LMFDB - Embedded newform 961.2.d.e.531.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,-1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	961.531
Dual form			961.2.d.e.628.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 1.53884i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 + 0.363271i) q^{4} -0.381966 q^{5} +1.61803 q^{6} +(-2.42705 + 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +(1.61803 + 1.17557i) q^{9} +(-0.190983 - 0.587785i) q^{10} +(-4.23607 + 3.07768i) q^{11} +(0.190983 + 0.587785i) q^{12} +(0.572949 - 1.76336i) q^{13} +(-3.92705 - 2.85317i) q^{14} +(-0.118034 + 0.363271i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(-3.42705 - 2.48990i) q^{17} +(-1.00000 + 3.07768i) q^{18} +(1.54508 + 4.75528i) q^{19} +(0.190983 - 0.138757i) q^{20} +(0.927051 + 2.85317i) q^{21} +(-6.85410 - 4.97980i) q^{22} +(2.80902 + 2.04087i) q^{23} +(1.80902 - 1.31433i) q^{24} -4.85410 q^{25} +3.00000 q^{26} +(4.04508 - 2.93893i) q^{27} +(0.572949 - 1.76336i) q^{28} +(1.97214 + 6.06961i) q^{29} -0.618034 q^{30} -3.38197 q^{32} +(1.61803 + 4.97980i) q^{33} +(2.11803 - 6.51864i) q^{34} +(0.927051 - 0.673542i) q^{35} -1.23607 q^{36} +4.23607 q^{37} +(-6.54508 + 4.75528i) q^{38} +(-1.50000 - 1.08981i) q^{39} +(-0.690983 - 0.502029i) q^{40} +(-0.763932 - 2.35114i) q^{41} +(-3.92705 + 2.85317i) q^{42} +(0.736068 + 2.26538i) q^{43} +(1.00000 - 3.07768i) q^{44} +(-0.618034 - 0.449028i) q^{45} +(-1.73607 + 5.34307i) q^{46} +(-1.73607 + 5.34307i) q^{47} +(3.92705 + 2.85317i) q^{48} +(0.618034 - 1.90211i) q^{49} +(-2.42705 - 7.46969i) q^{50} +(-3.42705 + 2.48990i) q^{51} +(0.354102 + 1.08981i) q^{52} +(0.572949 + 0.416272i) q^{53} +(6.54508 + 4.75528i) q^{54} +(1.61803 - 1.17557i) q^{55} -6.70820 q^{56} +5.00000 q^{57} +(-8.35410 + 6.06961i) q^{58} +(0.163119 - 0.502029i) q^{59} +(-0.0729490 - 0.224514i) q^{60} -10.9443 q^{61} -6.00000 q^{63} +(1.30902 + 4.02874i) q^{64} +(-0.218847 + 0.673542i) q^{65} +(-6.85410 + 4.97980i) q^{66} +0.236068 q^{67} +2.61803 q^{68} +(2.80902 - 2.04087i) q^{69} +(1.50000 + 1.08981i) q^{70} +(8.97214 + 6.51864i) q^{71} +(1.38197 + 4.25325i) q^{72} +(9.35410 - 6.79615i) q^{73} +(2.11803 + 6.51864i) q^{74} +(-1.50000 + 4.61653i) q^{75} +(-2.50000 - 1.81636i) q^{76} +(4.85410 - 14.9394i) q^{77} +(0.927051 - 2.85317i) q^{78} +(0.572949 - 1.76336i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.23607 - 2.35114i) q^{82} +(-2.19098 - 6.74315i) q^{83} +(-1.50000 - 1.08981i) q^{84} +(1.30902 + 0.951057i) q^{85} +(-3.11803 + 2.26538i) q^{86} +6.38197 q^{87} -11.7082 q^{88} +(-6.97214 + 5.06555i) q^{89} +(0.381966 - 1.17557i) q^{90} +(1.71885 + 5.29007i) q^{91} -2.14590 q^{92} -9.09017 q^{94} +(-0.590170 - 1.81636i) q^{95} +(-1.04508 + 3.21644i) q^{96} +(15.1353 - 10.9964i) q^{97} +3.23607 q^{98} -10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} + 5 q^{8} + 2 q^{9} - 3 q^{10} - 8 q^{11} + 3 q^{12} + 9 q^{13} - 9 q^{14} + 4 q^{15} - 6 q^{16} - 7 q^{17} - 4 q^{18} - 5 q^{19} + 3 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 + 5 * q^8 + 2 * q^9 - 3 * q^10 - 8 * q^11 + 3 * q^12 + 9 * q^13 - 9 * q^14 + 4 * q^15 - 6 * q^16 - 7 * q^17 - 4 * q^18 - 5 * q^19 + 3 * q^20 - 3 * q^21 - 14 * q^22 + 9 * q^23 + 5 * q^24 - 6 * q^25 + 12 * q^26 + 5 * q^27 + 9 * q^28 - 10 * q^29 + 2 * q^30 - 18 * q^32 + 2 * q^33 + 4 * q^34 - 3 * q^35 + 4 * q^36 + 8 * q^37 - 15 * q^38 - 6 * q^39 - 5 * q^40 - 12 * q^41 - 9 * q^42 - 6 * q^43 + 4 * q^44 + 2 * q^45 + 2 * q^46 + 2 * q^47 + 9 * q^48 - 2 * q^49 - 3 * q^50 - 7 * q^51 - 12 * q^52 + 9 * q^53 + 15 * q^54 + 2 * q^55 + 20 * q^57 - 20 * q^58 - 15 * q^59 - 7 * q^60 - 8 * q^61 - 24 * q^63 + 3 * q^64 - 21 * q^65 - 14 * q^66 - 8 * q^67 + 6 * q^68 + 9 * q^69 + 6 * q^70 + 18 * q^71 + 10 * q^72 + 24 * q^73 + 4 * q^74 - 6 * q^75 - 10 * q^76 + 6 * q^77 - 3 * q^78 + 9 * q^80 - q^81 + 4 * q^82 - 11 * q^83 - 6 * q^84 + 3 * q^85 - 8 * q^86 + 30 * q^87 - 20 * q^88 - 10 * q^89 + 6 * q^90 + 27 * q^91 - 22 * q^92 - 14 * q^94 + 20 * q^95 + 7 * q^96 + 27 * q^97 + 4 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.500000	+	1.53884i	0.353553	+	1.08813i	0.956844	+	0.290604i	$0.0938561\pi$
$2$	0.500000	+	1.53884i	0.353553	+	1.08813i	−0.603290	+	0.797522i	$0.706144\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i	−0.821362	−	0.570408i	$-0.806785\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i	0.999773	+	0.0213149i	$0.00678525\pi$
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	−0.381966			−0.170820			−0.0854102	−	0.996346i	$-0.527220\pi$
$5$	−0.381966			−0.170820			−0.0854102	+	0.996346i	$0.527220\pi$
$6$	1.61803			0.660560
$7$	−2.42705	+	1.76336i	−0.917339	+	0.666486i	−0.942860	−	0.333188i	$-0.891875\pi$
$7$	−2.42705	+	1.76336i	−0.917339	+	0.666486i	0.0255212	+	0.999674i	$0.491875\pi$
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$	1.61803	+	1.17557i	0.539345	+	0.391857i
$10$	−0.190983	−	0.587785i	−0.0603941	−	0.185874i
$11$	−4.23607	+	3.07768i	−1.27722	+	0.927957i	−0.999465	−	0.0326948i	$-0.989591\pi$
$11$	−4.23607	+	3.07768i	−1.27722	+	0.927957i	−0.277757	+	0.960651i	$0.589591\pi$
$12$	0.190983	+	0.587785i	0.0551320	+	0.169679i
$13$	0.572949	−	1.76336i	0.158907	−	0.489067i	−0.839628	−	0.543161i	$-0.817227\pi$
$13$	0.572949	−	1.76336i	0.158907	−	0.489067i	0.998536	+	0.0540944i	$0.0172272\pi$
$14$	−3.92705	−	2.85317i	−1.04955	−	0.762542i
$15$	−0.118034	+	0.363271i	−0.0304762	+	0.0937962i
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	−3.42705	−	2.48990i	−0.831182	−	0.603889i	0.0887115	−	0.996057i	$-0.471725\pi$
$17$	−3.42705	−	2.48990i	−0.831182	−	0.603889i	−0.919893	+	0.392168i	$0.871725\pi$
$18$	−1.00000	+	3.07768i	−0.235702	+	0.725417i
$19$	1.54508	+	4.75528i	0.354467	+	1.09094i	0.956318	+	0.292328i	$0.0944300\pi$
$19$	1.54508	+	4.75528i	0.354467	+	1.09094i	−0.601851	+	0.798608i	$0.705570\pi$
$20$	0.190983	−	0.138757i	0.0427051	−	0.0310271i
$21$	0.927051	+	2.85317i	0.202299	+	0.622613i
$22$	−6.85410	−	4.97980i	−1.46130	−	1.06170i
$23$	2.80902	+	2.04087i	0.585721	+	0.425551i	0.840782	−	0.541374i	$-0.182096\pi$
$23$	2.80902	+	2.04087i	0.585721	+	0.425551i	−0.255061	+	0.966925i	$0.582096\pi$
$24$	1.80902	−	1.31433i	0.369264	−	0.268286i
$25$	−4.85410			−0.970820
$26$	3.00000			0.588348
$27$	4.04508	−	2.93893i	0.778477	−	0.565597i
$28$	0.572949	−	1.76336i	0.108277	−	0.333243i
$29$	1.97214	+	6.06961i	0.366216	+	1.12710i	0.949216	+	0.314626i	$0.101879\pi$
$29$	1.97214	+	6.06961i	0.366216	+	1.12710i	−0.582999	+	0.812473i	$0.698121\pi$
$30$	−0.618034			−0.112837
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	1.61803	+	4.97980i	0.281664	+	0.866871i
$34$	2.11803	−	6.51864i	0.363240	−	1.11794i
$35$	0.927051	−	0.673542i	0.156700	−	0.113849i
$36$	−1.23607			−0.206011
$37$	4.23607			0.696405			0.348203	−	0.937419i	$-0.386792\pi$
$37$	4.23607			0.696405			0.348203	+	0.937419i	$0.386792\pi$
$38$	−6.54508	+	4.75528i	−1.06175	+	0.771409i
$39$	−1.50000	−	1.08981i	−0.240192	−	0.174510i
$40$	−0.690983	−	0.502029i	−0.109254	−	0.0793777i
$41$	−0.763932	−	2.35114i	−0.119306	−	0.367187i	0.873515	−	0.486798i	$-0.161835\pi$
$41$	−0.763932	−	2.35114i	−0.119306	−	0.367187i	−0.992821	+	0.119611i	$0.961835\pi$
$42$	−3.92705	+	2.85317i	−0.605957	+	0.440254i
$43$	0.736068	+	2.26538i	0.112249	+	0.345468i	0.991363	−	0.131144i	$-0.0418649\pi$
$43$	0.736068	+	2.26538i	0.112249	+	0.345468i	−0.879114	+	0.476611i	$0.841865\pi$
$44$	1.00000	−	3.07768i	0.150756	−	0.463978i
$45$	−0.618034	−	0.449028i	−0.0921311	−	0.0669371i
$46$	−1.73607	+	5.34307i	−0.255969	+	0.787792i
$47$	−1.73607	+	5.34307i	−0.253232	+	0.779367i	0.740941	+	0.671570i	$0.234380\pi$
$47$	−1.73607	+	5.34307i	−0.253232	+	0.779367i	−0.994173	+	0.107797i	$0.965620\pi$
$48$	3.92705	+	2.85317i	0.566821	+	0.411820i
$49$	0.618034	−	1.90211i	0.0882906	−	0.271730i
$50$	−2.42705	−	7.46969i	−0.343237	−	1.05637i
$51$	−3.42705	+	2.48990i	−0.479883	+	0.348655i
$52$	0.354102	+	1.08981i	0.0491051	+	0.151130i
$53$	0.572949	+	0.416272i	0.0787006	+	0.0571793i	0.626440	−	0.779470i	$-0.284511\pi$
$53$	0.572949	+	0.416272i	0.0787006	+	0.0571793i	−0.547739	+	0.836649i	$0.684511\pi$
$54$	6.54508	+	4.75528i	0.890673	+	0.647112i
$55$	1.61803	−	1.17557i	0.218176	−	0.158514i
$56$	−6.70820			−0.896421
$57$	5.00000			0.662266
$58$	−8.35410	+	6.06961i	−1.09695	+	0.796979i
$59$	0.163119	−	0.502029i	0.0212363	−	0.0653585i	−0.939877	−	0.341514i	$-0.889060\pi$
$59$	0.163119	−	0.502029i	0.0212363	−	0.0653585i	0.961113	+	0.276155i	$0.0890604\pi$
$60$	−0.0729490	−	0.224514i	−0.00941768	−	0.0289846i
$61$	−10.9443			−1.40127			−0.700635	−	0.713520i	$-0.747100\pi$
$61$	−10.9443			−1.40127			−0.700635	+	0.713520i	$0.747100\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	−0.218847	+	0.673542i	−0.0271446	+	0.0835426i
$66$	−6.85410	+	4.97980i	−0.843682	+	0.612971i
$67$	0.236068			0.0288403			0.0144201	−	0.999896i	$-0.495410\pi$
$67$	0.236068			0.0288403			0.0144201	+	0.999896i	$0.495410\pi$
$68$	2.61803			0.317483
$69$	2.80902	−	2.04087i	0.338166	−	0.245692i
$70$	1.50000	+	1.08981i	0.179284	+	0.130258i
$71$	8.97214	+	6.51864i	1.06480	+	0.773620i	0.974970	−	0.222337i	$-0.0713686\pi$
$71$	8.97214	+	6.51864i	1.06480	+	0.773620i	0.0898268	+	0.995957i	$0.471369\pi$
$72$	1.38197	+	4.25325i	0.162866	+	0.501251i
$73$	9.35410	−	6.79615i	1.09481	−	0.795430i	0.114609	−	0.993411i	$-0.463438\pi$
$73$	9.35410	−	6.79615i	1.09481	−	0.795430i	0.980206	+	0.197981i	$0.0634385\pi$
$74$	2.11803	+	6.51864i	0.246216	+	0.757776i
$75$	−1.50000	+	4.61653i	−0.173205	+	0.533070i
$76$	−2.50000	−	1.81636i	−0.286770	−	0.208350i
$77$	4.85410	−	14.9394i	0.553176	−	1.70250i
$78$	0.927051	−	2.85317i	0.104968	−	0.323058i
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	0.572949	−	1.76336i	0.0640576	−	0.197149i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	3.23607	−	2.35114i	0.357364	−	0.259640i
$83$	−2.19098	−	6.74315i	−0.240492	−	0.740157i	−0.996345	−	0.0854166i	$-0.972778\pi$
$83$	−2.19098	−	6.74315i	−0.240492	−	0.740157i	0.755854	−	0.654741i	$-0.227222\pi$
$84$	−1.50000	−	1.08981i	−0.163663	−	0.118908i
$85$	1.30902	+	0.951057i	0.141983	+	0.103157i
$86$	−3.11803	+	2.26538i	−0.336226	+	0.244283i
$87$	6.38197			0.684219
$88$	−11.7082			−1.24810
$89$	−6.97214	+	5.06555i	−0.739045	+	0.536948i	−0.892412	−	0.451222i	$-0.850988\pi$
$89$	−6.97214	+	5.06555i	−0.739045	+	0.536948i	0.153367	+	0.988169i	$0.450988\pi$
$90$	0.381966	−	1.17557i	0.0402628	−	0.123916i
$91$	1.71885	+	5.29007i	0.180184	+	0.554550i
$92$	−2.14590			−0.223725
$93$		0			0
$94$	−9.09017			−0.937579
$95$	−0.590170	−	1.81636i	−0.0605502	−	0.186354i
$96$	−1.04508	+	3.21644i	−0.106664	+	0.328277i
$97$	15.1353	−	10.9964i	1.53675	−	1.11652i	0.584421	−	0.811451i	$-0.301322\pi$
$97$	15.1353	−	10.9964i	1.53675	−	1.11652i	0.952331	−	0.305065i	$-0.0986782\pi$
$98$	3.23607			0.326892
$99$	−10.4721			−1.05249
$100$	2.42705	−	1.76336i	0.242705	−	0.176336i
$101$	−7.47214	−	5.42882i	−0.743505	−	0.540188i	0.150302	−	0.988640i	$-0.451976\pi$
$101$	−7.47214	−	5.42882i	−0.743505	−	0.540188i	−0.893807	+	0.448452i	$0.851976\pi$
$102$	−5.54508	−	4.02874i	−0.549045	−	0.398905i
$103$	−2.11803	−	6.51864i	−0.208696	−	0.642301i	−0.999541	−	0.0302843i	$-0.990359\pi$
$103$	−2.11803	−	6.51864i	−0.208696	−	0.642301i	0.790845	−	0.612016i	$-0.209641\pi$
$104$	3.35410	−	2.43690i	0.328897	−	0.238957i
$105$	−0.354102	−	1.08981i	−0.0345568	−	0.106355i
$106$	−0.354102	+	1.08981i	−0.0343934	+	0.105852i
$107$	8.16312	+	5.93085i	0.789158	+	0.573357i	0.907714	−	0.419590i	$-0.137826\pi$
$107$	8.16312	+	5.93085i	0.789158	+	0.573357i	−0.118555	+	0.992947i	$0.537826\pi$
$108$	−0.954915	+	2.93893i	−0.0918867	+	0.282798i
$109$	5.69098	−	17.5150i	0.545097	−	1.67764i	−0.175661	−	0.984451i	$-0.556206\pi$
$109$	5.69098	−	17.5150i	0.545097	−	1.67764i	0.720758	−	0.693186i	$-0.243794\pi$
$110$	2.61803	+	1.90211i	0.249620	+	0.181359i
$111$	1.30902	−	4.02874i	0.124246	−	0.382391i
$112$	−4.50000	−	13.8496i	−0.425210	−	1.30866i
$113$	−3.92705	+	2.85317i	−0.369426	+	0.268404i	−0.756973	−	0.653446i	$-0.773323\pi$
$113$	−3.92705	+	2.85317i	−0.369426	+	0.268404i	0.387547	+	0.921850i	$0.373323\pi$
$114$	2.50000	+	7.69421i	0.234146	+	0.720629i
$115$	−1.07295	−	0.779543i	−0.100053	−	0.0726928i
$116$	−3.19098	−	2.31838i	−0.296275	−	0.215257i
$117$	3.00000	−	2.17963i	0.277350	−	0.201507i
$118$	0.854102			0.0786265
$119$	12.7082			1.16496
$120$	−0.690983	+	0.502029i	−0.0630778	+	0.0458287i
$121$	5.07295	−	15.6129i	0.461177	−	1.41936i
$122$	−5.47214	−	16.8415i	−0.495424	−	1.52476i
$123$	−2.47214			−0.222905
$124$		0			0
$125$	3.76393			0.336656
$126$	−3.00000	−	9.23305i	−0.267261	−	0.822546i
$127$	−1.78115	+	5.48183i	−0.158052	+	0.486433i	−0.998457	−	0.0555247i	$-0.982317\pi$
$127$	−1.78115	+	5.48183i	−0.158052	+	0.486433i	0.840406	+	0.541958i	$0.182317\pi$
$128$	−11.0172	+	8.00448i	−0.973794	+	0.707503i
$129$	2.38197			0.209720
$130$	−1.14590			−0.100502
$131$	8.97214	−	6.51864i	0.783899	−	0.569536i	−0.122248	−	0.992500i	$-0.539010\pi$
$131$	8.97214	−	6.51864i	0.783899	−	0.569536i	0.906147	+	0.422964i	$0.139010\pi$
$132$	−2.61803	−	1.90211i	−0.227871	−	0.165558i
$133$	−12.1353	−	8.81678i	−1.05226	−	0.764512i
$134$	0.118034	+	0.363271i	0.0101966	+	0.0313819i
$135$	−1.54508	+	1.12257i	−0.132980	+	0.0966154i
$136$	−2.92705	−	9.00854i	−0.250993	−	0.772476i
$137$	−0.763932	+	2.35114i	−0.0652671	+	0.200872i	−0.978372	−	0.206853i	$-0.933678\pi$
$137$	−0.763932	+	2.35114i	−0.0652671	+	0.200872i	0.913105	+	0.407725i	$0.133678\pi$
$138$	4.54508	+	3.30220i	0.386903	+	0.281102i
$139$	0.263932	−	0.812299i	0.0223864	−	0.0688983i	−0.939239	−	0.343263i	$-0.888468\pi$
$139$	0.263932	−	0.812299i	0.0223864	−	0.0688983i	0.961626	+	0.274365i	$0.0884677\pi$
$140$	−0.218847	+	0.673542i	−0.0184960	+	0.0569247i
$141$	4.54508	+	3.30220i	0.382765	+	0.278095i
$142$	−5.54508	+	17.0660i	−0.465333	+	1.43215i
$143$	3.00000	+	9.23305i	0.250873	+	0.772106i
$144$	−7.85410	+	5.70634i	−0.654508	+	0.475528i
$145$	−0.753289	−	2.31838i	−0.0625572	−	0.192531i
$146$	15.1353	+	10.9964i	1.25260	+	0.910069i
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$	−2.11803	+	1.53884i	−0.174101	+	0.126492i
$149$	12.0344			0.985900			0.492950	−	0.870058i	$-0.335919\pi$
$149$	12.0344			0.985900			0.492950	+	0.870058i	$0.335919\pi$
$150$	−7.85410			−0.641285
$151$	14.9721	−	10.8779i	1.21842	−	0.885230i	0.222448	−	0.974945i	$-0.428595\pi$
$151$	14.9721	−	10.8779i	1.21842	−	0.885230i	0.995968	+	0.0897142i	$0.0285954\pi$
$152$	−3.45492	+	10.6331i	−0.280231	+	0.862461i
$153$	−2.61803	−	8.05748i	−0.211656	−	0.651409i
$154$	25.4164			2.04811
$155$		0			0
$156$	1.14590			0.0917453
$157$	−1.14590	−	3.52671i	−0.0914526	−	0.281462i	0.894860	−	0.446346i	$-0.147275\pi$
$157$	−1.14590	−	3.52671i	−0.0914526	−	0.281462i	−0.986313	+	0.164884i	$0.947275\pi$
$158$		0			0
$159$	0.572949	−	0.416272i	0.0454378	−	0.0330125i
$160$	1.29180			0.102125
$161$	−10.4164			−0.820928
$162$	−1.30902	+	0.951057i	−0.102846	+	0.0747221i
$163$	−0.572949	−	0.416272i	−0.0448768	−	0.0326049i	0.565121	−	0.825008i	$-0.308830\pi$
$163$	−0.572949	−	0.416272i	−0.0448768	−	0.0326049i	−0.609998	+	0.792403i	$0.708830\pi$
$164$	1.23607	+	0.898056i	0.0965207	+	0.0701264i
$165$	−0.618034	−	1.90211i	−0.0481139	−	0.148079i
$166$	9.28115	−	6.74315i	0.720357	−	0.523370i
$167$	1.47214	+	4.53077i	0.113917	+	0.350601i	0.991720	−	0.128422i	$-0.0409911\pi$
$167$	1.47214	+	4.53077i	0.113917	+	0.350601i	−0.877802	+	0.479023i	$0.840991\pi$
$168$	−2.07295	+	6.37988i	−0.159931	+	0.492219i
$169$	7.73607	+	5.62058i	0.595082	+	0.432352i
$170$	−0.809017	+	2.48990i	−0.0620488	+	0.190966i
$171$	−3.09017	+	9.51057i	−0.236311	+	0.727291i
$172$	−1.19098	−	0.865300i	−0.0908116	−	0.0659785i
$173$	3.73607	−	11.4984i	0.284048	−	0.874210i	−0.702634	−	0.711551i	$-0.747993\pi$
$173$	3.73607	−	11.4984i	0.284048	−	0.874210i	0.986682	−	0.162659i	$-0.0520070\pi$
$174$	3.19098	+	9.82084i	0.241908	+	0.744516i
$175$	11.7812	−	8.55951i	0.890571	−	0.647038i
$176$	−7.85410	−	24.1724i	−0.592025	−	1.82207i
$177$	−0.427051	−	0.310271i	−0.0320991	−	0.0233214i
$178$	−11.2812	−	8.19624i	−0.845558	−	0.614334i
$179$	−3.88197	+	2.82041i	−0.290152	+	0.210808i	−0.723333	−	0.690499i	$-0.757391\pi$
$179$	−3.88197	+	2.82041i	−0.290152	+	0.210808i	0.433181	+	0.901307i	$0.357391\pi$
$180$	0.472136			0.0351909
$181$	−17.0000			−1.26360			−0.631800	−	0.775131i	$-0.717684\pi$
$181$	−17.0000			−1.26360			−0.631800	+	0.775131i	$0.717684\pi$
$182$	−7.28115	+	5.29007i	−0.539715	+	0.392126i
$183$	−3.38197	+	10.4086i	−0.250002	+	0.769427i
$184$	2.39919	+	7.38394i	0.176870	+	0.544351i
$185$	−1.61803			−0.118960
$186$		0			0
$187$	22.1803			1.62199
$188$	−1.07295	−	3.30220i	−0.0782528	−	0.240838i
$189$	−4.63525	+	14.2658i	−0.337165	+	1.03769i
$190$	2.50000	−	1.81636i	0.181369	−	0.131772i
$191$	−4.90983			−0.355263			−0.177631	−	0.984097i	$-0.556843\pi$
$191$	−4.90983			−0.355263			−0.177631	+	0.984097i	$0.556843\pi$
$192$	4.23607			0.305712
$193$	3.73607	−	2.71441i	0.268928	−	0.195388i	−0.445146	−	0.895458i	$-0.646848\pi$
$193$	3.73607	−	2.71441i	0.268928	−	0.195388i	0.714074	+	0.700070i	$0.246848\pi$
$194$	24.4894	+	17.7926i	1.75823	+	1.27743i
$195$	0.572949	+	0.416272i	0.0410297	+	0.0298098i
$196$	0.381966	+	1.17557i	0.0272833	+	0.0839693i
$197$	−8.42705	+	6.12261i	−0.600403	+	0.436218i	−0.846022	−	0.533148i	$-0.821009\pi$
$197$	−8.42705	+	6.12261i	−0.600403	+	0.436218i	0.245619	+	0.969366i	$0.421009\pi$
$198$	−5.23607	−	16.1150i	−0.372111	−	1.14524i
$199$	4.10739	−	12.6412i	0.291165	−	0.896114i	−0.693317	−	0.720632i	$-0.743852\pi$
$199$	4.10739	−	12.6412i	0.291165	−	0.896114i	0.984483	−	0.175482i	$-0.0561484\pi$
$200$	−8.78115	−	6.37988i	−0.620921	−	0.451126i
$201$	0.0729490	−	0.224514i	0.00514543	−	0.0158360i
$202$	4.61803	−	14.2128i	0.324924	−	1.00001i
$203$	−15.4894	−	11.2537i	−1.08714	−	0.789853i
$204$	0.809017	−	2.48990i	0.0566425	−	0.174328i
$205$	0.291796	+	0.898056i	0.0203799	+	0.0627229i
$206$	8.97214	−	6.51864i	0.625118	−	0.454175i
$207$	2.14590	+	6.60440i	0.149150	+	0.459037i
$208$	7.28115	+	5.29007i	0.504857	+	0.366800i
$209$	−21.1803	−	15.3884i	−1.46507	−	1.06444i
$210$	1.50000	−	1.08981i	0.103510	−	0.0752043i
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−0.437694			−0.0300610
$213$	8.97214	−	6.51864i	0.614761	−	0.446650i
$214$	−5.04508	+	15.5272i	−0.344875	+	1.06142i
$215$	−0.281153	−	0.865300i	−0.0191745	−	0.0590130i
$216$	11.1803			0.760726
$217$		0			0
$218$	29.7984			2.01820
$219$	−3.57295	−	10.9964i	−0.241438	−	0.743068i
$220$	−0.381966	+	1.17557i	−0.0257521	+	0.0792569i
$221$	−6.35410	+	4.61653i	−0.427423	+	0.310541i
$222$	6.85410			0.460017
$223$	12.7082			0.851004			0.425502	−	0.904957i	$-0.360097\pi$
$223$	12.7082			0.851004			0.425502	+	0.904957i	$0.360097\pi$
$224$	8.20820	−	5.96361i	0.548434	−	0.398460i
$225$	−7.85410	−	5.70634i	−0.523607	−	0.380423i
$226$	−6.35410	−	4.61653i	−0.422669	−	0.307087i
$227$	6.71885	+	20.6785i	0.445946	+	1.37248i	0.881443	+	0.472290i	$0.156572\pi$
$227$	6.71885	+	20.6785i	0.445946	+	1.37248i	−0.435498	+	0.900190i	$0.643428\pi$
$228$	−2.50000	+	1.81636i	−0.165567	+	0.120291i
$229$	0.854102	+	2.62866i	0.0564406	+	0.173706i	0.975303	−	0.220872i	$-0.0708905\pi$
$229$	0.854102	+	2.62866i	0.0564406	+	0.173706i	−0.918862	+	0.394579i	$0.870890\pi$
$230$	0.663119	−	2.04087i	0.0437248	−	0.134571i
$231$	−12.7082	−	9.23305i	−0.836138	−	0.607490i
$232$	−4.40983	+	13.5721i	−0.289520	+	0.891049i
$233$	−1.79180	+	5.51458i	−0.117384	+	0.361272i	−0.992437	−	0.122756i	$-0.960827\pi$
$233$	−1.79180	+	5.51458i	−0.117384	+	0.361272i	0.875052	+	0.484028i	$0.160827\pi$
$234$	4.85410	+	3.52671i	0.317323	+	0.230548i
$235$	0.663119	−	2.04087i	0.0432571	−	0.133132i
$236$	0.100813	+	0.310271i	0.00656237	+	0.0201969i
$237$		0			0
$238$	6.35410	+	19.5559i	0.411875	+	1.26762i
$239$	10.8541	+	7.88597i	0.702093	+	0.510101i	0.880613	−	0.473836i	$-0.157131\pi$
$239$	10.8541	+	7.88597i	0.702093	+	0.510101i	−0.178520	+	0.983936i	$0.557131\pi$
$240$	−1.50000	−	1.08981i	−0.0968246	−	0.0703472i
$241$	−14.1353	+	10.2699i	−0.910532	+	0.661540i	−0.941149	−	0.337991i	$-0.890253\pi$
$241$	−14.1353	+	10.2699i	−0.910532	+	0.661540i	0.0306175	+	0.999531i	$0.490253\pi$
$242$	26.5623			1.70749
$243$	16.0000			1.02640
$244$	5.47214	−	3.97574i	0.350318	−	0.254521i
$245$	−0.236068	+	0.726543i	−0.0150818	+	0.0464171i
$246$	−1.23607	−	3.80423i	−0.0788088	−	0.242549i
$247$	9.27051			0.589868
$248$		0			0
$249$	−7.09017			−0.449321
$250$	1.88197	+	5.79210i	0.119026	+	0.366324i
$251$	5.23607	−	16.1150i	0.330498	−	1.01717i	−0.638400	−	0.769705i	$-0.720403\pi$
$251$	5.23607	−	16.1150i	0.330498	−	1.01717i	0.968898	−	0.247462i	$-0.0795967\pi$
$252$	3.00000	−	2.17963i	0.188982	−	0.137304i
$253$	−18.1803			−1.14299
$254$	−9.32624			−0.585180
$255$	1.30902	−	0.951057i	0.0819738	−	0.0595575i
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	20.5623	+	14.9394i	1.28264	+	0.931894i	0.999629	−	0.0272228i	$-0.00866637\pi$
$257$	20.5623	+	14.9394i	1.28264	+	0.931894i	0.283012	+	0.959116i	$0.408666\pi$
$258$	1.19098	+	3.66547i	0.0741474	+	0.228202i
$259$	−10.2812	+	7.46969i	−0.638840	+	0.464144i
$260$	−0.135255	−	0.416272i	−0.00838815	−	0.0258161i
$261$	−3.94427	+	12.1392i	−0.244144	+	0.751399i
$262$	14.5172	+	10.5474i	0.896877	+	0.651619i
$263$	−4.26393	+	13.1230i	−0.262925	+	0.809201i	0.729239	+	0.684259i	$0.239874\pi$
$263$	−4.26393	+	13.1230i	−0.262925	+	0.809201i	−0.992164	+	0.124942i	$0.960126\pi$
$264$	−3.61803	+	11.1352i	−0.222675	+	0.685322i
$265$	−0.218847	−	0.159002i	−0.0134437	−	0.00976740i
$266$	7.50000	−	23.0826i	0.459855	−	1.41529i
$267$	2.66312	+	8.19624i	0.162980	+	0.501602i
$268$	−0.118034	+	0.0857567i	−0.00721007	+	0.00523842i
$269$	1.11803	+	3.44095i	0.0681677	+	0.209799i	0.979338	−	0.202232i	$-0.0648196\pi$
$269$	1.11803	+	3.44095i	0.0681677	+	0.209799i	−0.911170	+	0.412031i	$0.864820\pi$
$270$	−2.50000	−	1.81636i	−0.152145	−	0.110540i
$271$	−8.54508	−	6.20837i	−0.519077	−	0.377131i	0.297179	−	0.954822i	$-0.403954\pi$
$271$	−8.54508	−	6.20837i	−0.519077	−	0.377131i	−0.816256	+	0.577690i	$0.803954\pi$
$272$	16.6353	−	12.0862i	1.00866	−	0.732835i
$273$	5.56231			0.336646
$274$	−4.00000			−0.241649
$275$	20.5623	−	14.9394i	1.23995	−	0.900879i
$276$	−0.663119	+	2.04087i	−0.0399151	+	0.122846i
$277$	0.718847	+	2.21238i	0.0431913	+	0.132929i	0.970327	−	0.241797i	$-0.0777368\pi$
$277$	0.718847	+	2.21238i	0.0431913	+	0.132929i	−0.927136	+	0.374726i	$0.877737\pi$
$278$	1.38197			0.0828848
$279$		0			0
$280$	2.56231			0.153127
$281$	−3.10081	−	9.54332i	−0.184979	−	0.569307i	0.814969	−	0.579505i	$-0.196754\pi$
$281$	−3.10081	−	9.54332i	−0.184979	−	0.569307i	−0.999948	+	0.0101977i	$0.996754\pi$
$282$	−2.80902	+	8.64527i	−0.167275	+	0.514818i
$283$	10.9721	−	7.97172i	0.652226	−	0.473870i	−0.211803	−	0.977312i	$-0.567933\pi$
$283$	10.9721	−	7.97172i	0.652226	−	0.473870i	0.864029	+	0.503443i	$0.167933\pi$
$284$	−6.85410			−0.406716
$285$	−1.90983			−0.113129
$286$	−12.7082	+	9.23305i	−0.751452	+	0.545962i
$287$	6.00000	+	4.35926i	0.354169	+	0.257319i
$288$	−5.47214	−	3.97574i	−0.322449	−	0.234273i
$289$	0.291796	+	0.898056i	0.0171645	+	0.0528268i
$290$	3.19098	−	2.31838i	0.187381	−	0.136140i
$291$	−5.78115	−	17.7926i	−0.338897	−	1.04302i
$292$	−2.20820	+	6.79615i	−0.129225	+	0.397715i
$293$	3.04508	+	2.21238i	0.177896	+	0.129249i	0.673170	−	0.739488i	$-0.264932\pi$
$293$	3.04508	+	2.21238i	0.177896	+	0.129249i	−0.495274	+	0.868737i	$0.664932\pi$
$294$	1.00000	−	3.07768i	0.0583212	−	0.179494i
$295$	−0.0623059	+	0.191758i	−0.00362759	+	0.0111646i
$296$	7.66312	+	5.56758i	0.445410	+	0.323609i
$297$	−8.09017	+	24.8990i	−0.469439	+	1.44479i
$298$	6.01722	+	18.5191i	0.348568	+	1.07278i
$299$	5.20820	−	3.78398i	0.301198	−	0.218833i
$300$	−0.927051	−	2.85317i	−0.0535233	−	0.164728i
$301$	−5.78115	−	4.20025i	−0.333220	−	0.242099i
$302$	24.2254	+	17.6008i	1.39402	+	1.01281i
$303$	−7.47214	+	5.42882i	−0.429263	+	0.311878i
$304$	−24.2705			−1.39201
$305$	4.18034			0.239366
$306$	11.0902	−	8.05748i	0.633983	−	0.460615i
$307$	−1.57295	+	4.84104i	−0.0897729	+	0.276293i	−0.985856	−	0.167593i	$-0.946400\pi$
$307$	−1.57295	+	4.84104i	−0.0897729	+	0.276293i	0.896083	+	0.443886i	$0.146400\pi$
$308$	3.00000	+	9.23305i	0.170941	+	0.526102i
$309$	−6.85410			−0.389916
$310$		0			0
$311$	7.52786			0.426866			0.213433	−	0.976958i	$-0.431535\pi$
$311$	7.52786			0.426866			0.213433	+	0.976958i	$0.431535\pi$
$312$	−1.28115	−	3.94298i	−0.0725310	−	0.223227i
$313$	1.00000	−	3.07768i	0.0565233	−	0.173961i	−0.918809	−	0.394702i	$-0.870848\pi$
$313$	1.00000	−	3.07768i	0.0565233	−	0.173961i	0.975332	+	0.220741i	$0.0708477\pi$
$314$	4.85410	−	3.52671i	0.273933	−	0.199024i
$315$	2.29180			0.129128
$316$		0			0
$317$	8.00000	−	5.81234i	0.449325	−	0.326454i	−0.340004	−	0.940424i	$-0.610429\pi$
$317$	8.00000	−	5.81234i	0.449325	−	0.326454i	0.789329	+	0.613970i	$0.210429\pi$
$318$	0.927051	+	0.673542i	0.0519864	+	0.0377704i
$319$	−27.0344	−	19.6417i	−1.51364	−	1.09972i
$320$	−0.500000	−	1.53884i	−0.0279508	−	0.0860239i
$321$	8.16312	−	5.93085i	0.455621	−	0.331028i
$322$	−5.20820	−	16.0292i	−0.290242	−	0.893273i
$323$	6.54508	−	20.1437i	0.364178	−	1.12083i
$324$	−0.500000	−	0.363271i	−0.0277778	−	0.0201817i
$325$	−2.78115	+	8.55951i	−0.154271	+	0.474796i
$326$	0.354102	−	1.08981i	0.0196119	−	0.0603592i
$327$	−14.8992	−	10.8249i	−0.823927	−	0.598618i
$328$	1.70820	−	5.25731i	0.0943198	−	0.290286i
$329$	−5.20820	−	16.0292i	−0.287138	−	0.883719i
$330$	2.61803	−	1.90211i	0.144118	−	0.104708i
$331$	6.88197	+	21.1805i	0.378267	+	1.16419i	0.941248	+	0.337716i	$0.109654\pi$
$331$	6.88197	+	21.1805i	0.378267	+	1.16419i	−0.562981	+	0.826470i	$0.690346\pi$
$332$	3.54508	+	2.57565i	0.194562	+	0.141357i
$333$	6.85410	+	4.97980i	0.375602	+	0.272891i
$334$	−6.23607	+	4.53077i	−0.341222	+	0.247913i
$335$	−0.0901699			−0.00492651
$336$	−14.5623			−0.794439
$337$	−22.6353	+	16.4455i	−1.23302	+	0.895842i	−0.997113	−	0.0759333i	$-0.975806\pi$
$337$	−22.6353	+	16.4455i	−1.23302	+	0.895842i	−0.235908	+	0.971775i	$0.575806\pi$
$338$	−4.78115	+	14.7149i	−0.260060	+	0.800384i
$339$	1.50000	+	4.61653i	0.0814688	+	0.250735i
$340$	−1.00000			−0.0542326
$341$		0			0
$342$	−16.1803			−0.874933
$343$	−4.63525	−	14.2658i	−0.250280	−	0.770283i
$344$	−1.64590	+	5.06555i	−0.0887409	+	0.273116i
$345$	−1.07295	+	0.779543i	−0.0577656	+	0.0419692i
$346$	19.5623			1.05168
$347$	32.1246			1.72454			0.862270	−	0.506449i	$-0.169042\pi$
$347$	32.1246			1.72454			0.862270	+	0.506449i	$0.169042\pi$
$348$	−3.19098	+	2.31838i	−0.171055	+	0.124278i
$349$	2.66312	+	1.93487i	0.142553	+	0.103571i	0.656776	−	0.754085i	$-0.271920\pi$
$349$	2.66312	+	1.93487i	0.142553	+	0.103571i	−0.514223	+	0.857657i	$0.671920\pi$
$350$	19.0623	+	13.8496i	1.01892	+	0.740291i
$351$	−2.86475	−	8.81678i	−0.152909	−	0.470605i
$352$	14.3262	−	10.4086i	0.763591	−	0.554781i
$353$	10.6976	+	32.9237i	0.569374	+	1.75235i	0.654584	+	0.755989i	$0.272844\pi$
$353$	10.6976	+	32.9237i	0.569374	+	1.75235i	−0.0852105	+	0.996363i	$0.527156\pi$
$354$	0.263932	−	0.812299i	0.0140278	−	0.0431732i
$355$	−3.42705	−	2.48990i	−0.181889	−	0.132150i
$356$	1.64590	−	5.06555i	0.0872324	−	0.268474i
$357$	3.92705	−	12.0862i	0.207842	−	0.639671i
$358$	−6.28115	−	4.56352i	−0.331969	−	0.241190i
$359$	−2.98936	+	9.20029i	−0.157772	+	0.485573i	−0.998431	−	0.0559918i	$-0.982168\pi$
$359$	−2.98936	+	9.20029i	−0.157772	+	0.485573i	0.840659	+	0.541565i	$0.182168\pi$
$360$	−0.527864	−	1.62460i	−0.0278209	−	0.0856239i
$361$	−4.85410	+	3.52671i	−0.255479	+	0.185616i
$362$	−8.50000	−	26.1603i	−0.446750	−	1.37496i
$363$	−13.2812	−	9.64932i	−0.697080	−	0.506458i
$364$	−2.78115	−	2.02063i	−0.145772	−	0.105910i
$365$	−3.57295	+	2.59590i	−0.187017	+	0.135876i
$366$	−17.7082			−0.925623
$367$	2.72949			0.142478			0.0712391	−	0.997459i	$-0.477305\pi$
$367$	2.72949			0.142478			0.0712391	+	0.997459i	$0.477305\pi$
$368$	−13.6353	+	9.90659i	−0.710787	+	0.516417i
$369$	1.52786	−	4.70228i	0.0795374	−	0.244791i
$370$	−0.809017	−	2.48990i	−0.0420588	−	0.129444i
$371$	−2.12461			−0.110304
$372$		0			0
$373$	−31.6525			−1.63890			−0.819452	−	0.573148i	$-0.805722\pi$
$373$	−31.6525			−1.63890			−0.819452	+	0.573148i	$0.805722\pi$
$374$	11.0902	+	34.1320i	0.573459	+	1.76493i
$375$	1.16312	−	3.57971i	0.0600632	−	0.184856i
$376$	−10.1631	+	7.38394i	−0.524123	+	0.380798i
$377$	11.8328			0.609421
$378$	−24.2705			−1.24834
$379$	−6.80902	+	4.94704i	−0.349756	+	0.254112i	−0.748767	−	0.662834i	$-0.769354\pi$
$379$	−6.80902	+	4.94704i	−0.349756	+	0.254112i	0.399011	+	0.916946i	$0.369354\pi$
$380$	0.954915	+	0.693786i	0.0489861	+	0.0355905i
$381$	4.66312	+	3.38795i	0.238899	+	0.173570i
$382$	−2.45492	−	7.55545i	−0.125604	−	0.386571i
$383$	−8.20820	+	5.96361i	−0.419420	+	0.304726i	−0.777404	−	0.629001i	$-0.783464\pi$
$383$	−8.20820	+	5.96361i	−0.419420	+	0.304726i	0.357985	+	0.933727i	$0.383464\pi$
$384$	4.20820	+	12.9515i	0.214749	+	0.660929i
$385$	−1.85410	+	5.70634i	−0.0944938	+	0.290822i
$386$	6.04508	+	4.39201i	0.307687	+	0.223547i
$387$	−1.47214	+	4.53077i	−0.0748329	+	0.230312i
$388$	−3.57295	+	10.9964i	−0.181389	+	0.558258i
$389$	23.5172	+	17.0863i	1.19237	+	0.866308i	0.993513	−	0.113721i	$-0.0362769\pi$
$389$	23.5172	+	17.0863i	1.19237	+	0.866308i	0.198858	+	0.980028i	$0.436277\pi$
$390$	−0.354102	+	1.08981i	−0.0179307	+	0.0551849i
$391$	−4.54508	−	13.9883i	−0.229855	−	0.707420i
$392$	3.61803	−	2.62866i	0.182738	−	0.132767i
$393$	−3.42705	−	10.5474i	−0.172872	−	0.532045i
$394$	−13.6353	−	9.90659i	−0.686934	−	0.499087i
$395$		0			0
$396$	5.23607	−	3.80423i	0.263122	−	0.191170i
$397$	29.7082			1.49101			0.745506	−	0.666499i	$-0.232208\pi$
$397$	29.7082			1.49101			0.745506	+	0.666499i	$0.232208\pi$
$398$	21.5066			1.07803
$399$	−12.1353	+	8.81678i	−0.607523	+	0.441391i
$400$	7.28115	−	22.4091i	0.364058	−	1.12045i
$401$	−7.36475	−	22.6664i	−0.367778	−	1.13190i	−0.948223	−	0.317605i	$-0.897122\pi$
$401$	−7.36475	−	22.6664i	−0.367778	−	1.13190i	0.580445	−	0.814299i	$-0.302878\pi$
$402$	0.381966			0.0190507
$403$		0			0
$404$	5.70820			0.283994
$405$	−0.118034	−	0.363271i	−0.00586516	−	0.0180511i
$406$	9.57295	−	29.4625i	0.475097	−	1.46220i
$407$	−17.9443	+	13.0373i	−0.889465	+	0.646234i
$408$	−9.47214			−0.468941
$409$	−16.1803			−0.800066			−0.400033	−	0.916501i	$-0.631001\pi$
$409$	−16.1803			−0.800066			−0.400033	+	0.916501i	$0.631001\pi$
$410$	−1.23607	+	0.898056i	−0.0610450	+	0.0443518i
$411$	2.00000	+	1.45309i	0.0986527	+	0.0716754i
$412$	3.42705	+	2.48990i	0.168839	+	0.122668i
$413$	0.489357	+	1.50609i	0.0240797	+	0.0741096i
$414$	−9.09017	+	6.60440i	−0.446757	+	0.324588i
$415$	0.836881	+	2.57565i	0.0410809	+	0.126434i
$416$	−1.93769	+	5.96361i	−0.0950033	+	0.292390i
$417$	−0.690983	−	0.502029i	−0.0338376	−	0.0245844i
$418$	13.0902	−	40.2874i	0.640261	−	1.97052i
$419$	−1.38197	+	4.25325i	−0.0675135	+	0.207785i	−0.979122	−	0.203275i	$-0.934841\pi$
$419$	−1.38197	+	4.25325i	−0.0675135	+	0.207785i	0.911608	+	0.411060i	$0.134841\pi$
$420$	0.572949	+	0.416272i	0.0279570	+	0.0203120i
$421$	5.94427	−	18.2946i	0.289706	−	0.891624i	−0.695242	−	0.718775i	$-0.744703\pi$
$421$	5.94427	−	18.2946i	0.289706	−	0.891624i	0.984948	−	0.172848i	$-0.0552970\pi$
$422$	−4.00000	−	12.3107i	−0.194717	−	0.599277i
$423$	−9.09017	+	6.60440i	−0.441979	+	0.321117i
$424$	0.489357	+	1.50609i	0.0237653	+	0.0731420i
$425$	16.6353	+	12.0862i	0.806928	+	0.586268i
$426$	14.5172	+	10.5474i	0.703362	+	0.511022i
$427$	26.5623	−	19.2986i	1.28544	−	0.933927i
$428$	−6.23607			−0.301432
$429$	9.70820			0.468717
$430$	1.19098	−	0.865300i	0.0574343	−	0.0417285i
$431$	7.65248	−	23.5519i	0.368607	−	1.13446i	−0.579085	−	0.815267i	$-0.696590\pi$
$431$	7.65248	−	23.5519i	0.368607	−	1.13446i	0.947692	−	0.319188i	$-0.103410\pi$
$432$	7.50000	+	23.0826i	0.360844	+	1.11056i
$433$	−27.4164			−1.31755			−0.658774	−	0.752341i	$-0.728925\pi$
$433$	−27.4164			−1.31755			−0.658774	+	0.752341i	$0.728925\pi$
$434$		0			0
$435$	−2.43769			−0.116878
$436$	3.51722	+	10.8249i	0.168444	+	0.518418i
$437$	−5.36475	+	16.5110i	−0.256631	+	0.789828i
$438$	15.1353	−	10.9964i	0.723190	−	0.525429i
$439$	−11.8328			−0.564749			−0.282375	−	0.959304i	$-0.591122\pi$
$439$	−11.8328			−0.564749			−0.282375	+	0.959304i	$0.591122\pi$
$440$	4.47214			0.213201
$441$	3.23607	−	2.35114i	0.154098	−	0.111959i
$442$	−10.2812	−	7.46969i	−0.489025	−	0.355297i
$443$	0.708204	+	0.514540i	0.0336478	+	0.0244465i	0.604482	−	0.796619i	$-0.293380\pi$
$443$	0.708204	+	0.514540i	0.0336478	+	0.0244465i	−0.570834	+	0.821065i	$0.693380\pi$
$444$	0.809017	+	2.48990i	0.0383942	+	0.118165i
$445$	2.66312	−	1.93487i	0.126244	−	0.0917216i
$446$	6.35410	+	19.5559i	0.300875	+	0.925999i
$447$	3.71885	−	11.4454i	0.175895	−	0.541350i
$448$	−10.2812	−	7.46969i	−0.485739	−	0.352910i
$449$	10.5279	−	32.4014i	0.496841	−	1.52912i	−0.317228	−	0.948349i	$-0.602752\pi$
$449$	10.5279	−	32.4014i	0.496841	−	1.52912i	0.814069	−	0.580769i	$-0.197248\pi$
$450$	4.85410	−	14.9394i	0.228825	−	0.704250i
$451$	10.4721	+	7.60845i	0.493114	+	0.358268i
$452$	0.927051	−	2.85317i	0.0436048	−	0.134202i
$453$	−5.71885	−	17.6008i	−0.268695	−	0.826958i
$454$	−28.4615	+	20.6785i	−1.33576	+	0.970489i
$455$	−0.656541	−	2.02063i	−0.0307791	−	0.0947284i
$456$	9.04508	+	6.57164i	0.423575	+	0.307745i
$457$	21.6353	+	15.7189i	1.01205	+	0.735301i	0.964639	−	0.263575i	$-0.0849015\pi$
$457$	21.6353	+	15.7189i	1.01205	+	0.735301i	0.0474155	+	0.998875i	$0.484902\pi$
$458$	−3.61803	+	2.62866i	−0.169060	+	0.122829i
$459$	−21.1803			−0.988614
$460$	0.819660			0.0382168
$461$	−25.6803	+	18.6579i	−1.19605	+	0.868983i	−0.993891	−	0.110369i	$-0.964797\pi$
$461$	−25.6803	+	18.6579i	−1.19605	+	0.868983i	−0.202162	+	0.979352i	$0.564797\pi$
$462$	7.85410	−	24.1724i	0.365406	−	1.12460i
$463$	−2.81966	−	8.67802i	−0.131041	−	0.403302i	0.863912	−	0.503642i	$-0.168007\pi$
$463$	−2.81966	−	8.67802i	−0.131041	−	0.403302i	−0.994953	+	0.100340i	$0.968007\pi$
$464$	−30.9787			−1.43815
$465$		0			0
$466$	−9.38197			−0.434611
$467$	11.9828	+	36.8792i	0.554497	+	1.70657i	0.697268	+	0.716810i	$0.254399\pi$
$467$	11.9828	+	36.8792i	0.554497	+	1.70657i	−0.142771	+	0.989756i	$0.545601\pi$
$468$	−0.708204	+	2.17963i	−0.0327367	+	0.100753i
$469$	−0.572949	+	0.416272i	−0.0264563	+	0.0192216i
$470$	3.47214			0.160158
$471$	−3.70820			−0.170865
$472$	0.954915	−	0.693786i	0.0439535	−	0.0319341i
$473$	−10.0902	−	7.33094i	−0.463947	−	0.337077i
$474$		0			0
$475$	−7.50000	−	23.0826i	−0.344124	−	1.05910i
$476$	−6.35410	+	4.61653i	−0.291240	+	0.211598i
$477$	0.437694	+	1.34708i	0.0200406	+	0.0616787i
$478$	−6.70820	+	20.6457i	−0.306826	+	0.944314i
$479$	−7.23607	−	5.25731i	−0.330624	−	0.240213i	0.410071	−	0.912054i	$-0.365504\pi$
$479$	−7.23607	−	5.25731i	−0.330624	−	0.240213i	−0.740696	+	0.671841i	$0.765504\pi$
$480$	0.399187	−	1.22857i	0.0182203	−	0.0560763i
$481$	2.42705	−	7.46969i	0.110664	−	0.340589i
$482$	−22.8713	−	16.6170i	−1.04176	−	0.756883i
$483$	−3.21885	+	9.90659i	−0.146463	+	0.450766i
$484$	3.13525	+	9.64932i	0.142512	+	0.438606i
$485$	−5.78115	+	4.20025i	−0.262509	+	0.190724i
$486$	8.00000	+	24.6215i	0.362887	+	1.11685i
$487$	−33.9164	−	24.6417i	−1.53690	−	1.11662i	−0.952243	−	0.305341i	$-0.901229\pi$
$487$	−33.9164	−	24.6417i	−1.53690	−	1.11662i	−0.584656	−	0.811281i	$-0.698771\pi$
$488$	−19.7984	−	14.3844i	−0.896230	−	0.651149i
$489$	−0.572949	+	0.416272i	−0.0259097	+	0.0188245i
$490$	−1.23607			−0.0558399
$491$	−21.5967			−0.974648			−0.487324	−	0.873221i	$-0.662027\pi$
$491$	−21.5967			−0.974648			−0.487324	+	0.873221i	$0.662027\pi$
$492$	1.23607	−	0.898056i	0.0557262	−	0.0404875i
$493$	8.35410	−	25.7113i	0.376250	−	1.15798i
$494$	4.63525	+	14.2658i	0.208550	+	0.641851i
$495$	4.00000			0.179787
$496$		0			0
$497$	−33.2705			−1.49239
$498$	−3.54508	−	10.9106i	−0.158859	−	0.488918i
$499$	−3.35410	+	10.3229i	−0.150150	+	0.462115i	−0.997637	−	0.0687012i	$-0.978114\pi$
$499$	−3.35410	+	10.3229i	−0.150150	+	0.462115i	0.847487	+	0.530816i	$0.178114\pi$
$500$	−1.88197	+	1.36733i	−0.0841641	+	0.0611488i
$501$	4.76393			0.212837
$502$	27.4164			1.22365
$503$	−16.0623	+	11.6699i	−0.716183	+	0.520337i	−0.885162	−	0.465282i	$-0.845953\pi$
$503$	−16.0623	+	11.6699i	−0.716183	+	0.520337i	0.168980	+	0.985620i	$0.445953\pi$
$504$	−10.8541	−	7.88597i	−0.483480	−	0.351269i
$505$	2.85410	+	2.07363i	0.127006	+	0.0922752i
$506$	−9.09017	−	27.9767i	−0.404107	−	1.24371i
$507$	7.73607	−	5.62058i	0.343571	−	0.249619i
$508$	−1.10081	−	3.38795i	−0.0488407	−	0.150316i
$509$	4.04508	−	12.4495i	0.179295	−	0.551814i	−0.820508	−	0.571635i	$-0.806310\pi$
$509$	4.04508	−	12.4495i	0.179295	−	0.551814i	0.999804	+	0.0198206i	$0.00630950\pi$
$510$	2.11803	+	1.53884i	0.0937881	+	0.0681411i
$511$	−10.7188	+	32.9892i	−0.474174	+	1.45936i
$512$	−1.63525	+	5.03280i	−0.0722687	+	0.222420i
$513$	20.2254	+	14.6946i	0.892974	+	0.648784i
$514$	−12.7082	+	39.1118i	−0.560535	+	1.72515i
$515$	0.809017	+	2.48990i	0.0356495	+	0.109718i
$516$	−1.19098	+	0.865300i	−0.0524301	+	0.0380927i
$517$	−9.09017	−	27.9767i	−0.399785	−	1.23041i
$518$	−16.6353	−	12.0862i	−0.730911	−	0.531038i
$519$	−9.78115	−	7.10642i	−0.429345	−	0.311937i
$520$	−1.28115	+	0.930812i	−0.0561823	+	0.0408188i
$521$	−27.0689			−1.18591			−0.592955	−	0.805236i	$-0.702039\pi$
$521$	−27.0689			−1.18591			−0.592955	+	0.805236i	$0.702039\pi$
$522$	−20.6525			−0.903934
$523$	−4.95492	+	3.59996i	−0.216663	+	0.157415i	−0.690823	−	0.723024i	$-0.742752\pi$
$523$	−4.95492	+	3.59996i	−0.216663	+	0.157415i	0.474160	+	0.880439i	$0.342752\pi$
$524$	−2.11803	+	6.51864i	−0.0925267	+	0.284768i
$525$	−4.50000	−	13.8496i	−0.196396	−	0.604445i
$526$	−22.3262			−0.973470
$527$		0			0
$528$	−25.4164			−1.10611
$529$	−3.38197	−	10.4086i	−0.147042	−	0.452549i
$530$	0.135255	−	0.416272i	0.00587510	−	0.0180817i
$531$	0.854102	−	0.620541i	0.0370649	−	0.0269292i
$532$	9.27051			0.401928
$533$	−4.58359			−0.198537
$534$	−11.2812	+	8.19624i	−0.488183	+	0.354686i
$535$	−3.11803	−	2.26538i	−0.134804	−	0.0979411i
$536$	0.427051	+	0.310271i	0.0184458	+	0.0134017i
$537$	1.48278	+	4.56352i	0.0639866	+	0.196931i
$538$	−4.73607	+	3.44095i	−0.204186	+	0.148350i
$539$	3.23607	+	9.95959i	0.139387	+	0.428990i
$540$	0.364745	−	1.12257i	0.0156961	−	0.0483077i
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	0.135293	−	0.990806i	$-0.456803\pi$
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	−0.900504	+	0.434847i	$0.856803\pi$
$542$	5.28115	−	16.2537i	0.226845	−	0.698157i
$543$	−5.25329	+	16.1680i	−0.225440	+	0.693834i
$544$	11.5902	+	8.42075i	0.496924	+	0.361037i
$545$	−2.17376	+	6.69015i	−0.0931137	+	0.286575i
$546$	2.78115	+	8.55951i	0.119022	+	0.366313i
$547$	8.32624	−	6.04937i	0.356004	−	0.258652i	−0.395379	−	0.918518i	$-0.629387\pi$
$547$	8.32624	−	6.04937i	0.356004	−	0.258652i	0.751384	+	0.659866i	$0.229387\pi$
$548$	−0.472136	−	1.45309i	−0.0201686	−	0.0620727i
$549$	−17.7082	−	12.8658i	−0.755768	−	0.549097i
$550$	33.2705	+	24.1724i	1.41866	+	1.03072i
$551$	−25.8156	+	18.7561i	−1.09978	+	0.799038i
$552$	7.76393			0.330455
$553$		0			0
$554$	−3.04508	+	2.21238i	−0.129373	+	0.0939952i
$555$	−0.500000	+	1.53884i	−0.0212238	+	0.0653202i
$556$	0.163119	+	0.502029i	0.00691778	+	0.0212908i
$557$	−0.111456			−0.00472255			−0.00236127	−	0.999997i	$-0.500752\pi$
$557$	−0.111456			−0.00472255			−0.00236127	+	0.999997i	$0.500752\pi$
$558$		0			0
$559$	4.41641			0.186794
$560$	1.71885	+	5.29007i	0.0726345	+	0.223546i
$561$	6.85410	−	21.0948i	0.289380	−	0.890621i
$562$	13.1353	−	9.54332i	0.554077	−	0.402561i
$563$	11.5623			0.487293			0.243647	−	0.969864i	$-0.421656\pi$
$563$	11.5623			0.487293			0.243647	+	0.969864i	$0.421656\pi$
$564$	−3.47214			−0.146203
$565$	1.50000	−	1.08981i	0.0631055	−	0.0458488i
$566$	17.7533	+	12.8985i	0.746226	+	0.542165i
$567$	−2.42705	−	1.76336i	−0.101927	−	0.0740540i
$568$	7.66312	+	23.5847i	0.321537	+	0.989590i
$569$	19.7984	−	14.3844i	0.829991	−	0.603024i	−0.0895658	−	0.995981i	$-0.528548\pi$
$569$	19.7984	−	14.3844i	0.829991	−	0.603024i	0.919557	+	0.392957i	$0.128548\pi$
$570$	−0.954915	−	2.93893i	−0.0399970	−	0.123098i
$571$	−2.16312	+	6.65740i	−0.0905237	+	0.278603i	−0.986061	−	0.166383i	$-0.946791\pi$
$571$	−2.16312	+	6.65740i	−0.0905237	+	0.278603i	0.895538	+	0.444986i	$0.146791\pi$
$572$	−4.85410	−	3.52671i	−0.202960	−	0.147459i
$573$	−1.51722	+	4.66953i	−0.0633828	+	0.195072i
$574$	−3.70820	+	11.4127i	−0.154777	+	0.476356i
$575$	−13.6353	−	9.90659i	−0.568629	−	0.413133i
$576$	−2.61803	+	8.05748i	−0.109085	+	0.335728i
$577$	−2.46556	−	7.58821i	−0.102643	−	0.315901i	0.886527	−	0.462676i	$-0.153111\pi$
$577$	−2.46556	−	7.58821i	−0.102643	−	0.315901i	−0.989170	+	0.146775i	$0.953111\pi$
$578$	−1.23607	+	0.898056i	−0.0514136	+	0.0373542i
$579$	−1.42705	−	4.39201i	−0.0593062	−	0.182526i
$580$	1.21885	+	0.885544i	0.0506099	+	0.0367702i
$581$	17.2082	+	12.5025i	0.713917	+	0.518691i
$582$	24.4894	−	17.7926i	1.01512	−	0.737525i
$583$	−3.70820			−0.153578
$584$	25.8541			1.06985
$585$	−1.14590	+	0.832544i	−0.0473771	+	0.0344214i
$586$	−1.88197	+	5.79210i	−0.0777433	+	0.239269i
$587$	12.3647	+	38.0548i	0.510348	+	1.57069i	0.791591	+	0.611052i	$0.209253\pi$
$587$	12.3647	+	38.0548i	0.510348	+	1.57069i	−0.281243	+	0.959637i	$0.590747\pi$
$588$	1.23607			0.0509746
$589$		0			0
$590$	−0.326238			−0.0134310
$591$	3.21885	+	9.90659i	0.132406	+	0.407503i
$592$	−6.35410	+	19.5559i	−0.261152	+	0.803743i
$593$	−33.8885	+	24.6215i	−1.39164	+	1.01108i	−0.395952	+	0.918271i	$0.629585\pi$
$593$	−33.8885	+	24.6215i	−1.39164	+	1.01108i	−0.995684	+	0.0928113i	$0.970415\pi$
$594$	−42.3607			−1.73808
$595$	−4.85410			−0.198999
$596$	−6.01722	+	4.37177i	−0.246475	+	0.179075i
$597$	−10.7533	−	7.81272i	−0.440103	−	0.319753i
$598$	8.42705	+	6.12261i	0.344608	+	0.250372i
$599$	1.60739	+	4.94704i	0.0656762	+	0.202131i	0.978509	−	0.206202i	$-0.0661104\pi$
$599$	1.60739	+	4.94704i	0.0656762	+	0.202131i	−0.912833	+	0.408333i	$0.866110\pi$
$600$	−8.78115	+	6.37988i	−0.358489	+	0.260458i
$601$	−6.79837	−	20.9232i	−0.277311	−	0.853477i	−0.988599	−	0.150575i	$-0.951887\pi$
$601$	−6.79837	−	20.9232i	−0.277311	−	0.853477i	0.711287	−	0.702902i	$-0.248113\pi$
$602$	3.57295	−	10.9964i	0.145623	−	0.448180i
$603$	0.381966	+	0.277515i	0.0155549	+	0.0113013i
$604$	−3.53444	+	10.8779i	−0.143814	+	0.442615i
$605$	−1.93769	+	5.96361i	−0.0787785	+	0.242455i
$606$	−12.0902	−	8.78402i	−0.491130	−	0.356827i
$607$	0.437694	−	1.34708i	0.0177655	−	0.0546765i	−0.941781	−	0.336228i	$-0.890849\pi$
$607$	0.437694	−	1.34708i	0.0177655	−	0.0546765i	0.959546	+	0.281551i	$0.0908489\pi$
$608$	−5.22542	−	16.0822i	−0.211919	−	0.652219i
$609$	−15.4894	+	11.2537i	−0.627660	+	0.456022i
$610$	2.09017	+	6.43288i	0.0846285	+	0.260460i
$611$	8.42705	+	6.12261i	0.340922	+	0.247694i
$612$	4.23607	+	3.07768i	0.171233	+	0.124408i
$613$	34.7426	−	25.2420i	1.40324	−	1.01952i	0.408980	−	0.912543i	$-0.365885\pi$
$613$	34.7426	−	25.2420i	1.40324	−	1.01952i	0.994262	−	0.106972i	$-0.0341155\pi$
$614$	−8.23607			−0.332381
$615$	0.944272			0.0380767
$616$	28.4164	−	20.6457i	1.14493	−	0.831840i
$617$	−3.01722	+	9.28605i	−0.121469	+	0.373842i	−0.993241	−	0.116069i	$-0.962971\pi$
$617$	−3.01722	+	9.28605i	−0.121469	+	0.373842i	0.871772	+	0.489911i	$0.162971\pi$
$618$	−3.42705	−	10.5474i	−0.137856	−	0.424278i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	17.3607			0.696660
$622$	3.76393	+	11.5842i	0.150920	+	0.464484i
$623$	7.98936	−	24.5887i	0.320087	−	0.985126i
$624$	7.28115	−	5.29007i	0.291479	−	0.211772i
$625$	22.8328			0.913313
$626$	5.23607			0.209275
$627$	−21.1803	+	15.3884i	−0.845861	+	0.614554i
$628$	1.85410	+	1.34708i	0.0739867	+	0.0537545i
$629$	−14.5172	−	10.5474i	−0.578840	−	0.420552i
$630$	1.14590	+	3.52671i	0.0456537	+	0.140508i
$631$	−34.1976	+	24.8460i	−1.36138	+	0.989103i	−0.363028	+	0.931778i	$0.618257\pi$
$631$	−34.1976	+	24.8460i	−1.36138	+	0.989103i	−0.998356	+	0.0573246i	$0.981743\pi$
$632$		0			0
$633$	−2.47214	+	7.60845i	−0.0982586	+	0.302409i
$634$	12.9443	+	9.40456i	0.514083	+	0.373503i
$635$	0.680340	−	2.09387i	0.0269985	−	0.0830927i
$636$	−0.135255	+	0.416272i	−0.00536321	+	0.0165063i
$637$	−3.00000	−	2.17963i	−0.118864	−	0.0863600i
$638$	16.7082	−	51.4226i	0.661484	−	2.03584i
$639$	6.85410	+	21.0948i	0.271144	+	0.834496i
$640$	4.20820	−	3.05744i	0.166344	−	0.120856i
$641$	9.24265	+	28.4459i	0.365063	+	1.12355i	0.949942	+	0.312427i	$0.101142\pi$
$641$	9.24265	+	28.4459i	0.365063	+	1.12355i	−0.584879	+	0.811120i	$0.698858\pi$
$642$	13.2082	+	9.59632i	0.521286	+	0.378737i
$643$	12.0172	+	8.73102i	0.473913	+	0.344318i	0.798964	−	0.601378i	$-0.205382\pi$
$643$	12.0172	+	8.73102i	0.473913	+	0.344318i	−0.325051	+	0.945696i	$0.605382\pi$
$644$	5.20820	−	3.78398i	0.205232	−	0.149110i
$645$	−0.909830			−0.0358245
$646$	34.2705			1.34836
$647$	4.76393	−	3.46120i	0.187289	−	0.136074i	−0.490190	−	0.871616i	$-0.663072\pi$
$647$	4.76393	−	3.46120i	0.187289	−	0.136074i	0.677479	+	0.735542i	$0.263072\pi$
$648$	−0.690983	+	2.12663i	−0.0271444	+	0.0835418i
$649$	0.854102	+	2.62866i	0.0335264	+	0.103184i
$650$	−14.5623			−0.571181
$651$		0			0
$652$	0.437694			0.0171414
$653$	2.57953	+	7.93897i	0.100945	+	0.310676i	0.988757	−	0.149529i	$-0.0477759\pi$
$653$	2.57953	+	7.93897i	0.100945	+	0.310676i	−0.887813	+	0.460205i	$0.847776\pi$
$654$	9.20820	−	28.3399i	0.360069	−	1.10818i
$655$	−3.42705	+	2.48990i	−0.133906	+	0.0972884i
$656$	12.0000			0.468521
$657$	23.1246			0.902177
$658$	22.0623	−	16.0292i	0.860078	−	0.624883i
$659$	30.4894	+	22.1518i	1.18770	+	0.862912i	0.993019	−	0.117955i	$-0.0376339\pi$
$659$	30.4894	+	22.1518i	1.18770	+	0.862912i	0.194678	+	0.980867i	$0.437634\pi$
$660$	1.00000	+	0.726543i	0.0389249	+	0.0282806i
$661$	−4.44427	−	13.6781i	−0.172862	−	0.532015i	0.826667	−	0.562691i	$-0.190234\pi$
$661$	−4.44427	−	13.6781i	−0.172862	−	0.532015i	−0.999529	+	0.0306761i	$0.990234\pi$
$662$	−29.1525	+	21.1805i	−1.13304	+	0.823204i
$663$	2.42705	+	7.46969i	0.0942588	+	0.290099i
$664$	4.89919	−	15.0781i	0.190125	−	0.585146i
$665$	4.63525	+	3.36771i	0.179747	+	0.130594i
$666$	−4.23607	+	13.0373i	−0.164144	+	0.505184i
$667$	−6.84752	+	21.0745i	−0.265137	+	0.816008i
$668$	−2.38197	−	1.73060i	−0.0921610	−	0.0669589i
$669$	3.92705	−	12.0862i	0.151829	−	0.467280i
$670$	−0.0450850	−	0.138757i	−0.00174178	−	0.00536066i
$671$	46.3607	−	33.6830i	1.78973	−	1.30032i
$672$	−3.13525	−	9.64932i	−0.120945	−	0.372231i
$673$	18.1353	+	13.1760i	0.699063	+	0.507899i	0.879627	−	0.475664i	$-0.157792\pi$
$673$	18.1353	+	13.1760i	0.699063	+	0.507899i	−0.180564	+	0.983563i	$0.557792\pi$
$674$	−36.6246	−	26.6093i	−1.41073	−	1.02495i
$675$	−19.6353	+	14.2658i	−0.755761	+	0.549093i
$676$	−5.90983			−0.227301
$677$	2.65248			0.101943			0.0509715	−	0.998700i	$-0.483768\pi$
$677$	2.65248			0.101943			0.0509715	+	0.998700i	$0.483768\pi$
$678$	−6.35410	+	4.61653i	−0.244028	+	0.177297i
$679$	−17.3435	+	53.3777i	−0.665581	+	2.04845i
$680$	1.11803	+	3.44095i	0.0428746	+	0.131955i
$681$	21.7426			0.833180
$682$		0			0
$683$	27.9443			1.06926			0.534629	−	0.845087i	$-0.320451\pi$
$683$	27.9443			1.06926			0.534629	+	0.845087i	$0.320451\pi$
$684$	−1.90983	−	5.87785i	−0.0730242	−	0.224745i
$685$	0.291796	−	0.898056i	0.0111490	−	0.0343130i
$686$	19.6353	−	14.2658i	0.749678	−	0.544673i
$687$	2.76393			0.105451
$688$	−11.5623			−0.440809
$689$	1.06231	−	0.771810i	0.0404706	−	0.0294036i
$690$	−1.73607	−	1.26133i	−0.0660910	−	0.0480179i
$691$	40.3156	+	29.2910i	1.53368	+	1.11428i	0.954150	+	0.299329i	$0.0967629\pi$
$691$	40.3156	+	29.2910i	1.53368	+	1.11428i	0.579528	+	0.814953i	$0.303237\pi$
$692$	2.30902	+	7.10642i	0.0877757	+	0.270146i
$693$	25.4164	−	18.4661i	0.965489	−	0.701469i
$694$	16.0623	+	49.4347i	0.609717	+	1.87652i
$695$	−0.100813	+	0.310271i	−0.00382406	+	0.0117692i
$696$	11.5451	+	8.38800i	0.437615	+	0.317946i
$697$	−3.23607	+	9.95959i	−0.122575	+	0.377246i
$698$	−1.64590	+	5.06555i	−0.0622982	+	0.191734i
$699$	4.69098	+	3.40820i	0.177429	+	0.128910i
$700$	−2.78115	+	8.55951i	−0.105118	+	0.323519i
$701$	−0.298374	−	0.918300i	−0.0112694	−	0.0346837i	0.945264	−	0.326307i	$-0.105804\pi$
$701$	−0.298374	−	0.918300i	−0.0112694	−	0.0346837i	−0.956533	+	0.291624i	$0.905804\pi$
$702$	12.1353	−	8.81678i	0.458016	−	0.332768i
$703$	6.54508	+	20.1437i	0.246853	+	0.759734i
$704$	−17.9443	−	13.0373i	−0.676300	−	0.491361i
$705$	−1.73607	−	1.26133i	−0.0653841	−	0.0475043i
$706$	−45.3156	+	32.9237i	−1.70547	+	1.23910i
$707$	27.7082			1.04207
$708$	0.326238			0.0122608
$709$	8.78115	−	6.37988i	0.329783	−	0.239601i	−0.410555	−	0.911836i	$-0.634665\pi$
$709$	8.78115	−	6.37988i	0.329783	−	0.239601i	0.740339	+	0.672234i	$0.234665\pi$
$710$	2.11803	−	6.51864i	0.0794884	−	0.244640i
$711$		0			0
$712$	−19.2705			−0.722193
$713$		0			0
$714$	20.5623			0.769525
$715$	−1.14590	−	3.52671i	−0.0428542	−	0.131892i
$716$	0.916408	−	2.82041i	0.0342478	−	0.105404i
$717$	10.8541	−	7.88597i	0.405354	−	0.294507i
$718$	−15.6525			−0.584145
$719$	43.6180			1.62668			0.813339	−	0.581790i	$-0.197647\pi$
$719$	43.6180			1.62668			0.813339	+	0.581790i	$0.197647\pi$
$720$	3.00000	−	2.17963i	0.111803	−	0.0812299i
$721$	16.6353	+	12.0862i	0.619529	+	0.450114i
$722$	−7.85410	−	5.70634i	−0.292299	−	0.212368i
$723$	5.39919	+	16.6170i	0.200798	+	0.617992i
$724$	8.50000	−	6.17561i	0.315900	−	0.229515i
$725$	−9.57295	−	29.4625i	−0.355530	−	1.09421i
$726$	8.20820	−	25.2623i	0.304635	−	0.937570i
$727$	−24.1353	−	17.5353i	−0.895127	−	0.650348i	0.0420827	−	0.999114i	$-0.486601\pi$
$727$	−24.1353	−	17.5353i	−0.895127	−	0.650348i	−0.937210	+	0.348766i	$0.886601\pi$
$728$	−3.84346	+	11.8290i	−0.142448	+	0.438410i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	−5.78115	−	4.20025i	−0.213970	−	0.155458i
$731$	3.11803	−	9.59632i	0.115325	−	0.354933i
$732$	−2.09017	−	6.43288i	−0.0772549	−	0.237766i
$733$	−8.13525	+	5.91061i	−0.300482	+	0.218313i	−0.727802	−	0.685787i	$-0.759458\pi$
$733$	−8.13525	+	5.91061i	−0.300482	+	0.218313i	0.427319	+	0.904101i	$0.359458\pi$
$734$	1.36475	+	4.20025i	0.0503737	+	0.155034i
$735$	0.618034	+	0.449028i	0.0227965	+	0.0165626i
$736$	−9.50000	−	6.90215i	−0.350175	−	0.254417i
$737$	−1.00000	+	0.726543i	−0.0368355	+	0.0267625i
$738$	8.00000			0.294484
$739$	−8.29180			−0.305019			−0.152509	−	0.988302i	$-0.548735\pi$
$739$	−8.29180			−0.305019			−0.152509	+	0.988302i	$0.548735\pi$
$740$	0.809017	−	0.587785i	0.0297401	−	0.0216074i
$741$	2.86475	−	8.81678i	0.105239	−	0.323892i
$742$	−1.06231	−	3.26944i	−0.0389985	−	0.120025i
$743$	23.5623			0.864417			0.432209	−	0.901774i	$-0.357734\pi$
$743$	23.5623			0.864417			0.432209	+	0.901774i	$0.357734\pi$
$744$		0			0
$745$	−4.59675			−0.168412
$746$	−15.8262	−	48.7082i	−0.579440	−	1.78333i
$747$	4.38197	−	13.4863i	0.160328	−	0.493438i
$748$	−11.0902	+	8.05748i	−0.405497	+	0.294611i
$749$	−30.2705			−1.10606
$750$	6.09017			0.222382
$751$	−11.1910	+	8.13073i	−0.408365	+	0.296694i	−0.772939	−	0.634480i	$-0.781214\pi$
$751$	−11.1910	+	8.13073i	−0.408365	+	0.296694i	0.364575	+	0.931174i	$0.381214\pi$
$752$	−22.0623	−	16.0292i	−0.804530	−	0.584525i
$753$	−13.7082	−	9.95959i	−0.499555	−	0.362948i
$754$	5.91641	+	18.2088i	0.215463	+	0.663127i
$755$	−5.71885	+	4.15499i	−0.208130	+	0.151215i
$756$	−2.86475	−	8.81678i	−0.104190	−	0.320663i
$757$	−0.888544	+	2.73466i	−0.0322947	+	0.0993928i	−0.965905	−	0.258898i	$-0.916641\pi$
$757$	−0.888544	+	2.73466i	−0.0322947	+	0.0993928i	0.933610	+	0.358291i	$0.116641\pi$
$758$	−11.0172	−	8.00448i	−0.400163	−	0.290736i
$759$	−5.61803	+	17.2905i	−0.203922	+	0.627607i
$760$	1.31966	−	4.06150i	0.0478691	−	0.147326i
$761$	−27.9164	−	20.2825i	−1.01197	−	0.735239i	−0.0473478	−	0.998878i	$-0.515077\pi$
$761$	−27.9164	−	20.2825i	−1.01197	−	0.735239i	−0.964621	+	0.263640i	$0.915077\pi$
$762$	−2.88197	+	8.86978i	−0.104403	+	0.321318i
$763$	17.0729	+	52.5451i	0.618082	+	1.90226i
$764$	2.45492	−	1.78360i	0.0888157	−	0.0645284i
$765$	1.00000	+	3.07768i	0.0361551	+	0.111274i
$766$	−13.2812	−	9.64932i	−0.479868	−	0.348644i
$767$	−0.791796	−	0.575274i	−0.0285901	−	0.0207719i
$768$	−10.9721	+	7.97172i	−0.395923	+	0.287655i
$769$	−11.2574			−0.405951			−0.202975	−	0.979184i	$-0.565061\pi$
$769$	−11.2574			−0.405951			−0.202975	+	0.979184i	$0.565061\pi$
$770$	−9.70820			−0.349859
$771$	20.5623	−	14.9394i	0.740533	−	0.538029i
$772$	−0.881966	+	2.71441i	−0.0317427	+	0.0976938i
$773$	2.44427	+	7.52270i	0.0879144	+	0.270573i	0.985342	−	0.170588i	$-0.0545668\pi$
$773$	2.44427	+	7.52270i	0.0879144	+	0.270573i	−0.897428	+	0.441161i	$0.854567\pi$
$774$	−7.70820			−0.277066
$775$		0			0
$776$	41.8328			1.50171
$777$	3.92705	+	12.0862i	0.140882	+	0.433591i
$778$	−14.5344	+	44.7324i	−0.521085	+	1.60373i
$779$	10.0000	−	7.26543i	0.358287	−	0.260311i
$780$	−0.437694			−0.0156720
$781$	−58.0689			−2.07787
$782$	19.2533	−	13.9883i	0.688496	−	0.500222i
$783$	25.8156	+	18.7561i	0.922574	+	0.670289i
$784$	7.85410	+	5.70634i	0.280504	+	0.203798i
$785$	0.437694	+	1.34708i	0.0156220	+	0.0480795i
$786$	14.5172	−	10.5474i	0.517812	−	0.376213i
$787$	−13.8156	−	42.5200i	−0.492473	−	1.51568i	−0.820858	−	0.571132i	$-0.806505\pi$
$787$	−13.8156	−	42.5200i	−0.492473	−	1.51568i	0.328386	−	0.944544i	$-0.393495\pi$
$788$	1.98936	−	6.12261i	0.0708679	−	0.218109i
$789$	11.1631	+	8.11048i	0.397418	+	0.288741i
$790$		0			0
$791$	4.50000	−	13.8496i	0.160002	−	0.492434i
$792$	−18.9443	−	13.7638i	−0.673155	−	0.489076i
$793$	−6.27051	+	19.2986i	−0.222672	+	0.685315i
$794$	14.8541	+	45.7162i	0.527152	+	1.62241i
$795$	−0.218847	+	0.159002i	−0.00776171	+	0.00563921i
$796$	2.53851	+	7.81272i	0.0899750	+	0.276915i
$797$	21.7984	+	15.8374i	0.772138	+	0.560991i	0.902609	−	0.430461i	$-0.141649\pi$
$797$	21.7984	+	15.8374i	0.772138	+	0.560991i	−0.130471	+	0.991452i	$0.541649\pi$
$798$	−19.6353	−	14.2658i	−0.695080	−	0.505006i
$799$	19.2533	−	13.9883i	0.681132	−	0.494872i
$800$	16.4164			0.580408
$801$	−17.2361			−0.609007
$802$	31.1976	−	22.6664i	1.10162	−	0.800377i
$803$	−18.7082	+	57.5779i	−0.660198	+	2.03188i
$804$	0.0450850	+	0.138757i	0.00159002	+	0.00489359i
$805$	3.97871			0.140231
$806$		0			0
$807$	3.61803			0.127361
$808$	−6.38197	−	19.6417i	−0.224517	−	0.690992i
$809$	−9.33282	+	28.7235i	−0.328124	+	1.00986i	0.641886	+	0.766800i	$0.278152\pi$
$809$	−9.33282	+	28.7235i	−0.328124	+	1.00986i	−0.970011	+	0.243063i	$0.921848\pi$
$810$	0.500000	−	0.363271i	0.0175682	−	0.0127641i
$811$	−28.7771			−1.01050			−0.505250	−	0.862973i	$-0.668600\pi$
$811$	−28.7771			−1.01050			−0.505250	+	0.862973i	$0.668600\pi$
$812$	11.8328			0.415250
$813$	−8.54508	+	6.20837i	−0.299689	+	0.217737i
$814$	−29.0344	−	21.0948i	−1.01766	−	0.739371i
$815$	0.218847	+	0.159002i	0.00766588	+	0.00556959i
$816$	−6.35410	−	19.5559i	−0.222438	−	0.684594i
$817$	−9.63525	+	7.00042i	−0.337095	+	0.244914i
$818$	−8.09017	−	24.8990i	−0.282866	−	0.870573i
$819$	−3.43769	+	10.5801i	−0.120123	+	0.369700i
$820$	−0.472136	−	0.343027i	−0.0164877	−	0.0119790i
$821$	7.27051	−	22.3763i	0.253743	−	0.780939i	−0.740332	−	0.672241i	$-0.765332\pi$
$821$	7.27051	−	22.3763i	0.253743	−	0.780939i	0.994075	−	0.108698i	$-0.0346682\pi$
$822$	−1.23607	+	3.80423i	−0.0431128	+	0.132688i
$823$	27.6074	+	20.0579i	0.962333	+	0.699176i	0.953691	−	0.300787i	$-0.0972492\pi$
$823$	27.6074	+	20.0579i	0.962333	+	0.699176i	0.00864171	+	0.999963i	$0.497249\pi$
$824$	4.73607	−	14.5761i	0.164989	−	0.507783i
$825$	−7.85410	−	24.1724i	−0.273445	−	0.841576i
$826$	−2.07295	+	1.50609i	−0.0721271	+	0.0524034i
$827$	−5.66312	−	17.4293i	−0.196926	−	0.606076i	−0.999949	−	0.0101274i	$-0.996776\pi$
$827$	−5.66312	−	17.4293i	−0.196926	−	0.606076i	0.803023	−	0.595948i	$-0.203224\pi$
$828$	−3.47214	−	2.52265i	−0.120665	−	0.0876683i
$829$	−6.70820	−	4.87380i	−0.232986	−	0.169274i	0.465167	−	0.885223i	$-0.345994\pi$
$829$	−6.70820	−	4.87380i	−0.232986	−	0.169274i	−0.698153	+	0.715949i	$0.745994\pi$
$830$	−3.54508	+	2.57565i	−0.123052	+	0.0894023i
$831$	2.32624			0.0806963
$832$	7.85410			0.272292
$833$	−6.85410	+	4.97980i	−0.237481	+	0.172540i
$834$	0.427051	−	1.31433i	0.0147876	−	0.0455114i
$835$	−0.562306	−	1.73060i	−0.0194594	−	0.0598899i
$836$	16.1803			0.559609
$837$		0			0
$838$	−7.23607			−0.249966
$839$	−3.45492	−	10.6331i	−0.119277	−	0.367097i	0.873538	−	0.486756i	$-0.161820\pi$
$839$	−3.45492	−	10.6331i	−0.119277	−	0.367097i	−0.992815	+	0.119659i	$0.961820\pi$
$840$	0.791796	−	2.43690i	0.0273196	−	0.0840810i
$841$	−9.48936	+	6.89442i	−0.327219	+	0.237739i
$842$	31.1246			1.07262
$843$	−10.0344			−0.345605
$844$	4.00000	−	2.90617i	0.137686	−	0.100035i
$845$	−2.95492	−	2.14687i	−0.101652	−	0.0738546i
$846$	−14.7082	−	10.6861i	−0.505678	−	0.367397i
$847$	15.2188	+	46.8388i	0.522926	+	1.60940i
$848$	−2.78115	+	2.02063i	−0.0955052	+	0.0693886i
$849$	−4.19098	−	12.8985i	−0.143834	−	0.442676i
$850$	−10.2812	+	31.6421i	−0.352641	+	1.08532i
$851$	11.8992	+	8.64527i	0.407899	+	0.296356i
$852$	−2.11803	+	6.51864i	−0.0725626	+	0.223325i
$853$	1.23607	−	3.80423i	0.0423222	−	0.130254i	−0.927663	−	0.373419i	$-0.878185\pi$
$853$	1.23607	−	3.80423i	0.0423222	−	0.130254i	0.969985	+	0.243164i	$0.0781855\pi$
$854$	42.9787	+	31.2259i	1.47070	+	1.06853i
$855$	1.18034	−	3.63271i	0.0403668	−	0.124236i
$856$	6.97214	+	21.4580i	0.238303	+	0.733420i
$857$	−11.4721	+	8.33499i	−0.391881	+	0.284718i	−0.766226	−	0.642571i	$-0.777868\pi$
$857$	−11.4721	+	8.33499i	−0.391881	+	0.284718i	0.374345	+	0.927289i	$0.377868\pi$
$858$	4.85410	+	14.9394i	0.165716	+	0.510022i
$859$	45.8779	+	33.3322i	1.56533	+	1.13728i	0.931459	+	0.363846i	$0.118536\pi$
$859$	45.8779	+	33.3322i	1.56533	+	1.13728i	0.633875	+	0.773436i	$0.281464\pi$
$860$	0.454915	+	0.330515i	0.0155125	+	0.0112705i
$861$	6.00000	−	4.35926i	0.204479	−	0.148563i
$862$	40.0689			1.36475
$863$	−40.5066			−1.37886			−0.689430	−	0.724352i	$-0.742139\pi$
$863$	−40.5066			−1.37886			−0.689430	+	0.724352i	$0.742139\pi$
$864$	−13.6803	+	9.93935i	−0.465415	+	0.338144i
$865$	−1.42705	+	4.39201i	−0.0485212	+	0.149333i
$866$	−13.7082	−	42.1895i	−0.465824	−	1.43366i
$867$	0.944272			0.0320692
$868$		0			0
$869$		0			0
$870$	−1.21885	−	3.75123i	−0.0413228	−	0.127178i
$871$	0.135255	−	0.416272i	0.00458294	−	0.0141048i
$872$	33.3156	−	24.2052i	1.12821	−	0.819691i
$873$	37.4164			1.26635
$874$	−28.0902			−0.950164
$875$	−9.13525	+	6.63715i	−0.308828	+	0.224377i
$876$	5.78115	+	4.20025i	0.195327	+	0.141913i
$877$	−24.0344	−	17.4620i	−0.811585	−	0.589651i	0.102704	−	0.994712i	$-0.467250\pi$
$877$	−24.0344	−	17.4620i	−0.811585	−	0.589651i	−0.914290	+	0.405061i	$0.867250\pi$
$878$	−5.91641	−	18.2088i	−0.199669	−	0.614518i
$879$	3.04508	−	2.21238i	0.102708	−	0.0746219i
$880$	3.00000	+	9.23305i	0.101130	+	0.311246i
$881$	−9.07295	+	27.9237i	−0.305675	+	0.940772i	0.673749	+	0.738960i	$0.264683\pi$
$881$	−9.07295	+	27.9237i	−0.305675	+	0.940772i	−0.979424	+	0.201812i	$0.935317\pi$
$882$	5.23607	+	3.80423i	0.176308	+	0.128095i
$883$	0.309017	−	0.951057i	0.0103992	−	0.0320056i	−0.945722	−	0.324976i	$-0.894644\pi$
$883$	0.309017	−	0.951057i	0.0103992	−	0.0320056i	0.956121	+	0.292970i	$0.0946438\pi$
$884$	1.50000	−	4.61653i	0.0504505	−	0.155271i
$885$	0.163119	+	0.118513i	0.00548318	+	0.00398377i
$886$	−0.437694	+	1.34708i	−0.0147046	+	0.0452562i
$887$	−14.8647	−	45.7490i	−0.499109	−	1.53610i	−0.810453	−	0.585803i	$-0.800779\pi$
$887$	−14.8647	−	45.7490i	−0.499109	−	1.53610i	0.311344	−	0.950297i	$-0.399221\pi$
$888$	7.66312	−	5.56758i	0.257157	−	0.186836i
$889$	−5.34346	−	16.4455i	−0.179214	−	0.551564i
$890$	4.30902	+	3.13068i	0.144439	+	0.104941i
$891$	−4.23607	−	3.07768i	−0.141914	−	0.103106i
$892$	−6.35410	+	4.61653i	−0.212751	+	0.154573i
$893$	−28.0902			−0.940002
$894$	19.4721			0.651246
$895$	1.48278	−	1.07730i	0.0495638	−	0.0360102i
$896$	12.6246	−	38.8546i	0.421759	−	1.29804i
$897$	−1.98936	−	6.12261i	−0.0664227	−	0.204428i
$898$	55.1246			1.83953
$899$		0			0
$900$	6.00000			0.200000
$901$	−0.927051	−	2.85317i	−0.0308845	−	0.0950529i
$902$	−6.47214	+	19.9192i	−0.215499	+	0.663236i
$903$	−5.78115	+	4.20025i	−0.192385	+	0.139776i
$904$	−10.8541			−0.361002
$905$	6.49342			0.215849
$906$	24.2254	−	17.6008i	0.804836	−	0.584747i
$907$	9.64590	+	7.00816i	0.320287	+	0.232702i	0.736298	−	0.676658i	$-0.236572\pi$
$907$	9.64590	+	7.00816i	0.320287	+	0.232702i	−0.416011	+	0.909360i	$0.636572\pi$
$908$	−10.8713	−	7.89848i	−0.360778	−	0.262120i
$909$	−5.70820	−	17.5680i	−0.189329	−	0.582695i
$910$	2.78115	−	2.02063i	0.0921943	−	0.0669831i
$911$	4.38197	+	13.4863i	0.145181	+	0.446821i	0.997034	−	0.0769594i	$-0.0245212\pi$
$911$	4.38197	+	13.4863i	0.145181	+	0.446821i	−0.851853	+	0.523781i	$0.824521\pi$
$912$	−7.50000	+	23.0826i	−0.248350	+	0.764342i
$913$	30.0344	+	21.8213i	0.993995	+	0.722180i
$914$	−13.3713	+	41.1527i	−0.442284	+	1.36121i
$915$	1.29180	−	3.97574i	0.0427055	−	0.131434i
$916$	−1.38197	−	1.00406i	−0.0456614	−	0.0331750i
$917$	−10.2812	+	31.6421i	−0.339514	+	1.04492i
$918$	−10.5902	−	32.5932i	−0.349528	−	1.07574i
$919$	−40.5517	+	29.4625i	−1.33768	+	0.971878i	−0.338150	+	0.941092i	$0.609801\pi$
$919$	−40.5517	+	29.4625i	−1.33768	+	0.971878i	−0.999526	+	0.0307862i	$0.990199\pi$
$920$	−0.916408	−	2.82041i	−0.0302131	−	0.0929863i
$921$	4.11803	+	2.99193i	0.135694	+	0.0985873i
$922$	−41.5517	−	30.1891i	−1.36843	−	0.994223i
$923$	16.6353	−	12.0862i	0.547556	−	0.397823i
$924$	9.70820			0.319376
$925$	−20.5623			−0.676084
$926$	11.9443	−	8.67802i	0.392513	−	0.285177i
$927$	4.23607	−	13.0373i	0.139131	−	0.428200i
$928$	−6.66970	−	20.5272i	−0.218944	−	0.673839i
$929$	33.5410			1.10045			0.550223	−	0.835018i	$-0.314543\pi$
$929$	33.5410			1.10045			0.550223	+	0.835018i	$0.314543\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	−1.10739	−	3.40820i	−0.0362738	−	0.111639i
$933$	2.32624	−	7.15942i	0.0761576	−	0.234389i
$934$	−50.7599	+	36.8792i	−1.66091	+	1.20672i
$935$	−8.47214			−0.277068
$936$	8.29180			0.271026
$937$	35.9894	−	26.1478i	1.17572	−	0.854211i	0.184038	−	0.982919i	$-0.441083\pi$
$937$	35.9894	−	26.1478i	1.17572	−	0.854211i	0.991683	+	0.128708i	$0.0410829\pi$
$938$	−0.927051	−	0.673542i	−0.0302693	−	0.0219919i
$939$	−2.61803	−	1.90211i	−0.0854363	−	0.0620731i
$940$	0.409830	+	1.26133i	0.0133672	+	0.0411400i
$941$	44.8328	−	32.5729i	1.46151	−	1.06185i	0.478541	−	0.878065i	$-0.341166\pi$
$941$	44.8328	−	32.5729i	1.46151	−	1.06185i	0.982967	−	0.183783i	$-0.0588342\pi$
$942$	−1.85410	−	5.70634i	−0.0604099	−	0.185923i
$943$	2.65248	−	8.16348i	0.0863765	−	0.265840i
$944$	2.07295	+	1.50609i	0.0674687	+	0.0490189i
$945$	1.77051	−	5.44907i	0.0575947	−	0.177258i
$946$	6.23607	−	19.1926i	0.202752	−	0.624007i
$947$	−29.1803	−	21.2008i	−0.948234	−	0.688932i	0.00215480	−	0.999998i	$-0.499314\pi$
$947$	−29.1803	−	21.2008i	−0.948234	−	0.688932i	−0.950388	+	0.311066i	$0.899314\pi$
$948$		0			0
$949$	−6.62461	−	20.3885i	−0.215044	−	0.661837i
$950$	31.7705	−	23.0826i	1.03077	−	0.748899i
$951$	−3.05573	−	9.40456i	−0.0990888	−	0.304964i
$952$	22.9894	+	16.7027i	0.745089	+	0.541339i
$953$	−7.45492	−	5.41631i	−0.241488	−	0.175452i	0.460458	−	0.887682i	$-0.347685\pi$
$953$	−7.45492	−	5.41631i	−0.241488	−	0.175452i	−0.701946	+	0.712230i	$0.747685\pi$
$954$	−1.85410	+	1.34708i	−0.0600288	+	0.0436135i
$955$	1.87539			0.0606861
$956$	−8.29180			−0.268176
$957$	−27.0344	+	19.6417i	−0.873899	+	0.634925i
$958$	4.47214	−	13.7638i	0.144488	−	0.444689i
$959$	−2.29180	−	7.05342i	−0.0740060	−	0.227767i
$960$	−1.61803			−0.0522218
$961$		0			0
$962$	12.7082			0.409729
$963$	6.23607	+	19.1926i	0.200954	+	0.618474i
$964$	3.33688	−	10.2699i	0.107474	−	0.330770i
$965$	−1.42705	+	1.03681i	−0.0459384	+	0.0333762i
$966$	−16.8541			−0.542272
$967$	−12.3475			−0.397070			−0.198535	−	0.980094i	$-0.563618\pi$
$967$	−12.3475			−0.397070			−0.198535	+	0.980094i	$0.563618\pi$
$968$	29.6976	−	21.5765i	0.954516	−	0.693496i
$969$	−17.1353	−	12.4495i	−0.550464	−	0.399935i
$970$	−9.35410	−	6.79615i	−0.300342	−	0.218211i
$971$	−0.135255	−	0.416272i	−0.00434054	−	0.0133588i	0.948863	−	0.315689i	$-0.102236\pi$
$971$	−0.135255	−	0.416272i	−0.00434054	−	0.0133588i	−0.953203	+	0.302330i	$0.902236\pi$
$972$	−8.00000	+	5.81234i	−0.256600	+	0.186431i
$973$	0.791796	+	2.43690i	0.0253838	+	0.0781234i
$974$	20.9615	−	64.5128i	0.671650	−	2.06712i
$975$	7.28115	+	5.29007i	0.233184	+	0.169418i
$976$	16.4164	−	50.5245i	0.525476	−	1.61725i
$977$	16.0902	−	49.5205i	0.514770	−	1.58430i	−0.268930	−	0.963160i	$-0.586670\pi$
$977$	16.0902	−	49.5205i	0.514770	−	1.58430i	0.783700	−	0.621140i	$-0.213330\pi$
$978$	−0.927051	−	0.673542i	−0.0296438	−	0.0215375i
$979$	13.9443	−	42.9161i	0.445661	−	1.37160i
$980$	−0.145898	−	0.449028i	−0.00466054	−	0.0143437i
$981$	29.7984	−	21.6498i	0.951389	−	0.691224i
$982$	−10.7984	−	33.2340i	−0.344590	−	1.06054i
$983$	−6.50000	−	4.72253i	−0.207318	−	0.150625i	0.479282	−	0.877661i	$-0.340897\pi$
$983$	−6.50000	−	4.72253i	−0.207318	−	0.150625i	−0.686599	+	0.727036i	$0.740897\pi$
$984$	−4.47214	−	3.24920i	−0.142566	−	0.103581i
$985$	3.21885	−	2.33863i	0.102561	−	0.0745149i
$986$	43.7426			1.39305
$987$	−16.8541			−0.536472
$988$	−4.63525	+	3.36771i	−0.147467	+	0.107141i
$989$	−2.55573	+	7.86572i	−0.0812674	+	0.250115i
$990$	2.00000	+	6.15537i	0.0635642	+	0.195630i
$991$	−16.2705			−0.516850			−0.258425	−	0.966031i	$-0.583203\pi$
$991$	−16.2705			−0.516850			−0.258425	+	0.966031i	$0.583203\pi$
$992$		0			0
$993$	22.2705			0.706733
$994$	−16.6353	−	51.1981i	−0.527638	−	1.62390i
$995$	−1.56888	+	4.82853i	−0.0497370	+	0.153075i
$996$	3.54508	−	2.57565i	0.112330	−	0.0816128i
$997$	53.2492			1.68642			0.843210	−	0.537584i	$-0.180663\pi$
$997$	53.2492			1.68642			0.843210	+	0.537584i	$0.180663\pi$
$998$	−17.5623			−0.555925
$999$	17.1353	−	12.4495i	0.542135	−	0.393884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.e.531.1		4
31.2	even	5		961.2.d.b.388.1		4
31.3	odd	30		961.2.c.f.439.2		4
31.4	even	5		961.2.d.b.374.1		4
31.5	even	3		961.2.g.g.844.1		8
31.6	odd	6		961.2.g.f.547.1		8
31.7	even	15		961.2.g.c.816.1		8
31.8	even	5	inner	961.2.d.e.628.1		4
31.9	even	15		961.2.g.g.448.1		8
31.10	even	15		961.2.g.c.338.1		8
31.11	odd	30		961.2.g.b.732.1		8
31.12	odd	30		961.2.g.b.235.1		8
31.13	odd	30		961.2.c.f.521.2		4
31.14	even	15		961.2.g.g.846.1		8
31.15	odd	10		961.2.a.d.1.2		2
31.16	even	5		961.2.a.e.1.2		2
31.17	odd	30		961.2.g.f.846.1		8
31.18	even	15		961.2.c.d.521.2		4
31.19	even	15		961.2.g.c.235.1		8
31.20	even	15		961.2.g.c.732.1		8
31.21	odd	30		961.2.g.b.338.1		8
31.22	odd	30		961.2.g.f.448.1		8
31.23	odd	10		961.2.d.f.628.1		4
31.24	odd	30		961.2.g.b.816.1		8
31.25	even	3		961.2.g.g.547.1		8
31.26	odd	6		961.2.g.f.844.1		8
31.27	odd	10		31.2.d.a.2.1	✓	4
31.28	even	15		961.2.c.d.439.2		4
31.29	odd	10		31.2.d.a.16.1	yes	4
31.30	odd	2		961.2.d.f.531.1		4
93.29	even	10		279.2.i.a.109.1		4
93.47	odd	10		8649.2.a.f.1.1		2
93.77	even	10		8649.2.a.g.1.1		2
93.89	even	10		279.2.i.a.64.1		4
124.27	even	10		496.2.n.b.33.1		4
124.91	even	10		496.2.n.b.481.1		4
155.27	even	20		775.2.bf.a.374.2		8
155.29	odd	10		775.2.k.c.326.1		4
155.58	even	20		775.2.bf.a.374.1		8
155.89	odd	10		775.2.k.c.126.1		4
155.122	even	20		775.2.bf.a.574.1		8
155.153	even	20		775.2.bf.a.574.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.2.1	✓	4	31.27	odd	10
31.2.d.a.16.1	yes	4	31.29	odd	10
279.2.i.a.64.1		4	93.89	even	10
279.2.i.a.109.1		4	93.29	even	10
496.2.n.b.33.1		4	124.27	even	10
496.2.n.b.481.1		4	124.91	even	10
775.2.k.c.126.1		4	155.89	odd	10
775.2.k.c.326.1		4	155.29	odd	10
775.2.bf.a.374.1		8	155.58	even	20
775.2.bf.a.374.2		8	155.27	even	20
775.2.bf.a.574.1		8	155.122	even	20
775.2.bf.a.574.2		8	155.153	even	20
961.2.a.d.1.2		2	31.15	odd	10
961.2.a.e.1.2		2	31.16	even	5
961.2.c.d.439.2		4	31.28	even	15
961.2.c.d.521.2		4	31.18	even	15
961.2.c.f.439.2		4	31.3	odd	30
961.2.c.f.521.2		4	31.13	odd	30
961.2.d.b.374.1		4	31.4	even	5
961.2.d.b.388.1		4	31.2	even	5
961.2.d.e.531.1		4	1.1	even	1	trivial
961.2.d.e.628.1		4	31.8	even	5	inner
961.2.d.f.531.1		4	31.30	odd	2
961.2.d.f.628.1		4	31.23	odd	10
961.2.g.b.235.1		8	31.12	odd	30
961.2.g.b.338.1		8	31.21	odd	30
961.2.g.b.732.1		8	31.11	odd	30
961.2.g.b.816.1		8	31.24	odd	30
961.2.g.c.235.1		8	31.19	even	15
961.2.g.c.338.1		8	31.10	even	15
961.2.g.c.732.1		8	31.20	even	15
961.2.g.c.816.1		8	31.7	even	15
961.2.g.f.448.1		8	31.22	odd	30
961.2.g.f.547.1		8	31.6	odd	6
961.2.g.f.844.1		8	31.26	odd	6
961.2.g.f.846.1		8	31.17	odd	30
961.2.g.g.448.1		8	31.9	even	15
961.2.g.g.547.1		8	31.25	even	3
961.2.g.g.844.1		8	31.5	even	3
961.2.g.g.846.1		8	31.14	even	15
8649.2.a.f.1.1		2	93.47	odd	10
8649.2.a.g.1.1		2	93.77	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 1.53884i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.500000 + 0.363271i) q^{4} -0.381966 q^{5} +1.61803 q^{6} +(-2.42705 + 1.76336i) q^{7} +(1.80902 + 1.31433i) q^{8} +(1.61803 + 1.17557i) q^{9} +(-0.190983 - 0.587785i) q^{10} +(-4.23607 + 3.07768i) q^{11} +(0.190983 + 0.587785i) q^{12} +(0.572949 - 1.76336i) q^{13} +(-3.92705 - 2.85317i) q^{14} +(-0.118034 + 0.363271i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(-3.42705 - 2.48990i) q^{17} +(-1.00000 + 3.07768i) q^{18} +(1.54508 + 4.75528i) q^{19} +(0.190983 - 0.138757i) q^{20} +(0.927051 + 2.85317i) q^{21} +(-6.85410 - 4.97980i) q^{22} +(2.80902 + 2.04087i) q^{23} +(1.80902 - 1.31433i) q^{24} -4.85410 q^{25} +3.00000 q^{26} +(4.04508 - 2.93893i) q^{27} +(0.572949 - 1.76336i) q^{28} +(1.97214 + 6.06961i) q^{29} -0.618034 q^{30} -3.38197 q^{32} +(1.61803 + 4.97980i) q^{33} +(2.11803 - 6.51864i) q^{34} +(0.927051 - 0.673542i) q^{35} -1.23607 q^{36} +4.23607 q^{37} +(-6.54508 + 4.75528i) q^{38} +(-1.50000 - 1.08981i) q^{39} +(-0.690983 - 0.502029i) q^{40} +(-0.763932 - 2.35114i) q^{41} +(-3.92705 + 2.85317i) q^{42} +(0.736068 + 2.26538i) q^{43} +(1.00000 - 3.07768i) q^{44} +(-0.618034 - 0.449028i) q^{45} +(-1.73607 + 5.34307i) q^{46} +(-1.73607 + 5.34307i) q^{47} +(3.92705 + 2.85317i) q^{48} +(0.618034 - 1.90211i) q^{49} +(-2.42705 - 7.46969i) q^{50} +(-3.42705 + 2.48990i) q^{51} +(0.354102 + 1.08981i) q^{52} +(0.572949 + 0.416272i) q^{53} +(6.54508 + 4.75528i) q^{54} +(1.61803 - 1.17557i) q^{55} -6.70820 q^{56} +5.00000 q^{57} +(-8.35410 + 6.06961i) q^{58} +(0.163119 - 0.502029i) q^{59} +(-0.0729490 - 0.224514i) q^{60} -10.9443 q^{61} -6.00000 q^{63} +(1.30902 + 4.02874i) q^{64} +(-0.218847 + 0.673542i) q^{65} +(-6.85410 + 4.97980i) q^{66} +0.236068 q^{67} +2.61803 q^{68} +(2.80902 - 2.04087i) q^{69} +(1.50000 + 1.08981i) q^{70} +(8.97214 + 6.51864i) q^{71} +(1.38197 + 4.25325i) q^{72} +(9.35410 - 6.79615i) q^{73} +(2.11803 + 6.51864i) q^{74} +(-1.50000 + 4.61653i) q^{75} +(-2.50000 - 1.81636i) q^{76} +(4.85410 - 14.9394i) q^{77} +(0.927051 - 2.85317i) q^{78} +(0.572949 - 1.76336i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.23607 - 2.35114i) q^{82} +(-2.19098 - 6.74315i) q^{83} +(-1.50000 - 1.08981i) q^{84} +(1.30902 + 0.951057i) q^{85} +(-3.11803 + 2.26538i) q^{86} +6.38197 q^{87} -11.7082 q^{88} +(-6.97214 + 5.06555i) q^{89} +(0.381966 - 1.17557i) q^{90} +(1.71885 + 5.29007i) q^{91} -2.14590 q^{92} -9.09017 q^{94} +(-0.590170 - 1.81636i) q^{95} +(-1.04508 + 3.21644i) q^{96} +(15.1353 - 10.9964i) q^{97} +3.23607 q^{98} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} + 5 q^{8} + 2 q^{9} - 3 q^{10} - 8 q^{11} + 3 q^{12} + 9 q^{13} - 9 q^{14} + 4 q^{15} - 6 q^{16} - 7 q^{17} - 4 q^{18} - 5 q^{19} + 3 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 + 5 * q^8 + 2 * q^9 - 3 * q^10 - 8 * q^11 + 3 * q^12 + 9 * q^13 - 9 * q^14 + 4 * q^15 - 6 * q^16 - 7 * q^17 - 4 * q^18 - 5 * q^19 + 3 * q^20 - 3 * q^21 - 14 * q^22 + 9 * q^23 + 5 * q^24 - 6 * q^25 + 12 * q^26 + 5 * q^27 + 9 * q^28 - 10 * q^29 + 2 * q^30 - 18 * q^32 + 2 * q^33 + 4 * q^34 - 3 * q^35 + 4 * q^36 + 8 * q^37 - 15 * q^38 - 6 * q^39 - 5 * q^40 - 12 * q^41 - 9 * q^42 - 6 * q^43 + 4 * q^44 + 2 * q^45 + 2 * q^46 + 2 * q^47 + 9 * q^48 - 2 * q^49 - 3 * q^50 - 7 * q^51 - 12 * q^52 + 9 * q^53 + 15 * q^54 + 2 * q^55 + 20 * q^57 - 20 * q^58 - 15 * q^59 - 7 * q^60 - 8 * q^61 - 24 * q^63 + 3 * q^64 - 21 * q^65 - 14 * q^66 - 8 * q^67 + 6 * q^68 + 9 * q^69 + 6 * q^70 + 18 * q^71 + 10 * q^72 + 24 * q^73 + 4 * q^74 - 6 * q^75 - 10 * q^76 + 6 * q^77 - 3 * q^78 + 9 * q^80 - q^81 + 4 * q^82 - 11 * q^83 - 6 * q^84 + 3 * q^85 - 8 * q^86 + 30 * q^87 - 20 * q^88 - 10 * q^89 + 6 * q^90 + 27 * q^91 - 22 * q^92 - 14 * q^94 + 20 * q^95 + 7 * q^96 + 27 * q^97 + 4 * q^98 - 24 * q^99

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