LMFDB - Embedded newform 1134.2.k.d.647.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 796x^12 - 2228x^11 + 5254x^10 - 10232x^9 + 16903x^8 - 23292x^7 + 26994x^6 - 25716x^5 + 19962x^4 - 12096x^3 + 5454x^2 - 1620*x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.7
Root			$0.500000 - 0.911095i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.d.971.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.330211 - 0.571943i) q^{5} +(-2.34953 + 1.21644i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.330211 - 0.571943i) q^{5} +(-2.34953 + 1.21644i) q^{7} -1.00000i q^{8} +(-0.571943 - 0.330211i) q^{10} +(-2.25192 - 1.30015i) q^{11} -5.87410i q^{13} +(-1.42653 + 2.22823i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.35656 + 4.08169i) q^{17} +(-3.59343 + 2.07467i) q^{19} -0.660423 q^{20} -2.60030 q^{22} +(-4.56456 + 2.63535i) q^{23} +(2.28192 - 3.95240i) q^{25} +(-2.93705 - 5.08712i) q^{26} +(-0.121294 + 2.64297i) q^{28} -7.43874i q^{29} +(-1.73804 - 1.00346i) q^{31} +(-0.866025 - 0.500000i) q^{32} +4.71312i q^{34} +(1.47157 + 0.942112i) q^{35} +(3.17112 + 5.49254i) q^{37} +(-2.07467 + 3.59343i) q^{38} +(-0.571943 + 0.330211i) q^{40} -7.90306 q^{41} -2.66007 q^{43} +(-2.25192 + 1.30015i) q^{44} +(-2.63535 + 4.56456i) q^{46} +(-0.874572 - 1.51480i) q^{47} +(4.04054 - 5.71612i) q^{49} -4.56384i q^{50} +(-5.08712 - 2.93705i) q^{52} +(-7.83672 - 4.52454i) q^{53} +1.71730i q^{55} +(1.21644 + 2.34953i) q^{56} +(-3.71937 - 6.44214i) q^{58} +(0.111972 - 0.193941i) q^{59} +(7.78008 - 4.49183i) q^{61} -2.00692 q^{62} -1.00000 q^{64} +(-3.35965 + 1.93970i) q^{65} +(5.67037 - 9.82137i) q^{67} +(2.35656 + 4.08169i) q^{68} +(1.74548 + 0.0801053i) q^{70} +3.89426i q^{71} +(-3.46836 - 2.00246i) q^{73} +(5.49254 + 3.17112i) q^{74} +4.14934i q^{76} +(6.87250 + 0.315400i) q^{77} +(5.08602 + 8.80925i) q^{79} +(-0.330211 + 0.571943i) q^{80} +(-6.84425 + 3.95153i) q^{82} -12.2888 q^{83} +3.11265 q^{85} +(-2.30369 + 1.33003i) q^{86} +(-1.30015 + 2.25192i) q^{88} +(7.52627 + 13.0359i) q^{89} +(7.14550 + 13.8014i) q^{91} +5.27070i q^{92} +(-1.51480 - 0.874572i) q^{94} +(2.37318 + 1.37016i) q^{95} +4.33520i q^{97} +(0.641153 - 6.97058i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 8 * q^7	$ 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.330211	−	0.571943i	−0.147675	−	0.255781i	0.782693	−	0.622408i	$-0.213846\pi$
$5$	−0.330211	−	0.571943i	−0.147675	−	0.255781i	−0.930368	+	0.366628i	$0.880512\pi$
$6$		0			0
$7$	−2.34953	+	1.21644i	−0.888037	+	0.459772i
$7$	−2.34953	+	1.21644i	−0.888037	+	0.459772i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.571943	−	0.330211i	−0.180864	−	0.104422i
$11$	−2.25192	−	1.30015i	−0.678980	−	0.392009i	0.120490	−	0.992714i	$-0.461553\pi$
$11$	−2.25192	−	1.30015i	−0.678980	−	0.392009i	−0.799471	+	0.600705i	$0.794887\pi$
$12$		0			0
$13$		−	5.87410i		−	1.62918i	−0.580035	−	0.814592i	$-0.696961\pi$
$13$		−	5.87410i		−	1.62918i	0.580035	−	0.814592i	$-0.303039\pi$
$14$	−1.42653	+	2.22823i	−0.381256	+	0.595520i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.35656	+	4.08169i	−0.571550	+	0.989954i	0.424857	+	0.905261i	$0.360324\pi$
$17$	−2.35656	+	4.08169i	−0.571550	+	0.989954i	−0.996407	+	0.0846936i	$0.973009\pi$
$18$		0			0
$19$	−3.59343	+	2.07467i	−0.824389	+	0.475961i	−0.851928	−	0.523659i	$-0.824566\pi$
$19$	−3.59343	+	2.07467i	−0.824389	+	0.475961i	0.0275384	+	0.999621i	$0.491233\pi$
$20$	−0.660423			−0.147675
$21$		0			0
$22$	−2.60030			−0.554385
$23$	−4.56456	+	2.63535i	−0.951776	+	0.549508i	−0.893632	−	0.448800i	$-0.851852\pi$
$23$	−4.56456	+	2.63535i	−0.951776	+	0.549508i	−0.0581439	+	0.998308i	$0.518518\pi$
$24$		0			0
$25$	2.28192	−	3.95240i	0.456384	−	0.790481i
$26$	−2.93705	−	5.08712i	−0.576003	−	0.997667i
$27$		0			0
$28$	−0.121294	+	2.64297i	−0.0229224	+	0.499474i
$29$		−	7.43874i		−	1.38134i	−0.723170	−	0.690670i	$-0.757316\pi$
$29$		−	7.43874i		−	1.38134i	0.723170	−	0.690670i	$-0.242684\pi$
$30$		0			0
$31$	−1.73804	−	1.00346i	−0.312162	−	0.180227i	0.335732	−	0.941958i	$-0.391017\pi$
$31$	−1.73804	−	1.00346i	−0.312162	−	0.180227i	−0.647894	+	0.761731i	$0.724350\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			4.71312i			0.808294i
$35$	1.47157	+	0.942112i	0.248742	+	0.159246i
$36$		0			0
$37$	3.17112	+	5.49254i	0.521329	+	0.902968i	0.999692	+	0.0248059i	$0.00789677\pi$
$37$	3.17112	+	5.49254i	0.521329	+	0.902968i	−0.478364	+	0.878162i	$0.658770\pi$
$38$	−2.07467	+	3.59343i	−0.336556	+	0.582931i
$39$		0			0
$40$	−0.571943	+	0.330211i	−0.0904321	+	0.0522110i
$41$	−7.90306			−1.23425			−0.617126	−	0.786865i	$-0.711703\pi$
$41$	−7.90306			−1.23425			−0.617126	+	0.786865i	$0.711703\pi$
$42$		0			0
$43$	−2.66007			−0.405656			−0.202828	−	0.979214i	$-0.565013\pi$
$43$	−2.66007			−0.405656			−0.202828	+	0.979214i	$0.565013\pi$
$44$	−2.25192	+	1.30015i	−0.339490	+	0.196005i
$45$		0			0
$46$	−2.63535	+	4.56456i	−0.388561	+	0.673007i
$47$	−0.874572	−	1.51480i	−0.127569	−	0.220957i	0.795165	−	0.606393i	$-0.207384\pi$
$47$	−0.874572	−	1.51480i	−0.127569	−	0.220957i	−0.922734	+	0.385436i	$0.874051\pi$
$48$		0			0
$49$	4.04054	−	5.71612i	0.577220	−	0.816588i
$50$		−	4.56384i		−	0.645425i
$51$		0			0
$52$	−5.08712	−	2.93705i	−0.705457	−	0.407296i
$53$	−7.83672	−	4.52454i	−1.07646	−	0.621493i	−0.146519	−	0.989208i	$-0.546807\pi$
$53$	−7.83672	−	4.52454i	−1.07646	−	0.621493i	−0.929938	+	0.367715i	$0.880140\pi$
$54$		0			0
$55$			1.71730i			0.231560i
$56$	1.21644	+	2.34953i	0.162554	+	0.313969i
$57$		0			0
$58$	−3.71937	−	6.44214i	−0.488377	−	0.845894i
$59$	0.111972	−	0.193941i	0.0145775	−	0.0252490i	−0.858645	−	0.512571i	$-0.828693\pi$
$59$	0.111972	−	0.193941i	0.0145775	−	0.0252490i	0.873222	+	0.487322i	$0.162026\pi$
$60$		0			0
$61$	7.78008	−	4.49183i	0.996137	−	0.575120i	0.0890340	−	0.996029i	$-0.471622\pi$
$61$	7.78008	−	4.49183i	0.996137	−	0.575120i	0.907103	+	0.420909i	$0.138289\pi$
$62$	−2.00692			−0.254879
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.35965	+	1.93970i	−0.416714	+	0.240590i
$66$		0			0
$67$	5.67037	−	9.82137i	0.692746	−	1.19987i	−0.278189	−	0.960526i	$-0.589734\pi$
$67$	5.67037	−	9.82137i	0.692746	−	1.19987i	0.970935	−	0.239345i	$-0.0769326\pi$
$68$	2.35656	+	4.08169i	0.285775	+	0.494977i
$69$		0			0
$70$	1.74548	+	0.0801053i	0.208624	+	0.00957442i
$71$			3.89426i			0.462163i	0.972934	+	0.231082i	$0.0742265\pi$
$71$			3.89426i			0.462163i	−0.972934	+	0.231082i	$0.925774\pi$
$72$		0			0
$73$	−3.46836	−	2.00246i	−0.405940	−	0.234370i	0.283104	−	0.959089i	$-0.408636\pi$
$73$	−3.46836	−	2.00246i	−0.405940	−	0.234370i	−0.689044	+	0.724720i	$0.741969\pi$
$74$	5.49254	+	3.17112i	0.638495	+	0.368635i
$75$		0			0
$76$			4.14934i			0.475961i
$77$	6.87250	+	0.315400i	0.783195	+	0.0359432i
$78$		0			0
$79$	5.08602	+	8.80925i	0.572222	+	0.991118i	0.996337	+	0.0855099i	$0.0272519\pi$
$79$	5.08602	+	8.80925i	0.572222	+	0.991118i	−0.424115	+	0.905608i	$0.639415\pi$
$80$	−0.330211	+	0.571943i	−0.0369188	+	0.0639452i
$81$		0			0
$82$	−6.84425	+	3.95153i	−0.755821	+	0.436374i
$83$	−12.2888			−1.34887			−0.674437	−	0.738332i	$-0.735614\pi$
$83$	−12.2888			−1.34887			−0.674437	+	0.738332i	$0.735614\pi$
$84$		0			0
$85$	3.11265			0.337615
$86$	−2.30369	+	1.33003i	−0.248413	+	0.143421i
$87$		0			0
$88$	−1.30015	+	2.25192i	−0.138596	+	0.240056i
$89$	7.52627	+	13.0359i	0.797783	+	1.38180i	0.921057	+	0.389428i	$0.127327\pi$
$89$	7.52627	+	13.0359i	0.797783	+	1.38180i	−0.123274	+	0.992373i	$0.539340\pi$
$90$		0			0
$91$	7.14550	+	13.8014i	0.749052	+	1.44678i
$92$			5.27070i			0.549508i
$93$		0			0
$94$	−1.51480	−	0.874572i	−0.156240	−	0.0902052i
$95$	2.37318	+	1.37016i	0.243483	+	0.140575i
$96$		0			0
$97$			4.33520i			0.440173i	0.975480	+	0.220087i	$0.0706340\pi$
$97$			4.33520i			0.440173i	−0.975480	+	0.220087i	$0.929366\pi$
$98$	0.641153	−	6.97058i	0.0647662	−	0.704134i
$99$		0			0
$100$	−2.28192	−	3.95240i	−0.228192	−	0.395240i
$101$	−2.53783	+	4.39565i	−0.252523	+	0.437384i	−0.964220	−	0.265104i	$-0.914594\pi$
$101$	−2.53783	+	4.39565i	−0.252523	+	0.437384i	0.711696	+	0.702487i	$0.247927\pi$
$102$		0			0
$103$	2.48292	−	1.43352i	0.244649	−	0.141248i	−0.372662	−	0.927967i	$-0.621555\pi$
$103$	2.48292	−	1.43352i	0.244649	−	0.141248i	0.617312	+	0.786719i	$0.288222\pi$
$104$	−5.87410			−0.576003
$105$		0			0
$106$	−9.04907			−0.878923
$107$	8.49932	−	4.90709i	0.821660	−	0.474386i	−0.0293282	−	0.999570i	$-0.509337\pi$
$107$	8.49932	−	4.90709i	0.821660	−	0.474386i	0.850989	+	0.525184i	$0.176003\pi$
$108$		0			0
$109$	3.84454	−	6.65893i	0.368240	−	0.637810i	−0.621051	−	0.783770i	$-0.713294\pi$
$109$	3.84454	−	6.65893i	0.368240	−	0.637810i	0.989290	+	0.145961i	$0.0466272\pi$
$110$	0.858648	+	1.48722i	0.0818688	+	0.141801i
$111$		0			0
$112$	2.22823	+	1.42653i	0.210548	+	0.134794i
$113$		−	0.544483i		−	0.0512207i	−0.999672	−	0.0256103i	$-0.991847\pi$
$113$		−	0.544483i		−	0.0512207i	0.999672	−	0.0256103i	$-0.00815291\pi$
$114$		0			0
$115$	3.01454	+	1.74044i	0.281107	+	0.162297i
$116$	−6.44214	−	3.71937i	−0.598138	−	0.345335i
$117$		0			0
$118$		−	0.223944i		−	0.0206157i
$119$	0.571674	−	12.4566i	0.0524052	−	1.14190i
$120$		0			0
$121$	−2.11923	−	3.67061i	−0.192657	−	0.333692i
$122$	4.49183	−	7.78008i	0.406671	−	0.704375i
$123$		0			0
$124$	−1.73804	+	1.00346i	−0.156081	+	0.0901134i
$125$	−6.31618			−0.564936
$126$		0			0
$127$	19.4512			1.72602			0.863009	−	0.505189i	$-0.168577\pi$
$127$	19.4512			1.72602			0.863009	+	0.505189i	$0.168577\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.93970	+	3.35965i	−0.170123	+	0.294661i
$131$	−8.35965	−	14.4793i	−0.730386	−	1.26507i	−0.956718	−	0.291016i	$-0.906007\pi$
$131$	−8.35965	−	14.4793i	−0.730386	−	1.26507i	0.226332	−	0.974050i	$-0.427327\pi$
$132$		0			0
$133$	5.91915	−	9.24568i	0.513255	−	0.801702i
$134$		−	11.3407i		−	0.979691i
$135$		0			0
$136$	4.08169	+	2.35656i	0.350002	+	0.202074i
$137$	−2.72325	−	1.57227i	−0.232663	−	0.134328i	0.379137	−	0.925340i	$-0.376221\pi$
$137$	−2.72325	−	1.57227i	−0.232663	−	0.134328i	−0.611800	+	0.791013i	$0.709554\pi$
$138$		0			0
$139$			16.8214i			1.42677i	0.700771	+	0.713386i	$0.252840\pi$
$139$			16.8214i			1.42677i	−0.700771	+	0.713386i	$0.747160\pi$
$140$	1.55168	−	0.803365i	0.131141	−	0.0678968i
$141$		0			0
$142$	1.94713	+	3.37253i	0.163399	+	0.283016i
$143$	−7.63721	+	13.2280i	−0.638655	+	1.10618i
$144$		0			0
$145$	−4.25453	+	2.45636i	−0.353320	+	0.203989i
$146$	−4.00491			−0.331449
$147$		0			0
$148$	6.34224			0.521329
$149$	18.0015	−	10.3931i	1.47474	−	0.851439i	0.475142	−	0.879909i	$-0.342397\pi$
$149$	18.0015	−	10.3931i	1.47474	−	0.851439i	0.999595	+	0.0284697i	$0.00906343\pi$
$150$		0			0
$151$	4.71396	−	8.16482i	0.383617	−	0.664443i	−0.607960	−	0.793968i	$-0.708012\pi$
$151$	4.71396	−	8.16482i	0.383617	−	0.664443i	0.991576	+	0.129525i	$0.0413451\pi$
$152$	2.07467	+	3.59343i	0.168278	+	0.291466i
$153$		0			0
$154$	6.10946	−	3.16311i	0.492315	−	0.254890i
$155$			1.32542i			0.106460i
$156$		0			0
$157$	4.00571	+	2.31270i	0.319690	+	0.184573i	0.651254	−	0.758859i	$-0.274243\pi$
$157$	4.00571	+	2.31270i	0.319690	+	0.184573i	−0.331564	+	0.943433i	$0.607576\pi$
$158$	8.80925	+	5.08602i	0.700826	+	0.404622i
$159$		0			0
$160$			0.660423i			0.0522110i
$161$	7.51880	−	11.7443i	0.592564	−	0.925583i
$162$		0			0
$163$	−5.76907	−	9.99233i	−0.451869	−	0.782659i	0.546634	−	0.837372i	$-0.315909\pi$
$163$	−5.76907	−	9.99233i	−0.451869	−	0.782659i	−0.998502	+	0.0547126i	$0.982576\pi$
$164$	−3.95153	+	6.84425i	−0.308563	+	0.534446i
$165$		0			0
$166$	−10.6424	+	6.14441i	−0.826013	+	0.476899i
$167$	−19.0063			−1.47076			−0.735378	−	0.677658i	$-0.762995\pi$
$167$	−19.0063			−1.47076			−0.735378	+	0.677658i	$0.762995\pi$
$168$		0			0
$169$	−21.5051			−1.65424
$170$	2.69564	−	1.55633i	0.206746	−	0.119365i
$171$		0			0
$172$	−1.33003	+	2.30369i	−0.101414	+	0.175654i
$173$	4.78911	+	8.29499i	0.364110	+	0.630656i	0.988633	−	0.150350i	$-0.0480400\pi$
$173$	4.78911	+	8.29499i	0.364110	+	0.630656i	−0.624523	+	0.781006i	$0.714707\pi$
$174$		0			0
$175$	−0.553567	+	12.0621i	−0.0418457	+	0.911809i
$176$			2.60030i			0.196005i
$177$		0			0
$178$	13.0359	+	7.52627i	0.977080	+	0.564118i
$179$	17.6588	+	10.1953i	1.31988	+	0.762032i	0.983709	−	0.179769i	$-0.0575350\pi$
$179$	17.6588	+	10.1953i	1.31988	+	0.762032i	0.336170	+	0.941801i	$0.390868\pi$
$180$		0			0
$181$		−	23.9866i		−	1.78291i	−0.453107	−	0.891456i	$-0.649684\pi$
$181$		−	23.9866i		−	1.78291i	0.453107	−	0.891456i	$-0.350316\pi$
$182$	13.0889	+	8.37958i	0.970211	+	0.621136i
$183$		0			0
$184$	2.63535	+	4.56456i	0.194280	+	0.336504i
$185$	2.09428	−	3.62740i	0.153974	−	0.266692i
$186$		0			0
$187$	10.6136	−	6.12776i	0.776143	−	0.448106i
$188$	−1.74914			−0.127569
$189$		0			0
$190$	2.74032			0.198803
$191$	4.94699	−	2.85615i	0.357952	−	0.206664i	−0.310230	−	0.950661i	$-0.600406\pi$
$191$	4.94699	−	2.85615i	0.357952	−	0.206664i	0.668182	+	0.743998i	$0.267073\pi$
$192$		0			0
$193$	−0.691202	+	1.19720i	−0.0497538	+	0.0861761i	−0.889830	−	0.456293i	$-0.849177\pi$
$193$	−0.691202	+	1.19720i	−0.0497538	+	0.0861761i	0.840076	+	0.542469i	$0.182510\pi$
$194$	2.16760	+	3.75439i	0.155625	+	0.269550i
$195$		0			0
$196$	−2.93003	−	6.35727i	−0.209288	−	0.454091i
$197$		−	5.94533i		−	0.423587i	−0.977314	−	0.211794i	$-0.932069\pi$
$197$		−	5.94533i		−	0.423587i	0.977314	−	0.211794i	$-0.0679305\pi$
$198$		0			0
$199$	−16.1647	−	9.33269i	−1.14588	−	0.661577i	−0.198003	−	0.980201i	$-0.563446\pi$
$199$	−16.1647	−	9.33269i	−1.14588	−	0.661577i	−0.947881	+	0.318625i	$0.896779\pi$
$200$	−3.95240	−	2.28192i	−0.279477	−	0.161356i
$201$		0			0
$202$			5.07566i			0.357122i
$203$	9.04879	+	17.4775i	0.635101	+	1.22668i
$204$		0			0
$205$	2.60968	+	4.52010i	0.182268	+	0.315698i
$206$	1.43352	−	2.48292i	0.0998777	−	0.172993i
$207$		0			0
$208$	−5.08712	+	2.93705i	−0.352729	+	0.203648i
$209$	10.7895			0.746326
$210$		0			0
$211$	−8.17368			−0.562699			−0.281350	−	0.959605i	$-0.590782\pi$
$211$	−8.17368			−0.562699			−0.281350	+	0.959605i	$0.590782\pi$
$212$	−7.83672	+	4.52454i	−0.538228	+	0.310746i
$213$		0			0
$214$	4.90709	−	8.49932i	0.335441	−	0.581002i
$215$	0.878384	+	1.52141i	0.0599053	+	0.103759i
$216$		0			0
$217$	5.30423	+	0.243427i	0.360075	+	0.0165249i
$218$		−	7.68907i		−	0.520770i
$219$		0			0
$220$	1.48722	+	0.858648i	0.100268	+	0.0578900i
$221$	23.9762	+	13.8427i	1.61282	+	0.931160i
$222$		0			0
$223$			27.1394i			1.81739i	0.417462	+	0.908695i	$0.362920\pi$
$223$			27.1394i			1.81739i	−0.417462	+	0.908695i	$0.637080\pi$
$224$	2.64297	+	0.121294i	0.176591	+	0.00810430i
$225$		0			0
$226$	−0.272242	−	0.471536i	−0.0181092	−	0.0313661i
$227$	6.29665	−	10.9061i	0.417924	−	0.723865i	−0.577807	−	0.816174i	$-0.696091\pi$
$227$	6.29665	−	10.9061i	0.417924	−	0.723865i	0.995730	+	0.0923086i	$0.0294246\pi$
$228$		0			0
$229$	−1.22382	+	0.706571i	−0.0808721	+	0.0466916i	−0.539891	−	0.841735i	$-0.681534\pi$
$229$	−1.22382	+	0.706571i	−0.0808721	+	0.0466916i	0.459019	+	0.888427i	$0.348201\pi$
$230$	3.48089			0.229523
$231$		0			0
$232$	−7.43874			−0.488377
$233$	−15.5393	+	8.97160i	−1.01801	+	0.587749i	−0.913527	−	0.406777i	$-0.866652\pi$
$233$	−15.5393	+	8.97160i	−1.01801	+	0.587749i	−0.104484	+	0.994527i	$0.533319\pi$
$234$		0			0
$235$	−0.577587	+	1.00041i	−0.0376776	+	0.0652596i
$236$	−0.111972	−	0.193941i	−0.00728875	−	0.0126245i
$237$		0			0
$238$	−5.73324	−	11.0736i	−0.371631	−	0.717795i
$239$		−	25.6164i		−	1.65699i	−0.559997	−	0.828494i	$-0.689198\pi$
$239$		−	25.6164i		−	1.65699i	0.559997	−	0.828494i	$-0.310802\pi$
$240$		0			0
$241$	−10.5993	−	6.11953i	−0.682764	−	0.394194i	0.118132	−	0.992998i	$-0.462309\pi$
$241$	−10.5993	−	6.11953i	−0.682764	−	0.394194i	−0.800896	+	0.598804i	$0.795643\pi$
$242$	−3.67061	−	2.11923i	−0.235956	−	0.136229i
$243$		0			0
$244$		−	8.98366i		−	0.575120i
$245$	−4.60353	−	0.423432i	−0.294109	−	0.0270521i
$246$		0			0
$247$	12.1868	+	21.1082i	0.775428	+	1.34308i
$248$	−1.00346	+	1.73804i	−0.0637198	+	0.110366i
$249$		0			0
$250$	−5.46997	+	3.15809i	−0.345951	+	0.199735i
$251$	22.2877			1.40679			0.703394	−	0.710800i	$-0.251667\pi$
$251$	22.2877			1.40679			0.703394	+	0.710800i	$0.251667\pi$
$252$		0			0
$253$	13.7054			0.861650
$254$	16.8453	−	9.72561i	1.05697	−	0.610239i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.1946	+	24.5858i	0.885436	+	1.53362i	0.845213	+	0.534429i	$0.179473\pi$
$257$	14.1946	+	24.5858i	0.885436	+	1.53362i	0.0402224	+	0.999191i	$0.487193\pi$
$258$		0			0
$259$	−14.1320	−	9.04738i	−0.878118	−	0.562177i
$260$			3.87939i			0.240590i
$261$		0			0
$262$	−14.4793	−	8.35965i	−0.894537	−	0.516461i
$263$	24.1449	+	13.9401i	1.48884	+	0.859582i	0.999919	−	0.0127465i	$-0.00405745\pi$
$263$	24.1449	+	13.9401i	1.48884	+	0.859582i	0.488921	+	0.872328i	$0.337391\pi$
$264$		0			0
$265$			5.97621i			0.367116i
$266$	0.503290	−	10.9666i	0.0308587	−	0.672403i
$267$		0			0
$268$	−5.67037	−	9.82137i	−0.346373	−	0.599936i
$269$	−3.06694	+	5.31209i	−0.186995	+	0.323884i	−0.944247	−	0.329238i	$-0.893208\pi$
$269$	−3.06694	+	5.31209i	−0.186995	+	0.323884i	0.757252	+	0.653123i	$0.226541\pi$
$270$		0			0
$271$	−2.98593	+	1.72393i	−0.181382	+	0.104721i	−0.587942	−	0.808903i	$-0.700062\pi$
$271$	−2.98593	+	1.72393i	−0.181382	+	0.104721i	0.406560	+	0.913624i	$0.366728\pi$
$272$	4.71312			0.285775
$273$		0			0
$274$	−3.14453			−0.189968
$275$	−10.2774	+	5.93367i	−0.619752	+	0.357814i
$276$		0			0
$277$	6.71559	−	11.6317i	0.403501	−	0.698884i	−0.590645	−	0.806931i	$-0.701127\pi$
$277$	6.71559	−	11.6317i	0.403501	−	0.698884i	0.994146	+	0.108048i	$0.0344600\pi$
$278$	8.41070	+	14.5678i	0.504440	+	0.873716i
$279$		0			0
$280$	0.942112	−	1.47157i	0.0563020	−	0.0879434i
$281$		−	26.4653i		−	1.57879i	−0.613889	−	0.789393i	$-0.710396\pi$
$281$		−	26.4653i		−	1.57879i	0.613889	−	0.789393i	$-0.289604\pi$
$282$		0			0
$283$	−6.64541	−	3.83673i	−0.395029	−	0.228070i	0.289308	−	0.957236i	$-0.406575\pi$
$283$	−6.64541	−	3.83673i	−0.395029	−	0.228070i	−0.684337	+	0.729166i	$0.739908\pi$
$284$	3.37253	+	1.94713i	0.200123	+	0.115541i
$285$		0			0
$286$			15.2744i			0.903195i
$287$	18.5685	−	9.61361i	1.09606	−	0.567474i
$288$		0			0
$289$	−2.60677	−	4.51506i	−0.153340	−	0.265592i
$290$	−2.45636	+	4.25453i	−0.144242	+	0.249835i
$291$		0			0
$292$	−3.46836	+	2.00246i	−0.202970	+	0.117185i
$293$	−3.32948			−0.194511			−0.0972553	−	0.995259i	$-0.531006\pi$
$293$	−3.32948			−0.194511			−0.0972553	+	0.995259i	$0.531006\pi$
$294$		0			0
$295$	−0.147898			−0.00861093
$296$	5.49254	−	3.17112i	0.319247	−	0.184318i
$297$		0			0
$298$	10.3931	−	18.0015i	0.602059	−	1.04280i
$299$	15.4803	+	26.8127i	0.895250	+	1.55062i
$300$		0			0
$301$	6.24990	−	3.23581i	0.360238	−	0.186509i
$302$		−	9.42792i		−	0.542516i
$303$		0			0
$304$	3.59343	+	2.07467i	0.206097	+	0.118990i
$305$	−5.13814	−	2.96651i	−0.294209	−	0.169862i
$306$		0			0
$307$		−	18.5385i		−	1.05805i	−0.848607	−	0.529024i	$-0.822558\pi$
$307$		−	18.5385i		−	1.05805i	0.848607	−	0.529024i	$-0.177442\pi$
$308$	3.70940	−	5.79406i	0.211363	−	0.330147i
$309$		0			0
$310$	0.662708	+	1.14784i	0.0376393	+	0.0651932i
$311$	−10.7758	+	18.6642i	−0.611039	+	1.05835i	0.380026	+	0.924976i	$0.375915\pi$
$311$	−10.7758	+	18.6642i	−0.611039	+	1.05835i	−0.991066	+	0.133376i	$0.957418\pi$
$312$		0			0
$313$	23.5767	−	13.6120i	1.33263	−	0.769396i	0.346930	−	0.937891i	$-0.387224\pi$
$313$	23.5767	−	13.6120i	1.33263	−	0.769396i	0.985702	+	0.168496i	$0.0538909\pi$
$314$	4.62539			0.261026
$315$		0			0
$316$	10.1720			0.572222
$317$	−19.4249	+	11.2149i	−1.09101	+	0.629894i	−0.933845	−	0.357678i	$-0.883568\pi$
$317$	−19.4249	+	11.2149i	−1.09101	+	0.629894i	−0.157164	+	0.987573i	$0.550235\pi$
$318$		0			0
$319$	−9.67147	+	16.7515i	−0.541498	+	0.937902i
$320$	0.330211	+	0.571943i	0.0184594	+	0.0319726i
$321$		0			0
$322$	0.639304	−	13.9303i	0.0356270	−	0.776305i
$323$		−	19.5563i		−	1.08814i
$324$		0			0
$325$	−23.2168	−	13.4042i	−1.28784	−	0.743533i
$326$	−9.99233	−	5.76907i	−0.553424	−	0.319519i
$327$		0			0
$328$			7.90306i			0.436374i
$329$	3.89750	+	2.49520i	0.214876	+	0.137565i
$330$		0			0
$331$	−1.46420	−	2.53608i	−0.0804799	−	0.139395i	0.822976	−	0.568076i	$-0.192312\pi$
$331$	−1.46420	−	2.53608i	−0.0804799	−	0.139395i	−0.903456	+	0.428680i	$0.858979\pi$
$332$	−6.14441	+	10.6424i	−0.337219	+	0.584080i
$333$		0			0
$334$	−16.4600	+	9.50317i	−0.900650	+	0.519991i
$335$	−7.48968			−0.409205
$336$		0			0
$337$	−24.8418			−1.35322			−0.676610	−	0.736341i	$-0.736552\pi$
$337$	−24.8418			−1.35322			−0.676610	+	0.736341i	$0.736552\pi$
$338$	−18.6240	+	10.7525i	−1.01301	+	0.584862i
$339$		0			0
$340$	1.55633	−	2.69564i	0.0844037	−	0.146192i
$341$	2.60929	+	4.51943i	0.141301	+	0.244741i
$342$		0			0
$343$	−2.54004	+	18.3453i	−0.137149	+	0.990550i
$344$			2.66007i			0.143421i
$345$		0			0
$346$	8.29499	+	4.78911i	0.445941	+	0.257464i
$347$	−13.4947	−	7.79117i	−0.724433	−	0.418252i	0.0919490	−	0.995764i	$-0.470690\pi$
$347$	−13.4947	−	7.79117i	−0.724433	−	0.418252i	−0.816382	+	0.577512i	$0.804024\pi$
$348$		0			0
$349$			16.1238i			0.863085i	0.902093	+	0.431542i	$0.142030\pi$
$349$			16.1238i			0.863085i	−0.902093	+	0.431542i	$0.857970\pi$
$350$	5.55164	+	10.7229i	0.296748	+	0.573161i
$351$		0			0
$352$	1.30015	+	2.25192i	0.0692981	+	0.120028i
$353$	10.9701	−	19.0008i	0.583880	−	1.01131i	−0.411134	−	0.911575i	$-0.634867\pi$
$353$	10.9701	−	19.0008i	0.583880	−	1.01131i	0.995014	−	0.0997345i	$-0.0317993\pi$
$354$		0			0
$355$	2.22729	−	1.28593i	0.118212	−	0.0682500i
$356$	15.0525			0.797783
$357$		0			0
$358$	20.3906			1.07768
$359$	9.77938	−	5.64613i	0.516136	−	0.297991i	−0.219216	−	0.975676i	$-0.570350\pi$
$359$	9.77938	−	5.64613i	0.516136	−	0.297991i	0.735352	+	0.677685i	$0.237017\pi$
$360$		0			0
$361$	−0.891506	+	1.54413i	−0.0469214	+	0.0812702i
$362$	−11.9933	−	20.7730i	−0.630355	−	1.09181i
$363$		0			0
$364$	15.5251	+	0.712494i	0.813735	+	0.0373448i
$365$			2.64493i			0.138442i
$366$		0			0
$367$	−10.7901	−	6.22965i	−0.563237	−	0.325185i	0.191207	−	0.981550i	$-0.438760\pi$
$367$	−10.7901	−	6.22965i	−0.563237	−	0.325185i	−0.754444	+	0.656365i	$0.772093\pi$
$368$	4.56456	+	2.63535i	0.237944	+	0.137377i
$369$		0			0
$370$		−	4.18856i		−	0.217753i
$371$	23.9164	+	1.09760i	1.24168	+	0.0569844i
$372$		0			0
$373$	9.19719	+	15.9300i	0.476212	+	0.824824i	0.999629	−	0.0272532i	$-0.00867605\pi$
$373$	9.19719	+	15.9300i	0.476212	+	0.824824i	−0.523416	+	0.852077i	$0.675343\pi$
$374$	6.12776	−	10.6136i	0.316859	−	0.548816i
$375$		0			0
$376$	−1.51480	+	0.874572i	−0.0781200	+	0.0451026i
$377$	−43.6959			−2.25046
$378$		0			0
$379$	−0.285278			−0.0146538			−0.00732688	−	0.999973i	$-0.502332\pi$
$379$	−0.285278			−0.0146538			−0.00732688	+	0.999973i	$0.502332\pi$
$380$	2.37318	−	1.37016i	0.121742	−	0.0702876i
$381$		0			0
$382$	2.85615	−	4.94699i	0.146133	−	0.253110i
$383$	1.39732	+	2.42022i	0.0713996	+	0.123668i	0.899515	−	0.436890i	$-0.143920\pi$
$383$	1.39732	+	2.42022i	0.0713996	+	0.123668i	−0.828115	+	0.560558i	$0.810587\pi$
$384$		0			0
$385$	−2.08899	−	4.03483i	−0.106465	−	0.205634i
$386$			1.38240i			0.0703625i
$387$		0			0
$388$	3.75439	+	2.16760i	0.190601	+	0.110043i
$389$	−6.71856	−	3.87896i	−0.340645	−	0.196671i	0.319912	−	0.947447i	$-0.396347\pi$
$389$	−6.71856	−	3.87896i	−0.340645	−	0.196671i	−0.660557	+	0.750776i	$0.729680\pi$
$390$		0			0
$391$		−	24.8415i		−	1.25629i
$392$	−5.71612	−	4.04054i	−0.288708	−	0.204078i
$393$		0			0
$394$	−2.97267	−	5.14881i	−0.149761	−	0.259393i
$395$	3.35893	−	5.81783i	0.169006	−	0.292727i
$396$		0			0
$397$	5.00629	−	2.89038i	0.251258	−	0.145064i	−0.369082	−	0.929397i	$-0.620328\pi$
$397$	5.00629	−	2.89038i	0.251258	−	0.145064i	0.620340	+	0.784333i	$0.286995\pi$
$398$	−18.6654			−0.935611
$399$		0			0
$400$	−4.56384			−0.228192
$401$	11.8154	−	6.82164i	0.590034	−	0.340656i	−0.175077	−	0.984555i	$-0.556017\pi$
$401$	11.8154	−	6.82164i	0.590034	−	0.340656i	0.765111	+	0.643898i	$0.222684\pi$
$402$		0			0
$403$	−5.89443	+	10.2095i	−0.293623	+	0.508569i
$404$	2.53783	+	4.39565i	0.126262	+	0.218692i
$405$		0			0
$406$	16.5752	+	10.6116i	0.822615	+	0.526644i
$407$		−	16.4917i		−	0.817463i
$408$		0			0
$409$	−25.3625	−	14.6431i	−1.25410	−	0.724053i	−0.282176	−	0.959363i	$-0.591056\pi$
$409$	−25.3625	−	14.6431i	−1.25410	−	0.724053i	−0.971921	+	0.235309i	$0.924390\pi$
$410$	4.52010	+	2.60968i	0.223232	+	0.128883i
$411$		0			0
$412$		−	2.86703i		−	0.141248i
$413$	−0.0271630	+	0.591876i	−0.00133661	+	0.0291243i
$414$		0			0
$415$	4.05791	+	7.02851i	0.199195	+	0.345016i
$416$	−2.93705	+	5.08712i	−0.144001	+	0.249417i
$417$		0			0
$418$	9.34398	−	5.39475i	0.457029	−	0.263866i
$419$	−20.8178			−1.01702			−0.508509	−	0.861057i	$-0.669803\pi$
$419$	−20.8178			−1.01702			−0.508509	+	0.861057i	$0.669803\pi$
$420$		0			0
$421$	−38.3993			−1.87147			−0.935734	−	0.352707i	$-0.885261\pi$
$421$	−38.3993			−1.87147			−0.935734	+	0.352707i	$0.885261\pi$
$422$	−7.07862	+	4.08684i	−0.344582	+	0.198944i
$423$		0			0
$424$	−4.52454	+	7.83672i	−0.219731	+	0.380585i
$425$	10.7550	+	18.6282i	0.521693	+	0.903599i
$426$		0			0
$427$	−12.8154	+	20.0177i	−0.620183	+	0.968723i
$428$		−	9.81417i		−	0.474386i
$429$		0			0
$430$	1.52141	+	0.878384i	0.0733687	+	0.0423595i
$431$	−17.2706	−	9.97120i	−0.831897	−	0.480296i	0.0226047	−	0.999744i	$-0.492804\pi$
$431$	−17.2706	−	9.97120i	−0.831897	−	0.480296i	−0.854502	+	0.519448i	$0.826137\pi$
$432$		0			0
$433$		−	28.2196i		−	1.35615i	−0.734993	−	0.678075i	$-0.762815\pi$
$433$		−	28.2196i		−	1.35615i	0.734993	−	0.678075i	$-0.237185\pi$
$434$	4.71531	−	2.44130i	0.226342	−	0.117186i
$435$		0			0
$436$	−3.84454	−	6.65893i	−0.184120	−	0.318905i
$437$	10.9349	−	18.9399i	0.523089	−	0.906017i
$438$		0			0
$439$	−7.91077	+	4.56728i	−0.377560	+	0.217985i	−0.676756	−	0.736207i	$-0.736615\pi$
$439$	−7.91077	+	4.56728i	−0.377560	+	0.217985i	0.299196	+	0.954192i	$0.403282\pi$
$440$	1.71730			0.0818688
$441$		0			0
$442$	27.6854			1.31686
$443$	−29.2751	+	16.9020i	−1.39090	+	0.803037i	−0.993415	−	0.114571i	$-0.963451\pi$
$443$	−29.2751	+	16.9020i	−1.39090	+	0.803037i	−0.397486	+	0.917608i	$0.630117\pi$
$444$		0			0
$445$	4.97052	−	8.60919i	0.235625	−	0.408115i
$446$	13.5697	+	23.5034i	0.642544	+	1.11292i
$447$		0			0
$448$	2.34953	−	1.21644i	0.111005	−	0.0574714i
$449$		−	27.0131i		−	1.27483i	−0.770522	−	0.637413i	$-0.780005\pi$
$449$		−	27.0131i		−	1.27483i	0.770522	−	0.637413i	$-0.219995\pi$
$450$		0			0
$451$	17.7971	+	10.2752i	0.838032	+	0.483838i
$452$	−0.471536	−	0.272242i	−0.0221792	−	0.0128052i
$453$		0			0
$454$		−	12.5933i		−	0.591033i
$455$	5.53406	−	8.64418i	0.259441	−	0.405246i
$456$		0			0
$457$	1.70305	+	2.94976i	0.0796651	+	0.137984i	0.903105	−	0.429419i	$-0.141282\pi$
$457$	1.70305	+	2.94976i	0.0796651	+	0.137984i	−0.823440	+	0.567403i	$0.807948\pi$
$458$	−0.706571	+	1.22382i	−0.0330159	+	0.0571852i
$459$		0			0
$460$	3.01454	−	1.74044i	0.140554	−	0.0811486i
$461$	1.67610			0.0780639			0.0390319	−	0.999238i	$-0.487573\pi$
$461$	1.67610			0.0780639			0.0390319	+	0.999238i	$0.487573\pi$
$462$		0			0
$463$	16.4467			0.764341			0.382170	−	0.924092i	$-0.375177\pi$
$463$	16.4467			0.764341			0.382170	+	0.924092i	$0.375177\pi$
$464$	−6.44214	+	3.71937i	−0.299069	+	0.172667i
$465$		0			0
$466$	−8.97160	+	15.5393i	−0.415601	+	0.719843i
$467$	1.83112	+	3.17159i	0.0847340	+	0.146764i	0.905278	−	0.424820i	$-0.139663\pi$
$467$	1.83112	+	3.17159i	0.0847340	+	0.146764i	−0.820544	+	0.571584i	$0.806329\pi$
$468$		0			0
$469$	−1.37556	+	29.9732i	−0.0635176	+	1.38404i
$470$			1.15517i			0.0532842i
$471$		0			0
$472$	−0.193941	−	0.111972i	−0.00892686	−	0.00515392i
$473$	5.99027	+	3.45848i	0.275433	+	0.159021i
$474$		0			0
$475$			18.9369i			0.868885i
$476$	−10.5019	−	6.72341i	−0.481355	−	0.308167i
$477$		0			0
$478$	−12.8082	−	22.1845i	−0.585834	−	1.01469i
$479$	−14.2133	+	24.6182i	−0.649422	+	1.12483i	0.333839	+	0.942630i	$0.391656\pi$
$479$	−14.2133	+	24.6182i	−0.649422	+	1.12483i	−0.983261	+	0.182202i	$0.941678\pi$
$480$		0			0
$481$	32.2637	−	18.6275i	1.47110	−	0.849340i
$482$	−12.2391			−0.557474
$483$		0			0
$484$	−4.23846			−0.192657
$485$	2.47949	−	1.43153i	0.112588	−	0.0650026i
$486$		0			0
$487$	−20.0702	+	34.7626i	−0.909467	+	1.57524i	−0.0946602	+	0.995510i	$0.530176\pi$
$487$	−20.0702	+	34.7626i	−0.909467	+	1.57524i	−0.814807	+	0.579733i	$0.803157\pi$
$488$	−4.49183	−	7.78008i	−0.203336	−	0.352188i
$489$		0			0
$490$	−4.19849	+	1.93506i	−0.189668	+	0.0874171i
$491$		−	8.45892i		−	0.381746i	−0.981615	−	0.190873i	$-0.938868\pi$
$491$		−	8.45892i		−	0.381746i	0.981615	−	0.190873i	$-0.0611318\pi$
$492$		0			0
$493$	30.3626	+	17.5299i	1.36746	+	0.789505i
$494$	21.1082	+	12.1868i	0.949702	+	0.548311i
$495$		0			0
$496$			2.00692i			0.0901134i
$497$	−4.73713	−	9.14966i	−0.212490	−	0.410418i
$498$		0			0
$499$	−5.74186	−	9.94519i	−0.257041	−	0.445208i	0.708407	−	0.705804i	$-0.249414\pi$
$499$	−5.74186	−	9.94519i	−0.257041	−	0.445208i	−0.965448	+	0.260596i	$0.916081\pi$
$500$	−3.15809	+	5.46997i	−0.141234	+	0.244625i
$501$		0			0
$502$	19.3017	−	11.1439i	0.861478	−	0.497375i
$503$	−1.99804			−0.0890883			−0.0445441	−	0.999007i	$-0.514184\pi$
$503$	−1.99804			−0.0890883			−0.0445441	+	0.999007i	$0.514184\pi$
$504$		0			0
$505$	3.35208			0.149166
$506$	11.8692	−	6.85269i	0.527650	−	0.304639i
$507$		0			0
$508$	9.72561	−	16.8453i	0.431504	−	0.747387i
$509$	−15.9306	−	27.5926i	−0.706112	−	1.22302i	−0.966289	−	0.257461i	$-0.917114\pi$
$509$	−15.9306	−	27.5926i	−0.706112	−	1.22302i	0.260177	−	0.965561i	$-0.416219\pi$
$510$		0			0
$511$	10.5849	+	0.485772i	0.468247	+	0.0214893i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	24.5858	+	14.1946i	1.08443	+	0.626098i
$515$	−1.63978	−	0.946726i	−0.0722572	−	0.0417177i
$516$		0			0
$517$			4.54829i			0.200034i
$518$	−16.7623	−	0.769275i	−0.736495	−	0.0338000i
$519$		0			0
$520$	1.93970	+	3.35965i	0.0850613	+	0.147330i
$521$	−0.864274	+	1.49697i	−0.0378645	+	0.0655833i	−0.884337	−	0.466850i	$-0.845389\pi$
$521$	−0.864274	+	1.49697i	−0.0378645	+	0.0655833i	0.846472	+	0.532433i	$0.178722\pi$
$522$		0			0
$523$	−38.4274	+	22.1861i	−1.68031	+	0.970130i	−0.718864	+	0.695151i	$0.755338\pi$
$523$	−38.4274	+	22.1861i	−1.68031	+	0.970130i	−0.961450	+	0.274979i	$0.911329\pi$
$524$	−16.7193			−0.730386
$525$		0			0
$526$	27.8801			1.21563
$527$	8.19162	−	4.72943i	0.356833	−	0.206017i
$528$		0			0
$529$	2.39013	−	4.13982i	0.103919	−	0.179992i
$530$	2.98811	+	5.17555i	0.129795	+	0.224812i
$531$		0			0
$532$	−5.04742	−	9.74897i	−0.218834	−	0.422672i
$533$			46.4234i			2.01082i
$534$		0			0
$535$	−5.61315	−	3.24075i	−0.242677	−	0.140110i
$536$	−9.82137	−	5.67037i	−0.424219	−	0.244923i
$537$		0			0
$538$			6.13388i			0.264450i
$539$	−16.5308	+	7.61896i	−0.712032	+	0.328172i
$540$		0			0
$541$	15.7052	+	27.2022i	0.675220	+	1.16952i	0.976404	+	0.215950i	$0.0692848\pi$
$541$	15.7052	+	27.2022i	0.675220	+	1.16952i	−0.301184	+	0.953566i	$0.597382\pi$
$542$	−1.72393	+	2.98593i	−0.0740490	+	0.128257i
$543$		0			0
$544$	4.08169	−	2.35656i	0.175001	−	0.101037i
$545$	−5.07804			−0.217519
$546$		0			0
$547$	−21.6668			−0.926406			−0.463203	−	0.886252i	$-0.653300\pi$
$547$	−21.6668			−0.926406			−0.463203	+	0.886252i	$0.653300\pi$
$548$	−2.72325	+	1.57227i	−0.116331	+	0.0671639i
$549$		0			0
$550$	−5.93367	+	10.2774i	−0.253013	+	0.438231i
$551$	15.4329	+	26.7306i	0.657464	+	1.13876i
$552$		0			0
$553$	−22.6657	−	14.5107i	−0.963843	−	0.617058i
$554$		−	13.4312i		−	0.570636i
$555$		0			0
$556$	14.5678	+	8.41070i	0.617811	+	0.356693i
$557$	−7.32110	−	4.22684i	−0.310205	−	0.179097i	0.336813	−	0.941571i	$-0.390651\pi$
$557$	−7.32110	−	4.22684i	−0.310205	−	0.179097i	−0.647018	+	0.762475i	$0.723984\pi$
$558$		0			0
$559$			15.6255i			0.660889i
$560$	0.0801053	−	1.74548i	0.00338507	−	0.0737599i
$561$		0			0
$562$	−13.2326	−	22.9196i	−0.558185	−	0.966805i
$563$	−19.9644	+	34.5794i	−0.841400	+	1.45735i	0.0473118	+	0.998880i	$0.484935\pi$
$563$	−19.9644	+	34.5794i	−0.841400	+	1.45735i	−0.888712	+	0.458467i	$0.848399\pi$
$564$		0			0
$565$	−0.311413	+	0.179795i	−0.0131013	+	0.00756401i
$566$	−7.67346			−0.322540
$567$		0			0
$568$	3.89426			0.163399
$569$	−17.2519	+	9.96037i	−0.723236	+	0.417560i	−0.815943	−	0.578133i	$-0.803781\pi$
$569$	−17.2519	+	9.96037i	−0.723236	+	0.417560i	0.0927066	+	0.995693i	$0.470448\pi$
$570$		0			0
$571$	4.50381	−	7.80082i	0.188478	−	0.326454i	−0.756265	−	0.654266i	$-0.772978\pi$
$571$	4.50381	−	7.80082i	0.188478	−	0.326454i	0.944743	+	0.327812i	$0.106311\pi$
$572$	7.63721	+	13.2280i	0.319328	+	0.553092i
$573$		0			0
$574$	11.2739	−	17.6099i	0.470565	−	0.735021i
$575$			24.0546i			1.00315i
$576$		0			0
$577$	−17.7359	−	10.2398i	−0.738355	−	0.426290i	0.0831158	−	0.996540i	$-0.473513\pi$
$577$	−17.7359	−	10.2398i	−0.738355	−	0.426290i	−0.821471	+	0.570250i	$0.806846\pi$
$578$	−4.51506	−	2.60677i	−0.187802	−	0.108427i
$579$		0			0
$580$			4.91271i			0.203989i
$581$	28.8729	−	14.9486i	1.19785	−	0.620174i
$582$		0			0
$583$	11.7651	+	20.3778i	0.487262	+	0.843963i
$584$	−2.00246	+	3.46836i	−0.0828622	+	0.143522i
$585$		0			0
$586$	−2.88342	+	1.66474i	−0.119113	+	0.0687699i
$587$	−22.2964			−0.920270			−0.460135	−	0.887849i	$-0.652199\pi$
$587$	−22.2964			−0.920270			−0.460135	+	0.887849i	$0.652199\pi$
$588$		0			0
$589$	8.32739			0.343124
$590$	−0.128083	+	0.0739488i	−0.00527310	+	0.00304442i
$591$		0			0
$592$	3.17112	−	5.49254i	0.130332	−	0.225742i
$593$	−18.9090	−	32.7513i	−0.776499	−	1.34494i	−0.933948	−	0.357409i	$-0.883660\pi$
$593$	−18.9090	−	32.7513i	−0.776499	−	1.34494i	0.157449	−	0.987527i	$-0.449673\pi$
$594$		0			0
$595$	−7.31326	+	3.78636i	−0.299815	+	0.155226i
$596$		−	20.7863i		−	0.851439i
$597$		0			0
$598$	26.8127	+	15.4803i	1.09645	+	0.633037i
$599$	−5.73495	−	3.31107i	−0.234324	−	0.135287i	0.378241	−	0.925707i	$-0.376529\pi$
$599$	−5.73495	−	3.31107i	−0.234324	−	0.135287i	−0.612565	+	0.790420i	$0.709862\pi$
$600$		0			0
$601$		−	29.5837i		−	1.20674i	−0.797460	−	0.603372i	$-0.793824\pi$
$601$		−	29.5837i		−	1.20674i	0.797460	−	0.603372i	$-0.206176\pi$
$602$	3.79466	−	5.92725i	0.154659	−	0.241577i
$603$		0			0
$604$	−4.71396	−	8.16482i	−0.191808	−	0.332222i
$605$	−1.39959	+	2.42416i	−0.0569013	+	0.0985560i
$606$		0			0
$607$	−9.92423	+	5.72975i	−0.402812	+	0.232564i	−0.687697	−	0.725998i	$-0.741378\pi$
$607$	−9.92423	+	5.72975i	−0.402812	+	0.232564i	0.284885	+	0.958562i	$0.408045\pi$
$608$	4.14934			0.168278
$609$		0			0
$610$	−5.93301			−0.240221
$611$	−8.89811	+	5.13733i	−0.359979	+	0.207834i
$612$		0			0
$613$	−2.47537	+	4.28746i	−0.0999791	+	0.173169i	−0.911676	−	0.410910i	$-0.865211\pi$
$613$	−2.47537	+	4.28746i	−0.0999791	+	0.173169i	0.811697	+	0.584079i	$0.198544\pi$
$614$	−9.26924	−	16.0548i	−0.374076	−	0.647919i
$615$		0			0
$616$	0.315400	−	6.87250i	0.0127078	−	0.276901i
$617$			10.1338i			0.407970i	0.978974	+	0.203985i	$0.0653893\pi$
$617$			10.1338i			0.407970i	−0.978974	+	0.203985i	$0.934611\pi$
$618$		0			0
$619$	22.1612	+	12.7948i	0.890732	+	0.514264i	0.874182	−	0.485599i	$-0.161398\pi$
$619$	22.1612	+	12.7948i	0.890732	+	0.514264i	0.0165502	+	0.999863i	$0.494732\pi$
$620$	1.14784	+	0.662708i	0.0460985	+	0.0266150i
$621$		0			0
$622$			21.5516i			0.864140i
$623$	−33.5405	−	21.4729i	−1.34377	−	0.860292i
$624$		0			0
$625$	−9.32393	−	16.1495i	−0.372957	−	0.645981i
$626$	13.6120	−	23.5767i	0.544045	−	0.942313i
$627$		0			0
$628$	4.00571	−	2.31270i	0.159845	−	0.0922866i
$629$	−29.8918			−1.19186
$630$		0			0
$631$	38.6494			1.53861			0.769305	−	0.638882i	$-0.220603\pi$
$631$	38.6494			1.53861			0.769305	+	0.638882i	$0.220603\pi$
$632$	8.80925	−	5.08602i	0.350413	−	0.202311i
$633$		0			0
$634$	−11.2149	+	19.4249i	−0.445403	+	0.771460i
$635$	−6.42302	−	11.1250i	−0.254890	−	0.441482i
$636$		0			0
$637$	−33.5771	−	23.7346i	−1.33037	−	0.940398i
$638$			19.3429i			0.765794i
$639$		0			0
$640$	0.571943	+	0.330211i	0.0226080	+	0.0130528i
$641$	13.2162	+	7.63037i	0.522008	+	0.301382i	0.737756	−	0.675068i	$-0.235886\pi$
$641$	13.2162	+	7.63037i	0.522008	+	0.301382i	−0.215748	+	0.976449i	$0.569219\pi$
$642$		0			0
$643$			0.0876859i			0.00345799i	0.999999	+	0.00172900i	$0.000550357\pi$
$643$			0.0876859i			0.00345799i	−0.999999	+	0.00172900i	$0.999450\pi$
$644$	−6.41149	−	12.3836i	−0.252648	−	0.487984i
$645$		0			0
$646$	−9.77817	−	16.9363i	−0.384717	−	0.666349i
$647$	21.1405	−	36.6165i	0.831121	−	1.43954i	−0.0660294	−	0.997818i	$-0.521033\pi$
$647$	21.1405	−	36.6165i	0.831121	−	1.43954i	0.897150	−	0.441726i	$-0.145634\pi$
$648$		0			0
$649$	−0.504304	+	0.291160i	−0.0197957	+	0.0114290i
$650$	−26.8085			−1.05152
$651$		0			0
$652$	−11.5381			−0.451869
$653$	−9.92733	+	5.73154i	−0.388486	+	0.224293i	−0.681504	−	0.731814i	$-0.738674\pi$
$653$	−9.92733	+	5.73154i	−0.388486	+	0.224293i	0.293018	+	0.956107i	$0.405340\pi$
$654$		0			0
$655$	−5.52090	+	9.56249i	−0.215720	+	0.373637i
$656$	3.95153	+	6.84425i	0.154281	+	0.267223i
$657$		0			0
$658$	4.62293	+	0.212161i	0.180221	+	0.00827089i
$659$		−	43.1305i		−	1.68013i	−0.542489	−	0.840063i	$-0.682518\pi$
$659$		−	43.1305i		−	1.68013i	0.542489	−	0.840063i	$-0.317482\pi$
$660$		0			0
$661$	−1.81381	−	1.04720i	−0.0705491	−	0.0407315i	0.464311	−	0.885672i	$-0.346302\pi$
$661$	−1.81381	−	1.04720i	−0.0705491	−	0.0407315i	−0.534860	+	0.844941i	$0.679636\pi$
$662$	−2.53608	−	1.46420i	−0.0985674	−	0.0569079i
$663$		0			0
$664$			12.2888i			0.476899i
$665$	−7.24257	−	0.332384i	−0.280855	−	0.0128893i
$666$		0			0
$667$	19.6037	+	33.9546i	0.759057	+	1.31473i
$668$	−9.50317	+	16.4600i	−0.367689	+	0.636856i
$669$		0			0
$670$	−6.48626	+	3.74484i	−0.250586	+	0.144676i
$671$	−23.3602			−0.901810
$672$		0			0
$673$	8.86436			0.341696			0.170848	−	0.985297i	$-0.445349\pi$
$673$	8.86436			0.341696			0.170848	+	0.985297i	$0.445349\pi$
$674$	−21.5137	+	12.4209i	−0.828675	+	0.478436i
$675$		0			0
$676$	−10.7525	+	18.6240i	−0.413560	+	0.716306i
$677$	2.70881	+	4.69180i	0.104108	+	0.180320i	0.913373	−	0.407123i	$-0.133468\pi$
$677$	2.70881	+	4.69180i	0.104108	+	0.180320i	−0.809265	+	0.587443i	$0.800135\pi$
$678$		0			0
$679$	−5.27352	−	10.1857i	−0.202379	−	0.390890i
$680$		−	3.11265i		−	0.119365i
$681$		0			0
$682$	4.51943	+	2.60929i	0.173058	+	0.0999151i
$683$	12.5852	+	7.26604i	0.481558	+	0.278027i	0.721065	−	0.692867i	$-0.243653\pi$
$683$	12.5852	+	7.26604i	0.481558	+	0.278027i	−0.239508	+	0.970894i	$0.576986\pi$
$684$		0			0
$685$			2.07672i			0.0793475i
$686$	6.97289	+	17.1575i	0.266226	+	0.655075i
$687$		0			0
$688$	1.33003	+	2.30369i	0.0507071	+	0.0878272i
$689$	−26.5776	+	46.0337i	−1.01253	+	1.75375i
$690$		0			0
$691$	3.28158	−	1.89462i	0.124837	−	0.0720748i	−0.436281	−	0.899810i	$-0.643705\pi$
$691$	3.28158	−	1.89462i	0.124837	−	0.0720748i	0.561118	+	0.827736i	$0.310371\pi$
$692$	9.57823			0.364110
$693$		0			0
$694$	−15.5823			−0.591497
$695$	9.62088	−	5.55462i	0.364941	−	0.210699i
$696$		0			0
$697$	18.6241	−	32.2578i	0.705437	−	1.22185i
$698$	8.06188	+	13.9636i	0.305147	+	0.528529i
$699$		0			0
$700$	10.1693	+	6.51045i	0.384363	+	0.246072i
$701$		−	29.5523i		−	1.11618i	−0.829782	−	0.558088i	$-0.811535\pi$
$701$		−	29.5523i		−	1.11618i	0.829782	−	0.558088i	$-0.188465\pi$
$702$		0			0
$703$	−22.7904	−	13.1580i	−0.859556	−	0.496265i
$704$	2.25192	+	1.30015i	0.0848725	+	0.0490012i
$705$		0			0
$706$		−	21.9402i		−	0.825730i
$707$	0.615647	−	13.4148i	0.0231538	−	0.504516i
$708$		0			0
$709$	2.27586	+	3.94191i	0.0854718	+	0.148041i	0.905592	−	0.424150i	$-0.139427\pi$
$709$	2.27586	+	3.94191i	0.0854718	+	0.148041i	−0.820120	+	0.572191i	$0.806094\pi$
$710$	1.28593	−	2.22729i	0.0482600	−	0.0835888i
$711$		0			0
$712$	13.0359	−	7.52627i	0.488540	−	0.282059i
$713$	10.5779			0.396144
$714$		0			0
$715$	10.0876			0.377254
$716$	17.6588	−	10.1953i	0.659939	−	0.381016i
$717$		0			0
$718$	5.64613	−	9.77938i	0.210712	−	0.364963i
$719$	14.0142	+	24.2733i	0.522641	+	0.905240i	0.999653	+	0.0263435i	$0.00838636\pi$
$719$	14.0142	+	24.2733i	0.522641	+	0.905240i	−0.477012	+	0.878897i	$0.658280\pi$
$720$		0			0
$721$	−4.08990	+	6.38841i	−0.152316	+	0.237917i
$722$			1.78301i			0.0663568i
$723$		0			0
$724$	−20.7730	−	11.9933i	−0.772024	−	0.445728i
$725$	−29.4009	−	16.9746i	−1.09192	−	0.630421i
$726$		0			0
$727$		−	18.8842i		−	0.700374i	−0.936680	−	0.350187i	$-0.886118\pi$
$727$		−	18.8842i		−	0.700374i	0.936680	−	0.350187i	$-0.113882\pi$
$728$	13.8014	−	7.14550i	0.511512	−	0.264830i
$729$		0			0
$730$	1.32247	+	2.29058i	0.0489467	+	0.0847782i
$731$	6.26861	−	10.8576i	0.231853	−	0.401581i
$732$		0			0
$733$	8.25128	−	4.76388i	0.304768	−	0.175958i	−0.339815	−	0.940492i	$-0.610364\pi$
$733$	8.25128	−	4.76388i	0.304768	−	0.175958i	0.644583	+	0.764534i	$0.277031\pi$
$734$	−12.4593			−0.459881
$735$		0			0
$736$	5.27070			0.194280
$737$	−25.5385	+	14.7446i	−0.940722	+	0.543126i
$738$		0			0
$739$	4.87463	−	8.44311i	0.179316	−	0.310585i	−0.762330	−	0.647188i	$-0.775945\pi$
$739$	4.87463	−	8.44311i	0.179316	−	0.310585i	0.941647	+	0.336603i	$0.109278\pi$
$740$	−2.09428	−	3.62740i	−0.0769872	−	0.133346i
$741$		0			0
$742$	21.2610	−	11.0077i	0.780517	−	0.404104i
$743$			33.0765i			1.21346i	0.794908	+	0.606729i	$0.207519\pi$
$743$			33.0765i			1.21346i	−0.794908	+	0.606729i	$0.792481\pi$
$744$		0			0
$745$	−11.8886	−	6.86387i	−0.435563	−	0.251473i
$746$	15.9300	+	9.19719i	0.583239	+	0.336733i
$747$		0			0
$748$		−	12.2555i		−	0.448106i
$749$	−14.0002	+	21.8682i	−0.511556	+	0.799048i
$750$		0			0
$751$	4.18103	+	7.24176i	0.152568	+	0.264256i	0.932171	−	0.362019i	$-0.117912\pi$
$751$	4.18103	+	7.24176i	0.152568	+	0.264256i	−0.779603	+	0.626274i	$0.784579\pi$
$752$	−0.874572	+	1.51480i	−0.0318924	+	0.0552392i
$753$		0			0
$754$	−37.8418	+	21.8480i	−1.37812	+	0.795656i
$755$	−6.22641			−0.226602
$756$		0			0
$757$	−18.1472			−0.659572			−0.329786	−	0.944056i	$-0.606977\pi$
$757$	−18.1472			−0.659572			−0.329786	+	0.944056i	$0.606977\pi$
$758$	−0.247058	+	0.142639i	−0.00897356	+	0.00518089i
$759$		0			0
$760$	1.37016	−	2.37318i	0.0497009	−	0.0860844i
$761$	4.08474	+	7.07498i	0.148072	+	0.256468i	0.930515	−	0.366254i	$-0.119360\pi$
$761$	4.08474	+	7.07498i	0.148072	+	0.256468i	−0.782443	+	0.622722i	$0.786027\pi$
$762$		0			0
$763$	−0.932638	+	20.3220i	−0.0337638	+	0.735705i
$764$		−	5.71230i		−	0.206664i
$765$		0			0
$766$	2.42022	+	1.39732i	0.0874463	+	0.0504871i
$767$	−1.13923	−	0.657734i	−0.0411352	−	0.0237494i
$768$		0			0
$769$		−	21.6670i		−	0.781333i	−0.920532	−	0.390667i	$-0.872245\pi$
$769$		−	21.6670i		−	0.781333i	0.920532	−	0.390667i	$-0.127755\pi$
$770$	−3.82653	−	2.44977i	−0.137899	−	0.0882836i
$771$		0			0
$772$	0.691202	+	1.19720i	0.0248769	+	0.0430881i
$773$	−5.35259	+	9.27095i	−0.192519	+	0.333453i	−0.946084	−	0.323920i	$-0.894999\pi$
$773$	−5.35259	+	9.27095i	−0.192519	+	0.333453i	0.753565	+	0.657373i	$0.228332\pi$
$774$		0			0
$775$	−7.93216	+	4.57964i	−0.284932	+	0.164505i
$776$	4.33520			0.155625
$777$		0			0
$778$	−7.75793			−0.278135
$779$	28.3991	−	16.3962i	1.01750	−	0.587456i
$780$		0			0
$781$	5.06311	−	8.76957i	0.181172	−	0.313800i
$782$	−12.4207	−	21.5133i	−0.444164	−	0.769315i
$783$		0			0
$784$	−6.97058	−	0.641153i	−0.248949	−	0.0228983i
$785$		−	3.05471i		−	0.109027i
$786$		0			0
$787$	21.4355	+	12.3758i	0.764093	+	0.441149i	0.830763	−	0.556626i	$-0.187904\pi$
$787$	21.4355	+	12.3758i	0.764093	+	0.441149i	−0.0666702	+	0.997775i	$0.521238\pi$
$788$	−5.14881	−	2.97267i	−0.183419	−	0.105897i
$789$		0			0
$790$		−	6.71785i		−	0.239010i
$791$	0.662332	+	1.27928i	0.0235498	+	0.0454859i
$792$		0			0
$793$	−26.3855	−	45.7010i	−0.936976	−	1.62289i
$794$	2.89038	−	5.00629i	0.102576	−	0.177666i
$795$		0			0
$796$	−16.1647	+	9.33269i	−0.572942	+	0.330788i
$797$	54.4419			1.92843			0.964215	−	0.265122i	$-0.0854121\pi$
$797$	54.4419			1.92843			0.964215	+	0.265122i	$0.0854121\pi$
$798$		0			0
$799$	8.24393			0.291649
$800$	−3.95240	+	2.28192i	−0.139739	+	0.0806781i
$801$		0			0
$802$	6.82164	−	11.8154i	0.240881	−	0.417217i
$803$	5.20698	+	9.01875i	0.183750	+	0.318265i
$804$		0			0
$805$	−9.19988	−	0.422211i	−0.324253	−	0.0148810i
$806$			11.7889i			0.415245i
$807$		0			0
$808$	4.39565	+	2.53783i	0.154638	+	0.0892805i
$809$	24.6546	+	14.2343i	0.866809	+	0.500452i	0.866286	−	0.499548i	$-0.166500\pi$
$809$	24.6546	+	14.2343i	0.866809	+	0.500452i	0.000522376		1.00000i	$0.499834\pi$
$810$		0			0
$811$		−	34.3732i		−	1.20701i	−0.797361	−	0.603503i	$-0.793771\pi$
$811$		−	34.3732i		−	1.20701i	0.797361	−	0.603503i	$-0.206229\pi$
$812$	19.6604	+	0.902275i	0.689944	+	0.0316636i
$813$		0			0
$814$	−8.24585	−	14.2822i	−0.289017	−	0.500592i
$815$	−3.81003	+	6.59916i	−0.133459	+	0.231158i
$816$		0			0
$817$	9.55877	−	5.51876i	0.334419	−	0.193077i
$818$	−29.2861			−1.02397
$819$		0			0
$820$	5.21936			0.182268
$821$	0.957060	−	0.552559i	0.0334016	−	0.0192844i	−0.483206	−	0.875507i	$-0.660528\pi$
$821$	0.957060	−	0.552559i	0.0334016	−	0.0192844i	0.516608	+	0.856222i	$0.327195\pi$
$822$		0			0
$823$	−17.4396	+	30.2063i	−0.607908	+	1.05293i	0.383677	+	0.923467i	$0.374658\pi$
$823$	−17.4396	+	30.2063i	−0.607908	+	1.05293i	−0.991585	+	0.129460i	$0.958676\pi$
$824$	−1.43352	−	2.48292i	−0.0499389	−	0.0864967i
$825$		0			0
$826$	0.272414	+	0.526162i	0.00947851	+	0.0183075i
$827$		−	17.3806i		−	0.604382i	−0.953247	−	0.302191i	$-0.902282\pi$
$827$		−	17.3806i		−	0.604382i	0.953247	−	0.302191i	$-0.0977181\pi$
$828$		0			0
$829$	45.2612	+	26.1315i	1.57199	+	0.907586i	0.995926	+	0.0901786i	$0.0287438\pi$
$829$	45.2612	+	26.1315i	1.57199	+	0.907586i	0.576060	+	0.817408i	$0.304590\pi$
$830$	7.02851	+	4.05791i	0.243963	+	0.140852i
$831$		0			0
$832$			5.87410i			0.203648i
$833$	13.8096	+	29.9626i	0.478475	+	1.03814i
$834$		0			0
$835$	6.27611	+	10.8705i	0.217194	+	0.376191i
$836$	5.39475	−	9.34398i	0.186581	−	0.323168i
$837$		0			0
$838$	−18.0288	+	10.4089i	−0.622794	+	0.359570i
$839$	28.2310			0.974644			0.487322	−	0.873222i	$-0.337974\pi$
$839$	28.2310			0.974644			0.487322	+	0.873222i	$0.337974\pi$
$840$		0			0
$841$	−26.3349			−0.908099
$842$	−33.2548	+	19.1997i	−1.14604	+	0.661664i
$843$		0			0
$844$	−4.08684	+	7.07862i	−0.140675	+	0.243656i
$845$	7.10123	+	12.2997i	0.244290	+	0.423122i
$846$		0			0
$847$	9.44427	+	6.04628i	0.324509	+	0.207753i
$848$			9.04907i			0.310746i
$849$		0			0
$850$	18.6282	+	10.7550i	0.638941	+	0.368893i
$851$	−28.9495	−	16.7140i	−0.992376	−	0.572949i
$852$		0			0
$853$			32.5436i			1.11427i	0.830422	+	0.557135i	$0.188099\pi$
$853$			32.5436i			1.11427i	−0.830422	+	0.557135i	$0.811901\pi$
$854$	−1.08966	+	23.7435i	−0.0372875	+	0.812487i
$855$		0			0
$856$	−4.90709	−	8.49932i	−0.167721	−	0.290501i
$857$	23.6268	−	40.9228i	0.807075	−	1.39789i	−0.107807	−	0.994172i	$-0.534383\pi$
$857$	23.6268	−	40.9228i	0.807075	−	1.39789i	0.914881	−	0.403723i	$-0.132284\pi$
$858$		0			0
$859$	−3.48645	+	2.01290i	−0.118956	+	0.0686794i	−0.558297	−	0.829641i	$-0.688545\pi$
$859$	−3.48645	+	2.01290i	−0.118956	+	0.0686794i	0.439341	+	0.898320i	$0.355212\pi$
$860$	1.75677			0.0599053
$861$		0			0
$862$	−19.9424			−0.679241
$863$	19.4653	−	11.2383i	0.662605	−	0.382555i	−0.130664	−	0.991427i	$-0.541711\pi$
$863$	19.4653	−	11.2383i	0.662605	−	0.382555i	0.793269	+	0.608871i	$0.208377\pi$
$864$		0			0
$865$	3.16284	−	5.47820i	0.107540	−	0.186264i
$866$	−14.1098	−	24.4389i	−0.479471	−	0.830469i
$867$		0			0
$868$	2.86293	−	4.47189i	0.0971742	−	0.151786i
$869$		−	26.4503i		−	0.897266i
$870$		0			0
$871$	−57.6917	−	33.3083i	−1.95481	−	1.12861i
$872$	−6.65893	−	3.84454i	−0.225500	−	0.130192i
$873$		0			0
$874$		−	21.8699i		−	0.739760i
$875$	14.8400	−	7.68326i	0.501684	−	0.259742i
$876$		0			0
$877$	6.82567	+	11.8224i	0.230487	+	0.399214i	0.957951	−	0.286931i	$-0.0926349\pi$
$877$	6.82567	+	11.8224i	0.230487	+	0.399214i	−0.727465	+	0.686145i	$0.759302\pi$
$878$	−4.56728	+	7.91077i	−0.154138	+	0.266975i
$879$		0			0
$880$	1.48722	−	0.858648i	0.0501342	−	0.0289450i
$881$	11.6865			0.393727			0.196863	−	0.980431i	$-0.436924\pi$
$881$	11.6865			0.393727			0.196863	+	0.980431i	$0.436924\pi$
$882$		0			0
$883$	−26.6602			−0.897187			−0.448593	−	0.893736i	$-0.648075\pi$
$883$	−26.6602			−0.897187			−0.448593	+	0.893736i	$0.648075\pi$
$884$	23.9762	−	13.8427i	0.806408	−	0.465580i
$885$		0			0
$886$	−16.9020	+	29.2751i	−0.567833	+	0.983515i
$887$	−6.50026	−	11.2588i	−0.218257	−	0.378033i	0.736018	−	0.676962i	$-0.236704\pi$
$887$	−6.50026	−	11.2588i	−0.218257	−	0.378033i	−0.954275	+	0.298929i	$0.903371\pi$
$888$		0			0
$889$	−45.7012	+	23.6613i	−1.53277	+	0.793574i
$890$		−	9.94104i		−	0.333224i
$891$		0			0
$892$	23.5034	+	13.5697i	0.786953	+	0.454347i
$893$	6.28543	+	3.62889i	0.210334	+	0.121436i
$894$		0			0
$895$		−	13.4664i		−	0.450133i
$896$	1.42653	−	2.22823i	0.0476570	−	0.0744400i
$897$		0			0
$898$	−13.5065	−	23.3940i	−0.450719	−	0.780668i
$899$	−7.46448	+	12.9289i	−0.248954	+	0.431202i
$900$		0			0
$901$	36.9355	−	21.3247i	1.23050	−	0.710429i
$902$	20.5503			0.684250
$903$		0			0
$904$	−0.544483			−0.0181092
$905$	−13.7190	+	7.92066i	−0.456034	+	0.263292i
$906$		0			0
$907$	−13.5506	+	23.4703i	−0.449940	+	0.779319i	−0.998382	−	0.0568698i	$-0.981888\pi$
$907$	−13.5506	+	23.4703i	−0.449940	+	0.779319i	0.548441	+	0.836189i	$0.315221\pi$
$908$	−6.29665	−	10.9061i	−0.208962	−	0.361932i
$909$		0			0
$910$	0.470547	−	10.2531i	0.0155985	−	0.339887i
$911$		−	37.3223i		−	1.23654i	−0.785964	−	0.618272i	$-0.787833\pi$
$911$		−	37.3223i		−	1.23654i	0.785964	−	0.618272i	$-0.212167\pi$
$912$		0			0
$913$	27.6735	+	15.9773i	0.915859	+	0.528771i
$914$	2.94976	+	1.70305i	0.0975694	+	0.0563317i
$915$		0			0
$916$			1.41314i			0.0466916i
$917$	37.2545	+	23.8506i	1.23025	+	0.787615i
$918$		0			0
$919$	−6.00814	−	10.4064i	−0.198190	−	0.343276i	0.749751	−	0.661720i	$-0.230173\pi$
$919$	−6.00814	−	10.4064i	−0.198190	−	0.343276i	−0.947942	+	0.318444i	$0.896840\pi$
$920$	1.74044	−	3.01454i	0.0573807	−	0.0993864i
$921$		0			0
$922$	1.45155	−	0.838051i	0.0478042	−	0.0275997i
$923$	22.8753			0.752949
$924$		0			0
$925$	28.9450			0.951705
$926$	14.2432	−	8.22333i	0.468061	−	0.270235i
$927$		0			0
$928$	−3.71937	+	6.44214i	−0.122094	+	0.211474i
$929$	−16.7460	−	29.0050i	−0.549419	−	0.951622i	−0.998314	−	0.0580375i	$-0.981516\pi$
$929$	−16.7460	−	29.0050i	−0.549419	−	0.951622i	0.448895	−	0.893584i	$-0.351818\pi$
$930$		0			0
$931$	−2.66036	+	28.9233i	−0.0871897	+	0.947922i
$932$			17.9432i			0.587749i
$933$		0			0
$934$	3.17159	+	1.83112i	0.103778	+	0.0599160i
$935$	−7.00946	−	4.04691i	−0.229234	−	0.132348i
$936$		0			0
$937$			28.5256i			0.931891i	0.884813	+	0.465946i	$0.154286\pi$
$937$			28.5256i			0.931891i	−0.884813	+	0.465946i	$0.845714\pi$
$938$	13.7953	+	26.6454i	0.450434	+	0.870002i
$939$		0			0
$940$	0.577587	+	1.00041i	0.0188388	+	0.0326298i
$941$	−4.05703	+	7.02698i	−0.132255	+	0.229073i	−0.924546	−	0.381071i	$-0.875555\pi$
$941$	−4.05703	+	7.02698i	−0.132255	+	0.229073i	0.792290	+	0.610144i	$0.208889\pi$
$942$		0			0
$943$	36.0740	−	20.8273i	1.17473	−	0.678231i
$944$	−0.223944			−0.00728875
$945$		0			0
$946$	6.91696			0.224890
$947$	−27.5208	+	15.8892i	−0.894307	+	0.516329i	−0.875349	−	0.483492i	$-0.839368\pi$
$947$	−27.5208	+	15.8892i	−0.894307	+	0.516329i	−0.0189584	+	0.999820i	$0.506035\pi$
$948$		0			0
$949$	−11.7626	+	20.3735i	−0.381831	+	0.661351i
$950$	9.46846	+	16.3998i	0.307197	+	0.532081i
$951$		0			0
$952$	−12.4566	−	0.571674i	−0.403722	−	0.0185281i
$953$			4.07356i			0.131956i	0.997821	+	0.0659778i	$0.0210166\pi$
$953$			4.07356i			0.131956i	−0.997821	+	0.0659778i	$0.978983\pi$
$954$		0			0
$955$	−3.26711	−	1.88627i	−0.105721	−	0.0610381i
$956$	−22.1845	−	12.8082i	−0.717497	−	0.414247i
$957$		0			0
$958$			28.4266i			0.918422i
$959$	8.31091	+	0.381413i	0.268373	+	0.0123165i
$960$		0			0
$961$	−13.4861	−	23.3587i	−0.435037	−	0.753505i
$962$	18.6275	−	32.2637i	0.600574	−	1.04022i
$963$		0			0
$964$	−10.5993	+	6.11953i	−0.341382	+	0.197097i
$965$	0.912971			0.0293896
$966$		0			0
$967$	−37.7138			−1.21279			−0.606397	−	0.795162i	$-0.707386\pi$
$967$	−37.7138			−1.21279			−0.606397	+	0.795162i	$0.707386\pi$
$968$	−3.67061	+	2.11923i	−0.117978	+	0.0681146i
$969$		0			0
$970$	1.43153	−	2.47949i	0.0459638	−	0.0796116i
$971$	−26.7525	−	46.3368i	−0.858530	−	1.48702i	−0.873331	−	0.487127i	$-0.838045\pi$
$971$	−26.7525	−	46.3368i	−0.858530	−	1.48702i	0.0148008	−	0.999890i	$-0.495289\pi$
$972$		0			0
$973$	−20.4622	−	39.5223i	−0.655989	−	1.26703i
$974$			40.1404i			1.28618i
$975$		0			0
$976$	−7.78008	−	4.49183i	−0.249034	−	0.143780i
$977$	−4.43220	−	2.55893i	−0.141799	−	0.0818675i	0.427422	−	0.904052i	$-0.359422\pi$
$977$	−4.43220	−	2.55893i	−0.141799	−	0.0818675i	−0.569221	+	0.822185i	$0.692755\pi$
$978$		0			0
$979$		−	39.1411i		−	1.25095i
$980$	−2.66847	+	3.77506i	−0.0852410	+	0.120590i
$981$		0			0
$982$	−4.22946	−	7.32564i	−0.134967	−	0.233770i
$983$	−9.18953	+	15.9167i	−0.293100	+	0.507665i	−0.974541	−	0.224208i	$-0.928020\pi$
$983$	−9.18953	+	15.9167i	−0.293100	+	0.507665i	0.681441	+	0.731873i	$0.261354\pi$
$984$		0			0
$985$	−3.40039	+	1.96322i	−0.108345	+	0.0625533i
$986$	35.0597			1.11653
$987$		0			0
$988$	24.3736			0.775428
$989$	12.1420	−	7.01020i	0.386094	−	0.222912i
$990$		0			0
$991$	11.8103	−	20.4561i	0.375168	−	0.649810i	−0.615184	−	0.788383i	$-0.710918\pi$
$991$	11.8103	−	20.4561i	0.375168	−	0.649810i	0.990352	+	0.138574i	$0.0442517\pi$
$992$	1.00346	+	1.73804i	0.0318599	+	0.0551830i
$993$		0			0
$994$	−8.67731	−	5.55527i	−0.275227	−	0.176202i
$995$			12.3270i			0.390793i
$996$		0			0
$997$	32.3902	+	18.7005i	1.02581	+	0.592250i	0.915781	−	0.401678i	$-0.131573\pi$
$997$	32.3902	+	18.7005i	1.02581	+	0.592250i	0.110027	+	0.993929i	$0.464906\pi$
$998$	−9.94519	−	5.74186i	−0.314809	−	0.181755i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.d.647.7	yes	16
3.2	odd	2		1134.2.k.c.647.2	✓	16
7.5	odd	6		1134.2.k.c.971.2	yes	16
9.2	odd	6		1134.2.t.h.1025.7		16
9.4	even	3		1134.2.l.g.269.7		16
9.5	odd	6		1134.2.l.h.269.2		16
9.7	even	3		1134.2.t.g.1025.2		16
21.5	even	6	inner	1134.2.k.d.971.7	yes	16
63.5	even	6		1134.2.t.g.593.2		16
63.40	odd	6		1134.2.t.h.593.7		16
63.47	even	6		1134.2.l.g.215.3		16
63.61	odd	6		1134.2.l.h.215.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.2	✓	16	3.2	odd	2
1134.2.k.c.971.2	yes	16	7.5	odd	6
1134.2.k.d.647.7	yes	16	1.1	even	1	trivial
1134.2.k.d.971.7	yes	16	21.5	even	6	inner
1134.2.l.g.215.3		16	63.47	even	6
1134.2.l.g.269.7		16	9.4	even	3
1134.2.l.h.215.6		16	63.61	odd	6
1134.2.l.h.269.2		16	9.5	odd	6
1134.2.t.g.593.2		16	63.5	even	6
1134.2.t.g.1025.2		16	9.7	even	3
1134.2.t.h.593.7		16	63.40	odd	6
1134.2.t.h.1025.7		16	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.330211 - 0.571943i) q^{5} +(-2.34953 + 1.21644i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.330211 - 0.571943i) q^{5} +(-2.34953 + 1.21644i) q^{7} -1.00000i q^{8} +(-0.571943 - 0.330211i) q^{10} +(-2.25192 - 1.30015i) q^{11} -5.87410i q^{13} +(-1.42653 + 2.22823i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.35656 + 4.08169i) q^{17} +(-3.59343 + 2.07467i) q^{19} -0.660423 q^{20} -2.60030 q^{22} +(-4.56456 + 2.63535i) q^{23} +(2.28192 - 3.95240i) q^{25} +(-2.93705 - 5.08712i) q^{26} +(-0.121294 + 2.64297i) q^{28} -7.43874i q^{29} +(-1.73804 - 1.00346i) q^{31} +(-0.866025 - 0.500000i) q^{32} +4.71312i q^{34} +(1.47157 + 0.942112i) q^{35} +(3.17112 + 5.49254i) q^{37} +(-2.07467 + 3.59343i) q^{38} +(-0.571943 + 0.330211i) q^{40} -7.90306 q^{41} -2.66007 q^{43} +(-2.25192 + 1.30015i) q^{44} +(-2.63535 + 4.56456i) q^{46} +(-0.874572 - 1.51480i) q^{47} +(4.04054 - 5.71612i) q^{49} -4.56384i q^{50} +(-5.08712 - 2.93705i) q^{52} +(-7.83672 - 4.52454i) q^{53} +1.71730i q^{55} +(1.21644 + 2.34953i) q^{56} +(-3.71937 - 6.44214i) q^{58} +(0.111972 - 0.193941i) q^{59} +(7.78008 - 4.49183i) q^{61} -2.00692 q^{62} -1.00000 q^{64} +(-3.35965 + 1.93970i) q^{65} +(5.67037 - 9.82137i) q^{67} +(2.35656 + 4.08169i) q^{68} +(1.74548 + 0.0801053i) q^{70} +3.89426i q^{71} +(-3.46836 - 2.00246i) q^{73} +(5.49254 + 3.17112i) q^{74} +4.14934i q^{76} +(6.87250 + 0.315400i) q^{77} +(5.08602 + 8.80925i) q^{79} +(-0.330211 + 0.571943i) q^{80} +(-6.84425 + 3.95153i) q^{82} -12.2888 q^{83} +3.11265 q^{85} +(-2.30369 + 1.33003i) q^{86} +(-1.30015 + 2.25192i) q^{88} +(7.52627 + 13.0359i) q^{89} +(7.14550 + 13.8014i) q^{91} +5.27070i q^{92} +(-1.51480 - 0.874572i) q^{94} +(2.37318 + 1.37016i) q^{95} +4.33520i q^{97} +(0.641153 - 6.97058i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 8 * q^7	\( 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more