LMFDB - Embedded newform 784.2.m.k.589.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			589.3
Character	$\chi$	$=$	784.589
Dual form			784.2.m.k.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913051 + 1.07997i) q^{2} +(-1.80111 - 1.80111i) q^{3} +(-0.332676 - 1.97214i) q^{4} +(1.37283 - 1.37283i) q^{5} +(3.58965 - 0.300642i) q^{6} +(2.43360 + 1.44138i) q^{8} +3.48800i q^{9} +O(q^{10})$	\(q+(-0.913051 + 1.07997i) q^{2} +(-1.80111 - 1.80111i) q^{3} +(-0.332676 - 1.97214i) q^{4} +(1.37283 - 1.37283i) q^{5} +(3.58965 - 0.300642i) q^{6} +(2.43360 + 1.44138i) q^{8} +3.48800i q^{9} +(0.229153 + 2.73608i) q^{10} +(-3.74749 + 3.74749i) q^{11} +(-2.95285 + 4.15122i) q^{12} +(3.61173 + 3.61173i) q^{13} -4.94523 q^{15} +(-3.77865 + 1.31216i) q^{16} -0.589630 q^{17} +(-3.76694 - 3.18472i) q^{18} +(0.376876 + 0.376876i) q^{19} +(-3.16411 - 2.25070i) q^{20} +(-0.625532 - 7.46884i) q^{22} +0.436515i q^{23} +(-1.78710 - 6.97927i) q^{24} +1.23069i q^{25} +(-7.19827 + 0.602871i) q^{26} +(0.878939 - 0.878939i) q^{27} +(2.68976 + 2.68976i) q^{29} +(4.51525 - 5.34071i) q^{30} +7.88237 q^{31} +(2.03300 - 5.27891i) q^{32} +13.4993 q^{33} +(0.538362 - 0.636783i) q^{34} +(6.87881 - 1.16037i) q^{36} +(2.12926 - 2.12926i) q^{37} +(-0.751121 + 0.0629081i) q^{38} -13.0103i q^{39} +(5.31969 - 1.36215i) q^{40} -2.95135i q^{41} +(-7.67329 + 7.67329i) q^{43} +(8.63727 + 6.14387i) q^{44} +(4.78842 + 4.78842i) q^{45} +(-0.471424 - 0.398561i) q^{46} +4.03543 q^{47} +(9.16913 + 4.44242i) q^{48} +(-1.32911 - 1.12368i) q^{50} +(1.06199 + 1.06199i) q^{51} +(5.92130 - 8.32437i) q^{52} +(0.667643 - 0.667643i) q^{53} +(0.146713 + 1.75175i) q^{54} +10.2893i q^{55} -1.35759i q^{57} +(-5.36075 + 0.448975i) q^{58} +(-0.0205828 + 0.0205828i) q^{59} +(1.64516 + 9.75267i) q^{60} +(-1.44796 - 1.44796i) q^{61} +(-7.19700 + 8.51273i) q^{62} +(3.84483 + 7.01550i) q^{64} +9.91658 q^{65} +(-12.3255 + 14.5789i) q^{66} +(4.57382 + 4.57382i) q^{67} +(0.196155 + 1.16283i) q^{68} +(0.786212 - 0.786212i) q^{69} -2.05630i q^{71} +(-5.02754 + 8.48840i) q^{72} +7.91736i q^{73} +(0.355417 + 4.24367i) q^{74} +(2.21660 - 2.21660i) q^{75} +(0.617873 - 0.868628i) q^{76} +(14.0507 + 11.8790i) q^{78} +13.0606 q^{79} +(-3.38607 + 6.98882i) q^{80} +7.29786 q^{81} +(3.18737 + 2.69473i) q^{82} +(-10.1551 - 10.1551i) q^{83} +(-0.809460 + 0.809460i) q^{85} +(-1.28083 - 15.2930i) q^{86} -9.68911i q^{87} +(-14.5215 + 3.71834i) q^{88} +3.87127i q^{89} +(-9.54343 + 0.799284i) q^{90} +(0.860868 - 0.145218i) q^{92} +(-14.1970 - 14.1970i) q^{93} +(-3.68455 + 4.35814i) q^{94} +1.03477 q^{95} +(-13.1696 + 5.84624i) q^{96} +12.0556 q^{97} +(-13.0712 - 13.0712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8}+O(q^{10}) $ 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8	$ 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27} + 12 q^{29} + 4 q^{30} + 28 q^{31} - 16 q^{32} + 16 q^{33} + 22 q^{34} - 36 q^{36} + 24 q^{37} + 20 q^{38} + 26 q^{40} - 20 q^{43} - 6 q^{44} - 28 q^{45} + 14 q^{46} - 20 q^{47} - 28 q^{48} + 28 q^{50} - 24 q^{51} - 16 q^{52} + 16 q^{53} + 64 q^{54} + 6 q^{58} - 20 q^{59} - 46 q^{60} + 8 q^{61} - 12 q^{62} + 40 q^{64} - 8 q^{65} - 20 q^{66} - 48 q^{67} + 20 q^{69} + 32 q^{72} + 8 q^{74} - 4 q^{75} + 18 q^{76} + 58 q^{78} + 36 q^{79} - 28 q^{80} + 2 q^{82} + 4 q^{83} + 20 q^{86} + 42 q^{88} + 10 q^{90} + 38 q^{92} - 8 q^{93} - 72 q^{94} + 4 q^{95} - 120 q^{96} + 24 q^{97} - 12 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 12 * q^13 - 20 * q^15 - 16 * q^16 + 8 * q^17 - 18 * q^18 - 4 * q^19 + 8 * q^20 + 18 * q^24 - 10 * q^26 + 12 * q^27 + 12 * q^29 + 4 * q^30 + 28 * q^31 - 16 * q^32 + 16 * q^33 + 22 * q^34 - 36 * q^36 + 24 * q^37 + 20 * q^38 + 26 * q^40 - 20 * q^43 - 6 * q^44 - 28 * q^45 + 14 * q^46 - 20 * q^47 - 28 * q^48 + 28 * q^50 - 24 * q^51 - 16 * q^52 + 16 * q^53 + 64 * q^54 + 6 * q^58 - 20 * q^59 - 46 * q^60 + 8 * q^61 - 12 * q^62 + 40 * q^64 - 8 * q^65 - 20 * q^66 - 48 * q^67 + 20 * q^69 + 32 * q^72 + 8 * q^74 - 4 * q^75 + 18 * q^76 + 58 * q^78 + 36 * q^79 - 28 * q^80 + 2 * q^82 + 4 * q^83 + 20 * q^86 + 42 * q^88 + 10 * q^90 + 38 * q^92 - 8 * q^93 - 72 * q^94 + 4 * q^95 - 120 * q^96 + 24 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−0.913051	+	1.07997i	−0.645625	+	0.763655i
$2$	−0.913051	+	1.07997i	−0.645625	+	0.763655i
$3$	−1.80111	−	1.80111i	−1.03987	−	1.03987i	−0.999171	−	0.0407003i	$-0.987041\pi$
$3$	−1.80111	−	1.80111i	−1.03987	−	1.03987i	−0.0407003	−	0.999171i	$-0.512959\pi$
$4$	−0.332676	−	1.97214i	−0.166338	−	0.986069i
$5$	1.37283	−	1.37283i	0.613947	−	0.613947i	−0.330025	−	0.943972i	$-0.607057\pi$
$5$	1.37283	−	1.37283i	0.613947	−	0.613947i	0.943972	+	0.330025i	$0.107057\pi$
$6$	3.58965	−	0.300642i	1.46547	−	0.122736i
$7$		0			0
$7$		0			0
$8$	2.43360	+	1.44138i	0.860408	+	0.509606i
$9$			3.48800i			1.16267i
$10$	0.229153	+	2.73608i	0.0724644	+	0.865223i
$11$	−3.74749	+	3.74749i	−1.12991	+	1.12991i	−0.139721	+	0.990191i	$0.544620\pi$
$11$	−3.74749	+	3.74749i	−1.12991	+	1.12991i	−0.990191	+	0.139721i	$0.955380\pi$
$12$	−2.95285	+	4.15122i	−0.852415	+	1.19835i
$13$	3.61173	+	3.61173i	1.00171	+	1.00171i	0.999999	+	0.00171617i	$0.000546274\pi$
$13$	3.61173	+	3.61173i	1.00171	+	1.00171i	0.00171617	+	0.999999i	$0.499454\pi$
$14$		0			0
$15$	−4.94523			−1.27685
$16$	−3.77865	+	1.31216i	−0.944663	+	0.328041i
$17$	−0.589630			−0.143006			−0.0715031	−	0.997440i	$-0.522780\pi$
$17$	−0.589630			−0.143006			−0.0715031	+	0.997440i	$0.522780\pi$
$18$	−3.76694	−	3.18472i	−0.887876	−	0.750646i
$19$	0.376876	+	0.376876i	0.0864612	+	0.0864612i	0.749015	−	0.662553i	$-0.230527\pi$
$19$	0.376876	+	0.376876i	0.0864612	+	0.0864612i	−0.662553	+	0.749015i	$0.730527\pi$
$20$	−3.16411	−	2.25070i	−0.707517	−	0.503272i
$21$		0			0
$22$	−0.625532	−	7.46884i	−0.133364	−	1.59236i
$23$			0.436515i			0.0910197i	0.998964	+	0.0455098i	$0.0144912\pi$
$23$			0.436515i			0.0910197i	−0.998964	+	0.0455098i	$0.985509\pi$
$24$	−1.78710	−	6.97927i	−0.364790	−	1.42464i
$25$			1.23069i			0.246138i
$26$	−7.19827	+	0.602871i	−1.41170	+	0.118233i
$27$	0.878939	−	0.878939i	0.169152	−	0.169152i
$28$		0			0
$29$	2.68976	+	2.68976i	0.499476	+	0.499476i	0.911275	−	0.411799i	$-0.135099\pi$
$29$	2.68976	+	2.68976i	0.499476	+	0.499476i	−0.411799	+	0.911275i	$0.635099\pi$
$30$	4.51525	−	5.34071i	0.824367	−	0.975075i
$31$	7.88237			1.41571			0.707857	−	0.706355i	$-0.249662\pi$
$31$	7.88237			1.41571			0.707857	+	0.706355i	$0.249662\pi$
$32$	2.03300	−	5.27891i	0.359388	−	0.933188i
$33$	13.4993			2.34993
$34$	0.538362	−	0.636783i	0.0923284	−	0.109207i
$35$		0			0
$36$	6.87881	−	1.16037i	1.14647	−	0.193395i
$37$	2.12926	−	2.12926i	0.350049	−	0.350049i	−0.510079	−	0.860128i	$-0.670384\pi$
$37$	2.12926	−	2.12926i	0.350049	−	0.350049i	0.860128	+	0.510079i	$0.170384\pi$
$38$	−0.751121	+	0.0629081i	−0.121848	+	0.0102050i
$39$		−	13.0103i		−	2.08331i
$40$	5.31969	−	1.36215i	0.841116	−	0.215374i
$41$		−	2.95135i		−	0.460923i	−0.973081	−	0.230461i	$-0.925976\pi$
$41$		−	2.95135i		−	0.460923i	0.973081	−	0.230461i	$-0.0740235\pi$
$42$		0			0
$43$	−7.67329	+	7.67329i	−1.17017	+	1.17017i	−0.187996	+	0.982170i	$0.560199\pi$
$43$	−7.67329	+	7.67329i	−1.17017	+	1.17017i	−0.982170	+	0.187996i	$0.939801\pi$
$44$	8.63727	+	6.14387i	1.30212	+	0.926224i
$45$	4.78842	+	4.78842i	0.713816	+	0.713816i
$46$	−0.471424	−	0.398561i	−0.0695076	−	0.0587645i
$47$	4.03543			0.588627			0.294314	−	0.955709i	$-0.404909\pi$
$47$	4.03543			0.588627			0.294314	+	0.955709i	$0.404909\pi$
$48$	9.16913	+	4.44242i	1.32345	+	0.641208i
$49$		0			0
$50$	−1.32911	−	1.12368i	−0.187964	−	0.158912i
$51$	1.06199	+	1.06199i	0.148708	+	0.148708i
$52$	5.92130	−	8.32437i	0.821137	−	1.15438i
$53$	0.667643	−	0.667643i	0.0917078	−	0.0917078i	−0.659765	−	0.751472i	$-0.729344\pi$
$53$	0.667643	−	0.667643i	0.0917078	−	0.0917078i	0.751472	+	0.659765i	$0.229344\pi$
$54$	0.146713	+	1.75175i	0.0199651	+	0.238382i
$55$			10.2893i			1.38741i
$56$		0			0
$57$		−	1.35759i		−	0.179817i
$58$	−5.36075	+	0.448975i	−0.703901	+	0.0589533i
$59$	−0.0205828	+	0.0205828i	−0.00267965	+	0.00267965i	−0.708445	−	0.705766i	$-0.750603\pi$
$59$	−0.0205828	+	0.0205828i	−0.00267965	+	0.00267965i	0.705766	+	0.708445i	$0.250603\pi$
$60$	1.64516	+	9.75267i	0.212389	+	1.25906i
$61$	−1.44796	−	1.44796i	−0.185392	−	0.185392i	0.608308	−	0.793701i	$-0.291848\pi$
$61$	−1.44796	−	1.44796i	−0.185392	−	0.185392i	−0.793701	+	0.608308i	$0.791848\pi$
$62$	−7.19700	+	8.51273i	−0.914020	+	1.08112i
$63$		0			0
$64$	3.84483	+	7.01550i	0.480604	+	0.876938i
$65$	9.91658			1.23000
$66$	−12.3255	+	14.5789i	−1.51717	+	1.79453i
$67$	4.57382	+	4.57382i	0.558781	+	0.558781i	0.928960	−	0.370179i	$-0.120704\pi$
$67$	4.57382	+	4.57382i	0.558781	+	0.558781i	−0.370179	+	0.928960i	$0.620704\pi$
$68$	0.196155	+	1.16283i	0.0237873	+	0.141014i
$69$	0.786212	−	0.786212i	0.0946488	−	0.0946488i
$70$		0			0
$71$		−	2.05630i		−	0.244037i	−0.992528	−	0.122019i	$-0.961063\pi$
$71$		−	2.05630i		−	0.244037i	0.992528	−	0.122019i	$-0.0389368\pi$
$72$	−5.02754	+	8.48840i	−0.592501	+	1.00037i
$73$			7.91736i			0.926657i	0.886187	+	0.463329i	$0.153345\pi$
$73$			7.91736i			0.926657i	−0.886187	+	0.463329i	$0.846655\pi$
$74$	0.355417	+	4.24367i	0.0413164	+	0.493317i
$75$	2.21660	−	2.21660i	0.255951	−	0.255951i
$76$	0.617873	−	0.868628i	0.0708749	−	0.0996384i
$77$		0			0
$78$	14.0507	+	11.8790i	1.59093	+	1.34504i
$79$	13.0606			1.46943			0.734714	−	0.678377i	$-0.237316\pi$
$79$	13.0606			1.46943			0.734714	+	0.678377i	$0.237316\pi$
$80$	−3.38607	+	6.98882i	−0.378574	+	0.781373i
$81$	7.29786			0.810874
$82$	3.18737	+	2.69473i	0.351986	+	0.297583i
$83$	−10.1551	−	10.1551i	−1.11467	−	1.11467i	−0.992510	−	0.122161i	$-0.961018\pi$
$83$	−10.1551	−	10.1551i	−1.11467	−	1.11467i	−0.122161	−	0.992510i	$-0.538982\pi$
$84$		0			0
$85$	−0.809460	+	0.809460i	−0.0877983	+	0.0877983i
$86$	−1.28083	−	15.2930i	−0.138115	−	1.64909i
$87$		−	9.68911i		−	1.03878i
$88$	−14.5215	+	3.71834i	−1.54799	+	0.396376i
$89$			3.87127i			0.410354i	0.978725	+	0.205177i	$0.0657771\pi$
$89$			3.87127i			0.410354i	−0.978725	+	0.205177i	$0.934223\pi$
$90$	−9.54343	+	0.799284i	−1.00597	+	0.0842519i
$91$		0			0
$92$	0.860868	−	0.145218i	0.0897517	−	0.0151400i
$93$	−14.1970	−	14.1970i	−1.47216	−	1.47216i
$94$	−3.68455	+	4.35814i	−0.380032	+	0.449508i
$95$	1.03477			0.106165
$96$	−13.1696	+	5.84624i	−1.34411	+	0.596679i
$97$	12.0556			1.22406			0.612029	−	0.790836i	$-0.290354\pi$
$97$	12.0556			1.22406			0.612029	+	0.790836i	$0.290354\pi$
$98$		0			0
$99$	−13.0712	−	13.0712i	−1.31371	−	1.31371i
$100$	2.42709	−	0.409420i	0.242709	−	0.0409420i
$101$	1.89869	−	1.89869i	0.188927	−	0.188927i	−0.606305	−	0.795232i	$-0.707349\pi$
$101$	1.89869	−	1.89869i	0.188927	−	0.188927i	0.795232	+	0.606305i	$0.207349\pi$
$102$	−2.11657	+	0.177267i	−0.209571	+	0.0175521i
$103$		−	0.0892702i		−	0.00879606i	−0.999990	−	0.00439803i	$-0.998600\pi$
$103$		−	0.0892702i		−	0.00879606i	0.999990	−	0.00439803i	$-0.00139994\pi$
$104$	3.58363	+	13.9954i	0.351404	+	1.37236i
$105$		0			0
$106$	0.111443	+	1.33063i	0.0108243	+	0.129242i
$107$	−10.3074	+	10.3074i	−0.996458	+	0.996458i	−0.999994	−	0.00353567i	$-0.998875\pi$
$107$	−10.3074	+	10.3074i	−0.996458	+	0.996458i	0.00353567	+	0.999994i	$0.498875\pi$
$108$	−2.02579	−	1.44099i	−0.194932	−	0.138659i
$109$	4.89306	+	4.89306i	0.468670	+	0.468670i	0.901483	−	0.432814i	$-0.142479\pi$
$109$	4.89306	+	4.89306i	0.468670	+	0.468670i	−0.432814	+	0.901483i	$0.642479\pi$
$110$	−11.1122	−	9.39468i	−1.05950	−	0.895747i
$111$	−7.67008			−0.728012
$112$		0			0
$113$	7.51142			0.706615			0.353307	−	0.935507i	$-0.385057\pi$
$113$	7.51142			0.706615			0.353307	+	0.935507i	$0.385057\pi$
$114$	1.46616	+	1.23955i	0.137318	+	0.116094i
$115$	0.599260	+	0.599260i	0.0558813	+	0.0558813i
$116$	4.40976	−	6.19939i	0.409436	−	0.575599i
$117$	−12.5977	+	12.5977i	−1.16466	+	1.16466i
$118$	−0.00343568	−	0.0410219i	−0.000316280	−	0.00377638i
$119$		0			0
$120$	−12.0347	−	7.12797i	−1.09861	−	0.650691i
$121$		−	17.0874i		−	1.55340i
$122$	2.88582	−	0.241694i	0.261270	−	0.0218819i
$123$	−5.31570	+	5.31570i	−0.479301	+	0.479301i
$124$	−2.62227	−	15.5451i	−0.235487	−	1.39599i
$125$	8.55366	+	8.55366i	0.765063	+	0.765063i
$126$		0			0
$127$	4.25202			0.377306			0.188653	−	0.982044i	$-0.439588\pi$
$127$	4.25202			0.377306			0.188653	+	0.982044i	$0.439588\pi$
$128$	−11.0871	−	2.25320i	−0.979968	−	0.199157i
$129$	27.6409			2.43365
$130$	−9.05434	+	10.7096i	−0.794118	+	0.939296i
$131$	−3.58025	−	3.58025i	−0.312808	−	0.312808i	0.533188	−	0.845996i	$-0.320994\pi$
$131$	−3.58025	−	3.58025i	−0.312808	−	0.312808i	−0.845996	+	0.533188i	$0.820994\pi$
$132$	−4.49089	−	26.6225i	−0.390882	−	2.31719i
$133$		0			0
$134$	−9.11572	+	0.763463i	−0.787479	+	0.0659531i
$135$		−	2.41326i		−	0.207701i
$136$	−1.43492	−	0.849882i	−0.123044	−	0.0728768i
$137$		−	0.278868i		−	0.0238253i	−0.999929	−	0.0119127i	$-0.996208\pi$
$137$		−	0.278868i		−	0.0238253i	0.999929	−	0.0119127i	$-0.00379201\pi$
$138$	0.131235	+	1.56694i	0.0111714	+	0.133387i
$139$	12.1095	−	12.1095i	1.02712	−	1.02712i	0.0274943	−	0.999622i	$-0.491247\pi$
$139$	12.1095	−	12.1095i	1.02712	−	1.02712i	0.999622	−	0.0274943i	$-0.00875280\pi$
$140$		0			0
$141$	−7.26825	−	7.26825i	−0.612097	−	0.612097i
$142$	2.22074	+	1.87750i	0.186360	+	0.157557i
$143$	−27.0699			−2.26370
$144$	−4.57683	−	13.1799i	−0.381402	−	1.09833i
$145$	7.38515			0.613304
$146$	−8.55052	−	7.22896i	−0.707646	−	0.598273i
$147$		0			0
$148$	−4.90756	−	3.49085i	−0.403399	−	0.286946i
$149$	−15.5122	+	15.5122i	−1.27081	+	1.27081i	−0.325146	+	0.945664i	$0.605413\pi$
$149$	−15.5122	+	15.5122i	−1.27081	+	1.27081i	−0.945664	+	0.325146i	$0.894587\pi$
$150$	0.369996	+	4.41774i	0.0302101	+	0.360707i
$151$		−	9.33891i		−	0.759990i	−0.924989	−	0.379995i	$-0.875926\pi$
$151$		−	9.33891i		−	0.759990i	0.924989	−	0.379995i	$-0.124074\pi$
$152$	0.373943	+	1.46039i	0.0303308	+	0.118453i
$153$		−	2.05663i		−	0.166269i
$154$		0			0
$155$	10.8211	−	10.8211i	0.869174	−	0.869174i
$156$	−25.6580	+	4.32820i	−2.05429	+	0.346533i
$157$	−8.25568	−	8.25568i	−0.658875	−	0.658875i	0.296239	−	0.955114i	$-0.404268\pi$
$157$	−8.25568	−	8.25568i	−0.658875	−	0.658875i	−0.955114	+	0.296239i	$0.904268\pi$
$158$	−11.9250	+	14.1050i	−0.948699	+	1.12214i
$159$	−2.40500			−0.190729
$160$	−4.45607	−	10.0380i	−0.352283	−	0.793574i
$161$		0			0
$162$	−6.66332	+	7.88148i	−0.523520	+	0.619228i
$163$	10.4581	+	10.4581i	0.819141	+	0.819141i	0.985984	−	0.166842i	$-0.0533571\pi$
$163$	10.4581	+	10.4581i	0.819141	+	0.819141i	−0.166842	+	0.985984i	$0.553357\pi$
$164$	−5.82046	+	0.981841i	−0.454502	+	0.0766689i
$165$	18.5322	−	18.5322i	1.44273	−	1.44273i
$166$	20.2394	−	1.69510i	1.57088	−	0.131565i
$167$			0.426814i			0.0330279i	0.999864	+	0.0165139i	$0.00525679\pi$
$167$			0.426814i			0.0330279i	−0.999864	+	0.0165139i	$0.994743\pi$
$168$		0			0
$169$			13.0892i			1.00686i
$170$	−0.135115	−	1.61327i	−0.0103629	−	0.123732i
$171$	−1.31454	+	1.31454i	−0.100525	+	0.100525i
$172$	17.6855	+	12.5801i	1.34851	+	0.959222i
$173$	−2.97755	−	2.97755i	−0.226379	−	0.226379i	0.584799	−	0.811178i	$-0.301173\pi$
$173$	−2.97755	−	2.97755i	−0.226379	−	0.226379i	−0.811178	+	0.584799i	$0.801173\pi$
$174$	10.4640	+	8.84665i	0.793271	+	0.670663i
$175$		0			0
$176$	9.24315	−	19.0778i	0.696729	−	1.43804i
$177$	0.0741437			0.00557298
$178$	−4.18087	−	3.53467i	−0.313369	−	0.264935i
$179$	9.93538	+	9.93538i	0.742605	+	0.742605i	0.973079	−	0.230473i	$-0.0740275\pi$
$179$	9.93538	+	9.93538i	0.742605	+	0.742605i	−0.230473	+	0.973079i	$0.574027\pi$
$180$	7.85043	−	11.0364i	0.585137	−	0.822606i
$181$	−10.0681	+	10.0681i	−0.748356	+	0.748356i	−0.974170	−	0.225814i	$-0.927496\pi$
$181$	−10.0681	+	10.0681i	−0.748356	+	0.748356i	0.225814	+	0.974170i	$0.427496\pi$
$182$		0			0
$183$			5.21587i			0.385568i
$184$	−0.629185	+	1.06230i	−0.0463841	+	0.0783141i
$185$		−	5.84622i		−	0.429823i
$186$	28.2950	−	2.36977i	2.07469	−	0.173760i
$187$	2.20963	−	2.20963i	0.161584	−	0.161584i
$188$	−1.34249	−	7.95842i	−0.0979110	−	0.580427i
$189$		0			0
$190$	−0.944798	+	1.11752i	−0.0685429	+	0.0810736i
$191$	9.64501			0.697888			0.348944	−	0.937144i	$-0.386540\pi$
$191$	9.64501			0.697888			0.348944	+	0.937144i	$0.386540\pi$
$192$	5.71072	−	19.5607i	0.412136	−	1.41167i
$193$	−19.5594			−1.40792			−0.703959	−	0.710241i	$-0.748586\pi$
$193$	−19.5594			−1.40792			−0.703959	+	0.710241i	$0.748586\pi$
$194$	−11.0073	+	13.0197i	−0.790281	+	0.934757i
$195$	−17.8609	−	17.8609i	−1.27904	−	1.27904i
$196$		0			0
$197$	−8.33252	+	8.33252i	−0.593668	+	0.593668i	−0.938620	−	0.344953i	$-0.887895\pi$
$197$	−8.33252	+	8.33252i	−0.593668	+	0.593668i	0.344953	+	0.938620i	$0.387895\pi$
$198$	26.0513	−	2.18186i	1.85138	−	0.155058i
$199$		−	2.70632i		−	0.191846i	−0.995389	−	0.0959230i	$-0.969420\pi$
$199$		−	2.70632i		−	0.191846i	0.995389	−	0.0959230i	$-0.0305803\pi$
$200$	−1.77389	+	2.99500i	−0.125433	+	0.211779i
$201$		−	16.4759i		−	1.16212i
$202$	0.316930	+	3.78413i	0.0222991	+	0.266251i
$203$		0			0
$204$	1.74109	−	2.44769i	0.121901	−	0.171372i
$205$	−4.05169	−	4.05169i	−0.282982	−	0.282982i
$206$	0.0964093	+	0.0815083i	0.00671715	+	0.00567895i
$207$	−1.52256			−0.105826
$208$	−18.3867	−	8.90830i	−1.27489	−	0.617680i
$209$	−2.82468			−0.195387
$210$		0			0
$211$	11.9853	+	11.9853i	0.825100	+	0.825100i	0.986834	−	0.161734i	$-0.0517087\pi$
$211$	11.9853	+	11.9853i	0.825100	+	0.825100i	−0.161734	+	0.986834i	$0.551709\pi$
$212$	−1.53879	−	1.09457i	−0.105685	−	0.0751757i
$213$	−3.70362	+	3.70362i	−0.253768	+	0.253768i
$214$	−1.72052	−	20.5430i	−0.117612	−	1.40429i
$215$			21.0682i			1.43684i
$216$	3.40587	−	0.872100i	0.231740	−	0.0593389i
$217$		0			0
$218$	−9.75197	+	0.816750i	−0.660487	+	0.0553173i
$219$	14.2600	−	14.2600i	0.963605	−	0.963605i
$220$	20.2920	−	3.42301i	1.36808	−	0.230779i
$221$	−2.12959	−	2.12959i	−0.143251	−	0.143251i
$222$	7.00317	−	8.28346i	0.470022	−	0.555950i
$223$	−2.50874			−0.167998			−0.0839988	−	0.996466i	$-0.526769\pi$
$223$	−2.50874			−0.167998			−0.0839988	+	0.996466i	$0.526769\pi$
$224$		0			0
$225$	−4.29264			−0.286176
$226$	−6.85831	+	8.11211i	−0.456208	+	0.539610i
$227$	−13.4012	−	13.4012i	−0.889471	−	0.889471i	0.105001	−	0.994472i	$-0.466515\pi$
$227$	−13.4012	−	13.4012i	−0.889471	−	0.889471i	−0.994472	+	0.105001i	$0.966515\pi$
$228$	−2.67735	+	0.451637i	−0.177312	+	0.0299104i
$229$	18.3747	−	18.3747i	1.21423	−	1.21423i	0.244610	−	0.969621i	$-0.421340\pi$
$229$	18.3747	−	18.3747i	1.21423	−	1.21423i	0.969621	−	0.244610i	$-0.0786601\pi$
$230$	−1.19434	+	0.100029i	−0.0787524	+	0.00659569i
$231$		0			0
$232$	2.66883	+	10.4228i	0.175217	+	0.684289i
$233$			14.1341i			0.925955i	0.886370	+	0.462977i	$0.153219\pi$
$233$			14.1341i			0.925955i	−0.886370	+	0.462977i	$0.846781\pi$
$234$	−2.10281	−	25.1075i	−0.137465	−	1.64133i
$235$	5.53995	−	5.53995i	0.361386	−	0.361386i
$236$	0.0474395	+	0.0337447i	0.00308805	+	0.00219659i
$237$	−23.5235	−	23.5235i	−1.52802	−	1.52802i
$238$		0			0
$239$	−2.15987			−0.139710			−0.0698550	−	0.997557i	$-0.522254\pi$
$239$	−2.15987			−0.139710			−0.0698550	+	0.997557i	$0.522254\pi$
$240$	18.6863	−	6.48895i	1.20620	−	0.418860i
$241$	9.71222			0.625619			0.312809	−	0.949816i	$-0.398730\pi$
$241$	9.71222			0.625619			0.312809	+	0.949816i	$0.398730\pi$
$242$	18.4539	+	15.6017i	1.18626	+	1.00291i
$243$	−15.7811	−	15.7811i	−1.01236	−	1.01236i
$244$	−2.37388	+	3.33728i	−0.151972	+	0.213647i
$245$		0			0
$246$	−0.887298	−	10.5943i	−0.0565720	−	0.675468i
$247$			2.72235i			0.173219i
$248$	19.1825	+	11.3615i	1.21809	+	0.721456i
$249$			36.5811i			2.31823i
$250$	−17.0476	+	1.42778i	−1.07819	+	0.0903006i
$251$	10.1748	−	10.1748i	0.642228	−	0.642228i	−0.308875	−	0.951103i	$-0.599952\pi$
$251$	10.1748	−	10.1748i	0.642228	−	0.642228i	0.951103	+	0.308875i	$0.0999525\pi$
$252$		0			0
$253$	−1.63584	−	1.63584i	−0.102844	−	0.102844i
$254$	−3.88231	+	4.59206i	−0.243598	+	0.288131i
$255$	2.91585			0.182598
$256$	12.5565	−	9.91643i	0.784778	−	0.619777i
$257$	−26.5109			−1.65371			−0.826853	−	0.562418i	$-0.809871\pi$
$257$	−26.5109			−1.65371			−0.826853	+	0.562418i	$0.809871\pi$
$258$	−25.2375	+	29.8514i	−1.57122	+	1.85847i
$259$		0			0
$260$	−3.29900	−	19.5569i	−0.204595	−	1.21286i
$261$	−9.38188	+	9.38188i	−0.580724	+	0.580724i
$262$	7.13552	−	0.597616i	0.440834	−	0.0369208i
$263$			20.7628i			1.28029i	0.768253	+	0.640146i	$0.221126\pi$
$263$			20.7628i			1.28029i	−0.768253	+	0.640146i	$0.778874\pi$
$264$	32.8519	+	19.4576i	2.02190	+	1.19754i
$265$		−	1.83312i		−	0.112607i
$266$		0			0
$267$	6.97259	−	6.97259i	0.426716	−	0.426716i
$268$	7.49860	−	10.5418i	0.458050	−	0.643943i
$269$	17.7004	+	17.7004i	1.07921	+	1.07921i	0.996580	+	0.0826332i	$0.0263330\pi$
$269$	17.7004	+	17.7004i	1.07921	+	1.07921i	0.0826332	+	0.996580i	$0.473667\pi$
$270$	2.60626	+	2.20343i	0.158612	+	0.134097i
$271$	5.64144			0.342693			0.171347	−	0.985211i	$-0.445188\pi$
$271$	5.64144			0.342693			0.171347	+	0.985211i	$0.445188\pi$
$272$	2.22801	−	0.773691i	0.135093	−	0.0469119i
$273$		0			0
$274$	0.301170	+	0.254621i	0.0181943	+	0.0153822i
$275$	−4.61199	−	4.61199i	−0.278114	−	0.278114i
$276$	−1.81207	−	1.28896i	−0.109074	−	0.0775866i
$277$	−13.5254	+	13.5254i	−0.812662	+	0.812662i	−0.985032	−	0.172371i	$-0.944857\pi$
$277$	−13.5254	+	13.5254i	−0.812662	+	0.812662i	0.172371	+	0.985032i	$0.444857\pi$
$278$	2.02132	+	24.1345i	0.121231	+	1.44749i
$279$			27.4937i			1.64600i
$280$		0			0
$281$		−	20.6400i		−	1.23128i	−0.788029	−	0.615639i	$-0.788898\pi$
$281$		−	20.6400i		−	1.23128i	0.788029	−	0.615639i	$-0.211102\pi$
$282$	14.4858	−	1.21322i	0.862616	−	0.0722460i
$283$	−16.7897	+	16.7897i	−0.998042	+	0.998042i	−0.999998	−	0.00195630i	$-0.999377\pi$
$283$	−16.7897	+	16.7897i	−0.998042	+	0.998042i	0.00195630	+	0.999998i	$0.499377\pi$
$284$	−4.05530	+	0.684079i	−0.240638	+	0.0405926i
$285$	−1.86374	−	1.86374i	−0.110398	−	0.110398i
$286$	24.7162	−	29.2347i	1.46150	−	1.72868i
$287$		0			0
$288$	18.4128	+	7.09112i	1.08499	+	0.417848i
$289$	−16.6523			−0.979549
$290$	−6.74302	+	7.97575i	−0.395964	+	0.468352i
$291$	−21.7134	−	21.7134i	−1.27286	−	1.27286i
$292$	15.6141	−	2.63391i	0.913748	−	0.154138i
$293$	−20.5268	+	20.5268i	−1.19919	+	1.19919i	−0.224778	+	0.974410i	$0.572166\pi$
$293$	−20.5268	+	20.5268i	−1.19919	+	1.19919i	−0.974410	+	0.224778i	$0.927834\pi$
$294$		0			0
$295$			0.0565132i			0.00329033i
$296$	8.25086	−	2.11270i	0.479572	−	0.122798i
$297$			6.58764i			0.382253i
$298$	−2.58930	−	30.9162i	−0.149994	−	1.79093i
$299$	−1.57658	+	1.57658i	−0.0911758	+	0.0911758i
$300$	−5.10886	−	3.63404i	−0.294960	−	0.209811i
$301$		0			0
$302$	10.0858	+	8.52690i	0.580370	+	0.490668i
$303$	−6.83950			−0.392919
$304$	−1.91860	−	0.929560i	−0.110040	−	0.0533139i
$305$	−3.97560			−0.227642
$306$	2.22110	+	1.87781i	0.126972	+	0.107347i
$307$	6.03127	+	6.03127i	0.344223	+	0.344223i	0.857952	−	0.513730i	$-0.171737\pi$
$307$	6.03127	+	6.03127i	0.344223	+	0.344223i	−0.513730	+	0.857952i	$0.671737\pi$
$308$		0			0
$309$	−0.160786	+	0.160786i	−0.00914677	+	0.00914677i
$310$	1.80627	+	21.5668i	0.102589	+	1.22491i
$311$			16.0181i			0.908305i	0.890924	+	0.454153i	$0.150058\pi$
$311$			16.0181i			0.908305i	−0.890924	+	0.454153i	$0.849942\pi$
$312$	18.7528	−	31.6618i	1.06167	−	1.79250i
$313$			17.7543i			1.00353i	0.865003	+	0.501766i	$0.167316\pi$
$313$			17.7543i			1.00353i	−0.865003	+	0.501766i	$0.832684\pi$
$314$	16.4538	−	1.37804i	0.928539	−	0.0777673i
$315$		0			0
$316$	−4.34493	−	25.7572i	−0.244421	−	1.44896i
$317$	−10.9913	−	10.9913i	−0.617335	−	0.617335i	0.327512	−	0.944847i	$-0.393790\pi$
$317$	−10.9913	−	10.9913i	−0.617335	−	0.617335i	−0.944847	+	0.327512i	$0.893790\pi$
$318$	2.19588	−	2.59733i	0.123139	−	0.145651i
$319$	−20.1597			−1.12873
$320$	14.9094	+	4.35278i	0.833459	+	0.243328i
$321$	37.1297			2.07238
$322$		0			0
$323$	−0.222217	−	0.222217i	−0.0123645	−	0.0123645i
$324$	−2.42782	−	14.3924i	−0.134879	−	0.799577i
$325$	−4.44492	+	4.44492i	−0.246560	+	0.246560i
$326$	−20.8432	+	1.74567i	−1.15440	+	0.0966835i
$327$		−	17.6259i		−	0.974713i
$328$	4.25402	−	7.18240i	0.234889	−	0.396582i
$329$		0			0
$330$	3.09340	+	36.9351i	0.170286	+	2.03321i
$331$	10.7479	−	10.7479i	0.590756	−	0.590756i	−0.347080	−	0.937836i	$-0.612827\pi$
$331$	10.7479	−	10.7479i	0.590756	−	0.590756i	0.937836	+	0.347080i	$0.112827\pi$
$332$	−16.6490	+	23.4057i	−0.913731	+	1.28455i
$333$	7.42687	+	7.42687i	0.406990	+	0.406990i
$334$	−0.460947	−	0.389703i	−0.0252219	−	0.0213236i
$335$	12.5581			0.686124
$336$		0			0
$337$	18.9202			1.03065			0.515325	−	0.856995i	$-0.327671\pi$
$337$	18.9202			1.03065			0.515325	+	0.856995i	$0.327671\pi$
$338$	−14.1360	−	11.9511i	−0.768897	−	0.650057i
$339$	−13.5289	−	13.5289i	−0.734789	−	0.734789i
$340$	1.86565	+	1.32708i	0.101179	+	0.0719710i
$341$	−29.5391	+	29.5391i	−1.59963	+	1.59963i
$342$	−0.219423	−	2.61991i	−0.0118651	−	0.141669i
$343$		0			0
$344$	−29.7339	+	7.61359i	−1.60314	+	0.410497i
$345$		−	2.15867i		−	0.116219i
$346$	5.93431	−	0.497012i	0.319031	−	0.0267196i
$347$	−4.33814	+	4.33814i	−0.232883	+	0.232883i	−0.813895	−	0.581012i	$-0.802657\pi$
$347$	−4.33814	+	4.33814i	−0.232883	+	0.232883i	0.581012	+	0.813895i	$0.302657\pi$
$348$	−19.1083	+	3.22333i	−1.02431	+	0.172789i
$349$	2.94202	+	2.94202i	0.157483	+	0.157483i	0.781450	−	0.623968i	$-0.214480\pi$
$349$	2.94202	+	2.94202i	0.157483	+	0.157483i	−0.623968	+	0.781450i	$0.714480\pi$
$350$		0			0
$351$	6.34899			0.338884
$352$	12.1640	+	27.4013i	0.648344	+	1.46050i
$353$	−26.0573			−1.38689			−0.693446	−	0.720508i	$-0.743908\pi$
$353$	−26.0573			−1.38689			−0.693446	+	0.720508i	$0.743908\pi$
$354$	−0.0676970	+	0.0800731i	−0.00359806	+	0.00425584i
$355$	−2.82294	−	2.82294i	−0.149826	−	0.149826i
$356$	7.63469	−	1.28788i	0.404638	−	0.0682574i
$357$		0			0
$358$	−19.8014	+	1.65842i	−1.04654	+	0.0876500i
$359$			29.6821i			1.56656i	0.621667	+	0.783282i	$0.286456\pi$
$359$			29.6821i			1.56656i	−0.621667	+	0.783282i	$0.713544\pi$
$360$	4.75116	+	18.5551i	0.250408	+	0.977937i
$361$		−	18.7159i		−	0.985049i
$362$	−1.68057	−	20.0660i	−0.0883288	−	1.05464i
$363$	−30.7763	+	30.7763i	−1.61534	+	1.61534i
$364$		0			0
$365$	10.8692	+	10.8692i	0.568919	+	0.568919i
$366$	−5.63299	−	4.76236i	−0.294441	−	0.248932i
$367$	4.43995			0.231764			0.115882	−	0.993263i	$-0.463031\pi$
$367$	4.43995			0.231764			0.115882	+	0.993263i	$0.463031\pi$
$368$	−0.572779	−	1.64944i	−0.0298582	−	0.0859830i
$369$	10.2943			0.535899
$370$	6.31375	+	5.33790i	0.328236	+	0.277504i
$371$		0			0
$372$	−23.2755	+	32.7215i	−1.20678	+	1.69653i
$373$	12.9411	−	12.9411i	0.670067	−	0.670067i	−0.287665	−	0.957731i	$-0.592879\pi$
$373$	12.9411	−	12.9411i	0.670067	−	0.670067i	0.957731	+	0.287665i	$0.0928788\pi$
$374$	0.368832	+	4.40385i	0.0190719	+	0.227718i
$375$		−	30.8122i		−	1.59113i
$376$	9.82062	+	5.81659i	0.506460	+	0.299968i
$377$			19.4294i			1.00066i
$378$		0			0
$379$	1.71717	−	1.71717i	0.0882050	−	0.0882050i	−0.661628	−	0.749833i	$-0.730134\pi$
$379$	1.71717	−	1.71717i	0.0882050	−	0.0882050i	0.749833	+	0.661628i	$0.230134\pi$
$380$	−0.344243	−	2.04071i	−0.0176593	−	0.104686i
$381$	−7.65836	−	7.65836i	−0.392350	−	0.392350i
$382$	−8.80638	+	10.4163i	−0.450574	+	0.532946i
$383$	11.7746			0.601652			0.300826	−	0.953679i	$-0.402738\pi$
$383$	11.7746			0.601652			0.300826	+	0.953679i	$0.402738\pi$
$384$	15.9108	+	24.0273i	0.811943	+	1.22614i
$385$		0			0
$386$	17.8587	−	21.1236i	0.908986	−	1.07516i
$387$	−26.7644	−	26.7644i	−1.36051	−	1.36051i
$388$	−4.01059	−	23.7752i	−0.203607	−	1.20700i
$389$	11.0528	−	11.0528i	0.560399	−	0.560399i	−0.369022	−	0.929421i	$-0.620307\pi$
$389$	11.0528	−	11.0528i	0.560399	−	0.560399i	0.929421	+	0.369022i	$0.120307\pi$
$390$	35.5971	−	2.98134i	1.80253	−	0.150966i
$391$		−	0.257382i		−	0.0130164i
$392$		0			0
$393$			12.8969i			0.650560i
$394$	−1.39087	−	16.6069i	−0.0700708	−	0.836643i
$395$	17.9299	−	17.9299i	0.902151	−	0.902151i
$396$	−21.4298	+	30.1268i	−1.07689	+	1.51393i
$397$	2.28633	+	2.28633i	0.114748	+	0.114748i	0.762149	−	0.647402i	$-0.224144\pi$
$397$	2.28633	+	2.28633i	0.114748	+	0.114748i	−0.647402	+	0.762149i	$0.724144\pi$
$398$	2.92275	+	2.47101i	0.146504	+	0.123861i
$399$		0			0
$400$	−1.61486	−	4.65034i	−0.0807432	−	0.232517i
$401$	4.74770			0.237089			0.118544	−	0.992949i	$-0.462177\pi$
$401$	4.74770			0.237089			0.118544	+	0.992949i	$0.462177\pi$
$402$	17.7935	+	15.0433i	0.887459	+	0.750294i
$403$	28.4690	+	28.4690i	1.41814	+	1.41814i
$404$	−4.37613	−	3.11283i	−0.217721	−	0.154869i
$405$	10.0187	−	10.0187i	0.497834	−	0.497834i
$406$		0			0
$407$			15.9588i			0.791048i
$408$	1.05373	+	4.11519i	0.0521672	+	0.203732i
$409$		−	3.09877i		−	0.153224i	−0.997061	−	0.0766121i	$-0.975590\pi$
$409$		−	3.09877i		−	0.153224i	0.997061	−	0.0766121i	$-0.0244103\pi$
$410$	8.07511	−	0.676309i	0.398801	−	0.0334005i
$411$	−0.502273	+	0.502273i	−0.0247753	+	0.0247753i
$412$	−0.176053	+	0.0296980i	−0.00867352	+	0.00146312i
$413$		0			0
$414$	1.39018	−	1.64433i	0.0683236	−	0.0808142i
$415$	−27.8825			−1.36870
$416$	26.4087	−	11.7233i	1.29479	−	0.574784i
$417$	−43.6212			−2.13614
$418$	2.57907	−	3.05057i	0.126147	−	0.149208i
$419$	−2.62329	−	2.62329i	−0.128156	−	0.128156i	0.640119	−	0.768276i	$-0.278885\pi$
$419$	−2.62329	−	2.62329i	−0.128156	−	0.128156i	−0.768276	+	0.640119i	$0.778885\pi$
$420$		0			0
$421$	−3.44059	+	3.44059i	−0.167684	+	0.167684i	−0.785961	−	0.618276i	$-0.787831\pi$
$421$	−3.44059	+	3.44059i	−0.167684	+	0.167684i	0.618276	+	0.785961i	$0.287831\pi$
$422$	−23.8869	+	2.00058i	−1.16280	+	0.0973869i
$423$			14.0756i			0.684377i
$424$	2.58710	−	0.662448i	0.125641	−	0.0321713i
$425$		−	0.725650i		−	0.0351992i
$426$	−0.618208	−	7.38139i	−0.0299523	−	0.357629i
$427$		0			0
$428$	23.7567	+	16.8987i	1.14832	+	0.816828i
$429$	48.7559	+	48.7559i	2.35396	+	2.35396i
$430$	−22.7531	−	19.2364i	−1.09725	−	0.927660i
$431$	−22.7890			−1.09771			−0.548853	−	0.835919i	$-0.684935\pi$
$431$	−22.7890			−1.09771			−0.548853	+	0.835919i	$0.684935\pi$
$432$	−2.16789	+	4.47452i	−0.104303	+	0.215280i
$433$	16.6448			0.799899			0.399950	−	0.916537i	$-0.369028\pi$
$433$	16.6448			0.799899			0.399950	+	0.916537i	$0.369028\pi$
$434$		0			0
$435$	−13.3015	−	13.3015i	−0.637757	−	0.637757i
$436$	8.02198	−	11.2776i	0.384183	−	0.540098i
$437$	−0.164512	+	0.164512i	−0.00786967	+	0.00786967i
$438$	2.38029	+	28.4206i	0.113735	+	1.35799i
$439$			30.8773i			1.47369i	0.676059	+	0.736847i	$0.263686\pi$
$439$			30.8773i			1.47369i	−0.676059	+	0.736847i	$0.736314\pi$
$440$	−14.8309	+	25.0401i	−0.707033	+	1.19374i
$441$		0			0
$442$	4.24431	−	0.355471i	0.201881	−	0.0169080i
$443$	10.0594	−	10.0594i	0.477937	−	0.477937i	−0.426534	−	0.904471i	$-0.640266\pi$
$443$	10.0594	−	10.0594i	0.477937	−	0.477937i	0.904471	+	0.426534i	$0.140266\pi$
$444$	2.55165	+	15.1265i	0.121096	+	0.717870i
$445$	5.31459	+	5.31459i	0.251936	+	0.251936i
$446$	2.29061	−	2.70937i	0.108463	−	0.128292i
$447$	55.8784			2.64296
$448$		0			0
$449$	14.7633			0.696725			0.348363	−	0.937360i	$-0.386738\pi$
$449$	14.7633			0.696725			0.348363	+	0.937360i	$0.386738\pi$
$450$	3.91940	−	4.63592i	0.184762	−	0.218540i
$451$	11.0601	+	11.0601i	0.520802	+	0.520802i
$452$	−2.49887	−	14.8135i	−0.117537	−	0.696771i
$453$	−16.8204	+	16.8204i	−0.790292	+	0.790292i
$454$	26.7090	−	2.23694i	1.25351	−	0.104985i
$455$		0			0
$456$	1.95680	−	3.30383i	0.0916358	−	0.154716i
$457$		−	2.08225i		−	0.0974035i	−0.998813	−	0.0487017i	$-0.984492\pi$
$457$		−	2.08225i		−	0.0974035i	0.998813	−	0.0487017i	$-0.0155084\pi$
$458$	3.06710	+	36.6211i	0.143316	+	1.71119i
$459$	−0.518249	+	0.518249i	−0.0241898	+	0.0241898i
$460$	0.982464	−	1.38118i	0.0458076	−	0.0643980i
$461$	−10.5211	−	10.5211i	−0.490015	−	0.490015i	0.418296	−	0.908311i	$-0.362628\pi$
$461$	−10.5211	−	10.5211i	−0.490015	−	0.490015i	−0.908311	+	0.418296i	$0.862628\pi$
$462$		0			0
$463$	26.5483			1.23380			0.616902	−	0.787040i	$-0.288387\pi$
$463$	26.5483			1.23380			0.616902	+	0.787040i	$0.288387\pi$
$464$	−13.6931	−	6.63426i	−0.635685	−	0.307988i
$465$	−38.9801			−1.80766
$466$	−15.2644	−	12.9051i	−0.707110	−	0.597819i
$467$	−6.84110	−	6.84110i	−0.316568	−	0.316568i	0.530879	−	0.847448i	$-0.321862\pi$
$467$	−6.84110	−	6.84110i	−0.316568	−	0.316568i	−0.847448	+	0.530879i	$0.821862\pi$
$468$	29.0354	+	20.6535i	1.34216	+	0.954708i
$469$		0			0
$470$	0.924729	+	11.0412i	0.0426546	+	0.509294i
$471$			29.7388i			1.37029i
$472$	−0.0797580	+	0.0204226i	−0.00367116	+	0.000940028i
$473$		−	57.5112i		−	2.64437i
$474$	46.8829	−	3.92655i	2.15340	−	0.180352i
$475$	−0.463816	+	0.463816i	−0.0212813	+	0.0212813i
$476$		0			0
$477$	2.32874	+	2.32874i	0.106626	+	0.106626i
$478$	1.97207	−	2.33259i	0.0902003	−	0.106690i
$479$	3.89284			0.177868			0.0889342	−	0.996038i	$-0.471654\pi$
$479$	3.89284			0.177868			0.0889342	+	0.996038i	$0.471654\pi$
$480$	−10.0537	+	26.1054i	−0.458885	+	1.19154i
$481$	15.3807			0.701298
$482$	−8.86775	+	10.4889i	−0.403915	+	0.477757i
$483$		0			0
$484$	−33.6987	+	5.68456i	−1.53176	+	0.258389i
$485$	16.5502	−	16.5502i	0.751507	−	0.751507i
$486$	31.4520	−	2.63418i	1.42669	−	0.119489i
$487$			2.88610i			0.130782i	0.997860	+	0.0653909i	$0.0208294\pi$
$487$			2.88610i			0.130782i	−0.997860	+	0.0653909i	$0.979171\pi$
$488$	−1.43669	−	5.61082i	−0.0650361	−	0.253990i
$489$		−	37.6724i		−	1.70360i
$490$		0			0
$491$	10.1200	−	10.1200i	0.456710	−	0.456710i	−0.440864	−	0.897574i	$-0.645328\pi$
$491$	10.1200	−	10.1200i	0.456710	−	0.456710i	0.897574	+	0.440864i	$0.145328\pi$
$492$	12.2517	+	8.71489i	0.552349	+	0.392898i
$493$	−1.58596	−	1.58596i	−0.0714282	−	0.0714282i
$494$	−2.94006	−	2.48564i	−0.132279	−	0.111834i
$495$	−35.8891			−1.61310
$496$	−29.7847	+	10.3430i	−1.33737	+	0.464413i
$497$		0			0
$498$	−39.5065	−	33.4004i	−1.77033	−	1.49671i
$499$	−13.5626	−	13.5626i	−0.607144	−	0.607144i	0.335055	−	0.942199i	$-0.391245\pi$
$499$	−13.5626	−	13.5626i	−0.607144	−	0.607144i	−0.942199	+	0.335055i	$0.891245\pi$
$500$	14.0234	−	19.7146i	0.627146	−	0.881663i
$501$	0.768739	−	0.768739i	0.0343447	−	0.0343447i
$502$	1.69838	+	20.2786i	0.0758024	+	0.905078i
$503$		−	25.3179i		−	1.12887i	−0.825477	−	0.564436i	$-0.809094\pi$
$503$		−	25.3179i		−	1.12887i	0.825477	−	0.564436i	$-0.190906\pi$
$504$		0			0
$505$		−	5.21315i		−	0.231982i
$506$	3.26026	−	0.273054i	0.144936	−	0.0121387i
$507$	23.5752	−	23.5752i	1.04701	−	1.04701i
$508$	−1.41454	−	8.38557i	−0.0627602	−	0.372049i
$509$	1.56374	+	1.56374i	0.0693116	+	0.0693116i	0.740913	−	0.671601i	$-0.234393\pi$
$509$	1.56374	+	1.56374i	0.0693116	+	0.0693116i	−0.671601	+	0.740913i	$0.734393\pi$
$510$	−2.66232	+	3.14904i	−0.117890	+	0.139442i
$511$		0			0
$512$	−0.755222	+	22.6148i	−0.0333764	+	0.999443i
$513$	0.662501			0.0292501
$514$	24.2058	−	28.6310i	1.06767	−	1.26286i
$515$	−0.122553	−	0.122553i	−0.00540032	−	0.00540032i
$516$	−9.19545	−	54.5117i	−0.404807	−	2.39974i
$517$	−15.1227	+	15.1227i	−0.665097	+	0.665097i
$518$		0			0
$519$			10.7258i			0.470809i
$520$	24.1330	+	14.2936i	1.05830	+	0.626815i
$521$		−	10.2874i		−	0.450699i	−0.974278	−	0.225349i	$-0.927648\pi$
$521$		−	10.2874i		−	0.450699i	0.974278	−	0.225349i	$-0.0723524\pi$
$522$	−1.56602	−	18.6983i	−0.0685430	−	0.818402i
$523$	−4.61761	+	4.61761i	−0.201914	+	0.201914i	−0.800820	−	0.598906i	$-0.795602\pi$
$523$	−4.61761	+	4.61761i	−0.201914	+	0.201914i	0.598906	+	0.800820i	$0.295602\pi$
$524$	−5.86969	+	8.25181i	−0.256418	+	0.360482i
$525$		0			0
$526$	−22.4233	−	18.9575i	−0.977701	−	0.826588i
$527$	−4.64768			−0.202456
$528$	−51.0092	+	17.7133i	−2.21989	+	0.770872i
$529$	22.8095			0.991715
$530$	1.97971	+	1.67373i	0.0859933	+	0.0727022i
$531$	−0.0717927	−	0.0717927i	−0.00311554	−	0.00311554i
$532$		0			0
$533$	10.6595	−	10.6595i	0.461713	−	0.461713i
$534$	1.16387	+	13.8965i	0.0503654	+	0.601362i
$535$			28.3007i			1.22355i
$536$	4.53823	+	17.7235i	0.196022	+	0.765538i
$537$		−	35.7894i		−	1.54443i
$538$	−35.2773	+	2.95456i	−1.52091	+	0.127380i
$539$		0			0
$540$	−4.75929	+	0.802834i	−0.204807	+	0.0345485i
$541$	−4.78373	−	4.78373i	−0.205669	−	0.205669i	0.596755	−	0.802424i	$-0.296456\pi$
$541$	−4.78373	−	4.78373i	−0.205669	−	0.205669i	−0.802424	+	0.596755i	$0.796456\pi$
$542$	−5.15092	+	6.09259i	−0.221251	+	0.261699i
$543$	36.2675			1.55639
$544$	−1.19872	+	3.11260i	−0.0513947	+	0.133452i
$545$	13.4346			0.575477
$546$		0			0
$547$	−1.78581	−	1.78581i	−0.0763555	−	0.0763555i	0.667898	−	0.744253i	$-0.267194\pi$
$547$	−1.78581	−	1.78581i	−0.0763555	−	0.0763555i	−0.744253	+	0.667898i	$0.767194\pi$
$548$	−0.549967	+	0.0927727i	−0.0234934	+	0.00396305i
$549$	5.05048	−	5.05048i	0.215549	−	0.215549i
$550$	9.19181	−	0.769835i	0.391940	−	0.0328259i
$551$			2.02741i			0.0863705i
$552$	3.04656	−	0.780095i	0.129670	−	0.0332030i
$553$		0			0
$554$	−2.25766	−	26.9564i	−0.0959188	−	1.14527i
$555$	−10.5297	+	10.5297i	−0.446961	+	0.446961i
$556$	−27.9102	−	19.8531i	−1.18366	−	0.841959i
$557$	−2.46688	−	2.46688i	−0.104525	−	0.104525i	0.652910	−	0.757435i	$-0.273548\pi$
$557$	−2.46688	−	2.46688i	−0.104525	−	0.104525i	−0.757435	+	0.652910i	$0.773548\pi$
$558$	−29.6924	−	25.1031i	−1.25698	−	1.06270i
$559$	−55.4278			−2.34435
$560$		0			0
$561$	−7.95959			−0.336054
$562$	22.2906	+	18.8453i	0.940271	+	0.794943i
$563$	28.1611	+	28.1611i	1.18685	+	1.18685i	0.977934	+	0.208915i	$0.0669933\pi$
$563$	28.1611	+	28.1611i	1.18685	+	1.18685i	0.208915	+	0.977934i	$0.433007\pi$
$564$	−11.9160	+	16.7520i	−0.501755	+	0.705385i
$565$	10.3119	−	10.3119i	0.433824	−	0.433824i
$566$	−2.80253	−	33.4622i	−0.117799	−	1.40652i
$567$		0			0
$568$	2.96391	−	5.00420i	0.124363	−	0.209972i
$569$		−	45.1863i		−	1.89431i	−0.320781	−	0.947153i	$-0.603945\pi$
$569$		−	45.1863i		−	1.89431i	0.320781	−	0.947153i	$-0.396055\pi$
$570$	3.71447	−	0.311095i	0.155582	−	0.0130303i
$571$	17.6006	−	17.6006i	0.736562	−	0.736562i	−0.235349	−	0.971911i	$-0.575623\pi$
$571$	17.6006	−	17.6006i	0.736562	−	0.736562i	0.971911	+	0.235349i	$0.0756234\pi$
$572$	9.00549	+	53.3856i	0.376539	+	2.23216i
$573$	−17.3717	−	17.3717i	−0.725714	−	0.725714i
$574$		0			0
$575$	−0.537214			−0.0224034
$576$	−24.4701	+	13.4108i	−1.01959	+	0.558782i
$577$	−10.9316			−0.455088			−0.227544	−	0.973768i	$-0.573070\pi$
$577$	−10.9316			−0.455088			−0.227544	+	0.973768i	$0.573070\pi$
$578$	15.2044	−	17.9840i	0.632421	−	0.748038i
$579$	35.2287	+	35.2287i	1.46405	+	1.46405i
$580$	−2.45686	−	14.5645i	−0.102016	−	0.604760i
$581$		0			0
$582$	43.2753	−	3.62441i	1.79382	−	0.150236i
$583$			5.00397i			0.207243i
$584$	−11.4119	+	19.2677i	−0.472230	+	0.797303i
$585$			34.5890i			1.43008i
$586$	−3.42633	−	40.9103i	−0.141541	−	1.68999i
$587$	7.44744	−	7.44744i	0.307389	−	0.307389i	−0.536507	−	0.843896i	$-0.680256\pi$
$587$	7.44744	−	7.44744i	0.307389	−	0.307389i	0.843896	+	0.536507i	$0.180256\pi$
$588$		0			0
$589$	2.97067	+	2.97067i	0.122404	+	0.122404i
$590$	−0.0610327	−	0.0515995i	−0.00251268	−	0.00212432i
$591$	30.0156			1.23468
$592$	−5.25181	+	10.8397i	−0.215848	+	0.445509i
$593$	25.2894			1.03851			0.519256	−	0.854619i	$-0.326209\pi$
$593$	25.2894			1.03851			0.519256	+	0.854619i	$0.326209\pi$
$594$	−7.11446	−	6.01485i	−0.291910	−	0.246792i
$595$		0			0
$596$	35.7528	+	25.4317i	1.46449	+	1.04172i
$597$	−4.87438	+	4.87438i	−0.199495	+	0.199495i
$598$	−0.263162	−	3.14215i	−0.0107615	−	0.128492i
$599$		−	17.8531i		−	0.729459i	−0.931114	−	0.364729i	$-0.881162\pi$
$599$		−	17.8531i		−	0.729459i	0.931114	−	0.364729i	$-0.118838\pi$
$600$	8.58931	−	2.19936i	0.350657	−	0.0897884i
$601$			15.3921i			0.627855i	0.949447	+	0.313928i	$0.101645\pi$
$601$			15.3921i			0.627855i	−0.949447	+	0.313928i	$0.898355\pi$
$602$		0			0
$603$	−15.9535	+	15.9535i	−0.649676	+	0.649676i
$604$	−18.4176	+	3.10683i	−0.749402	+	0.126415i
$605$	−23.4581	−	23.4581i	−0.953706	−	0.953706i
$606$	6.24482	−	7.38647i	0.253678	−	0.300055i
$607$	−30.2868			−1.22930			−0.614652	−	0.788798i	$-0.710704\pi$
$607$	−30.2868			−1.22930			−0.614652	+	0.788798i	$0.710704\pi$
$608$	2.75568	−	1.22330i	0.111758	−	0.0496115i
$609$		0			0
$610$	3.62992	−	4.29353i	0.146971	−	0.173840i
$611$	14.5749	+	14.5749i	0.589637	+	0.589637i
$612$	−4.05595	+	0.684190i	−0.163952	+	0.0276567i
$613$	10.8154	−	10.8154i	0.436831	−	0.436831i	−0.454113	−	0.890944i	$-0.650044\pi$
$613$	10.8154	−	10.8154i	0.436831	−	0.436831i	0.890944	+	0.454113i	$0.150044\pi$
$614$	−12.0204	+	1.00674i	−0.485106	+	0.0406287i
$615$			14.5951i			0.588531i
$616$		0			0
$617$		−	39.3266i		−	1.58323i	−0.611020	−	0.791615i	$-0.709241\pi$
$617$		−	39.3266i		−	1.58323i	0.611020	−	0.791615i	$-0.290759\pi$
$618$	−0.0268384	−	0.320449i	−0.00107960	−	0.0128904i
$619$	3.80053	−	3.80053i	0.152756	−	0.152756i	−0.626592	−	0.779348i	$-0.715551\pi$
$619$	3.80053	−	3.80053i	0.152756	−	0.152756i	0.779348	+	0.626592i	$0.215551\pi$
$620$	−24.9407	−	17.7408i	−1.00164	−	0.712489i
$621$	0.383670	+	0.383670i	0.0153962	+	0.0153962i
$622$	−17.2991	−	14.6254i	−0.693632	−	0.586424i
$623$		0			0
$624$	17.0716	+	49.1613i	0.683411	+	1.96803i
$625$	17.3320			0.693279
$626$	−19.1741	−	16.2106i	−0.766353	−	0.647905i
$627$	5.08756	+	5.08756i	0.203177	+	0.203177i
$628$	−13.5349	+	19.0278i	−0.540100	+	0.759292i
$629$	−1.25548	+	1.25548i	−0.0500592	+	0.0500592i
$630$		0			0
$631$		−	7.48252i		−	0.297875i	−0.988847	−	0.148937i	$-0.952415\pi$
$631$		−	7.48252i		−	0.297875i	0.988847	−	0.148937i	$-0.0475853\pi$
$632$	31.7842	+	18.8253i	1.26431	+	0.748828i
$633$		−	43.1736i		−	1.71600i
$634$	21.9060	−	1.83468i	0.869997	−	0.0728643i
$635$	5.83729	−	5.83729i	0.231646	−	0.231646i
$636$	0.800084	+	4.74298i	0.0317254	+	0.188072i
$637$		0			0
$638$	18.4068	−	21.7719i	0.728734	−	0.861958i
$639$	7.17236			0.283734
$640$	−18.3139	+	12.1274i	−0.723920	+	0.479377i
$641$	9.46770			0.373952			0.186976	−	0.982365i	$-0.440131\pi$
$641$	9.46770			0.373952			0.186976	+	0.982365i	$0.440131\pi$
$642$	−33.9013	+	40.0990i	−1.33798	+	1.58258i
$643$	20.6140	+	20.6140i	0.812939	+	0.812939i	0.985073	−	0.172135i	$-0.0550665\pi$
$643$	20.6140	+	20.6140i	0.812939	+	0.812939i	−0.172135	+	0.985073i	$0.555066\pi$
$644$		0			0
$645$	37.9462	−	37.9462i	1.49413	−	1.49413i
$646$	0.442884	−	0.0370925i	0.0174250	−	0.00145939i
$647$		−	34.8969i		−	1.37194i	−0.727630	−	0.685970i	$-0.759378\pi$
$647$		−	34.8969i		−	1.37194i	0.727630	−	0.685970i	$-0.240622\pi$
$648$	17.7601	+	10.5190i	0.697682	+	0.413226i
$649$		−	0.154268i		−	0.00605554i
$650$	−0.741946	−	8.85882i	−0.0291015	−	0.347471i
$651$		0			0
$652$	17.1456	−	24.1040i	0.671475	−	0.943984i
$653$	28.2132	+	28.2132i	1.10407	+	1.10407i	0.993915	+	0.110153i	$0.0351341\pi$
$653$	28.2132	+	28.2132i	1.10407	+	1.10407i	0.110153	+	0.993915i	$0.464866\pi$
$654$	19.0354	+	16.0933i	0.744344	+	0.629299i
$655$	−9.83014			−0.384095
$656$	3.87265	+	11.1521i	0.151202	+	0.435417i
$657$	−27.6157			−1.07739
$658$		0			0
$659$	−6.66795	−	6.66795i	−0.259746	−	0.259746i	0.565205	−	0.824951i	$-0.308797\pi$
$659$	−6.66795	−	6.66795i	−0.259746	−	0.259746i	−0.824951	+	0.565205i	$0.808797\pi$
$660$	−42.7133	−	30.3829i	−1.66261	−	1.18265i
$661$	−1.77464	+	1.77464i	−0.0690256	+	0.0690256i	−0.740777	−	0.671751i	$-0.765542\pi$
$661$	−1.77464	+	1.77464i	−0.0690256	+	0.0690256i	0.671751	+	0.740777i	$0.265542\pi$
$662$	1.79403	+	21.4207i	0.0697271	+	0.832540i
$663$			7.67124i			0.297926i
$664$	−10.0761	−	39.3510i	−0.391030	−	1.52711i
$665$		0			0
$666$	−14.8019	+	1.23969i	−0.573563	+	0.0480372i
$667$	−1.17412	+	1.17412i	−0.0454621	+	0.0454621i
$668$	0.841736	−	0.141991i	0.0325678	−	0.00549378i
$669$	4.51852	+	4.51852i	0.174696	+	0.174696i
$670$	−11.4662	+	13.5624i	−0.442979	+	0.523962i
$671$	10.8524			0.418954
$672$		0			0
$673$	−36.8448			−1.42026			−0.710131	−	0.704070i	$-0.751364\pi$
$673$	−36.8448			−1.42026			−0.710131	+	0.704070i	$0.751364\pi$
$674$	−17.2751	+	20.4333i	−0.665412	+	0.787060i
$675$	1.08170	+	1.08170i	0.0416346	+	0.0416346i
$676$	25.8138	−	4.35447i	0.992838	−	0.167480i
$677$	12.3669	−	12.3669i	0.475299	−	0.475299i	−0.428326	−	0.903624i	$-0.640896\pi$
$677$	12.3669	−	12.3669i	0.475299	−	0.475299i	0.903624	+	0.428326i	$0.140896\pi$
$678$	26.9634	−	2.25824i	1.03552	−	0.0867274i
$679$		0			0
$680$	−3.13665	+	0.803162i	−0.120285	+	0.0307999i
$681$			48.2742i			1.84987i
$682$	−4.93067	−	58.8721i	−0.188805	−	2.25433i
$683$	−23.5085	+	23.5085i	−0.899529	+	0.899529i	−0.995394	−	0.0958655i	$-0.969438\pi$
$683$	−23.5085	+	23.5085i	−0.899529	+	0.899529i	0.0958655	+	0.995394i	$0.469438\pi$
$684$	3.02977	+	2.15514i	0.115846	+	0.0824039i
$685$	−0.382838	−	0.382838i	−0.0146275	−	0.0146275i
$686$		0			0
$687$	−66.1896			−2.52529
$688$	18.9261	−	39.0633i	0.721551	−	1.48928i
$689$	4.82270			0.183730
$690$	2.33130	+	1.97097i	0.0887510	+	0.0750337i
$691$	−10.5025	−	10.5025i	−0.399532	−	0.399532i	0.478536	−	0.878068i	$-0.341168\pi$
$691$	−10.5025	−	10.5025i	−0.399532	−	0.399532i	−0.878068	+	0.478536i	$0.841168\pi$
$692$	−4.88157	+	6.86269i	−0.185570	+	0.260880i
$693$		0			0
$694$	−0.724122	−	8.64600i	−0.0274873	−	0.328198i
$695$		−	33.2486i		−	1.26119i
$696$	13.9657	−	23.5794i	0.529369	−	0.893776i
$697$			1.74020i			0.0659148i
$698$	−5.86351	+	0.491082i	−0.221937	+	0.0185877i
$699$	25.4571	−	25.4571i	0.962874	−	0.962874i
$700$		0			0
$701$	−21.3787	−	21.3787i	−0.807464	−	0.807464i	0.176785	−	0.984249i	$-0.443430\pi$
$701$	−21.3787	−	21.3787i	−0.807464	−	0.807464i	−0.984249	+	0.176785i	$0.943430\pi$
$702$	−5.79695	+	6.85672i	−0.218792	+	0.258790i
$703$	1.60493			0.0605313
$704$	−40.6990	−	11.8820i	−1.53390	−	0.447822i
$705$	−19.9561			−0.751591
$706$	23.7917	−	28.1412i	0.895412	−	1.05911i
$707$		0			0
$708$	−0.0246658	−	0.146222i	−0.000926998	−	0.00549535i
$709$	9.76517	−	9.76517i	0.366738	−	0.366738i	−0.499548	−	0.866286i	$-0.666500\pi$
$709$	9.76517	−	9.76517i	0.366738	−	0.366738i	0.866286	+	0.499548i	$0.166500\pi$
$710$	5.62618	−	0.471206i	0.211147	−	0.0176840i
$711$			45.5552i			1.70845i
$712$	−5.57999	+	9.42114i	−0.209119	+	0.353072i
$713$			3.44077i			0.128858i
$714$		0			0
$715$	−37.1623	+	37.1623i	−1.38979	+	1.38979i
$716$	16.2887	−	22.8992i	0.608736	−	0.855783i
$717$	3.89016	+	3.89016i	0.145281	+	0.145281i
$718$	−32.0559	−	27.1013i	−1.19631	−	1.01141i
$719$	44.3762			1.65495			0.827477	−	0.561500i	$-0.189775\pi$
$719$	44.3762			1.65495			0.827477	+	0.561500i	$0.189775\pi$
$720$	−24.3770	−	11.8106i	−0.908476	−	0.440155i
$721$		0			0
$722$	20.2127	+	17.0886i	0.752238	+	0.635972i
$723$	−17.4928	−	17.4928i	−0.650563	−	0.650563i
$724$	23.2051	+	16.5063i	0.862411	+	0.613451i
$725$	−3.31025	+	3.31025i	−0.122940	+	0.122940i
$726$	−5.13719	−	61.3379i	−0.190659	−	2.27646i
$727$			1.44539i			0.0536067i	0.999641	+	0.0268033i	$0.00853279\pi$
$727$			1.44539i			0.0536067i	−0.999641	+	0.0268033i	$0.991467\pi$
$728$		0			0
$729$			34.9533i			1.29457i
$730$	−21.6625	+	1.81428i	−0.801765	+	0.0671497i
$731$	4.52440	−	4.52440i	0.167341	−	0.167341i
$732$	10.2864	−	1.73519i	0.380197	−	0.0641346i
$733$	−28.8564	−	28.8564i	−1.06584	−	1.06584i	−0.997674	−	0.0681626i	$-0.978286\pi$
$733$	−28.8564	−	28.8564i	−1.06584	−	1.06584i	−0.0681626	−	0.997674i	$-0.521714\pi$
$734$	−4.05390	+	4.79502i	−0.149632	+	0.176987i
$735$		0			0
$736$	2.30432	+	0.887437i	0.0849385	+	0.0327114i
$737$	−34.2807			−1.26275
$738$	−9.39921	+	11.1175i	−0.345990	+	0.409242i
$739$	8.00319	+	8.00319i	0.294402	+	0.294402i	0.838816	−	0.544414i	$-0.183248\pi$
$739$	8.00319	+	8.00319i	0.294402	+	0.294402i	−0.544414	+	0.838816i	$0.683248\pi$
$740$	−11.5296	+	1.94490i	−0.423835	+	0.0714958i
$741$	4.90325	−	4.90325i	0.180125	−	0.180125i
$742$		0			0
$743$		−	9.66874i		−	0.354712i	−0.984147	−	0.177356i	$-0.943246\pi$
$743$		−	9.66874i		−	0.354712i	0.984147	−	0.177356i	$-0.0567544\pi$
$744$	−14.0866	−	55.0132i	−0.516438	−	2.01688i
$745$			42.5912i			1.56042i
$746$	2.16014	+	25.7920i	0.0790882	+	0.944311i
$747$	35.4211	−	35.4211i	1.29599	−	1.29599i
$748$	−5.09279	−	3.62261i	−0.186211	−	0.132456i
$749$		0			0
$750$	33.2763	+	28.1331i	1.21508	+	1.02728i
$751$	−51.7511			−1.88843			−0.944213	−	0.329336i	$-0.893175\pi$
$751$	−51.7511			−1.88843			−0.944213	+	0.329336i	$0.893175\pi$
$752$	−15.2485	+	5.29514i	−0.556055	+	0.193094i
$753$	−36.6519			−1.33567
$754$	−20.9832	−	17.7400i	−0.764162	−	0.646054i
$755$	−12.8207	−	12.8207i	−0.466594	−	0.466594i
$756$		0			0
$757$	−28.2783	+	28.2783i	−1.02779	+	1.02779i	−0.0281911	+	0.999603i	$0.508975\pi$
$757$	−28.2783	+	28.2783i	−1.02779	+	1.02779i	−0.999603	+	0.0281911i	$0.991025\pi$
$758$	0.286630	+	3.42236i	0.0104109	+	0.124306i
$759$			5.89265i			0.213890i
$760$	2.51822	+	1.49150i	0.0913454	+	0.0541024i
$761$			5.70643i			0.206858i	0.994637	+	0.103429i	$0.0329814\pi$
$761$			5.70643i			0.206858i	−0.994637	+	0.103429i	$0.967019\pi$
$762$	15.2633	−	1.27833i	0.552930	−	0.0463092i
$763$		0			0
$764$	−3.20866	−	19.0213i	−0.116085	−	0.688166i
$765$	−2.82340	−	2.82340i	−0.102080	−	0.102080i
$766$	−10.7508	+	12.7162i	−0.388441	+	0.459455i
$767$	−0.148679			−0.00536849
$768$	−40.4761	−	4.75497i	−1.46056	−	0.171580i
$769$	−39.6503			−1.42983			−0.714914	−	0.699212i	$-0.753534\pi$
$769$	−39.6503			−1.42983			−0.714914	+	0.699212i	$0.753534\pi$
$770$		0			0
$771$	47.7491	+	47.7491i	1.71964	+	1.71964i
$772$	6.50694	+	38.5738i	0.234190	+	1.38830i
$773$	−15.6985	+	15.6985i	−0.564635	+	0.564635i	−0.930620	−	0.365986i	$-0.880732\pi$
$773$	−15.6985	+	15.6985i	−0.564635	+	0.564635i	0.365986	+	0.930620i	$0.380732\pi$
$774$	53.3421	−	4.46752i	1.91734	−	0.160582i
$775$			9.70073i			0.348461i
$776$	29.3384	+	17.3767i	1.05319	+	0.623786i
$777$		0			0
$778$	1.84494	+	22.0285i	0.0661442	+	0.789759i
$779$	1.11229	−	1.11229i	0.0398519	−	0.0398519i
$780$	−29.2822	+	41.1659i	−1.04847	+	1.47398i
$781$	7.70595	+	7.70595i	0.275741	+	0.275741i
$782$	0.277966	+	0.235003i	0.00994003	+	0.00840370i
$783$	4.72827			0.168975
$784$		0			0
$785$	−22.6673			−0.809029
$786$	−13.9282	−	11.7755i	−0.496804	−	0.420018i
$787$	13.7970	+	13.7970i	0.491808	+	0.491808i	0.908876	−	0.417067i	$-0.136942\pi$
$787$	13.7970	+	13.7970i	0.491808	+	0.491808i	−0.417067	+	0.908876i	$0.636942\pi$
$788$	19.2049	+	13.6609i	0.684146	+	0.486648i
$789$	37.3962	−	37.3962i	1.33134	−	1.33134i
$790$	2.99286	+	35.7347i	0.106481	+	1.27138i
$791$		0			0
$792$	−12.9695	−	50.6509i	−0.460853	−	1.79980i
$793$		−	10.4593i		−	0.371420i
$794$	−4.55671	+	0.381635i	−0.161711	+	0.0135437i
$795$	−3.30165	+	3.30165i	−0.117097	+	0.117097i
$796$	−5.33724	+	0.900327i	−0.189173	+	0.0319113i
$797$	2.54421	+	2.54421i	0.0901206	+	0.0901206i	0.750730	−	0.660609i	$-0.229702\pi$
$797$	2.54421	+	2.54421i	0.0901206	+	0.0901206i	−0.660609	+	0.750730i	$0.729702\pi$
$798$		0			0
$799$	−2.37941			−0.0841774
$800$	6.49669	+	2.50199i	0.229693	+	0.0884588i
$801$	−13.5030			−0.477105
$802$	−4.33490	+	5.12738i	−0.153070	+	0.181054i
$803$	−29.6703	−	29.6703i	−1.04704	−	1.04704i
$804$	−32.4928	+	5.48113i	−1.14593	+	0.193305i
$805$		0			0
$806$	−56.7394	+	4.75205i	−1.99856	+	0.167384i
$807$		−	63.7608i		−	2.24449i
$808$	7.35740	−	1.88392i	0.258832	−	0.0662760i
$809$			22.3457i			0.785632i	0.919617	+	0.392816i	$0.128499\pi$
$809$			22.3457i			0.785632i	−0.919617	+	0.392816i	$0.871501\pi$
$810$	1.67232	+	19.9675i	0.0587595	+	0.701587i
$811$	−31.7484	+	31.7484i	−1.11484	+	1.11484i	−0.122349	+	0.992487i	$0.539043\pi$
$811$	−31.7484	+	31.7484i	−1.11484	+	1.11484i	−0.992487	+	0.122349i	$0.960957\pi$
$812$		0			0
$813$	−10.1609	−	10.1609i	−0.356357	−	0.356357i
$814$	−17.2350	−	14.5712i	−0.604088	−	0.510720i
$815$	28.7143			1.00582
$816$	−5.40639	−	2.61938i	−0.189262	−	0.0916968i
$817$	−5.78375			−0.202348
$818$	3.34658	+	2.82933i	0.117010	+	0.0989253i
$819$		0			0
$820$	−6.64259	+	9.33839i	−0.231969	+	0.326111i
$821$	−34.3939	+	34.3939i	−1.20036	+	1.20036i	−0.226297	+	0.974058i	$0.572662\pi$
$821$	−34.3939	+	34.3939i	−1.20036	+	1.20036i	−0.974058	+	0.226297i	$0.927338\pi$
$822$	−0.0838395	−	1.00104i	−0.00292424	−	0.0349153i
$823$			19.3122i			0.673180i	0.941651	+	0.336590i	$0.109274\pi$
$823$			19.3122i			0.673180i	−0.941651	+	0.336590i	$0.890726\pi$
$824$	0.128673	−	0.217248i	0.00448252	−	0.00756820i
$825$			16.6134i			0.578405i
$826$		0			0
$827$	14.4794	−	14.4794i	0.503498	−	0.503498i	−0.409025	−	0.912523i	$-0.634131\pi$
$827$	14.4794	−	14.4794i	0.503498	−	0.503498i	0.912523	+	0.409025i	$0.134131\pi$
$828$	0.506520	+	3.00271i	0.0176028	+	0.104351i
$829$	−1.01085	−	1.01085i	−0.0351084	−	0.0351084i	0.689335	−	0.724443i	$-0.257903\pi$
$829$	−1.01085	−	1.01085i	−0.0351084	−	0.0351084i	−0.724443	+	0.689335i	$0.757903\pi$
$830$	25.4582	−	30.1123i	0.883666	−	1.04521i
$831$	48.7214			1.69013
$832$	−11.4516	+	39.2246i	−0.397013	+	1.35987i
$833$		0			0
$834$	39.8284	−	47.1096i	1.37914	−	1.63127i
$835$	0.585942	+	0.585942i	0.0202774	+	0.0202774i
$836$	0.939701	+	5.57065i	0.0325002	+	0.192665i
$837$	6.92812	−	6.92812i	0.239471	−	0.239471i
$838$	5.22828	−	0.437880i	0.180608	−	0.0151263i
$839$		−	41.9512i		−	1.44832i	−0.689634	−	0.724158i	$-0.742228\pi$
$839$		−	41.9512i		−	1.44832i	0.689634	−	0.724158i	$-0.257772\pi$
$840$		0			0
$841$		−	14.5304i		−	0.501048i
$842$	−0.574304	−	6.85718i	−0.0197918	−	0.236314i
$843$	−37.1749	+	37.1749i	−1.28037	+	1.28037i
$844$	19.6494	−	27.6238i	0.676360	−	0.950851i
$845$	17.9693	+	17.9693i	0.618162	+	0.618162i
$846$	−15.2012	−	12.8517i	−0.522628	−	0.441851i
$847$		0			0
$848$	−1.64673	+	3.39885i	−0.0565491	+	0.116717i
$849$	60.4801			2.07567
$850$	0.783681	+	0.662556i	0.0268801	+	0.0227255i
$851$	0.929456	+	0.929456i	0.0318613	+	0.0318613i
$852$	8.53614	+	6.07194i	0.292443	+	0.208021i
$853$	34.5722	−	34.5722i	1.18373	−	1.18373i	0.204960	−	0.978770i	$-0.434294\pi$
$853$	34.5722	−	34.5722i	1.18373	−	1.18373i	0.978770	−	0.204960i	$-0.0657064\pi$
$854$		0			0
$855$			3.60928i			0.123435i
$856$	−39.9412	+	10.2272i	−1.36516	+	0.349560i
$857$		−	8.33684i		−	0.284781i	−0.989811	−	0.142391i	$-0.954521\pi$
$857$		−	8.33684i		−	0.284781i	0.989811	−	0.142391i	$-0.0454789\pi$
$858$	−97.1715	+	8.13834i	−3.31738	+	0.277838i
$859$	9.23577	−	9.23577i	0.315120	−	0.315120i	−0.531769	−	0.846889i	$-0.678473\pi$
$859$	9.23577	−	9.23577i	0.315120	−	0.315120i	0.846889	+	0.531769i	$0.178473\pi$
$860$	41.5494	−	7.00888i	1.41682	−	0.239001i
$861$		0			0
$862$	20.8075	−	24.6114i	0.708706	−	0.838269i
$863$	49.4383			1.68290			0.841450	−	0.540336i	$-0.181703\pi$
$863$	49.4383			1.68290			0.841450	+	0.540336i	$0.181703\pi$
$864$	−2.85295	−	6.42673i	−0.0970595	−	0.218642i
$865$	−8.17531			−0.277969
$866$	−15.1976	+	17.9759i	−0.516435	+	0.610847i
$867$	29.9927	+	29.9927i	1.01861	+	1.01861i
$868$		0			0
$869$	−48.9443	+	48.9443i	−1.66032	+	1.66032i
$870$	26.5101	−	2.22028i	0.898778	−	0.0752747i
$871$			33.0388i			1.11948i
$872$	4.85499	+	18.9605i	0.164411	+	0.642084i
$873$			42.0498i			1.42317i
$874$	−0.0274603	−	0.327876i	−0.000928860	−	0.0110906i
$875$		0			0
$876$	−32.8667	−	23.3788i	−1.11046	−	0.789897i
$877$	−38.0406	−	38.0406i	−1.28454	−	1.28454i	−0.938057	−	0.346482i	$-0.887376\pi$
$877$	−38.0406	−	38.0406i	−1.28454	−	1.28454i	−0.346482	−	0.938057i	$-0.612624\pi$
$878$	−33.3466	−	28.1926i	−1.12539	−	0.951454i
$879$	73.9420			2.49400
$880$	−13.5013	−	38.8798i	−0.455128	−	1.31064i
$881$	−26.2319			−0.883776			−0.441888	−	0.897070i	$-0.645691\pi$
$881$	−26.2319			−0.883776			−0.441888	+	0.897070i	$0.645691\pi$
$882$		0			0
$883$	−12.8278	−	12.8278i	−0.431688	−	0.431688i	0.457514	−	0.889202i	$-0.348740\pi$
$883$	−12.8278	−	12.8278i	−0.431688	−	0.431688i	−0.889202	+	0.457514i	$0.848740\pi$
$884$	−3.49138	+	4.90830i	−0.117428	+	0.165084i
$885$	0.101787	−	0.101787i	0.00342152	−	0.00342152i
$886$	1.67912	+	20.0486i	0.0564111	+	0.673547i
$887$		−	53.5372i		−	1.79760i	−0.438356	−	0.898801i	$-0.644439\pi$
$887$		−	53.5372i		−	1.79760i	0.438356	−	0.898801i	$-0.355561\pi$
$888$	−18.6659	−	11.0555i	−0.626387	−	0.370999i
$889$		0			0
$890$	−10.5921	+	0.887113i	−0.355048	+	0.0297361i
$891$	−27.3487	+	27.3487i	−0.916216	+	0.916216i
$892$	0.834597	+	4.94758i	0.0279444	+	0.165657i
$893$	1.52085	+	1.52085i	0.0508934	+	0.0508934i
$894$	−51.0198	+	60.3471i	−1.70636	+	2.01831i
$895$	27.2791			0.911841
$896$		0			0
$897$	5.67918			0.189622
$898$	−13.4797	+	15.9440i	−0.449823	+	0.532058i
$899$	21.2017	+	21.2017i	0.707115	+	0.707115i
$900$	1.42806	+	8.46567i	0.0476019	+	0.282189i
$901$	−0.393662	+	0.393662i	−0.0131148	+	0.0131148i
$902$	−22.0431	+	1.84616i	−0.733956	+	0.0614705i
$903$		0			0
$904$	18.2798	+	10.8268i	0.607977	+	0.360095i
$905$			27.6436i			0.918903i
$906$	−2.80767	−	33.5235i	−0.0932785	−	1.11374i
$907$	26.5916	−	26.5916i	0.882960	−	0.882960i	−0.110874	−	0.993834i	$-0.535365\pi$
$907$	26.5916	−	26.5916i	0.882960	−	0.882960i	0.993834	+	0.110874i	$0.0353651\pi$
$908$	−21.9708	+	30.8873i	−0.729127	+	1.02503i
$909$	6.62263	+	6.62263i	0.219659	+	0.219659i
$910$		0			0
$911$	18.6202			0.616914			0.308457	−	0.951238i	$-0.400187\pi$
$911$	18.6202			0.616914			0.308457	+	0.951238i	$0.400187\pi$
$912$	1.78138	+	5.12986i	0.0589874	+	0.169867i
$913$	76.1126			2.51896
$914$	2.24877	+	1.90120i	0.0743826	+	0.0628861i
$915$	7.16049	+	7.16049i	0.236719	+	0.236719i
$916$	−42.3502	−	30.1246i	−1.39929	−	0.995344i
$917$		0			0
$918$	−0.0865062	−	1.03288i	−0.00285513	−	0.0340902i
$919$		−	17.9678i		−	0.592702i	−0.955079	−	0.296351i	$-0.904230\pi$
$919$		−	17.9678i		−	0.592702i	0.955079	−	0.296351i	$-0.0957698\pi$
$920$	0.594597	+	2.32212i	0.0196033	+	0.0765581i
$921$		−	21.7260i		−	0.715894i
$922$	20.9687	−	1.75618i	0.690569	−	0.0578367i
$923$	7.42679	−	7.42679i	0.244456	−	0.244456i
$924$		0			0
$925$	2.62046	+	2.62046i	0.0861602	+	0.0861602i
$926$	−24.2400	+	28.6714i	−0.796574	+	0.942201i
$927$	0.311374			0.0102269
$928$	19.6673	−	8.73071i	0.645610	−	0.286599i
$929$	−26.2515			−0.861285			−0.430642	−	0.902523i	$-0.641713\pi$
$929$	−26.2515			−0.861285			−0.430642	+	0.902523i	$0.641713\pi$
$930$	35.5908	−	42.0974i	1.16707	−	1.38043i
$931$		0			0
$932$	27.8744	−	4.70207i	0.913055	−	0.154021i
$933$	28.8504	−	28.8504i	0.944521	−	0.944521i
$934$	13.6345	−	1.14192i	0.446133	−	0.0373647i
$935$		−	6.06689i		−	0.198409i
$936$	−48.8160	+	12.4997i	−1.59560	+	0.408566i
$937$		−	47.7798i		−	1.56090i	−0.625219	−	0.780449i	$-0.714990\pi$
$937$		−	47.7798i		−	1.56090i	0.625219	−	0.780449i	$-0.285010\pi$
$938$		0			0
$939$	31.9775	−	31.9775i	1.04355	−	1.04355i
$940$	−12.7685	−	9.08253i	−0.416464	−	0.296239i
$941$	−30.6179	−	30.6179i	−0.998115	−	0.998115i	0.00188368	−	0.999998i	$-0.499400\pi$
$941$	−30.6179	−	30.6179i	−0.998115	−	0.998115i	−0.999998	+	0.00188368i	$0.999400\pi$
$942$	−32.1170	−	27.1530i	−1.04643	−	0.884694i
$943$	1.28831			0.0419531
$944$	0.0507672	−	0.104783i	0.00165233	−	0.00341040i
$945$		0			0
$946$	62.1105	+	52.5107i	2.01939	+	1.70727i
$947$	13.1940	+	13.1940i	0.428748	+	0.428748i	0.888202	−	0.459454i	$-0.151955\pi$
$947$	13.1940	+	13.1940i	0.428748	+	0.428748i	−0.459454	+	0.888202i	$0.651955\pi$
$948$	−38.5659	+	54.2173i	−1.25256	+	1.76090i
$949$	−28.5954	+	28.5954i	−0.928246	+	0.928246i
$950$	−0.0774203	−	0.924396i	−0.00251185	−	0.0299914i
$951$			39.5932i			1.28390i
$952$		0			0
$953$			33.1972i			1.07536i	0.843148	+	0.537681i	$0.180700\pi$
$953$			33.1972i			1.07536i	−0.843148	+	0.537681i	$0.819300\pi$
$954$	−4.64122	+	0.388713i	−0.150265	+	0.0125851i
$955$	13.2409	−	13.2409i	0.428467	−	0.428467i
$956$	0.718534	+	4.25955i	0.0232391	+	0.137764i
$957$	36.3099	+	36.3099i	1.17373	+	1.17373i
$958$	−3.55436	+	4.20416i	−0.114836	+	0.135830i
$959$		0			0
$960$	−19.0136	−	34.6933i	−0.613661	−	1.11972i
$961$	31.1317			1.00425
$962$	−14.0433	+	16.6107i	−0.452775	+	0.535550i
$963$	−35.9523	−	35.9523i	−1.15855	−	1.15855i
$964$	−3.23102	−	19.1538i	−0.104064	−	0.616903i
$965$	−26.8517	+	26.8517i	−0.864387	+	0.864387i
$966$		0			0
$967$			13.2736i			0.426850i	0.976959	+	0.213425i	$0.0684619\pi$
$967$			13.2736i			0.426850i	−0.976959	+	0.213425i	$0.931538\pi$
$968$	24.6295	−	41.5839i	0.791622	−	1.33656i
$969$			0.800475i			0.0257150i
$970$	2.76256	+	32.9849i	0.0887006	+	1.05908i
$971$	−30.1077	+	30.1077i	−0.966203	+	0.966203i	−0.999447	−	0.0332439i	$-0.989416\pi$
$971$	−30.1077	+	30.1077i	−0.966203	+	0.966203i	0.0332439	+	0.999447i	$0.489416\pi$
$972$	−25.8725	+	36.3724i	−0.829860	+	1.16665i
$973$		0			0
$974$	−3.11691	−	2.63516i	−0.0998722	−	0.0844359i
$975$	16.0116			0.512781
$976$	7.37130	+	3.57138i	0.235950	+	0.114317i
$977$	48.8002			1.56126			0.780628	−	0.624996i	$-0.214900\pi$
$977$	48.8002			1.56126			0.780628	+	0.624996i	$0.214900\pi$
$978$	40.6851	+	34.3968i	1.30097	+	1.09989i
$979$	−14.5076	−	14.5076i	−0.463664	−	0.463664i
$980$		0			0
$981$	−17.0670	+	17.0670i	−0.544907	+	0.544907i
$982$	1.68924	+	20.1694i	0.0539057	+	0.643632i
$983$		−	53.0171i		−	1.69098i	−0.533990	−	0.845491i	$-0.679308\pi$
$983$		−	53.0171i		−	1.69098i	0.533990	−	0.845491i	$-0.320692\pi$
$984$	−20.5983	+	5.27434i	−0.656648	+	0.168140i
$985$			22.8782i			0.728961i
$986$	3.16086	−	0.264729i	0.100662	−	0.00843069i
$987$		0			0
$988$	5.36885	−	0.905659i	0.170806	−	0.0288128i
$989$	−3.34951	−	3.34951i	−0.106508	−	0.106508i
$990$	32.7686	−	38.7592i	1.04146	−	1.23185i
$991$	−13.8568			−0.440175			−0.220088	−	0.975480i	$-0.570634\pi$
$991$	−13.8568			−0.440175			−0.220088	+	0.975480i	$0.570634\pi$
$992$	16.0249	−	41.6103i	0.508791	−	1.32113i
$993$	−38.7162			−1.22862
$994$		0			0
$995$	−3.71531	−	3.71531i	−0.117783	−	0.117783i
$996$	72.1429	−	12.1696i	2.28593	−	0.385609i
$997$	18.9385	−	18.9385i	0.599787	−	0.599787i	−0.340469	−	0.940256i	$-0.610586\pi$
$997$	18.9385	−	18.9385i	0.599787	−	0.599787i	0.940256	+	0.340469i	$0.110586\pi$
$998$	27.0305	−	2.26386i	0.855635	−	0.0716614i
$999$		−	3.74299i		−	0.118423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.k.589.3		24
7.2	even	3		784.2.x.o.557.11		48
7.3	odd	6		112.2.w.c.93.6	yes	48
7.4	even	3		784.2.x.o.765.6		48
7.5	odd	6		112.2.w.c.109.11	yes	48
7.6	odd	2		784.2.m.j.589.3		24
16.5	even	4	inner	784.2.m.k.197.3		24
28.3	even	6		448.2.ba.c.401.2		48
28.19	even	6		448.2.ba.c.81.11		48
56.3	even	6		896.2.ba.e.289.11		48
56.5	odd	6		896.2.ba.f.417.11		48
56.19	even	6		896.2.ba.e.417.2		48
56.45	odd	6		896.2.ba.f.289.2		48
112.3	even	12		896.2.ba.e.737.2		48
112.5	odd	12		112.2.w.c.53.6	yes	48
112.19	even	12		896.2.ba.e.865.11		48
112.37	even	12		784.2.x.o.165.6		48
112.45	odd	12		896.2.ba.f.737.11		48
112.53	even	12		784.2.x.o.373.11		48
112.59	even	12		448.2.ba.c.177.11		48
112.61	odd	12		896.2.ba.f.865.2		48
112.69	odd	4		784.2.m.j.197.3		24
112.75	even	12		448.2.ba.c.305.2		48
112.101	odd	12		112.2.w.c.37.11	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.11	✓	48	112.101	odd	12
112.2.w.c.53.6	yes	48	112.5	odd	12
112.2.w.c.93.6	yes	48	7.3	odd	6
112.2.w.c.109.11	yes	48	7.5	odd	6
448.2.ba.c.81.11		48	28.19	even	6
448.2.ba.c.177.11		48	112.59	even	12
448.2.ba.c.305.2		48	112.75	even	12
448.2.ba.c.401.2		48	28.3	even	6
784.2.m.j.197.3		24	112.69	odd	4
784.2.m.j.589.3		24	7.6	odd	2
784.2.m.k.197.3		24	16.5	even	4	inner
784.2.m.k.589.3		24	1.1	even	1	trivial
784.2.x.o.165.6		48	112.37	even	12
784.2.x.o.373.11		48	112.53	even	12
784.2.x.o.557.11		48	7.2	even	3
784.2.x.o.765.6		48	7.4	even	3
896.2.ba.e.289.11		48	56.3	even	6
896.2.ba.e.417.2		48	56.19	even	6
896.2.ba.e.737.2		48	112.3	even	12
896.2.ba.e.865.11		48	112.19	even	12
896.2.ba.f.289.2		48	56.45	odd	6
896.2.ba.f.417.11		48	56.5	odd	6
896.2.ba.f.737.11		48	112.45	odd	12
896.2.ba.f.865.2		48	112.61	odd	12

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913051 + 1.07997i) q^{2} +(-1.80111 - 1.80111i) q^{3} +(-0.332676 - 1.97214i) q^{4} +(1.37283 - 1.37283i) q^{5} +(3.58965 - 0.300642i) q^{6} +(2.43360 + 1.44138i) q^{8} +3.48800i q^{9} +O(q^{10})\)	\(q+(-0.913051 + 1.07997i) q^{2} +(-1.80111 - 1.80111i) q^{3} +(-0.332676 - 1.97214i) q^{4} +(1.37283 - 1.37283i) q^{5} +(3.58965 - 0.300642i) q^{6} +(2.43360 + 1.44138i) q^{8} +3.48800i q^{9} +(0.229153 + 2.73608i) q^{10} +(-3.74749 + 3.74749i) q^{11} +(-2.95285 + 4.15122i) q^{12} +(3.61173 + 3.61173i) q^{13} -4.94523 q^{15} +(-3.77865 + 1.31216i) q^{16} -0.589630 q^{17} +(-3.76694 - 3.18472i) q^{18} +(0.376876 + 0.376876i) q^{19} +(-3.16411 - 2.25070i) q^{20} +(-0.625532 - 7.46884i) q^{22} +0.436515i q^{23} +(-1.78710 - 6.97927i) q^{24} +1.23069i q^{25} +(-7.19827 + 0.602871i) q^{26} +(0.878939 - 0.878939i) q^{27} +(2.68976 + 2.68976i) q^{29} +(4.51525 - 5.34071i) q^{30} +7.88237 q^{31} +(2.03300 - 5.27891i) q^{32} +13.4993 q^{33} +(0.538362 - 0.636783i) q^{34} +(6.87881 - 1.16037i) q^{36} +(2.12926 - 2.12926i) q^{37} +(-0.751121 + 0.0629081i) q^{38} -13.0103i q^{39} +(5.31969 - 1.36215i) q^{40} -2.95135i q^{41} +(-7.67329 + 7.67329i) q^{43} +(8.63727 + 6.14387i) q^{44} +(4.78842 + 4.78842i) q^{45} +(-0.471424 - 0.398561i) q^{46} +4.03543 q^{47} +(9.16913 + 4.44242i) q^{48} +(-1.32911 - 1.12368i) q^{50} +(1.06199 + 1.06199i) q^{51} +(5.92130 - 8.32437i) q^{52} +(0.667643 - 0.667643i) q^{53} +(0.146713 + 1.75175i) q^{54} +10.2893i q^{55} -1.35759i q^{57} +(-5.36075 + 0.448975i) q^{58} +(-0.0205828 + 0.0205828i) q^{59} +(1.64516 + 9.75267i) q^{60} +(-1.44796 - 1.44796i) q^{61} +(-7.19700 + 8.51273i) q^{62} +(3.84483 + 7.01550i) q^{64} +9.91658 q^{65} +(-12.3255 + 14.5789i) q^{66} +(4.57382 + 4.57382i) q^{67} +(0.196155 + 1.16283i) q^{68} +(0.786212 - 0.786212i) q^{69} -2.05630i q^{71} +(-5.02754 + 8.48840i) q^{72} +7.91736i q^{73} +(0.355417 + 4.24367i) q^{74} +(2.21660 - 2.21660i) q^{75} +(0.617873 - 0.868628i) q^{76} +(14.0507 + 11.8790i) q^{78} +13.0606 q^{79} +(-3.38607 + 6.98882i) q^{80} +7.29786 q^{81} +(3.18737 + 2.69473i) q^{82} +(-10.1551 - 10.1551i) q^{83} +(-0.809460 + 0.809460i) q^{85} +(-1.28083 - 15.2930i) q^{86} -9.68911i q^{87} +(-14.5215 + 3.71834i) q^{88} +3.87127i q^{89} +(-9.54343 + 0.799284i) q^{90} +(0.860868 - 0.145218i) q^{92} +(-14.1970 - 14.1970i) q^{93} +(-3.68455 + 4.35814i) q^{94} +1.03477 q^{95} +(-13.1696 + 5.84624i) q^{96} +12.0556 q^{97} +(-13.0712 - 13.0712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8}+O(q^{10}) \) 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8	\( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27} + 12 q^{29} + 4 q^{30} + 28 q^{31} - 16 q^{32} + 16 q^{33} + 22 q^{34} - 36 q^{36} + 24 q^{37} + 20 q^{38} + 26 q^{40} - 20 q^{43} - 6 q^{44} - 28 q^{45} + 14 q^{46} - 20 q^{47} - 28 q^{48} + 28 q^{50} - 24 q^{51} - 16 q^{52} + 16 q^{53} + 64 q^{54} + 6 q^{58} - 20 q^{59} - 46 q^{60} + 8 q^{61} - 12 q^{62} + 40 q^{64} - 8 q^{65} - 20 q^{66} - 48 q^{67} + 20 q^{69} + 32 q^{72} + 8 q^{74} - 4 q^{75} + 18 q^{76} + 58 q^{78} + 36 q^{79} - 28 q^{80} + 2 q^{82} + 4 q^{83} + 20 q^{86} + 42 q^{88} + 10 q^{90} + 38 q^{92} - 8 q^{93} - 72 q^{94} + 4 q^{95} - 120 q^{96} + 24 q^{97} - 12 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 12 * q^13 - 20 * q^15 - 16 * q^16 + 8 * q^17 - 18 * q^18 - 4 * q^19 + 8 * q^20 + 18 * q^24 - 10 * q^26 + 12 * q^27 + 12 * q^29 + 4 * q^30 + 28 * q^31 - 16 * q^32 + 16 * q^33 + 22 * q^34 - 36 * q^36 + 24 * q^37 + 20 * q^38 + 26 * q^40 - 20 * q^43 - 6 * q^44 - 28 * q^45 + 14 * q^46 - 20 * q^47 - 28 * q^48 + 28 * q^50 - 24 * q^51 - 16 * q^52 + 16 * q^53 + 64 * q^54 + 6 * q^58 - 20 * q^59 - 46 * q^60 + 8 * q^61 - 12 * q^62 + 40 * q^64 - 8 * q^65 - 20 * q^66 - 48 * q^67 + 20 * q^69 + 32 * q^72 + 8 * q^74 - 4 * q^75 + 18 * q^76 + 58 * q^78 + 36 * q^79 - 28 * q^80 + 2 * q^82 + 4 * q^83 + 20 * q^86 + 42 * q^88 + 10 * q^90 + 38 * q^92 - 8 * q^93 - 72 * q^94 + 4 * q^95 - 120 * q^96 + 24 * q^97 - 12 * q^99

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