LMFDB - Embedded newform 242.2.c.f.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,2,Mod(3,242)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			3.2
Root			$0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	242.3
Dual form			242.2.c.f.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.226216 + 0.696222i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.40126 + 1.01807i) q^{5} +(-0.592242 - 0.430289i) q^{6} +(1.46228 - 4.50045i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.99350 - 1.44836i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.226216 + 0.696222i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.40126 + 1.01807i) q^{5} +(-0.592242 - 0.430289i) q^{6} +(1.46228 - 4.50045i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.99350 - 1.44836i) q^{9} -1.73205 q^{10} +0.732051 q^{12} +(-2.42705 + 1.76336i) q^{13} +(1.46228 + 4.50045i) q^{14} +(-0.391818 + 1.20589i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.20378 + 3.05422i) q^{17} +(-0.761449 + 2.34350i) q^{18} +(0.391818 + 1.20589i) q^{19} +(1.40126 - 1.01807i) q^{20} +3.46410 q^{21} -1.26795 q^{23} +(-0.592242 + 0.430289i) q^{24} +(-0.618034 - 1.90211i) q^{25} +(0.927051 - 2.85317i) q^{26} +(3.23607 + 2.35114i) q^{27} +(-3.82831 - 2.78143i) q^{28} +(-0.927051 + 2.85317i) q^{29} +(-0.391818 - 1.20589i) q^{30} +(-0.158691 + 0.115296i) q^{31} +1.00000 q^{32} -5.19615 q^{34} +(6.63083 - 4.81758i) q^{35} +(-0.761449 - 2.34350i) q^{36} +(-2.22373 + 6.84395i) q^{37} +(-1.02579 - 0.745282i) q^{38} +(-1.77672 - 1.29087i) q^{39} +(-0.535233 + 1.64728i) q^{40} +(-0.248403 - 0.764504i) q^{41} +(-2.80252 + 2.03615i) q^{42} +4.26795 q^{45} +(1.02579 - 0.745282i) q^{46} +(-2.53275 - 7.79500i) q^{47} +(0.226216 - 0.696222i) q^{48} +(-12.4526 - 9.04737i) q^{49} +(1.61803 + 1.17557i) q^{50} +(-1.17545 + 3.61767i) q^{51} +(0.927051 + 2.85317i) q^{52} +(-9.05788 + 6.58093i) q^{53} -4.00000 q^{54} +4.73205 q^{56} +(-0.750932 + 0.545584i) q^{57} +(-0.927051 - 2.85317i) q^{58} +(2.92457 - 9.00090i) q^{59} +(1.02579 + 0.745282i) q^{60} +(-2.05158 - 1.49056i) q^{61} +(0.0606144 - 0.186552i) q^{62} +(-3.60322 - 11.0896i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.19615 q^{65} -10.1962 q^{67} +(4.20378 - 3.05422i) q^{68} +(-0.286831 - 0.882774i) q^{69} +(-2.53275 + 7.79500i) q^{70} +(7.65662 + 5.56286i) q^{71} +(1.99350 + 1.44836i) q^{72} +(-0.286831 + 0.882774i) q^{73} +(-2.22373 - 6.84395i) q^{74} +(1.18448 - 0.860577i) q^{75} +1.26795 q^{76} +2.19615 q^{78} +(3.82831 - 2.78143i) q^{79} +(-0.535233 - 1.64728i) q^{80} +(1.37948 - 4.24561i) q^{81} +(0.650326 + 0.472490i) q^{82} +(-6.63083 - 4.81758i) q^{83} +(1.07047 - 3.29456i) q^{84} +(2.78115 + 8.55951i) q^{85} -2.19615 q^{87} +6.46410 q^{89} +(-3.45284 + 2.50864i) q^{90} +(4.38685 + 13.5013i) q^{91} +(-0.391818 + 1.20589i) q^{92} +(-0.116170 - 0.0844022i) q^{93} +(6.63083 + 4.81758i) q^{94} +(-0.678648 + 2.08867i) q^{95} +(0.226216 + 0.696222i) q^{96} +(0.809017 - 0.587785i) q^{97} +15.3923 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}+O(q^{10}) $ 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 - 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$123$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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
$3$	0.226216	+	0.696222i	0.130606	+	0.401964i	0.994881	−	0.101056i	$-0.0322222\pi$
$3$	0.226216	+	0.696222i	0.130606	+	0.401964i	−0.864275	+	0.503020i	$0.832222\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	1.40126	+	1.01807i	0.626662	+	0.455296i	0.855242	−	0.518229i	$-0.173408\pi$
$5$	1.40126	+	1.01807i	0.626662	+	0.455296i	−0.228580	+	0.973525i	$0.573408\pi$
$6$	−0.592242	−	0.430289i	−0.241782	−	0.175665i
$7$	1.46228	−	4.50045i	0.552691	−	1.70101i	−0.149272	−	0.988796i	$-0.547693\pi$
$7$	1.46228	−	4.50045i	0.552691	−	1.70101i	0.701963	−	0.712213i	$-0.252307\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	1.99350	−	1.44836i	0.664500	−	0.482788i
$10$	−1.73205			−0.547723
$11$		0			0
$11$		0			0
$12$	0.732051			0.211325
$13$	−2.42705	+	1.76336i	−0.673143	+	0.489067i	−0.871076	−	0.491149i	$-0.836577\pi$
$13$	−2.42705	+	1.76336i	−0.673143	+	0.489067i	0.197933	+	0.980216i	$0.436577\pi$
$14$	1.46228	+	4.50045i	0.390812	+	1.20280i
$15$	−0.391818	+	1.20589i	−0.101167	+	0.311360i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.20378	+	3.05422i	1.01957	+	0.740758i	0.966194	−	0.257817i	$-0.0830032\pi$
$17$	4.20378	+	3.05422i	1.01957	+	0.740758i	0.0533716	+	0.998575i	$0.483003\pi$
$18$	−0.761449	+	2.34350i	−0.179475	+	0.552368i
$19$	0.391818	+	1.20589i	0.0898892	+	0.276650i	0.985888	−	0.167406i	$-0.0535390\pi$
$19$	0.391818	+	1.20589i	0.0898892	+	0.276650i	−0.895999	+	0.444056i	$0.853539\pi$
$20$	1.40126	−	1.01807i	0.313331	−	0.227648i
$21$	3.46410			0.755929
$22$		0			0
$23$	−1.26795			−0.264386			−0.132193	−	0.991224i	$-0.542202\pi$
$23$	−1.26795			−0.264386			−0.132193	+	0.991224i	$0.542202\pi$
$24$	−0.592242	+	0.430289i	−0.120891	+	0.0878323i
$25$	−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
$28$	−3.82831	−	2.78143i	−0.723482	−	0.525641i
$29$	−0.927051	+	2.85317i	−0.172149	+	0.529820i	−0.999492	−	0.0318771i	$-0.989851\pi$
$29$	−0.927051	+	2.85317i	−0.172149	+	0.529820i	0.827343	+	0.561697i	$0.189851\pi$
$30$	−0.391818	−	1.20589i	−0.0715358	−	0.220165i
$31$	−0.158691	+	0.115296i	−0.0285017	+	0.0207077i	−0.601945	−	0.798538i	$-0.705607\pi$
$31$	−0.158691	+	0.115296i	−0.0285017	+	0.0207077i	0.573443	+	0.819245i	$0.305607\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−5.19615			−0.891133
$35$	6.63083	−	4.81758i	1.12081	−	0.814319i
$36$	−0.761449	−	2.34350i	−0.126908	−	0.390583i
$37$	−2.22373	+	6.84395i	−0.365580	+	1.12514i	0.584038	+	0.811726i	$0.301472\pi$
$37$	−2.22373	+	6.84395i	−0.365580	+	1.12514i	−0.949617	+	0.313412i	$0.898528\pi$
$38$	−1.02579	−	0.745282i	−0.166406	−	0.120901i
$39$	−1.77672	−	1.29087i	−0.284504	−	0.206704i
$40$	−0.535233	+	1.64728i	−0.0846278	+	0.260458i
$41$	−0.248403	−	0.764504i	−0.0387940	−	0.119396i	0.929784	−	0.368105i	$-0.119993\pi$
$41$	−0.248403	−	0.764504i	−0.0387940	−	0.119396i	−0.968578	+	0.248710i	$0.919993\pi$
$42$	−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
$45$	4.26795			0.636228
$46$	1.02579	−	0.745282i	0.151245	−	0.109886i
$47$	−2.53275	−	7.79500i	−0.369440	−	1.13702i	−0.947154	−	0.320779i	$-0.896055\pi$
$47$	−2.53275	−	7.79500i	−0.369440	−	1.13702i	0.577714	−	0.816239i	$-0.303945\pi$
$48$	0.226216	−	0.696222i	0.0326515	−	0.100491i
$49$	−12.4526	−	9.04737i	−1.77895	−	1.29248i
$50$	1.61803	+	1.17557i	0.228825	+	0.166251i
$51$	−1.17545	+	3.61767i	−0.164596	+	0.506576i
$52$	0.927051	+	2.85317i	0.128559	+	0.395663i
$53$	−9.05788	+	6.58093i	−1.24420	+	0.903961i	−0.997870	−	0.0652267i	$-0.979223\pi$
$53$	−9.05788	+	6.58093i	−1.24420	+	0.903961i	−0.246325	+	0.969187i	$0.579223\pi$
$54$	−4.00000			−0.544331
$55$		0			0
$56$	4.73205			0.632347
$57$	−0.750932	+	0.545584i	−0.0994634	+	0.0722644i
$58$	−0.927051	−	2.85317i	−0.121728	−	0.374640i
$59$	2.92457	−	9.00090i	0.380746	−	1.17182i	−0.558773	−	0.829321i	$-0.688728\pi$
$59$	2.92457	−	9.00090i	0.380746	−	1.17182i	0.939519	−	0.342496i	$-0.111272\pi$
$60$	1.02579	+	0.745282i	0.132429	+	0.0962155i
$61$	−2.05158	−	1.49056i	−0.262679	−	0.190847i	0.448649	−	0.893708i	$-0.351906\pi$
$61$	−2.05158	−	1.49056i	−0.262679	−	0.190847i	−0.711327	+	0.702861i	$0.751906\pi$
$62$	0.0606144	−	0.186552i	0.00769804	−	0.0236921i
$63$	−3.60322	−	11.0896i	−0.453963	−	1.39715i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−5.19615			−0.644503
$66$		0			0
$67$	−10.1962			−1.24566			−0.622829	−	0.782358i	$-0.714017\pi$
$67$	−10.1962			−1.24566			−0.622829	+	0.782358i	$0.714017\pi$
$68$	4.20378	−	3.05422i	0.509783	−	0.370379i
$69$	−0.286831	−	0.882774i	−0.0345303	−	0.106273i
$70$	−2.53275	+	7.79500i	−0.302722	+	0.931681i
$71$	7.65662	+	5.56286i	0.908674	+	0.660190i	0.940679	−	0.339298i	$-0.110189\pi$
$71$	7.65662	+	5.56286i	0.908674	+	0.660190i	−0.0320055	+	0.999488i	$0.510189\pi$
$72$	1.99350	+	1.44836i	0.234936	+	0.170691i
$73$	−0.286831	+	0.882774i	−0.0335710	+	0.103321i	−0.966438	−	0.256900i	$-0.917299\pi$
$73$	−0.286831	+	0.882774i	−0.0335710	+	0.103321i	0.932867	+	0.360221i	$0.117299\pi$
$74$	−2.22373	−	6.84395i	−0.258504	−	0.795593i
$75$	1.18448	−	0.860577i	0.136772	−	0.0993709i
$76$	1.26795			0.145444
$77$		0			0
$78$	2.19615			0.248665
$79$	3.82831	−	2.78143i	0.430718	−	0.312935i	−0.351218	−	0.936294i	$-0.614232\pi$
$79$	3.82831	−	2.78143i	0.430718	−	0.312935i	0.781936	+	0.623359i	$0.214232\pi$
$80$	−0.535233	−	1.64728i	−0.0598409	−	0.184171i
$81$	1.37948	−	4.24561i	0.153276	−	0.471735i
$82$	0.650326	+	0.472490i	0.0718165	+	0.0521778i
$83$	−6.63083	−	4.81758i	−0.727828	−	0.528798i	0.161048	−	0.986947i	$-0.448513\pi$
$83$	−6.63083	−	4.81758i	−0.727828	−	0.528798i	−0.888876	+	0.458149i	$0.848513\pi$
$84$	1.07047	−	3.29456i	0.116797	−	0.359466i
$85$	2.78115	+	8.55951i	0.301658	+	0.928409i
$86$		0			0
$87$	−2.19615			−0.235452
$88$		0			0
$89$	6.46410			0.685193			0.342597	−	0.939483i	$-0.388694\pi$
$89$	6.46410			0.685193			0.342597	+	0.939483i	$0.388694\pi$
$90$	−3.45284	+	2.50864i	−0.363962	+	0.264434i
$91$	4.38685	+	13.5013i	0.459867	+	1.41533i
$92$	−0.391818	+	1.20589i	−0.0408498	+	0.125723i
$93$	−0.116170	−	0.0844022i	−0.0120462	−	0.00875210i
$94$	6.63083	+	4.81758i	0.683918	+	0.496895i
$95$	−0.678648	+	2.08867i	−0.0696279	+	0.214293i
$96$	0.226216	+	0.696222i	0.0230881	+	0.0710578i
$97$	0.809017	−	0.587785i	0.0821432	−	0.0596806i	−0.545956	−	0.837814i	$-0.683833\pi$
$97$	0.809017	−	0.587785i	0.0821432	−	0.0596806i	0.628099	+	0.778133i	$0.283833\pi$
$98$	15.3923			1.55486
$99$		0			0
$100$	−2.00000			−0.200000
$101$	−13.2617	+	9.63516i	−1.31958	+	0.958734i	−0.319647	+	0.947537i	$0.603564\pi$
$101$	−13.2617	+	9.63516i	−1.31958	+	0.958734i	−0.999937	+	0.0111969i	$0.996436\pi$
$102$	−1.17545	−	3.61767i	−0.116387	−	0.358203i
$103$	−2.59336	+	7.98156i	−0.255532	+	0.786446i	0.738193	+	0.674590i	$0.235680\pi$
$103$	−2.59336	+	7.98156i	−0.255532	+	0.786446i	−0.993724	+	0.111856i	$0.964320\pi$
$104$	−2.42705	−	1.76336i	−0.237992	−	0.172911i
$105$	4.85410	+	3.52671i	0.473712	+	0.344172i
$106$	3.45980	−	10.6482i	0.336046	−	1.03424i
$107$	3.89005	+	11.9723i	0.376065	+	1.15741i	0.942757	+	0.333480i	$0.108223\pi$
$107$	3.89005	+	11.9723i	0.376065	+	1.15741i	−0.566692	+	0.823930i	$0.691777\pi$
$108$	3.23607	−	2.35114i	0.311391	−	0.226239i
$109$	−2.07180			−0.198442			−0.0992211	−	0.995065i	$-0.531635\pi$
$109$	−2.07180			−0.198442			−0.0992211	+	0.995065i	$0.531635\pi$
$110$		0			0
$111$	−5.26795			−0.500012
$112$	−3.82831	+	2.78143i	−0.361741	+	0.262820i
$113$	3.35481	+	10.3251i	0.315594	+	0.971300i	0.975509	+	0.219959i	$0.0705924\pi$
$113$	3.35481	+	10.3251i	0.315594	+	0.971300i	−0.659915	+	0.751340i	$0.729408\pi$
$114$	0.286831	−	0.882774i	0.0268641	−	0.0826793i
$115$	−1.77672	−	1.29087i	−0.165680	−	0.120374i
$116$	2.42705	+	1.76336i	0.225346	+	0.163723i
$117$	−2.28435	+	7.03050i	−0.211188	+	0.649970i
$118$	2.92457	+	9.00090i	0.269228	+	0.828600i
$119$	19.8925	−	14.4527i	1.82354	−	1.32488i
$120$	−1.26795			−0.115747
$121$		0			0
$122$	2.53590			0.229589
$123$	0.476072	−	0.345887i	0.0429260	−	0.0311875i
$124$	0.0606144	+	0.186552i	0.00544334	+	0.0167529i
$125$	3.74663	−	11.5309i	0.335109	−	1.03136i
$126$	9.43334	+	6.85373i	0.840389	+	0.610578i
$127$	−11.2101	−	8.14459i	−0.994733	−	0.722716i	−0.0337803	−	0.999429i	$-0.510755\pi$
$127$	−11.2101	−	8.14459i	−0.994733	−	0.722716i	−0.960952	+	0.276714i	$0.910755\pi$
$128$	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
$134$	8.24886	−	5.99315i	0.712593	−	0.517729i
$135$	2.14093	+	6.58911i	0.184262	+	0.567101i
$136$	−1.60570	+	4.94183i	−0.137688	+	0.423759i
$137$	7.65662	+	5.56286i	0.654149	+	0.475267i	0.864682	−	0.502320i	$-0.167520\pi$
$137$	7.65662	+	5.56286i	0.654149	+	0.475267i	−0.210533	+	0.977587i	$0.567520\pi$
$138$	0.750932	+	0.545584i	0.0639236	+	0.0464432i
$139$	6.24095	−	19.2077i	0.529351	−	1.62917i	−0.226198	−	0.974081i	$-0.572629\pi$
$139$	6.24095	−	19.2077i	0.529351	−	1.62917i	0.755548	−	0.655093i	$-0.227371\pi$
$140$	−2.53275	−	7.79500i	−0.214056	−	0.658798i
$141$	4.85410	−	3.52671i	0.408789	−	0.297003i
$142$	−9.46410			−0.794210
$143$		0			0
$144$	−2.46410			−0.205342
$145$	−4.20378	+	3.05422i	−0.349105	+	0.253639i
$146$	−0.286831	−	0.882774i	−0.0237383	−	0.0730589i
$147$	3.48199	−	10.7165i	0.287190	−	0.883878i
$148$	5.82181	+	4.22979i	0.478550	+	0.347687i
$149$	12.1353	+	8.81678i	0.994159	+	0.722299i	0.960828	−	0.277146i	$-0.0893885\pi$
$149$	12.1353	+	8.81678i	0.994159	+	0.722299i	0.0333309	+	0.999444i	$0.489388\pi$
$150$	−0.452432	+	1.39244i	−0.0369409	+	0.113693i
$151$	−1.35730	−	4.17733i	−0.110455	−	0.339946i	0.880517	−	0.474015i	$-0.157196\pi$
$151$	−1.35730	−	4.17733i	−0.110455	−	0.339946i	−0.990972	+	0.134069i	$0.957196\pi$
$152$	−1.02579	+	0.745282i	−0.0832028	+	0.0604503i
$153$	12.8038			1.03513
$154$		0			0
$155$	−0.339746			−0.0272891
$156$	−1.77672	+	1.29087i	−0.142252	+	0.103352i
$157$	1.23607	+	3.80423i	0.0986490	+	0.303610i	0.988187	−	0.153250i	$-0.0489740\pi$
$157$	1.23607	+	3.80423i	0.0986490	+	0.303610i	−0.889538	+	0.456860i	$0.848974\pi$
$158$	−1.46228	+	4.50045i	−0.116333	+	0.358036i
$159$	−6.63083	−	4.81758i	−0.525859	−	0.382059i
$160$	1.40126	+	1.01807i	0.110779	+	0.0804858i
$161$	−1.85410	+	5.70634i	−0.146124	+	0.449723i
$162$	1.37948	+	4.24561i	0.108382	+	0.333567i
$163$	−17.9571	+	13.0466i	−1.40651	+	1.02189i	−0.412687	+	0.910873i	$0.635410\pi$
$163$	−17.9571	+	13.0466i	−1.40651	+	1.02189i	−0.993819	+	0.111013i	$0.964590\pi$
$164$	−0.803848			−0.0627700
$165$		0			0
$166$	8.19615			0.636145
$167$	−13.2617	+	9.63516i	−1.02622	+	0.745591i	−0.967548	−	0.252687i	$-0.918686\pi$
$167$	−13.2617	+	9.63516i	−1.02622	+	0.745591i	−0.0586694	+	0.998277i	$0.518686\pi$
$168$	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
$171$	2.52766	+	1.83645i	0.193295	+	0.140437i
$172$		0			0
$173$	−1.35730	−	4.17733i	−0.103193	−	0.317597i	0.886109	−	0.463477i	$-0.153398\pi$
$173$	−1.35730	−	4.17733i	−0.103193	−	0.317597i	−0.989302	+	0.145881i	$0.953398\pi$
$174$	1.77672	−	1.29087i	0.134693	−	0.0978603i
$175$	−9.46410			−0.715419
$176$		0			0
$177$	6.92820			0.520756
$178$	−5.22957	+	3.79950i	−0.391973	+	0.284785i
$179$	−4.28187	−	13.1782i	−0.320042	−	0.984987i	−0.973629	−	0.228136i	$-0.926737\pi$
$179$	−4.28187	−	13.1782i	−0.320042	−	0.984987i	0.653588	−	0.756851i	$-0.273263\pi$
$180$	1.31887	−	4.05906i	0.0983027	−	0.302545i
$181$	−5.82181	−	4.22979i	−0.432732	−	0.314398i	0.350009	−	0.936746i	$-0.386179\pi$
$181$	−5.82181	−	4.22979i	−0.432732	−	0.314398i	−0.782740	+	0.622349i	$0.786179\pi$
$182$	−11.4849	−	8.34429i	−0.851320	−	0.618520i
$183$	0.573661	−	1.76555i	0.0424063	−	0.130513i
$184$	−0.391818	−	1.20589i	−0.0288852	−	0.0888995i
$185$	−10.0837	+	7.32622i	−0.741366	+	0.538634i
$186$	0.143594			0.0105288
$187$		0			0
$188$	−8.19615			−0.597766
$189$	15.3132	−	11.1257i	1.11387	−	0.809277i
$190$	−0.678648	−	2.08867i	−0.0492343	−	0.151528i
$191$	−6.63277	+	20.4136i	−0.479931	+	1.47707i	0.359260	+	0.933237i	$0.383029\pi$
$191$	−6.63277	+	20.4136i	−0.479931	+	1.47707i	−0.839191	+	0.543837i	$0.816971\pi$
$192$	−0.592242	−	0.430289i	−0.0427414	−	0.0310534i
$193$	−8.30695	−	6.03535i	−0.597947	−	0.434434i	0.247203	−	0.968964i	$-0.420489\pi$
$193$	−8.30695	−	6.03535i	−0.597947	−	0.434434i	−0.845150	+	0.534530i	$0.820489\pi$
$194$	−0.309017	+	0.951057i	−0.0221861	+	0.0682819i
$195$	−1.17545	−	3.61767i	−0.0841760	−	0.259067i
$196$	−12.4526	+	9.04737i	−0.889474	+	0.646241i
$197$	−13.3923			−0.954162			−0.477081	−	0.878859i	$-0.658305\pi$
$197$	−13.3923			−0.954162			−0.477081	+	0.878859i	$0.658305\pi$
$198$		0			0
$199$	−0.392305			−0.0278098			−0.0139049	−	0.999903i	$-0.504426\pi$
$199$	−0.392305			−0.0278098			−0.0139049	+	0.999903i	$0.504426\pi$
$200$	1.61803	−	1.17557i	0.114412	−	0.0831254i
$201$	−2.30653	−	7.09878i	−0.162690	−	0.500710i
$202$	5.06550	−	15.5900i	0.356407	−	1.09691i
$203$	11.4849	+	8.34429i	0.806084	+	0.585654i
$204$	3.07738	+	2.23585i	0.215460	+	0.156540i
$205$	0.430246	−	1.32416i	0.0300497	−	0.0924834i
$206$	−2.59336	−	7.98156i	−0.180688	−	0.556101i
$207$	−2.52766	+	1.83645i	−0.175684	+	0.127642i
$208$	3.00000			0.208013
$209$		0			0
$210$	−6.00000			−0.414039
$211$	20.9183	−	15.1980i	1.44007	−	1.04627i	0.452046	−	0.891995i	$-0.350694\pi$
$211$	20.9183	−	15.1980i	1.44007	−	1.04627i	0.988027	−	0.154280i	$-0.0493057\pi$
$212$	3.45980	+	10.6482i	0.237620	+	0.731320i
$213$	−2.14093	+	6.58911i	−0.146694	+	0.451479i
$214$	−10.1843	−	7.39931i	−0.696183	−	0.505806i
$215$		0			0
$216$	−1.23607	+	3.80423i	−0.0841038	+	0.258845i
$217$	0.286831	+	0.882774i	0.0194713	+	0.0599266i
$218$	1.67612	−	1.21777i	0.113521	−	0.0824779i
$219$	−0.679492			−0.0459158
$220$		0			0
$221$	−15.5885			−1.04859
$222$	4.26186	−	3.09642i	0.286037	−	0.207818i
$223$	−6.30157	−	19.3942i	−0.421984	−	1.29873i	−0.905853	−	0.423593i	$-0.860769\pi$
$223$	−6.30157	−	19.3942i	−0.421984	−	1.29873i	0.483868	−	0.875141i	$-0.339231\pi$
$224$	1.46228	−	4.50045i	0.0977030	−	0.300699i
$225$	−3.98700	−	2.89673i	−0.265800	−	0.193115i
$226$	−8.78302	−	6.38124i	−0.584238	−	0.424473i
$227$	−5.06550	+	15.5900i	−0.336209	+	1.03475i	0.629914	+	0.776665i	$0.283090\pi$
$227$	−5.06550	+	15.5900i	−0.336209	+	1.03475i	−0.966123	+	0.258081i	$0.916910\pi$
$228$	0.286831	+	0.882774i	0.0189958	+	0.0584631i
$229$	10.6759	−	7.75650i	0.705484	−	0.512564i	−0.176230	−	0.984349i	$-0.556390\pi$
$229$	10.6759	−	7.75650i	0.705484	−	0.512564i	0.881714	+	0.471785i	$0.156390\pi$
$230$	2.19615			0.144810
$231$		0			0
$232$	−3.00000			−0.196960
$233$	5.50443	−	3.99920i	0.360607	−	0.261996i	−0.392698	−	0.919667i	$-0.628458\pi$
$233$	5.50443	−	3.99920i	0.360607	−	0.261996i	0.753305	+	0.657671i	$0.228458\pi$
$234$	−2.28435	−	7.03050i	−0.149332	−	0.459598i
$235$	4.38685	−	13.5013i	0.286167	−	0.880731i
$236$	−7.65662	−	5.56286i	−0.498403	−	0.362111i
$237$	2.80252	+	2.03615i	0.182043	+	0.132262i
$238$	−7.59825	+	23.3850i	−0.492521	+	1.51583i
$239$	−4.38685	−	13.5013i	−0.283762	−	0.873329i	−0.986767	−	0.162145i	$-0.948159\pi$
$239$	−4.38685	−	13.5013i	−0.283762	−	0.873329i	0.703005	−	0.711185i	$-0.251841\pi$
$240$	1.02579	−	0.745282i	0.0662146	−	0.0481077i
$241$	26.7846			1.72535			0.862674	−	0.505760i	$-0.168788\pi$
$241$	26.7846			1.72535			0.862674	+	0.505760i	$0.168788\pi$
$242$		0			0
$243$	15.2679			0.979439
$244$	−2.05158	+	1.49056i	−0.131339	+	0.0954236i
$245$	−8.23847	−	25.3554i	−0.526337	−	1.61990i
$246$	−0.181843	+	0.559656i	−0.0115939	+	0.0356824i
$247$	−3.07738	−	2.23585i	−0.195809	−	0.142263i
$248$	−0.158691	−	0.115296i	−0.0100769	−	0.00732127i
$249$	1.85410	−	5.70634i	0.117499	−	0.361625i
$250$	3.74663	+	11.5309i	0.236958	+	0.729281i
$251$	−7.38176	+	5.36316i	−0.465932	+	0.338520i	−0.795854	−	0.605489i	$-0.792978\pi$
$251$	−7.38176	+	5.36316i	−0.465932	+	0.338520i	0.329921	+	0.944008i	$0.392978\pi$
$252$	−11.6603			−0.734527
$253$		0			0
$254$	13.8564			0.869428
$255$	−5.33017	+	3.87260i	−0.333788	+	0.242511i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−5.99255	+	18.4432i	−0.373805	+	1.15045i	0.570476	+	0.821314i	$0.306759\pi$
$257$	−5.99255	+	18.4432i	−0.373805	+	1.15045i	−0.944281	+	0.329140i	$0.893241\pi$
$258$		0			0
$259$	27.5491	+	20.0156i	1.71182	+	1.24371i
$260$	−1.60570	+	4.94183i	−0.0995812	+	0.306480i
$261$	2.28435	+	7.03050i	0.141398	+	0.435177i
$262$		0			0
$263$	9.80385			0.604531			0.302266	−	0.953224i	$-0.402257\pi$
$263$	9.80385			0.604531			0.302266	+	0.953224i	$0.402257\pi$
$264$		0			0
$265$	−19.3923			−1.19126
$266$	−4.85410	+	3.52671i	−0.297624	+	0.216237i
$267$	1.46228	+	4.50045i	0.0894903	+	0.275423i
$268$	−3.15078	+	9.69712i	−0.192465	+	0.592346i
$269$	−7.75722	−	5.63595i	−0.472966	−	0.343630i	0.325630	−	0.945497i	$-0.394424\pi$
$269$	−7.75722	−	5.63595i	−0.472966	−	0.343630i	−0.798596	+	0.601867i	$0.794424\pi$
$270$	−5.60503	−	4.07230i	−0.341112	−	0.247832i
$271$	−5.06550	+	15.5900i	−0.307707	+	0.947026i	0.670946	+	0.741506i	$0.265888\pi$
$271$	−5.06550	+	15.5900i	−0.307707	+	0.947026i	−0.978653	+	0.205519i	$0.934112\pi$
$272$	−1.60570	−	4.94183i	−0.0973598	−	0.299643i
$273$	−8.40755	+	6.10844i	−0.508848	+	0.369700i
$274$	−9.46410			−0.571747
$275$		0			0
$276$	−0.928203			−0.0558713
$277$	6.73143	−	4.89067i	0.404453	−	0.293852i	−0.366900	−	0.930261i	$-0.619581\pi$
$277$	6.73143	−	4.89067i	0.404453	−	0.293852i	0.771352	+	0.636409i	$0.219581\pi$
$278$	6.24095	+	19.2077i	0.374308	+	1.15200i
$279$	−0.149360	+	0.459683i	−0.00894196	+	0.0275205i
$280$	6.63083	+	4.81758i	0.396268	+	0.287905i
$281$	−14.5623	−	10.5801i	−0.868714	−	0.631158i	0.0615273	−	0.998105i	$-0.480403\pi$
$281$	−14.5623	−	10.5801i	−0.868714	−	0.631158i	−0.930242	+	0.366947i	$0.880403\pi$
$282$	−1.85410	+	5.70634i	−0.110410	+	0.339808i
$283$	2.14093	+	6.58911i	0.127265	+	0.391682i	0.994307	−	0.106553i	$-0.0339815\pi$
$283$	2.14093	+	6.58911i	0.127265	+	0.391682i	−0.867042	+	0.498235i	$0.833982\pi$
$284$	7.65662	−	5.56286i	0.454337	−	0.330095i
$285$	−1.60770			−0.0952316
$286$		0			0
$287$	−3.80385			−0.224534
$288$	1.99350	−	1.44836i	0.117468	−	0.0853456i
$289$	3.09017	+	9.51057i	0.181775	+	0.559445i
$290$	1.60570	−	4.94183i	0.0942899	−	0.290195i
$291$	0.592242	+	0.430289i	0.0347178	+	0.0252240i
$292$	0.750932	+	0.545584i	0.0439450	+	0.0319279i
$293$	7.34985	−	22.6205i	0.429383	−	1.32150i	−0.469352	−	0.883011i	$-0.655512\pi$
$293$	7.34985	−	22.6205i	0.429383	−	1.32150i	0.898735	−	0.438493i	$-0.144488\pi$
$294$	3.48199	+	10.7165i	0.203074	+	0.624996i
$295$	13.2617	−	9.63516i	0.772123	−	0.560980i
$296$	−7.19615			−0.418268
$297$		0			0
$298$	−15.0000			−0.868927
$299$	3.07738	−	2.23585i	0.177969	−	0.129302i
$300$	−0.452432	−	1.39244i	−0.0261212	−	0.0803928i
$301$		0			0
$302$	3.55345	+	2.58173i	0.204478	+	0.148562i
$303$	−9.70820	−	7.05342i	−0.557722	−	0.405209i
$304$	0.391818	−	1.20589i	0.0224723	−	0.0691626i
$305$	−1.35730	−	4.17733i	−0.0777186	−	0.239193i
$306$	−10.3585	+	7.52591i	−0.592158	+	0.430228i
$307$	25.2679			1.44212			0.721059	−	0.692874i	$-0.243656\pi$
$307$	25.2679			1.44212			0.721059	+	0.692874i	$0.243656\pi$
$308$		0			0
$309$	−6.14359			−0.349497
$310$	0.274860	−	0.199698i	0.0156110	−	0.0113421i
$311$	2.71459	+	8.35466i	0.153930	+	0.473749i	0.998051	−	0.0624042i	$-0.0198768\pi$
$311$	2.71459	+	8.35466i	0.153930	+	0.473749i	−0.844120	+	0.536154i	$0.819877\pi$
$312$	0.678648	−	2.08867i	0.0384209	−	0.118247i
$313$	25.7143	+	18.6825i	1.45346	+	1.05600i	0.985008	+	0.172508i	$0.0551872\pi$
$313$	25.7143	+	18.6825i	1.45346	+	1.05600i	0.468450	+	0.883490i	$0.344813\pi$
$314$	−3.23607	−	2.35114i	−0.182622	−	0.132683i
$315$	6.24095	−	19.2077i	0.351638	−	1.08223i
$316$	−1.46228	−	4.50045i	−0.0822599	−	0.253170i
$317$	6.35597	−	4.61788i	0.356987	−	0.259366i	−0.394807	−	0.918764i	$-0.629189\pi$
$317$	6.35597	−	4.61788i	0.356987	−	0.259366i	0.751794	+	0.659398i	$0.229189\pi$
$318$	8.19615			0.459617
$319$		0			0
$320$	−1.73205			−0.0968246
$321$	−7.45541	+	5.41667i	−0.416120	+	0.302329i
$322$	−1.85410	−	5.70634i	−0.103325	−	0.318002i
$323$	−2.03595	+	6.26600i	−0.113283	+	0.348649i
$324$	−3.61153	−	2.62393i	−0.200641	−	0.145774i
$325$	4.85410	+	3.52671i	0.269257	+	0.195627i
$326$	6.85899	−	21.1098i	0.379884	−	1.16916i
$327$	−0.468674	−	1.44243i	−0.0259177	−	0.0797666i
$328$	0.650326	−	0.472490i	0.0359083	−	0.0260889i
$329$	−38.7846			−2.13826
$330$		0			0
$331$	28.7846			1.58215			0.791073	−	0.611722i	$-0.209523\pi$
$331$	28.7846			1.58215			0.791073	+	0.611722i	$0.209523\pi$
$332$	−6.63083	+	4.81758i	−0.363914	+	0.264399i
$333$	5.47951	+	16.8642i	0.300275	+	0.924152i
$334$	5.06550	−	15.5900i	0.277172	−	0.853047i
$335$	−14.2874	−	10.3804i	−0.780607	−	0.567144i
$336$	−2.80252	−	2.03615i	−0.152890	−	0.111081i
$337$	0.822064	−	2.53005i	0.0447807	−	0.137821i	−0.926166	−	0.377115i	$-0.876916\pi$
$337$	0.822064	−	2.53005i	0.0447807	−	0.137821i	0.970947	+	0.239294i	$0.0769161\pi$
$338$	−1.23607	−	3.80423i	−0.0672332	−	0.206923i
$339$	−6.42961	+	4.67139i	−0.349209	+	0.253715i
$340$	9.00000			0.488094
$341$		0			0
$342$	−3.12436			−0.168946
$343$	−32.1283	+	23.3426i	−1.73477	+	1.26038i
$344$		0			0
$345$	0.496805	−	1.52901i	0.0267471	−	0.0823191i
$346$	3.55345	+	2.58173i	0.191035	+	0.138795i
$347$	22.9699	+	16.6886i	1.23309	+	0.895890i	0.997118	−	0.0758708i	$-0.0241737\pi$
$347$	22.9699	+	16.6886i	1.23309	+	0.895890i	0.235969	+	0.971761i	$0.424174\pi$
$348$	−0.678648	+	2.08867i	−0.0363794	+	0.111964i
$349$	−6.77619	−	20.8550i	−0.362721	−	1.11634i	−0.951396	−	0.307971i	$-0.900350\pi$
$349$	−6.77619	−	20.8550i	−0.362721	−	1.11634i	0.588675	−	0.808370i	$-0.299650\pi$
$350$	7.65662	−	5.56286i	0.409264	−	0.297347i
$351$	−12.0000			−0.640513
$352$		0			0
$353$	21.9282			1.16712			0.583560	−	0.812070i	$-0.301659\pi$
$353$	21.9282			1.16712			0.583560	+	0.812070i	$0.301659\pi$
$354$	−5.60503	+	4.07230i	−0.297904	+	0.216440i
$355$	5.06550	+	15.5900i	0.268849	+	0.827432i
$356$	1.99752	−	6.14773i	0.105868	−	0.325829i
$357$	14.5623	+	10.5801i	0.770719	+	0.559960i
$358$	11.2101	+	8.14459i	0.592471	+	0.430455i
$359$	−2.03595	+	6.26600i	−0.107453	+	0.330707i	−0.990298	−	0.138957i	$-0.955625\pi$
$359$	−2.03595	+	6.26600i	−0.107453	+	0.330707i	0.882845	+	0.469664i	$0.155625\pi$
$360$	1.31887	+	4.05906i	0.0695105	+	0.213931i
$361$	14.0707	−	10.2229i	0.740562	−	0.538049i
$362$	7.19615			0.378221
$363$		0			0
$364$	14.1962			0.744081
$365$	−1.30065	+	0.944980i	−0.0680793	+	0.0494625i
$366$	0.573661	+	1.76555i	0.0299857	+	0.0922866i
$367$	2.65398	−	8.16811i	0.138537	−	0.426372i	−0.857587	−	0.514339i	$-0.828037\pi$
$367$	2.65398	−	8.16811i	0.138537	−	0.426372i	0.996123	+	0.0879676i	$0.0280372\pi$
$368$	1.02579	+	0.745282i	0.0534731	+	0.0388505i
$369$	−1.60247	−	1.16426i	−0.0834213	−	0.0606091i
$370$	3.85162	−	11.8541i	0.200236	−	0.616263i
$371$	16.3720	+	50.3877i	0.849990	+	2.61600i
$372$	−0.116170	+	0.0844022i	−0.00602311	+	0.00437605i
$373$	−11.3205			−0.586154			−0.293077	−	0.956089i	$-0.594679\pi$
$373$	−11.3205			−0.586154			−0.293077	+	0.956089i	$0.594679\pi$
$374$		0			0
$375$	8.87564			0.458336
$376$	6.63083	−	4.81758i	0.341959	−	0.248448i
$377$	−2.78115	−	8.55951i	−0.143237	−	0.440837i
$378$	−5.84914	+	18.0018i	−0.300847	+	0.925912i
$379$	−2.91869	−	2.12055i	−0.149923	−	0.108925i	0.510295	−	0.859999i	$-0.329536\pi$
$379$	−2.91869	−	2.12055i	−0.149923	−	0.108925i	−0.660218	+	0.751074i	$0.729536\pi$
$380$	1.77672	+	1.29087i	0.0911441	+	0.0662200i
$381$	3.13454	−	9.64713i	0.160587	−	0.494237i
$382$	−6.63277	−	20.4136i	−0.339362	−	1.04445i
$383$	0.549721	−	0.399395i	0.0280894	−	0.0204081i	−0.573652	−	0.819099i	$-0.694474\pi$
$383$	0.549721	−	0.399395i	0.0280894	−	0.0204081i	0.601741	+	0.798691i	$0.294474\pi$
$384$	0.732051			0.0373573
$385$		0			0
$386$	10.2679			0.522625
$387$		0			0
$388$	−0.309017	−	0.951057i	−0.0156880	−	0.0482826i
$389$	10.0926	−	31.0617i	0.511714	−	1.57489i	−0.277469	−	0.960735i	$-0.589496\pi$
$389$	10.0926	−	31.0617i	0.511714	−	1.57489i	0.789183	−	0.614158i	$-0.210504\pi$
$390$	3.07738	+	2.23585i	0.155829	+	0.113216i
$391$	−5.33017	−	3.87260i	−0.269558	−	0.195846i
$392$	4.75648	−	14.6390i	0.240239	−	0.739379i
$393$		0			0
$394$	10.8346	−	7.87180i	0.545839	−	0.396576i
$395$	8.19615			0.412393
$396$		0			0
$397$	5.58846			0.280477			0.140238	−	0.990118i	$-0.455213\pi$
$397$	5.58846			0.280477			0.140238	+	0.990118i	$0.455213\pi$
$398$	0.317381	−	0.230591i	0.0159089	−	0.0115585i
$399$	1.35730	+	4.17733i	0.0679498	+	0.209128i
$400$	−0.618034	+	1.90211i	−0.0309017	+	0.0951057i
$401$	5.98050	+	4.34509i	0.298652	+	0.216983i	0.727012	−	0.686625i	$-0.240908\pi$
$401$	5.98050	+	4.34509i	0.298652	+	0.216983i	−0.428360	+	0.903608i	$0.640908\pi$
$402$	6.03859	+	4.38729i	0.301177	+	0.218818i
$403$	0.181843	−	0.559656i	0.00905826	−	0.0278785i
$404$	5.06550	+	15.5900i	0.252018	+	0.775632i
$405$	6.25536	−	4.54479i	0.310831	−	0.225832i
$406$	−14.1962			−0.704543
$407$		0			0
$408$	−3.80385			−0.188319
$409$	2.15219	−	1.56366i	0.106419	−	0.0773179i	−0.533303	−	0.845924i	$-0.679049\pi$
$409$	2.15219	−	1.56366i	0.106419	−	0.0773179i	0.639722	+	0.768606i	$0.279049\pi$
$410$	0.430246	+	1.32416i	0.0212483	+	0.0653956i
$411$	−2.14093	+	6.58911i	−0.105604	+	0.325017i
$412$	6.78952	+	4.93287i	0.334496	+	0.243025i
$413$	−36.2315	−	26.3237i	−1.78284	−	1.29531i
$414$	0.965479	−	2.97144i	0.0474507	−	0.146038i
$415$	−4.38685	−	13.5013i	−0.215342	−	0.662755i
$416$	−2.42705	+	1.76336i	−0.118996	+	0.0864556i
$417$	14.7846			0.724005
$418$		0			0
$419$	−39.3731			−1.92350			−0.961750	−	0.273928i	$-0.911677\pi$
$419$	−39.3731			−1.92350			−0.961750	+	0.273928i	$0.911677\pi$
$420$	4.85410	−	3.52671i	0.236856	−	0.172086i
$421$	2.34496	+	7.21705i	0.114286	+	0.351738i	0.991798	−	0.127819i	$-0.0407976\pi$
$421$	2.34496	+	7.21705i	0.114286	+	0.351738i	−0.877511	+	0.479556i	$0.840798\pi$
$422$	−7.99007	+	24.5909i	−0.388950	+	1.19707i
$423$	−16.3390	−	11.8710i	−0.794431	−	0.577188i
$424$	−9.05788	−	6.58093i	−0.439889	−	0.319598i
$425$	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
$428$	12.5885			0.608486
$429$		0			0
$430$		0			0
$431$	−13.2617	+	9.63516i	−0.638791	+	0.464109i	−0.859435	−	0.511245i	$-0.829184\pi$
$431$	−13.2617	+	9.63516i	−0.638791	+	0.464109i	0.220643	+	0.975355i	$0.429184\pi$
$432$	−1.23607	−	3.80423i	−0.0594703	−	0.183031i
$433$	9.82198	−	30.2290i	0.472014	−	1.45271i	−0.377928	−	0.925835i	$-0.623363\pi$
$433$	9.82198	−	30.2290i	0.472014	−	1.45271i	0.849942	−	0.526876i	$-0.176637\pi$
$434$	−0.750932	−	0.545584i	−0.0360459	−	0.0261889i
$435$	−3.07738	−	2.23585i	−0.147549	−	0.107201i
$436$	−0.640220	+	1.97040i	−0.0306610	+	0.0943648i
$437$	−0.496805	−	1.52901i	−0.0237654	−	0.0731424i
$438$	0.549721	−	0.399395i	0.0262667	−	0.0190838i
$439$	−21.1244			−1.00821			−0.504105	−	0.863642i	$-0.668178\pi$
$439$	−21.1244			−1.00821			−0.504105	+	0.863642i	$0.668178\pi$
$440$		0			0
$441$	−37.9282			−1.80610
$442$	12.6113	−	9.16267i	0.599860	−	0.435824i
$443$	5.27548	+	16.2362i	0.250645	+	0.771407i	0.994656	+	0.103240i	$0.0329210\pi$
$443$	5.27548	+	16.2362i	0.250645	+	0.771407i	−0.744011	+	0.668167i	$0.767079\pi$
$444$	−1.62789	+	5.01012i	−0.0772560	+	0.237770i
$445$	9.05788	+	6.58093i	0.429385	+	0.311966i
$446$	16.4977	+	11.9863i	0.781190	+	0.567568i
$447$	−3.39324	+	10.4433i	−0.160495	+	0.493952i
$448$	1.46228	+	4.50045i	0.0690864	+	0.212626i
$449$	8.03209	−	5.83565i	0.379058	−	0.275401i	−0.381899	−	0.924204i	$-0.624730\pi$
$449$	8.03209	−	5.83565i	0.379058	−	0.275401i	0.760957	+	0.648803i	$0.224730\pi$
$450$	4.92820			0.232318
$451$		0			0
$452$	10.8564			0.510642
$453$	2.60131	−	1.88996i	0.122220	−	0.0887980i
$454$	−5.06550	−	15.5900i	−0.237736	−	0.731675i
$455$	−7.59825	+	23.3850i	−0.356212	+	1.09631i
$456$	−0.750932	−	0.545584i	−0.0351656	−	0.0255493i
$457$	4.20378	+	3.05422i	0.196644	+	0.142870i	0.681750	−	0.731585i	$-0.261219\pi$
$457$	4.20378	+	3.05422i	0.196644	+	0.142870i	−0.485106	+	0.874455i	$0.661219\pi$
$458$	−4.07784	+	12.5503i	−0.190545	+	0.586436i
$459$	6.42280	+	19.7673i	0.299791	+	0.922660i
$460$	−1.77672	+	1.29087i	−0.0828402	+	0.0601869i
$461$	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
$463$	28.7846			1.33773			0.668867	−	0.743382i	$-0.266780\pi$
$463$	28.7846			1.33773			0.668867	+	0.743382i	$0.266780\pi$
$464$	2.42705	−	1.76336i	0.112673	−	0.0818617i
$465$	−0.0768560	−	0.236539i	−0.00356411	−	0.0109692i
$466$	−2.10250	+	6.47084i	−0.0973966	+	0.299756i
$467$	−17.3648	−	12.6163i	−0.803548	−	0.583812i	0.108405	−	0.994107i	$-0.465426\pi$
$467$	−17.3648	−	12.6163i	−0.803548	−	0.583812i	−0.911953	+	0.410295i	$0.865426\pi$
$468$	5.98050	+	4.34509i	0.276449	+	0.200852i
$469$	−14.9097	+	45.8873i	−0.688465	+	2.11888i
$470$	4.38685	+	13.5013i	0.202350	+	0.622771i
$471$	−2.36897	+	1.72115i	−0.109156	+	0.0793066i
$472$	9.46410			0.435621
$473$		0			0
$474$	−3.46410			−0.159111
$475$	2.05158	−	1.49056i	0.0941332	−	0.0683918i
$476$	−7.59825	−	23.3850i	−0.348265	−	1.07185i
$477$	−8.52530	+	26.2382i	−0.390347	+	1.20136i
$478$	11.4849	+	8.34429i	0.525308	+	0.381659i
$479$	7.10690	+	5.16346i	0.324722	+	0.235925i	0.738188	−	0.674595i	$-0.235682\pi$
$479$	7.10690	+	5.16346i	0.324722	+	0.235925i	−0.413465	+	0.910520i	$0.635682\pi$
$480$	−0.391818	+	1.20589i	−0.0178840	+	0.0550412i
$481$	−6.67120	−	20.5318i	−0.304181	−	0.936171i
$482$	−21.6692	+	15.7436i	−0.987005	+	0.717101i
$483$	−4.39230			−0.199857
$484$		0			0
$485$	1.73205			0.0786484
$486$	−12.3520	+	8.97428i	−0.560299	+	0.407081i
$487$	−4.01128	−	12.3454i	−0.181768	−	0.559425i	0.818109	−	0.575063i	$-0.195022\pi$
$487$	−4.01128	−	12.3454i	−0.181768	−	0.559425i	−0.999878	+	0.0156373i	$0.995022\pi$
$488$	0.783636	−	2.41178i	0.0354735	−	0.109176i
$489$	−13.1455	−	9.55075i	−0.594459	−	0.431900i
$490$	21.5686	+	15.6705i	0.974370	+	0.707921i
$491$	−10.3128	+	31.7397i	−0.465412	+	1.43239i	0.393051	+	0.919517i	$0.371419\pi$
$491$	−10.3128	+	31.7397i	−0.465412	+	1.43239i	−0.858463	+	0.512875i	$0.828581\pi$
$492$	−0.181843	−	0.559656i	−0.00819813	−	0.0252312i
$493$	−12.6113	+	9.16267i	−0.567986	+	0.412666i
$494$	3.80385			0.171143
$495$		0			0
$496$	0.196152			0.00880750
$497$	36.2315	−	26.3237i	1.62521	−	1.18078i
$498$	1.85410	+	5.70634i	0.0830843	+	0.255707i
$499$	4.94427	−	15.2169i	0.221336	−	0.681202i	−0.777307	−	0.629122i	$-0.783415\pi$
$499$	4.94427	−	15.2169i	0.221336	−	0.681202i	0.998643	−	0.0520806i	$-0.0165853\pi$
$500$	−9.80881	−	7.12652i	−0.438663	−	0.318708i
$501$	−9.70820	−	7.05342i	−0.433731	−	0.315124i
$502$	2.81958	−	8.67778i	0.125844	−	0.387308i
$503$	−4.38685	−	13.5013i	−0.195600	−	0.601995i	−0.999969	−	0.00786508i	$-0.997496\pi$
$503$	−4.38685	−	13.5013i	−0.195600	−	0.601995i	0.804369	−	0.594130i	$-0.202504\pi$
$504$	9.43334	−	6.85373i	0.420195	−	0.305289i
$505$	−28.3923			−1.26344
$506$		0			0
$507$	−2.92820			−0.130046
$508$	−11.2101	+	8.14459i	−0.497366	+	0.361358i
$509$	3.99503	+	12.2955i	0.177077	+	0.544986i	0.999722	−	0.0235684i	$-0.00750275\pi$
$509$	3.99503	+	12.2955i	0.177077	+	0.544986i	−0.822645	+	0.568555i	$0.807503\pi$
$510$	2.03595	−	6.26600i	0.0901532	−	0.277463i
$511$	3.55345	+	2.58173i	0.157195	+	0.114209i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−1.56727	+	4.82357i	−0.0691967	+	0.212966i
$514$	−5.99255	−	18.4432i	−0.264320	−	0.813494i
$515$	−11.7598	+	8.54399i	−0.518198	+	0.376493i
$516$		0			0
$517$		0			0
$518$	−34.0526			−1.49618
$519$	2.60131	−	1.88996i	0.114185	−	0.0829600i
$520$	−1.60570	−	4.94183i	−0.0704146	−	0.216714i
$521$	2.92457	−	9.00090i	0.128128	−	0.394336i	−0.866330	−	0.499472i	$-0.833528\pi$
$521$	2.92457	−	9.00090i	0.128128	−	0.394336i	0.994458	+	0.105135i	$0.0335275\pi$
$522$	−5.98050	−	4.34509i	−0.261759	−	0.190179i
$523$	−2.05158	−	1.49056i	−0.0897095	−	0.0651778i	0.542026	−	0.840361i	$-0.317657\pi$
$523$	−2.05158	−	1.49056i	−0.0897095	−	0.0651778i	−0.631736	+	0.775184i	$0.717657\pi$
$524$		0			0
$525$	−2.14093	−	6.58911i	−0.0934380	−	0.287572i
$526$	−7.93148	+	5.76256i	−0.345829	+	0.251259i
$527$	−1.01924			−0.0443987
$528$		0			0
$529$	−21.3923			−0.930100
$530$	15.6887	−	11.3985i	0.681474	−	0.495120i
$531$	−7.20643	−	22.1791i	−0.312733	−	0.962492i
$532$	1.85410	−	5.70634i	0.0803855	−	0.247401i
$533$	1.95098	+	1.41747i	0.0845063	+	0.0613974i
$534$	−3.82831	−	2.78143i	−0.165667	−	0.120364i
$535$	−6.73776	+	20.7367i	−0.291299	+	0.896525i
$536$	−3.15078	−	9.69712i	−0.136093	−	0.418852i
$537$	8.20634	−	5.96225i	0.354130	−	0.257290i
$538$	9.58846			0.413388
$539$		0			0
$540$	6.92820			0.298142
$541$	24.2705	−	17.6336i	1.04347	−	0.758126i	0.0725107	−	0.997368i	$-0.476899\pi$
$541$	24.2705	−	17.6336i	1.04347	−	0.758126i	0.970960	+	0.239242i	$0.0768989\pi$
$542$	−5.06550	−	15.5900i	−0.217582	−	0.669648i
$543$	1.62789	−	5.01012i	0.0698593	−	0.215005i
$544$	4.20378	+	3.05422i	0.180235	+	0.130949i
$545$	−2.90312	−	2.10924i	−0.124356	−	0.0903500i
$546$	3.21140	−	9.88367i	0.137435	−	0.422982i
$547$	−7.41641	−	22.8254i	−0.317103	−	0.975942i	−0.974880	−	0.222730i	$-0.928503\pi$
$547$	−7.41641	−	22.8254i	−0.317103	−	0.975942i	0.657778	−	0.753212i	$-0.271497\pi$
$548$	7.65662	−	5.56286i	0.327075	−	0.237634i
$549$	−6.24871			−0.266688
$550$		0			0
$551$	−3.80385			−0.162049
$552$	0.750932	−	0.545584i	0.0319618	−	0.0232216i
$553$	−6.91960	−	21.2963i	−0.294251	−	0.905613i
$554$	−2.57118	+	7.91327i	−0.109239	+	0.336203i
$555$	−7.38176	−	5.36316i	−0.313338	−	0.227654i
$556$	−16.3390	−	11.8710i	−0.692929	−	0.503443i
$557$	11.4883	−	35.3573i	0.486775	−	1.49814i	−0.342619	−	0.939474i	$-0.611314\pi$
$557$	11.4883	−	35.3573i	0.486775	−	1.49814i	0.829394	−	0.558664i	$-0.188686\pi$
$558$	−0.149360	−	0.459683i	−0.00632292	−	0.0194599i
$559$		0			0
$560$	−8.19615			−0.346351
$561$		0			0
$562$	18.0000			0.759284
$563$	0.476072	−	0.345887i	0.0200640	−	0.0145774i	−0.577708	−	0.816243i	$-0.696053\pi$
$563$	0.476072	−	0.345887i	0.0200640	−	0.0145774i	0.597772	+	0.801666i	$0.296053\pi$
$564$	−1.85410	−	5.70634i	−0.0780718	−	0.240280i
$565$	−5.81071	+	17.8835i	−0.244458	+	0.752365i
$566$	−5.60503	−	4.07230i	−0.235597	−	0.171171i
$567$	−17.0900	−	12.4166i	−0.717711	−	0.521448i
$568$	−2.92457	+	9.00090i	−0.122712	+	0.377669i
$569$	12.9787	+	39.9444i	0.544096	+	1.67456i	0.723130	+	0.690712i	$0.242703\pi$
$569$	12.9787	+	39.9444i	0.544096	+	1.67456i	−0.179034	+	0.983843i	$0.557297\pi$
$570$	1.30065	−	0.944980i	0.0544783	−	0.0395808i
$571$	5.66025			0.236874			0.118437	−	0.992962i	$-0.462212\pi$
$571$	5.66025			0.236874			0.118437	+	0.992962i	$0.462212\pi$
$572$		0			0
$573$	−15.7128			−0.656412
$574$	3.07738	−	2.23585i	0.128447	−	0.0933224i
$575$	0.783636	+	2.41178i	0.0326799	+	0.100578i
$576$	−0.761449	+	2.34350i	−0.0317271	+	0.0976458i
$577$	−11.8179	−	8.58619i	−0.491985	−	0.357448i	0.313962	−	0.949435i	$-0.398343\pi$
$577$	−11.8179	−	8.58619i	−0.491985	−	0.357448i	−0.805947	+	0.591988i	$0.798343\pi$
$578$	−8.09017	−	5.87785i	−0.336507	−	0.244486i
$579$	2.32278	−	7.14877i	0.0965313	−	0.297093i
$580$	1.60570	+	4.94183i	0.0666730	+	0.205199i
$581$	−31.3774	+	22.7970i	−1.30175	+	0.945780i
$582$	−0.732051			−0.0303445
$583$		0			0
$584$	−0.928203			−0.0384093
$585$	−10.3585	+	7.52591i	−0.428273	+	0.311158i
$586$	7.34985	+	22.6205i	0.303619	+	0.934445i
$587$	9.45235	−	29.0914i	0.390140	−	1.20073i	−0.542542	−	0.840029i	$-0.682538\pi$
$587$	9.45235	−	29.0914i	0.390140	−	1.20073i	0.932682	−	0.360700i	$-0.117462\pi$
$588$	−9.11596	−	6.62313i	−0.375936	−	0.273133i
$589$	−0.201212	−	0.146189i	−0.00829078	−	0.00602361i
$590$	−5.06550	+	15.5900i	−0.208543	+	0.641830i
$591$	−3.02956	−	9.32401i	−0.124619	−	0.383539i
$592$	5.82181	−	4.22979i	0.239275	−	0.173843i
$593$	−23.1962			−0.952552			−0.476276	−	0.879296i	$-0.658014\pi$
$593$	−23.1962			−0.952552			−0.476276	+	0.879296i	$0.658014\pi$
$594$		0			0
$595$	42.5885			1.74596
$596$	12.1353	−	8.81678i	0.497079	−	0.361149i
$597$	−0.0887457	−	0.273131i	−0.00363212	−	0.0111785i
$598$	−1.17545	+	3.61767i	−0.0480679	+	0.147938i
$599$	3.07738	+	2.23585i	0.125738	+	0.0913542i	0.648877	−	0.760893i	$-0.275239\pi$
$599$	3.07738	+	2.23585i	0.125738	+	0.0913542i	−0.523139	+	0.852248i	$0.675239\pi$
$600$	1.18448	+	0.860577i	0.0483563	+	0.0351329i
$601$	−2.67617	+	8.23639i	−0.109163	+	0.335969i	−0.990685	−	0.136174i	$-0.956519\pi$
$601$	−2.67617	+	8.23639i	−0.109163	+	0.335969i	0.881522	+	0.472143i	$0.156519\pi$
$602$		0			0
$603$	−20.3260	+	14.7677i	−0.827740	+	0.601388i
$604$	−4.39230			−0.178720
$605$		0			0
$606$	12.0000			0.487467
$607$	−21.1931	+	15.3977i	−0.860203	+	0.624974i	−0.927940	−	0.372729i	$-0.878422\pi$
$607$	−21.1931	+	15.3977i	−0.860203	+	0.624974i	0.0677374	+	0.997703i	$0.478422\pi$
$608$	0.391818	+	1.20589i	0.0158903	+	0.0489054i
$609$	−3.21140	+	9.88367i	−0.130132	+	0.400506i
$610$	3.55345	+	2.58173i	0.143875	+	0.104531i
$611$	19.8925	+	14.4527i	0.804764	+	0.584695i
$612$	3.95661	−	12.1772i	0.159936	−	0.492233i
$613$	6.27938	+	19.3260i	0.253622	+	0.780568i	0.994098	+	0.108485i	$0.0346000\pi$
$613$	6.27938	+	19.3260i	0.253622	+	0.780568i	−0.740476	+	0.672083i	$0.765400\pi$
$614$	−20.4422	+	14.8521i	−0.824980	+	0.599383i
$615$	1.01924			0.0410996
$616$		0			0
$617$	10.6077			0.427050			0.213525	−	0.976938i	$-0.431506\pi$
$617$	10.6077			0.427050			0.213525	+	0.976938i	$0.431506\pi$
$618$	4.97027	−	3.61111i	0.199934	−	0.145260i
$619$	−9.33112	−	28.7182i	−0.375050	−	1.15428i	−0.943445	−	0.331528i	$-0.892436\pi$
$619$	−9.33112	−	28.7182i	−0.375050	−	1.15428i	0.568396	−	0.822755i	$-0.307564\pi$
$620$	−0.104987	+	0.323118i	−0.00421639	+	0.0129767i
$621$	−4.10317	−	2.98113i	−0.164655	−	0.119629i
$622$	−7.10690	−	5.16346i	−0.284961	−	0.207036i
$623$	9.45235	−	29.0914i	0.378701	−	1.16552i
$624$	0.678648	+	2.08867i	0.0271677	+	0.0836135i
$625$	8.89919	−	6.46564i	0.355967	−	0.258626i
$626$	−31.7846			−1.27037
$627$		0			0
$628$	4.00000			0.159617
$629$	−30.2510	+	21.9786i	−1.20619	+	0.876346i
$630$	6.24095	+	19.2077i	0.248646	+	0.765252i
$631$	−6.36218	+	19.5808i	−0.253275	+	0.779499i	0.740890	+	0.671626i	$0.234404\pi$
$631$	−6.36218	+	19.5808i	−0.253275	+	0.779499i	−0.994165	+	0.107873i	$0.965596\pi$
$632$	3.82831	+	2.78143i	0.152282	+	0.110639i
$633$	15.3132	+	11.1257i	0.608647	+	0.442208i
$634$	−2.42776	+	7.47189i	−0.0964188	+	0.296747i
$635$	−7.41641	−	22.8254i	−0.294311	−	0.905797i
$636$	−6.63083	+	4.81758i	−0.262929	+	0.191029i
$637$	46.1769			1.82960
$638$		0			0
$639$	23.3205			0.922545
$640$	1.40126	−	1.01807i	0.0553896	−	0.0402429i
$641$	1.13703	+	3.49940i	0.0449098	+	0.138218i	0.970997	−	0.239091i	$-0.0768494\pi$
$641$	1.13703	+	3.49940i	0.0449098	+	0.138218i	−0.926087	+	0.377309i	$0.876849\pi$
$642$	2.84771	−	8.76436i	0.112390	−	0.345902i
$643$	20.8758	+	15.1671i	0.823259	+	0.598133i	0.917644	−	0.397403i	$-0.130088\pi$
$643$	20.8758	+	15.1671i	0.823259	+	0.598133i	−0.0943850	+	0.995536i	$0.530088\pi$
$644$	4.85410	+	3.52671i	0.191278	+	0.138972i
$645$		0			0
$646$	−2.03595	−	6.26600i	−0.0801032	−	0.246532i
$647$	18.8667	−	13.7075i	0.741726	−	0.538895i	−0.151525	−	0.988453i	$-0.548418\pi$
$647$	18.8667	−	13.7075i	0.741726	−	0.538895i	0.893251	+	0.449558i	$0.148418\pi$
$648$	4.46410			0.175366
$649$		0			0
$650$	−6.00000			−0.235339
$651$	−0.549721	+	0.399395i	−0.0215452	+	0.0156535i
$652$	6.85899	+	21.1098i	0.268619	+	0.826723i
$653$	−0.573661	+	1.76555i	−0.0224491	+	0.0690912i	−0.961653	−	0.274267i	$-0.911565\pi$
$653$	−0.573661	+	1.76555i	−0.0224491	+	0.0690912i	0.939204	+	0.343359i	$0.111565\pi$
$654$	1.22700	+	0.891471i	0.0479797	+	0.0348593i
$655$		0			0
$656$	−0.248403	+	0.764504i	−0.00969849	+	0.0298489i
$657$	0.706780	+	2.17524i	0.0275741	+	0.0848644i
$658$	31.3774	−	22.7970i	1.22322	−	0.888720i
$659$	16.9808			0.661477			0.330738	−	0.943723i	$-0.392702\pi$
$659$	16.9808			0.661477			0.330738	+	0.943723i	$0.392702\pi$
$660$		0			0
$661$	−16.4115			−0.638335			−0.319168	−	0.947698i	$-0.603403\pi$
$661$	−16.4115			−0.638335			−0.319168	+	0.947698i	$0.603403\pi$
$662$	−23.2872	+	16.9192i	−0.905084	+	0.657582i
$663$	−3.52636	−	10.8530i	−0.136952	−	0.421496i
$664$	2.53275	−	7.79500i	0.0982898	−	0.302505i
$665$	8.40755	+	6.10844i	0.326031	+	0.236875i
$666$	−14.3455	−	10.4226i	−0.555878	−	0.403869i
$667$	1.17545	−	3.61767i	0.0455137	−	0.140077i
$668$	5.06550	+	15.5900i	0.195990	+	0.603196i
$669$	12.0772	−	8.77458i	0.466930	−	0.339245i
$670$	17.6603			0.682275
$671$		0			0
$672$	3.46410			0.133631
$673$	−0.750932	+	0.545584i	−0.0289463	+	0.0210307i	−0.602164	−	0.798372i	$-0.705695\pi$
$673$	−0.750932	+	0.545584i	−0.0289463	+	0.0210307i	0.573218	+	0.819403i	$0.305695\pi$
$674$	0.822064	+	2.53005i	0.0316647	+	0.0974540i
$675$	2.47214	−	7.60845i	0.0951526	−	0.292849i
$676$	3.23607	+	2.35114i	0.124464	+	0.0904285i
$677$	−3.72770	−	2.70834i	−0.143267	−	0.104090i	0.513843	−	0.857884i	$-0.328221\pi$
$677$	−3.72770	−	2.70834i	−0.143267	−	0.104090i	−0.657110	+	0.753794i	$0.728221\pi$
$678$	2.45589	−	7.55847i	0.0943181	−	0.290281i
$679$	−1.46228	−	4.50045i	−0.0561173	−	0.172711i
$680$	−7.28115	+	5.29007i	−0.279219	+	0.202865i
$681$	−12.0000			−0.459841
$682$		0			0
$683$	−5.41154			−0.207067			−0.103533	−	0.994626i	$-0.533015\pi$
$683$	−5.41154			−0.207067			−0.103533	+	0.994626i	$0.533015\pi$
$684$	2.52766	−	1.83645i	0.0966474	−	0.0702184i
$685$	5.06550	+	15.5900i	0.193543	+	0.595664i
$686$	12.2719	−	37.7691i	0.468545	−	1.44203i
$687$	7.81531	+	5.67815i	0.298173	+	0.216635i
$688$		0			0
$689$	10.3794	−	31.9445i	0.395424	−	1.21699i
$690$	0.496805	+	1.52901i	0.0189130	+	0.0582084i
$691$	33.3128	−	24.2032i	1.26728	−	0.920732i	0.268189	−	0.963366i	$-0.413575\pi$
$691$	33.3128	−	24.2032i	1.26728	−	0.920732i	0.999091	+	0.0426339i	$0.0135749\pi$
$692$	−4.39230			−0.166970
$693$		0			0
$694$	−28.3923			−1.07776
$695$	28.3000	−	20.5612i	1.07348	−	0.779930i
$696$	−0.678648	−	2.08867i	−0.0257241	−	0.0791706i
$697$	1.29074	−	3.97248i	0.0488902	−	0.150468i
$698$	17.7403	+	12.8891i	0.671480	+	0.487859i
$699$	4.02952	+	2.92762i	0.152410	+	0.110733i
$700$	−2.92457	+	9.00090i	−0.110538	+	0.340202i
$701$	−5.49575	−	16.9142i	−0.207571	−	0.638839i	−0.999598	−	0.0283526i	$-0.990974\pi$
$701$	−5.49575	−	16.9142i	−0.207571	−	0.638839i	0.792026	−	0.610487i	$-0.209026\pi$
$702$	9.70820	−	7.05342i	0.366413	−	0.266214i
$703$	−9.12436			−0.344132
$704$		0			0
$705$	10.3923			0.391397
$706$	−17.7403	+	12.8891i	−0.667665	+	0.485087i
$707$	23.9702	+	73.7727i	0.901492	+	2.77451i
$708$	2.14093	−	6.58911i	0.0804612	−	0.247634i
$709$	30.7426	+	22.3358i	1.15456	+	0.838840i	0.989081	−	0.147373i	$-0.0470816\pi$
$709$	30.7426	+	22.3358i	1.15456	+	0.838840i	0.165483	+	0.986213i	$0.447082\pi$
$710$	−13.2617	−	9.63516i	−0.497701	−	0.361601i
$711$	3.60322	−	11.0896i	0.135131	−	0.415891i
$712$	1.99752	+	6.14773i	0.0748601	+	0.230396i
$713$	0.201212	−	0.146189i	0.00753544	−	0.00547481i
$714$	−18.0000			−0.673633
$715$		0			0
$716$	−13.8564			−0.517838
$717$	8.40755	−	6.10844i	0.313986	−	0.228124i
$718$	−2.03595	−	6.26600i	−0.0759808	−	0.233845i
$719$	−14.4410	+	44.4448i	−0.538558	+	1.65751i	0.197274	+	0.980348i	$0.436791\pi$
$719$	−14.4410	+	44.4448i	−0.538558	+	1.65751i	−0.735832	+	0.677164i	$0.763209\pi$
$720$	−3.45284	−	2.50864i	−0.128680	−	0.0934914i
$721$	32.1283	+	23.3426i	1.19652	+	0.869324i
$722$	−5.37452	+	16.5411i	−0.200019	+	0.615595i
$723$	6.05911	+	18.6480i	0.225341	+	0.693528i
$724$	−5.82181	+	4.22979i	−0.216366	+	0.157199i
$725$	6.00000			0.222834
$726$		0			0
$727$	−36.9808			−1.37154			−0.685770	−	0.727818i	$-0.740535\pi$
$727$	−36.9808			−1.37154			−0.685770	+	0.727818i	$0.740535\pi$
$728$	−11.4849	+	8.34429i	−0.425660	+	0.309260i
$729$	−0.684593	−	2.10696i	−0.0253553	−	0.0780356i
$730$	0.496805	−	1.52901i	0.0183876	−	0.0565912i
$731$		0			0
$732$	−1.50186	−	1.09117i	−0.0555105	−	0.0403307i
$733$	5.13206	−	15.7949i	0.189557	−	0.583396i	−0.810440	−	0.585822i	$-0.800772\pi$
$733$	5.13206	−	15.7949i	0.189557	−	0.583396i	0.999997	+	0.00242517i	$0.000771958\pi$
$734$	2.65398	+	8.16811i	0.0979602	+	0.301490i
$735$	15.7893	−	11.4716i	0.582397	−	0.423137i
$736$	−1.26795			−0.0467372
$737$		0			0
$738$	1.98076			0.0729129
$739$	−8.68241	+	6.30814i	−0.319388	+	0.232049i	−0.735914	−	0.677075i	$-0.763247\pi$
$739$	−8.68241	+	6.30814i	−0.319388	+	0.232049i	0.416526	+	0.909124i	$0.363247\pi$
$740$	3.85162	+	11.8541i	0.141588	+	0.435764i
$741$	0.860492	−	2.64832i	0.0316110	−	0.0972885i
$742$	−42.8623	−	31.1413i	−1.57353	−	1.14323i
$743$	30.9013	+	22.4511i	1.13366	+	0.823652i	0.986223	−	0.165419i	$-0.0528977\pi$
$743$	30.9013	+	22.4511i	1.13366	+	0.823652i	0.147437	+	0.989071i	$0.452898\pi$
$744$	0.0443728	−	0.136566i	0.00162679	−	0.00500674i
$745$	8.02850	+	24.7092i	0.294141	+	0.905274i
$746$	9.15848	−	6.65403i	0.335316	−	0.243621i
$747$	−20.1962			−0.738939
$748$		0			0
$749$	59.5692			2.17661
$750$	−7.18055	+	5.21697i	−0.262197	+	0.190497i
$751$	1.23607	+	3.80423i	0.0451048	+	0.138818i	0.971073	−	0.238784i	$-0.0767487\pi$
$751$	1.23607	+	3.80423i	0.0451048	+	0.138818i	−0.925968	+	0.377602i	$0.876749\pi$
$752$	−2.53275	+	7.79500i	−0.0923599	+	0.284255i
$753$	−5.40382	−	3.92611i	−0.196926	−	0.143075i
$754$	7.28115	+	5.29007i	0.265164	+	0.192653i
$755$	2.35091	−	7.23535i	0.0855583	−	0.263321i
$756$	−5.84914	−	18.0018i	−0.212731	−	0.654719i
$757$	10.6759	−	7.75650i	0.388023	−	0.281915i	−0.376622	−	0.926367i	$-0.622914\pi$
$757$	10.6759	−	7.75650i	0.388023	−	0.281915i	0.764645	+	0.644452i	$0.222914\pi$
$758$	3.60770			0.131037
$759$		0			0
$760$	−2.19615			−0.0796628
$761$	−16.1648	+	11.7444i	−0.585973	+	0.425734i	−0.840872	−	0.541233i	$-0.817958\pi$
$761$	−16.1648	+	11.7444i	−0.585973	+	0.425734i	0.254900	+	0.966967i	$0.417958\pi$
$762$	3.13454	+	9.64713i	0.113553	+	0.349479i
$763$	−3.02956	+	9.32401i	−0.109677	+	0.337552i
$764$	17.3648	+	12.6163i	0.628237	+	0.456441i
$765$	17.9415	+	13.0353i	0.648676	+	0.471291i
$766$	−0.209975	+	0.646235i	−0.00758669	+	0.0233494i
$767$	8.77370	+	27.0027i	0.316800	+	0.975011i
$768$	−0.592242	+	0.430289i	−0.0213707	+	0.0155267i
$769$	34.5167			1.24470			0.622351	−	0.782738i	$-0.286178\pi$
$769$	34.5167			1.24470			0.622351	+	0.782738i	$0.286178\pi$
$770$		0			0
$771$	−14.1962			−0.511262
$772$	−8.30695	+	6.03535i	−0.298974	+	0.217217i
$773$	−5.56231	−	17.1190i	−0.200062	−	0.615728i	−0.999880	−	0.0154855i	$-0.995071\pi$
$773$	−5.56231	−	17.1190i	−0.200062	−	0.615728i	0.799818	−	0.600243i	$-0.204929\pi$
$774$		0			0
$775$	0.317381	+	0.230591i	0.0114007	+	0.00828307i
$776$	0.809017	+	0.587785i	0.0290420	+	0.0211003i
$777$	−7.70324	+	23.7081i	−0.276352	+	0.850524i
$778$	10.0926	+	31.0617i	0.361836	+	1.11362i
$779$	0.824581	−	0.599093i	0.0295437	−	0.0214647i
$780$	−3.80385			−0.136200
$781$		0			0
$782$	6.58846			0.235603
$783$	−9.70820	+	7.05342i	−0.346943	+	0.252069i
$784$	4.75648	+	14.6390i	0.169874	+	0.522820i
$785$	−2.14093	+	6.58911i	−0.0764132	+	0.235176i
$786$		0			0
$787$	−36.2315	−	26.3237i	−1.29151	−	0.938340i	−0.291679	−	0.956516i	$-0.594214\pi$
$787$	−36.2315	−	26.3237i	−1.29151	−	0.938340i	−0.999835	+	0.0181765i	$0.994214\pi$
$788$	−4.13845	+	12.7368i	−0.147426	+	0.453731i
$789$	2.21779	+	6.82565i	0.0789554	+	0.243000i
$790$	−6.63083	+	4.81758i	−0.235914	+	0.171402i
$791$	51.3731			1.82662
$792$		0			0
$793$	7.60770			0.270157
$794$	−4.52116	+	3.28481i	−0.160450	+	0.116574i
$795$	−4.38685	−	13.5013i	−0.155586	−	0.478843i
$796$	−0.121229	+	0.373104i	−0.00429684	+	0.0132243i
$797$	−29.8755	−	21.7059i	−1.05825	−	0.768861i	−0.0844830	−	0.996425i	$-0.526924\pi$
$797$	−29.8755	−	21.7059i	−1.05825	−	0.768861i	−0.973763	+	0.227564i	$0.926924\pi$
$798$	−3.55345	−	2.58173i	−0.125791	−	0.0913923i
$799$	13.1606	−	40.5040i	0.465587	−	1.43293i
$800$	−0.618034	−	1.90211i	−0.0218508	−	0.0672499i
$801$	12.8862	−	9.36236i	0.455311	−	0.330803i
$802$	−7.39230			−0.261031
$803$		0			0
$804$	−7.46410			−0.263239
$805$	−8.40755	+	6.10844i	−0.296327	+	0.215294i
$806$	0.181843	+	0.559656i	0.00640516	+	0.0197130i
$807$	2.16906	−	6.67569i	0.0763547	−	0.234995i
$808$	−13.2617	−	9.63516i	−0.466543	−	0.338964i
$809$	−14.5623	−	10.5801i	−0.511983	−	0.371978i	0.301592	−	0.953437i	$-0.402482\pi$
$809$	−14.5623	−	10.5801i	−0.511983	−	0.371978i	−0.813575	+	0.581459i	$0.802482\pi$
$810$	−2.38934	+	7.35362i	−0.0839527	+	0.258380i
$811$	2.14093	+	6.58911i	0.0751783	+	0.231375i	0.981583	−	0.191035i	$-0.0611843\pi$
$811$	2.14093	+	6.58911i	0.0751783	+	0.231375i	−0.906405	+	0.422410i	$0.861184\pi$
$812$	11.4849	−	8.34429i	0.403042	−	0.292827i
$813$	−12.0000			−0.420858
$814$		0			0
$815$	−38.4449			−1.34666
$816$	3.07738	−	2.23585i	0.107730	−	0.0782702i
$817$		0			0
$818$	−0.822064	+	2.53005i	−0.0287428	+	0.0884612i
$819$	28.3000	+	20.5612i	0.988883	+	0.718466i
$820$	−1.12640	−	0.818376i	−0.0393355	−	0.0285789i
$821$	−5.06550	+	15.5900i	−0.176787	+	0.544095i	−0.999711	−	0.0240573i	$-0.992342\pi$
$821$	−5.06550	+	15.5900i	−0.176787	+	0.544095i	0.822923	+	0.568152i	$0.192342\pi$
$822$	−2.14093	−	6.58911i	−0.0746736	−	0.229822i
$823$	−25.8885	+	18.8091i	−0.902418	+	0.655645i	−0.939086	−	0.343683i	$-0.888326\pi$
$823$	−25.8885	+	18.8091i	−0.902418	+	0.655645i	0.0366680	+	0.999328i	$0.488326\pi$
$824$	−8.39230			−0.292360
$825$		0			0
$826$	44.7846			1.55826
$827$	16.3390	−	11.8710i	0.568164	−	0.412795i	−0.266274	−	0.963897i	$-0.585793\pi$
$827$	16.3390	−	11.8710i	0.568164	−	0.412795i	0.834438	+	0.551102i	$0.185793\pi$
$828$	0.965479	+	2.97144i	0.0335527	+	0.103265i
$829$	4.57464	−	14.0793i	0.158884	−	0.488994i	−0.839650	−	0.543128i	$-0.817240\pi$
$829$	4.57464	−	14.0793i	0.158884	−	0.488994i	0.998534	+	0.0541339i	$0.0172398\pi$
$830$	11.4849	+	8.34429i	0.398648	+	0.289635i
$831$	4.92775	+	3.58022i	0.170942	+	0.124196i
$832$	0.927051	−	2.85317i	0.0321397	−	0.0989159i
$833$	−24.7154	−	76.0662i	−0.856338	−	2.63554i
$834$	−11.9610	+	8.69018i	−0.414176	+	0.300916i
$835$	−28.3923			−0.982556
$836$		0			0
$837$	−0.784610			−0.0271201
$838$	31.8535	−	23.1429i	1.10036	−	0.799458i
$839$	−15.5883	−	47.9759i	−0.538169	−	1.65631i	−0.736701	−	0.676218i	$-0.763618\pi$
$839$	−15.5883	−	47.9759i	−0.538169	−	1.65631i	0.198533	−	0.980094i	$-0.436382\pi$
$840$	−1.85410	+	5.70634i	−0.0639726	+	0.196887i
$841$	16.1803	+	11.7557i	0.557943	+	0.405369i
$842$	−6.13919	−	4.46038i	−0.211570	−	0.153715i
$843$	4.07189	−	12.5320i	0.140243	−	0.431625i
$844$	−7.99007	−	24.5909i	−0.275030	−	0.846454i
$845$	−5.60503	+	4.07230i	−0.192819	+	0.140091i
$846$	20.1962			0.694358
$847$		0			0
$848$	11.1962			0.384477
$849$	−4.10317	+	2.98113i	−0.140820	+	0.102312i
$850$	3.21140	+	9.88367i	0.110150	+	0.339007i
$851$	2.81958	−	8.67778i	0.0966540	−	0.297470i
$852$	5.60503	+	4.07230i	0.192025	+	0.139515i
$853$	8.78302	+	6.38124i	0.300725	+	0.218489i	0.727906	−	0.685676i	$-0.240494\pi$
$853$	8.78302	+	6.38124i	0.300725	+	0.218489i	−0.427182	+	0.904166i	$0.640494\pi$
$854$	3.70820	−	11.4127i	0.126892	−	0.390534i
$855$	1.67226	+	5.14668i	0.0571900	+	0.176013i
$856$	−10.1843	+	7.39931i	−0.348091	+	0.252903i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−24.7846			−0.845640			−0.422820	−	0.906214i	$-0.638960\pi$
$859$	−24.7846			−0.845640			−0.422820	+	0.906214i	$0.638960\pi$
$860$		0			0
$861$	−0.860492	−	2.64832i	−0.0293255	−	0.0902545i
$862$	5.06550	−	15.5900i	0.172532	−	0.530998i
$863$	3.07738	+	2.23585i	0.104755	+	0.0761091i	0.638930	−	0.769265i	$-0.279377\pi$
$863$	3.07738	+	2.23585i	0.104755	+	0.0761091i	−0.534175	+	0.845374i	$0.679377\pi$
$864$	3.23607	+	2.35114i	0.110093	+	0.0799874i
$865$	2.35091	−	7.23535i	0.0799332	−	0.246009i
$866$	9.82198	+	30.2290i	0.333765	+	1.02722i
$867$	−5.92242	+	4.30289i	−0.201136	+	0.146134i
$868$	0.928203			0.0315053
$869$		0			0
$870$	3.80385			0.128963
$871$	24.7466	−	17.9794i	0.838506	−	0.609210i
$872$	−0.640220	−	1.97040i	−0.0216806	−	0.0667260i
$873$	0.761449	−	2.34350i	0.0257712	−	0.0793155i
$874$	1.30065	+	0.944980i	0.0439952	+	0.0319644i
$875$	−46.4158	−	33.7230i	−1.56914	−	1.14005i
$876$	−0.209975	+	0.646235i	−0.00709438	+	0.0218343i
$877$	−1.99752	−	6.14773i	−0.0674514	−	0.207594i	0.911650	−	0.410968i	$-0.134809\pi$
$877$	−1.99752	−	6.14773i	−0.0674514	−	0.207594i	−0.979101	+	0.203374i	$0.934809\pi$
$878$	17.0900	−	12.4166i	0.576758	−	0.419039i
$879$	17.4115			0.587277
$880$		0			0
$881$	41.5359			1.39938			0.699690	−	0.714447i	$-0.253321\pi$
$881$	41.5359			1.39938			0.699690	+	0.714447i	$0.253321\pi$
$882$	30.6846	−	22.2936i	1.03320	−	0.750666i
$883$	−4.82304	−	14.8438i	−0.162308	−	0.499534i	0.836520	−	0.547937i	$-0.184587\pi$
$883$	−4.82304	−	14.8438i	−0.162308	−	0.499534i	−0.998828	+	0.0484034i	$0.984587\pi$
$884$	−4.81710	+	14.8255i	−0.162017	+	0.498636i
$885$	9.70820	+	7.05342i	0.326338	+	0.237098i
$886$	−13.8114	−	10.0346i	−0.464002	−	0.337117i
$887$	−14.1542	+	43.5620i	−0.475250	+	1.46267i	0.370369	+	0.928885i	$0.379231\pi$
$887$	−14.1542	+	43.5620i	−0.475250	+	1.46267i	−0.845620	+	0.533786i	$0.820769\pi$
$888$	−1.62789	−	5.01012i	−0.0546283	−	0.168129i
$889$	−53.0466	+	38.5406i	−1.77913	+	1.29261i
$890$	−11.1962			−0.375296
$891$		0			0
$892$	−20.3923			−0.682785
$893$	8.40755	−	6.10844i	0.281348	−	0.204411i
$894$	−3.39324	−	10.4433i	−0.113487	−	0.349277i
$895$	7.41641	−	22.8254i	0.247903	−	0.762968i
$896$	−3.82831	−	2.78143i	−0.127895	−	0.0929210i
$897$	2.25280	+	1.63675i	0.0752187	+	0.0546496i
$898$	−3.06798	+	9.44228i	−0.102380	+	0.315093i
$899$	−0.181843	−	0.559656i	−0.00606481	−	0.0186656i
$900$	−3.98700	+	2.89673i	−0.132900	+	0.0965575i
$901$	−58.1769			−1.93815
$902$		0			0
$903$		0			0
$904$	−8.78302	+	6.38124i	−0.292119	+	0.212237i
$905$	−3.85162	−	11.8541i	−0.128032	−	0.394042i
$906$	−0.993610	+	3.05802i	−0.0330105	+	0.101596i
$907$	−30.3941	−	22.0826i	−1.00922	−	0.733242i	−0.0451753	−	0.998979i	$-0.514385\pi$
$907$	−30.3941	−	22.0826i	−1.00922	−	0.733242i	−0.964045	+	0.265737i	$0.914385\pi$
$908$	13.2617	+	9.63516i	0.440103	+	0.319754i
$909$	−12.4819	+	38.4154i	−0.413999	+	1.27416i
$910$	−7.59825	−	23.3850i	−0.251880	−	0.775206i
$911$	25.5712	−	18.5785i	0.847210	−	0.615534i	−0.0771651	−	0.997018i	$-0.524587\pi$
$911$	25.5712	−	18.5785i	0.847210	−	0.615534i	0.924375	+	0.381484i	$0.124587\pi$
$912$	0.928203			0.0307359
$913$		0			0
$914$	−5.19615			−0.171873
$915$	2.60131	−	1.88996i	0.0859965	−	0.0624801i
$916$	−4.07784	−	12.5503i	−0.134735	−	0.414673i
$917$		0			0
$918$	−16.8151	−	12.2169i	−0.554981	−	0.403217i
$919$	−17.9145	−	13.0157i	−0.590946	−	0.429348i	0.251708	−	0.967803i	$-0.419008\pi$
$919$	−17.9145	−	13.0157i	−0.590946	−	0.429348i	−0.842654	+	0.538456i	$0.819008\pi$
$920$	0.678648	−	2.08867i	0.0223744	−	0.0688612i
$921$	5.71602	+	17.5921i	0.188349	+	0.579679i
$922$	−26.6976	+	19.3969i	−0.879237	+	0.638803i
$923$	−28.3923			−0.934544
$924$		0			0
$925$	14.3923			0.473216
$926$	−23.2872	+	16.9192i	−0.765266	+	0.555998i
$927$	6.39031	+	19.6674i	0.209885	+	0.645961i
$928$	−0.927051	+	2.85317i	−0.0304319	+	0.0936599i
$929$	−31.5517	−	22.9236i	−1.03518	−	0.752100i	−0.0658383	−	0.997830i	$-0.520972\pi$
$929$	−31.5517	−	22.9236i	−1.03518	−	0.752100i	−0.969338	+	0.245731i	$0.920972\pi$
$930$	0.201212	+	0.146189i	0.00659799	+	0.00479372i
$931$	6.03098	−	18.5614i	0.197657	−	0.608327i
$932$	−2.10250	−	6.47084i	−0.0688698	−	0.211960i
$933$	−5.20261	+	3.77992i	−0.170326	+	0.123749i
$934$	21.4641			0.702327
$935$		0			0
$936$	−7.39230			−0.241625
$937$	−28.6755	+	20.8340i	−0.936788	+	0.680616i	−0.947645	−	0.319325i	$-0.896544\pi$
$937$	−28.6755	+	20.8340i	−0.936788	+	0.680616i	0.0108576	+	0.999941i	$0.496544\pi$
$938$	−14.9097	−	45.8873i	−0.486818	−	1.49827i
$939$	−7.19019	+	22.1291i	−0.234643	+	0.722157i
$940$	−11.4849	−	8.34429i	−0.374597	−	0.272161i
$941$	27.9982	+	20.3419i	0.912716	+	0.663127i	0.941700	−	0.336453i	$-0.109227\pi$
$941$	27.9982	+	20.3419i	0.912716	+	0.663127i	−0.0289845	+	0.999580i	$0.509227\pi$
$942$	0.904865	−	2.78489i	0.0294821	−	0.0907365i
$943$	0.314962	+	0.969353i	0.0102566	+	0.0315665i
$944$	−7.65662	+	5.56286i	−0.249202	+	0.181056i
$945$	32.7846			1.06648
$946$		0			0
$947$	5.90897			0.192016			0.0960078	−	0.995381i	$-0.469393\pi$
$947$	5.90897			0.192016			0.0960078	+	0.995381i	$0.469393\pi$
$948$	2.80252	−	2.03615i	0.0910215	−	0.0661310i
$949$	−0.860492	−	2.64832i	−0.0279327	−	0.0859681i
$950$	−0.783636	+	2.41178i	−0.0254245	+	0.0782486i
$951$	4.65289	+	3.38052i	0.150880	+	0.109621i
$952$	19.8925	+	14.4527i	0.644719	+	0.468416i
$953$	−12.2335	+	37.6509i	−0.396282	+	1.21963i	0.531676	+	0.846948i	$0.321562\pi$
$953$	−12.2335	+	37.6509i	−0.396282	+	1.21963i	−0.927959	+	0.372683i	$0.878438\pi$
$954$	−8.52530	−	26.2382i	−0.276017	−	0.849493i
$955$	−30.0768	+	21.8520i	−0.973261	+	0.707115i
$956$	−14.1962			−0.459136
$957$		0			0
$958$	−8.78461			−0.283818
$959$	36.2315	−	26.3237i	1.16998	−	0.850038i
$960$	−0.391818	−	1.20589i	−0.0126459	−	0.0389200i
$961$	−9.56764	+	29.4462i	−0.308633	+	0.949876i
$962$	17.4654	+	12.6894i	0.563108	+	0.409122i
$963$	25.0951	+	18.2327i	0.808678	+	0.587539i
$964$	8.27690	−	25.4737i	0.266581	−	0.820452i
$965$	−5.49575	−	16.9142i	−0.176914	−	0.544486i
$966$	3.55345	−	2.58173i	0.114330	−	0.0830659i
$967$	−32.4449			−1.04336			−0.521678	−	0.853142i	$-0.674694\pi$
$967$	−32.4449			−1.04336			−0.521678	+	0.853142i	$0.674694\pi$
$968$		0			0
$969$	−4.82309			−0.154940
$970$	−1.40126	+	1.01807i	−0.0449917	+	0.0326884i
$971$	−1.25231	−	3.85421i	−0.0401885	−	0.123688i	0.928949	−	0.370207i	$-0.120713\pi$
$971$	−1.25231	−	3.85421i	−0.0401885	−	0.123688i	−0.969138	+	0.246519i	$0.920713\pi$
$972$	4.71806	−	14.5207i	0.151332	−	0.465751i
$973$	−77.3171	−	56.1742i	−2.47867	−	1.80086i
$974$	10.5017	+	7.62990i	0.336495	+	0.244478i
$975$	−1.35730	+	4.17733i	−0.0434683	+	0.133782i
$976$	0.783636	+	2.41178i	0.0250836	+	0.0771993i
$977$	−26.1478	+	18.9975i	−0.836544	+	0.607784i	−0.921403	−	0.388608i	$-0.872956\pi$
$977$	−26.1478	+	18.9975i	−0.836544	+	0.607784i	0.0848595	+	0.996393i	$0.472956\pi$
$978$	16.2487			0.519576
$979$		0			0
$980$	−26.6603			−0.851631
$981$	−4.13013	+	3.00071i	−0.131865	+	0.0958054i
$982$	−10.3128	−	31.7397i	−0.329096	−	1.01285i
$983$	9.92103	−	30.5338i	0.316432	−	0.973876i	−0.658730	−	0.752380i	$-0.728906\pi$
$983$	9.92103	−	30.5338i	0.316432	−	0.973876i	0.975161	−	0.221497i	$-0.0710942\pi$
$984$	0.476072	+	0.345887i	0.0151766	+	0.0110265i
$985$	−18.7661	−	13.6344i	−0.597937	−	0.434427i
$986$	4.81710	−	14.8255i	0.153408	−	0.472140i
$987$	−8.77370	−	27.0027i	−0.279270	−	0.859505i
$988$	−3.07738	+	2.23585i	−0.0979044	+	0.0711317i
$989$		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	$0.602897\pi$
$992$	−0.158691	+	0.115296i	−0.00503843	+	0.00366064i
$993$	6.51154	+	20.0405i	0.206638	+	0.635965i
$994$	−13.8392	+	42.5927i	−0.438953	+	1.35096i
$995$	−0.549721	−	0.399395i	−0.0174273	−	0.0126617i
$996$	−4.85410	−	3.52671i	−0.153808	−	0.111748i
$997$	3.85162	−	11.8541i	0.121982	−	0.375422i	−0.871357	−	0.490649i	$-0.836760\pi$
$997$	3.85162	−	11.8541i	0.121982	−	0.375422i	0.993339	+	0.115227i	$0.0367596\pi$
$998$	4.94427	+	15.2169i	0.156508	+	0.481683i
$999$	−23.2872	+	16.9192i	−0.736776	+	0.535299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.2.c.f.3.2		8
11.2	odd	10		242.2.a.c.1.2	✓	2
11.3	even	5	inner	242.2.c.f.27.1		8
11.4	even	5	inner	242.2.c.f.81.2		8
11.5	even	5	inner	242.2.c.f.9.1		8
11.6	odd	10		242.2.c.g.9.1		8
11.7	odd	10		242.2.c.g.81.2		8
11.8	odd	10		242.2.c.g.27.1		8
11.9	even	5		242.2.a.e.1.2	yes	2
11.10	odd	2		242.2.c.g.3.2		8
33.2	even	10		2178.2.a.y.1.2		2
33.20	odd	10		2178.2.a.s.1.2		2
44.31	odd	10		1936.2.a.v.1.1		2
44.35	even	10		1936.2.a.y.1.1		2
55.9	even	10		6050.2.a.cc.1.1		2
55.24	odd	10		6050.2.a.cv.1.1		2
88.13	odd	10		7744.2.a.cs.1.1		2
88.35	even	10		7744.2.a.bt.1.2		2
88.53	even	10		7744.2.a.cv.1.1		2
88.75	odd	10		7744.2.a.bq.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
242.2.a.c.1.2	✓	2	11.2	odd	10
242.2.a.e.1.2	yes	2	11.9	even	5
242.2.c.f.3.2		8	1.1	even	1	trivial
242.2.c.f.9.1		8	11.5	even	5	inner
242.2.c.f.27.1		8	11.3	even	5	inner
242.2.c.f.81.2		8	11.4	even	5	inner
242.2.c.g.3.2		8	11.10	odd	2
242.2.c.g.9.1		8	11.6	odd	10
242.2.c.g.27.1		8	11.8	odd	10
242.2.c.g.81.2		8	11.7	odd	10
1936.2.a.v.1.1		2	44.31	odd	10
1936.2.a.y.1.1		2	44.35	even	10
2178.2.a.s.1.2		2	33.20	odd	10
2178.2.a.y.1.2		2	33.2	even	10
6050.2.a.cc.1.1		2	55.9	even	10
6050.2.a.cv.1.1		2	55.24	odd	10
7744.2.a.bq.1.2		2	88.75	odd	10
7744.2.a.bt.1.2		2	88.35	even	10
7744.2.a.cs.1.1		2	88.13	odd	10
7744.2.a.cv.1.1		2	88.53	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.226216 + 0.696222i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.40126 + 1.01807i) q^{5} +(-0.592242 - 0.430289i) q^{6} +(1.46228 - 4.50045i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.99350 - 1.44836i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.226216 + 0.696222i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.40126 + 1.01807i) q^{5} +(-0.592242 - 0.430289i) q^{6} +(1.46228 - 4.50045i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.99350 - 1.44836i) q^{9} -1.73205 q^{10} +0.732051 q^{12} +(-2.42705 + 1.76336i) q^{13} +(1.46228 + 4.50045i) q^{14} +(-0.391818 + 1.20589i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.20378 + 3.05422i) q^{17} +(-0.761449 + 2.34350i) q^{18} +(0.391818 + 1.20589i) q^{19} +(1.40126 - 1.01807i) q^{20} +3.46410 q^{21} -1.26795 q^{23} +(-0.592242 + 0.430289i) q^{24} +(-0.618034 - 1.90211i) q^{25} +(0.927051 - 2.85317i) q^{26} +(3.23607 + 2.35114i) q^{27} +(-3.82831 - 2.78143i) q^{28} +(-0.927051 + 2.85317i) q^{29} +(-0.391818 - 1.20589i) q^{30} +(-0.158691 + 0.115296i) q^{31} +1.00000 q^{32} -5.19615 q^{34} +(6.63083 - 4.81758i) q^{35} +(-0.761449 - 2.34350i) q^{36} +(-2.22373 + 6.84395i) q^{37} +(-1.02579 - 0.745282i) q^{38} +(-1.77672 - 1.29087i) q^{39} +(-0.535233 + 1.64728i) q^{40} +(-0.248403 - 0.764504i) q^{41} +(-2.80252 + 2.03615i) q^{42} +4.26795 q^{45} +(1.02579 - 0.745282i) q^{46} +(-2.53275 - 7.79500i) q^{47} +(0.226216 - 0.696222i) q^{48} +(-12.4526 - 9.04737i) q^{49} +(1.61803 + 1.17557i) q^{50} +(-1.17545 + 3.61767i) q^{51} +(0.927051 + 2.85317i) q^{52} +(-9.05788 + 6.58093i) q^{53} -4.00000 q^{54} +4.73205 q^{56} +(-0.750932 + 0.545584i) q^{57} +(-0.927051 - 2.85317i) q^{58} +(2.92457 - 9.00090i) q^{59} +(1.02579 + 0.745282i) q^{60} +(-2.05158 - 1.49056i) q^{61} +(0.0606144 - 0.186552i) q^{62} +(-3.60322 - 11.0896i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.19615 q^{65} -10.1962 q^{67} +(4.20378 - 3.05422i) q^{68} +(-0.286831 - 0.882774i) q^{69} +(-2.53275 + 7.79500i) q^{70} +(7.65662 + 5.56286i) q^{71} +(1.99350 + 1.44836i) q^{72} +(-0.286831 + 0.882774i) q^{73} +(-2.22373 - 6.84395i) q^{74} +(1.18448 - 0.860577i) q^{75} +1.26795 q^{76} +2.19615 q^{78} +(3.82831 - 2.78143i) q^{79} +(-0.535233 - 1.64728i) q^{80} +(1.37948 - 4.24561i) q^{81} +(0.650326 + 0.472490i) q^{82} +(-6.63083 - 4.81758i) q^{83} +(1.07047 - 3.29456i) q^{84} +(2.78115 + 8.55951i) q^{85} -2.19615 q^{87} +6.46410 q^{89} +(-3.45284 + 2.50864i) q^{90} +(4.38685 + 13.5013i) q^{91} +(-0.391818 + 1.20589i) q^{92} +(-0.116170 - 0.0844022i) q^{93} +(6.63083 + 4.81758i) q^{94} +(-0.678648 + 2.08867i) q^{95} +(0.226216 + 0.696222i) q^{96} +(0.809017 - 0.587785i) q^{97} +15.3923 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 6 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 6 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 6 q^{7} - 2 q^{8} - 2 q^{9} - 8 q^{12} - 6 q^{13} - 6 q^{14} + 6 q^{15} - 2 q^{16} - 2 q^{18} - 6 q^{19} - 24 q^{23} + 2 q^{24} + 4 q^{25} - 6 q^{26} + 8 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{30} + 10 q^{31} + 8 q^{32} + 6 q^{35} - 2 q^{36} + 4 q^{37} - 6 q^{38} + 6 q^{39} + 12 q^{41} + 48 q^{45} + 6 q^{46} + 6 q^{47} + 2 q^{48} - 10 q^{49} + 4 q^{50} + 18 q^{51} - 6 q^{52} - 12 q^{53} - 32 q^{54} + 24 q^{56} + 12 q^{57} + 6 q^{58} - 12 q^{59} + 6 q^{60} - 12 q^{61} + 10 q^{62} + 6 q^{63} - 2 q^{64} - 40 q^{67} - 12 q^{69} + 6 q^{70} + 12 q^{71} - 2 q^{72} - 12 q^{73} + 4 q^{74} - 4 q^{75} + 24 q^{76} - 24 q^{78} + 6 q^{79} - 2 q^{81} + 12 q^{82} - 6 q^{83} - 18 q^{85} + 24 q^{87} + 24 q^{89} - 12 q^{90} - 18 q^{91} + 6 q^{92} - 28 q^{93} + 6 q^{94} - 6 q^{95} + 2 q^{96} + 2 q^{97} + 40 q^{98}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more