LMFDB - Embedded newform 242.2.c.f.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [242,2,Mod(3,242)] 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("242.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.93237972891$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$-0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	242.81
Dual form			242.2.c.f.3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.844250 + 2.59833i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.40126 + 1.01807i) q^{5} +(2.21028 - 1.60586i) q^{6} +(0.391818 + 1.20589i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-3.61153 - 2.62393i) q^{9} +1.73205 q^{10} -2.73205 q^{12} +(-2.42705 - 1.76336i) q^{13} +(0.391818 - 1.20589i) q^{14} +(-1.46228 - 4.50045i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.20378 + 3.05422i) q^{17} +(1.37948 + 4.24561i) q^{18} +(1.46228 - 4.50045i) q^{19} +(-1.40126 - 1.01807i) q^{20} -3.46410 q^{21} -4.73205 q^{23} +(2.21028 + 1.60586i) q^{24} +(-0.618034 + 1.90211i) q^{25} +(0.927051 + 2.85317i) q^{26} +(3.23607 - 2.35114i) q^{27} +(-1.02579 + 0.745282i) q^{28} +(-0.927051 - 2.85317i) q^{29} +(-1.46228 + 4.50045i) q^{30} +(8.24886 + 5.99315i) q^{31} +1.00000 q^{32} +5.19615 q^{34} +(-1.77672 - 1.29087i) q^{35} +(1.37948 - 4.24561i) q^{36} +(0.987665 + 3.03972i) q^{37} +(-3.82831 + 2.78143i) q^{38} +(6.63083 - 4.81758i) q^{39} +(0.535233 + 1.64728i) q^{40} +(-3.45980 + 10.6482i) q^{41} +(2.80252 + 2.03615i) q^{42} +7.73205 q^{45} +(3.82831 + 2.78143i) q^{46} +(0.678648 - 2.08867i) q^{47} +(-0.844250 - 2.59833i) q^{48} +(4.36247 - 3.16952i) q^{49} +(1.61803 - 1.17557i) q^{50} +(-4.38685 - 13.5013i) q^{51} +(0.927051 - 2.85317i) q^{52} +(-0.650326 - 0.472490i) q^{53} -4.00000 q^{54} +1.26795 q^{56} +(10.4591 + 7.59901i) q^{57} +(-0.927051 + 2.85317i) q^{58} +(0.783636 + 2.41178i) q^{59} +(3.82831 - 2.78143i) q^{60} +(-7.65662 + 5.56286i) q^{61} +(-3.15078 - 9.69712i) q^{62} +(1.74911 - 5.38322i) q^{63} +(-0.809017 - 0.587785i) q^{64} +5.19615 q^{65} +0.196152 q^{67} +(-4.20378 - 3.05422i) q^{68} +(3.99503 - 12.2955i) q^{69} +(0.678648 + 2.08867i) q^{70} +(2.05158 - 1.49056i) q^{71} +(-3.61153 + 2.62393i) q^{72} +(3.99503 + 12.2955i) q^{73} +(0.987665 - 3.03972i) q^{74} +(-4.42055 - 3.21172i) q^{75} +4.73205 q^{76} -8.19615 q^{78} +(1.02579 + 0.745282i) q^{79} +(0.535233 - 1.64728i) q^{80} +(-0.761449 - 2.34350i) q^{81} +(9.05788 - 6.58093i) q^{82} +(1.77672 - 1.29087i) q^{83} +(-1.07047 - 3.29456i) q^{84} +(2.78115 - 8.55951i) q^{85} +8.19615 q^{87} -0.464102 q^{89} +(-6.25536 - 4.54479i) q^{90} +(1.17545 - 3.61767i) q^{91} +(-1.46228 - 4.50045i) q^{92} +(-22.5363 + 16.3736i) q^{93} +(-1.77672 + 1.29087i) q^{94} +(2.53275 + 7.79500i) q^{95} +(-0.844250 + 2.59833i) q^{96} +(0.809017 + 0.587785i) q^{97} -5.39230 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 6 q^{7} - 2 q^{8} - 2 q^{9} - 8 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{18} - 6 q^{19} - 24 q^{23} + 2 q^{24} + 4 q^{25} - 6 q^{26} + 8 q^{27}+ \cdots + 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 6 * q^7 - 2 * q^8 - 2 * q^9 - 8 * q^12 - 6 * q^13 - 6 * q^14 + 6 * q^15 - 2 * q^16 - 2 * q^18 - 6 * q^19 - 24 * q^23 + 2 * q^24 + 4 * q^25 - 6 * q^26 + 8 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 10 * q^31 + 8 * q^32 + 6 * q^35 - 2 * q^36 + 4 * q^37 - 6 * q^38 + 6 * q^39 + 12 * q^41 + 48 * q^45 + 6 * q^46 + 6 * q^47 + 2 * q^48 - 10 * q^49 + 4 * q^50 + 18 * q^51 - 6 * q^52 - 12 * q^53 - 32 * q^54 + 24 * q^56 + 12 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 + 10 * q^62 + 6 * q^63 - 2 * q^64 - 40 * q^67 - 12 * q^69 + 6 * q^70 + 12 * q^71 - 2 * q^72 - 12 * q^73 + 4 * q^74 - 4 * q^75 + 24 * q^76 - 24 * q^78 + 6 * q^79 - 2 * q^81 + 12 * q^82 - 6 * q^83 - 18 * q^85 + 24 * q^87 + 24 * q^89 - 12 * q^90 - 18 * q^91 + 6 * q^92 - 28 * q^93 + 6 * q^94 - 6 * q^95 + 2 * q^96 + 2 * q^97 + 40 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.844250	+	2.59833i	−0.487428	+	1.50015i	0.341005	+	0.940061i	$0.389233\pi$
$3$	−0.844250	+	2.59833i	−0.487428	+	1.50015i	−0.828433	+	0.560088i	$0.810767\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.40126	+	1.01807i	−0.626662	+	0.455296i	−0.855242	−	0.518229i	$-0.826592\pi$
$5$	−1.40126	+	1.01807i	−0.626662	+	0.455296i	0.228580	+	0.973525i	$0.426592\pi$
$6$	2.21028	−	1.60586i	0.902341	−	0.655589i
$7$	0.391818	+	1.20589i	0.148093	+	0.455784i	0.997396	−	0.0721223i	$-0.0229772\pi$
$7$	0.391818	+	1.20589i	0.148093	+	0.455784i	−0.849303	+	0.527906i	$0.822977\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−3.61153	−	2.62393i	−1.20384	−	0.874644i
$10$	1.73205			0.547723
$11$		0			0
$11$		0			0
$12$	−2.73205			−0.788675
$13$	−2.42705	−	1.76336i	−0.673143	−	0.489067i	0.197933	−	0.980216i	$-0.436577\pi$
$13$	−2.42705	−	1.76336i	−0.673143	−	0.489067i	−0.871076	+	0.491149i	$0.836577\pi$
$14$	0.391818	−	1.20589i	0.104718	−	0.322288i
$15$	−1.46228	−	4.50045i	−0.377560	−	1.16201i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.20378	+	3.05422i	−1.01957	+	0.740758i	−0.966194	−	0.257817i	$-0.916997\pi$
$17$	−4.20378	+	3.05422i	−1.01957	+	0.740758i	−0.0533716	+	0.998575i	$0.516997\pi$
$18$	1.37948	+	4.24561i	0.325147	+	1.00070i
$19$	1.46228	−	4.50045i	0.335471	−	1.03247i	−0.631019	−	0.775768i	$-0.717363\pi$
$19$	1.46228	−	4.50045i	0.335471	−	1.03247i	0.966490	−	0.256706i	$-0.0826371\pi$
$20$	−1.40126	−	1.01807i	−0.313331	−	0.227648i
$21$	−3.46410			−0.755929
$22$		0			0
$23$	−4.73205			−0.986701			−0.493350	−	0.869831i	$-0.664228\pi$
$23$	−4.73205			−0.986701			−0.493350	+	0.869831i	$0.664228\pi$
$24$	2.21028	+	1.60586i	0.451171	+	0.327795i
$25$	−0.618034	+	1.90211i	−0.123607	+	0.380423i
$26$	0.927051	+	2.85317i	0.181810	+	0.559553i
$27$	3.23607	−	2.35114i	0.622782	−	0.452477i
$28$	−1.02579	+	0.745282i	−0.193857	+	0.140845i
$29$	−0.927051	−	2.85317i	−0.172149	−	0.529820i	0.827343	−	0.561697i	$-0.189851\pi$
$29$	−0.927051	−	2.85317i	−0.172149	−	0.529820i	−0.999492	+	0.0318771i	$0.989851\pi$
$30$	−1.46228	+	4.50045i	−0.266975	+	0.821666i
$31$	8.24886	+	5.99315i	1.48154	+	1.07640i	0.977057	+	0.212979i	$0.0683166\pi$
$31$	8.24886	+	5.99315i	1.48154	+	1.07640i	0.504482	+	0.863422i	$0.331683\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	5.19615			0.891133
$35$	−1.77672	−	1.29087i	−0.300321	−	0.218196i
$36$	1.37948	−	4.24561i	0.229914	−	0.707602i
$37$	0.987665	+	3.03972i	0.162371	+	0.499727i	0.998833	−	0.0482981i	$-0.0153798\pi$
$37$	0.987665	+	3.03972i	0.162371	+	0.499727i	−0.836462	+	0.548025i	$0.815380\pi$
$38$	−3.82831	+	2.78143i	−0.621034	+	0.451207i
$39$	6.63083	−	4.81758i	1.06178	−	0.771430i
$40$	0.535233	+	1.64728i	0.0846278	+	0.260458i
$41$	−3.45980	+	10.6482i	−0.540330	+	1.66297i	0.191511	+	0.981490i	$0.438661\pi$
$41$	−3.45980	+	10.6482i	−0.540330	+	1.66297i	−0.731841	+	0.681475i	$0.761339\pi$
$42$	2.80252	+	2.03615i	0.432438	+	0.314184i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	7.73205			1.15263
$46$	3.82831	+	2.78143i	0.564453	+	0.410099i
$47$	0.678648	−	2.08867i	0.0989910	−	0.304663i	−0.889282	−	0.457359i	$-0.848795\pi$
$47$	0.678648	−	2.08867i	0.0989910	−	0.304663i	0.988273	+	0.152696i	$0.0487955\pi$
$48$	−0.844250	−	2.59833i	−0.121857	−	0.375037i
$49$	4.36247	−	3.16952i	0.623209	−	0.452788i
$50$	1.61803	−	1.17557i	0.228825	−	0.166251i
$51$	−4.38685	−	13.5013i	−0.614282	−	1.89057i
$52$	0.927051	−	2.85317i	0.128559	−	0.395663i
$53$	−0.650326	−	0.472490i	−0.0893292	−	0.0649015i	0.542224	−	0.840234i	$-0.317582\pi$
$53$	−0.650326	−	0.472490i	−0.0893292	−	0.0649015i	−0.631553	+	0.775332i	$0.717582\pi$
$54$	−4.00000			−0.544331
$55$		0			0
$56$	1.26795			0.169437
$57$	10.4591	+	7.59901i	1.38535	+	1.00651i
$58$	−0.927051	+	2.85317i	−0.121728	+	0.374640i
$59$	0.783636	+	2.41178i	0.102021	+	0.313987i	0.989020	−	0.147784i	$-0.0472141\pi$
$59$	0.783636	+	2.41178i	0.102021	+	0.313987i	−0.886999	+	0.461771i	$0.847214\pi$
$60$	3.82831	−	2.78143i	0.494233	−	0.359081i
$61$	−7.65662	+	5.56286i	−0.980330	+	0.712251i	−0.957782	−	0.287495i	$-0.907178\pi$
$61$	−7.65662	+	5.56286i	−0.980330	+	0.712251i	−0.0225474	+	0.999746i	$0.507178\pi$
$62$	−3.15078	−	9.69712i	−0.400150	−	1.23154i
$63$	1.74911	−	5.38322i	0.220368	−	0.678222i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	5.19615			0.644503
$66$		0			0
$67$	0.196152			0.0239638			0.0119819	−	0.999928i	$-0.496186\pi$
$67$	0.196152			0.0239638			0.0119819	+	0.999928i	$0.496186\pi$
$68$	−4.20378	−	3.05422i	−0.509783	−	0.370379i
$69$	3.99503	−	12.2955i	0.480946	−	1.48020i
$70$	0.678648	+	2.08867i	0.0811140	+	0.249643i
$71$	2.05158	−	1.49056i	0.243478	−	0.176897i	−0.459353	−	0.888254i	$-0.651919\pi$
$71$	2.05158	−	1.49056i	0.243478	−	0.176897i	0.702832	+	0.711356i	$0.251919\pi$
$72$	−3.61153	+	2.62393i	−0.425623	+	0.309233i
$73$	3.99503	+	12.2955i	0.467583	+	1.43907i	0.855704	+	0.517465i	$0.173124\pi$
$73$	3.99503	+	12.2955i	0.467583	+	1.43907i	−0.388121	+	0.921609i	$0.626876\pi$
$74$	0.987665	−	3.03972i	0.114814	−	0.353360i
$75$	−4.42055	−	3.21172i	−0.510441	−	0.370857i
$76$	4.73205			0.542803
$77$		0			0
$78$	−8.19615			−0.928032
$79$	1.02579	+	0.745282i	0.115411	+	0.0838508i	0.643993	−	0.765031i	$-0.277276\pi$
$79$	1.02579	+	0.745282i	0.115411	+	0.0838508i	−0.528583	+	0.848882i	$0.677276\pi$
$80$	0.535233	−	1.64728i	0.0598409	−	0.184171i
$81$	−0.761449	−	2.34350i	−0.0846055	−	0.260389i
$82$	9.05788	−	6.58093i	1.00028	−	0.726743i
$83$	1.77672	−	1.29087i	0.195021	−	0.141691i	−0.485990	−	0.873965i	$-0.661541\pi$
$83$	1.77672	−	1.29087i	0.195021	−	0.141691i	0.681011	+	0.732274i	$0.261541\pi$
$84$	−1.07047	−	3.29456i	−0.116797	−	0.359466i
$85$	2.78115	−	8.55951i	0.301658	−	0.928409i
$86$		0			0
$87$	8.19615			0.878720
$88$		0			0
$89$	−0.464102			−0.0491947			−0.0245973	−	0.999697i	$-0.507830\pi$
$89$	−0.464102			−0.0491947			−0.0245973	+	0.999697i	$0.507830\pi$
$90$	−6.25536	−	4.54479i	−0.659373	−	0.479062i
$91$	1.17545	−	3.61767i	0.123221	−	0.379235i
$92$	−1.46228	−	4.50045i	−0.152454	−	0.469204i
$93$	−22.5363	+	16.3736i	−2.33691	+	1.69786i
$94$	−1.77672	+	1.29087i	−0.183255	+	0.133143i
$95$	2.53275	+	7.79500i	0.259855	+	0.799751i
$96$	−0.844250	+	2.59833i	−0.0861659	+	0.265191i
$97$	0.809017	+	0.587785i	0.0821432	+	0.0596806i	0.628099	−	0.778133i	$-0.283833\pi$
$97$	0.809017	+	0.587785i	0.0821432	+	0.0596806i	−0.545956	+	0.837814i	$0.683833\pi$
$98$	−5.39230			−0.544705
$99$		0			0
$100$	−2.00000			−0.200000
$101$	3.55345	+	2.58173i	0.353581	+	0.256892i	0.750370	−	0.661018i	$-0.229875\pi$
$101$	3.55345	+	2.58173i	0.353581	+	0.256892i	−0.396789	+	0.917910i	$0.629875\pi$
$102$	−4.38685	+	13.5013i	−0.434363	+	1.33683i
$103$	3.82943	+	11.7858i	0.377325	+	1.16129i	0.941896	+	0.335903i	$0.109042\pi$
$103$	3.82943	+	11.7858i	0.377325	+	1.16129i	−0.564571	+	0.825384i	$0.690958\pi$
$104$	−2.42705	+	1.76336i	−0.237992	+	0.172911i
$105$	4.85410	−	3.52671i	0.473712	−	0.344172i
$106$	0.248403	+	0.764504i	0.0241270	+	0.0742552i
$107$	−5.74415	+	17.6787i	−0.555308	+	1.70906i	0.139821	+	0.990177i	$0.455347\pi$
$107$	−5.74415	+	17.6787i	−0.555308	+	1.70906i	−0.695129	+	0.718885i	$0.744653\pi$
$108$	3.23607	+	2.35114i	0.311391	+	0.226239i
$109$	−15.9282			−1.52565			−0.762823	−	0.646608i	$-0.776187\pi$
$109$	−15.9282			−1.52565			−0.762823	+	0.646608i	$0.776187\pi$
$110$		0			0
$111$	−8.73205			−0.828810
$112$	−1.02579	−	0.745282i	−0.0969283	−	0.0704225i
$113$	−5.20892	+	16.0314i	−0.490014	+	1.50811i	0.334572	+	0.942370i	$0.391408\pi$
$113$	−5.20892	+	16.0314i	−0.490014	+	1.50811i	−0.824586	+	0.565737i	$0.808592\pi$
$114$	−3.99503	−	12.2955i	−0.374169	−	1.15157i
$115$	6.63083	−	4.81758i	0.618328	−	0.449241i
$116$	2.42705	−	1.76336i	0.225346	−	0.163723i
$117$	4.13845	+	12.7368i	0.382600	+	1.17752i
$118$	0.783636	−	2.41178i	0.0721395	−	0.222023i
$119$	−5.33017	−	3.87260i	−0.488616	−	0.355000i
$120$	−4.73205			−0.431975
$121$		0			0
$122$	9.46410			0.856840
$123$	−24.7466	−	17.9794i	−2.23132	−	1.62115i
$124$	−3.15078	+	9.69712i	−0.282949	+	0.870827i
$125$	−3.74663	−	11.5309i	−0.335109	−	1.03136i
$126$	−4.57924	+	3.32701i	−0.407951	+	0.296394i
$127$	11.2101	−	8.14459i	0.994733	−	0.722716i	0.0337803	−	0.999429i	$-0.489245\pi$
$127$	11.2101	−	8.14459i	0.994733	−	0.722716i	0.960952	+	0.276714i	$0.0892454\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	−4.20378	−	3.05422i	−0.368696	−	0.267873i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	6.00000			0.520266
$134$	−0.158691	−	0.115296i	−0.0137088	−	0.00996001i
$135$	−2.14093	+	6.58911i	−0.184262	+	0.567101i
$136$	1.60570	+	4.94183i	0.137688	+	0.423759i
$137$	2.05158	−	1.49056i	0.175279	−	0.127347i	−0.496687	−	0.867930i	$-0.665450\pi$
$137$	2.05158	−	1.49056i	0.175279	−	0.127347i	0.671966	+	0.740582i	$0.265450\pi$
$138$	−10.4591	+	7.59901i	−0.890341	+	0.646870i
$139$	3.02956	+	9.32401i	0.256964	+	0.790852i	0.993436	+	0.114385i	$0.0364899\pi$
$139$	3.02956	+	9.32401i	0.256964	+	0.790852i	−0.736473	+	0.676467i	$0.763510\pi$
$140$	0.678648	−	2.08867i	0.0573563	−	0.176524i
$141$	4.85410	+	3.52671i	0.408789	+	0.297003i
$142$	−2.53590			−0.212808
$143$		0			0
$144$	4.46410			0.372008
$145$	4.20378	+	3.05422i	0.349105	+	0.253639i
$146$	3.99503	−	12.2955i	0.330631	−	1.01758i
$147$	4.55245	+	14.0110i	0.375480	+	1.15561i
$148$	−2.58574	+	1.87865i	−0.212547	+	0.154424i
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.0333309	−	0.999444i	$-0.489388\pi$
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.960828	+	0.277146i	$0.0893885\pi$
$150$	1.68850	+	5.19667i	0.137865	+	0.424306i
$151$	5.06550	−	15.5900i	0.412225	−	1.26870i	−0.502485	−	0.864586i	$-0.667581\pi$
$151$	5.06550	−	15.5900i	0.412225	−	1.26870i	0.914710	−	0.404111i	$-0.132419\pi$
$152$	−3.82831	−	2.78143i	−0.310517	−	0.225604i
$153$	23.1962			1.87530
$154$		0			0
$155$	−17.6603			−1.41851
$156$	6.63083	+	4.81758i	0.530891	+	0.385715i
$157$	1.23607	−	3.80423i	0.0986490	−	0.303610i	−0.889538	−	0.456860i	$-0.848974\pi$
$157$	1.23607	−	3.80423i	0.0986490	−	0.303610i	0.988187	+	0.153250i	$0.0489740\pi$
$158$	−0.391818	−	1.20589i	−0.0311714	−	0.0959356i
$159$	1.77672	−	1.29087i	0.140903	−	0.102372i
$160$	−1.40126	+	1.01807i	−0.110779	+	0.0804858i
$161$	−1.85410	−	5.70634i	−0.146124	−	0.449723i
$162$	−0.761449	+	2.34350i	−0.0598251	+	0.184123i
$163$	−9.54951	−	6.93813i	−0.747976	−	0.543436i	0.147223	−	0.989103i	$-0.452966\pi$
$163$	−9.54951	−	6.93813i	−0.747976	−	0.543436i	−0.895199	+	0.445667i	$0.852966\pi$
$164$	−11.1962			−0.874273
$165$		0			0
$166$	−2.19615			−0.170454
$167$	3.55345	+	2.58173i	0.274974	+	0.199780i	0.716722	−	0.697359i	$-0.245642\pi$
$167$	3.55345	+	2.58173i	0.274974	+	0.199780i	−0.441748	+	0.897139i	$0.645642\pi$
$168$	−1.07047	+	3.29456i	−0.0825883	+	0.254181i
$169$	−1.23607	−	3.80423i	−0.0950822	−	0.292633i
$170$	−7.28115	+	5.29007i	−0.558439	+	0.405730i
$171$	−17.0900	+	12.4166i	−1.30690	+	0.949520i
$172$		0			0
$173$	5.06550	−	15.5900i	0.385123	−	1.18529i	−0.551268	−	0.834328i	$-0.685856\pi$
$173$	5.06550	−	15.5900i	0.385123	−	1.18529i	0.936391	−	0.350958i	$-0.114144\pi$
$174$	−6.63083	−	4.81758i	−0.502682	−	0.365220i
$175$	−2.53590			−0.191696
$176$		0			0
$177$	−6.92820			−0.520756
$178$	0.375466	+	0.272792i	0.0281424	+	0.0204466i
$179$	4.28187	−	13.1782i	0.320042	−	0.984987i	−0.653588	−	0.756851i	$-0.726737\pi$
$179$	4.28187	−	13.1782i	0.320042	−	0.984987i	0.973629	−	0.228136i	$-0.0732631\pi$
$180$	2.38934	+	7.35362i	0.178091	+	0.548106i
$181$	2.58574	−	1.87865i	0.192197	−	0.139639i	−0.487525	−	0.873109i	$-0.662100\pi$
$181$	2.58574	−	1.87865i	0.192197	−	0.139639i	0.679722	+	0.733470i	$0.262100\pi$
$182$	−3.07738	+	2.23585i	−0.228110	+	0.165732i
$183$	−7.99007	−	24.5909i	−0.590643	−	1.81781i
$184$	−1.46228	+	4.50045i	−0.107801	+	0.331777i
$185$	−4.47864	−	3.25392i	−0.329276	−	0.239233i
$186$	27.8564			2.04253
$187$		0			0
$188$	2.19615			0.160171
$189$	4.10317	+	2.98113i	0.298462	+	0.216845i
$190$	2.53275	−	7.79500i	0.183745	−	0.565509i
$191$	−4.49184	−	13.8245i	−0.325018	−	1.00030i	−0.971432	−	0.237316i	$-0.923732\pi$
$191$	−4.49184	−	13.8245i	−0.325018	−	1.00030i	0.646414	−	0.762987i	$-0.276268\pi$
$192$	2.21028	−	1.60586i	0.159513	−	0.115893i
$193$	−11.1095	+	8.07150i	−0.799677	+	0.580999i	−0.910819	−	0.412805i	$-0.864549\pi$
$193$	−11.1095	+	8.07150i	−0.799677	+	0.580999i	0.111143	+	0.993804i	$0.464549\pi$
$194$	−0.309017	−	0.951057i	−0.0221861	−	0.0682819i
$195$	−4.38685	+	13.5013i	−0.314149	+	0.966851i
$196$	4.36247	+	3.16952i	0.311605	+	0.226394i
$197$	7.39230			0.526680			0.263340	−	0.964703i	$-0.415176\pi$
$197$	7.39230			0.526680			0.263340	+	0.964703i	$0.415176\pi$
$198$		0			0
$199$	20.3923			1.44557			0.722786	−	0.691072i	$-0.242861\pi$
$199$	20.3923			1.44557			0.722786	+	0.691072i	$0.242861\pi$
$200$	1.61803	+	1.17557i	0.114412	+	0.0831254i
$201$	−0.165602	+	0.509670i	−0.0116806	+	0.0359493i
$202$	−1.35730	−	4.17733i	−0.0954991	−	0.293916i
$203$	3.07738	−	2.23585i	0.215990	−	0.156926i
$204$	11.4849	−	8.34429i	0.804106	−	0.584217i
$205$	−5.99255	−	18.4432i	−0.418538	−	1.28813i
$206$	3.82943	−	11.7858i	0.266809	−	0.821154i
$207$	17.0900	+	12.4166i	1.18783	+	0.863012i
$208$	3.00000			0.208013
$209$		0			0
$210$	−6.00000			−0.414039
$211$	−1.50186	−	1.09117i	−0.103393	−	0.0751191i	0.534888	−	0.844923i	$-0.320354\pi$
$211$	−1.50186	−	1.09117i	−0.103393	−	0.0751191i	−0.638280	+	0.769804i	$0.720354\pi$
$212$	0.248403	−	0.764504i	0.0170604	−	0.0525064i
$213$	2.14093	+	6.58911i	0.146694	+	0.451479i
$214$	15.0384	−	10.9260i	1.02800	−	0.746887i
$215$		0			0
$216$	−1.23607	−	3.80423i	−0.0841038	−	0.258845i
$217$	−3.99503	+	12.2955i	−0.271201	+	0.834670i
$218$	12.8862	+	9.36236i	0.872763	+	0.634099i
$219$	−35.3205			−2.38674
$220$		0			0
$221$	15.5885			1.04859
$222$	7.06438	+	5.13257i	0.474130	+	0.344476i
$223$	0.121229	−	0.373104i	0.00811809	−	0.0249849i	−0.946915	−	0.321483i	$-0.895819\pi$
$223$	0.121229	−	0.373104i	0.00811809	−	0.0249849i	0.955034	+	0.296498i	$0.0958188\pi$
$224$	0.391818	+	1.20589i	0.0261794	+	0.0805720i
$225$	7.22307	−	5.24787i	0.481538	−	0.349858i
$226$	13.6371	−	9.90795i	0.907128	−	0.659067i
$227$	1.35730	+	4.17733i	0.0900870	+	0.277259i	0.985942	−	0.167087i	$-0.0534361\pi$
$227$	1.35730	+	4.17733i	0.0900870	+	0.277259i	−0.895855	+	0.444346i	$0.853436\pi$
$228$	−3.99503	+	12.2955i	−0.264578	+	0.814286i
$229$	2.26836	+	1.64806i	0.149897	+	0.108907i	0.660206	−	0.751084i	$-0.270469\pi$
$229$	2.26836	+	1.64806i	0.149897	+	0.108907i	−0.510309	+	0.859991i	$0.670469\pi$
$230$	−8.19615			−0.540438
$231$		0			0
$232$	−3.00000			−0.196960
$233$	13.9120	+	10.1076i	0.911404	+	0.662174i	0.941370	−	0.337377i	$-0.109540\pi$
$233$	13.9120	+	10.1076i	0.911404	+	0.662174i	−0.0299655	+	0.999551i	$0.509540\pi$
$234$	4.13845	−	12.7368i	0.270539	−	0.832633i
$235$	1.17545	+	3.61767i	0.0766781	+	0.235991i
$236$	−2.05158	+	1.49056i	−0.133547	+	0.0970274i
$237$	−2.80252	+	2.03615i	−0.182043	+	0.132262i
$238$	2.03595	+	6.26600i	0.131971	+	0.406164i
$239$	−1.17545	+	3.61767i	−0.0760338	+	0.234008i	−0.981849	−	0.189666i	$-0.939260\pi$
$239$	−1.17545	+	3.61767i	−0.0760338	+	0.234008i	0.905815	+	0.423674i	$0.139260\pi$
$240$	3.82831	+	2.78143i	0.247116	+	0.179541i
$241$	−14.7846			−0.952360			−0.476180	−	0.879348i	$-0.657979\pi$
$241$	−14.7846			−0.952360			−0.476180	+	0.879348i	$0.657979\pi$
$242$		0			0
$243$	18.7321			1.20166
$244$	−7.65662	−	5.56286i	−0.490165	−	0.356126i
$245$	−2.88614	+	8.88263i	−0.184389	+	0.567490i
$246$	9.45235	+	29.0914i	0.602660	+	1.85480i
$247$	−11.4849	+	8.34429i	−0.730769	+	0.530934i
$248$	8.24886	−	5.99315i	0.523803	−	0.380565i
$249$	1.85410	+	5.70634i	0.117499	+	0.361625i
$250$	−3.74663	+	11.5309i	−0.236958	+	0.729281i
$251$	12.2359	+	8.88987i	0.772321	+	0.561124i	0.902664	−	0.430345i	$-0.141608\pi$
$251$	12.2359	+	8.88987i	0.772321	+	0.561124i	−0.130344	+	0.991469i	$0.541608\pi$
$252$	5.66025			0.356562
$253$		0			0
$254$	−13.8564			−0.869428
$255$	19.8925	+	14.4527i	1.24572	+	0.905065i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	0.430246	+	1.32416i	0.0268380	+	0.0825989i	0.963578	−	0.267426i	$-0.0861731\pi$
$257$	0.430246	+	1.32416i	0.0268380	+	0.0825989i	−0.936740	+	0.350025i	$0.886173\pi$
$258$		0			0
$259$	−3.27859	+	2.38203i	−0.203722	+	0.148012i
$260$	1.60570	+	4.94183i	0.0995812	+	0.306480i
$261$	−4.13845	+	12.7368i	−0.256164	+	0.788391i
$262$		0			0
$263$	20.1962			1.24535			0.622674	−	0.782481i	$-0.286046\pi$
$263$	20.1962			1.24535			0.622674	+	0.782481i	$0.286046\pi$
$264$		0			0
$265$	1.39230			0.0855286
$266$	−4.85410	−	3.52671i	−0.297624	−	0.216237i
$267$	0.391818	−	1.20589i	0.0239789	−	0.0737994i
$268$	0.0606144	+	0.186552i	0.00370262	+	0.0113955i
$269$	17.4654	−	12.6894i	1.06489	−	0.773685i	0.0898999	−	0.995951i	$-0.471345\pi$
$269$	17.4654	−	12.6894i	1.06489	−	0.773685i	0.974986	+	0.222266i	$0.0713453\pi$
$270$	5.60503	−	4.07230i	0.341112	−	0.247832i
$271$	1.35730	+	4.17733i	0.0824499	+	0.253755i	0.983780	−	0.179377i	$-0.0574083\pi$
$271$	1.35730	+	4.17733i	0.0824499	+	0.253755i	−0.901330	+	0.433132i	$0.857408\pi$
$272$	1.60570	−	4.94183i	0.0973598	−	0.299643i
$273$	8.40755	+	6.10844i	0.508848	+	0.369700i
$274$	−2.53590			−0.153199
$275$		0			0
$276$	12.9282			0.778186
$277$	−21.2937	−	15.4708i	−1.27942	−	0.929551i	−0.279881	−	0.960035i	$-0.590295\pi$
$277$	−21.2937	−	15.4708i	−1.27942	−	0.929551i	−0.999535	+	0.0304839i	$0.990295\pi$
$278$	3.02956	−	9.32401i	0.181701	−	0.559217i
$279$	−14.0654	−	43.2889i	−0.842075	−	2.59164i
$280$	−1.77672	+	1.29087i	−0.106180	+	0.0771440i
$281$	−14.5623	+	10.5801i	−0.868714	+	0.631158i	−0.930242	−	0.366947i	$-0.880403\pi$
$281$	−14.5623	+	10.5801i	−0.868714	+	0.631158i	0.0615273	+	0.998105i	$0.480403\pi$
$282$	−1.85410	−	5.70634i	−0.110410	−	0.339808i
$283$	−2.14093	+	6.58911i	−0.127265	+	0.391682i	−0.994307	−	0.106553i	$-0.966018\pi$
$283$	−2.14093	+	6.58911i	−0.127265	+	0.391682i	0.867042	+	0.498235i	$0.166018\pi$
$284$	2.05158	+	1.49056i	0.121739	+	0.0884487i
$285$	−22.3923			−1.32641
$286$		0			0
$287$	−14.1962			−0.837972
$288$	−3.61153	−	2.62393i	−0.212812	−	0.154617i
$289$	3.09017	−	9.51057i	0.181775	−	0.559445i
$290$	−1.60570	−	4.94183i	−0.0942899	−	0.290195i
$291$	−2.21028	+	1.60586i	−0.129569	+	0.0941371i
$292$	−10.4591	+	7.59901i	−0.612075	+	0.444698i
$293$	−5.49575	−	16.9142i	−0.321065	−	0.988136i	−0.973186	−	0.230021i	$-0.926120\pi$
$293$	−5.49575	−	16.9142i	−0.321065	−	0.988136i	0.652121	−	0.758115i	$-0.273880\pi$
$294$	4.55245	−	14.0110i	0.265505	−	0.817139i
$295$	−3.55345	−	2.58173i	−0.206890	−	0.150314i
$296$	3.19615			0.185773
$297$		0			0
$298$	−15.0000			−0.868927
$299$	11.4849	+	8.34429i	0.664191	+	0.482563i
$300$	1.68850	−	5.19667i	0.0974856	−	0.300030i
$301$		0			0
$302$	−13.2617	+	9.63516i	−0.763122	+	0.554441i
$303$	−9.70820	+	7.05342i	−0.557722	+	0.405209i
$304$	1.46228	+	4.50045i	0.0838677	+	0.258118i
$305$	5.06550	−	15.5900i	0.290050	−	0.892681i
$306$	−18.7661	−	13.6344i	−1.07279	−	0.779424i
$307$	28.7321			1.63982			0.819912	−	0.572489i	$-0.194022\pi$
$307$	28.7321			1.63982			0.819912	+	0.572489i	$0.194022\pi$
$308$		0			0
$309$	−33.8564			−1.92602
$310$	14.2874	+	10.3804i	0.811472	+	0.589569i
$311$	−10.1310	+	31.1800i	−0.574476	+	1.76806i	0.0634789	+	0.997983i	$0.479780\pi$
$311$	−10.1310	+	31.1800i	−0.574476	+	1.76806i	−0.637955	+	0.770073i	$0.720220\pi$
$312$	−2.53275	−	7.79500i	−0.143389	−	0.441305i
$313$	−7.91592	+	5.75125i	−0.447434	+	0.325080i	−0.788582	−	0.614930i	$-0.789184\pi$
$313$	−7.91592	+	5.75125i	−0.447434	+	0.325080i	0.341148	+	0.940010i	$0.389184\pi$
$314$	−3.23607	+	2.35114i	−0.182622	+	0.132683i
$315$	3.02956	+	9.32401i	0.170696	+	0.525349i
$316$	−0.391818	+	1.20589i	−0.0220415	+	0.0678367i
$317$	−16.0642	−	11.6713i	−0.902254	−	0.655526i	0.0367902	−	0.999323i	$-0.488287\pi$
$317$	−16.0642	−	11.6713i	−0.902254	−	0.655526i	−0.939044	+	0.343797i	$0.888287\pi$
$318$	−2.19615			−0.123154
$319$		0			0
$320$	1.73205			0.0968246
$321$	−41.0856	−	29.8504i	−2.29318	−	1.66609i
$322$	−1.85410	+	5.70634i	−0.103325	+	0.318002i
$323$	7.59825	+	23.3850i	0.422778	+	1.30118i
$324$	1.99350	−	1.44836i	0.110750	−	0.0804646i
$325$	4.85410	−	3.52671i	0.269257	−	0.195627i
$326$	3.64759	+	11.2261i	0.202021	+	0.621758i
$327$	13.4474	−	41.3868i	0.743642	−	2.28870i
$328$	9.05788	+	6.58093i	0.500138	+	0.363371i
$329$	2.78461			0.153521
$330$		0			0
$331$	−12.7846			−0.702706			−0.351353	−	0.936243i	$-0.614278\pi$
$331$	−12.7846			−0.702706			−0.351353	+	0.936243i	$0.614278\pi$
$332$	1.77672	+	1.29087i	0.0975104	+	0.0708455i
$333$	4.40904	−	13.5696i	0.241614	−	0.743611i
$334$	−1.35730	−	4.17733i	−0.0742680	−	0.228573i
$335$	−0.274860	+	0.199698i	−0.0150172	+	0.0109106i
$336$	2.80252	−	2.03615i	0.152890	−	0.111081i
$337$	−4.53027	−	13.9427i	−0.246779	−	0.759509i	−0.995339	−	0.0964411i	$-0.969254\pi$
$337$	−4.53027	−	13.9427i	−0.246779	−	0.759509i	0.748559	−	0.663068i	$-0.230746\pi$
$338$	−1.23607	+	3.80423i	−0.0672332	+	0.206923i
$339$	−37.2573	−	27.0690i	−2.02354	−	1.47019i
$340$	9.00000			0.488094
$341$		0			0
$342$	21.1244			1.14227
$343$	12.7119	+	9.23576i	0.686380	+	0.498684i
$344$		0			0
$345$	6.91960	+	21.2963i	0.372539	+	1.14656i
$346$	−13.2617	+	9.63516i	−0.712951	+	0.517989i
$347$	6.15475	−	4.47169i	0.330405	−	0.240053i	−0.410198	−	0.911997i	$-0.634540\pi$
$347$	6.15475	−	4.47169i	0.330405	−	0.240053i	0.740602	+	0.671944i	$0.234540\pi$
$348$	2.53275	+	7.79500i	0.135770	+	0.417856i
$349$	−2.49432	+	7.67673i	−0.133518	+	0.410926i	−0.995357	−	0.0962565i	$-0.969313\pi$
$349$	−2.49432	+	7.67673i	−0.133518	+	0.410926i	0.861839	+	0.507183i	$0.169313\pi$
$350$	2.05158	+	1.49056i	0.109662	+	0.0796740i
$351$	−12.0000			−0.640513
$352$		0			0
$353$	8.07180			0.429618			0.214809	−	0.976656i	$-0.431087\pi$
$353$	8.07180			0.429618			0.214809	+	0.976656i	$0.431087\pi$
$354$	5.60503	+	4.07230i	0.297904	+	0.216440i
$355$	−1.35730	+	4.17733i	−0.0720378	+	0.221710i
$356$	−0.143415	−	0.441387i	−0.00760099	−	0.0233935i
$357$	14.5623	−	10.5801i	0.770719	−	0.559960i
$358$	−11.2101	+	8.14459i	−0.592471	+	0.430455i
$359$	7.59825	+	23.3850i	0.401020	+	1.23421i	0.924173	+	0.381975i	$0.124756\pi$
$359$	7.59825	+	23.3850i	0.401020	+	1.23421i	−0.523152	+	0.852239i	$0.675244\pi$
$360$	2.38934	−	7.35362i	0.125929	−	0.387570i
$361$	−2.74443	−	1.99395i	−0.144444	−	0.104945i
$362$	−3.19615			−0.167986
$363$		0			0
$364$	3.80385			0.199376
$365$	−18.1158	−	13.1619i	−0.948222	−	0.688924i
$366$	−7.99007	+	24.5909i	−0.417648	+	1.28539i
$367$	−6.98022	−	21.4829i	−0.364364	−	1.12140i	−0.950378	−	0.311097i	$-0.899304\pi$
$367$	−6.98022	−	21.4829i	−0.364364	−	1.12140i	0.586014	−	0.810301i	$-0.300696\pi$
$368$	3.82831	−	2.78143i	0.199564	−	0.144992i
$369$	40.4353	−	29.3780i	2.10498	−	1.52936i
$370$	1.71069	+	5.26495i	0.0889344	+	0.273712i
$371$	0.314962	−	0.969353i	0.0163520	−	0.0503263i
$372$	−22.5363	−	16.3736i	−1.16845	−	0.848931i
$373$	23.3205			1.20749			0.603745	−	0.797177i	$-0.293674\pi$
$373$	23.3205			1.20749			0.603745	+	0.797177i	$0.293674\pi$
$374$		0			0
$375$	33.1244			1.71053
$376$	−1.77672	−	1.29087i	−0.0916276	−	0.0665713i
$377$	−2.78115	+	8.55951i	−0.143237	+	0.440837i
$378$	−1.56727	−	4.82357i	−0.0806117	−	0.248097i
$379$	−19.7338	+	14.3374i	−1.01366	+	0.736465i	−0.964973	−	0.262350i	$-0.915503\pi$
$379$	−19.7338	+	14.3374i	−1.01366	+	0.736465i	−0.0486838	+	0.998814i	$0.515503\pi$
$380$	−6.63083	+	4.81758i	−0.340154	+	0.247137i
$381$	11.6983	+	36.0036i	0.599321	+	1.84452i
$382$	−4.49184	+	13.8245i	−0.229823	+	0.707321i
$383$	28.5749	+	20.7609i	1.46011	+	1.06083i	0.983335	+	0.181805i	$0.0581941\pi$
$383$	28.5749	+	20.7609i	1.46011	+	1.06083i	0.476774	+	0.879026i	$0.341806\pi$
$384$	−2.73205			−0.139419
$385$		0			0
$386$	13.7321			0.698943
$387$		0			0
$388$	−0.309017	+	0.951057i	−0.0156880	+	0.0482826i
$389$	4.74024	+	14.5890i	0.240340	+	0.739690i	0.996368	+	0.0851509i	$0.0271372\pi$
$389$	4.74024	+	14.5890i	0.240340	+	0.739690i	−0.756028	+	0.654539i	$0.772863\pi$
$390$	11.4849	−	8.34429i	0.581562	−	0.422529i
$391$	19.8925	−	14.4527i	1.00601	−	0.730906i
$392$	−1.66631	−	5.12839i	−0.0841616	−	0.259023i
$393$		0			0
$394$	−5.98050	−	4.34509i	−0.301293	−	0.218902i
$395$	−2.19615			−0.110500
$396$		0			0
$397$	−25.5885			−1.28425			−0.642124	−	0.766601i	$-0.721947\pi$
$397$	−25.5885			−1.28425			−0.642124	+	0.766601i	$0.721947\pi$
$398$	−16.4977	−	11.9863i	−0.826956	−	0.600819i
$399$	−5.06550	+	15.5900i	−0.253592	+	0.780477i
$400$	−0.618034	−	1.90211i	−0.0309017	−	0.0951057i
$401$	−10.8346	+	7.87180i	−0.541054	+	0.393099i	−0.824476	−	0.565896i	$-0.808530\pi$
$401$	−10.8346	+	7.87180i	−0.541054	+	0.393099i	0.283422	+	0.958995i	$0.408530\pi$
$402$	0.433551	−	0.314993i	0.0216236	−	0.0157104i
$403$	−9.45235	−	29.0914i	−0.470855	−	1.44914i
$404$	−1.35730	+	4.17733i	−0.0675280	+	0.207830i
$405$	3.45284	+	2.50864i	0.171573	+	0.124655i
$406$	−3.80385			−0.188782
$407$		0			0
$408$	−14.1962			−0.702814
$409$	−11.8604	−	8.61708i	−0.586459	−	0.426087i	0.254588	−	0.967050i	$-0.418060\pi$
$409$	−11.8604	−	8.61708i	−0.586459	−	0.426087i	−0.841047	+	0.540962i	$0.818060\pi$
$410$	−5.99255	+	18.4432i	−0.295951	+	0.910844i
$411$	2.14093	+	6.58911i	0.105604	+	0.325017i
$412$	−10.0256	+	7.28401i	−0.493925	+	0.358858i
$413$	−2.60131	+	1.88996i	−0.128002	+	0.0929988i
$414$	−6.52778	−	20.0905i	−0.320823	−	0.987392i
$415$	−1.17545	+	3.61767i	−0.0577007	+	0.177585i
$416$	−2.42705	−	1.76336i	−0.118996	−	0.0864556i
$417$	−26.7846			−1.31165
$418$		0			0
$419$	33.3731			1.63038			0.815191	−	0.579193i	$-0.196632\pi$
$419$	33.3731			1.63038			0.815191	+	0.579193i	$0.196632\pi$
$420$	4.85410	+	3.52671i	0.236856	+	0.172086i
$421$	−7.28923	+	22.4340i	−0.355256	+	1.09336i	0.600606	+	0.799545i	$0.294926\pi$
$421$	−7.28923	+	22.4340i	−0.355256	+	1.09336i	−0.955861	+	0.293819i	$0.905074\pi$
$422$	0.573661	+	1.76555i	0.0279254	+	0.0859455i
$423$	−7.93148	+	5.76256i	−0.385642	+	0.280185i
$424$	−0.650326	+	0.472490i	−0.0315826	+	0.0229461i
$425$	−3.21140	−	9.88367i	−0.155776	−	0.479428i
$426$	2.14093	−	6.58911i	0.103729	−	0.319244i
$427$	−9.70820	−	7.05342i	−0.469813	−	0.341339i
$428$	−18.5885			−0.898507
$429$		0			0
$430$		0			0
$431$	3.55345	+	2.58173i	0.171164	+	0.124358i	0.670069	−	0.742299i	$-0.266264\pi$
$431$	3.55345	+	2.58173i	0.171164	+	0.124358i	−0.498905	+	0.866656i	$0.666264\pi$
$432$	−1.23607	+	3.80423i	−0.0594703	+	0.183031i
$433$	−3.02361	−	9.30572i	−0.145305	−	0.447204i	0.851745	−	0.523957i	$-0.175545\pi$
$433$	−3.02361	−	9.30572i	−0.145305	−	0.447204i	−0.997050	+	0.0767528i	$0.975545\pi$
$434$	10.4591	−	7.59901i	0.502055	−	0.364764i
$435$	−11.4849	+	8.34429i	−0.550660	+	0.400078i
$436$	−4.92209	−	15.1486i	−0.235725	−	0.725487i
$437$	−6.91960	+	21.2963i	−0.331009	+	1.01874i
$438$	28.5749	+	20.7609i	1.36536	+	0.991993i
$439$	3.12436			0.149117			0.0745587	−	0.997217i	$-0.476245\pi$
$439$	3.12436			0.149117			0.0745587	+	0.997217i	$0.476245\pi$
$440$		0			0
$441$	−24.0718			−1.14628
$442$	−12.6113	−	9.16267i	−0.599860	−	0.435824i
$443$	9.55734	−	29.4145i	0.454083	−	1.39752i	−0.418126	−	0.908389i	$-0.637313\pi$
$443$	9.55734	−	29.4145i	0.454083	−	1.39752i	0.872208	−	0.489134i	$-0.162687\pi$
$444$	−2.69835	−	8.30467i	−0.128058	−	0.394122i
$445$	0.650326	−	0.472490i	0.0308284	−	0.0223982i
$446$	−0.317381	+	0.230591i	−0.0150284	+	0.0109188i
$447$	12.6638	+	38.9750i	0.598975	+	1.84346i
$448$	0.391818	−	1.20589i	0.0185117	−	0.0569730i
$449$	−3.17798	−	2.30894i	−0.149978	−	0.108966i	0.510266	−	0.860017i	$-0.329547\pi$
$449$	−3.17798	−	2.30894i	−0.149978	−	0.108966i	−0.660244	+	0.751051i	$0.729547\pi$
$450$	−8.92820			−0.420880
$451$		0			0
$452$	−16.8564			−0.792859
$453$	36.2315	+	26.3237i	1.70230	+	1.23680i
$454$	1.35730	−	4.17733i	0.0637011	−	0.196052i
$455$	2.03595	+	6.26600i	0.0954466	+	0.293754i
$456$	10.4591	−	7.59901i	0.489794	−	0.355856i
$457$	−4.20378	+	3.05422i	−0.196644	+	0.142870i	−0.681750	−	0.731585i	$-0.738781\pi$
$457$	−4.20378	+	3.05422i	−0.196644	+	0.142870i	0.485106	+	0.874455i	$0.338781\pi$
$458$	−0.866437	−	2.66662i	−0.0404859	−	0.124603i
$459$	−6.42280	+	19.7673i	−0.299791	+	0.922660i
$460$	6.63083	+	4.81758i	0.309164	+	0.224621i
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$	−12.7846			−0.594151			−0.297076	−	0.954854i	$-0.596011\pi$
$463$	−12.7846			−0.594151			−0.297076	+	0.954854i	$0.596011\pi$
$464$	2.42705	+	1.76336i	0.112673	+	0.0818617i
$465$	14.9097	−	45.8873i	0.691419	−	2.12797i
$466$	−5.31390	−	16.3545i	−0.246162	−	0.757608i
$467$	−11.7598	+	8.54399i	−0.544178	+	0.395369i	−0.825634	−	0.564206i	$-0.809183\pi$
$467$	−11.7598	+	8.54399i	−0.544178	+	0.395369i	0.281456	+	0.959574i	$0.409183\pi$
$468$	−10.8346	+	7.87180i	−0.500830	+	0.363874i
$469$	0.0768560	+	0.236539i	0.00354888	+	0.0109223i
$470$	1.17545	−	3.61767i	0.0542196	−	0.166871i
$471$	8.84110	+	6.42344i	0.407376	+	0.295976i
$472$	2.53590			0.116724
$473$		0			0
$474$	3.46410			0.159111
$475$	7.65662	+	5.56286i	0.351310	+	0.255241i
$476$	2.03595	−	6.26600i	0.0933174	−	0.287201i
$477$	1.10889	+	3.41283i	0.0507728	+	0.156263i
$478$	3.07738	−	2.23585i	0.140756	−	0.102265i
$479$	−26.5233	+	19.2703i	−1.21188	+	0.880483i	−0.995400	−	0.0958040i	$-0.969458\pi$
$479$	−26.5233	+	19.2703i	−1.21188	+	0.880483i	−0.216481	+	0.976287i	$0.569458\pi$
$480$	−1.46228	−	4.50045i	−0.0667438	−	0.205416i
$481$	2.96300	−	9.11916i	0.135101	−	0.415798i
$482$	11.9610	+	8.69018i	0.544809	+	0.395827i
$483$	16.3923			0.745876
$484$		0			0
$485$	−1.73205			−0.0786484
$486$	−15.1545	−	11.0104i	−0.687424	−	0.499443i
$487$	12.0457	−	37.0729i	0.545844	−	1.67993i	−0.173132	−	0.984899i	$-0.555389\pi$
$487$	12.0457	−	37.0729i	0.545844	−	1.67993i	0.718976	−	0.695035i	$-0.244611\pi$
$488$	2.92457	+	9.00090i	0.132389	+	0.407451i
$489$	26.0898	−	18.9553i	1.17982	−	0.857189i
$490$	7.55601	−	5.48976i	0.341346	−	0.248002i
$491$	12.1669	+	37.4460i	0.549087	+	1.68991i	0.711070	+	0.703121i	$0.248211\pi$
$491$	12.1669	+	37.4460i	0.549087	+	1.68991i	−0.161983	+	0.986794i	$0.551789\pi$
$492$	9.45235	−	29.0914i	0.426145	−	1.31154i
$493$	12.6113	+	9.16267i	0.567986	+	0.412666i
$494$	14.1962			0.638715
$495$		0			0
$496$	−10.1962			−0.457821
$497$	2.60131	+	1.88996i	0.116684	+	0.0847762i
$498$	1.85410	−	5.70634i	0.0830843	−	0.255707i
$499$	4.94427	+	15.2169i	0.221336	+	0.681202i	0.998643	+	0.0520806i	$0.0165853\pi$
$499$	4.94427	+	15.2169i	0.221336	+	0.681202i	−0.777307	+	0.629122i	$0.783415\pi$
$500$	9.80881	−	7.12652i	0.438663	−	0.318708i
$501$	−9.70820	+	7.05342i	−0.433731	+	0.315124i
$502$	−4.67368	−	14.3841i	−0.208597	−	0.641995i
$503$	−1.17545	+	3.61767i	−0.0524109	+	0.161304i	−0.973836	−	0.227252i	$-0.927026\pi$
$503$	−1.17545	+	3.61767i	−0.0524109	+	0.161304i	0.921425	+	0.388556i	$0.127026\pi$
$504$	−4.57924	−	3.32701i	−0.203976	−	0.148197i
$505$	−7.60770			−0.338538
$506$		0			0
$507$	10.9282			0.485339
$508$	11.2101	+	8.14459i	0.497366	+	0.361358i
$509$	−0.286831	+	0.882774i	−0.0127135	+	0.0391283i	−0.957212	−	0.289387i	$-0.906548\pi$
$509$	−0.286831	+	0.882774i	−0.0127135	+	0.0391283i	0.944498	+	0.328516i	$0.106548\pi$
$510$	−7.59825	−	23.3850i	−0.336456	−	1.03551i
$511$	−13.2617	+	9.63516i	−0.586661	+	0.426234i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−5.84914	−	18.0018i	−0.258246	−	0.794798i
$514$	0.430246	−	1.32416i	0.0189773	−	0.0584062i
$515$	−17.3648	−	12.6163i	−0.765186	−	0.555940i
$516$		0			0
$517$		0			0
$518$	4.05256			0.178059
$519$	36.2315	+	26.3237i	1.59039	+	1.15548i
$520$	1.60570	−	4.94183i	0.0704146	−	0.216714i
$521$	0.783636	+	2.41178i	0.0343317	+	0.105662i	0.966754	−	0.255709i	$-0.0823088\pi$
$521$	0.783636	+	2.41178i	0.0343317	+	0.105662i	−0.932422	+	0.361371i	$0.882309\pi$
$522$	10.8346	−	7.87180i	0.474218	−	0.344539i
$523$	−7.65662	+	5.56286i	−0.334801	+	0.243247i	−0.742465	−	0.669885i	$-0.766343\pi$
$523$	−7.65662	+	5.56286i	−0.334801	+	0.243247i	0.407664	+	0.913132i	$0.366343\pi$
$524$		0			0
$525$	2.14093	−	6.58911i	0.0934380	−	0.287572i
$526$	−16.3390	−	11.8710i	−0.712416	−	0.517600i
$527$	−52.9808			−2.30788
$528$		0			0
$529$	−0.607695			−0.0264215
$530$	−1.12640	−	0.818376i	−0.0489276	−	0.0355480i
$531$	3.49823	−	10.7664i	0.151810	−	0.467224i
$532$	1.85410	+	5.70634i	0.0803855	+	0.247401i
$533$	27.1736	−	19.7428i	1.17702	−	0.855156i
$534$	−1.02579	+	0.745282i	−0.0443904	+	0.0322515i
$535$	−9.94916	−	30.6204i	−0.430140	−	1.32383i
$536$	0.0606144	−	0.186552i	0.00261814	−	0.00805782i
$537$	30.6265	+	22.2514i	1.32163	+	0.960220i
$538$	−21.5885			−0.930744
$539$		0			0
$540$	−6.92820			−0.298142
$541$	24.2705	+	17.6336i	1.04347	+	0.758126i	0.970960	−	0.239242i	$-0.0768989\pi$
$541$	24.2705	+	17.6336i	1.04347	+	0.758126i	0.0725107	+	0.997368i	$0.476899\pi$
$542$	1.35730	−	4.17733i	0.0583009	−	0.179432i
$543$	2.69835	+	8.30467i	0.115797	+	0.356388i
$544$	−4.20378	+	3.05422i	−0.180235	+	0.130949i
$545$	22.3195	−	16.2161i	0.956064	−	0.694621i
$546$	−3.21140	−	9.88367i	−0.137435	−	0.422982i
$547$	−7.41641	+	22.8254i	−0.317103	+	0.975942i	0.657778	+	0.753212i	$0.271497\pi$
$547$	−7.41641	+	22.8254i	−0.317103	+	0.975942i	−0.974880	+	0.222730i	$0.928503\pi$
$548$	2.05158	+	1.49056i	0.0876394	+	0.0636737i
$549$	42.2487			1.80313
$550$		0			0
$551$	−14.1962			−0.604776
$552$	−10.4591	−	7.59901i	−0.445170	−	0.323435i
$553$	−0.496805	+	1.52901i	−0.0211263	+	0.0650201i
$554$	8.13348	+	25.0323i	0.345559	+	1.06352i
$555$	12.2359	−	8.88987i	0.519383	−	0.377354i
$556$	−7.93148	+	5.76256i	−0.336370	+	0.244387i
$557$	−7.78009	−	23.9447i	−0.329653	−	1.01457i	−0.969296	−	0.245896i	$-0.920918\pi$
$557$	−7.78009	−	23.9447i	−0.329653	−	1.01457i	0.639643	−	0.768672i	$-0.279082\pi$
$558$	−14.0654	+	43.2889i	−0.595437	+	1.83257i
$559$		0			0
$560$	2.19615			0.0928044
$561$		0			0
$562$	18.0000			0.759284
$563$	−24.7466	−	17.9794i	−1.04294	−	0.757743i	−0.0720860	−	0.997398i	$-0.522966\pi$
$563$	−24.7466	−	17.9794i	−1.04294	−	0.757743i	−0.970858	+	0.239655i	$0.922966\pi$
$564$	−1.85410	+	5.70634i	−0.0780718	+	0.240280i
$565$	−9.02211	−	27.7672i	−0.379563	−	1.16817i
$566$	5.60503	−	4.07230i	0.235597	−	0.171171i
$567$	2.52766	−	1.83645i	0.106152	−	0.0771237i
$568$	−0.783636	−	2.41178i	−0.0328806	−	0.101196i
$569$	12.9787	−	39.9444i	0.544096	−	1.67456i	−0.179034	−	0.983843i	$-0.557297\pi$
$569$	12.9787	−	39.9444i	0.544096	−	1.67456i	0.723130	−	0.690712i	$-0.242703\pi$
$570$	18.1158	+	13.1619i	0.758785	+	0.551290i
$571$	−11.6603			−0.487966			−0.243983	−	0.969779i	$-0.578454\pi$
$571$	−11.6603			−0.487966			−0.243983	+	0.969779i	$0.578454\pi$
$572$		0			0
$573$	39.7128			1.65903
$574$	11.4849	+	8.34429i	0.479372	+	0.348284i
$575$	2.92457	−	9.00090i	0.121963	−	0.375363i
$576$	1.37948	+	4.24561i	0.0574785	+	0.176901i
$577$	−28.6330	+	20.8031i	−1.19201	+	0.866043i	−0.993475	−	0.114051i	$-0.963617\pi$
$577$	−28.6330	+	20.8031i	−1.19201	+	0.866043i	−0.198532	+	0.980095i	$0.563617\pi$
$578$	−8.09017	+	5.87785i	−0.336507	+	0.244486i
$579$	−11.5933	−	35.6805i	−0.481801	−	1.48283i
$580$	−1.60570	+	4.94183i	−0.0666730	+	0.205199i
$581$	2.25280	+	1.63675i	0.0934618	+	0.0679039i
$582$	2.73205			0.113247
$583$		0			0
$584$	12.9282			0.534973
$585$	−18.7661	−	13.6344i	−0.775882	−	0.563711i
$586$	−5.49575	+	16.9142i	−0.227027	+	0.698718i
$587$	−0.181843	−	0.559656i	−0.00750548	−	0.0230995i	0.947234	−	0.320544i	$-0.103866\pi$
$587$	−0.181843	−	0.559656i	−0.00750548	−	0.0230995i	−0.954739	+	0.297444i	$0.903866\pi$
$588$	−11.9185	+	8.65928i	−0.491510	+	0.357103i
$589$	39.0340	−	28.3599i	1.60837	−	1.16855i
$590$	1.35730	+	4.17733i	0.0558790	+	0.171978i
$591$	−6.24095	+	19.2077i	−0.256719	+	0.790098i
$592$	−2.58574	−	1.87865i	−0.106273	−	0.0772121i
$593$	−12.8038			−0.525791			−0.262896	−	0.964824i	$-0.584677\pi$
$593$	−12.8038			−0.525791			−0.262896	+	0.964824i	$0.584677\pi$
$594$		0			0
$595$	11.4115			0.467828
$596$	12.1353	+	8.81678i	0.497079	+	0.361149i
$597$	−17.2162	+	52.9860i	−0.704612	+	2.16857i
$598$	−4.38685	−	13.5013i	−0.179392	−	0.552111i
$599$	11.4849	−	8.34429i	0.469261	−	0.340938i	−0.327892	−	0.944715i	$-0.606338\pi$
$599$	11.4849	−	8.34429i	0.469261	−	0.340938i	0.797153	+	0.603777i	$0.206338\pi$
$600$	−4.42055	+	3.21172i	−0.180468	+	0.131118i
$601$	2.67617	+	8.23639i	0.109163	+	0.335969i	0.990685	−	0.136174i	$-0.0434805\pi$
$601$	2.67617	+	8.23639i	0.109163	+	0.335969i	−0.881522	+	0.472143i	$0.843481\pi$
$602$		0			0
$603$	−0.708411	−	0.514691i	−0.0288487	−	0.0209598i
$604$	16.3923			0.666993
$605$		0			0
$606$	12.0000			0.487467
$607$	−12.7856	−	9.28927i	−0.518951	−	0.377040i	0.297258	−	0.954797i	$-0.403928\pi$
$607$	−12.7856	−	9.28927i	−0.518951	−	0.377040i	−0.816208	+	0.577757i	$0.803928\pi$
$608$	1.46228	−	4.50045i	0.0593035	−	0.182517i
$609$	3.21140	+	9.88367i	0.130132	+	0.400506i
$610$	−13.2617	+	9.63516i	−0.536949	+	0.390116i
$611$	−5.33017	+	3.87260i	−0.215636	+	0.156669i
$612$	7.16801	+	22.0609i	0.289749	+	0.891757i
$613$	−4.42528	+	13.6196i	−0.178735	+	0.550091i	−0.999784	−	0.0207668i	$-0.993389\pi$
$613$	−4.42528	+	13.6196i	−0.178735	+	0.550091i	0.821049	+	0.570858i	$0.193389\pi$
$614$	−23.2447	−	16.8883i	−0.938080	−	0.681555i
$615$	52.9808			2.13639
$616$		0			0
$617$	31.3923			1.26381			0.631903	−	0.775047i	$-0.282274\pi$
$617$	31.3923			1.26381			0.631903	+	0.775047i	$0.282274\pi$
$618$	27.3904	+	19.9003i	1.10180	+	0.800507i
$619$	−6.11973	+	18.8346i	−0.245973	+	0.757026i	0.749502	+	0.662002i	$0.230293\pi$
$619$	−6.11973	+	18.8346i	−0.245973	+	0.757026i	−0.995475	+	0.0950240i	$0.969707\pi$
$620$	−5.45732	−	16.7959i	−0.219171	−	0.674540i
$621$	−15.3132	+	11.1257i	−0.614499	+	0.446460i
$622$	26.5233	−	19.2703i	1.06349	−	0.772669i
$623$	−0.181843	−	0.559656i	−0.00728540	−	0.0224221i
$624$	−2.53275	+	7.79500i	−0.101391	+	0.312050i
$625$	8.89919	+	6.46564i	0.355967	+	0.258626i
$626$	9.78461			0.391072
$627$		0			0
$628$	4.00000			0.159617
$629$	−13.4359	−	9.76176i	−0.535725	−	0.389227i
$630$	3.02956	−	9.32401i	0.120700	−	0.371478i
$631$	3.27201	+	10.0702i	0.130257	+	0.400889i	0.994822	−	0.101631i	$-0.0324062\pi$
$631$	3.27201	+	10.0702i	0.130257	+	0.400889i	−0.864565	+	0.502520i	$0.832406\pi$
$632$	1.02579	−	0.745282i	0.0408038	−	0.0296457i
$633$	4.10317	−	2.98113i	0.163086	−	0.118489i
$634$	6.13597	+	18.8846i	0.243690	+	0.750002i
$635$	−7.41641	+	22.8254i	−0.294311	+	0.905797i
$636$	1.77672	+	1.29087i	0.0704517	+	0.0511862i
$637$	−16.1769			−0.640953
$638$		0			0
$639$	−11.3205			−0.447832
$640$	−1.40126	−	1.01807i	−0.0553896	−	0.0402429i
$641$	11.8417	−	36.4450i	0.467719	−	1.43949i	−0.387813	−	0.921738i	$-0.626769\pi$
$641$	11.8417	−	36.4450i	0.467719	−	1.43949i	0.855531	−	0.517751i	$-0.173231\pi$
$642$	15.6933	+	48.2990i	0.619365	+	1.90621i
$643$	29.2833	−	21.2756i	1.15482	−	0.839026i	0.165706	−	0.986175i	$-0.447010\pi$
$643$	29.2833	−	21.2756i	1.15482	−	0.839026i	0.989114	+	0.147149i	$0.0470096\pi$
$644$	4.85410	−	3.52671i	0.191278	−	0.138972i
$645$		0			0
$646$	7.59825	−	23.3850i	0.298949	−	0.920071i
$647$	−9.15848	−	6.65403i	−0.360057	−	0.261597i	0.393019	−	0.919530i	$-0.371431\pi$
$647$	−9.15848	−	6.65403i	−0.360057	−	0.261597i	−0.753076	+	0.657934i	$0.771431\pi$
$648$	−2.46410			−0.0967991
$649$		0			0
$650$	−6.00000			−0.235339
$651$	−28.5749	−	20.7609i	−1.11994	−	0.813683i
$652$	3.64759	−	11.2261i	0.142851	−	0.439649i
$653$	7.99007	+	24.5909i	0.312676	+	0.962316i	0.976701	+	0.214606i	$0.0688468\pi$
$653$	7.99007	+	24.5909i	0.312676	+	0.962316i	−0.664025	+	0.747710i	$0.731153\pi$
$654$	−35.2057	+	25.5785i	−1.37665	+	1.00020i
$655$		0			0
$656$	−3.45980	−	10.6482i	−0.135083	−	0.415741i
$657$	17.8342	−	54.8881i	0.695780	−	2.14139i
$658$	−2.25280	−	1.63675i	−0.0878232	−	0.0638073i
$659$	−34.9808			−1.36266			−0.681329	−	0.731978i	$-0.738597\pi$
$659$	−34.9808			−1.36266			−0.681329	+	0.731978i	$0.738597\pi$
$660$		0			0
$661$	−47.5885			−1.85098			−0.925488	−	0.378776i	$-0.876345\pi$
$661$	−47.5885			−1.85098			−0.925488	+	0.378776i	$0.876345\pi$
$662$	10.3430	+	7.51461i	0.401991	+	0.292063i
$663$	−13.1606	+	40.5040i	−0.511114	+	1.57305i
$664$	−0.678648	−	2.08867i	−0.0263367	−	0.0810559i
$665$	−8.40755	+	6.10844i	−0.326031	+	0.236875i
$666$	−11.5430	+	8.38649i	−0.447283	+	0.324970i
$667$	4.38685	+	13.5013i	0.169860	+	0.522774i
$668$	−1.35730	+	4.17733i	−0.0525154	+	0.161626i
$669$	0.867102	+	0.629986i	0.0335241	+	0.0243567i
$670$	0.339746			0.0131255
$671$		0			0
$672$	−3.46410			−0.133631
$673$	10.4591	+	7.59901i	0.403170	+	0.292920i	0.770831	−	0.637040i	$-0.219841\pi$
$673$	10.4591	+	7.59901i	0.403170	+	0.292920i	−0.367661	+	0.929960i	$0.619841\pi$
$674$	−4.53027	+	13.9427i	−0.174499	+	0.537054i
$675$	2.47214	+	7.60845i	0.0951526	+	0.292849i
$676$	3.23607	−	2.35114i	0.124464	−	0.0904285i
$677$	−20.5428	+	14.9252i	−0.789524	+	0.573623i	−0.907822	−	0.419355i	$-0.862256\pi$
$677$	−20.5428	+	14.9252i	−0.789524	+	0.573623i	0.118298	+	0.992978i	$0.462256\pi$
$678$	14.2310	+	43.7986i	0.546539	+	1.68207i
$679$	−0.391818	+	1.20589i	−0.0150366	+	0.0462779i
$680$	−7.28115	−	5.29007i	−0.279219	−	0.202865i
$681$	−12.0000			−0.459841
$682$		0			0
$683$	−36.5885			−1.40002			−0.700009	−	0.714134i	$-0.746821\pi$
$683$	−36.5885			−1.40002			−0.700009	+	0.714134i	$0.746821\pi$
$684$	−17.0900	−	12.4166i	−0.653451	−	0.474760i
$685$	−1.35730	+	4.17733i	−0.0518596	+	0.159608i
$686$	−4.85553	−	14.9438i	−0.185385	−	0.570556i
$687$	−6.19728	+	4.50258i	−0.236441	+	0.171784i
$688$		0			0
$689$	0.745208	+	2.29351i	0.0283902	+	0.0873759i
$690$	6.91960	−	21.2963i	0.263425	−	0.810738i
$691$	−17.1325	−	12.4475i	−0.651750	−	0.473524i	0.212117	−	0.977244i	$-0.431964\pi$
$691$	−17.1325	−	12.4475i	−0.651750	−	0.473524i	−0.863867	+	0.503720i	$0.831964\pi$
$692$	16.3923			0.623142
$693$		0			0
$694$	−7.60770			−0.288784
$695$	−13.7377	−	9.98104i	−0.521102	−	0.378602i
$696$	2.53275	−	7.79500i	0.0960037	−	0.295469i
$697$	−17.9777	−	55.3295i	−0.680952	−	2.09576i
$698$	6.53022	−	4.74448i	0.247173	−	0.179581i
$699$	−38.0082	+	27.6146i	−1.43760	+	1.04448i
$700$	−0.783636	−	2.41178i	−0.0296186	−	0.0911568i
$701$	7.34985	−	22.6205i	0.277600	−	0.854365i	−0.710920	−	0.703273i	$-0.751721\pi$
$701$	7.34985	−	22.6205i	0.277600	−	0.854365i	0.988520	−	0.151092i	$-0.0482789\pi$
$702$	9.70820	+	7.05342i	0.366413	+	0.266214i
$703$	15.1244			0.570426
$704$		0			0
$705$	−10.3923			−0.391397
$706$	−6.53022	−	4.74448i	−0.245768	−	0.178561i
$707$	−1.72098	+	5.29664i	−0.0647242	+	0.199201i
$708$	−2.14093	−	6.58911i	−0.0804612	−	0.247634i
$709$	30.7426	−	22.3358i	1.15456	−	0.838840i	0.165483	−	0.986213i	$-0.447082\pi$
$709$	30.7426	−	22.3358i	1.15456	−	0.838840i	0.989081	+	0.147373i	$0.0470816\pi$
$710$	3.55345	−	2.58173i	0.133359	−	0.0968907i
$711$	−1.74911	−	5.38322i	−0.0655969	−	0.201887i
$712$	−0.143415	+	0.441387i	−0.00537472	+	0.0165417i
$713$	−39.0340	−	28.3599i	−1.46184	−	1.06209i
$714$	−18.0000			−0.673633
$715$		0			0
$716$	13.8564			0.517838
$717$	−8.40755	−	6.10844i	−0.313986	−	0.228124i
$718$	7.59825	−	23.3850i	0.283564	−	0.872721i
$719$	−13.3705	−	41.1503i	−0.498637	−	1.53465i	−0.811212	−	0.584753i	$-0.801192\pi$
$719$	−13.3705	−	41.1503i	−0.498637	−	1.53465i	0.312575	−	0.949893i	$-0.398808\pi$
$720$	−6.25536	+	4.54479i	−0.233124	+	0.169374i
$721$	−12.7119	+	9.23576i	−0.473417	+	0.343958i
$722$	1.04828	+	3.22627i	0.0390129	+	0.120069i
$723$	12.4819	−	38.4154i	0.464207	−	1.42868i
$724$	2.58574	+	1.87865i	0.0960983	+	0.0698195i
$725$	6.00000			0.222834
$726$		0			0
$727$	14.9808			0.555606			0.277803	−	0.960638i	$-0.410394\pi$
$727$	14.9808			0.555606			0.277803	+	0.960638i	$0.410394\pi$
$728$	−3.07738	−	2.23585i	−0.114055	−	0.0828659i
$729$	−13.5302	+	41.6416i	−0.501118	+	1.54228i
$730$	6.91960	+	21.2963i	0.256106	+	0.788213i
$731$		0			0
$732$	20.9183	−	15.1980i	0.773162	−	0.561735i
$733$	11.5549	+	35.5622i	0.426788	+	1.31352i	0.901271	+	0.433255i	$0.142635\pi$
$733$	11.5549	+	35.5622i	0.426788	+	1.31352i	−0.474483	+	0.880265i	$0.657365\pi$
$734$	−6.98022	+	21.4829i	−0.257645	+	0.792948i
$735$	−20.6434	−	14.9983i	−0.761444	−	0.553221i
$736$	−4.73205			−0.174426
$737$		0			0
$738$	−49.9808			−1.83982
$739$	−5.87989	−	4.27199i	−0.216295	−	0.157148i	0.474362	−	0.880330i	$-0.342679\pi$
$739$	−5.87989	−	4.27199i	−0.216295	−	0.157148i	−0.690657	+	0.723182i	$0.742679\pi$
$740$	1.71069	−	5.26495i	0.0628861	−	0.193543i
$741$	−11.9851	−	36.8864i	−0.440284	−	1.35505i
$742$	−0.824581	+	0.599093i	−0.0302713	+	0.0219934i
$743$	22.4938	−	16.3427i	0.825217	−	0.599555i	−0.0929851	−	0.995667i	$-0.529641\pi$
$743$	22.4938	−	16.3427i	0.825217	−	0.599555i	0.918202	+	0.396112i	$0.129641\pi$
$744$	8.60810	+	26.4930i	0.315588	+	0.971281i
$745$	−8.02850	+	24.7092i	−0.294141	+	0.905274i
$746$	−18.8667	−	13.7075i	−0.690759	−	0.501865i
$747$	−9.80385			−0.358704
$748$		0			0
$749$	−23.5692			−0.861201
$750$	−26.7982	−	19.4700i	−0.978531	−	0.710944i
$751$	1.23607	−	3.80423i	0.0451048	−	0.138818i	−0.925968	−	0.377602i	$-0.876749\pi$
$751$	1.23607	−	3.80423i	0.0451048	−	0.138818i	0.971073	+	0.238784i	$0.0767487\pi$
$752$	0.678648	+	2.08867i	0.0247478	+	0.0761658i
$753$	−33.4290	+	24.2876i	−1.21822	+	0.885089i
$754$	7.28115	−	5.29007i	0.265164	−	0.192653i
$755$	8.77370	+	27.0027i	0.319308	+	0.982728i
$756$	−1.56727	+	4.82357i	−0.0570011	+	0.175431i
$757$	2.26836	+	1.64806i	0.0824450	+	0.0598998i	0.628244	−	0.778016i	$-0.283774\pi$
$757$	2.26836	+	1.64806i	0.0824450	+	0.0598998i	−0.545799	+	0.837916i	$0.683774\pi$
$758$	24.3923			0.885968
$759$		0			0
$760$	8.19615			0.297306
$761$	25.8730	+	18.7978i	0.937895	+	0.681420i	0.947913	−	0.318529i	$-0.103189\pi$
$761$	25.8730	+	18.7978i	0.937895	+	0.681420i	−0.0100182	+	0.999950i	$0.503189\pi$
$762$	11.6983	−	36.0036i	0.423784	−	1.30427i
$763$	−6.24095	−	19.2077i	−0.225938	−	0.695365i
$764$	11.7598	−	8.54399i	0.425454	−	0.309111i
$765$	−32.5038	+	23.6154i	−1.17518	+	0.853817i
$766$	−10.9146	−	33.5918i	−0.394362	−	1.21372i
$767$	2.35091	−	7.23535i	0.0848863	−	0.261253i
$768$	2.21028	+	1.60586i	0.0797564	+	0.0579465i
$769$	−10.5167			−0.379240			−0.189620	−	0.981858i	$-0.560726\pi$
$769$	−10.5167			−0.379240			−0.189620	+	0.981858i	$0.560726\pi$
$770$		0			0
$771$	−3.80385			−0.136992
$772$	−11.1095	−	8.07150i	−0.399838	−	0.290500i
$773$	−5.56231	+	17.1190i	−0.200062	+	0.615728i	0.799818	+	0.600243i	$0.204929\pi$
$773$	−5.56231	+	17.1190i	−0.200062	+	0.615728i	−0.999880	+	0.0154855i	$0.995071\pi$
$774$		0			0
$775$	−16.4977	+	11.9863i	−0.592616	+	0.430560i
$776$	0.809017	−	0.587785i	0.0290420	−	0.0211003i
$777$	−3.42137	−	10.5299i	−0.122741	−	0.377758i
$778$	4.74024	−	14.5890i	0.169946	−	0.523040i
$779$	42.8623	+	31.1413i	1.53570	+	1.11575i
$780$	−14.1962			−0.508304
$781$		0			0
$782$	−24.5885			−0.879281
$783$	−9.70820	−	7.05342i	−0.346943	−	0.252069i
$784$	−1.66631	+	5.12839i	−0.0595112	+	0.183157i
$785$	2.14093	+	6.58911i	0.0764132	+	0.235176i
$786$		0			0
$787$	−2.60131	+	1.88996i	−0.0927265	+	0.0673698i	−0.633183	−	0.774003i	$-0.718252\pi$
$787$	−2.60131	+	1.88996i	−0.0927265	+	0.0673698i	0.540456	+	0.841372i	$0.318252\pi$
$788$	2.28435	+	7.03050i	0.0813765	+	0.250451i
$789$	−17.0506	+	52.4764i	−0.607018	+	1.86821i
$790$	1.77672	+	1.29087i	0.0632130	+	0.0459270i
$791$	−21.3731			−0.759939
$792$		0			0
$793$	28.3923			1.00824
$794$	20.7015	+	15.0405i	0.734669	+	0.533768i
$795$	−1.17545	+	3.61767i	−0.0416890	+	0.128306i
$796$	6.30157	+	19.3942i	0.223353	+	0.687410i
$797$	−18.6655	+	13.5613i	−0.661165	+	0.480365i	−0.867056	−	0.498210i	$-0.833991\pi$
$797$	−18.6655	+	13.5613i	−0.661165	+	0.480365i	0.205891	+	0.978575i	$0.433991\pi$
$798$	13.2617	−	9.63516i	0.469457	−	0.341081i
$799$	3.52636	+	10.8530i	0.124754	+	0.383952i
$800$	−0.618034	+	1.90211i	−0.0218508	+	0.0672499i
$801$	1.67612	+	1.21777i	0.0592227	+	0.0430278i
$802$	13.3923			0.472899
$803$		0			0
$804$	−0.535898			−0.0188997
$805$	8.40755	+	6.10844i	0.296327	+	0.215294i
$806$	−9.45235	+	29.0914i	−0.332945	+	1.02470i
$807$	18.2261	+	56.0940i	0.641588	+	1.97460i
$808$	3.55345	−	2.58173i	0.125010	−	0.0908250i
$809$	−14.5623	+	10.5801i	−0.511983	+	0.371978i	−0.813575	−	0.581459i	$-0.802482\pi$
$809$	−14.5623	+	10.5801i	−0.511983	+	0.371978i	0.301592	+	0.953437i	$0.402482\pi$
$810$	−1.31887	−	4.05906i	−0.0463403	−	0.142621i
$811$	−2.14093	+	6.58911i	−0.0751783	+	0.231375i	−0.981583	−	0.191035i	$-0.938816\pi$
$811$	−2.14093	+	6.58911i	−0.0751783	+	0.231375i	0.906405	+	0.422410i	$0.138816\pi$
$812$	3.07738	+	2.23585i	0.107995	+	0.0784628i
$813$	−12.0000			−0.420858
$814$		0			0
$815$	20.4449			0.716152
$816$	11.4849	+	8.34429i	0.402053	+	0.292109i
$817$		0			0
$818$	4.53027	+	13.9427i	0.158397	+	0.487496i
$819$	−13.7377	+	9.98104i	−0.480035	+	0.348766i
$820$	15.6887	−	11.3985i	0.547873	−	0.398053i
$821$	1.35730	+	4.17733i	0.0473700	+	0.145790i	0.971944	−	0.235213i	$-0.0755788\pi$
$821$	1.35730	+	4.17733i	0.0473700	+	0.145790i	−0.924574	+	0.381003i	$0.875579\pi$
$822$	2.14093	−	6.58911i	0.0746736	−	0.229822i
$823$	−25.8885	−	18.8091i	−0.902418	−	0.655645i	0.0366680	−	0.999328i	$-0.488326\pi$
$823$	−25.8885	−	18.8091i	−0.902418	−	0.655645i	−0.939086	+	0.343683i	$0.888326\pi$
$824$	12.3923			0.431706
$825$		0			0
$826$	3.21539			0.111878
$827$	7.93148	+	5.76256i	0.275805	+	0.200384i	0.717085	−	0.696985i	$-0.245476\pi$
$827$	7.93148	+	5.76256i	0.275805	+	0.200384i	−0.441281	+	0.897369i	$0.645476\pi$
$828$	−6.52778	+	20.0905i	−0.226856	+	0.698192i
$829$	7.78604	+	23.9630i	0.270420	+	0.832268i	0.990395	+	0.138268i	$0.0441534\pi$
$829$	7.78604	+	23.9630i	0.270420	+	0.832268i	−0.719975	+	0.694000i	$0.755847\pi$
$830$	3.07738	−	2.23585i	0.106817	−	0.0776073i
$831$	58.1756	−	42.2670i	2.01809	−	1.46623i
$832$	0.927051	+	2.85317i	0.0321397	+	0.0989159i
$833$	−8.65842	+	26.6479i	−0.299996	+	0.923294i
$834$	21.6692	+	15.7436i	0.750343	+	0.545156i
$835$	−7.60770			−0.263275
$836$		0			0
$837$	40.7846			1.40972
$838$	−26.9994	−	19.6162i	−0.932678	−	0.677630i
$839$	2.60961	−	8.03154i	0.0900936	−	0.277280i	−0.895850	−	0.444356i	$-0.853433\pi$
$839$	2.60961	−	8.03154i	0.0900936	−	0.277280i	0.985944	+	0.167076i	$0.0534326\pi$
$840$	−1.85410	−	5.70634i	−0.0639726	−	0.196887i
$841$	16.1803	−	11.7557i	0.557943	−	0.405369i
$842$	19.0835	−	13.8649i	0.657660	−	0.477818i
$843$	−15.1965	−	46.7700i	−0.523395	−	1.61085i
$844$	0.573661	−	1.76555i	0.0197462	−	0.0607726i
$845$	5.60503	+	4.07230i	0.192819	+	0.140091i
$846$	9.80385			0.337063
$847$		0			0
$848$	0.803848			0.0276042
$849$	−15.3132	−	11.1257i	−0.525549	−	0.381834i
$850$	−3.21140	+	9.88367i	−0.110150	+	0.339007i
$851$	−4.67368	−	14.3841i	−0.160212	−	0.493081i
$852$	−5.60503	+	4.07230i	−0.192025	+	0.139515i
$853$	−13.6371	+	9.90795i	−0.466926	+	0.339242i	−0.796242	−	0.604978i	$-0.793182\pi$
$853$	−13.6371	+	9.90795i	−0.466926	+	0.339242i	0.329316	+	0.944220i	$0.393182\pi$
$854$	3.70820	+	11.4127i	0.126892	+	0.390534i
$855$	11.3065	−	34.7977i	0.386673	−	1.19006i
$856$	15.0384	+	10.9260i	0.514001	+	0.373444i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	16.7846			0.572683			0.286342	−	0.958128i	$-0.407561\pi$
$859$	16.7846			0.572683			0.286342	+	0.958128i	$0.407561\pi$
$860$		0			0
$861$	11.9851	−	36.8864i	0.408451	−	1.25708i
$862$	−1.35730	−	4.17733i	−0.0462297	−	0.142280i
$863$	11.4849	−	8.34429i	0.390952	−	0.284043i	−0.374894	−	0.927068i	$-0.622321\pi$
$863$	11.4849	−	8.34429i	0.390952	−	0.284043i	0.765845	+	0.643025i	$0.222321\pi$
$864$	3.23607	−	2.35114i	0.110093	−	0.0799874i
$865$	8.77370	+	27.0027i	0.298315	+	0.918119i
$866$	−3.02361	+	9.30572i	−0.102746	+	0.316221i
$867$	22.1028	+	16.0586i	0.750649	+	0.545378i
$868$	−12.9282			−0.438812
$869$		0			0
$870$	14.1962			0.481295
$871$	−0.476072	−	0.345887i	−0.0161311	−	0.0117199i
$872$	−4.92209	+	15.1486i	−0.166683	+	0.512997i
$873$	−1.37948	−	4.24561i	−0.0466884	−	0.143692i
$874$	18.1158	−	13.1619i	0.612775	−	0.445207i
$875$	12.4371	−	9.03606i	0.420450	−	0.305475i
$876$	−10.9146	−	33.5918i	−0.368771	−	1.13496i
$877$	0.143415	−	0.441387i	0.00484279	−	0.0149046i	−0.948606	−	0.316460i	$-0.897506\pi$
$877$	0.143415	−	0.441387i	0.00484279	−	0.0149046i	0.953449	+	0.301555i	$0.0975058\pi$
$878$	−2.52766	−	1.83645i	−0.0853043	−	0.0619772i
$879$	48.5885			1.63885
$880$		0			0
$881$	48.4641			1.63280			0.816399	−	0.577489i	$-0.195967\pi$
$881$	48.4641			1.63280			0.816399	+	0.577489i	$0.195967\pi$
$882$	19.4745	+	14.1490i	0.655740	+	0.476423i
$883$	−11.2458	+	34.6111i	−0.378453	+	1.16476i	0.562667	+	0.826684i	$0.309775\pi$
$883$	−11.2458	+	34.6111i	−0.378453	+	1.16476i	−0.941120	+	0.338074i	$0.890225\pi$
$884$	4.81710	+	14.8255i	0.162017	+	0.498636i
$885$	9.70820	−	7.05342i	0.326338	−	0.237098i
$886$	−25.0214	+	18.1791i	−0.840612	+	0.610740i
$887$	−17.3656	−	53.4457i	−0.583079	−	1.79453i	−0.606853	−	0.794814i	$-0.707568\pi$
$887$	−17.3656	−	53.4457i	−0.583079	−	1.79453i	0.0237742	−	0.999717i	$-0.492432\pi$
$888$	−2.69835	+	8.30467i	−0.0905508	+	0.278687i
$889$	14.2138	+	10.3269i	0.476715	+	0.346354i
$890$	−0.803848			−0.0269450
$891$		0			0
$892$	0.392305			0.0131353
$893$	−8.40755	−	6.10844i	−0.281348	−	0.204411i
$894$	12.6638	−	38.9750i	0.423539	−	1.30352i
$895$	7.41641	+	22.8254i	0.247903	+	0.762968i
$896$	−1.02579	+	0.745282i	−0.0342693	+	0.0248981i
$897$	−31.3774	+	22.7970i	−1.04766	+	0.761170i
$898$	1.21388	+	3.73594i	0.0405078	+	0.124670i
$899$	9.45235	−	29.0914i	0.315254	−	0.970251i
$900$	7.22307	+	5.24787i	0.240769	+	0.174929i
$901$	4.17691			0.139153
$902$		0			0
$903$		0			0
$904$	13.6371	+	9.90795i	0.453564	+	0.329533i
$905$	−1.71069	+	5.26495i	−0.0568651	+	0.175013i
$906$	−13.8392	−	42.5927i	−0.459777	−	1.41505i
$907$	36.8663	−	26.7849i	1.22412	−	0.889379i	0.227689	−	0.973734i	$-0.426883\pi$
$907$	36.8663	−	26.7849i	1.22412	−	0.889379i	0.996436	+	0.0843555i	$0.0268831\pi$
$908$	−3.55345	+	2.58173i	−0.117925	+	0.0856778i
$909$	−6.05911	−	18.6480i	−0.200968	−	0.618516i
$910$	2.03595	−	6.26600i	0.0674909	−	0.207716i
$911$	42.3863	+	30.7954i	1.40432	+	1.02030i	0.994118	+	0.108303i	$0.0345417\pi$
$911$	42.3863	+	30.7954i	1.40432	+	1.02030i	0.410202	+	0.911995i	$0.365458\pi$
$912$	−12.9282			−0.428096
$913$		0			0
$914$	5.19615			0.171873
$915$	36.2315	+	26.3237i	1.19778	+	0.870236i
$916$	−0.866437	+	2.66662i	−0.0286279	+	0.0881075i
$917$		0			0
$918$	16.8151	−	12.2169i	0.554981	−	0.403217i
$919$	−40.3347	+	29.3049i	−1.33052	+	0.966678i	−0.330782	+	0.943707i	$0.607313\pi$
$919$	−40.3347	+	29.3049i	−1.33052	+	0.966678i	−0.999736	+	0.0229710i	$0.992687\pi$
$920$	−2.53275	−	7.79500i	−0.0835023	−	0.256994i
$921$	−24.2570	+	74.6555i	−0.799297	+	2.45998i
$922$	−26.6976	−	19.3969i	−0.879237	−	0.638803i
$923$	−7.60770			−0.250410
$924$		0			0
$925$	−6.39230			−0.210178
$926$	10.3430	+	7.51461i	0.339891	+	0.246945i
$927$	17.0950	−	52.6129i	0.561473	−	1.72804i
$928$	−0.927051	−	2.85317i	−0.0304319	−	0.0936599i
$929$	−31.5517	+	22.9236i	−1.03518	+	0.752100i	−0.969338	−	0.245731i	$-0.920972\pi$
$929$	−31.5517	+	22.9236i	−1.03518	+	0.752100i	−0.0658383	+	0.997830i	$0.520972\pi$
$930$	−39.0340	+	28.3599i	−1.27998	+	0.929957i
$931$	−7.88508	−	24.2678i	−0.258423	−	0.795345i
$932$	−5.31390	+	16.3545i	−0.174063	+	0.535710i
$933$	−72.4630	−	52.6475i	−2.37233	−	1.72360i
$934$	14.5359			0.475629
$935$		0			0
$936$	13.3923			0.437741
$937$	18.9673	+	13.7805i	0.619634	+	0.450191i	0.852794	−	0.522248i	$-0.174906\pi$
$937$	18.9673	+	13.7805i	0.619634	+	0.450191i	−0.233159	+	0.972439i	$0.574906\pi$
$938$	0.0768560	−	0.236539i	0.00250944	−	0.00772326i
$939$	−8.26066	−	25.4237i	−0.269576	−	0.829671i
$940$	−3.07738	+	2.23585i	−0.100373	+	0.0729252i
$941$	44.8133	−	32.5588i	1.46087	−	1.06139i	0.477738	−	0.878503i	$-0.341457\pi$
$941$	44.8133	−	32.5588i	1.46087	−	1.06139i	0.983135	−	0.182883i	$-0.0585431\pi$
$942$	−3.37700	−	10.3933i	−0.110029	−	0.338633i
$943$	16.3720	−	50.3877i	0.533144	−	1.64085i
$944$	−2.05158	−	1.49056i	−0.0667734	−	0.0485137i
$945$	−8.78461			−0.285763
$946$		0			0
$947$	−59.9090			−1.94678			−0.973390	−	0.229155i	$-0.926404\pi$
$947$	−59.9090			−1.94678			−0.973390	+	0.229155i	$0.926404\pi$
$948$	−2.80252	−	2.03615i	−0.0910215	−	0.0661310i
$949$	11.9851	−	36.8864i	0.389053	−	1.19738i
$950$	−2.92457	−	9.00090i	−0.0948855	−	0.292028i
$951$	43.8881	−	31.8866i	1.42317	−	1.03399i
$952$	−5.33017	+	3.87260i	−0.172752	+	0.125512i
$953$	−2.59931	−	7.99985i	−0.0841999	−	0.259141i	0.900089	−	0.435706i	$-0.143501\pi$
$953$	−2.59931	−	7.99985i	−0.0841999	−	0.259141i	−0.984289	+	0.176565i	$0.943501\pi$
$954$	1.10889	−	3.41283i	0.0359018	−	0.110494i
$955$	20.3686	+	14.7986i	0.659111	+	0.478872i
$956$	−3.80385			−0.123025
$957$		0			0
$958$	32.7846			1.05922
$959$	2.60131	+	1.88996i	0.0840005	+	0.0610300i
$960$	−1.46228	+	4.50045i	−0.0471950	+	0.145251i
$961$	22.5464	+	69.3905i	0.727302	+	2.23840i
$962$	−7.75722	+	5.63595i	−0.250103	+	0.181710i
$963$	67.1328	−	48.7749i	2.16333	−	1.57175i
$964$	−4.56870	−	14.0610i	−0.147148	−	0.452874i
$965$	7.34985	−	22.6205i	0.236600	−	0.728180i
$966$	−13.2617	−	9.63516i	−0.426687	−	0.310006i
$967$	26.4449			0.850409			0.425205	−	0.905097i	$-0.360202\pi$
$967$	26.4449			0.850409			0.425205	+	0.905097i	$0.360202\pi$
$968$		0			0
$969$	−67.1769			−2.15803
$970$	1.40126	+	1.01807i	0.0449917	+	0.0326884i
$971$	10.5228	−	32.3859i	0.337693	−	1.03931i	−0.627687	−	0.778466i	$-0.715998\pi$
$971$	10.5228	−	32.3859i	0.337693	−	1.03931i	0.965380	−	0.260847i	$-0.0840019\pi$
$972$	5.78852	+	17.8152i	0.185667	+	0.571424i
$973$	−10.0567	+	7.30663i	−0.322403	+	0.234240i
$974$	−31.5361	+	22.9123i	−1.01048	+	0.734158i
$975$	5.06550	+	15.5900i	0.162226	+	0.499280i
$976$	2.92457	−	9.00090i	0.0936131	−	0.288112i
$977$	1.87733	+	1.36396i	0.0600611	+	0.0436370i	0.617411	−	0.786641i	$-0.288182\pi$
$977$	1.87733	+	1.36396i	0.0600611	+	0.0436370i	−0.557350	+	0.830278i	$0.688182\pi$
$978$	−32.2487			−1.03120
$979$		0			0
$980$	−9.33975			−0.298347
$981$	57.5252	+	41.7945i	1.83664	+	1.33440i
$982$	12.1669	−	37.4460i	0.388263	−	1.19495i
$983$	−13.6292	−	41.9465i	−0.434705	−	1.33788i	−0.893389	−	0.449285i	$-0.851679\pi$
$983$	−13.6292	−	41.9465i	−0.434705	−	1.33788i	0.458684	−	0.888600i	$-0.348321\pi$
$984$	−24.7466	+	17.9794i	−0.788892	+	0.573164i
$985$	−10.3585	+	7.52591i	−0.330050	+	0.239796i
$986$	−4.81710	−	14.8255i	−0.153408	−	0.472140i
$987$	−2.35091	+	7.23535i	−0.0748302	+	0.230304i
$988$	−11.4849	−	8.34429i	−0.365384	−	0.265467i
$989$		0			0
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	8.24886	+	5.99315i	0.261902	+	0.190283i
$993$	10.7934	−	33.2187i	0.342518	−	1.05416i
$994$	−0.993610	−	3.05802i	−0.0315154	−	0.0969944i
$995$	−28.5749	+	20.7609i	−0.905885	+	0.658164i
$996$	−4.85410	+	3.52671i	−0.153808	+	0.111748i
$997$	1.71069	+	5.26495i	0.0541780	+	0.166743i	0.974484	−	0.224456i	$-0.0720605\pi$
$997$	1.71069	+	5.26495i	0.0541780	+	0.166743i	−0.920306	+	0.391199i	$0.872061\pi$
$998$	4.94427	−	15.2169i	0.156508	−	0.481683i
$999$	10.3430	+	7.51461i	0.327237	+	0.237752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.2.c.f.81.1		8
11.2	odd	10		242.2.c.g.27.2		8
11.3	even	5	inner	242.2.c.f.3.1		8
11.4	even	5	inner	242.2.c.f.9.2		8
11.5	even	5		242.2.a.e.1.1	yes	2
11.6	odd	10		242.2.a.c.1.1	✓	2
11.7	odd	10		242.2.c.g.9.2		8
11.8	odd	10		242.2.c.g.3.1		8
11.9	even	5	inner	242.2.c.f.27.2		8
11.10	odd	2		242.2.c.g.81.1		8
33.5	odd	10		2178.2.a.s.1.1		2
33.17	even	10		2178.2.a.y.1.1		2
44.27	odd	10		1936.2.a.v.1.2		2
44.39	even	10		1936.2.a.y.1.2		2
55.39	odd	10		6050.2.a.cv.1.2		2
55.49	even	10		6050.2.a.cc.1.2		2
88.5	even	10		7744.2.a.cv.1.2		2
88.27	odd	10		7744.2.a.bq.1.1		2
88.61	odd	10		7744.2.a.cs.1.2		2
88.83	even	10		7744.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
242.2.a.c.1.1	✓	2	11.6	odd	10
242.2.a.e.1.1	yes	2	11.5	even	5
242.2.c.f.3.1		8	11.3	even	5	inner
242.2.c.f.9.2		8	11.4	even	5	inner
242.2.c.f.27.2		8	11.9	even	5	inner
242.2.c.f.81.1		8	1.1	even	1	trivial
242.2.c.g.3.1		8	11.8	odd	10
242.2.c.g.9.2		8	11.7	odd	10
242.2.c.g.27.2		8	11.2	odd	10
242.2.c.g.81.1		8	11.10	odd	2
1936.2.a.v.1.2		2	44.27	odd	10
1936.2.a.y.1.2		2	44.39	even	10
2178.2.a.s.1.1		2	33.5	odd	10
2178.2.a.y.1.1		2	33.17	even	10
6050.2.a.cc.1.2		2	55.49	even	10
6050.2.a.cv.1.2		2	55.39	odd	10
7744.2.a.bq.1.1		2	88.27	odd	10
7744.2.a.bt.1.1		2	88.83	even	10
7744.2.a.cs.1.2		2	88.61	odd	10
7744.2.a.cv.1.2		2	88.5	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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.844250 + 2.59833i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.40126 + 1.01807i) q^{5} +(2.21028 - 1.60586i) q^{6} +(0.391818 + 1.20589i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-3.61153 - 2.62393i) q^{9} +1.73205 q^{10} -2.73205 q^{12} +(-2.42705 - 1.76336i) q^{13} +(0.391818 - 1.20589i) q^{14} +(-1.46228 - 4.50045i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.20378 + 3.05422i) q^{17} +(1.37948 + 4.24561i) q^{18} +(1.46228 - 4.50045i) q^{19} +(-1.40126 - 1.01807i) q^{20} -3.46410 q^{21} -4.73205 q^{23} +(2.21028 + 1.60586i) q^{24} +(-0.618034 + 1.90211i) q^{25} +(0.927051 + 2.85317i) q^{26} +(3.23607 - 2.35114i) q^{27} +(-1.02579 + 0.745282i) q^{28} +(-0.927051 - 2.85317i) q^{29} +(-1.46228 + 4.50045i) q^{30} +(8.24886 + 5.99315i) q^{31} +1.00000 q^{32} +5.19615 q^{34} +(-1.77672 - 1.29087i) q^{35} +(1.37948 - 4.24561i) q^{36} +(0.987665 + 3.03972i) q^{37} +(-3.82831 + 2.78143i) q^{38} +(6.63083 - 4.81758i) q^{39} +(0.535233 + 1.64728i) q^{40} +(-3.45980 + 10.6482i) q^{41} +(2.80252 + 2.03615i) q^{42} +7.73205 q^{45} +(3.82831 + 2.78143i) q^{46} +(0.678648 - 2.08867i) q^{47} +(-0.844250 - 2.59833i) q^{48} +(4.36247 - 3.16952i) q^{49} +(1.61803 - 1.17557i) q^{50} +(-4.38685 - 13.5013i) q^{51} +(0.927051 - 2.85317i) q^{52} +(-0.650326 - 0.472490i) q^{53} -4.00000 q^{54} +1.26795 q^{56} +(10.4591 + 7.59901i) q^{57} +(-0.927051 + 2.85317i) q^{58} +(0.783636 + 2.41178i) q^{59} +(3.82831 - 2.78143i) q^{60} +(-7.65662 + 5.56286i) q^{61} +(-3.15078 - 9.69712i) q^{62} +(1.74911 - 5.38322i) q^{63} +(-0.809017 - 0.587785i) q^{64} +5.19615 q^{65} +0.196152 q^{67} +(-4.20378 - 3.05422i) q^{68} +(3.99503 - 12.2955i) q^{69} +(0.678648 + 2.08867i) q^{70} +(2.05158 - 1.49056i) q^{71} +(-3.61153 + 2.62393i) q^{72} +(3.99503 + 12.2955i) q^{73} +(0.987665 - 3.03972i) q^{74} +(-4.42055 - 3.21172i) q^{75} +4.73205 q^{76} -8.19615 q^{78} +(1.02579 + 0.745282i) q^{79} +(0.535233 - 1.64728i) q^{80} +(-0.761449 - 2.34350i) q^{81} +(9.05788 - 6.58093i) q^{82} +(1.77672 - 1.29087i) q^{83} +(-1.07047 - 3.29456i) q^{84} +(2.78115 - 8.55951i) q^{85} +8.19615 q^{87} -0.464102 q^{89} +(-6.25536 - 4.54479i) q^{90} +(1.17545 - 3.61767i) q^{91} +(-1.46228 - 4.50045i) q^{92} +(-22.5363 + 16.3736i) q^{93} +(-1.77672 + 1.29087i) q^{94} +(2.53275 + 7.79500i) q^{95} +(-0.844250 + 2.59833i) q^{96} +(0.809017 + 0.587785i) q^{97} -5.39230 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 6 q^{7} - 2 q^{8} - 2 q^{9} - 8 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{18} - 6 q^{19} - 24 q^{23} + 2 q^{24} + 4 q^{25} - 6 q^{26} + 8 q^{27}+ \cdots + 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 6 * q^7 - 2 * q^8 - 2 * q^9 - 8 * q^12 - 6 * q^13 - 6 * q^14 + 6 * q^15 - 2 * q^16 - 2 * q^18 - 6 * q^19 - 24 * q^23 + 2 * q^24 + 4 * q^25 - 6 * q^26 + 8 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 10 * q^31 + 8 * q^32 + 6 * q^35 - 2 * q^36 + 4 * q^37 - 6 * q^38 + 6 * q^39 + 12 * q^41 + 48 * q^45 + 6 * q^46 + 6 * q^47 + 2 * q^48 - 10 * q^49 + 4 * q^50 + 18 * q^51 - 6 * q^52 - 12 * q^53 - 32 * q^54 + 24 * q^56 + 12 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 + 10 * q^62 + 6 * q^63 - 2 * q^64 - 40 * q^67 - 12 * q^69 + 6 * q^70 + 12 * q^71 - 2 * q^72 - 12 * q^73 + 4 * q^74 - 4 * q^75 + 24 * q^76 - 24 * q^78 + 6 * q^79 - 2 * q^81 + 12 * q^82 - 6 * q^83 - 18 * q^85 + 24 * q^87 + 24 * q^89 - 12 * q^90 - 18 * q^91 + 6 * q^92 - 28 * q^93 + 6 * q^94 - 6 * q^95 + 2 * q^96 + 2 * q^97 + 40 * q^98

Introduction

L-functions

Modular forms

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