LMFDB - Embedded newform 1110.2.u.f.191.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.14
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.f.401.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.392697 - 1.68695i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.47053 - 0.915172i) q^{6} -0.873718 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.69158 - 1.32492i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.392697 - 1.68695i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.47053 - 0.915172i) q^{6} -0.873718 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.69158 - 1.32492i) q^{9} -1.00000 q^{10} +3.24582 q^{11} +(1.68695 + 0.392697i) q^{12} +(2.80064 + 2.80064i) q^{13} +(-0.617812 - 0.617812i) q^{14} +(0.915172 + 1.47053i) q^{15} -1.00000 q^{16} +(2.67922 - 2.67922i) q^{17} +(-0.966374 - 2.84009i) q^{18} +(2.24528 + 2.24528i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-0.343107 + 1.47392i) q^{21} +(2.29514 + 2.29514i) q^{22} +(3.93841 - 3.93841i) q^{23} +(0.915172 + 1.47053i) q^{24} -1.00000i q^{25} +3.96070i q^{26} +(-3.29204 + 4.02026i) q^{27} -0.873718i q^{28} +(0.0117303 + 0.0117303i) q^{29} +(-0.392697 + 1.68695i) q^{30} +(5.20171 - 5.20171i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.27463 - 5.47553i) q^{33} +3.78900 q^{34} +(0.617812 - 0.617812i) q^{35} +(1.32492 - 2.69158i) q^{36} +(-2.06314 + 5.72219i) q^{37} +3.17531i q^{38} +(5.82434 - 3.62473i) q^{39} -1.00000i q^{40} +12.1119 q^{41} +(-1.28483 + 0.799603i) q^{42} +(8.06425 + 8.06425i) q^{43} +3.24582i q^{44} +(2.84009 - 0.966374i) q^{45} +5.56975 q^{46} -3.06944i q^{47} +(-0.392697 + 1.68695i) q^{48} -6.23662 q^{49} +(0.707107 - 0.707107i) q^{50} +(-3.46758 - 5.57183i) q^{51} +(-2.80064 + 2.80064i) q^{52} -9.17714i q^{53} +(-5.17058 + 0.514925i) q^{54} +(-2.29514 + 2.29514i) q^{55} +(0.617812 - 0.617812i) q^{56} +(4.66939 - 2.90596i) q^{57} +0.0165891i q^{58} +(-7.96028 + 7.96028i) q^{59} +(-1.47053 + 0.915172i) q^{60} +(-6.64635 + 6.64635i) q^{61} +7.35632 q^{62} +(2.35168 + 1.15761i) q^{63} -1.00000i q^{64} -3.96070 q^{65} +(4.77308 - 2.97049i) q^{66} -7.74070i q^{67} +(2.67922 + 2.67922i) q^{68} +(-5.09728 - 8.19049i) q^{69} +0.873718 q^{70} +0.580983i q^{71} +(2.84009 - 0.966374i) q^{72} -11.0501i q^{73} +(-5.50506 + 2.58734i) q^{74} +(-1.68695 - 0.392697i) q^{75} +(-2.24528 + 2.24528i) q^{76} -2.83593 q^{77} +(6.68150 + 1.55536i) q^{78} +(0.763562 + 0.763562i) q^{79} +(0.707107 - 0.707107i) q^{80} +(5.48918 + 7.13224i) q^{81} +(8.56443 + 8.56443i) q^{82} -6.26833i q^{83} +(-1.47392 - 0.343107i) q^{84} +3.78900i q^{85} +11.4046i q^{86} +(0.0243948 - 0.0151819i) q^{87} +(-2.29514 + 2.29514i) q^{88} +(-6.49421 - 6.49421i) q^{89} +(2.69158 + 1.32492i) q^{90} +(-2.44697 - 2.44697i) q^{91} +(3.93841 + 3.93841i) q^{92} +(-6.73230 - 10.8177i) q^{93} +(2.17042 - 2.17042i) q^{94} -3.17531 q^{95} +(-1.47053 + 0.915172i) q^{96} +(7.15350 + 7.15350i) q^{97} +(-4.40995 - 4.40995i) q^{98} +(-8.73639 - 4.30045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q + 24 * q^7 - 8 * q^9	$ 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) $ 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.392697	−	1.68695i	0.226724	−	0.973959i
$3$	0.392697	−	1.68695i	0.226724	−	0.973959i
$4$			1.00000i			0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	1.47053	−	0.915172i	0.600341	−	0.373618i
$7$	−0.873718			−0.330234			−0.165117	−	0.986274i	$-0.552800\pi$
$7$	−0.873718			−0.330234			−0.165117	+	0.986274i	$0.552800\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.69158	−	1.32492i	−0.897193	−	0.441640i
$10$	−1.00000			−0.316228
$11$	3.24582			0.978653			0.489326	−	0.872101i	$-0.337243\pi$
$11$	3.24582			0.978653			0.489326	+	0.872101i	$0.337243\pi$
$12$	1.68695	+	0.392697i	0.486980	+	0.113362i
$13$	2.80064	+	2.80064i	0.776758	+	0.776758i	0.979278	−	0.202520i	$-0.0649131\pi$
$13$	2.80064	+	2.80064i	0.776758	+	0.776758i	−0.202520	+	0.979278i	$0.564913\pi$
$14$	−0.617812	−	0.617812i	−0.165117	−	0.165117i
$15$	0.915172	+	1.47053i	0.236297	+	0.379689i
$16$	−1.00000			−0.250000
$17$	2.67922	−	2.67922i	0.649807	−	0.649807i	−0.303139	−	0.952946i	$-0.598035\pi$
$17$	2.67922	−	2.67922i	0.649807	−	0.649807i	0.952946	+	0.303139i	$0.0980347\pi$
$18$	−0.966374	−	2.84009i	−0.227777	−	0.669416i
$19$	2.24528	+	2.24528i	0.515103	+	0.515103i	0.916086	−	0.400982i	$-0.131331\pi$
$19$	2.24528	+	2.24528i	0.515103	+	0.515103i	−0.400982	+	0.916086i	$0.631331\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	−0.343107	+	1.47392i	−0.0748720	+	0.321635i
$22$	2.29514	+	2.29514i	0.489326	+	0.489326i
$23$	3.93841	−	3.93841i	0.821215	−	0.821215i	−0.165067	−	0.986282i	$-0.552784\pi$
$23$	3.93841	−	3.93841i	0.821215	−	0.821215i	0.986282	+	0.165067i	$0.0527842\pi$
$24$	0.915172	+	1.47053i	0.186809	+	0.300171i
$25$		−	1.00000i		−	0.200000i
$26$			3.96070i			0.776758i
$27$	−3.29204	+	4.02026i	−0.633554	+	0.773699i
$28$		−	0.873718i		−	0.165117i
$29$	0.0117303	+	0.0117303i	0.00217826	+	0.00217826i	0.708195	−	0.706017i	$-0.249510\pi$
$29$	0.0117303	+	0.0117303i	0.00217826	+	0.00217826i	−0.706017	+	0.708195i	$0.749510\pi$
$30$	−0.392697	+	1.68695i	−0.0716964	+	0.307993i
$31$	5.20171	−	5.20171i	0.934254	−	0.934254i	−0.0637143	−	0.997968i	$-0.520295\pi$
$31$	5.20171	−	5.20171i	0.934254	−	0.934254i	0.997968	+	0.0637143i	$0.0202946\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.27463	−	5.47553i	0.221884	−	0.953168i
$34$	3.78900			0.649807
$35$	0.617812	−	0.617812i	0.104429	−	0.104429i
$36$	1.32492	−	2.69158i	0.220820	−	0.448596i
$37$	−2.06314	+	5.72219i	−0.339179	+	0.940722i
$37$	−2.06314	+	5.72219i	−0.339179	+	0.940722i
$38$			3.17531i			0.515103i
$39$	5.82434	−	3.62473i	0.932640	−	0.580421i
$40$		−	1.00000i		−	0.158114i
$41$	12.1119			1.89157			0.945783	−	0.324799i	$-0.105297\pi$
$41$	12.1119			1.89157			0.945783	+	0.324799i	$0.105297\pi$
$42$	−1.28483	+	0.799603i	−0.198253	+	0.123381i
$43$	8.06425	+	8.06425i	1.22979	+	1.22979i	0.964044	+	0.265743i	$0.0856174\pi$
$43$	8.06425	+	8.06425i	1.22979	+	1.22979i	0.265743	+	0.964044i	$0.414383\pi$
$44$			3.24582i			0.489326i
$45$	2.84009	−	0.966374i	0.423376	−	0.144059i
$46$	5.56975			0.821215
$47$		−	3.06944i		−	0.447724i	−0.974621	−	0.223862i	$-0.928133\pi$
$47$		−	3.06944i		−	0.447724i	0.974621	−	0.223862i	$-0.0718666\pi$
$48$	−0.392697	+	1.68695i	−0.0566810	+	0.243490i
$49$	−6.23662			−0.890945
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	−3.46758	−	5.57183i	−0.485559	−	0.780213i
$52$	−2.80064	+	2.80064i	−0.388379	+	0.388379i
$53$		−	9.17714i		−	1.26058i	−0.776361	−	0.630289i	$-0.782937\pi$
$53$		−	9.17714i		−	1.26058i	0.776361	−	0.630289i	$-0.217063\pi$
$54$	−5.17058	+	0.514925i	−0.703626	+	0.0700724i
$55$	−2.29514	+	2.29514i	−0.309477	+	0.309477i
$56$	0.617812	−	0.617812i	0.0825586	−	0.0825586i
$57$	4.66939	−	2.90596i	0.618476	−	0.384903i
$58$			0.0165891i			0.00217826i
$59$	−7.96028	+	7.96028i	−1.03634	+	1.03634i	−0.0370254	+	0.999314i	$0.511788\pi$
$59$	−7.96028	+	7.96028i	−1.03634	+	1.03634i	−0.999314	+	0.0370254i	$0.988212\pi$
$60$	−1.47053	+	0.915172i	−0.189845	+	0.118148i
$61$	−6.64635	+	6.64635i	−0.850978	+	0.850978i	−0.990254	−	0.139276i	$-0.955522\pi$
$61$	−6.64635	+	6.64635i	−0.850978	+	0.850978i	0.139276	+	0.990254i	$0.455522\pi$
$62$	7.35632			0.934254
$63$	2.35168	+	1.15761i	0.296284	+	0.145845i
$64$		−	1.00000i		−	0.125000i
$65$	−3.96070			−0.491265
$66$	4.77308	−	2.97049i	0.587526	−	0.365642i
$67$		−	7.74070i		−	0.945677i	−0.881149	−	0.472838i	$-0.843229\pi$
$67$		−	7.74070i		−	0.945677i	0.881149	−	0.472838i	$-0.156771\pi$
$68$	2.67922	+	2.67922i	0.324904	+	0.324904i
$69$	−5.09728	−	8.19049i	−0.613641	−	0.986019i
$70$	0.873718			0.104429
$71$			0.580983i			0.0689500i	0.999406	+	0.0344750i	$0.0109759\pi$
$71$			0.580983i			0.0689500i	−0.999406	+	0.0344750i	$0.989024\pi$
$72$	2.84009	−	0.966374i	0.334708	−	0.113888i
$73$		−	11.0501i		−	1.29332i	−0.762780	−	0.646658i	$-0.776166\pi$
$73$		−	11.0501i		−	1.29332i	0.762780	−	0.646658i	$-0.223834\pi$
$74$	−5.50506	+	2.58734i	−0.639950	+	0.300772i
$75$	−1.68695	−	0.392697i	−0.194792	−	0.0453448i
$76$	−2.24528	+	2.24528i	−0.257552	+	0.257552i
$77$	−2.83593			−0.323185
$78$	6.68150	+	1.55536i	0.756531	+	0.176110i
$79$	0.763562	+	0.763562i	0.0859075	+	0.0859075i	0.748755	−	0.662847i	$-0.230652\pi$
$79$	0.763562	+	0.763562i	0.0859075	+	0.0859075i	−0.662847	+	0.748755i	$0.730652\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	5.48918	+	7.13224i	0.609909	+	0.792471i
$82$	8.56443	+	8.56443i	0.945783	+	0.945783i
$83$		−	6.26833i		−	0.688039i	−0.938963	−	0.344019i	$-0.888211\pi$
$83$		−	6.26833i		−	0.688039i	0.938963	−	0.344019i	$-0.111789\pi$
$84$	−1.47392	−	0.343107i	−0.160817	−	0.0374360i
$85$			3.78900i			0.410974i
$86$			11.4046i			1.22979i
$87$	0.0243948	−	0.0151819i	0.00261540	−	0.00162767i
$88$	−2.29514	+	2.29514i	−0.244663	+	0.244663i
$89$	−6.49421	−	6.49421i	−0.688385	−	0.688385i	0.273490	−	0.961875i	$-0.411822\pi$
$89$	−6.49421	−	6.49421i	−0.688385	−	0.688385i	−0.961875	+	0.273490i	$0.911822\pi$
$90$	2.69158	+	1.32492i	0.283717	+	0.139659i
$91$	−2.44697	−	2.44697i	−0.256512	−	0.256512i
$92$	3.93841	+	3.93841i	0.410607	+	0.410607i
$93$	−6.73230	−	10.8177i	−0.698107	−	1.12174i
$94$	2.17042	−	2.17042i	0.223862	−	0.223862i
$95$	−3.17531			−0.325780
$96$	−1.47053	+	0.915172i	−0.150085	+	0.0934044i
$97$	7.15350	+	7.15350i	0.726328	+	0.726328i	0.969886	−	0.243558i	$-0.0783147\pi$
$97$	7.15350	+	7.15350i	0.726328	+	0.726328i	−0.243558	+	0.969886i	$0.578315\pi$
$98$	−4.40995	−	4.40995i	−0.445473	−	0.445473i
$99$	−8.73639	−	4.30045i	−0.878040	−	0.432212i
$100$	1.00000			0.100000
$101$	−9.86993			−0.982095			−0.491048	−	0.871133i	$-0.663386\pi$
$101$	−9.86993			−0.982095			−0.491048	+	0.871133i	$0.663386\pi$
$102$	1.48793	−	6.39183i	0.147327	−	0.632886i
$103$	−4.80415	+	4.80415i	−0.473367	+	0.473367i	−0.903002	−	0.429636i	$-0.858642\pi$
$103$	−4.80415	+	4.80415i	−0.473367	+	0.473367i	0.429636	+	0.903002i	$0.358642\pi$
$104$	−3.96070			−0.388379
$105$	−0.799603	−	1.28483i	−0.0780332	−	0.125386i
$106$	6.48922	−	6.48922i	0.630289	−	0.630289i
$107$			14.7208i			1.42312i	0.702628	+	0.711558i	$0.252010\pi$
$107$			14.7208i			1.42312i	−0.702628	+	0.711558i	$0.747990\pi$
$108$	−4.02026	−	3.29204i	−0.386849	−	0.316777i
$109$	12.8578	+	12.8578i	1.23155	+	1.23155i	0.963368	+	0.268184i	$0.0864235\pi$
$109$	12.8578	+	12.8578i	1.23155	+	1.23155i	0.268184	+	0.963368i	$0.413577\pi$
$110$	−3.24582			−0.309477
$111$	8.84284	+	5.72750i	0.839325	+	0.543630i
$112$	0.873718			0.0825586
$113$	−3.10020	−	3.10020i	−0.291643	−	0.291643i	0.546086	−	0.837729i	$-0.316117\pi$
$113$	−3.10020	−	3.10020i	−0.291643	−	0.291643i	−0.837729	+	0.546086i	$0.816117\pi$
$114$	5.35658	+	1.24694i	0.501690	+	0.116786i
$115$			5.56975i			0.519382i
$116$	−0.0117303	+	0.0117303i	−0.00108913	+	0.00108913i
$117$	−3.82752	−	11.2488i	−0.353854	−	1.03995i
$118$	−11.2575			−1.03634
$119$	−2.34089	+	2.34089i	−0.214589	+	0.214589i
$120$	−1.68695	−	0.392697i	−0.153996	−	0.0358482i
$121$	−0.464630			−0.0422391
$122$	−9.39935			−0.850978
$123$	4.75632	−	20.4322i	0.428863	−	1.84231i
$124$	5.20171	+	5.20171i	0.467127	+	0.467127i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	0.844338	+	2.48144i	0.0752196	+	0.221064i
$127$	−0.948940			−0.0842048			−0.0421024	−	0.999113i	$-0.513406\pi$
$127$	−0.948940			−0.0842048			−0.0421024	+	0.999113i	$0.513406\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	16.7708	−	10.4372i	1.47658	−	0.918940i
$130$	−2.80064	−	2.80064i	−0.245632	−	0.245632i
$131$	11.7356	+	11.7356i	1.02535	+	1.02535i	0.999670	+	0.0256765i	$0.00817399\pi$
$131$	11.7356	+	11.7356i	1.02535	+	1.02535i	0.0256765	+	0.999670i	$0.491826\pi$
$132$	5.47553	+	1.27463i	0.476584	+	0.110942i
$133$	−1.96174	−	1.96174i	−0.170105	−	0.170105i
$134$	5.47350	−	5.47350i	0.472838	−	0.472838i
$135$	−0.514925	−	5.17058i	−0.0443177	−	0.445012i
$136$			3.78900i			0.324904i
$137$		−	21.3281i		−	1.82218i	−0.412209	−	0.911089i	$-0.635243\pi$
$137$		−	21.3281i		−	1.82218i	0.412209	−	0.911089i	$-0.364757\pi$
$138$	2.18723	−	9.39587i	0.186189	−	0.799830i
$139$		−	14.6182i		−	1.23990i	−0.784641	−	0.619951i	$-0.787153\pi$
$139$		−	14.6182i		−	1.23990i	0.784641	−	0.619951i	$-0.212847\pi$
$140$	0.617812	+	0.617812i	0.0522146	+	0.0522146i
$141$	−5.17799	−	1.20536i	−0.436065	−	0.101510i
$142$	−0.410817	+	0.410817i	−0.0344750	+	0.0344750i
$143$	9.09039	+	9.09039i	0.760176	+	0.760176i
$144$	2.69158	+	1.32492i	0.224298	+	0.110410i
$145$	−0.0165891			−0.00137765
$146$	7.81360	−	7.81360i	0.646658	−	0.646658i
$147$	−2.44910	+	10.5208i	−0.201999	+	0.867744i
$148$	−5.72219	−	2.06314i	−0.470361	−	0.169589i
$149$			4.27966i			0.350604i	0.984515	+	0.175302i	$0.0560902\pi$
$149$			4.27966i			0.350604i	−0.984515	+	0.175302i	$0.943910\pi$
$150$	−0.915172	−	1.47053i	−0.0747235	−	0.120068i
$151$			16.2675i			1.32383i	0.749577	+	0.661917i	$0.230257\pi$
$151$			16.2675i			1.32383i	−0.749577	+	0.661917i	$0.769743\pi$
$152$	−3.17531			−0.257552
$153$	−10.7611	+	3.66159i	−0.869983	+	0.296022i
$154$	−2.00531	−	2.00531i	−0.161592	−	0.161592i
$155$			7.35632i			0.590874i
$156$	3.62473	+	5.82434i	0.290210	+	0.466320i
$157$	−18.4593			−1.47321			−0.736607	−	0.676321i	$-0.763573\pi$
$157$	−18.4593			−1.47321			−0.736607	+	0.676321i	$0.763573\pi$
$158$			1.07984i			0.0859075i
$159$	−15.4813	−	3.60384i	−1.22775	−	0.285803i
$160$	1.00000			0.0790569
$161$	−3.44106	+	3.44106i	−0.271193	+	0.271193i
$162$	−1.16182	+	8.92469i	−0.0912812	+	0.701190i
$163$	−7.65805	+	7.65805i	−0.599825	+	0.599825i	−0.940266	−	0.340441i	$-0.889424\pi$
$163$	−7.65805	+	7.65805i	−0.599825	+	0.599825i	0.340441	+	0.940266i	$0.389424\pi$
$164$			12.1119i			0.945783i
$165$	2.97049	+	4.77308i	0.231252	+	0.371584i
$166$	4.43238	−	4.43238i	0.344019	−	0.344019i
$167$	−12.4791	+	12.4791i	−0.965665	+	0.965665i	−0.999430	−	0.0337648i	$-0.989250\pi$
$167$	−12.4791	+	12.4791i	−0.965665	+	0.965665i	0.0337648	+	0.999430i	$0.489250\pi$
$168$	−0.799603	−	1.28483i	−0.0616907	−	0.0991267i
$169$			2.68718i			0.206706i
$170$	−2.67922	+	2.67922i	−0.205487	+	0.205487i
$171$	−3.06854	−	9.01817i	−0.234657	−	0.689637i
$172$	−8.06425	+	8.06425i	−0.614894	+	0.614894i
$173$	9.17456			0.697529			0.348765	−	0.937210i	$-0.386601\pi$
$173$	9.17456			0.697529			0.348765	+	0.937210i	$0.386601\pi$
$174$	0.0279850	+	0.00651450i	0.00212153	+	0.000493863i
$175$			0.873718i			0.0660469i
$176$	−3.24582			−0.244663
$177$	10.3026	+	16.5545i	0.774389	+	1.24432i
$178$		−	9.18420i		−	0.688385i
$179$	−10.0110	−	10.0110i	−0.748257	−	0.748257i	0.225895	−	0.974152i	$-0.427470\pi$
$179$	−10.0110	−	10.0110i	−0.748257	−	0.748257i	−0.974152	+	0.225895i	$0.927470\pi$
$180$	0.966374	+	2.84009i	0.0720293	+	0.211688i
$181$	−22.6754			−1.68545			−0.842724	−	0.538346i	$-0.819049\pi$
$181$	−22.6754			−1.68545			−0.842724	+	0.538346i	$0.819049\pi$
$182$		−	3.46054i		−	0.256512i
$183$	8.60203	+	13.8220i	0.635880	+	1.02175i
$184$			5.56975i			0.410607i
$185$	−2.58734	−	5.50506i	−0.190225	−	0.404740i
$186$	2.88881	−	12.4097i	0.211818	−	0.909925i
$187$	8.69629	−	8.69629i	0.635936	−	0.635936i
$188$	3.06944			0.223862
$189$	2.87632	−	3.51257i	0.209221	−	0.255502i
$190$	−2.24528	−	2.24528i	−0.162890	−	0.162890i
$191$	6.59688	−	6.59688i	0.477333	−	0.477333i	−0.426945	−	0.904278i	$-0.640410\pi$
$191$	6.59688	−	6.59688i	0.477333	−	0.477333i	0.904278	+	0.426945i	$0.140410\pi$
$192$	−1.68695	−	0.392697i	−0.121745	−	0.0283405i
$193$	−0.721641	−	0.721641i	−0.0519448	−	0.0519448i	0.680657	−	0.732602i	$-0.261694\pi$
$193$	−0.721641	−	0.721641i	−0.0519448	−	0.0519448i	−0.732602	+	0.680657i	$0.761694\pi$
$194$			10.1166i			0.726328i
$195$	−1.55536	+	6.68150i	−0.111381	+	0.478472i
$196$		−	6.23662i		−	0.445473i
$197$		−	14.8081i		−	1.05504i	−0.849544	−	0.527518i	$-0.823123\pi$
$197$		−	14.8081i		−	1.05504i	0.849544	−	0.527518i	$-0.176877\pi$
$198$	−3.13668	−	9.21844i	−0.222914	−	0.655126i
$199$	−15.3316	+	15.3316i	−1.08683	+	1.08683i	−0.0909720	+	0.995853i	$0.528997\pi$
$199$	−15.3316	+	15.3316i	−1.08683	+	1.08683i	−0.995853	+	0.0909720i	$0.971003\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	−13.0581	−	3.03975i	−0.921050	−	0.214408i
$202$	−6.97910	−	6.97910i	−0.491048	−	0.491048i
$203$	−0.0102490	−	0.0102490i	−0.000719336	−	0.000719336i
$204$	5.57183	−	3.46758i	0.390106	−	0.242779i
$205$	−8.56443	+	8.56443i	−0.598166	+	0.598166i
$206$	−6.79409			−0.473367
$207$	−15.8186	+	5.38246i	−1.09947	+	0.374107i
$208$	−2.80064	−	2.80064i	−0.194190	−	0.194190i
$209$	7.28779	+	7.28779i	0.504107	+	0.504107i
$210$	0.343107	−	1.47392i	0.0236766	−	0.101710i
$211$	−14.8756			−1.02408			−0.512039	−	0.858962i	$-0.671109\pi$
$211$	−14.8756			−1.02408			−0.512039	+	0.858962i	$0.671109\pi$
$212$	9.17714			0.630289
$213$	0.980088	+	0.228151i	0.0671545	+	0.0156326i
$214$	−10.4092	+	10.4092i	−0.711558	+	0.711558i
$215$	−11.4046			−0.777786
$216$	−0.514925	−	5.17058i	−0.0350362	−	0.351813i
$217$	−4.54482	+	4.54482i	−0.308523	+	0.308523i
$218$			18.1836i			1.23155i
$219$	−18.6409	−	4.33935i	−1.25964	−	0.293226i
$220$	−2.29514	−	2.29514i	−0.154739	−	0.154739i
$221$	15.0071			1.00949
$222$	2.20288	+	10.3028i	0.147847	+	0.691478i
$223$	6.18301			0.414045			0.207022	−	0.978336i	$-0.433623\pi$
$223$	6.18301			0.414045			0.207022	+	0.978336i	$0.433623\pi$
$224$	0.617812	+	0.617812i	0.0412793	+	0.0412793i
$225$	−1.32492	+	2.69158i	−0.0883279	+	0.179439i
$226$		−	4.38435i		−	0.291643i
$227$	16.9434	−	16.9434i	1.12457	−	1.12457i	0.133527	−	0.991045i	$-0.457370\pi$
$227$	16.9434	−	16.9434i	1.12457	−	1.12457i	0.991045	−	0.133527i	$-0.0426304\pi$
$228$	2.90596	+	4.66939i	0.192452	+	0.309238i
$229$	7.05363			0.466117			0.233058	−	0.972463i	$-0.425127\pi$
$229$	7.05363			0.466117			0.233058	+	0.972463i	$0.425127\pi$
$230$	−3.93841	+	3.93841i	−0.259691	+	0.259691i
$231$	−1.11366	+	4.78407i	−0.0732737	+	0.314769i
$232$	−0.0165891			−0.00108913
$233$	4.46090			0.292243			0.146122	−	0.989267i	$-0.453321\pi$
$233$	4.46090			0.292243			0.146122	+	0.989267i	$0.453321\pi$
$234$	5.24761	−	10.6605i	0.343047	−	0.696902i
$235$	2.17042	+	2.17042i	0.141583	+	0.141583i
$236$	−7.96028	−	7.96028i	−0.518170	−	0.518170i
$237$	1.58794	−	0.988240i	0.103148	−	0.0641931i
$238$	−3.31051			−0.214589
$239$	−17.0743	+	17.0743i	−1.10444	+	1.10444i	−0.110576	+	0.993868i	$0.535270\pi$
$239$	−17.0743	+	17.0743i	−1.10444	+	1.10444i	−0.993868	+	0.110576i	$0.964730\pi$
$240$	−0.915172	−	1.47053i	−0.0590741	−	0.0949223i
$241$	−3.79899	−	3.79899i	−0.244715	−	0.244715i	0.574083	−	0.818797i	$-0.305359\pi$
$241$	−3.79899	−	3.79899i	−0.244715	−	0.244715i	−0.818797	+	0.574083i	$0.805359\pi$
$242$	−0.328543	−	0.328543i	−0.0211195	−	0.0211195i
$243$	14.1873	−	6.45914i	0.910116	−	0.414354i
$244$	−6.64635	−	6.64635i	−0.425489	−	0.425489i
$245$	4.40995	−	4.40995i	0.281742	−	0.281742i
$246$	17.8110	−	11.0845i	1.13559	−	0.706722i
$247$			12.5765i			0.800221i
$248$			7.35632i			0.467127i
$249$	−10.5743	−	2.46156i	−0.670122	−	0.155995i
$250$			1.00000i			0.0632456i
$251$	−2.59871	−	2.59871i	−0.164029	−	0.164029i	0.620320	−	0.784349i	$-0.287003\pi$
$251$	−2.59871	−	2.59871i	−0.164029	−	0.164029i	−0.784349	+	0.620320i	$0.787003\pi$
$252$	−1.15761	+	2.35168i	−0.0729223	+	0.148142i
$253$	12.7834	−	12.7834i	0.803684	−	0.803684i
$254$	−0.671002	−	0.671002i	−0.0421024	−	0.0421024i
$255$	6.39183	+	1.48793i	0.400272	+	0.0931777i
$256$	1.00000			0.0625000
$257$	13.1036	−	13.1036i	0.817381	−	0.817381i	−0.168346	−	0.985728i	$-0.553843\pi$
$257$	13.1036	−	13.1036i	0.817381	−	0.817381i	0.985728	+	0.168346i	$0.0538427\pi$
$258$	19.2389	+	4.47855i	1.19776	+	0.278822i
$259$	1.80260	−	4.99958i	0.112008	−	0.310659i
$260$		−	3.96070i		−	0.245632i
$261$	−0.0160313	−	0.0471146i	−0.000992312	−	0.00291632i
$262$			16.5967i			1.02535i
$263$	3.79960			0.234293			0.117147	−	0.993115i	$-0.462625\pi$
$263$	3.79960			0.234293			0.117147	+	0.993115i	$0.462625\pi$
$264$	2.97049	+	4.77308i	0.182821	+	0.293763i
$265$	6.48922	+	6.48922i	0.398630	+	0.398630i
$266$		−	2.77433i		−	0.170105i
$267$	−13.5056	+	8.40513i	−0.826532	+	0.514385i
$268$	7.74070			0.472838
$269$			12.5379i			0.764450i	0.924069	+	0.382225i	$0.124842\pi$
$269$			12.5379i			0.764450i	−0.924069	+	0.382225i	$0.875158\pi$
$270$	3.29204	−	4.02026i	0.200347	−	0.244665i
$271$	−16.9560			−1.03000			−0.515001	−	0.857189i	$-0.672209\pi$
$271$	−16.9560			−1.03000			−0.515001	+	0.857189i	$0.672209\pi$
$272$	−2.67922	+	2.67922i	−0.162452	+	0.162452i
$273$	−5.08883	+	3.16699i	−0.307990	+	0.191675i
$274$	15.0812	−	15.0812i	0.911089	−	0.911089i
$275$		−	3.24582i		−	0.195731i
$276$	8.19049	−	5.09728i	0.493009	−	0.306820i
$277$	13.7206	−	13.7206i	0.824392	−	0.824392i	−0.162342	−	0.986735i	$-0.551905\pi$
$277$	13.7206	−	13.7206i	0.824392	−	0.824392i	0.986735	+	0.162342i	$0.0519048\pi$
$278$	10.3366	−	10.3366i	0.619951	−	0.619951i
$279$	−20.8926	+	7.10896i	−1.25081	+	0.425602i
$280$			0.873718i			0.0522146i
$281$	16.4710	−	16.4710i	0.982575	−	0.982575i	−0.0172753	−	0.999851i	$-0.505499\pi$
$281$	16.4710	−	16.4710i	0.982575	−	0.982575i	0.999851	+	0.0172753i	$0.00549917\pi$
$282$	−2.80907	−	4.51371i	−0.167278	−	0.268788i
$283$	−0.457464	+	0.457464i	−0.0271934	+	0.0271934i	−0.720573	−	0.693379i	$-0.756121\pi$
$283$	−0.457464	+	0.457464i	−0.0271934	+	0.0271934i	0.693379	+	0.720573i	$0.256121\pi$
$284$	−0.580983			−0.0344750
$285$	−1.24694	+	5.35658i	−0.0738621	+	0.317296i
$286$			12.8557i			0.760176i
$287$	−10.5824			−0.624660
$288$	0.966374	+	2.84009i	0.0569441	+	0.167354i
$289$			2.64352i			0.155501i
$290$	−0.0117303	−	0.0117303i	−0.000688826	−	0.000688826i
$291$	14.8767	−	9.25842i	0.872090	−	0.542738i
$292$	11.0501			0.646658
$293$		−	6.48865i		−	0.379071i	−0.981874	−	0.189536i	$-0.939302\pi$
$293$		−	6.48865i		−	0.379071i	0.981874	−	0.189536i	$-0.0606983\pi$
$294$	−9.17113	+	5.70758i	−0.534871	+	0.332873i
$295$		−	11.2575i		−	0.655439i
$296$	−2.58734	−	5.50506i	−0.150386	−	0.319975i
$297$	−10.6854	+	13.0490i	−0.620029	+	0.757182i
$298$	−3.02618	+	3.02618i	−0.175302	+	0.175302i
$299$	22.0601			1.27577
$300$	0.392697	−	1.68695i	0.0226724	−	0.0973959i
$301$	−7.04588	−	7.04588i	−0.406118	−	0.406118i
$302$	−11.5029	+	11.5029i	−0.661917	+	0.661917i
$303$	−3.87590	+	16.6501i	−0.222664	+	0.956520i
$304$	−2.24528	−	2.24528i	−0.128776	−	0.128776i
$305$		−	9.39935i		−	0.538205i
$306$	−10.1984	−	5.02011i	−0.583002	−	0.286981i
$307$			4.82152i			0.275178i	0.990489	+	0.137589i	$0.0439354\pi$
$307$			4.82152i			0.275178i	−0.990489	+	0.137589i	$0.956065\pi$
$308$		−	2.83593i		−	0.161592i
$309$	6.21776	+	9.99091i	0.353716	+	0.568363i
$310$	−5.20171	+	5.20171i	−0.295437	+	0.295437i
$311$	−6.45365	−	6.45365i	−0.365953	−	0.365953i	0.500046	−	0.865999i	$-0.333316\pi$
$311$	−6.45365	−	6.45365i	−0.365953	−	0.365953i	−0.865999	+	0.500046i	$0.833316\pi$
$312$	−1.55536	+	6.68150i	−0.0880548	+	0.378265i
$313$	−23.6394	−	23.6394i	−1.33618	−	1.33618i	−0.899729	−	0.436449i	$-0.856236\pi$
$313$	−23.6394	−	23.6394i	−1.33618	−	1.33618i	−0.436449	−	0.899729i	$-0.643764\pi$
$314$	−13.0527	−	13.0527i	−0.736607	−	0.736607i
$315$	−2.48144	+	0.844338i	−0.139813	+	0.0475731i
$316$	−0.763562	+	0.763562i	−0.0429537	+	0.0429537i
$317$	−2.73418			−0.153567			−0.0767834	−	0.997048i	$-0.524465\pi$
$317$	−2.73418			−0.153567			−0.0767834	+	0.997048i	$0.524465\pi$
$318$	−8.39867	−	13.4953i	−0.470974	−	0.756777i
$319$	0.0380744	+	0.0380744i	0.00213176	+	0.00213176i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	24.8332	+	5.78083i	1.38606	+	0.322654i
$322$	−4.86639			−0.271193
$323$	12.0312			0.669436
$324$	−7.13224	+	5.48918i	−0.396236	+	0.304955i
$325$	2.80064	−	2.80064i	0.155352	−	0.155352i
$326$	−10.8301			−0.599825
$327$	26.7396	−	16.6412i	1.47870	−	0.920259i
$328$	−8.56443	+	8.56443i	−0.472891	+	0.472891i
$329$			2.68183i			0.147854i
$330$	−1.27463	+	5.47553i	−0.0701659	+	0.301418i
$331$	−15.9221	−	15.9221i	−0.875158	−	0.875158i	0.117871	−	0.993029i	$-0.462393\pi$
$331$	−15.9221	−	15.9221i	−0.875158	−	0.875158i	−0.993029	+	0.117871i	$0.962393\pi$
$332$	6.26833			0.344019
$333$	13.1345	−	12.6682i	0.719769	−	0.694214i
$334$	−17.6482			−0.965665
$335$	5.47350	+	5.47350i	0.299049	+	0.299049i
$336$	0.343107	−	1.47392i	0.0187180	−	0.0804087i
$337$			6.36440i			0.346691i	0.984861	+	0.173346i	$0.0554577\pi$
$337$			6.36440i			0.346691i	−0.984861	+	0.173346i	$0.944542\pi$
$338$	−1.90012	+	1.90012i	−0.103353	+	0.103353i
$339$	−6.44732	+	4.01244i	−0.350170	+	0.217926i
$340$	−3.78900			−0.205487
$341$	16.8838	−	16.8838i	0.914310	−	0.914310i
$342$	4.20703	−	8.54659i	0.227490	−	0.462147i
$343$	11.5651			0.624455
$344$	−11.4046			−0.614894
$345$	9.39587	+	2.18723i	0.505857	+	0.117756i
$346$	6.48740	+	6.48740i	0.348765	+	0.348765i
$347$	−11.1501	−	11.1501i	−0.598571	−	0.598571i	0.341361	−	0.939932i	$-0.389112\pi$
$347$	−11.1501	−	11.1501i	−0.598571	−	0.598571i	−0.939932	+	0.341361i	$0.889112\pi$
$348$	0.0151819	+	0.0243948i	0.000813836	+	0.00130770i
$349$	−5.32513			−0.285048			−0.142524	−	0.989791i	$-0.545522\pi$
$349$	−5.32513			−0.285048			−0.142524	+	0.989791i	$0.545522\pi$
$350$	−0.617812	+	0.617812i	−0.0330234	+	0.0330234i
$351$	−20.4791	+	2.03946i	−1.09309	+	0.108859i
$352$	−2.29514	−	2.29514i	−0.122332	−	0.122332i
$353$	1.76426	+	1.76426i	0.0939022	+	0.0939022i	0.752497	−	0.658595i	$-0.228849\pi$
$353$	1.76426	+	1.76426i	0.0939022	+	0.0939022i	−0.658595	+	0.752497i	$0.728849\pi$
$354$	−4.42080	+	18.9909i	−0.234963	+	1.00935i
$355$	−0.410817	−	0.410817i	−0.0218039	−	0.0218039i
$356$	6.49421	−	6.49421i	0.344192	−	0.344192i
$357$	3.02969	+	4.86821i	0.160348	+	0.257653i
$358$		−	14.1577i		−	0.748257i
$359$			31.2814i			1.65097i	0.564426	+	0.825483i	$0.309097\pi$
$359$			31.2814i			1.65097i	−0.564426	+	0.825483i	$0.690903\pi$
$360$	−1.32492	+	2.69158i	−0.0698293	+	0.141859i
$361$		−	8.91741i		−	0.469337i
$362$	−16.0339	−	16.0339i	−0.842724	−	0.842724i
$363$	−0.182459	+	0.783806i	−0.00957661	+	0.0411391i
$364$	2.44697	−	2.44697i	0.128256	−	0.128256i
$365$	7.81360	+	7.81360i	0.408983	+	0.408983i
$366$	−3.69110	+	15.8562i	−0.192937	+	0.828817i
$367$	9.81757			0.512473			0.256237	−	0.966614i	$-0.417517\pi$
$367$	9.81757			0.512473			0.256237	+	0.966614i	$0.417517\pi$
$368$	−3.93841	+	3.93841i	−0.205304	+	0.205304i
$369$	−32.6002	−	16.0473i	−1.69710	−	0.835390i
$370$	2.06314	−	5.72219i	0.107258	−	0.297482i
$371$			8.01823i			0.416286i
$372$	10.8177	−	6.73230i	0.560871	−	0.349054i
$373$			22.1399i			1.14636i	0.819429	+	0.573181i	$0.194291\pi$
$373$			22.1399i			1.14636i	−0.819429	+	0.573181i	$0.805709\pi$
$374$	12.2984			0.635936
$375$	1.47053	−	0.915172i	0.0759379	−	0.0472593i
$376$	2.17042	+	2.17042i	0.111931	+	0.111931i
$377$			0.0657046i			0.00338396i
$378$	4.51762	−	0.449899i	0.232362	−	0.0231403i
$379$	−5.96113			−0.306203			−0.153101	−	0.988211i	$-0.548926\pi$
$379$	−5.96113			−0.306203			−0.153101	+	0.988211i	$0.548926\pi$
$380$		−	3.17531i		−	0.162890i
$381$	−0.372646	+	1.60081i	−0.0190912	+	0.0820121i
$382$	9.32939			0.477333
$383$	9.16947	−	9.16947i	0.468538	−	0.468538i	−0.432903	−	0.901441i	$-0.642511\pi$
$383$	9.16947	−	9.16947i	0.468538	−	0.468538i	0.901441	+	0.432903i	$0.142511\pi$
$384$	−0.915172	−	1.47053i	−0.0467022	−	0.0750427i
$385$	2.00531	−	2.00531i	0.102200	−	0.102200i
$386$		−	1.02055i		−	0.0519448i
$387$	−11.0211	−	32.3900i	−0.560233	−	1.64648i
$388$	−7.15350	+	7.15350i	−0.363164	+	0.363164i
$389$	−6.40269	+	6.40269i	−0.324629	+	0.324629i	−0.850540	−	0.525911i	$-0.823725\pi$
$389$	−6.40269	+	6.40269i	−0.324629	+	0.324629i	0.525911	+	0.850540i	$0.323725\pi$
$390$	−5.82434	+	3.62473i	−0.294927	+	0.183545i
$391$		−	21.1038i		−	1.06726i
$392$	4.40995	−	4.40995i	0.222736	−	0.222736i
$393$	24.4059	−	15.1888i	1.23112	−	0.766175i
$394$	10.4709	−	10.4709i	0.527518	−	0.527518i
$395$	−1.07984			−0.0543327
$396$	4.30045	−	8.73639i	0.216106	−	0.439020i
$397$			2.29166i			0.115015i	0.998345	+	0.0575075i	$0.0183153\pi$
$397$			2.29166i			0.115015i	−0.998345	+	0.0575075i	$0.981685\pi$
$398$	−21.6821			−1.08683
$399$	−4.07973	+	2.53899i	−0.204242	+	0.127108i
$400$			1.00000i			0.0500000i
$401$	−17.9575	−	17.9575i	−0.896756	−	0.896756i	0.0983914	−	0.995148i	$-0.468630\pi$
$401$	−17.9575	−	17.9575i	−0.896756	−	0.896756i	−0.995148	+	0.0983914i	$0.968630\pi$
$402$	−7.08407	−	11.3829i	−0.353321	−	0.567729i
$403$	29.1362			1.45138
$404$		−	9.86993i		−	0.491048i
$405$	−8.92469	−	1.16182i	−0.443472	−	0.0577313i
$406$		−	0.0144942i		−	0.000719336i
$407$	−6.69660	+	18.5732i	−0.331938	+	0.920640i
$408$	6.39183	+	1.48793i	0.316443	+	0.0736634i
$409$	2.75786	−	2.75786i	0.136367	−	0.136367i	−0.635628	−	0.771995i	$-0.719259\pi$
$409$	2.75786	−	2.75786i	0.136367	−	0.136367i	0.771995	+	0.635628i	$0.219259\pi$
$410$	−12.1119			−0.598166
$411$	−35.9793	−	8.37547i	−1.77473	−	0.413131i
$412$	−4.80415	−	4.80415i	−0.236683	−	0.236683i
$413$	6.95504	−	6.95504i	0.342235	−	0.342235i
$414$	−14.9914	−	7.37947i	−0.736788	−	0.362681i
$415$	4.43238	+	4.43238i	0.217577	+	0.217577i
$416$		−	3.96070i		−	0.194190i
$417$	−24.6602	−	5.74054i	−1.20761	−	0.281115i
$418$			10.3065i			0.504107i
$419$			9.86970i			0.482166i	0.970504	+	0.241083i	$0.0775027\pi$
$419$			9.86970i			0.482166i	−0.970504	+	0.241083i	$0.922497\pi$
$420$	1.28483	−	0.799603i	0.0626932	−	0.0390166i
$421$	−5.59923	+	5.59923i	−0.272890	+	0.272890i	−0.830262	−	0.557373i	$-0.811809\pi$
$421$	−5.59923	+	5.59923i	−0.272890	+	0.272890i	0.557373	+	0.830262i	$0.311809\pi$
$422$	−10.5186	−	10.5186i	−0.512039	−	0.512039i
$423$	−4.06676	+	8.26165i	−0.197733	+	0.401695i
$424$	6.48922	+	6.48922i	0.315144	+	0.315144i
$425$	−2.67922	−	2.67922i	−0.129961	−	0.129961i
$426$	0.531700	+	0.854354i	0.0257609	+	0.0413936i
$427$	5.80703	−	5.80703i	0.281022	−	0.281022i
$428$	−14.7208			−0.711558
$429$	18.9048	−	11.7652i	0.912731	−	0.568030i
$430$	−8.06425	−	8.06425i	−0.388893	−	0.388893i
$431$	−16.1018	−	16.1018i	−0.775598	−	0.775598i	0.203481	−	0.979079i	$-0.434774\pi$
$431$	−16.1018	−	16.1018i	−0.775598	−	0.775598i	−0.979079	+	0.203481i	$0.934774\pi$
$432$	3.29204	−	4.02026i	0.158388	−	0.193425i
$433$	32.3378			1.55405			0.777027	−	0.629468i	$-0.216727\pi$
$433$	32.3378			1.55405			0.777027	+	0.629468i	$0.216727\pi$
$434$	−6.42735			−0.308523
$435$	−0.00651450	+	0.0279850i	−0.000312347	+	0.00134178i
$436$	−12.8578	+	12.8578i	−0.615776	+	0.615776i
$437$	17.6857			0.846021
$438$	−10.1128	−	16.2495i	−0.483206	−	0.776432i
$439$	18.7980	−	18.7980i	0.897177	−	0.897177i	−0.0980082	−	0.995186i	$-0.531247\pi$
$439$	18.7980	−	18.7980i	0.897177	−	0.897177i	0.995186	+	0.0980082i	$0.0312472\pi$
$440$		−	3.24582i		−	0.154739i
$441$	16.7863	+	8.26301i	0.799349	+	0.393477i
$442$	10.6116	+	10.6116i	0.504743	+	0.504743i
$443$	−14.1166			−0.670698			−0.335349	−	0.942094i	$-0.608854\pi$
$443$	−14.1166			−0.670698			−0.335349	+	0.942094i	$0.608854\pi$
$444$	−5.72750	+	8.84284i	−0.271815	+	0.419662i
$445$	9.18420			0.435373
$446$	4.37205	+	4.37205i	0.207022	+	0.207022i
$447$	7.21957	+	1.68061i	0.341474	+	0.0794903i
$448$			0.873718i			0.0412793i
$449$	6.93149	−	6.93149i	0.327117	−	0.327117i	−0.524372	−	0.851489i	$-0.675700\pi$
$449$	6.93149	−	6.93149i	0.327117	−	0.327117i	0.851489	+	0.524372i	$0.175700\pi$
$450$	−2.84009	+	0.966374i	−0.133883	+	0.0455553i
$451$	39.3132			1.85119
$452$	3.10020	−	3.10020i	0.145821	−	0.145821i
$453$	27.4425	+	6.38822i	1.28936	+	0.300145i
$454$	23.9616			1.12457
$455$	3.46054			0.162233
$456$	−1.24694	+	5.35658i	−0.0583931	+	0.250845i
$457$	14.8024	+	14.8024i	0.692425	+	0.692425i	0.962765	−	0.270340i	$-0.0871361\pi$
$457$	14.8024	+	14.8024i	0.692425	+	0.692425i	−0.270340	+	0.962765i	$0.587136\pi$
$458$	4.98767	+	4.98767i	0.233058	+	0.233058i
$459$	1.95105	+	19.5913i	0.0910671	+	0.914443i
$460$	−5.56975			−0.259691
$461$	−5.43289	+	5.43289i	−0.253035	+	0.253035i	−0.822214	−	0.569179i	$-0.807261\pi$
$461$	−5.43289	+	5.43289i	−0.253035	+	0.253035i	0.569179	+	0.822214i	$0.307261\pi$
$462$	−4.17033	+	2.59537i	−0.194021	+	0.120747i
$463$	−1.14209	−	1.14209i	−0.0530773	−	0.0530773i	0.680070	−	0.733147i	$-0.261949\pi$
$463$	−1.14209	−	1.14209i	−0.0530773	−	0.0530773i	−0.733147	+	0.680070i	$0.761949\pi$
$464$	−0.0117303	−	0.0117303i	−0.000544565	−	0.000544565i
$465$	12.4097	+	2.88881i	0.575487	+	0.133965i
$466$	3.15433	+	3.15433i	0.146122	+	0.146122i
$467$	8.44172	−	8.44172i	0.390636	−	0.390636i	−0.484278	−	0.874914i	$-0.660918\pi$
$467$	8.44172	−	8.44172i	0.390636	−	0.390636i	0.874914	+	0.484278i	$0.160918\pi$
$468$	11.2488	−	3.82752i	0.519974	−	0.176927i
$469$			6.76319i			0.312295i
$470$			3.06944i			0.141583i
$471$	−7.24893	+	31.1399i	−0.334013	+	1.43485i
$472$		−	11.2575i		−	0.518170i
$473$	26.1751	+	26.1751i	1.20353	+	1.20353i
$474$	1.82163	+	0.424050i	0.0836704	+	0.0194773i
$475$	2.24528	−	2.24528i	0.103021	−	0.103021i
$476$	−2.34089	−	2.34089i	−0.107294	−	0.107294i
$477$	−12.1590	+	24.7010i	−0.556721	+	1.13098i
$478$	−24.1467			−1.10444
$479$	−9.71035	+	9.71035i	−0.443677	+	0.443677i	−0.893246	−	0.449569i	$-0.851578\pi$
$479$	−9.71035	+	9.71035i	−0.443677	+	0.443677i	0.449569	+	0.893246i	$0.351578\pi$
$480$	0.392697	−	1.68695i	0.0179241	−	0.0769982i
$481$	−21.8039	+	10.2477i	−0.994173	+	0.467254i
$482$		−	5.37258i		−	0.244715i
$483$	4.45359	+	7.15618i	0.202645	+	0.325617i
$484$		−	0.464630i		−	0.0211195i
$485$	−10.1166			−0.459370
$486$	14.5992	+	5.46463i	0.662235	+	0.247881i
$487$	−3.87550	−	3.87550i	−0.175616	−	0.175616i	0.613826	−	0.789442i	$-0.289630\pi$
$487$	−3.87550	−	3.87550i	−0.175616	−	0.175616i	−0.789442	+	0.613826i	$0.789630\pi$
$488$		−	9.39935i		−	0.425489i
$489$	9.91143	+	15.9260i	0.448210	+	0.720199i
$490$	6.23662			0.281742
$491$			37.5934i			1.69657i	0.529541	+	0.848284i	$0.322364\pi$
$491$			37.5934i			1.69657i	−0.529541	+	0.848284i	$0.677636\pi$
$492$	20.4322	+	4.75632i	0.921154	+	0.214432i
$493$	0.0628561			0.00283090
$494$	−8.89290	+	8.89290i	−0.400111	+	0.400111i
$495$	9.21844	−	3.13668i	0.414338	−	0.140983i
$496$	−5.20171	+	5.20171i	−0.233563	+	0.233563i
$497$		−	0.507616i		−	0.0227697i
$498$	−5.73660	−	9.21777i	−0.257063	−	0.413058i
$499$	−13.8728	+	13.8728i	−0.621031	+	0.621031i	−0.945795	−	0.324764i	$-0.894715\pi$
$499$	−13.8728	+	13.8728i	−0.621031	+	0.621031i	0.324764	+	0.945795i	$0.394715\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	16.1511	+	25.9522i	0.721579	+	1.15946i
$502$		−	3.67514i		−	0.164029i
$503$	11.0121	−	11.0121i	0.491005	−	0.491005i	−0.417618	−	0.908623i	$-0.637135\pi$
$503$	11.0121	−	11.0121i	0.491005	−	0.491005i	0.908623	+	0.417618i	$0.137135\pi$
$504$	−2.48144	+	0.844338i	−0.110532	+	0.0376098i
$505$	6.97910	−	6.97910i	0.310566	−	0.310566i
$506$	18.0784			0.803684
$507$	4.53313	+	1.05525i	0.201323	+	0.0468652i
$508$		−	0.948940i		−	0.0421024i
$509$	8.43066			0.373683			0.186841	−	0.982390i	$-0.440175\pi$
$509$	8.43066			0.373683			0.186841	+	0.982390i	$0.440175\pi$
$510$	3.46758	+	5.57183i	0.153547	+	0.246725i
$511$			9.65467i			0.427098i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−16.4182	+	1.63505i	−0.724880	+	0.0721890i
$514$	18.5313			0.817381
$515$		−	6.79409i		−	0.299383i
$516$	10.4372	+	16.7708i	0.459470	+	0.738292i
$517$		−	9.96287i		−	0.438167i
$518$	4.80987	−	2.26060i	0.211334	−	0.0993251i
$519$	3.60283	−	15.4770i	0.158147	−	0.679365i
$520$	2.80064	−	2.80064i	0.122816	−	0.122816i
$521$	−10.1891			−0.446392			−0.223196	−	0.974774i	$-0.571649\pi$
$521$	−10.1891			−0.446392			−0.223196	+	0.974774i	$0.571649\pi$
$522$	0.0219792	−	0.0446509i	0.000962005	−	0.00195432i
$523$	21.5024	+	21.5024i	0.940233	+	0.940233i	0.998312	−	0.0580790i	$-0.0184975\pi$
$523$	21.5024	+	21.5024i	0.940233	+	0.940233i	−0.0580790	+	0.998312i	$0.518498\pi$
$524$	−11.7356	+	11.7356i	−0.512673	+	0.512673i
$525$	1.47392	+	0.343107i	0.0643269	+	0.0149744i
$526$	2.68672	+	2.68672i	0.117147	+	0.117147i
$527$		−	27.8731i		−	1.21417i
$528$	−1.27463	+	5.47553i	−0.0554710	+	0.238292i
$529$		−	8.02212i		−	0.348788i
$530$			9.17714i			0.398630i
$531$	31.9724	−	10.8790i	1.38748	−	0.472108i
$532$	1.96174	−	1.96174i	0.0850524	−	0.0850524i
$533$	33.9212	+	33.9212i	1.46929	+	1.46929i
$534$	−15.4933	−	3.60661i	−0.670459	−	0.156073i
$535$	−10.4092	−	10.4092i	−0.450029	−	0.450029i
$536$	5.47350	+	5.47350i	0.236419	+	0.236419i
$537$	−20.8193	+	12.9567i	−0.898420	+	0.559124i
$538$	−8.86564	+	8.86564i	−0.382225	+	0.382225i
$539$	−20.2430			−0.871926
$540$	5.17058	−	0.514925i	0.222506	−	0.0221588i
$541$	−14.4179	−	14.4179i	−0.619875	−	0.619875i	0.325625	−	0.945499i	$-0.394425\pi$
$541$	−14.4179	−	14.4179i	−0.619875	−	0.619875i	−0.945499	+	0.325625i	$0.894425\pi$
$542$	−11.9897	−	11.9897i	−0.515001	−	0.515001i
$543$	−8.90456	+	38.2522i	−0.382131	+	1.64156i
$544$	−3.78900			−0.162452
$545$	−18.1836			−0.778902
$546$	−5.83774	−	1.35894i	−0.249832	−	0.0581574i
$547$	−16.2982	+	16.2982i	−0.696862	+	0.696862i	−0.963732	−	0.266870i	$-0.914010\pi$
$547$	−16.2982	+	16.2982i	−0.696862	+	0.696862i	0.266870	+	0.963732i	$0.414010\pi$
$548$	21.3281			0.911089
$549$	26.6950	−	9.08329i	1.13932	−	0.387665i
$550$	2.29514	−	2.29514i	0.0978653	−	0.0978653i
$551$			0.0526756i			0.00224406i
$552$	9.39587	+	2.18723i	0.399915	+	0.0930945i
$553$	−0.667138	−	0.667138i	−0.0283696	−	0.0283696i
$554$	19.4039			0.824392
$555$	−10.3028	+	2.20288i	−0.437329	+	0.0935069i
$556$	14.6182			0.619951
$557$	13.8613	+	13.8613i	0.587322	+	0.587322i	0.936905	−	0.349583i	$-0.113677\pi$
$557$	13.8613	+	13.8613i	0.587322	+	0.587322i	−0.349583	+	0.936905i	$0.613677\pi$
$558$	−19.8001	−	9.74653i	−0.838206	−	0.412603i
$559$			45.1702i			1.91049i
$560$	−0.617812	+	0.617812i	−0.0261073	+	0.0261073i
$561$	−11.2552	−	18.0852i	−0.475193	−	0.763557i
$562$	23.2935			0.982575
$563$	−9.05310	+	9.05310i	−0.381543	+	0.381543i	−0.871658	−	0.490115i	$-0.836955\pi$
$563$	−9.05310	+	9.05310i	−0.381543	+	0.381543i	0.490115	+	0.871658i	$0.336955\pi$
$564$	1.20536	−	5.17799i	0.0507549	−	0.218033i
$565$	4.38435			0.184451
$566$	−0.646951			−0.0271934
$567$	−4.79600	−	6.23157i	−0.201413	−	0.261701i
$568$	−0.410817	−	0.410817i	−0.0172375	−	0.0172375i
$569$	−22.3048	−	22.3048i	−0.935066	−	0.935066i	0.0629509	−	0.998017i	$-0.479949\pi$
$569$	−22.3048	−	22.3048i	−0.935066	−	0.935066i	−0.998017	+	0.0629509i	$0.979949\pi$
$570$	−4.66939	+	2.90596i	−0.195579	+	0.121717i
$571$	−15.8222			−0.662138			−0.331069	−	0.943607i	$-0.607409\pi$
$571$	−15.8222			−0.662138			−0.331069	+	0.943607i	$0.607409\pi$
$572$	−9.09039	+	9.09039i	−0.380088	+	0.380088i
$573$	−8.53800	−	13.7192i	−0.356680	−	0.573126i
$574$	−7.48290	−	7.48290i	−0.312330	−	0.312330i
$575$	−3.93841	−	3.93841i	−0.164243	−	0.164243i
$576$	−1.32492	+	2.69158i	−0.0552049	+	0.112149i
$577$	−16.3027	−	16.3027i	−0.678689	−	0.678689i	0.281014	−	0.959704i	$-0.409329\pi$
$577$	−16.3027	−	16.3027i	−0.678689	−	0.678689i	−0.959704	+	0.281014i	$0.909329\pi$
$578$	−1.86925	+	1.86925i	−0.0777505	+	0.0777505i
$579$	−1.50076	+	0.933983i	−0.0623693	+	0.0388150i
$580$		−	0.0165891i		−	0.000688826i
$581$			5.47675i			0.227214i
$582$	17.0661	+	3.97275i	0.707414	+	0.164676i
$583$		−	29.7874i		−	1.23367i
$584$	7.81360	+	7.81360i	0.323329	+	0.323329i
$585$	10.6605	+	5.24761i	0.440759	+	0.216962i
$586$	4.58817	−	4.58817i	0.189536	−	0.189536i
$587$	−12.6200	−	12.6200i	−0.520882	−	0.520882i	0.396956	−	0.917838i	$-0.370067\pi$
$587$	−12.6200	−	12.6200i	−0.520882	−	0.520882i	−0.917838	+	0.396956i	$0.870067\pi$
$588$	−10.5208	−	2.44910i	−0.433872	−	0.100999i
$589$	23.3586			0.962474
$590$	7.96028	−	7.96028i	0.327719	−	0.327719i
$591$	−24.9805	−	5.81512i	−1.02756	−	0.239202i
$592$	2.06314	−	5.72219i	0.0847946	−	0.235180i
$593$			21.6189i			0.887782i	0.896081	+	0.443891i	$0.146402\pi$
$593$			21.6189i			0.887782i	−0.896081	+	0.443891i	$0.853598\pi$
$594$	−16.7828	+	1.67136i	−0.688606	+	0.0685765i
$595$		−	3.31051i		−	0.135718i
$596$	−4.27966			−0.175302
$597$	19.8429	+	31.8842i	0.812114	+	1.30493i
$598$	15.5989	+	15.5989i	0.637885	+	0.637885i
$599$		−	0.728152i		−	0.0297515i	−0.999889	−	0.0148757i	$-0.995265\pi$
$599$		−	0.728152i		−	0.0297515i	0.999889	−	0.0148757i	$-0.00473527\pi$
$600$	1.47053	−	0.915172i	0.0600341	−	0.0373618i
$601$	39.4004			1.60718			0.803588	−	0.595186i	$-0.202921\pi$
$601$	39.4004			1.60718			0.803588	+	0.595186i	$0.202921\pi$
$602$		−	9.96438i		−	0.406118i
$603$	−10.2558	+	20.8347i	−0.417648	+	0.848454i
$604$	−16.2675			−0.661917
$605$	0.328543	−	0.328543i	0.0133572	−	0.0133572i
$606$	−14.5140	+	9.03269i	−0.589592	+	0.366928i
$607$	18.6181	−	18.6181i	0.755684	−	0.755684i	−0.219850	−	0.975534i	$-0.570557\pi$
$607$	18.6181	−	18.6181i	0.755684	−	0.755684i	0.975534	+	0.219850i	$0.0705567\pi$
$608$		−	3.17531i		−	0.128776i
$609$	−0.0213142	+	0.0132647i	−0.000863694	+	0.000537513i
$610$	6.64635	−	6.64635i	0.269103	−	0.269103i
$611$	8.59641	−	8.59641i	0.347774	−	0.347774i
$612$	−3.66159	−	10.7611i	−0.148011	−	0.434991i
$613$			34.7946i			1.40534i	0.711516	+	0.702670i	$0.248009\pi$
$613$			34.7946i			1.40534i	−0.711516	+	0.702670i	$0.751991\pi$
$614$	−3.40933	+	3.40933i	−0.137589	+	0.137589i
$615$	11.0845	+	17.8110i	0.446970	+	0.718207i
$616$	2.00531	−	2.00531i	0.0807962	−	0.0807962i
$617$	−9.78568			−0.393957			−0.196978	−	0.980408i	$-0.563113\pi$
$617$	−9.78568			−0.393957			−0.196978	+	0.980408i	$0.563113\pi$
$618$	−2.66802	+	11.4613i	−0.107324	+	0.461040i
$619$			36.0295i			1.44815i	0.689723	+	0.724074i	$0.257732\pi$
$619$			36.0295i			1.44815i	−0.689723	+	0.724074i	$0.742268\pi$
$620$	−7.35632			−0.295437
$621$	2.86800	+	28.7988i	0.115089	+	1.15566i
$622$		−	9.12683i		−	0.365953i
$623$	5.67411	+	5.67411i	0.227328	+	0.227328i
$624$	−5.82434	+	3.62473i	−0.233160	+	0.145105i
$625$	−1.00000			−0.0400000
$626$		−	33.4312i		−	1.33618i
$627$	15.1560	−	9.43222i	0.605273	−	0.376687i
$628$		−	18.4593i		−	0.736607i
$629$	9.80340	+	20.8586i	0.390887	+	0.831689i
$630$	−2.35168	−	1.15761i	−0.0936932	−	0.0461201i
$631$	−0.797835	+	0.797835i	−0.0317613	+	0.0317613i	−0.722809	−	0.691048i	$-0.757149\pi$
$631$	−0.797835	+	0.797835i	−0.0317613	+	0.0317613i	0.691048	+	0.722809i	$0.257149\pi$
$632$	−1.07984			−0.0429537
$633$	−5.84160	+	25.0943i	−0.232183	+	0.997409i
$634$	−1.93336	−	1.93336i	−0.0767834	−	0.0767834i
$635$	0.671002	−	0.671002i	0.0266279	−	0.0266279i
$636$	3.60384	−	15.4813i	0.142902	−	0.613875i
$637$	−17.4665	−	17.4665i	−0.692049	−	0.692049i
$638$			0.0538454i			0.00213176i
$639$	0.769756	−	1.56376i	0.0304511	−	0.0618615i
$640$			1.00000i			0.0395285i
$641$		−	0.310559i		−	0.0122663i	−0.999981	−	0.00613317i	$-0.998048\pi$
$641$		−	0.310559i		−	0.0122663i	0.999981	−	0.00613317i	$-0.00195226\pi$
$642$	13.4721	+	21.6474i	0.531701	+	0.854355i
$643$	24.4682	−	24.4682i	0.964931	−	0.964931i	−0.0344744	−	0.999406i	$-0.510976\pi$
$643$	24.4682	−	24.4682i	0.964931	−	0.964931i	0.999406	+	0.0344744i	$0.0109757\pi$
$644$	−3.44106	−	3.44106i	−0.135597	−	0.135597i
$645$	−4.47855	+	19.2389i	−0.176343	+	0.757531i
$646$	8.50737	+	8.50737i	0.334718	+	0.334718i
$647$	−4.14891	−	4.14891i	−0.163111	−	0.163111i	0.620833	−	0.783943i	$-0.286795\pi$
$647$	−4.14891	−	4.14891i	−0.163111	−	0.163111i	−0.783943	+	0.620833i	$0.786795\pi$
$648$	−8.92469	−	1.16182i	−0.350595	−	0.0456406i
$649$	−25.8377	+	25.8377i	−1.01422	+	1.01422i
$650$	3.96070			0.155352
$651$	5.88213	+	9.45161i	0.230539	+	0.370438i
$652$	−7.65805	−	7.65805i	−0.299912	−	0.299912i
$653$	6.38197	+	6.38197i	0.249746	+	0.249746i	0.820866	−	0.571120i	$-0.193491\pi$
$653$	6.38197	+	6.38197i	0.249746	+	0.249746i	−0.571120	+	0.820866i	$0.693491\pi$
$654$	30.6748	+	7.14067i	1.19948	+	0.279222i
$655$	−16.5967			−0.648486
$656$	−12.1119			−0.472891
$657$	−14.6405	+	29.7422i	−0.571180	+	1.16035i
$658$	−1.89634	+	1.89634i	−0.0739270	+	0.0739270i
$659$	40.6095			1.58192			0.790960	−	0.611867i	$-0.209581\pi$
$659$	40.6095			1.58192			0.790960	+	0.611867i	$0.209581\pi$
$660$	−4.77308	+	2.97049i	−0.185792	+	0.115626i
$661$	18.2484	−	18.2484i	0.709782	−	0.709782i	−0.256707	−	0.966489i	$-0.582637\pi$
$661$	18.2484	−	18.2484i	0.709782	−	0.709782i	0.966489	+	0.256707i	$0.0826375\pi$
$662$		−	22.5172i		−	0.875158i
$663$	5.89324	−	25.3162i	0.228875	−	0.983198i
$664$	4.43238	+	4.43238i	0.172010	+	0.172010i
$665$	2.77433			0.107584
$666$	18.2453	+	0.329742i	0.706991	+	0.0127772i
$667$	0.0923973			0.00357764
$668$	−12.4791	−	12.4791i	−0.482833	−	0.482833i
$669$	2.42805	−	10.4304i	0.0938738	−	0.403263i
$670$			7.74070i			0.299049i
$671$	−21.5729	+	21.5729i	−0.832811	+	0.832811i
$672$	1.28483	−	0.799603i	0.0495633	−	0.0308453i
$673$	43.2033			1.66536			0.832682	−	0.553752i	$-0.186804\pi$
$673$	43.2033			1.66536			0.832682	+	0.553752i	$0.186804\pi$
$674$	−4.50031	+	4.50031i	−0.173346	+	0.173346i
$675$	4.02026	+	3.29204i	0.154740	+	0.126711i
$676$	−2.68718			−0.103353
$677$	−20.8361			−0.800797			−0.400399	−	0.916341i	$-0.631128\pi$
$677$	−20.8361			−0.800797			−0.400399	+	0.916341i	$0.631128\pi$
$678$	−7.39616	−	1.72172i	−0.284048	−	0.0661223i
$679$	−6.25014	−	6.25014i	−0.239859	−	0.239859i
$680$	−2.67922	−	2.67922i	−0.102744	−	0.102744i
$681$	−21.9290	−	35.2362i	−0.840320	−	1.35025i
$682$	23.8773			0.914310
$683$	−28.5744	+	28.5744i	−1.09337	+	1.09337i	−0.0982022	+	0.995166i	$0.531309\pi$
$683$	−28.5744	+	28.5744i	−1.09337	+	1.09337i	−0.995166	+	0.0982022i	$0.968691\pi$
$684$	9.01817	−	3.06854i	0.344818	−	0.117328i
$685$	15.0812	+	15.0812i	0.576223	+	0.576223i
$686$	8.17774	+	8.17774i	0.312228	+	0.312228i
$687$	2.76994	−	11.8991i	0.105680	−	0.453979i
$688$	−8.06425	−	8.06425i	−0.307447	−	0.307447i
$689$	25.7019	−	25.7019i	0.979164	−	0.979164i
$690$	5.09728	+	8.19049i	0.194050	+	0.311807i
$691$		−	34.9094i		−	1.32802i	−0.747725	−	0.664008i	$-0.768854\pi$
$691$		−	34.9094i		−	1.32802i	0.747725	−	0.664008i	$-0.231146\pi$
$692$			9.17456i			0.348765i
$693$	7.63314	+	3.75738i	0.289959	+	0.142731i
$694$		−	15.7687i		−	0.598571i
$695$	10.3366	+	10.3366i	0.392091	+	0.392091i
$696$	−0.00651450	+	0.0279850i	−0.000246932	+	0.00106077i
$697$	32.4506	−	32.4506i	1.22915	−	1.22915i
$698$	−3.76544	−	3.76544i	−0.142524	−	0.142524i
$699$	1.75178	−	7.52530i	0.0662585	−	0.284633i
$700$	−0.873718			−0.0330234
$701$	−5.73772	+	5.73772i	−0.216711	+	0.216711i	−0.807111	−	0.590400i	$-0.798970\pi$
$701$	−5.73772	+	5.73772i	−0.216711	+	0.216711i	0.590400	+	0.807111i	$0.298970\pi$
$702$	−15.9230	−	13.0388i	−0.600977	−	0.492118i
$703$	−17.4803	+	8.21559i	−0.659281	+	0.309857i
$704$		−	3.24582i		−	0.122332i
$705$	4.51371	−	2.80907i	0.169996	−	0.105796i
$706$			2.49504i			0.0939022i
$707$	8.62354			0.324322
$708$	−16.5545	+	10.3026i	−0.622158	+	0.387195i
$709$	−18.6081	−	18.6081i	−0.698842	−	0.698842i	0.265319	−	0.964161i	$-0.414523\pi$
$709$	−18.6081	−	18.6081i	−0.698842	−	0.698842i	−0.964161	+	0.265319i	$0.914523\pi$
$710$		−	0.580983i		−	0.0218039i
$711$	−1.04353	−	3.06685i	−0.0391354	−	0.115016i
$712$	9.18420			0.344192
$713$		−	40.9729i		−	1.53445i
$714$	−1.30003	+	5.58466i	−0.0486524	+	0.209001i
$715$	−12.8557			−0.480778
$716$	10.0110	−	10.0110i	0.374129	−	0.374129i
$717$	22.0984	+	35.5084i	0.825279	+	1.32609i
$718$	−22.1193	+	22.1193i	−0.825483	+	0.825483i
$719$		−	18.6694i		−	0.696252i	−0.937448	−	0.348126i	$-0.886818\pi$
$719$		−	18.6694i		−	0.696252i	0.937448	−	0.348126i	$-0.113182\pi$
$720$	−2.84009	+	0.966374i	−0.105844	+	0.0360146i
$721$	4.19747	−	4.19747i	0.156322	−	0.156322i
$722$	6.30556	−	6.30556i	0.234669	−	0.234669i
$723$	−7.90055	+	4.91684i	−0.293825	+	0.182859i
$724$		−	22.6754i		−	0.842724i
$725$	0.0117303	−	0.0117303i	0.000435652	−	0.000435652i
$726$	−0.683252	+	0.425216i	−0.0253579	+	0.0157813i
$727$	20.9335	−	20.9335i	0.776381	−	0.776381i	−0.202833	−	0.979213i	$-0.565015\pi$
$727$	20.9335	−	20.9335i	0.776381	−	0.776381i	0.979213	+	0.202833i	$0.0650147\pi$
$728$	3.46054			0.128256
$729$	−5.32492	−	26.4697i	−0.197219	−	0.980359i
$730$			11.0501i			0.408983i
$731$	43.2119			1.59825
$732$	−13.8220	+	8.60203i	−0.510877	+	0.317940i
$733$		−	45.5805i		−	1.68355i	−0.539825	−	0.841777i	$-0.681510\pi$
$733$		−	45.5805i		−	1.68355i	0.539825	−	0.841777i	$-0.318490\pi$
$734$	6.94207	+	6.94207i	0.256237	+	0.256237i
$735$	−5.70758	−	9.17113i	−0.210527	−	0.338282i
$736$	−5.56975			−0.205304
$737$		−	25.1249i		−	0.925489i
$738$	−11.7047	−	34.3990i	−0.430854	−	1.26624i
$739$			30.7839i			1.13240i	0.824267	+	0.566202i	$0.191588\pi$
$739$			30.7839i			1.13240i	−0.824267	+	0.566202i	$0.808412\pi$
$740$	5.50506	−	2.58734i	0.202370	−	0.0951124i
$741$	21.2158	+	4.93874i	0.779383	+	0.181429i
$742$	−5.66975	+	5.66975i	−0.208143	+	0.208143i
$743$	−5.50584			−0.201990			−0.100995	−	0.994887i	$-0.532203\pi$
$743$	−5.50584			−0.201990			−0.100995	+	0.994887i	$0.532203\pi$
$744$	12.4097	+	2.88881i	0.454963	+	0.105909i
$745$	−3.02618	−	3.02618i	−0.110871	−	0.110871i
$746$	−15.6553	+	15.6553i	−0.573181	+	0.573181i
$747$	−8.30503	+	16.8717i	−0.303865	+	0.617303i
$748$	8.69629	+	8.69629i	0.317968	+	0.317968i
$749$		−	12.8618i		−	0.469962i
$750$	1.68695	+	0.392697i	0.0615986	+	0.0143393i
$751$			45.1238i			1.64659i	0.567613	+	0.823295i	$0.307867\pi$
$751$			45.1238i			1.64659i	−0.567613	+	0.823295i	$0.692133\pi$
$752$			3.06944i			0.111931i
$753$	−5.40440	+	3.36339i	−0.196947	+	0.122569i
$754$	−0.0464602	+	0.0464602i	−0.00169198	+	0.00169198i
$755$	−11.5029	−	11.5029i	−0.418633	−	0.418633i
$756$	3.51257	+	2.87632i	0.127751	+	0.104611i
$757$	14.1289	+	14.1289i	0.513524	+	0.513524i	0.915605	−	0.402080i	$-0.131713\pi$
$757$	14.1289	+	14.1289i	0.513524	+	0.513524i	−0.402080	+	0.915605i	$0.631713\pi$
$758$	−4.21515	−	4.21515i	−0.153101	−	0.153101i
$759$	−16.5449	−	26.5849i	−0.600541	−	0.964970i
$760$	2.24528	−	2.24528i	0.0814450	−	0.0814450i
$761$	−0.980959			−0.0355597			−0.0177799	−	0.999842i	$-0.505660\pi$
$761$	−0.980959			−0.0355597			−0.0177799	+	0.999842i	$0.505660\pi$
$762$	−1.39545	+	0.868444i	−0.0505517	+	0.0314604i
$763$	−11.2341	−	11.2341i	−0.406701	−	0.406701i
$764$	6.59688	+	6.59688i	0.238667	+	0.238667i
$765$	5.02011	−	10.1984i	0.181502	−	0.368723i
$766$	12.9676			0.468538
$767$	−44.5878			−1.60997
$768$	0.392697	−	1.68695i	0.0141702	−	0.0608724i
$769$	−5.20667	+	5.20667i	−0.187757	+	0.187757i	−0.794726	−	0.606968i	$-0.792385\pi$
$769$	−5.20667	+	5.20667i	−0.187757	+	0.187757i	0.606968	+	0.794726i	$0.292385\pi$
$770$	2.83593			0.102200
$771$	−16.9594	−	27.2509i	−0.610776	−	0.981416i
$772$	0.721641	−	0.721641i	0.0259724	−	0.0259724i
$773$		−	19.8914i		−	0.715444i	−0.933828	−	0.357722i	$-0.883554\pi$
$773$		−	19.8914i		−	0.715444i	0.933828	−	0.357722i	$-0.116446\pi$
$774$	15.1101	−	30.6963i	0.543123	−	1.10336i
$775$	−5.20171	−	5.20171i	−0.186851	−	0.186851i
$776$	−10.1166			−0.363164
$777$	−7.72614	−	5.00422i	−0.277174	−	0.179525i
$778$	−9.05477			−0.324629
$779$	27.1947	+	27.1947i	0.974352	+	0.974352i
$780$	−6.68150	−	1.55536i	−0.239236	−	0.0556907i
$781$			1.88577i			0.0674781i
$782$	14.9226	−	14.9226i	0.533631	−	0.533631i
$783$	−0.0857753	+	0.00854215i	−0.00306536	+	0.000305272i
$784$	6.23662			0.222736
$785$	13.0527	−	13.0527i	0.465871	−	0.465871i
$786$	27.9977	+	6.51747i	0.998646	+	0.232471i
$787$	−8.14992			−0.290513			−0.145257	−	0.989394i	$-0.546401\pi$
$787$	−8.14992			−0.290513			−0.145257	+	0.989394i	$0.546401\pi$
$788$	14.8081			0.527518
$789$	1.49209	−	6.40972i	0.0531199	−	0.228192i
$790$	−0.763562	−	0.763562i	−0.0271663	−	0.0271663i
$791$	2.70870	+	2.70870i	0.0963104	+	0.0963104i
$792$	9.21844	−	3.13668i	0.327563	−	0.111457i
$793$	−37.2281			−1.32201
$794$	−1.62045	+	1.62045i	−0.0575075	+	0.0575075i
$795$	13.4953	−	8.39867i	0.478628	−	0.297870i
$796$	−15.3316	−	15.3316i	−0.543413	−	0.543413i
$797$	10.4496	+	10.4496i	0.370146	+	0.370146i	0.867530	−	0.497385i	$-0.165706\pi$
$797$	10.4496	+	10.4496i	0.370146	+	0.370146i	−0.497385	+	0.867530i	$0.665706\pi$
$798$	−4.68014	−	1.08947i	−0.165675	−	0.0385668i
$799$	−8.22373	−	8.22373i	−0.290935	−	0.290935i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	8.87537	+	26.0840i	0.313596	+	0.921632i
$802$		−	25.3958i		−	0.896756i
$803$		−	35.8667i		−	1.26571i
$804$	3.03975	−	13.0581i	0.107204	−	0.460525i
$805$		−	4.86639i		−	0.171518i
$806$	20.6024	+	20.6024i	0.725689	+	0.725689i
$807$	21.1508	+	4.92360i	0.744543	+	0.173319i
$808$	6.97910	−	6.97910i	0.245524	−	0.245524i
$809$	13.8558	+	13.8558i	0.487143	+	0.487143i	0.907404	−	0.420260i	$-0.138061\pi$
$809$	13.8558	+	13.8558i	0.487143	+	0.487143i	−0.420260	+	0.907404i	$0.638061\pi$
$810$	−5.48918	−	7.13224i	−0.192870	−	0.250601i
$811$	−8.21906			−0.288610			−0.144305	−	0.989533i	$-0.546095\pi$
$811$	−8.21906			−0.288610			−0.144305	+	0.989533i	$0.546095\pi$
$812$	0.0102490	−	0.0102490i	0.000359668	−	0.000359668i
$813$	−6.65857	+	28.6038i	−0.233526	+	1.00318i
$814$	−17.8685	+	8.39804i	−0.626289	+	0.294351i
$815$		−	10.8301i		−	0.379362i
$816$	3.46758	+	5.57183i	0.121390	+	0.195053i
$817$			36.2131i			1.26693i
$818$	3.90020			0.136367
$819$	3.34417	+	9.82825i	0.116855	+	0.343427i
$820$	−8.56443	−	8.56443i	−0.299083	−	0.299083i
$821$			31.5158i			1.09991i	0.835194	+	0.549955i	$0.185355\pi$
$821$			31.5158i			1.09991i	−0.835194	+	0.549955i	$0.814645\pi$
$822$	−19.5188	−	31.3635i	−0.680798	−	1.09393i
$823$	2.89732			0.100994			0.0504971	−	0.998724i	$-0.483919\pi$
$823$	2.89732			0.100994			0.0504971	+	0.998724i	$0.483919\pi$
$824$		−	6.79409i		−	0.236683i
$825$	−5.47553	−	1.27463i	−0.190634	−	0.0443768i
$826$	9.83591			0.342235
$827$	−19.0188	+	19.0188i	−0.661348	+	0.661348i	−0.955698	−	0.294350i	$-0.904897\pi$
$827$	−19.0188	+	19.0188i	−0.661348	+	0.661348i	0.294350	+	0.955698i	$0.404897\pi$
$828$	−5.38246	−	15.8186i	−0.187053	−	0.549734i
$829$	38.2891	−	38.2891i	1.32984	−	1.32984i	0.424328	−	0.905509i	$-0.360510\pi$
$829$	38.2891	−	38.2891i	1.32984	−	1.32984i	0.905509	−	0.424328i	$-0.139490\pi$
$830$			6.26833i			0.217577i
$831$	−17.7579	−	28.5340i	−0.616015	−	0.989834i
$832$	2.80064	−	2.80064i	0.0970948	−	0.0970948i
$833$	−16.7093	+	16.7093i	−0.578943	+	0.578943i
$834$	−13.3782	−	21.4965i	−0.463249	−	0.744364i
$835$		−	17.6482i		−	0.610740i
$836$	−7.28779	+	7.28779i	−0.252054	+	0.252054i
$837$	3.78795	+	38.0364i	0.130931	+	1.31473i
$838$	−6.97893	+	6.97893i	−0.241083	+	0.241083i
$839$	−28.1427			−0.971595			−0.485797	−	0.874071i	$-0.661471\pi$
$839$	−28.1427			−0.971595			−0.485797	+	0.874071i	$0.661471\pi$
$840$	1.47392	+	0.343107i	0.0508549	+	0.0118383i
$841$		−	28.9997i		−	0.999991i
$842$	−7.91851			−0.272890
$843$	−21.3175	−	34.2537i	−0.734215	−	1.17976i
$844$		−	14.8756i		−	0.512039i
$845$	−1.90012	−	1.90012i	−0.0653662	−	0.0653662i
$846$	−8.71750	+	2.96623i	−0.299714	+	0.101981i
$847$	0.405955			0.0139488
$848$			9.17714i			0.315144i
$849$	0.592072	+	0.951362i	0.0203199	+	0.0326506i
$850$		−	3.78900i		−	0.129961i
$851$	14.4108	+	30.6618i	0.493996	+	1.05107i
$852$	−0.228151	+	0.980088i	−0.00781631	+	0.0335773i
$853$	15.2906	−	15.2906i	0.523541	−	0.523541i	−0.395098	−	0.918639i	$-0.629289\pi$
$853$	15.2906	−	15.2906i	0.523541	−	0.523541i	0.918639	+	0.395098i	$0.129289\pi$
$854$	8.21239			0.281022
$855$	8.54659	+	4.20703i	0.292287	+	0.143877i
$856$	−10.4092	−	10.4092i	−0.355779	−	0.355779i
$857$	11.5743	−	11.5743i	0.395369	−	0.395369i	−0.481227	−	0.876596i	$-0.659809\pi$
$857$	11.5743	−	11.5743i	0.395369	−	0.395369i	0.876596	+	0.481227i	$0.159809\pi$
$858$	21.6870	+	5.04842i	0.740381	+	0.172350i
$859$	9.96139	+	9.96139i	0.339878	+	0.339878i	0.856321	−	0.516443i	$-0.172744\pi$
$859$	9.96139	+	9.96139i	0.339878	+	0.339878i	−0.516443	+	0.856321i	$0.672744\pi$
$860$		−	11.4046i		−	0.388893i
$861$	−4.15568	+	17.8520i	−0.141625	+	0.608393i
$862$		−	22.7714i		−	0.775598i
$863$			35.5287i			1.20941i	0.796450	+	0.604705i	$0.206709\pi$
$863$			35.5287i			1.20941i	−0.796450	+	0.604705i	$0.793291\pi$
$864$	5.17058	−	0.514925i	0.175907	−	0.0175181i
$865$	−6.48740	+	6.48740i	−0.220578	+	0.220578i
$866$	22.8662	+	22.8662i	0.777027	+	0.777027i
$867$	4.45947	+	1.03810i	0.151452	+	0.0352558i
$868$	−4.54482	−	4.54482i	−0.154261	−	0.154261i
$869$	2.47839	+	2.47839i	0.0840736	+	0.0840736i
$870$	−0.0243948	+	0.0151819i	−0.000827061	+	0.000514715i
$871$	21.6789	−	21.6789i	0.734562	−	0.734562i
$872$	−18.1836			−0.615776
$873$	−9.77640	−	28.7320i	−0.330881	−	0.972431i
$874$	12.5057	+	12.5057i	0.423010	+	0.423010i
$875$	−0.617812	−	0.617812i	−0.0208859	−	0.0208859i
$876$	4.33935	−	18.6409i	0.146613	−	0.629819i
$877$	−20.3035			−0.685599			−0.342800	−	0.939409i	$-0.611375\pi$
$877$	−20.3035			−0.685599			−0.342800	+	0.939409i	$0.611375\pi$
$878$	26.5843			0.897177
$879$	−10.9460	−	2.54808i	−0.369200	−	0.0859445i
$880$	2.29514	−	2.29514i	0.0773693	−	0.0773693i
$881$	−6.22716			−0.209798			−0.104899	−	0.994483i	$-0.533452\pi$
$881$	−6.22716			−0.209798			−0.104899	+	0.994483i	$0.533452\pi$
$882$	6.02690	+	17.7126i	0.202936	+	0.596413i
$883$	−23.8218	+	23.8218i	−0.801669	+	0.801669i	−0.983356	−	0.181687i	$-0.941844\pi$
$883$	−23.8218	+	23.8218i	−0.801669	+	0.801669i	0.181687	+	0.983356i	$0.441844\pi$
$884$			15.0071i			0.504743i
$885$	−18.9909	−	4.42080i	−0.638371	−	0.148604i
$886$	−9.98191	−	9.98191i	−0.335349	−	0.335349i
$887$	−43.3246			−1.45470			−0.727350	−	0.686267i	$-0.759248\pi$
$887$	−43.3246			−1.45470			−0.727350	+	0.686267i	$0.759248\pi$
$888$	−10.3028	+	2.20288i	−0.345739	+	0.0739237i
$889$	0.829106			0.0278073
$890$	6.49421	+	6.49421i	0.217686	+	0.217686i
$891$	17.8169	+	23.1500i	0.596889	+	0.775554i
$892$			6.18301i			0.207022i
$893$	6.89177	−	6.89177i	0.230624	−	0.230624i
$894$	3.91663	+	6.29338i	0.130992	+	0.210482i
$895$	14.1577			0.473239
$896$	−0.617812	+	0.617812i	−0.0206396	+	0.0206396i
$897$	8.66295	−	37.2143i	0.289248	−	1.24255i
$898$	9.80260			0.327117
$899$	0.122035			0.00407009
$900$	−2.69158	−	1.32492i	−0.0897193	−	0.0441640i
$901$	−24.5876	−	24.5876i	−0.819132	−	0.819132i
$902$	27.7986	+	27.7986i	0.925593	+	0.925593i
$903$	−14.6529	+	9.11913i	−0.487619	+	0.303466i
$904$	4.38435			0.145821
$905$	16.0339	−	16.0339i	0.532985	−	0.532985i
$906$	14.8876	+	23.9219i	0.494608	+	0.794752i
$907$	−12.4807	−	12.4807i	−0.414413	−	0.414413i	0.468859	−	0.883273i	$-0.344665\pi$
$907$	−12.4807	−	12.4807i	−0.414413	−	0.414413i	−0.883273	+	0.468859i	$0.844665\pi$
$908$	16.9434	+	16.9434i	0.562286	+	0.562286i
$909$	26.5657	+	13.0769i	0.881128	+	0.433732i
$910$	2.44697	+	2.44697i	0.0811163	+	0.0811163i
$911$	−35.6884	+	35.6884i	−1.18241	+	1.18241i	−0.203291	+	0.979118i	$0.565164\pi$
$911$	−35.6884	+	35.6884i	−1.18241	+	1.18241i	−0.979118	+	0.203291i	$0.934836\pi$
$912$	−4.66939	+	2.90596i	−0.154619	+	0.0962258i
$913$		−	20.3459i		−	0.673351i
$914$			20.9337i			0.692425i
$915$	−15.8562	−	3.69110i	−0.524190	−	0.122024i
$916$			7.05363i			0.233058i
$917$	−10.2536	−	10.2536i	−0.338605	−	0.338605i
$918$	−12.4735	+	15.2327i	−0.411688	+	0.502755i
$919$	10.4021	−	10.4021i	0.343134	−	0.343134i	−0.514411	−	0.857544i	$-0.671989\pi$
$919$	10.4021	−	10.4021i	0.343134	−	0.343134i	0.857544	+	0.514411i	$0.171989\pi$
$920$	−3.93841	−	3.93841i	−0.129845	−	0.129845i
$921$	8.13364	+	1.89340i	0.268013	+	0.0623895i
$922$	−7.68326			−0.253035
$923$	−1.62713	+	1.62713i	−0.0535575	+	0.0535575i
$924$	−4.78407	−	1.11366i	−0.157384	−	0.0366368i
$925$	5.72219	+	2.06314i	0.188144	+	0.0678357i
$926$		−	1.61515i		−	0.0530773i
$927$	19.2958	−	6.56563i	0.633758	−	0.215644i
$928$		−	0.0165891i		−	0.000544565i
$929$	16.9964			0.557632			0.278816	−	0.960344i	$-0.410058\pi$
$929$	16.9964			0.557632			0.278816	+	0.960344i	$0.410058\pi$
$930$	6.73230	+	10.8177i	0.220761	+	0.354726i
$931$	−14.0030	−	14.0030i	−0.458929	−	0.458929i
$932$			4.46090i			0.146122i
$933$	−13.4213	+	8.35263i	−0.439393	+	0.273453i
$934$	11.9384			0.390636
$935$			12.2984i			0.402201i
$936$	10.6605	+	5.24761i	0.348451	+	0.171524i
$937$	−18.6700			−0.609923			−0.304961	−	0.952365i	$-0.598644\pi$
$937$	−18.6700			−0.609923			−0.304961	+	0.952365i	$0.598644\pi$
$938$	−4.78230	+	4.78230i	−0.156147	+	0.156147i
$939$	−49.1615	+	30.5953i	−1.60433	+	0.998439i
$940$	−2.17042	+	2.17042i	−0.0707914	+	0.0707914i
$941$			16.2052i			0.528275i	0.964485	+	0.264137i	$0.0850872\pi$
$941$			16.2052i			0.528275i	−0.964485	+	0.264137i	$0.914913\pi$
$942$	−27.1450	+	16.8935i	−0.884432	+	0.550419i
$943$	47.7017	−	47.7017i	1.55338	−	1.55338i
$944$	7.96028	−	7.96028i	0.259085	−	0.259085i
$945$	0.449899	+	4.51762i	0.0146352	+	0.146958i
$946$			37.0172i			1.20353i
$947$	30.9113	−	30.9113i	1.00448	−	1.00448i	0.00449357	−	0.999990i	$-0.498570\pi$
$947$	30.9113	−	30.9113i	1.00448	−	1.00448i	0.999990	−	0.00449357i	$-0.00143035\pi$
$948$	0.988240	+	1.58794i	0.0320965	+	0.0515738i
$949$	30.9474	−	30.9474i	1.00459	−	1.00459i
$950$	3.17531			0.103021
$951$	−1.07370	+	4.61241i	−0.0348172	+	0.149568i
$952$		−	3.31051i		−	0.107294i
$953$	−60.8196			−1.97014			−0.985070	−	0.172157i	$-0.944926\pi$
$953$	−60.8196			−1.97014			−0.985070	+	0.172157i	$0.944926\pi$
$954$	−26.0639	+	8.86855i	−0.843851	+	0.287130i
$955$			9.32939i			0.301892i
$956$	−17.0743	−	17.0743i	−0.552222	−	0.552222i
$957$	0.0791812	−	0.0492778i	0.00255957	−	0.00159292i
$958$	−13.7325			−0.443677
$959$			18.6347i			0.601746i
$960$	1.47053	−	0.915172i	0.0474612	−	0.0295371i
$961$		−	23.1155i		−	0.745661i
$962$	−22.6639	−	8.17150i	−0.730713	−	0.263460i
$963$	19.5039	−	39.6222i	0.628504	−	1.27681i
$964$	3.79899	−	3.79899i	0.122357	−	0.122357i
$965$	1.02055			0.0328528
$966$	−1.91102	+	8.20934i	−0.0614860	+	0.264131i
$967$	−32.1280	−	32.1280i	−1.03317	−	1.03317i	−0.999431	−	0.0337345i	$-0.989260\pi$
$967$	−32.1280	−	32.1280i	−1.03317	−	1.03317i	−0.0337345	−	0.999431i	$-0.510740\pi$
$968$	0.328543	−	0.328543i	0.0105598	−	0.0105598i
$969$	4.72463	−	20.2960i	0.151777	−	0.652003i
$970$	−7.15350	−	7.15350i	−0.229685	−	0.229685i
$971$		−	46.3264i		−	1.48668i	−0.668911	−	0.743342i	$-0.733239\pi$
$971$		−	46.3264i		−	1.48668i	0.668911	−	0.743342i	$-0.266761\pi$
$972$	6.45914	+	14.1873i	0.207177	+	0.455058i
$973$			12.7722i			0.409458i
$974$		−	5.48079i		−	0.175616i
$975$	−3.62473	−	5.82434i	−0.116084	−	0.186528i
$976$	6.64635	−	6.64635i	0.212744	−	0.212744i
$977$	20.5956	+	20.5956i	0.658912	+	0.658912i	0.955123	−	0.296211i	$-0.0957230\pi$
$977$	20.5956	+	20.5956i	0.658912	+	0.658912i	−0.296211	+	0.955123i	$0.595723\pi$
$978$	−4.25296	+	18.2698i	−0.135995	+	0.584205i
$979$	−21.0791	−	21.0791i	−0.673690	−	0.673690i
$980$	4.40995	+	4.40995i	0.140871	+	0.140871i
$981$	−17.5722	−	51.6432i	−0.561037	−	1.64884i
$982$	−26.5826	+	26.5826i	−0.848284	+	0.848284i
$983$	5.10058			0.162683			0.0813416	−	0.996686i	$-0.474080\pi$
$983$	5.10058			0.162683			0.0813416	+	0.996686i	$0.474080\pi$
$984$	11.0845	+	17.8110i	0.353361	+	0.567793i
$985$	10.4709	+	10.4709i	0.333632	+	0.333632i
$986$	0.0444460	+	0.0444460i	0.00141545	+	0.00141545i
$987$	4.52410	+	1.05315i	0.144004	+	0.0335220i
$988$	−12.5765			−0.400111
$989$	63.5206			2.01984
$990$	8.73639	+	4.30045i	0.277661	+	0.136677i
$991$	−37.2894	+	37.2894i	−1.18454	+	1.18454i	−0.205980	+	0.978556i	$0.566038\pi$
$991$	−37.2894	+	37.2894i	−1.18454	+	1.18454i	−0.978556	+	0.205980i	$0.933962\pi$
$992$	−7.35632			−0.233563
$993$	−33.1123	+	20.6072i	−1.05079	+	0.653949i
$994$	0.358938	−	0.358938i	0.0113848	−	0.0113848i
$995$		−	21.6821i		−	0.687369i
$996$	2.46156	−	10.5743i	0.0779974	−	0.335061i
$997$	−20.2213	−	20.2213i	−0.640416	−	0.640416i	0.310242	−	0.950658i	$-0.399590\pi$
$997$	−20.2213	−	20.2213i	−0.640416	−	0.640416i	−0.950658	+	0.310242i	$0.899590\pi$
$998$	−19.6191			−0.621031
$999$	−16.2127	−	27.1320i	−0.512947	−	0.858420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.191.14	yes	40
3.2	odd	2	inner	1110.2.u.f.191.2	✓	40
37.31	odd	4	inner	1110.2.u.f.401.2	yes	40
111.68	even	4	inner	1110.2.u.f.401.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.2	✓	40	3.2	odd	2	inner
1110.2.u.f.191.14	yes	40	1.1	even	1	trivial
1110.2.u.f.401.2	yes	40	37.31	odd	4	inner
1110.2.u.f.401.14	yes	40	111.68	even	4	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.392697 - 1.68695i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.47053 - 0.915172i) q^{6} -0.873718 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.69158 - 1.32492i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.392697 - 1.68695i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.47053 - 0.915172i) q^{6} -0.873718 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.69158 - 1.32492i) q^{9} -1.00000 q^{10} +3.24582 q^{11} +(1.68695 + 0.392697i) q^{12} +(2.80064 + 2.80064i) q^{13} +(-0.617812 - 0.617812i) q^{14} +(0.915172 + 1.47053i) q^{15} -1.00000 q^{16} +(2.67922 - 2.67922i) q^{17} +(-0.966374 - 2.84009i) q^{18} +(2.24528 + 2.24528i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-0.343107 + 1.47392i) q^{21} +(2.29514 + 2.29514i) q^{22} +(3.93841 - 3.93841i) q^{23} +(0.915172 + 1.47053i) q^{24} -1.00000i q^{25} +3.96070i q^{26} +(-3.29204 + 4.02026i) q^{27} -0.873718i q^{28} +(0.0117303 + 0.0117303i) q^{29} +(-0.392697 + 1.68695i) q^{30} +(5.20171 - 5.20171i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.27463 - 5.47553i) q^{33} +3.78900 q^{34} +(0.617812 - 0.617812i) q^{35} +(1.32492 - 2.69158i) q^{36} +(-2.06314 + 5.72219i) q^{37} +3.17531i q^{38} +(5.82434 - 3.62473i) q^{39} -1.00000i q^{40} +12.1119 q^{41} +(-1.28483 + 0.799603i) q^{42} +(8.06425 + 8.06425i) q^{43} +3.24582i q^{44} +(2.84009 - 0.966374i) q^{45} +5.56975 q^{46} -3.06944i q^{47} +(-0.392697 + 1.68695i) q^{48} -6.23662 q^{49} +(0.707107 - 0.707107i) q^{50} +(-3.46758 - 5.57183i) q^{51} +(-2.80064 + 2.80064i) q^{52} -9.17714i q^{53} +(-5.17058 + 0.514925i) q^{54} +(-2.29514 + 2.29514i) q^{55} +(0.617812 - 0.617812i) q^{56} +(4.66939 - 2.90596i) q^{57} +0.0165891i q^{58} +(-7.96028 + 7.96028i) q^{59} +(-1.47053 + 0.915172i) q^{60} +(-6.64635 + 6.64635i) q^{61} +7.35632 q^{62} +(2.35168 + 1.15761i) q^{63} -1.00000i q^{64} -3.96070 q^{65} +(4.77308 - 2.97049i) q^{66} -7.74070i q^{67} +(2.67922 + 2.67922i) q^{68} +(-5.09728 - 8.19049i) q^{69} +0.873718 q^{70} +0.580983i q^{71} +(2.84009 - 0.966374i) q^{72} -11.0501i q^{73} +(-5.50506 + 2.58734i) q^{74} +(-1.68695 - 0.392697i) q^{75} +(-2.24528 + 2.24528i) q^{76} -2.83593 q^{77} +(6.68150 + 1.55536i) q^{78} +(0.763562 + 0.763562i) q^{79} +(0.707107 - 0.707107i) q^{80} +(5.48918 + 7.13224i) q^{81} +(8.56443 + 8.56443i) q^{82} -6.26833i q^{83} +(-1.47392 - 0.343107i) q^{84} +3.78900i q^{85} +11.4046i q^{86} +(0.0243948 - 0.0151819i) q^{87} +(-2.29514 + 2.29514i) q^{88} +(-6.49421 - 6.49421i) q^{89} +(2.69158 + 1.32492i) q^{90} +(-2.44697 - 2.44697i) q^{91} +(3.93841 + 3.93841i) q^{92} +(-6.73230 - 10.8177i) q^{93} +(2.17042 - 2.17042i) q^{94} -3.17531 q^{95} +(-1.47053 + 0.915172i) q^{96} +(7.15350 + 7.15350i) q^{97} +(-4.40995 - 4.40995i) q^{98} +(-8.73639 - 4.30045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q + 24 * q^7 - 8 * q^9	\( 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) \) 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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