LMFDB - Embedded newform 920.2.bv.a.17.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [920,2,Mod(17,920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

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

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			17.4
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.4

$q$-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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.47093	+	1.34923i	−1.42659	+	0.778978i	−0.992541	−	0.121910i	$-0.961098\pi$
$3$	−2.47093	+	1.34923i	−1.42659	+	0.778978i	−0.434051	+	0.900888i	$0.642916\pi$
$4$		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	0.835211	−	0.549930i	$-0.185346\pi$
$7$	0.191158	+	0.255357i	0.0722509	+	0.0965159i	−0.762960	+	0.646446i	$0.776255\pi$
$8$		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
$13$	−4.13246	−	3.09352i	−1.14614	−	0.857989i	−0.154623	−	0.987974i	$-0.549416\pi$
$13$	−4.13246	−	3.09352i	−1.14614	−	0.857989i	−0.991516	+	0.129984i	$0.958507\pi$
$14$		0			0
$15$	−0.231747	−	6.29094i	−0.0598369	−	1.62431i
$16$		0			0
$17$	−0.227137	−	3.17579i	−0.0550889	−	0.770243i	−0.947649	−	0.319314i	$-0.896547\pi$
$17$	−0.227137	−	3.17579i	−0.0550889	−	0.770243i	0.892560	−	0.450929i	$-0.148907\pi$
$18$		0			0
$19$	3.00031	+	3.46254i	0.688319	+	0.794362i	0.987125	−	0.159952i	$-0.0511339\pi$
$19$	3.00031	+	3.46254i	0.688319	+	0.794362i	−0.298806	+	0.954314i	$0.596588\pi$
$20$		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	0.988556	−	0.150856i	$-0.0482030\pi$
$29$	5.27704	+	4.57258i	0.979921	+	0.849107i	−0.00863436	+	0.999963i	$0.502748\pi$
$30$		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
$33$	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	0.195481	−	0.980707i	$-0.437373\pi$
$37$	4.74880	−	1.03304i	0.780698	−	0.169830i	0.585217	+	0.810877i	$0.301010\pi$
$38$		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
$43$	−1.90880	−	3.49571i	−0.291090	−	0.533091i	0.690681	−	0.723160i	$-0.257311\pi$
$43$	−1.90880	−	3.49571i	−0.291090	−	0.533091i	−0.981771	+	0.190068i	$0.939129\pi$
$44$		0			0
$45$	5.63109	+	9.46647i	0.839433	+	1.41118i
$46$		0			0
$47$	−3.43722	−	3.43722i	−0.501370	−	0.501370i	0.410493	−	0.911864i	$-0.365357\pi$
$47$	−3.43722	−	3.43722i	−0.501370	−	0.501370i	−0.911864	+	0.410493i	$0.865357\pi$
$48$		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	−0.283223	−	0.959054i	$-0.591404\pi$
$53$	4.05640	−	3.03658i	0.557189	−	0.417107i	0.840412	+	0.541947i	$0.182313\pi$
$54$		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	−0.0101170	−	0.999949i	$-0.503220\pi$
$59$	2.01165	−	0.289231i	0.261894	−	0.0376547i	0.272011	+	0.962294i	$0.412311\pi$
$60$		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
$63$	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	0.919896	−	0.392164i	$-0.128273\pi$
$67$	−0.262976	−	0.705066i	−0.0321276	−	0.0861375i	−0.952023	+	0.306026i	$0.901001\pi$
$68$		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
$73$	7.11789	+	0.509081i	0.833086	+	0.0595835i	0.481364	−	0.876521i	$-0.340142\pi$
$73$	7.11789	+	0.509081i	0.833086	+	0.0595835i	0.351722	+	0.936104i	$0.385596\pi$
$74$		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	0.999340	+	0.0363153i	$0.0115621\pi$
$79$	0.450734	+	3.13492i	0.0507115	+	0.352706i	−0.948629	+	0.316391i	$0.897529\pi$
$80$		0			0
$81$	−0.202267	−	0.442902i	−0.0224741	−	0.0492114i
$82$		0			0
$83$	−0.313966	−	1.44328i	−0.0344622	−	0.158420i	0.956700	−	0.291076i	$-0.0940132\pi$
$83$	−0.313966	−	1.44328i	−0.0344622	−	0.158420i	−0.991162	+	0.132656i	$0.957650\pi$
$84$		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	0.840236	−	0.542220i	$-0.182416\pi$
$89$	11.8297	+	3.47350i	1.25394	+	0.368191i	0.413706	+	0.910411i	$0.364234\pi$
$90$		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	−0.181784	−	0.983338i	$-0.558187\pi$
$97$	3.86140	−	17.7506i	0.392066	−	1.80230i	0.573850	−	0.818960i	$-0.305449\pi$
$98$		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
$103$	3.88377	−	10.4128i	0.382679	−	1.02600i	−0.592692	−	0.805429i	$-0.701935\pi$
$103$	3.88377	−	10.4128i	0.382679	−	1.02600i	0.975371	−	0.220572i	$-0.0707925\pi$
$104$		0			0
$105$	1.56213	−	1.26174i	0.152449	−	0.123133i
$106$		0			0
$107$	−9.19283	+	16.8354i	−0.888704	+	1.62754i	−0.115569	+	0.993299i	$0.536869\pi$
$107$	−9.19283	+	16.8354i	−0.888704	+	1.62754i	−0.773136	+	0.634241i	$0.781313\pi$
$108$		0			0
$109$	−12.4592	+	14.3786i	−1.19337	+	1.37722i	−0.285283	+	0.958443i	$0.592088\pi$
$109$	−12.4592	+	14.3786i	−1.19337	+	1.37722i	−0.908088	+	0.418780i	$0.862458\pi$
$110$		0			0
$111$	−10.3401	+	8.95979i	−0.981443	+	0.850425i
$112$		0			0
$113$	−16.3985	+	6.11631i	−1.54264	+	0.575374i	−0.969716	−	0.244236i	$-0.921463\pi$
$113$	−16.3985	+	6.11631i	−1.54264	+	0.575374i	−0.572922	+	0.819610i	$0.694190\pi$
$114$		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	0.597285	+	0.802029i	$0.296246\pi$
$127$	−4.27483	+	11.4613i	−0.379330	+	1.01702i	−0.976615	+	0.214994i	$0.931027\pi$
$128$		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
$133$	−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	−0.578963	+	0.815354i	$0.696542\pi$
$137$	−16.3201	+	16.3201i	−1.39432	+	1.39432i	−0.815354	+	0.578963i	$0.803458\pi$
$138$		0			0
$139$		−	13.8056i		−	1.17098i	−0.810681	−	0.585488i	$-0.800903\pi$
$139$		−	13.8056i		−	1.17098i	0.810681	−	0.585488i	$-0.199097\pi$
$140$		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	−0.885233	−	0.465147i	$-0.846001\pi$
$149$	−8.02048	−	17.5624i	−0.657064	−	1.43877i	0.228170	−	0.973621i	$-0.426726\pi$
$150$		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
$153$	−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	−0.0507328	−	0.998712i	$-0.516156\pi$
$157$	−3.04579	−	0.217839i	−0.243081	−	0.0173855i	−0.192348	+	0.981327i	$0.561610\pi$
$158$		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	−0.924595	−	0.380951i	$-0.875597\pi$
$163$	−6.06826	−	16.2696i	−0.475302	−	1.27434i	0.449293	−	0.893385i	$-0.351676\pi$
$164$		0			0
$165$	12.8940	+	25.6870i	1.00380	+	1.99973i
$166$		0			0
$167$	16.4315	−	1.17521i	1.27151	−	0.0909402i	0.580785	−	0.814057i	$-0.302746\pi$
$167$	16.4315	−	1.17521i	1.27151	−	0.0909402i	0.690726	+	0.723117i	$0.257291\pi$
$168$		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	−0.456830	−	0.889554i	$-0.651015\pi$
$173$	−18.2117	−	6.79263i	−1.38461	−	0.516434i	−0.927783	+	0.373120i	$0.878288\pi$
$174$		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	0.674792	−	0.738008i	$-0.264233\pi$
$179$	−3.70390	−	5.76338i	−0.276843	−	0.430775i	−0.951634	+	0.307233i	$0.900597\pi$
$180$		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
$187$	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	0.422165	−	0.906519i	$-0.361270\pi$
$191$	7.90289	+	1.13626i	0.571833	+	0.0822172i	0.149668	+	0.988736i	$0.452179\pi$
$192$		0			0
$193$	−14.8218	+	3.22428i	−1.06689	+	0.232089i	−0.711542	−	0.702644i	$-0.752003\pi$
$193$	−14.8218	+	3.22428i	−1.06689	+	0.232089i	−0.355352	+	0.934732i	$0.615639\pi$
$194$		0			0
$195$	−18.5035	+	26.7140i	−1.32506	+	1.91303i
$196$		0			0
$197$	11.2972	−	15.0913i	0.804893	−	1.07521i	−0.190720	−	0.981644i	$-0.561082\pi$
$197$	11.2972	−	15.0913i	0.804893	−	1.07521i	0.995613	−	0.0935664i	$-0.0298267\pi$
$198$		0			0
$199$	8.94437	−	2.62631i	0.634050	−	0.186174i	0.0511151	−	0.998693i	$-0.483722\pi$
$199$	8.94437	−	2.62631i	0.634050	−	0.186174i	0.582935	+	0.812519i	$0.301904\pi$
$200$		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	−0.978884	−	0.204416i	$-0.934471\pi$
$211$	−15.1346	−	17.4663i	−1.04191	−	1.20243i	−0.0630253	−	0.998012i	$-0.520075\pi$
$212$		0			0
$213$	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	−0.936866	−	0.349689i	$-0.886287\pi$
$223$	−15.0593	−	20.1169i	−1.00844	−	1.34712i	−0.0715786	−	0.997435i	$-0.522804\pi$
$224$		0			0
$225$	−24.5628	+	1.81216i	−1.63752	+	0.120811i
$226$		0			0
$227$	2.01279	−	1.09907i	0.133594	−	0.0729478i	−0.411062	−	0.911607i	$-0.634842\pi$
$227$	2.01279	−	1.09907i	0.133594	−	0.0729478i	0.544656	+	0.838660i	$0.316660\pi$
$228$		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	−0.207339	−	0.978269i	$-0.566480\pi$
$233$	7.68616	−	4.19696i	0.503537	−	0.274952i	0.710876	+	0.703317i	$0.248299\pi$
$234$		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	−0.631759	−	0.775165i	$-0.717667\pi$
$239$	5.19130	−	8.07783i	0.335798	−	0.522511i	0.967557	+	0.252653i	$0.0813032\pi$
$240$		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
$243$	−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	−0.164188	−	0.986429i	$-0.552500\pi$
$251$	−16.1155	−	7.35971i	−1.01720	−	0.464540i	−0.853014	+	0.521889i	$0.825228\pi$
$252$		0			0
$253$	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	−0.937841	−	0.347066i	$-0.887178\pi$
$257$	0.638793	−	8.93150i	0.0398468	−	0.557131i	0.977687	−	0.210065i	$-0.0673676\pi$
$258$		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	0.180173	+	0.983635i	$0.442334\pi$
$263$	−13.2070	+	17.6425i	−0.814378	+	1.08788i	−0.994551	+	0.104247i	$0.966757\pi$
$264$		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	0.414298	−	0.910141i	$-0.364027\pi$
$269$	9.10920	+	1.30971i	0.555398	+	0.0798541i	0.141100	+	0.989995i	$0.454936\pi$
$270$		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
$273$	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	0.999578	+	0.0290345i	$0.00924325\pi$
$277$	17.1195	+	17.1195i	1.02861	+	1.02861i	0.0290345	+	0.999578i	$0.490757\pi$
$278$		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
$283$	11.5763	−	8.66593i	0.688141	−	0.515136i	−0.197032	−	0.980397i	$-0.563130\pi$
$283$	11.5763	−	8.66593i	0.688141	−	0.515136i	0.885174	+	0.465261i	$0.154039\pi$
$284$		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	0.461504	−	0.887138i	$-0.347310\pi$
$293$	17.8800	−	1.27881i	1.04456	−	0.0747086i	0.583059	+	0.812430i	$0.301856\pi$
$294$		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	0.692375	−	0.721538i	$-0.256565\pi$
$307$	8.05467	+	4.39818i	0.459704	+	0.251018i	−0.232670	+	0.972556i	$0.574746\pi$
$308$		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
$313$	−2.41447	−	11.0992i	−0.136474	−	0.627361i	−0.993667	−	0.112366i	$-0.964157\pi$
$313$	−2.41447	−	11.0992i	−0.136474	−	0.627361i	0.857193	−	0.514996i	$-0.172206\pi$
$314$		0			0
$315$	−1.34090	+	3.24753i	−0.0755514	+	0.182978i
$316$		0			0
$317$	24.3390	+	5.29462i	1.36701	+	0.297375i	0.835414	−	0.549621i	$-0.185228\pi$
$317$	24.3390	+	5.29462i	1.36701	+	0.297375i	0.531598	+	0.846997i	$0.321592\pi$
$318$		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	−0.985394	−	0.170291i	$-0.945529\pi$
$331$	−28.1933	−	18.1187i	−1.54964	−	0.995895i	−0.564250	−	0.825604i	$-0.690834\pi$
$332$		0			0
$333$	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	−0.838695	−	0.544601i	$-0.816681\pi$
$337$	1.33800	−	2.45036i	0.0728855	−	0.133480i	0.911581	+	0.411122i	$0.134863\pi$
$338$		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	−0.986659	−	0.162798i	$-0.947948\pi$
$347$	−30.2838	+	11.2953i	−1.62572	+	0.606361i	−0.639058	+	0.769159i	$0.720675\pi$
$348$		0			0
$349$	−24.6327	+	21.3444i	−1.31856	+	1.14254i	−0.339132	+	0.940739i	$0.610133\pi$
$349$	−24.6327	+	21.3444i	−1.31856	+	1.14254i	−0.979427	+	0.201799i	$0.935321\pi$
$350$		0			0
$351$	18.3289	−	21.1527i	0.978324	−	1.12905i
$352$		0			0
$353$	−11.9250	+	21.8390i	−0.634702	+	1.16237i	0.340330	+	0.940306i	$0.389461\pi$
$353$	−11.9250	+	21.8390i	−0.634702	+	1.16237i	−0.975032	+	0.222064i	$0.928721\pi$
$354$		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	0.447415	−	0.894326i	$-0.352345\pi$
$359$	−3.41487	−	2.19460i	−0.180230	−	0.115827i	−0.627645	+	0.778500i	$0.715981\pi$
$360$		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	−0.404795	−	0.914408i	$-0.632657\pi$
$367$	9.76278	−	9.76278i	0.509613	−	0.509613i	0.914408	+	0.404795i	$0.132657\pi$
$368$		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	0.418892	−	0.908036i	$-0.362419\pi$
$373$	8.16402	+	1.77597i	0.422717	+	0.0919564i	0.00382530	+	0.999993i	$0.498782\pi$
$374$		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	0.750670	−	0.660678i	$-0.229731\pi$
$379$	−4.67661	−	10.2403i	−0.240221	−	0.526011i	−0.990891	+	0.134666i	$0.957004\pi$
$380$		0			0
$381$	−4.90107	−	34.0877i	−0.251090	−	1.74637i
$382$		0			0
$383$	8.16491	+	4.45838i	0.417207	+	0.227812i	0.674119	−	0.738622i	$-0.264523\pi$
$383$	8.16491	+	4.45838i	0.417207	+	0.227812i	−0.256912	+	0.966435i	$0.582705\pi$
$384$		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	−0.924901	−	0.380208i	$-0.875852\pi$
$389$	−0.628717	+	1.37670i	−0.0318772	+	0.0698013i	0.893024	+	0.450010i	$0.148580\pi$
$390$		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	0.206526	−	0.978441i	$-0.433784\pi$
$397$	10.9626	−	0.784061i	0.550197	−	0.0393509i	0.343671	+	0.939090i	$0.388330\pi$
$398$		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
$403$	−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	0.651836	−	0.758360i	$-0.273999\pi$
$409$	−6.24459	−	9.71677i	−0.308775	−	0.480464i	−0.960611	+	0.277897i	$0.910363\pi$
$410$		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	−0.672975	−	0.739666i	$-0.734984\pi$
$419$	−5.72563	+	3.67964i	−0.279715	+	0.179762i	0.393260	+	0.919427i	$0.371347\pi$
$420$		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
$423$	−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	0.915911	−	0.401382i	$-0.131470\pi$
$431$	13.4728	+	11.6743i	0.648962	+	0.562329i	−0.266949	+	0.963711i	$0.586015\pi$
$432$		0			0
$433$	2.39587	−	33.4986i	0.115138	−	1.60984i	−0.531509	−	0.847053i	$-0.678375\pi$
$433$	2.39587	−	33.4986i	0.115138	−	1.60984i	0.646647	−	0.762789i	$-0.276171\pi$
$434$		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	0.337653	−	0.941271i	$-0.390367\pi$
$439$	−3.19723	−	1.46013i	−0.152596	−	0.0696881i	−0.490249	+	0.871582i	$0.663094\pi$
$440$		0			0
$441$	−22.2523	−	25.6805i	−1.05963	−	1.22288i
$442$		0			0
$443$	−1.85444	−	25.9285i	−0.0881072	−	1.23190i	−0.828602	−	0.559838i	$-0.810863\pi$
$443$	−1.85444	−	25.9285i	−0.0881072	−	1.23190i	0.740495	−	0.672062i	$-0.234591\pi$
$444$		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	−0.690756	−	0.723088i	$-0.742722\pi$
$449$	−12.6424	+	5.77358i	−0.596631	+	0.272472i	0.0941247	+	0.995560i	$0.469995\pi$
$450$		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	−0.129474	−	0.991583i	$-0.541329\pi$
$457$	13.5683	−	7.40886i	0.634699	−	0.346572i	0.764173	+	0.645011i	$0.223147\pi$
$458$		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	−0.732569	−	0.680693i	$-0.761679\pi$
$463$	−11.9635	+	6.53256i	−0.555991	+	0.303594i	0.176578	+	0.984287i	$0.443497\pi$
$464$		0			0
$465$	−2.24970	−	6.73404i	−0.104327	−	0.312284i
$466$		0			0
$467$	−10.1700	−	13.5855i	−0.470612	−	0.628664i	0.500942	−	0.865481i	$-0.332987\pi$
$467$	−10.1700	−	13.5855i	−0.470612	−	0.628664i	−0.971554	+	0.236817i	$0.923896\pi$
$468$		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	−0.727219	−	0.686406i	$-0.759187\pi$
$479$	−28.5207	−	32.9146i	−1.30314	−	1.50391i	−0.575925	−	0.817502i	$-0.695358\pi$
$480$		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	0.838896	+	0.544292i	$0.183202\pi$
$487$	−1.52098	+	21.2661i	−0.0689221	+	0.963657i	−0.907818	+	0.419365i	$0.862253\pi$
$488$		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
$493$	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	0.643413	−	0.765519i	$-0.277518\pi$
$499$	23.3456	+	3.35659i	1.04509	+	0.150261i	0.401678	+	0.915781i	$0.368427\pi$
$500$		0			0
$501$	−39.0156	+	25.0738i	−1.74309	+	1.12021i
$502$		0			0
$503$	19.1159	+	35.0082i	0.852338	+	1.56094i	0.827650	+	0.561245i	$0.189677\pi$
$503$	19.1159	+	35.0082i	0.852338	+	1.56094i	0.0246878	+	0.999695i	$0.492141\pi$
$504$		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	$-0.741243\pi$
$509$	6.39700	−	21.7862i	0.283542	−	0.965655i	0.970930	−	0.239365i	$-0.0769391\pi$
$510$		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	0.905881	+	0.423531i	$0.139210\pi$
$521$	8.50895	+	28.9788i	0.372784	+	1.26958i	−0.533098	+	0.846054i	$0.678972\pi$
$522$		0			0
$523$	−20.4894	+	1.46543i	−0.895938	+	0.0640787i	−0.511709	−	0.859159i	$-0.670987\pi$
$523$	−20.4894	+	1.46543i	−0.895938	+	0.0640787i	−0.384229	+	0.923238i	$0.625533\pi$
$524$		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	0.980959	+	0.194217i	$0.0622164\pi$
$541$	11.2889	+	24.7192i	0.485346	+	1.06276i	−0.495612	+	0.868544i	$0.665056\pi$
$542$		0			0
$543$	−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	0.166703	−	0.986007i	$-0.446688\pi$
$547$	−2.13442	−	0.464314i	−0.0912612	−	0.0198527i	−0.257964	+	0.966155i	$0.583052\pi$
$548$		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	−0.912241	−	0.409653i	$-0.865650\pi$
$557$	2.07071	−	9.51889i	0.0877387	−	0.403328i	0.999980	+	0.00632509i	$0.00201335\pi$
$558$		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	−0.901282	−	0.433233i	$-0.857373\pi$
$563$	1.50834	−	4.04402i	0.0635690	−	0.170435i	0.964851	+	0.262798i	$0.0846454\pi$
$564$		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	−0.940364	−	0.340169i	$-0.889516\pi$
$569$	−11.2072	+	12.9338i	−0.469830	+	0.542213i	0.470534	+	0.882382i	$0.344061\pi$
$570$		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
$573$	−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	−0.785565	−	0.618780i	$-0.787627\pi$
$577$	−23.3973	+	8.72672i	−0.974040	+	0.363298i	−0.188476	+	0.982078i	$0.560355\pi$
$578$		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	−0.644906	−	0.764261i	$-0.723104\pi$
$587$	8.30941	−	22.2784i	0.342966	−	0.919528i	0.987873	−	0.155266i	$-0.0496236\pi$
$588$		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	0.886065	+	0.463561i	$0.153428\pi$
$593$	−2.73951	+	12.5933i	−0.112498	+	0.517146i	−0.998563	+	0.0535849i	$0.982935\pi$
$594$		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	$0.0846076\pi$
$599$			12.8581i			0.525368i	−0.964882	+	0.262684i	$0.915392\pi$
$600$		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
$603$	−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	−0.961722	−	0.274026i	$-0.911645\pi$
$607$	−4.94579	−	22.7354i	−0.200743	−	0.922802i	0.760979	−	0.648776i	$-0.224719\pi$
$608$		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	0.712707	−	0.701461i	$-0.247469\pi$
$613$	12.5755	+	6.86674i	0.507919	+	0.277345i	−0.204788	+	0.978806i	$0.565651\pi$
$614$		0			0
$615$	2.48145	+	3.56543i	0.100062	+	0.143772i
$616$		0			0
$617$	15.1480	+	1.08341i	0.609835	+	0.0436163i	0.372842	−	0.927895i	$-0.378383\pi$
$617$	15.1480	+	1.08341i	0.609835	+	0.0436163i	0.236993	+	0.971511i	$0.423838\pi$
$618$		0			0
$619$	18.5706	−	40.6639i	0.746414	−	1.63442i	−0.0262919	−	0.999654i	$-0.508370\pi$
$619$	18.5706	−	40.6639i	0.746414	−	1.63442i	0.772706	−	0.634764i	$-0.218903\pi$
$620$		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	−0.0815678	−	0.996668i	$-0.525993\pi$
$631$	3.03854	−	0.436875i	0.120962	−	0.0173917i	0.202530	+	0.979276i	$0.435084\pi$
$632$		0			0
$633$	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	−0.864352	−	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	$-0.321043\pi$
$643$	−7.93740	−	7.93740i	−0.313020	−	0.313020i	−0.846079	+	0.533058i	$0.821043\pi$
$644$		0			0
$645$	−21.5489	+	12.8183i	−0.848489	+	0.504719i
$646$		0			0
$647$	17.5701	+	32.1772i	0.690750	+	1.26502i	0.953861	+	0.300249i	$0.0970699\pi$
$647$	17.5701	+	32.1772i	0.690750	+	1.26502i	−0.263110	+	0.964766i	$0.584748\pi$
$648$		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	−0.0172723	−	0.999851i	$-0.505498\pi$
$653$	9.77101	−	2.12555i	0.382369	−	0.0831794i	0.399642	+	0.916671i	$0.369135\pi$
$654$		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	−0.0388560	−	0.999245i	$-0.512371\pi$
$659$	12.0317	−	3.53283i	0.468689	−	0.137619i	0.507545	+	0.861625i	$0.330553\pi$
$660$		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
$663$	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	0.999771	+	0.0213765i	$0.00680486\pi$
$673$	0.342916	+	4.79459i	0.0132184	+	0.184818i	−0.986553	+	0.163441i	$0.947741\pi$
$674$		0			0
$675$	22.7736	−	14.7080i	0.876556	−	0.566111i
$676$		0			0
$677$	0.905472	+	0.677828i	0.0348001	+	0.0260510i	0.616536	−	0.787327i	$-0.288535\pi$
$677$	0.905472	+	0.677828i	0.0348001	+	0.0260510i	−0.581736	+	0.813378i	$0.697626\pi$
$678$		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	−0.970210	−	0.242267i	$-0.922109\pi$
$683$	−24.2872	−	32.4439i	−0.929323	−	1.24143i	0.0408865	−	0.999164i	$-0.486982\pi$
$684$		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	−0.307754	−	0.951466i	$-0.599577\pi$
$701$	5.55420	−	2.53652i	0.209779	−	0.0958030i	0.517534	+	0.855663i	$0.326850\pi$
$702$		0			0
$703$	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	0.988289	−	0.152594i	$-0.0487627\pi$
$709$	18.5484	+	21.4060i	0.696600	+	0.803919i	−0.291689	+	0.956513i	$0.594217\pi$
$710$		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	0.392557	−	0.919728i	$-0.371591\pi$
$719$	−12.3866	−	10.7331i	−0.461943	−	0.400275i	−0.854500	+	0.519452i	$0.826136\pi$
$720$		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	0.169885	−	0.985464i	$-0.445660\pi$
$727$	19.7853	−	4.30402i	0.733795	−	0.159627i	0.563910	+	0.825836i	$0.309297\pi$
$728$		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	−0.993578	−	0.113149i	$-0.963906\pi$
$733$	−14.9339	−	27.3494i	−0.551596	−	1.01017i	0.441982	−	0.897024i	$-0.354276\pi$
$734$		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	$-0.709740\pi$
$739$	8.97815	−	30.5768i	0.330267	−	1.12478i	0.942527	−	0.334129i	$-0.108442\pi$
$740$		0			0
$741$	35.9978	+	56.0137i	1.32241	+	2.05771i
$742$		0			0
$743$	20.3742	−	15.2520i	0.747458	−	0.559540i	−0.156236	−	0.987720i	$-0.549936\pi$
$743$	20.3742	−	15.2520i	0.747458	−	0.559540i	0.903694	+	0.428180i	$0.140845\pi$
$744$		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	0.998514	−	0.0544949i	$-0.0173549\pi$
$751$	3.53649	+	12.0442i	0.129048	+	0.439499i	−0.869466	+	0.493993i	$0.835537\pi$
$752$		0			0
$753$	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	0.832680	−	0.553754i	$-0.186805\pi$
$757$	−4.38153	−	11.7473i	−0.159249	−	0.426964i	−0.991930	+	0.126790i	$0.959533\pi$
$758$		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
$763$	−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	−0.936410	−	0.350907i	$-0.885873\pi$
$769$	−3.79339	−	26.3836i	−0.136793	−	0.951417i	0.799617	−	0.600510i	$-0.205036\pi$
$770$		0			0
$771$	10.4722	+	22.9310i	0.377148	+	0.825839i
$772$		0			0
$773$	7.89966	+	36.3141i	0.284131	+	1.30613i	0.868924	+	0.494946i	$0.164812\pi$
$773$	7.89966	+	36.3141i	0.284131	+	1.30613i	−0.584793	+	0.811183i	$0.698824\pi$
$774$		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	0.596346	+	0.802728i	$0.296619\pi$
$787$	−7.84305	+	36.0539i	−0.279575	+	1.28518i	−0.875920	+	0.482456i	$0.839745\pi$
$788$		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	−0.893406	−	0.449249i	$-0.851691\pi$
$797$	−0.916435	+	1.67833i	−0.0324618	+	0.0594493i	0.860945	+	0.508699i	$0.169873\pi$
$798$		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	−0.227149	+	0.973860i	$0.572940\pi$
$809$	−34.7977	+	30.1524i	−1.22342	+	1.06010i	−0.996274	+	0.0862421i	$0.972514\pi$
$810$		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
$813$	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	0.669545	+	0.742771i	$0.266489\pi$
$821$	−5.21892	+	36.2984i	−0.182142	+	1.26682i	−0.851687	+	0.524051i	$0.824420\pi$
$822$		0			0
$823$	−2.16138	+	9.93569i	−0.0753408	+	0.346336i	−0.999351	−	0.0360326i	$-0.988528\pi$
$823$	−2.16138	+	9.93569i	−0.0753408	+	0.346336i	0.924010	+	0.382369i	$0.124892\pi$
$824$		0			0
$825$	−64.2679	+	0.144180i	−2.23752	+	0.00501969i
$826$		0			0
$827$	−7.46991	+	7.46991i	−0.259754	+	0.259754i	−0.824954	−	0.565200i	$-0.808799\pi$
$827$	−7.46991	+	7.46991i	−0.259754	+	0.259754i	0.565200	+	0.824954i	$0.308799\pi$
$828$		0			0
$829$			28.2182i			0.980057i	0.871706	+	0.490029i	$0.163014\pi$
$829$			28.2182i			0.980057i	−0.871706	+	0.490029i	$0.836986\pi$
$830$		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	0.809288	−	0.587412i	$-0.199853\pi$
$839$	−4.76827	−	10.4411i	−0.164619	−	0.360465i	−0.973907	+	0.226947i	$0.927126\pi$
$840$		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	−0.989388	−	0.145298i	$-0.953586\pi$
$853$	−9.83689	−	26.3737i	−0.336809	−	0.903019i	0.652579	−	0.757720i	$-0.273687\pi$
$854$		0			0
$855$	−15.8831	+	47.9002i	−0.543190	+	1.63815i
$856$		0			0
$857$	11.6102	−	0.830376i	0.396596	−	0.0283651i	0.128383	−	0.991725i	$-0.459021\pi$
$857$	11.6102	−	0.830376i	0.396596	−	0.0283651i	0.268213	+	0.963360i	$0.413567\pi$
$858$		0			0
$859$	14.5817	+	49.6607i	0.497521	+	1.69440i	0.699181	+	0.714944i	$0.253548\pi$
$859$	14.5817	+	49.6607i	0.497521	+	1.69440i	−0.201661	+	0.979455i	$0.564634\pi$
$860$		0			0
$861$	0.613367	−	0.0881889i	0.0209035	−	0.00300547i
$862$		0			0
$863$	−47.9200	−	17.8732i	−1.63122	−	0.608412i	−0.643608	−	0.765355i	$-0.722563\pi$
$863$	−47.9200	−	17.8732i	−1.63122	−	0.608412i	−0.987608	+	0.156943i	$0.949836\pi$
$864$		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	−0.969021	−	0.246979i	$-0.920562\pi$
$877$	−19.3351	−	35.4096i	−0.652900	−	1.19570i	0.316120	−	0.948719i	$-0.397620\pi$
$878$		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
$883$	−35.2432	+	7.66670i	−1.18603	+	0.258005i	−0.761960	−	0.647625i	$-0.775763\pi$
$883$	−35.2432	+	7.66670i	−1.18603	+	0.258005i	−0.424070	+	0.905629i	$0.639399\pi$
$884$		0			0
$885$	−2.28573	−	12.5881i	−0.0768339	−	0.423145i
$886$		0			0
$887$	−21.1342	+	28.2320i	−0.709617	+	0.947938i	−0.999960	−	0.00898495i	$-0.997140\pi$
$887$	−21.1342	+	28.2320i	−0.709617	+	0.947938i	0.290342	+	0.956923i	$0.406231\pi$
$888$		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	0.944856	−	0.327486i	$-0.106201\pi$
$907$	27.0094	+	20.2190i	0.896832	+	0.671360i	−0.0480238	+	0.998846i	$0.515292\pi$
$908$		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
$913$	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	−0.490125	−	0.871652i	$-0.663049\pi$
$929$	15.4337	−	24.0153i	0.506363	−	0.787916i	0.996488	+	0.0837363i	$0.0266854\pi$
$930$		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	0.893063	+	0.449931i	$0.148551\pi$
$937$	2.23830	+	31.2955i	0.0731220	+	1.02238i	−0.819941	+	0.572448i	$0.805994\pi$
$938$		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
$943$	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	0.963334	+	0.268306i	$0.0864637\pi$
$947$	−0.873303	+	12.2104i	−0.0283785	+	0.396784i	−0.991712	+	0.128478i	$0.958991\pi$
$948$		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	−0.565285	−	0.824896i	$-0.691234\pi$
$953$	11.8993	−	15.8956i	0.385456	−	0.514909i	0.950741	+	0.309987i	$0.100325\pi$
$954$		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	0.986535	−	0.163550i	$-0.0522945\pi$
$967$	25.5921	+	25.5921i	0.822985	+	0.822985i	−0.163550	+	0.986535i	$0.552294\pi$
$968$		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
$973$	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	−0.483958	−	0.875091i	$-0.660801\pi$
$977$	−44.4716	−	16.5871i	−1.42277	−	0.530667i	−0.938814	+	0.344424i	$0.888074\pi$
$978$		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	−0.683320	−	0.730119i	$-0.739465\pi$
$983$	−39.3722	+	2.81596i	−1.25578	+	0.0898150i	−0.572458	+	0.819934i	$0.694010\pi$
$984$		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	−0.954514	−	0.298168i	$-0.903625\pi$
$991$	−3.27709	+	7.17582i	−0.104100	+	0.227947i	0.850413	+	0.526115i	$0.176352\pi$
$992$		0			0
$993$	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	0.978263	−	0.207370i	$-0.0664904\pi$
$997$	42.0804	+	22.9777i	1.33270	+	0.727710i	0.354438	+	0.935079i	$0.384672\pi$
$998$		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.17.4	✓	720
5.3	odd	4	inner	920.2.bv.a.753.4	yes	720
23.19	odd	22	inner	920.2.bv.a.617.4	yes	720
115.88	even	44	inner	920.2.bv.a.433.4	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.4	✓	720	1.1	even	1	trivial
920.2.bv.a.433.4	yes	720	115.88	even	44	inner
920.2.bv.a.617.4	yes	720	23.19	odd	22	inner
920.2.bv.a.753.4	yes	720	5.3	odd	4	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

Related objects

Downloads

Learn more