LMFDB - Embedded newform 920.2.bv.a.753.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			753.4
Character	$\chi$	$=$	920.753
Dual form			920.2.bv.a.617.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34923 - 2.47093i) q^{3} +(2.23473 - 0.0773038i) q^{5} +(0.255357 - 0.191158i) q^{7} +(-2.66315 + 4.14394i) q^{9} +(-4.15304 + 1.89663i) q^{11} +(3.09352 - 4.13246i) q^{13} +(-3.20618 - 5.41756i) q^{15} +(-3.17579 + 0.227137i) q^{17} +(-3.00031 - 3.46254i) q^{19} +(-0.816873 - 0.373054i) q^{21} +(-3.37622 - 3.40605i) q^{23} +(4.98805 - 0.345507i) q^{25} +(5.40822 + 0.386803i) q^{27} +(-5.27704 - 4.57258i) q^{29} +(1.08214 - 0.317745i) q^{31} +(10.2898 + 7.70288i) q^{33} +(0.555877 - 0.446927i) q^{35} +(-1.03304 - 4.74880i) q^{37} +(-14.3849 - 2.06824i) q^{39} +(-0.580499 + 0.373064i) q^{41} +(3.49571 - 1.90880i) q^{43} +(-5.63109 + 9.46647i) q^{45} +(-3.43722 + 3.43722i) q^{47} +(-1.94346 + 6.61882i) q^{49} +(4.84612 + 7.54070i) q^{51} +(3.03658 + 4.05640i) q^{53} +(-9.13431 + 4.55950i) q^{55} +(-4.50759 + 12.0853i) q^{57} +(-2.01165 + 0.289231i) q^{59} +(-1.29502 - 4.41043i) q^{61} +(0.112093 + 1.56727i) q^{63} +(6.59374 - 9.47409i) q^{65} +(-0.705066 + 0.262976i) q^{67} +(-3.86081 + 12.9379i) q^{69} +(3.29427 - 7.21344i) q^{71} +(-0.509081 + 7.11789i) q^{73} +(-7.58375 - 11.8590i) q^{75} +(-0.697952 + 1.27820i) q^{77} +(-0.450734 - 3.13492i) q^{79} +(-0.202267 - 0.442902i) q^{81} +(1.44328 - 0.313966i) q^{83} +(-7.07949 + 0.753092i) q^{85} +(-4.17859 + 19.2087i) q^{87} +(-11.8297 - 3.47350i) q^{89} -1.64661i q^{91} +(-2.24518 - 2.24518i) q^{93} +(-6.97256 - 7.50592i) q^{95} +(-17.7506 - 3.86140i) q^{97} +(3.20064 - 22.2610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.34923	−	2.47093i	−0.778978	−	1.42659i	−0.900888	−	0.434051i	$-0.857084\pi$
$3$	−1.34923	−	2.47093i	−0.778978	−	1.42659i	0.121910	−	0.992541i	$-0.461098\pi$
$4$		0			0
$5$	2.23473	−	0.0773038i	0.999402	−	0.0345713i
$5$	2.23473	−	0.0773038i	0.999402	−	0.0345713i
$6$		0			0
$7$	0.255357	−	0.191158i	0.0965159	−	0.0722509i	−0.549930	−	0.835211i	$-0.685346\pi$
$7$	0.255357	−	0.191158i	0.0965159	−	0.0722509i	0.646446	+	0.762960i	$0.276255\pi$
$8$		0			0
$9$	−2.66315	+	4.14394i	−0.887717	+	1.38131i
$10$		0			0
$11$	−4.15304	+	1.89663i	−1.25219	+	0.571855i	−0.927449	−	0.373949i	$-0.878004\pi$
$11$	−4.15304	+	1.89663i	−1.25219	+	0.571855i	−0.324739	+	0.945804i	$0.605276\pi$
$12$		0			0
$13$	3.09352	−	4.13246i	0.857989	−	1.14614i	−0.129984	−	0.991516i	$-0.541493\pi$
$13$	3.09352	−	4.13246i	0.857989	−	1.14614i	0.987974	−	0.154623i	$-0.0494163\pi$
$14$		0			0
$15$	−3.20618	−	5.41756i	−0.827832	−	1.39881i
$16$		0			0
$17$	−3.17579	+	0.227137i	−0.770243	+	0.0550889i	−0.450929	−	0.892560i	$-0.648907\pi$
$17$	−3.17579	+	0.227137i	−0.770243	+	0.0550889i	−0.319314	+	0.947649i	$0.603453\pi$
$18$		0			0
$19$	−3.00031	−	3.46254i	−0.688319	−	0.794362i	0.298806	−	0.954314i	$-0.403412\pi$
$19$	−3.00031	−	3.46254i	−0.688319	−	0.794362i	−0.987125	+	0.159952i	$0.948866\pi$
$20$		0			0
$21$	−0.816873	−	0.373054i	−0.178256	−	0.0814070i
$22$		0			0
$23$	−3.37622	−	3.40605i	−0.703990	−	0.710210i
$23$	−3.37622	−	3.40605i	−0.703990	−	0.710210i
$24$		0			0
$25$	4.98805	−	0.345507i	0.997610	−	0.0691013i
$26$		0			0
$27$	5.40822	+	0.386803i	1.04081	+	0.0744404i
$28$		0			0
$29$	−5.27704	−	4.57258i	−0.979921	−	0.849107i	0.00863436	−	0.999963i	$-0.497252\pi$
$29$	−5.27704	−	4.57258i	−0.979921	−	0.849107i	−0.988556	+	0.150856i	$0.951797\pi$
$30$		0			0
$31$	1.08214	−	0.317745i	0.194358	−	0.0570687i	−0.183105	−	0.983093i	$-0.558615\pi$
$31$	1.08214	−	0.317745i	0.194358	−	0.0570687i	0.377463	+	0.926025i	$0.376797\pi$
$32$		0			0
$33$	10.2898	+	7.70288i	1.79123	+	1.34090i
$34$		0			0
$35$	0.555877	−	0.446927i	0.0939604	−	0.0755444i
$36$		0			0
$37$	−1.03304	−	4.74880i	−0.169830	−	0.780698i	−0.980707	−	0.195481i	$-0.937373\pi$
$37$	−1.03304	−	4.74880i	−0.169830	−	0.780698i	0.810877	−	0.585217i	$-0.198990\pi$
$38$		0			0
$39$	−14.3849	−	2.06824i	−2.30343	−	0.331183i
$40$		0			0
$41$	−0.580499	+	0.373064i	−0.0906587	+	0.0582628i	−0.585185	−	0.810900i	$-0.698978\pi$
$41$	−0.580499	+	0.373064i	−0.0906587	+	0.0582628i	0.494526	+	0.869163i	$0.335342\pi$
$42$		0			0
$43$	3.49571	−	1.90880i	0.533091	−	0.291090i	−0.190068	−	0.981771i	$-0.560871\pi$
$43$	3.49571	−	1.90880i	0.533091	−	0.291090i	0.723160	+	0.690681i	$0.242689\pi$
$44$		0			0
$45$	−5.63109	+	9.46647i	−0.839433	+	1.41118i
$46$		0			0
$47$	−3.43722	+	3.43722i	−0.501370	+	0.501370i	−0.911864	−	0.410493i	$-0.865357\pi$
$47$	−3.43722	+	3.43722i	−0.501370	+	0.501370i	0.410493	+	0.911864i	$0.365357\pi$
$48$		0			0
$49$	−1.94346	+	6.61882i	−0.277637	+	0.945546i
$50$		0			0
$51$	4.84612	+	7.54070i	0.678592	+	1.05591i
$52$		0			0
$53$	3.03658	+	4.05640i	0.417107	+	0.557189i	0.959054	−	0.283223i	$-0.0914037\pi$
$53$	3.03658	+	4.05640i	0.417107	+	0.557189i	−0.541947	+	0.840412i	$0.682313\pi$
$54$		0			0
$55$	−9.13431	+	4.55950i	−1.23167	+	0.614803i
$56$		0			0
$57$	−4.50759	+	12.0853i	−0.597045	+	1.60074i
$58$		0			0
$59$	−2.01165	+	0.289231i	−0.261894	+	0.0376547i	−0.272011	−	0.962294i	$-0.587689\pi$
$59$	−2.01165	+	0.289231i	−0.261894	+	0.0376547i	0.0101170	+	0.999949i	$0.496780\pi$
$60$		0			0
$61$	−1.29502	−	4.41043i	−0.165810	−	0.564698i	−0.999914	−	0.0130906i	$-0.995833\pi$
$61$	−1.29502	−	4.41043i	−0.165810	−	0.564698i	0.834104	−	0.551607i	$-0.185985\pi$
$62$		0			0
$63$	0.112093	+	1.56727i	0.0141224	+	0.197457i
$64$		0			0
$65$	6.59374	−	9.47409i	0.817853	−	1.17512i
$66$		0			0
$67$	−0.705066	+	0.262976i	−0.0861375	+	0.0321276i	−0.392164	−	0.919896i	$-0.628273\pi$
$67$	−0.705066	+	0.262976i	−0.0861375	+	0.0321276i	0.306026	+	0.952023i	$0.401001\pi$
$68$		0			0
$69$	−3.86081	+	12.9379i	−0.464787	+	1.55754i
$70$		0			0
$71$	3.29427	−	7.21344i	0.390958	−	0.856078i	−0.607150	−	0.794587i	$-0.707687\pi$
$71$	3.29427	−	7.21344i	0.390958	−	0.856078i	0.998108	−	0.0614909i	$-0.0195855\pi$
$72$		0			0
$73$	−0.509081	+	7.11789i	−0.0595835	+	0.833086i	0.876521	+	0.481364i	$0.159858\pi$
$73$	−0.509081	+	7.11789i	−0.0595835	+	0.833086i	−0.936104	+	0.351722i	$0.885596\pi$
$74$		0			0
$75$	−7.58375	−	11.8590i	−0.875696	−	1.36935i
$76$		0			0
$77$	−0.697952	+	1.27820i	−0.0795390	+	0.145665i
$78$		0			0
$79$	−0.450734	−	3.13492i	−0.0507115	−	0.352706i	−0.999340	−	0.0363153i	$-0.988438\pi$
$79$	−0.450734	−	3.13492i	−0.0507115	−	0.352706i	0.948629	−	0.316391i	$-0.102471\pi$
$80$		0			0
$81$	−0.202267	−	0.442902i	−0.0224741	−	0.0492114i
$82$		0			0
$83$	1.44328	−	0.313966i	0.158420	−	0.0344622i	−0.132656	−	0.991162i	$-0.542350\pi$
$83$	1.44328	−	0.313966i	0.158420	−	0.0344622i	0.291076	+	0.956700i	$0.405987\pi$
$84$		0			0
$85$	−7.07949	+	0.753092i	−0.767878	+	0.0816843i
$86$		0			0
$87$	−4.17859	+	19.2087i	−0.447992	+	2.05938i
$88$		0			0
$89$	−11.8297	−	3.47350i	−1.25394	−	0.368191i	−0.413706	−	0.910411i	$-0.635766\pi$
$89$	−11.8297	−	3.47350i	−1.25394	−	0.368191i	−0.840236	+	0.542220i	$0.817584\pi$
$90$		0			0
$91$		−	1.64661i		−	0.172611i
$92$		0			0
$93$	−2.24518	−	2.24518i	−0.232814	−	0.232814i
$94$		0			0
$95$	−6.97256	−	7.50592i	−0.715369	−	0.770091i
$96$		0			0
$97$	−17.7506	−	3.86140i	−1.80230	−	0.392066i	−0.818960	−	0.573850i	$-0.805449\pi$
$97$	−17.7506	−	3.86140i	−1.80230	−	0.392066i	−0.983338	+	0.181784i	$0.941813\pi$
$98$		0			0
$99$	3.20064	−	22.2610i	0.321677	−	2.23731i
$100$		0			0
$101$	−2.78246	−	1.78818i	−0.276865	−	0.177930i	0.394838	−	0.918751i	$-0.370801\pi$
$101$	−2.78246	−	1.78818i	−0.276865	−	0.177930i	−0.671703	+	0.740820i	$0.734437\pi$
$102$		0			0
$103$	10.4128	+	3.88377i	1.02600	+	0.382679i	0.805429	−	0.592692i	$-0.201935\pi$
$103$	10.4128	+	3.88377i	1.02600	+	0.382679i	0.220572	+	0.975371i	$0.429208\pi$
$104$		0			0
$105$	−1.85433	−	0.770527i	−0.180964	−	0.0751957i
$106$		0			0
$107$	16.8354	+	9.19283i	1.62754	+	0.888704i	0.993299	+	0.115569i	$0.0368690\pi$
$107$	16.8354	+	9.19283i	1.62754	+	0.888704i	0.634241	+	0.773136i	$0.281313\pi$
$108$		0			0
$109$	12.4592	−	14.3786i	1.19337	−	1.37722i	0.285283	−	0.958443i	$-0.407912\pi$
$109$	12.4592	−	14.3786i	1.19337	−	1.37722i	0.908088	−	0.418780i	$-0.137542\pi$
$110$		0			0
$111$	−10.3401	+	8.95979i	−0.981443	+	0.850425i
$112$		0			0
$113$	−6.11631	−	16.3985i	−0.575374	−	1.54264i	−0.819610	−	0.572922i	$-0.805810\pi$
$113$	−6.11631	−	16.3985i	−0.575374	−	1.54264i	0.244236	−	0.969716i	$-0.421463\pi$
$114$		0			0
$115$	−7.80824	−	7.35061i	−0.728122	−	0.685448i
$116$		0			0
$117$	8.88618	+	23.8248i	0.821527	+	2.20260i
$118$		0			0
$119$	−0.767542	+	0.665079i	−0.0703605	+	0.0609677i
$120$		0			0
$121$	6.44706	−	7.44030i	0.586096	−	0.676391i
$122$		0			0
$123$	1.70504	+	0.931023i	0.153738	+	0.0839476i
$124$		0			0
$125$	11.1202	−	1.15771i	0.994624	−	0.103549i
$126$		0			0
$127$	11.4613	+	4.27483i	1.01702	+	0.379330i	0.802029	−	0.597285i	$-0.203754\pi$
$127$	11.4613	+	4.27483i	1.01702	+	0.379330i	0.214994	+	0.976615i	$0.431027\pi$
$128$		0			0
$129$	−9.43304	−	6.06225i	−0.830533	−	0.533751i
$130$		0			0
$131$	1.56280	−	10.8695i	0.136542	−	0.949673i	−0.800220	−	0.599707i	$-0.795284\pi$
$131$	1.56280	−	10.8695i	0.136542	−	0.949673i	0.936762	−	0.349967i	$-0.113807\pi$
$132$		0			0
$133$	−1.42804	−	0.310652i	−0.123827	−	0.0269369i
$134$		0			0
$135$	12.1158	+	0.446326i	1.04276	+	0.0384136i
$136$		0			0
$137$	16.3201	+	16.3201i	1.39432	+	1.39432i	0.815354	+	0.578963i	$0.196542\pi$
$137$	16.3201	+	16.3201i	1.39432	+	1.39432i	0.578963	+	0.815354i	$0.303458\pi$
$138$		0			0
$139$			13.8056i			1.17098i	0.810681	+	0.585488i	$0.199097\pi$
$139$			13.8056i			1.17098i	−0.810681	+	0.585488i	$0.800903\pi$
$140$		0			0
$141$	13.1307	+	3.85553i	1.10581	+	0.324694i
$142$		0			0
$143$	−5.00977	+	23.0295i	−0.418938	+	1.92583i
$144$		0			0
$145$	−12.1462	−	9.81055i	−1.00869	−	0.814722i
$146$		0			0
$147$	18.9768	−	4.12816i	1.56518	−	0.340485i
$148$		0			0
$149$	8.02048	+	17.5624i	0.657064	+	1.43877i	0.885233	+	0.465147i	$0.153999\pi$
$149$	8.02048	+	17.5624i	0.657064	+	1.43877i	−0.228170	+	0.973621i	$0.573274\pi$
$150$		0			0
$151$	−1.62791	−	11.3223i	−0.132477	−	0.921399i	−0.942311	−	0.334740i	$-0.891352\pi$
$151$	−1.62791	−	11.3223i	−0.132477	−	0.921399i	0.809833	−	0.586660i	$-0.199557\pi$
$152$		0			0
$153$	7.51638	−	13.7652i	0.607663	−	1.11285i
$154$		0			0
$155$	2.39373	−	0.793728i	0.192269	−	0.0637538i
$156$		0			0
$157$	−0.217839	+	3.04579i	−0.0173855	+	0.243081i	0.981327	+	0.192348i	$0.0616102\pi$
$157$	−0.217839	+	3.04579i	−0.0173855	+	0.243081i	−0.998712	+	0.0507328i	$0.983844\pi$
$158$		0			0
$159$	5.92603	−	12.9762i	0.469965	−	1.02908i
$160$		0			0
$161$	−1.51323	−	0.224368i	−0.119260	−	0.0176826i
$162$		0			0
$163$	16.2696	−	6.06826i	1.27434	−	0.475302i	0.380951	−	0.924595i	$-0.375597\pi$
$163$	16.2696	−	6.06826i	1.27434	−	0.475302i	0.893385	+	0.449293i	$0.148324\pi$
$164$		0			0
$165$	23.5905	+	16.4184i	1.83652	+	1.27817i
$166$		0			0
$167$	−1.17521	−	16.4315i	−0.0909402	−	1.27151i	−0.814057	−	0.580785i	$-0.802746\pi$
$167$	−1.17521	−	16.4315i	−0.0909402	−	1.27151i	0.723117	−	0.690726i	$-0.242709\pi$
$168$		0			0
$169$	−3.84484	−	13.0943i	−0.295757	−	1.00726i
$170$		0			0
$171$	22.3389	−	3.21184i	1.70830	−	0.245616i
$172$		0			0
$173$	6.79263	−	18.2117i	0.516434	−	1.38461i	−0.373120	−	0.927783i	$-0.621712\pi$
$173$	6.79263	−	18.2117i	0.516434	−	1.38461i	0.889554	−	0.456830i	$-0.151015\pi$
$174$		0			0
$175$	1.20769	−	1.04173i	0.0912926	−	0.0787476i
$176$		0			0
$177$	3.42884	+	4.58040i	0.257728	+	0.344284i
$178$		0			0
$179$	3.70390	+	5.76338i	0.276843	+	0.430775i	0.951634	−	0.307233i	$-0.0994030\pi$
$179$	3.70390	+	5.76338i	0.276843	+	0.430775i	−0.674792	+	0.738008i	$0.735767\pi$
$180$		0			0
$181$	−3.70057	+	12.6030i	−0.275061	+	0.936772i	0.699871	+	0.714269i	$0.253241\pi$
$181$	−3.70057	+	12.6030i	−0.275061	+	0.936772i	−0.974932	+	0.222503i	$0.928577\pi$
$182$		0			0
$183$	−9.15058	+	9.15058i	−0.676431	+	0.676431i
$184$		0			0
$185$	−2.67566	−	10.5324i	−0.196719	−	0.774360i
$186$		0			0
$187$	12.7584	−	6.96661i	0.932987	−	0.509449i
$188$		0			0
$189$	1.45497	−	0.935051i	0.105833	−	0.0680149i
$190$		0			0
$191$	7.90289	+	1.13626i	0.571833	+	0.0822172i	0.422165	−	0.906519i	$-0.361270\pi$
$191$	7.90289	+	1.13626i	0.571833	+	0.0822172i	0.149668	+	0.988736i	$0.452179\pi$
$192$		0			0
$193$	−3.22428	−	14.8218i	−0.232089	−	1.06689i	−0.934732	−	0.355352i	$-0.884361\pi$
$193$	−3.22428	−	14.8218i	−0.232089	−	1.06689i	0.702644	−	0.711542i	$-0.252003\pi$
$194$		0			0
$195$	−32.3063	−	3.50995i	−2.31350	−	0.251352i
$196$		0			0
$197$	−15.0913	−	11.2972i	−1.07521	−	0.804893i	−0.0935664	−	0.995613i	$-0.529827\pi$
$197$	−15.0913	−	11.2972i	−1.07521	−	0.804893i	−0.981644	+	0.190720i	$0.938918\pi$
$198$		0			0
$199$	−8.94437	+	2.62631i	−0.634050	+	0.186174i	−0.582935	−	0.812519i	$-0.698096\pi$
$199$	−8.94437	+	2.62631i	−0.634050	+	0.186174i	−0.0511151	+	0.998693i	$0.516278\pi$
$200$		0			0
$201$	1.60109	+	1.38735i	0.112932	+	0.0978564i
$202$		0			0
$203$	−2.22161	−	0.158893i	−0.155927	−	0.0111521i
$204$		0			0
$205$	−1.26842	+	0.878573i	−0.0885903	+	0.0613622i
$206$		0			0
$207$	23.1058	−	4.92004i	1.60597	−	0.341966i
$208$		0			0
$209$	19.0276	+	8.68960i	1.31616	+	0.601072i
$210$		0			0
$211$	−15.1346	−	17.4663i	−1.04191	−	1.20243i	−0.978884	−	0.204416i	$-0.934471\pi$
$211$	−15.1346	−	17.4663i	−1.04191	−	1.20243i	−0.0630253	−	0.998012i	$-0.520075\pi$
$212$		0			0
$213$	−22.2686	+	1.59268i	−1.52582	+	0.109129i
$214$		0			0
$215$	7.66442	−	4.53590i	0.522709	−	0.309346i
$216$		0			0
$217$	0.215593	−	0.287998i	0.0146354	−	0.0195506i
$218$		0			0
$219$	18.2747	−	8.34576i	1.23489	−	0.563954i
$220$		0			0
$221$	−8.88576	+	13.8265i	−0.597721	+	0.930072i
$222$		0			0
$223$	20.1169	−	15.0593i	1.34712	−	1.00844i	0.349689	−	0.936866i	$-0.386287\pi$
$223$	20.1169	−	15.0593i	1.34712	−	1.00844i	0.997435	−	0.0715786i	$-0.0228037\pi$
$224$		0			0
$225$	−11.8522	+	21.5903i	−0.790145	+	1.43936i
$226$		0			0
$227$	−1.09907	−	2.01279i	−0.0729478	−	0.133594i	0.838660	−	0.544656i	$-0.183340\pi$
$227$	−1.09907	−	2.01279i	−0.0729478	−	0.133594i	−0.911607	+	0.411062i	$0.865158\pi$
$228$		0			0
$229$	19.5250			1.29025			0.645125	−	0.764077i	$-0.276805\pi$
$229$	19.5250			1.29025			0.645125	+	0.764077i	$0.276805\pi$
$230$		0			0
$231$	4.10005			0.269763
$232$		0			0
$233$	4.19696	+	7.68616i	0.274952	+	0.503537i	0.978269	−	0.207339i	$-0.0664804\pi$
$233$	4.19696	+	7.68616i	0.274952	+	0.503537i	−0.703317	+	0.710876i	$0.748299\pi$
$234$		0			0
$235$	−7.41556	+	7.94698i	−0.483738	+	0.518404i
$236$		0			0
$237$	−7.13803	+	5.34346i	−0.463665	+	0.347095i
$238$		0			0
$239$	−5.19130	+	8.07783i	−0.335798	+	0.522511i	−0.967557	−	0.252653i	$-0.918697\pi$
$239$	−5.19130	+	8.07783i	−0.335798	+	0.522511i	0.631759	+	0.775165i	$0.282333\pi$
$240$		0			0
$241$	10.0367	−	4.58359i	0.646519	−	0.295255i	−0.0650392	−	0.997883i	$-0.520717\pi$
$241$	10.0367	−	4.58359i	0.646519	−	0.295255i	0.711558	+	0.702628i	$0.247990\pi$
$242$		0			0
$243$	8.92643	−	11.9243i	0.572631	−	0.764945i
$244$		0			0
$245$	−3.83146	+	14.9415i	−0.244783	+	0.954579i
$246$		0			0
$247$	−23.5904	+	1.68722i	−1.50102	+	0.107355i
$248$		0			0
$249$	−2.72310	−	3.14262i	−0.172569	−	0.199156i
$250$		0			0
$251$	−16.1155	−	7.35971i	−1.01720	−	0.464540i	−0.164188	−	0.986429i	$-0.552500\pi$
$251$	−16.1155	−	7.35971i	−1.01720	−	0.464540i	−0.853014	+	0.521889i	$0.825228\pi$
$252$		0			0
$253$	20.4816	+	7.74201i	1.28767	+	0.486736i
$254$		0			0
$255$	11.4127	+	16.4768i	0.714691	+	1.03182i
$256$		0			0
$257$	−8.93150	−	0.638793i	−0.557131	−	0.0398468i	−0.210065	−	0.977687i	$-0.567368\pi$
$257$	−8.93150	−	0.638793i	−0.557131	−	0.0398468i	−0.347066	+	0.937841i	$0.612822\pi$
$258$		0			0
$259$	−1.17156	−	1.01517i	−0.0727975	−	0.0630793i
$260$		0			0
$261$	33.0021	−	9.69028i	2.04278	−	0.599813i
$262$		0			0
$263$	−17.6425	−	13.2070i	−1.08788	−	0.814378i	−0.104247	−	0.994551i	$-0.533243\pi$
$263$	−17.6425	−	13.2070i	−1.08788	−	0.814378i	−0.983635	+	0.180173i	$0.942334\pi$
$264$		0			0
$265$	7.09952	+	8.83022i	0.436120	+	0.542436i
$266$		0			0
$267$	7.37815	+	33.9168i	0.451536	+	2.07568i
$268$		0			0
$269$	−9.10920	−	1.30971i	−0.555398	−	0.0798541i	−0.141100	−	0.989995i	$-0.545064\pi$
$269$	−9.10920	−	1.30971i	−0.555398	−	0.0798541i	−0.414298	+	0.910141i	$0.635973\pi$
$270$		0			0
$271$	−14.0938	+	9.05752i	−0.856136	+	0.550205i	−0.893483	−	0.449097i	$-0.851746\pi$
$271$	−14.0938	+	9.05752i	−0.856136	+	0.550205i	0.0373468	+	0.999302i	$0.488109\pi$
$272$		0			0
$273$	−4.06865	+	2.22165i	−0.246246	+	0.134460i
$274$		0			0
$275$	−20.0603	+	10.8954i	−1.20968	+	0.657016i
$276$		0			0
$277$	17.1195	−	17.1195i	1.02861	−	1.02861i	0.0290345	−	0.999578i	$-0.490757\pi$
$277$	17.1195	−	17.1195i	1.02861	−	1.02861i	0.999578	−	0.0290345i	$-0.00924325\pi$
$278$		0			0
$279$	−1.56519	+	5.33053i	−0.0937052	+	0.319131i
$280$		0			0
$281$	−6.80305	−	10.5858i	−0.405836	−	0.631493i	0.576833	−	0.816862i	$-0.304288\pi$
$281$	−6.80305	−	10.5858i	−0.405836	−	0.631493i	−0.982669	+	0.185369i	$0.940652\pi$
$282$		0			0
$283$	8.66593	+	11.5763i	0.515136	+	0.688141i	0.980397	−	0.197032i	$-0.0631304\pi$
$283$	8.66593	+	11.5763i	0.515136	+	0.688141i	−0.465261	+	0.885174i	$0.654039\pi$
$284$		0			0
$285$	−9.13902	+	27.3559i	−0.541349	+	1.62042i
$286$		0			0
$287$	−0.0769204	+	0.206232i	−0.00454047	+	0.0121735i
$288$		0			0
$289$	−6.79289	+	0.976670i	−0.399582	+	0.0574512i
$290$		0			0
$291$	14.4084	+	49.0704i	0.844633	+	2.87656i
$292$		0			0
$293$	1.27881	+	17.8800i	0.0747086	+	1.04456i	0.887138	+	0.461504i	$0.152690\pi$
$293$	1.27881	+	17.8800i	0.0747086	+	1.04456i	−0.812430	+	0.583059i	$0.801856\pi$
$294$		0			0
$295$	−4.47313	+	0.801861i	−0.260436	+	0.0466862i
$296$		0			0
$297$	−23.1942	+	8.65097i	−1.34586	+	0.501980i
$298$		0			0
$299$	−24.5198	+	3.41541i	−1.41802	+	0.197518i
$300$		0			0
$301$	0.527772	−	1.15566i	0.0304203	−	0.0666111i
$302$		0			0
$303$	−0.664285	+	9.28792i	−0.0381622	+	0.533577i
$304$		0			0
$305$	−3.23496	−	9.75601i	−0.185233	−	0.558628i
$306$		0			0
$307$	4.39818	−	8.05467i	0.251018	−	0.459704i	−0.721538	−	0.692375i	$-0.756565\pi$
$307$	4.39818	−	8.05467i	0.251018	−	0.459704i	0.972556	+	0.232670i	$0.0747463\pi$
$308$		0			0
$309$	−4.45272	−	30.9693i	−0.253306	−	1.76178i
$310$		0			0
$311$	9.77141	+	21.3964i	0.554086	+	1.21328i	0.954847	+	0.297097i	$0.0960184\pi$
$311$	9.77141	+	21.3964i	0.554086	+	1.21328i	−0.400761	+	0.916183i	$0.631254\pi$
$312$		0			0
$313$	11.0992	−	2.41447i	0.627361	−	0.136474i	0.112366	−	0.993667i	$-0.464157\pi$
$313$	11.0992	−	2.41447i	0.627361	−	0.136474i	0.514996	+	0.857193i	$0.327794\pi$
$314$		0			0
$315$	0.371654	+	3.49376i	0.0209403	+	0.196851i
$316$		0			0
$317$	5.29462	−	24.3390i	0.297375	−	1.36701i	−0.549621	−	0.835414i	$-0.685228\pi$
$317$	5.29462	−	24.3390i	0.297375	−	1.36701i	0.846997	−	0.531598i	$-0.178408\pi$
$318$		0			0
$319$	30.5882	+	8.98151i	1.71261	+	0.502868i
$320$		0			0
$321$		−	54.0024i		−	3.01412i
$322$		0			0
$323$	10.3148	+	10.3148i	0.573933	+	0.573933i
$324$		0			0
$325$	14.0029	−	21.6818i	0.776738	−	1.20269i
$326$		0			0
$327$	−52.3389	−	11.3856i	−2.89435	−	0.629626i
$328$		0			0
$329$	−0.220667	+	1.53477i	−0.0121658	+	0.0846147i
$330$		0			0
$331$	−28.1933	−	18.1187i	−1.54964	−	0.995895i	−0.985394	−	0.170291i	$-0.945529\pi$
$331$	−28.1933	−	18.1187i	−1.54964	−	0.995895i	−0.564250	−	0.825604i	$-0.690834\pi$
$332$		0			0
$333$	22.4299	+	8.36592i	1.22915	+	0.458450i
$334$		0			0
$335$	−1.55530	+	0.642185i	−0.0849754	+	0.0350863i
$336$		0			0
$337$	−2.45036	−	1.33800i	−0.133480	−	0.0728855i	0.411122	−	0.911581i	$-0.365137\pi$
$337$	−2.45036	−	1.33800i	−0.133480	−	0.0728855i	−0.544601	+	0.838695i	$0.683319\pi$
$338$		0			0
$339$	−32.2671	+	37.2383i	−1.75251	+	2.02251i
$340$		0			0
$341$	−3.89152	+	3.37203i	−0.210738	+	0.182605i
$342$		0			0
$343$	1.54927	+	4.15375i	0.0836527	+	0.224282i
$344$		0			0
$345$	−7.62772	+	29.2113i	−0.410663	+	1.57268i
$346$		0			0
$347$	11.2953	+	30.2838i	0.606361	+	1.62572i	0.769159	+	0.639058i	$0.220675\pi$
$347$	11.2953	+	30.2838i	0.606361	+	1.62572i	−0.162798	+	0.986659i	$0.552052\pi$
$348$		0			0
$349$	24.6327	−	21.3444i	1.31856	−	1.14254i	0.339132	−	0.940739i	$-0.389867\pi$
$349$	24.6327	−	21.3444i	1.31856	−	1.14254i	0.979427	−	0.201799i	$-0.0646787\pi$
$350$		0			0
$351$	18.3289	−	21.1527i	0.978324	−	1.12905i
$352$		0			0
$353$	−21.8390	−	11.9250i	−1.16237	−	0.634702i	−0.222064	−	0.975032i	$-0.571279\pi$
$353$	−21.8390	−	11.9250i	−1.16237	−	0.634702i	−0.940306	+	0.340330i	$0.889461\pi$
$354$		0			0
$355$	6.80418	−	16.3748i	0.361128	−	0.869083i
$356$		0			0
$357$	2.67896	+	0.999199i	0.141785	+	0.0528832i
$358$		0			0
$359$	3.41487	+	2.19460i	0.180230	+	0.115827i	0.627645	−	0.778500i	$-0.284019\pi$
$359$	3.41487	+	2.19460i	0.180230	+	0.115827i	−0.447415	+	0.894326i	$0.647655\pi$
$360$		0			0
$361$	−0.283360	+	1.97081i	−0.0149137	+	0.103727i
$362$		0			0
$363$	−27.0830	−	5.89155i	−1.42149	−	0.309226i
$364$		0			0
$365$	−0.587420	+	15.9459i	−0.0307470	+	0.834648i
$366$		0			0
$367$	−9.76278	−	9.76278i	−0.509613	−	0.509613i	0.404795	−	0.914408i	$-0.367343\pi$
$367$	−9.76278	−	9.76278i	−0.509613	−	0.509613i	−0.914408	+	0.404795i	$0.867343\pi$
$368$		0			0
$369$		−	3.39908i		−	0.176949i
$370$		0			0
$371$	1.55083	+	0.455363i	0.0805148	+	0.0236413i
$372$		0			0
$373$	−1.77597	+	8.16402i	−0.0919564	+	0.422717i	0.908036	+	0.418892i	$0.137581\pi$
$373$	−1.77597	+	8.16402i	−0.0919564	+	0.422717i	−0.999993	+	0.00382530i	$0.998782\pi$
$374$		0			0
$375$	−17.8644	−	25.9153i	−0.922512	−	1.33826i
$376$		0			0
$377$	−35.2207	+	7.66179i	−1.81396	+	0.394602i
$378$		0			0
$379$	4.67661	+	10.2403i	0.240221	+	0.526011i	0.990891	−	0.134666i	$-0.0429963\pi$
$379$	4.67661	+	10.2403i	0.240221	+	0.526011i	−0.750670	+	0.660678i	$0.770269\pi$
$380$		0			0
$381$	−4.90107	−	34.0877i	−0.251090	−	1.74637i
$382$		0			0
$383$	−4.45838	+	8.16491i	−0.227812	+	0.417207i	−0.966435	−	0.256912i	$-0.917295\pi$
$383$	−4.45838	+	8.16491i	−0.227812	+	0.417207i	0.738622	+	0.674119i	$0.235477\pi$
$384$		0			0
$385$	−1.46093	+	2.91040i	−0.0744557	+	0.148328i
$386$		0			0
$387$	−1.39964	+	19.5695i	−0.0711475	+	0.994772i
$388$		0			0
$389$	0.628717	−	1.37670i	0.0318772	−	0.0698013i	−0.893024	−	0.450010i	$-0.851420\pi$
$389$	0.628717	−	1.37670i	0.0318772	−	0.0698013i	0.924901	+	0.380208i	$0.124148\pi$
$390$		0			0
$391$	11.4958	+	10.0500i	0.581368	+	0.508252i
$392$		0			0
$393$	−28.9664	+	10.8039i	−1.46116	+	0.544985i
$394$		0			0
$395$	−1.24961	−	6.97087i	−0.0628747	−	0.350742i
$396$		0			0
$397$	−0.784061	−	10.9626i	−0.0393509	−	0.550197i	−0.978441	−	0.206526i	$-0.933784\pi$
$397$	−0.784061	−	10.9626i	−0.0393509	−	0.550197i	0.939090	−	0.343671i	$-0.111670\pi$
$398$		0			0
$399$	1.15916	+	3.94774i	0.0580306	+	0.197634i
$400$		0			0
$401$	−6.84218	+	0.983757i	−0.341682	+	0.0491265i	−0.311020	−	0.950403i	$-0.600671\pi$
$401$	−6.84218	+	0.983757i	−0.341682	+	0.0491265i	−0.0306620	+	0.999530i	$0.509762\pi$
$402$		0			0
$403$	2.03456	−	5.45486i	0.101348	−	0.271726i
$404$		0			0
$405$	−0.486250	−	0.974132i	−0.0241619	−	0.0484050i
$406$		0			0
$407$	13.2970	+	17.7627i	0.659106	+	0.880462i
$408$		0			0
$409$	6.24459	+	9.71677i	0.308775	+	0.480464i	0.960611	−	0.277897i	$-0.0896373\pi$
$409$	6.24459	+	9.71677i	0.308775	+	0.480464i	−0.651836	+	0.758360i	$0.726001\pi$
$410$		0			0
$411$	18.3062	−	62.3452i	0.902979	−	3.07526i
$412$		0			0
$413$	−0.458399	+	0.458399i	−0.0225563	+	0.0225563i
$414$		0			0
$415$	3.20106	−	0.813200i	0.157134	−	0.0399184i
$416$		0			0
$417$	34.1127	−	18.6269i	1.67050	−	0.912165i
$418$		0			0
$419$	5.72563	−	3.67964i	0.279715	−	0.179762i	−0.393260	−	0.919427i	$-0.628653\pi$
$419$	5.72563	−	3.67964i	0.279715	−	0.179762i	0.672975	+	0.739666i	$0.265016\pi$
$420$		0			0
$421$	24.1849	+	3.47726i	1.17870	+	0.169471i	0.703688	−	0.710509i	$-0.251535\pi$
$421$	24.1849	+	3.47726i	1.17870	+	0.169471i	0.475011	+	0.879980i	$0.342444\pi$
$422$		0			0
$423$	−5.08981	−	23.3975i	−0.247475	−	1.13763i
$424$		0			0
$425$	−15.7625	+	2.23023i	−0.764595	+	0.108182i
$426$		0			0
$427$	−1.17378	−	0.878681i	−0.0568032	−	0.0425224i
$428$		0			0
$429$	63.6637	−	18.6934i	3.07371	−	0.902524i
$430$		0			0
$431$	13.4728	+	11.6743i	0.648962	+	0.562329i	0.915911	−	0.401382i	$-0.131470\pi$
$431$	13.4728	+	11.6743i	0.648962	+	0.562329i	−0.266949	+	0.963711i	$0.586015\pi$
$432$		0			0
$433$	33.4986	+	2.39587i	1.60984	+	0.115138i	0.847053	−	0.531509i	$-0.178375\pi$
$433$	33.4986	+	2.39587i	1.60984	+	0.115138i	0.762789	+	0.646647i	$0.223829\pi$
$434$		0			0
$435$	−7.85312	+	43.2492i	−0.376528	+	2.07364i
$436$		0			0
$437$	−1.66388	+	21.9095i	−0.0795944	+	1.04807i
$438$		0			0
$439$	3.19723	+	1.46013i	0.152596	+	0.0696881i	0.490249	−	0.871582i	$-0.336906\pi$
$439$	3.19723	+	1.46013i	0.152596	+	0.0696881i	−0.337653	+	0.941271i	$0.609633\pi$
$440$		0			0
$441$	−22.2523	−	25.6805i	−1.05963	−	1.22288i
$442$		0			0
$443$	25.9285	−	1.85444i	1.23190	−	0.0881072i	0.559838	−	0.828602i	$-0.310863\pi$
$443$	25.9285	−	1.85444i	1.23190	−	0.0881072i	0.672062	+	0.740495i	$0.265409\pi$
$444$		0			0
$445$	−26.7046	−	6.84787i	−1.26592	−	0.324620i
$446$		0			0
$447$	32.5740	−	43.5138i	1.54070	−	2.05813i
$448$		0			0
$449$	12.6424	−	5.77358i	0.596631	−	0.272472i	−0.0941247	−	0.995560i	$-0.530005\pi$
$449$	12.6424	−	5.77358i	0.596631	−	0.272472i	0.690756	+	0.723088i	$0.257278\pi$
$450$		0			0
$451$	1.70327	−	2.65034i	0.0802039	−	0.124800i
$452$		0			0
$453$	−25.7803	+	19.2989i	−1.21126	+	0.906741i
$454$		0			0
$455$	−0.127289	−	3.67972i	−0.00596739	−	0.172508i
$456$		0			0
$457$	−7.40886	−	13.5683i	−0.346572	−	0.634699i	0.645011	−	0.764173i	$-0.276853\pi$
$457$	−7.40886	−	13.5683i	−0.346572	−	0.634699i	−0.991583	+	0.129474i	$0.958671\pi$
$458$		0			0
$459$	−17.2632			−0.805779
$460$		0			0
$461$	−19.1442			−0.891635			−0.445818	−	0.895124i	$-0.647087\pi$
$461$	−19.1442			−0.891635			−0.445818	+	0.895124i	$0.647087\pi$
$462$		0			0
$463$	−6.53256	−	11.9635i	−0.303594	−	0.555991i	0.680693	−	0.732569i	$-0.261679\pi$
$463$	−6.53256	−	11.9635i	−0.303594	−	0.555991i	−0.984287	+	0.176578i	$0.943497\pi$
$464$		0			0
$465$	−5.19094	−	4.84382i	−0.240724	−	0.224627i
$466$		0			0
$467$	−13.5855	+	10.1700i	−0.628664	+	0.470612i	−0.865481	−	0.500942i	$-0.832987\pi$
$467$	−13.5855	+	10.1700i	−0.628664	+	0.470612i	0.236817	+	0.971554i	$0.423896\pi$
$468$		0			0
$469$	−0.129774	+	0.201932i	−0.00599239	+	0.00932434i
$470$		0			0
$471$	7.81986	−	3.57121i	0.360320	−	0.164553i
$472$		0			0
$473$	−10.8975	+	14.5574i	−0.501069	+	0.669350i
$474$		0			0
$475$	−16.1620	−	16.2347i	−0.741565	−	0.744899i
$476$		0			0
$477$	−24.8964	+	1.78062i	−1.13993	+	0.0815291i
$478$		0			0
$479$	28.5207	+	32.9146i	1.30314	+	1.50391i	0.727219	+	0.686406i	$0.240813\pi$
$479$	28.5207	+	32.9146i	1.30314	+	1.50391i	0.575925	+	0.817502i	$0.304642\pi$
$480$		0			0
$481$	−22.8200	−	10.4215i	−1.04050	−	0.475181i
$482$		0			0
$483$	1.48730	+	4.04182i	0.0676747	+	0.183909i
$484$		0			0
$485$	−39.9663	−	7.25701i	−1.81478	−	0.329524i
$486$		0			0
$487$	21.2661	+	1.52098i	0.963657	+	0.0689221i	0.544292	−	0.838896i	$-0.316798\pi$
$487$	21.2661	+	1.52098i	0.963657	+	0.0689221i	0.419365	+	0.907818i	$0.362253\pi$
$488$		0			0
$489$	−36.9457	−	32.0136i	−1.67074	−	1.44771i
$490$		0			0
$491$	36.4623	−	10.7063i	1.64552	−	0.483168i	0.677810	−	0.735237i	$-0.262929\pi$
$491$	36.4623	−	10.7063i	1.64552	−	0.483168i	0.967709	+	0.252069i	$0.0811112\pi$
$492$		0			0
$493$	17.7974	+	13.3230i	0.801554	+	0.600036i
$494$		0			0
$495$	5.43172	−	49.9947i	0.244138	−	2.24710i
$496$		0			0
$497$	−0.537692	−	2.47173i	−0.0241188	−	0.110872i
$498$		0			0
$499$	−23.3456	−	3.35659i	−1.04509	−	0.150261i	−0.401678	−	0.915781i	$-0.631573\pi$
$499$	−23.3456	−	3.35659i	−1.04509	−	0.150261i	−0.643413	+	0.765519i	$0.722482\pi$
$500$		0			0
$501$	−39.0156	+	25.0738i	−1.74309	+	1.12021i
$502$		0			0
$503$	−35.0082	+	19.1159i	−1.56094	+	0.852338i	−0.561245	+	0.827650i	$0.689677\pi$
$503$	−35.0082	+	19.1159i	−1.56094	+	0.852338i	−0.999695	+	0.0246878i	$0.992141\pi$
$504$		0			0
$505$	−6.35628	−	3.78100i	−0.282851	−	0.168252i
$506$		0			0
$507$	−27.1676	+	27.1676i	−1.20656	+	1.20656i
$508$		0			0
$509$	−6.39700	+	21.7862i	−0.283542	+	0.965655i	0.687388	+	0.726291i	$0.258757\pi$
$509$	−6.39700	+	21.7862i	−0.283542	+	0.965655i	−0.970930	+	0.239365i	$0.923061\pi$
$510$		0			0
$511$	1.23064	+	1.91492i	0.0544404	+	0.0847110i
$512$		0			0
$513$	−14.8870	−	19.8867i	−0.657278	−	0.878020i
$514$		0			0
$515$	23.5700	+	7.87423i	1.03862	+	0.346980i
$516$		0			0
$517$	7.75578	−	20.7941i	0.341099	−	0.914521i
$518$		0			0
$519$	−54.1647	+	7.78771i	−2.37757	+	0.341843i
$520$		0			0
$521$	8.50895	+	28.9788i	0.372784	+	1.26958i	0.905881	+	0.423531i	$0.139210\pi$
$521$	8.50895	+	28.9788i	0.372784	+	1.26958i	−0.533098	+	0.846054i	$0.678972\pi$
$522$		0			0
$523$	−1.46543	−	20.4894i	−0.0640787	−	0.895938i	−0.923238	−	0.384229i	$-0.874467\pi$
$523$	−1.46543	−	20.4894i	−0.0640787	−	0.895938i	0.859159	−	0.511709i	$-0.170987\pi$
$524$		0			0
$525$	−4.20350	−	1.57857i	−0.183456	−	0.0688946i
$526$		0			0
$527$	−3.36448	+	1.25489i	−0.146559	+	0.0546637i
$528$		0			0
$529$	−0.202313	+	22.9991i	−0.00879623	+	0.999961i
$530$		0			0
$531$	4.15876	−	9.10641i	0.180475	−	0.395185i
$532$		0			0
$533$	−0.254114	+	3.55297i	−0.0110069	+	0.153896i
$534$		0			0
$535$	38.3333	+	19.2421i	1.65729	+	0.831907i
$536$		0			0
$537$	9.24350	−	16.9282i	0.398887	−	0.730506i
$538$		0			0
$539$	−4.48218	−	31.1743i	−0.193061	−	1.34277i
$540$		0			0
$541$	11.2889	+	24.7192i	0.485346	+	1.06276i	0.980959	+	0.194217i	$0.0622164\pi$
$541$	11.2889	+	24.7192i	0.485346	+	1.06276i	−0.495612	+	0.868544i	$0.665056\pi$
$542$		0			0
$543$	36.1340	−	7.86047i	1.55066	−	0.337325i
$544$		0			0
$545$	26.7313	−	33.0955i	1.14505	−	1.41766i
$546$		0			0
$547$	−0.464314	+	2.13442i	−0.0198527	+	0.0912612i	−0.986007	−	0.166703i	$-0.946688\pi$
$547$	−0.464314	+	2.13442i	−0.0198527	+	0.0912612i	0.966155	+	0.257964i	$0.0830516\pi$
$548$		0			0
$549$	21.7254	+	6.37915i	0.927218	+	0.272256i
$550$		0			0
$551$			31.9911i			1.36287i
$552$		0			0
$553$	−0.714363	−	0.714363i	−0.0303778	−	0.0303778i
$554$		0			0
$555$	−22.4148	+	20.8220i	−0.951456	+	0.883847i
$556$		0			0
$557$	−9.51889	−	2.07071i	−0.403328	−	0.0877387i	0.00632509	−	0.999980i	$-0.497987\pi$
$557$	−9.51889	−	2.07071i	−0.403328	−	0.0877387i	−0.409653	+	0.912241i	$0.634350\pi$
$558$		0			0
$559$	2.92601	−	20.3508i	0.123757	−	0.860749i
$560$		0			0
$561$	−34.4280	−	22.1255i	−1.45355	−	0.934141i
$562$		0			0
$563$	4.04402	+	1.50834i	0.170435	+	0.0635690i	0.433233	−	0.901282i	$-0.357373\pi$
$563$	4.04402	+	1.50834i	0.170435	+	0.0635690i	−0.262798	+	0.964851i	$0.584645\pi$
$564$		0			0
$565$	−14.9360	−	36.1733i	−0.628361	−	1.52182i
$566$		0			0
$567$	−0.136315	−	0.0744334i	−0.00572467	−	0.00312591i
$568$		0			0
$569$	11.2072	−	12.9338i	0.469830	−	0.542213i	−0.470534	−	0.882382i	$-0.655939\pi$
$569$	11.2072	−	12.9338i	0.469830	−	0.542213i	0.940364	+	0.340169i	$0.110484\pi$
$570$		0			0
$571$	−6.63720	+	5.75116i	−0.277758	+	0.240679i	−0.782588	−	0.622540i	$-0.786101\pi$
$571$	−6.63720	+	5.75116i	−0.277758	+	0.240679i	0.504830	+	0.863219i	$0.331555\pi$
$572$		0			0
$573$	−7.85518	−	21.0606i	−0.328155	−	0.879818i
$574$		0			0
$575$	−18.0175	−	15.8230i	−0.751384	−	0.659866i
$576$		0			0
$577$	8.72672	+	23.3973i	0.363298	+	0.974040i	0.982078	+	0.188476i	$0.0603547\pi$
$577$	8.72672	+	23.3973i	0.363298	+	0.974040i	−0.618780	+	0.785565i	$0.712373\pi$
$578$		0			0
$579$	−32.2733	+	27.9649i	−1.34123	+	1.16218i
$580$		0			0
$581$	0.308534	−	0.356067i	0.0128001	−	0.0147722i
$582$		0			0
$583$	−20.3045	−	11.0871i	−0.840927	−	0.459181i
$584$		0			0
$585$	21.7000	+	52.5550i	0.897183	+	2.17288i
$586$		0			0
$587$	−22.2784	−	8.30941i	−0.919528	−	0.342966i	−0.155266	−	0.987873i	$-0.549624\pi$
$587$	−22.2784	−	8.30941i	−0.919528	−	0.342966i	−0.764261	+	0.644906i	$0.776896\pi$
$588$		0			0
$589$	−4.34696	−	2.79362i	−0.179113	−	0.115109i
$590$		0			0
$591$	−7.55297	+	52.5321i	−0.310688	+	2.16088i
$592$		0			0
$593$	−12.5933	−	2.73951i	−0.517146	−	0.112498i	−0.0535849	−	0.998563i	$-0.517065\pi$
$593$	−12.5933	−	2.73951i	−0.517146	−	0.112498i	−0.463561	+	0.886065i	$0.653428\pi$
$594$		0			0
$595$	−1.66384	+	1.54561i	−0.0682107	+	0.0633637i
$596$		0			0
$597$	18.5574	+	18.5574i	0.759505	+	0.759505i
$598$		0			0
$599$		−	12.8581i		−	0.525368i	−0.964882	−	0.262684i	$-0.915392\pi$
$599$		−	12.8581i		−	0.525368i	0.964882	−	0.262684i	$-0.0846076\pi$
$600$		0			0
$601$	−16.2507	−	4.77162i	−0.662878	−	0.194639i	−0.0670488	−	0.997750i	$-0.521358\pi$
$601$	−16.2507	−	4.77162i	−0.662878	−	0.194639i	−0.595829	+	0.803111i	$0.703176\pi$
$602$		0			0
$603$	0.787940	−	3.62210i	0.0320874	−	0.147503i
$604$		0			0
$605$	13.8323	−	17.1255i	0.562362	−	0.696249i
$606$		0			0
$607$	−22.7354	+	4.94579i	−0.922802	+	0.200743i	−0.648776	−	0.760979i	$-0.724719\pi$
$607$	−22.7354	+	4.94579i	−0.922802	+	0.200743i	−0.274026	+	0.961722i	$0.588355\pi$
$608$		0			0
$609$	2.60485	+	5.70384i	0.105554	+	0.231131i
$610$		0			0
$611$	3.57107	+	24.8373i	0.144470	+	1.00481i
$612$		0			0
$613$	−6.86674	+	12.5755i	−0.277345	+	0.507919i	−0.978806	−	0.204788i	$-0.934349\pi$
$613$	−6.86674	+	12.5755i	−0.277345	+	0.507919i	0.701461	+	0.712707i	$0.252531\pi$
$614$		0			0
$615$	3.88228	+	1.94878i	0.156549	+	0.0785824i
$616$		0			0
$617$	1.08341	−	15.1480i	0.0436163	−	0.609835i	−0.927895	−	0.372842i	$-0.878383\pi$
$617$	1.08341	−	15.1480i	0.0436163	−	0.609835i	0.971511	−	0.236993i	$-0.0761620\pi$
$618$		0			0
$619$	−18.5706	+	40.6639i	−0.746414	+	1.63442i	0.0262919	+	0.999654i	$0.491630\pi$
$619$	−18.5706	+	40.6639i	−0.746414	+	1.63442i	−0.772706	+	0.634764i	$0.781097\pi$
$620$		0			0
$621$	−16.9418	−	19.7266i	−0.679853	−	0.791600i
$622$		0			0
$623$	−3.68478	+	1.37435i	−0.147627	+	0.0550622i
$624$		0			0
$625$	24.7613	−	3.44681i	0.990450	−	0.137872i
$626$		0			0
$627$	−4.20117	−	58.7401i	−0.167779	−	2.34585i
$628$		0			0
$629$	4.35935	+	14.8466i	0.173818	+	0.591971i
$630$		0			0
$631$	3.03854	−	0.436875i	0.120962	−	0.0173917i	−0.0815678	−	0.996668i	$-0.525993\pi$
$631$	3.03854	−	0.436875i	0.120962	−	0.0173917i	0.202530	+	0.979276i	$0.435084\pi$
$632$		0			0
$633$	−22.7379	+	60.9626i	−0.903749	+	2.42304i
$634$		0			0
$635$	25.9433	+	8.66710i	1.02953	+	0.343943i
$636$		0			0
$637$	21.3399	+	28.5068i	0.845518	+	1.12948i
$638$		0			0
$639$	21.1190	+	32.8618i	0.835454	+	1.29999i
$640$		0			0
$641$	3.40954	−	11.6118i	0.134669	−	0.458639i	−0.864352	−	0.502887i	$-0.832271\pi$
$641$	3.40954	−	11.6118i	0.134669	−	0.458639i	0.999021	+	0.0442482i	$0.0140893\pi$
$642$		0			0
$643$	7.93740	−	7.93740i	0.313020	−	0.313020i	−0.533058	−	0.846079i	$-0.678957\pi$
$643$	7.93740	−	7.93740i	0.313020	−	0.313020i	0.846079	+	0.533058i	$0.178957\pi$
$644$		0			0
$645$	−21.5489	−	12.8183i	−0.848489	−	0.504719i
$646$		0			0
$647$	32.1772	−	17.5701i	1.26502	−	0.690750i	0.300249	−	0.953861i	$-0.402930\pi$
$647$	32.1772	−	17.5701i	1.26502	−	0.690750i	0.964766	+	0.263110i	$0.0847483\pi$
$648$		0			0
$649$	7.80588	−	5.01653i	0.306407	−	0.196916i
$650$		0			0
$651$	−1.00251	−	0.144139i	−0.0392914	−	0.00564924i
$652$		0			0
$653$	2.12555	+	9.77101i	0.0831794	+	0.382369i	0.999851	−	0.0172723i	$-0.00549821\pi$
$653$	2.12555	+	9.77101i	0.0831794	+	0.382369i	−0.916671	+	0.399642i	$0.869135\pi$
$654$		0			0
$655$	2.65218	−	24.4112i	0.103629	−	0.953826i
$656$		0			0
$657$	−28.1404	−	21.0656i	−1.09786	−	0.821848i
$658$		0			0
$659$	−12.0317	+	3.53283i	−0.468689	+	0.137619i	−0.507545	−	0.861625i	$-0.669447\pi$
$659$	−12.0317	+	3.53283i	−0.468689	+	0.137619i	0.0388560	+	0.999245i	$0.487629\pi$
$660$		0			0
$661$	−7.38771	−	6.40149i	−0.287349	−	0.248989i	0.499244	−	0.866462i	$-0.333611\pi$
$661$	−7.38771	−	6.40149i	−0.287349	−	0.248989i	−0.786592	+	0.617473i	$0.788157\pi$
$662$		0			0
$663$	46.1533	+	3.30095i	1.79244	+	0.128198i
$664$		0			0
$665$	−3.21531	−	0.583830i	−0.124684	−	0.0226400i
$666$		0			0
$667$	2.24201	+	33.4119i	0.0868108	+	1.29371i
$668$		0			0
$669$	−64.3527	−	29.3889i	−2.48802	−	1.13624i
$670$		0			0
$671$	13.7432	+	15.8605i	0.530551	+	0.612288i
$672$		0			0
$673$	−4.79459	+	0.342916i	−0.184818	+	0.0132184i	−0.163441	−	0.986553i	$-0.552259\pi$
$673$	−4.79459	+	0.342916i	−0.184818	+	0.0132184i	−0.0213765	+	0.999771i	$0.506805\pi$
$674$		0			0
$675$	27.1101	+	0.0608193i	1.04347	+	0.00234093i
$676$		0			0
$677$	0.677828	−	0.905472i	0.0260510	−	0.0348001i	−0.787327	−	0.616536i	$-0.788535\pi$
$677$	0.677828	−	0.905472i	0.0260510	−	0.0348001i	0.813378	+	0.581736i	$0.197626\pi$
$678$		0			0
$679$	−5.27088	+	2.40713i	−0.202278	+	0.0923771i
$680$		0			0
$681$	−3.49058	+	5.43144i	−0.133759	+	0.208133i
$682$		0			0
$683$	32.4439	−	24.2872i	1.24143	−	0.929323i	0.242267	−	0.970210i	$-0.422109\pi$
$683$	32.4439	−	24.2872i	1.24143	−	0.929323i	0.999164	+	0.0408865i	$0.0130182\pi$
$684$		0			0
$685$	37.7326	+	35.2093i	1.44169	+	1.34528i
$686$		0			0
$687$	−26.3437	−	48.2450i	−1.00508	−	1.84066i
$688$		0			0
$689$	26.1567			0.996489
$690$		0			0
$691$	−30.7526			−1.16988			−0.584942	−	0.811075i	$-0.698883\pi$
$691$	−30.7526			−1.16988			−0.584942	+	0.811075i	$0.698883\pi$
$692$		0			0
$693$	−3.43805	−	6.29633i	−0.130601	−	0.239178i
$694$		0			0
$695$	1.06723	+	30.8518i	0.0404822	+	1.17028i
$696$		0			0
$697$	1.75881	−	1.31663i	0.0666196	−	0.0498708i
$698$		0			0
$699$	13.3293	−	20.7408i	0.504160	−	0.784489i
$700$		0			0
$701$	5.55420	−	2.53652i	0.209779	−	0.0958030i	−0.307754	−	0.951466i	$-0.599577\pi$
$701$	5.55420	−	2.53652i	0.209779	−	0.0958030i	0.517534	+	0.855663i	$0.326850\pi$
$702$		0			0
$703$	−13.3435	+	17.8248i	−0.503259	+	0.672276i
$704$		0			0
$705$	29.6417	+	7.60102i	1.11637	+	0.286271i
$706$		0			0
$707$	−1.05235	+	0.0752652i	−0.0395775	+	0.00283064i
$708$		0			0
$709$	−18.5484	−	21.4060i	−0.696600	−	0.803919i	0.291689	−	0.956513i	$-0.405783\pi$
$709$	−18.5484	−	21.4060i	−0.696600	−	0.803919i	−0.988289	+	0.152594i	$0.951237\pi$
$710$		0			0
$711$	14.1913	+	6.48096i	0.532216	+	0.243055i
$712$		0			0
$713$	−4.73579	−	2.61304i	−0.177357	−	0.0978593i
$714$		0			0
$715$	−9.41522	+	51.8521i	−0.352109	+	1.93916i
$716$		0			0
$717$	26.9640	+	1.92850i	1.00699	+	0.0720213i
$718$		0			0
$719$	12.3866	+	10.7331i	0.461943	+	0.400275i	0.854500	−	0.519452i	$-0.173864\pi$
$719$	12.3866	+	10.7331i	0.461943	+	0.400275i	−0.392557	+	0.919728i	$0.628409\pi$
$720$		0			0
$721$	3.40139	−	0.998738i	0.126674	−	0.0371950i
$722$		0			0
$723$	−24.8675	−	18.6156i	−0.924833	−	0.692321i
$724$		0			0
$725$	−27.9020	−	20.9850i	−1.03625	−	0.779363i
$726$		0			0
$727$	−4.30402	−	19.7853i	−0.159627	−	0.733795i	−0.985464	−	0.169885i	$-0.945660\pi$
$727$	−4.30402	−	19.7853i	−0.159627	−	0.733795i	0.825836	−	0.563910i	$-0.190703\pi$
$728$		0			0
$729$	−42.9538	−	6.17583i	−1.59088	−	0.228734i
$730$		0			0
$731$	−10.6681	+	6.85597i	−0.394574	+	0.253577i
$732$		0			0
$733$	27.3494	−	14.9339i	1.01017	−	0.551596i	0.113149	−	0.993578i	$-0.463906\pi$
$733$	27.3494	−	14.9339i	1.01017	−	0.551596i	0.897024	+	0.441982i	$0.145724\pi$
$734$		0			0
$735$	42.0890	−	10.6923i	1.55248	−	0.394391i
$736$		0			0
$737$	2.42940	−	2.42940i	0.0894881	−	0.0894881i
$738$		0			0
$739$	−8.97815	+	30.5768i	−0.330267	+	1.12478i	0.612261	+	0.790656i	$0.290260\pi$
$739$	−8.97815	+	30.5768i	−0.330267	+	1.12478i	−0.942527	+	0.334129i	$0.891558\pi$
$740$		0			0
$741$	35.9978	+	56.0137i	1.32241	+	2.05771i
$742$		0			0
$743$	15.2520	+	20.3742i	0.559540	+	0.747458i	0.987720	−	0.156236i	$-0.0499359\pi$
$743$	15.2520	+	20.3742i	0.559540	+	0.747458i	−0.428180	+	0.903694i	$0.640845\pi$
$744$		0			0
$745$	19.2813	+	38.6273i	0.706411	+	1.41519i
$746$		0			0
$747$	−2.54261	+	6.81700i	−0.0930292	+	0.249421i
$748$		0			0
$749$	6.05632	−	0.870768i	0.221293	−	0.0318172i
$750$		0			0
$751$	3.53649	+	12.0442i	0.129048	+	0.439499i	0.998514	−	0.0544949i	$-0.0173549\pi$
$751$	3.53649	+	12.0442i	0.129048	+	0.439499i	−0.869466	+	0.493993i	$0.835537\pi$
$752$		0			0
$753$	3.55821	+	49.7502i	0.129668	+	1.81300i
$754$		0			0
$755$	−4.51320	−	25.1766i	−0.164252	−	0.916269i
$756$		0			0
$757$	−11.7473	+	4.38153i	−0.426964	+	0.159249i	−0.553754	−	0.832680i	$-0.686805\pi$
$757$	−11.7473	+	4.38153i	−0.426964	+	0.159249i	0.126790	+	0.991930i	$0.459533\pi$
$758$		0			0
$759$	−8.50437	−	61.0543i	−0.308689	−	2.21613i
$760$		0			0
$761$	0.945262	−	2.06983i	0.0342657	−	0.0750315i	−0.891725	−	0.452577i	$-0.850505\pi$
$761$	0.945262	−	2.06983i	0.0342657	−	0.0750315i	0.925991	+	0.377546i	$0.123232\pi$
$762$		0			0
$763$	0.432944	−	6.05335i	0.0156736	−	0.219146i
$764$		0			0
$765$	15.7330	−	31.3426i	0.568827	−	1.13319i
$766$		0			0
$767$	−5.02784	+	9.20779i	−0.181545	+	0.332474i
$768$		0			0
$769$	3.79339	+	26.3836i	0.136793	+	0.951417i	0.936410	+	0.350907i	$0.114127\pi$
$769$	3.79339	+	26.3836i	0.136793	+	0.951417i	−0.799617	+	0.600510i	$0.794964\pi$
$770$		0			0
$771$	10.4722	+	22.9310i	0.377148	+	0.825839i
$772$		0			0
$773$	−36.3141	+	7.89966i	−1.30613	+	0.284131i	−0.811183	−	0.584793i	$-0.801176\pi$
$773$	−36.3141	+	7.89966i	−1.30613	+	0.284131i	−0.494946	+	0.868924i	$0.664812\pi$
$774$		0			0
$775$	5.28798	−	1.95881i	0.189950	−	0.0703627i
$776$		0			0
$777$	−0.927695	+	4.26455i	−0.0332809	+	0.152990i
$778$		0			0
$779$	3.03343	+	0.890695i	0.108684	+	0.0319125i
$780$		0			0
$781$			36.2057i			1.29554i
$782$		0			0
$783$	−26.7707	−	26.7707i	−0.956706	−	0.956706i
$784$		0			0
$785$	−0.251361	+	6.82337i	−0.00897146	+	0.243536i
$786$		0			0
$787$	36.0539	+	7.84305i	1.28518	+	0.279575i	0.802728	−	0.596346i	$-0.203381\pi$
$787$	36.0539	+	7.84305i	1.28518	+	0.279575i	0.482456	+	0.875920i	$0.339745\pi$
$788$		0			0
$789$	−8.82980	+	61.4126i	−0.314349	+	2.18635i
$790$		0			0
$791$	−4.69654	−	3.01828i	−0.166990	−	0.107318i
$792$		0			0
$793$	−22.2321	−	8.29215i	−0.789485	−	0.294463i
$794$		0			0
$795$	12.2400	−	29.4564i	0.434107	−	1.04471i
$796$		0			0
$797$	1.67833	+	0.916435i	0.0594493	+	0.0324618i	0.508699	−	0.860945i	$-0.330127\pi$
$797$	1.67833	+	0.916435i	0.0594493	+	0.0324618i	−0.449249	+	0.893406i	$0.648309\pi$
$798$		0			0
$799$	10.1352	−	11.6966i	0.358557	−	0.413797i
$800$		0			0
$801$	45.8982	−	39.7710i	1.62173	−	1.40524i
$802$		0			0
$803$	−11.3858	−	30.5264i	−0.401795	−	1.07725i
$804$		0			0
$805$	−3.39902	−	0.384422i	−0.119800	−	0.0135491i
$806$		0			0
$807$	9.05422	+	24.2753i	0.318723	+	0.854531i
$808$		0			0
$809$	34.7977	−	30.1524i	1.22342	−	1.06010i	0.227149	−	0.973860i	$-0.427060\pi$
$809$	34.7977	−	30.1524i	1.22342	−	1.06010i	0.996274	−	0.0862421i	$-0.0274858\pi$
$810$		0			0
$811$	0.598397	−	0.690587i	0.0210126	−	0.0242498i	−0.745146	−	0.666901i	$-0.767620\pi$
$811$	0.598397	−	0.690587i	0.0210126	−	0.0242498i	0.766159	+	0.642652i	$0.222166\pi$
$812$		0			0
$813$	41.3963	+	22.6041i	1.45183	+	0.792759i
$814$		0			0
$815$	35.8891	−	14.8186i	1.25714	−	0.519074i
$816$		0			0
$817$	−17.0975	−	6.37705i	−0.598167	−	0.223105i
$818$		0			0
$819$	6.82344	+	4.38516i	0.238430	+	0.153230i
$820$		0			0
$821$	−5.21892	+	36.2984i	−0.182142	+	1.26682i	0.669545	+	0.742771i	$0.266489\pi$
$821$	−5.21892	+	36.2984i	−0.182142	+	1.26682i	−0.851687	+	0.524051i	$0.824420\pi$
$822$		0			0
$823$	−9.93569	−	2.16138i	−0.346336	−	0.0753408i	0.0360326	−	0.999351i	$-0.488528\pi$
$823$	−9.93569	−	2.16138i	−0.346336	−	0.0753408i	−0.382369	+	0.924010i	$0.624892\pi$
$824$		0			0
$825$	53.9876	+	34.8671i	1.87961	+	1.21392i
$826$		0			0
$827$	7.46991	+	7.46991i	0.259754	+	0.259754i	0.824954	−	0.565200i	$-0.191201\pi$
$827$	7.46991	+	7.46991i	0.259754	+	0.259754i	−0.565200	+	0.824954i	$0.691201\pi$
$828$		0			0
$829$		−	28.2182i		−	0.980057i	−0.871706	−	0.490029i	$-0.836986\pi$
$829$		−	28.2182i		−	0.980057i	0.871706	−	0.490029i	$-0.163014\pi$
$830$		0			0
$831$	−65.3993	−	19.2030i	−2.26868	−	0.666144i
$832$		0			0
$833$	4.66865	−	21.4615i	0.161759	−	0.743595i
$834$		0			0
$835$	−3.89649	−	36.6292i	−0.134844	−	1.26761i
$836$		0			0
$837$	5.97535	−	1.29986i	0.206538	−	0.0449297i
$838$		0			0
$839$	4.76827	+	10.4411i	0.164619	+	0.360465i	0.973907	−	0.226947i	$-0.0728743\pi$
$839$	4.76827	+	10.4411i	0.164619	+	0.360465i	−0.809288	+	0.587412i	$0.800147\pi$
$840$		0			0
$841$	2.81152	+	19.5545i	0.0969489	+	0.674294i
$842$		0			0
$843$	−16.9778	+	31.0925i	−0.584746	+	1.07088i
$844$		0			0
$845$	−9.60444	−	28.9651i	−0.330403	−	0.996430i
$846$		0			0
$847$	0.224029	−	3.13234i	0.00769774	−	0.107628i
$848$		0			0
$849$	16.9120	−	37.0320i	0.580417	−	1.27094i
$850$		0			0
$851$	−12.6869	+	19.5516i	−0.434900	+	0.670219i
$852$		0			0
$853$	26.3737	−	9.83689i	0.903019	−	0.336809i	0.145298	−	0.989388i	$-0.453586\pi$
$853$	26.3737	−	9.83689i	0.903019	−	0.336809i	0.757720	+	0.652579i	$0.226313\pi$
$854$		0			0
$855$	49.6731	−	8.90449i	1.69878	−	0.304527i
$856$		0			0
$857$	−0.830376	−	11.6102i	−0.0283651	−	0.396596i	−0.991725	−	0.128383i	$-0.959021\pi$
$857$	−0.830376	−	11.6102i	−0.0283651	−	0.396596i	0.963360	−	0.268213i	$-0.0864332\pi$
$858$		0			0
$859$	−14.5817	−	49.6607i	−0.497521	−	1.69440i	−0.699181	−	0.714944i	$-0.746452\pi$
$859$	−14.5817	−	49.6607i	−0.497521	−	1.69440i	0.201661	−	0.979455i	$-0.435366\pi$
$860$		0			0
$861$	0.613367	−	0.0881889i	0.0209035	−	0.00300547i
$862$		0			0
$863$	17.8732	−	47.9200i	0.608412	−	1.63122i	−0.156943	−	0.987608i	$-0.550164\pi$
$863$	17.8732	−	47.9200i	0.608412	−	1.63122i	0.765355	−	0.643608i	$-0.222563\pi$
$864$		0			0
$865$	13.7719	−	41.2234i	0.468257	−	1.40164i
$866$		0			0
$867$	11.5784	+	15.4670i	0.393225	+	0.525287i
$868$		0			0
$869$	7.81770	+	12.1646i	0.265197	+	0.412655i
$870$		0			0
$871$	−1.09440	+	3.72718i	−0.0370823	+	0.126291i
$872$		0			0
$873$	63.2739	−	63.2739i	2.14150	−	2.14150i
$874$		0			0
$875$	2.61833	−	2.42135i	0.0885156	−	0.0818566i
$876$		0			0
$877$	−35.4096	+	19.3351i	−1.19570	+	0.652900i	−0.948719	−	0.316120i	$-0.897620\pi$
$877$	−35.4096	+	19.3351i	−1.19570	+	0.652900i	−0.246979	+	0.969021i	$0.579438\pi$
$878$		0			0
$879$	42.4549	−	27.2841i	1.43197	−	0.920271i
$880$		0			0
$881$	2.99299	+	0.430327i	0.100836	+	0.0144981i	0.192548	−	0.981287i	$-0.438325\pi$
$881$	2.99299	+	0.430327i	0.100836	+	0.0144981i	−0.0917119	+	0.995786i	$0.529234\pi$
$882$		0			0
$883$	−7.66670	−	35.2432i	−0.258005	−	1.18603i	−0.905629	−	0.424070i	$-0.860601\pi$
$883$	−7.66670	−	35.2432i	−0.258005	−	1.18603i	0.647625	−	0.761960i	$-0.275763\pi$
$884$		0			0
$885$	8.01662	+	9.97089i	0.269476	+	0.335168i
$886$		0			0
$887$	28.2320	+	21.1342i	0.947938	+	0.709617i	0.956923	−	0.290342i	$-0.0937691\pi$
$887$	28.2320	+	21.1342i	0.947938	+	0.709617i	−0.00898495	+	0.999960i	$0.502860\pi$
$888$		0			0
$889$	3.74388	−	1.09930i	0.125566	−	0.0368694i
$890$		0			0
$891$	1.68004	+	1.45577i	0.0562835	+	0.0487700i
$892$		0			0
$893$	22.2143	+	1.58880i	0.743372	+	0.0531670i
$894$		0			0
$895$	8.72276	+	12.5933i	0.291570	+	0.420947i
$896$		0			0
$897$	41.5220	+	55.9785i	1.38638	+	1.86907i
$898$		0			0
$899$	−7.16341	−	3.27142i	−0.238913	−	0.109108i
$900$		0			0
$901$	−10.5649	−	12.1926i	−0.351968	−	0.406193i
$902$		0			0
$903$	−3.56764	+	0.255163i	−0.118724	+	0.00849128i
$904$		0			0
$905$	−7.29552	+	28.4504i	−0.242511	+	0.945722i
$906$		0			0
$907$	20.2190	−	27.0094i	0.671360	−	0.896832i	−0.327486	−	0.944856i	$-0.606201\pi$
$907$	20.2190	−	27.0094i	0.671360	−	0.896832i	0.998846	+	0.0480238i	$0.0152923\pi$
$908$		0			0
$909$	14.8202	−	6.76817i	0.491556	−	0.224486i
$910$		0			0
$911$	−15.9877	+	24.8773i	−0.529695	+	0.824221i	−0.998245	−	0.0592155i	$-0.981140\pi$
$911$	−15.9877	+	24.8773i	−0.529695	+	0.824221i	0.468550	+	0.883437i	$0.344776\pi$
$912$		0			0
$913$	−5.39851	+	4.04127i	−0.178665	+	0.133747i
$914$		0			0
$915$	−19.7417	+	21.1565i	−0.652641	+	0.699411i
$916$		0			0
$917$	−1.67872	−	3.07435i	−0.0554362	−	0.101524i
$918$		0			0
$919$	−50.7741			−1.67488			−0.837442	−	0.546526i	$-0.815950\pi$
$919$	−50.7741			−1.67488			−0.837442	+	0.546526i	$0.815950\pi$
$920$		0			0
$921$	−25.8367			−0.851348
$922$		0			0
$923$	−19.6184	−	35.9284i	−0.645747	−	1.18260i
$924$		0			0
$925$	−6.79358	−	23.3303i	−0.223372	−	0.767096i
$926$		0			0
$927$	−43.8249	+	32.8069i	−1.43940	+	1.07752i
$928$		0			0
$929$	−15.4337	+	24.0153i	−0.506363	+	0.787916i	−0.996488	−	0.0837363i	$-0.973315\pi$
$929$	−15.4337	+	24.0153i	−0.506363	+	0.787916i	0.490125	+	0.871652i	$0.336951\pi$
$930$		0			0
$931$	28.7490	−	13.1292i	0.942209	−	0.430292i
$932$		0			0
$933$	39.6852	−	53.0132i	1.29923	−	1.73557i
$934$		0			0
$935$	27.9730	−	16.5548i	0.914817	−	0.541399i
$936$		0			0
$937$	31.2955	−	2.23830i	1.02238	−	0.0731220i	0.449931	−	0.893063i	$-0.351449\pi$
$937$	31.2955	−	2.23830i	1.02238	−	0.0731220i	0.572448	+	0.819941i	$0.305994\pi$
$938$		0			0
$939$	−20.9413	−	24.1675i	−0.683393	−	0.788678i
$940$		0			0
$941$	−10.4386	−	4.76713i	−0.340287	−	0.155404i	0.237940	−	0.971280i	$-0.423528\pi$
$941$	−10.4386	−	4.76713i	−0.340287	−	0.155404i	−0.578227	+	0.815876i	$0.696255\pi$
$942$		0			0
$943$	3.23057	+	0.717662i	0.105202	+	0.0233703i
$944$		0			0
$945$	3.17918	−	2.20206i	0.103419	−	0.0716331i
$946$		0			0
$947$	12.2104	+	0.873303i	0.396784	+	0.0283785i	0.268306	−	0.963334i	$-0.413536\pi$
$947$	12.2104	+	0.873303i	0.396784	+	0.0283785i	0.128478	+	0.991712i	$0.458991\pi$
$948$		0			0
$949$	27.8396	+	24.1231i	0.903710	+	0.783069i
$950$		0			0
$951$	−67.2835	+	19.7562i	−2.18182	+	0.640640i
$952$		0			0
$953$	15.8956	+	11.8993i	0.514909	+	0.385456i	0.824896	−	0.565285i	$-0.191234\pi$
$953$	15.8956	+	11.8993i	0.514909	+	0.385456i	−0.309987	+	0.950741i	$0.600325\pi$
$954$		0			0
$955$	17.7487	+	1.92832i	0.574333	+	0.0623990i
$956$		0			0
$957$	−19.0779	−	87.6995i	−0.616700	−	2.83492i
$958$		0			0
$959$	7.28715	+	1.04773i	0.235314	+	0.0338331i
$960$		0			0
$961$	−25.0088	+	16.0722i	−0.806735	+	0.518457i
$962$		0			0
$963$	−82.9298	+	45.2831i	−2.67238	+	1.45923i
$964$		0			0
$965$	−8.35117	−	32.8734i	−0.268834	−	1.05823i
$966$		0			0
$967$	25.5921	−	25.5921i	0.822985	−	0.822985i	−0.163550	−	0.986535i	$-0.552294\pi$
$967$	25.5921	−	25.5921i	0.822985	−	0.822985i	0.986535	+	0.163550i	$0.0522945\pi$
$968$		0			0
$969$	11.5702	−	39.4044i	0.371687	−	1.26585i
$970$		0			0
$971$	−13.6108	−	21.1788i	−0.436792	−	0.679661i	0.551164	−	0.834397i	$-0.314184\pi$
$971$	−13.6108	−	21.1788i	−0.436792	−	0.679661i	−0.987956	+	0.154736i	$0.950547\pi$
$972$		0			0
$973$	2.63905	+	3.52536i	0.0846041	+	0.113018i
$974$		0			0
$975$	−72.4672	−	5.34639i	−2.32081	−	0.171221i
$976$		0			0
$977$	−16.5871	+	44.4716i	−0.530667	+	1.42277i	0.344424	+	0.938814i	$0.388074\pi$
$977$	−16.5871	+	44.4716i	−0.530667	+	1.42277i	−0.875091	+	0.483958i	$0.839199\pi$
$978$		0			0
$979$	55.7170	−	8.01090i	1.78072	−	0.256029i
$980$		0			0
$981$	26.4036	+	89.9225i	0.843003	+	2.87101i
$982$		0			0
$983$	−2.81596	−	39.3722i	−0.0898150	−	1.25578i	−0.819934	−	0.572458i	$-0.805990\pi$
$983$	−2.81596	−	39.3722i	−0.0898150	−	1.25578i	0.730119	−	0.683320i	$-0.239465\pi$
$984$		0			0
$985$	−34.5983	−	24.0796i	−1.10239	−	0.767240i
$986$		0			0
$987$	4.09004	−	1.52551i	0.130187	−	0.0485574i
$988$		0			0
$989$	−18.3038	−	5.46203i	−0.582026	−	0.173682i
$990$		0			0
$991$	−3.27709	+	7.17582i	−0.104100	+	0.227947i	−0.954514	−	0.298168i	$-0.903625\pi$
$991$	−3.27709	+	7.17582i	−0.104100	+	0.227947i	0.850413	+	0.526115i	$0.176352\pi$
$992$		0			0
$993$	−6.73088	+	94.1100i	−0.213598	+	2.98649i
$994$		0			0
$995$	−19.7853	+	6.56052i	−0.627235	+	0.207983i
$996$		0			0
$997$	22.9777	−	42.0804i	0.727710	−	1.33270i	−0.207370	−	0.978263i	$-0.566490\pi$
$997$	22.9777	−	42.0804i	0.727710	−	1.33270i	0.935079	−	0.354438i	$-0.115328\pi$
$998$		0			0
$999$	−3.75004	−	26.0821i	−0.118646	−	0.825202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.753.4	yes	720
5.2	odd	4	inner	920.2.bv.a.17.4	✓	720
23.19	odd	22	inner	920.2.bv.a.433.4	yes	720
115.42	even	44	inner	920.2.bv.a.617.4	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.4	✓	720	5.2	odd	4	inner
920.2.bv.a.433.4	yes	720	23.19	odd	22	inner
920.2.bv.a.617.4	yes	720	115.42	even	44	inner
920.2.bv.a.753.4	yes	720	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34923 - 2.47093i) q^{3} +(2.23473 - 0.0773038i) q^{5} +(0.255357 - 0.191158i) q^{7} +(-2.66315 + 4.14394i) q^{9} +(-4.15304 + 1.89663i) q^{11} +(3.09352 - 4.13246i) q^{13} +(-3.20618 - 5.41756i) q^{15} +(-3.17579 + 0.227137i) q^{17} +(-3.00031 - 3.46254i) q^{19} +(-0.816873 - 0.373054i) q^{21} +(-3.37622 - 3.40605i) q^{23} +(4.98805 - 0.345507i) q^{25} +(5.40822 + 0.386803i) q^{27} +(-5.27704 - 4.57258i) q^{29} +(1.08214 - 0.317745i) q^{31} +(10.2898 + 7.70288i) q^{33} +(0.555877 - 0.446927i) q^{35} +(-1.03304 - 4.74880i) q^{37} +(-14.3849 - 2.06824i) q^{39} +(-0.580499 + 0.373064i) q^{41} +(3.49571 - 1.90880i) q^{43} +(-5.63109 + 9.46647i) q^{45} +(-3.43722 + 3.43722i) q^{47} +(-1.94346 + 6.61882i) q^{49} +(4.84612 + 7.54070i) q^{51} +(3.03658 + 4.05640i) q^{53} +(-9.13431 + 4.55950i) q^{55} +(-4.50759 + 12.0853i) q^{57} +(-2.01165 + 0.289231i) q^{59} +(-1.29502 - 4.41043i) q^{61} +(0.112093 + 1.56727i) q^{63} +(6.59374 - 9.47409i) q^{65} +(-0.705066 + 0.262976i) q^{67} +(-3.86081 + 12.9379i) q^{69} +(3.29427 - 7.21344i) q^{71} +(-0.509081 + 7.11789i) q^{73} +(-7.58375 - 11.8590i) q^{75} +(-0.697952 + 1.27820i) q^{77} +(-0.450734 - 3.13492i) q^{79} +(-0.202267 - 0.442902i) q^{81} +(1.44328 - 0.313966i) q^{83} +(-7.07949 + 0.753092i) q^{85} +(-4.17859 + 19.2087i) q^{87} +(-11.8297 - 3.47350i) q^{89} -1.64661i q^{91} +(-2.24518 - 2.24518i) q^{93} +(-6.97256 - 7.50592i) q^{95} +(-17.7506 - 3.86140i) q^{97} +(3.20064 - 22.2610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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