LMFDB - Embedded newform 637.2.k.d.459.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(459,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			459.1
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	637.459
Dual form			637.2.k.d.569.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18890i q^{2} +(0.895644 + 1.55130i) q^{3} -2.79129 q^{4} +(-1.89564 + 1.09445i) q^{5} +(3.39564 - 1.96048i) q^{6} +1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +O(q^{10})$	\(q-2.18890i q^{2} +(0.895644 + 1.55130i) q^{3} -2.79129 q^{4} +(-1.89564 + 1.09445i) q^{5} +(3.39564 - 1.96048i) q^{6} +1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +(2.39564 + 4.14938i) q^{10} +(1.10436 - 0.637600i) q^{11} +(-2.50000 - 4.33013i) q^{12} +(3.50000 - 0.866025i) q^{13} +(-3.39564 - 1.96048i) q^{15} -1.79129 q^{16} +3.00000 q^{17} +(0.395644 + 0.228425i) q^{18} +(5.68693 + 3.28335i) q^{19} +(5.29129 - 3.05493i) q^{20} +(-1.39564 - 2.41733i) q^{22} +7.58258 q^{23} +(-2.68693 + 1.55130i) q^{24} +(-0.104356 + 0.180750i) q^{25} +(-1.89564 - 7.66115i) q^{26} +5.00000 q^{27} +(1.10436 - 1.91280i) q^{29} +(-4.29129 + 7.43273i) q^{30} +(-7.50000 - 4.33013i) q^{31} +7.38505i q^{32} +(1.97822 + 1.14213i) q^{33} -6.56670i q^{34} +(0.291288 - 0.504525i) q^{36} -6.92820i q^{37} +(7.18693 - 12.4481i) q^{38} +(4.47822 + 4.65390i) q^{39} +(-1.89564 - 3.28335i) q^{40} +(2.20871 + 1.27520i) q^{41} +(2.18693 + 3.78788i) q^{43} +(-3.08258 + 1.77973i) q^{44} -0.456850i q^{45} -16.5975i q^{46} +(-3.70871 + 2.14123i) q^{47} +(-1.60436 - 2.77883i) q^{48} +(0.395644 + 0.228425i) q^{50} +(2.68693 + 4.65390i) q^{51} +(-9.76951 + 2.41733i) q^{52} +(6.08258 - 10.5353i) q^{53} -10.9445i q^{54} +(-1.39564 + 2.41733i) q^{55} +11.7629i q^{57} +(-4.18693 - 2.41733i) q^{58} -8.85095i q^{59} +(9.47822 + 5.47225i) q^{60} +(-6.37386 + 11.0399i) q^{61} +(-9.47822 + 16.4168i) q^{62} +12.5826 q^{64} +(-5.68693 + 5.47225i) q^{65} +(2.50000 - 4.33013i) q^{66} +(-9.87386 + 5.70068i) q^{67} -8.37386 q^{68} +(6.79129 + 11.7629i) q^{69} +(-0.791288 + 0.456850i) q^{71} +(-0.313068 - 0.180750i) q^{72} +(3.00000 + 1.73205i) q^{73} -15.1652 q^{74} -0.373864 q^{75} +(-15.8739 - 9.16478i) q^{76} +(10.1869 - 9.80238i) q^{78} +(3.00000 + 5.19615i) q^{79} +(3.39564 - 1.96048i) q^{80} +(4.79129 + 8.29875i) q^{81} +(2.79129 - 4.83465i) q^{82} +3.55945i q^{83} +(-5.68693 + 3.28335i) q^{85} +(8.29129 - 4.78698i) q^{86} +3.95644 q^{87} +(1.10436 + 1.91280i) q^{88} +2.91190i q^{89} -1.00000 q^{90} -21.1652 q^{92} -15.5130i q^{93} +(4.68693 + 8.11800i) q^{94} -14.3739 q^{95} +(-11.4564 + 6.61438i) q^{96} +(-13.1869 + 7.61348i) q^{97} +0.266150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9}+O(q^{10}) $ 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9	$ 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9} + 5 q^{10} + 9 q^{11} - 10 q^{12} + 14 q^{13} - 9 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{18} + 9 q^{19} + 12 q^{20} - q^{22} + 12 q^{23} + 3 q^{24} - 5 q^{25} - 3 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} - 30 q^{31} - 15 q^{33} - 8 q^{36} + 15 q^{38} - 5 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} + 6 q^{44} - 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} - 7 q^{52} + 6 q^{53} - q^{55} - 3 q^{58} + 15 q^{60} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 9 q^{65} + 10 q^{66} - 12 q^{67} - 6 q^{68} + 18 q^{69} + 6 q^{71} - 15 q^{72} + 12 q^{73} - 24 q^{74} + 26 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} + 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 24 q^{86} - 30 q^{87} + 9 q^{88} - 4 q^{90} - 48 q^{92} + 5 q^{94} - 30 q^{95} - 39 q^{97}+O(q^{100}) $ 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9 + 5 * q^10 + 9 * q^11 - 10 * q^12 + 14 * q^13 - 9 * q^15 + 2 * q^16 + 12 * q^17 - 3 * q^18 + 9 * q^19 + 12 * q^20 - q^22 + 12 * q^23 + 3 * q^24 - 5 * q^25 - 3 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 - 30 * q^31 - 15 * q^33 - 8 * q^36 + 15 * q^38 - 5 * q^39 - 3 * q^40 + 18 * q^41 - 5 * q^43 + 6 * q^44 - 24 * q^47 - 11 * q^48 - 3 * q^50 - 3 * q^51 - 7 * q^52 + 6 * q^53 - q^55 - 3 * q^58 + 15 * q^60 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 9 * q^65 + 10 * q^66 - 12 * q^67 - 6 * q^68 + 18 * q^69 + 6 * q^71 - 15 * q^72 + 12 * q^73 - 24 * q^74 + 26 * q^75 - 36 * q^76 + 27 * q^78 + 12 * q^79 + 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 24 * q^86 - 30 * q^87 + 9 * q^88 - 4 * q^90 - 48 * q^92 + 5 * q^94 - 30 * q^95 - 39 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	2.18890i		−	1.54779i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$		−	2.18890i		−	1.54779i	0.633316	−	0.773893i	$-0.281693\pi$
$3$	0.895644	+	1.55130i	0.517100	+	0.895644i	0.999803	+	0.0198595i	$0.00632191\pi$
$3$	0.895644	+	1.55130i	0.517100	+	0.895644i	−0.482703	+	0.875784i	$0.660345\pi$
$4$	−2.79129			−1.39564
$5$	−1.89564	+	1.09445i	−0.847758	+	0.489453i	−0.859894	−	0.510473i	$-0.829470\pi$
$5$	−1.89564	+	1.09445i	−0.847758	+	0.489453i	0.0121359	+	0.999926i	$0.496137\pi$
$6$	3.39564	−	1.96048i	1.38627	−	0.800361i
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	−0.104356	+	0.180750i	−0.0347854	+	0.0602500i
$10$	2.39564	+	4.14938i	0.757569	+	1.31215i
$11$	1.10436	−	0.637600i	0.332976	−	0.192244i	−0.324186	−	0.945993i	$-0.605090\pi$
$11$	1.10436	−	0.637600i	0.332976	−	0.192244i	0.657162	+	0.753750i	$0.271757\pi$
$12$	−2.50000	−	4.33013i	−0.721688	−	1.25000i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$		0			0
$15$	−3.39564	−	1.96048i	−0.876751	−	0.506193i
$16$	−1.79129			−0.447822
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	0.395644	+	0.228425i	0.0932542	+	0.0538403i
$19$	5.68693	+	3.28335i	1.30467	+	0.753253i	0.981202	−	0.192986i	$-0.0618172\pi$
$19$	5.68693	+	3.28335i	1.30467	+	0.753253i	0.323470	+	0.946238i	$0.395150\pi$
$20$	5.29129	−	3.05493i	1.18317	−	0.683102i
$21$		0			0
$22$	−1.39564	−	2.41733i	−0.297552	−	0.515376i
$23$	7.58258			1.58108			0.790538	−	0.612413i	$-0.209801\pi$
$23$	7.58258			1.58108			0.790538	+	0.612413i	$0.209801\pi$
$24$	−2.68693	+	1.55130i	−0.548468	+	0.316658i
$25$	−0.104356	+	0.180750i	−0.0208712	+	0.0361500i
$26$	−1.89564	−	7.66115i	−0.371766	−	1.50248i
$27$	5.00000			0.962250
$28$		0			0
$29$	1.10436	−	1.91280i	0.205074	−	0.355198i	−0.745082	−	0.666972i	$-0.767590\pi$
$29$	1.10436	−	1.91280i	0.205074	−	0.355198i	0.950156	+	0.311774i	$0.100923\pi$
$30$	−4.29129	+	7.43273i	−0.783478	+	1.35702i
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.987829	+	0.155543i	$0.950287\pi$
$32$			7.38505i			1.30551i
$33$	1.97822	+	1.14213i	0.344364	+	0.198819i
$34$		−	6.56670i		−	1.12618i
$35$		0			0
$36$	0.291288	−	0.504525i	0.0485480	−	0.0840876i
$37$		−	6.92820i		−	1.13899i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$		−	6.92820i		−	1.13899i	0.821995	−	0.569495i	$-0.192861\pi$
$38$	7.18693	−	12.4481i	1.16587	−	2.01935i
$39$	4.47822	+	4.65390i	0.717089	+	0.745221i
$40$	−1.89564	−	3.28335i	−0.299728	−	0.519143i
$41$	2.20871	+	1.27520i	0.344943	+	0.199153i	0.662456	−	0.749101i	$-0.269514\pi$
$41$	2.20871	+	1.27520i	0.344943	+	0.199153i	−0.317513	+	0.948254i	$0.602848\pi$
$42$		0			0
$43$	2.18693	+	3.78788i	0.333504	+	0.577646i	0.983196	−	0.182551i	$-0.0584356\pi$
$43$	2.18693	+	3.78788i	0.333504	+	0.577646i	−0.649692	+	0.760197i	$0.725102\pi$
$44$	−3.08258	+	1.77973i	−0.464716	+	0.268304i
$45$		−	0.456850i		−	0.0681032i
$46$		−	16.5975i		−	2.44717i
$47$	−3.70871	+	2.14123i	−0.540971	+	0.312330i	−0.745472	−	0.666536i	$-0.767776\pi$
$47$	−3.70871	+	2.14123i	−0.540971	+	0.312330i	0.204501	+	0.978866i	$0.434443\pi$
$48$	−1.60436	−	2.77883i	−0.231569	−	0.401089i
$49$		0			0
$50$	0.395644	+	0.228425i	0.0559525	+	0.0323042i
$51$	2.68693	+	4.65390i	0.376246	+	0.651677i
$52$	−9.76951	+	2.41733i	−1.35479	+	0.335223i
$53$	6.08258	−	10.5353i	0.835506	−	1.44714i	−0.0581117	−	0.998310i	$-0.518508\pi$
$53$	6.08258	−	10.5353i	0.835506	−	1.44714i	0.893618	−	0.448829i	$-0.148159\pi$
$54$		−	10.9445i		−	1.48936i
$55$	−1.39564	+	2.41733i	−0.188189	+	0.325952i
$56$		0			0
$57$			11.7629i			1.55803i
$58$	−4.18693	−	2.41733i	−0.549771	−	0.317410i
$59$		−	8.85095i		−	1.15230i	−0.817345	−	0.576148i	$-0.804555\pi$
$59$		−	8.85095i		−	1.15230i	0.817345	−	0.576148i	$-0.195445\pi$
$60$	9.47822	+	5.47225i	1.22363	+	0.706465i
$61$	−6.37386	+	11.0399i	−0.816090	+	1.41351i	0.0924533	+	0.995717i	$0.470529\pi$
$61$	−6.37386	+	11.0399i	−0.816090	+	1.41351i	−0.908543	+	0.417792i	$0.862804\pi$
$62$	−9.47822	+	16.4168i	−1.20374	+	2.08493i
$63$		0			0
$64$	12.5826			1.57282
$65$	−5.68693	+	5.47225i	−0.705377	+	0.678749i
$66$	2.50000	−	4.33013i	0.307729	−	0.533002i
$67$	−9.87386	+	5.70068i	−1.20628	+	0.696449i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−9.87386	+	5.70068i	−1.20628	+	0.696449i	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−8.37386			−1.01548
$69$	6.79129	+	11.7629i	0.817575	+	1.41608i
$70$		0			0
$71$	−0.791288	+	0.456850i	−0.0939086	+	0.0542181i	−0.546219	−	0.837643i	$-0.683933\pi$
$71$	−0.791288	+	0.456850i	−0.0939086	+	0.0542181i	0.452310	+	0.891861i	$0.350600\pi$
$72$	−0.313068	−	0.180750i	−0.0368954	−	0.0213016i
$73$	3.00000	+	1.73205i	0.351123	+	0.202721i	0.665180	−	0.746683i	$-0.268355\pi$
$73$	3.00000	+	1.73205i	0.351123	+	0.202721i	−0.314057	+	0.949404i	$0.601688\pi$
$74$	−15.1652			−1.76291
$75$	−0.373864			−0.0431700
$76$	−15.8739	−	9.16478i	−1.82086	−	1.05127i
$77$		0			0
$78$	10.1869	−	9.80238i	1.15344	−	1.10990i
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$	3.39564	−	1.96048i	0.379645	−	0.219188i
$81$	4.79129	+	8.29875i	0.532365	+	0.922084i
$82$	2.79129	−	4.83465i	0.308246	−	0.533898i
$83$			3.55945i			0.390701i	0.980734	+	0.195350i	$0.0625844\pi$
$83$			3.55945i			0.390701i	−0.980734	+	0.195350i	$0.937416\pi$
$84$		0			0
$85$	−5.68693	+	3.28335i	−0.616834	+	0.356129i
$86$	8.29129	−	4.78698i	0.894073	−	0.516193i
$87$	3.95644			0.424175
$88$	1.10436	+	1.91280i	0.117725	+	0.203905i
$89$			2.91190i			0.308661i	0.988019	+	0.154330i	$0.0493220\pi$
$89$			2.91190i			0.308661i	−0.988019	+	0.154330i	$0.950678\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−21.1652			−2.20662
$93$		−	15.5130i		−	1.60862i
$94$	4.68693	+	8.11800i	0.483420	+	0.837308i
$95$	−14.3739			−1.47473
$96$	−11.4564	+	6.61438i	−1.16927	+	0.675077i
$97$	−13.1869	+	7.61348i	−1.33893	+	0.773032i	−0.986649	−	0.162863i	$-0.947927\pi$
$97$	−13.1869	+	7.61348i	−1.33893	+	0.773032i	−0.352281	+	0.935894i	$0.614594\pi$
$98$		0			0
$99$			0.266150i			0.0267491i
$100$	0.291288	−	0.504525i	0.0291288	−	0.0504525i
$101$	−4.89564	−	8.47950i	−0.487135	−	0.843742i	0.512756	−	0.858534i	$-0.328625\pi$
$101$	−4.89564	−	8.47950i	−0.487135	−	0.843742i	−0.999891	+	0.0147923i	$0.995291\pi$
$102$	10.1869	−	5.88143i	1.00866	−	0.582348i
$103$	2.29129	+	3.96863i	0.225767	+	0.391040i	0.956549	−	0.291570i	$-0.0941778\pi$
$103$	2.29129	+	3.96863i	0.225767	+	0.391040i	−0.730782	+	0.682611i	$0.760844\pi$
$104$	1.50000	+	6.06218i	0.147087	+	0.594445i
$105$		0			0
$106$	−23.0608	−	13.3142i	−2.23986	−	1.29319i
$107$	−9.79129			−0.946560			−0.473280	−	0.880912i	$-0.656930\pi$
$107$	−9.79129			−0.946560			−0.473280	+	0.880912i	$0.656930\pi$
$108$	−13.9564			−1.34296
$109$	−6.87386	−	3.96863i	−0.658397	−	0.380126i	0.133269	−	0.991080i	$-0.457453\pi$
$109$	−6.87386	−	3.96863i	−0.658397	−	0.380126i	−0.791666	+	0.610954i	$0.790786\pi$
$110$	5.29129	+	3.05493i	0.504505	+	0.291276i
$111$	10.7477	−	6.20520i	1.02013	−	0.588972i
$112$		0			0
$113$	−0.708712	−	1.22753i	−0.0666700	−	0.115476i	0.830764	−	0.556625i	$-0.187904\pi$
$113$	−0.708712	−	1.22753i	−0.0666700	−	0.115476i	−0.897434	+	0.441150i	$0.854571\pi$
$114$	25.7477			2.41150
$115$	−14.3739	+	8.29875i	−1.34037	+	0.773863i
$116$	−3.08258	+	5.33918i	−0.286210	+	0.495730i
$117$	−0.208712	+	0.723000i	−0.0192954	+	0.0668414i
$118$	−19.3739			−1.78351
$119$		0			0
$120$	3.39564	−	5.88143i	0.309978	−	0.536898i
$121$	−4.68693	+	8.11800i	−0.426085	+	0.738000i
$122$	24.1652	+	13.9518i	2.18781	+	1.26313i
$123$			4.56850i			0.411928i
$124$	20.9347	+	12.0866i	1.87999	+	1.08541i
$125$		−	11.4014i		−	1.01977i
$126$		0			0
$127$	7.97822	−	13.8187i	0.707953	−	1.22621i	−0.257663	−	0.966235i	$-0.582952\pi$
$127$	7.97822	−	13.8187i	0.707953	−	1.22621i	0.965615	−	0.259975i	$-0.0837143\pi$
$128$		−	12.7719i		−	1.12889i
$129$	−3.91742	+	6.78518i	−0.344910	+	0.597402i
$130$	11.9782	+	12.4481i	1.05056	+	1.09177i
$131$	1.81307	+	3.14033i	0.158409	+	0.274372i	0.934295	−	0.356501i	$-0.116030\pi$
$131$	1.81307	+	3.14033i	0.158409	+	0.274372i	−0.775886	+	0.630873i	$0.782697\pi$
$132$	−5.52178	−	3.18800i	−0.480609	−	0.277480i
$133$		0			0
$134$	12.4782	+	21.6129i	1.07795	+	1.86707i
$135$	−9.47822	+	5.47225i	−0.815755	+	0.470977i
$136$			5.19615i			0.445566i
$137$		−	17.1497i		−	1.46520i	−0.680660	−	0.732599i	$-0.738307\pi$
$137$		−	17.1497i		−	1.46520i	0.680660	−	0.732599i	$-0.261693\pi$
$138$	25.7477	−	14.8655i	2.19179	−	1.26543i
$139$	0.395644	+	0.685275i	0.0335581	+	0.0581243i	0.882317	−	0.470656i	$-0.155983\pi$
$139$	0.395644	+	0.685275i	0.0335581	+	0.0581243i	−0.848759	+	0.528781i	$0.822649\pi$
$140$		0			0
$141$	−6.64337	−	3.83555i	−0.559473	−	0.323012i
$142$	1.00000	+	1.73205i	0.0839181	+	0.145350i
$143$	3.31307	−	3.18800i	0.277053	−	0.266594i
$144$	0.186932	−	0.323775i	0.0155776	−	0.0269813i
$145$			4.83465i			0.401496i
$146$	3.79129	−	6.56670i	0.313769	−	0.543464i
$147$		0			0
$148$			19.3386i			1.58962i
$149$	−1.89564	−	1.09445i	−0.155297	−	0.0896609i	0.420338	−	0.907368i	$-0.361912\pi$
$149$	−1.89564	−	1.09445i	−0.155297	−	0.0896609i	−0.575635	+	0.817707i	$0.695245\pi$
$150$			0.818350i			0.0668180i
$151$	10.5000	+	6.06218i	0.854478	+	0.493333i	0.862159	−	0.506637i	$-0.169112\pi$
$151$	10.5000	+	6.06218i	0.854478	+	0.493333i	−0.00768132	+	0.999970i	$0.502445\pi$
$152$	−5.68693	+	9.85005i	−0.461271	+	0.798945i
$153$	−0.313068	+	0.542250i	−0.0253101	+	0.0438383i
$154$		0			0
$155$	18.9564			1.52262
$156$	−12.5000	−	12.9904i	−1.00080	−	1.04006i
$157$	−10.9782	+	19.0148i	−0.876157	+	1.51755i	−0.0206325	+	0.999787i	$0.506568\pi$
$157$	−10.9782	+	19.0148i	−0.876157	+	1.51755i	−0.855525	+	0.517762i	$0.826765\pi$
$158$	11.3739	−	6.56670i	0.904856	−	0.522419i
$159$	21.7913			1.72816
$160$	−8.08258	−	13.9994i	−0.638984	−	1.10675i
$161$		0			0
$162$	18.1652	−	10.4877i	1.42719	−	0.823988i
$163$	−6.00000	−	3.46410i	−0.469956	−	0.271329i	0.246265	−	0.969202i	$-0.420797\pi$
$163$	−6.00000	−	3.46410i	−0.469956	−	0.271329i	−0.716221	+	0.697873i	$0.754130\pi$
$164$	−6.16515	−	3.55945i	−0.481417	−	0.277946i
$165$	−5.00000			−0.389249
$166$	7.79129			0.604721
$167$	17.2913	+	9.98313i	1.33804	+	0.772518i	0.986517	−	0.163661i	$-0.0523304\pi$
$167$	17.2913	+	9.98313i	1.33804	+	0.772518i	0.351523	+	0.936179i	$0.385664\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	7.18693	+	12.4481i	0.551213	+	0.954728i
$171$	−1.18693	+	0.685275i	−0.0907669	+	0.0524043i
$172$	−6.10436	−	10.5731i	−0.465453	−	0.806188i
$173$	3.87386	−	6.70973i	0.294524	−	0.510131i	−0.680350	−	0.732888i	$-0.738172\pi$
$173$	3.87386	−	6.70973i	0.294524	−	0.510131i	0.974874	+	0.222756i	$0.0715054\pi$
$174$		−	8.66025i		−	0.656532i
$175$		0			0
$176$	−1.97822	+	1.14213i	−0.149114	+	0.0860910i
$177$	13.7305	−	7.92730i	1.03205	−	0.595853i
$178$	6.37386			0.477741
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$			1.27520i			0.0950478i
$181$	9.16515			0.681240			0.340620	−	0.940201i	$-0.389363\pi$
$181$	9.16515			0.681240			0.340620	+	0.940201i	$0.389363\pi$
$182$		0			0
$183$	−22.8348			−1.68800
$184$			13.1334i			0.968208i
$185$	7.58258	+	13.1334i	0.557482	+	0.965587i
$186$	−33.9564			−2.48981
$187$	3.31307	−	1.91280i	0.242276	−	0.139878i
$188$	10.3521	−	5.97678i	0.755003	−	0.435901i
$189$		0			0
$190$			31.4630i			2.28256i
$191$	0.313068	−	0.542250i	0.0226528	−	0.0392358i	−0.854477	−	0.519490i	$-0.826122\pi$
$191$	0.313068	−	0.542250i	0.0226528	−	0.0392358i	0.877130	+	0.480254i	$0.159455\pi$
$192$	11.2695	+	19.5194i	0.813307	+	1.40869i
$193$	10.7477	−	6.20520i	0.773638	−	0.446660i	−0.0605327	−	0.998166i	$-0.519280\pi$
$193$	10.7477	−	6.20520i	0.773638	−	0.446660i	0.834171	+	0.551506i	$0.185947\pi$
$194$	16.6652	+	28.8649i	1.19649	+	2.07238i
$195$	−13.5826	−	3.92095i	−0.972668	−	0.280785i
$196$		0			0
$197$	−9.47822	−	5.47225i	−0.675295	−	0.389882i	0.122785	−	0.992433i	$-0.460817\pi$
$197$	−9.47822	−	5.47225i	−0.675295	−	0.389882i	−0.798080	+	0.602551i	$0.794151\pi$
$198$	0.582576			0.0414019
$199$	−11.0000			−0.779769			−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000			−0.779769			−0.389885	+	0.920864i	$0.627485\pi$
$200$	−0.313068	−	0.180750i	−0.0221373	−	0.0127810i
$201$	−17.6869	−	10.2116i	−1.24754	−	0.720268i
$202$	−18.5608	+	10.7161i	−1.30593	+	0.753981i
$203$		0			0
$204$	−7.50000	−	12.9904i	−0.525105	−	0.909509i
$205$	−5.58258			−0.389904
$206$	8.68693	−	5.01540i	0.605247	−	0.349440i
$207$	−0.791288	+	1.37055i	−0.0549983	+	0.0952599i
$208$	−6.26951	+	1.55130i	−0.434712	+	0.107563i
$209$	8.37386			0.579232
$210$		0			0
$211$	−0.708712	+	1.22753i	−0.0487898	+	0.0845063i	−0.889389	−	0.457151i	$-0.848870\pi$
$211$	−0.708712	+	1.22753i	−0.0487898	+	0.0845063i	0.840599	+	0.541658i	$0.182203\pi$
$212$	−16.9782	+	29.4071i	−1.16607	+	2.01969i
$213$	−1.41742	−	0.818350i	−0.0971203	−	0.0560724i
$214$			21.4322i			1.46507i
$215$	−8.29129	−	4.78698i	−0.565461	−	0.326469i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−8.68693	+	15.0462i	−0.588353	+	1.01906i
$219$			6.20520i			0.419309i
$220$	3.89564	−	6.74745i	0.262644	−	0.454913i
$221$	10.5000	−	2.59808i	0.706306	−	0.174766i
$222$	−13.5826	−	23.5257i	−0.911603	−	1.57894i
$223$	−17.9347	−	10.3546i	−1.20099	−	0.693394i	−0.240217	−	0.970719i	$-0.577219\pi$
$223$	−17.9347	−	10.3546i	−1.20099	−	0.693394i	−0.960776	+	0.277325i	$0.910552\pi$
$224$		0			0
$225$	−0.0217804	−	0.0377247i	−0.00145203	−	0.00251498i
$226$	−2.68693	+	1.55130i	−0.178732	+	0.103191i
$227$			12.3151i			0.817379i	0.912673	+	0.408689i	$0.134014\pi$
$227$			12.3151i			0.817379i	−0.912673	+	0.408689i	$0.865986\pi$
$228$		−	32.8335i		−	2.17445i
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	−0.684969	−	0.728572i	$-0.740184\pi$
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	0.288478	+	0.957487i	$0.406851\pi$
$230$	18.1652	+	31.4630i	1.19777	+	2.07461i
$231$		0			0
$232$	3.31307	+	1.91280i	0.217514	+	0.125582i
$233$	3.47822	+	6.02445i	0.227866	+	0.394675i	0.957175	−	0.289509i	$-0.0934919\pi$
$233$	3.47822	+	6.02445i	0.227866	+	0.394675i	−0.729310	+	0.684184i	$0.760159\pi$
$234$	1.58258	+	0.456850i	0.103456	+	0.0298652i
$235$	4.68693	−	8.11800i	0.305742	−	0.529560i
$236$			24.7056i			1.60820i
$237$	−5.37386	+	9.30780i	−0.349070	+	0.604607i
$238$		0			0
$239$		−	13.2288i		−	0.855697i	−0.903850	−	0.427849i	$-0.859272\pi$
$239$		−	13.2288i		−	0.855697i	0.903850	−	0.427849i	$-0.140728\pi$
$240$	6.08258	+	3.51178i	0.392629	+	0.226684i
$241$		−	4.11165i		−	0.264855i	−0.991193	−	0.132427i	$-0.957723\pi$
$241$		−	4.11165i		−	0.264855i	0.991193	−	0.132427i	$-0.0422771\pi$
$242$	17.7695	+	10.2592i	1.14227	+	0.659488i
$243$	−1.08258	+	1.87508i	−0.0694473	+	0.120286i
$244$	17.7913	−	30.8154i	1.13897	−	1.97275i
$245$		0			0
$246$	10.0000			0.637577
$247$	22.7477	+	6.56670i	1.44740	+	0.417829i
$248$	7.50000	−	12.9904i	0.476250	−	0.824890i
$249$	−5.52178	+	3.18800i	−0.349929	+	0.202031i
$250$	−24.9564			−1.57838
$251$	−10.5826	−	18.3296i	−0.667966	−	1.15695i	−0.978472	−	0.206380i	$-0.933832\pi$
$251$	−10.5826	−	18.3296i	−0.667966	−	1.15695i	0.310506	−	0.950572i	$-0.399502\pi$
$252$		0			0
$253$	8.37386	−	4.83465i	0.526460	−	0.303952i
$254$	−30.2477	−	17.4635i	−1.89791	−	1.09576i
$255$	−10.1869	−	5.88143i	−0.637930	−	0.368309i
$256$	−2.79129			−0.174455
$257$	−27.9564			−1.74387			−0.871937	−	0.489617i	$-0.837136\pi$
$257$	−27.9564			−1.74387			−0.871937	+	0.489617i	$0.837136\pi$
$258$	14.8521	+	8.57485i	0.924650	+	0.533847i
$259$		0			0
$260$	15.8739	−	15.2746i	0.984455	−	0.947292i
$261$	0.230493	+	0.399225i	0.0142671	+	0.0247114i
$262$	6.87386	−	3.96863i	0.424669	−	0.245183i
$263$	13.6652	+	23.6687i	0.842629	+	1.45948i	0.887664	+	0.460491i	$0.152327\pi$
$263$	13.6652	+	23.6687i	0.842629	+	1.45948i	−0.0450348	+	0.998985i	$0.514340\pi$
$264$	−1.97822	+	3.42638i	−0.121751	+	0.210879i
$265$			26.6283i			1.63576i
$266$		0			0
$267$	−4.51723	+	2.60803i	−0.276450	+	0.159609i
$268$	27.5608	−	15.9122i	1.68354	−	0.971994i
$269$	11.2087			0.683407			0.341704	−	0.939808i	$-0.388996\pi$
$269$	11.2087			0.683407			0.341704	+	0.939808i	$0.388996\pi$
$270$	11.9782	+	20.7469i	0.728971	+	1.26262i
$271$		−	28.7219i		−	1.74473i	−0.488856	−	0.872364i	$-0.662586\pi$
$271$		−	28.7219i		−	1.74473i	0.488856	−	0.872364i	$-0.337414\pi$
$272$	−5.37386			−0.325838
$273$		0			0
$274$	−37.5390			−2.26781
$275$			0.266150i			0.0160494i
$276$	−18.9564	−	32.8335i	−1.14104	−	1.97635i
$277$	−15.7477			−0.946189			−0.473095	−	0.881012i	$-0.656863\pi$
$277$	−15.7477			−0.946189			−0.473095	+	0.881012i	$0.656863\pi$
$278$	1.50000	−	0.866025i	0.0899640	−	0.0519408i
$279$	1.56534	−	0.903750i	0.0937145	−	0.0541061i
$280$		0			0
$281$		−	6.39590i		−	0.381548i	−0.981634	−	0.190774i	$-0.938900\pi$
$281$		−	6.39590i		−	0.381548i	0.981634	−	0.190774i	$-0.0610997\pi$
$282$	−8.39564	+	14.5417i	−0.499953	+	0.865945i
$283$	−12.3739	−	21.4322i	−0.735550	−	1.27401i	−0.954482	−	0.298270i	$-0.903591\pi$
$283$	−12.3739	−	21.4322i	−0.735550	−	1.27401i	0.218932	−	0.975740i	$-0.429743\pi$
$284$	2.20871	−	1.27520i	0.131063	−	0.0756692i
$285$	−12.8739	−	22.2982i	−0.762582	−	1.32083i
$286$	−6.97822	−	7.25198i	−0.412631	−	0.428818i
$287$		0			0
$288$	−1.33485	−	0.770675i	−0.0786567	−	0.0454125i
$289$	−8.00000			−0.470588
$290$	10.5826			0.621430
$291$	−23.6216	−	13.6379i	−1.38472	−	0.799470i
$292$	−8.37386	−	4.83465i	−0.490043	−	0.282927i
$293$	−6.79129	+	3.92095i	−0.396751	+	0.229064i	−0.685081	−	0.728467i	$-0.740233\pi$
$293$	−6.79129	+	3.92095i	−0.396751	+	0.229064i	0.288330	+	0.957531i	$0.406900\pi$
$294$		0			0
$295$	9.68693	+	16.7783i	0.563995	+	0.976868i
$296$	12.0000			0.697486
$297$	5.52178	−	3.18800i	0.320406	−	0.184987i
$298$	−2.39564	+	4.14938i	−0.138776	+	0.240367i
$299$	26.5390	−	6.56670i	1.53479	−	0.379762i
$300$	1.04356			0.0602500
$301$		0			0
$302$	13.2695	−	22.9835i	0.763574	−	1.32255i
$303$	8.76951	−	15.1892i	0.503795	−	0.872599i
$304$	−10.1869	−	5.88143i	−0.584261	−	0.337323i
$305$		−	27.9035i		−	1.59775i
$306$	1.18693	+	0.685275i	0.0678524	+	0.0391746i
$307$			24.1733i			1.37964i	0.723980	+	0.689820i	$0.242311\pi$
$307$			24.1733i			1.37964i	−0.723980	+	0.689820i	$0.757689\pi$
$308$		0			0
$309$	−4.10436	+	7.10895i	−0.233489	+	0.404414i
$310$		−	41.4938i		−	2.35669i
$311$	−2.76951	+	4.79693i	−0.157044	+	0.272009i	−0.933802	−	0.357791i	$-0.883530\pi$
$311$	−2.76951	+	4.79693i	−0.157044	+	0.272009i	0.776757	+	0.629800i	$0.216863\pi$
$312$	−8.06080	+	7.75650i	−0.456353	+	0.439126i
$313$	10.3739	+	17.9681i	0.586365	+	1.01561i	0.994704	+	0.102784i	$0.0327751\pi$
$313$	10.3739	+	17.9681i	0.586365	+	1.01561i	−0.408338	+	0.912831i	$0.633892\pi$
$314$	41.6216	+	24.0302i	2.34884	+	1.35610i
$315$		0			0
$316$	−8.37386	−	14.5040i	−0.471067	−	0.815911i
$317$	16.0390	−	9.26013i	0.900841	−	0.520101i	0.0233679	−	0.999727i	$-0.492561\pi$
$317$	16.0390	−	9.26013i	0.900841	−	0.520101i	0.877473	+	0.479626i	$0.159228\pi$
$318$		−	47.6990i		−	2.67483i
$319$		−	2.81655i		−	0.157697i
$320$	−23.8521	+	13.7710i	−1.33337	+	0.769823i
$321$	−8.76951	−	15.1892i	−0.489466	−	0.847780i
$322$		0			0
$323$	17.0608	+	9.85005i	0.949288	+	0.548072i
$324$	−13.3739	−	23.1642i	−0.742992	−	1.28690i
$325$	−0.208712	+	0.723000i	−0.0115773	+	0.0401048i
$326$	−7.58258	+	13.1334i	−0.419960	+	0.727392i
$327$		−	14.2179i		−	0.786252i
$328$	−2.20871	+	3.82560i	−0.121956	+	0.211234i
$329$		0			0
$330$			10.9445i			0.602475i
$331$	−0.939205	−	0.542250i	−0.0516234	−	0.0298048i	0.473966	−	0.880543i	$-0.342822\pi$
$331$	−0.939205	−	0.542250i	−0.0516234	−	0.0298048i	−0.525590	+	0.850738i	$0.676155\pi$
$332$		−	9.93545i		−	0.545279i
$333$	1.25227	+	0.723000i	0.0686241	+	0.0396202i
$334$	21.8521	−	37.8489i	1.19569	−	2.07100i
$335$	12.4782	−	21.6129i	0.681758	−	1.18084i
$336$		0			0
$337$	−12.9564			−0.705782			−0.352891	−	0.935664i	$-0.614801\pi$
$337$	−12.9564			−0.705782			−0.352891	+	0.935664i	$0.614801\pi$
$338$	−13.2695	−	25.1724i	−0.721766	−	1.36920i
$339$	1.26951	−	2.19885i	0.0689502	−	0.119425i
$340$	15.8739	−	9.16478i	0.860881	−	0.497030i
$341$	−11.0436			−0.598042
$342$	1.50000	+	2.59808i	0.0811107	+	0.140488i
$343$		0			0
$344$	−6.56080	+	3.78788i	−0.353734	+	0.204229i
$345$	−25.7477	−	14.8655i	−1.38621	−	0.800329i
$346$	−14.6869	−	8.47950i	−0.789574	−	0.455861i
$347$	−4.41742			−0.237140			−0.118570	−	0.992946i	$-0.537831\pi$
$347$	−4.41742			−0.237140			−0.118570	+	0.992946i	$0.537831\pi$
$348$	−11.0436			−0.591997
$349$	−9.24773	−	5.33918i	−0.495019	−	0.285800i	0.231635	−	0.972803i	$-0.425593\pi$
$349$	−9.24773	−	5.33918i	−0.495019	−	0.285800i	−0.726654	+	0.687003i	$0.758926\pi$
$350$		0			0
$351$	17.5000	−	4.33013i	0.934081	−	0.231125i
$352$	4.70871	+	8.15573i	0.250975	+	0.434702i
$353$	−23.2259	+	13.4095i	−1.23619	+	0.713716i	−0.968314	−	0.249737i	$-0.919656\pi$
$353$	−23.2259	+	13.4095i	−1.23619	+	0.713716i	−0.267879	+	0.963453i	$0.586323\pi$
$354$	−17.3521	−	30.0547i	−0.922253	−	1.59739i
$355$	1.00000	−	1.73205i	0.0530745	−	0.0919277i
$356$		−	8.12795i		−	0.430781i
$357$		0			0
$358$	17.0608	−	9.85005i	0.901691	−	0.520592i
$359$	10.9782	−	6.33828i	0.579408	−	0.334522i	−0.181490	−	0.983393i	$-0.558092\pi$
$359$	10.9782	−	6.33828i	0.579408	−	0.334522i	0.760898	+	0.648871i	$0.224759\pi$
$360$	0.791288			0.0417045
$361$	12.0608	+	20.8899i	0.634779	+	1.09947i
$362$		−	20.0616i		−	1.05441i
$363$	−16.7913			−0.881314
$364$		0			0
$365$	−7.58258			−0.396890
$366$			49.9832i			2.61266i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−13.5826			−0.708041
$369$	−0.460985	+	0.266150i	−0.0239979	+	0.0138552i
$370$	28.7477	−	16.5975i	1.49452	−	0.862863i
$371$		0			0
$372$			43.3013i			2.24507i
$373$	−18.3956	+	31.8622i	−0.952490	+	1.64976i	−0.212481	+	0.977165i	$0.568154\pi$
$373$	−18.3956	+	31.8622i	−0.952490	+	1.64976i	−0.740009	+	0.672596i	$0.765179\pi$
$374$	−4.18693	−	7.25198i	−0.216501	−	0.374991i
$375$	17.6869	−	10.2116i	0.913349	−	0.527322i
$376$	−3.70871	−	6.42368i	−0.191262	−	0.331276i
$377$	2.20871	−	7.65120i	0.113754	−	0.394057i
$378$		0			0
$379$	−3.93920	−	2.27430i	−0.202343	−	0.116823i	0.395405	−	0.918507i	$-0.370604\pi$
$379$	−3.93920	−	2.27430i	−0.202343	−	0.116823i	−0.597748	+	0.801684i	$0.703938\pi$
$380$	40.1216			2.05819
$381$	28.5826			1.46433
$382$	−1.18693	−	0.685275i	−0.0607287	−	0.0350617i
$383$	3.39564	+	1.96048i	0.173509	+	0.100176i	0.584240	−	0.811581i	$-0.301393\pi$
$383$	3.39564	+	1.96048i	0.173509	+	0.100176i	−0.410730	+	0.911757i	$0.634726\pi$
$384$	19.8131	−	11.4391i	1.01108	−	0.583748i
$385$		0			0
$386$	−13.5826	−	23.5257i	−0.691335	−	1.19743i
$387$	−0.912878			−0.0464042
$388$	36.8085	−	21.2514i	1.86867	−	1.07888i
$389$	−18.1652	+	31.4630i	−0.921010	+	1.59524i	−0.123154	+	0.992388i	$0.539301\pi$
$389$	−18.1652	+	31.4630i	−0.921010	+	1.59524i	−0.797856	+	0.602848i	$0.794033\pi$
$390$	−8.58258	+	29.7309i	−0.434596	+	1.50548i
$391$	22.7477			1.15040
$392$		0			0
$393$	−3.24773	+	5.62523i	−0.163826	+	0.283755i
$394$	−11.9782	+	20.7469i	−0.603454	+	1.04521i
$395$	−11.3739	−	6.56670i	−0.572281	−	0.330407i
$396$		−	0.742901i		−	0.0373322i
$397$	−13.1216	−	7.57575i	−0.658554	−	0.380216i	0.133172	−	0.991093i	$-0.457484\pi$
$397$	−13.1216	−	7.57575i	−0.658554	−	0.380216i	−0.791726	+	0.610877i	$0.790817\pi$
$398$			24.0779i			1.20692i
$399$		0			0
$400$	0.186932	−	0.323775i	0.00934659	−	0.0161888i
$401$			29.5601i			1.47616i	0.674712	+	0.738081i	$0.264268\pi$
$401$			29.5601i			1.47616i	−0.674712	+	0.738081i	$0.735732\pi$
$402$	−22.3521	+	38.7149i	−1.11482	+	1.93093i
$403$	−30.0000	−	8.66025i	−1.49441	−	0.431398i
$404$	13.6652	+	23.6687i	0.679867	+	1.17756i
$405$	−18.1652	−	10.4877i	−0.902634	−	0.521136i
$406$		0			0
$407$	−4.41742	−	7.65120i	−0.218964	−	0.379256i
$408$	−8.06080	+	4.65390i	−0.399069	+	0.230402i
$409$		−	0.361500i		−	0.0178750i	−0.999960	−	0.00893751i	$-0.997155\pi$
$409$		−	0.361500i		−	0.0178750i	0.999960	−	0.00893751i	$-0.00284494\pi$
$410$			12.2197i			0.603488i
$411$	26.6044	−	15.3600i	1.31230	−	0.757655i
$412$	−6.39564	−	11.0776i	−0.315091	−	0.545753i
$413$		0			0
$414$	3.00000	+	1.73205i	0.147442	+	0.0851257i
$415$	−3.89564	−	6.74745i	−0.191230	−	0.331219i
$416$	6.39564	+	25.8477i	0.313572	+	1.26729i
$417$	−0.708712	+	1.22753i	−0.0347058	+	0.0601122i
$418$		−	18.3296i		−	0.896528i
$419$	12.8739	−	22.2982i	0.628929	−	1.08934i	−0.358838	−	0.933400i	$-0.616827\pi$
$419$	12.8739	−	22.2982i	0.628929	−	1.08934i	0.987767	−	0.155938i	$-0.0498399\pi$
$420$		0			0
$421$			20.0616i			0.977743i	0.872356	+	0.488872i	$0.162591\pi$
$421$			20.0616i			0.977743i	−0.872356	+	0.488872i	$0.837409\pi$
$422$	2.68693	+	1.55130i	0.130798	+	0.0755161i
$423$		−	0.893800i		−	0.0434580i
$424$	18.2477	+	10.5353i	0.886188	+	0.511641i
$425$	−0.313068	+	0.542250i	−0.0151860	+	0.0263030i
$426$	−1.79129	+	3.10260i	−0.0867882	+	0.150322i
$427$		0			0
$428$	27.3303			1.32106
$429$	7.91288	+	2.28425i	0.382037	+	0.110285i
$430$	−10.4782	+	18.1488i	−0.505305	+	0.875213i
$431$	13.5172	−	7.80418i	0.651102	−	0.375914i	−0.137776	−	0.990463i	$-0.543995\pi$
$431$	13.5172	−	7.80418i	0.651102	−	0.375914i	0.788878	+	0.614549i	$0.210662\pi$
$432$	−8.95644			−0.430917
$433$	11.2477	+	19.4816i	0.540531	+	0.936228i	0.998874	+	0.0474518i	$0.0151101\pi$
$433$	11.2477	+	19.4816i	0.540531	+	0.936228i	−0.458342	+	0.888776i	$0.651557\pi$
$434$		0			0
$435$	−7.50000	+	4.33013i	−0.359597	+	0.207614i
$436$	19.1869	+	11.0776i	0.918887	+	0.530520i
$437$	43.1216	+	24.8963i	2.06279	+	1.19095i
$438$	13.5826			0.649001
$439$	−11.5390			−0.550727			−0.275364	−	0.961340i	$-0.588798\pi$
$439$	−11.5390			−0.550727			−0.275364	+	0.961340i	$0.588798\pi$
$440$	−4.18693	−	2.41733i	−0.199604	−	0.115242i
$441$		0			0
$442$	−5.68693	−	22.9835i	−0.270500	−	1.09321i
$443$	−1.58258	−	2.74110i	−0.0751904	−	0.130234i	0.825979	−	0.563701i	$-0.190623\pi$
$443$	−1.58258	−	2.74110i	−0.0751904	−	0.130234i	−0.901169	+	0.433468i	$0.857290\pi$
$444$	−30.0000	+	17.3205i	−1.42374	+	0.821995i
$445$	−3.18693	−	5.51993i	−0.151075	−	0.261670i
$446$	−22.6652	+	39.2572i	−1.07323	+	1.85888i
$447$		−	3.92095i		−	0.185455i
$448$		0			0
$449$	−17.2087	+	9.93545i	−0.812129	+	0.468883i	−0.847695	−	0.530484i	$-0.822010\pi$
$449$	−17.2087	+	9.93545i	−0.812129	+	0.468883i	0.0355654	+	0.999367i	$0.488677\pi$
$450$	−0.0825757	+	0.0476751i	−0.00389266	+	0.00224743i
$451$	3.25227			0.153144
$452$	1.97822	+	3.42638i	0.0930476	+	0.161163i
$453$			21.7182i			1.02041i
$454$	26.9564			1.26513
$455$		0			0
$456$	−20.3739			−0.954094
$457$			8.94630i			0.418490i	0.977863	+	0.209245i	$0.0671007\pi$
$457$			8.94630i			0.418490i	−0.977863	+	0.209245i	$0.932899\pi$
$458$	7.58258	+	13.1334i	0.354310	+	0.613684i
$459$	15.0000			0.700140
$460$	40.1216	−	23.1642i	1.87068	−	1.08004i
$461$	−15.4782	+	8.93635i	−0.720893	+	0.416208i	−0.815081	−	0.579347i	$-0.803308\pi$
$461$	−15.4782	+	8.93635i	−0.720893	+	0.416208i	0.0941885	+	0.995554i	$0.469974\pi$
$462$		0			0
$463$		−	7.93725i		−	0.368875i	−0.982844	−	0.184438i	$-0.940954\pi$
$463$		−	7.93725i		−	0.368875i	0.982844	−	0.184438i	$-0.0590464\pi$
$464$	−1.97822	+	3.42638i	−0.0918365	+	0.159066i
$465$	16.9782	+	29.4071i	0.787346	+	1.36372i
$466$	13.1869	−	7.61348i	0.610873	−	0.352688i
$467$	5.91742	+	10.2493i	0.273826	+	0.474280i	0.969838	−	0.243750i	$-0.0783775\pi$
$467$	5.91742	+	10.2493i	0.273826	+	0.474280i	−0.696012	+	0.718030i	$0.745044\pi$
$468$	0.582576	−	2.01810i	0.0269296	−	0.0932868i
$469$		0			0
$470$	−17.7695	−	10.2592i	−0.819646	−	0.473223i
$471$	−39.3303			−1.81224
$472$	15.3303			0.705634
$473$	4.83030	+	2.78878i	0.222098	+	0.128228i
$474$	20.3739	+	11.7629i	0.935803	+	0.540286i
$475$	−1.18693	+	0.685275i	−0.0544602	+	0.0314426i
$476$		0			0
$477$	1.26951	+	2.19885i	0.0581268	+	0.100678i
$478$	−28.9564			−1.32444
$479$	8.85208	−	5.11075i	0.404462	−	0.233516i	−0.283945	−	0.958840i	$-0.591643\pi$
$479$	8.85208	−	5.11075i	0.404462	−	0.233516i	0.688407	+	0.725324i	$0.258310\pi$
$480$	14.4782	−	25.0770i	0.660837	−	1.14460i
$481$	−6.00000	−	24.2487i	−0.273576	−	1.10565i
$482$	−9.00000			−0.409939
$483$		0			0
$484$	13.0826	−	22.6597i	0.594663	−	1.02999i
$485$	16.6652	−	28.8649i	0.756726	−	1.31069i
$486$	4.10436	+	2.36965i	0.186177	+	0.107490i
$487$		−	10.3169i		−	0.467501i	−0.972297	−	0.233751i	$-0.924900\pi$
$487$		−	10.3169i		−	0.467501i	0.972297	−	0.233751i	$-0.0750999\pi$
$488$	−19.1216	−	11.0399i	−0.865594	−	0.499751i
$489$		−	12.4104i		−	0.561218i
$490$		0			0
$491$	−18.5608	+	32.1482i	−0.837637	+	1.45083i	0.0542283	+	0.998529i	$0.482730\pi$
$491$	−18.5608	+	32.1482i	−0.837637	+	1.45083i	−0.891865	+	0.452301i	$0.850603\pi$
$492$		−	12.7520i		−	0.574905i
$493$	3.31307	−	5.73840i	0.149213	−	0.258445i
$494$	14.3739	−	49.7925i	0.646711	−	2.24027i
$495$	−0.291288	−	0.504525i	−0.0130924	−	0.0226767i
$496$	13.4347	+	7.75650i	0.603234	+	0.348277i
$497$		0			0
$498$	6.97822	+	12.0866i	0.312701	+	0.541615i
$499$	36.5608	−	21.1084i	1.63669	−	0.944941i	0.654723	−	0.755869i	$-0.272785\pi$
$499$	36.5608	−	21.1084i	1.63669	−	0.944941i	0.981963	−	0.189072i	$-0.0605479\pi$
$500$			31.8245i			1.42323i
$501$			35.7653i			1.59788i
$502$	−40.1216	+	23.1642i	−1.79071	+	1.03387i
$503$	−11.0608	−	19.1579i	−0.493176	−	0.854207i	0.506793	−	0.862068i	$-0.330831\pi$
$503$	−11.0608	−	19.1579i	−0.493176	−	0.854207i	−0.999969	+	0.00786127i	$0.997498\pi$
$504$		0			0
$505$	18.5608	+	10.7161i	0.825945	+	0.476859i
$506$	−10.5826	−	18.3296i	−0.470453	−	0.814848i
$507$	19.7042	+	12.4104i	0.875093	+	0.551165i
$508$	−22.2695	+	38.5719i	−0.988050	+	1.71135i
$509$			21.9844i			0.974440i	0.873279	+	0.487220i	$0.161989\pi$
$509$			21.9844i			0.974440i	−0.873279	+	0.487220i	$0.838011\pi$
$510$	−12.8739	+	22.2982i	−0.570064	+	0.987380i
$511$		0			0
$512$		−	19.4340i		−	0.858868i
$513$	28.4347	+	16.4168i	1.25542	+	0.724818i
$514$			61.1939i			2.69915i
$515$	−8.68693	−	5.01540i	−0.382792	−	0.221005i
$516$	10.9347	−	18.9394i	0.481372	−	0.833760i
$517$	−2.73049	+	4.72935i	−0.120087	+	0.207997i
$518$		0			0
$519$	13.8784			0.609195
$520$	−9.47822	−	9.85005i	−0.415647	−	0.431953i
$521$	12.7913	−	22.1552i	0.560396	−	0.970635i	−0.437065	−	0.899430i	$-0.643982\pi$
$521$	12.7913	−	22.1552i	0.560396	−	0.970635i	0.997462	−	0.0712054i	$-0.0226846\pi$
$522$	0.873864	−	0.504525i	0.0382480	−	0.0220825i
$523$	12.3303			0.539166			0.269583	−	0.962977i	$-0.413114\pi$
$523$	12.3303			0.539166			0.269583	+	0.962977i	$0.413114\pi$
$524$	−5.06080	−	8.76555i	−0.221082	−	0.382925i
$525$		0			0
$526$	51.8085	−	29.9117i	2.25896	−	1.30421i
$527$	−22.5000	−	12.9904i	−0.980115	−	0.565870i
$528$	−3.54356	−	2.04588i	−0.154214	−	0.0890353i
$529$	34.4955			1.49980
$530$	58.2867			2.53181
$531$	1.59981	+	0.923651i	0.0694259	+	0.0400830i
$532$		0			0
$533$	8.83485	+	2.55040i	0.382680	+	0.110470i
$534$	5.70871	+	9.88778i	0.247040	+	0.427886i
$535$	18.5608	−	10.7161i	0.802453	−	0.463297i
$536$	−9.87386	−	17.1020i	−0.426486	−	0.738695i
$537$	−8.06080	+	13.9617i	−0.347849	+	0.602492i
$538$		−	24.5348i		−	1.05777i
$539$		0			0
$540$	26.4564	−	15.2746i	1.13850	−	0.657316i
$541$	26.0608	−	15.0462i	1.12044	−	0.646887i	0.178928	−	0.983862i	$-0.442737\pi$
$541$	26.0608	−	15.0462i	1.12044	−	0.646887i	0.941513	+	0.336975i	$0.109404\pi$
$542$	−62.8693			−2.70047
$543$	8.20871	+	14.2179i	0.352270	+	0.610149i
$544$			22.1552i			0.949895i
$545$	17.3739			0.744215
$546$		0			0
$547$	15.7477			0.673324			0.336662	−	0.941626i	$-0.390702\pi$
$547$	15.7477			0.673324			0.336662	+	0.941626i	$0.390702\pi$
$548$			47.8698i			2.04490i
$549$	−1.33030	−	2.30415i	−0.0567759	−	0.0983388i
$550$	0.582576			0.0248411
$551$	12.5608	−	7.25198i	0.535108	−	0.308945i
$552$	−20.3739	+	11.7629i	−0.867169	+	0.500660i
$553$		0			0
$554$			34.4702i			1.46450i
$555$	−13.5826	+	23.5257i	−0.576548	+	0.998611i
$556$	−1.10436	−	1.91280i	−0.0468351	−	0.0811208i
$557$	−24.0998	+	13.9140i	−1.02114	+	0.589556i	−0.914434	−	0.404734i	$-0.867364\pi$
$557$	−24.0998	+	13.9140i	−1.02114	+	0.589556i	−0.106707	+	0.994290i	$0.534031\pi$
$558$	−1.97822	−	3.42638i	−0.0837447	−	0.145050i
$559$	10.9347	+	11.3636i	0.462487	+	0.480630i
$560$		0			0
$561$	5.93466	+	3.42638i	0.250561	+	0.144662i
$562$	−14.0000			−0.590554
$563$	0.330303			0.0139206			0.00696030	−	0.999976i	$-0.497784\pi$
$563$	0.330303			0.0139206			0.00696030	+	0.999976i	$0.497784\pi$
$564$	18.5436	+	10.7061i	0.780825	+	0.450809i
$565$	2.68693	+	1.55130i	0.113040	+	0.0652637i
$566$	−46.9129	+	27.0852i	−1.97190	+	1.13847i
$567$		0			0
$568$	−0.791288	−	1.37055i	−0.0332017	−	0.0575070i
$569$	−10.7477			−0.450568			−0.225284	−	0.974293i	$-0.572331\pi$
$569$	−10.7477			−0.450568			−0.225284	+	0.974293i	$0.572331\pi$
$570$	−48.8085	+	28.1796i	−2.04436	+	1.18031i
$571$	12.4782	−	21.6129i	0.522197	−	0.904472i	−0.477469	−	0.878648i	$-0.658446\pi$
$571$	12.4782	−	21.6129i	0.522197	−	0.904472i	0.999667	−	0.0258237i	$-0.00822085\pi$
$572$	−9.24773	+	8.89863i	−0.386667	+	0.372070i
$573$	1.12159			0.0468551
$574$		0			0
$575$	−0.791288	+	1.37055i	−0.0329990	+	0.0571559i
$576$	−1.31307	+	2.27430i	−0.0547112	+	0.0947625i
$577$	17.1261	+	9.88778i	0.712970	+	0.411634i	0.812160	−	0.583435i	$-0.198292\pi$
$577$	17.1261	+	9.88778i	0.712970	+	0.411634i	−0.0991895	+	0.995069i	$0.531625\pi$
$578$			17.5112i			0.728370i
$579$	19.2523	+	11.1153i	0.800097	+	0.461936i
$580$		−	13.4949i		−	0.560345i
$581$		0			0
$582$	−29.8521	+	51.7053i	−1.23741	+	2.14325i
$583$		−	15.5130i		−	0.642483i
$584$	−3.00000	+	5.19615i	−0.124141	+	0.215018i
$585$	−0.395644	−	1.59898i	−0.0163579	−	0.0661095i
$586$	8.58258	+	14.8655i	0.354543	+	0.614086i
$587$	−30.7259	−	17.7396i	−1.26820	−	0.732193i	−0.293549	−	0.955944i	$-0.594836\pi$
$587$	−30.7259	−	17.7396i	−1.26820	−	0.732193i	−0.974646	+	0.223751i	$0.928170\pi$
$588$		0			0
$589$	−28.4347	−	49.2503i	−1.17163	−	2.02932i
$590$	36.7259	−	21.2037i	1.51198	−	0.872944i
$591$		−	19.6048i		−	0.806432i
$592$			12.4104i			0.510065i
$593$	−16.9782	+	9.80238i	−0.697212	+	0.402535i	−0.806308	−	0.591496i	$-0.798538\pi$
$593$	−16.9782	+	9.80238i	−0.697212	+	0.402535i	0.109096	+	0.994031i	$0.465204\pi$
$594$	−6.97822	−	12.0866i	−0.286320	−	0.495920i
$595$		0			0
$596$	5.29129	+	3.05493i	0.216740	+	0.125135i
$597$	−9.85208	−	17.0643i	−0.403219	−	0.698396i
$598$	−14.3739	−	58.0913i	−0.587791	−	2.37553i
$599$	10.1869	−	17.6443i	0.416227	−	0.720926i	−0.579330	−	0.815093i	$-0.696686\pi$
$599$	10.1869	−	17.6443i	0.416227	−	0.720926i	0.995556	+	0.0941675i	$0.0300189\pi$
$600$		−	0.647551i		−	0.0264361i
$601$	0.686932	−	1.18980i	0.0280205	−	0.0485330i	−0.851675	−	0.524070i	$-0.824413\pi$
$601$	0.686932	−	1.18980i	0.0280205	−	0.0485330i	0.879696	+	0.475537i	$0.157746\pi$
$602$		0			0
$603$		−	2.37960i		−	0.0969049i
$604$	−29.3085	−	16.9213i	−1.19255	−	0.688517i
$605$		−	20.5185i		−	0.834194i
$606$	−33.2477	−	19.1956i	−1.35060	−	0.779767i
$607$	3.87386	−	6.70973i	0.157235	−	0.272339i	−0.776635	−	0.629950i	$-0.783075\pi$
$607$	3.87386	−	6.70973i	0.157235	−	0.272339i	0.933871	+	0.357611i	$0.116409\pi$
$608$	−24.2477	+	41.9983i	−0.983375	+	1.70326i
$609$		0			0
$610$	−61.0780			−2.47298
$611$	−11.1261	+	10.7061i	−0.450115	+	0.433124i
$612$	0.873864	−	1.51358i	0.0353238	−	0.0611827i
$613$	−32.3085	+	18.6533i	−1.30493	+	0.753401i	−0.981245	−	0.192764i	$-0.938255\pi$
$613$	−32.3085	+	18.6533i	−1.30493	+	0.753401i	−0.323684	+	0.946165i	$0.604921\pi$
$614$	52.9129			2.13539
$615$	−5.00000	−	8.66025i	−0.201619	−	0.349215i
$616$		0			0
$617$	−24.0826	+	13.9041i	−0.969528	+	0.559757i	−0.899092	−	0.437759i	$-0.855772\pi$
$617$	−24.0826	+	13.9041i	−0.969528	+	0.559757i	−0.0704357	+	0.997516i	$0.522439\pi$
$618$	15.5608	+	8.98403i	0.625947	+	0.361391i
$619$	−10.7477	−	6.20520i	−0.431988	−	0.249408i	0.268205	−	0.963362i	$-0.413569\pi$
$619$	−10.7477	−	6.20520i	−0.431988	−	0.249408i	−0.700193	+	0.713954i	$0.746903\pi$
$620$	−52.9129			−2.12503
$621$	37.9129			1.52139
$622$	10.5000	+	6.06218i	0.421012	+	0.243071i
$623$		0			0
$624$	−8.02178	−	8.33648i	−0.321128	−	0.333726i
$625$	11.9564	+	20.7092i	0.478258	+	0.828366i
$626$	39.3303	−	22.7074i	1.57196	−	0.907569i
$627$	7.50000	+	12.9904i	0.299521	+	0.518786i
$628$	30.6434	−	53.0759i	1.22280	−	2.11796i
$629$		−	20.7846i		−	0.828737i
$630$		0			0
$631$	−10.4347	+	6.02445i	−0.415397	+	0.239830i	−0.693106	−	0.720836i	$-0.743758\pi$
$631$	−10.4347	+	6.02445i	−0.415397	+	0.239830i	0.277709	+	0.960665i	$0.410425\pi$
$632$	−9.00000	+	5.19615i	−0.358001	+	0.206692i
$633$	−2.53901			−0.100917
$634$	−20.2695	−	35.1078i	−0.805005	−	1.39431i
$635$			34.9271i			1.38604i
$636$	−60.8258			−2.41190
$637$		0			0
$638$	−6.16515			−0.244081
$639$		−	0.190700i		−	0.00754399i
$640$	13.9782	+	24.2110i	0.552538	+	0.957023i
$641$	15.6261			0.617195			0.308598	−	0.951193i	$-0.400140\pi$
$641$	15.6261			0.617195			0.308598	+	0.951193i	$0.400140\pi$
$642$	−33.2477	+	19.1956i	−1.31218	+	0.757589i
$643$	−11.7523	+	6.78518i	−0.463464	+	0.267581i	−0.713500	−	0.700655i	$-0.752891\pi$
$643$	−11.7523	+	6.78518i	−0.463464	+	0.267581i	0.250035	+	0.968237i	$0.419558\pi$
$644$		0			0
$645$		−	17.1497i		−	0.675269i
$646$	21.5608	−	37.3444i	0.848298	−	1.46930i
$647$	−14.5390	−	25.1823i	−0.571588	−	0.990019i	−0.996403	−	0.0847389i	$-0.972994\pi$
$647$	−14.5390	−	25.1823i	−0.571588	−	0.990019i	0.424816	−	0.905280i	$-0.360339\pi$
$648$	−14.3739	+	8.29875i	−0.564659	+	0.326006i
$649$	−5.64337	−	9.77461i	−0.221522	−	0.383687i
$650$	1.58258	+	0.456850i	0.0620737	+	0.0179191i
$651$		0			0
$652$	16.7477	+	9.66930i	0.655892	+	0.378679i
$653$	11.2087			0.438631			0.219315	−	0.975654i	$-0.429618\pi$
$653$	11.2087			0.438631			0.219315	+	0.975654i	$0.429618\pi$
$654$	−31.1216			−1.21695
$655$	−6.87386	−	3.96863i	−0.268584	−	0.155067i
$656$	−3.95644	−	2.28425i	−0.154473	−	0.0891850i
$657$	−0.626136	+	0.361500i	−0.0244279	+	0.0141035i
$658$		0			0
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	0.801660	−	0.597781i	$-0.203951\pi$
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	−0.918523	+	0.395367i	$0.870617\pi$
$660$	13.9564			0.543254
$661$	−16.2523	+	9.38325i	−0.632140	+	0.364966i	−0.781580	−	0.623804i	$-0.785586\pi$
$661$	−16.2523	+	9.38325i	−0.632140	+	0.364966i	0.149440	+	0.988771i	$0.452253\pi$
$662$	−1.18693	+	2.05583i	−0.0461314	+	0.0799020i
$663$	13.4347	+	13.9617i	0.521759	+	0.542228i
$664$	−6.16515			−0.239254
$665$		0			0
$666$	1.58258	−	2.74110i	0.0613236	−	0.106216i
$667$	8.37386	−	14.5040i	0.324237	−	0.561595i
$668$	−48.2650	−	27.8658i	−1.86743	−	1.07816i
$669$		−	37.0961i		−	1.43422i
$670$	−47.3085	−	27.3136i	−1.82769	−	1.05522i
$671$			16.2559i			0.627552i
$672$		0			0
$673$	14.2477	−	24.6778i	0.549210	−	0.951259i	−0.449119	−	0.893472i	$-0.648262\pi$
$673$	14.2477	−	24.6778i	0.549210	−	0.951259i	0.998329	−	0.0577870i	$-0.0184044\pi$
$674$			28.3604i			1.09240i
$675$	−0.521780	+	0.903750i	−0.0200833	+	0.0347854i
$676$	−32.0998	+	16.9213i	−1.23461	+	0.650819i
$677$	−16.8956	−	29.2641i	−0.649352	−	1.12471i	−0.983278	−	0.182112i	$-0.941707\pi$
$677$	−16.8956	−	29.2641i	−0.649352	−	1.12471i	0.333925	−	0.942599i	$-0.391627\pi$
$678$	−4.81307	−	2.77883i	−0.184845	−	0.106720i
$679$		0			0
$680$	−5.68693	−	9.85005i	−0.218084	−	0.377732i
$681$	−19.1044	+	11.0299i	−0.732081	+	0.422667i
$682$			24.1733i			0.925642i
$683$			25.0671i			0.959164i	0.877497	+	0.479582i	$0.159212\pi$
$683$			25.0671i			0.959164i	−0.877497	+	0.479582i	$0.840788\pi$
$684$	3.31307	−	1.91280i	0.126678	−	0.0731378i
$685$	18.7695	+	32.5097i	0.717146	+	1.24213i
$686$		0			0
$687$	−10.7477	−	6.20520i	−0.410051	−	0.236743i
$688$	−3.91742	−	6.78518i	−0.149350	−	0.258682i
$689$	12.1652	−	42.1413i	0.463455	−	1.60546i
$690$	−32.5390	+	56.3592i	−1.23874	+	2.14556i
$691$			29.3694i			1.11727i	0.829415	+	0.558633i	$0.188674\pi$
$691$			29.3694i			1.11727i	−0.829415	+	0.558633i	$0.811326\pi$
$692$	−10.8131	+	18.7288i	−0.411051	+	0.711962i
$693$		0			0
$694$			9.66930i			0.367042i
$695$	−1.50000	−	0.866025i	−0.0568982	−	0.0328502i
$696$			6.85275i			0.259753i
$697$	6.62614	+	3.82560i	0.250983	+	0.144905i
$698$	−11.6869	+	20.2424i	−0.442357	+	0.766185i
$699$	−6.23049	+	10.7915i	−0.235659	+	0.408173i
$700$		0			0
$701$	31.9129			1.20533			0.602666	−	0.797993i	$-0.294105\pi$
$701$	31.9129			1.20533			0.602666	+	0.797993i	$0.294105\pi$
$702$	−9.47822	−	38.3058i	−0.357732	−	1.44576i
$703$	22.7477	−	39.4002i	0.857947	−	1.48601i
$704$	13.8956	−	8.02265i	0.523712	−	0.302365i
$705$	16.7913			0.632396
$706$	29.3521	+	50.8393i	1.10468	+	1.91336i
$707$		0			0
$708$	−38.3258	+	22.1274i	−1.44037	+	0.831598i
$709$	6.31307	+	3.64485i	0.237092	+	0.136885i	0.613840	−	0.789431i	$-0.289624\pi$
$709$	6.31307	+	3.64485i	0.237092	+	0.136885i	−0.376747	+	0.926316i	$0.622957\pi$
$710$	−3.79129	−	2.18890i	−0.142284	−	0.0821480i
$711$	−1.25227			−0.0469639
$712$	−5.04356			−0.189015
$713$	−56.8693	−	32.8335i	−2.12977	−	1.22962i
$714$		0			0
$715$	−2.79129	+	9.66930i	−0.104388	+	0.361611i
$716$	−12.5608	−	21.7559i	−0.469419	−	0.813057i
$717$	20.5218	−	11.8483i	0.766400	−	0.442481i
$718$	−13.8739	−	24.0302i	−0.517768	−	0.896800i
$719$	2.91742	−	5.05313i	0.108802	−	0.188450i	−0.806483	−	0.591257i	$-0.798632\pi$
$719$	2.91742	−	5.05313i	0.108802	−	0.188450i	0.915285	+	0.402807i	$0.131965\pi$
$720$			0.818350i			0.0304981i
$721$		0			0
$722$	45.7259	−	26.3999i	1.70174	−	0.982502i
$723$	6.37841	−	3.68258i	0.237216	−	0.136956i
$724$	−25.5826			−0.950769
$725$	0.230493	+	0.399225i	0.00856028	+	0.0148268i
$726$			36.7545i			1.36409i
$727$	27.7477			1.02911			0.514553	−	0.857459i	$-0.327958\pi$
$727$	27.7477			1.02911			0.514553	+	0.857459i	$0.327958\pi$
$728$		0			0
$729$	24.8693			0.921086
$730$			16.5975i			0.614301i
$731$	6.56080	+	11.3636i	0.242660	+	0.420299i
$732$	63.7386			2.35585
$733$	−7.81307	+	4.51088i	−0.288582	+	0.166613i	−0.637302	−	0.770614i	$-0.719950\pi$
$733$	−7.81307	+	4.51088i	−0.288582	+	0.166613i	0.348720	+	0.937227i	$0.386616\pi$
$734$	−34.1216	+	19.7001i	−1.25945	+	0.727144i
$735$		0			0
$736$			55.9977i			2.06410i
$737$	−7.26951	+	12.5912i	−0.267776	+	0.463801i
$738$	0.582576	+	1.00905i	0.0214449	+	0.0371437i
$739$	10.7477	−	6.20520i	0.395362	−	0.228262i	−0.289119	−	0.957293i	$-0.593362\pi$
$739$	10.7477	−	6.20520i	0.395362	−	0.228262i	0.684481	+	0.729031i	$0.260029\pi$
$740$	−21.1652	−	36.6591i	−0.778046	−	1.34762i
$741$	10.1869	+	41.1700i	0.374226	+	1.51242i
$742$		0			0
$743$	4.64792	+	2.68348i	0.170516	+	0.0984472i	0.582829	−	0.812595i	$-0.301946\pi$
$743$	4.64792	+	2.68348i	0.170516	+	0.0984472i	−0.412313	+	0.911042i	$0.635279\pi$
$744$	26.8693			0.985077
$745$	4.79129			0.175539
$746$	69.7432	+	40.2662i	2.55348	+	1.47425i
$747$	−0.643371	−	0.371450i	−0.0235397	−	0.0135907i
$748$	−9.24773	+	5.33918i	−0.338130	+	0.195220i
$749$		0			0
$750$	−22.3521	−	38.7149i	−0.816183	−	1.41367i
$751$	−3.74773			−0.136757			−0.0683783	−	0.997659i	$-0.521782\pi$
$751$	−3.74773			−0.136757			−0.0683783	+	0.997659i	$0.521782\pi$
$752$	6.64337	−	3.83555i	0.242259	−	0.139868i
$753$	18.9564	−	32.8335i	0.690811	−	1.19652i
$754$	−16.7477	−	4.83465i	−0.609916	−	0.176068i
$755$	−26.5390			−0.965854
$756$		0			0
$757$	−3.00000	+	5.19615i	−0.109037	+	0.188857i	−0.915380	−	0.402590i	$-0.868110\pi$
$757$	−3.00000	+	5.19615i	−0.109037	+	0.188857i	0.806343	+	0.591448i	$0.201443\pi$
$758$	−4.97822	+	8.62253i	−0.180817	+	0.313184i
$759$	15.0000	+	8.66025i	0.544466	+	0.314347i
$760$		−	24.8963i		−	0.903082i
$761$	−27.7259	−	16.0076i	−1.00506	−	0.580274i	−0.0953219	−	0.995447i	$-0.530388\pi$
$761$	−27.7259	−	16.0076i	−1.00506	−	0.580274i	−0.909743	+	0.415172i	$0.863721\pi$
$762$		−	62.5644i		−	2.26647i
$763$		0			0
$764$	−0.873864	+	1.51358i	−0.0316153	+	0.0547593i
$765$		−	1.37055i		−	0.0495524i
$766$	4.29129	−	7.43273i	0.155051	−	0.268555i
$767$	−7.66515	−	30.9783i	−0.276773	−	1.11856i
$768$	−2.50000	−	4.33013i	−0.0902110	−	0.156250i
$769$	21.8739	+	12.6289i	0.788792	+	0.455409i	0.839537	−	0.543303i	$-0.182826\pi$
$769$	21.8739	+	12.6289i	0.788792	+	0.455409i	−0.0507453	+	0.998712i	$0.516160\pi$
$770$		0			0
$771$	−25.0390	−	43.3688i	−0.901758	−	1.56189i
$772$	−30.0000	+	17.3205i	−1.07972	+	0.623379i
$773$			22.8981i			0.823586i	0.911277	+	0.411793i	$0.135097\pi$
$773$			22.8981i			0.823586i	−0.911277	+	0.411793i	$0.864903\pi$
$774$			1.99820i			0.0718238i
$775$	1.56534	−	0.903750i	0.0562287	−	0.0324637i
$776$	−13.1869	−	22.8404i	−0.473383	−	0.819924i
$777$		0			0
$778$	68.8693	+	39.7617i	2.46908	+	1.42553i
$779$	8.37386	+	14.5040i	0.300025	+	0.519658i
$780$	37.9129	+	10.9445i	1.35750	+	0.391876i
$781$	−0.582576	+	1.00905i	−0.0208462	+	0.0361067i
$782$		−	49.7925i		−	1.78058i
$783$	5.52178	−	9.56400i	0.197332	−	0.341790i
$784$		0			0
$785$		−	48.0605i		−	1.71535i
$786$	12.3131	+	7.10895i	0.439193	+	0.253568i
$787$			5.48220i			0.195419i	0.995215	+	0.0977097i	$0.0311517\pi$
$787$			5.48220i			0.195419i	−0.995215	+	0.0977097i	$0.968848\pi$
$788$	26.4564	+	15.2746i	0.942472	+	0.544136i
$789$	−24.4782	+	42.3975i	−0.871448	+	1.50939i
$790$	−14.3739	+	24.8963i	−0.511399	+	0.885769i
$791$		0			0
$792$	−0.460985			−0.0163804
$793$	−12.7477	+	44.1594i	−0.452685	+	1.56815i
$794$	−16.5826	+	28.7219i	−0.588494	+	1.01930i
$795$	−41.3085	+	23.8495i	−1.46506	+	0.845854i
$796$	30.7042			1.08828
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	0.739975	−	0.672634i	$-0.234837\pi$
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	−0.952506	+	0.304520i	$0.901504\pi$
$798$		0			0
$799$	−11.1261	+	6.42368i	−0.393614	+	0.227253i
$800$	−1.33485	−	0.770675i	−0.0471940	−	0.0272475i
$801$	−0.526326	−	0.303875i	−0.0185968	−	0.0107369i
$802$	64.7042			2.28478
$803$	4.41742			0.155888
$804$	49.3693	+	28.5034i	1.74112	+	1.00524i
$805$		0			0
$806$	−18.9564	+	65.6670i	−0.667712	+	2.31302i
$807$	10.0390	+	17.3881i	0.353390	+	0.612090i
$808$	14.6869	−	8.47950i	0.516684	−	0.298308i
$809$	14.6216	+	25.3253i	0.514068	+	0.890391i	0.999867	+	0.0163209i	$0.00519535\pi$
$809$	14.6216	+	25.3253i	0.514068	+	0.890391i	−0.485799	+	0.874071i	$0.661471\pi$
$810$	−22.9564	+	39.7617i	−0.806607	+	1.39708i
$811$			12.0489i			0.423094i	0.977368	+	0.211547i	$0.0678502\pi$
$811$			12.0489i			0.423094i	−0.977368	+	0.211547i	$0.932150\pi$
$812$		0			0
$813$	44.5562	−	25.7246i	1.56266	−	0.902200i
$814$	−16.7477	+	9.66930i	−0.587008	+	0.338909i
$815$	15.1652			0.531212
$816$	−4.81307	−	8.33648i	−0.168491	−	0.291835i
$817$			28.7219i			1.00485i
$818$	−0.791288			−0.0276667
$819$		0			0
$820$	15.5826			0.544167
$821$		−	49.6972i		−	1.73444i	−0.497922	−	0.867222i	$-0.665904\pi$
$821$		−	49.6972i		−	1.73444i	0.497922	−	0.867222i	$-0.334096\pi$
$822$	−33.6216	−	58.2343i	−1.17269	−	2.03115i
$823$	32.4955			1.13272			0.566360	−	0.824158i	$-0.308351\pi$
$823$	32.4955			1.13272			0.566360	+	0.824158i	$0.308351\pi$
$824$	−6.87386	+	3.96863i	−0.239462	+	0.138254i
$825$	−0.412878	+	0.238375i	−0.0143746	+	0.00829917i
$826$		0			0
$827$		−	0.989150i		−	0.0343961i	−0.999852	−	0.0171981i	$-0.994525\pi$
$827$		−	0.989150i		−	0.0343961i	0.999852	−	0.0171981i	$-0.00547458\pi$
$828$	2.20871	−	3.82560i	0.0767581	−	0.132949i
$829$	10.3131	+	17.8628i	0.358188	+	0.620399i	0.987658	−	0.156625i	$-0.0500615\pi$
$829$	10.3131	+	17.8628i	0.358188	+	0.620399i	−0.629470	+	0.777024i	$0.716728\pi$
$830$	−14.7695	+	8.52718i	−0.512657	+	0.295983i
$831$	−14.1044	−	24.4295i	−0.489275	−	0.847449i
$832$	44.0390	−	10.8968i	1.52678	−	0.377780i
$833$		0			0
$834$	2.68693	+	1.55130i	0.0930408	+	0.0537172i
$835$	−43.7042			−1.51245
$836$	−23.3739			−0.808402
$837$	−37.5000	−	21.6506i	−1.29619	−	0.748355i
$838$	−48.8085	−	28.1796i	−1.68606	−	0.973449i
$839$	40.2695	−	23.2496i	1.39026	−	0.802666i	0.396914	−	0.917856i	$-0.370081\pi$
$839$	40.2695	−	23.2496i	1.39026	−	0.802666i	0.993343	+	0.115190i	$0.0367477\pi$
$840$		0			0
$841$	12.0608	+	20.8899i	0.415889	+	0.720342i
$842$	43.9129			1.51334
$843$	9.92197	−	5.72845i	0.341731	−	0.197298i
$844$	1.97822	−	3.42638i	0.0680931	−	0.117941i
$845$	−15.1652	+	24.0779i	−0.521697	+	0.828305i
$846$	−1.95644			−0.0672638
$847$		0			0
$848$	−10.8956	+	18.8718i	−0.374158	+	0.648061i
$849$	22.1652	−	38.3912i	0.760706	−	1.31758i
$850$	1.18693	+	0.685275i	0.0407114	+	0.0235048i
$851$		−	52.5336i		−	1.80083i
$852$	3.95644	+	2.28425i	0.135545	+	0.0782572i
$853$		−	17.6066i		−	0.602837i	−0.953492	−	0.301419i	$-0.902540\pi$
$853$		−	17.6066i		−	0.602837i	0.953492	−	0.301419i	$-0.0974601\pi$
$854$		0			0
$855$	1.50000	−	2.59808i	0.0512989	−	0.0888523i
$856$		−	16.9590i		−	0.579647i
$857$	23.7695	−	41.1700i	0.811951	−	1.40634i	−0.0995459	−	0.995033i	$-0.531739\pi$
$857$	23.7695	−	41.1700i	0.811951	−	1.40634i	0.911497	−	0.411307i	$-0.134928\pi$
$858$	5.00000	−	17.3205i	0.170697	−	0.591312i
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	−0.960381	+	0.278691i	$0.910099\pi$
$860$	23.1434	+	13.3618i	0.789182	+	0.455635i
$861$		0			0
$862$	−17.0826	−	29.5879i	−0.581835	−	1.00777i
$863$	2.66970	−	1.54135i	0.0908776	−	0.0524682i	−0.453873	−	0.891067i	$-0.649958\pi$
$863$	2.66970	−	1.54135i	0.0908776	−	0.0524682i	0.544750	+	0.838598i	$0.316625\pi$
$864$			36.9253i			1.25622i
$865$			16.9590i			0.576624i
$866$	42.6434	−	24.6202i	1.44908	−	0.836627i
$867$	−7.16515	−	12.4104i	−0.243341	−	0.421479i
$868$		0			0
$869$	6.62614	+	3.82560i	0.224776	+	0.129775i
$870$	9.47822	+	16.4168i	0.321342	+	0.556580i
$871$	−29.6216	+	28.5034i	−1.00369	+	0.965800i
$872$	6.87386	−	11.9059i	0.232778	−	0.403184i
$873$		−	3.17805i		−	0.107561i
$874$	54.4955	−	94.3889i	1.84334	−	3.19275i
$875$		0			0
$876$		−	17.3205i		−	0.585206i
$877$	−30.2477	−	17.4635i	−1.02139	−	0.589702i	−0.106886	−	0.994271i	$-0.534088\pi$
$877$	−30.2477	−	17.4635i	−1.02139	−	0.589702i	−0.914507	+	0.404570i	$0.867421\pi$
$878$			25.2578i			0.852408i
$879$	−12.1652	−	7.02355i	−0.410320	−	0.236899i
$880$	2.50000	−	4.33013i	0.0842750	−	0.145969i
$881$	3.70871	−	6.42368i	0.124950	−	0.216419i	−0.796764	−	0.604291i	$-0.793456\pi$
$881$	3.70871	−	6.42368i	0.124950	−	0.216419i	0.921713	+	0.387872i	$0.126790\pi$
$882$		0			0
$883$	−53.2432			−1.79178			−0.895888	−	0.444280i	$-0.853459\pi$
$883$	−53.2432			−1.79178			−0.895888	+	0.444280i	$0.853459\pi$
$884$	−29.3085	+	7.25198i	−0.985752	+	0.243910i
$885$	−17.3521	+	30.0547i	−0.583284	+	1.01028i
$886$	−6.00000	+	3.46410i	−0.201574	+	0.116379i
$887$	−31.5826			−1.06044			−0.530220	−	0.847860i	$-0.677891\pi$
$887$	−31.5826			−1.06044			−0.530220	+	0.847860i	$0.677891\pi$
$888$	10.7477	+	18.6156i	0.360670	+	0.624699i
$889$		0			0
$890$	−12.0826	+	6.97588i	−0.405009	+	0.233832i
$891$	10.5826	+	6.10985i	0.354530	+	0.204688i
$892$	50.0608	+	28.9026i	1.67616	+	0.967731i
$893$	−28.1216			−0.941053
$894$	−8.58258			−0.287044
$895$	−17.0608	−	9.85005i	−0.570279	−	0.329251i
$896$		0			0
$897$	33.9564	+	35.2886i	1.13377	+	1.17825i
$898$	21.7477	+	37.6682i	0.725731	+	1.25700i
$899$	−16.5653	+	9.56400i	−0.552485	+	0.318977i
$900$	0.0607953	+	0.105301i	0.00202651	+	0.00351002i
$901$	18.2477	−	31.6060i	0.607920	−	1.05295i
$902$		−	7.11890i		−	0.237034i
$903$		0			0
$904$	2.12614	−	1.22753i	0.0707142	−	0.0408269i
$905$	−17.3739	+	10.0308i	−0.577527	+	0.333435i
$906$	47.5390			1.57938
$907$	−11.5390	−	19.9862i	−0.383147	−	0.663630i	0.608363	−	0.793659i	$-0.291826\pi$
$907$	−11.5390	−	19.9862i	−0.383147	−	0.663630i	−0.991510	+	0.130029i	$0.958493\pi$
$908$		−	34.3749i		−	1.14077i
$909$	2.04356			0.0677806
$910$		0			0
$911$	−1.87841			−0.0622345			−0.0311172	−	0.999516i	$-0.509907\pi$
$911$	−1.87841			−0.0622345			−0.0311172	+	0.999516i	$0.509907\pi$
$912$		−	21.0707i		−	0.697719i
$913$	2.26951	+	3.93090i	0.0751097	+	0.130094i
$914$	19.5826			0.647734
$915$	43.2867	−	24.9916i	1.43102	−	0.826197i
$916$	16.7477	−	9.66930i	0.553360	−	0.319483i
$917$		0			0
$918$		−	32.8335i		−	1.08367i
$919$	9.95644	−	17.2451i	0.328433	−	0.568862i	−0.653768	−	0.756695i	$-0.726813\pi$
$919$	9.95644	−	17.2451i	0.328433	−	0.568862i	0.982201	+	0.187833i	$0.0601463\pi$
$920$	−14.3739	−	24.8963i	−0.473892	−	0.820805i
$921$	−37.5000	+	21.6506i	−1.23567	+	0.713413i
$922$	19.5608	+	33.8803i	0.644200	+	1.11579i
$923$	−2.37386	+	2.28425i	−0.0781367	+	0.0751870i
$924$		0			0
$925$	1.25227	+	0.723000i	0.0411745	+	0.0237721i
$926$	−17.3739			−0.570941
$927$	−0.956439			−0.0314136
$928$	14.1261	+	8.15573i	0.463713	+	0.267725i
$929$	23.1606	+	13.3718i	0.759875	+	0.438714i	0.829251	−	0.558877i	$-0.188767\pi$
$929$	23.1606	+	13.3718i	0.759875	+	0.438714i	−0.0693760	+	0.997591i	$0.522101\pi$
$930$	64.3693	−	37.1636i	2.11075	−	1.21864i
$931$		0			0
$932$	−9.70871	−	16.8160i	−0.318019	−	0.550826i
$933$	−9.92197			−0.324831
$934$	22.4347	−	12.9527i	0.734084	−	0.423824i
$935$	−4.18693	+	7.25198i	−0.136927	+	0.237165i
$936$	−1.25227	−	0.361500i	−0.0409318	−	0.0118160i
$937$	34.4955			1.12692			0.563459	−	0.826144i	$-0.309470\pi$
$937$	34.4955			1.12692			0.563459	+	0.826144i	$0.309470\pi$
$938$		0			0
$939$	−18.5826	+	32.1860i	−0.606419	+	1.05035i
$940$	−13.0826	+	22.6597i	−0.426707	+	0.739077i
$941$	−1.96099	−	1.13218i	−0.0639263	−	0.0369079i	0.467696	−	0.883889i	$-0.345084\pi$
$941$	−1.96099	−	1.13218i	−0.0639263	−	0.0369079i	−0.531622	+	0.846981i	$0.678417\pi$
$942$			86.0901i			2.80497i
$943$	16.7477	+	9.66930i	0.545381	+	0.314876i
$944$			15.8546i			0.516024i
$945$		0			0
$946$	6.10436	−	10.5731i	0.198470	−	0.343760i
$947$			56.8915i			1.84873i	0.381514	+	0.924363i	$0.375403\pi$
$947$			56.8915i			1.84873i	−0.381514	+	0.924363i	$0.624597\pi$
$948$	15.0000	−	25.9808i	0.487177	−	0.843816i
$949$	12.0000	+	3.46410i	0.389536	+	0.112449i
$950$	1.50000	+	2.59808i	0.0486664	+	0.0842927i
$951$	28.7305	+	16.5876i	0.931650	+	0.537888i
$952$		0			0
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	0.961553	−	0.274620i	$-0.0885520\pi$
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	−0.718604	+	0.695419i	$0.755219\pi$
$954$	4.81307	−	2.77883i	0.155829	−	0.0899678i
$955$			1.37055i			0.0443500i
$956$			36.9253i			1.19425i
$957$	4.36932	−	2.52263i	0.141240	−	0.0815449i
$958$	−11.1869	−	19.3763i	−0.361433	−	0.626021i
$959$		0			0
$960$	−42.7259	−	24.6678i	−1.37897	−	0.796151i
$961$	22.0000	+	38.1051i	0.709677	+	1.22920i
$962$	−53.0780	+	13.1334i	−1.71130	+	0.423438i
$963$	1.02178	−	1.76978i	0.0329264	−	0.0570302i
$964$			11.4768i			0.369643i
$965$	−13.5826	+	23.5257i	−0.437239	+	0.757319i
$966$		0			0
$967$			23.8118i			0.765735i	0.923803	+	0.382867i	$0.125063\pi$
$967$			23.8118i			0.765735i	−0.923803	+	0.382867i	$0.874937\pi$
$968$	−14.0608	−	8.11800i	−0.451931	−	0.260923i
$969$			35.2886i			1.13363i
$970$	−63.1824	−	36.4784i	−2.02866	−	1.17125i
$971$	24.8739	−	43.0828i	0.798240	−	1.38259i	−0.122521	−	0.992466i	$-0.539098\pi$
$971$	24.8739	−	43.0828i	0.798240	−	1.38259i	0.920761	−	0.390127i	$-0.127569\pi$
$972$	3.02178	−	5.23388i	0.0969237	−	0.167877i
$973$		0			0
$974$	−22.5826			−0.723592
$975$	−1.30852	+	0.323775i	−0.0419063	+	0.0103691i
$976$	11.4174	−	19.7756i	0.365463	−	0.633000i
$977$	−49.2042	+	28.4080i	−1.57418	+	0.908854i	−0.578533	+	0.815659i	$0.696375\pi$
$977$	−49.2042	+	28.4080i	−1.57418	+	0.908854i	−0.995648	+	0.0931946i	$0.970292\pi$
$978$	−27.1652			−0.868646
$979$	1.85663	+	3.21578i	0.0593381	+	0.102777i
$980$		0			0
$981$	1.43466	−	0.828301i	0.0458051	−	0.0264456i
$982$	70.3693	+	40.6277i	2.24558	+	1.29648i
$983$	−21.7259	−	12.5435i	−0.692950	−	0.400075i	0.111766	−	0.993735i	$-0.464349\pi$
$983$	−21.7259	−	12.5435i	−0.692950	−	0.400075i	−0.804716	+	0.593660i	$0.797683\pi$
$984$	−7.91288			−0.252253
$985$	23.9564			0.763316
$986$	−12.5608	−	7.25198i	−0.400017	−	0.230950i
$987$		0			0
$988$	−63.4955	−	18.3296i	−2.02006	−	0.583141i
$989$	16.5826	+	28.7219i	0.527295	+	0.913302i
$990$	−1.10436	+	0.637600i	−0.0350987	+	0.0202643i
$991$	13.3131	+	23.0589i	0.422904	+	0.732490i	0.996222	−	0.0868421i	$-0.0276776\pi$
$991$	13.3131	+	23.0589i	0.422904	+	0.732490i	−0.573319	+	0.819333i	$0.694344\pi$
$992$	31.9782	−	55.3879i	1.01531	−	1.75857i
$993$		−	1.94265i		−	0.0616482i
$994$		0			0
$995$	20.8521	−	12.0390i	0.661055	−	0.381661i
$996$	15.4129	−	8.89863i	0.488376	−	0.281964i
$997$	−50.0780			−1.58599			−0.792994	−	0.609230i	$-0.791479\pi$
$997$	−50.0780			−1.58599			−0.792994	+	0.609230i	$0.791479\pi$
$998$	−46.2042	−	80.0280i	−1.46257	−	2.53324i
$999$		−	34.6410i		−	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.d.459.1		4
7.2	even	3		637.2.u.e.30.1		4
7.3	odd	6		637.2.q.f.589.2	yes	4
7.4	even	3		637.2.q.e.589.2	yes	4
7.5	odd	6		637.2.u.d.30.1		4
7.6	odd	2		637.2.k.f.459.1		4
13.10	even	6		637.2.u.e.361.1		4
91.10	odd	6		637.2.q.f.491.2	yes	4
91.23	even	6	inner	637.2.k.d.569.2		4
91.32	odd	12		8281.2.a.bs.1.1		4
91.45	even	12		8281.2.a.bq.1.1		4
91.46	odd	12		8281.2.a.bs.1.4		4
91.59	even	12		8281.2.a.bq.1.4		4
91.62	odd	6		637.2.u.d.361.1		4
91.75	odd	6		637.2.k.f.569.2		4
91.88	even	6		637.2.q.e.491.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.d.459.1		4	1.1	even	1	trivial
637.2.k.d.569.2		4	91.23	even	6	inner
637.2.k.f.459.1		4	7.6	odd	2
637.2.k.f.569.2		4	91.75	odd	6
637.2.q.e.491.2	✓	4	91.88	even	6
637.2.q.e.589.2	yes	4	7.4	even	3
637.2.q.f.491.2	yes	4	91.10	odd	6
637.2.q.f.589.2	yes	4	7.3	odd	6
637.2.u.d.30.1		4	7.5	odd	6
637.2.u.d.361.1		4	91.62	odd	6
637.2.u.e.30.1		4	7.2	even	3
637.2.u.e.361.1		4	13.10	even	6
8281.2.a.bq.1.1		4	91.45	even	12
8281.2.a.bq.1.4		4	91.59	even	12
8281.2.a.bs.1.1		4	91.32	odd	12
8281.2.a.bs.1.4		4	91.46	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.18890i q^{2} +(0.895644 + 1.55130i) q^{3} -2.79129 q^{4} +(-1.89564 + 1.09445i) q^{5} +(3.39564 - 1.96048i) q^{6} +1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +O(q^{10})\)	\(q-2.18890i q^{2} +(0.895644 + 1.55130i) q^{3} -2.79129 q^{4} +(-1.89564 + 1.09445i) q^{5} +(3.39564 - 1.96048i) q^{6} +1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +(2.39564 + 4.14938i) q^{10} +(1.10436 - 0.637600i) q^{11} +(-2.50000 - 4.33013i) q^{12} +(3.50000 - 0.866025i) q^{13} +(-3.39564 - 1.96048i) q^{15} -1.79129 q^{16} +3.00000 q^{17} +(0.395644 + 0.228425i) q^{18} +(5.68693 + 3.28335i) q^{19} +(5.29129 - 3.05493i) q^{20} +(-1.39564 - 2.41733i) q^{22} +7.58258 q^{23} +(-2.68693 + 1.55130i) q^{24} +(-0.104356 + 0.180750i) q^{25} +(-1.89564 - 7.66115i) q^{26} +5.00000 q^{27} +(1.10436 - 1.91280i) q^{29} +(-4.29129 + 7.43273i) q^{30} +(-7.50000 - 4.33013i) q^{31} +7.38505i q^{32} +(1.97822 + 1.14213i) q^{33} -6.56670i q^{34} +(0.291288 - 0.504525i) q^{36} -6.92820i q^{37} +(7.18693 - 12.4481i) q^{38} +(4.47822 + 4.65390i) q^{39} +(-1.89564 - 3.28335i) q^{40} +(2.20871 + 1.27520i) q^{41} +(2.18693 + 3.78788i) q^{43} +(-3.08258 + 1.77973i) q^{44} -0.456850i q^{45} -16.5975i q^{46} +(-3.70871 + 2.14123i) q^{47} +(-1.60436 - 2.77883i) q^{48} +(0.395644 + 0.228425i) q^{50} +(2.68693 + 4.65390i) q^{51} +(-9.76951 + 2.41733i) q^{52} +(6.08258 - 10.5353i) q^{53} -10.9445i q^{54} +(-1.39564 + 2.41733i) q^{55} +11.7629i q^{57} +(-4.18693 - 2.41733i) q^{58} -8.85095i q^{59} +(9.47822 + 5.47225i) q^{60} +(-6.37386 + 11.0399i) q^{61} +(-9.47822 + 16.4168i) q^{62} +12.5826 q^{64} +(-5.68693 + 5.47225i) q^{65} +(2.50000 - 4.33013i) q^{66} +(-9.87386 + 5.70068i) q^{67} -8.37386 q^{68} +(6.79129 + 11.7629i) q^{69} +(-0.791288 + 0.456850i) q^{71} +(-0.313068 - 0.180750i) q^{72} +(3.00000 + 1.73205i) q^{73} -15.1652 q^{74} -0.373864 q^{75} +(-15.8739 - 9.16478i) q^{76} +(10.1869 - 9.80238i) q^{78} +(3.00000 + 5.19615i) q^{79} +(3.39564 - 1.96048i) q^{80} +(4.79129 + 8.29875i) q^{81} +(2.79129 - 4.83465i) q^{82} +3.55945i q^{83} +(-5.68693 + 3.28335i) q^{85} +(8.29129 - 4.78698i) q^{86} +3.95644 q^{87} +(1.10436 + 1.91280i) q^{88} +2.91190i q^{89} -1.00000 q^{90} -21.1652 q^{92} -15.5130i q^{93} +(4.68693 + 8.11800i) q^{94} -14.3739 q^{95} +(-11.4564 + 6.61438i) q^{96} +(-13.1869 + 7.61348i) q^{97} +0.266150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9}+O(q^{10}) \) 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9	\( 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9} + 5 q^{10} + 9 q^{11} - 10 q^{12} + 14 q^{13} - 9 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{18} + 9 q^{19} + 12 q^{20} - q^{22} + 12 q^{23} + 3 q^{24} - 5 q^{25} - 3 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} - 30 q^{31} - 15 q^{33} - 8 q^{36} + 15 q^{38} - 5 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} + 6 q^{44} - 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} - 7 q^{52} + 6 q^{53} - q^{55} - 3 q^{58} + 15 q^{60} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 9 q^{65} + 10 q^{66} - 12 q^{67} - 6 q^{68} + 18 q^{69} + 6 q^{71} - 15 q^{72} + 12 q^{73} - 24 q^{74} + 26 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} + 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 24 q^{86} - 30 q^{87} + 9 q^{88} - 4 q^{90} - 48 q^{92} + 5 q^{94} - 30 q^{95} - 39 q^{97}+O(q^{100}) \) 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9 + 5 * q^10 + 9 * q^11 - 10 * q^12 + 14 * q^13 - 9 * q^15 + 2 * q^16 + 12 * q^17 - 3 * q^18 + 9 * q^19 + 12 * q^20 - q^22 + 12 * q^23 + 3 * q^24 - 5 * q^25 - 3 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 - 30 * q^31 - 15 * q^33 - 8 * q^36 + 15 * q^38 - 5 * q^39 - 3 * q^40 + 18 * q^41 - 5 * q^43 + 6 * q^44 - 24 * q^47 - 11 * q^48 - 3 * q^50 - 3 * q^51 - 7 * q^52 + 6 * q^53 - q^55 - 3 * q^58 + 15 * q^60 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 9 * q^65 + 10 * q^66 - 12 * q^67 - 6 * q^68 + 18 * q^69 + 6 * q^71 - 15 * q^72 + 12 * q^73 - 24 * q^74 + 26 * q^75 - 36 * q^76 + 27 * q^78 + 12 * q^79 + 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 24 * q^86 - 30 * q^87 + 9 * q^88 - 4 * q^90 - 48 * q^92 + 5 * q^94 - 30 * q^95 - 39 * q^97

Introduction

L-functions

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