.27417i	0.883189	+	0.105576i
$465$		0			0
$466$	1.15510	+	4.88803i	0.0535092	+	0.226434i
$467$	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
$470$	24.4088	−	5.76811i	1.12589	−	0.266063i
$471$		0			0
$472$	−13.4633	+	2.34668i	−0.619700	+	0.108015i
$473$	−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
$482$	−2.94928	−	3.13016i	−0.134336	−	0.142575i
$483$		0			0
$484$	0.834466	−	14.0111i	0.0379303	−	0.636866i
$485$	−18.7597			−0.851836
$486$		0			0
$487$			4.23920i			0.192097i	0.995377	+	0.0960483i	$0.0306203\pi$
$487$			4.23920i			0.192097i	−0.995377	+	0.0960483i	$0.969380\pi$
$488$	21.7198	+	7.95371i	0.983208	+	0.360048i
$489$		0			0
$490$	1.91651	+	39.4249i	0.0865793	+	1.78104i
$491$	14.4458	+	8.34027i	0.651928	+	0.376391i	0.789195	−	0.614143i	$-0.210498\pi$
$491$	14.4458	+	8.34027i	0.651928	+	0.376391i	−0.137266	+	0.990534i	$0.543832\pi$
$492$		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
$497$	−9.30917	+	1.59854i	−0.417573	+	0.0717043i
$498$		0			0
$499$	26.1648	+	15.1063i	1.17130	+	0.676249i	0.953985	−	0.299853i	$-0.0969378\pi$
$499$	26.1648	+	15.1063i	1.17130	+	0.676249i	0.217312	+	0.976102i	$0.430271\pi$
$500$	−21.0531	−	42.0575i	−0.941525	−	1.88087i
$501$		0			0
$502$	5.18284	+	21.9321i	0.231322	+	0.978879i
$503$	−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
$506$	3.79758	+	16.0701i	0.168823	+	0.714404i
$507$		0			0
$508$	0.293086	+	0.585493i	0.0130036	+	0.0259771i
$509$	−9.96494	−	5.75326i	−0.441688	−	0.255009i	0.262625	−	0.964898i	$-0.415412\pi$
$509$	−9.96494	−	5.75326i	−0.441688	−	0.255009i	−0.704313	+	0.709889i	$0.748745\pi$
$510$		0			0
$511$	−29.7264	+	5.10452i	−1.31502	+	0.225811i
$512$	−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
$518$	−21.4452	+	9.12039i	−0.942250	+	0.400727i
$519$		0			0
$520$	−10.6804	+	29.1658i	−0.468368	+	1.27901i
$521$			28.7291i			1.25865i	0.777144	+	0.629323i	$0.216668\pi$
$521$			28.7291i			1.25865i	−0.777144	+	0.629323i	$0.783332\pi$
$522$		0			0
$523$	20.1932			0.882986			0.441493	−	0.897265i	$-0.354449\pi$
$523$	20.1932			0.882986			0.441493	+	0.897265i	$0.354449\pi$
$524$	−0.274210	+	4.60412i	−0.0119789	+	0.201132i
$525$		0			0
$526$	−1.44598	−	1.53466i	−0.0630475	−	0.0669142i
$527$	−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
$536$	−0.987843	−	5.66743i	−0.0426683	−	0.244796i
$537$		0			0
$538$	−25.1107	+	5.93398i	−1.08260	+	0.255832i
$539$	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	$0.260437\pi$
$542$	5.03821	+	21.3201i	0.216409	+	0.915775i
$543$		0			0
$544$	−6.51604	+	14.9709i	−0.279373	+	0.641872i
$545$	4.42653	+	2.55566i	0.189612	+	0.109472i
$546$		0			0
$547$	6.72258	−	3.88128i	0.287437	−	0.165952i	−0.349349	−	0.936993i	$-0.613597\pi$
$547$	6.72258	−	3.88128i	0.287437	−	0.165952i	0.636785	+	0.771041i	$0.280264\pi$
$548$	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
$553$	22.4604	+	27.0118i	0.955113	+	1.14866i
$554$	−19.1422	+	18.0361i	−0.813276	+	0.766280i
$555$		0			0
$556$	−1.05991	+	17.7963i	−0.0449501	+	0.754733i
$557$	−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
$560$	−22.9368	−	35.4185i	−0.969258	−	1.49670i
$561$		0			0
$562$	20.3237	−	19.1492i	0.857302	−	0.807762i
$563$	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	0.137388	−	0.990517i	$-0.456129\pi$
$571$	−15.5735	−	8.99137i	−0.651731	−	0.376277i	−0.789119	+	0.614240i	$0.789463\pi$
$572$	9.82908	−	4.92024i	0.410974	−	0.205726i
$573$		0			0
$574$	16.8998	+	2.06323i	0.705385	+	0.0861176i
$575$			63.7667i			2.65926i
$576$		0			0
$577$		−	13.5843i		−	0.565523i	−0.959190	−	0.282762i	$-0.908749\pi$
$577$		−	13.5843i		−	0.565523i	0.959190	−	0.282762i	$-0.0912505\pi$
$578$	−2.81955	−	11.9314i	−0.117278	−	0.496282i
$579$		0			0
$580$	−17.0982	−	34.1569i	−0.709966	−	1.41829i
$581$	−34.8366	+	28.9668i	−1.44527	+	1.20174i
$582$		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
$590$	18.6839	+	19.8297i	0.769203	+	0.816378i
$591$		0			0
$592$	14.9294	−	19.9443i	0.613593	−	0.819707i
$593$			0.875544i			0.0359543i	0.999838	+	0.0179772i	$0.00572261\pi$
$593$			0.875544i			0.0359543i	−0.999838	+	0.0179772i	$0.994277\pi$
$594$		0			0
$595$	−28.5652	−	10.5419i	−1.17106	−	0.432175i
$596$	−0.242679	+	4.07469i	−0.00994052	+	0.166906i
$597$		0			0
$598$	16.5873	−	15.6288i	0.678305	−	0.639109i
$599$	12.3931	+	7.15518i	0.506370	+	0.292353i	0.731340	−	0.682013i	$-0.238895\pi$
$599$	12.3931	+	7.15518i	0.506370	+	0.292353i	−0.224970	+	0.974366i	$0.572229\pi$
$600$		0			0
$601$	30.3634	−	17.5303i	1.23855	−	0.715076i	0.269751	−	0.962930i	$-0.413059\pi$
$601$	30.3634	−	17.5303i	1.23855	−	0.715076i	0.968797	+	0.247854i	$0.0797252\pi$
$602$	−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	$-0.108865\pi$
$608$	−0.443746	−	0.193139i	−0.0179963	−	0.00783282i
$609$		0			0
$610$	−10.6050	−	44.8768i	−0.429382	−	1.81701i
$611$			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	$0.500961\pi$
$614$	2.38752	+	10.1032i	0.0963526	+	0.407733i
$615$		0			0
$616$	−2.68774	+	14.6892i	−0.108292	+	0.591843i
$617$	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
$623$	−20.2579	+	3.47862i	−0.811614	+	0.139368i
$624$		0			0
$625$	−19.6376	+	34.0133i	−0.785503	+	1.36053i
$626$	−14.4129	−	15.2969i	−0.576057	−	0.611386i
$627$		0			0
$628$	−15.7644	−	0.938889i	−0.629067	−	0.0374658i
$629$		−	17.9768i		−	0.716782i
$630$		0			0
$631$			21.2923i			0.847634i	0.905748	+	0.423817i	$0.139310\pi$
$631$			21.2923i			0.847634i	−0.905748	+	0.423817i	$0.860690\pi$
$632$	−35.2652	−	12.9140i	−1.40277	−	0.513691i
$633$		0			0
$634$	−22.0384	+	20.7649i	−0.875256	+	0.824679i
$635$	0.652661	−	1.13044i	0.0259001	−	0.0448603i
$636$		0			0
$637$	−18.9553	−	3.51752i	−0.751037	−	0.139369i
$638$	−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	$0.869446\pi$
$644$	3.41653	+	30.7729i	0.134630	+	1.21262i
$645$		0			0
$646$	−0.339852	+	0.0803114i	−0.0133713	+	0.00315981i
$647$	−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
$650$	41.3089	−	9.76182i	1.62027	−	0.382890i
$651$		0			0
$652$	−11.9825	−	23.9372i	−0.469271	−	0.937454i
$653$	−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	0.452492	−	0.891768i	$-0.350535\pi$
$659$	37.2494	−	21.5060i	1.45103	−	0.837754i	0.998540	+	0.0540142i	$0.0172016\pi$
$660$		0			0
$661$	−37.6797	−	21.7544i	−1.46557	−	0.846148i	−0.466312	−	0.884620i	$-0.654418\pi$
$661$	−37.6797	−	21.7544i	−1.46557	−	0.846148i	−0.999260	+	0.0384716i	$0.987751\pi$
$662$	−16.4726	−	17.4829i	−0.640226	−	0.679491i
$663$		0			0
$664$	16.6550	−	45.4809i	0.646338	−	1.76500i
$665$	0.312467	−	0.846688i	0.0121169	−	0.0328331i
$666$		0			0
$667$			28.0275i			1.08523i
$668$	1.50561	−	25.2799i	0.0582539	−	0.978109i
$669$		0			0
$670$	−8.34739	+	7.86503i	−0.322488	+	0.303853i
$671$	−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	−0.804628	−	0.593779i	$-0.797635\pi$
$677$	−18.0239	+	10.4061i	−0.692714	+	0.399939i	0.111914	+	0.993718i	$0.464302\pi$
$678$		0			0
$679$	7.95878	+	9.57156i	0.305430	+	0.367323i
$680$	32.0672	−	5.58937i	1.22972	−	0.214343i
$681$		0			0
$682$	4.90572	−	1.15929i	0.187850	−	0.0443913i
$683$		−	10.0088i		−	0.382976i	−0.981495	−	0.191488i	$-0.938669\pi$
$683$		−	10.0088i		−	0.382976i	0.981495	−	0.191488i	$-0.0613313\pi$
$684$		0			0
$685$		−	48.4378i		−	1.85071i
$686$	19.3022	−	17.7038i	0.736963	−	0.675933i
$687$		0			0
$688$	5.09201	−	42.5969i	0.194131	−	1.62399i
$689$	−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
$698$	4.83124	+	5.12754i	0.182865	+	0.194080i
$699$		0			0
$700$	−23.1464	+	52.8172i	−0.874851	+	1.99630i
$701$	−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
$704$	−5.40105	−	15.0227i	−0.203560	−	0.566188i
$705$		0			0
$706$	11.6531	+	12.3678i	0.438570	+	0.465468i
$707$	4.82174	+	5.79883i	0.181340	+	0.218087i
$708$		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
$716$	−7.33396	−	14.6509i	−0.274083	−	0.547531i
$717$		0			0
$718$	−38.0367	+	8.98855i	−1.41952	+	0.335450i
$719$	−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
$722$	6.17716	+	26.1398i	0.229890	+	0.972821i
$723$		0			0
$724$	−3.30347	−	6.59929i	−0.122773	−	0.245261i
$725$	−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	0.888715	−	0.458460i	$-0.151599\pi$
$733$	25.3422	+	14.6313i	0.936034	+	0.540419i	0.0473190	+	0.998880i	$0.484932\pi$
$734$	30.3979	−	28.6413i	1.12201	−	1.05717i
$735$		0			0
$736$	−19.6788	−	26.6147i	−0.725370	−	0.981031i
$737$	4.05876			0.149506
$738$		0			0
$739$		−	11.9818i		−	0.440757i	−0.975414	−	0.220378i	$-0.929271\pi$
$739$		−	11.9818i		−	0.440757i	0.975414	−	0.220378i	$-0.0707292\pi$
$740$	−49.5792	−	2.95282i	−1.82257	−	0.108548i
$741$		0			0
$742$	7.95008	−	3.38107i	0.291857	−	0.124123i
$743$	−30.9885	−	17.8912i	−1.13686	−	0.656365i	−0.191207	−	0.981550i	$-0.561240\pi$
$743$	−30.9885	−	17.8912i	−1.13686	−	0.656365i	−0.945651	+	0.325184i	$0.894574\pi$
$744$		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
$749$	40.5569	−	6.96430i	1.48192	−	0.254470i
$750$		0			0
$751$	5.11442	+	2.95281i	0.186628	+	0.107750i	0.590403	−	0.807109i	$-0.298969\pi$
$751$	5.11442	+	2.95281i	0.186628	+	0.107750i	−0.403775	+	0.914858i	$0.632302\pi$
$752$	17.6661	+	2.11179i	0.644216	+	0.0770091i
$753$		0			0
$754$	18.1566	−	4.29063i	0.661223	−	0.156255i
$755$	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	$0.584584\pi$
$758$	22.1611	−	5.23696i	0.804929	−	0.190215i
$759$		0			0
$760$	0.165672	+	0.950488i	0.00600955	+	0.0344778i
$761$	24.8767	+	14.3626i	0.901781	+	0.520643i	0.877777	−	0.479069i	$-0.159025\pi$
$761$	24.8767	+	14.3626i	0.901781	+	0.520643i	0.0240032	+	0.999712i	$0.492359\pi$
$762$		0			0
$763$	−0.574003	−	3.34273i	−0.0207803	−	0.121015i
$764$	−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	0.403025	−	0.915189i	$-0.367959\pi$
$769$	−5.21450	−	3.01059i	−0.188040	−	0.108565i	−0.591065	+	0.806624i	$0.701292\pi$
$770$	27.3960	−	11.6512i	0.987283	−	0.419879i
$771$		0			0
$772$	1.39595	−	23.4386i	0.0502413	−	0.843574i
$773$			32.8018i			1.17980i	0.807476	+	0.589900i	$0.200833\pi$
$773$			32.8018i			1.17980i	−0.807476	+	0.589900i	$0.799167\pi$
$774$		0			0
$775$	19.4660			0.699241
$776$	−12.4961	−	4.57605i	−0.448585	−	0.164271i
$777$		0			0
$778$	−4.45804	+	4.20043i	−0.159828	+	0.150593i
$779$	−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	$0.156270\pi$
$788$	36.3648	−	18.2035i	1.29544	−	0.648473i
$789$		0			0
$790$	17.2187	+	72.8639i	0.612613	+	2.59238i
$791$	36.6990	+	13.5436i	1.30487	+	0.481556i
$792$		0			0
$793$	22.5227			0.799805
$794$	−39.3565	+	9.30045i	−1.39671	+	0.330061i
$795$		0			0
$796$	40.7366	−	20.3919i	1.44387	−	0.722772i
$797$	24.2935	+	14.0259i	0.860520	+	0.496822i	0.864186	−	0.503172i	$-0.167834\pi$
$797$	24.2935	+	14.0259i	0.860520	+	0.496822i	−0.00366627	+	0.999993i	$0.501167\pi$
$798$		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
$805$	47.4621	−	39.4649i	1.67282	−	1.39095i
$806$	−4.77100	−	5.06360i	−0.168051	−	0.178358i
$807$		0			0
$808$	−7.57065	−	2.77235i	−0.266335	−	0.0975309i
$809$	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	$0.456848\pi$
$812$	−10.1736	+	23.2148i	−0.357022	+	0.814681i
$813$		0			0
$814$	12.0535	+	12.7927i	0.422474	+	0.448384i
$815$	−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	0.311447	−	0.950264i	$-0.399186\pi$
$823$	−10.2067	−	5.89282i	−0.355782	−	0.205411i	−0.667229	+	0.744853i	$0.732520\pi$
$824$	−5.73144	+	0.999002i	−0.199664	+	0.0348019i
$825$		0			0
$826$	2.19090	−	17.9456i	0.0762313	−	0.624407i
$827$		−	6.80800i		−	0.236737i	−0.992970	−	0.118369i	$-0.962234\pi$
$827$		−	6.80800i		−	0.236737i	0.992970	−	0.118369i	$-0.0377665\pi$
$828$		0			0
$829$			6.20652i			0.215561i	0.994175	+	0.107781i	$0.0343744\pi$
$829$			6.20652i			0.215561i	−0.994175	+	0.107781i	$0.965626\pi$
$830$	−93.9714	+	22.2066i	−3.26179	+	0.770804i
$831$		0			0
$832$	−14.2288	+	16.8225i	−0.493294	+	0.583216i
$833$	6.74007	+	19.0469i	0.233530	+	0.659934i
$834$		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
$842$	11.4494	−	10.7878i	0.394571	−	0.371770i
$843$		0			0
$844$	46.3944	+	2.76314i	1.59696	+	0.0951112i
$845$		−	21.5898i		−	0.742713i
$846$		0			0
$847$	17.4194	+	6.42854i	0.598536	+	0.220887i
$848$	−5.53455	+	7.39367i	−0.190057	+	0.253900i
$849$		0			0
$850$	−30.5055	−	32.3764i	−1.04633	−	1.11050i
$851$	31.5609	+	18.2217i	1.08189	+	0.624631i
$852$		0			0
$853$	−25.2532	+	14.5799i	−0.864652	+	0.499207i	−0.865567	−	0.500793i	$-0.833042\pi$
$853$	−25.2532	+	14.5799i	−0.864652	+	0.499207i	0.000915480		1.00000i	$0.499709\pi$
$854$	−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	0.130139	−	0.991496i	$-0.458458\pi$
$857$	30.8516	−	17.8122i	1.05387	−	0.608452i	0.923730	+	0.383044i	$0.125124\pi$
$858$		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	$0.171168\pi$
$860$	−76.4793	+	38.2840i	−2.60792	+	1.30547i
$861$		0			0
$862$	−46.1126	+	10.8970i	−1.57060	+	0.371153i
$863$		−	7.37519i		−	0.251054i	−0.992090	−	0.125527i	$-0.959938\pi$
$863$		−	7.37519i		−	0.251054i	0.992090	−	0.125527i	$-0.0400622\pi$
$864$		0			0
$865$	30.3825			1.03304
$866$	9.32488	−	2.20359i	0.316872	−	0.0748810i
$867$		0			0
$868$	9.39405	−	1.04296i	0.318855	−	0.0354004i
$869$	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
$875$	61.3208	−	10.5298i	2.07302	−	0.355973i
$876$		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	$0.277236\pi$
$878$	−0.0370030	+	0.0348648i	−0.00124879	+	0.00117663i
$879$		0			0
$880$	−19.0721	+	25.4786i	−0.642919	+	0.858884i
$881$		−	15.9543i		−	0.537513i	−0.963208	−	0.268756i	$-0.913387\pi$
$881$		−	15.9543i		−	0.537513i	0.963208	−	0.268756i	$-0.0866126\pi$
$882$		0			0
$883$		−	53.4055i		−	1.79724i	−0.438731	−	0.898619i	$-0.644572\pi$
$883$		−	53.4055i		−	1.79724i	0.438731	−	0.898619i	$-0.355428\pi$
$884$	−0.945209	+	15.8705i	−0.0317908	+	0.533782i
$885$		0			0
$886$	14.5814	+	15.4757i	0.489873	+	0.519917i
$887$	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
$889$	−0.853663	+	0.146588i	−0.0286309	+	0.00491641i
$890$	−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
$896$	−6.63895	−	29.1877i	−0.221792	−	0.975094i
$897$		0			0
$898$	−7.16712	−	30.3289i	−0.239170	−	1.01209i
$899$	8.55594			0.285357
$900$		0			0
$901$			6.66427i			0.222019i
$902$	−2.95316	−	12.4968i	−0.0983295	−	0.416099i
$903$		0			0
$904$	−41.1981	+	7.18092i	−1.37023	+	0.238834i
$905$	−7.35637	+	12.7416i	−0.244534	+	0.423545i
$906$		0			0
$907$	−24.9768	+	14.4203i	−0.829340	+	0.478819i	−0.853627	−	0.520886i	$-0.825602\pi$
$907$	−24.9768	+	14.4203i	−0.829340	+	0.478819i	0.0242869	+	0.999705i	$0.492268\pi$
$908$	−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	−0.440279	−	0.897861i	$-0.645121\pi$
$911$	3.53596	−	2.04149i	0.117152	−	0.0676376i	0.557431	+	0.830223i	$0.311787\pi$
$912$		0			0
$913$	29.5934	+	17.0857i	0.979398	+	0.565456i
$914$	−18.2918	+	17.2348i	−0.605039	+	0.570077i
$915$		0			0
$916$	19.8951	+	1.18490i	0.657352	+	0.0391504i
$917$	−5.72411	−	2.11246i	−0.189027	−	0.0697595i
$918$		0			0
$919$			0.244050i			0.00805047i	0.999992	+	0.00402523i	$0.00128128\pi$
$919$			0.244050i			0.00805047i	−0.999992	+	0.00402523i	$0.998719\pi$
$920$	−22.6910	+	61.9641i	−0.748101	+	2.04289i
$921$		0			0
$922$	−33.2678	−	35.3081i	−1.09562	−	1.16281i
$923$	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	−0.772768	−	0.634688i	$-0.781129\pi$
$929$	−18.5771	+	10.7255i	−0.609496	+	0.351893i	0.163272	+	0.986581i	$0.447795\pi$
$930$		0			0
$931$	−0.564559	+	0.199779i	−0.0185027	+	0.00654751i
$932$	6.35174	−	3.17956i	0.208058	−	0.104150i
$933$		0			0
$934$	−0.685521	−	2.90090i	−0.0224309	−	0.0949205i
$935$			22.9651i			0.751040i
$936$		0			0
$937$			57.2133i			1.86908i	0.355863	+	0.934538i	$0.384187\pi$
$937$			57.2133i			1.86908i	−0.355863	+	0.934538i	$0.615813\pi$
$938$	7.55425	+	0.922268i	0.246655	+	0.0301131i
$939$		0			0
$940$	−15.8774	−	31.7180i	−0.517863	−	1.03453i
$941$	8.14635	+	4.70330i	0.265564	+	0.153323i	0.626870	−	0.779124i	$-0.284336\pi$
$941$	8.14635	+	4.70330i	0.265564	+	0.153323i	−0.361306	+	0.932447i	$0.617669\pi$
$942$		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	−0.932725	−	0.360589i	$-0.882576\pi$
$947$	−33.4447	+	19.3093i	−1.08681	+	0.627469i	−0.154083	+	0.988058i	$0.549242\pi$
$948$		0			0
$949$	15.6985	−	27.1906i	0.509594	−	0.882643i
$950$	0.959655	−	0.904200i	0.0311353	−	0.0293361i
$951$		0			0
$952$	−16.4562	−	13.9900i	−0.533350	−	0.453418i
$953$	−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
$956$	11.5683	+	0.688978i	0.374144	+	0.0222831i
$957$		0			0
$958$	1.23869	−	1.16711i	0.0400203	−	0.0377077i
$959$	−24.7138	+	20.5496i	−0.798051	+	0.663582i
$960$		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	0.344232	−	0.938885i	$-0.388139\pi$
$967$	−9.22794	−	5.32776i	−0.296751	−	0.171329i	−0.640982	+	0.767556i	$0.721473\pi$
$968$	−19.5549	+	3.40846i	−0.628518	+	0.109552i
$969$		0			0
$970$	6.10140	+	25.8192i	0.195904	+	0.829003i
$971$	−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
$974$	5.83444	−	1.37875i	0.186948	−	0.0441781i
$975$		0			0
$976$	3.88263	−	32.4799i	0.124280	−	1.03966i
$977$	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
$986$	−13.4081	−	14.2305i	−0.427002	−	0.453190i
$987$		0			0
$988$	−0.470410	−	0.0280165i	−0.0149657	−	0.000891324i
$989$	62.7552			1.99550
$990$		0			0
$991$		−	27.3007i		−	0.867235i	−0.901097	−	0.433617i	$-0.857237\pi$
$991$		−	27.3007i		−	0.867235i	0.901097	−	0.433617i	$-0.142763\pi$
$992$	−8.12466	+	6.00734i	−0.257958	+	0.190733i
$993$		0			0
$994$	5.22778	+	12.2924i	0.165815	+	0.389890i
$995$	−78.6523	−	45.4099i	−2.49344	−	1.43959i
$996$		0			0
$997$	28.4727	−	16.4387i	0.901740	−	0.520620i	0.0239754	−	0.999713i	$-0.492368\pi$
$997$	28.4727	−	16.4387i	0.901740	−	0.520620i	0.877764	+	0.479093i	$0.159034\pi$
$998$	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.307.16		80
3.2	odd	2		252.2.bi.c.139.26	yes	80
4.3	odd	2	inner	756.2.bi.c.307.10		80
7.6	odd	2	inner	756.2.bi.c.307.15		80
9.2	odd	6		252.2.bi.c.223.32	yes	80
9.7	even	3	inner	756.2.bi.c.559.9		80
12.11	even	2		252.2.bi.c.139.31	yes	80
21.20	even	2		252.2.bi.c.139.25	✓	80
28.27	even	2	inner	756.2.bi.c.307.9		80
36.7	odd	6	inner	756.2.bi.c.559.15		80
36.11	even	6		252.2.bi.c.223.25	yes	80
63.20	even	6		252.2.bi.c.223.31	yes	80
63.34	odd	6	inner	756.2.bi.c.559.10		80
84.83	odd	2		252.2.bi.c.139.32	yes	80
252.83	odd	6		252.2.bi.c.223.26	yes	80
252.223	even	6	inner	756.2.bi.c.559.16		80

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

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)

\(f(q)\)	\(=\)	\(q+(-0.325239 - 1.37631i) q^{2} +(-1.78844 + 0.895257i) q^{4} +(3.45303 + 1.99361i) q^{5} +(-0.447766 - 2.60759i) q^{7} +(1.81382 + 2.17027i) q^{8} +(1.62076 - 5.40083i) q^{10} +(-1.72816 + 0.997755i) q^{11} +(2.38515 + 1.37707i) q^{13} +(-3.44321 + 1.46435i) q^{14} +(2.39703 - 3.20222i) q^{16} -2.88632i q^{17} +0.0855521 q^{19} +(-7.96033 - 0.474099i) q^{20} +(1.93528 + 2.05397i) q^{22} +(5.06735 + 2.92564i) q^{23} +(5.44896 + 9.43788i) q^{25} +(1.11952 - 3.73057i) q^{26} +(3.13526 + 4.26264i) q^{28} +(2.39499 + 4.14825i) q^{29} +(0.893108 - 1.54691i) q^{31} +(-5.18685 - 2.25756i) q^{32} +(-3.97246 + 0.938743i) q^{34} +(3.65236 - 9.89675i) q^{35} +6.22828 q^{37} +(-0.0278249 - 0.117746i) q^{38} +(1.93650 + 11.1101i) q^{40} +(-3.94059 - 2.27510i) q^{41} +(9.28817 - 5.36253i) q^{43} +(2.19747 - 3.33157i) q^{44} +(2.37847 - 7.92576i) q^{46} +(2.22398 + 3.85205i) q^{47} +(-6.59901 + 2.33518i) q^{49} +(11.2172 - 10.5690i) q^{50} +(-5.49852 - 0.327479i) q^{52} -2.30892 q^{53} -7.95654 q^{55} +(4.84700 - 5.70146i) q^{56} +(4.93031 - 4.64541i) q^{58} +(-2.41588 + 4.18443i) q^{59} +(7.08218 - 4.08890i) q^{61} +(-2.41949 - 0.726076i) q^{62} +(-1.42013 + 7.87294i) q^{64} +(5.49066 + 9.51011i) q^{65} +(-1.76145 - 1.01697i) q^{67} +(2.58400 + 5.16201i) q^{68} +(-14.8089 - 1.80795i) q^{70} -3.57003i q^{71} -11.4000i q^{73} +(-2.02568 - 8.57202i) q^{74} +(-0.153005 + 0.0765911i) q^{76} +(3.37555 + 4.05957i) q^{77} +(-11.4989 + 6.63892i) q^{79} +(14.6610 - 6.27865i) q^{80} +(-1.84960 + 6.16341i) q^{82} +(-8.56210 - 14.8300i) q^{83} +(5.75420 - 9.96656i) q^{85} +(-10.4014 - 11.0393i) q^{86} +(-5.29997 - 1.94083i) q^{88} -7.76882i q^{89} +(2.52283 - 6.83608i) q^{91} +(-11.6818 - 0.695744i) q^{92} +(4.57827 - 4.31372i) q^{94} +(0.295414 + 0.170557i) q^{95} +(-4.07462 + 2.35248i) q^{97} +(5.36018 + 8.32277i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56}+ \cdots - 20 q^{98}+O(q^{100}) \) 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

Introduction

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