LMFDB - Embedded newform 630.2.p.c.307.2

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			307.2
Root			$1.69230i$ of defining polynomial
Character	$\chi$	$=$	630.307
Dual form			630.2.p.c.433.2

$q$-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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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	0.783659	−	0.621191i	$-0.213351\pi$
$13$	0.585786	+	0.585786i	0.162468	+	0.162468i	−0.621191	+	0.783659i	$0.713351\pi$
$14$	−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	−0.466759	−	0.884385i	$-0.654578\pi$
$17$	1.72192	−	1.72192i	0.417626	−	0.417626i	0.884385	+	0.466759i	$0.154578\pi$
$18$		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	−0.664916	−	0.746918i	$-0.731533\pi$
$23$	0.393270	−	0.393270i	0.0820024	−	0.0820024i	0.746918	+	0.664916i	$0.231533\pi$
$24$		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	$0.357322\pi$
$29$			9.70636i			1.80243i	−0.433377	+	0.901213i	$0.642678\pi$
$30$		0			0
$31$		−	6.39327i		−	1.14827i	−0.818762	−	0.574133i	$-0.805339\pi$
$31$		−	6.39327i		−	1.14827i	0.818762	−	0.574133i	$-0.194661\pi$
$32$	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	0.331556	−	0.943435i	$-0.392426\pi$
$37$	−3.72192	−	3.72192i	−0.611879	−	0.611879i	−0.943435	+	0.331556i	$0.892426\pi$
$38$	−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	$0.0127863\pi$
$41$			0.514280i			0.0803170i	−0.999193	+	0.0401585i	$0.987214\pi$
$42$		0			0
$43$	7.16246	−	7.16246i	1.09226	−	1.09226i	0.0969783	−	0.995286i	$-0.469082\pi$
$43$	7.16246	−	7.16246i	1.09226	−	1.09226i	0.995286	−	0.0969783i	$-0.0309177\pi$
$44$		−	0.0296189i		−	0.00446522i
$45$		0			0
$46$	−0.556167			−0.0820024
$47$	7.77786	−	7.77786i	1.13452	−	1.13452i	0.145101	−	0.989417i	$-0.453649\pi$
$47$	7.77786	−	7.77786i	1.13452	−	1.13452i	0.989417	−	0.145101i	$-0.0463508\pi$
$48$		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	−0.188435	−	0.982086i	$-0.560341\pi$
$53$	5.77786	−	5.77786i	0.793651	−	0.793651i	0.982086	+	0.188435i	$0.0603415\pi$
$54$		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	$-0.759039\pi$
$61$		−	10.7273i		−	1.37349i	0.726898	−	0.686745i	$-0.240961\pi$
$62$	−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	0.838022	−	0.545637i	$-0.183712\pi$
$67$	2.39327	+	2.39327i	0.292384	+	0.292384i	−0.545637	+	0.838022i	$0.683712\pi$
$68$	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	0.940345	−	0.340222i	$-0.110502\pi$
$73$	5.12745	+	5.12745i	0.600123	+	0.600123i	−0.340222	+	0.940345i	$0.610502\pi$
$74$			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	$0.187367\pi$
$79$			9.86988i			1.11045i	−0.831701	+	0.555224i	$0.812633\pi$
$80$	−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	0.698792	−	0.715325i	$-0.253721\pi$
$83$	−0.150629	−	0.150629i	−0.0165337	−	0.0165337i	−0.715325	+	0.698792i	$0.753721\pi$
$84$		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	−0.821301	−	0.570494i	$-0.806752\pi$
$97$	−2.47016	+	2.47016i	−0.250807	+	0.250807i	0.570494	+	0.821301i	$0.306752\pi$
$98$	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	$0.219541\pi$
$101$			12.7897i			1.27262i	−0.771433	+	0.636311i	$0.780459\pi$
$102$		0			0
$103$	−8.06462	−	8.06462i	−0.794631	−	0.794631i	0.187612	−	0.982243i	$-0.439925\pi$
$103$	−8.06462	−	8.06462i	−0.794631	−	0.794631i	−0.982243	+	0.187612i	$0.939925\pi$
$104$	0.828427			0.0812340
$105$		0			0
$106$	−8.17113			−0.793651
$107$	1.22170	+	1.22170i	0.118106	+	0.118106i	0.763690	−	0.645584i	$-0.223386\pi$
$107$	1.22170	+	1.22170i	0.118106	+	0.118106i	−0.645584	+	0.763690i	$0.723386\pi$
$108$		0			0
$109$			14.8984i			1.42701i	0.700649	+	0.713506i	$0.252894\pi$
$109$			14.8984i			1.42701i	−0.700649	+	0.713506i	$0.747106\pi$
$110$	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	−0.703735	−	0.710462i	$-0.748486\pi$
$113$	0.0715065	−	0.0715065i	0.00672676	−	0.00672676i	0.710462	+	0.703735i	$0.248486\pi$
$114$		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	0.925372	−	0.379059i	$-0.123752\pi$
$127$	6.15663	+	6.15663i	0.546313	+	0.546313i	−0.379059	+	0.925372i	$0.623752\pi$
$128$	−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	$0.0633253\pi$
$131$			4.52401i			0.395265i	−0.980276	+	0.197632i	$0.936675\pi$
$132$		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	0.427043	−	0.904231i	$-0.359555\pi$
$137$	−5.58535	−	5.58535i	−0.477188	−	0.477188i	−0.904231	+	0.427043i	$0.859555\pi$
$138$		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	$0.103618\pi$
$149$			7.80748i			0.639614i	−0.947483	+	0.319807i	$0.896382\pi$
$150$		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	−0.315147	+	0.949043i	$0.602054\pi$
$157$	−15.8403	+	15.8403i	−1.26419	+	1.26419i	−0.949043	+	0.315147i	$0.897946\pi$
$158$	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	−0.593081	−	0.805143i	$-0.702089\pi$
$163$	2.70742	−	2.70742i	0.212061	−	0.212061i	0.805143	+	0.593081i	$0.202089\pi$
$164$	−0.514280			−0.0401585
$165$		0			0
$166$			0.213022i			0.0165337i
$167$	−13.7779	+	13.7779i	−1.06616	+	1.06616i	−0.0685129	+	0.997650i	$0.521825\pi$
$167$	−13.7779	+	13.7779i	−1.06616	+	1.06616i	−0.997650	+	0.0685129i	$0.978175\pi$
$168$		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	0.980450	−	0.196770i	$-0.0630451\pi$
$173$	10.3077	+	10.3077i	0.783680	+	0.783680i	−0.196770	+	0.980450i	$0.563045\pi$
$174$		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	$0.222881\pi$
$179$			17.2422i			1.28874i	−0.764713	+	0.644371i	$0.777119\pi$
$180$		0			0
$181$			22.4015i			1.66509i	0.553957	+	0.832545i	$0.313117\pi$
$181$			22.4015i			1.66509i	−0.553957	+	0.832545i	$0.686883\pi$
$182$	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	−0.506561	−	0.862204i	$-0.669083\pi$
$193$	4.94076	−	4.94076i	0.355644	−	0.355644i	0.862204	+	0.506561i	$0.169083\pi$
$194$	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	0.903098	−	0.429435i	$-0.141287\pi$
$197$	6.64818	+	6.64818i	0.473663	+	0.473663i	−0.429435	+	0.903098i	$0.641287\pi$
$198$		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	−0.967438	−	0.253108i	$-0.918547\pi$
$223$	−18.2266	−	18.2266i	−1.22055	−	1.22055i	−0.253108	−	0.967438i	$-0.581453\pi$
$224$	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	−0.937796	−	0.347186i	$-0.887137\pi$
$227$	−8.89844	+	8.89844i	−0.590610	+	0.590610i	0.347186	+	0.937796i	$0.387137\pi$
$228$		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	−0.631961	−	0.775000i	$-0.717750\pi$
$233$	2.18340	−	2.18340i	0.143039	−	0.143039i	0.775000	+	0.631961i	$0.217750\pi$
$234$		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	$-0.800683\pi$
$239$		−	18.1201i		−	1.17209i	0.810277	−	0.586047i	$-0.199317\pi$
$240$		0			0
$241$			19.6257i			1.26420i	0.774885	+	0.632102i	$0.217808\pi$
$241$			19.6257i			1.26420i	−0.774885	+	0.632102i	$0.782192\pi$
$242$	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	$-0.638160\pi$
$251$		−	28.7478i		−	1.81455i	0.420543	−	0.907273i	$-0.361840\pi$
$252$		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	−0.0278275	−	0.999613i	$-0.508859\pi$
$257$	15.5789	−	15.5789i	0.971785	−	0.971785i	0.999613	+	0.0278275i	$0.00885890\pi$
$258$		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	−0.896273	−	0.443502i	$-0.853736\pi$
$263$	−7.34271	+	7.34271i	−0.452771	+	0.452771i	0.443502	+	0.896273i	$0.353736\pi$
$264$		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	$-0.902747\pi$
$271$		−	9.90353i		−	0.601596i	0.953688	−	0.300798i	$-0.0972531\pi$
$272$	−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	0.789771	−	0.613402i	$-0.210199\pi$
$277$	2.93538	+	2.93538i	0.176370	+	0.176370i	−0.613402	+	0.789771i	$0.710199\pi$
$278$	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	0.202929	−	0.979194i	$-0.434954\pi$
$283$	−13.0588	−	13.0588i	−0.776265	−	0.776265i	−0.979194	+	0.202929i	$0.934954\pi$
$284$		−	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	0.0135130	−	0.999909i	$-0.495699\pi$
$293$	−16.8844	−	16.8844i	−0.986396	−	0.986396i	−0.999909	+	0.0135130i	$0.995699\pi$
$294$		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	−0.297368	−	0.954763i	$-0.596109\pi$
$307$	11.5185	−	11.5185i	0.657395	−	0.657395i	0.954763	+	0.297368i	$0.0961088\pi$
$308$	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	$-0.912277\pi$
$311$		−	9.59762i		−	0.544231i	0.962265	−	0.272115i	$-0.0877233\pi$
$312$		0			0
$313$	0.529400	+	0.529400i	0.0299234	+	0.0299234i	0.721910	−	0.691987i	$-0.243264\pi$
$313$	0.529400	+	0.529400i	0.0299234	+	0.0299234i	−0.691987	+	0.721910i	$0.743264\pi$
$314$	22.4015			1.26419
$315$		0			0
$316$	−9.86988			−0.555224
$317$	−19.8576	−	19.8576i	−1.11531	−	1.11531i	−0.992420	−	0.122895i	$-0.960782\pi$
$317$	−19.8576	−	19.8576i	−1.11531	−	1.11531i	−0.122895	−	0.992420i	$-0.539218\pi$
$318$		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	0.872735	−	0.488194i	$-0.162344\pi$
$337$	7.05924	+	7.05924i	0.384541	+	0.384541i	−0.488194	+	0.872735i	$0.662344\pi$
$338$	−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	0.950540	+	0.310601i	$0.100530\pi$
$347$	23.4925	+	23.4925i	1.26114	+	1.26114i	0.310601	+	0.950540i	$0.399470\pi$
$348$		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	0.876998	−	0.480493i	$-0.159542\pi$
$353$	7.44966	+	7.44966i	0.396505	+	0.396505i	−0.480493	+	0.876998i	$0.659542\pi$
$354$		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	$-0.855608\pi$
$359$		−	16.6063i		−	0.876447i	0.898866	−	0.438223i	$-0.144392\pi$
$360$		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	−0.778108	−	0.628130i	$-0.783821\pi$
$367$	−2.87317	+	2.87317i	−0.149978	+	0.149978i	0.628130	+	0.778108i	$0.283821\pi$
$368$	−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	−0.746114	−	0.665818i	$-0.768083\pi$
$373$	−1.55078	+	1.55078i	−0.0802964	+	0.0802964i	0.665818	+	0.746114i	$0.268083\pi$
$374$	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	$0.0569366\pi$
$379$			6.92743i			0.355838i	−0.984045	+	0.177919i	$0.943063\pi$
$380$	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	0.790041	−	0.613054i	$-0.210059\pi$
$383$	3.46372	+	3.46372i	0.176988	+	0.176988i	−0.613054	+	0.790041i	$0.710059\pi$
$384$		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	$0.217660\pi$
$389$			24.9198i			1.26348i	−0.775178	+	0.631742i	$0.782340\pi$
$390$		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	−0.961209	−	0.275822i	$-0.911050\pi$
$397$	−13.6562	+	13.6562i	−0.685387	+	0.685387i	0.275822	+	0.961209i	$0.411050\pi$
$398$	−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	0.986544	−	0.163494i	$-0.0522763\pi$
$433$	17.1266	+	17.1266i	0.823051	+	0.823051i	−0.163494	+	0.986544i	$0.552276\pi$
$434$	−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	−0.673207	−	0.739454i	$-0.735084\pi$
$443$	1.39433	−	1.39433i	0.0662466	−	0.0662466i	0.739454	+	0.673207i	$0.235084\pi$
$444$		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	$0.0507433\pi$
$449$			6.72730i			0.317481i	−0.987320	+	0.158740i	$0.949257\pi$
$450$		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	0.200516	−	0.979690i	$-0.435738\pi$
$457$	−16.6569	−	16.6569i	−0.779175	−	0.779175i	−0.979690	+	0.200516i	$0.935738\pi$
$458$	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	$0.0868018\pi$
$461$			11.5655i			0.538657i	−0.963048	+	0.269329i	$0.913198\pi$
$462$		0			0
$463$	−12.4160	+	12.4160i	−0.577021	+	0.577021i	−0.934081	−	0.357061i	$-0.883779\pi$
$463$	−12.4160	+	12.4160i	−0.577021	+	0.577021i	0.357061	+	0.934081i	$0.383779\pi$
$464$		−	9.70636i		−	0.450606i
$465$		0			0
$466$	−3.08780			−0.143039
$467$	−6.14975	+	6.14975i	−0.284577	+	0.284577i	−0.834931	−	0.550355i	$-0.814493\pi$
$467$	−6.14975	+	6.14975i	−0.284577	+	0.284577i	0.550355	+	0.834931i	$0.314493\pi$
$468$		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	0.0159910	−	0.999872i	$-0.494910\pi$
$487$	−21.7124	−	21.7124i	−0.983881	−	0.983881i	−0.999872	+	0.0159910i	$0.994910\pi$
$488$	−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	$-0.737649\pi$
$499$		−	32.7928i		−	1.46801i	0.679144	−	0.734005i	$-0.262351\pi$
$500$	−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	0.797097	−	0.603852i	$-0.206368\pi$
$503$	4.33403	+	4.33403i	0.193245	+	0.193245i	−0.603852	+	0.797097i	$0.706368\pi$
$504$		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	$0.0716039\pi$
$521$			10.1828i			0.446116i	−0.974805	+	0.223058i	$0.928396\pi$
$522$		0			0
$523$	7.86522	+	7.86522i	0.343922	+	0.343922i	0.857840	−	0.513917i	$-0.171806\pi$
$523$	7.86522	+	7.86522i	0.343922	+	0.343922i	−0.513917	+	0.857840i	$0.671806\pi$
$524$	−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	0.923019	−	0.384755i	$-0.125714\pi$
$547$	12.5889	+	12.5889i	0.538264	+	0.538264i	−0.384755	+	0.923019i	$0.625714\pi$
$548$	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	−0.999110	−	0.0421733i	$-0.986572\pi$
$557$	−24.5752	−	24.5752i	−1.04128	−	1.04128i	−0.0421733	−	0.999110i	$-0.513428\pi$
$558$		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	0.562180	−	0.827015i	$-0.309963\pi$
$563$	−6.28391	−	6.28391i	−0.264835	−	0.264835i	−0.827015	+	0.562180i	$0.809963\pi$
$564$		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	$0.102298\pi$
$569$			15.0696i			0.631749i	−0.948801	+	0.315875i	$0.897702\pi$
$570$		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	−0.345406	−	0.938453i	$-0.612259\pi$
$577$	14.2455	−	14.2455i	0.593048	−	0.593048i	0.938453	+	0.345406i	$0.112259\pi$
$578$	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	−0.820646	−	0.571437i	$-0.806386\pi$
$587$	−6.03786	+	6.03786i	−0.249209	+	0.249209i	0.571437	+	0.820646i	$0.306386\pi$
$588$		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	0.202895	−	0.979200i	$-0.434965\pi$
$593$	−18.9043	−	18.9043i	−0.776305	−	0.776305i	−0.979200	+	0.202895i	$0.934965\pi$
$594$		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	$-0.835675\pi$
$599$		−	24.1620i		−	0.987233i	0.869680	−	0.493617i	$-0.164325\pi$
$600$		0			0
$601$		−	46.4416i		−	1.89439i	−0.320652	−	0.947197i	$-0.603902\pi$
$601$		−	46.4416i		−	1.89439i	0.320652	−	0.947197i	$-0.396098\pi$
$602$	−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	−0.999981	−	0.00612457i	$-0.998050\pi$
$607$	−24.4860	+	24.4860i	−0.993857	+	0.993857i	0.00612457	+	0.999981i	$0.498050\pi$
$608$	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	−0.219569	+	0.975597i	$0.570465\pi$
$613$	−29.5909	+	29.5909i	−1.19517	+	1.19517i	−0.975597	+	0.219569i	$0.929535\pi$
$614$	−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	0.966672	+	0.256019i	$0.0824110\pi$
$617$	30.3710	+	30.3710i	1.22269	+	1.22269i	0.256019	+	0.966672i	$0.417589\pi$
$618$		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	0.821165	−	0.570691i	$-0.193325\pi$
$643$	6.35138	+	6.35138i	0.250474	+	0.250474i	−0.570691	+	0.821165i	$0.693325\pi$
$644$	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	0.452274	−	0.891879i	$-0.350613\pi$
$647$	34.1901	−	34.1901i	1.34415	−	1.34415i	0.891879	−	0.452274i	$-0.149387\pi$
$648$		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	−0.197565	+	0.980290i	$0.563303\pi$
$653$	−30.0988	+	30.0988i	−1.17786	+	1.17786i	−0.980290	+	0.197565i	$0.936697\pi$
$654$		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	$-0.820925\pi$
$659$		−	27.3843i		−	1.06674i	0.845881	−	0.533371i	$-0.179075\pi$
$660$		0			0
$661$			22.5855i			0.878475i	0.898371	+	0.439238i	$0.144751\pi$
$661$			22.5855i			0.878475i	−0.898371	+	0.439238i	$0.855249\pi$
$662$	−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	−0.276894	−	0.960900i	$-0.589305\pi$
$673$	17.7447	−	17.7447i	0.684006	−	0.684006i	0.960900	+	0.276894i	$0.0893052\pi$
$674$		−	9.98327i		−	0.384541i
$675$		0			0
$676$	12.3137			0.473604
$677$	−18.4477	+	18.4477i	−0.709003	+	0.709003i	−0.966326	−	0.257322i	$-0.917160\pi$
$677$	−18.4477	+	18.4477i	−0.709003	+	0.709003i	0.257322	+	0.966326i	$0.417160\pi$
$678$		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	−0.732566	−	0.680696i	$-0.761678\pi$
$683$	−1.35560	+	1.35560i	−0.0518704	+	0.0518704i	0.680696	+	0.732566i	$0.261678\pi$
$684$		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	$0.0257268\pi$
$691$			4.24455i			0.161470i	−0.996736	+	0.0807352i	$0.974273\pi$
$692$	−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	$-0.778259\pi$
$709$		−	34.1694i		−	1.28326i	0.767015	−	0.641629i	$-0.221741\pi$
$710$	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	−0.511563	−	0.859246i	$-0.670933\pi$
$727$	9.37456	−	9.37456i	0.347683	−	0.347683i	0.859246	+	0.511563i	$0.170933\pi$
$728$	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	0.531489	−	0.847065i	$-0.321633\pi$
$733$	−8.54390	−	8.54390i	−0.315576	−	0.315576i	−0.847065	+	0.531489i	$0.821633\pi$
$734$	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	$0.148153\pi$
$739$			24.4015i			0.897624i	−0.893626	+	0.448812i	$0.851847\pi$
$740$	−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	−0.939851	−	0.341584i	$-0.889036\pi$
$743$	−16.3076	+	16.3076i	−0.598267	+	0.598267i	0.341584	+	0.939851i	$0.389036\pi$
$744$		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	0.236608	−	0.971605i	$-0.423964\pi$
$757$	−20.2224	−	20.2224i	−0.734997	−	0.734997i	−0.971605	+	0.236608i	$0.923964\pi$
$758$	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	$-0.862266\pi$
$761$		−	23.1354i		−	0.838657i	0.907835	−	0.419329i	$-0.137734\pi$
$762$		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	0.987393	−	0.158289i	$-0.0505977\pi$
$773$	23.0515	+	23.0515i	0.829104	+	0.829104i	−0.158289	+	0.987393i	$0.550598\pi$
$774$		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	−0.127996	−	0.991775i	$-0.540855\pi$
$787$	24.2320	−	24.2320i	0.863779	−	0.863779i	0.991775	+	0.127996i	$0.0408545\pi$
$788$	−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	−0.324627	−	0.945842i	$-0.605239\pi$
$797$	17.5376	−	17.5376i	0.621215	−	0.621215i	0.945842	+	0.324627i	$0.105239\pi$
$798$		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	$0.114961\pi$
$809$			20.1011i			0.706718i	−0.935488	+	0.353359i	$0.885039\pi$
$810$		0			0
$811$			27.6340i			0.970360i	0.874414	+	0.485180i	$0.161246\pi$
$811$			27.6340i			0.970360i	−0.874414	+	0.485180i	$0.838754\pi$
$812$	−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	−0.899803	−	0.436296i	$-0.856290\pi$
$823$	−13.2971	+	13.2971i	−0.463507	+	0.463507i	0.436296	+	0.899803i	$0.356290\pi$
$824$	−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	0.630040	−	0.776563i	$-0.283038\pi$
$827$	−4.21364	−	4.21364i	−0.146523	−	0.146523i	−0.776563	+	0.630040i	$0.783038\pi$
$828$		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	−0.999179	−	0.0405092i	$-0.987102\pi$
$853$	−30.3653	−	30.3653i	−1.03969	−	1.03969i	−0.0405092	−	0.999179i	$-0.512898\pi$
$854$	−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	0.139680	−	0.990197i	$-0.455393\pi$
$857$	33.0766	−	33.0766i	1.12988	−	1.12988i	0.990197	−	0.139680i	$-0.0446072\pi$
$858$		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	−0.867375	−	0.497655i	$-0.834194\pi$
$863$	−10.8612	+	10.8612i	−0.369720	+	0.369720i	0.497655	+	0.867375i	$0.334194\pi$
$864$		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	0.600350	−	0.799737i	$-0.295028\pi$
$877$	−5.90470	−	5.90470i	−0.199388	−	0.199388i	−0.799737	+	0.600350i	$0.795028\pi$
$878$	−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	$-0.963663\pi$
$881$		−	6.76200i		−	0.227818i	0.993491	−	0.113909i	$-0.0363372\pi$
$882$		0			0
$883$	24.6192	−	24.6192i	0.828501	−	0.828501i	−0.158808	−	0.987309i	$-0.550765\pi$
$883$	24.6192	−	24.6192i	0.828501	−	0.828501i	0.987309	+	0.158808i	$0.0507651\pi$
$884$			2.01735i			0.0678508i
$885$		0			0
$886$	−1.97188			−0.0662466
$887$	−6.92132	+	6.92132i	−0.232395	+	0.232395i	−0.813692	−	0.581297i	$-0.802546\pi$
$887$	−6.92132	+	6.92132i	−0.232395	+	0.232395i	0.581297	+	0.813692i	$0.302546\pi$
$888$		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	0.595106	−	0.803647i	$-0.297110\pi$
$907$	−6.28050	−	6.28050i	−0.208540	−	0.208540i	−0.803647	+	0.595106i	$0.797110\pi$
$908$	−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	$0.0492504\pi$
$919$			9.34358i			0.308216i	−0.988054	+	0.154108i	$0.950750\pi$
$920$	−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	−0.994870	−	0.101158i	$-0.967745\pi$
$937$	−27.3569	+	27.3569i	−0.893713	+	0.893713i	0.101158	+	0.994870i	$0.467745\pi$
$938$	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	$-0.656991\pi$
$941$		−	54.0397i		−	1.76164i	0.473448	−	0.880822i	$-0.343009\pi$
$942$		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	0.109585	−	0.993977i	$-0.465048\pi$
$947$	−27.2157	−	27.2157i	−0.884393	−	0.884393i	−0.993977	+	0.109585i	$0.965048\pi$
$948$		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	−0.628497	−	0.777812i	$-0.716330\pi$
$953$	4.60945	−	4.60945i	0.149315	−	0.149315i	0.777812	+	0.628497i	$0.216330\pi$
$954$		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	0.999999	+	0.00150238i	$0.000478222\pi$
$967$	31.1433	+	31.1433i	1.00150	+	1.00150i	0.00150238	+	0.999999i	$0.499522\pi$
$968$	−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	$0.000314191\pi$
$971$			0.0615153i			0.00197412i	−1.00000		0.000987061i	$0.999686\pi$
$972$		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	0.693823	−	0.720145i	$-0.255925\pi$
$977$	−0.822738	−	0.822738i	−0.0263217	−	0.0263217i	−0.720145	+	0.693823i	$0.755925\pi$
$978$		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	0.949542	−	0.313639i	$-0.101548\pi$
$983$	19.9374	+	19.9374i	0.635903	+	0.635903i	−0.313639	+	0.949542i	$0.601548\pi$
$984$		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	−0.999896	−	0.0144253i	$-0.995408\pi$
$997$	−31.1165	+	31.1165i	−0.985471	+	0.985471i	0.0144253	+	0.999896i	$0.495408\pi$
$998$	−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.307.2		8
3.2	odd	2		210.2.m.b.97.3	yes	8
5.3	odd	4		630.2.p.b.433.1		8
7.6	odd	2		630.2.p.b.307.1		8
12.11	even	2		1680.2.cz.a.97.3		8
15.2	even	4		1050.2.m.b.643.1		8
15.8	even	4		210.2.m.a.13.4	✓	8
15.14	odd	2		1050.2.m.a.307.1		8
21.20	even	2		210.2.m.a.97.4	yes	8
35.13	even	4	inner	630.2.p.c.433.2		8
60.23	odd	4		1680.2.cz.b.433.2		8
84.83	odd	2		1680.2.cz.b.97.2		8
105.62	odd	4		1050.2.m.a.643.1		8
105.83	odd	4		210.2.m.b.13.3	yes	8
105.104	even	2		1050.2.m.b.307.1		8
420.83	even	4		1680.2.cz.a.433.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.4	✓	8	15.8	even	4
210.2.m.a.97.4	yes	8	21.20	even	2
210.2.m.b.13.3	yes	8	105.83	odd	4
210.2.m.b.97.3	yes	8	3.2	odd	2
630.2.p.b.307.1		8	7.6	odd	2
630.2.p.b.433.1		8	5.3	odd	4
630.2.p.c.307.2		8	1.1	even	1	trivial
630.2.p.c.433.2		8	35.13	even	4	inner
1050.2.m.a.307.1		8	15.14	odd	2
1050.2.m.a.643.1		8	105.62	odd	4
1050.2.m.b.307.1		8	105.104	even	2
1050.2.m.b.643.1		8	15.2	even	4
1680.2.cz.a.97.3		8	12.11	even	2
1680.2.cz.a.433.3		8	420.83	even	4
1680.2.cz.b.97.2		8	84.83	odd	2
1680.2.cz.b.433.2		8	60.23	odd	4

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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