LMFDB - Embedded newform 630.2.p.c.433.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(307,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("630.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.p (of order $4$, degree $2$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.2
Root			$-1.69230i$ of defining polynomial
Character	$\chi$	$=$	630.433
Dual form			630.2.p.c.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.489528 + 2.18183i) q^{5} +(2.19663 - 1.47472i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.489528 + 2.18183i) q^{5} +(2.19663 - 1.47472i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.88893 - 1.19663i) q^{10} -0.0296189 q^{11} +(0.585786 - 0.585786i) q^{13} +(-0.510472 + 2.59604i) q^{14} -1.00000 q^{16} +(1.72192 + 1.72192i) q^{17} +5.77786 q^{19} +(2.18183 - 0.489528i) q^{20} +(0.0209438 - 0.0209438i) q^{22} +(0.393270 + 0.393270i) q^{23} +(-4.52072 + 2.13613i) q^{25} +0.828427i q^{26} +(-1.47472 - 2.19663i) q^{28} -9.70636i q^{29} +6.39327i q^{31} +(0.707107 - 0.707107i) q^{32} -2.43516 q^{34} +(4.29289 + 4.07076i) q^{35} +(-3.72192 + 3.72192i) q^{37} +(-4.08557 + 4.08557i) q^{38} +(-1.19663 + 1.88893i) q^{40} -0.514280i q^{41} +(7.16246 + 7.16246i) q^{43} +0.0296189i q^{44} -0.556167 q^{46} +(7.77786 + 7.77786i) q^{47} +(2.65041 - 6.47884i) q^{49} +(1.68616 - 4.70711i) q^{50} +(-0.585786 - 0.585786i) q^{52} +(5.77786 + 5.77786i) q^{53} +(-0.0144993 - 0.0646234i) q^{55} +(2.59604 + 0.510472i) q^{56} +(6.86343 + 6.86343i) q^{58} -12.8070 q^{59} +10.7273i q^{61} +(-4.52072 - 4.52072i) q^{62} +1.00000i q^{64} +(1.56484 + 0.991325i) q^{65} +(2.39327 - 2.39327i) q^{67} +(1.72192 - 1.72192i) q^{68} +(-5.91399 + 0.157074i) q^{70} -6.64818 q^{71} +(5.12745 - 5.12745i) q^{73} -5.26358i q^{74} -5.77786i q^{76} +(-0.0650620 + 0.0436796i) q^{77} -9.86988i q^{79} +(-0.489528 - 2.18183i) q^{80} +(0.363651 + 0.363651i) q^{82} +(-0.150629 + 0.150629i) q^{83} +(-2.91399 + 4.59985i) q^{85} -10.1292 q^{86} +(-0.0209438 - 0.0209438i) q^{88} +4.38416 q^{89} +(0.422889 - 2.15063i) q^{91} +(0.393270 - 0.393270i) q^{92} -10.9996 q^{94} +(2.82843 + 12.6063i) q^{95} +(-2.47016 - 2.47016i) q^{97} +(2.70711 + 6.45535i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^7	$ 8 q + 8 q^{7} + 4 q^{10} - 8 q^{11} + 16 q^{13} - 8 q^{14} - 8 q^{16} + 12 q^{17} + 8 q^{19} + 4 q^{20} + 8 q^{22} - 16 q^{23} - 4 q^{25} - 4 q^{28} - 16 q^{34} + 40 q^{35} - 28 q^{37} - 4 q^{38} - 8 q^{46} + 24 q^{47} - 4 q^{49} - 16 q^{52} + 8 q^{53} - 28 q^{55} - 4 q^{56} - 12 q^{58} + 8 q^{59} - 4 q^{62} + 16 q^{65} + 12 q^{68} + 4 q^{70} - 8 q^{71} + 28 q^{73} - 44 q^{77} - 24 q^{82} - 16 q^{83} + 28 q^{85} - 8 q^{86} - 8 q^{88} - 64 q^{89} - 8 q^{91} - 16 q^{92} - 8 q^{94} + 28 q^{97} + 16 q^{98}+O(q^{100}) $ 8 * q + 8 * q^7 + 4 * q^10 - 8 * q^11 + 16 * q^13 - 8 * q^14 - 8 * q^16 + 12 * q^17 + 8 * q^19 + 4 * q^20 + 8 * q^22 - 16 * q^23 - 4 * q^25 - 4 * q^28 - 16 * q^34 + 40 * q^35 - 28 * q^37 - 4 * q^38 - 8 * q^46 + 24 * q^47 - 4 * q^49 - 16 * q^52 + 8 * q^53 - 28 * q^55 - 4 * q^56 - 12 * q^58 + 8 * q^59 - 4 * q^62 + 16 * q^65 + 12 * q^68 + 4 * q^70 - 8 * q^71 + 28 * q^73 - 44 * q^77 - 24 * q^82 - 16 * q^83 + 28 * q^85 - 8 * q^86 - 8 * q^88 - 64 * q^89 - 8 * q^91 - 16 * q^92 - 8 * q^94 + 28 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.489528	+	2.18183i	0.218924	+	0.975742i
$5$	0.489528	+	2.18183i	0.218924	+	0.975742i
$6$		0			0
$7$	2.19663	−	1.47472i	0.830250	−	0.557391i
$7$	2.19663	−	1.47472i	0.830250	−	0.557391i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−1.88893	−	1.19663i	−0.597333	−	0.378409i
$11$	−0.0296189			−0.00893045			−0.00446522	−	0.999990i	$-0.501421\pi$
$11$	−0.0296189			−0.00893045			−0.00446522	+	0.999990i	$0.501421\pi$
$12$		0			0
$13$	0.585786	−	0.585786i	0.162468	−	0.162468i	−0.621191	−	0.783659i	$-0.713351\pi$
$13$	0.585786	−	0.585786i	0.162468	−	0.162468i	0.783659	+	0.621191i	$0.213351\pi$
$14$	−0.510472	+	2.59604i	−0.136429	+	0.693821i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.72192	+	1.72192i	0.417626	+	0.417626i	0.884385	−	0.466759i	$-0.154578\pi$
$17$	1.72192	+	1.72192i	0.417626	+	0.417626i	−0.466759	+	0.884385i	$0.654578\pi$
$18$		0			0
$19$	5.77786			1.32553			0.662767	−	0.748826i	$-0.269382\pi$
$19$	5.77786			1.32553			0.662767	+	0.748826i	$0.269382\pi$
$20$	2.18183	−	0.489528i	0.487871	−	0.109462i
$21$		0			0
$22$	0.0209438	−	0.0209438i	0.00446522	−	0.00446522i
$23$	0.393270	+	0.393270i	0.0820024	+	0.0820024i	0.746918	−	0.664916i	$-0.231533\pi$
$23$	0.393270	+	0.393270i	0.0820024	+	0.0820024i	−0.664916	+	0.746918i	$0.731533\pi$
$24$		0			0
$25$	−4.52072	+	2.13613i	−0.904145	+	0.427226i
$26$			0.828427i			0.162468i
$27$		0			0
$28$	−1.47472	−	2.19663i	−0.278696	−	0.415125i
$29$		−	9.70636i		−	1.80243i	−0.433377	−	0.901213i	$-0.642678\pi$
$29$		−	9.70636i		−	1.80243i	0.433377	−	0.901213i	$-0.357322\pi$
$30$		0			0
$31$			6.39327i			1.14827i	0.818762	+	0.574133i	$0.194661\pi$
$31$			6.39327i			1.14827i	−0.818762	+	0.574133i	$0.805339\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	−2.43516			−0.417626
$35$	4.29289	+	4.07076i	0.725631	+	0.688084i
$36$		0			0
$37$	−3.72192	+	3.72192i	−0.611879	+	0.611879i	−0.943435	−	0.331556i	$-0.892426\pi$
$37$	−3.72192	+	3.72192i	−0.611879	+	0.611879i	0.331556	+	0.943435i	$0.392426\pi$
$38$	−4.08557	+	4.08557i	−0.662767	+	0.662767i
$39$		0			0
$40$	−1.19663	+	1.88893i	−0.189205	+	0.298666i
$41$		−	0.514280i		−	0.0803170i	−0.999193	−	0.0401585i	$-0.987214\pi$
$41$		−	0.514280i		−	0.0803170i	0.999193	−	0.0401585i	$-0.0127863\pi$
$42$		0			0
$43$	7.16246	+	7.16246i	1.09226	+	1.09226i	0.995286	+	0.0969783i	$0.0309177\pi$
$43$	7.16246	+	7.16246i	1.09226	+	1.09226i	0.0969783	+	0.995286i	$0.469082\pi$
$44$			0.0296189i			0.00446522i
$45$		0			0
$46$	−0.556167			−0.0820024
$47$	7.77786	+	7.77786i	1.13452	+	1.13452i	0.989417	+	0.145101i	$0.0463508\pi$
$47$	7.77786	+	7.77786i	1.13452	+	1.13452i	0.145101	+	0.989417i	$0.453649\pi$
$48$		0			0
$49$	2.65041	−	6.47884i	0.378630	−	0.925548i
$50$	1.68616	−	4.70711i	0.238459	−	0.665685i
$51$		0			0
$52$	−0.585786	−	0.585786i	−0.0812340	−	0.0812340i
$53$	5.77786	+	5.77786i	0.793651	+	0.793651i	0.982086	−	0.188435i	$-0.0603415\pi$
$53$	5.77786	+	5.77786i	0.793651	+	0.793651i	−0.188435	+	0.982086i	$0.560341\pi$
$54$		0			0
$55$	−0.0144993	−	0.0646234i	−0.00195509	−	0.00871381i
$56$	2.59604	+	0.510472i	0.346910	+	0.0682147i
$57$		0			0
$58$	6.86343	+	6.86343i	0.901213	+	0.901213i
$59$	−12.8070			−1.66734			−0.833668	−	0.552267i	$-0.813763\pi$
$59$	−12.8070			−1.66734			−0.833668	+	0.552267i	$0.813763\pi$
$60$		0			0
$61$			10.7273i			1.37349i	0.726898	+	0.686745i	$0.240961\pi$
$61$			10.7273i			1.37349i	−0.726898	+	0.686745i	$0.759039\pi$
$62$	−4.52072	−	4.52072i	−0.574133	−	0.574133i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	1.56484	+	0.991325i	0.194095	+	0.122959i
$66$		0			0
$67$	2.39327	−	2.39327i	0.292384	−	0.292384i	−0.545637	−	0.838022i	$-0.683712\pi$
$67$	2.39327	−	2.39327i	0.292384	−	0.292384i	0.838022	+	0.545637i	$0.183712\pi$
$68$	1.72192	−	1.72192i	0.208813	−	0.208813i
$69$		0			0
$70$	−5.91399	+	0.157074i	−0.706858	+	0.0187739i
$71$	−6.64818			−0.788994			−0.394497	−	0.918897i	$-0.629081\pi$
$71$	−6.64818			−0.788994			−0.394497	+	0.918897i	$0.629081\pi$
$72$		0			0
$73$	5.12745	−	5.12745i	0.600123	−	0.600123i	−0.340222	−	0.940345i	$-0.610502\pi$
$73$	5.12745	−	5.12745i	0.600123	−	0.600123i	0.940345	+	0.340222i	$0.110502\pi$
$74$		−	5.26358i		−	0.611879i
$75$		0			0
$76$		−	5.77786i		−	0.662767i
$77$	−0.0650620	+	0.0436796i	−0.00741450	+	0.00497775i
$78$		0			0
$79$		−	9.86988i		−	1.11045i	−0.831701	−	0.555224i	$-0.812633\pi$
$79$		−	9.86988i		−	1.11045i	0.831701	−	0.555224i	$-0.187367\pi$
$80$	−0.489528	−	2.18183i	−0.0547309	−	0.243935i
$81$		0			0
$82$	0.363651	+	0.363651i	0.0401585	+	0.0401585i
$83$	−0.150629	+	0.150629i	−0.0165337	+	0.0165337i	−0.715325	−	0.698792i	$-0.753721\pi$
$83$	−0.150629	+	0.150629i	−0.0165337	+	0.0165337i	0.698792	+	0.715325i	$0.253721\pi$
$84$		0			0
$85$	−2.91399	+	4.59985i	−0.316067	+	0.498923i
$86$	−10.1292			−1.09226
$87$		0			0
$88$	−0.0209438	−	0.0209438i	−0.00223261	−	0.00223261i
$89$	4.38416			0.464720			0.232360	−	0.972630i	$-0.425355\pi$
$89$	4.38416			0.464720			0.232360	+	0.972630i	$0.425355\pi$
$90$		0			0
$91$	0.422889	−	2.15063i	0.0443308	−	0.225447i
$92$	0.393270	−	0.393270i	0.0410012	−	0.0410012i
$93$		0			0
$94$	−10.9996			−1.13452
$95$	2.82843	+	12.6063i	0.290191	+	1.29338i
$96$		0			0
$97$	−2.47016	−	2.47016i	−0.250807	−	0.250807i	0.570494	−	0.821301i	$-0.306752\pi$
$97$	−2.47016	−	2.47016i	−0.250807	−	0.250807i	−0.821301	+	0.570494i	$0.806752\pi$
$98$	2.70711	+	6.45535i	0.273459	+	0.652089i
$99$		0			0
$100$	2.13613	+	4.52072i	0.213613	+	0.452072i
$101$		−	12.7897i		−	1.27262i	−0.771433	−	0.636311i	$-0.780459\pi$
$101$		−	12.7897i		−	1.27262i	0.771433	−	0.636311i	$-0.219541\pi$
$102$		0			0
$103$	−8.06462	+	8.06462i	−0.794631	+	0.794631i	−0.982243	−	0.187612i	$-0.939925\pi$
$103$	−8.06462	+	8.06462i	−0.794631	+	0.794631i	0.187612	+	0.982243i	$0.439925\pi$
$104$	0.828427			0.0812340
$105$		0			0
$106$	−8.17113			−0.793651
$107$	1.22170	−	1.22170i	0.118106	−	0.118106i	−0.645584	−	0.763690i	$-0.723386\pi$
$107$	1.22170	−	1.22170i	0.118106	−	0.118106i	0.763690	+	0.645584i	$0.223386\pi$
$108$		0			0
$109$		−	14.8984i		−	1.42701i	−0.700649	−	0.713506i	$-0.747106\pi$
$109$		−	14.8984i		−	1.42701i	0.700649	−	0.713506i	$-0.252894\pi$
$110$	0.0559482	+	0.0354431i	0.00533445	+	0.00337936i
$111$		0			0
$112$	−2.19663	+	1.47472i	−0.207562	+	0.139348i
$113$	0.0715065	+	0.0715065i	0.00672676	+	0.00672676i	0.710462	−	0.703735i	$-0.248486\pi$
$113$	0.0715065	+	0.0715065i	0.00672676	+	0.00672676i	−0.703735	+	0.710462i	$0.748486\pi$
$114$		0			0
$115$	−0.665529	+	1.05056i	−0.0620609	+	0.0979655i
$116$	−9.70636			−0.901213
$117$		0			0
$118$	9.05595	−	9.05595i	0.833668	−	0.833668i
$119$	6.32176	+	1.24308i	0.579515	+	0.113953i
$120$		0			0
$121$	−10.9991			−0.999920
$122$	−7.58535	−	7.58535i	−0.686745	−	0.686745i
$123$		0			0
$124$	6.39327			0.574133
$125$	−6.87368	−	8.81774i	−0.614801	−	0.788682i
$126$		0			0
$127$	6.15663	−	6.15663i	0.546313	−	0.546313i	−0.379059	−	0.925372i	$-0.623752\pi$
$127$	6.15663	−	6.15663i	0.546313	−	0.546313i	0.925372	+	0.379059i	$0.123752\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−1.80748	+	0.405538i	−0.158527	+	0.0355681i
$131$		−	4.52401i		−	0.395265i	−0.980276	−	0.197632i	$-0.936675\pi$
$131$		−	4.52401i		−	0.395265i	0.980276	−	0.197632i	$-0.0633253\pi$
$132$		0			0
$133$	12.6919	−	8.52072i	1.10052	−	0.738841i
$134$			3.38459i			0.292384i
$135$		0			0
$136$			2.43516i			0.208813i
$137$	−5.58535	+	5.58535i	−0.477188	+	0.477188i	−0.904231	−	0.427043i	$-0.859555\pi$
$137$	−5.58535	+	5.58535i	−0.477188	+	0.477188i	0.427043	+	0.904231i	$0.359555\pi$
$138$		0			0
$139$	−16.6063			−1.40853			−0.704264	−	0.709939i	$-0.748723\pi$
$139$	−16.6063			−1.40853			−0.704264	+	0.709939i	$0.748723\pi$
$140$	4.07076	−	4.29289i	0.344042	−	0.362816i
$141$		0			0
$142$	4.70097	−	4.70097i	0.394497	−	0.394497i
$143$	−0.0173504	+	0.0173504i	−0.00145091	+	0.00145091i
$144$		0			0
$145$	21.1776	−	4.75154i	1.75870	−	0.394594i
$146$			7.25132i			0.600123i
$147$		0			0
$148$	3.72192	+	3.72192i	0.305940	+	0.305940i
$149$		−	7.80748i		−	0.639614i	−0.947483	−	0.319807i	$-0.896382\pi$
$149$		−	7.80748i		−	0.639614i	0.947483	−	0.319807i	$-0.103618\pi$
$150$		0			0
$151$	0.870315			0.0708252			0.0354126	−	0.999373i	$-0.488725\pi$
$151$	0.870315			0.0708252			0.0354126	+	0.999373i	$0.488725\pi$
$152$	4.08557	+	4.08557i	0.331383	+	0.331383i
$153$		0			0
$154$	0.0151196	−	0.0768919i	0.00121838	−	0.00619613i
$155$	−13.9490	+	3.12969i	−1.12041	+	0.251382i
$156$		0			0
$157$	−15.8403	−	15.8403i	−1.26419	−	1.26419i	−0.949043	−	0.315147i	$-0.897946\pi$
$157$	−15.8403	−	15.8403i	−1.26419	−	1.26419i	−0.315147	−	0.949043i	$-0.602054\pi$
$158$	6.97906	+	6.97906i	0.555224	+	0.555224i
$159$		0			0
$160$	1.88893	+	1.19663i	0.149333	+	0.0946023i
$161$	1.44383	+	0.283908i	0.113790	+	0.0223751i
$162$		0			0
$163$	2.70742	+	2.70742i	0.212061	+	0.212061i	0.805143	−	0.593081i	$-0.202089\pi$
$163$	2.70742	+	2.70742i	0.212061	+	0.212061i	−0.593081	+	0.805143i	$0.702089\pi$
$164$	−0.514280			−0.0401585
$165$		0			0
$166$		−	0.213022i		−	0.0165337i
$167$	−13.7779	−	13.7779i	−1.06616	−	1.06616i	−0.997650	−	0.0685129i	$-0.978175\pi$
$167$	−13.7779	−	13.7779i	−1.06616	−	1.06616i	−0.0685129	−	0.997650i	$-0.521825\pi$
$168$		0			0
$169$			12.3137i			0.947208i
$170$	−1.19208	−	5.31309i	−0.0914282	−	0.407495i
$171$		0			0
$172$	7.16246	−	7.16246i	0.546132	−	0.546132i
$173$	10.3077	−	10.3077i	0.783680	−	0.783680i	−0.196770	−	0.980450i	$-0.563045\pi$
$173$	10.3077	−	10.3077i	0.783680	−	0.783680i	0.980450	+	0.196770i	$0.0630451\pi$
$174$		0			0
$175$	−6.78019	+	11.3591i	−0.512534	+	0.858667i
$176$	0.0296189			0.00223261
$177$		0			0
$178$	−3.10007	+	3.10007i	−0.232360	+	0.232360i
$179$		−	17.2422i		−	1.28874i	−0.764713	−	0.644371i	$-0.777119\pi$
$179$		−	17.2422i		−	1.28874i	0.764713	−	0.644371i	$-0.222881\pi$
$180$		0			0
$181$		−	22.4015i		−	1.66509i	−0.553957	−	0.832545i	$-0.686883\pi$
$181$		−	22.4015i		−	1.66509i	0.553957	−	0.832545i	$-0.313117\pi$
$182$	1.22170	+	1.81975i	0.0905582	+	0.134889i
$183$		0			0
$184$			0.556167i			0.0410012i
$185$	−9.94255	−	6.29859i	−0.730991	−	0.463081i
$186$		0			0
$187$	−0.0510013	−	0.0510013i	−0.00372959	−	0.00372959i
$188$	7.77786	−	7.77786i	0.567259	−	0.567259i
$189$		0			0
$190$	−10.9140	−	6.91399i	−0.791784	−	0.501594i
$191$	22.5644			1.63270			0.816351	−	0.577555i	$-0.195993\pi$
$191$	22.5644			1.63270			0.816351	+	0.577555i	$0.195993\pi$
$192$		0			0
$193$	4.94076	+	4.94076i	0.355644	+	0.355644i	0.862204	−	0.506561i	$-0.169083\pi$
$193$	4.94076	+	4.94076i	0.355644	+	0.355644i	−0.506561	+	0.862204i	$0.669083\pi$
$194$	3.49334			0.250807
$195$		0			0
$196$	−6.47884	−	2.65041i	−0.462774	−	0.189315i
$197$	6.64818	−	6.64818i	0.473663	−	0.473663i	−0.429435	−	0.903098i	$-0.641287\pi$
$197$	6.64818	−	6.64818i	0.473663	−	0.473663i	0.903098	+	0.429435i	$0.141287\pi$
$198$		0			0
$199$	12.2631			0.869311			0.434656	−	0.900597i	$-0.356870\pi$
$199$	12.2631			0.869311			0.434656	+	0.900597i	$0.356870\pi$
$200$	−4.70711	−	1.68616i	−0.332843	−	0.119230i
$201$		0			0
$202$	9.04368	+	9.04368i	0.636311	+	0.636311i
$203$	−14.3141	−	21.3213i	−1.00466	−	1.49646i
$204$		0			0
$205$	1.12207	−	0.251755i	0.0783687	−	0.0175833i
$206$		−	11.4051i		−	0.794631i
$207$		0			0
$208$	−0.585786	+	0.585786i	−0.0406170	+	0.0406170i
$209$	−0.171134			−0.0118376
$210$		0			0
$211$	−4.62829			−0.318625			−0.159312	−	0.987228i	$-0.550928\pi$
$211$	−4.62829			−0.318625			−0.159312	+	0.987228i	$0.550928\pi$
$212$	5.77786	−	5.77786i	0.396825	−	0.396825i
$213$		0			0
$214$			1.72774i			0.118106i
$215$	−12.1210	+	19.1335i	−0.826646	+	1.30489i
$216$		0			0
$217$	9.42827	+	14.0437i	0.640033	+	0.953347i
$218$	10.5348	+	10.5348i	0.713506	+	0.713506i
$219$		0			0
$220$	−0.0646234	+	0.0144993i	−0.00435691	+	0.000977543i
$221$	2.01735			0.135702
$222$		0			0
$223$	−18.2266	+	18.2266i	−1.22055	+	1.22055i	−0.253108	+	0.967438i	$0.581453\pi$
$223$	−18.2266	+	18.2266i	−1.22055	+	1.22055i	−0.967438	+	0.253108i	$0.918547\pi$
$224$	0.510472	−	2.59604i	0.0341073	−	0.173455i
$225$		0			0
$226$	−0.101125			−0.00672676
$227$	−8.89844	−	8.89844i	−0.590610	−	0.590610i	0.347186	−	0.937796i	$-0.387137\pi$
$227$	−8.89844	−	8.89844i	−0.590610	−	0.590610i	−0.937796	+	0.347186i	$0.887137\pi$
$228$		0			0
$229$	−13.3137			−0.879795			−0.439897	−	0.898048i	$-0.644985\pi$
$229$	−13.3137			−0.879795			−0.439897	+	0.898048i	$0.644985\pi$
$230$	−0.272260	−	1.21346i	−0.0179523	−	0.0800132i
$231$		0			0
$232$	6.86343	−	6.86343i	0.450606	−	0.450606i
$233$	2.18340	+	2.18340i	0.143039	+	0.143039i	0.775000	−	0.631961i	$-0.217750\pi$
$233$	2.18340	+	2.18340i	0.143039	+	0.143039i	−0.631961	+	0.775000i	$0.717750\pi$
$234$		0			0
$235$	−13.1625	+	20.7774i	−0.858624	+	1.35537i
$236$			12.8070i			0.833668i
$237$		0			0
$238$	−5.34915	+	3.59117i	−0.346734	+	0.232781i
$239$			18.1201i			1.17209i	0.810277	+	0.586047i	$0.199317\pi$
$239$			18.1201i			1.17209i	−0.810277	+	0.586047i	$0.800683\pi$
$240$		0			0
$241$		−	19.6257i		−	1.26420i	−0.774885	−	0.632102i	$-0.782192\pi$
$241$		−	19.6257i		−	1.26420i	0.774885	−	0.632102i	$-0.217808\pi$
$242$	7.77755	−	7.77755i	0.499960	−	0.499960i
$243$		0			0
$244$	10.7273			0.686745
$245$	15.4331	+	2.61116i	0.985987	+	0.166821i
$246$		0			0
$247$	3.38459	−	3.38459i	0.215357	−	0.215357i
$248$	−4.52072	+	4.52072i	−0.287066	+	0.287066i
$249$		0			0
$250$	11.0955	+	1.37465i	0.701742	+	0.0869406i
$251$			28.7478i			1.81455i	0.420543	+	0.907273i	$0.361840\pi$
$251$			28.7478i			1.81455i	−0.420543	+	0.907273i	$0.638160\pi$
$252$		0			0
$253$	−0.0116482	−	0.0116482i	−0.000732318	−	0.000732318i
$254$			8.70680i			0.546313i
$255$		0			0
$256$	1.00000			0.0625000
$257$	15.5789	+	15.5789i	0.971785	+	0.971785i	0.999613	−	0.0278275i	$-0.00885890\pi$
$257$	15.5789	+	15.5789i	0.971785	+	0.971785i	−0.0278275	+	0.999613i	$0.508859\pi$
$258$		0			0
$259$	−2.68691	+	13.6645i	−0.166957	+	0.849069i
$260$	0.991325	−	1.56484i	0.0614794	−	0.0970474i
$261$		0			0
$262$	3.19896	+	3.19896i	0.197632	+	0.197632i
$263$	−7.34271	−	7.34271i	−0.452771	−	0.452771i	0.443502	−	0.896273i	$-0.353736\pi$
$263$	−7.34271	−	7.34271i	−0.452771	−	0.452771i	−0.896273	+	0.443502i	$0.853736\pi$
$264$		0			0
$265$	−9.77786	+	15.4347i	−0.600649	+	0.948147i
$266$	−2.94944	+	14.9996i	−0.180842	+	0.919682i
$267$		0			0
$268$	−2.39327	−	2.39327i	−0.146192	−	0.146192i
$269$	−16.6069			−1.01254			−0.506271	−	0.862375i	$-0.668976\pi$
$269$	−16.6069			−1.01254			−0.506271	+	0.862375i	$0.668976\pi$
$270$		0			0
$271$			9.90353i			0.601596i	0.953688	+	0.300798i	$0.0972531\pi$
$271$			9.90353i			0.601596i	−0.953688	+	0.300798i	$0.902747\pi$
$272$	−1.72192	−	1.72192i	−0.104407	−	0.104407i
$273$		0			0
$274$		−	7.89887i		−	0.477188i
$275$	0.133899	−	0.0632699i	0.00807442	−	0.00381532i
$276$		0			0
$277$	2.93538	−	2.93538i	0.176370	−	0.176370i	−0.613402	−	0.789771i	$-0.710199\pi$
$277$	2.93538	−	2.93538i	0.176370	−	0.176370i	0.789771	+	0.613402i	$0.210199\pi$
$278$	11.7424	−	11.7424i	0.704264	−	0.704264i
$279$		0			0
$280$	0.157074	+	5.91399i	0.00938694	+	0.353429i
$281$	4.70995			0.280972			0.140486	−	0.990083i	$-0.455133\pi$
$281$	4.70995			0.280972			0.140486	+	0.990083i	$0.455133\pi$
$282$		0			0
$283$	−13.0588	+	13.0588i	−0.776265	+	0.776265i	−0.979194	−	0.202929i	$-0.934954\pi$
$283$	−13.0588	+	13.0588i	−0.776265	+	0.776265i	0.202929	+	0.979194i	$0.434954\pi$
$284$			6.64818i			0.394497i
$285$		0			0
$286$		−	0.0245371i		−	0.00145091i
$287$	−0.758418	−	1.12969i	−0.0447680	−	0.0666832i
$288$		0			0
$289$		−	11.0700i		−	0.651177i
$290$	−11.6150	+	18.3347i	−0.682054	+	1.07665i
$291$		0			0
$292$	−5.12745	−	5.12745i	−0.300062	−	0.300062i
$293$	−16.8844	+	16.8844i	−0.986396	+	0.986396i	−0.999909	−	0.0135130i	$-0.995699\pi$
$293$	−16.8844	+	16.8844i	−0.986396	+	0.986396i	0.0135130	+	0.999909i	$0.495699\pi$
$294$		0			0
$295$	−6.26941	−	27.9427i	−0.365019	−	1.62689i
$296$	−5.26358			−0.305940
$297$		0			0
$298$	5.52072	+	5.52072i	0.319807	+	0.319807i
$299$	0.460744			0.0266455
$300$		0			0
$301$	26.2959	+	5.17070i	1.51567	+	0.298034i
$302$	−0.615405	+	0.615405i	−0.0354126	+	0.0354126i
$303$		0			0
$304$	−5.77786			−0.331383
$305$	−23.4051	+	5.25132i	−1.34017	+	0.300689i
$306$		0			0
$307$	11.5185	+	11.5185i	0.657395	+	0.657395i	0.954763	−	0.297368i	$-0.0961088\pi$
$307$	11.5185	+	11.5185i	0.657395	+	0.657395i	−0.297368	+	0.954763i	$0.596109\pi$
$308$	0.0436796	+	0.0650620i	0.00248888	+	0.00370725i
$309$		0			0
$310$	7.65041	−	12.0765i	0.434514	−	0.685896i
$311$			9.59762i			0.544231i	0.962265	+	0.272115i	$0.0877233\pi$
$311$			9.59762i			0.544231i	−0.962265	+	0.272115i	$0.912277\pi$
$312$		0			0
$313$	0.529400	−	0.529400i	0.0299234	−	0.0299234i	−0.691987	−	0.721910i	$-0.743264\pi$
$313$	0.529400	−	0.529400i	0.0299234	−	0.0299234i	0.721910	+	0.691987i	$0.243264\pi$
$314$	22.4015			1.26419
$315$		0			0
$316$	−9.86988			−0.555224
$317$	−19.8576	+	19.8576i	−1.11531	+	1.11531i	−0.122895	+	0.992420i	$0.539218\pi$
$317$	−19.8576	+	19.8576i	−1.11531	+	1.11531i	−0.992420	+	0.122895i	$0.960782\pi$
$318$		0			0
$319$			0.287492i			0.0160965i
$320$	−2.18183	+	0.489528i	−0.121968	+	0.0273655i
$321$		0			0
$322$	−1.22170	+	0.820191i	−0.0680825	+	0.0457074i
$323$	9.94900	+	9.94900i	0.553577	+	0.553577i
$324$		0			0
$325$	−1.39686	+	3.89949i	−0.0774840	+	0.216305i
$326$	−3.82887			−0.212061
$327$		0			0
$328$	0.363651	−	0.363651i	0.0200793	−	0.0200793i
$329$	28.5553	+	5.61497i	1.57430	+	0.309563i
$330$		0			0
$331$	4.64353			0.255231			0.127616	−	0.991824i	$-0.459268\pi$
$331$	4.64353			0.255231			0.127616	+	0.991824i	$0.459268\pi$
$332$	0.150629	+	0.150629i	0.00826685	+	0.00826685i
$333$		0			0
$334$	19.4848			1.06616
$335$	6.39327	+	4.05012i	0.349302	+	0.221282i
$336$		0			0
$337$	7.05924	−	7.05924i	0.384541	−	0.384541i	−0.488194	−	0.872735i	$-0.662344\pi$
$337$	7.05924	−	7.05924i	0.384541	−	0.384541i	0.872735	+	0.488194i	$0.162344\pi$
$338$	−8.70711	−	8.70711i	−0.473604	−	0.473604i
$339$		0			0
$340$	4.59985	+	2.91399i	0.249462	+	0.158034i
$341$		−	0.189362i		−	0.0102545i
$342$		0			0
$343$	−3.73248	−	18.1402i	−0.201535	−	0.979481i
$344$			10.1292i			0.546132i
$345$		0			0
$346$			14.5773i			0.783680i
$347$	23.4925	−	23.4925i	1.26114	−	1.26114i	0.310601	−	0.950540i	$-0.399470\pi$
$347$	23.4925	−	23.4925i	1.26114	−	1.26114i	0.950540	−	0.310601i	$-0.100530\pi$
$348$		0			0
$349$	−20.1819			−1.08031			−0.540156	−	0.841565i	$-0.681635\pi$
$349$	−20.1819			−1.08031			−0.540156	+	0.841565i	$0.681635\pi$
$350$	−3.23777	−	12.8264i	−0.173066	−	0.685601i
$351$		0			0
$352$	−0.0209438	+	0.0209438i	−0.00111631	+	0.00111631i
$353$	7.44966	−	7.44966i	0.396505	−	0.396505i	−0.480493	−	0.876998i	$-0.659542\pi$
$353$	7.44966	−	7.44966i	0.396505	−	0.396505i	0.876998	+	0.480493i	$0.159542\pi$
$354$		0			0
$355$	−3.25447	−	14.5052i	−0.172729	−	0.769854i
$356$		−	4.38416i		−	0.232360i
$357$		0			0
$358$	12.1921	+	12.1921i	0.644371	+	0.644371i
$359$			16.6063i			0.876447i	0.898866	+	0.438223i	$0.144392\pi$
$359$			16.6063i			0.876447i	−0.898866	+	0.438223i	$0.855608\pi$
$360$		0			0
$361$	14.3837			0.757038
$362$	15.8403	+	15.8403i	0.832545	+	0.832545i
$363$		0			0
$364$	−2.15063	−	0.422889i	−0.112724	−	0.0221654i
$365$	13.6972	+	8.67718i	0.716947	+	0.454184i
$366$		0			0
$367$	−2.87317	−	2.87317i	−0.149978	−	0.149978i	0.628130	−	0.778108i	$-0.283821\pi$
$367$	−2.87317	−	2.87317i	−0.149978	−	0.149978i	−0.778108	+	0.628130i	$0.783821\pi$
$368$	−0.393270	−	0.393270i	−0.0205006	−	0.0205006i
$369$		0			0
$370$	11.4842	−	2.57667i	0.597036	−	0.133955i
$371$	21.2126	+	4.17113i	1.10130	+	0.216554i
$372$		0			0
$373$	−1.55078	−	1.55078i	−0.0802964	−	0.0802964i	0.665818	−	0.746114i	$-0.268083\pi$
$373$	−1.55078	−	1.55078i	−0.0802964	−	0.0802964i	−0.746114	+	0.665818i	$0.768083\pi$
$374$	0.0721268			0.00372959
$375$		0			0
$376$			10.9996i			0.567259i
$377$	−5.68585	−	5.68585i	−0.292836	−	0.292836i
$378$		0			0
$379$		−	6.92743i		−	0.355838i	−0.984045	−	0.177919i	$-0.943063\pi$
$379$		−	6.92743i		−	0.355838i	0.984045	−	0.177919i	$-0.0569366\pi$
$380$	12.6063	−	2.82843i	0.646689	−	0.145095i
$381$		0			0
$382$	−15.9554	+	15.9554i	−0.816351	+	0.816351i
$383$	3.46372	−	3.46372i	0.176988	−	0.176988i	−0.613054	−	0.790041i	$-0.710059\pi$
$383$	3.46372	−	3.46372i	0.176988	−	0.176988i	0.790041	+	0.613054i	$0.210059\pi$
$384$		0			0
$385$	−0.127151	−	0.120572i	−0.00648021	−	0.00614489i
$386$	−6.98729			−0.355644
$387$		0			0
$388$	−2.47016	+	2.47016i	−0.125403	+	0.125403i
$389$		−	24.9198i		−	1.26348i	−0.775178	−	0.631742i	$-0.782340\pi$
$389$		−	24.9198i		−	1.26348i	0.775178	−	0.631742i	$-0.217660\pi$
$390$		0			0
$391$			1.35436i			0.0684927i
$392$	6.45535	−	2.70711i	0.326045	−	0.136730i
$393$		0			0
$394$			9.40194i			0.473663i
$395$	21.5343	−	4.83158i	1.08351	−	0.243103i
$396$		0			0
$397$	−13.6562	−	13.6562i	−0.685387	−	0.685387i	0.275822	−	0.961209i	$-0.411050\pi$
$397$	−13.6562	−	13.6562i	−0.685387	−	0.685387i	−0.961209	+	0.275822i	$0.911050\pi$
$398$	−8.67135	+	8.67135i	−0.434656	+	0.434656i
$399$		0			0
$400$	4.52072	−	2.13613i	0.226036	−	0.106806i
$401$	−13.0125			−0.649811			−0.324905	−	0.945747i	$-0.605332\pi$
$401$	−13.0125			−0.649811			−0.324905	+	0.945747i	$0.605332\pi$
$402$		0			0
$403$	3.74509	+	3.74509i	0.186556	+	0.186556i
$404$	−12.7897			−0.636311
$405$		0			0
$406$	25.1981	+	4.95482i	1.25056	+	0.245904i
$407$	0.110239	−	0.110239i	0.00546436	−	0.00546436i
$408$		0			0
$409$	10.6154			0.524898			0.262449	−	0.964946i	$-0.415470\pi$
$409$	10.6154			0.524898			0.262449	+	0.964946i	$0.415470\pi$
$410$	−0.615405	+	0.971440i	−0.0303927	+	0.0479760i
$411$		0			0
$412$	8.06462	+	8.06462i	0.397315	+	0.397315i
$413$	−28.1324	+	18.8868i	−1.38430	+	0.929358i
$414$		0			0
$415$	−0.402384	−	0.254909i	−0.0197522	−	0.0125130i
$416$		−	0.828427i		−	0.0406170i
$417$		0			0
$418$	0.121010	−	0.121010i	0.00591880	−	0.00591880i
$419$	−9.83560			−0.480501			−0.240250	−	0.970711i	$-0.577230\pi$
$419$	−9.83560			−0.480501			−0.240250	+	0.970711i	$0.577230\pi$
$420$		0			0
$421$	−32.5963			−1.58865			−0.794323	−	0.607495i	$-0.792174\pi$
$421$	−32.5963			−1.58865			−0.794323	+	0.607495i	$0.792174\pi$
$422$	3.27270	−	3.27270i	0.159312	−	0.159312i
$423$		0			0
$424$			8.17113i			0.396825i
$425$	−11.4625	−	4.10607i	−0.556015	−	0.199174i
$426$		0			0
$427$	15.8198	+	23.5640i	0.765571	+	1.14034i
$428$	−1.22170	−	1.22170i	−0.0590530	−	0.0590530i
$429$		0			0
$430$	−4.95855	−	22.1002i	−0.239123	−	1.06577i
$431$	29.3746			1.41492			0.707462	−	0.706751i	$-0.249840\pi$
$431$	29.3746			1.41492			0.707462	+	0.706751i	$0.249840\pi$
$432$		0			0
$433$	17.1266	−	17.1266i	0.823051	−	0.823051i	−0.163494	−	0.986544i	$-0.552276\pi$
$433$	17.1266	−	17.1266i	0.823051	−	0.823051i	0.986544	+	0.163494i	$0.0522763\pi$
$434$	−16.5972	−	3.26358i	−0.796690	−	0.156657i
$435$		0			0
$436$	−14.8984			−0.713506
$437$	2.27226	+	2.27226i	0.108697	+	0.108697i
$438$		0			0
$439$	2.29872			0.109712			0.0548561	−	0.998494i	$-0.482530\pi$
$439$	2.29872			0.109712			0.0548561	+	0.998494i	$0.482530\pi$
$440$	0.0354431	−	0.0559482i	0.00168968	−	0.00266722i
$441$		0			0
$442$	−1.42648	+	1.42648i	−0.0678508	+	0.0678508i
$443$	1.39433	+	1.39433i	0.0662466	+	0.0662466i	0.739454	−	0.673207i	$-0.235084\pi$
$443$	1.39433	+	1.39433i	0.0662466	+	0.0662466i	−0.673207	+	0.739454i	$0.735084\pi$
$444$		0			0
$445$	2.14617	+	9.56546i	0.101738	+	0.453446i
$446$		−	25.7764i		−	1.22055i
$447$		0			0
$448$	1.47472	+	2.19663i	0.0696739	+	0.103781i
$449$		−	6.72730i		−	0.317481i	−0.987320	−	0.158740i	$-0.949257\pi$
$449$		−	6.72730i		−	0.317481i	0.987320	−	0.158740i	$-0.0507433\pi$
$450$		0			0
$451$			0.0152324i			0.000717267i
$452$	0.0715065	−	0.0715065i	0.00336338	−	0.00336338i
$453$		0			0
$454$	12.5843			0.590610
$455$	4.89931	−	0.130124i	0.229683	−	0.00610031i
$456$		0			0
$457$	−16.6569	+	16.6569i	−0.779175	+	0.779175i	−0.979690	−	0.200516i	$-0.935738\pi$
$457$	−16.6569	+	16.6569i	−0.779175	+	0.779175i	0.200516	+	0.979690i	$0.435738\pi$
$458$	9.41421	−	9.41421i	0.439897	−	0.439897i
$459$		0			0
$460$	1.05056	+	0.665529i	0.0489827	+	0.0310305i
$461$		−	11.5655i		−	0.538657i	−0.963048	−	0.269329i	$-0.913198\pi$
$461$		−	11.5655i		−	0.538657i	0.963048	−	0.269329i	$-0.0868018\pi$
$462$		0			0
$463$	−12.4160	−	12.4160i	−0.577021	−	0.577021i	0.357061	−	0.934081i	$-0.383779\pi$
$463$	−12.4160	−	12.4160i	−0.577021	−	0.577021i	−0.934081	+	0.357061i	$0.883779\pi$
$464$			9.70636i			0.450606i
$465$		0			0
$466$	−3.08780			−0.143039
$467$	−6.14975	−	6.14975i	−0.284577	−	0.284577i	0.550355	−	0.834931i	$-0.314493\pi$
$467$	−6.14975	−	6.14975i	−0.284577	−	0.284577i	−0.834931	+	0.550355i	$0.814493\pi$
$468$		0			0
$469$	1.72774	−	8.78654i	0.0797796	−	0.405725i
$470$	−5.38459	−	23.9991i	−0.248373	−	1.10700i
$471$		0			0
$472$	−9.05595	−	9.05595i	−0.416834	−	0.416834i
$473$	−0.212144	−	0.212144i	−0.00975441	−	0.00975441i
$474$		0			0
$475$	−26.1201	+	12.3423i	−1.19847	+	0.566302i
$476$	1.24308	−	6.32176i	0.0569764	−	0.289758i
$477$		0			0
$478$	−12.8129	−	12.8129i	−0.586047	−	0.586047i
$479$	−6.82843			−0.311999			−0.155999	−	0.987757i	$-0.549860\pi$
$479$	−6.82843			−0.311999			−0.155999	+	0.987757i	$0.549860\pi$
$480$		0			0
$481$			4.36050i			0.198822i
$482$	13.8775	+	13.8775i	0.632102	+	0.632102i
$483$		0			0
$484$			10.9991i			0.499960i
$485$	4.18025	−	6.59868i	0.189815	−	0.299630i
$486$		0			0
$487$	−21.7124	+	21.7124i	−0.983881	+	0.983881i	−0.999872	−	0.0159910i	$-0.994910\pi$
$487$	−21.7124	+	21.7124i	−0.983881	+	0.983881i	0.0159910	+	0.999872i	$0.494910\pi$
$488$	−7.58535	+	7.58535i	−0.343373	+	0.343373i
$489$		0			0
$490$	−12.7592	+	9.06651i	−0.576404	+	0.409583i
$491$	−14.8991			−0.672385			−0.336192	−	0.941793i	$-0.609139\pi$
$491$	−14.8991			−0.672385			−0.336192	+	0.941793i	$0.609139\pi$
$492$		0			0
$493$	16.7135	−	16.7135i	0.752740	−	0.752740i
$494$			4.78654i			0.215357i
$495$		0			0
$496$		−	6.39327i		−	0.287066i
$497$	−14.6036	+	9.80419i	−0.655062	+	0.439778i
$498$		0			0
$499$			32.7928i			1.46801i	0.679144	+	0.734005i	$0.262351\pi$
$499$			32.7928i			1.46801i	−0.679144	+	0.734005i	$0.737649\pi$
$500$	−8.81774	+	6.87368i	−0.394341	+	0.307400i
$501$		0			0
$502$	−20.3278	−	20.3278i	−0.907273	−	0.907273i
$503$	4.33403	−	4.33403i	0.193245	−	0.193245i	−0.603852	−	0.797097i	$-0.706368\pi$
$503$	4.33403	−	4.33403i	0.193245	−	0.193245i	0.797097	+	0.603852i	$0.206368\pi$
$504$		0			0
$505$	27.9049	−	6.26092i	1.24175	−	0.278607i
$506$	0.0164731			0.000732318
$507$		0			0
$508$	−6.15663	−	6.15663i	−0.273157	−	0.273157i
$509$	12.2581			0.543329			0.271665	−	0.962392i	$-0.412426\pi$
$509$	12.2581			0.543329			0.271665	+	0.962392i	$0.412426\pi$
$510$		0			0
$511$	3.70159	−	18.8247i	0.163749	−	0.832756i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−22.0319			−0.971785
$515$	−21.5435	−	13.6477i	−0.949318	−	0.601391i
$516$		0			0
$517$	−0.230372	−	0.230372i	−0.0101318	−	0.0101318i
$518$	−7.76231	−	11.5622i	−0.341056	−	0.508013i
$519$		0			0
$520$	0.405538	+	1.80748i	0.0177840	+	0.0792634i
$521$		−	10.1828i		−	0.446116i	−0.974805	−	0.223058i	$-0.928396\pi$
$521$		−	10.1828i		−	0.446116i	0.974805	−	0.223058i	$-0.0716039\pi$
$522$		0			0
$523$	7.86522	−	7.86522i	0.343922	−	0.343922i	−0.513917	−	0.857840i	$-0.671806\pi$
$523$	7.86522	−	7.86522i	0.343922	−	0.343922i	0.857840	+	0.513917i	$0.171806\pi$
$524$	−4.52401			−0.197632
$525$		0			0
$526$	10.3842			0.452771
$527$	−11.0087	+	11.0087i	−0.479545	+	0.479545i
$528$		0			0
$529$		−	22.6907i		−	0.986551i
$530$	−4.00000	−	17.8280i	−0.173749	−	0.774398i
$531$		0			0
$532$	−8.52072	−	12.6919i	−0.369420	−	0.550262i
$533$	−0.301258	−	0.301258i	−0.0130489	−	0.0130489i
$534$		0			0
$535$	3.26358	+	2.06747i	0.141097	+	0.0893847i
$536$	3.38459			0.146192
$537$		0			0
$538$	11.7429	−	11.7429i	0.506271	−	0.506271i
$539$	−0.0785023	+	0.191896i	−0.00338133	+	0.00826556i
$540$		0			0
$541$	17.5312			0.753725			0.376862	−	0.926269i	$-0.377003\pi$
$541$	17.5312			0.753725			0.376862	+	0.926269i	$0.377003\pi$
$542$	−7.00285	−	7.00285i	−0.300798	−	0.300798i
$543$		0			0
$544$	2.43516			0.104407
$545$	32.5058	−	7.29320i	1.39239	−	0.312407i
$546$		0			0
$547$	12.5889	−	12.5889i	0.538264	−	0.538264i	−0.384755	−	0.923019i	$-0.625714\pi$
$547$	12.5889	−	12.5889i	0.538264	−	0.538264i	0.923019	+	0.384755i	$0.125714\pi$
$548$	5.58535	+	5.58535i	0.238594	+	0.238594i
$549$		0			0
$550$	−0.0499424	+	0.139420i	−0.00212955	+	0.00594487i
$551$		−	56.0820i		−	2.38917i
$552$		0			0
$553$	−14.5553	−	21.6805i	−0.618954	−	0.921949i
$554$			4.15125i			0.176370i
$555$		0			0
$556$			16.6063i			0.704264i
$557$	−24.5752	+	24.5752i	−1.04128	+	1.04128i	−0.0421733	+	0.999110i	$0.513428\pi$
$557$	−24.5752	+	24.5752i	−1.04128	+	1.04128i	−0.999110	+	0.0421733i	$0.986572\pi$
$558$		0			0
$559$	8.39134			0.354916
$560$	−4.29289	−	4.07076i	−0.181408	−	0.172021i
$561$		0			0
$562$	−3.33044	+	3.33044i	−0.140486	+	0.140486i
$563$	−6.28391	+	6.28391i	−0.264835	+	0.264835i	−0.827015	−	0.562180i	$-0.809963\pi$
$563$	−6.28391	+	6.28391i	−0.264835	+	0.264835i	0.562180	+	0.827015i	$0.309963\pi$
$564$		0			0
$565$	−0.121010	+	0.191019i	−0.00509094	+	0.00803623i
$566$		−	18.4679i		−	0.776265i
$567$		0			0
$568$	−4.70097	−	4.70097i	−0.197248	−	0.197248i
$569$		−	15.0696i		−	0.631749i	−0.948801	−	0.315875i	$-0.897702\pi$
$569$		−	15.0696i		−	0.631749i	0.948801	−	0.315875i	$-0.102298\pi$
$570$		0			0
$571$	28.0757			1.17493			0.587466	−	0.809249i	$-0.300126\pi$
$571$	28.0757			1.17493			0.587466	+	0.809249i	$0.300126\pi$
$572$	0.0173504	+	0.0173504i	0.000725456	+	0.000725456i
$573$		0			0
$574$	1.33509	+	0.262525i	0.0557256	+	0.0109576i
$575$	−2.61794	−	0.937789i	−0.109176	−	0.0391085i
$576$		0			0
$577$	14.2455	+	14.2455i	0.593048	+	0.593048i	0.938453	−	0.345406i	$-0.112259\pi$
$577$	14.2455	+	14.2455i	0.593048	+	0.593048i	−0.345406	+	0.938453i	$0.612259\pi$
$578$	7.82768	+	7.82768i	0.325588	+	0.325588i
$579$		0			0
$580$	−4.75154	−	21.1776i	−0.197297	−	0.879351i
$581$	−0.108742	+	0.553013i	−0.00451136	+	0.0229428i
$582$		0			0
$583$	−0.171134	−	0.171134i	−0.00708766	−	0.00708766i
$584$	7.25132			0.300062
$585$		0			0
$586$		−	23.8781i		−	0.986396i
$587$	−6.03786	−	6.03786i	−0.249209	−	0.249209i	0.571437	−	0.820646i	$-0.306386\pi$
$587$	−6.03786	−	6.03786i	−0.249209	−	0.249209i	−0.820646	+	0.571437i	$0.806386\pi$
$588$		0			0
$589$			36.9394i			1.52206i
$590$	24.1916	+	15.3254i	0.995954	+	0.630935i
$591$		0			0
$592$	3.72192	−	3.72192i	0.152970	−	0.152970i
$593$	−18.9043	+	18.9043i	−0.776305	+	0.776305i	−0.979200	−	0.202895i	$-0.934965\pi$
$593$	−18.9043	+	18.9043i	−0.776305	+	0.776305i	0.202895	+	0.979200i	$0.434965\pi$
$594$		0			0
$595$	0.382499	+	14.4015i	0.0156809	+	0.590404i
$596$	−7.80748			−0.319807
$597$		0			0
$598$	−0.325795	+	0.325795i	−0.0133228	+	0.0133228i
$599$			24.1620i			0.987233i	0.869680	+	0.493617i	$0.164325\pi$
$599$			24.1620i			0.987233i	−0.869680	+	0.493617i	$0.835675\pi$
$600$		0			0
$601$			46.4416i			1.89439i	0.320652	+	0.947197i	$0.396098\pi$
$601$			46.4416i			1.89439i	−0.320652	+	0.947197i	$0.603902\pi$
$602$	−22.2503	+	14.9378i	−0.906853	+	0.608819i
$603$		0			0
$604$		−	0.870315i		−	0.0354126i
$605$	−5.38438	−	23.9982i	−0.218906	−	0.975664i
$606$		0			0
$607$	−24.4860	−	24.4860i	−0.993857	−	0.993857i	0.00612457	−	0.999981i	$-0.498050\pi$
$607$	−24.4860	−	24.4860i	−0.993857	−	0.993857i	−0.999981	+	0.00612457i	$0.998050\pi$
$608$	4.08557	−	4.08557i	0.165692	−	0.165692i
$609$		0			0
$610$	12.8367	−	20.2631i	0.519741	−	0.820431i
$611$	9.11233			0.368646
$612$		0			0
$613$	−29.5909	−	29.5909i	−1.19517	−	1.19517i	−0.975597	−	0.219569i	$-0.929535\pi$
$613$	−29.5909	−	29.5909i	−1.19517	−	1.19517i	−0.219569	−	0.975597i	$-0.570465\pi$
$614$	−16.2896			−0.657395
$615$		0			0
$616$	−0.0768919	−	0.0151196i	−0.00309806	−	0.000609188i
$617$	30.3710	−	30.3710i	1.22269	−	1.22269i	0.256019	−	0.966672i	$-0.417589\pi$
$617$	30.3710	−	30.3710i	1.22269	−	1.22269i	0.966672	−	0.256019i	$-0.0824110\pi$
$618$		0			0
$619$	41.0141			1.64850			0.824248	−	0.566229i	$-0.191598\pi$
$619$	41.0141			1.64850			0.824248	+	0.566229i	$0.191598\pi$
$620$	3.12969	+	13.9490i	0.125691	+	0.560205i
$621$		0			0
$622$	−6.78654	−	6.78654i	−0.272115	−	0.272115i
$623$	9.63039	−	6.46540i	0.385833	−	0.259031i
$624$		0			0
$625$	15.8739	−	19.3137i	0.634956	−	0.772548i
$626$			0.748684i			0.0299234i
$627$		0			0
$628$	−15.8403	+	15.8403i	−0.632095	+	0.632095i
$629$	−12.8177			−0.511073
$630$		0			0
$631$	−4.08948			−0.162800			−0.0813998	−	0.996682i	$-0.525939\pi$
$631$	−4.08948			−0.162800			−0.0813998	+	0.996682i	$0.525939\pi$
$632$	6.97906	−	6.97906i	0.277612	−	0.277612i
$633$		0			0
$634$		−	28.0829i		−	1.11531i
$635$	16.4465	+	10.4189i	0.652661	+	0.413460i
$636$		0			0
$637$	−2.24264	−	5.34779i	−0.0888567	−	0.211887i
$638$	−0.203288	−	0.203288i	−0.00804823	−	0.00804823i
$639$		0			0
$640$	1.19663	−	1.88893i	0.0473011	−	0.0746666i
$641$	−11.8151			−0.466668			−0.233334	−	0.972397i	$-0.574964\pi$
$641$	−11.8151			−0.466668			−0.233334	+	0.972397i	$0.574964\pi$
$642$		0			0
$643$	6.35138	−	6.35138i	0.250474	−	0.250474i	−0.570691	−	0.821165i	$-0.693325\pi$
$643$	6.35138	−	6.35138i	0.250474	−	0.250474i	0.821165	+	0.570691i	$0.193325\pi$
$644$	0.283908	−	1.44383i	0.0111875	−	0.0568950i
$645$		0			0
$646$	−14.0700			−0.553577
$647$	34.1901	+	34.1901i	1.34415	+	1.34415i	0.891879	+	0.452274i	$0.149387\pi$
$647$	34.1901	+	34.1901i	1.34415	+	1.34415i	0.452274	+	0.891879i	$0.350613\pi$
$648$		0			0
$649$	0.379331			0.0148900
$650$	−1.76963	−	3.74509i	−0.0694105	−	0.146895i
$651$		0			0
$652$	2.70742	−	2.70742i	0.106031	−	0.106031i
$653$	−30.0988	−	30.0988i	−1.17786	−	1.17786i	−0.980290	−	0.197565i	$-0.936697\pi$
$653$	−30.0988	−	30.0988i	−1.17786	−	1.17786i	−0.197565	−	0.980290i	$-0.563303\pi$
$654$		0			0
$655$	9.87061	−	2.21463i	0.385677	−	0.0865328i
$656$			0.514280i			0.0200793i
$657$		0			0
$658$	−24.1620	+	16.2213i	−0.941934	+	0.632370i
$659$			27.3843i			1.06674i	0.845881	+	0.533371i	$0.179075\pi$
$659$			27.3843i			1.06674i	−0.845881	+	0.533371i	$0.820925\pi$
$660$		0			0
$661$		−	22.5855i		−	0.878475i	−0.898371	−	0.439238i	$-0.855249\pi$
$661$		−	22.5855i		−	0.878475i	0.898371	−	0.439238i	$-0.144751\pi$
$662$	−3.28347	+	3.28347i	−0.127616	+	0.127616i
$663$		0			0
$664$	−0.213022			−0.00826685
$665$	24.8038	+	23.5203i	0.961848	+	0.912078i
$666$		0			0
$667$	3.81722	−	3.81722i	0.147803	−	0.147803i
$668$	−13.7779	+	13.7779i	−0.533082	+	0.533082i
$669$		0			0
$670$	−7.38459	+	1.65685i	−0.285292	+	0.0640099i
$671$		−	0.317731i		−	0.0122659i
$672$		0			0
$673$	17.7447	+	17.7447i	0.684006	+	0.684006i	0.960900	−	0.276894i	$-0.0893052\pi$
$673$	17.7447	+	17.7447i	0.684006	+	0.684006i	−0.276894	+	0.960900i	$0.589305\pi$
$674$			9.98327i			0.384541i
$675$		0			0
$676$	12.3137			0.473604
$677$	−18.4477	−	18.4477i	−0.709003	−	0.709003i	0.257322	−	0.966326i	$-0.417160\pi$
$677$	−18.4477	−	18.4477i	−0.709003	−	0.709003i	−0.966326	+	0.257322i	$0.917160\pi$
$678$		0			0
$679$	−9.06884	−	1.78325i	−0.348030	−	0.0684349i
$680$	−5.31309	+	1.19208i	−0.203748	+	0.0457141i
$681$		0			0
$682$	0.133899	+	0.133899i	0.00512726	+	0.00512726i
$683$	−1.35560	−	1.35560i	−0.0518704	−	0.0518704i	0.680696	−	0.732566i	$-0.261678\pi$
$683$	−1.35560	−	1.35560i	−0.0518704	−	0.0518704i	−0.732566	+	0.680696i	$0.761678\pi$
$684$		0			0
$685$	−14.9204	−	9.45207i	−0.570081	−	0.361145i
$686$	15.4664	+	10.1878i	0.590508	+	0.388973i
$687$		0			0
$688$	−7.16246	−	7.16246i	−0.273066	−	0.273066i
$689$	6.76919			0.257886
$690$		0			0
$691$		−	4.24455i		−	0.161470i	−0.996736	−	0.0807352i	$-0.974273\pi$
$691$		−	4.24455i		−	0.161470i	0.996736	−	0.0807352i	$-0.0257268\pi$
$692$	−10.3077	−	10.3077i	−0.391840	−	0.391840i
$693$		0			0
$694$			33.2234i			1.26114i
$695$	−8.12925	−	36.2320i	−0.308360	−	1.37436i
$696$		0			0
$697$	0.885547	−	0.885547i	0.0335425	−	0.0335425i
$698$	14.2708	−	14.2708i	0.540156	−	0.540156i
$699$		0			0
$700$	11.3591	+	6.78019i	0.429333	+	0.256267i
$701$	−11.1047			−0.419419			−0.209710	−	0.977764i	$-0.567252\pi$
$701$	−11.1047			−0.419419			−0.209710	+	0.977764i	$0.567252\pi$
$702$		0			0
$703$	−21.5047	+	21.5047i	−0.811066	+	0.811066i
$704$		−	0.0296189i		−	0.00111631i
$705$		0			0
$706$			10.5354i			0.396505i
$707$	−18.8612	−	28.0943i	−0.709348	−	1.05659i
$708$		0			0
$709$			34.1694i			1.28326i	0.767015	+	0.641629i	$0.221741\pi$
$709$			34.1694i			1.28326i	−0.767015	+	0.641629i	$0.778259\pi$
$710$	12.5580	+	7.95544i	0.471292	+	0.298562i
$711$		0			0
$712$	3.10007	+	3.10007i	0.116180	+	0.116180i
$713$	−2.51428	+	2.51428i	−0.0941605	+	0.0941605i
$714$		0			0
$715$	−0.0463490	−	0.0293620i	−0.00173335	−	0.00109808i
$716$	−17.2422			−0.644371
$717$		0			0
$718$	−11.7424	−	11.7424i	−0.438223	−	0.438223i
$719$	−27.7960			−1.03662			−0.518308	−	0.855194i	$-0.673438\pi$
$719$	−27.7960			−1.03662			−0.518308	+	0.855194i	$0.673438\pi$
$720$		0			0
$721$	−5.82198	+	29.6081i	−0.216822	+	1.10266i
$722$	−10.1708	+	10.1708i	−0.378519	+	0.378519i
$723$		0			0
$724$	−22.4015			−0.832545
$725$	20.7340	+	43.8798i	0.770043	+	1.62965i
$726$		0			0
$727$	9.37456	+	9.37456i	0.347683	+	0.347683i	0.859246	−	0.511563i	$-0.170933\pi$
$727$	9.37456	+	9.37456i	0.347683	+	0.347683i	−0.511563	+	0.859246i	$0.670933\pi$
$728$	1.81975	−	1.22170i	0.0674445	−	0.0452791i
$729$		0			0
$730$	−15.8211	+	3.54972i	−0.585565	+	0.131381i
$731$			24.6663i			0.912316i
$732$		0			0
$733$	−8.54390	+	8.54390i	−0.315576	+	0.315576i	−0.847065	−	0.531489i	$-0.821633\pi$
$733$	−8.54390	+	8.54390i	−0.315576	+	0.315576i	0.531489	+	0.847065i	$0.321633\pi$
$734$	4.06327			0.149978
$735$		0			0
$736$	0.556167			0.0205006
$737$	−0.0708861	+	0.0708861i	−0.00261112	+	0.00261112i
$738$		0			0
$739$		−	24.4015i		−	0.897624i	−0.893626	−	0.448812i	$-0.851847\pi$
$739$		−	24.4015i		−	0.897624i	0.893626	−	0.448812i	$-0.148153\pi$
$740$	−6.29859	+	9.94255i	−0.231541	+	0.365496i
$741$		0			0
$742$	−17.9490	+	12.0501i	−0.658928	+	0.442374i
$743$	−16.3076	−	16.3076i	−0.598267	−	0.598267i	0.341584	−	0.939851i	$-0.389036\pi$
$743$	−16.3076	−	16.3076i	−0.598267	−	0.598267i	−0.939851	+	0.341584i	$0.889036\pi$
$744$		0			0
$745$	17.0346	−	3.82198i	0.624098	−	0.140027i
$746$	2.19314			0.0802964
$747$		0			0
$748$	−0.0510013	+	0.0510013i	−0.00186479	+	0.00186479i
$749$	0.881963	−	4.48528i	0.0322262	−	0.163889i
$750$		0			0
$751$	27.6503			1.00897			0.504486	−	0.863420i	$-0.331682\pi$
$751$	27.6503			1.00897			0.504486	+	0.863420i	$0.331682\pi$
$752$	−7.77786	−	7.77786i	−0.283630	−	0.283630i
$753$		0			0
$754$	8.04101			0.292836
$755$	0.426043	+	1.89887i	0.0155053	+	0.0691071i
$756$		0			0
$757$	−20.2224	+	20.2224i	−0.734997	+	0.734997i	−0.971605	−	0.236608i	$-0.923964\pi$
$757$	−20.2224	+	20.2224i	−0.734997	+	0.734997i	0.236608	+	0.971605i	$0.423964\pi$
$758$	4.89844	+	4.89844i	0.177919	+	0.177919i
$759$		0			0
$760$	−6.91399	+	10.9140i	−0.250797	+	0.395892i
$761$			23.1354i			0.838657i	0.907835	+	0.419329i	$0.137734\pi$
$761$			23.1354i			0.838657i	−0.907835	+	0.419329i	$0.862266\pi$
$762$		0			0
$763$	−21.9710	−	32.7264i	−0.795404	−	1.18478i
$764$		−	22.5644i		−	0.816351i
$765$		0			0
$766$			4.89844i			0.176988i
$767$	−7.50219	+	7.50219i	−0.270888	+	0.270888i
$768$		0			0
$769$	25.1546			0.907098			0.453549	−	0.891231i	$-0.350158\pi$
$769$	25.1546			0.907098			0.453549	+	0.891231i	$0.350158\pi$
$770$	0.175166	−	0.00465235i	0.00631255	−	0.000167659i
$771$		0			0
$772$	4.94076	−	4.94076i	0.177822	−	0.177822i
$773$	23.0515	−	23.0515i	0.829104	−	0.829104i	−0.158289	−	0.987393i	$-0.550598\pi$
$773$	23.0515	−	23.0515i	0.829104	−	0.829104i	0.987393	+	0.158289i	$0.0505977\pi$
$774$		0			0
$775$	−13.6569	−	28.9022i	−0.490569	−	1.03820i
$776$		−	3.49334i		−	0.125403i
$777$		0			0
$778$	17.6210	+	17.6210i	0.631742	+	0.631742i
$779$		−	2.97144i		−	0.106463i
$780$		0			0
$781$	0.196912			0.00704607
$782$	−0.957674	−	0.957674i	−0.0342463	−	0.0342463i
$783$		0			0
$784$	−2.65041	+	6.47884i	−0.0946575	+	0.231387i
$785$	26.8064	−	42.3149i	0.956762	−	1.51028i
$786$		0			0
$787$	24.2320	+	24.2320i	0.863779	+	0.863779i	0.991775	−	0.127996i	$-0.0408545\pi$
$787$	24.2320	+	24.2320i	0.863779	+	0.863779i	−0.127996	+	0.991775i	$0.540855\pi$
$788$	−6.64818	−	6.64818i	−0.236832	−	0.236832i
$789$		0			0
$790$	−11.8106	+	18.6435i	−0.420204	+	0.663307i
$791$	0.262525	+	0.0516217i	0.00933433	+	0.00183546i
$792$		0			0
$793$	6.28391	+	6.28391i	0.223148	+	0.223148i
$794$	19.3128			0.685387
$795$		0			0
$796$		−	12.2631i		−	0.434656i
$797$	17.5376	+	17.5376i	0.621215	+	0.621215i	0.945842	−	0.324627i	$-0.105239\pi$
$797$	17.5376	+	17.5376i	0.621215	+	0.621215i	−0.324627	+	0.945842i	$0.605239\pi$
$798$		0			0
$799$			26.7857i			0.947609i
$800$	−1.68616	+	4.70711i	−0.0596149	+	0.166421i
$801$		0			0
$802$	9.20119	−	9.20119i	0.324905	−	0.324905i
$803$	−0.151870	+	0.151870i	−0.00535937	+	0.00535937i
$804$		0			0
$805$	0.0873592	+	3.28917i	0.00307901	+	0.115928i
$806$	−5.29636			−0.186556
$807$		0			0
$808$	9.04368	−	9.04368i	0.318156	−	0.318156i
$809$		−	20.1011i		−	0.706718i	−0.935488	−	0.353359i	$-0.885039\pi$
$809$		−	20.1011i		−	0.706718i	0.935488	−	0.353359i	$-0.114961\pi$
$810$		0			0
$811$		−	27.6340i		−	0.970360i	−0.874414	−	0.485180i	$-0.838754\pi$
$811$		−	27.6340i		−	0.970360i	0.874414	−	0.485180i	$-0.161246\pi$
$812$	−21.3213	+	14.3141i	−0.748232	+	0.502328i
$813$		0			0
$814$			0.155902i			0.00546436i
$815$	−4.58175	+	7.23247i	−0.160492	+	0.253342i
$816$		0			0
$817$	41.3837	+	41.3837i	1.44783	+	1.44783i
$818$	−7.50623	+	7.50623i	−0.262449	+	0.262449i
$819$		0			0
$820$	−0.251755	−	1.12207i	−0.00879165	−	0.0391844i
$821$	6.07616			0.212059			0.106030	−	0.994363i	$-0.466186\pi$
$821$	6.07616			0.212059			0.106030	+	0.994363i	$0.466186\pi$
$822$		0			0
$823$	−13.2971	−	13.2971i	−0.463507	−	0.463507i	0.436296	−	0.899803i	$-0.356290\pi$
$823$	−13.2971	−	13.2971i	−0.463507	−	0.463507i	−0.899803	+	0.436296i	$0.856290\pi$
$824$	−11.4051			−0.397315
$825$		0			0
$826$	6.53764	−	33.2476i	0.227473	−	1.15683i
$827$	−4.21364	+	4.21364i	−0.146523	+	0.146523i	−0.776563	−	0.630040i	$-0.783038\pi$
$827$	−4.21364	+	4.21364i	−0.146523	+	0.146523i	0.630040	+	0.776563i	$0.283038\pi$
$828$		0			0
$829$	−25.3382			−0.880034			−0.440017	−	0.897990i	$-0.645028\pi$
$829$	−25.3382			−0.880034			−0.440017	+	0.897990i	$0.645028\pi$
$830$	0.464776	−	0.104280i	0.0161326	−	0.00361962i
$831$		0			0
$832$	0.585786	+	0.585786i	0.0203085	+	0.0203085i
$833$	15.7198	−	6.59223i	0.544659	−	0.228407i
$834$		0			0
$835$	23.3162	−	36.8055i	0.806892	−	1.27371i
$836$			0.171134i			0.00591880i
$837$		0			0
$838$	6.95482	−	6.95482i	0.240250	−	0.240250i
$839$	8.27672			0.285744			0.142872	−	0.989741i	$-0.454366\pi$
$839$	8.27672			0.285744			0.142872	+	0.989741i	$0.454366\pi$
$840$		0			0
$841$	−65.2134			−2.24874
$842$	23.0491	−	23.0491i	0.794323	−	0.794323i
$843$		0			0
$844$			4.62829i			0.159312i
$845$	−26.8664	+	6.02791i	−0.924231	+	0.207366i
$846$		0			0
$847$	−24.1611	+	16.2206i	−0.830184	+	0.557347i
$848$	−5.77786	−	5.77786i	−0.198413	−	0.198413i
$849$		0			0
$850$	11.0087	−	5.20181i	0.377594	−	0.178421i
$851$	−2.92743			−0.100351
$852$		0			0
$853$	−30.3653	+	30.3653i	−1.03969	+	1.03969i	−0.0405092	+	0.999179i	$0.512898\pi$
$853$	−30.3653	+	30.3653i	−1.03969	+	1.03969i	−0.999179	+	0.0405092i	$0.987102\pi$
$854$	−27.8485	−	5.47599i	−0.952956	−	0.187384i
$855$		0			0
$856$	1.72774			0.0590530
$857$	33.0766	+	33.0766i	1.12988	+	1.12988i	0.990197	+	0.139680i	$0.0446072\pi$
$857$	33.0766	+	33.0766i	1.12988	+	1.12988i	0.139680	+	0.990197i	$0.455393\pi$
$858$		0			0
$859$	−1.87687			−0.0640380			−0.0320190	−	0.999487i	$-0.510194\pi$
$859$	−1.87687			−0.0640380			−0.0320190	+	0.999487i	$0.510194\pi$
$860$	19.1335	+	12.1210i	0.652446	+	0.413323i
$861$		0			0
$862$	−20.7710	+	20.7710i	−0.707462	+	0.707462i
$863$	−10.8612	−	10.8612i	−0.369720	−	0.369720i	0.497655	−	0.867375i	$-0.334194\pi$
$863$	−10.8612	−	10.8612i	−0.369720	−	0.369720i	−0.867375	+	0.497655i	$0.834194\pi$
$864$		0			0
$865$	27.5355	+	17.4437i	0.936236	+	0.593104i
$866$			24.2206i			0.823051i
$867$		0			0
$868$	14.0437	−	9.42827i	0.476674	−	0.320016i
$869$			0.292335i			0.00991680i
$870$		0			0
$871$		−	2.80389i		−	0.0950062i
$872$	10.5348	−	10.5348i	0.356753	−	0.356753i
$873$		0			0
$874$	−3.21346			−0.108697
$875$	−28.1027	−	9.23260i	−0.950043	−	0.312119i
$876$		0			0
$877$	−5.90470	+	5.90470i	−0.199388	+	0.199388i	−0.799737	−	0.600350i	$-0.795028\pi$
$877$	−5.90470	+	5.90470i	−0.199388	+	0.199388i	0.600350	+	0.799737i	$0.295028\pi$
$878$	−1.62544	+	1.62544i	−0.0548561	+	0.0548561i
$879$		0			0
$880$	0.0144993	+	0.0646234i	0.000488771	+	0.00217845i
$881$			6.76200i			0.227818i	0.993491	+	0.113909i	$0.0363372\pi$
$881$			6.76200i			0.227818i	−0.993491	+	0.113909i	$0.963663\pi$
$882$		0			0
$883$	24.6192	+	24.6192i	0.828501	+	0.828501i	0.987309	−	0.158808i	$-0.0507651\pi$
$883$	24.6192	+	24.6192i	0.828501	+	0.828501i	−0.158808	+	0.987309i	$0.550765\pi$
$884$		−	2.01735i		−	0.0678508i
$885$		0			0
$886$	−1.97188			−0.0662466
$887$	−6.92132	−	6.92132i	−0.232395	−	0.232395i	0.581297	−	0.813692i	$-0.302546\pi$
$887$	−6.92132	−	6.92132i	−0.232395	−	0.232395i	−0.813692	+	0.581297i	$0.802546\pi$
$888$		0			0
$889$	4.44457	−	22.6032i	0.149066	−	0.758086i
$890$	−8.28137	−	5.24623i	−0.277592	−	0.175854i
$891$		0			0
$892$	18.2266	+	18.2266i	0.610273	+	0.610273i
$893$	44.9394	+	44.9394i	1.50384	+	1.50384i
$894$		0			0
$895$	37.6195	−	8.44054i	1.25748	−	0.282136i
$896$	−2.59604	−	0.510472i	−0.0867276	−	0.0170537i
$897$		0			0
$898$	4.75692	+	4.75692i	0.158740	+	0.158740i
$899$	62.0554			2.06966
$900$		0			0
$901$			19.8980i			0.662898i
$902$	−0.0107710	−	0.0107710i	−0.000358634	−	0.000358634i
$903$		0			0
$904$			0.101125i			0.00336338i
$905$	48.8762	−	10.9662i	1.62470	−	0.364528i
$906$		0			0
$907$	−6.28050	+	6.28050i	−0.208540	+	0.208540i	−0.803647	−	0.595106i	$-0.797110\pi$
$907$	−6.28050	+	6.28050i	−0.208540	+	0.208540i	0.595106	+	0.803647i	$0.297110\pi$
$908$	−8.89844	+	8.89844i	−0.295305	+	0.295305i
$909$		0			0
$910$	−3.37233	+	3.55635i	−0.111792	+	0.117892i
$911$	−19.9873			−0.662209			−0.331104	−	0.943594i	$-0.607421\pi$
$911$	−19.9873			−0.662209			−0.331104	+	0.943594i	$0.607421\pi$
$912$		0			0
$913$	0.00446148	−	0.00446148i	0.000147653	−	0.000147653i
$914$		−	23.5563i		−	0.779175i
$915$		0			0
$916$			13.3137i			0.439897i
$917$	−6.67165	−	9.93761i	−0.220317	−	0.328169i
$918$		0			0
$919$		−	9.34358i		−	0.308216i	−0.988054	−	0.154108i	$-0.950750\pi$
$919$		−	9.34358i		−	0.308216i	0.988054	−	0.154108i	$-0.0492504\pi$
$920$	−1.21346	+	0.272260i	−0.0400066	+	0.00897613i
$921$		0			0
$922$	8.17802	+	8.17802i	0.269329	+	0.269329i
$923$	−3.89441	+	3.89441i	−0.128186	+	0.128186i
$924$		0			0
$925$	8.87526	−	24.7763i	0.291817	−	0.814638i
$926$	17.5589			0.577021
$927$		0			0
$928$	−6.86343	−	6.86343i	−0.225303	−	0.225303i
$929$	13.8699			0.455056			0.227528	−	0.973772i	$-0.426936\pi$
$929$	13.8699			0.455056			0.227528	+	0.973772i	$0.426936\pi$
$930$		0			0
$931$	15.3137	−	37.4338i	0.501887	−	1.22684i
$932$	2.18340	−	2.18340i	0.0715197	−	0.0715197i
$933$		0			0
$934$	8.69706			0.284577
$935$	0.0863094	−	0.136243i	0.00282262	−	0.00445561i
$936$		0			0
$937$	−27.3569	−	27.3569i	−0.893713	−	0.893713i	0.101158	−	0.994870i	$-0.467745\pi$
$937$	−27.3569	−	27.3569i	−0.893713	−	0.893713i	−0.994870	+	0.101158i	$0.967745\pi$
$938$	4.99132	+	7.43472i	0.162973	+	0.242752i
$939$		0			0
$940$	20.7774	+	13.1625i	0.677685	+	0.429312i
$941$			54.0397i			1.76164i	0.473448	+	0.880822i	$0.343009\pi$
$941$			54.0397i			1.76164i	−0.473448	+	0.880822i	$0.656991\pi$
$942$		0			0
$943$	0.202251	−	0.202251i	0.00658619	−	0.00658619i
$944$	12.8070			0.416834
$945$		0			0
$946$	0.300018			0.00975441
$947$	−27.2157	+	27.2157i	−0.884393	+	0.884393i	−0.993977	−	0.109585i	$-0.965048\pi$
$947$	−27.2157	+	27.2157i	−0.884393	+	0.884393i	0.109585	+	0.993977i	$0.465048\pi$
$948$		0			0
$949$		−	6.00719i		−	0.195002i
$950$	9.74242	−	27.1970i	0.316086	−	0.882388i
$951$		0			0
$952$	3.59117	+	5.34915i	0.116391	+	0.173367i
$953$	4.60945	+	4.60945i	0.149315	+	0.149315i	0.777812	−	0.628497i	$-0.216330\pi$
$953$	4.60945	+	4.60945i	0.149315	+	0.149315i	−0.628497	+	0.777812i	$0.716330\pi$
$954$		0			0
$955$	11.0459	+	49.2316i	0.357437	+	1.59310i
$956$	18.1201			0.586047
$957$		0			0
$958$	4.82843	−	4.82843i	0.155999	−	0.155999i
$959$	−4.03215	+	20.5058i	−0.130205	+	0.662166i
$960$		0			0
$961$	−9.87390			−0.318513
$962$	−3.08334	−	3.08334i	−0.0994108	−	0.0994108i
$963$		0			0
$964$	−19.6257			−0.632102
$965$	−8.36124	+	13.1985i	−0.269158	+	0.424875i
$966$		0			0
$967$	31.1433	−	31.1433i	1.00150	−	1.00150i	0.00150238	−	0.999999i	$-0.499522\pi$
$967$	31.1433	−	31.1433i	1.00150	−	1.00150i	0.999999	−	0.00150238i	$-0.000478222\pi$
$968$	−7.77755	−	7.77755i	−0.249980	−	0.249980i
$969$		0			0
$970$	1.71009	+	7.62185i	0.0549076	+	0.244723i
$971$		−	0.0615153i		−	0.00197412i	−1.00000		0.000987061i	$-0.999686\pi$
$971$		−	0.0615153i		−	0.00197412i	1.00000		0.000987061i	$-0.000314191\pi$
$972$		0			0
$973$	−36.4780	+	24.4896i	−1.16943	+	0.785101i
$974$		−	30.7059i		−	0.983881i
$975$		0			0
$976$		−	10.7273i		−	0.343373i
$977$	−0.822738	+	0.822738i	−0.0263217	+	0.0263217i	−0.720145	−	0.693823i	$-0.755925\pi$
$977$	−0.822738	+	0.822738i	−0.0263217	+	0.0263217i	0.693823	+	0.720145i	$0.255925\pi$
$978$		0			0
$979$	−0.129854			−0.00415015
$980$	2.61116	−	15.4331i	0.0834104	−	0.492994i
$981$		0			0
$982$	10.5352	−	10.5352i	0.336192	−	0.336192i
$983$	19.9374	−	19.9374i	0.635903	−	0.635903i	−0.313639	−	0.949542i	$-0.601548\pi$
$983$	19.9374	−	19.9374i	0.635903	−	0.635903i	0.949542	+	0.313639i	$0.101548\pi$
$984$		0			0
$985$	17.7596	+	11.2507i	0.565869	+	0.358477i
$986$			23.6365i			0.752740i
$987$		0			0
$988$	−3.38459	−	3.38459i	−0.107678	−	0.107678i
$989$			5.63356i			0.179137i
$990$		0			0
$991$	24.6283			0.782344			0.391172	−	0.920318i	$-0.372070\pi$
$991$	24.6283			0.782344			0.391172	+	0.920318i	$0.372070\pi$
$992$	4.52072	+	4.52072i	0.143533	+	0.143533i
$993$		0			0
$994$	3.39371	−	17.2589i	0.107642	−	0.547420i
$995$	6.00315	+	26.7560i	0.190313	+	0.848224i
$996$		0			0
$997$	−31.1165	−	31.1165i	−0.985471	−	0.985471i	0.0144253	−	0.999896i	$-0.495408\pi$
$997$	−31.1165	−	31.1165i	−0.985471	−	0.985471i	−0.999896	+	0.0144253i	$0.995408\pi$
$998$	−23.1880	−	23.1880i	−0.734005	−	0.734005i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.p.c.433.2		8
3.2	odd	2		210.2.m.b.13.3	yes	8
5.2	odd	4		630.2.p.b.307.1		8
7.6	odd	2		630.2.p.b.433.1		8
12.11	even	2		1680.2.cz.a.433.3		8
15.2	even	4		210.2.m.a.97.4	yes	8
15.8	even	4		1050.2.m.b.307.1		8
15.14	odd	2		1050.2.m.a.643.1		8
21.20	even	2		210.2.m.a.13.4	✓	8
35.27	even	4	inner	630.2.p.c.307.2		8
60.47	odd	4		1680.2.cz.b.97.2		8
84.83	odd	2		1680.2.cz.b.433.2		8
105.62	odd	4		210.2.m.b.97.3	yes	8
105.83	odd	4		1050.2.m.a.307.1		8
105.104	even	2		1050.2.m.b.643.1		8
420.167	even	4		1680.2.cz.a.97.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.4	✓	8	21.20	even	2
210.2.m.a.97.4	yes	8	15.2	even	4
210.2.m.b.13.3	yes	8	3.2	odd	2
210.2.m.b.97.3	yes	8	105.62	odd	4
630.2.p.b.307.1		8	5.2	odd	4
630.2.p.b.433.1		8	7.6	odd	2
630.2.p.c.307.2		8	35.27	even	4	inner
630.2.p.c.433.2		8	1.1	even	1	trivial
1050.2.m.a.307.1		8	105.83	odd	4
1050.2.m.a.643.1		8	15.14	odd	2
1050.2.m.b.307.1		8	15.8	even	4
1050.2.m.b.643.1		8	105.104	even	2
1680.2.cz.a.97.3		8	420.167	even	4
1680.2.cz.a.433.3		8	12.11	even	2
1680.2.cz.b.97.2		8	60.47	odd	4
1680.2.cz.b.433.2		8	84.83	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.489528 + 2.18183i) q^{5} +(2.19663 - 1.47472i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.489528 + 2.18183i) q^{5} +(2.19663 - 1.47472i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.88893 - 1.19663i) q^{10} -0.0296189 q^{11} +(0.585786 - 0.585786i) q^{13} +(-0.510472 + 2.59604i) q^{14} -1.00000 q^{16} +(1.72192 + 1.72192i) q^{17} +5.77786 q^{19} +(2.18183 - 0.489528i) q^{20} +(0.0209438 - 0.0209438i) q^{22} +(0.393270 + 0.393270i) q^{23} +(-4.52072 + 2.13613i) q^{25} +0.828427i q^{26} +(-1.47472 - 2.19663i) q^{28} -9.70636i q^{29} +6.39327i q^{31} +(0.707107 - 0.707107i) q^{32} -2.43516 q^{34} +(4.29289 + 4.07076i) q^{35} +(-3.72192 + 3.72192i) q^{37} +(-4.08557 + 4.08557i) q^{38} +(-1.19663 + 1.88893i) q^{40} -0.514280i q^{41} +(7.16246 + 7.16246i) q^{43} +0.0296189i q^{44} -0.556167 q^{46} +(7.77786 + 7.77786i) q^{47} +(2.65041 - 6.47884i) q^{49} +(1.68616 - 4.70711i) q^{50} +(-0.585786 - 0.585786i) q^{52} +(5.77786 + 5.77786i) q^{53} +(-0.0144993 - 0.0646234i) q^{55} +(2.59604 + 0.510472i) q^{56} +(6.86343 + 6.86343i) q^{58} -12.8070 q^{59} +10.7273i q^{61} +(-4.52072 - 4.52072i) q^{62} +1.00000i q^{64} +(1.56484 + 0.991325i) q^{65} +(2.39327 - 2.39327i) q^{67} +(1.72192 - 1.72192i) q^{68} +(-5.91399 + 0.157074i) q^{70} -6.64818 q^{71} +(5.12745 - 5.12745i) q^{73} -5.26358i q^{74} -5.77786i q^{76} +(-0.0650620 + 0.0436796i) q^{77} -9.86988i q^{79} +(-0.489528 - 2.18183i) q^{80} +(0.363651 + 0.363651i) q^{82} +(-0.150629 + 0.150629i) q^{83} +(-2.91399 + 4.59985i) q^{85} -10.1292 q^{86} +(-0.0209438 - 0.0209438i) q^{88} +4.38416 q^{89} +(0.422889 - 2.15063i) q^{91} +(0.393270 - 0.393270i) q^{92} -10.9996 q^{94} +(2.82843 + 12.6063i) q^{95} +(-2.47016 - 2.47016i) q^{97} +(2.70711 + 6.45535i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^7	\( 8 q + 8 q^{7} + 4 q^{10} - 8 q^{11} + 16 q^{13} - 8 q^{14} - 8 q^{16} + 12 q^{17} + 8 q^{19} + 4 q^{20} + 8 q^{22} - 16 q^{23} - 4 q^{25} - 4 q^{28} - 16 q^{34} + 40 q^{35} - 28 q^{37} - 4 q^{38} - 8 q^{46} + 24 q^{47} - 4 q^{49} - 16 q^{52} + 8 q^{53} - 28 q^{55} - 4 q^{56} - 12 q^{58} + 8 q^{59} - 4 q^{62} + 16 q^{65} + 12 q^{68} + 4 q^{70} - 8 q^{71} + 28 q^{73} - 44 q^{77} - 24 q^{82} - 16 q^{83} + 28 q^{85} - 8 q^{86} - 8 q^{88} - 64 q^{89} - 8 q^{91} - 16 q^{92} - 8 q^{94} + 28 q^{97} + 16 q^{98}+O(q^{100}) \) 8 * q + 8 * q^7 + 4 * q^10 - 8 * q^11 + 16 * q^13 - 8 * q^14 - 8 * q^16 + 12 * q^17 + 8 * q^19 + 4 * q^20 + 8 * q^22 - 16 * q^23 - 4 * q^25 - 4 * q^28 - 16 * q^34 + 40 * q^35 - 28 * q^37 - 4 * q^38 - 8 * q^46 + 24 * q^47 - 4 * q^49 - 16 * q^52 + 8 * q^53 - 28 * q^55 - 4 * q^56 - 12 * q^58 + 8 * q^59 - 4 * q^62 + 16 * q^65 + 12 * q^68 + 4 * q^70 - 8 * q^71 + 28 * q^73 - 44 * q^77 - 24 * q^82 - 16 * q^83 + 28 * q^85 - 8 * q^86 - 8 * q^88 - 64 * q^89 - 8 * q^91 - 16 * q^92 - 8 * q^94 + 28 * q^97 + 16 * q^98

Introduction

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