LMFDB - Embedded newform 920.2.bv.a.433.4

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			433.4
Character	$\chi$	$=$	920.433
Dual form			920.2.bv.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.47093 - 1.34923i) q^{3} +(-0.998659 - 2.00067i) q^{5} +(0.191158 - 0.255357i) q^{7} +(2.66315 + 4.14394i) q^{9} +(-4.15304 - 1.89663i) q^{11} +(-4.13246 + 3.09352i) q^{13} +(-0.231747 + 6.29094i) q^{15} +(-0.227137 + 3.17579i) q^{17} +(3.00031 - 3.46254i) q^{19} +(-0.816873 + 0.373054i) q^{21} +(-3.40605 - 3.37622i) q^{23} +(-3.00536 + 3.99597i) q^{25} +(-0.386803 - 5.40822i) q^{27} +(5.27704 - 4.57258i) q^{29} +(1.08214 + 0.317745i) q^{31} +(7.70288 + 10.2898i) q^{33} +(-0.701787 - 0.127429i) q^{35} +(4.74880 + 1.03304i) q^{37} +(14.3849 - 2.06824i) q^{39} +(-0.580499 - 0.373064i) q^{41} +(-1.90880 + 3.49571i) q^{43} +(5.63109 - 9.46647i) q^{45} +(-3.43722 + 3.43722i) q^{47} +(1.94346 + 6.61882i) q^{49} +(4.84612 - 7.54070i) q^{51} +(4.05640 + 3.03658i) q^{53} +(0.352940 + 10.2029i) q^{55} +(-12.0853 + 4.50759i) q^{57} +(2.01165 + 0.289231i) q^{59} +(-1.29502 + 4.41043i) q^{61} +(1.56727 + 0.112093i) q^{63} +(10.3160 + 5.17832i) q^{65} +(-0.262976 + 0.705066i) q^{67} +(3.86081 + 12.9379i) q^{69} +(3.29427 + 7.21344i) q^{71} +(7.11789 - 0.509081i) q^{73} +(12.8175 - 5.81885i) q^{75} +(-1.27820 + 0.697952i) q^{77} +(0.450734 - 3.13492i) q^{79} +(-0.202267 + 0.442902i) q^{81} +(-0.313966 + 1.44328i) q^{83} +(6.58055 - 2.71711i) q^{85} +(-19.2087 + 4.17859i) q^{87} +(11.8297 - 3.47350i) q^{89} +1.64661i q^{91} +(-2.24518 - 2.24518i) q^{93} +(-9.92369 - 2.54473i) q^{95} +(3.86140 + 17.7506i) q^{97} +(-3.20064 - 22.2610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−2.47093	−	1.34923i	−1.42659	−	0.778978i	−0.434051	−	0.900888i	$-0.642916\pi$
$3$	−2.47093	−	1.34923i	−1.42659	−	0.778978i	−0.992541	+	0.121910i	$0.961098\pi$
$4$		0			0
$5$	−0.998659	−	2.00067i	−0.446614	−	0.894727i
$5$	−0.998659	−	2.00067i	−0.446614	−	0.894727i
$6$		0			0
$7$	0.191158	−	0.255357i	0.0722509	−	0.0965159i	−0.762960	−	0.646446i	$-0.776255\pi$
$7$	0.191158	−	0.255357i	0.0722509	−	0.0965159i	0.835211	+	0.549930i	$0.185346\pi$
$8$		0			0
$9$	2.66315	+	4.14394i	0.887717	+	1.38131i
$10$		0			0
$11$	−4.15304	−	1.89663i	−1.25219	−	0.571855i	−0.324739	−	0.945804i	$-0.605276\pi$
$11$	−4.15304	−	1.89663i	−1.25219	−	0.571855i	−0.927449	+	0.373949i	$0.878004\pi$
$12$		0			0
$13$	−4.13246	+	3.09352i	−1.14614	+	0.857989i	−0.991516	−	0.129984i	$-0.958507\pi$
$13$	−4.13246	+	3.09352i	−1.14614	+	0.857989i	−0.154623	+	0.987974i	$0.549416\pi$
$14$		0			0
$15$	−0.231747	+	6.29094i	−0.0598369	+	1.62431i
$16$		0			0
$17$	−0.227137	+	3.17579i	−0.0550889	+	0.770243i	0.892560	+	0.450929i	$0.148907\pi$
$17$	−0.227137	+	3.17579i	−0.0550889	+	0.770243i	−0.947649	+	0.319314i	$0.896547\pi$
$18$		0			0
$19$	3.00031	−	3.46254i	0.688319	−	0.794362i	−0.298806	−	0.954314i	$-0.596588\pi$
$19$	3.00031	−	3.46254i	0.688319	−	0.794362i	0.987125	+	0.159952i	$0.0511339\pi$
$20$		0			0
$21$	−0.816873	+	0.373054i	−0.178256	+	0.0814070i
$22$		0			0
$23$	−3.40605	−	3.37622i	−0.710210	−	0.703990i
$23$	−3.40605	−	3.37622i	−0.710210	−	0.703990i
$24$		0			0
$25$	−3.00536	+	3.99597i	−0.601072	+	0.799195i
$26$		0			0
$27$	−0.386803	−	5.40822i	−0.0744404	−	1.04081i
$28$		0			0
$29$	5.27704	−	4.57258i	0.979921	−	0.849107i	−0.00863436	−	0.999963i	$-0.502748\pi$
$29$	5.27704	−	4.57258i	0.979921	−	0.849107i	0.988556	+	0.150856i	$0.0482030\pi$
$30$		0			0
$31$	1.08214	+	0.317745i	0.194358	+	0.0570687i	0.377463	−	0.926025i	$-0.376797\pi$
$31$	1.08214	+	0.317745i	0.194358	+	0.0570687i	−0.183105	+	0.983093i	$0.558615\pi$
$32$		0			0
$33$	7.70288	+	10.2898i	1.34090	+	1.79123i
$34$		0			0
$35$	−0.701787	−	0.127429i	−0.118624	−	0.0215395i
$36$		0			0
$37$	4.74880	+	1.03304i	0.780698	+	0.169830i	0.585217	−	0.810877i	$-0.301010\pi$
$37$	4.74880	+	1.03304i	0.780698	+	0.169830i	0.195481	+	0.980707i	$0.437373\pi$
$38$		0			0
$39$	14.3849	−	2.06824i	2.30343	−	0.331183i
$40$		0			0
$41$	−0.580499	−	0.373064i	−0.0906587	−	0.0582628i	0.494526	−	0.869163i	$-0.335342\pi$
$41$	−0.580499	−	0.373064i	−0.0906587	−	0.0582628i	−0.585185	+	0.810900i	$0.698978\pi$
$42$		0			0
$43$	−1.90880	+	3.49571i	−0.291090	+	0.533091i	−0.981771	−	0.190068i	$-0.939129\pi$
$43$	−1.90880	+	3.49571i	−0.291090	+	0.533091i	0.690681	+	0.723160i	$0.257311\pi$
$44$		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
$53$	4.05640	+	3.03658i	0.557189	+	0.417107i	0.840412	−	0.541947i	$-0.182313\pi$
$53$	4.05640	+	3.03658i	0.557189	+	0.417107i	−0.283223	+	0.959054i	$0.591404\pi$
$54$		0			0
$55$	0.352940	+	10.2029i	0.0475905	+	1.37576i
$56$		0			0
$57$	−12.0853	+	4.50759i	−1.60074	+	0.597045i
$58$		0			0
$59$	2.01165	+	0.289231i	0.261894	+	0.0376547i	0.272011	−	0.962294i	$-0.412311\pi$
$59$	2.01165	+	0.289231i	0.261894	+	0.0376547i	−0.0101170	+	0.999949i	$0.503220\pi$
$60$		0			0
$61$	−1.29502	+	4.41043i	−0.165810	+	0.564698i	0.834104	+	0.551607i	$0.185985\pi$
$61$	−1.29502	+	4.41043i	−0.165810	+	0.564698i	−0.999914	+	0.0130906i	$0.995833\pi$
$62$		0			0
$63$	1.56727	+	0.112093i	0.197457	+	0.0141224i
$64$		0			0
$65$	10.3160	+	5.17832i	1.27955	+	0.642292i
$66$		0			0
$67$	−0.262976	+	0.705066i	−0.0321276	+	0.0861375i	−0.952023	−	0.306026i	$-0.901001\pi$
$67$	−0.262976	+	0.705066i	−0.0321276	+	0.0861375i	0.919896	+	0.392164i	$0.128273\pi$
$68$		0			0
$69$	3.86081	+	12.9379i	0.464787	+	1.55754i
$70$		0			0
$71$	3.29427	+	7.21344i	0.390958	+	0.856078i	0.998108	+	0.0614909i	$0.0195855\pi$
$71$	3.29427	+	7.21344i	0.390958	+	0.856078i	−0.607150	+	0.794587i	$0.707687\pi$
$72$		0			0
$73$	7.11789	−	0.509081i	0.833086	−	0.0595835i	0.351722	−	0.936104i	$-0.385596\pi$
$73$	7.11789	−	0.509081i	0.833086	−	0.0595835i	0.481364	+	0.876521i	$0.340142\pi$
$74$		0			0
$75$	12.8175	−	5.81885i	1.48004	−	0.671903i
$76$		0			0
$77$	−1.27820	+	0.697952i	−0.145665	+	0.0795390i
$78$		0			0
$79$	0.450734	−	3.13492i	0.0507115	−	0.352706i	−0.948629	−	0.316391i	$-0.897529\pi$
$79$	0.450734	−	3.13492i	0.0507115	−	0.352706i	0.999340	−	0.0363153i	$-0.0115621\pi$
$80$		0			0
$81$	−0.202267	+	0.442902i	−0.0224741	+	0.0492114i
$82$		0			0
$83$	−0.313966	+	1.44328i	−0.0344622	+	0.158420i	−0.991162	−	0.132656i	$-0.957650\pi$
$83$	−0.313966	+	1.44328i	−0.0344622	+	0.158420i	0.956700	+	0.291076i	$0.0940132\pi$
$84$		0			0
$85$	6.58055	−	2.71711i	0.713761	−	0.294712i
$86$		0			0
$87$	−19.2087	+	4.17859i	−2.05938	+	0.447992i
$88$		0			0
$89$	11.8297	−	3.47350i	1.25394	−	0.368191i	0.413706	−	0.910411i	$-0.364234\pi$
$89$	11.8297	−	3.47350i	1.25394	−	0.368191i	0.840236	+	0.542220i	$0.182416\pi$
$90$		0			0
$91$			1.64661i			0.172611i
$92$		0			0
$93$	−2.24518	−	2.24518i	−0.232814	−	0.232814i
$94$		0			0
$95$	−9.92369	−	2.54473i	−1.01815	−	0.261084i
$96$		0			0
$97$	3.86140	+	17.7506i	0.392066	+	1.80230i	0.573850	+	0.818960i	$0.305449\pi$
$97$	3.86140	+	17.7506i	0.392066	+	1.80230i	−0.181784	+	0.983338i	$0.558187\pi$
$98$		0			0
$99$	−3.20064	−	22.2610i	−0.321677	−	2.23731i
$100$		0			0
$101$	−2.78246	+	1.78818i	−0.276865	+	0.177930i	−0.671703	−	0.740820i	$-0.734437\pi$
$101$	−2.78246	+	1.78818i	−0.276865	+	0.177930i	0.394838	+	0.918751i	$0.370801\pi$
$102$		0			0
$103$	3.88377	+	10.4128i	0.382679	+	1.02600i	0.975371	+	0.220572i	$0.0707925\pi$
$103$	3.88377	+	10.4128i	0.382679	+	1.02600i	−0.592692	+	0.805429i	$0.701935\pi$
$104$		0			0
$105$	1.56213	+	1.26174i	0.152449	+	0.123133i
$106$		0			0
$107$	−9.19283	−	16.8354i	−0.888704	−	1.62754i	−0.773136	−	0.634241i	$-0.781313\pi$
$107$	−9.19283	−	16.8354i	−0.888704	−	1.62754i	−0.115569	−	0.993299i	$-0.536869\pi$
$108$		0			0
$109$	−12.4592	−	14.3786i	−1.19337	−	1.37722i	−0.908088	−	0.418780i	$-0.862458\pi$
$109$	−12.4592	−	14.3786i	−1.19337	−	1.37722i	−0.285283	−	0.958443i	$-0.592088\pi$
$110$		0			0
$111$	−10.3401	−	8.95979i	−0.981443	−	0.850425i
$112$		0			0
$113$	−16.3985	−	6.11631i	−1.54264	−	0.575374i	−0.572922	−	0.819610i	$-0.694190\pi$
$113$	−16.3985	−	6.11631i	−1.54264	−	0.575374i	−0.969716	+	0.244236i	$0.921463\pi$
$114$		0			0
$115$	−3.35322	+	10.1861i	−0.312689	+	0.949856i
$116$		0			0
$117$	−23.8248	−	8.88618i	−2.20260	−	0.821527i
$118$		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
$123$	0.931023	+	1.70504i	0.0839476	+	0.153738i
$124$		0			0
$125$	10.9960	+	2.02212i	0.983508	+	0.180864i
$126$		0			0
$127$	−4.27483	−	11.4613i	−0.379330	−	1.01702i	−0.976615	−	0.214994i	$-0.931027\pi$
$127$	−4.27483	−	11.4613i	−0.379330	−	1.01702i	0.597285	−	0.802029i	$-0.296246\pi$
$128$		0			0
$129$	9.43304	−	6.06225i	0.830533	−	0.533751i
$130$		0			0
$131$	1.56280	+	10.8695i	0.136542	+	0.949673i	0.936762	+	0.349967i	$0.113807\pi$
$131$	1.56280	+	10.8695i	0.136542	+	0.949673i	−0.800220	+	0.599707i	$0.795284\pi$
$132$		0			0
$133$	−0.310652	−	1.42804i	−0.0269369	−	0.123827i
$134$		0			0
$135$	−10.4338	+	6.17483i	−0.897996	+	0.531445i
$136$		0			0
$137$	−16.3201	−	16.3201i	−1.39432	−	1.39432i	−0.815354	−	0.578963i	$-0.803458\pi$
$137$	−16.3201	−	16.3201i	−1.39432	−	1.39432i	−0.578963	−	0.815354i	$-0.696542\pi$
$138$		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
$143$	23.0295	−	5.00977i	1.92583	−	0.418938i
$144$		0			0
$145$	−14.4182	−	5.99116i	−1.19737	−	0.497539i
$146$		0			0
$147$	4.12816	−	18.9768i	0.340485	−	1.56518i
$148$		0			0
$149$	−8.02048	+	17.5624i	−0.657064	+	1.43877i	0.228170	+	0.973621i	$0.426726\pi$
$149$	−8.02048	+	17.5624i	−0.657064	+	1.43877i	−0.885233	+	0.465147i	$0.846001\pi$
$150$		0			0
$151$	−1.62791	+	11.3223i	−0.132477	+	0.921399i	0.809833	+	0.586660i	$0.199557\pi$
$151$	−1.62791	+	11.3223i	−0.132477	+	0.921399i	−0.942311	+	0.334740i	$0.891352\pi$
$152$		0			0
$153$	−13.7652	+	7.51638i	−1.11285	+	0.607663i
$154$		0			0
$155$	−0.444986	−	2.48232i	−0.0357421	−	0.199385i
$156$		0			0
$157$	−3.04579	+	0.217839i	−0.243081	+	0.0173855i	−0.192348	−	0.981327i	$-0.561610\pi$
$157$	−3.04579	+	0.217839i	−0.243081	+	0.0173855i	−0.0507328	+	0.998712i	$0.516156\pi$
$158$		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
$163$	−6.06826	+	16.2696i	−0.475302	+	1.27434i	0.449293	+	0.893385i	$0.351676\pi$
$163$	−6.06826	+	16.2696i	−0.475302	+	1.27434i	−0.924595	+	0.380951i	$0.875597\pi$
$164$		0			0
$165$	12.8940	−	25.6870i	1.00380	−	1.99973i
$166$		0			0
$167$	16.4315	+	1.17521i	1.27151	+	0.0909402i	0.690726	−	0.723117i	$-0.257291\pi$
$167$	16.4315	+	1.17521i	1.27151	+	0.0909402i	0.580785	+	0.814057i	$0.302746\pi$
$168$		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
$173$	−18.2117	+	6.79263i	−1.38461	+	0.516434i	−0.927783	−	0.373120i	$-0.878288\pi$
$173$	−18.2117	+	6.79263i	−1.38461	+	0.516434i	−0.456830	+	0.889554i	$0.651015\pi$
$174$		0			0
$175$	0.445902	+	1.53130i	0.0337070	+	0.115756i
$176$		0			0
$177$	−4.58040	−	3.42884i	−0.344284	−	0.257728i
$178$		0			0
$179$	−3.70390	+	5.76338i	−0.276843	+	0.430775i	−0.951634	−	0.307233i	$-0.900597\pi$
$179$	−3.70390	+	5.76338i	−0.276843	+	0.430775i	0.674792	+	0.738008i	$0.264233\pi$
$180$		0			0
$181$	−3.70057	−	12.6030i	−0.275061	−	0.936772i	−0.974932	−	0.222503i	$-0.928577\pi$
$181$	−3.70057	−	12.6030i	−0.275061	−	0.936772i	0.699871	−	0.714269i	$-0.253241\pi$
$182$		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
$187$	6.96661	−	12.7584i	0.509449	−	0.932987i
$188$		0			0
$189$	−1.45497	−	0.935051i	−0.105833	−	0.0680149i
$190$		0			0
$191$	7.90289	−	1.13626i	0.571833	−	0.0822172i	0.149668	−	0.988736i	$-0.452179\pi$
$191$	7.90289	−	1.13626i	0.571833	−	0.0822172i	0.422165	+	0.906519i	$0.361270\pi$
$192$		0			0
$193$	−14.8218	−	3.22428i	−1.06689	−	0.232089i	−0.355352	−	0.934732i	$-0.615639\pi$
$193$	−14.8218	−	3.22428i	−1.06689	−	0.232089i	−0.711542	+	0.702644i	$0.752003\pi$
$194$		0			0
$195$	−18.5035	−	26.7140i	−1.32506	−	1.91303i
$196$		0			0
$197$	11.2972	+	15.0913i	0.804893	+	1.07521i	0.995613	+	0.0935664i	$0.0298267\pi$
$197$	11.2972	+	15.0913i	0.804893	+	1.07521i	−0.190720	+	0.981644i	$0.561082\pi$
$198$		0			0
$199$	8.94437	+	2.62631i	0.634050	+	0.186174i	0.582935	−	0.812519i	$-0.301904\pi$
$199$	8.94437	+	2.62631i	0.634050	+	0.186174i	0.0511151	+	0.998693i	$0.483722\pi$
$200$		0			0
$201$	1.60109	−	1.38735i	0.112932	−	0.0978564i
$202$		0			0
$203$	−0.158893	−	2.22161i	−0.0111521	−	0.155927i
$204$		0			0
$205$	−0.166658	+	1.53395i	−0.0116399	+	0.107136i
$206$		0			0
$207$	4.92004	−	23.1058i	0.341966	−	1.60597i
$208$		0			0
$209$	−19.0276	+	8.68960i	−1.31616	+	0.601072i
$210$		0			0
$211$	−15.1346	+	17.4663i	−1.04191	+	1.20243i	−0.0630253	+	0.998012i	$0.520075\pi$
$211$	−15.1346	+	17.4663i	−1.04191	+	1.20243i	−0.978884	+	0.204416i	$0.934471\pi$
$212$		0			0
$213$	1.59268	−	22.2686i	0.109129	−	1.52582i
$214$		0			0
$215$	8.90001	+	0.327861i	0.606976	+	0.0223599i
$216$		0			0
$217$	0.287998	−	0.215593i	0.0195506	−	0.0146354i
$218$		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
$223$	−15.0593	+	20.1169i	−1.00844	+	1.34712i	−0.0715786	+	0.997435i	$0.522804\pi$
$223$	−15.0593	+	20.1169i	−1.00844	+	1.34712i	−0.936866	+	0.349689i	$0.886287\pi$
$224$		0			0
$225$	−24.5628	−	1.81216i	−1.63752	−	0.120811i
$226$		0			0
$227$	2.01279	+	1.09907i	0.133594	+	0.0729478i	0.544656	−	0.838660i	$-0.316660\pi$
$227$	2.01279	+	1.09907i	0.133594	+	0.0729478i	−0.411062	+	0.911607i	$0.634842\pi$
$228$		0			0
$229$	−19.5250			−1.29025			−0.645125	−	0.764077i	$-0.723195\pi$
$229$	−19.5250			−1.29025			−0.645125	+	0.764077i	$0.723195\pi$
$230$		0			0
$231$	4.10005			0.269763
$232$		0			0
$233$	7.68616	+	4.19696i	0.503537	+	0.274952i	0.710876	−	0.703317i	$-0.248299\pi$
$233$	7.68616	+	4.19696i	0.503537	+	0.274952i	−0.207339	+	0.978269i	$0.566480\pi$
$234$		0			0
$235$	10.3094	+	3.44413i	0.672508	+	0.224671i
$236$		0			0
$237$	−5.34346	+	7.13803i	−0.347095	+	0.463665i
$238$		0			0
$239$	5.19130	+	8.07783i	0.335798	+	0.522511i	0.967557	−	0.252653i	$-0.0813032\pi$
$239$	5.19130	+	8.07783i	0.335798	+	0.522511i	−0.631759	+	0.775165i	$0.717667\pi$
$240$		0			0
$241$	10.0367	+	4.58359i	0.646519	+	0.295255i	0.711558	−	0.702628i	$-0.247990\pi$
$241$	10.0367	+	4.58359i	0.646519	+	0.295255i	−0.0650392	+	0.997883i	$0.520717\pi$
$242$		0			0
$243$	−11.9243	+	8.92643i	−0.764945	+	0.572631i
$244$		0			0
$245$	11.3012	−	10.4982i	0.722009	−	0.670704i
$246$		0			0
$247$	−1.68722	+	23.5904i	−0.107355	+	1.50102i
$248$		0			0
$249$	2.72310	−	3.14262i	0.172569	−	0.199156i
$250$		0			0
$251$	−16.1155	+	7.35971i	−1.01720	+	0.464540i	−0.853014	−	0.521889i	$-0.825228\pi$
$251$	−16.1155	+	7.35971i	−1.01720	+	0.464540i	−0.164188	+	0.986429i	$0.552500\pi$
$252$		0			0
$253$	7.74201	+	20.4816i	0.486736	+	1.28767i
$254$		0			0
$255$	−19.9261	−	2.16489i	−1.24782	−	0.135571i
$256$		0			0
$257$	0.638793	+	8.93150i	0.0398468	+	0.557131i	0.977687	+	0.210065i	$0.0673676\pi$
$257$	0.638793	+	8.93150i	0.0398468	+	0.557131i	−0.937841	+	0.347066i	$0.887178\pi$
$258$		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
$263$	−13.2070	−	17.6425i	−0.814378	−	1.08788i	−0.994551	−	0.104247i	$-0.966757\pi$
$263$	−13.2070	−	17.6425i	−0.814378	−	1.08788i	0.180173	−	0.983635i	$-0.442334\pi$
$264$		0			0
$265$	2.02424	−	11.1480i	0.124348	−	0.684818i
$266$		0			0
$267$	−33.9168	−	7.37815i	−2.07568	−	0.451536i
$268$		0			0
$269$	9.10920	−	1.30971i	0.555398	−	0.0798541i	0.141100	−	0.989995i	$-0.454936\pi$
$269$	9.10920	−	1.30971i	0.555398	−	0.0798541i	0.414298	+	0.910141i	$0.364027\pi$
$270$		0			0
$271$	−14.0938	−	9.05752i	−0.856136	−	0.550205i	0.0373468	−	0.999302i	$-0.488109\pi$
$271$	−14.0938	−	9.05752i	−0.856136	−	0.550205i	−0.893483	+	0.449097i	$0.851746\pi$
$272$		0			0
$273$	2.22165	−	4.06865i	0.134460	−	0.246246i
$274$		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	−0.982669	−	0.185369i	$-0.940652\pi$
$281$	−6.80305	+	10.5858i	−0.405836	+	0.631493i	0.576833	+	0.816862i	$0.304288\pi$
$282$		0			0
$283$	11.5763	+	8.66593i	0.688141	+	0.515136i	0.885174	−	0.465261i	$-0.154039\pi$
$283$	11.5763	+	8.66593i	0.688141	+	0.515136i	−0.197032	+	0.980397i	$0.563130\pi$
$284$		0			0
$285$	21.0873	+	19.6772i	1.24911	+	1.16558i
$286$		0			0
$287$	−0.206232	+	0.0769204i	−0.0121735	+	0.00454047i
$288$		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
$293$	17.8800	+	1.27881i	1.04456	+	0.0747086i	0.583059	−	0.812430i	$-0.301856\pi$
$293$	17.8800	+	1.27881i	1.04456	+	0.0747086i	0.461504	+	0.887138i	$0.347310\pi$
$294$		0			0
$295$	−1.43029	−	4.31348i	−0.0832748	−	0.251141i
$296$		0			0
$297$	−8.65097	+	23.1942i	−0.501980	+	1.34586i
$298$		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
$303$	9.28792	−	0.664285i	0.533577	−	0.0381622i
$304$		0			0
$305$	10.1171	−	1.81361i	0.579303	−	0.103847i
$306$		0			0
$307$	8.05467	−	4.39818i	0.459704	−	0.251018i	−0.232670	−	0.972556i	$-0.574746\pi$
$307$	8.05467	−	4.39818i	0.459704	−	0.251018i	0.692375	+	0.721538i	$0.256565\pi$
$308$		0			0
$309$	4.45272	−	30.9693i	0.253306	−	1.76178i
$310$		0			0
$311$	9.77141	−	21.3964i	0.554086	−	1.21328i	−0.400761	−	0.916183i	$-0.631254\pi$
$311$	9.77141	−	21.3964i	0.554086	−	1.21328i	0.954847	−	0.297097i	$-0.0960184\pi$
$312$		0			0
$313$	−2.41447	+	11.0992i	−0.136474	+	0.627361i	0.857193	+	0.514996i	$0.172206\pi$
$313$	−2.41447	+	11.0992i	−0.136474	+	0.627361i	−0.993667	+	0.112366i	$0.964157\pi$
$314$		0			0
$315$	−1.34090	−	3.24753i	−0.0755514	−	0.182978i
$316$		0			0
$317$	24.3390	−	5.29462i	1.36701	−	0.297375i	0.531598	−	0.846997i	$-0.321592\pi$
$317$	24.3390	−	5.29462i	1.36701	−	0.297375i	0.835414	+	0.549621i	$0.185228\pi$
$318$		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
$325$	0.0579034	−	25.8104i	0.00321191	−	1.43170i
$326$		0			0
$327$	11.3856	+	52.3389i	0.629626	+	2.89435i
$328$		0			0
$329$	0.220667	+	1.53477i	0.0121658	+	0.0846147i
$330$		0			0
$331$	−28.1933	+	18.1187i	−1.54964	+	0.995895i	−0.564250	+	0.825604i	$0.690834\pi$
$331$	−28.1933	+	18.1187i	−1.54964	+	0.995895i	−0.985394	+	0.170291i	$0.945529\pi$
$332$		0			0
$333$	8.36592	+	22.4299i	0.458450	+	1.22915i
$334$		0			0
$335$	1.67323	−	0.177992i	0.0914182	−	0.00972476i
$336$		0			0
$337$	1.33800	+	2.45036i	0.0728855	+	0.133480i	0.911581	−	0.411122i	$-0.134863\pi$
$337$	1.33800	+	2.45036i	0.0728855	+	0.133480i	−0.838695	+	0.544601i	$0.816681\pi$
$338$		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
$343$	4.15375	+	1.54927i	0.224282	+	0.0836527i
$344$		0			0
$345$	22.0289	−	20.6448i	1.18600	−	1.11148i
$346$		0			0
$347$	−30.2838	−	11.2953i	−1.62572	−	0.606361i	−0.639058	−	0.769159i	$-0.720675\pi$
$347$	−30.2838	−	11.2953i	−1.62572	−	0.606361i	−0.986659	+	0.162798i	$0.947948\pi$
$348$		0			0
$349$	−24.6327	−	21.3444i	−1.31856	−	1.14254i	−0.979427	−	0.201799i	$-0.935321\pi$
$349$	−24.6327	−	21.3444i	−1.31856	−	1.14254i	−0.339132	−	0.940739i	$-0.610133\pi$
$350$		0			0
$351$	18.3289	+	21.1527i	0.978324	+	1.12905i
$352$		0			0
$353$	−11.9250	−	21.8390i	−0.634702	−	1.16237i	−0.975032	−	0.222064i	$-0.928721\pi$
$353$	−11.9250	−	21.8390i	−0.634702	−	1.16237i	0.340330	−	0.940306i	$-0.389461\pi$
$354$		0			0
$355$	11.1419	−	13.7945i	0.591349	−	0.732137i
$356$		0			0
$357$	−0.999199	−	2.67896i	−0.0528832	−	0.141785i
$358$		0			0
$359$	−3.41487	+	2.19460i	−0.180230	+	0.115827i	−0.627645	−	0.778500i	$-0.715981\pi$
$359$	−3.41487	+	2.19460i	−0.180230	+	0.115827i	0.447415	+	0.894326i	$0.352345\pi$
$360$		0			0
$361$	−0.283360	−	1.97081i	−0.0149137	−	0.103727i
$362$		0			0
$363$	−5.89155	−	27.0830i	−0.309226	−	1.42149i
$364$		0			0
$365$	−8.12685	−	13.7321i	−0.425379	−	0.718773i
$366$		0			0
$367$	9.76278	+	9.76278i	0.509613	+	0.509613i	0.914408	−	0.404795i	$-0.132657\pi$
$367$	9.76278	+	9.76278i	0.509613	+	0.509613i	−0.404795	+	0.914408i	$0.632657\pi$
$368$		0			0
$369$		−	3.39908i		−	0.176949i
$370$		0			0
$371$	1.55083	−	0.455363i	0.0805148	−	0.0236413i
$372$		0			0
$373$	8.16402	−	1.77597i	0.422717	−	0.0919564i	0.00382530	−	0.999993i	$-0.498782\pi$
$373$	8.16402	−	1.77597i	0.422717	−	0.0919564i	0.418892	+	0.908036i	$0.362419\pi$
$374$		0			0
$375$	−24.4419	−	19.8326i	−1.26218	−	1.02415i
$376$		0			0
$377$	−7.66179	+	35.2207i	−0.394602	+	1.81396i
$378$		0			0
$379$	−4.67661	+	10.2403i	−0.240221	+	0.526011i	−0.990891	−	0.134666i	$-0.957004\pi$
$379$	−4.67661	+	10.2403i	−0.240221	+	0.526011i	0.750670	+	0.660678i	$0.229731\pi$
$380$		0			0
$381$	−4.90107	+	34.0877i	−0.251090	+	1.74637i
$382$		0			0
$383$	8.16491	−	4.45838i	0.417207	−	0.227812i	−0.256912	−	0.966435i	$-0.582705\pi$
$383$	8.16491	−	4.45838i	0.417207	−	0.227812i	0.674119	+	0.738622i	$0.264523\pi$
$384$		0			0
$385$	2.67286	+	1.86025i	0.136222	+	0.0948070i
$386$		0			0
$387$	−19.5695	+	1.39964i	−0.994772	+	0.0711475i
$388$		0			0
$389$	−0.628717	−	1.37670i	−0.0318772	−	0.0698013i	0.893024	−	0.450010i	$-0.148580\pi$
$389$	−0.628717	−	1.37670i	−0.0318772	−	0.0698013i	−0.924901	+	0.380208i	$0.875852\pi$
$390$		0			0
$391$	11.4958	−	10.0500i	0.581368	−	0.508252i
$392$		0			0
$393$	10.8039	−	28.9664i	0.544985	−	1.46116i
$394$		0			0
$395$	−6.72207	+	2.22895i	−0.338224	+	0.112151i
$396$		0			0
$397$	10.9626	+	0.784061i	0.550197	+	0.0393509i	0.343671	−	0.939090i	$-0.388330\pi$
$397$	10.9626	+	0.784061i	0.550197	+	0.0393509i	0.206526	+	0.978441i	$0.433784\pi$
$398$		0			0
$399$	−1.15916	+	3.94774i	−0.0580306	+	0.197634i
$400$		0			0
$401$	−6.84218	−	0.983757i	−0.341682	−	0.0491265i	−0.0306620	−	0.999530i	$-0.509762\pi$
$401$	−6.84218	−	0.983757i	−0.341682	−	0.0491265i	−0.311020	+	0.950403i	$0.600671\pi$
$402$		0			0
$403$	−5.45486	+	2.03456i	−0.271726	+	0.101348i
$404$		0			0
$405$	1.08810	−	0.0376394i	0.0540680	−	0.00187032i
$406$		0			0
$407$	−17.7627	−	13.2970i	−0.880462	−	0.659106i
$408$		0			0
$409$	−6.24459	+	9.71677i	−0.308775	+	0.480464i	−0.960611	−	0.277897i	$-0.910363\pi$
$409$	−6.24459	+	9.71677i	−0.308775	+	0.480464i	0.651836	+	0.758360i	$0.273999\pi$
$410$		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
$417$	18.6269	−	34.1127i	0.912165	−	1.67050i
$418$		0			0
$419$	−5.72563	−	3.67964i	−0.279715	−	0.179762i	0.393260	−	0.919427i	$-0.371347\pi$
$419$	−5.72563	−	3.67964i	−0.279715	−	0.179762i	−0.672975	+	0.739666i	$0.734984\pi$
$420$		0			0
$421$	24.1849	−	3.47726i	1.17870	−	0.169471i	0.475011	−	0.879980i	$-0.342444\pi$
$421$	24.1849	−	3.47726i	1.17870	−	0.169471i	0.703688	+	0.710509i	$0.251535\pi$
$422$		0			0
$423$	−23.3975	−	5.08981i	−1.13763	−	0.247475i
$424$		0			0
$425$	−12.0078	−	10.4520i	−0.582462	−	0.506998i
$426$		0			0
$427$	0.878681	+	1.17378i	0.0425224	+	0.0568032i
$428$		0			0
$429$	−63.6637	−	18.6934i	−3.07371	−	0.902524i
$430$		0			0
$431$	13.4728	−	11.6743i	0.648962	−	0.562329i	−0.266949	−	0.963711i	$-0.586015\pi$
$431$	13.4728	−	11.6743i	0.648962	−	0.562329i	0.915911	+	0.401382i	$0.131470\pi$
$432$		0			0
$433$	2.39587	+	33.4986i	0.115138	+	1.60984i	0.646647	+	0.762789i	$0.276171\pi$
$433$	2.39587	+	33.4986i	0.115138	+	1.60984i	−0.531509	+	0.847053i	$0.678375\pi$
$434$		0			0
$435$	27.5429	+	34.2572i	1.32058	+	1.64251i
$436$		0			0
$437$	−21.9095	+	1.66388i	−1.04807	+	0.0795944i
$438$		0			0
$439$	−3.19723	+	1.46013i	−0.152596	+	0.0696881i	−0.490249	−	0.871582i	$-0.663094\pi$
$439$	−3.19723	+	1.46013i	−0.152596	+	0.0696881i	0.337653	+	0.941271i	$0.390367\pi$
$440$		0			0
$441$	−22.2523	+	25.6805i	−1.05963	+	1.22288i
$442$		0			0
$443$	−1.85444	+	25.9285i	−0.0881072	+	1.23190i	0.740495	+	0.672062i	$0.234591\pi$
$443$	−1.85444	+	25.9285i	−0.0881072	+	1.23190i	−0.828602	+	0.559838i	$0.810863\pi$
$444$		0			0
$445$	−18.7631	−	20.1984i	−0.889458	−	0.957497i
$446$		0			0
$447$	43.5138	−	32.5740i	2.05813	−	1.54070i
$448$		0			0
$449$	−12.6424	−	5.77358i	−0.596631	−	0.272472i	0.0941247	−	0.995560i	$-0.469995\pi$
$449$	−12.6424	−	5.77358i	−0.596631	−	0.272472i	−0.690756	+	0.723088i	$0.742722\pi$
$450$		0			0
$451$	1.70327	+	2.65034i	0.0802039	+	0.124800i
$452$		0			0
$453$	19.2989	−	25.7803i	0.906741	−	1.21126i
$454$		0			0
$455$	3.29431	−	1.64440i	0.154440	−	0.0770905i
$456$		0			0
$457$	13.5683	+	7.40886i	0.634699	+	0.346572i	0.764173	−	0.645011i	$-0.223147\pi$
$457$	13.5683	+	7.40886i	0.634699	+	0.346572i	−0.129474	+	0.991583i	$0.541329\pi$
$458$		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
$463$	−11.9635	−	6.53256i	−0.555991	−	0.303594i	0.176578	−	0.984287i	$-0.443497\pi$
$463$	−11.9635	−	6.53256i	−0.555991	−	0.303594i	−0.732569	+	0.680693i	$0.761679\pi$
$464$		0			0
$465$	−2.24970	+	6.73404i	−0.104327	+	0.312284i
$466$		0			0
$467$	−10.1700	+	13.5855i	−0.470612	+	0.628664i	−0.971554	−	0.236817i	$-0.923896\pi$
$467$	−10.1700	+	13.5855i	−0.470612	+	0.628664i	0.500942	+	0.865481i	$0.332987\pi$
$468$		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
$473$	14.5574	−	10.8975i	0.669350	−	0.501069i
$474$		0			0
$475$	4.81922	+	22.3954i	0.221121	+	1.02757i
$476$		0			0
$477$	−1.78062	+	24.8964i	−0.0815291	+	1.13993i
$478$		0			0
$479$	−28.5207	+	32.9146i	−1.30314	+	1.50391i	−0.575925	+	0.817502i	$0.695358\pi$
$479$	−28.5207	+	32.9146i	−1.30314	+	1.50391i	−0.727219	+	0.686406i	$0.759187\pi$
$480$		0			0
$481$	−22.8200	+	10.4215i	−1.04050	+	0.475181i
$482$		0			0
$483$	4.04182	+	1.48730i	0.183909	+	0.0676747i
$484$		0			0
$485$	31.6568	−	25.4522i	1.43746	−	1.15572i
$486$		0			0
$487$	−1.52098	−	21.2661i	−0.0689221	−	0.963657i	−0.907818	−	0.419365i	$-0.862253\pi$
$487$	−1.52098	−	21.2661i	−0.0689221	−	0.963657i	0.838896	−	0.544292i	$-0.183202\pi$
$488$		0			0
$489$	36.9457	−	32.0136i	1.67074	−	1.44771i
$490$		0			0
$491$	36.4623	+	10.7063i	1.64552	+	0.483168i	0.967709	−	0.252069i	$-0.0811112\pi$
$491$	36.4623	+	10.7063i	1.64552	+	0.483168i	0.677810	+	0.735237i	$0.262929\pi$
$492$		0			0
$493$	13.3230	+	17.7974i	0.600036	+	0.801554i
$494$		0			0
$495$	−41.3405	+	28.6346i	−1.85812	+	1.28703i
$496$		0			0
$497$	2.47173	+	0.537692i	0.110872	+	0.0241188i
$498$		0			0
$499$	23.3456	−	3.35659i	1.04509	−	0.150261i	0.401678	−	0.915781i	$-0.368427\pi$
$499$	23.3456	−	3.35659i	1.04509	−	0.150261i	0.643413	+	0.765519i	$0.277518\pi$
$500$		0			0
$501$	−39.0156	−	25.0738i	−1.74309	−	1.12021i
$502$		0			0
$503$	19.1159	−	35.0082i	0.852338	−	1.56094i	0.0246878	−	0.999695i	$-0.492141\pi$
$503$	19.1159	−	35.0082i	0.852338	−	1.56094i	0.827650	−	0.561245i	$-0.189677\pi$
$504$		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	0.970930	+	0.239365i	$0.0769391\pi$
$509$	6.39700	+	21.7862i	0.283542	+	0.965655i	−0.687388	+	0.726291i	$0.741243\pi$
$510$		0			0
$511$	1.23064	−	1.91492i	0.0544404	−	0.0847110i
$512$		0			0
$513$	−19.8867	−	14.8870i	−0.878020	−	0.657278i
$514$		0			0
$515$	16.9540	−	18.1689i	0.747081	−	0.800620i
$516$		0			0
$517$	20.7941	−	7.75578i	0.914521	−	0.341099i
$518$		0			0
$519$	54.1647	+	7.78771i	2.37757	+	0.341843i
$520$		0			0
$521$	8.50895	−	28.9788i	0.372784	−	1.26958i	−0.533098	−	0.846054i	$-0.678972\pi$
$521$	8.50895	−	28.9788i	0.372784	−	1.26958i	0.905881	−	0.423531i	$-0.139210\pi$
$522$		0			0
$523$	−20.4894	−	1.46543i	−0.895938	−	0.0640787i	−0.384229	−	0.923238i	$-0.625533\pi$
$523$	−20.4894	−	1.46543i	−0.895938	−	0.0640787i	−0.511709	+	0.859159i	$0.670987\pi$
$524$		0			0
$525$	0.964286	−	4.38536i	0.0420849	−	0.191393i
$526$		0			0
$527$	−1.25489	+	3.36448i	−0.0546637	+	0.146559i
$528$		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
$533$	3.55297	−	0.254114i	0.153896	−	0.0110069i
$534$		0			0
$535$	−24.5016	+	35.2046i	−1.05930	+	1.52203i
$536$		0			0
$537$	16.9282	−	9.24350i	0.730506	−	0.398887i
$538$		0			0
$539$	4.48218	−	31.1743i	0.193061	−	1.34277i
$540$		0			0
$541$	11.2889	−	24.7192i	0.485346	−	1.06276i	−0.495612	−	0.868544i	$-0.665056\pi$
$541$	11.2889	−	24.7192i	0.485346	−	1.06276i	0.980959	−	0.194217i	$-0.0622164\pi$
$542$		0			0
$543$	−7.86047	+	36.1340i	−0.337325	+	1.55066i
$544$		0			0
$545$	−16.3245	+	39.2860i	−0.699263	+	1.68283i
$546$		0			0
$547$	−2.13442	+	0.464314i	−0.0912612	+	0.0198527i	−0.257964	−	0.966155i	$-0.583052\pi$
$547$	−2.13442	+	0.464314i	−0.0912612	+	0.0198527i	0.166703	+	0.986007i	$0.446688\pi$
$548$		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
$555$	−7.59930	+	29.6350i	−0.322572	+	1.25794i
$556$		0			0
$557$	2.07071	+	9.51889i	0.0877387	+	0.403328i	0.999980	−	0.00632509i	$-0.00201335\pi$
$557$	2.07071	+	9.51889i	0.0877387	+	0.403328i	−0.912241	+	0.409653i	$0.865650\pi$
$558$		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
$563$	1.50834	+	4.04402i	0.0635690	+	0.170435i	0.964851	−	0.262798i	$-0.0846454\pi$
$563$	1.50834	+	4.04402i	0.0635690	+	0.170435i	−0.901282	+	0.433233i	$0.857373\pi$
$564$		0			0
$565$	4.13975	+	38.9160i	0.174161	+	1.63721i
$566$		0			0
$567$	0.0744334	+	0.136315i	0.00312591	+	0.00572467i
$568$		0			0
$569$	−11.2072	−	12.9338i	−0.469830	−	0.542213i	0.470534	−	0.882382i	$-0.344061\pi$
$569$	−11.2072	−	12.9338i	−0.469830	−	0.542213i	−0.940364	+	0.340169i	$0.889516\pi$
$570$		0			0
$571$	−6.63720	−	5.75116i	−0.277758	−	0.240679i	0.504830	−	0.863219i	$-0.331555\pi$
$571$	−6.63720	−	5.75116i	−0.277758	−	0.240679i	−0.782588	+	0.622540i	$0.786101\pi$
$572$		0			0
$573$	−21.0606	−	7.85518i	−0.879818	−	0.328155i
$574$		0			0
$575$	23.7277	−	3.46373i	0.989512	−	0.144447i
$576$		0			0
$577$	−23.3973	−	8.72672i	−0.974040	−	0.363298i	−0.188476	−	0.982078i	$-0.560355\pi$
$577$	−23.3973	−	8.72672i	−0.974040	−	0.363298i	−0.785565	+	0.618780i	$0.787627\pi$
$578$		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
$583$	−11.0871	−	20.3045i	−0.459181	−	0.840927i
$584$		0			0
$585$	6.01451	+	56.5398i	0.248669	+	2.33763i
$586$		0			0
$587$	8.30941	+	22.2784i	0.342966	+	0.919528i	0.987873	+	0.155266i	$0.0496236\pi$
$587$	8.30941	+	22.2784i	0.342966	+	0.919528i	−0.644906	+	0.764261i	$0.723104\pi$
$588$		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
$593$	−2.73951	−	12.5933i	−0.112498	−	0.517146i	−0.998563	−	0.0535849i	$-0.982935\pi$
$593$	−2.73951	−	12.5933i	−0.112498	−	0.517146i	0.886065	−	0.463561i	$-0.153428\pi$
$594$		0			0
$595$	0.564091	−	2.19979i	0.0231255	−	0.0901825i
$596$		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	−0.595829	−	0.803111i	$-0.703176\pi$
$601$	−16.2507	+	4.77162i	−0.662878	+	0.194639i	−0.0670488	+	0.997750i	$0.521358\pi$
$602$		0			0
$603$	−3.62210	+	0.787940i	−0.147503	+	0.0320874i
$604$		0			0
$605$	8.44717	−	20.3288i	0.343426	−	0.826481i
$606$		0			0
$607$	−4.94579	+	22.7354i	−0.200743	+	0.922802i	0.760979	+	0.648776i	$0.224719\pi$
$607$	−4.94579	+	22.7354i	−0.200743	+	0.922802i	−0.961722	+	0.274026i	$0.911645\pi$
$608$		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
$613$	12.5755	−	6.86674i	0.507919	−	0.277345i	−0.204788	−	0.978806i	$-0.565651\pi$
$613$	12.5755	−	6.86674i	0.507919	−	0.277345i	0.712707	+	0.701461i	$0.247469\pi$
$614$		0			0
$615$	2.48145	−	3.56543i	0.100062	−	0.143772i
$616$		0			0
$617$	15.1480	−	1.08341i	0.609835	−	0.0436163i	0.236993	−	0.971511i	$-0.423838\pi$
$617$	15.1480	−	1.08341i	0.609835	−	0.0436163i	0.372842	+	0.927895i	$0.378383\pi$
$618$		0			0
$619$	18.5706	+	40.6639i	0.746414	+	1.63442i	0.772706	+	0.634764i	$0.218903\pi$
$619$	18.5706	+	40.6639i	0.746414	+	1.63442i	−0.0262919	+	0.999654i	$0.508370\pi$
$620$		0			0
$621$	−16.9418	+	19.7266i	−0.679853	+	0.791600i
$622$		0			0
$623$	1.37435	−	3.68478i	0.0550622	−	0.147627i
$624$		0			0
$625$	−6.93562	−	24.0187i	−0.277425	−	0.960747i
$626$		0			0
$627$	58.7401	+	4.20117i	2.34585	+	0.167779i
$628$		0			0
$629$	−4.35935	+	14.8466i	−0.173818	+	0.591971i
$630$		0			0
$631$	3.03854	+	0.436875i	0.120962	+	0.0173917i	0.202530	−	0.979276i	$-0.435084\pi$
$631$	3.03854	+	0.436875i	0.120962	+	0.0173917i	−0.0815678	+	0.996668i	$0.525993\pi$
$632$		0			0
$633$	60.9626	−	22.7379i	2.42304	−	0.903749i
$634$		0			0
$635$	−18.6611	+	19.9984i	−0.740544	+	0.793613i
$636$		0			0
$637$	−28.5068	−	21.3399i	−1.12948	−	0.845518i
$638$		0			0
$639$	−21.1190	+	32.8618i	−0.835454	+	1.29999i
$640$		0			0
$641$	3.40954	+	11.6118i	0.134669	+	0.458639i	0.999021	−	0.0442482i	$-0.0140893\pi$
$641$	3.40954	+	11.6118i	0.134669	+	0.458639i	−0.864352	+	0.502887i	$0.832271\pi$
$642$		0			0
$643$	−7.93740	+	7.93740i	−0.313020	+	0.313020i	−0.846079	−	0.533058i	$-0.821043\pi$
$643$	−7.93740	+	7.93740i	−0.313020	+	0.313020i	0.533058	+	0.846079i	$0.321043\pi$
$644$		0			0
$645$	−21.5489	−	12.8183i	−0.848489	−	0.504719i
$646$		0			0
$647$	17.5701	−	32.1772i	0.690750	−	1.26502i	−0.263110	−	0.964766i	$-0.584748\pi$
$647$	17.5701	−	32.1772i	0.690750	−	1.26502i	0.953861	−	0.300249i	$-0.0970699\pi$
$648$		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
$653$	9.77101	+	2.12555i	0.382369	+	0.0831794i	0.399642	−	0.916671i	$-0.369135\pi$
$653$	9.77101	+	2.12555i	0.382369	+	0.0831794i	−0.0172723	+	0.999851i	$0.505498\pi$
$654$		0			0
$655$	20.1856	−	13.9816i	0.788717	−	0.546306i
$656$		0			0
$657$	21.0656	+	28.1404i	0.821848	+	1.09786i
$658$		0			0
$659$	12.0317	+	3.53283i	0.468689	+	0.137619i	0.507545	−	0.861625i	$-0.330553\pi$
$659$	12.0317	+	3.53283i	0.468689	+	0.137619i	−0.0388560	+	0.999245i	$0.512371\pi$
$660$		0			0
$661$	−7.38771	+	6.40149i	−0.287349	+	0.248989i	−0.786592	−	0.617473i	$-0.788157\pi$
$661$	−7.38771	+	6.40149i	−0.287349	+	0.248989i	0.499244	+	0.866462i	$0.333611\pi$
$662$		0			0
$663$	3.30095	+	46.1533i	0.128198	+	1.79244i
$664$		0			0
$665$	−2.54681	+	2.04764i	−0.0987610	+	0.0794041i
$666$		0			0
$667$	−33.4119	−	2.24201i	−1.29371	−	0.0868108i
$668$		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
$673$	0.342916	−	4.79459i	0.0132184	−	0.184818i	−0.986553	−	0.163441i	$-0.947741\pi$
$673$	0.342916	−	4.79459i	0.0132184	−	0.184818i	0.999771	−	0.0213765i	$-0.00680486\pi$
$674$		0			0
$675$	22.7736	+	14.7080i	0.876556	+	0.566111i
$676$		0			0
$677$	0.905472	−	0.677828i	0.0348001	−	0.0260510i	−0.581736	−	0.813378i	$-0.697626\pi$
$677$	0.905472	−	0.677828i	0.0348001	−	0.0260510i	0.616536	+	0.787327i	$0.288535\pi$
$678$		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
$683$	−24.2872	+	32.4439i	−0.929323	+	1.24143i	0.0408865	+	0.999164i	$0.486982\pi$
$683$	−24.2872	+	32.4439i	−0.929323	+	1.24143i	−0.970210	+	0.242267i	$0.922109\pi$
$684$		0			0
$685$	−16.3529	+	48.9492i	−0.624811	+	1.87025i
$686$		0			0
$687$	48.2450	+	26.3437i	1.84066	+	1.00508i
$688$		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
$693$	−6.29633	−	3.43805i	−0.239178	−	0.130601i
$694$		0			0
$695$	27.6204	−	13.7871i	1.04770	−	0.522974i
$696$		0			0
$697$	1.31663	−	1.75881i	0.0498708	−	0.0666196i
$698$		0			0
$699$	−13.3293	−	20.7408i	−0.504160	−	0.784489i
$700$		0			0
$701$	5.55420	+	2.53652i	0.209779	+	0.0958030i	0.517534	−	0.855663i	$-0.326850\pi$
$701$	5.55420	+	2.53652i	0.209779	+	0.0958030i	−0.307754	+	0.951466i	$0.599577\pi$
$702$		0			0
$703$	17.8248	−	13.3435i	0.672276	−	0.503259i
$704$		0			0
$705$	−20.8268	−	22.4199i	−0.784382	−	0.844383i
$706$		0			0
$707$	−0.0752652	+	1.05235i	−0.00283064	+	0.0395775i
$708$		0			0
$709$	18.5484	−	21.4060i	0.696600	−	0.803919i	−0.291689	−	0.956513i	$-0.594217\pi$
$709$	18.5484	−	21.4060i	0.696600	−	0.803919i	0.988289	+	0.152594i	$0.0487627\pi$
$710$		0			0
$711$	14.1913	−	6.48096i	0.532216	−	0.243055i
$712$		0			0
$713$	−2.61304	−	4.73579i	−0.0978593	−	0.177357i
$714$		0			0
$715$	−33.0216	−	41.0715i	−1.23494	−	1.53599i
$716$		0			0
$717$	−1.92850	−	26.9640i	−0.0720213	−	1.00699i
$718$		0			0
$719$	−12.3866	+	10.7331i	−0.461943	+	0.400275i	−0.854500	−	0.519452i	$-0.826136\pi$
$719$	−12.3866	+	10.7331i	−0.461943	+	0.400275i	0.392557	+	0.919728i	$0.371591\pi$
$720$		0			0
$721$	3.40139	+	0.998738i	0.126674	+	0.0371950i
$722$		0			0
$723$	−18.6156	−	24.8675i	−0.692321	−	0.924833i
$724$		0			0
$725$	2.41251	+	34.8292i	0.0895983	+	1.29352i
$726$		0			0
$727$	19.7853	+	4.30402i	0.733795	+	0.159627i	0.563910	−	0.825836i	$-0.309297\pi$
$727$	19.7853	+	4.30402i	0.733795	+	0.159627i	0.169885	+	0.985464i	$0.445660\pi$
$728$		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
$733$	−14.9339	+	27.3494i	−0.551596	+	1.01017i	0.441982	+	0.897024i	$0.354276\pi$
$733$	−14.9339	+	27.3494i	−0.551596	+	1.01017i	−0.993578	+	0.113149i	$0.963906\pi$
$734$		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	0.942527	+	0.334129i	$0.108442\pi$
$739$	8.97815	+	30.5768i	0.330267	+	1.12478i	−0.612261	+	0.790656i	$0.709740\pi$
$740$		0			0
$741$	35.9978	−	56.0137i	1.32241	−	2.05771i
$742$		0			0
$743$	20.3742	+	15.2520i	0.747458	+	0.559540i	0.903694	−	0.428180i	$-0.140845\pi$
$743$	20.3742	+	15.2520i	0.747458	+	0.559540i	−0.156236	+	0.987720i	$0.549936\pi$
$744$		0			0
$745$	43.1463	−	1.49252i	1.58076	−	0.0546816i
$746$		0			0
$747$	−6.81700	+	2.54261i	−0.249421	+	0.0930292i
$748$		0			0
$749$	−6.05632	−	0.870768i	−0.221293	−	0.0318172i
$750$		0			0
$751$	3.53649	−	12.0442i	0.129048	−	0.439499i	−0.869466	−	0.493993i	$-0.835537\pi$
$751$	3.53649	−	12.0442i	0.129048	−	0.439499i	0.998514	+	0.0544949i	$0.0173549\pi$
$752$		0			0
$753$	49.7502	+	3.55821i	1.81300	+	0.129668i
$754$		0			0
$755$	24.2780	−	8.05026i	0.883567	−	0.292979i
$756$		0			0
$757$	−4.38153	+	11.7473i	−0.159249	+	0.426964i	−0.991930	−	0.126790i	$-0.959533\pi$
$757$	−4.38153	+	11.7473i	−0.159249	+	0.426964i	0.832680	+	0.553754i	$0.186805\pi$
$758$		0			0
$759$	8.50437	−	61.0543i	0.308689	−	2.21613i
$760$		0			0
$761$	0.945262	+	2.06983i	0.0342657	+	0.0750315i	0.925991	−	0.377546i	$-0.123232\pi$
$761$	0.945262	+	2.06983i	0.0342657	+	0.0750315i	−0.891725	+	0.452577i	$0.850505\pi$
$762$		0			0
$763$	−6.05335	+	0.432944i	−0.219146	+	0.0156736i
$764$		0			0
$765$	28.7845	+	20.0334i	1.04071	+	0.724308i
$766$		0			0
$767$	−9.20779	+	5.02784i	−0.332474	+	0.181545i
$768$		0			0
$769$	−3.79339	+	26.3836i	−0.136793	+	0.951417i	0.799617	+	0.600510i	$0.205036\pi$
$769$	−3.79339	+	26.3836i	−0.136793	+	0.951417i	−0.936410	+	0.350907i	$0.885873\pi$
$770$		0			0
$771$	10.4722	−	22.9310i	0.377148	−	0.825839i
$772$		0			0
$773$	7.89966	−	36.3141i	0.284131	−	1.30613i	−0.584793	−	0.811183i	$-0.698824\pi$
$773$	7.89966	−	36.3141i	0.284131	−	1.30613i	0.868924	−	0.494946i	$-0.164812\pi$
$774$		0			0
$775$	−4.52192	+	3.36927i	−0.162432	+	0.121028i
$776$		0			0
$777$	−4.26455	+	0.927695i	−0.152990	+	0.0332809i
$778$		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
$785$	3.47753	+	5.87608i	0.124118	+	0.209726i
$786$		0			0
$787$	−7.84305	−	36.0539i	−0.279575	−	1.28518i	−0.875920	−	0.482456i	$-0.839745\pi$
$787$	−7.84305	−	36.0539i	−0.279575	−	1.28518i	0.596346	−	0.802728i	$-0.296619\pi$
$788$		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
$793$	−8.29215	−	22.2321i	−0.294463	−	0.789485i
$794$		0			0
$795$	−20.0430	+	24.8148i	−0.710852	+	0.880091i
$796$		0			0
$797$	−0.916435	−	1.67833i	−0.0324618	−	0.0594493i	0.860945	−	0.508699i	$-0.169873\pi$
$797$	−0.916435	−	1.67833i	−0.0324618	−	0.0594493i	−0.893406	+	0.449249i	$0.851691\pi$
$798$		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
$803$	−30.5264	−	11.3858i	−1.07725	−	0.401795i
$804$		0			0
$805$	1.96009	+	2.80341i	0.0690841	+	0.0988074i
$806$		0			0
$807$	−24.2753	−	9.05422i	−0.854531	−	0.318723i
$808$		0			0
$809$	−34.7977	−	30.1524i	−1.22342	−	1.06010i	−0.996274	−	0.0862421i	$-0.972514\pi$
$809$	−34.7977	−	30.1524i	−1.22342	−	1.06010i	−0.227149	−	0.973860i	$-0.572940\pi$
$810$		0			0
$811$	0.598397	+	0.690587i	0.0210126	+	0.0242498i	0.766159	−	0.642652i	$-0.222166\pi$
$811$	0.598397	+	0.690587i	0.0210126	+	0.0242498i	−0.745146	+	0.666901i	$0.767620\pi$
$812$		0			0
$813$	22.6041	+	41.3963i	0.792759	+	1.45183i
$814$		0			0
$815$	38.6103	−	4.10723i	1.35246	−	0.143870i
$816$		0			0
$817$	6.37705	+	17.0975i	0.223105	+	0.598167i
$818$		0			0
$819$	−6.82344	+	4.38516i	−0.238430	+	0.153230i
$820$		0			0
$821$	−5.21892	−	36.2984i	−0.182142	−	1.26682i	−0.851687	−	0.524051i	$-0.824420\pi$
$821$	−5.21892	−	36.2984i	−0.182142	−	1.26682i	0.669545	−	0.742771i	$-0.266489\pi$
$822$		0			0
$823$	−2.16138	−	9.93569i	−0.0753408	−	0.346336i	0.924010	−	0.382369i	$-0.124892\pi$
$823$	−2.16138	−	9.93569i	−0.0753408	−	0.346336i	−0.999351	+	0.0360326i	$0.988528\pi$
$824$		0			0
$825$	−64.2679	−	0.144180i	−2.23752	−	0.00501969i
$826$		0			0
$827$	−7.46991	−	7.46991i	−0.259754	−	0.259754i	0.565200	−	0.824954i	$-0.308799\pi$
$827$	−7.46991	−	7.46991i	−0.259754	−	0.259754i	−0.824954	+	0.565200i	$0.808799\pi$
$828$		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
$833$	−21.4615	+	4.66865i	−0.743595	+	0.161759i
$834$		0			0
$835$	−14.0583	−	34.0477i	−0.486508	−	1.17827i
$836$		0			0
$837$	1.29986	−	5.97535i	0.0449297	−	0.206538i
$838$		0			0
$839$	−4.76827	+	10.4411i	−0.164619	+	0.360465i	−0.973907	−	0.226947i	$-0.927126\pi$
$839$	−4.76827	+	10.4411i	−0.164619	+	0.360465i	0.809288	+	0.587412i	$0.199853\pi$
$840$		0			0
$841$	2.81152	−	19.5545i	0.0969489	−	0.674294i
$842$		0			0
$843$	31.0925	−	16.9778i	1.07088	−	0.584746i
$844$		0			0
$845$	−30.0371	+	5.38451i	−1.03331	+	0.185233i
$846$		0			0
$847$	3.13234	−	0.224029i	0.107628	−	0.00769774i
$848$		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
$853$	−9.83689	+	26.3737i	−0.336809	+	0.903019i	0.652579	+	0.757720i	$0.273687\pi$
$853$	−9.83689	+	26.3737i	−0.336809	+	0.903019i	−0.989388	+	0.145298i	$0.953586\pi$
$854$		0			0
$855$	−15.8831	−	47.9002i	−0.543190	−	1.63815i
$856$		0			0
$857$	11.6102	+	0.830376i	0.396596	+	0.0283651i	0.268213	−	0.963360i	$-0.413567\pi$
$857$	11.6102	+	0.830376i	0.396596	+	0.0283651i	0.128383	+	0.991725i	$0.459021\pi$
$858$		0			0
$859$	14.5817	−	49.6607i	0.497521	−	1.69440i	−0.201661	−	0.979455i	$-0.564634\pi$
$859$	14.5817	−	49.6607i	0.497521	−	1.69440i	0.699181	−	0.714944i	$-0.253548\pi$
$860$		0			0
$861$	0.613367	+	0.0881889i	0.0209035	+	0.00300547i
$862$		0			0
$863$	−47.9200	+	17.8732i	−1.63122	+	0.608412i	−0.987608	−	0.156943i	$-0.949836\pi$
$863$	−47.9200	+	17.8732i	−1.63122	+	0.608412i	−0.643608	+	0.765355i	$0.722563\pi$
$864$		0			0
$865$	31.7771	+	29.6522i	1.08045	+	1.00820i
$866$		0			0
$867$	−15.4670	−	11.5784i	−0.525287	−	0.393225i
$868$		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
$877$	−19.3351	+	35.4096i	−0.652900	+	1.19570i	0.316120	+	0.948719i	$0.397620\pi$
$877$	−19.3351	+	35.4096i	−0.652900	+	1.19570i	−0.969021	+	0.246979i	$0.920562\pi$
$878$		0			0
$879$	−42.4549	−	27.2841i	−1.43197	−	0.920271i
$880$		0			0
$881$	2.99299	−	0.430327i	0.100836	−	0.0144981i	−0.0917119	−	0.995786i	$-0.529234\pi$
$881$	2.99299	−	0.430327i	0.100836	−	0.0144981i	0.192548	+	0.981287i	$0.438325\pi$
$882$		0			0
$883$	−35.2432	−	7.66670i	−1.18603	−	0.258005i	−0.424070	−	0.905629i	$-0.639399\pi$
$883$	−35.2432	−	7.66670i	−1.18603	−	0.258005i	−0.761960	+	0.647625i	$0.775763\pi$
$884$		0			0
$885$	−2.28573	+	12.5881i	−0.0768339	+	0.423145i
$886$		0			0
$887$	−21.1342	−	28.2320i	−0.709617	−	0.947938i	0.290342	−	0.956923i	$-0.406231\pi$
$887$	−21.1342	−	28.2320i	−0.709617	−	0.947938i	−0.999960	+	0.00898495i	$0.997140\pi$
$888$		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
$893$	1.58880	+	22.2143i	0.0531670	+	0.743372i
$894$		0			0
$895$	15.2296	+	1.65463i	0.509068	+	0.0553082i
$896$		0			0
$897$	−55.9785	−	41.5220i	−1.86907	−	1.38638i
$898$		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
$903$	0.255163	−	3.56764i	0.00849128	−	0.118724i
$904$		0			0
$905$	−21.5188	+	19.9897i	−0.715309	+	0.664480i
$906$		0			0
$907$	27.0094	−	20.2190i	0.896832	−	0.671360i	−0.0480238	−	0.998846i	$-0.515292\pi$
$907$	27.0094	−	20.2190i	0.896832	−	0.671360i	0.944856	+	0.327486i	$0.106201\pi$
$908$		0			0
$909$	−14.8202	−	6.76817i	−0.491556	−	0.224486i
$910$		0			0
$911$	−15.9877	−	24.8773i	−0.529695	−	0.824221i	0.468550	−	0.883437i	$-0.344776\pi$
$911$	−15.9877	−	24.8773i	−0.529695	−	0.824221i	−0.998245	+	0.0592155i	$0.981140\pi$
$912$		0			0
$913$	4.04127	−	5.39851i	0.133747	−	0.178665i
$914$		0			0
$915$	−27.4456	−	9.16899i	−0.907324	−	0.303117i
$916$		0			0
$917$	3.07435	+	1.67872i	0.101524	+	0.0554362i
$918$		0			0
$919$	50.7741			1.67488			0.837442	−	0.546526i	$-0.184050\pi$
$919$	50.7741			1.67488			0.837442	+	0.546526i	$0.184050\pi$
$920$		0			0
$921$	−25.8367			−0.851348
$922$		0			0
$923$	−35.9284	−	19.6184i	−1.18260	−	0.645747i
$924$		0			0
$925$	−18.3998	+	15.8714i	−0.604983	+	0.521849i
$926$		0			0
$927$	−32.8069	+	43.8249i	−1.07752	+	1.43940i
$928$		0			0
$929$	15.4337	+	24.0153i	0.506363	+	0.787916i	0.996488	−	0.0837363i	$-0.0266854\pi$
$929$	15.4337	+	24.0153i	0.506363	+	0.787916i	−0.490125	+	0.871652i	$0.663049\pi$
$930$		0			0
$931$	28.7490	+	13.1292i	0.942209	+	0.430292i
$932$		0			0
$933$	−53.0132	+	39.6852i	−1.73557	+	1.29923i
$934$		0			0
$935$	−32.4826	−	1.19660i	−1.06230	−	0.0391331i
$936$		0			0
$937$	2.23830	−	31.2955i	0.0731220	−	1.02238i	−0.819941	−	0.572448i	$-0.805994\pi$
$937$	2.23830	−	31.2955i	0.0731220	−	1.02238i	0.893063	−	0.449931i	$-0.148551\pi$
$938$		0			0
$939$	20.9413	−	24.1675i	0.683393	−	0.788678i
$940$		0			0
$941$	−10.4386	+	4.76713i	−0.340287	+	0.155404i	−0.578227	−	0.815876i	$-0.696255\pi$
$941$	−10.4386	+	4.76713i	−0.340287	+	0.155404i	0.237940	+	0.971280i	$0.423528\pi$
$942$		0			0
$943$	0.717662	+	3.23057i	0.0233703	+	0.105202i
$944$		0			0
$945$	−0.417712	+	3.84471i	−0.0135882	+	0.125068i
$946$		0			0
$947$	−0.873303	−	12.2104i	−0.0283785	−	0.396784i	−0.991712	−	0.128478i	$-0.958991\pi$
$947$	−0.873303	−	12.2104i	−0.0283785	−	0.396784i	0.963334	−	0.268306i	$-0.0864637\pi$
$948$		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
$953$	11.8993	+	15.8956i	0.385456	+	0.514909i	0.950741	−	0.309987i	$-0.100325\pi$
$953$	11.8993	+	15.8956i	0.385456	+	0.514909i	−0.565285	+	0.824896i	$0.691234\pi$
$954$		0			0
$955$	−10.1656	−	14.6763i	−0.328950	−	0.474915i
$956$		0			0
$957$	87.6995	+	19.0779i	2.83492	+	0.616700i
$958$		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
$963$	45.2831	−	82.9298i	1.45923	−	2.67238i
$964$		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	−0.987956	−	0.154736i	$-0.950547\pi$
$971$	−13.6108	+	21.1788i	−0.436792	+	0.679661i	0.551164	+	0.834397i	$0.314184\pi$
$972$		0			0
$973$	3.52536	+	2.63905i	0.113018	+	0.0846041i
$974$		0			0
$975$	−34.9672	+	63.6975i	−1.11985	+	2.03995i
$976$		0			0
$977$	−44.4716	+	16.5871i	−1.42277	+	0.530667i	−0.938814	−	0.344424i	$-0.888074\pi$
$977$	−44.4716	+	16.5871i	−1.42277	+	0.530667i	−0.483958	+	0.875091i	$0.660801\pi$
$978$		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
$983$	−39.3722	−	2.81596i	−1.25578	−	0.0898150i	−0.572458	−	0.819934i	$-0.694010\pi$
$983$	−39.3722	−	2.81596i	−1.25578	−	0.0898150i	−0.683320	+	0.730119i	$0.739465\pi$
$984$		0			0
$985$	18.9107	−	37.6730i	0.602544	−	1.20036i
$986$		0			0
$987$	1.52551	−	4.09004i	0.0485574	−	0.130187i
$988$		0			0
$989$	18.3038	−	5.46203i	0.582026	−	0.173682i
$990$		0			0
$991$	−3.27709	−	7.17582i	−0.104100	−	0.227947i	0.850413	−	0.526115i	$-0.176352\pi$
$991$	−3.27709	−	7.17582i	−0.104100	−	0.227947i	−0.954514	+	0.298168i	$0.903625\pi$
$992$		0			0
$993$	94.1100	−	6.73088i	2.98649	−	0.213598i
$994$		0			0
$995$	−3.67801	−	20.5175i	−0.116601	−	0.650449i
$996$		0			0
$997$	42.0804	−	22.9777i	1.33270	−	0.727710i	0.354438	−	0.935079i	$-0.384672\pi$
$997$	42.0804	−	22.9777i	1.33270	−	0.727710i	0.978263	+	0.207370i	$0.0664904\pi$
$998$		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.433.4	yes	720
5.2	odd	4	inner	920.2.bv.a.617.4	yes	720
23.17	odd	22	inner	920.2.bv.a.753.4	yes	720
115.17	even	44	inner	920.2.bv.a.17.4	✓	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.4	✓	720	115.17	even	44	inner
920.2.bv.a.433.4	yes	720	1.1	even	1	trivial
920.2.bv.a.617.4	yes	720	5.2	odd	4	inner
920.2.bv.a.753.4	yes	720	23.17	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47093 - 1.34923i) q^{3} +(-0.998659 - 2.00067i) q^{5} +(0.191158 - 0.255357i) q^{7} +(2.66315 + 4.14394i) q^{9} +(-4.15304 - 1.89663i) q^{11} +(-4.13246 + 3.09352i) q^{13} +(-0.231747 + 6.29094i) q^{15} +(-0.227137 + 3.17579i) q^{17} +(3.00031 - 3.46254i) q^{19} +(-0.816873 + 0.373054i) q^{21} +(-3.40605 - 3.37622i) q^{23} +(-3.00536 + 3.99597i) q^{25} +(-0.386803 - 5.40822i) q^{27} +(5.27704 - 4.57258i) q^{29} +(1.08214 + 0.317745i) q^{31} +(7.70288 + 10.2898i) q^{33} +(-0.701787 - 0.127429i) q^{35} +(4.74880 + 1.03304i) q^{37} +(14.3849 - 2.06824i) q^{39} +(-0.580499 - 0.373064i) q^{41} +(-1.90880 + 3.49571i) q^{43} +(5.63109 - 9.46647i) q^{45} +(-3.43722 + 3.43722i) q^{47} +(1.94346 + 6.61882i) q^{49} +(4.84612 - 7.54070i) q^{51} +(4.05640 + 3.03658i) q^{53} +(0.352940 + 10.2029i) q^{55} +(-12.0853 + 4.50759i) q^{57} +(2.01165 + 0.289231i) q^{59} +(-1.29502 + 4.41043i) q^{61} +(1.56727 + 0.112093i) q^{63} +(10.3160 + 5.17832i) q^{65} +(-0.262976 + 0.705066i) q^{67} +(3.86081 + 12.9379i) q^{69} +(3.29427 + 7.21344i) q^{71} +(7.11789 - 0.509081i) q^{73} +(12.8175 - 5.81885i) q^{75} +(-1.27820 + 0.697952i) q^{77} +(0.450734 - 3.13492i) q^{79} +(-0.202267 + 0.442902i) q^{81} +(-0.313966 + 1.44328i) q^{83} +(6.58055 - 2.71711i) q^{85} +(-19.2087 + 4.17859i) q^{87} +(11.8297 - 3.47350i) q^{89} +1.64661i q^{91} +(-2.24518 - 2.24518i) q^{93} +(-9.92369 - 2.54473i) q^{95} +(3.86140 + 17.7506i) q^{97} +(-3.20064 - 22.2610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 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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