LMFDB - Embedded newform 1110.2.u.f.401.2

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			401.2
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.f.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.392697 + 1.68695i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.915172 - 1.47053i) q^{6} -0.873718 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.69158 - 1.32492i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.392697 + 1.68695i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.915172 - 1.47053i) 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} +(-1.47053 + 0.915172i) q^{15} -1.00000 q^{16} +(-2.67922 - 2.67922i) q^{17} +(2.84009 - 0.966374i) 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} +(-1.47053 + 0.915172i) 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} +(3.62473 + 5.82434i) q^{39} +1.00000i q^{40} -12.1119 q^{41} +(0.799603 + 1.28483i) q^{42} +(8.06425 - 8.06425i) q^{43} +3.24582i q^{44} +(-0.966374 - 2.84009i) 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} +(5.57183 - 3.46758i) q^{51} +(-2.80064 - 2.80064i) q^{52} -9.17714i q^{53} +(0.514925 + 5.17058i) q^{54} +(-2.29514 - 2.29514i) q^{55} +(-0.617812 - 0.617812i) q^{56} +(2.90596 + 4.66939i) q^{57} -0.0165891i q^{58} +(7.96028 + 7.96028i) q^{59} +(0.915172 + 1.47053i) 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} +(2.97049 + 4.77308i) q^{66} +7.74070i q^{67} +(-2.67922 + 2.67922i) q^{68} +(8.19049 - 5.09728i) q^{69} +0.873718 q^{70} +0.580983i q^{71} +(-0.966374 - 2.84009i) 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} +(-0.0151819 - 0.0243948i) 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} +(-10.8177 + 6.73230i) q^{93} +(2.17042 + 2.17042i) q^{94} +3.17531 q^{95} +(0.915172 + 1.47053i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$6$	−0.915172	−	1.47053i	−0.373618	−	0.600341i
$7$	−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	$-0.662757\pi$
$11$	−3.24582			−0.978653			−0.489326	+	0.872101i	$0.662757\pi$
$12$	1.68695	+	0.392697i	0.486980	+	0.113362i
$13$	2.80064	−	2.80064i	0.776758	−	0.776758i	−0.202520	−	0.979278i	$-0.564913\pi$
$13$	2.80064	−	2.80064i	0.776758	−	0.776758i	0.979278	+	0.202520i	$0.0649131\pi$
$14$	0.617812	−	0.617812i	0.165117	−	0.165117i
$15$	−1.47053	+	0.915172i	−0.379689	+	0.236297i
$16$	−1.00000			−0.250000
$17$	−2.67922	−	2.67922i	−0.649807	−	0.649807i	0.303139	−	0.952946i	$-0.401965\pi$
$17$	−2.67922	−	2.67922i	−0.649807	−	0.649807i	−0.952946	+	0.303139i	$0.901965\pi$
$18$	2.84009	−	0.966374i	0.669416	−	0.227777i
$19$	2.24528	−	2.24528i	0.515103	−	0.515103i	−0.400982	−	0.916086i	$-0.631331\pi$
$19$	2.24528	−	2.24528i	0.515103	−	0.515103i	0.916086	+	0.400982i	$0.131331\pi$
$20$	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	$-0.447216\pi$
$23$	−3.93841	−	3.93841i	−0.821215	−	0.821215i	−0.986282	+	0.165067i	$0.947216\pi$
$24$	−1.47053	+	0.915172i	−0.300171	+	0.186809i
$25$			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	$-0.750490\pi$
$29$	−0.0117303	+	0.0117303i	−0.00217826	+	0.00217826i	0.706017	+	0.708195i	$0.250490\pi$
$30$	0.392697	−	1.68695i	0.0716964	−	0.307993i
$31$	5.20171	+	5.20171i	0.934254	+	0.934254i	0.997968	−	0.0637143i	$-0.0202946\pi$
$31$	5.20171	+	5.20171i	0.934254	+	0.934254i	−0.0637143	+	0.997968i	$0.520295\pi$
$32$	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
$39$	3.62473	+	5.82434i	0.580421	+	0.932640i
$40$			1.00000i			0.158114i
$41$	−12.1119			−1.89157			−0.945783	−	0.324799i	$-0.894703\pi$
$41$	−12.1119			−1.89157			−0.945783	+	0.324799i	$0.894703\pi$
$42$	0.799603	+	1.28483i	0.123381	+	0.198253i
$43$	8.06425	−	8.06425i	1.22979	−	1.22979i	0.265743	−	0.964044i	$-0.414383\pi$
$43$	8.06425	−	8.06425i	1.22979	−	1.22979i	0.964044	−	0.265743i	$-0.0856174\pi$
$44$			3.24582i			0.489326i
$45$	−0.966374	−	2.84009i	−0.144059	−	0.423376i
$46$	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
$51$	5.57183	−	3.46758i	0.780213	−	0.485559i
$52$	−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	$-0.217063\pi$
$54$	0.514925	+	5.17058i	0.0700724	+	0.703626i
$55$	−2.29514	−	2.29514i	−0.309477	−	0.309477i
$56$	−0.617812	−	0.617812i	−0.0825586	−	0.0825586i
$57$	2.90596	+	4.66939i	0.384903	+	0.618476i
$58$		−	0.0165891i		−	0.00217826i
$59$	7.96028	+	7.96028i	1.03634	+	1.03634i	0.999314	+	0.0370254i	$0.0117882\pi$
$59$	7.96028	+	7.96028i	1.03634	+	1.03634i	0.0370254	+	0.999314i	$0.488212\pi$
$60$	0.915172	+	1.47053i	0.118148	+	0.189845i
$61$	−6.64635	−	6.64635i	−0.850978	−	0.850978i	0.139276	−	0.990254i	$-0.455522\pi$
$61$	−6.64635	−	6.64635i	−0.850978	−	0.850978i	−0.990254	+	0.139276i	$0.955522\pi$
$62$	−7.35632			−0.934254
$63$	2.35168	+	1.15761i	0.296284	+	0.145845i
$64$			1.00000i			0.125000i
$65$	3.96070			0.491265
$66$	2.97049	+	4.77308i	0.365642	+	0.587526i
$67$			7.74070i			0.945677i	0.881149	+	0.472838i	$0.156771\pi$
$67$			7.74070i			0.945677i	−0.881149	+	0.472838i	$0.843229\pi$
$68$	−2.67922	+	2.67922i	−0.324904	+	0.324904i
$69$	8.19049	−	5.09728i	0.986019	−	0.613641i
$70$	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	$0.989024\pi$
$72$	−0.966374	−	2.84009i	−0.113888	−	0.334708i
$73$			11.0501i			1.29332i	0.762780	+	0.646658i	$0.223834\pi$
$73$			11.0501i			1.29332i	−0.762780	+	0.646658i	$0.776166\pi$
$74$	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	−0.662847	−	0.748755i	$-0.730652\pi$
$79$	0.763562	−	0.763562i	0.0859075	−	0.0859075i	0.748755	+	0.662847i	$0.230652\pi$
$80$	−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
$87$	−0.0151819	−	0.0243948i	−0.00162767	−	0.00261540i
$88$	−2.29514	−	2.29514i	−0.244663	−	0.244663i
$89$	6.49421	−	6.49421i	0.688385	−	0.688385i	−0.273490	−	0.961875i	$-0.588178\pi$
$89$	6.49421	−	6.49421i	0.688385	−	0.688385i	0.961875	+	0.273490i	$0.0881780\pi$
$90$	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
$93$	−10.8177	+	6.73230i	−1.12174	+	0.698107i
$94$	2.17042	+	2.17042i	0.223862	+	0.223862i
$95$	3.17531			0.325780
$96$	0.915172	+	1.47053i	0.0934044	+	0.150085i
$97$	7.15350	−	7.15350i	0.726328	−	0.726328i	−0.243558	−	0.969886i	$-0.578315\pi$
$97$	7.15350	−	7.15350i	0.726328	−	0.726328i	0.969886	+	0.243558i	$0.0783147\pi$
$98$	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	$-0.336614\pi$
$101$	9.86993			0.982095			0.491048	+	0.871133i	$0.336614\pi$
$102$	−1.48793	+	6.39183i	−0.147327	+	0.632886i
$103$	−4.80415	−	4.80415i	−0.473367	−	0.473367i	0.429636	−	0.903002i	$-0.358642\pi$
$103$	−4.80415	−	4.80415i	−0.473367	−	0.473367i	−0.903002	+	0.429636i	$0.858642\pi$
$104$	3.96070			0.388379
$105$	1.28483	−	0.799603i	0.125386	−	0.0780332i
$106$	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	0.268184	−	0.963368i	$-0.413577\pi$
$109$	12.8578	−	12.8578i	1.23155	−	1.23155i	0.963368	−	0.268184i	$-0.0864235\pi$
$110$	3.24582			0.309477
$111$	10.4632	−	1.23332i	0.993125	−	0.117062i
$112$	0.873718			0.0825586
$113$	3.10020	−	3.10020i	0.291643	−	0.291643i	−0.546086	−	0.837729i	$-0.683883\pi$
$113$	3.10020	−	3.10020i	0.291643	−	0.291643i	0.837729	+	0.546086i	$0.183883\pi$
$114$	−5.35658	−	1.24694i	−0.501690	−	0.116786i
$115$		−	5.56975i		−	0.519382i
$116$	0.0117303	+	0.0117303i	0.00108913	+	0.00108913i
$117$	−11.2488	+	3.82752i	−1.03995	+	0.353854i
$118$	−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
$126$	−2.48144	+	0.844338i	−0.221064	+	0.0752196i
$127$	−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
$129$	10.4372	+	16.7708i	0.918940	+	1.47658i
$130$	−2.80064	+	2.80064i	−0.245632	+	0.245632i
$131$	−11.7356	+	11.7356i	−1.02535	+	1.02535i	−0.0256765	+	0.999670i	$0.508174\pi$
$131$	−11.7356	+	11.7356i	−1.02535	+	1.02535i	−0.999670	+	0.0256765i	$0.991826\pi$
$132$	−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
$135$	5.17058	−	0.514925i	0.445012	−	0.0443177i
$136$		−	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	$0.212847\pi$
$139$			14.6182i			1.23990i	−0.784641	+	0.619951i	$0.787153\pi$
$140$	−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	$0.943910\pi$
$150$	1.47053	−	0.915172i	0.120068	−	0.0747235i
$151$		−	16.2675i		−	1.32383i	−0.749577	−	0.661917i	$-0.769743\pi$
$151$		−	16.2675i		−	1.32383i	0.749577	−	0.661917i	$-0.230257\pi$
$152$	3.17531			0.257552
$153$	3.66159	+	10.7611i	0.296022	+	0.869983i
$154$	−2.00531	+	2.00531i	−0.161592	+	0.161592i
$155$			7.35632i			0.590874i
$156$	5.82434	−	3.62473i	0.466320	−	0.290210i
$157$	−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
$162$	−8.92469	−	1.16182i	−0.701190	−	0.0912812i
$163$	−7.65805	−	7.65805i	−0.599825	−	0.599825i	0.340441	−	0.940266i	$-0.389424\pi$
$163$	−7.65805	−	7.65805i	−0.599825	−	0.599825i	−0.940266	+	0.340441i	$0.889424\pi$
$164$			12.1119i			0.945783i
$165$	4.77308	−	2.97049i	0.371584	−	0.231252i
$166$	4.43238	+	4.43238i	0.344019	+	0.344019i
$167$	12.4791	+	12.4791i	0.965665	+	0.965665i	0.999430	−	0.0337648i	$-0.0107497\pi$
$167$	12.4791	+	12.4791i	0.965665	+	0.965665i	−0.0337648	+	0.999430i	$0.510750\pi$
$168$	1.28483	−	0.799603i	0.0991267	−	0.0616907i
$169$		−	2.68718i		−	0.206706i
$170$	2.67922	+	2.67922i	0.205487	+	0.205487i
$171$	−9.01817	+	3.06854i	−0.689637	+	0.234657i
$172$	−8.06425	−	8.06425i	−0.614894	−	0.614894i
$173$	−9.17456			−0.697529			−0.348765	−	0.937210i	$-0.613399\pi$
$173$	−9.17456			−0.697529			−0.348765	+	0.937210i	$0.613399\pi$
$174$	0.0279850	+	0.00651450i	0.00212153	+	0.000493863i
$175$		−	0.873718i		−	0.0660469i
$176$	3.24582			0.244663
$177$	−16.5545	+	10.3026i	−1.24432	+	0.774389i
$178$			9.18420i			0.688385i
$179$	10.0110	−	10.0110i	0.748257	−	0.748257i	−0.225895	−	0.974152i	$-0.572530\pi$
$179$	10.0110	−	10.0110i	0.748257	−	0.748257i	0.974152	+	0.225895i	$0.0725305\pi$
$180$	−2.84009	+	0.966374i	−0.211688	+	0.0720293i
$181$	−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
$183$	13.8220	−	8.60203i	1.02175	−	0.635880i
$184$		−	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	$-0.359590\pi$
$191$	−6.59688	−	6.59688i	−0.477333	−	0.477333i	−0.904278	+	0.426945i	$0.859590\pi$
$192$	−1.68695	−	0.392697i	−0.121745	−	0.0283405i
$193$	−0.721641	+	0.721641i	−0.0519448	+	0.0519448i	−0.732602	−	0.680657i	$-0.761694\pi$
$193$	−0.721641	+	0.721641i	−0.0519448	+	0.0519448i	0.680657	+	0.732602i	$0.261694\pi$
$194$			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	$-0.176877\pi$
$198$	−9.21844	+	3.13668i	−0.655126	+	0.222914i
$199$	−15.3316	−	15.3316i	−1.08683	−	1.08683i	−0.995853	−	0.0909720i	$-0.971003\pi$
$199$	−15.3316	−	15.3316i	−1.08683	−	1.08683i	−0.0909720	−	0.995853i	$-0.528997\pi$
$200$	−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
$204$	−3.46758	−	5.57183i	−0.242779	−	0.390106i
$205$	−8.56443	−	8.56443i	−0.598166	−	0.598166i
$206$	6.79409			0.473367
$207$	5.38246	+	15.8186i	0.374107	+	1.09947i
$208$	−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
$216$	5.17058	−	0.514925i	0.351813	−	0.0350362i
$217$	−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
$222$	−6.52652	+	8.27070i	−0.438031	+	0.555093i
$223$	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	−0.991045	−	0.133527i	$-0.957370\pi$
$227$	−16.9434	−	16.9434i	−1.12457	−	1.12457i	−0.133527	−	0.991045i	$-0.542630\pi$
$228$	4.66939	−	2.90596i	0.309238	−	0.192452i
$229$	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	$-0.546679\pi$
$233$	−4.46090			−0.292243			−0.146122	+	0.989267i	$0.546679\pi$
$234$	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
$237$	0.988240	+	1.58794i	0.0641931	+	0.103148i
$238$	−3.31051			−0.214589
$239$	17.0743	+	17.0743i	1.10444	+	1.10444i	0.993868	+	0.110576i	$0.0352697\pi$
$239$	17.0743	+	17.0743i	1.10444	+	1.10444i	0.110576	+	0.993868i	$0.464730\pi$
$240$	1.47053	−	0.915172i	0.0949223	−	0.0590741i
$241$	−3.79899	+	3.79899i	−0.244715	+	0.244715i	−0.818797	−	0.574083i	$-0.805359\pi$
$241$	−3.79899	+	3.79899i	−0.244715	+	0.244715i	0.574083	+	0.818797i	$0.305359\pi$
$242$	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
$246$	11.0845	+	17.8110i	0.706722	+	1.13559i
$247$		−	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	$-0.712997\pi$
$251$	2.59871	−	2.59871i	0.164029	−	0.164029i	0.784349	+	0.620320i	$0.212997\pi$
$252$	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	$-0.446157\pi$
$257$	−13.1036	−	13.1036i	−0.817381	−	0.817381i	−0.985728	+	0.168346i	$0.946157\pi$
$258$	−19.2389	−	4.47855i	−1.19776	−	0.278822i
$259$	1.80260	+	4.99958i	0.112008	+	0.310659i
$260$		−	3.96070i		−	0.245632i
$261$	0.0471146	−	0.0160313i	0.00291632	−	0.000992312i
$262$		−	16.5967i		−	1.02535i
$263$	−3.79960			−0.234293			−0.117147	−	0.993115i	$-0.537375\pi$
$263$	−3.79960			−0.234293			−0.117147	+	0.993115i	$0.537375\pi$
$264$	4.77308	−	2.97049i	0.293763	−	0.182821i
$265$	6.48922	−	6.48922i	0.398630	−	0.398630i
$266$		−	2.77433i		−	0.170105i
$267$	8.40513	+	13.5056i	0.514385	+	0.826532i
$268$	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
$273$	−3.16699	−	5.08883i	−0.191675	−	0.307990i
$274$	15.0812	+	15.0812i	0.911089	+	0.911089i
$275$		−	3.24582i		−	0.195731i
$276$	−5.09728	−	8.19049i	−0.306820	−	0.493009i
$277$	13.7206	+	13.7206i	0.824392	+	0.824392i	0.986735	−	0.162342i	$-0.0519048\pi$
$277$	13.7206	+	13.7206i	0.824392	+	0.824392i	−0.162342	+	0.986735i	$0.551905\pi$
$278$	−10.3366	−	10.3366i	−0.619951	−	0.619951i
$279$	−7.10896	−	20.8926i	−0.425602	−	1.25081i
$280$		−	0.873718i		−	0.0522146i
$281$	−16.4710	−	16.4710i	−0.982575	−	0.982575i	0.0172753	−	0.999851i	$-0.494501\pi$
$281$	−16.4710	−	16.4710i	−0.982575	−	0.982575i	−0.999851	+	0.0172753i	$0.994501\pi$
$282$	−4.51371	+	2.80907i	−0.268788	+	0.167278i
$283$	−0.457464	−	0.457464i	−0.0271934	−	0.0271934i	0.693379	−	0.720573i	$-0.256121\pi$
$283$	−0.457464	−	0.457464i	−0.0271934	−	0.0271934i	−0.720573	+	0.693379i	$0.756121\pi$
$284$	0.580983			0.0344750
$285$	−1.24694	+	5.35658i	−0.0738621	+	0.317296i
$286$		−	12.8557i		−	0.760176i
$287$	10.5824			0.624660
$288$	−2.84009	+	0.966374i	−0.167354	+	0.0569441i
$289$		−	2.64352i		−	0.155501i
$290$	0.0117303	−	0.0117303i	0.000688826	−	0.000688826i
$291$	9.25842	+	14.8767i	0.542738	+	0.872090i
$292$	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	$-0.0606983\pi$
$294$	5.70758	+	9.17113i	0.332873	+	0.534871i
$295$			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	$-0.956065\pi$
$307$		−	4.82152i		−	0.275178i	0.990489	−	0.137589i	$-0.0439354\pi$
$308$		−	2.83593i		−	0.161592i
$309$	9.99091	−	6.21776i	0.568363	−	0.353716i
$310$	−5.20171	−	5.20171i	−0.295437	−	0.295437i
$311$	6.45365	−	6.45365i	0.365953	−	0.365953i	−0.500046	−	0.865999i	$-0.666684\pi$
$311$	6.45365	−	6.45365i	0.365953	−	0.365953i	0.865999	+	0.500046i	$0.166684\pi$
$312$	−1.55536	+	6.68150i	−0.0880548	+	0.378265i
$313$	−23.6394	+	23.6394i	−1.33618	+	1.33618i	−0.436449	+	0.899729i	$0.643764\pi$
$313$	−23.6394	+	23.6394i	−1.33618	+	1.33618i	−0.899729	+	0.436449i	$0.856236\pi$
$314$	13.0527	−	13.0527i	0.736607	−	0.736607i
$315$	0.844338	+	2.48144i	0.0475731	+	0.139813i
$316$	−0.763562	−	0.763562i	−0.0429537	−	0.0429537i
$317$	2.73418			0.153567			0.0767834	−	0.997048i	$-0.475535\pi$
$317$	2.73418			0.153567			0.0767834	+	0.997048i	$0.475535\pi$
$318$	−13.4953	+	8.39867i	−0.756777	+	0.470974i
$319$	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
$327$	16.6412	+	26.7396i	0.920259	+	1.47870i
$328$	−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	−0.993029	−	0.117871i	$-0.962393\pi$
$331$	−15.9221	+	15.9221i	−0.875158	+	0.875158i	0.117871	+	0.993029i	$0.462393\pi$
$332$	−6.26833			−0.344019
$333$	−2.02833	+	18.1352i	−0.111152	+	0.993803i
$334$	−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	$-0.944542\pi$
$337$		−	6.36440i		−	0.346691i	0.984861	−	0.173346i	$-0.0554577\pi$
$338$	1.90012	+	1.90012i	0.103353	+	0.103353i
$339$	4.01244	+	6.44732i	0.217926	+	0.350170i
$340$	−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	$-0.610888\pi$
$347$	11.1501	−	11.1501i	0.598571	−	0.598571i	0.939932	+	0.341361i	$0.110888\pi$
$348$	−0.0243948	+	0.0151819i	−0.00130770	+	0.000813836i
$349$	−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
$351$	−2.03946	−	20.4791i	−0.108859	−	1.09309i
$352$	−2.29514	+	2.29514i	−0.122332	+	0.122332i
$353$	−1.76426	+	1.76426i	−0.0939022	+	0.0939022i	−0.752497	−	0.658595i	$-0.771151\pi$
$353$	−1.76426	+	1.76426i	−0.0939022	+	0.0939022i	0.658595	+	0.752497i	$0.271151\pi$
$354$	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
$357$	−4.86821	+	3.02969i	−0.257653	+	0.160348i
$358$			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
$372$	6.73230	+	10.8177i	0.349054	+	0.560871i
$373$		−	22.1399i		−	1.14636i	−0.819429	−	0.573181i	$-0.805709\pi$
$373$		−	22.1399i		−	1.14636i	0.819429	−	0.573181i	$-0.194291\pi$
$374$	−12.2984			−0.635936
$375$	−0.915172	−	1.47053i	−0.0472593	−	0.0759379i
$376$	2.17042	−	2.17042i	0.111931	−	0.111931i
$377$			0.0657046i			0.00338396i
$378$	−0.449899	−	4.51762i	−0.0231403	−	0.232362i
$379$	−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	$-0.357489\pi$
$383$	−9.16947	−	9.16947i	−0.468538	−	0.468538i	−0.901441	+	0.432903i	$0.857489\pi$
$384$	1.47053	−	0.915172i	0.0750427	−	0.0467022i
$385$	2.00531	+	2.00531i	0.102200	+	0.102200i
$386$		−	1.02055i		−	0.0519448i
$387$	−32.3900	+	11.0211i	−1.64648	+	0.560233i
$388$	−7.15350	−	7.15350i	−0.363164	−	0.363164i
$389$	6.40269	+	6.40269i	0.324629	+	0.324629i	0.850540	−	0.525911i	$-0.176275\pi$
$389$	6.40269	+	6.40269i	0.324629	+	0.324629i	−0.525911	+	0.850540i	$0.676275\pi$
$390$	−3.62473	−	5.82434i	−0.183545	−	0.294927i
$391$			21.1038i			1.06726i
$392$	−4.40995	−	4.40995i	−0.222736	−	0.222736i
$393$	−15.1888	−	24.4059i	−0.766175	−	1.23112i
$394$	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	$-0.981685\pi$
$397$		−	2.29166i		−	0.115015i	0.998345	−	0.0575075i	$-0.0183153\pi$
$398$	21.6821			1.08683
$399$	−2.53899	−	4.07973i	−0.127108	−	0.204242i
$400$		−	1.00000i		−	0.0500000i
$401$	17.9575	−	17.9575i	0.896756	−	0.896756i	−0.0983914	−	0.995148i	$-0.531370\pi$
$401$	17.9575	−	17.9575i	0.896756	−	0.896756i	0.995148	+	0.0983914i	$0.0313697\pi$
$402$	11.3829	−	7.08407i	0.567729	−	0.353321i
$403$	29.1362			1.45138
$404$		−	9.86993i		−	0.491048i
$405$	−1.16182	+	8.92469i	−0.0577313	+	0.443472i
$406$			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	0.771995	−	0.635628i	$-0.219259\pi$
$409$	2.75786	+	2.75786i	0.136367	+	0.136367i	−0.635628	+	0.771995i	$0.719259\pi$
$410$	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	$0.922497\pi$
$420$	−0.799603	−	1.28483i	−0.0390166	−	0.0626932i
$421$	−5.59923	−	5.59923i	−0.272890	−	0.272890i	0.557373	−	0.830262i	$-0.311809\pi$
$421$	−5.59923	−	5.59923i	−0.272890	−	0.272890i	−0.830262	+	0.557373i	$0.811809\pi$
$422$	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
$426$	0.854354	−	0.531700i	0.0413936	−	0.0257609i
$427$	5.80703	+	5.80703i	0.281022	+	0.281022i
$428$	14.7208			0.711558
$429$	−11.7652	−	18.9048i	−0.568030	−	0.912731i
$430$	−8.06425	+	8.06425i	−0.388893	+	0.388893i
$431$	16.1018	−	16.1018i	0.775598	−	0.775598i	−0.203481	−	0.979079i	$-0.565226\pi$
$431$	16.1018	−	16.1018i	0.775598	−	0.775598i	0.979079	+	0.203481i	$0.0652255\pi$
$432$	−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
$438$	16.2495	−	10.1128i	0.776432	−	0.483206i
$439$	18.7980	+	18.7980i	0.897177	+	0.897177i	0.995186	−	0.0980082i	$-0.0312472\pi$
$439$	18.7980	+	18.7980i	0.897177	+	0.897177i	−0.0980082	+	0.995186i	$0.531247\pi$
$440$		−	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	$-0.391146\pi$
$443$	14.1166			0.670698			0.335349	+	0.942094i	$0.391146\pi$
$444$	−1.23332	−	10.4632i	−0.0585310	−	0.496562i
$445$	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	$-0.324300\pi$
$449$	−6.93149	−	6.93149i	−0.327117	−	0.327117i	−0.851489	+	0.524372i	$0.824300\pi$
$450$	0.966374	+	2.84009i	0.0455553	+	0.133883i
$451$	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	−0.270340	−	0.962765i	$-0.587136\pi$
$457$	14.8024	−	14.8024i	0.692425	−	0.692425i	0.962765	+	0.270340i	$0.0871361\pi$
$458$	−4.98767	+	4.98767i	−0.233058	+	0.233058i
$459$	−19.5913	+	1.95105i	−0.914443	+	0.0910671i
$460$	−5.56975			−0.259691
$461$	5.43289	+	5.43289i	0.253035	+	0.253035i	0.822214	−	0.569179i	$-0.192739\pi$
$461$	5.43289	+	5.43289i	0.253035	+	0.253035i	−0.569179	+	0.822214i	$0.692739\pi$
$462$	−2.59537	−	4.17033i	−0.120747	−	0.194021i
$463$	−1.14209	+	1.14209i	−0.0530773	+	0.0530773i	−0.733147	−	0.680070i	$-0.761949\pi$
$463$	−1.14209	+	1.14209i	−0.0530773	+	0.0530773i	0.680070	+	0.733147i	$0.261949\pi$
$464$	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	$-0.339082\pi$
$467$	−8.44172	−	8.44172i	−0.390636	−	0.390636i	−0.874914	+	0.484278i	$0.839082\pi$
$468$	3.82752	+	11.2488i	0.176927	+	0.519974i
$469$		−	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	$-0.148422\pi$
$479$	9.71035	+	9.71035i	0.443677	+	0.443677i	−0.449569	+	0.893246i	$0.648422\pi$
$480$	−0.392697	+	1.68695i	−0.0179241	+	0.0769982i
$481$	−21.8039	−	10.2477i	−0.994173	−	0.467254i
$482$		−	5.37258i		−	0.244715i
$483$	−7.15618	+	4.45359i	−0.325617	+	0.202645i
$484$			0.464630i			0.0211195i
$485$	10.1166			0.459370
$486$	5.46463	−	14.5992i	0.247881	−	0.662235i
$487$	−3.87550	+	3.87550i	−0.175616	+	0.175616i	−0.789442	−	0.613826i	$-0.789630\pi$
$487$	−3.87550	+	3.87550i	−0.175616	+	0.175616i	0.613826	+	0.789442i	$0.289630\pi$
$488$		−	9.39935i		−	0.425489i
$489$	15.9260	−	9.91143i	0.720199	−	0.448210i
$490$	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
$495$	3.13668	+	9.21844i	0.140983	+	0.414338i
$496$	−5.20171	−	5.20171i	−0.233563	−	0.233563i
$497$		−	0.507616i		−	0.0227697i
$498$	−9.21777	+	5.73660i	−0.413058	+	0.257063i
$499$	−13.8728	−	13.8728i	−0.621031	−	0.621031i	0.324764	−	0.945795i	$-0.394715\pi$
$499$	−13.8728	−	13.8728i	−0.621031	−	0.621031i	−0.945795	+	0.324764i	$0.894715\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$	−25.9522	+	16.1511i	−1.15946	+	0.721579i
$502$			3.67514i			0.164029i
$503$	−11.0121	−	11.0121i	−0.491005	−	0.491005i	0.417618	−	0.908623i	$-0.362865\pi$
$503$	−11.0121	−	11.0121i	−0.491005	−	0.491005i	−0.908623	+	0.417618i	$0.862865\pi$
$504$	0.844338	+	2.48144i	0.0376098	+	0.110532i
$505$	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	$-0.559825\pi$
$509$	−8.43066			−0.373683			−0.186841	+	0.982390i	$0.559825\pi$
$510$	−5.57183	+	3.46758i	−0.246725	+	0.153547i
$511$		−	9.65467i		−	0.427098i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.63505	−	16.4182i	−0.0721890	−	0.724880i
$514$	18.5313			0.817381
$515$		−	6.79409i		−	0.299383i
$516$	16.7708	−	10.4372i	0.738292	−	0.459470i
$517$			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	$-0.428351\pi$
$521$	10.1891			0.446392			0.223196	+	0.974774i	$0.428351\pi$
$522$	−0.0219792	+	0.0446509i	−0.000962005	+	0.00195432i
$523$	21.5024	−	21.5024i	0.940233	−	0.940233i	−0.0580790	−	0.998312i	$-0.518498\pi$
$523$	21.5024	−	21.5024i	0.940233	−	0.940233i	0.998312	+	0.0580790i	$0.0184975\pi$
$524$	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
$531$	−10.8790	−	31.9724i	−0.472108	−	1.38748i
$532$	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
$537$	12.9567	+	20.8193i	0.559124	+	0.898420i
$538$	−8.86564	−	8.86564i	−0.382225	−	0.382225i
$539$	20.2430			0.871926
$540$	−0.514925	−	5.17058i	−0.0221588	−	0.222506i
$541$	−14.4179	+	14.4179i	−0.619875	+	0.619875i	−0.945499	−	0.325625i	$-0.894425\pi$
$541$	−14.4179	+	14.4179i	−0.619875	+	0.619875i	0.325625	+	0.945499i	$0.394425\pi$
$542$	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	0.266870	−	0.963732i	$-0.414010\pi$
$547$	−16.2982	−	16.2982i	−0.696862	−	0.696862i	−0.963732	+	0.266870i	$0.914010\pi$
$548$	−21.3281			−0.911089
$549$	9.08329	+	26.6950i	0.387665	+	1.13932i
$550$	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
$555$	8.27070	+	6.52652i	0.351072	+	0.277035i
$556$	14.6182			0.619951
$557$	−13.8613	+	13.8613i	−0.587322	+	0.587322i	−0.936905	−	0.349583i	$-0.886323\pi$
$557$	−13.8613	+	13.8613i	−0.587322	+	0.587322i	0.349583	+	0.936905i	$0.386323\pi$
$558$	19.8001	+	9.74653i	0.838206	+	0.412603i
$559$		−	45.1702i		−	1.91049i
$560$	0.617812	+	0.617812i	0.0261073	+	0.0261073i
$561$	−18.0852	+	11.2552i	−0.763557	+	0.475193i
$562$	23.2935			0.982575
$563$	9.05310	+	9.05310i	0.381543	+	0.381543i	0.871658	−	0.490115i	$-0.163045\pi$
$563$	9.05310	+	9.05310i	0.381543	+	0.381543i	−0.490115	+	0.871658i	$0.663045\pi$
$564$	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	$-0.520051\pi$
$569$	22.3048	−	22.3048i	0.935066	−	0.935066i	0.998017	+	0.0629509i	$0.0200512\pi$
$570$	−2.90596	−	4.66939i	−0.121717	−	0.195579i
$571$	−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
$573$	13.7192	−	8.53800i	0.573126	−	0.356680i
$574$	−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	−0.959704	−	0.281014i	$-0.909329\pi$
$577$	−16.3027	+	16.3027i	−0.678689	+	0.678689i	0.281014	+	0.959704i	$0.409329\pi$
$578$	1.86925	+	1.86925i	0.0777505	+	0.0777505i
$579$	−0.933983	−	1.50076i	−0.0388150	−	0.0623693i
$580$			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	$-0.629933\pi$
$587$	12.6200	−	12.6200i	0.520882	−	0.520882i	0.917838	+	0.396956i	$0.129933\pi$
$588$	−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	$0.853598\pi$
$594$	−1.67136	−	16.7828i	−0.0685765	−	0.688606i
$595$			3.31051i			0.135718i
$596$	4.27966			0.175302
$597$	31.8842	−	19.8429i	1.30493	−	0.812114i
$598$	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	$-0.00473527\pi$
$600$	−0.915172	−	1.47053i	−0.0373618	−	0.0600341i
$601$	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
$606$	−9.03269	−	14.5140i	−0.366928	−	0.589592i
$607$	18.6181	+	18.6181i	0.755684	+	0.755684i	0.975534	−	0.219850i	$-0.0705567\pi$
$607$	18.6181	+	18.6181i	0.755684	+	0.755684i	−0.219850	+	0.975534i	$0.570557\pi$
$608$		−	3.17531i		−	0.128776i
$609$	0.0132647	+	0.0213142i	0.000537513	+	0.000863694i
$610$	6.64635	+	6.64635i	0.269103	+	0.269103i
$611$	−8.59641	−	8.59641i	−0.347774	−	0.347774i
$612$	10.7611	−	3.66159i	0.434991	−	0.148011i
$613$		−	34.7946i		−	1.40534i	−0.711516	−	0.702670i	$-0.751991\pi$
$613$		−	34.7946i		−	1.40534i	0.711516	−	0.702670i	$-0.248009\pi$
$614$	3.40933	+	3.40933i	0.137589	+	0.137589i
$615$	17.8110	−	11.0845i	0.718207	−	0.446970i
$616$	2.00531	+	2.00531i	0.0807962	+	0.0807962i
$617$	9.78568			0.393957			0.196978	−	0.980408i	$-0.436887\pi$
$617$	9.78568			0.393957			0.196978	+	0.980408i	$0.436887\pi$
$618$	−2.66802	+	11.4613i	−0.107324	+	0.461040i
$619$		−	36.0295i		−	1.44815i	−0.689723	−	0.724074i	$-0.742268\pi$
$619$		−	36.0295i		−	1.44815i	0.689723	−	0.724074i	$-0.257732\pi$
$620$	7.35632			0.295437
$621$	−28.7988	+	2.86800i	−1.15566	+	0.115089i
$622$			9.12683i			0.365953i
$623$	−5.67411	+	5.67411i	−0.227328	+	0.227328i
$624$	−3.62473	−	5.82434i	−0.145105	−	0.233160i
$625$	−1.00000			−0.0400000
$626$		−	33.4312i		−	1.33618i
$627$	−9.43222	−	15.1560i	−0.376687	−	0.605273i
$628$			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	0.691048	−	0.722809i	$-0.257149\pi$
$631$	−0.797835	−	0.797835i	−0.0317613	−	0.0317613i	−0.722809	+	0.691048i	$0.757149\pi$
$632$	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	$-0.00195226\pi$
$642$	21.6474	−	13.4721i	0.854355	−	0.531701i
$643$	24.4682	+	24.4682i	0.964931	+	0.964931i	0.999406	−	0.0344744i	$-0.0109757\pi$
$643$	24.4682	+	24.4682i	0.964931	+	0.964931i	−0.0344744	+	0.999406i	$0.510976\pi$
$644$	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	$-0.713205\pi$
$647$	4.14891	−	4.14891i	0.163111	−	0.163111i	0.783943	+	0.620833i	$0.213205\pi$
$648$	−1.16182	+	8.92469i	−0.0456406	+	0.350595i
$649$	−25.8377	−	25.8377i	−1.01422	−	1.01422i
$650$	−3.96070			−0.155352
$651$	9.45161	−	5.88213i	0.370438	−	0.230539i
$652$	−7.65805	+	7.65805i	−0.299912	+	0.299912i
$653$	−6.38197	+	6.38197i	−0.249746	+	0.249746i	−0.820866	−	0.571120i	$-0.806509\pi$
$653$	−6.38197	+	6.38197i	−0.249746	+	0.249746i	0.571120	+	0.820866i	$0.306509\pi$
$654$	−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	$-0.790419\pi$
$659$	−40.6095			−1.58192			−0.790960	+	0.611867i	$0.790419\pi$
$660$	−2.97049	−	4.77308i	−0.115626	−	0.185792i
$661$	18.2484	+	18.2484i	0.709782	+	0.709782i	0.966489	−	0.256707i	$-0.0826375\pi$
$661$	18.2484	+	18.2484i	0.709782	+	0.709782i	−0.256707	+	0.966489i	$0.582637\pi$
$662$		−	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
$666$	−11.3893	−	14.2578i	−0.441326	−	0.552478i
$667$	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
$672$	−0.799603	−	1.28483i	−0.0308453	−	0.0495633i
$673$	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	$-0.368872\pi$
$677$	20.8361			0.800797			0.400399	+	0.916341i	$0.368872\pi$
$678$	−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
$681$	35.2362	−	21.9290i	1.35025	−	0.840320i
$682$	23.8773			0.914310
$683$	28.5744	+	28.5744i	1.09337	+	1.09337i	0.995166	+	0.0982022i	$0.0313092\pi$
$683$	28.5744	+	28.5744i	1.09337	+	1.09337i	0.0982022	+	0.995166i	$0.468691\pi$
$684$	3.06854	+	9.01817i	0.117328	+	0.344818i
$685$	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
$690$	−8.19049	+	5.09728i	−0.311807	+	0.194050i
$691$			34.9094i			1.32802i	0.747725	+	0.664008i	$0.231146\pi$
$691$			34.9094i			1.32802i	−0.747725	+	0.664008i	$0.768854\pi$
$692$			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	$-0.201030\pi$
$701$	5.73772	+	5.73772i	0.216711	+	0.216711i	−0.590400	+	0.807111i	$0.701030\pi$
$702$	15.9230	+	13.0388i	0.600977	+	0.492118i
$703$	−17.4803	−	8.21559i	−0.659281	−	0.309857i
$704$		−	3.24582i		−	0.122332i
$705$	2.80907	+	4.51371i	0.105796	+	0.169996i
$706$		−	2.49504i		−	0.0939022i
$707$	−8.62354			−0.324322
$708$	10.3026	+	16.5545i	0.387195	+	0.622158i
$709$	−18.6081	+	18.6081i	−0.698842	+	0.698842i	−0.964161	−	0.265319i	$-0.914523\pi$
$709$	−18.6081	+	18.6081i	−0.698842	+	0.698842i	0.265319	+	0.964161i	$0.414523\pi$
$710$		−	0.580983i		−	0.0218039i
$711$	−3.06685	+	1.04353i	−0.115016	+	0.0391354i
$712$	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
$717$	−35.5084	+	22.0984i	−1.32609	+	0.825279i
$718$	−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	$-0.113182\pi$
$720$	0.966374	+	2.84009i	0.0360146	+	0.105844i
$721$	4.19747	+	4.19747i	0.156322	+	0.156322i
$722$	−6.30556	−	6.30556i	−0.234669	−	0.234669i
$723$	−4.91684	−	7.90055i	−0.182859	−	0.293825i
$724$			22.6754i			0.842724i
$725$	−0.0117303	−	0.0117303i	−0.000435652	−	0.000435652i
$726$	0.425216	+	0.683252i	0.0157813	+	0.0253579i
$727$	20.9335	+	20.9335i	0.776381	+	0.776381i	0.979213	−	0.202833i	$-0.0650147\pi$
$727$	20.9335	+	20.9335i	0.776381	+	0.776381i	−0.202833	+	0.979213i	$0.565015\pi$
$728$	−3.46054			−0.128256
$729$	−5.32492	−	26.4697i	−0.197219	−	0.980359i
$730$		−	11.0501i		−	0.408983i
$731$	−43.2119			−1.59825
$732$	−8.60203	−	13.8220i	−0.317940	−	0.510877i
$733$			45.5805i			1.68355i	0.539825	+	0.841777i	$0.318490\pi$
$733$			45.5805i			1.68355i	−0.539825	+	0.841777i	$0.681510\pi$
$734$	−6.94207	+	6.94207i	−0.256237	+	0.256237i
$735$	9.17113	−	5.70758i	0.338282	−	0.210527i
$736$	−5.56975			−0.205304
$737$		−	25.1249i		−	0.925489i
$738$	−34.3990	+	11.7047i	−1.26624	+	0.430854i
$739$		−	30.7839i		−	1.13240i	−0.824267	−	0.566202i	$-0.808412\pi$
$739$		−	30.7839i		−	1.13240i	0.824267	−	0.566202i	$-0.191588\pi$
$740$	−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	$-0.467797\pi$
$743$	5.50584			0.201990			0.100995	+	0.994887i	$0.467797\pi$
$744$	−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	$-0.692133\pi$
$751$		−	45.1238i		−	1.64659i	0.567613	−	0.823295i	$-0.307867\pi$
$752$			3.06944i			0.111931i
$753$	3.36339	+	5.40440i	0.122569	+	0.196947i
$754$	−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	−0.402080	−	0.915605i	$-0.631713\pi$
$757$	14.1289	−	14.1289i	0.513524	−	0.513524i	0.915605	+	0.402080i	$0.131713\pi$
$758$	4.21515	−	4.21515i	0.153101	−	0.153101i
$759$	−26.5849	+	16.5449i	−0.964970	+	0.600541i
$760$	2.24528	+	2.24528i	0.0814450	+	0.0814450i
$761$	0.980959			0.0355597			0.0177799	−	0.999842i	$-0.494340\pi$
$761$	0.980959			0.0355597			0.0177799	+	0.999842i	$0.494340\pi$
$762$	0.868444	+	1.39545i	0.0314604	+	0.0505517i
$763$	−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	0.606968	−	0.794726i	$-0.292385\pi$
$769$	−5.20667	−	5.20667i	−0.187757	−	0.187757i	−0.794726	+	0.606968i	$0.792385\pi$
$770$	−2.83593			−0.102200
$771$	27.2509	−	16.9594i	0.981416	−	0.610776i
$772$	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
$777$	−9.14190	+	1.07758i	−0.327964	+	0.0386579i
$778$	−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
$783$	0.00854215	+	0.0857753i	0.000305272	+	0.00306536i
$784$	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
$792$	3.13668	+	9.21844i	0.111457	+	0.327563i
$793$	−37.2281			−1.32201
$794$	1.62045	+	1.62045i	0.0575075	+	0.0575075i
$795$	8.39867	+	13.4953i	0.297870	+	0.478628i
$796$	−15.3316	+	15.3316i	−0.543413	+	0.543413i
$797$	−10.4496	+	10.4496i	−0.370146	+	0.370146i	−0.867530	−	0.497385i	$-0.834294\pi$
$797$	−10.4496	+	10.4496i	−0.370146	+	0.370146i	0.497385	+	0.867530i	$0.334294\pi$
$798$	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
$801$	−26.0840	+	8.87537i	−0.921632	+	0.313596i
$802$			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	$-0.861939\pi$
$809$	−13.8558	+	13.8558i	−0.487143	+	0.487143i	0.420260	+	0.907404i	$0.361939\pi$
$810$	−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
$816$	−5.57183	+	3.46758i	−0.195053	+	0.121390i
$817$		−	36.2131i		−	1.26693i
$818$	−3.90020			−0.136367
$819$	9.82825	−	3.34417i	0.343427	−	0.116855i
$820$	−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	$0.814645\pi$
$822$	−31.3635	+	19.5188i	−1.09393	+	0.680798i
$823$	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	$-0.0951030\pi$
$827$	19.0188	+	19.0188i	0.661348	+	0.661348i	−0.294350	+	0.955698i	$0.595103\pi$
$828$	15.8186	−	5.38246i	0.549734	−	0.187053i
$829$	38.2891	+	38.2891i	1.32984	+	1.32984i	0.905509	+	0.424328i	$0.139490\pi$
$829$	38.2891	+	38.2891i	1.32984	+	1.32984i	0.424328	+	0.905509i	$0.360510\pi$
$830$			6.26833i			0.217577i
$831$	−28.5340	+	17.7579i	−0.989834	+	0.616015i
$832$	2.80064	+	2.80064i	0.0970948	+	0.0970948i
$833$	16.7093	+	16.7093i	0.578943	+	0.578943i
$834$	21.4965	−	13.3782i	0.744364	−	0.463249i
$835$			17.6482i			0.610740i
$836$	7.28779	+	7.28779i	0.252054	+	0.252054i
$837$	38.0364	−	3.78795i	1.31473	−	0.130931i
$838$	−6.97893	−	6.97893i	−0.241083	−	0.241083i
$839$	28.1427			0.971595			0.485797	−	0.874071i	$-0.338529\pi$
$839$	28.1427			0.971595			0.485797	+	0.874071i	$0.338529\pi$
$840$	1.47392	+	0.343107i	0.0508549	+	0.0118383i
$841$			28.9997i			0.999991i
$842$	7.91851			0.272890
$843$	34.2537	−	21.3175i	1.17976	−	0.734215i
$844$			14.8756i			0.512039i
$845$	1.90012	−	1.90012i	0.0653662	−	0.0653662i
$846$	−2.96623	−	8.71750i	−0.101981	−	0.299714i
$847$	0.405955			0.0139488
$848$			9.17714i			0.315144i
$849$	0.951362	−	0.592072i	0.0326506	−	0.0203199i
$850$			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	0.918639	−	0.395098i	$-0.129289\pi$
$853$	15.2906	+	15.2906i	0.523541	+	0.523541i	−0.395098	+	0.918639i	$0.629289\pi$
$854$	−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	$-0.340191\pi$
$857$	−11.5743	−	11.5743i	−0.395369	−	0.395369i	−0.876596	+	0.481227i	$0.840191\pi$
$858$	21.6870	+	5.04842i	0.740381	+	0.172350i
$859$	9.96139	−	9.96139i	0.339878	−	0.339878i	−0.516443	−	0.856321i	$-0.672744\pi$
$859$	9.96139	−	9.96139i	0.339878	−	0.339878i	0.856321	+	0.516443i	$0.172744\pi$
$860$		−	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	$0.793291\pi$
$864$	−0.514925	−	5.17058i	−0.0175181	−	0.175907i
$865$	−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
$870$	0.0151819	+	0.0243948i	0.000514715	+	0.000827061i
$871$	21.6789	+	21.6789i	0.734562	+	0.734562i
$872$	18.1836			0.615776
$873$	−28.7320	+	9.77640i	−0.972431	+	0.330881i
$874$	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	$-0.466548\pi$
$881$	6.22716			0.209798			0.104899	+	0.994483i	$0.466548\pi$
$882$	−17.7126	+	6.02690i	−0.596413	+	0.202936i
$883$	−23.8218	−	23.8218i	−0.801669	−	0.801669i	0.181687	−	0.983356i	$-0.441844\pi$
$883$	−23.8218	−	23.8218i	−0.801669	−	0.801669i	−0.983356	+	0.181687i	$0.941844\pi$
$884$			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	$-0.240752\pi$
$887$	43.3246			1.45470			0.727350	+	0.686267i	$0.240752\pi$
$888$	8.27070	+	6.52652i	0.277547	+	0.219016i
$889$	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
$894$	6.29338	−	3.91663i	0.210482	−	0.130992i
$895$	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
$903$	−9.11913	−	14.6529i	−0.303466	−	0.487619i
$904$	4.38435			0.145821
$905$	−16.0339	−	16.0339i	−0.532985	−	0.532985i
$906$	−23.9219	+	14.8876i	−0.794752	+	0.494608i
$907$	−12.4807	+	12.4807i	−0.414413	+	0.414413i	−0.883273	−	0.468859i	$-0.844665\pi$
$907$	−12.4807	+	12.4807i	−0.414413	+	0.414413i	0.468859	+	0.883273i	$0.344665\pi$
$908$	−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	0.979118	+	0.203291i	$0.0651638\pi$
$911$	35.6884	+	35.6884i	1.18241	+	1.18241i	0.203291	+	0.979118i	$0.434836\pi$
$912$	−2.90596	−	4.66939i	−0.0962258	−	0.154619i
$913$			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	0.857544	−	0.514411i	$-0.171989\pi$
$919$	10.4021	+	10.4021i	0.343134	+	0.343134i	−0.514411	+	0.857544i	$0.671989\pi$
$920$	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
$927$	6.56563	+	19.2958i	0.215644	+	0.633758i
$928$			0.0165891i			0.000544565i
$929$	−16.9964			−0.557632			−0.278816	−	0.960344i	$-0.589942\pi$
$929$	−16.9964			−0.557632			−0.278816	+	0.960344i	$0.589942\pi$
$930$	10.8177	−	6.73230i	0.354726	−	0.220761i
$931$	−14.0030	+	14.0030i	−0.458929	+	0.458929i
$932$			4.46090i			0.146122i
$933$	8.35263	+	13.4213i	0.273453	+	0.439393i
$934$	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
$939$	−30.5953	−	49.1615i	−0.998439	−	1.60433i
$940$	−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	$0.914913\pi$
$942$	16.8935	+	27.1450i	0.550419	+	0.884432i
$943$	47.7017	+	47.7017i	1.55338	+	1.55338i
$944$	−7.96028	−	7.96028i	−0.259085	−	0.259085i
$945$	−4.51762	+	0.449899i	−0.146958	+	0.0146352i
$946$		−	37.0172i		−	1.20353i
$947$	−30.9113	−	30.9113i	−1.00448	−	1.00448i	−0.999990	−	0.00449357i	$-0.998570\pi$
$947$	−30.9113	−	30.9113i	−1.00448	−	1.00448i	−0.00449357	−	0.999990i	$-0.501430\pi$
$948$	1.58794	−	0.988240i	0.0515738	−	0.0320965i
$949$	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	$-0.0550735\pi$
$953$	60.8196			1.97014			0.985070	+	0.172157i	$0.0550735\pi$
$954$	−8.86855	−	26.0639i	−0.287130	−	0.843851i
$955$		−	9.32939i		−	0.301892i
$956$	17.0743	−	17.0743i	0.552222	−	0.552222i
$957$	0.0492778	+	0.0791812i	0.00159292	+	0.00255957i
$958$	−13.7325			−0.443677
$959$			18.6347i			0.601746i
$960$	−0.915172	−	1.47053i	−0.0295371	−	0.0474612i
$961$			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	−0.0337345	+	0.999431i	$0.510740\pi$
$967$	−32.1280	+	32.1280i	−1.03317	+	1.03317i	−0.999431	+	0.0337345i	$0.989260\pi$
$968$	−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
$975$	−5.82434	+	3.62473i	−0.186528	+	0.116084i
$976$	6.64635	+	6.64635i	0.212744	+	0.212744i
$977$	−20.5956	+	20.5956i	−0.658912	+	0.658912i	−0.955123	−	0.296211i	$-0.904277\pi$
$977$	−20.5956	+	20.5956i	−0.658912	+	0.658912i	0.296211	+	0.955123i	$0.404277\pi$
$978$	−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
$981$	−51.6432	+	17.5722i	−1.64884	+	0.561037i
$982$	−26.5826	−	26.5826i	−0.848284	−	0.848284i
$983$	−5.10058			−0.162683			−0.0813416	−	0.996686i	$-0.525920\pi$
$983$	−5.10058			−0.162683			−0.0813416	+	0.996686i	$0.525920\pi$
$984$	17.8110	−	11.0845i	0.567793	−	0.353361i
$985$	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	−0.978556	−	0.205980i	$-0.933962\pi$
$991$	−37.2894	−	37.2894i	−1.18454	−	1.18454i	−0.205980	−	0.978556i	$-0.566038\pi$
$992$	7.35632			0.233563
$993$	−20.6072	−	33.1123i	−0.653949	−	1.05079i
$994$	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	−0.950658	−	0.310242i	$-0.899590\pi$
$997$	−20.2213	+	20.2213i	−0.640416	+	0.640416i	0.310242	+	0.950658i	$0.399590\pi$
$998$	19.6191			0.621031
$999$	−29.7966	−	10.5433i	−0.942723	−	0.333576i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.2	✓	40	111.80	even	4	inner
1110.2.u.f.191.14	yes	40	37.6	odd	4	inner
1110.2.u.f.401.2	yes	40	1.1	even	1	trivial
1110.2.u.f.401.14	yes	40	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.392697 + 1.68695i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.915172 - 1.47053i) q^{6} -0.873718 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.69158 - 1.32492i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.392697 + 1.68695i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.915172 - 1.47053i) 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} +(-1.47053 + 0.915172i) q^{15} -1.00000 q^{16} +(-2.67922 - 2.67922i) q^{17} +(2.84009 - 0.966374i) 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} +(-1.47053 + 0.915172i) 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} +(3.62473 + 5.82434i) q^{39} +1.00000i q^{40} -12.1119 q^{41} +(0.799603 + 1.28483i) q^{42} +(8.06425 - 8.06425i) q^{43} +3.24582i q^{44} +(-0.966374 - 2.84009i) 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} +(5.57183 - 3.46758i) q^{51} +(-2.80064 - 2.80064i) q^{52} -9.17714i q^{53} +(0.514925 + 5.17058i) q^{54} +(-2.29514 - 2.29514i) q^{55} +(-0.617812 - 0.617812i) q^{56} +(2.90596 + 4.66939i) q^{57} -0.0165891i q^{58} +(7.96028 + 7.96028i) q^{59} +(0.915172 + 1.47053i) 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} +(2.97049 + 4.77308i) q^{66} +7.74070i q^{67} +(-2.67922 + 2.67922i) q^{68} +(8.19049 - 5.09728i) q^{69} +0.873718 q^{70} +0.580983i q^{71} +(-0.966374 - 2.84009i) 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} +(-0.0151819 - 0.0243948i) 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} +(-10.8177 + 6.73230i) q^{93} +(2.17042 + 2.17042i) q^{94} +3.17531 q^{95} +(0.915172 + 1.47053i) 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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