LMFDB - Embedded newform 343.2.g.h.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(30,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([32]))

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

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

chi := DirichletCharacter("343.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.g (of order $21$, degree $12$, 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:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			275.1
Character	$\chi$	$=$	343.275
Dual form			343.2.g.h.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.189695 + 2.53130i) q^{2} +(-1.83277 + 0.565334i) q^{3} +(-4.39385 - 0.662266i) q^{4} +(-1.83323 - 1.70099i) q^{5} +(-1.08336 - 4.74653i) q^{6} +(1.38019 - 6.04701i) q^{8} +(0.560718 - 0.382291i) q^{9} +O(q^{10})$	\(q+(-0.189695 + 2.53130i) q^{2} +(-1.83277 + 0.565334i) q^{3} +(-4.39385 - 0.662266i) q^{4} +(-1.83323 - 1.70099i) q^{5} +(-1.08336 - 4.74653i) q^{6} +(1.38019 - 6.04701i) q^{8} +(0.560718 - 0.382291i) q^{9} +(4.65347 - 4.31779i) q^{10} +(2.53345 + 1.72727i) q^{11} +(8.42730 - 1.27021i) q^{12} +(0.101149 - 0.0487107i) q^{13} +(4.32151 + 2.08113i) q^{15} +(6.55286 + 2.02129i) q^{16} +(-0.208963 + 0.532430i) q^{17} +(0.861329 + 1.49187i) q^{18} +(1.46037 - 2.52943i) q^{19} +(6.92842 + 8.68796i) q^{20} +(-4.85283 + 6.08526i) q^{22} +(-2.58072 - 6.57557i) q^{23} +(0.889011 + 11.8630i) q^{24} +(0.0937177 + 1.25058i) q^{25} +(0.104114 + 0.265278i) q^{26} +(2.77598 - 3.48096i) q^{27} +(0.419642 + 0.526214i) q^{29} +(-6.08773 + 10.5443i) q^{30} +(-2.54599 - 4.40979i) q^{31} +(-1.82747 + 4.65633i) q^{32} +(-5.61970 - 1.73345i) q^{33} +(-1.30810 - 0.629948i) q^{34} +(-2.71689 + 1.30838i) q^{36} +(2.64694 - 0.398963i) q^{37} +(6.12572 + 4.17645i) q^{38} +(-0.157844 + 0.146458i) q^{39} +(-12.8161 + 8.73786i) q^{40} +(-0.963373 + 4.22081i) q^{41} +(-2.61140 - 11.4413i) q^{43} +(-9.98766 - 9.26719i) q^{44} +(-1.67820 - 0.252947i) q^{45} +(17.1343 - 5.28524i) q^{46} +(-0.248641 + 3.31788i) q^{47} -13.1526 q^{48} -3.18336 q^{50} +(0.0819805 - 1.09395i) q^{51} +(-0.476692 + 0.147040i) q^{52} +(1.38385 + 0.208582i) q^{53} +(8.28478 + 7.68715i) q^{54} +(-1.70631 - 7.47585i) q^{55} +(-1.24654 + 5.46145i) q^{57} +(-1.41161 + 0.962420i) q^{58} +(-9.39310 + 8.71553i) q^{59} +(-17.6098 - 12.0061i) q^{60} +(-0.539069 + 0.0812516i) q^{61} +(11.6455 - 5.60817i) q^{62} +(0.916925 + 0.441568i) q^{64} +(-0.268285 - 0.0827550i) q^{65} +(5.45391 - 13.8963i) q^{66} +(-2.29219 - 3.97020i) q^{67} +(1.27076 - 2.20102i) q^{68} +(8.44726 + 10.5925i) q^{69} +(0.460966 - 0.578033i) q^{71} +(-1.53782 - 3.91830i) q^{72} +(-1.01418 - 13.5333i) q^{73} +(0.507783 + 6.77590i) q^{74} +(-0.878756 - 2.23903i) q^{75} +(-8.09178 + 10.1468i) q^{76} +(-0.340788 - 0.427334i) q^{78} +(2.00436 - 3.47166i) q^{79} +(-8.57470 - 14.8518i) q^{80} +(-3.86362 + 9.84433i) q^{81} +(-10.5014 - 3.23926i) q^{82} +(-7.54999 - 3.63588i) q^{83} +(1.28873 - 0.620621i) q^{85} +(29.4568 - 4.43990i) q^{86} +(-1.06659 - 0.727190i) q^{87} +(13.9415 - 12.9358i) q^{88} +(8.36412 - 5.70256i) q^{89} +(0.958632 - 4.20004i) q^{90} +(6.98452 + 30.6012i) q^{92} +(7.15922 + 6.64279i) q^{93} +(-8.35140 - 1.25877i) q^{94} +(-6.97971 + 2.15295i) q^{95} +(0.716955 - 9.56710i) q^{96} -12.9089 q^{97} +2.08087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} + 12 q^{4} - 7 q^{5} - 20 q^{8} - 15 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 + 12 * q^4 - 7 * q^5 - 20 * q^8 - 15 * q^9	$ 48 q + 8 q^{2} - 7 q^{3} + 12 q^{4} - 7 q^{5} - 20 q^{8} - 15 q^{9} - 7 q^{10} - 3 q^{11} + 63 q^{12} + 14 q^{13} - 12 q^{15} + 18 q^{16} - 14 q^{17} + 2 q^{18} - 21 q^{19} - 14 q^{20} - 20 q^{22} - 27 q^{23} + 77 q^{24} + 17 q^{25} + 21 q^{26} - 7 q^{27} + 12 q^{29} + 11 q^{30} - 35 q^{31} - 60 q^{32} - 7 q^{33} - 70 q^{34} - 12 q^{36} - 6 q^{37} - 35 q^{38} + 35 q^{39} - 105 q^{40} + 42 q^{41} - 30 q^{43} + 13 q^{44} + 35 q^{45} + 69 q^{46} + 42 q^{47} + 84 q^{48} + 40 q^{50} + 53 q^{51} + 7 q^{52} - 31 q^{53} - 70 q^{54} + 7 q^{55} - 12 q^{57} - 47 q^{58} - 35 q^{59} - 91 q^{60} + 14 q^{61} + 28 q^{62} - 32 q^{64} + 35 q^{65} + 35 q^{66} + 11 q^{67} - 77 q^{68} - 70 q^{69} + 19 q^{71} - 124 q^{72} + 35 q^{73} + 13 q^{74} + 119 q^{75} - 119 q^{76} + 28 q^{78} + 15 q^{79} - 70 q^{80} - 125 q^{81} + 98 q^{82} - 26 q^{85} + 9 q^{86} - 35 q^{87} + 49 q^{88} + 14 q^{89} + 182 q^{90} - 38 q^{92} + 46 q^{93} - 14 q^{94} + 128 q^{95} - 98 q^{96} - 16 q^{99}+O(q^{100}) $ 48 * q + 8 * q^2 - 7 * q^3 + 12 * q^4 - 7 * q^5 - 20 * q^8 - 15 * q^9 - 7 * q^10 - 3 * q^11 + 63 * q^12 + 14 * q^13 - 12 * q^15 + 18 * q^16 - 14 * q^17 + 2 * q^18 - 21 * q^19 - 14 * q^20 - 20 * q^22 - 27 * q^23 + 77 * q^24 + 17 * q^25 + 21 * q^26 - 7 * q^27 + 12 * q^29 + 11 * q^30 - 35 * q^31 - 60 * q^32 - 7 * q^33 - 70 * q^34 - 12 * q^36 - 6 * q^37 - 35 * q^38 + 35 * q^39 - 105 * q^40 + 42 * q^41 - 30 * q^43 + 13 * q^44 + 35 * q^45 + 69 * q^46 + 42 * q^47 + 84 * q^48 + 40 * q^50 + 53 * q^51 + 7 * q^52 - 31 * q^53 - 70 * q^54 + 7 * q^55 - 12 * q^57 - 47 * q^58 - 35 * q^59 - 91 * q^60 + 14 * q^61 + 28 * q^62 - 32 * q^64 + 35 * q^65 + 35 * q^66 + 11 * q^67 - 77 * q^68 - 70 * q^69 + 19 * q^71 - 124 * q^72 + 35 * q^73 + 13 * q^74 + 119 * q^75 - 119 * q^76 + 28 * q^78 + 15 * q^79 - 70 * q^80 - 125 * q^81 + 98 * q^82 - 26 * q^85 + 9 * q^86 - 35 * q^87 + 49 * q^88 + 14 * q^89 + 182 * q^90 - 38 * q^92 + 46 * q^93 - 14 * q^94 + 128 * q^95 - 98 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{19}{21}\right)$

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 $

$2$	−0.189695	+	2.53130i	−0.134135	+	1.78990i	0.372795	+	0.927914i	$0.378399\pi$
$2$	−0.189695	+	2.53130i	−0.134135	+	1.78990i	−0.506930	+	0.861987i	$0.669220\pi$
$3$	−1.83277	+	0.565334i	−1.05815	+	0.326396i	−0.774527	−	0.632541i	$-0.782012\pi$
$3$	−1.83277	+	0.565334i	−1.05815	+	0.326396i	−0.283622	+	0.958936i	$0.591536\pi$
$4$	−4.39385	−	0.662266i	−2.19692	−	0.331133i
$5$	−1.83323	−	1.70099i	−0.819845	−	0.760705i	0.153963	−	0.988077i	$-0.450796\pi$
$5$	−1.83323	−	1.70099i	−0.819845	−	0.760705i	−0.973808	+	0.227372i	$0.926987\pi$
$6$	−1.08336	−	4.74653i	−0.442282	−	1.93776i
$7$		0			0
$7$		0			0
$8$	1.38019	−	6.04701i	0.487971	−	2.13794i
$9$	0.560718	−	0.382291i	0.186906	−	0.127430i
$10$	4.65347	−	4.31779i	1.47156	−	1.36540i
$11$	2.53345	+	1.72727i	0.763863	+	0.520793i	0.881454	−	0.472269i	$-0.156565\pi$
$11$	2.53345	+	1.72727i	0.763863	+	0.520793i	−0.117592	+	0.993062i	$0.537517\pi$
$12$	8.42730	−	1.27021i	2.43275	−	0.366678i
$13$	0.101149	−	0.0487107i	0.0280536	−	0.0135099i	−0.419804	−	0.907615i	$-0.637901\pi$
$13$	0.101149	−	0.0487107i	0.0280536	−	0.0135099i	0.447858	+	0.894105i	$0.352187\pi$
$14$		0			0
$15$	4.32151	+	2.08113i	1.11581	+	0.537345i
$16$	6.55286	+	2.02129i	1.63822	+	0.505323i
$17$	−0.208963	+	0.532430i	−0.0506810	+	0.129133i	−0.953972	−	0.299895i	$-0.903049\pi$
$17$	−0.208963	+	0.532430i	−0.0506810	+	0.129133i	0.903291	+	0.429028i	$0.141144\pi$
$18$	0.861329	+	1.49187i	0.203017	+	0.351636i
$19$	1.46037	−	2.52943i	0.335031	−	0.580291i	−0.648460	−	0.761249i	$-0.724587\pi$
$19$	1.46037	−	2.52943i	0.335031	−	0.580291i	0.983491	+	0.180958i	$0.0579199\pi$
$20$	6.92842	+	8.68796i	1.54924	+	1.94269i
$21$		0			0
$22$	−4.85283	+	6.08526i	−1.03463	+	1.29738i
$23$	−2.58072	−	6.57557i	−0.538118	−	1.37110i	−0.898778	−	0.438405i	$-0.855544\pi$
$23$	−2.58072	−	6.57557i	−0.538118	−	1.37110i	0.360660	−	0.932697i	$-0.382552\pi$
$24$	0.889011	+	11.8630i	0.181469	+	2.42153i
$25$	0.0937177	+	1.25058i	0.0187435	+	0.250115i
$26$	0.104114	+	0.265278i	0.0204185	+	0.0520254i
$27$	2.77598	−	3.48096i	0.534237	−	0.669912i
$28$		0			0
$29$	0.419642	+	0.526214i	0.0779255	+	0.0977155i	0.819266	−	0.573413i	$-0.194381\pi$
$29$	0.419642	+	0.526214i	0.0779255	+	0.0977155i	−0.741341	+	0.671129i	$0.765810\pi$
$30$	−6.08773	+	10.5443i	−1.11146	+	1.92511i
$31$	−2.54599	−	4.40979i	−0.457274	−	0.792022i	0.541542	−	0.840674i	$-0.317841\pi$
$31$	−2.54599	−	4.40979i	−0.457274	−	0.792022i	−0.998816	+	0.0486519i	$0.984507\pi$
$32$	−1.82747	+	4.65633i	−0.323055	+	0.823130i
$33$	−5.61970	−	1.73345i	−0.978265	−	0.301755i
$34$	−1.30810	−	0.629948i	−0.224338	−	0.108035i
$35$		0			0
$36$	−2.71689	+	1.30838i	−0.452814	+	0.218064i
$37$	2.64694	−	0.398963i	0.435155	−	0.0655891i	0.0721880	−	0.997391i	$-0.477002\pi$
$37$	2.64694	−	0.398963i	0.435155	−	0.0655891i	0.362967	+	0.931802i	$0.381764\pi$
$38$	6.12572	+	4.17645i	0.993723	+	0.677509i
$39$	−0.157844	+	0.146458i	−0.0252753	+	0.0234521i
$40$	−12.8161	+	8.73786i	−2.02640	+	1.38158i
$41$	−0.963373	+	4.22081i	−0.150454	+	0.659180i	0.842300	+	0.539010i	$0.181201\pi$
$41$	−0.963373	+	4.22081i	−0.150454	+	0.659180i	−0.992753	+	0.120171i	$0.961656\pi$
$42$		0			0
$43$	−2.61140	−	11.4413i	−0.398235	−	1.74478i	−0.634338	−	0.773056i	$-0.718727\pi$
$43$	−2.61140	−	11.4413i	−0.398235	−	1.74478i	0.236103	−	0.971728i	$-0.424130\pi$
$44$	−9.98766	−	9.26719i	−1.50570	−	1.39708i
$45$	−1.67820	−	0.252947i	−0.250171	−	0.0377072i
$46$	17.1343	−	5.28524i	2.52632	−	0.779266i
$47$	−0.248641	+	3.31788i	−0.0362680	+	0.483963i	0.949265	+	0.314478i	$0.101829\pi$
$47$	−0.248641	+	3.31788i	−0.0362680	+	0.483963i	−0.985533	+	0.169485i	$0.945790\pi$
$48$	−13.1526			−1.89841
$49$		0			0
$50$	−3.18336			−0.450196
$51$	0.0819805	−	1.09395i	0.0114796	−	0.153184i
$52$	−0.476692	+	0.147040i	−0.0661052	+	0.0203908i
$53$	1.38385	+	0.208582i	0.190086	+	0.0286509i	0.243395	−	0.969927i	$-0.421739\pi$
$53$	1.38385	+	0.208582i	0.190086	+	0.0286509i	−0.0533091	+	0.998578i	$0.516977\pi$
$54$	8.28478	+	7.68715i	1.12742	+	1.04609i
$55$	−1.70631	−	7.47585i	−0.230079	−	1.00804i
$56$		0			0
$57$	−1.24654	+	5.46145i	−0.165108	+	0.723386i
$58$	−1.41161	+	0.962420i	−0.185354	+	0.126372i
$59$	−9.39310	+	8.71553i	−1.22288	+	1.13466i	−0.236247	+	0.971693i	$0.575918\pi$
$59$	−9.39310	+	8.71553i	−1.22288	+	1.13466i	−0.986631	+	0.162972i	$0.947892\pi$
$60$	−17.6098	−	12.0061i	−2.27341	−	1.54999i
$61$	−0.539069	+	0.0812516i	−0.0690207	+	0.0104032i	−0.183462	−	0.983027i	$-0.558730\pi$
$61$	−0.539069	+	0.0812516i	−0.0690207	+	0.0104032i	0.114441	+	0.993430i	$0.463492\pi$
$62$	11.6455	−	5.60817i	1.47898	−	0.712238i
$63$		0			0
$64$	0.916925	+	0.441568i	0.114616	+	0.0551960i
$65$	−0.268285	−	0.0827550i	−0.0332767	−	0.0102645i
$66$	5.45391	−	13.8963i	0.671330	−	1.71052i
$67$	−2.29219	−	3.97020i	−0.280036	−	0.485037i	0.691357	−	0.722513i	$-0.257013\pi$
$67$	−2.29219	−	3.97020i	−0.280036	−	0.485037i	−0.971393	+	0.237476i	$0.923680\pi$
$68$	1.27076	−	2.20102i	0.154103	−	0.266913i
$69$	8.44726	+	10.5925i	1.01693	+	1.27519i
$70$		0			0
$71$	0.460966	−	0.578033i	0.0547066	−	0.0685999i	−0.753725	−	0.657189i	$-0.771745\pi$
$71$	0.460966	−	0.578033i	0.0547066	−	0.0685999i	0.808432	+	0.588590i	$0.200317\pi$
$72$	−1.53782	−	3.91830i	−0.181234	−	0.461776i
$73$	−1.01418	−	13.5333i	−0.118701	−	1.58396i	−0.665309	−	0.746568i	$-0.731700\pi$
$73$	−1.01418	−	13.5333i	−0.118701	−	1.58396i	0.546608	−	0.837389i	$-0.315919\pi$
$74$	0.507783	+	6.77590i	0.0590286	+	0.787682i
$75$	−0.878756	−	2.23903i	−0.101470	−	0.258541i
$76$	−8.09178	+	10.1468i	−0.928190	+	1.16391i
$77$		0			0
$78$	−0.340788	−	0.427334i	−0.0385866	−	0.0483861i
$79$	2.00436	−	3.47166i	0.225509	−	0.390592i	−0.730963	−	0.682417i	$-0.760929\pi$
$79$	2.00436	−	3.47166i	0.225509	−	0.390592i	0.956472	+	0.291824i	$0.0942623\pi$
$80$	−8.57470	−	14.8518i	−0.958681	−	1.66048i
$81$	−3.86362	+	9.84433i	−0.429291	+	1.09381i
$82$	−10.5014	−	3.23926i	−1.15969	−	0.357716i
$83$	−7.54999	−	3.63588i	−0.828719	−	0.399090i	−0.0290846	−	0.999577i	$-0.509259\pi$
$83$	−7.54999	−	3.63588i	−0.828719	−	0.399090i	−0.799635	+	0.600487i	$0.794973\pi$
$84$		0			0
$85$	1.28873	−	0.620621i	0.139783	−	0.0673158i
$86$	29.4568	−	4.43990i	3.17641	−	0.478766i
$87$	−1.06659	−	0.727190i	−0.114351	−	0.0779630i
$88$	13.9415	−	12.9358i	1.48617	−	1.37896i
$89$	8.36412	−	5.70256i	0.886595	−	0.604470i	−0.0320798	−	0.999485i	$-0.510213\pi$
$89$	8.36412	−	5.70256i	0.886595	−	0.604470i	0.918675	+	0.395015i	$0.129261\pi$
$90$	0.958632	−	4.20004i	0.101049	−	0.442723i
$91$		0			0
$92$	6.98452	+	30.6012i	0.728187	+	3.19039i
$93$	7.15922	+	6.64279i	0.742377	+	0.688825i
$94$	−8.35140	−	1.25877i	−0.861381	−	0.129832i
$95$	−6.97971	+	2.15295i	−0.716103	+	0.220889i
$96$	0.716955	−	9.56710i	0.0731739	−	0.976438i
$97$	−12.9089			−1.31070			−0.655352	−	0.755324i	$-0.727480\pi$
$97$	−12.9089			−1.31070			−0.655352	+	0.755324i	$0.727480\pi$
$98$		0			0
$99$	2.08087			0.209135
$100$	0.416433	−	5.55691i	0.0416433	−	0.555691i
$101$	17.7356	−	5.47071i	1.76476	−	0.544356i	0.769244	−	0.638955i	$-0.220633\pi$
$101$	17.7356	−	5.47071i	1.76476	−	0.544356i	0.995515	+	0.0945990i	$0.0301569\pi$
$102$	2.75358	+	0.415035i	0.272645	+	0.0410946i
$103$	−4.87994	−	4.52792i	−0.480834	−	0.446149i	0.402134	−	0.915581i	$-0.368268\pi$
$103$	−4.87994	−	4.52792i	−0.480834	−	0.446149i	−0.882969	+	0.469431i	$0.844459\pi$
$104$	−0.154949	−	0.678878i	−0.0151940	−	0.0665695i
$105$		0			0
$106$	−0.790492	+	3.46337i	−0.0767794	+	0.336392i
$107$	−7.40226	+	5.04677i	−0.715603	+	0.487890i	−0.865562	−	0.500802i	$-0.833038\pi$
$107$	−7.40226	+	5.04677i	−0.715603	+	0.487890i	0.149958	+	0.988692i	$0.452086\pi$
$108$	−14.5025	+	13.4564i	−1.39551	+	1.29484i
$109$	−2.88882	−	1.96956i	−0.276698	−	0.188650i	0.417018	−	0.908898i	$-0.363075\pi$
$109$	−2.88882	−	1.96956i	−0.276698	−	0.188650i	−0.693716	+	0.720249i	$0.744028\pi$
$110$	19.2473	−	2.90106i	1.83516	−	0.276606i
$111$	−4.62569	+	2.22761i	−0.439051	+	0.211436i
$112$		0			0
$113$	−5.22517	−	2.51631i	−0.491543	−	0.236714i	0.171657	−	0.985157i	$-0.445088\pi$
$113$	−5.22517	−	2.51631i	−0.491543	−	0.236714i	−0.663200	+	0.748442i	$0.730802\pi$
$114$	−13.5881	−	4.19138i	−1.27264	−	0.392558i
$115$	−6.45391	+	16.4443i	−0.601831	+	1.53344i
$116$	−1.49535	−	2.59002i	−0.138840	−	0.240477i
$117$	0.0380943	−	0.0659813i	0.00352182	−	0.00609997i
$118$	−20.2798	−	25.4301i	−1.86691	−	2.34103i
$119$		0			0
$120$	18.5491	−	23.2598i	1.69329	−	2.12332i
$121$	−0.583879	−	1.48770i	−0.0530800	−	0.135246i
$122$	−0.103414	−	1.37996i	−0.00936264	−	0.124936i
$123$	−0.620530	−	8.28040i	−0.0559513	−	0.746618i
$124$	8.26625	+	21.0621i	0.742331	+	1.89143i
$125$	−5.84076	+	7.32408i	−0.522413	+	0.655086i
$126$		0			0
$127$	−9.58196	−	12.0154i	−0.850261	−	1.06619i	−0.997029	−	0.0770231i	$-0.975458\pi$
$127$	−9.58196	−	12.0154i	−0.850261	−	1.06619i	0.146768	−	0.989171i	$-0.453113\pi$
$128$	−6.29378	+	10.9011i	−0.556297	+	0.963534i
$129$	11.2543	+	19.4929i	0.990882	+	1.71626i
$130$	0.260370	−	0.663413i	0.0228360	−	0.0581851i
$131$	0.416111	+	0.128353i	0.0363558	+	0.0112143i	0.312880	−	0.949793i	$-0.398706\pi$
$131$	0.416111	+	0.128353i	0.0363558	+	0.0112143i	−0.276524	+	0.961007i	$0.589183\pi$
$132$	23.5441	+	11.3382i	2.04925	+	0.986867i
$133$		0			0
$134$	10.4846	−	5.04911i	0.905731	−	0.436177i
$135$	−11.0101	+	1.65950i	−0.947596	+	0.142827i
$136$	2.93120	+	1.99846i	0.251348	+	0.171366i
$137$	4.25872	−	3.95152i	0.363847	−	0.337601i	−0.476970	−	0.878919i	$-0.658265\pi$
$137$	4.25872	−	3.95152i	0.363847	−	0.337601i	0.840818	+	0.541318i	$0.182075\pi$
$138$	−28.4153	+	19.3732i	−2.41887	+	1.64916i
$139$	−1.61838	+	7.09059i	−0.137269	+	0.601416i	0.858759	+	0.512380i	$0.171236\pi$
$139$	−1.61838	+	7.09059i	−0.137269	+	0.601416i	−0.996028	+	0.0890367i	$0.971621\pi$
$140$		0			0
$141$	−1.42001	−	6.22148i	−0.119587	−	0.523943i
$142$	1.37573	+	1.27649i	0.115449	+	0.107121i
$143$	0.340392	+	0.0513058i	0.0284650	+	0.00429041i
$144$	4.44703	−	1.37173i	0.370586	−	0.114311i
$145$	0.125784	−	1.67848i	0.0104458	−	0.139390i
$146$	34.4493			2.85105
$147$		0			0
$148$	−11.8945			−0.977721
$149$	−0.673366	+	8.98545i	−0.0551643	+	0.736117i	0.899213	+	0.437512i	$0.144140\pi$
$149$	−0.673366	+	8.98545i	−0.0551643	+	0.736117i	−0.954377	+	0.298605i	$0.903479\pi$
$150$	5.83437	−	1.79966i	0.476374	−	0.146942i
$151$	−9.58261	−	1.44435i	−0.779821	−	0.117539i	−0.252944	−	0.967481i	$-0.581399\pi$
$151$	−9.58261	−	1.44435i	−0.779821	−	0.117539i	−0.526877	+	0.849942i	$0.676637\pi$
$152$	−13.2799	−	12.3219i	−1.07714	−	0.999441i
$153$	0.0863737	+	0.378428i	0.00698290	+	0.0305941i
$154$		0			0
$155$	−2.83361	+	12.4149i	−0.227601	+	0.997185i
$156$	0.790538	−	0.538980i	0.0632937	−	0.0431529i
$157$	3.37647	−	3.13290i	0.269471	−	0.250033i	−0.533849	−	0.845580i	$-0.679255\pi$
$157$	3.37647	−	3.13290i	0.269471	−	0.250033i	0.803321	+	0.595547i	$0.203065\pi$
$158$	8.40761	+	5.73221i	0.668873	+	0.456030i
$159$	−2.65419	+	0.400055i	−0.210491	+	0.0317264i
$160$	11.2705	−	5.42760i	0.891013	−	0.429089i
$161$		0			0
$162$	−24.1861	−	11.6474i	−1.90024	−	0.915106i
$163$	17.2062	+	5.30741i	1.34769	+	0.415708i	0.882838	−	0.469678i	$-0.155630\pi$
$163$	17.2062	+	5.30741i	1.34769	+	0.415708i	0.464855	+	0.885387i	$0.346106\pi$
$164$	7.02821	−	17.9076i	0.548811	−	1.39835i
$165$	7.35362	+	12.7369i	0.572479	+	0.991563i
$166$	10.6357	−	18.4216i	0.825492	−	1.42979i
$167$	2.65610	+	3.33064i	0.205535	+	0.257733i	0.873906	−	0.486096i	$-0.161579\pi$
$167$	2.65610	+	3.33064i	0.205535	+	0.257733i	−0.668371	+	0.743828i	$0.733008\pi$
$168$		0			0
$169$	−8.09751	+	10.1540i	−0.622885	+	0.781073i
$170$	1.32651	+	3.37990i	0.101739	+	0.259227i
$171$	−0.148124	−	1.97658i	−0.0113273	−	0.151153i
$172$	3.89692	+	52.0008i	0.297137	+	3.96502i
$173$	7.93603	+	20.2207i	0.603366	+	1.53735i	0.826720	+	0.562613i	$0.190204\pi$
$173$	7.93603	+	20.2207i	0.603366	+	1.53735i	−0.223355	+	0.974737i	$0.571701\pi$
$174$	2.04307	−	2.56192i	0.154884	−	0.194219i
$175$		0			0
$176$	13.1100	+	16.4394i	0.988204	+	1.23917i
$177$	12.2882	−	21.2838i	0.923637	−	1.59979i
$178$	12.8483	+	22.2539i	0.963019	+	1.66800i
$179$	3.09956	−	7.89754i	0.231672	−	0.590290i	−0.767009	−	0.641636i	$-0.778256\pi$
$179$	3.09956	−	7.89754i	0.231672	−	0.590290i	0.998681	+	0.0513463i	$0.0163512\pi$
$180$	7.20622	+	2.22282i	0.537120	+	0.165679i
$181$	6.46864	+	3.11513i	0.480810	+	0.231546i	0.658558	−	0.752530i	$-0.271167\pi$
$181$	6.46864	+	3.11513i	0.480810	+	0.231546i	−0.177748	+	0.984076i	$0.556881\pi$
$182$		0			0
$183$	0.942054	−	0.453669i	0.0696387	−	0.0335362i
$184$	−43.3244	+	6.53011i	−3.19392	+	0.481406i
$185$	−5.53108	−	3.77103i	−0.406653	−	0.277252i
$186$	−18.1730	+	16.8620i	−1.33251	+	1.23639i
$187$	−1.44905	+	0.987945i	−0.105965	+	0.0722457i
$188$	3.28981	−	14.4136i	0.239934	−	1.05122i
$189$		0			0
$190$	−4.12576	−	18.0762i	−0.299314	−	1.31138i
$191$	−6.17389	−	5.72853i	−0.446727	−	0.414502i	0.424465	−	0.905444i	$-0.360462\pi$
$191$	−6.17389	−	5.72853i	−0.446727	−	0.414502i	−0.871192	+	0.490942i	$0.836653\pi$
$192$	−1.93014	−	0.290922i	−0.139296	−	0.0209955i
$193$	−11.3950	+	3.51489i	−0.820229	+	0.253007i	−0.676343	−	0.736587i	$-0.736436\pi$
$193$	−11.3950	+	3.51489i	−0.820229	+	0.253007i	−0.143886	+	0.989594i	$0.545960\pi$
$194$	2.44876	−	32.6764i	0.175811	−	2.34603i
$195$	0.538489			0.0385620
$196$		0			0
$197$	9.92588			0.707190			0.353595	−	0.935399i	$-0.384959\pi$
$197$	9.92588			0.707190			0.353595	+	0.935399i	$0.384959\pi$
$198$	−0.394730	+	5.26731i	−0.0280523	+	0.374332i
$199$	12.1859	−	3.75885i	0.863834	−	0.266458i	0.168990	−	0.985618i	$-0.445949\pi$
$199$	12.1859	−	3.75885i	0.863834	−	0.266458i	0.694844	+	0.719160i	$0.255473\pi$
$200$	7.69159	+	1.15932i	0.543878	+	0.0819764i
$201$	6.44555	+	5.98059i	0.454634	+	0.421839i
$202$	10.4837	+	45.9320i	0.737629	+	3.23176i
$203$		0			0
$204$	−1.08470	+	4.75237i	−0.0759440	+	0.332733i
$205$	8.94563	−	6.09903i	0.624790	−	0.425975i
$206$	12.3872	−	11.4937i	0.863059	−	0.800802i
$207$	−3.96084	−	2.70046i	−0.275297	−	0.187695i
$208$	0.761273	−	0.114743i	0.0527848	−	0.00795603i
$209$	8.06877	−	3.88572i	0.558129	−	0.268781i
$210$		0			0
$211$	13.5039	+	6.50313i	0.929646	+	0.447694i	0.836505	−	0.547959i	$-0.184595\pi$
$211$	13.5039	+	6.50313i	0.929646	+	0.447694i	0.0931407	+	0.995653i	$0.470309\pi$
$212$	−5.94228	−	1.83295i	−0.408117	−	0.125888i
$213$	−0.518062	+	1.32000i	−0.0354970	+	0.0904449i
$214$	−11.3707	−	19.6947i	−0.777288	−	1.34630i
$215$	−14.6742	+	25.4165i	−1.00077	+	1.73339i
$216$	−17.2180	−	21.5907i	−1.17154	−	1.46906i
$217$		0			0
$218$	5.53355	−	6.93885i	0.374779	−	0.469958i
$219$	9.50961	+	24.2301i	0.642600	+	1.63732i
$220$	2.54628	+	33.9777i	0.171670	+	2.29078i
$221$	0.00479864	+	0.0640334i	0.000322791	+	0.00430735i
$222$	−4.76129	−	12.1316i	−0.319557	−	0.814218i
$223$	16.3223	−	20.4675i	1.09302	−	1.37060i	0.170183	−	0.985413i	$-0.445564\pi$
$223$	16.3223	−	20.4675i	1.09302	−	1.37060i	0.922837	−	0.385191i	$-0.125864\pi$
$224$		0			0
$225$	0.530633	+	0.665393i	0.0353756	+	0.0443595i
$226$	7.36073	−	12.7492i	0.489628	−	0.848061i
$227$	−4.10658	−	7.11280i	−0.272563	−	0.472093i	0.696954	−	0.717116i	$-0.254538\pi$
$227$	−4.10658	−	7.11280i	−0.272563	−	0.472093i	−0.969517	+	0.245022i	$0.921205\pi$
$228$	9.09403	−	23.1712i	0.602267	−	1.53455i
$229$	24.0467	+	7.41741i	1.58905	+	0.490157i	0.958284	−	0.285818i	$-0.0922652\pi$
$229$	24.0467	+	7.41741i	1.58905	+	0.490157i	0.630765	+	0.775974i	$0.282741\pi$
$230$	−40.4012	−	19.4562i	−2.66398	−	1.28290i
$231$		0			0
$232$	3.76121	−	1.81130i	0.246935	−	0.118918i
$233$	−16.0522	+	2.41948i	−1.05161	+	0.158505i	−0.652031	−	0.758192i	$-0.726083\pi$
$233$	−16.0522	+	2.41948i	−1.05161	+	0.158505i	−0.399582	+	0.916698i	$0.630845\pi$
$234$	0.159792	+	0.108944i	0.0104459	+	0.00712192i
$235$	6.09949	−	5.65950i	0.397887	−	0.369185i
$236$	47.0438	−	32.0739i	3.06229	−	2.08784i
$237$	−1.71089	+	7.49588i	−0.111134	+	0.486910i
$238$		0			0
$239$	−2.77591	−	12.1620i	−0.179559	−	0.786697i	−0.981834	−	0.189743i	$-0.939235\pi$
$239$	−2.77591	−	12.1620i	−0.179559	−	0.786697i	0.802275	−	0.596954i	$-0.203623\pi$
$240$	24.1117	+	22.3724i	1.55640	+	1.44413i
$241$	−15.3037	−	2.30666i	−0.985799	−	0.148585i	−0.363694	−	0.931519i	$-0.618484\pi$
$241$	−15.3037	−	2.30666i	−0.985799	−	0.148585i	−0.622106	+	0.782933i	$0.713723\pi$
$242$	3.87658	−	1.19577i	0.249196	−	0.0768668i
$243$	0.517608	−	6.90699i	0.0332046	−	0.443084i
$244$	2.42240			0.155078
$245$		0			0
$246$	21.0779			1.34388
$247$	0.0245041	−	0.326984i	0.00155916	−	0.0208055i
$248$	−30.1800	+	9.30930i	−1.91643	+	0.591141i
$249$	15.8929	+	2.39546i	1.00717	+	0.151806i
$250$	−17.4315	−	16.1741i	−1.10246	−	1.02294i
$251$	−4.07904	−	17.8715i	−0.257467	−	1.12804i	−0.923949	−	0.382515i	$-0.875058\pi$
$251$	−4.07904	−	17.8715i	−0.257467	−	1.12804i	0.666482	−	0.745521i	$-0.267799\pi$
$252$		0			0
$253$	4.81970	−	21.1165i	0.303012	−	1.32758i
$254$	32.2323	−	21.9756i	2.02243	−	1.37887i
$255$	−2.01109	+	1.86602i	−0.125939	+	0.116855i
$256$	−24.7185	−	16.8528i	−1.54490	−	1.05330i
$257$	−15.6781	+	2.36310i	−0.977974	+	0.147406i	−0.618531	−	0.785761i	$-0.712272\pi$
$257$	−15.6781	+	2.36310i	−0.977974	+	0.147406i	−0.359444	+	0.933167i	$0.617034\pi$
$258$	−51.4774	+	24.7902i	−3.20484	+	1.54337i
$259$		0			0
$260$	1.12400	+	0.541289i	0.0697074	+	0.0335693i
$261$	0.436468	+	0.134632i	0.0270167	+	0.00833354i
$262$	−0.403835	+	1.02896i	−0.0249490	+	0.0635691i
$263$	−3.84895	−	6.66658i	−0.237336	−	0.411079i	0.722613	−	0.691253i	$-0.242941\pi$
$263$	−3.84895	−	6.66658i	−0.237336	−	0.411079i	−0.959949	+	0.280174i	$0.909608\pi$
$264$	−18.2384	+	31.5899i	−1.12250	+	1.94422i
$265$	−2.18212	−	2.73629i	−0.134046	−	0.168089i
$266$		0			0
$267$	−12.1056	+	15.1800i	−0.740853	+	0.929000i
$268$	7.44222	+	18.9625i	0.454606	+	1.15832i
$269$	0.0241621	+	0.322420i	0.00147319	+	0.0196583i	0.997892	−	0.0648973i	$-0.0206720\pi$
$269$	0.0241621	+	0.322420i	0.00147319	+	0.0196583i	−0.996419	+	0.0845556i	$0.973053\pi$
$270$	−2.11214	−	28.1846i	−0.128541	−	1.71526i
$271$	−6.05922	−	15.4386i	−0.368071	−	0.937831i	−0.988178	−	0.153313i	$-0.951006\pi$
$271$	−6.05922	−	15.4386i	−0.368071	−	0.937831i	0.620106	−	0.784518i	$-0.287089\pi$
$272$	−2.44550	+	3.06656i	−0.148280	+	0.185938i
$273$		0			0
$274$	9.19463	+	11.5297i	0.555468	+	0.696535i
$275$	−1.92266	+	3.33014i	−0.115941	+	0.200815i
$276$	−30.1009	−	52.1363i	−1.81186	−	3.13823i
$277$	−4.52128	+	11.5200i	−0.271657	+	0.692171i	0.728319	+	0.685238i	$0.240302\pi$
$277$	−4.52128	+	11.5200i	−0.271657	+	0.692171i	−0.999976	+	0.00693272i	$0.997793\pi$
$278$	−17.6414	−	5.44166i	−1.05806	−	0.326369i
$279$	−3.11341	−	1.49934i	−0.186395	−	0.0897631i
$280$		0			0
$281$	−27.1803	+	13.0893i	−1.62144	+	0.780843i	−0.999997	−	0.00261720i	$-0.999167\pi$
$281$	−27.1803	+	13.0893i	−1.62144	+	0.780843i	−0.621441	+	0.783461i	$0.713453\pi$
$282$	16.0178	−	2.41430i	0.953846	−	0.143769i
$283$	−7.99440	−	5.45049i	−0.475218	−	0.323998i	0.301915	−	0.953335i	$-0.402374\pi$
$283$	−7.99440	−	5.45049i	−0.475218	−	0.323998i	−0.777132	+	0.629337i	$0.783327\pi$
$284$	−2.40823	+	2.23451i	−0.142902	+	0.132594i
$285$	11.5750	−	7.89173i	0.685646	−	0.467466i
$286$	−0.194441	+	0.851902i	−0.0114975	+	0.0503740i
$287$		0			0
$288$	0.755375	+	3.30951i	0.0445109	+	0.195015i
$289$	12.2221	+	11.3404i	0.718945	+	0.667084i
$290$	4.22487	+	0.636796i	0.248093	+	0.0373940i
$291$	23.6591	−	7.29785i	1.38692	−	0.427808i
$292$	−4.50650	+	60.1350i	−0.263723	+	3.51914i
$293$	30.7981			1.79924			0.899622	−	0.436670i	$-0.143842\pi$
$293$	30.7981			1.79924			0.899622	+	0.436670i	$0.143842\pi$
$294$		0			0
$295$	32.0447			1.86571
$296$	1.24076	−	16.5567i	0.0721175	−	0.962341i
$297$	13.0454	−	4.02396i	0.756969	−	0.233494i
$298$	−22.6171	−	3.40899i	−1.31018	−	0.197477i
$299$	−0.581338	−	0.539403i	−0.0336196	−	0.0311945i
$300$	2.37828	+	10.4199i	0.137310	+	0.601596i
$301$		0			0
$302$	5.47385	−	23.9825i	0.314984	−	1.38004i
$303$	−29.4125	+	20.0531i	−1.68970	+	1.15202i
$304$	14.6823	−	13.6232i	0.842087	−	0.781342i
$305$	1.12644	+	0.767997i	0.0645001	+	0.0439754i
$306$	−0.974300	+	0.146852i	−0.0556970	+	0.00839497i
$307$	−14.2885	+	6.88098i	−0.815488	+	0.392718i	−0.794652	−	0.607065i	$-0.792347\pi$
$307$	−14.2885	+	6.88098i	−0.815488	+	0.392718i	−0.0208354	+	0.999783i	$0.506633\pi$
$308$		0			0
$309$	11.5036	+	5.53983i	0.654416	+	0.315150i
$310$	−30.8882	−	9.52776i	−1.75433	−	0.541140i
$311$	0.736155	−	1.87569i	0.0417435	−	0.106361i	−0.908482	−	0.417925i	$-0.862758\pi$
$311$	0.736155	−	1.87569i	0.0417435	−	0.106361i	0.950225	+	0.311564i	$0.100853\pi$
$312$	0.667779	+	1.15663i	0.0378055	+	0.0654811i
$313$	9.03444	−	15.6481i	0.510656	−	0.884483i	−0.489267	−	0.872134i	$-0.662736\pi$
$313$	9.03444	−	15.6481i	0.510656	−	0.884483i	0.999924	−	0.0123491i	$-0.00393093\pi$
$314$	7.28982	+	9.14115i	0.411389	+	0.515865i
$315$		0			0
$316$	−11.1060	+	13.9265i	−0.624763	+	0.783428i
$317$	−6.91259	−	17.6130i	−0.388250	−	0.989244i	−0.982715	−	0.185123i	$-0.940732\pi$
$317$	−6.91259	−	17.6130i	−0.388250	−	0.989244i	0.594466	−	0.804121i	$-0.297364\pi$
$318$	−0.509173	−	6.79445i	−0.0285530	−	0.381014i
$319$	0.154224	+	2.05797i	0.00863486	+	0.115224i
$320$	−0.929831	−	2.36917i	−0.0519792	−	0.132441i
$321$	10.7135	−	13.4343i	0.597970	−	0.749830i
$322$		0			0
$323$	1.04158	+	1.30610i	0.0579551	+	0.0726733i
$324$	23.4957	−	40.6957i	1.30532	−	2.26087i
$325$	0.0703959	+	0.121929i	0.00390486	+	0.00676342i
$326$	−16.6986	+	42.5473i	−0.924849	+	2.35648i
$327$	6.40799	+	1.97660i	0.354362	+	0.109306i
$328$	24.1937	+	11.6511i	1.33587	+	0.643322i
$329$		0			0
$330$	−33.6358	+	16.1981i	−1.85159	+	0.891678i
$331$	−25.9902	+	3.91739i	−1.42855	+	0.215319i	−0.817343	−	0.576151i	$-0.804554\pi$
$331$	−25.9902	+	3.91739i	−1.42855	+	0.215319i	−0.611207	+	0.791471i	$0.709316\pi$
$332$	30.7656	+	20.9756i	1.68848	+	1.15119i
$333$	1.33167	−	1.23561i	0.0729750	−	0.0677109i
$334$	−8.93470	+	6.09158i	−0.488885	+	0.333316i
$335$	−2.55114	+	11.1773i	−0.139384	+	0.610680i
$336$		0			0
$337$	5.51251	+	24.1519i	0.300285	+	1.31564i	0.869698	+	0.493584i	$0.164314\pi$
$337$	5.51251	+	24.1519i	0.300285	+	1.31564i	−0.569413	+	0.822052i	$0.692829\pi$
$338$	−24.1667	−	22.4234i	−1.31449	−	1.21967i
$339$	10.9991	+	1.65784i	0.597388	+	0.0900417i
$340$	−6.07351	+	1.87343i	−0.329382	+	0.101601i
$341$	1.16678	−	15.5696i	0.0631847	−	0.843141i
$342$	5.03142			0.272068
$343$		0			0
$344$	−72.7899			−3.92457
$345$	2.53200	−	33.7872i	0.136318	−	1.81904i
$346$	−52.6901	+	16.2527i	−2.83264	+	0.873753i
$347$	23.3233	+	3.51542i	1.25206	+	0.188717i	0.741398	−	0.671065i	$-0.234163\pi$
$347$	23.3233	+	3.51542i	1.25206	+	0.188717i	0.510660	+	0.859783i	$0.329401\pi$
$348$	4.20485	+	3.90153i	0.225404	+	0.209144i
$349$	−4.43195	−	19.4176i	−0.237237	−	1.03940i	−0.943479	−	0.331432i	$-0.892468\pi$
$349$	−4.43195	−	19.4176i	−0.237237	−	1.03940i	0.706243	−	0.707970i	$-0.250389\pi$
$350$		0			0
$351$	0.111226	−	0.487315i	0.00593683	−	0.0260110i
$352$	−12.6726	+	8.64000i	−0.675450	+	0.460514i
$353$	5.70595	−	5.29435i	0.303697	−	0.281790i	−0.513571	−	0.858047i	$-0.671678\pi$
$353$	5.70595	−	5.29435i	0.303697	−	0.281790i	0.817268	+	0.576257i	$0.195487\pi$
$354$	51.5447	+	35.1426i	2.73957	+	1.86781i
$355$	−1.82828	+	0.275569i	−0.0970352	+	0.0146257i
$356$	−40.5273	+	19.5169i	−2.14794	+	1.03439i
$357$		0			0
$358$	19.4031	+	9.34403i	1.02549	+	0.493848i
$359$	−1.90254	−	0.586856i	−0.100412	−	0.0309731i	0.244142	−	0.969740i	$-0.421494\pi$
$359$	−1.90254	−	0.586856i	−0.100412	−	0.0309731i	−0.344554	+	0.938766i	$0.611970\pi$
$360$	−3.84581	+	9.79895i	−0.202692	+	0.516450i
$361$	5.23466	+	9.06670i	0.275509	+	0.477195i
$362$	−9.11241	+	15.7832i	−0.478938	+	0.829545i
$363$	1.91116	+	2.39652i	0.100310	+	0.125785i
$364$		0			0
$365$	−21.1608	+	26.5348i	−1.10761	+	1.38889i
$366$	0.969672	+	2.47068i	0.0506856	+	0.129145i
$367$	−1.27087	−	16.9586i	−0.0663391	−	0.885233i	−0.926761	−	0.375651i	$-0.877419\pi$
$367$	−1.27087	−	16.9586i	−0.0663391	−	0.885233i	0.860422	−	0.509582i	$-0.170200\pi$
$368$	−3.61998	−	48.3052i	−0.188704	−	2.51808i
$369$	1.07340	+	2.73498i	0.0558789	+	0.142377i
$370$	10.5948	−	13.2855i	0.550799	−	0.690680i
$371$		0			0
$372$	−27.0572	−	33.9287i	−1.40285	−	1.75912i
$373$	−6.73436	+	11.6643i	−0.348692	+	0.603952i	−0.986017	−	0.166643i	$-0.946707\pi$
$373$	−6.73436	+	11.6643i	−0.348692	+	0.603952i	0.637325	+	0.770595i	$0.280041\pi$
$374$	−2.22591	−	3.85539i	−0.115099	−	0.199357i
$375$	6.56420	−	16.7253i	0.338974	−	0.863692i
$376$	19.7201	+	6.08285i	1.01699	+	0.313699i
$377$	0.0680785	+	0.0327849i	0.00350622	+	0.00168851i
$378$		0			0
$379$	19.6351	−	9.45578i	1.00859	−	0.485711i	0.144744	−	0.989469i	$-0.453764\pi$
$379$	19.6351	−	9.45578i	1.00859	−	0.485711i	0.863845	+	0.503758i	$0.168050\pi$
$380$	32.0936	−	4.83733i	1.64637	−	0.248150i
$381$	24.3542	+	16.6044i	1.24770	+	0.850670i
$382$	15.6718	−	14.5413i	0.801839	−	0.743998i
$383$	−27.7342	+	18.9089i	−1.41715	+	0.966199i	−0.418845	+	0.908058i	$0.637565\pi$
$383$	−27.7342	+	18.9089i	−1.41715	+	0.966199i	−0.998308	+	0.0581409i	$0.981483\pi$
$384$	5.37225	−	23.5374i	0.274151	−	1.20114i
$385$		0			0
$386$	−6.73567	−	29.5109i	−0.342837	−	1.50207i
$387$	−5.83817	−	5.41703i	−0.296771	−	0.275363i
$388$	56.7198	+	8.54914i	2.87951	+	0.434017i
$389$	−4.12938	+	1.27375i	−0.209368	+	0.0645815i	−0.397665	−	0.917531i	$-0.630179\pi$
$389$	−4.12938	+	1.27375i	−0.209368	+	0.0645815i	0.188297	+	0.982112i	$0.439703\pi$
$390$	−0.102149	+	1.36308i	−0.00517249	+	0.0690221i
$391$	4.04031			0.204327
$392$		0			0
$393$	−0.835197			−0.0421301
$394$	−1.88289	+	25.1254i	−0.0948586	+	1.26580i
$395$	−9.57971	+	2.95495i	−0.482007	+	0.148680i
$396$	−9.14302	−	1.37809i	−0.459454	−	0.0692516i
$397$	−7.21135	−	6.69116i	−0.361927	−	0.335820i	0.478158	−	0.878274i	$-0.341305\pi$
$397$	−7.21135	−	6.69116i	−0.361927	−	0.335820i	−0.840085	+	0.542454i	$0.817495\pi$
$398$	7.20318	+	31.5592i	0.361063	+	1.58192i
$399$		0			0
$400$	−1.91366	+	8.38429i	−0.0956829	+	0.419214i
$401$	4.67025	−	3.18412i	0.233221	−	0.159007i	−0.441071	−	0.897472i	$-0.645401\pi$
$401$	4.67025	−	3.18412i	0.233221	−	0.159007i	0.674292	+	0.738465i	$0.264449\pi$
$402$	−16.3614	+	15.1811i	−0.816031	+	0.757167i
$403$	−0.472328	−	0.322028i	−0.0235284	−	0.0160414i
$404$	−81.5506	+	12.2918i	−4.05729	+	0.611539i
$405$	23.8280	−	11.4749i	1.18402	−	0.570195i
$406$		0			0
$407$	7.39501	+	3.56125i	0.366557	+	0.176525i
$408$	−6.50200	−	2.00560i	−0.321897	−	0.0992921i
$409$	0.195464	−	0.498034i	0.00966507	−	0.0246262i	−0.925960	−	0.377622i	$-0.876742\pi$
$409$	0.195464	−	0.498034i	0.00966507	−	0.0246262i	0.935625	+	0.352996i	$0.114837\pi$
$410$	13.7415	+	23.8011i	0.678647	+	1.17545i
$411$	−5.57132	+	9.64981i	−0.274813	+	0.475990i
$412$	18.4430	+	23.1268i	0.908622	+	1.13938i
$413$		0			0
$414$	7.58702	−	9.51382i	0.372882	−	0.467579i
$415$	7.65626	+	19.5078i	0.375831	+	0.957602i
$416$	0.0419662	+	0.559999i	0.00205756	+	0.0274562i
$417$	−1.04244	−	13.9103i	−0.0510483	−	0.681192i
$418$	8.30532	+	21.1616i	0.406226	+	1.03505i
$419$	−15.9399	+	19.9880i	−0.778715	+	0.976477i	0.221285	+	0.975209i	$0.428975\pi$
$419$	−15.9399	+	19.9880i	−0.778715	+	0.976477i	−0.999999	+	0.00126797i	$0.999596\pi$
$420$		0			0
$421$	4.76920	+	5.98038i	0.232436	+	0.291466i	0.884347	−	0.466829i	$-0.154604\pi$
$421$	4.76920	+	5.98038i	0.232436	+	0.291466i	−0.651911	+	0.758296i	$0.726032\pi$
$422$	−19.0230	+	32.9488i	−0.926025	+	1.60392i
$423$	1.12898	+	1.95545i	0.0548929	+	0.0950773i
$424$	3.17127	−	8.08026i	0.154010	−	0.392412i
$425$	−0.685428	−	0.211426i	−0.0332481	−	0.0102557i
$426$	−3.24305	−	1.56177i	−0.157126	−	0.0756679i
$427$		0			0
$428$	35.8667	−	17.2725i	1.73368	−	0.834897i
$429$	−0.652864	+	0.0984034i	−0.0315206	+	0.00475096i
$430$	−61.5532	−	41.9663i	−2.96836	−	2.02379i
$431$	−9.01208	+	8.36199i	−0.434097	+	0.402783i	−0.866722	−	0.498791i	$-0.833778\pi$
$431$	−9.01208	+	8.36199i	−0.434097	+	0.402783i	0.432626	+	0.901574i	$0.357587\pi$
$432$	25.2266	−	17.1992i	1.21372	−	0.827498i
$433$	−1.96603	+	8.61375i	−0.0944815	+	0.413950i	−0.999945	−	0.0104733i	$-0.996666\pi$
$433$	−1.96603	+	8.61375i	−0.0944815	+	0.413950i	0.905464	+	0.424424i	$0.139523\pi$
$434$		0			0
$435$	0.718366	+	3.14737i	0.0344430	+	0.150905i
$436$	11.3886	+	10.5671i	0.545417	+	0.506073i
$437$	−20.4012	−	3.07499i	−0.975924	−	0.147097i
$438$	−63.1376	+	19.4754i	−3.01683	+	0.930570i
$439$	2.23547	−	29.8302i	0.106693	−	1.42372i	−0.644988	−	0.764192i	$-0.723138\pi$
$439$	2.23547	−	29.8302i	0.106693	−	1.42372i	0.751681	−	0.659527i	$-0.229243\pi$
$440$	−47.5615			−2.26741
$441$		0			0
$442$	−0.162998			−0.00775303
$443$	2.18778	−	29.1939i	0.103945	−	1.38705i	−0.664576	−	0.747221i	$-0.731388\pi$
$443$	2.18778	−	29.1939i	0.103945	−	1.38705i	0.768521	−	0.639825i	$-0.220993\pi$
$444$	21.7998	−	6.72436i	1.03457	−	0.319124i
$445$	−25.0333	−	3.77317i	−1.18669	−	0.178865i
$446$	48.7131	+	45.1992i	2.30663	+	2.14024i
$447$	−3.84565	−	16.8489i	−0.181893	−	0.796926i
$448$		0			0
$449$	−0.0866596	+	0.379680i	−0.00408972	+	0.0179182i	−0.976932	−	0.213552i	$-0.931497\pi$
$449$	−0.0866596	+	0.379680i	−0.00408972	+	0.0179182i	0.972842	+	0.231471i	$0.0743537\pi$
$450$	−1.78497	+	1.21697i	−0.0841443	+	0.0573686i
$451$	−9.73116	+	9.02919i	−0.458222	+	0.425168i
$452$	21.2921	+	14.5167i	1.00150	+	0.682809i
$453$	18.3792	−	2.77022i	0.863531	−	0.130156i
$454$	18.7836	−	9.04573i	0.881560	−	0.424537i
$455$		0			0
$456$	31.3050	+	15.0757i	1.46599	+	0.705983i
$457$	−15.3268	−	4.72769i	−0.716957	−	0.221152i	−0.0852507	−	0.996360i	$-0.527169\pi$
$457$	−15.3268	−	4.72769i	−0.716957	−	0.221152i	−0.631707	+	0.775207i	$0.717645\pi$
$458$	−23.3372	+	59.4623i	−1.09048	+	2.77849i
$459$	1.27329	+	2.20541i	0.0594322	+	0.102940i
$460$	39.2480	−	67.9795i	1.82995	−	3.16956i
$461$	5.90274	+	7.40180i	0.274918	+	0.344736i	0.900053	−	0.435780i	$-0.143528\pi$
$461$	5.90274	+	7.40180i	0.274918	+	0.344736i	−0.625135	+	0.780517i	$0.714956\pi$
$462$		0			0
$463$	18.9064	−	23.7078i	0.878653	−	1.10180i	−0.115445	−	0.993314i	$-0.536830\pi$
$463$	18.9064	−	23.7078i	0.878653	−	1.10180i	0.994098	−	0.108482i	$-0.0345990\pi$
$464$	1.68622	+	4.29643i	0.0782809	+	0.199457i
$465$	−1.82519	−	24.3555i	−0.0846412	−	1.12946i
$466$	−3.07941	−	41.0919i	−0.142651	−	1.90354i
$467$	1.88254	+	4.79663i	0.0871135	+	0.221961i	0.967791	−	0.251755i	$-0.0810076\pi$
$467$	1.88254	+	4.79663i	0.0871135	+	0.221961i	−0.880678	+	0.473716i	$0.842912\pi$
$468$	−0.211078	+	0.264683i	−0.00975706	+	0.0122350i
$469$		0			0
$470$	13.1689	+	16.5132i	0.607435	+	0.761699i
$471$	−4.41714	+	7.65071i	−0.203531	+	0.352526i
$472$	39.7386	+	68.8293i	1.82912	+	3.16812i
$473$	13.1464	−	33.4966i	0.604473	−	1.54017i
$474$	−18.6498	−	5.75270i	−0.856614	−	0.264230i
$475$	3.30010	+	1.58925i	0.151419	+	0.0729196i
$476$		0			0
$477$	0.855688	−	0.412077i	0.0391792	−	0.0188677i
$478$	31.3124	−	4.71958i	1.43220	−	0.215869i
$479$	2.73651	+	1.86572i	0.125034	+	0.0852470i	0.624222	−	0.781247i	$-0.285416\pi$
$479$	2.73651	+	1.86572i	0.125034	+	0.0852470i	−0.499188	+	0.866494i	$0.666368\pi$
$480$	−17.5878	+	16.3191i	−0.802772	+	0.744863i
$481$	0.248302	−	0.169289i	0.0113216	−	0.00771892i
$482$	8.74190	−	38.3008i	0.398183	−	1.74455i
$483$		0			0
$484$	1.58022	+	6.92341i	0.0718283	+	0.314700i
$485$	23.6650	+	21.9579i	1.07457	+	0.997058i
$486$	17.3855	+	2.62044i	0.788623	+	0.118866i
$487$	21.4027	−	6.60185i	0.969848	−	0.299158i	0.230942	−	0.972967i	$-0.425819\pi$
$487$	21.4027	−	6.60185i	0.969848	−	0.299158i	0.738906	+	0.673809i	$0.235343\pi$
$488$	−0.252689	+	3.37190i	−0.0114387	+	0.152639i
$489$	−34.5354			−1.56174
$490$		0			0
$491$	−2.67157			−0.120566			−0.0602832	−	0.998181i	$-0.519200\pi$
$491$	−2.67157			−0.120566			−0.0602832	+	0.998181i	$0.519200\pi$
$492$	−2.75731	+	36.7937i	−0.124309	+	1.65879i
$493$	−0.367862	+	0.113470i	−0.0165677	+	0.00511045i
$494$	0.823047	+	0.124054i	0.0370306	+	0.00558147i
$495$	−3.81471	−	3.53953i	−0.171458	−	0.159090i
$496$	−7.77008	−	34.0430i	−0.348887	−	1.52857i
$497$		0			0
$498$	−9.07844	+	39.7752i	−0.406815	+	1.78237i
$499$	22.5686	−	15.3870i	1.01031	−	0.688816i	0.0593816	−	0.998235i	$-0.481087\pi$
$499$	22.5686	−	15.3870i	1.01031	−	0.688816i	0.950926	+	0.309420i	$0.100135\pi$
$500$	30.5139	−	28.3127i	1.36462	−	1.26618i
$501$	−6.75093	−	4.60271i	−0.301609	−	0.205634i
$502$	46.0118	−	6.93517i	2.05361	−	0.309532i
$503$	23.5891	−	11.3599i	1.05179	−	0.506514i	0.173593	−	0.984818i	$-0.444462\pi$
$503$	23.5891	−	11.3599i	1.05179	−	0.506514i	0.878195	+	0.478303i	$0.158748\pi$
$504$		0			0
$505$	−41.8190	−	20.1390i	−1.86092	−	0.896173i
$506$	52.5379	+	16.2058i	2.33560	+	0.720436i
$507$	9.10048	−	23.1876i	0.404166	−	1.02980i
$508$	34.1443	+	59.1396i	1.51491	+	2.62390i
$509$	8.40029	−	14.5497i	0.372336	−	0.644905i	−0.617588	−	0.786502i	$-0.711890\pi$
$509$	8.40029	−	14.5497i	0.372336	−	0.644905i	0.989924	+	0.141596i	$0.0452235\pi$
$510$	−4.34197	−	5.44465i	−0.192265	−	0.241093i
$511$		0			0
$512$	31.6520	−	39.6903i	1.39883	−	1.75408i
$513$	−4.75091	−	12.1051i	−0.209758	−	0.534454i
$514$	−3.00765	−	40.1343i	−0.132662	−	1.77025i
$515$	1.24410	+	16.6014i	0.0548218	+	0.731546i
$516$	−36.5400	−	93.1023i	−1.60858	−	4.09860i
$517$	−6.36081	+	7.97621i	−0.279748	+	0.350793i
$518$		0			0
$519$	−25.9763	−	32.5733i	−1.14024	−	1.42981i
$520$	−0.870705	+	1.50811i	−0.0381829	+	0.0661348i
$521$	−0.144196	−	0.249755i	−0.00631735	−	0.0109420i	0.862849	−	0.505461i	$-0.168678\pi$
$521$	−0.144196	−	0.249755i	−0.00631735	−	0.0109420i	−0.869167	+	0.494519i	$0.835344\pi$
$522$	−0.423591	+	1.07929i	−0.0185401	+	0.0472393i
$523$	20.2588	+	6.24901i	0.885856	+	0.273250i	0.704106	−	0.710095i	$-0.251348\pi$
$523$	20.2588	+	6.24901i	0.885856	+	0.273250i	0.181749	+	0.983345i	$0.441824\pi$
$524$	−1.74332	−	0.839541i	−0.0761575	−	0.0366755i
$525$		0			0
$526$	17.6052	−	8.47824i	0.767625	−	0.369669i
$527$	2.87992	−	0.434079i	0.125451	−	0.0189088i
$528$	−33.3213	−	22.7181i	−1.45013	−	0.988679i
$529$	−19.7179	+	18.2955i	−0.857298	+	0.795457i
$530$	7.34030	−	5.00453i	0.318842	−	0.217383i
$531$	−1.93501	+	8.47785i	−0.0839725	+	0.367907i
$532$		0			0
$533$	0.108155	+	0.473857i	0.00468470	+	0.0205250i
$534$	−36.1288	−	33.5226i	−1.56344	−	1.45066i
$535$	22.1545	+	3.33926i	0.957824	+	0.144369i
$536$	−27.1715	+	8.38129i	−1.17363	+	0.362017i
$537$	−1.21602	+	16.2266i	−0.0524751	+	0.700231i
$538$	−0.820727			−0.0353840
$539$		0			0
$540$	49.4756			2.12909
$541$	−0.957475	+	12.7766i	−0.0411651	+	0.549310i	0.938052	+	0.346495i	$0.112628\pi$
$541$	−0.957475	+	12.7766i	−0.0411651	+	0.549310i	−0.979217	+	0.202815i	$0.934991\pi$
$542$	40.2293	−	12.4091i	1.72800	−	0.533016i
$543$	−13.6166	−	2.05237i	−0.584345	−	0.0880758i
$544$	−2.09729	−	1.94600i	−0.0899206	−	0.0834342i
$545$	1.94566	+	8.52449i	0.0833429	+	0.365149i
$546$		0			0
$547$	−4.62670	+	20.2709i	−0.197823	+	0.866721i	0.774406	+	0.632689i	$0.218049\pi$
$547$	−4.62670	+	20.2709i	−0.197823	+	0.866721i	−0.972229	+	0.234031i	$0.924808\pi$
$548$	−21.3291	+	14.5420i	−0.911135	+	0.621201i
$549$	−0.271204	+	0.251641i	−0.0115747	+	0.0107398i
$550$	−8.06488	−	5.49854i	−0.343888	−	0.234459i
$551$	1.94385	−	0.292988i	0.0828108	−	0.0124817i
$552$	75.7119	−	36.4610i	3.22251	−	1.55188i
$553$		0			0
$554$	−28.3030	−	13.6300i	−1.20248	−	0.579083i
$555$	12.2691	+	3.78451i	0.520794	+	0.160644i
$556$	11.8068	−	30.0832i	0.500719	−	1.27581i
$557$	−18.5479	−	32.1260i	−0.785902	−	1.36122i	−0.928459	−	0.371435i	$-0.878866\pi$
$557$	−18.5479	−	32.1260i	−0.785902	−	1.36122i	0.142557	−	0.989787i	$-0.454468\pi$
$558$	4.38588	−	7.59656i	0.185669	−	0.321588i
$559$	−0.821455	−	1.03007i	−0.0347438	−	0.0435674i
$560$		0			0
$561$	2.09725	−	2.62987i	0.0885460	−	0.111033i
$562$	−27.9771	−	71.2844i	−1.18014	−	3.00695i
$563$	1.21402	+	16.1999i	0.0511646	+	0.682745i	0.962535	+	0.271157i	$0.0874064\pi$
$563$	1.21402	+	16.1999i	0.0511646	+	0.682745i	−0.911370	+	0.411587i	$0.864975\pi$
$564$	2.11904	+	28.2766i	0.0892277	+	1.19066i
$565$	5.29872	+	13.5009i	0.222919	+	0.567988i
$566$	15.3133	−	19.2023i	0.643667	−	0.807133i
$567$		0			0
$568$	−2.85915	−	3.58526i	−0.119967	−	0.150434i
$569$	−2.47058	+	4.27917i	−0.103572	+	0.179392i	−0.913154	−	0.407615i	$-0.866361\pi$
$569$	−2.47058	+	4.27917i	−0.103572	+	0.179392i	0.809582	+	0.587007i	$0.199694\pi$
$570$	17.7806	+	30.7970i	0.744749	+	1.28994i
$571$	−4.82316	+	12.2892i	−0.201843	+	0.514288i	−0.995574	−	0.0939813i	$-0.970041\pi$
$571$	−4.82316	+	12.2892i	−0.201843	+	0.514288i	0.793731	+	0.608269i	$0.208136\pi$
$572$	−1.46165	−	0.450860i	−0.0611147	−	0.0188514i
$573$	14.5538	+	7.00876i	0.607995	+	0.292795i
$574$		0			0
$575$	7.98140	−	3.84364i	0.332847	−	0.160291i
$576$	0.682944	−	0.102937i	0.0284560	−	0.00428905i
$577$	−13.4939	−	9.19998i	−0.561758	−	0.383000i	0.248892	−	0.968531i	$-0.419934\pi$
$577$	−13.4939	−	9.19998i	−0.561758	−	0.383000i	−0.810650	+	0.585531i	$0.800886\pi$
$578$	−31.0245	+	28.7865i	−1.29045	+	1.19736i
$579$	18.8973	−	12.8839i	0.785344	−	0.535438i
$580$	−1.66427	+	7.29166i	−0.0691052	+	0.302770i
$581$		0			0
$582$	13.9851	+	61.2726i	0.579700	+	2.53983i
$583$	3.14563	+	2.91872i	0.130279	+	0.120881i
$584$	−83.2360	−	12.5458i	−3.44433	−	0.519149i
$585$	−0.182069	+	0.0561608i	−0.00752762	+	0.00232196i
$586$	−5.84224	+	77.9593i	−0.241341	+	3.22047i
$587$	−30.8688			−1.27409			−0.637045	−	0.770827i	$-0.719843\pi$
$587$	−30.8688			−1.27409			−0.637045	+	0.770827i	$0.719843\pi$
$588$		0			0
$589$	−14.8723			−0.612804
$590$	−6.07872	+	81.1148i	−0.250257	+	3.33944i
$591$	−18.1918	+	5.61144i	−0.748312	+	0.230824i
$592$	18.1515	+	2.73590i	0.746022	+	0.112445i
$593$	0.504847	+	0.468430i	0.0207316	+	0.0192361i	0.690471	−	0.723361i	$-0.257404\pi$
$593$	0.504847	+	0.468430i	0.0207316	+	0.0192361i	−0.669739	+	0.742597i	$0.733594\pi$
$594$	7.71122	+	33.7851i	0.316395	+	1.38622i
$595$		0			0
$596$	8.90942	−	39.0347i	0.364944	−	1.59892i
$597$	−20.2089	+	13.7782i	−0.827094	+	0.563903i
$598$	1.47567	−	1.36922i	0.0603446	−	0.0559916i
$599$	6.88987	+	4.69744i	0.281513	+	0.191932i	0.695842	−	0.718195i	$-0.255031\pi$
$599$	6.88987	+	4.69744i	0.281513	+	0.191932i	−0.414329	+	0.910127i	$0.635984\pi$
$600$	−14.7523	+	2.22355i	−0.602260	+	0.0907762i
$601$	−15.9481	+	7.68018i	−0.650535	+	0.313281i	−0.729889	−	0.683565i	$-0.760428\pi$
$601$	−15.9481	+	7.68018i	−0.650535	+	0.313281i	0.0793543	+	0.996846i	$0.474714\pi$
$602$		0			0
$603$	−2.80305	−	1.34988i	−0.114149	−	0.0549712i
$604$	41.1479	+	12.6925i	1.67429	+	0.516449i
$605$	−1.46018	+	3.72047i	−0.0593646	+	0.151258i
$606$	−45.1810	−	78.2558i	−1.83535	−	3.17893i
$607$	−14.9314	+	25.8620i	−0.606047	+	1.04970i	0.385838	+	0.922567i	$0.373912\pi$
$607$	−14.9314	+	25.8620i	−0.606047	+	1.04970i	−0.991885	+	0.127138i	$0.959421\pi$
$608$	9.10906	+	11.4224i	0.369421	+	0.463240i
$609$		0			0
$610$	−2.15771	+	2.70569i	−0.0873633	+	0.109550i
$611$	0.136467	+	0.347712i	0.00552085	+	0.0140669i
$612$	−0.128893	−	1.71996i	−0.00521018	−	0.0695251i
$613$	2.89501	+	38.6313i	0.116928	+	1.56030i	0.679576	+	0.733605i	$0.262164\pi$
$613$	2.89501	+	38.6313i	0.116928	+	1.56030i	−0.562648	+	0.826697i	$0.690217\pi$
$614$	−14.7074	−	37.4738i	−0.593542	−	1.51232i
$615$	−12.9473	+	16.2354i	−0.522085	+	0.654673i
$616$		0			0
$617$	17.1126	+	21.4585i	0.688928	+	0.863888i	0.996142	−	0.0877519i	$-0.0279683\pi$
$617$	17.1126	+	21.4585i	0.688928	+	0.863888i	−0.307214	+	0.951640i	$0.599397\pi$
$618$	−16.2052	+	28.0682i	−0.651867	+	1.12907i
$619$	13.4647	+	23.3216i	0.541194	+	0.937375i	0.998836	+	0.0482388i	$0.0153608\pi$
$619$	13.4647	+	23.3216i	0.541194	+	0.937375i	−0.457642	+	0.889137i	$0.651306\pi$
$620$	20.6724	−	52.6724i	0.830223	−	2.11537i
$621$	−30.0534	−	9.27023i	−1.20600	−	0.372002i
$622$	4.60830	+	2.21924i	0.184776	+	0.0889834i
$623$		0			0
$624$	−1.33037	+	0.640671i	−0.0532573	+	0.0256474i
$625$	29.3660	−	4.42621i	1.17464	−	0.177048i
$626$	37.8963	+	25.8373i	1.51464	+	1.03266i
$627$	−12.5915	+	11.6832i	−0.502854	+	0.466581i
$628$	−16.9105	+	11.5294i	−0.674802	+	0.460072i
$629$	−0.340695	+	1.49268i	−0.0135844	+	0.0595171i
$630$		0			0
$631$	1.46048	+	6.39877i	0.0581407	+	0.254731i	0.995643	−	0.0932484i	$-0.0297251\pi$
$631$	1.46048	+	6.39877i	0.0581407	+	0.254731i	−0.937502	+	0.347979i	$0.886868\pi$
$632$	−18.2268	−	16.9120i	−0.725022	−	0.672722i
$633$	−28.4259	−	4.28452i	−1.12983	−	0.170294i
$634$	45.8951	−	14.1568i	1.82273	−	0.562237i
$635$	−2.87212	+	38.3258i	−0.113977	+	1.52091i
$636$	11.9270			0.472938
$637$		0			0
$638$	−5.23860			−0.207398
$639$	0.0374951	−	0.500337i	0.00148328	−	0.0197930i
$640$	30.0806	−	9.27865i	1.18904	−	0.366771i
$641$	12.1731	+	1.83479i	0.480807	+	0.0724700i	0.384974	−	0.922927i	$-0.374210\pi$
$641$	12.1731	+	1.83479i	0.480807	+	0.0724700i	0.0958331	+	0.995397i	$0.469448\pi$
$642$	31.9740	+	29.6675i	1.26191	+	1.17088i
$643$	−2.52492	−	11.0624i	−0.0995731	−	0.436258i	−0.999999	−	0.00124928i	$-0.999602\pi$
$643$	−2.52492	−	11.0624i	−0.0995731	−	0.436258i	0.900426	−	0.435009i	$-0.143255\pi$
$644$		0			0
$645$	12.5256	−	54.8784i	0.493196	−	2.16083i
$646$	−3.50372	+	2.38879i	−0.137852	+	0.0939858i
$647$	−22.1233	+	20.5274i	−0.869755	+	0.807015i	−0.982433	−	0.186617i	$-0.940248\pi$
$647$	−22.1233	+	20.5274i	−0.869755	+	0.807015i	0.112678	+	0.993632i	$0.464057\pi$
$648$	54.1962	+	36.9504i	2.12903	+	1.45155i
$649$	−38.8510	+	5.85585i	−1.52504	+	0.229862i
$650$	−0.321994	+	0.155064i	−0.0126296	+	0.00608211i
$651$		0			0
$652$	−72.0864	−	34.7150i	−2.82312	−	1.35954i
$653$	−9.63678	−	2.97255i	−0.377116	−	0.116325i	0.100402	−	0.994947i	$-0.467987\pi$
$653$	−9.63678	−	2.97255i	−0.377116	−	0.116325i	−0.477518	+	0.878622i	$0.658463\pi$
$654$	−6.21894	+	15.8456i	−0.243180	+	0.619612i
$655$	−0.544499	−	0.943101i	−0.0212754	−	0.0368500i
$656$	−14.8443	+	25.7112i	−0.579574	+	1.00385i
$657$	−5.74234	−	7.20067i	−0.224030	−	0.280925i
$658$		0			0
$659$	14.6394	−	18.3572i	0.570269	−	0.715094i	−0.410150	−	0.912018i	$-0.634524\pi$
$659$	14.6394	−	18.3572i	0.570269	−	0.715094i	0.980419	+	0.196924i	$0.0630952\pi$
$660$	−23.8755	−	60.8338i	−0.929353	−	2.36795i
$661$	2.81870	+	37.6129i	0.109635	+	1.46297i	0.732566	+	0.680696i	$0.238322\pi$
$661$	2.81870	+	37.6129i	0.109635	+	1.46297i	−0.622932	+	0.782276i	$0.714059\pi$
$662$	−4.98589	−	66.5321i	−0.193782	−	2.58584i
$663$	−0.0449950	−	0.114645i	−0.00174746	−	0.00445246i
$664$	−32.4066	+	40.6367i	−1.25762	+	1.57701i
$665$		0			0
$666$	2.87509	+	3.60525i	0.111407	+	0.139700i
$667$	2.37718	−	4.11740i	0.0920448	−	0.159426i
$668$	−9.46471	−	16.3934i	−0.366201	−	0.634278i
$669$	−18.3440	+	46.7396i	−0.709218	+	1.80706i
$670$	−27.8091	−	8.57798i	−1.07436	−	0.331396i
$671$	−1.50605	−	0.725274i	−0.0581403	−	0.0279989i
$672$		0			0
$673$	−11.1185	+	5.35440i	−0.428588	+	0.206397i	−0.635726	−	0.771915i	$-0.719299\pi$
$673$	−11.1185	+	5.35440i	−0.428588	+	0.206397i	0.207138	+	0.978312i	$0.433585\pi$
$674$	−62.1814	+	9.37233i	−2.39514	+	0.361009i
$675$	4.61337	+	3.14534i	0.177569	+	0.121064i
$676$	42.3038	−	39.2522i	1.62707	−	1.50970i
$677$	12.1426	−	8.27869i	0.466678	−	0.318176i	−0.307050	−	0.951693i	$-0.599342\pi$
$677$	12.1426	−	8.27869i	0.466678	−	0.318176i	0.773728	+	0.633517i	$0.218390\pi$
$678$	−6.28297	+	27.5275i	−0.241296	+	1.05719i
$679$		0			0
$680$	−1.97421	−	8.64956i	−0.0757073	−	0.331695i
$681$	11.5475	+	10.7145i	0.442501	+	0.410581i
$682$	39.1900	+	5.90695i	1.50066	+	0.226189i
$683$	−16.7566	+	5.16874i	−0.641175	+	0.197776i	−0.598259	−	0.801303i	$-0.704141\pi$
$683$	−16.7566	+	5.16874i	−0.641175	+	0.197776i	−0.0429153	+	0.999079i	$0.513665\pi$
$684$	−0.658186	+	8.78289i	−0.0251664	+	0.335822i
$685$	−14.5287			−0.555113
$686$		0			0
$687$	−48.2653			−1.84143
$688$	6.01404	−	80.2518i	0.229283	−	3.05957i
$689$	0.150135	−	0.0463105i	0.00571968	−	0.00176429i
$690$	85.0453	+	12.8185i	3.23762	+	0.487993i
$691$	−11.1985	−	10.3907i	−0.426012	−	0.395282i	0.437819	−	0.899063i	$-0.355751\pi$
$691$	−11.1985	−	10.3907i	−0.426012	−	0.395282i	−0.863831	+	0.503781i	$0.831942\pi$
$692$	−21.4782	−	94.1023i	−0.816480	−	3.57723i
$693$		0			0
$694$	−13.3229	+	58.3714i	−0.505730	+	2.21575i
$695$	15.0279	−	10.2458i	0.570040	−	0.388647i
$696$	−5.86943	+	5.44603i	−0.222480	+	0.206431i
$697$	−2.04598	−	1.39492i	−0.0774969	−	0.0528365i
$698$	49.9926	−	7.53517i	1.89225	−	0.285210i
$699$	28.0521	−	13.5092i	1.06103	−	0.510964i
$700$		0			0
$701$	24.2530	+	11.6796i	0.916024	+	0.441134i	0.831650	−	0.555300i	$-0.187397\pi$
$701$	24.2530	+	11.6796i	0.916024	+	0.441134i	0.0843742	+	0.996434i	$0.473111\pi$
$702$	1.21244	+	0.373989i	0.0457607	+	0.0141153i
$703$	2.85636	−	7.27789i	0.107730	−	0.274491i
$704$	1.56027	+	2.70247i	0.0588049	+	0.101853i
$705$	−7.97945	+	13.8208i	−0.300523	+	0.520522i
$706$	12.3192	+	15.4478i	0.463640	+	0.581386i
$707$		0			0
$708$	−68.0879	+	85.3796i	−2.55890	+	3.20876i
$709$	2.51904	+	6.41840i	0.0946044	+	0.241048i	0.970341	−	0.241742i	$-0.0777187\pi$
$709$	2.51904	+	6.41840i	0.0946044	+	0.241048i	−0.875736	+	0.482790i	$0.839623\pi$
$710$	−0.350733	−	4.68021i	−0.0131628	−	0.175645i
$711$	−0.203302	−	2.71287i	−0.00762441	−	0.101741i
$712$	−22.9394	−	58.4485i	−0.859689	−	2.19045i
$713$	−22.4264	+	28.1218i	−0.839876	+	1.05317i
$714$		0			0
$715$	−0.536745	−	0.673057i	−0.0200731	−	0.0251709i
$716$	−18.8492	+	32.6478i	−0.704429	+	1.22011i
$717$	11.9632	+	20.7209i	0.446774	+	0.773836i
$718$	1.84641	−	4.70458i	0.0689075	−	0.175573i
$719$	10.2616	+	3.16530i	0.382695	+	0.118046i	0.480133	−	0.877196i	$-0.340589\pi$
$719$	10.2616	+	3.16530i	0.382695	+	0.118046i	−0.0974380	+	0.995242i	$0.531065\pi$
$720$	−10.4857	−	5.04965i	−0.390779	−	0.188189i
$721$		0			0
$722$	−23.9436	+	11.5306i	−0.891087	+	0.429125i
$723$	29.3522	−	4.42413i	1.09162	−	0.164535i
$724$	−26.3592	−	17.9714i	−0.979631	−	0.667901i
$725$	−0.618743	+	0.574110i	−0.0229795	+	0.0213219i
$726$	−6.42886	+	4.38312i	−0.238597	+	0.162673i
$727$	−2.87093	+	12.5784i	−0.106477	+	0.466506i	0.893375	+	0.449311i	$0.148331\pi$
$727$	−2.87093	+	12.5784i	−0.106477	+	0.466506i	−0.999852	+	0.0171945i	$0.994527\pi$
$728$		0			0
$729$	−4.10362	−	17.9791i	−0.151986	−	0.665893i
$730$	−63.1535	−	58.5979i	−2.33742	−	2.16881i
$731$	6.63738	+	1.00042i	0.245492	+	0.0370020i
$732$	−4.43969	+	1.36946i	−0.164096	+	0.0506168i
$733$	1.54086	−	20.5613i	0.0569129	−	0.759450i	−0.893620	−	0.448825i	$-0.851843\pi$
$733$	1.54086	−	20.5613i	0.0569129	−	0.759450i	0.950533	−	0.310625i	$-0.100538\pi$
$734$	43.1685			1.59338
$735$		0			0
$736$	35.3342			1.30244
$737$	1.05047	−	14.0175i	0.0386945	−	0.516342i
$738$	−7.12667	+	2.19829i	−0.262336	+	0.0809200i
$739$	−29.0803	−	4.38315i	−1.06974	−	0.161237i	−0.409512	−	0.912305i	$-0.634301\pi$
$739$	−29.0803	−	4.38315i	−1.06974	−	0.161237i	−0.660225	+	0.751068i	$0.729539\pi$
$740$	21.8053	+	20.2324i	0.801579	+	0.743757i
$741$	0.139945	+	0.613139i	0.00514101	+	0.0225242i
$742$		0			0
$743$	−11.1327	+	48.7754i	−0.408418	+	1.78940i	0.183089	+	0.983096i	$0.441390\pi$
$743$	−11.1327	+	48.7754i	−0.408418	+	1.78940i	−0.591507	+	0.806300i	$0.701467\pi$
$744$	50.0501	−	34.1236i	1.83492	−	1.25103i
$745$	16.5186	−	15.3270i	0.605193	−	0.561537i
$746$	−28.2483	−	19.2594i	−1.03424	−	0.705135i
$747$	−5.62338	+	0.847588i	−0.205749	+	0.0310116i
$748$	7.02118	−	3.38122i	0.256720	−	0.123630i
$749$		0			0
$750$	41.0916	+	19.7887i	1.50045	+	0.722581i
$751$	−15.2846	−	4.71468i	−0.557744	−	0.172041i	0.00305184	−	0.999995i	$-0.499029\pi$
$751$	−15.2846	−	4.71468i	−0.557744	−	0.172041i	−0.560796	+	0.827954i	$0.689505\pi$
$752$	−8.33572	+	21.2391i	−0.303972	+	0.774509i
$753$	17.5793	+	30.4482i	0.640624	+	1.10959i
$754$	−0.0959026	+	0.166108i	−0.00349257	+	0.00604930i
$755$	15.1103	+	18.9477i	0.549920	+	0.689578i
$756$		0			0
$757$	19.1325	−	23.9913i	0.695381	−	0.871980i	−0.301288	−	0.953533i	$-0.597417\pi$
$757$	19.1325	−	23.9913i	0.695381	−	0.871980i	0.996669	+	0.0815531i	$0.0259880\pi$
$758$	20.2108	+	51.4962i	0.734088	+	1.87043i
$759$	3.10447	+	41.4263i	0.112685	+	1.50368i
$760$	3.38561	+	45.1778i	0.122809	+	1.63877i
$761$	1.35735	+	3.45847i	0.0492038	+	0.125369i	0.953363	−	0.301827i	$-0.0975965\pi$
$761$	1.35735	+	3.45847i	0.0492038	+	0.125369i	−0.904159	+	0.427196i	$0.859501\pi$
$762$	−46.6507	+	58.4981i	−1.68998	+	2.11916i
$763$		0			0
$764$	23.3333	+	29.2590i	0.844169	+	1.05855i
$765$	0.485358	−	0.840665i	0.0175482	−	0.0303943i
$766$	−42.6031	−	73.7907i	−1.53931	−	2.66616i
$767$	−0.525562	+	1.33911i	−0.0189769	+	0.0483525i
$768$	54.8306	+	16.9130i	1.97853	+	0.610296i
$769$	11.0453	+	5.31912i	0.398302	+	0.191812i	0.622303	−	0.782777i	$-0.286197\pi$
$769$	11.0453	+	5.31912i	0.398302	+	0.191812i	−0.224000	+	0.974589i	$0.571912\pi$
$770$		0			0
$771$	27.3984	−	13.1944i	0.986730	−	0.475184i
$772$	52.3956	−	7.89736i	1.88576	−	0.284232i
$773$	2.65160	+	1.80783i	0.0953714	+	0.0650231i	0.610067	−	0.792350i	$-0.291143\pi$
$773$	2.65160	+	1.80783i	0.0953714	+	0.0650231i	−0.514695	+	0.857373i	$0.672095\pi$
$774$	14.8196	−	13.7506i	0.532680	−	0.494255i
$775$	5.27618	−	3.59724i	0.189526	−	0.129217i
$776$	−17.8168	+	78.0604i	−0.639585	+	2.80221i
$777$		0			0
$778$	−2.44091	−	10.6943i	−0.0875110	−	0.383411i
$779$	9.26937	+	8.60072i	0.332110	+	0.308153i
$780$	−2.36604	−	0.356622i	−0.0847177	−	0.0127691i
$781$	2.16625	−	0.668201i	0.0775147	−	0.0239101i
$782$	−0.766426	+	10.2272i	−0.0274073	+	0.365725i
$783$	2.99665			0.107091
$784$		0			0
$785$	−11.5189			−0.411126
$786$	0.158433	−	2.11414i	0.00565111	−	0.0754088i
$787$	−26.2473	+	8.09623i	−0.935616	+	0.288599i	−0.724826	−	0.688932i	$-0.758080\pi$
$787$	−26.2473	+	8.09623i	−0.935616	+	0.288599i	−0.210790	+	0.977531i	$0.567604\pi$
$788$	−43.6128	−	6.57357i	−1.55364	−	0.234174i
$789$	10.8231	+	10.0423i	0.385312	+	0.357517i
$790$	−5.66265	−	24.8097i	−0.201468	−	0.882689i
$791$		0			0
$792$	2.87200	−	12.5830i	0.102052	−	0.447119i
$793$	−0.0505684	+	0.0344770i	−0.00179574	+	0.00122431i
$794$	18.3053	−	16.9848i	0.649631	−	0.602769i
$795$	5.54623	+	3.78135i	0.196704	+	0.134111i
$796$	−56.0322	+	8.44550i	−1.98601	+	0.299343i
$797$	−11.4923	+	5.53441i	−0.407079	+	0.196039i	−0.626206	−	0.779657i	$-0.715393\pi$
$797$	−11.4923	+	5.53441i	−0.407079	+	0.196039i	0.219127	+	0.975696i	$0.429679\pi$
$798$		0			0
$799$	−1.71458	−	0.825700i	−0.0606576	−	0.0292112i
$800$	−5.99436	−	1.84901i	−0.211933	−	0.0653725i
$801$	2.50987	−	6.39506i	0.0886820	−	0.225958i
$802$	7.17405	+	12.4258i	0.253324	+	0.438771i
$803$	20.8064	−	36.0377i	0.734242	−	1.27174i
$804$	−24.3600	−	30.5465i	−0.859111	−	1.07729i
$805$		0			0
$806$	0.904749	−	1.13452i	0.0318684	−	0.0399617i
$807$	−0.226559	−	0.577262i	−0.00797524	−	0.0203206i
$808$	−8.60292	−	114.798i	−0.302650	−	4.03858i
$809$	−1.94509	−	25.9554i	−0.0683857	−	0.912544i	−0.920890	−	0.389823i	$-0.872536\pi$
$809$	−1.94509	−	25.9554i	−0.0683857	−	0.912544i	0.852504	−	0.522721i	$-0.175083\pi$
$810$	24.5265	+	62.4925i	0.861774	+	2.19576i
$811$	23.7523	−	29.7844i	0.834056	−	1.04587i	−0.164176	−	0.986431i	$-0.552496\pi$
$811$	23.7523	−	29.7844i	0.834056	−	1.04587i	0.998232	−	0.0594419i	$-0.0189321\pi$
$812$		0			0
$813$	19.8331	+	24.8700i	0.695578	+	0.872227i
$814$	−10.4174	+	18.0435i	−0.365129	+	0.632423i
$815$	−22.5150	−	38.9972i	−0.788668	−	1.36601i
$816$	2.74841	−	7.00282i	0.0962135	−	0.245148i
$817$	−32.7536	−	10.1031i	−1.14590	−	0.353464i
$818$	1.22360	+	0.589253i	0.0427820	+	0.0206027i
$819$		0			0
$820$	−43.3449	+	20.8738i	−1.51367	+	0.728945i
$821$	−2.39671	+	0.361246i	−0.0836457	+	0.0126076i	−0.190732	−	0.981642i	$-0.561086\pi$
$821$	−2.39671	+	0.361246i	−0.0836457	+	0.0126076i	0.107086	+	0.994250i	$0.465848\pi$
$822$	−23.3697	−	15.9332i	−0.815113	−	0.555735i
$823$	25.7611	−	23.9028i	0.897976	−	0.833200i	−0.0886728	−	0.996061i	$-0.528263\pi$
$823$	25.7611	−	23.9028i	0.897976	−	0.833200i	0.986649	+	0.162861i	$0.0520721\pi$
$824$	−34.1156	+	23.2596i	−1.18847	+	0.810288i
$825$	1.64114	−	7.19032i	0.0571373	−	0.250335i
$826$		0			0
$827$	−4.24922	−	18.6170i	−0.147760	−	0.647378i	−0.993505	−	0.113791i	$-0.963701\pi$
$827$	−4.24922	−	18.6170i	−0.147760	−	0.647378i	0.845745	−	0.533587i	$-0.179156\pi$
$828$	15.6149	+	14.4885i	0.542655	+	0.503511i
$829$	16.7324	+	2.52200i	0.581140	+	0.0875928i	0.433032	−	0.901378i	$-0.357444\pi$
$829$	16.7324	+	2.52200i	0.581140	+	0.0875928i	0.148108	+	0.988971i	$0.452682\pi$
$830$	−50.8326	+	15.6798i	−1.76443	+	0.544253i
$831$	1.77379	−	23.6696i	0.0615320	−	0.821088i
$832$	0.114255			0.00396108
$833$		0			0
$834$	35.4090			1.22611
$835$	0.796144	−	10.6238i	0.0275517	−	0.367652i
$836$	−38.0263	+	11.7296i	−1.31517	+	0.405676i
$837$	−22.4179	−	3.37896i	−0.774877	−	0.116794i
$838$	−47.5719	−	44.1403i	−1.64335	−	1.52480i
$839$	1.27299	+	5.57734i	0.0439486	+	0.192551i	0.992137	−	0.125158i	$-0.0399437\pi$
$839$	1.27299	+	5.57734i	0.0439486	+	0.192551i	−0.948188	+	0.317709i	$0.897087\pi$
$840$		0			0
$841$	6.35231	−	27.8313i	0.219045	−	0.959699i
$842$	−16.0429	+	10.9378i	−0.552873	+	0.376943i
$843$	42.4153	−	39.3556i	1.46086	−	1.35548i
$844$	−55.0272	−	37.5169i	−1.89411	−	1.29138i
$845$	32.1163	−	4.84076i	1.10484	−	0.166527i
$846$	−5.16400	+	2.48685i	−0.177542	+	0.0854997i
$847$		0			0
$848$	8.64657	+	4.16397i	0.296924	+	0.142991i
$849$	17.7332	+	5.46997i	0.608602	+	0.187729i
$850$	0.665206	−	1.69492i	0.0228164	−	0.0581352i
$851$	−9.45444	−	16.3756i	−0.324094	−	0.561347i
$852$	3.15048	−	5.45678i	0.107934	−	0.186946i
$853$	−14.7109	−	18.4469i	−0.503693	−	0.631611i	0.463365	−	0.886168i	$-0.346642\pi$
$853$	−14.7109	−	18.4469i	−0.503693	−	0.631611i	−0.967058	+	0.254556i	$0.918071\pi$
$854$		0			0
$855$	−3.09059	+	3.87548i	−0.105696	+	0.132539i
$856$	20.3014	+	51.7270i	0.693886	+	1.76799i
$857$	−1.28111	−	17.0952i	−0.0437618	−	0.583961i	−0.975381	−	0.220526i	$-0.929223\pi$
$857$	−1.28111	−	17.0952i	−0.0437618	−	0.583961i	0.931619	−	0.363436i	$-0.118396\pi$
$858$	−0.125244	−	1.67126i	−0.00427575	−	0.0570560i
$859$	2.44295	+	6.22455i	0.0833525	+	0.212379i	0.966473	−	0.256767i	$-0.0826572\pi$
$859$	2.44295	+	6.22455i	0.0833525	+	0.212379i	−0.883121	+	0.469146i	$0.844562\pi$
$860$	81.3087	−	101.958i	2.77261	−	3.47674i
$861$		0			0
$862$	−19.4572	−	24.3985i	−0.662714	−	0.831017i
$863$	24.2811	−	42.0560i	0.826537	−	1.43160i	−0.0742018	−	0.997243i	$-0.523641\pi$
$863$	24.2811	−	42.0560i	0.826537	−	1.43160i	0.900739	−	0.434361i	$-0.143026\pi$
$864$	11.1355	+	19.2872i	0.378837	+	0.656164i
$865$	19.8466	−	50.5682i	0.674804	−	1.71937i
$866$	−21.4311	−	6.61061i	−0.728257	−	0.224638i
$867$	−28.8113	−	13.8748i	−0.978484	−	0.471213i
$868$		0			0
$869$	11.0745	−	5.33318i	0.375675	−	0.180916i
$870$	−8.10320	+	1.22136i	−0.274724	+	0.0414080i
$871$	−0.425244	−	0.289926i	−0.0144088	−	0.00982378i
$872$	−15.8971	+	14.7503i	−0.538343	+	0.499509i
$873$	−7.23827	+	4.93497i	−0.244978	+	0.167023i
$874$	11.6537	−	51.0584i	0.394194	−	1.72708i
$875$		0			0
$876$	−25.7370	−	112.761i	−0.869573	−	3.80985i
$877$	−16.6416	−	15.4411i	−0.561946	−	0.521409i	0.347253	−	0.937771i	$-0.387114\pi$
$877$	−16.6416	−	15.4411i	−0.561946	−	0.521409i	−0.909199	+	0.416362i	$0.863305\pi$
$878$	75.0853	+	11.3173i	2.53400	+	0.381940i
$879$	−56.4457	+	17.4112i	−1.90387	+	0.587265i
$880$	3.92962	−	52.4372i	0.132468	−	1.76766i
$881$	−44.2276			−1.49007			−0.745033	−	0.667028i	$-0.767566\pi$
$881$	−44.2276			−1.49007			−0.745033	+	0.667028i	$0.767566\pi$
$882$		0			0
$883$	−4.79853			−0.161483			−0.0807417	−	0.996735i	$-0.525729\pi$
$883$	−4.79853			−0.161483			−0.0807417	+	0.996735i	$0.525729\pi$
$884$	0.0213226	−	0.284531i	0.000717158	−	0.00956981i
$885$	−58.7305	+	18.1160i	−1.97420	+	0.608961i
$886$	73.4836	+	11.0759i	2.46873	+	0.372101i
$887$	−11.6869	−	10.8439i	−0.392409	−	0.364102i	0.459152	−	0.888358i	$-0.348153\pi$
$887$	−11.6869	−	10.8439i	−0.392409	−	0.364102i	−0.851561	+	0.524255i	$0.824344\pi$
$888$	7.08607	+	31.0461i	0.237793	+	1.04184i
$889$		0			0
$890$	14.2997	−	62.6511i	0.479328	−	2.10007i
$891$	−26.7921	+	18.2666i	−0.897570	+	0.611953i
$892$	−85.2724	+	79.1212i	−2.85513	+	2.64917i
$893$	8.02924	+	5.47424i	0.268688	+	0.183189i
$894$	43.3792	−	6.53836i	1.45082	−	0.218676i
$895$	−19.1158	+	9.20569i	−0.638971	+	0.307712i
$896$		0			0
$897$	1.37040	+	0.659950i	0.0457563	+	0.0220351i
$898$	−0.944647	−	0.291385i	−0.0315233	−	0.00972364i
$899$	1.25209	−	3.19027i	0.0417595	−	0.106401i
$900$	−1.89085	−	3.27506i	−0.0630285	−	0.109169i
$901$	−0.400229	+	0.693216i	−0.0133335	+	0.0230944i
$902$	−21.0097	−	26.3453i	−0.699545	−	0.877202i
$903$		0			0
$904$	−22.4279	+	28.1237i	−0.745940	+	0.935379i
$905$	−6.55969	−	16.7138i	−0.218052	−	0.555587i
$906$	3.52583	+	47.0489i	0.117138	+	1.56309i
$907$	0.297026	+	3.96353i	0.00986257	+	0.131607i	0.999962	−	0.00876377i	$-0.00278963\pi$
$907$	0.297026	+	3.96353i	0.00986257	+	0.131607i	−0.990099	+	0.140371i	$0.955171\pi$
$908$	13.3331	+	33.9722i	0.442475	+	1.12741i
$909$	7.85327	−	9.84769i	0.260477	−	0.326627i
$910$		0			0
$911$	−11.1773	−	14.0159i	−0.370320	−	0.464366i	0.561400	−	0.827545i	$-0.310263\pi$
$911$	−11.1773	−	14.0159i	−0.370320	−	0.464366i	−0.931720	+	0.363179i	$0.881691\pi$
$912$	−19.2076	+	33.2685i	−0.636026	+	1.10163i
$913$	−12.8473	−	22.2522i	−0.425184	−	0.736441i
$914$	14.8746	−	37.8999i	0.492009	−	1.25362i
$915$	−2.49869	−	0.770743i	−0.0826040	−	0.0254800i
$916$	−100.745	−	48.5163i	−3.32871	−	1.60302i
$917$		0			0
$918$	−5.82408	+	2.80473i	−0.192223	+	0.0925699i
$919$	4.18525	−	0.630824i	0.138059	−	0.0208090i	−0.0796494	−	0.996823i	$-0.525380\pi$
$919$	4.18525	−	0.630824i	0.138059	−	0.0208090i	0.217708	+	0.976014i	$0.430142\pi$
$920$	90.5312	+	61.7232i	2.98473	+	2.03495i
$921$	22.2974	−	20.6890i	0.734726	−	0.681726i
$922$	−19.8559	+	13.5375i	−0.653920	+	0.445835i
$923$	0.0184698	−	0.0809214i	0.000607940	−	0.00266356i
$924$		0			0
$925$	0.746999	+	3.27282i	0.0245612	+	0.107610i
$926$	56.4252	+	52.3550i	1.85425	+	1.72049i
$927$	−4.46725	−	0.673330i	−0.146724	−	0.0221151i
$928$	−3.21711	+	0.992346i	−0.105607	+	0.0325754i
$929$	−3.31443	+	44.2280i	−0.108743	+	1.45107i	0.629742	+	0.776805i	$0.283161\pi$
$929$	−3.31443	+	44.2280i	−0.108743	+	1.45107i	−0.738485	+	0.674270i	$0.764458\pi$
$930$	61.9973			2.03297
$931$		0			0
$932$	72.1331			2.36280
$933$	−0.288809	+	3.85388i	−0.00945517	+	0.126170i
$934$	−12.4988	+	3.85538i	−0.408974	+	0.126152i
$935$	4.33692	+	0.653686i	0.141832	+	0.0213778i
$936$	−0.346412	−	0.321423i	−0.0113228	−	0.0105060i
$937$	10.5931	+	46.4115i	0.346062	+	1.51620i	0.786033	+	0.618184i	$0.212131\pi$
$937$	10.5931	+	46.4115i	0.346062	+	1.51620i	−0.439971	+	0.898012i	$0.645011\pi$
$938$		0			0
$939$	−7.71162	+	33.7868i	−0.251659	+	1.10259i
$940$	−30.5483	+	20.8275i	−0.996377	+	0.679318i
$941$	16.1729	−	15.0063i	0.527223	−	0.489191i	−0.371060	−	0.928609i	$-0.621006\pi$
$941$	16.1729	−	15.0063i	0.527223	−	0.489191i	0.898283	+	0.439418i	$0.144815\pi$
$942$	−18.5284	−	12.6324i	−0.603686	−	0.411586i
$943$	30.2405	−	4.55802i	0.984765	−	0.148430i
$944$	−79.1683	+	38.1255i	−2.57671	+	1.24088i
$945$		0			0
$946$	82.2961	+	39.6317i	2.67568	+	1.28854i
$947$	−1.82871	−	0.564083i	−0.0594252	−	0.0183302i	0.264900	−	0.964276i	$-0.414661\pi$
$947$	−1.82871	−	0.564083i	−0.0594252	−	0.0183302i	−0.324325	+	0.945946i	$0.605137\pi$
$948$	12.4816	−	31.8027i	0.405385	−	1.03290i
$949$	−0.761802	−	1.31948i	−0.0247291	−	0.0428321i
$950$	−4.64888	+	8.05209i	−0.150829	+	0.261244i
$951$	22.6264	+	28.3726i	0.733711	+	0.920045i
$952$		0			0
$953$	35.4370	−	44.4366i	1.14792	−	1.43944i	0.268573	−	0.963259i	$-0.413448\pi$
$953$	35.4370	−	44.4366i	1.14792	−	1.43944i	0.879345	−	0.476185i	$-0.157981\pi$
$954$	0.880773	+	2.24417i	0.0285161	+	0.0726578i
$955$	1.57399	+	21.0034i	0.0509331	+	0.679654i
$956$	4.14240	+	55.2765i	0.133975	+	1.78777i
$957$	−1.44610	−	3.68459i	−0.0467457	−	0.119106i
$958$	−5.24181	+	6.57302i	−0.169355	+	0.212365i
$959$		0			0
$960$	3.04354	+	3.81648i	0.0982298	+	0.123176i
$961$	2.53583	−	4.39218i	0.0818008	−	0.141683i
$962$	0.381420	+	0.660640i	0.0122975	+	0.0212999i
$963$	−2.22124	+	5.65963i	−0.0715786	+	0.182379i
$964$	65.7146	+	20.2703i	2.11652	+	0.652861i
$965$	26.8684	+	12.9391i	0.864924	+	0.416525i
$966$		0			0
$967$	−31.8007	+	15.3144i	−1.02264	+	0.492479i	−0.868562	−	0.495580i	$-0.834956\pi$
$967$	−31.8007	+	15.3144i	−1.02264	+	0.492479i	−0.154080	+	0.988058i	$0.549241\pi$
$968$	−9.80200	+	1.47741i	−0.315048	+	0.0474859i
$969$	−2.64736	−	1.80494i	−0.0850453	−	0.0579829i
$970$	−60.0713	+	55.7380i	−1.92877	+	1.78964i
$971$	17.1779	−	11.7117i	0.551265	−	0.375846i	−0.255418	−	0.966831i	$-0.582213\pi$
$971$	17.1779	−	11.7117i	0.551265	−	0.375846i	0.806683	+	0.590984i	$0.201261\pi$
$972$	−6.84855	+	30.0055i	−0.219667	+	0.962426i
$973$		0			0
$974$	12.6513	+	55.4290i	0.405374	+	1.77606i
$975$	−0.197950	−	0.183671i	−0.00633948	−	0.00588217i
$976$	−3.69668	−	0.557185i	−0.118328	−	0.0178351i
$977$	51.7384	−	15.9592i	1.65526	−	0.510579i	0.680293	−	0.732940i	$-0.261853\pi$
$977$	51.7384	−	15.9592i	1.65526	−	0.510579i	0.974964	+	0.222361i	$0.0713764\pi$
$978$	6.55119	−	87.4195i	0.209484	−	2.79537i
$979$	31.0399			0.992040
$980$		0			0
$981$	−2.37276			−0.0757563
$982$	0.506784	−	6.76256i	0.0161721	−	0.215802i
$983$	−19.5794	+	6.03946i	−0.624487	+	0.192629i	−0.590819	−	0.806804i	$-0.701195\pi$
$983$	−19.5794	+	6.03946i	−0.624487	+	0.192629i	−0.0336683	+	0.999433i	$0.510719\pi$
$984$	−50.9281	−	7.67617i	−1.62353	−	0.244707i
$985$	−18.1964	−	16.8838i	−0.579786	−	0.537963i
$986$	−0.217446	−	0.952694i	−0.00692490	−	0.0303400i
$987$		0			0
$988$	−0.324217	+	1.42049i	−0.0103147	+	0.0451918i
$989$	−68.4939	+	46.6983i	−2.17798	+	1.48492i
$990$	9.68326	−	8.98475i	0.307754	−	0.285554i
$991$	13.4028	+	9.13786i	0.425753	+	0.290274i	0.757179	−	0.653208i	$-0.226577\pi$
$991$	13.4028	+	9.13786i	0.425753	+	0.290274i	−0.331426	+	0.943481i	$0.607530\pi$
$992$	25.1862	−	3.79620i	0.799661	−	0.120530i
$993$	45.4193	−	21.8728i	1.44134	−	0.694112i
$994$		0			0
$995$	−28.7332	−	13.8372i	−0.910905	−	0.438669i
$996$	−68.2444	−	21.0506i	−2.16241	−	0.667014i
$997$	−12.0822	+	30.7849i	−0.382647	+	0.974968i	0.601700	+	0.798722i	$0.294490\pi$
$997$	−12.0822	+	30.7849i	−0.382647	+	0.974968i	−0.984346	+	0.176245i	$0.943605\pi$
$998$	34.6680	+	60.0467i	1.09739	+	1.90074i
$999$	5.95908	−	10.3214i	0.188537	−	0.326556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.g.h.275.1		48
7.2	even	3		343.2.e.c.148.8		48
7.3	odd	6		49.2.g.a.4.1	✓	48
7.4	even	3		343.2.g.g.263.1		48
7.5	odd	6		343.2.e.d.148.8		48
7.6	odd	2		343.2.g.i.275.1		48
21.17	even	6		441.2.bb.d.298.4		48
28.3	even	6		784.2.bg.c.641.4		48
49.9	even	21		2401.2.a.i.1.2		24
49.12	odd	42		343.2.e.d.197.8		48
49.17	odd	42		343.2.g.i.116.1		48
49.20	odd	14		49.2.g.a.37.1	yes	48
49.29	even	7		343.2.g.g.30.1		48
49.32	even	21	inner	343.2.g.h.116.1		48
49.37	even	21		343.2.e.c.197.8		48
49.40	odd	42		2401.2.a.h.1.2		24
147.20	even	14		441.2.bb.d.37.4		48
196.167	even	14		784.2.bg.c.625.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.4.1	✓	48	7.3	odd	6
49.2.g.a.37.1	yes	48	49.20	odd	14
343.2.e.c.148.8		48	7.2	even	3
343.2.e.c.197.8		48	49.37	even	21
343.2.e.d.148.8		48	7.5	odd	6
343.2.e.d.197.8		48	49.12	odd	42
343.2.g.g.30.1		48	49.29	even	7
343.2.g.g.263.1		48	7.4	even	3
343.2.g.h.116.1		48	49.32	even	21	inner
343.2.g.h.275.1		48	1.1	even	1	trivial
343.2.g.i.116.1		48	49.17	odd	42
343.2.g.i.275.1		48	7.6	odd	2
441.2.bb.d.37.4		48	147.20	even	14
441.2.bb.d.298.4		48	21.17	even	6
784.2.bg.c.625.4		48	196.167	even	14
784.2.bg.c.641.4		48	28.3	even	6
2401.2.a.h.1.2		24	49.40	odd	42
2401.2.a.i.1.2		24	49.9	even	21

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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.189695 + 2.53130i) q^{2} +(-1.83277 + 0.565334i) q^{3} +(-4.39385 - 0.662266i) q^{4} +(-1.83323 - 1.70099i) q^{5} +(-1.08336 - 4.74653i) q^{6} +(1.38019 - 6.04701i) q^{8} +(0.560718 - 0.382291i) q^{9} +O(q^{10})\)	\(q+(-0.189695 + 2.53130i) q^{2} +(-1.83277 + 0.565334i) q^{3} +(-4.39385 - 0.662266i) q^{4} +(-1.83323 - 1.70099i) q^{5} +(-1.08336 - 4.74653i) q^{6} +(1.38019 - 6.04701i) q^{8} +(0.560718 - 0.382291i) q^{9} +(4.65347 - 4.31779i) q^{10} +(2.53345 + 1.72727i) q^{11} +(8.42730 - 1.27021i) q^{12} +(0.101149 - 0.0487107i) q^{13} +(4.32151 + 2.08113i) q^{15} +(6.55286 + 2.02129i) q^{16} +(-0.208963 + 0.532430i) q^{17} +(0.861329 + 1.49187i) q^{18} +(1.46037 - 2.52943i) q^{19} +(6.92842 + 8.68796i) q^{20} +(-4.85283 + 6.08526i) q^{22} +(-2.58072 - 6.57557i) q^{23} +(0.889011 + 11.8630i) q^{24} +(0.0937177 + 1.25058i) q^{25} +(0.104114 + 0.265278i) q^{26} +(2.77598 - 3.48096i) q^{27} +(0.419642 + 0.526214i) q^{29} +(-6.08773 + 10.5443i) q^{30} +(-2.54599 - 4.40979i) q^{31} +(-1.82747 + 4.65633i) q^{32} +(-5.61970 - 1.73345i) q^{33} +(-1.30810 - 0.629948i) q^{34} +(-2.71689 + 1.30838i) q^{36} +(2.64694 - 0.398963i) q^{37} +(6.12572 + 4.17645i) q^{38} +(-0.157844 + 0.146458i) q^{39} +(-12.8161 + 8.73786i) q^{40} +(-0.963373 + 4.22081i) q^{41} +(-2.61140 - 11.4413i) q^{43} +(-9.98766 - 9.26719i) q^{44} +(-1.67820 - 0.252947i) q^{45} +(17.1343 - 5.28524i) q^{46} +(-0.248641 + 3.31788i) q^{47} -13.1526 q^{48} -3.18336 q^{50} +(0.0819805 - 1.09395i) q^{51} +(-0.476692 + 0.147040i) q^{52} +(1.38385 + 0.208582i) q^{53} +(8.28478 + 7.68715i) q^{54} +(-1.70631 - 7.47585i) q^{55} +(-1.24654 + 5.46145i) q^{57} +(-1.41161 + 0.962420i) q^{58} +(-9.39310 + 8.71553i) q^{59} +(-17.6098 - 12.0061i) q^{60} +(-0.539069 + 0.0812516i) q^{61} +(11.6455 - 5.60817i) q^{62} +(0.916925 + 0.441568i) q^{64} +(-0.268285 - 0.0827550i) q^{65} +(5.45391 - 13.8963i) q^{66} +(-2.29219 - 3.97020i) q^{67} +(1.27076 - 2.20102i) q^{68} +(8.44726 + 10.5925i) q^{69} +(0.460966 - 0.578033i) q^{71} +(-1.53782 - 3.91830i) q^{72} +(-1.01418 - 13.5333i) q^{73} +(0.507783 + 6.77590i) q^{74} +(-0.878756 - 2.23903i) q^{75} +(-8.09178 + 10.1468i) q^{76} +(-0.340788 - 0.427334i) q^{78} +(2.00436 - 3.47166i) q^{79} +(-8.57470 - 14.8518i) q^{80} +(-3.86362 + 9.84433i) q^{81} +(-10.5014 - 3.23926i) q^{82} +(-7.54999 - 3.63588i) q^{83} +(1.28873 - 0.620621i) q^{85} +(29.4568 - 4.43990i) q^{86} +(-1.06659 - 0.727190i) q^{87} +(13.9415 - 12.9358i) q^{88} +(8.36412 - 5.70256i) q^{89} +(0.958632 - 4.20004i) q^{90} +(6.98452 + 30.6012i) q^{92} +(7.15922 + 6.64279i) q^{93} +(-8.35140 - 1.25877i) q^{94} +(-6.97971 + 2.15295i) q^{95} +(0.716955 - 9.56710i) q^{96} -12.9089 q^{97} +2.08087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} + 12 q^{4} - 7 q^{5} - 20 q^{8} - 15 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 + 12 * q^4 - 7 * q^5 - 20 * q^8 - 15 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} + 12 q^{4} - 7 q^{5} - 20 q^{8} - 15 q^{9} - 7 q^{10} - 3 q^{11} + 63 q^{12} + 14 q^{13} - 12 q^{15} + 18 q^{16} - 14 q^{17} + 2 q^{18} - 21 q^{19} - 14 q^{20} - 20 q^{22} - 27 q^{23} + 77 q^{24} + 17 q^{25} + 21 q^{26} - 7 q^{27} + 12 q^{29} + 11 q^{30} - 35 q^{31} - 60 q^{32} - 7 q^{33} - 70 q^{34} - 12 q^{36} - 6 q^{37} - 35 q^{38} + 35 q^{39} - 105 q^{40} + 42 q^{41} - 30 q^{43} + 13 q^{44} + 35 q^{45} + 69 q^{46} + 42 q^{47} + 84 q^{48} + 40 q^{50} + 53 q^{51} + 7 q^{52} - 31 q^{53} - 70 q^{54} + 7 q^{55} - 12 q^{57} - 47 q^{58} - 35 q^{59} - 91 q^{60} + 14 q^{61} + 28 q^{62} - 32 q^{64} + 35 q^{65} + 35 q^{66} + 11 q^{67} - 77 q^{68} - 70 q^{69} + 19 q^{71} - 124 q^{72} + 35 q^{73} + 13 q^{74} + 119 q^{75} - 119 q^{76} + 28 q^{78} + 15 q^{79} - 70 q^{80} - 125 q^{81} + 98 q^{82} - 26 q^{85} + 9 q^{86} - 35 q^{87} + 49 q^{88} + 14 q^{89} + 182 q^{90} - 38 q^{92} + 46 q^{93} - 14 q^{94} + 128 q^{95} - 98 q^{96} - 16 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 + 12 * q^4 - 7 * q^5 - 20 * q^8 - 15 * q^9 - 7 * q^10 - 3 * q^11 + 63 * q^12 + 14 * q^13 - 12 * q^15 + 18 * q^16 - 14 * q^17 + 2 * q^18 - 21 * q^19 - 14 * q^20 - 20 * q^22 - 27 * q^23 + 77 * q^24 + 17 * q^25 + 21 * q^26 - 7 * q^27 + 12 * q^29 + 11 * q^30 - 35 * q^31 - 60 * q^32 - 7 * q^33 - 70 * q^34 - 12 * q^36 - 6 * q^37 - 35 * q^38 + 35 * q^39 - 105 * q^40 + 42 * q^41 - 30 * q^43 + 13 * q^44 + 35 * q^45 + 69 * q^46 + 42 * q^47 + 84 * q^48 + 40 * q^50 + 53 * q^51 + 7 * q^52 - 31 * q^53 - 70 * q^54 + 7 * q^55 - 12 * q^57 - 47 * q^58 - 35 * q^59 - 91 * q^60 + 14 * q^61 + 28 * q^62 - 32 * q^64 + 35 * q^65 + 35 * q^66 + 11 * q^67 - 77 * q^68 - 70 * q^69 + 19 * q^71 - 124 * q^72 + 35 * q^73 + 13 * q^74 + 119 * q^75 - 119 * q^76 + 28 * q^78 + 15 * q^79 - 70 * q^80 - 125 * q^81 + 98 * q^82 - 26 * q^85 + 9 * q^86 - 35 * q^87 + 49 * q^88 + 14 * q^89 + 182 * q^90 - 38 * q^92 + 46 * q^93 - 14 * q^94 + 128 * q^95 - 98 * q^96 - 16 * q^99

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