LMFDB - Embedded newform 847.2.f.d.729.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	847.729
Dual form			847.2.f.d.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.224514i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.500000 - 0.363271i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.454915 + 1.40008i) q^{8} +(0.309017 - 0.224514i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.224514i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.500000 - 0.363271i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.454915 + 1.40008i) q^{8} +(0.309017 - 0.224514i) q^{9} -0.381966 q^{10} +3.00000 q^{12} +(1.00000 - 0.726543i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-2.54508 - 1.84911i) q^{16} +(-2.50000 - 1.81636i) q^{17} +(0.0450850 - 0.138757i) q^{18} +(-0.545085 - 1.67760i) q^{19} +(1.50000 - 1.08981i) q^{20} -1.61803 q^{21} +5.09017 q^{23} +(1.92705 - 1.40008i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(0.145898 - 0.449028i) q^{26} +(-4.42705 - 3.21644i) q^{27} +(1.50000 + 1.08981i) q^{28} +(-1.42705 + 4.39201i) q^{29} +(0.190983 + 0.587785i) q^{30} +(3.42705 - 2.48990i) q^{31} -4.14590 q^{32} -1.18034 q^{34} +(-0.809017 + 0.587785i) q^{35} +(0.218847 + 0.673542i) q^{36} +(2.00000 - 6.15537i) q^{37} +(-0.545085 - 0.396027i) q^{38} +(-1.61803 - 1.17557i) q^{39} +(0.454915 - 1.40008i) q^{40} +(-3.45492 - 10.6331i) q^{41} +(-0.500000 + 0.363271i) q^{42} -12.5623 q^{43} -0.381966 q^{45} +(1.57295 - 1.14281i) q^{46} +(-2.04508 - 6.29412i) q^{47} +(-1.57295 + 4.84104i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.23607 - 0.898056i) q^{50} +(-1.54508 + 4.75528i) q^{51} +(0.708204 + 2.17963i) q^{52} +(1.92705 - 1.40008i) q^{53} -2.09017 q^{54} +1.47214 q^{56} +(-2.30902 + 1.67760i) q^{57} +(0.545085 + 1.67760i) q^{58} +(3.42705 - 10.5474i) q^{59} +(-2.42705 - 1.76336i) q^{60} +(6.16312 + 4.47777i) q^{61} +(0.500000 - 1.53884i) q^{62} +(-0.118034 - 0.363271i) q^{63} +(3.80902 - 2.76741i) q^{64} -1.23607 q^{65} -8.32624 q^{67} +(4.63525 - 3.36771i) q^{68} +(-2.54508 - 7.83297i) q^{69} +(-0.118034 + 0.363271i) q^{70} +(13.0172 + 9.45756i) q^{71} +(0.454915 + 0.330515i) q^{72} +(-4.39919 + 13.5393i) q^{73} +(-0.763932 - 2.35114i) q^{74} +(-5.23607 + 3.80423i) q^{75} +3.27051 q^{76} -0.763932 q^{78} +(-5.16312 + 3.75123i) q^{79} +(0.972136 + 2.99193i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(-3.45492 - 2.51014i) q^{82} +(-2.19098 - 1.59184i) q^{83} +(0.927051 - 2.85317i) q^{84} +(0.954915 + 2.93893i) q^{85} +(-3.88197 + 2.82041i) q^{86} +7.47214 q^{87} +6.85410 q^{89} +(-0.118034 + 0.0857567i) q^{90} +(-0.381966 - 1.17557i) q^{91} +(-2.91641 + 8.97578i) q^{92} +(-5.54508 - 4.02874i) q^{93} +(-2.04508 - 1.48584i) q^{94} +(-0.545085 + 1.67760i) q^{95} +(2.07295 + 6.37988i) q^{96} +(-5.66312 + 4.11450i) q^{97} -0.381966 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 2 q^{3} - 9 q^{4} - q^{5} - 2 q^{6} - q^{7} + 13 q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 - 2 * q^3 - 9 * q^4 - q^5 - 2 * q^6 - q^7 + 13 * q^8 - q^9	$ 4 q - q^{2} - 2 q^{3} - 9 q^{4} - q^{5} - 2 q^{6} - q^{7} + 13 q^{8} - q^{9} - 6 q^{10} + 12 q^{12} + 4 q^{13} + 4 q^{14} - 2 q^{15} + q^{16} - 10 q^{17} - 11 q^{18} + 9 q^{19} + 6 q^{20} - 2 q^{21} - 2 q^{23} + q^{24} + 4 q^{25} + 14 q^{26} - 11 q^{27} + 6 q^{28} + q^{29} + 3 q^{30} + 7 q^{31} - 30 q^{32} + 40 q^{34} - q^{35} + 21 q^{36} + 8 q^{37} + 9 q^{38} - 2 q^{39} + 13 q^{40} - 25 q^{41} - 2 q^{42} - 10 q^{43} - 6 q^{45} + 13 q^{46} + 3 q^{47} - 13 q^{48} - q^{49} + 4 q^{50} + 5 q^{51} - 24 q^{52} + q^{53} + 14 q^{54} - 12 q^{56} - 7 q^{57} - 9 q^{58} + 7 q^{59} - 3 q^{60} + 9 q^{61} + 2 q^{62} + 4 q^{63} + 13 q^{64} + 4 q^{65} - 2 q^{67} - 15 q^{68} + q^{69} + 4 q^{70} + 23 q^{71} + 13 q^{72} + 7 q^{73} - 12 q^{74} - 12 q^{75} - 54 q^{76} - 12 q^{78} - 5 q^{79} - 14 q^{80} - 14 q^{81} - 25 q^{82} - 11 q^{83} - 3 q^{84} + 15 q^{85} - 20 q^{86} + 12 q^{87} + 14 q^{89} + 4 q^{90} - 6 q^{91} + 42 q^{92} - 11 q^{93} + 3 q^{94} + 9 q^{95} + 15 q^{96} - 7 q^{97} - 6 q^{98}+O(q^{100}) $ 4 * q - q^2 - 2 * q^3 - 9 * q^4 - q^5 - 2 * q^6 - q^7 + 13 * q^8 - q^9 - 6 * q^10 + 12 * q^12 + 4 * q^13 + 4 * q^14 - 2 * q^15 + q^16 - 10 * q^17 - 11 * q^18 + 9 * q^19 + 6 * q^20 - 2 * q^21 - 2 * q^23 + q^24 + 4 * q^25 + 14 * q^26 - 11 * q^27 + 6 * q^28 + q^29 + 3 * q^30 + 7 * q^31 - 30 * q^32 + 40 * q^34 - q^35 + 21 * q^36 + 8 * q^37 + 9 * q^38 - 2 * q^39 + 13 * q^40 - 25 * q^41 - 2 * q^42 - 10 * q^43 - 6 * q^45 + 13 * q^46 + 3 * q^47 - 13 * q^48 - q^49 + 4 * q^50 + 5 * q^51 - 24 * q^52 + q^53 + 14 * q^54 - 12 * q^56 - 7 * q^57 - 9 * q^58 + 7 * q^59 - 3 * q^60 + 9 * q^61 + 2 * q^62 + 4 * q^63 + 13 * q^64 + 4 * q^65 - 2 * q^67 - 15 * q^68 + q^69 + 4 * q^70 + 23 * q^71 + 13 * q^72 + 7 * q^73 - 12 * q^74 - 12 * q^75 - 54 * q^76 - 12 * q^78 - 5 * q^79 - 14 * q^80 - 14 * q^81 - 25 * q^82 - 11 * q^83 - 3 * q^84 + 15 * q^85 - 20 * q^86 + 12 * q^87 + 14 * q^89 + 4 * q^90 - 6 * q^91 + 42 * q^92 - 11 * q^93 + 3 * q^94 + 9 * q^95 + 15 * q^96 - 7 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.309017	−	0.224514i	0.218508	−	0.158755i	−0.473147	−	0.880984i	$-0.656882\pi$
$2$	0.309017	−	0.224514i	0.218508	−	0.158755i	0.691655	+	0.722228i	$0.256882\pi$
$3$	−0.500000	−	1.53884i	−0.288675	−	0.888451i	−0.985273	−	0.170989i	$-0.945304\pi$
$3$	−0.500000	−	1.53884i	−0.288675	−	0.888451i	0.696598	−	0.717462i	$-0.254696\pi$
$4$	−0.572949	+	1.76336i	−0.286475	+	0.881678i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i	0.392000	−	0.919965i	$-0.371783\pi$
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i	−0.753804	+	0.657099i	$0.771783\pi$
$6$	−0.500000	−	0.363271i	−0.204124	−	0.148305i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.454915	+	1.40008i	0.160837	+	0.495005i
$9$	0.309017	−	0.224514i	0.103006	−	0.0748380i
$10$	−0.381966			−0.120788
$11$		0			0
$11$		0			0
$12$	3.00000			0.866025
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	−0.440411	−	0.897796i	$-0.645167\pi$
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	0.717761	+	0.696290i	$0.245167\pi$
$14$	−0.118034	−	0.363271i	−0.0315459	−	0.0970883i
$15$	−0.500000	+	1.53884i	−0.129099	+	0.397327i
$16$	−2.54508	−	1.84911i	−0.636271	−	0.462278i
$17$	−2.50000	−	1.81636i	−0.606339	−	0.440531i	0.241784	−	0.970330i	$-0.422267\pi$
$17$	−2.50000	−	1.81636i	−0.606339	−	0.440531i	−0.848123	+	0.529799i	$0.822267\pi$
$18$	0.0450850	−	0.138757i	0.0106266	−	0.0327054i
$19$	−0.545085	−	1.67760i	−0.125051	−	0.384868i	0.868859	−	0.495059i	$-0.164854\pi$
$19$	−0.545085	−	1.67760i	−0.125051	−	0.384868i	−0.993910	+	0.110191i	$0.964854\pi$
$20$	1.50000	−	1.08981i	0.335410	−	0.243690i
$21$	−1.61803			−0.353084
$22$		0			0
$23$	5.09017			1.06137			0.530687	−	0.847568i	$-0.321934\pi$
$23$	5.09017			1.06137			0.530687	+	0.847568i	$0.321934\pi$
$24$	1.92705	−	1.40008i	0.393358	−	0.285791i
$25$	−1.23607	−	3.80423i	−0.247214	−	0.760845i
$26$	0.145898	−	0.449028i	0.0286130	−	0.0880616i
$27$	−4.42705	−	3.21644i	−0.851986	−	0.619004i
$28$	1.50000	+	1.08981i	0.283473	+	0.205955i
$29$	−1.42705	+	4.39201i	−0.264997	+	0.815576i	0.726697	+	0.686958i	$0.241054\pi$
$29$	−1.42705	+	4.39201i	−0.264997	+	0.815576i	−0.991694	+	0.128618i	$0.958946\pi$
$30$	0.190983	+	0.587785i	0.0348686	+	0.107314i
$31$	3.42705	−	2.48990i	0.615517	−	0.447199i	−0.235836	−	0.971793i	$-0.575783\pi$
$31$	3.42705	−	2.48990i	0.615517	−	0.447199i	0.851353	+	0.524594i	$0.175783\pi$
$32$	−4.14590			−0.732898
$33$		0			0
$34$	−1.18034			−0.202427
$35$	−0.809017	+	0.587785i	−0.136749	+	0.0993538i
$36$	0.218847	+	0.673542i	0.0364745	+	0.112257i
$37$	2.00000	−	6.15537i	0.328798	−	1.01194i	−0.640899	−	0.767625i	$-0.721438\pi$
$37$	2.00000	−	6.15537i	0.328798	−	1.01194i	0.969697	−	0.244311i	$-0.0785617\pi$
$38$	−0.545085	−	0.396027i	−0.0884245	−	0.0642441i
$39$	−1.61803	−	1.17557i	−0.259093	−	0.188242i
$40$	0.454915	−	1.40008i	0.0719284	−	0.221373i
$41$	−3.45492	−	10.6331i	−0.539567	−	1.66062i	−0.733569	−	0.679615i	$-0.762147\pi$
$41$	−3.45492	−	10.6331i	−0.539567	−	1.66062i	0.194001	−	0.981001i	$-0.437853\pi$
$42$	−0.500000	+	0.363271i	−0.0771517	+	0.0560540i
$43$	−12.5623			−1.91573			−0.957867	−	0.287213i	$-0.907271\pi$
$43$	−12.5623			−1.91573			−0.957867	+	0.287213i	$0.907271\pi$
$44$		0			0
$45$	−0.381966			−0.0569401
$46$	1.57295	−	1.14281i	0.231919	−	0.168499i
$47$	−2.04508	−	6.29412i	−0.298306	−	0.918092i	−0.982091	−	0.188408i	$-0.939667\pi$
$47$	−2.04508	−	6.29412i	−0.298306	−	0.918092i	0.683784	−	0.729684i	$-0.260333\pi$
$48$	−1.57295	+	4.84104i	−0.227036	+	0.698744i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−1.23607	−	0.898056i	−0.174806	−	0.127004i
$51$	−1.54508	+	4.75528i	−0.216355	+	0.665873i
$52$	0.708204	+	2.17963i	0.0982102	+	0.302260i
$53$	1.92705	−	1.40008i	0.264701	−	0.192316i	−0.447516	−	0.894276i	$-0.647691\pi$
$53$	1.92705	−	1.40008i	0.264701	−	0.192316i	0.712217	+	0.701960i	$0.247691\pi$
$54$	−2.09017			−0.284436
$55$		0			0
$56$	1.47214			0.196722
$57$	−2.30902	+	1.67760i	−0.305837	+	0.222203i
$58$	0.545085	+	1.67760i	0.0715732	+	0.220280i
$59$	3.42705	−	10.5474i	0.446164	−	1.37315i	−0.435038	−	0.900412i	$-0.643265\pi$
$59$	3.42705	−	10.5474i	0.446164	−	1.37315i	0.881202	−	0.472740i	$-0.156735\pi$
$60$	−2.42705	−	1.76336i	−0.313331	−	0.227648i
$61$	6.16312	+	4.47777i	0.789107	+	0.573319i	0.907698	−	0.419624i	$-0.137838\pi$
$61$	6.16312	+	4.47777i	0.789107	+	0.573319i	−0.118592	+	0.992943i	$0.537838\pi$
$62$	0.500000	−	1.53884i	0.0635001	−	0.195433i
$63$	−0.118034	−	0.363271i	−0.0148709	−	0.0457679i
$64$	3.80902	−	2.76741i	0.476127	−	0.345927i
$65$	−1.23607			−0.153315
$66$		0			0
$67$	−8.32624			−1.01721			−0.508606	−	0.860999i	$-0.669839\pi$
$67$	−8.32624			−1.01721			−0.508606	+	0.860999i	$0.669839\pi$
$68$	4.63525	−	3.36771i	0.562107	−	0.408395i
$69$	−2.54508	−	7.83297i	−0.306392	−	0.942978i
$70$	−0.118034	+	0.363271i	−0.0141078	+	0.0434192i
$71$	13.0172	+	9.45756i	1.54486	+	1.12241i	0.947194	+	0.320661i	$0.103905\pi$
$71$	13.0172	+	9.45756i	1.54486	+	1.12241i	0.597666	+	0.801745i	$0.296095\pi$
$72$	0.454915	+	0.330515i	0.0536123	+	0.0389516i
$73$	−4.39919	+	13.5393i	−0.514886	+	1.58466i	0.268604	+	0.963251i	$0.413438\pi$
$73$	−4.39919	+	13.5393i	−0.514886	+	1.58466i	−0.783490	+	0.621405i	$0.786562\pi$
$74$	−0.763932	−	2.35114i	−0.0888053	−	0.273315i
$75$	−5.23607	+	3.80423i	−0.604609	+	0.439274i
$76$	3.27051			0.375153
$77$		0			0
$78$	−0.763932			−0.0864983
$79$	−5.16312	+	3.75123i	−0.580896	+	0.422046i	−0.839047	−	0.544059i	$-0.816887\pi$
$79$	−5.16312	+	3.75123i	−0.580896	+	0.422046i	0.258151	+	0.966105i	$0.416887\pi$
$80$	0.972136	+	2.99193i	0.108688	+	0.334508i
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$	−3.45492	−	2.51014i	−0.381532	−	0.277199i
$83$	−2.19098	−	1.59184i	−0.240492	−	0.174727i	0.461011	−	0.887395i	$-0.347487\pi$
$83$	−2.19098	−	1.59184i	−0.240492	−	0.174727i	−0.701502	+	0.712667i	$0.747487\pi$
$84$	0.927051	−	2.85317i	0.101150	−	0.311306i
$85$	0.954915	+	2.93893i	0.103575	+	0.318771i
$86$	−3.88197	+	2.82041i	−0.418603	+	0.304133i
$87$	7.47214			0.801097
$88$		0			0
$89$	6.85410			0.726533			0.363267	−	0.931685i	$-0.381661\pi$
$89$	6.85410			0.726533			0.363267	+	0.931685i	$0.381661\pi$
$90$	−0.118034	+	0.0857567i	−0.0124419	+	0.00903955i
$91$	−0.381966	−	1.17557i	−0.0400409	−	0.123233i
$92$	−2.91641	+	8.97578i	−0.304057	+	0.935790i
$93$	−5.54508	−	4.02874i	−0.574999	−	0.417761i
$94$	−2.04508	−	1.48584i	−0.210934	−	0.153253i
$95$	−0.545085	+	1.67760i	−0.0559245	+	0.172118i
$96$	2.07295	+	6.37988i	0.211569	+	0.651144i
$97$	−5.66312	+	4.11450i	−0.575003	+	0.417764i	−0.836919	−	0.547327i	$-0.815646\pi$
$97$	−5.66312	+	4.11450i	−0.575003	+	0.417764i	0.261916	+	0.965091i	$0.415646\pi$
$98$	−0.381966			−0.0385844
$99$		0			0
$100$	7.41641			0.741641
$101$	11.9721	−	8.69827i	1.19127	−	0.865510i	0.197874	−	0.980227i	$-0.436596\pi$
$101$	11.9721	−	8.69827i	1.19127	−	0.865510i	0.993398	+	0.114718i	$0.0365963\pi$
$102$	0.590170	+	1.81636i	0.0584355	+	0.179846i
$103$	2.73607	−	8.42075i	0.269593	−	0.829721i	−0.721007	−	0.692928i	$-0.756320\pi$
$103$	2.73607	−	8.42075i	0.269593	−	0.829721i	0.990600	−	0.136793i	$-0.0436796\pi$
$104$	1.47214	+	1.06957i	0.144355	+	0.104880i
$105$	1.30902	+	0.951057i	0.127747	+	0.0928136i
$106$	0.281153	−	0.865300i	0.0273080	−	0.0840453i
$107$	0.836881	+	2.57565i	0.0809043	+	0.248998i	0.983325	−	0.181859i	$-0.0582114\pi$
$107$	0.836881	+	2.57565i	0.0809043	+	0.248998i	−0.902420	+	0.430857i	$0.858211\pi$
$108$	8.20820	−	5.96361i	0.789835	−	0.573849i
$109$	−1.52786			−0.146343			−0.0731714	−	0.997319i	$-0.523312\pi$
$109$	−1.52786			−0.146343			−0.0731714	+	0.997319i	$0.523312\pi$
$110$		0			0
$111$	−10.4721			−0.993971
$112$	−2.54508	+	1.84911i	−0.240488	+	0.174725i
$113$	0.0450850	+	0.138757i	0.00424124	+	0.0130532i	0.953155	−	0.302483i	$-0.0978156\pi$
$113$	0.0450850	+	0.138757i	0.00424124	+	0.0130532i	−0.948914	+	0.315536i	$0.897816\pi$
$114$	−0.336881	+	1.03681i	−0.0315518	+	0.0971065i
$115$	−4.11803	−	2.99193i	−0.384009	−	0.278999i
$116$	−6.92705	−	5.03280i	−0.643161	−	0.467283i
$117$	0.145898	−	0.449028i	0.0134883	−	0.0415127i
$118$	−1.30902	−	4.02874i	−0.120505	−	0.370876i
$119$	−2.50000	+	1.81636i	−0.229175	+	0.166505i
$120$	−2.38197			−0.217443
$121$		0			0
$122$	2.90983			0.263444
$123$	−14.6353	+	10.6331i	−1.31962	+	0.958758i
$124$	2.42705	+	7.46969i	0.217956	+	0.670798i
$125$	−2.78115	+	8.55951i	−0.248754	+	0.765586i
$126$	−0.118034	−	0.0857567i	−0.0105153	−	0.00763982i
$127$	−2.38197	−	1.73060i	−0.211365	−	0.153566i	0.477066	−	0.878868i	$-0.341700\pi$
$127$	−2.38197	−	1.73060i	−0.211365	−	0.153566i	−0.688431	+	0.725302i	$0.741700\pi$
$128$	3.11803	−	9.59632i	0.275598	−	0.848203i
$129$	6.28115	+	19.3314i	0.553025	+	1.70203i
$130$	−0.381966	+	0.277515i	−0.0335006	+	0.0243396i
$131$	18.9443			1.65517			0.827584	−	0.561341i	$-0.189715\pi$
$131$	18.9443			1.65517			0.827584	+	0.561341i	$0.189715\pi$
$132$		0			0
$133$	−1.76393			−0.152952
$134$	−2.57295	+	1.86936i	−0.222269	+	0.161488i
$135$	1.69098	+	5.20431i	0.145537	+	0.447916i
$136$	1.40576	−	4.32650i	0.120543	−	0.370994i
$137$	12.3992	+	9.00854i	1.05933	+	0.769651i	0.973965	−	0.226698i	$-0.0727931\pi$
$137$	12.3992	+	9.00854i	1.05933	+	0.769651i	0.0853690	+	0.996349i	$0.472793\pi$
$138$	−2.54508	−	1.84911i	−0.216652	−	0.157407i
$139$	3.69098	−	11.3597i	0.313065	−	0.963515i	−0.663478	−	0.748195i	$-0.730921\pi$
$139$	3.69098	−	11.3597i	0.313065	−	0.963515i	0.976544	−	0.215320i	$-0.0690794\pi$
$140$	−0.572949	−	1.76336i	−0.0484230	−	0.149031i
$141$	−8.66312	+	6.29412i	−0.729566	+	0.530061i
$142$	6.14590			0.515752
$143$		0			0
$144$	−1.20163			−0.100136
$145$	3.73607	−	2.71441i	0.310264	−	0.225420i
$146$	1.68034	+	5.17155i	0.139066	+	0.428001i
$147$	−0.500000	+	1.53884i	−0.0412393	+	0.126922i
$148$	9.70820	+	7.05342i	0.798009	+	0.579788i
$149$	7.16312	+	5.20431i	0.586826	+	0.426354i	0.841178	−	0.540758i	$-0.181862\pi$
$149$	7.16312	+	5.20431i	0.586826	+	0.426354i	−0.254353	+	0.967112i	$0.581862\pi$
$150$	−0.763932	+	2.35114i	−0.0623748	+	0.191970i
$151$	0.0172209	+	0.0530006i	0.00140142	+	0.00431312i	0.951755	−	0.306860i	$-0.0992782\pi$
$151$	0.0172209	+	0.0530006i	0.00140142	+	0.00431312i	−0.950353	+	0.311173i	$0.899278\pi$
$152$	2.10081	−	1.52633i	0.170398	−	0.123802i
$153$	−1.18034			−0.0954248
$154$		0			0
$155$	−4.23607			−0.340249
$156$	3.00000	−	2.17963i	0.240192	−	0.174510i
$157$	6.14590	+	18.9151i	0.490496	+	1.50959i	0.823860	+	0.566793i	$0.191816\pi$
$157$	6.14590	+	18.9151i	0.490496	+	1.50959i	−0.333364	+	0.942798i	$0.608184\pi$
$158$	−0.753289	+	2.31838i	−0.0599284	+	0.184441i
$159$	−3.11803	−	2.26538i	−0.247276	−	0.179657i
$160$	3.35410	+	2.43690i	0.265165	+	0.192654i
$161$	1.57295	−	4.84104i	0.123966	−	0.381527i
$162$	0.909830	+	2.80017i	0.0714830	+	0.220002i
$163$	7.04508	−	5.11855i	0.551814	−	0.400916i	−0.276640	−	0.960974i	$-0.589221\pi$
$163$	7.04508	−	5.11855i	0.551814	−	0.400916i	0.828454	+	0.560058i	$0.189221\pi$
$164$	20.7295			1.61870
$165$		0			0
$166$	−1.03444			−0.0802883
$167$	−5.23607	+	3.80423i	−0.405179	+	0.294380i	−0.771647	−	0.636051i	$-0.780567\pi$
$167$	−5.23607	+	3.80423i	−0.405179	+	0.294380i	0.366468	+	0.930431i	$0.380567\pi$
$168$	−0.736068	−	2.26538i	−0.0567889	−	0.174778i
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$	0.954915	+	0.693786i	0.0732386	+	0.0532110i
$171$	−0.545085	−	0.396027i	−0.0416837	−	0.0302850i
$172$	7.19756	−	22.1518i	0.548809	−	1.68906i
$173$	−4.75329	−	14.6291i	−0.361386	−	1.11223i	−0.952213	−	0.305433i	$-0.901199\pi$
$173$	−4.75329	−	14.6291i	−0.361386	−	1.11223i	0.590828	−	0.806798i	$-0.298801\pi$
$174$	2.30902	−	1.67760i	0.175046	−	0.127178i
$175$	−4.00000			−0.302372
$176$		0			0
$177$	−17.9443			−1.34877
$178$	2.11803	−	1.53884i	0.158753	−	0.115341i
$179$	−1.16312	−	3.57971i	−0.0869356	−	0.267560i	0.898133	−	0.439725i	$-0.144924\pi$
$179$	−1.16312	−	3.57971i	−0.0869356	−	0.267560i	−0.985068	+	0.172164i	$0.944924\pi$
$180$	0.218847	−	0.673542i	0.0163119	−	0.0502029i
$181$	6.00000	+	4.35926i	0.445976	+	0.324021i	0.788005	−	0.615669i	$-0.211114\pi$
$181$	6.00000	+	4.35926i	0.445976	+	0.324021i	−0.342029	+	0.939690i	$0.611114\pi$
$182$	−0.381966	−	0.277515i	−0.0283132	−	0.0205707i
$183$	3.80902	−	11.7229i	0.281571	−	0.866585i
$184$	2.31559	+	7.12667i	0.170708	+	0.525385i
$185$	−5.23607	+	3.80423i	−0.384963	+	0.279692i
$186$	−2.61803			−0.191964
$187$		0			0
$188$	12.2705			0.894919
$189$	−4.42705	+	3.21644i	−0.322021	+	0.233962i
$190$	0.208204	+	0.640786i	0.0151047	+	0.0464875i
$191$	4.87132	−	14.9924i	0.352477	−	1.08481i	−0.604982	−	0.796239i	$-0.706820\pi$
$191$	4.87132	−	14.9924i	0.352477	−	1.08481i	0.957458	−	0.288572i	$-0.0931804\pi$
$192$	−6.16312	−	4.47777i	−0.444785	−	0.323155i
$193$	12.3992	+	9.00854i	0.892513	+	0.648449i	0.936532	−	0.350582i	$-0.114016\pi$
$193$	12.3992	+	9.00854i	0.892513	+	0.648449i	−0.0440190	+	0.999031i	$0.514016\pi$
$194$	−0.826238	+	2.54290i	−0.0593204	+	0.182569i
$195$	0.618034	+	1.90211i	0.0442583	+	0.136213i
$196$	1.50000	−	1.08981i	0.107143	−	0.0778438i
$197$	−4.29180			−0.305778			−0.152889	−	0.988243i	$-0.548858\pi$
$197$	−4.29180			−0.305778			−0.152889	+	0.988243i	$0.548858\pi$
$198$		0			0
$199$	−8.23607			−0.583839			−0.291920	−	0.956443i	$-0.594294\pi$
$199$	−8.23607			−0.583839			−0.291920	+	0.956443i	$0.594294\pi$
$200$	4.76393	−	3.46120i	0.336861	−	0.244744i
$201$	4.16312	+	12.8128i	0.293644	+	0.903743i
$202$	1.74671	−	5.37582i	0.122898	−	0.378242i
$203$	3.73607	+	2.71441i	0.262221	+	0.190514i
$204$	−7.50000	−	5.44907i	−0.525105	−	0.381511i
$205$	−3.45492	+	10.6331i	−0.241302	+	0.742650i
$206$	−1.04508	−	3.21644i	−0.0728145	−	0.224100i
$207$	1.57295	−	1.14281i	0.109328	−	0.0794311i
$208$	−3.88854			−0.269622
$209$		0			0
$210$	0.618034			0.0426484
$211$	−12.6353	+	9.18005i	−0.869847	+	0.631981i	−0.930546	−	0.366175i	$-0.880667\pi$
$211$	−12.6353	+	9.18005i	−0.869847	+	0.631981i	0.0606990	+	0.998156i	$0.480667\pi$
$212$	1.36475	+	4.20025i	0.0937311	+	0.288475i
$213$	8.04508	−	24.7602i	0.551240	−	1.69654i
$214$	0.836881	+	0.608030i	0.0572080	+	0.0415641i
$215$	10.1631	+	7.38394i	0.693119	+	0.503580i
$216$	2.48936	−	7.66145i	0.169379	−	0.521296i
$217$	−1.30902	−	4.02874i	−0.0888619	−	0.273489i
$218$	−0.472136	+	0.343027i	−0.0319771	+	0.0232327i
$219$	23.0344			1.55652
$220$		0			0
$221$	−3.81966			−0.256938
$222$	−3.23607	+	2.35114i	−0.217191	+	0.157798i
$223$	0.628677	+	1.93487i	0.0420993	+	0.129568i	0.969897	−	0.243515i	$-0.0783005\pi$
$223$	0.628677	+	1.93487i	0.0420993	+	0.129568i	−0.927798	+	0.373083i	$0.878301\pi$
$224$	−1.28115	+	3.94298i	−0.0856006	+	0.263452i
$225$	−1.23607	−	0.898056i	−0.0824045	−	0.0598704i
$226$	0.0450850	+	0.0327561i	0.00299901	+	0.00217891i
$227$	−4.95492	+	15.2497i	−0.328869	+	1.01216i	0.640794	+	0.767713i	$0.278605\pi$
$227$	−4.95492	+	15.2497i	−0.328869	+	1.01216i	−0.969664	+	0.244443i	$0.921395\pi$
$228$	−1.63525	−	5.03280i	−0.108297	−	0.333305i
$229$	−5.47214	+	3.97574i	−0.361609	+	0.262724i	−0.753723	−	0.657192i	$-0.771744\pi$
$229$	−5.47214	+	3.97574i	−0.361609	+	0.262724i	0.392114	+	0.919917i	$0.371744\pi$
$230$	−1.94427			−0.128201
$231$		0			0
$232$	−6.79837			−0.446335
$233$	23.7984	−	17.2905i	1.55908	−	1.13274i	0.622327	−	0.782757i	$-0.286187\pi$
$233$	23.7984	−	17.2905i	1.55908	−	1.13274i	0.936756	−	0.349983i	$-0.113813\pi$
$234$	−0.0557281	−	0.171513i	−0.00364306	−	0.0112122i
$235$	−2.04508	+	6.29412i	−0.133407	+	0.410583i
$236$	16.6353	+	12.0862i	1.08286	+	0.786746i
$237$	8.35410	+	6.06961i	0.542657	+	0.394264i
$238$	−0.364745	+	1.12257i	−0.0236429	+	0.0727654i
$239$	−5.28115	−	16.2537i	−0.341609	−	1.05137i	−0.963374	−	0.268161i	$-0.913584\pi$
$239$	−5.28115	−	16.2537i	−0.341609	−	1.05137i	0.621765	−	0.783204i	$-0.286416\pi$
$240$	4.11803	−	2.99193i	0.265818	−	0.193128i
$241$	16.2705			1.04808			0.524038	−	0.851695i	$-0.324425\pi$
$241$	16.2705			1.04808			0.524038	+	0.851695i	$0.324425\pi$
$242$		0			0
$243$	−3.94427			−0.253025
$244$	−11.4271	+	8.30224i	−0.731542	+	0.531496i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	−2.13525	+	6.57164i	−0.136139	+	0.418992i
$247$	−1.76393	−	1.28157i	−0.112236	−	0.0815445i
$248$	5.04508	+	3.66547i	0.320363	+	0.232758i
$249$	−1.35410	+	4.16750i	−0.0858127	+	0.264104i
$250$	1.06231	+	3.26944i	0.0671861	+	0.206778i
$251$	−18.6074	+	13.5191i	−1.17449	+	0.853316i	−0.991539	−	0.129807i	$-0.958564\pi$
$251$	−18.6074	+	13.5191i	−1.17449	+	0.853316i	−0.182949	+	0.983122i	$0.558564\pi$
$252$	0.708204			0.0446127
$253$		0			0
$254$	−1.12461			−0.0705644
$255$	4.04508	−	2.93893i	0.253313	−	0.184043i
$256$	1.71885	+	5.29007i	0.107428	+	0.330629i
$257$	−2.64590	+	8.14324i	−0.165047	+	0.507961i	−0.999040	−	0.0438137i	$-0.986049\pi$
$257$	−2.64590	+	8.14324i	−0.165047	+	0.507961i	0.833993	+	0.551775i	$0.186049\pi$
$258$	6.28115	+	4.56352i	0.391048	+	0.284113i
$259$	−5.23607	−	3.80423i	−0.325353	−	0.236383i
$260$	0.708204	−	2.17963i	0.0439209	−	0.135175i
$261$	0.545085	+	1.67760i	0.0337399	+	0.103841i
$262$	5.85410	−	4.25325i	0.361668	−	0.262767i
$263$	−17.1246			−1.05595			−0.527974	−	0.849260i	$-0.677048\pi$
$263$	−17.1246			−1.05595			−0.527974	+	0.849260i	$0.677048\pi$
$264$		0			0
$265$	−2.38197			−0.146323
$266$	−0.545085	+	0.396027i	−0.0334213	+	0.0242820i
$267$	−3.42705	−	10.5474i	−0.209732	−	0.645489i
$268$	4.77051	−	14.6821i	0.291405	−	0.896853i
$269$	−13.6353	−	9.90659i	−0.831356	−	0.604016i	0.0885865	−	0.996068i	$-0.471765\pi$
$269$	−13.6353	−	9.90659i	−0.831356	−	0.604016i	−0.919943	+	0.392053i	$0.871765\pi$
$270$	1.69098	+	1.22857i	0.102910	+	0.0747685i
$271$	−1.48278	+	4.56352i	−0.0900724	+	0.277214i	−0.985938	−	0.167110i	$-0.946556\pi$
$271$	−1.48278	+	4.56352i	−0.0900724	+	0.277214i	0.895866	+	0.444325i	$0.146556\pi$
$272$	3.00407	+	9.24556i	0.182148	+	0.560595i
$273$	−1.61803	+	1.17557i	−0.0979279	+	0.0711488i
$274$	5.85410			0.353659
$275$		0			0
$276$	15.2705			0.919177
$277$	−18.6353	+	13.5393i	−1.11968	+	0.813498i	−0.984161	−	0.177276i	$-0.943271\pi$
$277$	−18.6353	+	13.5393i	−1.11968	+	0.813498i	−0.135523	+	0.990774i	$0.543271\pi$
$278$	−1.40983	−	4.33901i	−0.0845560	−	0.260237i
$279$	0.500000	−	1.53884i	0.0299342	−	0.0921280i
$280$	−1.19098	−	0.865300i	−0.0711748	−	0.0517116i
$281$	20.3713	+	14.8006i	1.21525	+	0.882932i	0.995697	−	0.0926686i	$-0.0295397\pi$
$281$	20.3713	+	14.8006i	1.21525	+	0.882932i	0.219554	+	0.975600i	$0.429540\pi$
$282$	−1.26393	+	3.88998i	−0.0752661	+	0.231645i
$283$	3.69098	+	11.3597i	0.219406	+	0.675263i	0.998811	+	0.0487426i	$0.0155214\pi$
$283$	3.69098	+	11.3597i	0.219406	+	0.675263i	−0.779405	+	0.626520i	$0.784479\pi$
$284$	−24.1353	+	17.5353i	−1.43216	+	1.04053i
$285$	2.85410			0.169062
$286$		0			0
$287$	−11.1803			−0.659955
$288$	−1.28115	+	0.930812i	−0.0754927	+	0.0548486i
$289$	−2.30244	−	7.08618i	−0.135438	−	0.416834i
$290$	0.545085	−	1.67760i	0.0320085	−	0.0985120i
$291$	9.16312	+	6.65740i	0.537152	+	0.390263i
$292$	−21.3541	−	15.5147i	−1.24965	−	0.907927i
$293$	−3.39919	+	10.4616i	−0.198583	+	0.611174i	0.801333	+	0.598218i	$0.204124\pi$
$293$	−3.39919	+	10.4616i	−0.198583	+	0.611174i	−0.999916	+	0.0129565i	$0.995876\pi$
$294$	0.190983	+	0.587785i	0.0111384	+	0.0342803i
$295$	−8.97214	+	6.51864i	−0.522378	+	0.379530i
$296$	9.52786			0.553796
$297$		0			0
$298$	3.38197			0.195912
$299$	5.09017	−	3.69822i	0.294372	−	0.213874i
$300$	−3.70820	−	11.4127i	−0.214093	−	0.658911i
$301$	−3.88197	+	11.9475i	−0.223753	+	0.688640i
$302$	0.0172209	+	0.0125117i	0.000990953	+	0.000719969i
$303$	−19.3713	−	14.0741i	−1.11285	−	0.808535i
$304$	−1.71478	+	5.27756i	−0.0983495	+	0.302689i
$305$	−2.35410	−	7.24518i	−0.134795	−	0.414858i
$306$	−0.364745	+	0.265003i	−0.0208511	+	0.0151492i
$307$	−23.1803			−1.32297			−0.661486	−	0.749958i	$-0.730074\pi$
$307$	−23.1803			−1.32297			−0.661486	+	0.749958i	$0.730074\pi$
$308$		0			0
$309$	−14.3262			−0.814991
$310$	−1.30902	+	0.951057i	−0.0743472	+	0.0540164i
$311$	2.78115	+	8.55951i	0.157705	+	0.485365i	0.998425	−	0.0561046i	$-0.0178680\pi$
$311$	2.78115	+	8.55951i	0.157705	+	0.485365i	−0.840720	+	0.541470i	$0.817868\pi$
$312$	0.909830	−	2.80017i	0.0515090	−	0.158528i
$313$	−14.8262	−	10.7719i	−0.838029	−	0.608863i	0.0837907	−	0.996483i	$-0.473297\pi$
$313$	−14.8262	−	10.7719i	−0.838029	−	0.608863i	−0.921819	+	0.387620i	$0.873297\pi$
$314$	6.14590	+	4.46526i	0.346833	+	0.251989i
$315$	−0.118034	+	0.363271i	−0.00665046	+	0.0204680i
$316$	−3.65654	−	11.2537i	−0.205697	−	0.633069i
$317$	3.59017	−	2.60841i	0.201644	−	0.146503i	−0.482381	−	0.875962i	$-0.660228\pi$
$317$	3.59017	−	2.60841i	0.201644	−	0.146503i	0.684025	+	0.729459i	$0.260228\pi$
$318$	−1.47214			−0.0825533
$319$		0			0
$320$	−4.70820			−0.263197
$321$	3.54508	−	2.57565i	0.197867	−	0.143759i
$322$	−0.600813	−	1.84911i	−0.0334820	−	0.103047i
$323$	−1.68441	+	5.18407i	−0.0937228	+	0.288449i
$324$	−11.5623	−	8.40051i	−0.642350	−	0.466695i
$325$	−4.00000	−	2.90617i	−0.221880	−	0.161205i
$326$	1.02786	−	3.16344i	0.0569281	−	0.175207i
$327$	0.763932	+	2.35114i	0.0422455	+	0.130018i
$328$	13.3156	−	9.67435i	0.735231	−	0.534176i
$329$	−6.61803			−0.364864
$330$		0			0
$331$	6.18034			0.339702			0.169851	−	0.985470i	$-0.445671\pi$
$331$	6.18034			0.339702			0.169851	+	0.985470i	$0.445671\pi$
$332$	4.06231	−	2.95144i	0.222948	−	0.161981i
$333$	−0.763932	−	2.35114i	−0.0418632	−	0.128842i
$334$	−0.763932	+	2.35114i	−0.0418005	+	0.128649i
$335$	6.73607	+	4.89404i	0.368031	+	0.267390i
$336$	4.11803	+	2.99193i	0.224657	+	0.163223i
$337$	8.01722	−	24.6745i	0.436726	−	1.34410i	−0.454582	−	0.890705i	$-0.650211\pi$
$337$	8.01722	−	24.6745i	0.436726	−	1.34410i	0.891308	−	0.453399i	$-0.149789\pi$
$338$	1.35410	+	4.16750i	0.0736534	+	0.226682i
$339$	0.190983	−	0.138757i	0.0103728	−	0.00753626i
$340$	−5.72949			−0.310725
$341$		0			0
$342$	−0.257354			−0.0139161
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−5.71478	−	17.5883i	−0.308120	−	0.948297i
$345$	−2.54508	+	7.83297i	−0.137023	+	0.421713i
$346$	−4.75329	−	3.45347i	−0.255538	−	0.185660i
$347$	−1.89919	−	1.37984i	−0.101954	−	0.0740737i	0.535640	−	0.844446i	$-0.320070\pi$
$347$	−1.89919	−	1.37984i	−0.101954	−	0.0740737i	−0.637594	+	0.770373i	$0.720070\pi$
$348$	−4.28115	+	13.1760i	−0.229494	+	0.706310i
$349$	10.1353	+	31.1931i	0.542528	+	1.66973i	0.726797	+	0.686853i	$0.241008\pi$
$349$	10.1353	+	31.1931i	0.542528	+	1.66973i	−0.184269	+	0.982876i	$0.558992\pi$
$350$	−1.23607	+	0.898056i	−0.0660706	+	0.0480031i
$351$	−6.76393			−0.361032
$352$		0			0
$353$	24.0902			1.28219			0.641095	−	0.767461i	$-0.278480\pi$
$353$	24.0902			1.28219			0.641095	+	0.767461i	$0.278480\pi$
$354$	−5.54508	+	4.02874i	−0.294718	+	0.214125i
$355$	−4.97214	−	15.3027i	−0.263894	−	0.812181i
$356$	−3.92705	+	12.0862i	−0.208133	+	0.640568i
$357$	4.04508	+	2.93893i	0.214089	+	0.155544i
$358$	−1.16312	−	0.845055i	−0.0614727	−	0.0446626i
$359$	−4.82624	+	14.8536i	−0.254719	+	0.783945i	0.739166	+	0.673524i	$0.235220\pi$
$359$	−4.82624	+	14.8536i	−0.254719	+	0.783945i	−0.993885	+	0.110421i	$0.964780\pi$
$360$	−0.173762	−	0.534785i	−0.00915807	−	0.0281856i
$361$	12.8541	−	9.33905i	0.676532	−	0.491529i
$362$	2.83282			0.148889
$363$		0			0
$364$	2.29180			0.120123
$365$	11.5172	−	8.36775i	0.602839	−	0.437988i
$366$	−1.45492	−	4.47777i	−0.0760496	−	0.234057i
$367$	10.1459	−	31.2259i	0.529612	−	1.62998i	−0.225401	−	0.974266i	$-0.572369\pi$
$367$	10.1459	−	31.2259i	0.529612	−	1.62998i	0.755012	−	0.655711i	$-0.227631\pi$
$368$	−12.9549	−	9.41230i	−0.675322	−	0.490650i
$369$	−3.45492	−	2.51014i	−0.179856	−	0.130673i
$370$	−0.763932	+	2.35114i	−0.0397149	+	0.122230i
$371$	−0.736068	−	2.26538i	−0.0382147	−	0.117613i
$372$	10.2812	−	7.46969i	0.533053	−	0.387286i
$373$	−15.4377			−0.799334			−0.399667	−	0.916661i	$-0.630874\pi$
$373$	−15.4377			−0.799334			−0.399667	+	0.916661i	$0.630874\pi$
$374$		0			0
$375$	14.5623			0.751994
$376$	7.88197	−	5.72658i	0.406481	−	0.295326i
$377$	1.76393	+	5.42882i	0.0908471	+	0.279599i
$378$	−0.645898	+	1.98787i	−0.0332214	+	0.102245i
$379$	−25.9443	−	18.8496i	−1.33267	−	0.968240i	−0.999680	−	0.0253087i	$-0.991943\pi$
$379$	−25.9443	−	18.8496i	−1.33267	−	0.968240i	−0.332988	−	0.942931i	$-0.608057\pi$
$380$	−2.64590	−	1.92236i	−0.135732	−	0.0986149i
$381$	−1.47214	+	4.53077i	−0.0754198	+	0.232118i
$382$	−1.86068	−	5.72658i	−0.0952007	−	0.292998i
$383$	27.9894	−	20.3355i	1.43019	−	1.03909i	0.440208	−	0.897896i	$-0.354905\pi$
$383$	27.9894	−	20.3355i	1.43019	−	1.03909i	0.989981	−	0.141197i	$-0.0450953\pi$
$384$	−16.3262			−0.833145
$385$		0			0
$386$	5.85410			0.297966
$387$	−3.88197	+	2.82041i	−0.197331	+	0.143370i
$388$	−4.01064	−	12.3435i	−0.203610	−	0.626646i
$389$	−10.5623	+	32.5074i	−0.535530	+	1.64819i	0.206971	+	0.978347i	$0.433640\pi$
$389$	−10.5623	+	32.5074i	−0.535530	+	1.64819i	−0.742501	+	0.669845i	$0.766360\pi$
$390$	0.618034	+	0.449028i	0.0312954	+	0.0227374i
$391$	−12.7254	−	9.24556i	−0.643552	−	0.467568i
$392$	0.454915	−	1.40008i	0.0229767	−	0.0707149i
$393$	−9.47214	−	29.1522i	−0.477806	−	1.47054i
$394$	−1.32624	+	0.963568i	−0.0668149	+	0.0485439i
$395$	6.38197			0.321112
$396$		0			0
$397$	−0.819660			−0.0411376			−0.0205688	−	0.999788i	$-0.506548\pi$
$397$	−0.819660			−0.0411376			−0.0205688	+	0.999788i	$0.506548\pi$
$398$	−2.54508	+	1.84911i	−0.127574	+	0.0926876i
$399$	0.881966	+	2.71441i	0.0441535	+	0.135891i
$400$	−3.88854	+	11.9677i	−0.194427	+	0.598385i
$401$	14.1803	+	10.3026i	0.708132	+	0.514488i	0.882571	−	0.470180i	$-0.155811\pi$
$401$	14.1803	+	10.3026i	0.708132	+	0.514488i	−0.174438	+	0.984668i	$0.555811\pi$
$402$	4.16312	+	3.02468i	0.207638	+	0.150857i
$403$	1.61803	−	4.97980i	0.0806000	−	0.248061i
$404$	8.47871	+	26.0948i	0.421832	+	1.29826i
$405$	6.23607	−	4.53077i	0.309873	−	0.225136i
$406$	1.76393			0.0875425
$407$		0			0
$408$	−7.36068			−0.364408
$409$	14.3262	−	10.4086i	0.708387	−	0.514673i	−0.174266	−	0.984699i	$-0.555755\pi$
$409$	14.3262	−	10.4086i	0.708387	−	0.514673i	0.882653	+	0.470025i	$0.155755\pi$
$410$	1.31966	+	4.06150i	0.0651734	+	0.200583i
$411$	7.66312	−	23.5847i	0.377994	−	1.16335i
$412$	13.2812	+	9.64932i	0.654315	+	0.475388i
$413$	−8.97214	−	6.51864i	−0.441490	−	0.320761i
$414$	0.229490	−	0.706298i	0.0112788	−	0.0347127i
$415$	0.836881	+	2.57565i	0.0410809	+	0.126434i
$416$	−4.14590	+	3.01217i	−0.203269	+	0.147684i
$417$	−19.3262			−0.946410
$418$		0			0
$419$	29.8885			1.46015			0.730075	−	0.683367i	$-0.239485\pi$
$419$	29.8885			1.46015			0.730075	+	0.683367i	$0.239485\pi$
$420$	−2.42705	+	1.76336i	−0.118428	+	0.0860430i
$421$	0.236068	+	0.726543i	0.0115052	+	0.0354095i	0.956644	−	0.291259i	$-0.0940740\pi$
$421$	0.236068	+	0.726543i	0.0115052	+	0.0354095i	−0.945139	+	0.326668i	$0.894074\pi$
$422$	−1.84346	+	5.67358i	−0.0897382	+	0.276186i
$423$	−2.04508	−	1.48584i	−0.0994354	−	0.0722441i
$424$	2.83688	+	2.06111i	0.137771	+	0.100097i
$425$	−3.81966	+	11.7557i	−0.185281	+	0.570235i
$426$	−3.07295	−	9.45756i	−0.148885	−	0.458221i
$427$	6.16312	−	4.47777i	0.298254	−	0.216694i
$428$	−5.02129			−0.242713
$429$		0			0
$430$	4.79837			0.231398
$431$	11.2082	−	8.14324i	0.539880	−	0.392246i	−0.284160	−	0.958777i	$-0.591715\pi$
$431$	11.2082	−	8.14324i	0.539880	−	0.392246i	0.824041	+	0.566531i	$0.191715\pi$
$432$	5.31966	+	16.3722i	0.255942	+	0.787709i
$433$	−2.77051	+	8.52675i	−0.133142	+	0.409770i	−0.995296	−	0.0968764i	$-0.969115\pi$
$433$	−2.77051	+	8.52675i	−0.133142	+	0.409770i	0.862154	+	0.506646i	$0.169115\pi$
$434$	−1.30902	−	0.951057i	−0.0628348	−	0.0456522i
$435$	−6.04508	−	4.39201i	−0.289840	−	0.210581i
$436$	0.875388	−	2.69417i	0.0419235	−	0.129027i
$437$	−2.77458	−	8.53926i	−0.132726	−	0.408488i
$438$	7.11803	−	5.17155i	0.340113	−	0.247106i
$439$	3.38197			0.161412			0.0807062	−	0.996738i	$-0.474282\pi$
$439$	3.38197			0.161412			0.0807062	+	0.996738i	$0.474282\pi$
$440$		0			0
$441$	−0.381966			−0.0181889
$442$	−1.18034	+	0.857567i	−0.0561430	+	0.0407903i
$443$	0.954915	+	2.93893i	0.0453694	+	0.139633i	0.971175	−	0.238367i	$-0.0766121\pi$
$443$	0.954915	+	2.93893i	0.0453694	+	0.139633i	−0.925806	+	0.378000i	$0.876612\pi$
$444$	6.00000	−	18.4661i	0.284747	−	0.876362i
$445$	−5.54508	−	4.02874i	−0.262862	−	0.190981i
$446$	0.628677	+	0.456761i	0.0297687	+	0.0216282i
$447$	4.42705	−	13.6251i	0.209392	−	0.644443i
$448$	−1.45492	−	4.47777i	−0.0687383	−	0.211555i
$449$	−9.97214	+	7.24518i	−0.470614	+	0.341921i	−0.797681	−	0.603080i	$-0.793940\pi$
$449$	−9.97214	+	7.24518i	−0.470614	+	0.341921i	0.327066	+	0.945001i	$0.393940\pi$
$450$	−0.583592			−0.0275108
$451$		0			0
$452$	−0.270510			−0.0127237
$453$	0.0729490	−	0.0530006i	0.00342744	−	0.00249018i
$454$	1.89261	+	5.82485i	0.0888245	+	0.273374i
$455$	−0.381966	+	1.17557i	−0.0179068	+	0.0551116i
$456$	−3.39919	−	2.46965i	−0.159182	−	0.115652i
$457$	0.118034	+	0.0857567i	0.00552140	+	0.00401153i	0.590543	−	0.807007i	$-0.298914\pi$
$457$	0.118034	+	0.0857567i	0.00552140	+	0.00401153i	−0.585021	+	0.811018i	$0.698914\pi$
$458$	−0.798374	+	2.45714i	−0.0373056	+	0.114815i
$459$	5.22542	+	16.0822i	0.243902	+	0.750653i
$460$	7.63525	−	5.54734i	0.355996	−	0.258646i
$461$	−18.5066			−0.861937			−0.430969	−	0.902367i	$-0.641828\pi$
$461$	−18.5066			−0.861937			−0.430969	+	0.902367i	$0.641828\pi$
$462$		0			0
$463$	22.2361			1.03340			0.516699	−	0.856167i	$-0.327161\pi$
$463$	22.2361			1.03340			0.516699	+	0.856167i	$0.327161\pi$
$464$	11.7533	−	8.53926i	0.545633	−	0.396425i
$465$	2.11803	+	6.51864i	0.0982215	+	0.302295i
$466$	3.47214	−	10.6861i	0.160844	−	0.495026i
$467$	3.64590	+	2.64890i	0.168712	+	0.122576i	0.668937	−	0.743319i	$-0.266749\pi$
$467$	3.64590	+	2.64890i	0.168712	+	0.122576i	−0.500225	+	0.865895i	$0.666749\pi$
$468$	0.708204	+	0.514540i	0.0327367	+	0.0237846i
$469$	−2.57295	+	7.91872i	−0.118808	+	0.365653i
$470$	0.781153	+	2.40414i	0.0360319	+	0.110895i
$471$	26.0344	−	18.9151i	1.19960	−	0.871563i
$472$	16.3262			0.751476
$473$		0			0
$474$	3.94427			0.181166
$475$	−5.70820	+	4.14725i	−0.261910	+	0.190289i
$476$	−1.77051	−	5.44907i	−0.0811512	−	0.249758i
$477$	0.281153	−	0.865300i	0.0128731	−	0.0396194i
$478$	−5.28115	−	3.83698i	−0.241554	−	0.175499i
$479$	−17.6074	−	12.7925i	−0.804502	−	0.584505i	0.107729	−	0.994180i	$-0.465642\pi$
$479$	−17.6074	−	12.7925i	−0.804502	−	0.584505i	−0.912231	+	0.409675i	$0.865642\pi$
$480$	2.07295	−	6.37988i	0.0946167	−	0.291200i
$481$	−2.47214	−	7.60845i	−0.112720	−	0.346916i
$482$	5.02786	−	3.65296i	0.229013	−	0.166388i
$483$	−8.23607			−0.374754
$484$		0			0
$485$	7.00000			0.317854
$486$	−1.21885	+	0.885544i	−0.0552880	+	0.0401691i
$487$	−10.0729	−	31.0013i	−0.456449	−	1.40481i	−0.869426	−	0.494064i	$-0.835511\pi$
$487$	−10.0729	−	31.0013i	−0.456449	−	1.40481i	0.412977	−	0.910742i	$-0.364489\pi$
$488$	−3.46556	+	10.6659i	−0.156878	+	0.482822i
$489$	−11.3992	−	8.28199i	−0.515489	−	0.374525i
$490$	0.309017	+	0.224514i	0.0139600	+	0.0101425i
$491$	6.84346	−	21.0620i	0.308841	−	0.950515i	−0.669375	−	0.742925i	$-0.733438\pi$
$491$	6.84346	−	21.0620i	0.308841	−	0.950515i	0.978216	−	0.207590i	$-0.0665620\pi$
$492$	−10.3647	−	31.8994i	−0.467279	−	1.43814i
$493$	11.5451	−	8.38800i	0.519964	−	0.377776i
$494$	−0.832816			−0.0374702
$495$		0			0
$496$	−13.3262			−0.598366
$497$	13.0172	−	9.45756i	0.583902	−	0.424230i
$498$	0.517221	+	1.59184i	0.0231772	+	0.0713322i
$499$	−3.11803	+	9.59632i	−0.139582	+	0.429590i	−0.996275	−	0.0862375i	$-0.972516\pi$
$499$	−3.11803	+	9.59632i	−0.139582	+	0.429590i	0.856692	+	0.515828i	$0.172516\pi$
$500$	−13.5000	−	9.80832i	−0.603738	−	0.438642i
$501$	8.47214	+	6.15537i	0.378507	+	0.275002i
$502$	−2.71478	+	8.35524i	−0.121167	+	0.372913i
$503$	−10.7639	−	33.1280i	−0.479940	−	1.47710i	−0.839178	−	0.543857i	$-0.816963\pi$
$503$	−10.7639	−	33.1280i	−0.479940	−	1.47710i	0.359238	−	0.933246i	$-0.383037\pi$
$504$	0.454915	−	0.330515i	0.0202635	−	0.0147223i
$505$	−14.7984			−0.658519
$506$		0			0
$507$	18.5623			0.824381
$508$	4.41641	−	3.20871i	0.195946	−	0.142363i
$509$	−3.31966	−	10.2169i	−0.147141	−	0.452855i	0.850139	−	0.526559i	$-0.176518\pi$
$509$	−3.31966	−	10.2169i	−0.147141	−	0.452855i	−0.997280	+	0.0737042i	$0.976518\pi$
$510$	0.590170	−	1.81636i	0.0261332	−	0.0804296i
$511$	11.5172	+	8.36775i	0.509492	+	0.370168i
$512$	18.0451	+	13.1105i	0.797488	+	0.579409i
$513$	−2.98278	+	9.18005i	−0.131693	+	0.405309i
$514$	1.01064	+	3.11044i	0.0445776	+	0.137196i
$515$	−7.16312	+	5.20431i	−0.315645	+	0.229329i
$516$	−37.6869			−1.65907
$517$		0			0
$518$	−2.47214			−0.108619
$519$	−20.1353	+	14.6291i	−0.883840	+	0.642147i
$520$	−0.562306	−	1.73060i	−0.0246587	−	0.0758918i
$521$	−3.78115	+	11.6372i	−0.165655	+	0.509835i	−0.999084	−	0.0427924i	$-0.986375\pi$
$521$	−3.78115	+	11.6372i	−0.165655	+	0.509835i	0.833429	+	0.552627i	$0.186375\pi$
$522$	0.545085	+	0.396027i	0.0238577	+	0.0173336i
$523$	−13.3992	−	9.73508i	−0.585906	−	0.425685i	0.254943	−	0.966956i	$-0.417943\pi$
$523$	−13.3992	−	9.73508i	−0.585906	−	0.425685i	−0.840848	+	0.541271i	$0.817943\pi$
$524$	−10.8541	+	33.4055i	−0.474164	+	1.45933i
$525$	2.00000	+	6.15537i	0.0872872	+	0.268642i
$526$	−5.29180	+	3.84471i	−0.230733	+	0.167638i
$527$	−13.0902			−0.570217
$528$		0			0
$529$	2.90983			0.126514
$530$	−0.736068	+	0.534785i	−0.0319727	+	0.0232296i
$531$	−1.30902	−	4.02874i	−0.0568065	−	0.174832i
$532$	1.01064	−	3.11044i	0.0438169	−	0.134855i
$533$	−11.1803	−	8.12299i	−0.484274	−	0.351846i
$534$	−3.42705	−	2.48990i	−0.148303	−	0.107748i
$535$	0.836881	−	2.57565i	0.0361815	−	0.111355i
$536$	−3.78773	−	11.6574i	−0.163605	−	0.503525i
$537$	−4.92705	+	3.57971i	−0.212618	+	0.154476i
$538$	−6.43769			−0.277549
$539$		0			0
$540$	−10.1459			−0.436610
$541$	−0.572949	+	0.416272i	−0.0246330	+	0.0178969i	−0.600034	−	0.799975i	$-0.704846\pi$
$541$	−0.572949	+	0.416272i	−0.0246330	+	0.0178969i	0.575401	+	0.817872i	$0.304846\pi$
$542$	0.566371	+	1.74311i	0.0243277	+	0.0748730i
$543$	3.70820	−	11.4127i	0.159134	−	0.489765i
$544$	10.3647	+	7.53043i	0.444385	+	0.322864i
$545$	1.23607	+	0.898056i	0.0529473	+	0.0384685i
$546$	−0.236068	+	0.726543i	−0.0101028	+	0.0310931i
$547$	−0.534442	−	1.64484i	−0.0228511	−	0.0703284i	0.938981	−	0.343970i	$-0.111772\pi$
$547$	−0.534442	−	1.64484i	−0.0228511	−	0.0703284i	−0.961832	+	0.273641i	$0.911772\pi$
$548$	−22.9894	+	16.7027i	−0.982057	+	0.713506i
$549$	2.90983			0.124189
$550$		0			0
$551$	8.14590			0.347027
$552$	9.80902	−	7.12667i	0.417499	−	0.303331i
$553$	1.97214	+	6.06961i	0.0838638	+	0.258106i
$554$	−2.71885	+	8.36775i	−0.115513	+	0.355512i
$555$	8.47214	+	6.15537i	0.359622	+	0.261281i
$556$	17.9164	+	13.0170i	0.759825	+	0.552045i
$557$	−3.01722	+	9.28605i	−0.127844	+	0.393463i	−0.994408	−	0.105602i	$-0.966323\pi$
$557$	−3.01722	+	9.28605i	−0.127844	+	0.393463i	0.866565	+	0.499065i	$0.166323\pi$
$558$	−0.190983	−	0.587785i	−0.00808496	−	0.0248829i
$559$	−12.5623	+	9.12705i	−0.531329	+	0.386033i
$560$	3.14590			0.132938
$561$		0			0
$562$	9.61803			0.405712
$563$	25.8713	−	18.7966i	1.09035	−	0.792183i	0.110889	−	0.993833i	$-0.464630\pi$
$563$	25.8713	−	18.7966i	1.09035	−	0.792183i	0.979458	+	0.201650i	$0.0646303\pi$
$564$	−6.13525	−	18.8824i	−0.258341	−	0.795091i
$565$	0.0450850	−	0.138757i	0.00189674	−	0.00583756i
$566$	3.69098	+	2.68166i	0.155144	+	0.112718i
$567$	6.23607	+	4.53077i	0.261890	+	0.190274i
$568$	−7.31966	+	22.5276i	−0.307126	+	0.945237i
$569$	11.5279	+	35.4791i	0.483273	+	1.48736i	0.834466	+	0.551059i	$0.185776\pi$
$569$	11.5279	+	35.4791i	0.483273	+	1.48736i	−0.351193	+	0.936303i	$0.614224\pi$
$570$	0.881966	−	0.640786i	0.0369415	−	0.0268396i
$571$	34.3050			1.43562			0.717809	−	0.696240i	$-0.245145\pi$
$571$	34.3050			1.43562			0.717809	+	0.696240i	$0.245145\pi$
$572$		0			0
$573$	−25.5066			−1.06555
$574$	−3.45492	+	2.51014i	−0.144205	+	0.104771i
$575$	−6.29180	−	19.3642i	−0.262386	−	0.807541i
$576$	0.555728	−	1.71036i	0.0231553	−	0.0712648i
$577$	−7.80902	−	5.67358i	−0.325094	−	0.236194i	0.413252	−	0.910617i	$-0.364393\pi$
$577$	−7.80902	−	5.67358i	−0.325094	−	0.236194i	−0.738346	+	0.674422i	$0.764393\pi$
$578$	−2.30244	−	1.67282i	−0.0957688	−	0.0695801i
$579$	7.66312	−	23.5847i	0.318468	−	0.980145i
$580$	2.64590	+	8.14324i	0.109865	+	0.338130i
$581$	−2.19098	+	1.59184i	−0.0908973	+	0.0660407i
$582$	4.32624			0.179328
$583$		0			0
$584$	−20.9574			−0.867225
$585$	−0.381966	+	0.277515i	−0.0157924	+	0.0114738i
$586$	1.29837	+	3.99598i	0.0536353	+	0.165073i
$587$	0.309017	−	0.951057i	0.0127545	−	0.0392543i	−0.944477	−	0.328578i	$-0.893431\pi$
$587$	0.309017	−	0.951057i	0.0127545	−	0.0392543i	0.957231	+	0.289324i	$0.0934305\pi$
$588$	−2.42705	−	1.76336i	−0.100090	−	0.0727196i
$589$	−6.04508	−	4.39201i	−0.249083	−	0.180970i
$590$	−1.30902	+	4.02874i	−0.0538914	+	0.165861i
$591$	2.14590	+	6.60440i	0.0882705	+	0.271669i
$592$	−16.4721	+	11.9677i	−0.677001	+	0.491870i
$593$	11.1246			0.456833			0.228417	−	0.973564i	$-0.426645\pi$
$593$	11.1246			0.456833			0.228417	+	0.973564i	$0.426645\pi$
$594$		0			0
$595$	3.09017			0.126685
$596$	−13.2812	+	9.64932i	−0.544017	+	0.395252i
$597$	4.11803	+	12.6740i	0.168540	+	0.518713i
$598$	0.742646	−	2.28563i	0.0303690	−	0.0934663i
$599$	12.9443	+	9.40456i	0.528889	+	0.384260i	0.819942	−	0.572447i	$-0.194006\pi$
$599$	12.9443	+	9.40456i	0.528889	+	0.384260i	−0.291053	+	0.956707i	$0.594006\pi$
$600$	−7.70820	−	5.60034i	−0.314686	−	0.228633i
$601$	4.23607	−	13.0373i	0.172793	−	0.531802i	−0.826733	−	0.562595i	$-0.809803\pi$
$601$	4.23607	−	13.0373i	0.172793	−	0.531802i	0.999526	+	0.0307929i	$0.00980324\pi$
$602$	1.48278	+	4.56352i	0.0604336	+	0.185995i
$603$	−2.57295	+	1.86936i	−0.104779	+	0.0761261i
$604$	−0.103326			−0.00420426
$605$		0			0
$606$	−9.14590			−0.371527
$607$	−16.3435	+	11.8742i	−0.663361	+	0.481960i	−0.867796	−	0.496920i	$-0.834464\pi$
$607$	−16.3435	+	11.8742i	−0.663361	+	0.481960i	0.204436	+	0.978880i	$0.434464\pi$
$608$	2.25987	+	6.95515i	0.0916497	+	0.282069i
$609$	2.30902	−	7.10642i	0.0935661	−	0.287967i
$610$	−2.35410	−	1.71036i	−0.0953148	−	0.0692503i
$611$	−6.61803	−	4.80828i	−0.267737	−	0.194522i
$612$	0.676275	−	2.08136i	0.0273368	−	0.0841340i
$613$	−0.274575	−	0.845055i	−0.0110900	−	0.0341315i	0.945358	−	0.326033i	$-0.105712\pi$
$613$	−0.274575	−	0.845055i	−0.0110900	−	0.0341315i	−0.956448	+	0.291902i	$0.905712\pi$
$614$	−7.16312	+	5.20431i	−0.289080	+	0.210029i
$615$	18.0902			0.729466
$616$		0			0
$617$	9.41641			0.379090			0.189545	−	0.981872i	$-0.439299\pi$
$617$	9.41641			0.379090			0.189545	+	0.981872i	$0.439299\pi$
$618$	−4.42705	+	3.21644i	−0.178082	+	0.129384i
$619$	−12.2705	−	37.7647i	−0.493193	−	1.51789i	−0.819753	−	0.572717i	$-0.805889\pi$
$619$	−12.2705	−	37.7647i	−0.493193	−	1.51789i	0.326560	−	0.945177i	$-0.394111\pi$
$620$	2.42705	−	7.46969i	0.0974727	−	0.299990i
$621$	−22.5344	−	16.3722i	−0.904276	−	0.656995i
$622$	2.78115	+	2.02063i	0.111514	+	0.0810197i
$623$	2.11803	−	6.51864i	0.0848572	−	0.261164i
$624$	1.94427	+	5.98385i	0.0778332	+	0.239546i
$625$	−8.89919	+	6.46564i	−0.355967	+	0.258626i
$626$	−7.00000			−0.279776
$627$		0			0
$628$	−36.8754			−1.47149
$629$	−16.1803	+	11.7557i	−0.645152	+	0.468731i
$630$	0.0450850	+	0.138757i	0.00179623	+	0.00552822i
$631$	5.51064	−	16.9600i	0.219375	−	0.675168i	−0.779439	−	0.626478i	$-0.784496\pi$
$631$	5.51064	−	16.9600i	0.219375	−	0.675168i	0.998814	−	0.0486891i	$-0.0155044\pi$
$632$	−7.60081	−	5.52231i	−0.302344	−	0.219666i
$633$	20.4443	+	14.8536i	0.812587	+	0.590379i
$634$	0.523799	−	1.61209i	0.0208027	−	0.0640241i
$635$	0.909830	+	2.80017i	0.0361055	+	0.111121i
$636$	5.78115	−	4.20025i	0.229238	−	0.166551i
$637$	−1.23607			−0.0489748
$638$		0			0
$639$	6.14590			0.243128
$640$	−8.16312	+	5.93085i	−0.322676	+	0.234438i
$641$	9.78115	+	30.1033i	0.386332	+	1.18901i	0.935509	+	0.353302i	$0.114941\pi$
$641$	9.78115	+	30.1033i	0.386332	+	1.18901i	−0.549177	+	0.835706i	$0.685059\pi$
$642$	0.517221	−	1.59184i	0.0204131	−	0.0628250i
$643$	−1.28115	−	0.930812i	−0.0505237	−	0.0367076i	0.562237	−	0.826976i	$-0.309941\pi$
$643$	−1.28115	−	0.930812i	−0.0505237	−	0.0367076i	−0.612760	+	0.790269i	$0.709941\pi$
$644$	7.63525	+	5.54734i	0.300871	+	0.218596i
$645$	6.28115	−	19.3314i	0.247320	−	0.761173i
$646$	0.643386	+	1.98014i	0.0253137	+	0.0779075i
$647$	−5.00000	+	3.63271i	−0.196570	+	0.142817i	−0.681717	−	0.731616i	$-0.738766\pi$
$647$	−5.00000	+	3.63271i	−0.196570	+	0.142817i	0.485146	+	0.874433i	$0.338766\pi$
$648$	−11.3475			−0.445773
$649$		0			0
$650$	−1.88854			−0.0740748
$651$	−5.54508	+	4.02874i	−0.217329	+	0.157899i
$652$	4.98936	+	15.3557i	0.195398	+	0.601374i
$653$	5.63525	−	17.3435i	0.220525	−	0.678705i	−0.778191	−	0.628028i	$-0.783862\pi$
$653$	5.63525	−	17.3435i	0.220525	−	0.678705i	0.998715	−	0.0506766i	$-0.0161378\pi$
$654$	0.763932	+	0.555029i	0.0298721	+	0.0217034i
$655$	−15.3262	−	11.1352i	−0.598846	−	0.435087i
$656$	−10.8688	+	33.4508i	−0.424356	+	1.30603i
$657$	1.68034	+	5.17155i	0.0655563	+	0.201762i
$658$	−2.04508	+	1.48584i	−0.0797257	+	0.0579241i
$659$	31.4721			1.22598			0.612990	−	0.790091i	$-0.289967\pi$
$659$	31.4721			1.22598			0.612990	+	0.790091i	$0.289967\pi$
$660$		0			0
$661$	−34.5623			−1.34432			−0.672159	−	0.740407i	$-0.734633\pi$
$661$	−34.5623			−1.34432			−0.672159	+	0.740407i	$0.734633\pi$
$662$	1.90983	−	1.38757i	0.0742277	−	0.0539295i
$663$	1.90983	+	5.87785i	0.0741717	+	0.228277i
$664$	1.23200	−	3.79171i	0.0478110	−	0.147147i
$665$	1.42705	+	1.03681i	0.0553387	+	0.0402059i
$666$	−0.763932	−	0.555029i	−0.0296018	−	0.0215069i
$667$	−7.26393	+	22.3561i	−0.281261	+	0.865631i
$668$	−3.70820	−	11.4127i	−0.143475	−	0.441570i
$669$	2.66312	−	1.93487i	0.102962	−	0.0748064i
$670$	3.18034			0.122867
$671$		0			0
$672$	6.70820			0.258775
$673$	5.32624	−	3.86974i	0.205311	−	0.149167i	−0.480378	−	0.877061i	$-0.659501\pi$
$673$	5.32624	−	3.86974i	0.205311	−	0.149167i	0.685690	+	0.727894i	$0.259501\pi$
$674$	−3.06231	−	9.42481i	−0.117956	−	0.363030i
$675$	−6.76393	+	20.8172i	−0.260344	+	0.801256i
$676$	−17.2082	−	12.5025i	−0.661854	−	0.480865i
$677$	29.3435	+	21.3193i	1.12776	+	0.819366i	0.985367	−	0.170444i	$-0.0545202\pi$
$677$	29.3435	+	21.3193i	1.12776	+	0.819366i	0.142393	+	0.989810i	$0.454520\pi$
$678$	0.0278640	−	0.0857567i	0.00107011	−	0.00329347i
$679$	2.16312	+	6.65740i	0.0830129	+	0.255487i
$680$	−3.68034	+	2.67392i	−0.141135	+	0.102540i
$681$	25.9443			0.994187
$682$		0			0
$683$	0.493422			0.0188803			0.00944014	−	0.999955i	$-0.496995\pi$
$683$	0.493422			0.0188803			0.00944014	+	0.999955i	$0.496995\pi$
$684$	1.01064	−	0.734275i	0.0386429	−	0.0280757i
$685$	−4.73607	−	14.5761i	−0.180956	−	0.556925i
$686$	−0.118034	+	0.363271i	−0.00450656	+	0.0138698i
$687$	8.85410	+	6.43288i	0.337805	+	0.245430i
$688$	31.9721	+	23.2291i	1.21893	+	0.885602i
$689$	0.909830	−	2.80017i	0.0346618	−	0.106678i
$690$	0.972136	+	2.99193i	0.0370086	+	0.113901i
$691$	−15.0000	+	10.8981i	−0.570627	+	0.414585i	−0.835333	−	0.549744i	$-0.814725\pi$
$691$	−15.0000	+	10.8981i	−0.570627	+	0.414585i	0.264706	+	0.964329i	$0.414725\pi$
$692$	28.5197			1.08416
$693$		0			0
$694$	−0.896674			−0.0340373
$695$	−9.66312	+	7.02067i	−0.366543	+	0.266309i
$696$	3.39919	+	10.4616i	0.128846	+	0.396547i
$697$	−10.6763	+	32.8582i	−0.404393	+	1.24459i
$698$	10.1353	+	7.36369i	0.383625	+	0.278720i
$699$	−38.5066	−	27.9767i	−1.45645	−	1.05817i
$700$	2.29180	−	7.05342i	0.0866217	−	0.266594i
$701$	5.71885	+	17.6008i	0.215998	+	0.664773i	0.999081	+	0.0428564i	$0.0136458\pi$
$701$	5.71885	+	17.6008i	0.215998	+	0.664773i	−0.783083	+	0.621917i	$0.786354\pi$
$702$	−2.09017	+	1.51860i	−0.0788884	+	0.0573158i
$703$	−11.4164			−0.430578
$704$		0			0
$705$	10.7082			0.403294
$706$	7.44427	−	5.40858i	0.280169	−	0.203555i
$707$	−4.57295	−	14.0741i	−0.171983	−	0.529311i
$708$	10.2812	−	31.6421i	0.386389	−	1.18918i
$709$	5.69098	+	4.13474i	0.213729	+	0.155283i	0.689499	−	0.724286i	$-0.257831\pi$
$709$	5.69098	+	4.13474i	0.213729	+	0.155283i	−0.475770	+	0.879570i	$0.657831\pi$
$710$	−4.97214	−	3.61247i	−0.186601	−	0.135574i
$711$	−0.753289	+	2.31838i	−0.0282505	+	0.0869462i
$712$	3.11803	+	9.59632i	0.116853	+	0.359637i
$713$	17.4443	−	12.6740i	0.653293	−	0.474645i
$714$	1.90983			0.0714736
$715$		0			0
$716$	6.97871			0.260807
$717$	−22.3713	+	16.2537i	−0.835472	+	0.607006i
$718$	1.84346	+	5.67358i	0.0687973	+	0.211736i
$719$	−0.892609	+	2.74717i	−0.0332887	+	0.102452i	−0.966320	−	0.257342i	$-0.917153\pi$
$719$	−0.892609	+	2.74717i	−0.0332887	+	0.102452i	0.933032	+	0.359794i	$0.117153\pi$
$720$	0.972136	+	0.706298i	0.0362294	+	0.0263222i
$721$	−7.16312	−	5.20431i	−0.266768	−	0.193819i
$722$	1.87539	−	5.77185i	0.0697947	−	0.214806i
$723$	−8.13525	−	25.0377i	−0.302553	−	0.931164i
$724$	−11.1246	+	8.08250i	−0.413443	+	0.300384i
$725$	18.4721			0.686038
$726$		0			0
$727$	−12.4508			−0.461776			−0.230888	−	0.972980i	$-0.574163\pi$
$727$	−12.4508			−0.461776			−0.230888	+	0.972980i	$0.574163\pi$
$728$	1.47214	−	1.06957i	0.0545610	−	0.0396409i
$729$	9.11803	+	28.0624i	0.337705	+	1.03935i
$730$	1.68034	−	5.17155i	0.0621922	−	0.191408i
$731$	31.4058	+	22.8176i	1.16158	+	0.843940i
$732$	18.4894	+	13.4333i	0.683386	+	0.496509i
$733$	16.3607	−	50.3530i	0.604295	−	1.85983i	0.102733	−	0.994709i	$-0.467241\pi$
$733$	16.3607	−	50.3530i	0.604295	−	1.85983i	0.501563	−	0.865121i	$-0.332759\pi$
$734$	−3.87539	−	11.9272i	−0.143043	−	0.440242i
$735$	1.30902	−	0.951057i	0.0482838	−	0.0350802i
$736$	−21.1033			−0.777879
$737$		0			0
$738$	−1.63119			−0.0600449
$739$	9.20820	−	6.69015i	0.338729	−	0.246101i	−0.405396	−	0.914141i	$-0.632866\pi$
$739$	9.20820	−	6.69015i	0.338729	−	0.246101i	0.744125	+	0.668040i	$0.232866\pi$
$740$	−3.70820	−	11.4127i	−0.136316	−	0.419538i
$741$	−1.09017	+	3.35520i	−0.0400484	+	0.123256i
$742$	−0.736068	−	0.534785i	−0.0270219	−	0.0196326i
$743$	12.0623	+	8.76378i	0.442523	+	0.321512i	0.786637	−	0.617416i	$-0.211821\pi$
$743$	12.0623	+	8.76378i	0.442523	+	0.321512i	−0.344114	+	0.938928i	$0.611821\pi$
$744$	3.11803	−	9.59632i	0.114313	−	0.351818i
$745$	−2.73607	−	8.42075i	−0.100242	−	0.308512i
$746$	−4.77051	+	3.46598i	−0.174661	+	0.126898i
$747$	−1.03444			−0.0378482
$748$		0			0
$749$	2.70820			0.0989556
$750$	4.50000	−	3.26944i	0.164317	−	0.119383i
$751$	12.7639	+	39.2833i	0.465762	+	1.43347i	0.858021	+	0.513615i	$0.171694\pi$
$751$	12.7639	+	39.2833i	0.465762	+	1.43347i	−0.392259	+	0.919855i	$0.628306\pi$
$752$	−6.43363	+	19.8007i	−0.234610	+	0.722056i
$753$	30.1074	+	21.8743i	1.09717	+	0.797144i
$754$	1.76393	+	1.28157i	0.0642386	+	0.0466721i
$755$	0.0172209	−	0.0530006i	0.000626734	−	0.00192889i
$756$	−3.13525	−	9.64932i	−0.114028	−	0.350942i
$757$	11.9443	−	8.67802i	0.434122	−	0.315408i	−0.349173	−	0.937058i	$-0.613537\pi$
$757$	11.9443	−	8.67802i	0.434122	−	0.315408i	0.783295	+	0.621650i	$0.213537\pi$
$758$	−12.2492			−0.444912
$759$		0			0
$760$	−2.59675			−0.0941939
$761$	−12.3820	+	8.99602i	−0.448846	+	0.326106i	−0.789140	−	0.614213i	$-0.789473\pi$
$761$	−12.3820	+	8.99602i	−0.448846	+	0.326106i	0.340294	+	0.940319i	$0.389473\pi$
$762$	0.562306	+	1.73060i	0.0203702	+	0.0626930i
$763$	−0.472136	+	1.45309i	−0.0170925	+	0.0526052i
$764$	23.6459	+	17.1798i	0.855479	+	0.621542i
$765$	0.954915	+	0.693786i	0.0345250	+	0.0250839i
$766$	4.08359	−	12.5680i	0.147546	−	0.454100i
$767$	−4.23607	−	13.0373i	−0.152956	−	0.470749i
$768$	7.28115	−	5.29007i	0.262736	−	0.190889i
$769$	48.5623			1.75120			0.875601	−	0.483035i	$-0.160466\pi$
$769$	48.5623			1.75120			0.875601	+	0.483035i	$0.160466\pi$
$770$		0			0
$771$	13.8541			0.498943
$772$	−22.9894	+	16.7027i	−0.827405	+	0.601145i
$773$	12.4336	+	38.2668i	0.447207	+	1.37636i	0.880046	+	0.474889i	$0.157512\pi$
$773$	12.4336	+	38.2668i	0.447207	+	1.37636i	−0.432839	+	0.901471i	$0.642488\pi$
$774$	−0.566371	+	1.74311i	−0.0203578	+	0.0626548i
$775$	−13.7082	−	9.95959i	−0.492413	−	0.357759i
$776$	−8.33688	−	6.05710i	−0.299277	−	0.217437i
$777$	−3.23607	+	9.95959i	−0.116093	+	0.357298i
$778$	4.03444	+	12.4167i	0.144642	+	0.445162i
$779$	−15.9549	+	11.5919i	−0.571644	+	0.415324i
$780$	−3.70820			−0.132775
$781$		0			0
$782$	−6.00813			−0.214850
$783$	20.4443	−	14.8536i	0.730619	−	0.530826i
$784$	0.972136	+	2.99193i	0.0347191	+	0.106855i
$785$	6.14590	−	18.9151i	0.219357	−	0.675110i
$786$	−9.47214	−	6.88191i	−0.337860	−	0.245470i
$787$	−16.6353	−	12.0862i	−0.592983	−	0.430827i	0.250398	−	0.968143i	$-0.419438\pi$
$787$	−16.6353	−	12.0862i	−0.592983	−	0.430827i	−0.843381	+	0.537316i	$0.819438\pi$
$788$	2.45898	−	7.56796i	0.0875975	−	0.269598i
$789$	8.56231	+	26.3521i	0.304826	+	0.938158i
$790$	1.97214	−	1.43284i	0.0701654	−	0.0509782i
$791$	0.145898			0.00518754
$792$		0			0
$793$	9.41641			0.334386
$794$	−0.253289	+	0.184025i	−0.00898889	+	0.00653081i
$795$	1.19098	+	3.66547i	0.0422398	+	0.130001i
$796$	4.71885	−	14.5231i	0.167255	−	0.514758i
$797$	−26.0795	−	18.9479i	−0.923784	−	0.671169i	0.0206788	−	0.999786i	$-0.493417\pi$
$797$	−26.0795	−	18.9479i	−0.923784	−	0.671169i	−0.944463	+	0.328618i	$0.893417\pi$
$798$	0.881966	+	0.640786i	0.0312213	+	0.0226836i
$799$	−6.31966	+	19.4499i	−0.223574	+	0.688088i
$800$	5.12461	+	15.7719i	0.181182	+	0.557622i
$801$	2.11803	−	1.53884i	0.0748371	−	0.0543723i
$802$	6.69505			0.236410
$803$		0			0
$804$	−24.9787			−0.880931
$805$	−4.11803	+	2.99193i	−0.145142	+	0.105452i
$806$	−0.618034	−	1.90211i	−0.0217693	−	0.0669991i
$807$	−8.42705	+	25.9358i	−0.296646	+	0.912983i
$808$	17.6246	+	12.8050i	0.620032	+	0.450479i
$809$	−26.2984	−	19.1069i	−0.924602	−	0.671762i	0.0200635	−	0.999799i	$-0.493613\pi$
$809$	−26.2984	−	19.1069i	−0.924602	−	0.671762i	−0.944665	+	0.328036i	$0.893613\pi$
$810$	0.909830	−	2.80017i	0.0319682	−	0.0983879i
$811$	0.360680	+	1.11006i	0.0126652	+	0.0389794i	0.957189	−	0.289462i	$-0.0934765\pi$
$811$	0.360680	+	1.11006i	0.0126652	+	0.0389794i	−0.944524	+	0.328442i	$0.893477\pi$
$812$	−6.92705	+	5.03280i	−0.243092	+	0.176617i
$813$	7.76393			0.272293
$814$		0			0
$815$	−8.70820			−0.305035
$816$	12.7254	−	9.24556i	0.445479	−	0.323659i
$817$	6.84752	+	21.0745i	0.239565	+	0.737304i
$818$	2.09017	−	6.43288i	0.0730811	−	0.224920i
$819$	−0.381966	−	0.277515i	−0.0133470	−	0.00969714i
$820$	−16.7705	−	12.1845i	−0.585652	−	0.425501i
$821$	17.5106	−	53.8922i	0.611126	−	1.88085i	0.163760	−	0.986500i	$-0.447638\pi$
$821$	17.5106	−	53.8922i	0.611126	−	1.88085i	0.447366	−	0.894351i	$-0.352362\pi$
$822$	−2.92705	−	9.00854i	−0.102093	−	0.314209i
$823$	25.7984	−	18.7436i	0.899275	−	0.653361i	−0.0390048	−	0.999239i	$-0.512419\pi$
$823$	25.7984	−	18.7436i	0.899275	−	0.653361i	0.938280	+	0.345878i	$0.112419\pi$
$824$	13.0344			0.454076
$825$		0			0
$826$	−4.23607			−0.147392
$827$	15.8541	−	11.5187i	0.551301	−	0.400544i	−0.276964	−	0.960880i	$-0.589328\pi$
$827$	15.8541	−	11.5187i	0.551301	−	0.400544i	0.828265	+	0.560337i	$0.189328\pi$
$828$	1.11397	+	3.42844i	0.0387131	+	0.119147i
$829$	−14.8262	+	45.6305i	−0.514937	+	1.58481i	0.268461	+	0.963291i	$0.413485\pi$
$829$	−14.8262	+	45.6305i	−0.514937	+	1.58481i	−0.783397	+	0.621521i	$0.786515\pi$
$830$	0.836881	+	0.608030i	0.0290486	+	0.0211050i
$831$	30.1525	+	21.9071i	1.04598	+	0.759947i
$832$	1.79837	−	5.53483i	0.0623474	−	0.191886i
$833$	0.954915	+	2.93893i	0.0330858	+	0.101828i
$834$	−5.97214	+	4.33901i	−0.206798	+	0.150248i
$835$	6.47214			0.223978
$836$		0			0
$837$	−23.1803			−0.801230
$838$	9.23607	−	6.71040i	0.319055	−	0.231807i
$839$	9.45492	+	29.0992i	0.326420	+	1.00462i	0.970796	+	0.239908i	$0.0771173\pi$
$839$	9.45492	+	29.0992i	0.326420	+	1.00462i	−0.644376	+	0.764709i	$0.722883\pi$
$840$	−0.736068	+	2.26538i	−0.0253968	+	0.0781632i
$841$	6.20820	+	4.51052i	0.214076	+	0.155535i
$842$	0.236068	+	0.171513i	0.00813544	+	0.00591074i
$843$	12.5902	−	38.7486i	0.433628	−	1.33457i
$844$	−8.94834	−	27.5402i	−0.308014	−	0.947971i
$845$	9.28115	−	6.74315i	0.319281	−	0.231971i
$846$	−0.965558			−0.0331966
$847$		0			0
$848$	−7.49342			−0.257325
$849$	15.6353	−	11.3597i	0.536601	−	0.389863i
$850$	1.45898	+	4.49028i	0.0500426	+	0.154015i
$851$	10.1803	−	31.3319i	0.348978	−	1.07404i
$852$	39.0517	+	28.3727i	1.33789	+	0.972032i
$853$	28.2426	+	20.5195i	0.967010	+	0.702574i	0.954768	−	0.297351i	$-0.0961033\pi$
$853$	28.2426	+	20.5195i	0.967010	+	0.702574i	0.0122416	+	0.999925i	$0.496103\pi$
$854$	0.899187	−	2.76741i	0.0307695	−	0.0946989i
$855$	0.208204	+	0.640786i	0.00712042	+	0.0219144i
$856$	−3.22542	+	2.34341i	−0.110243	+	0.0800960i
$857$	−15.0902			−0.515470			−0.257735	−	0.966216i	$-0.582976\pi$
$857$	−15.0902			−0.515470			−0.257735	+	0.966216i	$0.582976\pi$
$858$		0			0
$859$	21.5623			0.735696			0.367848	−	0.929886i	$-0.380095\pi$
$859$	21.5623			0.735696			0.367848	+	0.929886i	$0.380095\pi$
$860$	−18.8435	+	13.6906i	−0.642557	+	0.466845i
$861$	5.59017	+	17.2048i	0.190512	+	0.586337i
$862$	1.63525	−	5.03280i	0.0556970	−	0.171418i
$863$	38.7877	+	28.1809i	1.32035	+	0.959290i	0.999928	+	0.0120153i	$0.00382467\pi$
$863$	38.7877	+	28.1809i	1.32035	+	0.959290i	0.320422	+	0.947275i	$0.396175\pi$
$864$	18.3541	+	13.3350i	0.624419	+	0.453667i
$865$	−4.75329	+	14.6291i	−0.161617	+	0.497405i
$866$	1.05824	+	3.25693i	0.0359605	+	0.110675i
$867$	−9.75329	+	7.08618i	−0.331239	+	0.240659i
$868$	7.85410			0.266586
$869$		0			0
$870$	−2.85410			−0.0967631
$871$	−8.32624	+	6.04937i	−0.282124	+	0.204975i
$872$	−0.695048	−	2.13914i	−0.0235373	−	0.0724404i
$873$	−0.826238	+	2.54290i	−0.0279639	+	0.0860641i
$874$	−2.77458	−	2.01585i	−0.0938514	−	0.0681870i
$875$	7.28115	+	5.29007i	0.246148	+	0.178837i
$876$	−13.1976	+	40.6179i	−0.445904	+	1.37235i
$877$	4.01722	+	12.3637i	0.135652	+	0.417494i	0.995691	−	0.0927348i	$-0.0295609\pi$
$877$	4.01722	+	12.3637i	0.135652	+	0.417494i	−0.860039	+	0.510228i	$0.829561\pi$
$878$	1.04508	−	0.759299i	0.0352699	−	0.0256251i
$879$	17.7984			0.600324
$880$		0			0
$881$	14.1459			0.476587			0.238294	−	0.971193i	$-0.423412\pi$
$881$	14.1459			0.476587			0.238294	+	0.971193i	$0.423412\pi$
$882$	−0.118034	+	0.0857567i	−0.00397441	+	0.00288758i
$883$	9.77458	+	30.0830i	0.328941	+	1.01238i	0.969630	+	0.244575i	$0.0786485\pi$
$883$	9.77458	+	30.0830i	0.328941	+	1.01238i	−0.640690	+	0.767800i	$0.721351\pi$
$884$	2.18847	−	6.73542i	0.0736062	−	0.226537i
$885$	14.5172	+	10.5474i	0.487991	+	0.354546i
$886$	0.954915	+	0.693786i	0.0320810	+	0.0233082i
$887$	17.6803	−	54.4145i	0.593648	−	1.82706i	0.0323024	−	0.999478i	$-0.489716\pi$
$887$	17.6803	−	54.4145i	0.593648	−	1.82706i	0.561345	−	0.827582i	$-0.310284\pi$
$888$	−4.76393	−	14.6619i	−0.159867	−	0.492020i
$889$	−2.38197	+	1.73060i	−0.0798886	+	0.0580424i
$890$	−2.61803			−0.0877567
$891$		0			0
$892$	−3.77206			−0.126298
$893$	−9.44427	+	6.86167i	−0.316041	+	0.229617i
$894$	−1.69098	−	5.20431i	−0.0565549	−	0.174058i
$895$	−1.16312	+	3.57971i	−0.0388788	+	0.119657i
$896$	−8.16312	−	5.93085i	−0.272711	−	0.198136i
$897$	−8.23607	−	5.98385i	−0.274994	−	0.199795i
$898$	−1.45492	+	4.47777i	−0.0485511	+	0.149425i
$899$	6.04508	+	18.6049i	0.201615	+	0.620507i
$900$	2.29180	−	1.66509i	0.0763932	−	0.0555029i
$901$	−7.36068			−0.245220
$902$		0			0
$903$	20.3262			0.676415
$904$	−0.173762	+	0.126246i	−0.00577924	+	0.00419886i
$905$	−2.29180	−	7.05342i	−0.0761819	−	0.234464i
$906$	0.0106431	−	0.0327561i	0.000353594	−	0.00108825i
$907$	12.7533	+	9.26581i	0.423466	+	0.307666i	0.779031	−	0.626986i	$-0.215711\pi$
$907$	12.7533	+	9.26581i	0.423466	+	0.307666i	−0.355565	+	0.934652i	$0.615711\pi$
$908$	−24.0517	−	17.4746i	−0.798182	−	0.579914i
$909$	1.74671	−	5.37582i	0.0579348	−	0.178305i
$910$	0.145898	+	0.449028i	0.00483647	+	0.0148851i
$911$	36.5517	−	26.5563i	1.21101	−	0.879851i	0.215688	−	0.976462i	$-0.430800\pi$
$911$	36.5517	−	26.5563i	1.21101	−	0.879851i	0.995322	+	0.0966115i	$0.0308004\pi$
$912$	8.97871			0.297315
$913$		0			0
$914$	0.0557281			0.00184332
$915$	−9.97214	+	7.24518i	−0.329669	+	0.239518i
$916$	−3.87539	−	11.9272i	−0.128046	−	0.394086i
$917$	5.85410	−	18.0171i	0.193319	−	0.594976i
$918$	5.22542	+	3.79649i	0.172465	+	0.125303i
$919$	12.0451	+	8.75127i	0.397331	+	0.288678i	0.768453	−	0.639906i	$-0.221027\pi$
$919$	12.0451	+	8.75127i	0.397331	+	0.288678i	−0.371122	+	0.928584i	$0.621027\pi$
$920$	2.31559	−	7.12667i	0.0763429	−	0.234959i
$921$	11.5902	+	35.6709i	0.381909	+	1.17540i
$922$	−5.71885	+	4.15499i	−0.188340	+	0.136837i
$923$	19.8885			0.654639
$924$		0			0
$925$	−25.8885			−0.851210
$926$	6.87132	−	4.99231i	0.225806	−	0.164057i
$927$	−1.04508	−	3.21644i	−0.0343251	−	0.105642i
$928$	5.91641	−	18.2088i	0.194216	−	0.597734i
$929$	−19.4164	−	14.1068i	−0.637032	−	0.462831i	0.221797	−	0.975093i	$-0.428808\pi$
$929$	−19.4164	−	14.1068i	−0.637032	−	0.462831i	−0.858829	+	0.512262i	$0.828808\pi$
$930$	2.11803	+	1.53884i	0.0694531	+	0.0504606i
$931$	−0.545085	+	1.67760i	−0.0178644	+	0.0549811i
$932$	16.8541	+	51.8716i	0.552074	+	1.69911i
$933$	11.7812	−	8.55951i	0.385698	−	0.280226i
$934$	1.72136			0.0563246
$935$		0			0
$936$	0.695048			0.0227184
$937$	41.8435	−	30.4011i	1.36697	−	0.993159i	0.368999	−	0.929430i	$-0.379701\pi$
$937$	41.8435	−	30.4011i	1.36697	−	0.993159i	0.997967	−	0.0637293i	$-0.0202994\pi$
$938$	0.982779	+	3.02468i	0.0320889	+	0.0987594i
$939$	−9.16312	+	28.2012i	−0.299027	+	0.920311i
$940$	−9.92705	−	7.21242i	−0.323785	−	0.235243i
$941$	−21.8992	−	15.9107i	−0.713893	−	0.518674i	0.170534	−	0.985352i	$-0.445451\pi$
$941$	−21.8992	−	15.9107i	−0.713893	−	0.518674i	−0.884427	+	0.466678i	$0.845451\pi$
$942$	3.79837	−	11.6902i	0.123758	−	0.380887i
$943$	−17.5861	−	54.1245i	−0.572682	−	1.76254i
$944$	−28.2254	+	20.5070i	−0.918659	+	0.667445i
$945$	5.47214			0.178009
$946$		0			0
$947$	6.29180			0.204456			0.102228	−	0.994761i	$-0.467403\pi$
$947$	6.29180			0.204456			0.102228	+	0.994761i	$0.467403\pi$
$948$	−15.4894	+	11.2537i	−0.503071	+	0.365502i
$949$	5.43769	+	16.7355i	0.176515	+	0.543257i
$950$	−0.832816	+	2.56314i	−0.0270201	+	0.0831593i
$951$	−5.80902	−	4.22050i	−0.188370	−	0.136859i
$952$	−3.68034	−	2.67392i	−0.119281	−	0.0866624i
$953$	−1.92705	+	5.93085i	−0.0624233	+	0.192119i	−0.977405	−	0.211377i	$-0.932205\pi$
$953$	−1.92705	+	5.93085i	−0.0624233	+	0.192119i	0.914981	+	0.403496i	$0.132205\pi$
$954$	−0.107391	−	0.330515i	−0.00347691	−	0.0107008i
$955$	−12.7533	+	9.26581i	−0.412687	+	0.299834i
$956$	31.6869			1.02483
$957$		0			0
$958$	−8.31308			−0.268583
$959$	12.3992	−	9.00854i	0.400391	−	0.290901i
$960$	2.35410	+	7.24518i	0.0759783	+	0.233837i
$961$	−4.03444	+	12.4167i	−0.130143	+	0.400540i
$962$	−2.47214	−	1.79611i	−0.0797049	−	0.0579090i
$963$	0.836881	+	0.608030i	0.0269681	+	0.0195935i
$964$	−9.32217	+	28.6907i	−0.300247	+	0.924065i
$965$	−4.73607	−	14.5761i	−0.152459	−	0.469222i
$966$	−2.54508	+	1.84911i	−0.0818868	+	0.0594942i
$967$	27.4508			0.882760			0.441380	−	0.897320i	$-0.354489\pi$
$967$	27.4508			0.882760			0.441380	+	0.897320i	$0.354489\pi$
$968$		0			0
$969$	8.81966			0.283328
$970$	2.16312	−	1.57160i	0.0694536	−	0.0504610i
$971$	−8.72949	−	26.8666i	−0.280143	−	0.862190i	−0.987813	−	0.155647i	$-0.950254\pi$
$971$	−8.72949	−	26.8666i	−0.280143	−	0.862190i	0.707670	−	0.706543i	$-0.249746\pi$
$972$	2.25987	−	6.95515i	0.0724853	−	0.223087i
$973$	−9.66312	−	7.02067i	−0.309785	−	0.225072i
$974$	−10.0729	−	7.31843i	−0.322758	−	0.234497i
$975$	−2.47214	+	7.60845i	−0.0791717	+	0.243665i
$976$	−7.40576	−	22.7926i	−0.237053	−	0.729573i
$977$	8.75329	−	6.35964i	0.280043	−	0.203463i	−0.438893	−	0.898539i	$-0.644629\pi$
$977$	8.75329	−	6.35964i	0.280043	−	0.203463i	0.718936	+	0.695076i	$0.244629\pi$
$978$	−5.38197			−0.172096
$979$		0			0
$980$	−1.85410			−0.0592271
$981$	−0.472136	+	0.343027i	−0.0150741	+	0.0109520i
$982$	−2.61397	−	8.04497i	−0.0834151	−	0.256725i
$983$	−3.82624	+	11.7759i	−0.122038	+	0.375594i	−0.993350	−	0.115135i	$-0.963270\pi$
$983$	−3.82624	+	11.7759i	−0.122038	+	0.375594i	0.871312	+	0.490730i	$0.163270\pi$
$984$	−21.5451	−	15.6534i	−0.686832	−	0.499013i
$985$	3.47214	+	2.52265i	0.110631	+	0.0803785i
$986$	1.68441	−	5.18407i	0.0536424	−	0.165094i
$987$	3.30902	+	10.1841i	0.105327	+	0.324164i
$988$	3.27051	−	2.37616i	0.104049	−	0.0755959i
$989$	−63.9443			−2.03331
$990$		0			0
$991$	−0.729490			−0.0231730			−0.0115865	−	0.999933i	$-0.503688\pi$
$991$	−0.729490			−0.0231730			−0.0115865	+	0.999933i	$0.503688\pi$
$992$	−14.2082	+	10.3229i	−0.451111	+	0.327751i
$993$	−3.09017	−	9.51057i	−0.0980636	−	0.301809i
$994$	1.89919	−	5.84510i	0.0602386	−	0.185395i
$995$	6.66312	+	4.84104i	0.211235	+	0.153471i
$996$	−6.57295	−	4.77553i	−0.208272	−	0.151318i
$997$	−17.2639	+	53.1329i	−0.546754	+	1.68274i	0.170028	+	0.985439i	$0.445614\pi$
$997$	−17.2639	+	53.1329i	−0.546754	+	1.68274i	−0.716782	+	0.697297i	$0.754386\pi$
$998$	1.19098	+	3.66547i	0.0376999	+	0.116028i
$999$	−28.6525	+	20.8172i	−0.906524	+	0.658628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.d.729.1		4
11.2	odd	10		847.2.a.h.1.1	yes	2
11.3	even	5		847.2.f.l.148.1		4
11.4	even	5	inner	847.2.f.d.323.1		4
11.5	even	5		847.2.f.l.372.1		4
11.6	odd	10		847.2.f.c.372.1		4
11.7	odd	10		847.2.f.j.323.1		4
11.8	odd	10		847.2.f.c.148.1		4
11.9	even	5		847.2.a.d.1.2	✓	2
11.10	odd	2		847.2.f.j.729.1		4
33.2	even	10		7623.2.a.t.1.2		2
33.20	odd	10		7623.2.a.bx.1.1		2
77.13	even	10		5929.2.a.s.1.1		2
77.20	odd	10		5929.2.a.i.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.d.1.2	✓	2	11.9	even	5
847.2.a.h.1.1	yes	2	11.2	odd	10
847.2.f.c.148.1		4	11.8	odd	10
847.2.f.c.372.1		4	11.6	odd	10
847.2.f.d.323.1		4	11.4	even	5	inner
847.2.f.d.729.1		4	1.1	even	1	trivial
847.2.f.j.323.1		4	11.7	odd	10
847.2.f.j.729.1		4	11.10	odd	2
847.2.f.l.148.1		4	11.3	even	5
847.2.f.l.372.1		4	11.5	even	5
5929.2.a.i.1.2		2	77.20	odd	10
5929.2.a.s.1.1		2	77.13	even	10
7623.2.a.t.1.2		2	33.2	even	10
7623.2.a.bx.1.1		2	33.20	odd	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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.224514i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.500000 - 0.363271i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.454915 + 1.40008i) q^{8} +(0.309017 - 0.224514i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.224514i) q^{2} +(-0.500000 - 1.53884i) q^{3} +(-0.572949 + 1.76336i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.500000 - 0.363271i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.454915 + 1.40008i) q^{8} +(0.309017 - 0.224514i) q^{9} -0.381966 q^{10} +3.00000 q^{12} +(1.00000 - 0.726543i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-2.54508 - 1.84911i) q^{16} +(-2.50000 - 1.81636i) q^{17} +(0.0450850 - 0.138757i) q^{18} +(-0.545085 - 1.67760i) q^{19} +(1.50000 - 1.08981i) q^{20} -1.61803 q^{21} +5.09017 q^{23} +(1.92705 - 1.40008i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(0.145898 - 0.449028i) q^{26} +(-4.42705 - 3.21644i) q^{27} +(1.50000 + 1.08981i) q^{28} +(-1.42705 + 4.39201i) q^{29} +(0.190983 + 0.587785i) q^{30} +(3.42705 - 2.48990i) q^{31} -4.14590 q^{32} -1.18034 q^{34} +(-0.809017 + 0.587785i) q^{35} +(0.218847 + 0.673542i) q^{36} +(2.00000 - 6.15537i) q^{37} +(-0.545085 - 0.396027i) q^{38} +(-1.61803 - 1.17557i) q^{39} +(0.454915 - 1.40008i) q^{40} +(-3.45492 - 10.6331i) q^{41} +(-0.500000 + 0.363271i) q^{42} -12.5623 q^{43} -0.381966 q^{45} +(1.57295 - 1.14281i) q^{46} +(-2.04508 - 6.29412i) q^{47} +(-1.57295 + 4.84104i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.23607 - 0.898056i) q^{50} +(-1.54508 + 4.75528i) q^{51} +(0.708204 + 2.17963i) q^{52} +(1.92705 - 1.40008i) q^{53} -2.09017 q^{54} +1.47214 q^{56} +(-2.30902 + 1.67760i) q^{57} +(0.545085 + 1.67760i) q^{58} +(3.42705 - 10.5474i) q^{59} +(-2.42705 - 1.76336i) q^{60} +(6.16312 + 4.47777i) q^{61} +(0.500000 - 1.53884i) q^{62} +(-0.118034 - 0.363271i) q^{63} +(3.80902 - 2.76741i) q^{64} -1.23607 q^{65} -8.32624 q^{67} +(4.63525 - 3.36771i) q^{68} +(-2.54508 - 7.83297i) q^{69} +(-0.118034 + 0.363271i) q^{70} +(13.0172 + 9.45756i) q^{71} +(0.454915 + 0.330515i) q^{72} +(-4.39919 + 13.5393i) q^{73} +(-0.763932 - 2.35114i) q^{74} +(-5.23607 + 3.80423i) q^{75} +3.27051 q^{76} -0.763932 q^{78} +(-5.16312 + 3.75123i) q^{79} +(0.972136 + 2.99193i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(-3.45492 - 2.51014i) q^{82} +(-2.19098 - 1.59184i) q^{83} +(0.927051 - 2.85317i) q^{84} +(0.954915 + 2.93893i) q^{85} +(-3.88197 + 2.82041i) q^{86} +7.47214 q^{87} +6.85410 q^{89} +(-0.118034 + 0.0857567i) q^{90} +(-0.381966 - 1.17557i) q^{91} +(-2.91641 + 8.97578i) q^{92} +(-5.54508 - 4.02874i) q^{93} +(-2.04508 - 1.48584i) q^{94} +(-0.545085 + 1.67760i) q^{95} +(2.07295 + 6.37988i) q^{96} +(-5.66312 + 4.11450i) q^{97} -0.381966 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 2 q^{3} - 9 q^{4} - q^{5} - 2 q^{6} - q^{7} + 13 q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 - 2 * q^3 - 9 * q^4 - q^5 - 2 * q^6 - q^7 + 13 * q^8 - q^9	\( 4 q - q^{2} - 2 q^{3} - 9 q^{4} - q^{5} - 2 q^{6} - q^{7} + 13 q^{8} - q^{9} - 6 q^{10} + 12 q^{12} + 4 q^{13} + 4 q^{14} - 2 q^{15} + q^{16} - 10 q^{17} - 11 q^{18} + 9 q^{19} + 6 q^{20} - 2 q^{21} - 2 q^{23} + q^{24} + 4 q^{25} + 14 q^{26} - 11 q^{27} + 6 q^{28} + q^{29} + 3 q^{30} + 7 q^{31} - 30 q^{32} + 40 q^{34} - q^{35} + 21 q^{36} + 8 q^{37} + 9 q^{38} - 2 q^{39} + 13 q^{40} - 25 q^{41} - 2 q^{42} - 10 q^{43} - 6 q^{45} + 13 q^{46} + 3 q^{47} - 13 q^{48} - q^{49} + 4 q^{50} + 5 q^{51} - 24 q^{52} + q^{53} + 14 q^{54} - 12 q^{56} - 7 q^{57} - 9 q^{58} + 7 q^{59} - 3 q^{60} + 9 q^{61} + 2 q^{62} + 4 q^{63} + 13 q^{64} + 4 q^{65} - 2 q^{67} - 15 q^{68} + q^{69} + 4 q^{70} + 23 q^{71} + 13 q^{72} + 7 q^{73} - 12 q^{74} - 12 q^{75} - 54 q^{76} - 12 q^{78} - 5 q^{79} - 14 q^{80} - 14 q^{81} - 25 q^{82} - 11 q^{83} - 3 q^{84} + 15 q^{85} - 20 q^{86} + 12 q^{87} + 14 q^{89} + 4 q^{90} - 6 q^{91} + 42 q^{92} - 11 q^{93} + 3 q^{94} + 9 q^{95} + 15 q^{96} - 7 q^{97} - 6 q^{98}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 - 9 * q^4 - q^5 - 2 * q^6 - q^7 + 13 * q^8 - q^9 - 6 * q^10 + 12 * q^12 + 4 * q^13 + 4 * q^14 - 2 * q^15 + q^16 - 10 * q^17 - 11 * q^18 + 9 * q^19 + 6 * q^20 - 2 * q^21 - 2 * q^23 + q^24 + 4 * q^25 + 14 * q^26 - 11 * q^27 + 6 * q^28 + q^29 + 3 * q^30 + 7 * q^31 - 30 * q^32 + 40 * q^34 - q^35 + 21 * q^36 + 8 * q^37 + 9 * q^38 - 2 * q^39 + 13 * q^40 - 25 * q^41 - 2 * q^42 - 10 * q^43 - 6 * q^45 + 13 * q^46 + 3 * q^47 - 13 * q^48 - q^49 + 4 * q^50 + 5 * q^51 - 24 * q^52 + q^53 + 14 * q^54 - 12 * q^56 - 7 * q^57 - 9 * q^58 + 7 * q^59 - 3 * q^60 + 9 * q^61 + 2 * q^62 + 4 * q^63 + 13 * q^64 + 4 * q^65 - 2 * q^67 - 15 * q^68 + q^69 + 4 * q^70 + 23 * q^71 + 13 * q^72 + 7 * q^73 - 12 * q^74 - 12 * q^75 - 54 * q^76 - 12 * q^78 - 5 * q^79 - 14 * q^80 - 14 * q^81 - 25 * q^82 - 11 * q^83 - 3 * q^84 + 15 * q^85 - 20 * q^86 + 12 * q^87 + 14 * q^89 + 4 * q^90 - 6 * q^91 + 42 * q^92 - 11 * q^93 + 3 * q^94 + 9 * q^95 + 15 * q^96 - 7 * q^97 - 6 * q^98

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