LMFDB - Embedded newform 624.2.cn.d.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			401.1
Root			$0.500000 - 2.74530i$ of defining polynomial
Character	$\chi$	$=$	624.401
Dual form			624.2.cn.d.305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73022 + 0.0795432i) q^{3} +(-0.313444 + 0.313444i) q^{5} +(0.0745867 + 0.278362i) q^{7} +(2.98735 - 0.275255i) q^{9} +O(q^{10})$	\(q+(-1.73022 + 0.0795432i) q^{3} +(-0.313444 + 0.313444i) q^{5} +(0.0745867 + 0.278362i) q^{7} +(2.98735 - 0.275255i) q^{9} +(0.150860 - 0.563016i) q^{11} +(-1.79144 - 3.12902i) q^{13} +(0.517396 - 0.567261i) q^{15} +(-2.79907 + 4.84812i) q^{17} +(6.79127 - 1.81971i) q^{19} +(-0.151194 - 0.475695i) q^{21} +(3.32595 + 5.76071i) q^{23} +4.80351i q^{25} +(-5.14688 + 0.713876i) q^{27} +(3.57681 - 2.06507i) q^{29} +(1.03573 + 1.03573i) q^{31} +(-0.216237 + 0.986144i) q^{33} +(-0.110630 - 0.0638720i) q^{35} +(6.72147 + 1.80101i) q^{37} +(3.34848 + 5.27140i) q^{39} +(7.36988 + 1.97475i) q^{41} +(3.26299 + 1.88389i) q^{43} +(-0.850089 + 1.02264i) q^{45} +(3.71799 + 3.71799i) q^{47} +(5.99026 - 3.45848i) q^{49} +(4.45737 - 8.61098i) q^{51} -3.64778i q^{53} +(0.129188 + 0.223760i) q^{55} +(-11.6057 + 3.68871i) q^{57} +(-3.29111 + 0.881850i) q^{59} +(-5.25554 + 9.10286i) q^{61} +(0.299437 + 0.811032i) q^{63} +(1.54229 + 0.419256i) q^{65} +(-2.29144 + 8.55177i) q^{67} +(-6.21286 - 9.70277i) q^{69} +(-3.98229 - 14.8621i) q^{71} +(3.52053 - 3.52053i) q^{73} +(-0.382086 - 8.31114i) q^{75} +0.167974 q^{77} -1.10886 q^{79} +(8.84847 - 1.64456i) q^{81} +(-8.23032 + 8.23032i) q^{83} +(-0.642265 - 2.39697i) q^{85} +(-6.02442 + 3.85755i) q^{87} +(-3.64478 + 13.6025i) q^{89} +(0.737380 - 0.732051i) q^{91} +(-1.87442 - 1.70965i) q^{93} +(-1.55830 + 2.69906i) q^{95} +(2.59245 - 0.694645i) q^{97} +(0.295697 - 1.72345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73} + 96 q^{79} + 24 q^{81} - 24 q^{85} - 48 q^{87} + 16 q^{91} - 24 q^{93} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.73022	+	0.0795432i	−0.998945	+	0.0459243i
$3$	−1.73022	+	0.0795432i	−0.998945	+	0.0459243i
$4$		0			0
$5$	−0.313444	+	0.313444i	−0.140176	+	0.140176i	−0.773713	−	0.633536i	$-0.781603\pi$
$5$	−0.313444	+	0.313444i	−0.140176	+	0.140176i	0.633536	+	0.773713i	$0.281603\pi$
$6$		0			0
$7$	0.0745867	+	0.278362i	0.0281911	+	0.105211i	0.978588	−	0.205830i	$-0.0659892\pi$
$7$	0.0745867	+	0.278362i	0.0281911	+	0.105211i	−0.950397	+	0.311040i	$0.899323\pi$
$8$		0			0
$9$	2.98735	−	0.275255i	0.995782	−	0.0917517i
$10$		0			0
$11$	0.150860	−	0.563016i	0.0454859	−	0.169756i	−0.939446	−	0.342696i	$-0.888660\pi$
$11$	0.150860	−	0.563016i	0.0454859	−	0.169756i	0.984932	+	0.172940i	$0.0553267\pi$
$12$		0			0
$13$	−1.79144	−	3.12902i	−0.496856	−	0.867833i
$13$	−1.79144	−	3.12902i	−0.496856	−	0.867833i
$14$		0			0
$15$	0.517396	−	0.567261i	0.133591	−	0.146466i
$16$		0			0
$17$	−2.79907	+	4.84812i	−0.678873	+	1.17584i	0.296448	+	0.955049i	$0.404198\pi$
$17$	−2.79907	+	4.84812i	−0.678873	+	1.17584i	−0.975321	+	0.220793i	$0.929135\pi$
$18$		0			0
$19$	6.79127	−	1.81971i	1.55802	−	0.417471i	0.625986	−	0.779834i	$-0.284696\pi$
$19$	6.79127	−	1.81971i	1.55802	−	0.417471i	0.932037	+	0.362363i	$0.118030\pi$
$20$		0			0
$21$	−0.151194	−	0.475695i	−0.0329931	−	0.103805i
$22$		0			0
$23$	3.32595	+	5.76071i	0.693509	+	1.20119i	0.970681	+	0.240372i	$0.0772694\pi$
$23$	3.32595	+	5.76071i	0.693509	+	1.20119i	−0.277172	+	0.960820i	$0.589397\pi$
$24$		0			0
$25$			4.80351i			0.960701i
$26$		0			0
$27$	−5.14688	+	0.713876i	−0.990518	+	0.137386i
$28$		0			0
$29$	3.57681	−	2.06507i	0.664198	−	0.383475i	−0.129677	−	0.991556i	$-0.541394\pi$
$29$	3.57681	−	2.06507i	0.664198	−	0.383475i	0.793874	+	0.608082i	$0.208061\pi$
$30$		0			0
$31$	1.03573	+	1.03573i	0.186022	+	0.186022i	0.793974	−	0.607952i	$-0.208009\pi$
$31$	1.03573	+	1.03573i	0.186022	+	0.186022i	−0.607952	+	0.793974i	$0.708009\pi$
$32$		0			0
$33$	−0.216237	+	0.986144i	−0.0376420	+	0.171666i
$34$		0			0
$35$	−0.110630	−	0.0638720i	−0.0186998	−	0.0107963i
$36$		0			0
$37$	6.72147	+	1.80101i	1.10500	+	0.296085i	0.764800	−	0.644268i	$-0.222838\pi$
$37$	6.72147	+	1.80101i	1.10500	+	0.296085i	0.340202	+	0.940352i	$0.389504\pi$
$38$		0			0
$39$	3.34848	+	5.27140i	0.536186	+	0.844100i
$40$		0			0
$41$	7.36988	+	1.97475i	1.15098	+	0.308404i	0.783358	−	0.621570i	$-0.213505\pi$
$41$	7.36988	+	1.97475i	1.15098	+	0.308404i	0.367623	+	0.929975i	$0.380172\pi$
$42$		0			0
$43$	3.26299	+	1.88389i	0.497602	+	0.287290i	0.727723	−	0.685872i	$-0.240579\pi$
$43$	3.26299	+	1.88389i	0.497602	+	0.287290i	−0.230121	+	0.973162i	$0.573912\pi$
$44$		0			0
$45$	−0.850089	+	1.02264i	−0.126724	+	0.152447i
$46$		0			0
$47$	3.71799	+	3.71799i	0.542325	+	0.542325i	0.924210	−	0.381885i	$-0.124725\pi$
$47$	3.71799	+	3.71799i	0.542325	+	0.542325i	−0.381885	+	0.924210i	$0.624725\pi$
$48$		0			0
$49$	5.99026	−	3.45848i	0.855751	−	0.494068i
$50$		0			0
$51$	4.45737	−	8.61098i	0.624157	−	1.20578i
$52$		0			0
$53$		−	3.64778i		−	0.501062i	−0.968109	−	0.250531i	$-0.919395\pi$
$53$		−	3.64778i		−	0.501062i	0.968109	−	0.250531i	$-0.0806052\pi$
$54$		0			0
$55$	0.129188	+	0.223760i	0.0174197	+	0.0301718i
$56$		0			0
$57$	−11.6057	+	3.68871i	−1.53721	+	0.488582i
$58$		0			0
$59$	−3.29111	+	0.881850i	−0.428466	+	0.114807i	−0.466606	−	0.884465i	$-0.654523\pi$
$59$	−3.29111	+	0.881850i	−0.428466	+	0.114807i	0.0381400	+	0.999272i	$0.487857\pi$
$60$		0			0
$61$	−5.25554	+	9.10286i	−0.672903	+	1.16550i	0.304174	+	0.952616i	$0.401620\pi$
$61$	−5.25554	+	9.10286i	−0.672903	+	1.16550i	−0.977077	+	0.212886i	$0.931714\pi$
$62$		0			0
$63$	0.299437	+	0.811032i	0.0377255	+	0.102180i
$64$		0			0
$65$	1.54229	+	0.419256i	0.191297	+	0.0520023i
$66$		0			0
$67$	−2.29144	+	8.55177i	−0.279944	+	1.04476i	0.672512	+	0.740087i	$0.265215\pi$
$67$	−2.29144	+	8.55177i	−0.279944	+	1.04476i	−0.952455	+	0.304678i	$0.901451\pi$
$68$		0			0
$69$	−6.21286	−	9.70277i	−0.747941	−	1.16808i
$70$		0			0
$71$	−3.98229	−	14.8621i	−0.472611	−	1.76381i	−0.630334	−	0.776324i	$-0.717082\pi$
$71$	−3.98229	−	14.8621i	−0.472611	−	1.76381i	0.157723	−	0.987483i	$-0.449585\pi$
$72$		0			0
$73$	3.52053	−	3.52053i	0.412047	−	0.412047i	−0.470404	−	0.882451i	$-0.655892\pi$
$73$	3.52053	−	3.52053i	0.412047	−	0.412047i	0.882451	+	0.470404i	$0.155892\pi$
$74$		0			0
$75$	−0.382086	−	8.31114i	−0.0441195	−	0.959687i
$76$		0			0
$77$	0.167974			0.0191424
$78$		0			0
$79$	−1.10886			−0.124757			−0.0623783	−	0.998053i	$-0.519869\pi$
$79$	−1.10886			−0.124757			−0.0623783	+	0.998053i	$0.519869\pi$
$80$		0			0
$81$	8.84847	−	1.64456i	0.983163	−	0.182729i
$82$		0			0
$83$	−8.23032	+	8.23032i	−0.903395	+	0.903395i	−0.995728	−	0.0923332i	$-0.970567\pi$
$83$	−8.23032	+	8.23032i	−0.903395	+	0.903395i	0.0923332	+	0.995728i	$0.470567\pi$
$84$		0			0
$85$	−0.642265	−	2.39697i	−0.0696634	−	0.259987i
$86$		0			0
$87$	−6.02442	+	3.85755i	−0.645886	+	0.413573i
$88$		0			0
$89$	−3.64478	+	13.6025i	−0.386346	+	1.44186i	0.449687	+	0.893186i	$0.351535\pi$
$89$	−3.64478	+	13.6025i	−0.386346	+	1.44186i	−0.836034	+	0.548678i	$0.815131\pi$
$90$		0			0
$91$	0.737380	−	0.732051i	0.0772985	−	0.0767398i
$92$		0			0
$93$	−1.87442	−	1.70965i	−0.194369	−	0.177283i
$94$		0			0
$95$	−1.55830	+	2.69906i	−0.159879	+	0.276918i
$96$		0			0
$97$	2.59245	−	0.694645i	0.263223	−	0.0705305i	−0.124794	−	0.992183i	$-0.539827\pi$
$97$	2.59245	−	0.694645i	0.263223	−	0.0705305i	0.388017	+	0.921652i	$0.373160\pi$
$98$		0			0
$99$	0.295697	−	1.72345i	0.0297187	−	0.173213i
$100$		0			0
$101$	−7.12030	−	12.3327i	−0.708497	−	1.22715i	−0.965415	−	0.260719i	$-0.916040\pi$
$101$	−7.12030	−	12.3327i	−0.708497	−	1.22715i	0.256918	−	0.966433i	$-0.417293\pi$
$102$		0			0
$103$		−	4.60903i		−	0.454141i	−0.973878	−	0.227071i	$-0.927085\pi$
$103$		−	4.60903i		−	0.454141i	0.973878	−	0.227071i	$-0.0729148\pi$
$104$		0			0
$105$	0.196494	+	0.101713i	0.0191759	+	0.00992617i
$106$		0			0
$107$	11.7017	−	6.75600i	1.13125	−	0.653127i	0.187001	−	0.982360i	$-0.440123\pi$
$107$	11.7017	−	6.75600i	1.13125	−	0.653127i	0.944249	+	0.329232i	$0.106790\pi$
$108$		0			0
$109$	2.06188	+	2.06188i	0.197492	+	0.197492i	0.798924	−	0.601432i	$-0.205403\pi$
$109$	2.06188	+	2.06188i	0.197492	+	0.197492i	−0.601432	+	0.798924i	$0.705403\pi$
$110$		0			0
$111$	−11.7729	−	2.58151i	−1.11743	−	0.245026i
$112$		0			0
$113$	−9.02108	−	5.20832i	−0.848632	−	0.489958i	0.0115570	−	0.999933i	$-0.496321\pi$
$113$	−9.02108	−	5.20832i	−0.848632	−	0.489958i	−0.860189	+	0.509975i	$0.829655\pi$
$114$		0			0
$115$	−2.84816	−	0.763163i	−0.265592	−	0.0711653i
$116$		0			0
$117$	−6.21292	−	8.85435i	−0.574385	−	0.818585i
$118$		0			0
$119$	−1.55830	−	0.417546i	−0.142850	−	0.0382764i
$120$		0			0
$121$	9.23205	+	5.33013i	0.839277	+	0.484557i
$122$		0			0
$123$	−12.9086	−	2.83054i	−1.16393	−	0.255221i
$124$		0			0
$125$	−3.07285	−	3.07285i	−0.274844	−	0.274844i
$126$		0			0
$127$	0.209104	−	0.120726i	0.0185550	−	0.0107127i	−0.490694	−	0.871332i	$-0.663257\pi$
$127$	0.209104	−	0.120726i	0.0185550	−	0.0107127i	0.509249	+	0.860619i	$0.329923\pi$
$128$		0			0
$129$	−5.79555	−	3.00000i	−0.510270	−	0.264135i
$130$		0			0
$131$		−	8.09043i		−	0.706864i	−0.935460	−	0.353432i	$-0.885015\pi$
$131$		−	8.09043i		−	0.706864i	0.935460	−	0.353432i	$-0.114985\pi$
$132$		0			0
$133$	1.01308	+	1.75470i	0.0878449	+	0.152152i
$134$		0			0
$135$	1.38950	−	1.83702i	0.119589	−	0.158105i
$136$		0			0
$137$	0.0798882	−	0.0214060i	0.00682531	−	0.00182884i	−0.255405	−	0.966834i	$-0.582209\pi$
$137$	0.0798882	−	0.0214060i	0.00682531	−	0.00182884i	0.262230	+	0.965005i	$0.415542\pi$
$138$		0			0
$139$	−3.12073	+	5.40526i	−0.264697	+	0.458468i	−0.967484	−	0.252932i	$-0.918605\pi$
$139$	−3.12073	+	5.40526i	−0.264697	+	0.458468i	0.702788	+	0.711400i	$0.251938\pi$
$140$		0			0
$141$	−6.72870	−	6.13721i	−0.566658	−	0.516847i
$142$		0			0
$143$	−2.03194	+	0.536566i	−0.169920	+	0.0448699i
$144$		0			0
$145$	−0.473846	+	1.76842i	−0.0393507	+	0.146859i
$146$		0			0
$147$	−10.0894	+	6.46042i	−0.832158	+	0.532846i
$148$		0			0
$149$	−3.76251	−	14.0419i	−0.308237	−	1.15036i	−0.930123	−	0.367249i	$-0.880300\pi$
$149$	−3.76251	−	14.0419i	−0.308237	−	1.15036i	0.621886	−	0.783108i	$-0.286367\pi$
$150$		0			0
$151$	6.40358	−	6.40358i	0.521116	−	0.521116i	−0.396793	−	0.917908i	$-0.629877\pi$
$151$	6.40358	−	6.40358i	0.521116	−	0.521116i	0.917908	+	0.396793i	$0.129877\pi$
$152$		0			0
$153$	−7.02730	+	15.2535i	−0.568124	+	1.23317i
$154$		0			0
$155$	−0.649285			−0.0521519
$156$		0			0
$157$	−10.2127			−0.815065			−0.407532	−	0.913191i	$-0.633611\pi$
$157$	−10.2127			−0.815065			−0.407532	+	0.913191i	$0.633611\pi$
$158$		0			0
$159$	0.290157	+	6.31148i	0.0230109	+	0.500533i
$160$		0			0
$161$	−1.35549	+	1.35549i	−0.106828	+	0.106828i
$162$		0			0
$163$	3.59245	+	13.4072i	0.281382	+	1.05013i	0.951442	+	0.307827i	$0.0996017\pi$
$163$	3.59245	+	13.4072i	0.281382	+	1.05013i	−0.670060	+	0.742307i	$0.733732\pi$
$164$		0			0
$165$	−0.241323	−	0.376879i	−0.0187870	−	0.0293400i
$166$		0			0
$167$	3.47123	−	12.9548i	0.268612	−	1.00247i	−0.691391	−	0.722481i	$-0.743002\pi$
$167$	3.47123	−	12.9548i	0.268612	−	1.00247i	0.960003	−	0.279991i	$-0.0903316\pi$
$168$		0			0
$169$	−6.58150	+	11.2109i	−0.506269	+	0.862376i
$170$		0			0
$171$	19.7870	−	7.30545i	1.51315	−	0.558662i
$172$		0			0
$173$	−0.551099	+	0.954532i	−0.0418993	+	0.0725717i	−0.886215	−	0.463275i	$-0.846674\pi$
$173$	−0.551099	+	0.954532i	−0.0418993	+	0.0725717i	0.844315	+	0.535847i	$0.180008\pi$
$174$		0			0
$175$	−1.33711	+	0.358278i	−0.101076	+	0.0270833i
$176$		0			0
$177$	5.62421	−	1.78758i	0.422741	−	0.134363i
$178$		0			0
$179$	2.79777	+	4.84589i	0.209115	+	0.362199i	0.951436	−	0.307846i	$-0.0996082\pi$
$179$	2.79777	+	4.84589i	0.209115	+	0.362199i	−0.742321	+	0.670045i	$0.766275\pi$
$180$		0			0
$181$		−	14.4687i		−	1.07545i	−0.843119	−	0.537727i	$-0.819283\pi$
$181$		−	14.4687i		−	1.07545i	0.843119	−	0.537727i	$-0.180717\pi$
$182$		0			0
$183$	8.36919	−	16.1680i	0.618668	−	1.19518i
$184$		0			0
$185$	−2.67132	+	1.54229i	−0.196399	+	0.113391i
$186$		0			0
$187$	2.30731	+	2.30731i	0.168727	+	0.168727i
$188$		0			0
$189$	−0.582605	−	1.37945i	−0.0423783	−	0.100340i
$190$		0			0
$191$	−5.78136	−	3.33787i	−0.418324	−	0.241520i	0.276036	−	0.961147i	$-0.410979\pi$
$191$	−5.78136	−	3.33787i	−0.418324	−	0.241520i	−0.694360	+	0.719628i	$0.744312\pi$
$192$		0			0
$193$	5.88685	+	1.57738i	0.423745	+	0.113542i	0.464388	−	0.885632i	$-0.346274\pi$
$193$	5.88685	+	1.57738i	0.423745	+	0.113542i	−0.0406437	+	0.999174i	$0.512941\pi$
$194$		0			0
$195$	−2.70185	−	0.602728i	−0.193484	−	0.0431623i
$196$		0			0
$197$	14.2844	+	3.82748i	1.01772	+	0.272697i	0.728851	−	0.684672i	$-0.240055\pi$
$197$	14.2844	+	3.82748i	1.01772	+	0.272697i	0.288868	+	0.957369i	$0.406721\pi$
$198$		0			0
$199$	−13.4064	−	7.74017i	−0.950352	−	0.548686i	−0.0571619	−	0.998365i	$-0.518205\pi$
$199$	−13.4064	−	7.74017i	−0.950352	−	0.548686i	−0.893190	+	0.449679i	$0.851538\pi$
$200$		0			0
$201$	3.28447	−	14.9787i	0.231668	−	1.05652i
$202$		0			0
$203$	0.841620	+	0.841620i	0.0590701	+	0.0590701i
$204$		0			0
$205$	−2.92902	+	1.69107i	−0.204572	+	0.118109i
$206$		0			0
$207$	11.5214	+	16.2938i	0.800795	+	1.13249i
$208$		0			0
$209$		−	4.09812i		−	0.283473i
$210$		0			0
$211$	9.40721	+	16.2938i	0.647619	+	1.12171i	0.983690	+	0.179872i	$0.0575684\pi$
$211$	9.40721	+	16.2938i	0.647619	+	1.12171i	−0.336071	+	0.941837i	$0.609098\pi$
$212$		0			0
$213$	8.07243	+	25.3980i	0.553114	+	1.74024i
$214$		0			0
$215$	−1.61326	+	0.432272i	−0.110023	+	0.0294807i
$216$		0			0
$217$	−0.211055	+	0.365558i	−0.0143274	+	0.0248157i
$218$		0			0
$219$	−5.81127	+	6.37133i	−0.392689	+	0.430535i
$220$		0			0
$221$	20.1842	+	0.0732075i	1.35774	+	0.00492447i
$222$		0			0
$223$	1.86235	−	6.95039i	0.124712	−	0.465432i	−0.875117	−	0.483911i	$-0.839216\pi$
$223$	1.86235	−	6.95039i	0.124712	−	0.465432i	0.999829	+	0.0184790i	$0.00588239\pi$
$224$		0			0
$225$	1.32219	+	14.3497i	0.0881460	+	0.956649i
$226$		0			0
$227$	1.38733	+	5.17758i	0.0920803	+	0.343648i	0.996561	−	0.0828671i	$-0.0264077\pi$
$227$	1.38733	+	5.17758i	0.0920803	+	0.343648i	−0.904480	+	0.426515i	$0.859741\pi$
$228$		0			0
$229$	−8.24846	+	8.24846i	−0.545074	+	0.545074i	−0.925012	−	0.379938i	$-0.875945\pi$
$229$	−8.24846	+	8.24846i	−0.545074	+	0.545074i	0.379938	+	0.925012i	$0.375945\pi$
$230$		0			0
$231$	−0.290633	+	0.0133612i	−0.0191222	+	0.000879103i
$232$		0			0
$233$	9.54763			0.625486			0.312743	−	0.949838i	$-0.398752\pi$
$233$	9.54763			0.625486			0.312743	+	0.949838i	$0.398752\pi$
$234$		0			0
$235$	−2.33077			−0.152042
$236$		0			0
$237$	1.91858	−	0.0882024i	0.124625	−	0.00572936i
$238$		0			0
$239$	−20.6375	+	20.6375i	−1.33493	+	1.33493i	−0.434036	+	0.900895i	$0.642911\pi$
$239$	−20.6375	+	20.6375i	−1.33493	+	1.33493i	−0.900895	+	0.434036i	$0.857089\pi$
$240$		0			0
$241$	−2.88685	−	10.7739i	−0.185958	−	0.694006i	−0.994423	−	0.105462i	$-0.966368\pi$
$241$	−2.88685	−	10.7739i	−0.185958	−	0.694006i	0.808465	−	0.588544i	$-0.200299\pi$
$242$		0			0
$243$	−15.1790	+	3.54930i	−0.973734	+	0.227688i
$244$		0			0
$245$	−0.793572	+	2.96165i	−0.0506994	+	0.189213i
$246$		0			0
$247$	−17.8601	−	17.9901i	−1.13641	−	1.14468i
$248$		0			0
$249$	13.5856	−	14.8950i	0.860954	−	0.943930i
$250$		0			0
$251$	2.23476	−	3.87071i	0.141057	−	0.244317i	−0.786838	−	0.617159i	$-0.788283\pi$
$251$	2.23476	−	3.87071i	0.141057	−	0.244317i	0.927895	+	0.372842i	$0.121617\pi$
$252$		0			0
$253$	3.74513	−	1.00350i	0.235454	−	0.0630898i
$254$		0			0
$255$	1.30192	+	4.09620i	0.0815297	+	0.256514i
$256$		0			0
$257$	5.97416	+	10.3475i	0.372658	+	0.645462i	0.989973	−	0.141254i	$-0.0451133\pi$
$257$	5.97416	+	10.3475i	0.372658	+	0.645462i	−0.617316	+	0.786715i	$0.711780\pi$
$258$		0			0
$259$			2.00533i			0.124605i
$260$		0			0
$261$	10.1168	−	7.15363i	0.626211	−	0.442798i
$262$		0			0
$263$	−2.38262	+	1.37560i	−0.146918	+	0.0848234i	−0.571657	−	0.820493i	$-0.693699\pi$
$263$	−2.38262	+	1.37560i	−0.146918	+	0.0848234i	0.424739	+	0.905316i	$0.360366\pi$
$264$		0			0
$265$	1.14338	+	1.14338i	0.0702371	+	0.0702371i
$266$		0			0
$267$	5.22430	−	23.8253i	0.319722	−	1.45809i
$268$		0			0
$269$	−5.40423	−	3.12013i	−0.329502	−	0.190238i	0.326118	−	0.945329i	$-0.394259\pi$
$269$	−5.40423	−	3.12013i	−0.329502	−	0.190238i	−0.655620	+	0.755091i	$0.727593\pi$
$270$		0			0
$271$	21.6057	+	5.78922i	1.31245	+	0.351670i	0.846144	−	0.532954i	$-0.178918\pi$
$271$	21.6057	+	5.78922i	1.31245	+	0.351670i	0.466306	+	0.884624i	$0.345585\pi$
$272$		0			0
$273$	−1.21760	+	1.32527i	−0.0736927	+	0.0802087i
$274$		0			0
$275$	2.70445	+	0.724656i	0.163085	+	0.0436984i
$276$		0			0
$277$	−4.84833	−	2.79919i	−0.291308	−	0.168187i	0.347224	−	0.937782i	$-0.387125\pi$
$277$	−4.84833	−	2.79919i	−0.291308	−	0.168187i	−0.638532	+	0.769596i	$0.720458\pi$
$278$		0			0
$279$	3.37917	+	2.80899i	0.202305	+	0.168170i
$280$		0			0
$281$	8.82870	+	8.82870i	0.526676	+	0.526676i	0.919580	−	0.392903i	$-0.128529\pi$
$281$	8.82870	+	8.82870i	0.526676	+	0.526676i	−0.392903	+	0.919580i	$0.628529\pi$
$282$		0			0
$283$	5.93983	−	3.42936i	0.353086	−	0.203854i	−0.312958	−	0.949767i	$-0.601320\pi$
$283$	5.93983	−	3.42936i	0.353086	−	0.203854i	0.666044	+	0.745913i	$0.267986\pi$
$284$		0			0
$285$	2.48152	−	4.79393i	0.146993	−	0.283968i
$286$		0			0
$287$			2.19878i			0.129790i
$288$		0			0
$289$	−7.16953	−	12.4180i	−0.421737	−	0.730470i
$290$		0			0
$291$	−4.43026	+	1.40810i	−0.259707	+	0.0825445i
$292$		0			0
$293$	−26.4232	+	7.08007i	−1.54366	+	0.413622i	−0.927446	−	0.373957i	$-0.878001\pi$
$293$	−26.4232	+	7.08007i	−1.54366	+	0.413622i	−0.616213	+	0.787579i	$0.711334\pi$
$294$		0			0
$295$	0.755168	−	1.30799i	0.0439676	−	0.0761541i
$296$		0			0
$297$	−0.374533	+	3.00547i	−0.0217326	+	0.174395i
$298$		0			0
$299$	12.0671	−	20.7269i	0.697861	−	1.19867i
$300$		0			0
$301$	−0.281026	+	1.04880i	−0.0161981	+	0.0604521i
$302$		0			0
$303$	13.3007	+	20.7720i	0.764105	+	1.19332i
$304$		0			0
$305$	−1.20592	−	4.50056i	−0.0690508	−	0.257701i
$306$		0			0
$307$	15.4869	−	15.4869i	0.883883	−	0.883883i	−0.110044	−	0.993927i	$-0.535099\pi$
$307$	15.4869	−	15.4869i	0.883883	−	0.883883i	0.993927	+	0.110044i	$0.0350992\pi$
$308$		0			0
$309$	0.366617	+	7.97465i	0.0208561	+	0.453662i
$310$		0			0
$311$	31.8012			1.80328			0.901642	−	0.432484i	$-0.142363\pi$
$311$	31.8012			1.80328			0.901642	+	0.432484i	$0.142363\pi$
$312$		0			0
$313$	−23.7424			−1.34200			−0.670999	−	0.741458i	$-0.734135\pi$
$313$	−23.7424			−1.34200			−0.670999	+	0.741458i	$0.734135\pi$
$314$		0			0
$315$	−0.348070	−	0.160356i	−0.0196115	−	0.00903506i
$316$		0			0
$317$	−16.8936	+	16.8936i	−0.948841	+	0.948841i	−0.998754	−	0.0499128i	$-0.984106\pi$
$317$	−16.8936	+	16.8936i	−0.948841	+	0.948841i	0.0499128	+	0.998754i	$0.484106\pi$
$318$		0			0
$319$	−0.623073	−	2.32534i	−0.0348854	−	0.130194i
$320$		0			0
$321$	−19.7092	+	12.6202i	−1.10006	+	0.704390i
$322$		0			0
$323$	−10.1870	+	38.0184i	−0.566820	+	2.11540i
$324$		0			0
$325$	15.0303	−	8.60519i	0.833728	−	0.477330i
$326$		0			0
$327$	−3.73152	−	3.40351i	−0.206354	−	0.188214i
$328$		0			0
$329$	−0.757633	+	1.31226i	−0.0417697	+	0.0723472i
$330$		0			0
$331$	−15.9259	+	4.26733i	−0.875367	+	0.234554i	−0.668407	−	0.743795i	$-0.733024\pi$
$331$	−15.9259	+	4.26733i	−0.875367	+	0.234554i	−0.206960	+	0.978349i	$0.566357\pi$
$332$		0			0
$333$	20.5751	+	3.53013i	1.12751	+	0.193450i
$334$		0			0
$335$	−1.96226	−	3.39874i	−0.107210	−	0.185693i
$336$		0			0
$337$		−	3.24846i		−	0.176955i	−0.996078	−	0.0884775i	$-0.971800\pi$
$337$		−	3.24846i		−	0.176955i	0.996078	−	0.0884775i	$-0.0282001\pi$
$338$		0			0
$339$	16.0228	+	8.29400i	0.870238	+	0.450468i
$340$		0			0
$341$	0.739381	−	0.426882i	0.0400397	−	0.0231169i
$342$		0			0
$343$	2.83592	+	2.83592i	0.153125	+	0.153125i
$344$		0			0
$345$	4.98866	+	1.09389i	0.268580	+	0.0588930i
$346$		0			0
$347$	−7.11715	−	4.10909i	−0.382069	−	0.220587i	0.296649	−	0.954986i	$-0.404131\pi$
$347$	−7.11715	−	4.10909i	−0.382069	−	0.220587i	−0.678718	+	0.734399i	$0.737464\pi$
$348$		0			0
$349$	7.73980	+	2.07387i	0.414302	+	0.111012i	0.459948	−	0.887946i	$-0.347868\pi$
$349$	7.73980	+	2.07387i	0.414302	+	0.111012i	−0.0456462	+	0.998958i	$0.514535\pi$
$350$		0			0
$351$	11.4541	+	14.8258i	0.611372	+	0.791343i
$352$		0			0
$353$	−2.70035	−	0.723557i	−0.143725	−	0.0385111i	0.186239	−	0.982504i	$-0.440370\pi$
$353$	−2.70035	−	0.723557i	−0.143725	−	0.0385111i	−0.329964	+	0.943993i	$0.607037\pi$
$354$		0			0
$355$	5.90666	+	3.41021i	0.313493	+	0.180995i
$356$		0			0
$357$	2.72943	+	0.598496i	0.144457	+	0.0316758i
$358$		0			0
$359$	11.6531	+	11.6531i	0.615028	+	0.615028i	0.944252	−	0.329224i	$-0.106787\pi$
$359$	11.6531	+	11.6531i	0.615028	+	0.615028i	−0.329224	+	0.944252i	$0.606787\pi$
$360$		0			0
$361$	26.3555	−	15.2163i	1.38713	−	0.800860i
$362$		0			0
$363$	−16.3975	−	8.48796i	−0.860645	−	0.445503i
$364$		0			0
$365$			2.20698i			0.115519i
$366$		0			0
$367$	−18.5929	−	32.2039i	−0.970544	−	1.68103i	−0.693918	−	0.720054i	$-0.744117\pi$
$367$	−18.5929	−	32.2039i	−0.970544	−	1.68103i	−0.276626	−	0.960978i	$-0.589216\pi$
$368$		0			0
$369$	22.5599	+	3.87067i	1.17442	+	0.201499i
$370$		0			0
$371$	1.01540	−	0.272076i	0.0527171	−	0.0141255i
$372$		0			0
$373$	3.94412	−	6.83141i	0.204219	−	0.353717i	−0.745665	−	0.666321i	$-0.767868\pi$
$373$	3.94412	−	6.83141i	0.204219	−	0.353717i	0.949883	+	0.312604i	$0.101201\pi$
$374$		0			0
$375$	5.56114	+	5.07229i	0.287176	+	0.261932i
$376$		0			0
$377$	−12.8693	−	7.49246i	−0.662802	−	0.385881i
$378$		0			0
$379$	−0.481911	+	1.79852i	−0.0247541	+	0.0923837i	−0.977198	−	0.212331i	$-0.931894\pi$
$379$	−0.481911	+	1.79852i	−0.0247541	+	0.0923837i	0.952444	+	0.304715i	$0.0985611\pi$
$380$		0			0
$381$	−0.352194	+	0.225517i	−0.0180435	+	0.0115536i
$382$		0			0
$383$	0.745523	+	2.78233i	0.0380945	+	0.142170i	0.982354	−	0.187032i	$-0.0598868\pi$
$383$	0.745523	+	2.78233i	0.0380945	+	0.142170i	−0.944259	+	0.329202i	$0.893220\pi$
$384$		0			0
$385$	−0.0526505	+	0.0526505i	−0.00268332	+	0.00268332i
$386$		0			0
$387$	10.2662	+	4.72967i	0.521862	+	0.240423i
$388$		0			0
$389$	23.4187			1.18738			0.593688	−	0.804695i	$-0.297671\pi$
$389$	23.4187			1.18738			0.593688	+	0.804695i	$0.297671\pi$
$390$		0			0
$391$	−37.2382			−1.88322
$392$		0			0
$393$	0.643539	+	13.9983i	0.0324623	+	0.706119i
$394$		0			0
$395$	0.347566	−	0.347566i	0.0174879	−	0.0174879i
$396$		0			0
$397$	4.76427	+	17.7805i	0.239112	+	0.892378i	0.976252	+	0.216638i	$0.0695092\pi$
$397$	4.76427	+	17.7805i	0.239112	+	0.892378i	−0.737140	+	0.675740i	$0.763824\pi$
$398$		0			0
$399$	−1.89242	−	2.95544i	−0.0947397	−	0.147957i
$400$		0			0
$401$	1.75607	−	6.55376i	0.0876942	−	0.327279i	−0.908117	−	0.418717i	$-0.862480\pi$
$401$	1.75607	−	6.55376i	0.0876942	−	0.327279i	0.995811	+	0.0914383i	$0.0291464\pi$
$402$		0			0
$403$	1.38537	−	5.09625i	0.0690100	−	0.253862i
$404$		0			0
$405$	−2.25802	+	3.28898i	−0.112202	+	0.163431i
$406$		0			0
$407$	2.02800	−	3.51260i	0.100524	−	0.174113i
$408$		0			0
$409$	−28.2895	+	7.58014i	−1.39882	+	0.374814i	−0.877923	−	0.478803i	$-0.841071\pi$
$409$	−28.2895	+	7.58014i	−1.39882	+	0.374814i	−0.520902	+	0.853617i	$0.674404\pi$
$410$		0			0
$411$	−0.136522	+	0.0433917i	−0.00673412	+	0.00214035i
$412$		0			0
$413$	−0.490946	−	0.850344i	−0.0241579	−	0.0418427i
$414$		0			0
$415$		−	5.15949i		−	0.253269i
$416$		0			0
$417$	4.96960	−	9.60053i	0.243362	−	0.470140i
$418$		0			0
$419$	8.00397	−	4.62109i	0.391020	−	0.225755i	−0.291582	−	0.956546i	$-0.594182\pi$
$419$	8.00397	−	4.62109i	0.391020	−	0.225755i	0.682602	+	0.730791i	$0.260848\pi$
$420$		0			0
$421$	−18.4490	−	18.4490i	−0.899149	−	0.899149i	0.0962115	−	0.995361i	$-0.469327\pi$
$421$	−18.4490	−	18.4490i	−0.899149	−	0.899149i	−0.995361	+	0.0962115i	$0.969327\pi$
$422$		0			0
$423$	12.1303	+	10.0835i	0.589796	+	0.490278i
$424$		0			0
$425$	−23.2880	−	13.4453i	−1.12963	−	0.652194i
$426$		0			0
$427$	−2.92588	−	0.783987i	−0.141593	−	0.0379398i
$428$		0			0
$429$	3.47304	−	1.09001i	0.167680	−	0.0526260i
$430$		0			0
$431$	21.6015	+	5.78811i	1.04051	+	0.278803i	0.738324	−	0.674446i	$-0.235617\pi$
$431$	21.6015	+	5.78811i	1.04051	+	0.278803i	0.302184	+	0.953249i	$0.402284\pi$
$432$		0			0
$433$	3.41910	+	1.97402i	0.164311	+	0.0948652i	0.579901	−	0.814687i	$-0.303091\pi$
$433$	3.41910	+	1.97402i	0.164311	+	0.0948652i	−0.415589	+	0.909552i	$0.636425\pi$
$434$		0			0
$435$	0.679193	−	3.09745i	0.0325648	−	0.148511i
$436$		0			0
$437$	33.0703	+	33.0703i	1.58197	+	1.58197i
$438$		0			0
$439$	−15.8569	+	9.15500i	−0.756810	+	0.436944i	−0.828149	−	0.560508i	$-0.810606\pi$
$439$	−15.8569	+	9.15500i	−0.756810	+	0.436944i	0.0713394	+	0.997452i	$0.477273\pi$
$440$		0			0
$441$	16.9430	−	11.9805i	0.806810	−	0.570501i
$442$		0			0
$443$		−	5.86371i		−	0.278593i	−0.990251	−	0.139297i	$-0.955516\pi$
$443$		−	5.86371i		−	0.278593i	0.990251	−	0.139297i	$-0.0444841\pi$
$444$		0			0
$445$	−3.12119	−	5.40607i	−0.147959	−	0.256272i
$446$		0			0
$447$	7.62693	+	23.9963i	0.360741	+	1.13499i
$448$		0			0
$449$	27.5332	−	7.37750i	1.29937	−	0.348166i	0.458160	−	0.888870i	$-0.348509\pi$
$449$	27.5332	−	7.37750i	1.29937	−	0.348166i	0.841213	+	0.540704i	$0.181842\pi$
$450$		0			0
$451$	2.22364	−	3.85145i	0.104707	−	0.181358i
$452$		0			0
$453$	−10.5703	+	11.5890i	−0.496634	+	0.544498i
$454$		0			0
$455$	−0.00167052	+	0.460585i	−7.83154e−5	+	0.0215925i
$456$		0			0
$457$	−4.96154	+	18.5167i	−0.232091	+	0.866175i	0.747348	+	0.664433i	$0.231327\pi$
$457$	−4.96154	+	18.5167i	−0.232091	+	0.866175i	−0.979439	+	0.201742i	$0.935340\pi$
$458$		0			0
$459$	10.9455	−	26.9509i	0.510892	−	1.25796i
$460$		0			0
$461$	7.67398	+	28.6397i	0.357413	+	1.33388i	0.877421	+	0.479722i	$0.159262\pi$
$461$	7.67398	+	28.6397i	0.357413	+	1.33388i	−0.520007	+	0.854162i	$0.674071\pi$
$462$		0			0
$463$	−18.2554	+	18.2554i	−0.848400	+	0.848400i	−0.989934	−	0.141533i	$-0.954797\pi$
$463$	−18.2554	+	18.2554i	−0.848400	+	0.848400i	0.141533	+	0.989934i	$0.454797\pi$
$464$		0			0
$465$	1.12341	−	0.0516463i	0.0520968	−	0.00239504i
$466$		0			0
$467$	−32.4456			−1.50140			−0.750701	−	0.660642i	$-0.770284\pi$
$467$	−32.4456			−1.50140			−0.750701	+	0.660642i	$0.770284\pi$
$468$		0			0
$469$	−2.55139			−0.117812
$470$		0			0
$471$	17.6703	−	0.812354i	0.814205	−	0.0374313i
$472$		0			0
$473$	1.55291	−	1.55291i	0.0714031	−	0.0714031i
$474$		0			0
$475$	8.74101	+	32.6219i	0.401065	+	1.49680i
$476$		0			0
$477$	−1.00407	−	10.8972i	−0.0459733	−	0.498948i
$478$		0			0
$479$	−2.14571	+	8.00792i	−0.0980402	+	0.365891i	−0.997463	−	0.0711890i	$-0.977321\pi$
$479$	−2.14571	+	8.00792i	−0.0980402	+	0.365891i	0.899423	+	0.437080i	$0.143987\pi$
$480$		0			0
$481$	−6.40570	−	24.2580i	−0.292075	−	1.10607i
$482$		0			0
$483$	2.23748	−	2.45312i	0.101809	−	0.111621i
$484$		0			0
$485$	−0.594856	+	1.03032i	−0.0270110	+	0.0467845i
$486$		0			0
$487$	31.0359	−	8.31604i	1.40637	−	0.376836i	0.525742	−	0.850644i	$-0.323788\pi$
$487$	31.0359	−	8.31604i	1.40637	−	0.376836i	0.880628	+	0.473808i	$0.157121\pi$
$488$		0			0
$489$	−7.28219	−	22.9117i	−0.329312	−	1.03610i
$490$		0			0
$491$	−13.2100	−	22.8803i	−0.596157	−	1.03257i	−0.993383	−	0.114853i	$-0.963360\pi$
$491$	−13.2100	−	22.8803i	−0.596157	−	1.03257i	0.397226	−	0.917721i	$-0.369973\pi$
$492$		0			0
$493$			23.1211i			1.04132i
$494$		0			0
$495$	0.447520	+	0.632890i	0.0201145	+	0.0284463i
$496$		0			0
$497$	3.84001	−	2.21703i	0.172248	−	0.0994475i
$498$		0			0
$499$	9.27427	+	9.27427i	0.415173	+	0.415173i	0.883536	−	0.468363i	$-0.155156\pi$
$499$	9.27427	+	9.27427i	0.415173	+	0.415173i	−0.468363	+	0.883536i	$0.655156\pi$
$500$		0			0
$501$	−4.97553	+	22.6908i	−0.222290	+	1.01375i
$502$		0			0
$503$	−26.4513	−	15.2717i	−1.17941	−	0.680931i	−0.223529	−	0.974697i	$-0.571758\pi$
$503$	−26.4513	−	15.2717i	−1.17941	−	0.680931i	−0.955877	+	0.293767i	$0.905091\pi$
$504$		0			0
$505$	6.09744	+	1.63380i	0.271332	+	0.0727033i
$506$		0			0
$507$	10.4957	−	19.9208i	0.466131	−	0.884716i
$508$		0			0
$509$	−23.0380	−	6.17302i	−1.02114	−	0.273614i	−0.290865	−	0.956764i	$-0.593943\pi$
$509$	−23.0380	−	6.17302i	−1.02114	−	0.273614i	−0.730278	+	0.683150i	$0.760610\pi$
$510$		0			0
$511$	1.24256	+	0.717395i	0.0549678	+	0.0317357i
$512$		0			0
$513$	−33.6548	+	14.2140i	−1.48590	+	0.627562i
$514$		0			0
$515$	1.44467	+	1.44467i	0.0636599	+	0.0636599i
$516$		0			0
$517$	2.65418	−	1.53239i	0.116731	−	0.0673946i
$518$		0			0
$519$	0.877598	−	1.69539i	0.0385223	−	0.0744193i
$520$		0			0
$521$		−	42.5422i		−	1.86381i	−0.362704	−	0.931904i	$-0.618146\pi$
$521$		−	42.5422i		−	1.86381i	0.362704	−	0.931904i	$-0.381854\pi$
$522$		0			0
$523$	−17.0400	−	29.5141i	−0.745107	−	1.29056i	−0.950145	−	0.311809i	$-0.899065\pi$
$523$	−17.0400	−	29.5141i	−0.745107	−	1.29056i	0.205037	−	0.978754i	$-0.434268\pi$
$524$		0			0
$525$	2.28500	−	0.726259i	0.0997257	−	0.0316965i
$526$		0			0
$527$	−7.92040	+	2.12227i	−0.345018	+	0.0924473i
$528$		0			0
$529$	−10.6239	+	18.4011i	−0.461908	+	0.800048i
$530$		0			0
$531$	−9.58895	+	3.54029i	−0.416125	+	0.153635i
$532$		0			0
$533$	−7.02365	−	26.5981i	−0.304228	−	1.15209i
$534$		0			0
$535$	−1.55021	+	5.78547i	−0.0670215	+	0.250128i
$536$		0			0
$537$	−5.22623	−	8.16192i	−0.225529	−	0.352213i
$538$		0			0
$539$	−1.04349	−	3.89436i	−0.0449463	−	0.167742i
$540$		0			0
$541$	18.5013	−	18.5013i	0.795434	−	0.795434i	−0.186938	−	0.982372i	$-0.559856\pi$
$541$	18.5013	−	18.5013i	0.795434	−	0.795434i	0.982372	+	0.186938i	$0.0598564\pi$
$542$		0			0
$543$	1.15089	+	25.0342i	0.0493895	+	1.07432i
$544$		0			0
$545$	−1.29257			−0.0553676
$546$		0			0
$547$	−39.5058			−1.68915			−0.844573	−	0.535440i	$-0.820146\pi$
$547$	−39.5058			−1.68915			−0.844573	+	0.535440i	$0.820146\pi$
$548$		0			0
$549$	−13.1945	+	28.6400i	−0.563128	+	1.22233i
$550$		0			0
$551$	20.5332	−	20.5332i	0.874746	−	0.874746i
$552$		0			0
$553$	−0.0827063	−	0.308664i	−0.00351703	−	0.0131257i
$554$		0			0
$555$	4.49930	−	2.88099i	0.190985	−	0.122291i
$556$		0			0
$557$	4.08768	−	15.2554i	0.173201	−	0.646394i	−0.823650	−	0.567098i	$-0.808066\pi$
$557$	4.08768	−	15.2554i	0.173201	−	0.646394i	0.996851	−	0.0792958i	$-0.0252672\pi$
$558$		0			0
$559$	0.0492717	−	13.5848i	0.00208397	−	0.574577i
$560$		0			0
$561$	−4.17568	−	3.80862i	−0.176298	−	0.160800i
$562$		0			0
$563$	−10.6906	+	18.5166i	−0.450555	+	0.780383i	−0.998421	−	0.0561827i	$-0.982107\pi$
$563$	−10.6906	+	18.5166i	−0.450555	+	0.780383i	0.547866	+	0.836566i	$0.315440\pi$
$564$		0			0
$565$	4.46012	−	1.19509i	0.187639	−	0.0502777i
$566$		0			0
$567$	1.11776	+	2.34041i	0.0469416	+	0.0982880i
$568$		0			0
$569$	14.5203	+	25.1500i	0.608725	+	1.05434i	0.991451	+	0.130480i	$0.0416519\pi$
$569$	14.5203	+	25.1500i	0.608725	+	1.05434i	−0.382726	+	0.923862i	$0.625015\pi$
$570$		0			0
$571$		−	9.91137i		−	0.414778i	−0.978259	−	0.207389i	$-0.933503\pi$
$571$		−	9.91137i		−	0.414778i	0.978259	−	0.207389i	$-0.0664966\pi$
$572$		0			0
$573$	10.2685	+	5.31539i	0.428974	+	0.222054i
$574$		0			0
$575$	−27.6716	+	15.9762i	−1.15399	+	0.666254i
$576$		0			0
$577$	−4.91283	−	4.91283i	−0.204524	−	0.204524i	0.597411	−	0.801935i	$-0.296196\pi$
$577$	−4.91283	−	4.91283i	−0.204524	−	0.204524i	−0.801935	+	0.597411i	$0.796196\pi$
$578$		0			0
$579$	−10.3110	−	2.26095i	−0.428512	−	0.0939621i
$580$		0			0
$581$	−2.90488	−	1.67713i	−0.120515	−	0.0695791i
$582$		0			0
$583$	−2.05376	−	0.550304i	−0.0850581	−	0.0227913i
$584$		0			0
$585$	4.72275	+	0.827940i	0.195262	+	0.0342311i
$586$		0			0
$587$	23.2001	+	6.21644i	0.957569	+	0.256580i	0.703571	−	0.710625i	$-0.251588\pi$
$587$	23.2001	+	6.21644i	0.957569	+	0.256580i	0.253998	+	0.967205i	$0.418254\pi$
$588$		0			0
$589$	8.91863	+	5.14917i	0.367486	+	0.212168i
$590$		0			0
$591$	−25.0196	−	5.48618i	−1.02917	−	0.225671i
$592$		0			0
$593$	−22.0744	−	22.0744i	−0.906489	−	0.906489i	0.0894984	−	0.995987i	$-0.471474\pi$
$593$	−22.0744	−	22.0744i	−0.906489	−	0.906489i	−0.995987	+	0.0894984i	$0.971474\pi$
$594$		0			0
$595$	0.619319	−	0.357564i	0.0253896	−	0.0146587i
$596$		0			0
$597$	23.8117	+	12.3258i	0.974548	+	0.504463i
$598$		0			0
$599$		−	35.2538i		−	1.44043i	−0.693750	−	0.720216i	$-0.744043\pi$
$599$		−	35.2538i		−	1.44043i	0.693750	−	0.720216i	$-0.255957\pi$
$600$		0			0
$601$	−10.0883	−	17.4735i	−0.411512	−	0.712759i	0.583544	−	0.812082i	$-0.301666\pi$
$601$	−10.0883	−	17.4735i	−0.411512	−	0.712759i	−0.995055	+	0.0993227i	$0.968332\pi$
$602$		0			0
$603$	−4.49140	+	26.1778i	−0.182904	+	1.06604i
$604$		0			0
$605$	−4.56443	+	1.22304i	−0.185570	+	0.0497234i
$606$		0			0
$607$	−2.42837	+	4.20607i	−0.0985647	+	0.170719i	−0.911091	−	0.412206i	$-0.864758\pi$
$607$	−2.42837	+	4.20607i	−0.0985647	+	0.170719i	0.812526	+	0.582925i	$0.198092\pi$
$608$		0			0
$609$	−1.52314	−	1.38925i	−0.0617206	−	0.0562951i
$610$		0			0
$611$	4.97311	−	18.2942i	0.201190	−	0.740105i
$612$		0			0
$613$	−0.235455	+	0.878731i	−0.00950994	+	0.0354916i	−0.970518	−	0.241030i	$-0.922515\pi$
$613$	−0.235455	+	0.878731i	−0.00950994	+	0.0354916i	0.961008	+	0.276521i	$0.0891816\pi$
$614$		0			0
$615$	4.93334	−	3.15891i	0.198932	−	0.127380i
$616$		0			0
$617$	−11.6445	−	43.4580i	−0.468792	−	1.74956i	−0.644002	−	0.765024i	$-0.722727\pi$
$617$	−11.6445	−	43.4580i	−0.468792	−	1.74956i	0.175210	−	0.984531i	$-0.443940\pi$
$618$		0			0
$619$	−11.7433	+	11.7433i	−0.472003	+	0.472003i	−0.902562	−	0.430559i	$-0.858316\pi$
$619$	−11.7433	+	11.7433i	−0.472003	+	0.472003i	0.430559	+	0.902562i	$0.358316\pi$
$620$		0			0
$621$	−21.2307	−	27.2754i	−0.851959	−	1.09452i
$622$		0			0
$623$	−4.05827			−0.162591
$624$		0			0
$625$	−22.0912			−0.883648
$626$		0			0
$627$	0.325977	+	7.09066i	0.0130183	+	0.283174i
$628$		0			0
$629$	−27.5454	+	27.5454i	−1.09831	+	1.09831i
$630$		0			0
$631$	−9.44656	−	35.2551i	−0.376062	−	1.40348i	−0.851787	−	0.523888i	$-0.824481\pi$
$631$	−9.44656	−	35.2551i	−0.376062	−	1.40348i	0.475725	−	0.879594i	$-0.342186\pi$
$632$		0			0
$633$	−17.5726	−	27.4436i	−0.698449	−	1.09078i
$634$		0			0
$635$	−0.0277015	+	0.103384i	−0.00109930	+	0.00410265i
$636$		0			0
$637$	−21.5528	−	12.5480i	−0.853953	−	0.497168i
$638$		0			0
$639$	−15.9873	−	43.3021i	−0.632450	−	1.71300i
$640$		0			0
$641$	0.424453	−	0.735175i	0.0167649	−	0.0290377i	−0.857521	−	0.514449i	$-0.827997\pi$
$641$	0.424453	−	0.735175i	0.0167649	−	0.0290377i	0.874286	+	0.485411i	$0.161330\pi$
$642$		0			0
$643$	16.6824	−	4.47005i	0.657891	−	0.176281i	0.0855970	−	0.996330i	$-0.472720\pi$
$643$	16.6824	−	4.47005i	0.657891	−	0.176281i	0.572294	+	0.820048i	$0.306054\pi$
$644$		0			0
$645$	2.75692	−	0.876250i	0.108553	−	0.0345023i
$646$		0			0
$647$	7.87623	+	13.6420i	0.309646	+	0.536323i	0.978285	−	0.207264i	$-0.0664560\pi$
$647$	7.87623	+	13.6420i	0.309646	+	0.536323i	−0.668639	+	0.743588i	$0.733123\pi$
$648$		0			0
$649$			1.98598i			0.0779567i
$650$		0			0
$651$	0.336095	−	0.649285i	0.0131726	−	0.0254475i
$652$		0			0
$653$	−21.3400	+	12.3207i	−0.835099	+	0.482145i	−0.855595	−	0.517645i	$-0.826809\pi$
$653$	−21.3400	+	12.3207i	−0.835099	+	0.482145i	0.0204964	+	0.999790i	$0.493475\pi$
$654$		0			0
$655$	2.53590	+	2.53590i	0.0990857	+	0.0990857i
$656$		0			0
$657$	9.54799	−	11.4861i	0.372503	−	0.448115i
$658$		0			0
$659$	−15.3411	−	8.85721i	−0.597606	−	0.345028i	0.170493	−	0.985359i	$-0.445464\pi$
$659$	−15.3411	−	8.85721i	−0.597606	−	0.345028i	−0.768099	+	0.640331i	$0.778797\pi$
$660$		0			0
$661$	−9.15665	−	2.45352i	−0.356153	−	0.0954308i	0.0763064	−	0.997084i	$-0.475687\pi$
$661$	−9.15665	−	2.45352i	−0.356153	−	0.0954308i	−0.432459	+	0.901654i	$0.642354\pi$
$662$		0			0
$663$	−34.9290	+	1.47885i	−1.35653	+	0.0574339i
$664$		0			0
$665$	−0.867544	−	0.232458i	−0.0336419	−	0.00901432i
$666$		0			0
$667$	23.7926	+	13.7367i	0.921253	+	0.531886i
$668$		0			0
$669$	−2.66943	+	12.1739i	−0.103206	+	0.470669i
$670$		0			0
$671$	4.33221	+	4.33221i	0.167243	+	0.167243i
$672$		0			0
$673$	−0.150089	+	0.0866536i	−0.00578549	+	0.00334025i	−0.502890	−	0.864350i	$-0.667730\pi$
$673$	−0.150089	+	0.0866536i	−0.00578549	+	0.00334025i	0.497104	+	0.867691i	$0.334397\pi$
$674$		0			0
$675$	−3.42911	−	24.7231i	−0.131986	−	0.951591i
$676$		0			0
$677$		−	2.12205i		−	0.0815568i	−0.999168	−	0.0407784i	$-0.987016\pi$
$677$		−	2.12205i		−	0.0815568i	0.999168	−	0.0407784i	$-0.0129838\pi$
$678$		0			0
$679$	0.386725	+	0.669827i	0.0148411	+	0.0257056i
$680$		0			0
$681$	−2.81223	−	8.84802i	−0.107765	−	0.339057i
$682$		0			0
$683$	30.9953	−	8.30516i	1.18600	−	0.317788i	0.388697	−	0.921365i	$-0.372925\pi$
$683$	30.9953	−	8.30516i	1.18600	−	0.317788i	0.797305	+	0.603577i	$0.206258\pi$
$684$		0			0
$685$	−0.0183309	+	0.0317500i	−0.000700388	+	0.00121311i
$686$		0			0
$687$	13.6156	−	14.9278i	0.519466	−	0.569531i
$688$		0			0
$689$	−11.4140	+	6.53478i	−0.434838	+	0.248955i
$690$		0			0
$691$	−7.89090	+	29.4492i	−0.300184	+	1.12030i	0.636829	+	0.771005i	$0.280246\pi$
$691$	−7.89090	+	29.4492i	−0.300184	+	1.12030i	−0.937012	+	0.349296i	$0.886421\pi$
$692$		0			0
$693$	0.501797	−	0.0462358i	0.0190617	−	0.00175635i
$694$		0			0
$695$	−0.716073	−	2.67242i	−0.0271622	−	0.101371i
$696$		0			0
$697$	−30.2026	+	30.2026i	−1.14401	+	1.14401i
$698$		0			0
$699$	−16.5195	+	0.759450i	−0.624826	+	0.0287250i
$700$		0			0
$701$	−1.23549			−0.0466638			−0.0233319	−	0.999728i	$-0.507427\pi$
$701$	−1.23549			−0.0466638			−0.0233319	+	0.999728i	$0.507427\pi$
$702$		0			0
$703$	48.9246			1.84523
$704$		0			0
$705$	4.03274	−	0.185397i	0.151882	−	0.00698244i
$706$		0			0
$707$	2.90188	−	2.90188i	0.109136	−	0.109136i
$708$		0			0
$709$	4.09728	+	15.2913i	0.153877	+	0.574276i	0.999199	+	0.0400188i	$0.0127418\pi$
$709$	4.09728	+	15.2913i	0.153877	+	0.574276i	−0.845322	+	0.534257i	$0.820592\pi$
$710$		0			0
$711$	−3.31255	+	0.305220i	−0.124230	+	0.0114466i
$712$		0			0
$713$	−2.52175	+	9.41131i	−0.0944404	+	0.352456i
$714$		0			0
$715$	0.468717	−	0.805084i	0.0175290	−	0.0301084i
$716$		0			0
$717$	34.0660	−	37.3491i	1.27222	−	1.39483i
$718$		0			0
$719$	−1.55033	+	2.68525i	−0.0578176	+	0.100143i	−0.893486	−	0.449092i	$-0.851748\pi$
$719$	−1.55033	+	2.68525i	−0.0578176	+	0.100143i	0.835668	+	0.549235i	$0.185081\pi$
$720$		0			0
$721$	1.28298	−	0.343773i	0.0477806	−	0.0128028i
$722$		0			0
$723$	5.85188	+	18.4116i	0.217634	+	0.684734i
$724$		0			0
$725$	9.91959	+	17.1812i	0.368404	+	0.638095i
$726$		0			0
$727$			20.0877i			0.745011i	0.928030	+	0.372506i	$0.121501\pi$
$727$			20.0877i			0.745011i	−0.928030	+	0.372506i	$0.878499\pi$
$728$		0			0
$729$	25.9808	−	7.34847i	0.962250	−	0.272166i
$730$		0			0
$731$	−18.2667	+	10.5463i	−0.675617	+	0.390067i
$732$		0			0
$733$	35.4832	+	35.4832i	1.31060	+	1.31060i	0.920972	+	0.389628i	$0.127396\pi$
$733$	35.4832	+	35.4832i	1.31060	+	1.31060i	0.389628	+	0.920972i	$0.372604\pi$
$734$		0			0
$735$	1.13748	−	5.18744i	0.0419565	−	0.191342i
$736$		0			0
$737$	4.46910	+	2.58023i	0.164621	+	0.0950442i
$738$		0			0
$739$	22.4899	+	6.02615i	0.827305	+	0.221676i	0.647538	−	0.762034i	$-0.275799\pi$
$739$	22.4899	+	6.02615i	0.827305	+	0.221676i	0.179767	+	0.983709i	$0.442466\pi$
$740$		0			0
$741$	32.3329	+	29.7062i	1.18778	+	1.09129i
$742$		0			0
$743$	−25.8872	−	6.93645i	−0.949709	−	0.254474i	−0.249470	−	0.968382i	$-0.580257\pi$
$743$	−25.8872	−	6.93645i	−0.949709	−	0.254474i	−0.700239	+	0.713909i	$0.746923\pi$
$744$		0			0
$745$	5.58069	+	3.22201i	0.204461	+	0.118045i
$746$		0			0
$747$	−22.3214	+	26.8522i	−0.816696	+	0.982472i
$748$		0			0
$749$	2.75341	+	2.75341i	0.100607	+	0.100607i
$750$		0			0
$751$	15.4295	−	8.90822i	0.563030	−	0.325065i	−0.191331	−	0.981526i	$-0.561280\pi$
$751$	15.4295	−	8.90822i	0.563030	−	0.325065i	0.754361	+	0.656460i	$0.227947\pi$
$752$		0			0
$753$	−3.55874	+	6.87496i	−0.129688	+	0.250537i
$754$		0			0
$755$			4.01433i			0.146096i
$756$		0			0
$757$	−12.3906	−	21.4612i	−0.450345	−	0.780020i	0.548062	−	0.836438i	$-0.315366\pi$
$757$	−12.3906	−	21.4612i	−0.450345	−	0.780020i	−0.998407	+	0.0564171i	$0.982032\pi$
$758$		0			0
$759$	−6.40009	+	2.03419i	−0.232308	+	0.0738363i
$760$		0			0
$761$	14.6883	−	3.93572i	0.532451	−	0.142670i	0.0174313	−	0.999848i	$-0.494451\pi$
$761$	14.6883	−	3.93572i	0.532451	−	0.142670i	0.515020	+	0.857178i	$0.327785\pi$
$762$		0			0
$763$	−0.420159	+	0.727738i	−0.0152108	+	0.0263459i
$764$		0			0
$765$	−2.57845	−	6.98378i	−0.0932239	−	0.252499i
$766$		0			0
$767$	8.65515	+	8.71816i	0.312519	+	0.314794i
$768$		0			0
$769$	4.74330	−	17.7022i	0.171048	−	0.638359i	−0.826143	−	0.563460i	$-0.809470\pi$
$769$	4.74330	−	17.7022i	0.171048	−	0.638359i	0.997191	−	0.0748992i	$-0.0238635\pi$
$770$		0			0
$771$	−11.1597	−	17.4284i	−0.401907	−	0.627667i
$772$		0			0
$773$	8.71254	+	32.5156i	0.313368	+	1.16951i	0.925499	+	0.378750i	$0.123646\pi$
$773$	8.71254	+	32.5156i	0.313368	+	1.16951i	−0.612131	+	0.790757i	$0.709687\pi$
$774$		0			0
$775$	−4.97512	+	4.97512i	−0.178712	+	0.178712i
$776$		0			0
$777$	−0.159510	−	3.46967i	−0.00572240	−	0.124474i
$778$		0			0
$779$	53.6443			1.92201
$780$		0			0
$781$	−8.96837			−0.320914
$782$		0			0
$783$	−16.9352	+	13.1821i	−0.605216	+	0.471089i
$784$		0			0
$785$	3.20112	−	3.20112i	0.114253	−	0.114253i
$786$		0			0
$787$	2.43856	+	9.10084i	0.0869253	+	0.324410i	0.995672	−	0.0929388i	$-0.0296261\pi$
$787$	2.43856	+	9.10084i	0.0869253	+	0.324410i	−0.908746	+	0.417349i	$0.862959\pi$
$788$		0			0
$789$	4.01304	−	2.56962i	0.142868	−	0.0914810i
$790$		0			0
$791$	0.776944	−	2.89959i	0.0276249	−	0.103098i
$792$		0			0
$793$	37.8980	+	0.137455i	1.34580	+	0.00488116i
$794$		0			0
$795$	−2.06924	−	1.88735i	−0.0733886	−	0.0669374i
$796$		0			0
$797$	23.4250	−	40.5734i	0.829757	−	1.43718i	−0.0684710	−	0.997653i	$-0.521812\pi$
$797$	23.4250	−	40.5734i	0.829757	−	1.43718i	0.898228	−	0.439529i	$-0.144855\pi$
$798$		0			0
$799$	−28.4322	+	7.61838i	−1.00586	+	0.269519i
$800$		0			0
$801$	−7.14407	+	41.6387i	−0.252423	+	1.47123i
$802$		0			0
$803$	−1.45101	−	2.51322i	−0.0512050	−	0.0886896i
$804$		0			0
$805$		−	0.849740i		−	0.0299494i
$806$		0			0
$807$	9.59871	+	4.96866i	0.337891	+	0.174905i
$808$		0			0
$809$	35.1892	−	20.3165i	1.23719	−	0.714289i	0.268667	−	0.963233i	$-0.413417\pi$
$809$	35.1892	−	20.3165i	1.23719	−	0.714289i	0.968518	+	0.248944i	$0.0800835\pi$
$810$		0			0
$811$	−16.5531	−	16.5531i	−0.581257	−	0.581257i	0.353992	−	0.935249i	$-0.384824\pi$
$811$	−16.5531	−	16.5531i	−0.581257	−	0.581257i	−0.935249	+	0.353992i	$0.884824\pi$
$812$		0			0
$813$	−37.8431	−	8.29806i	−1.32722	−	0.291026i
$814$		0			0
$815$	−5.32844	−	3.07638i	−0.186647	−	0.107761i
$816$		0			0
$817$	25.5880	+	6.85628i	0.895210	+	0.239871i
$818$		0			0
$819$	2.00131	−	2.38986i	0.0699314	−	0.0835083i
$820$		0			0
$821$	−3.40155	−	0.911442i	−0.118715	−	0.0318095i	0.198972	−	0.980005i	$-0.436240\pi$
$821$	−3.40155	−	0.911442i	−0.118715	−	0.0318095i	−0.317687	+	0.948196i	$0.602906\pi$
$822$		0			0
$823$	−8.97945	−	5.18429i	−0.313004	−	0.180713i	0.335266	−	0.942124i	$-0.391174\pi$
$823$	−8.97945	−	5.18429i	−0.313004	−	0.180713i	−0.648270	+	0.761411i	$0.724507\pi$
$824$		0			0
$825$	−4.73695	−	1.03870i	−0.164919	−	0.0361627i
$826$		0			0
$827$	−5.61338	−	5.61338i	−0.195196	−	0.195196i	0.602741	−	0.797937i	$-0.294075\pi$
$827$	−5.61338	−	5.61338i	−0.195196	−	0.195196i	−0.797937	+	0.602741i	$0.794075\pi$
$828$		0			0
$829$	−1.76277	+	1.01774i	−0.0612237	+	0.0353475i	−0.530299	−	0.847810i	$-0.677920\pi$
$829$	−1.76277	+	1.01774i	−0.0612237	+	0.0353475i	0.469076	+	0.883158i	$0.344587\pi$
$830$		0			0
$831$	8.61135	+	4.45757i	0.298725	+	0.154631i
$832$		0			0
$833$			38.7220i			1.34164i
$834$		0			0
$835$	2.97257	+	5.14864i	0.102870	+	0.178176i
$836$		0			0
$837$	−6.07015	−	4.59138i	−0.209815	−	0.158701i
$838$		0			0
$839$	−15.0893	+	4.04316i	−0.520940	+	0.139585i	−0.509701	−	0.860351i	$-0.670244\pi$
$839$	−15.0893	+	4.04316i	−0.520940	+	0.139585i	−0.0112385	+	0.999937i	$0.503577\pi$
$840$		0			0
$841$	−5.97094	+	10.3420i	−0.205894	+	0.356620i
$842$		0			0
$843$	−15.9779	−	14.5734i	−0.550308	−	0.501933i
$844$		0			0
$845$	−1.45105	−	5.57692i	−0.0499178	−	0.191852i
$846$		0			0
$847$	−0.795114	+	2.96740i	−0.0273204	+	0.101961i
$848$		0			0
$849$	−10.0044	+	6.40603i	−0.343352	+	0.219854i
$850$		0			0
$851$	11.9802	+	44.7105i	0.410674	+	1.53266i
$852$		0			0
$853$	21.4461	−	21.4461i	0.734300	−	0.734300i	−0.237168	−	0.971469i	$-0.576219\pi$
$853$	21.4461	−	21.4461i	0.734300	−	0.734300i	0.971469	+	0.237168i	$0.0762193\pi$
$854$		0			0
$855$	−3.91226	+	8.49196i	−0.133797	+	0.290419i
$856$		0			0
$857$	−17.8872			−0.611017			−0.305508	−	0.952189i	$-0.598826\pi$
$857$	−17.8872			−0.611017			−0.305508	+	0.952189i	$0.598826\pi$
$858$		0			0
$859$	1.29875			0.0443127			0.0221564	−	0.999755i	$-0.492947\pi$
$859$	1.29875			0.0443127			0.0221564	+	0.999755i	$0.492947\pi$
$860$		0			0
$861$	−0.174898	−	3.80438i	−0.00596051	−	0.129653i
$862$		0			0
$863$	15.1285	−	15.1285i	0.514979	−	0.514979i	−0.401069	−	0.916048i	$-0.631361\pi$
$863$	15.1285	−	15.1285i	0.514979	−	0.514979i	0.916048	+	0.401069i	$0.131361\pi$
$864$		0			0
$865$	−0.126454	−	0.471931i	−0.00429955	−	0.0160461i
$866$		0			0
$867$	13.3927	+	20.9156i	0.454838	+	0.710331i
$868$		0			0
$869$	−0.167282	+	0.624307i	−0.00567467	+	0.0211781i
$870$		0			0
$871$	30.8636	−	8.15001i	1.04577	−	0.276153i
$872$		0			0
$873$	7.55334	−	2.78873i	0.255642	−	0.0943842i
$874$		0			0
$875$	0.626170	−	1.08456i	0.0211684	−	0.0366647i
$876$		0			0
$877$	21.4896	−	5.75813i	0.725654	−	0.194438i	0.122961	−	0.992412i	$-0.460761\pi$
$877$	21.4896	−	5.75813i	0.725654	−	0.194438i	0.602693	+	0.797973i	$0.294094\pi$
$878$		0			0
$879$	45.1549	−	14.3519i	1.52304	−	0.484077i
$880$		0			0
$881$	10.2514	+	17.7560i	0.345379	+	0.598214i	0.985423	−	0.170125i	$-0.0544171\pi$
$881$	10.2514	+	17.7560i	0.345379	+	0.598214i	−0.640044	+	0.768338i	$0.721084\pi$
$882$		0			0
$883$			27.7709i			0.934566i	0.884108	+	0.467283i	$0.154767\pi$
$883$			27.7709i			0.934566i	−0.884108	+	0.467283i	$0.845233\pi$
$884$		0			0
$885$	−1.20257	+	2.32318i	−0.0404239	+	0.0780929i
$886$		0			0
$887$	11.4360	−	6.60256i	0.383982	−	0.221692i	−0.295567	−	0.955322i	$-0.595509\pi$
$887$	11.4360	−	6.60256i	0.383982	−	0.221692i	0.679549	+	0.733630i	$0.262175\pi$
$888$		0			0
$889$	0.0492020	+	0.0492020i	0.00165018	+	0.00165018i
$890$		0			0
$891$	0.408961	−	5.22993i	0.0137007	−	0.175209i
$892$		0			0
$893$	32.0156	+	18.4842i	1.07136	+	0.618550i
$894$		0			0
$895$	−2.39586	−	0.641969i	−0.0800848	−	0.0214587i
$896$		0			0
$897$	−19.2302	+	36.8221i	−0.642076	+	1.22945i
$898$		0			0
$899$	5.84346	+	1.56575i	0.194890	+	0.0522207i
$900$		0			0
$901$	17.6849	+	10.2104i	0.589170	+	0.340157i
$902$		0			0
$903$	0.402813	−	1.83702i	0.0134048	−	0.0611322i
$904$		0			0
$905$	4.53514	+	4.53514i	0.150753	+	0.150753i
$906$		0			0
$907$	24.2160	−	13.9811i	0.804079	−	0.464235i	−0.0408168	−	0.999167i	$-0.512996\pi$
$907$	24.2160	−	13.9811i	0.804079	−	0.464235i	0.844895	+	0.534932i	$0.179663\pi$
$908$		0			0
$909$	−24.6655	−	34.8822i	−0.818101	−	1.15697i
$910$		0			0
$911$			33.2713i			1.10233i	0.834397	+	0.551164i	$0.185816\pi$
$911$			33.2713i			1.10233i	−0.834397	+	0.551164i	$0.814184\pi$
$912$		0			0
$913$	3.39218	+	5.87543i	0.112265	+	0.194448i
$914$		0			0
$915$	2.44450	+	7.69105i	0.0808127	+	0.254258i
$916$		0			0
$917$	2.25207	−	0.603439i	0.0743697	−	0.0199273i
$918$		0			0
$919$	7.21868	−	12.5031i	0.238122	−	0.412440i	−0.722053	−	0.691837i	$-0.756801\pi$
$919$	7.21868	−	12.5031i	0.238122	−	0.412440i	0.960175	+	0.279398i	$0.0901348\pi$
$920$		0			0
$921$	−25.5639	+	28.0276i	−0.842358	+	0.923542i
$922$		0			0
$923$	−39.3698	+	39.0852i	−1.29587	+	1.28650i
$924$		0			0
$925$	−8.65117	+	32.2866i	−0.284449	+	1.06158i
$926$		0			0
$927$	−1.26866	−	13.7688i	−0.0416682	−	0.452226i
$928$		0			0
$929$	−3.64463	−	13.6019i	−0.119576	−	0.446265i	0.880012	−	0.474951i	$-0.157534\pi$
$929$	−3.64463	−	13.6019i	−0.119576	−	0.446265i	−0.999588	+	0.0286860i	$0.990868\pi$
$930$		0			0
$931$	34.3880	−	34.3880i	1.12702	−	1.12702i
$932$		0			0
$933$	−55.0233	+	2.52957i	−1.80138	+	0.0828145i
$934$		0			0
$935$	−1.44642			−0.0473031
$936$		0			0
$937$	25.6098			0.836635			0.418317	−	0.908301i	$-0.362620\pi$
$937$	25.6098			0.836635			0.418317	+	0.908301i	$0.362620\pi$
$938$		0			0
$939$	41.0796	−	1.88854i	1.34058	−	0.0616303i
$940$		0			0
$941$	24.7798	−	24.7798i	0.807800	−	0.807800i	−0.176501	−	0.984300i	$-0.556478\pi$
$941$	24.7798	−	24.7798i	0.807800	−	0.807800i	0.984300	+	0.176501i	$0.0564779\pi$
$942$		0			0
$943$	13.1359	+	49.0237i	0.427762	+	1.59643i
$944$		0			0
$945$	0.614994	+	0.249766i	0.0200058	+	0.00812488i
$946$		0			0
$947$	−2.97658	+	11.1087i	−0.0967258	+	0.360986i	−0.997275	−	0.0737675i	$-0.976498\pi$
$947$	−2.97658	+	11.1087i	−0.0967258	+	0.360986i	0.900550	+	0.434753i	$0.143164\pi$
$948$		0			0
$949$	−17.3226	−	4.70898i	−0.562316	−	0.152860i
$950$		0			0
$951$	27.8860	−	30.5735i	0.904265	−	0.991414i
$952$		0			0
$953$	−24.2758	+	42.0469i	−0.786370	+	1.36203i	0.141807	+	0.989894i	$0.454709\pi$
$953$	−24.2758	+	42.0469i	−0.786370	+	1.36203i	−0.928177	+	0.372139i	$0.878624\pi$
$954$		0			0
$955$	2.85837	−	0.765897i	0.0924946	−	0.0247838i
$956$		0			0
$957$	1.26302	+	3.97380i	0.0408277	+	0.128455i
$958$		0			0
$959$	0.0119172	+	0.0206412i	0.000384826	+	0.000666539i
$960$		0			0
$961$		−	28.8545i		−	0.930792i
$962$		0			0
$963$	33.0975	−	23.4035i	1.06655	−	0.754167i
$964$		0			0
$965$	−2.33962	+	1.35078i	−0.0753150	+	0.0434831i
$966$		0			0
$967$	−15.4257	−	15.4257i	−0.496058	−	0.496058i	0.414150	−	0.910209i	$-0.364079\pi$
$967$	−15.4257	−	15.4257i	−0.496058	−	0.496058i	−0.910209	+	0.414150i	$0.864079\pi$
$968$		0			0
$969$	14.6017	−	66.5906i	0.469073	−	2.13920i
$970$		0			0
$971$	6.63550	+	3.83101i	0.212943	+	0.122943i	0.602679	−	0.797984i	$-0.294100\pi$
$971$	6.63550	+	3.83101i	0.212943	+	0.122943i	−0.389735	+	0.920927i	$0.627433\pi$
$972$		0			0
$973$	−1.73738	−	0.465530i	−0.0556979	−	0.0149242i
$974$		0			0
$975$	−25.3212	+	16.0844i	−0.810928	+	0.515115i
$976$		0			0
$977$	19.4850	+	5.22099i	0.623381	+	0.167034i	0.556664	−	0.830738i	$-0.312081\pi$
$977$	19.4850	+	5.22099i	0.623381	+	0.167034i	0.0667166	+	0.997772i	$0.478748\pi$
$978$		0			0
$979$	7.10859	+	4.10415i	0.227191	+	0.131169i
$980$		0			0
$981$	6.72710	+	5.59201i	0.214780	+	0.178539i
$982$		0			0
$983$	−0.922992	−	0.922992i	−0.0294389	−	0.0294389i	0.692234	−	0.721673i	$-0.256627\pi$
$983$	−0.922992	−	0.922992i	−0.0294389	−	0.0294389i	−0.721673	+	0.692234i	$0.756627\pi$
$984$		0			0
$985$	−5.67705	+	3.27765i	−0.180886	+	0.104435i
$986$		0			0
$987$	1.20649	−	2.33077i	0.0384031	−	0.0741891i
$988$		0			0
$989$			25.0629i			0.796953i
$990$		0			0
$991$	10.2983	+	17.8371i	0.327135	+	0.566614i	0.981942	−	0.189182i	$-0.0605836\pi$
$991$	10.2983	+	17.8371i	0.327135	+	0.566614i	−0.654807	+	0.755796i	$0.727250\pi$
$992$		0			0
$993$	27.2159	−	8.65024i	0.863672	−	0.274507i
$994$		0			0
$995$	6.62826	−	1.77604i	0.210130	−	0.0563041i
$996$		0			0
$997$	16.0894	−	27.8677i	0.509558	−	0.882580i	−0.490381	−	0.871508i	$-0.663142\pi$
$997$	16.0894	−	27.8677i	0.509558	−	0.882580i	0.999939	−	0.0110718i	$-0.00352433\pi$
$998$		0			0
$999$	−35.8803	−	4.47130i	−1.13520	−	0.141466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.d.401.1		16
3.2	odd	2	inner	624.2.cn.d.401.3		16
4.3	odd	2		78.2.k.a.11.2	✓	16
12.11	even	2		78.2.k.a.11.3	yes	16
13.6	odd	12	inner	624.2.cn.d.305.3		16
39.32	even	12	inner	624.2.cn.d.305.1		16
52.3	odd	6		1014.2.g.c.437.6		16
52.11	even	12		1014.2.g.d.239.6		16
52.15	even	12		1014.2.g.c.239.2		16
52.19	even	12		78.2.k.a.71.3	yes	16
52.23	odd	6		1014.2.g.d.437.2		16
156.11	odd	12		1014.2.g.d.239.2		16
156.23	even	6		1014.2.g.d.437.6		16
156.71	odd	12		78.2.k.a.71.2	yes	16
156.107	even	6		1014.2.g.c.437.2		16
156.119	odd	12		1014.2.g.c.239.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.11.2	✓	16	4.3	odd	2
78.2.k.a.11.3	yes	16	12.11	even	2
78.2.k.a.71.2	yes	16	156.71	odd	12
78.2.k.a.71.3	yes	16	52.19	even	12
624.2.cn.d.305.1		16	39.32	even	12	inner
624.2.cn.d.305.3		16	13.6	odd	12	inner
624.2.cn.d.401.1		16	1.1	even	1	trivial
624.2.cn.d.401.3		16	3.2	odd	2	inner
1014.2.g.c.239.2		16	52.15	even	12
1014.2.g.c.239.6		16	156.119	odd	12
1014.2.g.c.437.2		16	156.107	even	6
1014.2.g.c.437.6		16	52.3	odd	6
1014.2.g.d.239.2		16	156.11	odd	12
1014.2.g.d.239.6		16	52.11	even	12
1014.2.g.d.437.2		16	52.23	odd	6
1014.2.g.d.437.6		16	156.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73022 + 0.0795432i) q^{3} +(-0.313444 + 0.313444i) q^{5} +(0.0745867 + 0.278362i) q^{7} +(2.98735 - 0.275255i) q^{9} +O(q^{10})\)	\(q+(-1.73022 + 0.0795432i) q^{3} +(-0.313444 + 0.313444i) q^{5} +(0.0745867 + 0.278362i) q^{7} +(2.98735 - 0.275255i) q^{9} +(0.150860 - 0.563016i) q^{11} +(-1.79144 - 3.12902i) q^{13} +(0.517396 - 0.567261i) q^{15} +(-2.79907 + 4.84812i) q^{17} +(6.79127 - 1.81971i) q^{19} +(-0.151194 - 0.475695i) q^{21} +(3.32595 + 5.76071i) q^{23} +4.80351i q^{25} +(-5.14688 + 0.713876i) q^{27} +(3.57681 - 2.06507i) q^{29} +(1.03573 + 1.03573i) q^{31} +(-0.216237 + 0.986144i) q^{33} +(-0.110630 - 0.0638720i) q^{35} +(6.72147 + 1.80101i) q^{37} +(3.34848 + 5.27140i) q^{39} +(7.36988 + 1.97475i) q^{41} +(3.26299 + 1.88389i) q^{43} +(-0.850089 + 1.02264i) q^{45} +(3.71799 + 3.71799i) q^{47} +(5.99026 - 3.45848i) q^{49} +(4.45737 - 8.61098i) q^{51} -3.64778i q^{53} +(0.129188 + 0.223760i) q^{55} +(-11.6057 + 3.68871i) q^{57} +(-3.29111 + 0.881850i) q^{59} +(-5.25554 + 9.10286i) q^{61} +(0.299437 + 0.811032i) q^{63} +(1.54229 + 0.419256i) q^{65} +(-2.29144 + 8.55177i) q^{67} +(-6.21286 - 9.70277i) q^{69} +(-3.98229 - 14.8621i) q^{71} +(3.52053 - 3.52053i) q^{73} +(-0.382086 - 8.31114i) q^{75} +0.167974 q^{77} -1.10886 q^{79} +(8.84847 - 1.64456i) q^{81} +(-8.23032 + 8.23032i) q^{83} +(-0.642265 - 2.39697i) q^{85} +(-6.02442 + 3.85755i) q^{87} +(-3.64478 + 13.6025i) q^{89} +(0.737380 - 0.732051i) q^{91} +(-1.87442 - 1.70965i) q^{93} +(-1.55830 + 2.69906i) q^{95} +(2.59245 - 0.694645i) q^{97} +(0.295697 - 1.72345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73} + 96 q^{79} + 24 q^{81} - 24 q^{85} - 48 q^{87} + 16 q^{91} - 24 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Introduction

L-functions

Modular forms

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