LMFDB - Embedded newform 1110.2.u.f.191.12

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			191.12
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.f.401.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.912090 - 1.47244i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.68612 - 0.396230i) q^{6} -2.79858 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33618 - 2.68600i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.912090 - 1.47244i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.68612 - 0.396230i) q^{6} -2.79858 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33618 - 2.68600i) q^{9} -1.00000 q^{10} -4.26033 q^{11} +(1.47244 + 0.912090i) q^{12} +(1.77526 + 1.77526i) q^{13} +(-1.97890 - 1.97890i) q^{14} +(0.396230 + 1.68612i) q^{15} -1.00000 q^{16} +(-5.48863 + 5.48863i) q^{17} +(0.954468 - 2.84412i) q^{18} +(0.485369 + 0.485369i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-2.55256 + 4.12076i) q^{21} +(-3.01251 - 3.01251i) q^{22} +(-1.36769 + 1.36769i) q^{23} +(0.396230 + 1.68612i) q^{24} -1.00000i q^{25} +2.51060i q^{26} +(-5.17371 - 0.482424i) q^{27} -2.79858i q^{28} +(7.02801 + 7.02801i) q^{29} +(-0.912090 + 1.47244i) q^{30} +(-3.79775 + 3.79775i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.88581 + 6.27310i) q^{33} -7.76210 q^{34} +(1.97890 - 1.97890i) q^{35} +(2.68600 - 1.33618i) q^{36} +(2.97703 - 5.30446i) q^{37} +0.686416i q^{38} +(4.23317 - 0.994773i) q^{39} -1.00000i q^{40} -7.88519 q^{41} +(-4.71875 + 1.10888i) q^{42} +(-3.72198 - 3.72198i) q^{43} -4.26033i q^{44} +(2.84412 + 0.954468i) q^{45} -1.93421 q^{46} -2.41387i q^{47} +(-0.912090 + 1.47244i) q^{48} +0.832067 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.07558 + 13.0878i) q^{51} +(-1.77526 + 1.77526i) q^{52} +2.32891i q^{53} +(-3.31724 - 3.99949i) q^{54} +(3.01251 - 3.01251i) q^{55} +(1.97890 - 1.97890i) q^{56} +(1.15738 - 0.271978i) q^{57} +9.93910i q^{58} +(4.84986 - 4.84986i) q^{59} +(-1.68612 + 0.396230i) q^{60} +(3.08764 - 3.08764i) q^{61} -5.37083 q^{62} +(3.73942 + 7.51700i) q^{63} -1.00000i q^{64} -2.51060 q^{65} +(-7.18343 + 1.68807i) q^{66} +0.631981i q^{67} +(-5.48863 - 5.48863i) q^{68} +(0.766391 + 3.26131i) q^{69} +2.79858 q^{70} -12.9487i q^{71} +(2.84412 + 0.954468i) q^{72} -8.24407i q^{73} +(5.85590 - 1.64574i) q^{74} +(-1.47244 - 0.912090i) q^{75} +(-0.485369 + 0.485369i) q^{76} +11.9229 q^{77} +(3.69671 + 2.28989i) q^{78} +(-4.17614 - 4.17614i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-5.42923 + 7.17798i) q^{81} +(-5.57567 - 5.57567i) q^{82} +12.6041i q^{83} +(-4.12076 - 2.55256i) q^{84} -7.76210i q^{85} -5.26367i q^{86} +(16.7585 - 3.93817i) q^{87} +(3.01251 - 3.01251i) q^{88} +(1.13309 + 1.13309i) q^{89} +(1.33618 + 2.68600i) q^{90} +(-4.96821 - 4.96821i) q^{91} +(-1.36769 - 1.36769i) q^{92} +(2.12808 + 9.05586i) q^{93} +(1.70686 - 1.70686i) q^{94} -0.686416 q^{95} +(-1.68612 + 0.396230i) q^{96} +(3.82220 + 3.82220i) q^{97} +(0.588360 + 0.588360i) q^{98} +(5.69258 + 11.4433i) 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
$3$	0.912090	−	1.47244i	0.526596	−	0.850116i
$3$	0.912090	−	1.47244i	0.526596	−	0.850116i
$4$			1.00000i			0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	1.68612	−	0.396230i	0.688356	−	0.161760i
$7$	−2.79858			−1.05776			−0.528882	−	0.848695i	$-0.677389\pi$
$7$	−2.79858			−1.05776			−0.528882	+	0.848695i	$0.677389\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.33618	−	2.68600i	−0.445394	−	0.895335i
$10$	−1.00000			−0.316228
$11$	−4.26033			−1.28454			−0.642269	−	0.766479i	$-0.722007\pi$
$11$	−4.26033			−1.28454			−0.642269	+	0.766479i	$0.722007\pi$
$12$	1.47244	+	0.912090i	0.425058	+	0.263298i
$13$	1.77526	+	1.77526i	0.492368	+	0.492368i	0.909052	−	0.416683i	$-0.136808\pi$
$13$	1.77526	+	1.77526i	0.492368	+	0.492368i	−0.416683	+	0.909052i	$0.636808\pi$
$14$	−1.97890	−	1.97890i	−0.528882	−	0.528882i
$15$	0.396230	+	1.68612i	0.102306	+	0.435354i
$16$	−1.00000			−0.250000
$17$	−5.48863	+	5.48863i	−1.33119	+	1.33119i	−0.426882	+	0.904307i	$0.640388\pi$
$17$	−5.48863	+	5.48863i	−1.33119	+	1.33119i	−0.904307	+	0.426882i	$0.859612\pi$
$18$	0.954468	−	2.84412i	0.224970	−	0.670364i
$19$	0.485369	+	0.485369i	0.111351	+	0.111351i	0.760587	−	0.649236i	$-0.224911\pi$
$19$	0.485369	+	0.485369i	0.111351	+	0.111351i	−0.649236	+	0.760587i	$0.724911\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	−2.55256	+	4.12076i	−0.557014	+	0.899223i
$22$	−3.01251	−	3.01251i	−0.642269	−	0.642269i
$23$	−1.36769	+	1.36769i	−0.285184	+	0.285184i	−0.835172	−	0.549989i	$-0.814632\pi$
$23$	−1.36769	+	1.36769i	−0.285184	+	0.285184i	0.549989	+	0.835172i	$0.314632\pi$
$24$	0.396230	+	1.68612i	0.0808801	+	0.344178i
$25$		−	1.00000i		−	0.200000i
$26$			2.51060i			0.492368i
$27$	−5.17371	−	0.482424i	−0.995681	−	0.0928426i
$28$		−	2.79858i		−	0.528882i
$29$	7.02801	+	7.02801i	1.30507	+	1.30507i	0.924929	+	0.380139i	$0.124124\pi$
$29$	7.02801	+	7.02801i	1.30507	+	1.30507i	0.380139	+	0.924929i	$0.375876\pi$
$30$	−0.912090	+	1.47244i	−0.166524	+	0.268830i
$31$	−3.79775	+	3.79775i	−0.682096	+	0.682096i	−0.960472	−	0.278376i	$-0.910204\pi$
$31$	−3.79775	+	3.79775i	−0.682096	+	0.682096i	0.278376	+	0.960472i	$0.410204\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.88581	+	6.27310i	−0.676432	+	1.09201i
$34$	−7.76210			−1.33119
$35$	1.97890	−	1.97890i	0.334495	−	0.334495i
$36$	2.68600	−	1.33618i	0.447667	−	0.222697i
$37$	2.97703	−	5.30446i	0.489421	−	0.872048i
$37$	2.97703	−	5.30446i	0.489421	−	0.872048i
$38$			0.686416i			0.111351i
$39$	4.23317	−	0.994773i	0.677849	−	0.159291i
$40$		−	1.00000i		−	0.158114i
$41$	−7.88519			−1.23146			−0.615730	−	0.787957i	$-0.711139\pi$
$41$	−7.88519			−1.23146			−0.615730	+	0.787957i	$0.711139\pi$
$42$	−4.71875	+	1.10888i	−0.728119	+	0.171104i
$43$	−3.72198	−	3.72198i	−0.567596	−	0.567596i	0.363858	−	0.931454i	$-0.381459\pi$
$43$	−3.72198	−	3.72198i	−0.567596	−	0.567596i	−0.931454	+	0.363858i	$0.881459\pi$
$44$		−	4.26033i		−	0.642269i
$45$	2.84412	+	0.954468i	0.423976	+	0.142284i
$46$	−1.93421			−0.285184
$47$		−	2.41387i		−	0.352099i	−0.984381	−	0.176050i	$-0.943668\pi$
$47$		−	2.41387i		−	0.352099i	0.984381	−	0.176050i	$-0.0563319\pi$
$48$	−0.912090	+	1.47244i	−0.131649	+	0.212529i
$49$	0.832067			0.118867
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	3.07558	+	13.0878i	0.430667	+	1.83266i
$52$	−1.77526	+	1.77526i	−0.246184	+	0.246184i
$53$			2.32891i			0.319900i	0.987125	+	0.159950i	$0.0511334\pi$
$53$			2.32891i			0.319900i	−0.987125	+	0.159950i	$0.948867\pi$
$54$	−3.31724	−	3.99949i	−0.451419	−	0.544262i
$55$	3.01251	−	3.01251i	0.406207	−	0.406207i
$56$	1.97890	−	1.97890i	0.264441	−	0.264441i
$57$	1.15738	−	0.271978i	0.153299	−	0.0360244i
$58$			9.93910i			1.30507i
$59$	4.84986	−	4.84986i	0.631398	−	0.631398i	−0.317020	−	0.948419i	$-0.602682\pi$
$59$	4.84986	−	4.84986i	0.631398	−	0.631398i	0.948419	+	0.317020i	$0.102682\pi$
$60$	−1.68612	+	0.396230i	−0.217677	+	0.0511531i
$61$	3.08764	−	3.08764i	0.395332	−	0.395332i	−0.481251	−	0.876583i	$-0.659817\pi$
$61$	3.08764	−	3.08764i	0.395332	−	0.395332i	0.876583	+	0.481251i	$0.159817\pi$
$62$	−5.37083			−0.682096
$63$	3.73942	+	7.51700i	0.471122	+	0.947054i
$64$		−	1.00000i		−	0.125000i
$65$	−2.51060			−0.311401
$66$	−7.18343	+	1.68807i	−0.884219	+	0.207787i
$67$			0.631981i			0.0772088i	0.999255	+	0.0386044i	$0.0122912\pi$
$67$			0.631981i			0.0772088i	−0.999255	+	0.0386044i	$0.987709\pi$
$68$	−5.48863	−	5.48863i	−0.665595	−	0.665595i
$69$	0.766391	+	3.26131i	0.0922627	+	0.392615i
$70$	2.79858			0.334495
$71$		−	12.9487i		−	1.53672i	−0.640015	−	0.768362i	$-0.721072\pi$
$71$		−	12.9487i		−	1.53672i	0.640015	−	0.768362i	$-0.278928\pi$
$72$	2.84412	+	0.954468i	0.335182	+	0.112485i
$73$		−	8.24407i		−	0.964895i	−0.875925	−	0.482448i	$-0.839748\pi$
$73$		−	8.24407i		−	0.964895i	0.875925	−	0.482448i	$-0.160252\pi$
$74$	5.85590	−	1.64574i	0.680734	−	0.191313i
$75$	−1.47244	−	0.912090i	−0.170023	−	0.105319i
$76$	−0.485369	+	0.485369i	−0.0556757	+	0.0556757i
$77$	11.9229			1.35874
$78$	3.69671	+	2.28989i	0.418570	+	0.259279i
$79$	−4.17614	−	4.17614i	−0.469852	−	0.469852i	0.432014	−	0.901867i	$-0.357803\pi$
$79$	−4.17614	−	4.17614i	−0.469852	−	0.469852i	−0.901867	+	0.432014i	$0.857803\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	−5.42923	+	7.17798i	−0.603248	+	0.797554i
$82$	−5.57567	−	5.57567i	−0.615730	−	0.615730i
$83$			12.6041i			1.38348i	0.722147	+	0.691740i	$0.243156\pi$
$83$			12.6041i			1.38348i	−0.722147	+	0.691740i	$0.756844\pi$
$84$	−4.12076	−	2.55256i	−0.449611	−	0.278507i
$85$		−	7.76210i		−	0.841918i
$86$		−	5.26367i		−	0.567596i
$87$	16.7585	−	3.93817i	1.79670	−	0.422216i
$88$	3.01251	−	3.01251i	0.321135	−	0.321135i
$89$	1.13309	+	1.13309i	0.120107	+	0.120107i	0.764606	−	0.644498i	$-0.222934\pi$
$89$	1.13309	+	1.13309i	0.120107	+	0.120107i	−0.644498	+	0.764606i	$0.722934\pi$
$90$	1.33618	+	2.68600i	0.140846	+	0.283130i
$91$	−4.96821	−	4.96821i	−0.520810	−	0.520810i
$92$	−1.36769	−	1.36769i	−0.142592	−	0.142592i
$93$	2.12808	+	9.05586i	0.220672	+	0.939049i
$94$	1.70686	−	1.70686i	0.176050	−	0.176050i
$95$	−0.686416			−0.0704248
$96$	−1.68612	+	0.396230i	−0.172089	+	0.0404400i
$97$	3.82220	+	3.82220i	0.388086	+	0.388086i	0.874004	−	0.485918i	$-0.161515\pi$
$97$	3.82220	+	3.82220i	0.388086	+	0.388086i	−0.485918	+	0.874004i	$0.661515\pi$
$98$	0.588360	+	0.588360i	0.0594333	+	0.0594333i
$99$	5.69258	+	11.4433i	0.572126	+	1.15009i
$100$	1.00000			0.100000
$101$	−12.5328			−1.24706			−0.623529	−	0.781800i	$-0.714302\pi$
$101$	−12.5328			−1.24706			−0.623529	+	0.781800i	$0.714302\pi$
$102$	−7.07974	+	11.4293i	−0.700998	+	1.13167i
$103$	−3.72362	+	3.72362i	−0.366899	+	0.366899i	−0.866345	−	0.499446i	$-0.833537\pi$
$103$	−3.72362	+	3.72362i	−0.366899	+	0.366899i	0.499446	+	0.866345i	$0.333537\pi$
$104$	−2.51060			−0.246184
$105$	−1.10888	−	4.71875i	−0.108216	−	0.460503i
$106$	−1.64679	+	1.64679i	−0.159950	+	0.159950i
$107$			14.1218i			1.36521i	0.730789	+	0.682603i	$0.239152\pi$
$107$			14.1218i			1.36521i	−0.730789	+	0.682603i	$0.760848\pi$
$108$	0.482424	−	5.17371i	0.0464213	−	0.497840i
$109$	2.78175	+	2.78175i	0.266443	+	0.266443i	0.827665	−	0.561222i	$-0.189669\pi$
$109$	2.78175	+	2.78175i	0.266443	+	0.266443i	−0.561222	+	0.827665i	$0.689669\pi$
$110$	4.26033			0.406207
$111$	−5.09520	−	9.22166i	−0.483615	−	0.875281i
$112$	2.79858			0.264441
$113$	12.0063	+	12.0063i	1.12946	+	1.12946i	0.990265	+	0.139196i	$0.0444517\pi$
$113$	12.0063	+	12.0063i	1.12946	+	1.12946i	0.139196	+	0.990265i	$0.455548\pi$
$114$	1.01071	+	0.626073i	0.0946615	+	0.0586371i
$115$		−	1.93421i		−	0.180366i
$116$	−7.02801	+	7.02801i	−0.652534	+	0.652534i
$117$	2.39628	−	7.14042i	0.221536	−	0.660133i
$118$	6.85874			0.631398
$119$	15.3604	−	15.3604i	1.40809	−	1.40809i
$120$	−1.47244	−	0.912090i	−0.134415	−	0.0832621i
$121$	7.15042			0.650038
$122$	4.36658			0.395332
$123$	−7.19201	+	11.6105i	−0.648481	+	1.04688i
$124$	−3.79775	−	3.79775i	−0.341048	−	0.341048i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−2.67116	+	7.95949i	−0.237966	+	0.709088i
$127$	−13.9419			−1.23715			−0.618573	−	0.785728i	$-0.712289\pi$
$127$	−13.9419			−1.23715			−0.618573	+	0.785728i	$0.712289\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−8.87518	+	2.08562i	−0.781416	+	0.183629i
$130$	−1.77526	−	1.77526i	−0.155701	−	0.155701i
$131$	1.96386	+	1.96386i	0.171583	+	0.171583i	0.787675	−	0.616091i	$-0.211285\pi$
$131$	1.96386	+	1.96386i	0.171583	+	0.171583i	−0.616091	+	0.787675i	$0.711285\pi$
$132$	−6.27310	−	3.88581i	−0.546003	−	0.338216i
$133$	−1.35835	−	1.35835i	−0.117784	−	0.117784i
$134$	−0.446878	+	0.446878i	−0.0386044	+	0.0386044i
$135$	3.99949	−	3.31724i	0.344221	−	0.285503i
$136$		−	7.76210i		−	0.665595i
$137$			6.74701i			0.576436i	0.957565	+	0.288218i	$0.0930627\pi$
$137$			6.74701i			0.576436i	−0.957565	+	0.288218i	$0.906937\pi$
$138$	−1.76417	+	2.84801i	−0.150176	+	0.242439i
$139$		−	17.7822i		−	1.50827i	−0.656720	−	0.754135i	$-0.728057\pi$
$139$		−	17.7822i		−	1.50827i	0.656720	−	0.754135i	$-0.271943\pi$
$140$	1.97890	+	1.97890i	0.167247	+	0.167247i
$141$	−3.55429	−	2.20167i	−0.299325	−	0.185414i
$142$	9.15610	−	9.15610i	0.768362	−	0.768362i
$143$	−7.56319	−	7.56319i	−0.632466	−	0.632466i
$144$	1.33618	+	2.68600i	0.111349	+	0.223834i
$145$	−9.93910			−0.825398
$146$	5.82944	−	5.82944i	0.482448	−	0.482448i
$147$	0.758920	−	1.22517i	0.0625947	−	0.101050i
$148$	5.30446	+	2.97703i	0.436024	+	0.244710i
$149$			2.23999i			0.183507i	0.995782	+	0.0917534i	$0.0292471\pi$
$149$			2.23999i			0.183507i	−0.995782	+	0.0917534i	$0.970753\pi$
$150$	−0.396230	−	1.68612i	−0.0323520	−	0.137671i
$151$			3.40280i			0.276916i	0.990368	+	0.138458i	$0.0442146\pi$
$151$			3.40280i			0.276916i	−0.990368	+	0.138458i	$0.955785\pi$
$152$	−0.686416			−0.0556757
$153$	22.0763	+	7.40867i	1.78476	+	0.598956i
$154$	8.43076	+	8.43076i	0.679370	+	0.679370i
$155$		−	5.37083i		−	0.431395i
$156$	0.994773	+	4.23317i	0.0796456	+	0.338925i
$157$	−14.8138			−1.18227			−0.591134	−	0.806574i	$-0.701319\pi$
$157$	−14.8138			−1.18227			−0.591134	+	0.806574i	$0.701319\pi$
$158$		−	5.90595i		−	0.469852i
$159$	3.42919	+	2.12418i	0.271952	+	0.168458i
$160$	1.00000			0.0790569
$161$	3.82760	−	3.82760i	0.301657	−	0.301657i
$162$	−8.91465	+	1.23655i	−0.700401	+	0.0971528i
$163$	7.65234	−	7.65234i	0.599378	−	0.599378i	−0.340769	−	0.940147i	$-0.610687\pi$
$163$	7.65234	−	7.65234i	0.599378	−	0.599378i	0.940147	+	0.340769i	$0.110687\pi$
$164$		−	7.88519i		−	0.615730i
$165$	−1.68807	−	7.18343i	−0.131416	−	0.559229i
$166$	−8.91245	+	8.91245i	−0.691740	+	0.691740i
$167$	−11.7216	+	11.7216i	−0.907044	+	0.907044i	−0.996033	−	0.0889886i	$-0.971637\pi$
$167$	−11.7216	+	11.7216i	−0.907044	+	0.907044i	0.0889886	+	0.996033i	$0.471637\pi$
$168$	−1.10888	−	4.71875i	−0.0855521	−	0.364059i
$169$		−	6.69691i		−	0.515147i
$170$	5.48863	−	5.48863i	0.420959	−	0.420959i
$171$	0.655162	−	1.95224i	0.0501015	−	0.149292i
$172$	3.72198	−	3.72198i	0.283798	−	0.283798i
$173$	4.86504			0.369882			0.184941	−	0.982750i	$-0.440791\pi$
$173$	4.86504			0.369882			0.184941	+	0.982750i	$0.440791\pi$
$174$	14.6348	+	9.06536i	1.10946	+	0.687243i
$175$			2.79858i			0.211553i
$176$	4.26033			0.321135
$177$	−2.71764	−	11.5647i	−0.204270	−	0.869254i
$178$			1.60243i			0.120107i
$179$	−9.23529	−	9.23529i	−0.690278	−	0.690278i	0.272015	−	0.962293i	$-0.412310\pi$
$179$	−9.23529	−	9.23529i	−0.690278	−	0.690278i	−0.962293	+	0.272015i	$0.912310\pi$
$180$	−0.954468	+	2.84412i	−0.0711418	+	0.211988i
$181$	19.4997			1.44940			0.724699	−	0.689065i	$-0.241979\pi$
$181$	19.4997			1.44940			0.724699	+	0.689065i	$0.241979\pi$
$182$		−	7.02611i		−	0.520810i
$183$	−1.73017	−	7.36258i	−0.127898	−	0.544258i
$184$		−	1.93421i		−	0.142592i
$185$	1.64574	+	5.85590i	0.120997	+	0.430534i
$186$	−4.89868	+	7.90824i	−0.359189	+	0.579861i
$187$	23.3834	−	23.3834i	1.70996	−	1.70996i
$188$	2.41387			0.176050
$189$	14.4791	+	1.35010i	1.05320	+	0.0982056i
$190$	−0.485369	−	0.485369i	−0.0352124	−	0.0352124i
$191$	−2.29567	+	2.29567i	−0.166109	+	0.166109i	−0.785267	−	0.619158i	$-0.787474\pi$
$191$	−2.29567	+	2.29567i	−0.166109	+	0.166109i	0.619158	+	0.785267i	$0.287474\pi$
$192$	−1.47244	−	0.912090i	−0.106264	−	0.0658244i
$193$	19.1715	+	19.1715i	1.37999	+	1.37999i	0.844608	+	0.535385i	$0.179834\pi$
$193$	19.1715	+	19.1715i	1.37999	+	1.37999i	0.535385	+	0.844608i	$0.320166\pi$
$194$			5.40541i			0.388086i
$195$	−2.28989	+	3.69671i	−0.163982	+	0.264727i
$196$			0.832067i			0.0594333i
$197$		−	16.7875i		−	1.19606i	−0.801473	−	0.598031i	$-0.795950\pi$
$197$		−	16.7875i		−	1.19606i	0.801473	−	0.598031i	$-0.204050\pi$
$198$	−4.06635	+	12.1169i	−0.288983	+	0.861109i
$199$	−5.65815	+	5.65815i	−0.401096	+	0.401096i	−0.878619	−	0.477523i	$-0.841535\pi$
$199$	−5.65815	+	5.65815i	−0.401096	+	0.401096i	0.477523	+	0.878619i	$0.341535\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	0.930557	+	0.576424i	0.0656364	+	0.0406578i
$202$	−8.86201	−	8.86201i	−0.623529	−	0.623529i
$203$	−19.6685	−	19.6685i	−1.38046	−	1.38046i
$204$	−13.0878	+	3.07558i	−0.916332	+	0.215333i
$205$	5.57567	−	5.57567i	0.389422	−	0.389422i
$206$	−5.26599			−0.366899
$207$	5.50111	+	1.84614i	0.382354	+	0.128316i
$208$	−1.77526	−	1.77526i	−0.123092	−	0.123092i
$209$	−2.06783	−	2.06783i	−0.143035	−	0.143035i
$210$	2.55256	−	4.12076i	0.176143	−	0.284359i
$211$	13.9231			0.958504			0.479252	−	0.877677i	$-0.340908\pi$
$211$	13.9231			0.958504			0.479252	+	0.877677i	$0.340908\pi$
$212$	−2.32891			−0.159950
$213$	−19.0662	−	11.8104i	−1.30639	−	0.809233i
$214$	−9.98563	+	9.98563i	−0.682603	+	0.682603i
$215$	5.26367			0.358979
$216$	3.99949	−	3.31724i	0.272131	−	0.225710i
$217$	10.6283	−	10.6283i	0.721497	−	0.721497i
$218$			3.93399i			0.266443i
$219$	−12.1389	−	7.51934i	−0.820273	−	0.508110i
$220$	3.01251	+	3.01251i	0.203103	+	0.203103i
$221$	−19.4875			−1.31087
$222$	2.91785	−	10.1235i	0.195833	−	0.679448i
$223$	−7.53292			−0.504442			−0.252221	−	0.967670i	$-0.581161\pi$
$223$	−7.53292			−0.504442			−0.252221	+	0.967670i	$0.581161\pi$
$224$	1.97890	+	1.97890i	0.132221	+	0.132221i
$225$	−2.68600	+	1.33618i	−0.179067	+	0.0890788i
$226$			16.9795i			1.12946i
$227$	0.877238	−	0.877238i	0.0582243	−	0.0582243i	−0.677395	−	0.735619i	$-0.736891\pi$
$227$	0.877238	−	0.877238i	0.0582243	−	0.0582243i	0.735619	+	0.677395i	$0.236891\pi$
$228$	0.271978	+	1.15738i	0.0180122	+	0.0766493i
$229$	22.3271			1.47542			0.737708	−	0.675120i	$-0.235908\pi$
$229$	22.3271			1.47542			0.737708	+	0.675120i	$0.235908\pi$
$230$	1.36769	−	1.36769i	0.0901830	−	0.0901830i
$231$	10.8748	−	17.5558i	0.715506	−	1.15509i
$232$	−9.93910			−0.652534
$233$	−9.79418			−0.641638			−0.320819	−	0.947140i	$-0.603958\pi$
$233$	−9.79418			−0.641638			−0.320819	+	0.947140i	$0.603958\pi$
$234$	6.74347	−	3.35461i	0.440834	−	0.219298i
$235$	1.70686	+	1.70686i	0.111344	+	0.111344i
$236$	4.84986	+	4.84986i	0.315699	+	0.315699i
$237$	−9.95815	+	2.34011i	−0.646851	+	0.152007i
$238$	21.7229			1.40809
$239$	2.87846	−	2.87846i	0.186192	−	0.186192i	−0.607856	−	0.794048i	$-0.707970\pi$
$239$	2.87846	−	2.87846i	0.186192	−	0.186192i	0.794048	+	0.607856i	$0.207970\pi$
$240$	−0.396230	−	1.68612i	−0.0255765	−	0.108839i
$241$	7.88502	+	7.88502i	0.507919	+	0.507919i	0.913887	−	0.405968i	$-0.133066\pi$
$241$	7.88502	+	7.88502i	0.507919	+	0.507919i	−0.405968	+	0.913887i	$0.633066\pi$
$242$	5.05611	+	5.05611i	0.325019	+	0.325019i
$243$	5.61723	+	14.5412i	0.360345	+	0.932819i
$244$	3.08764	+	3.08764i	0.197666	+	0.197666i
$245$	−0.588360	+	0.588360i	−0.0375889	+	0.0375889i
$246$	−13.2954	+	3.12435i	−0.847683	+	0.199201i
$247$			1.72331i			0.109652i
$248$		−	5.37083i		−	0.341048i
$249$	18.5588	+	11.4961i	1.17612	+	0.728534i
$250$			1.00000i			0.0632456i
$251$	19.0180	+	19.0180i	1.20040	+	1.20040i	0.974043	+	0.226361i	$0.0726829\pi$
$251$	19.0180	+	19.0180i	1.20040	+	1.20040i	0.226361	+	0.974043i	$0.427317\pi$
$252$	−7.51700	+	3.73942i	−0.473527	+	0.235561i
$253$	5.82682	−	5.82682i	0.366329	−	0.366329i
$254$	−9.85843	−	9.85843i	−0.618573	−	0.618573i
$255$	−11.4293	−	7.07974i	−0.715728	−	0.443350i
$256$	1.00000			0.0625000
$257$	1.79625	−	1.79625i	0.112047	−	0.112047i	−0.648860	−	0.760907i	$-0.724754\pi$
$257$	1.79625	−	1.79625i	0.112047	−	0.112047i	0.760907	+	0.648860i	$0.224754\pi$
$258$	−7.75046	−	4.80094i	−0.482523	−	0.298894i
$259$	−8.33147	+	14.8450i	−0.517692	+	0.922421i
$260$		−	2.51060i		−	0.155701i
$261$	9.48655	−	28.2680i	0.587203	−	1.74974i
$262$			2.77732i			0.171583i
$263$	−25.6368			−1.58083			−0.790417	−	0.612569i	$-0.790136\pi$
$263$	−25.6368			−1.58083			−0.790417	+	0.612569i	$0.790136\pi$
$264$	−1.68807	−	7.18343i	−0.103894	−	0.442110i
$265$	−1.64679	−	1.64679i	−0.101161	−	0.101161i
$266$		−	1.92099i		−	0.117784i
$267$	2.70189	−	0.634931i	0.165353	−	0.0388572i
$268$	−0.631981			−0.0386044
$269$			20.7163i			1.26310i	0.775337	+	0.631548i	$0.217580\pi$
$269$			20.7163i			1.26310i	−0.775337	+	0.631548i	$0.782420\pi$
$270$	5.17371	+	0.482424i	0.314862	+	0.0293594i
$271$	7.12296			0.432689			0.216345	−	0.976317i	$-0.430587\pi$
$271$	7.12296			0.432689			0.216345	+	0.976317i	$0.430587\pi$
$272$	5.48863	−	5.48863i	0.332797	−	0.332797i
$273$	−11.8469	+	2.78396i	−0.717005	+	0.168493i
$274$	−4.77085	+	4.77085i	−0.288218	+	0.288218i
$275$			4.26033i			0.256908i
$276$	−3.26131	+	0.766391i	−0.196308	+	0.0461313i
$277$	−9.36210	+	9.36210i	−0.562514	+	0.562514i	−0.930021	−	0.367507i	$-0.880211\pi$
$277$	−9.36210	+	9.36210i	−0.562514	+	0.562514i	0.367507	+	0.930021i	$0.380211\pi$
$278$	12.5739	−	12.5739i	0.754135	−	0.754135i
$279$	15.2753	+	5.12628i	0.914506	+	0.306903i
$280$			2.79858i			0.167247i
$281$	−19.0275	+	19.0275i	−1.13509	+	1.13509i	−0.145769	+	0.989319i	$0.546566\pi$
$281$	−19.0275	+	19.0275i	−1.13509	+	1.13509i	−0.989319	+	0.145769i	$0.953434\pi$
$282$	−0.956448	−	4.07008i	−0.0569556	−	0.242370i
$283$	−18.3350	+	18.3350i	−1.08990	+	1.08990i	−0.0943643	+	0.995538i	$0.530082\pi$
$283$	−18.3350	+	18.3350i	−1.08990	+	1.08990i	−0.995538	+	0.0943643i	$0.969918\pi$
$284$	12.9487			0.768362
$285$	−0.626073	+	1.01071i	−0.0370854	+	0.0598692i
$286$		−	10.6960i		−	0.632466i
$287$	22.0674			1.30260
$288$	−0.954468	+	2.84412i	−0.0562426	+	0.167591i
$289$		−	43.2502i		−	2.54413i
$290$	−7.02801	−	7.02801i	−0.412699	−	0.412699i
$291$	9.11417	−	2.14179i	0.534282	−	0.125554i
$292$	8.24407			0.482448
$293$			0.782467i			0.0457122i	0.999739	+	0.0228561i	$0.00727596\pi$
$293$			0.782467i			0.0457122i	−0.999739	+	0.0228561i	$0.992724\pi$
$294$	1.40296	−	0.329690i	0.0818226	−	0.0192279i
$295$			6.85874i			0.399331i
$296$	1.64574	+	5.85590i	0.0956567	+	0.340367i
$297$	22.0417	+	2.05529i	1.27899	+	0.119260i
$298$	−1.58391	+	1.58391i	−0.0917534	+	0.0917534i
$299$	−4.85602			−0.280831
$300$	0.912090	−	1.47244i	0.0526596	−	0.0850116i
$301$	10.4163	+	10.4163i	0.600383	+	0.600383i
$302$	−2.40614	+	2.40614i	−0.138458	+	0.138458i
$303$	−11.4310	+	18.4538i	−0.656695	+	1.06014i
$304$	−0.485369	−	0.485369i	−0.0278378	−	0.0278378i
$305$			4.36658i			0.250030i
$306$	10.3716	+	20.8490i	0.592904	+	1.19186i
$307$			8.87492i			0.506519i	0.967398	+	0.253259i	$0.0815026\pi$
$307$			8.87492i			0.506519i	−0.967398	+	0.253259i	$0.918497\pi$
$308$			11.9229i			0.679370i
$309$	2.08654	+	8.87909i	0.118699	+	0.505114i
$310$	3.79775	−	3.79775i	0.215698	−	0.215698i
$311$	−2.73004	−	2.73004i	−0.154806	−	0.154806i	0.625454	−	0.780261i	$-0.284914\pi$
$311$	−2.73004	−	2.73004i	−0.154806	−	0.154806i	−0.780261	+	0.625454i	$0.784914\pi$
$312$	−2.28989	+	3.69671i	−0.129640	+	0.209285i
$313$	−4.51817	−	4.51817i	−0.255382	−	0.255382i	0.567791	−	0.823173i	$-0.307798\pi$
$313$	−4.51817	−	4.51817i	−0.255382	−	0.255382i	−0.823173	+	0.567791i	$0.807798\pi$
$314$	−10.4749	−	10.4749i	−0.591134	−	0.591134i
$315$	−7.95949	−	2.67116i	−0.448467	−	0.150503i
$316$	4.17614	−	4.17614i	0.234926	−	0.234926i
$317$	−2.30629			−0.129534			−0.0647670	−	0.997900i	$-0.520630\pi$
$317$	−2.30629			−0.129534			−0.0647670	+	0.997900i	$0.520630\pi$
$318$	0.922783	+	3.92682i	0.0517471	+	0.220205i
$319$	−29.9416	−	29.9416i	−1.67641	−	1.67641i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	20.7936	+	12.8804i	1.16058	+	0.718912i
$322$	5.41304			0.301657
$323$	−5.32803			−0.296459
$324$	−7.17798	−	5.42923i	−0.398777	−	0.301624i
$325$	1.77526	−	1.77526i	0.0984737	−	0.0984737i
$326$	10.8220			0.599378
$327$	6.63317	−	1.55876i	0.366815	−	0.0861998i
$328$	5.57567	−	5.57567i	0.307865	−	0.307865i
$329$			6.75542i			0.372438i
$330$	3.88581	−	6.27310i	0.213907	−	0.345323i
$331$	9.28631	+	9.28631i	0.510422	+	0.510422i	0.914656	−	0.404234i	$-0.132462\pi$
$331$	9.28631	+	9.28631i	0.510422	+	0.510422i	−0.404234	+	0.914656i	$0.632462\pi$
$332$	−12.6041			−0.691740
$333$	−18.2257	−	0.908592i	−0.998760	−	0.0497906i
$334$	−16.5768			−0.907044
$335$	−0.446878	−	0.446878i	−0.0244156	−	0.0244156i
$336$	2.55256	−	4.12076i	0.139254	−	0.224806i
$337$			32.6463i			1.77836i	0.457560	+	0.889179i	$0.348723\pi$
$337$			32.6463i			1.77836i	−0.457560	+	0.889179i	$0.651277\pi$
$338$	4.73543	−	4.73543i	0.257573	−	0.257573i
$339$	28.6295	−	6.72779i	1.55494	−	0.365403i
$340$	7.76210			0.420959
$341$	16.1797	−	16.1797i	0.876178	−	0.876178i
$342$	1.84371	−	0.917176i	0.0996967	−	0.0495952i
$343$	17.2615			0.932032
$344$	5.26367			0.283798
$345$	−2.84801	−	1.76417i	−0.153332	−	0.0949799i
$346$	3.44010	+	3.44010i	0.184941	+	0.184941i
$347$	1.60797	+	1.60797i	0.0863203	+	0.0863203i	0.748948	−	0.662628i	$-0.230559\pi$
$347$	1.60797	+	1.60797i	0.0863203	+	0.0863203i	−0.662628	+	0.748948i	$0.730559\pi$
$348$	3.93817	+	16.7585i	0.211108	+	0.898351i
$349$	−26.5611			−1.42178			−0.710892	−	0.703301i	$-0.751709\pi$
$349$	−26.5611			−1.42178			−0.710892	+	0.703301i	$0.751709\pi$
$350$	−1.97890	+	1.97890i	−0.105776	+	0.105776i
$351$	−8.32825	−	10.0411i	−0.444529	−	0.535955i
$352$	3.01251	+	3.01251i	0.160567	+	0.160567i
$353$	13.7402	+	13.7402i	0.731319	+	0.731319i	0.970881	−	0.239562i	$-0.0770040\pi$
$353$	13.7402	+	13.7402i	0.731319	+	0.731319i	−0.239562	+	0.970881i	$0.577004\pi$
$354$	6.25579	−	10.0991i	0.332492	−	0.536762i
$355$	9.15610	+	9.15610i	0.485955	+	0.485955i
$356$	−1.13309	+	1.13309i	−0.0600537	+	0.0600537i
$357$	−8.60725	−	36.6274i	−0.455544	−	1.93853i
$358$		−	13.0607i		−	0.690278i
$359$		−	27.5625i		−	1.45469i	−0.686270	−	0.727347i	$-0.740753\pi$
$359$		−	27.5625i		−	1.45469i	0.686270	−	0.727347i	$-0.259247\pi$
$360$	−2.68600	+	1.33618i	−0.141565	+	0.0704230i
$361$		−	18.5288i		−	0.975202i
$362$	13.7883	+	13.7883i	0.724699	+	0.724699i
$363$	6.52183	−	10.5286i	0.342307	−	0.552608i
$364$	4.96821	−	4.96821i	0.260405	−	0.260405i
$365$	5.82944	+	5.82944i	0.305127	+	0.305127i
$366$	3.98272	−	6.42955i	0.208180	−	0.336078i
$367$	10.1661			0.530669			0.265334	−	0.964156i	$-0.414518\pi$
$367$	10.1661			0.530669			0.265334	+	0.964156i	$0.414518\pi$
$368$	1.36769	−	1.36769i	0.0712959	−	0.0712959i
$369$	10.5361	+	21.1797i	0.548485	+	1.10257i
$370$	−2.97703	+	5.30446i	−0.154768	+	0.275766i
$371$		−	6.51765i		−	0.338379i
$372$	−9.05586	+	2.12808i	−0.469525	+	0.110336i
$373$			29.8152i			1.54377i	0.635759	+	0.771887i	$0.280687\pi$
$373$			29.8152i			1.54377i	−0.635759	+	0.771887i	$0.719313\pi$
$374$	33.0691			1.70996
$375$	1.68612	−	0.396230i	0.0870709	−	0.0204612i
$376$	1.70686	+	1.70686i	0.0880248	+	0.0880248i
$377$			24.9531i			1.28515i
$378$	9.28357	+	11.1929i	0.477495	+	0.575701i
$379$	11.8696			0.609703			0.304851	−	0.952400i	$-0.401393\pi$
$379$	11.8696			0.609703			0.304851	+	0.952400i	$0.401393\pi$
$380$		−	0.686416i		−	0.0352124i
$381$	−12.7163	+	20.5287i	−0.651475	+	1.05172i
$382$	−3.24657			−0.166109
$383$	2.09268	−	2.09268i	0.106931	−	0.106931i	−0.651617	−	0.758548i	$-0.725909\pi$
$383$	2.09268	−	2.09268i	0.106931	−	0.106931i	0.758548	+	0.651617i	$0.225909\pi$
$384$	−0.396230	−	1.68612i	−0.0202200	−	0.0860445i
$385$	−8.43076	+	8.43076i	−0.429671	+	0.429671i
$386$			27.1126i			1.37999i
$387$	−5.02400	+	14.9705i	−0.255385	+	0.760993i
$388$	−3.82220	+	3.82220i	−0.194043	+	0.194043i
$389$	−6.62618	+	6.62618i	−0.335961	+	0.335961i	−0.854845	−	0.518884i	$-0.826348\pi$
$389$	−6.62618	+	6.62618i	−0.335961	+	0.335961i	0.518884	+	0.854845i	$0.326348\pi$
$390$	−4.23317	+	0.994773i	−0.214355	+	0.0503723i
$391$		−	15.0135i		−	0.759266i
$392$	−0.588360	+	0.588360i	−0.0297167	+	0.0297167i
$393$	4.68289	−	1.10046i	0.236220	−	0.0555106i
$394$	11.8706	−	11.8706i	0.598031	−	0.598031i
$395$	5.90595			0.297161
$396$	−11.4433	+	5.69258i	−0.575046	+	0.286063i
$397$			0.443718i			0.0222695i	0.999938	+	0.0111348i	$0.00354438\pi$
$397$			0.443718i			0.0222695i	−0.999938	+	0.0111348i	$0.996456\pi$
$398$	−8.00183			−0.401096
$399$	−3.23902	+	0.761154i	−0.162154	+	0.0381054i
$400$			1.00000i			0.0500000i
$401$	−17.4046	−	17.4046i	−0.869144	−	0.869144i	0.123233	−	0.992378i	$-0.460674\pi$
$401$	−17.4046	−	17.4046i	−0.869144	−	0.869144i	−0.992378	+	0.123233i	$0.960674\pi$
$402$	0.250410	+	1.06560i	0.0124893	+	0.0531471i
$403$	−13.4840			−0.671685
$404$		−	12.5328i		−	0.623529i
$405$	−1.23655	−	8.91465i	−0.0614448	−	0.442972i
$406$		−	27.8154i		−	1.38046i
$407$	−12.6831	+	22.5988i	−0.628680	+	1.12018i
$408$	−11.4293	−	7.07974i	−0.565833	−	0.350499i
$409$	−25.8916	+	25.8916i	−1.28026	+	1.28026i	−0.339738	+	0.940520i	$0.610338\pi$
$409$	−25.8916	+	25.8916i	−1.28026	+	1.28026i	−0.940520	+	0.339738i	$0.889662\pi$
$410$	7.88519			0.389422
$411$	9.93459	+	6.15388i	0.490037	+	0.303549i
$412$	−3.72362	−	3.72362i	−0.183449	−	0.183449i
$413$	−13.5727	+	13.5727i	−0.667871	+	0.667871i
$414$	2.58446	+	5.19529i	0.127019	+	0.255335i
$415$	−8.91245	−	8.91245i	−0.437495	−	0.437495i
$416$		−	2.51060i		−	0.123092i
$417$	−26.1833	−	16.2190i	−1.28220	−	0.794248i
$418$		−	2.92436i		−	0.143035i
$419$		−	39.7747i		−	1.94312i	−0.236791	−	0.971561i	$-0.576096\pi$
$419$		−	39.7747i		−	1.94312i	0.236791	−	0.971561i	$-0.423904\pi$
$420$	4.71875	−	1.10888i	0.230251	−	0.0541079i
$421$	−9.15823	+	9.15823i	−0.446345	+	0.446345i	−0.894137	−	0.447793i	$-0.852210\pi$
$421$	−9.15823	+	9.15823i	−0.446345	+	0.446345i	0.447793	+	0.894137i	$0.352210\pi$
$422$	9.84510	+	9.84510i	0.479252	+	0.479252i
$423$	−6.48367	+	3.22537i	−0.315247	+	0.156823i
$424$	−1.64679	−	1.64679i	−0.0799751	−	0.0799751i
$425$	5.48863	+	5.48863i	0.266238	+	0.266238i
$426$	−5.13065	−	21.8330i	−0.248581	−	1.05781i
$427$	−8.64102	+	8.64102i	−0.418168	+	0.418168i
$428$	−14.1218			−0.682603
$429$	−18.0347	+	4.23806i	−0.870723	+	0.204616i
$430$	3.72198	+	3.72198i	0.179490	+	0.179490i
$431$	22.4447	+	22.4447i	1.08112	+	1.08112i	0.996405	+	0.0847166i	$0.0269985\pi$
$431$	22.4447	+	22.4447i	1.08112	+	1.08112i	0.0847166	+	0.996405i	$0.473002\pi$
$432$	5.17371	+	0.482424i	0.248920	+	0.0232106i
$433$	−25.9555			−1.24734			−0.623671	−	0.781687i	$-0.714359\pi$
$433$	−25.9555			−1.24734			−0.623671	+	0.781687i	$0.714359\pi$
$434$	15.0307			0.721497
$435$	−9.06536	+	14.6348i	−0.434651	+	0.701684i
$436$	−2.78175	+	2.78175i	−0.133222	+	0.133222i
$437$	−1.32767			−0.0635111
$438$	−3.26655	−	13.9005i	−0.156082	−	0.664191i
$439$	14.5503	−	14.5503i	0.694446	−	0.694446i	−0.268761	−	0.963207i	$-0.586614\pi$
$439$	14.5503	−	14.5503i	0.694446	−	0.694446i	0.963207	+	0.268761i	$0.0866141\pi$
$440$			4.26033i			0.203103i
$441$	−1.11179	−	2.23493i	−0.0529425	−	0.106425i
$442$	−13.7797	−	13.7797i	−0.655436	−	0.655436i
$443$	−15.0026			−0.712797			−0.356399	−	0.934334i	$-0.615995\pi$
$443$	−15.0026			−0.712797			−0.356399	+	0.934334i	$0.615995\pi$
$444$	9.22166	−	5.09520i	0.437640	−	0.241807i
$445$	−1.60243			−0.0759626
$446$	−5.32658	−	5.32658i	−0.252221	−	0.252221i
$447$	3.29825	+	2.04307i	0.156002	+	0.0966339i
$448$			2.79858i			0.132221i
$449$	19.8528	−	19.8528i	0.936912	−	0.936912i	−0.0612124	−	0.998125i	$-0.519497\pi$
$449$	19.8528	−	19.8528i	0.936912	−	0.936912i	0.998125	+	0.0612124i	$0.0194967\pi$
$450$	−2.84412	−	0.954468i	−0.134073	−	0.0449940i
$451$	33.5935			1.58186
$452$	−12.0063	+	12.0063i	−0.564730	+	0.564730i
$453$	5.01043	+	3.10366i	0.235411	+	0.145823i
$454$	1.24060			0.0582243
$455$	7.02611			0.329389
$456$	−0.626073	+	1.01071i	−0.0293186	+	0.0473308i
$457$	19.3136	+	19.3136i	0.903451	+	0.903451i	0.995733	−	0.0922815i	$-0.0294160\pi$
$457$	19.3136	+	19.3136i	0.903451	+	0.903451i	−0.0922815	+	0.995733i	$0.529416\pi$
$458$	15.7876	+	15.7876i	0.737708	+	0.737708i
$459$	31.0444	−	25.7487i	1.44903	−	1.20185i
$460$	1.93421			0.0901830
$461$	−9.75740	+	9.75740i	−0.454447	+	0.454447i	−0.896828	−	0.442380i	$-0.854134\pi$
$461$	−9.75740	+	9.75740i	−0.454447	+	0.454447i	0.442380	+	0.896828i	$0.354134\pi$
$462$	20.1034	−	4.72421i	0.935296	−	0.219790i
$463$	−13.2936	−	13.2936i	−0.617806	−	0.617806i	0.327163	−	0.944968i	$-0.393908\pi$
$463$	−13.2936	−	13.2936i	−0.617806	−	0.617806i	−0.944968	+	0.327163i	$0.893908\pi$
$464$	−7.02801	−	7.02801i	−0.326267	−	0.326267i
$465$	−7.90824	−	4.89868i	−0.366736	−	0.227171i
$466$	−6.92553	−	6.92553i	−0.320819	−	0.320819i
$467$	16.8533	−	16.8533i	0.779876	−	0.779876i	−0.199934	−	0.979809i	$-0.564073\pi$
$467$	16.8533	−	16.8533i	0.779876	−	0.779876i	0.979809	+	0.199934i	$0.0640727\pi$
$468$	7.14042	+	2.39628i	0.330066	+	0.110768i
$469$		−	1.76865i		−	0.0816687i
$470$			2.41387i			0.111344i
$471$	−13.5115	+	21.8124i	−0.622577	+	1.00506i
$472$			6.85874i			0.315699i
$473$	15.8569	+	15.8569i	0.729099	+	0.729099i
$474$	−8.69618	−	5.38676i	−0.399429	−	0.247422i
$475$	0.485369	−	0.485369i	0.0222703	−	0.0222703i
$476$	15.3604	+	15.3604i	0.704043	+	0.704043i
$477$	6.25546	−	3.11185i	0.286418	−	0.142482i
$478$	4.07076			0.186192
$479$	1.79186	−	1.79186i	0.0818722	−	0.0818722i	−0.664985	−	0.746857i	$-0.731562\pi$
$479$	1.79186	−	1.79186i	0.0818722	−	0.0818722i	0.746857	+	0.664985i	$0.231562\pi$
$480$	0.912090	−	1.47244i	0.0416310	−	0.0672076i
$481$	14.7018	−	4.13179i	0.670344	−	0.188393i
$482$			11.1511i			0.507919i
$483$	−2.14481	−	9.12704i	−0.0975922	−	0.415295i
$484$			7.15042i			0.325019i
$485$	−5.40541			−0.245447
$486$	−6.31021	+	14.2542i	−0.286237	+	0.646582i
$487$	−8.70006	−	8.70006i	−0.394237	−	0.394237i	0.481957	−	0.876195i	$-0.339926\pi$
$487$	−8.70006	−	8.70006i	−0.394237	−	0.394237i	−0.876195	+	0.481957i	$0.839926\pi$
$488$			4.36658i			0.197666i
$489$	−4.28802	−	18.2473i	−0.193911	−	0.825170i
$490$	−0.832067			−0.0375889
$491$			1.24916i			0.0563736i	0.999603	+	0.0281868i	$0.00897333\pi$
$491$			1.24916i			0.0563736i	−0.999603	+	0.0281868i	$0.991027\pi$
$492$	−11.6105	−	7.19201i	−0.523442	−	0.324241i
$493$	−77.1483			−3.47459
$494$	−1.21857	+	1.21857i	−0.0548259	+	0.0548259i
$495$	−12.1169	−	4.06635i	−0.544613	−	0.182769i
$496$	3.79775	−	3.79775i	0.170524	−	0.170524i
$497$			36.2379i			1.62549i
$498$	4.99412	+	21.2520i	0.223792	+	0.952326i
$499$	26.1302	−	26.1302i	1.16975	−	1.16975i	0.187479	−	0.982269i	$-0.439968\pi$
$499$	26.1302	−	26.1302i	1.16975	−	1.16975i	0.982269	−	0.187479i	$-0.0600316\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	6.56824	+	27.9505i	0.293447	+	1.24874i
$502$			26.8955i			1.20040i
$503$	25.6242	−	25.6242i	1.14253	−	1.14253i	0.154538	−	0.987987i	$-0.450611\pi$
$503$	25.6242	−	25.6242i	1.14253	−	1.14253i	0.987987	−	0.154538i	$-0.0493890\pi$
$504$	−7.95949	−	2.67116i	−0.354544	−	0.118983i
$505$	8.86201	−	8.86201i	0.394354	−	0.394354i
$506$	8.24037			0.366329
$507$	−9.86082	−	6.10818i	−0.437934	−	0.271274i
$508$		−	13.9419i		−	0.618573i
$509$	−35.7638			−1.58520			−0.792601	−	0.609741i	$-0.791274\pi$
$509$	−35.7638			−1.58520			−0.792601	+	0.609741i	$0.791274\pi$
$510$	−3.07558	−	13.0878i	−0.136189	−	0.579539i
$511$			23.0717i			1.02063i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.27700	−	2.74531i	−0.100532	−	0.121209i
$514$	2.54028			0.112047
$515$		−	5.26599i		−	0.232047i
$516$	−2.08562	−	8.87518i	−0.0918145	−	0.390708i
$517$			10.2839i			0.452285i
$518$	−16.3882	+	4.60574i	−0.720057	+	0.202365i
$519$	4.43736	−	7.16350i	0.194778	−	0.314443i
$520$	1.77526	−	1.77526i	0.0778503	−	0.0778503i
$521$	−9.65846			−0.423145			−0.211572	−	0.977362i	$-0.567858\pi$
$521$	−9.65846			−0.423145			−0.211572	+	0.977362i	$0.567858\pi$
$522$	26.6965	−	13.2805i	1.16847	−	0.581270i
$523$	7.75116	+	7.75116i	0.338934	+	0.338934i	0.855966	−	0.517032i	$-0.172963\pi$
$523$	7.75116	+	7.75116i	0.338934	+	0.338934i	−0.517032	+	0.855966i	$0.672963\pi$
$524$	−1.96386	+	1.96386i	−0.0857916	+	0.0857916i
$525$	4.12076	+	2.55256i	0.179845	+	0.111403i
$526$	−18.1280	−	18.1280i	−0.790417	−	0.790417i
$527$		−	41.6889i		−	1.81600i
$528$	3.88581	−	6.27310i	0.169108	−	0.273002i
$529$			19.2588i			0.837341i
$530$		−	2.32891i		−	0.101161i
$531$	−19.5071	−	6.54645i	−0.846534	−	0.284092i
$532$	1.35835	−	1.35835i	0.0588918	−	0.0588918i
$533$	−13.9983	−	13.9983i	−0.606332	−	0.606332i
$534$	2.35949	+	1.46156i	0.102105	+	0.0632480i
$535$	−9.98563	−	9.98563i	−0.431716	−	0.431716i
$536$	−0.446878	−	0.446878i	−0.0193022	−	0.0193022i
$537$	−22.0219	+	5.17503i	−0.950314	+	0.223319i
$538$	−14.6486	+	14.6486i	−0.631548	+	0.631548i
$539$	−3.54488			−0.152689
$540$	3.31724	+	3.99949i	0.142751	+	0.172111i
$541$	−12.0747	−	12.0747i	−0.519132	−	0.519132i	0.398177	−	0.917309i	$-0.369643\pi$
$541$	−12.0747	−	12.0747i	−0.519132	−	0.519132i	−0.917309	+	0.398177i	$0.869643\pi$
$542$	5.03670	+	5.03670i	0.216345	+	0.216345i
$543$	17.7855	−	28.7122i	0.763247	−	1.23216i
$544$	7.76210			0.332797
$545$	−3.93399			−0.168513
$546$	−10.3456	−	6.40845i	−0.442749	−	0.274256i
$547$	−21.3535	+	21.3535i	−0.913010	+	0.913010i	−0.996508	−	0.0834976i	$-0.973391\pi$
$547$	−21.3535	+	21.3535i	−0.913010	+	0.913010i	0.0834976	+	0.996508i	$0.473391\pi$
$548$	−6.74701			−0.288218
$549$	−12.4191	−	4.16776i	−0.530033	−	0.177876i
$550$	−3.01251	+	3.01251i	−0.128454	+	0.128454i
$551$			6.82236i			0.290642i
$552$	−2.84801	−	1.76417i	−0.121220	−	0.0750882i
$553$	11.6873	+	11.6873i	0.496993	+	0.496993i
$554$	−13.2400			−0.562514
$555$	10.1235	+	2.91785i	0.429721	+	0.123856i
$556$	17.7822			0.754135
$557$	−10.3385	−	10.3385i	−0.438055	−	0.438055i	0.453302	−	0.891357i	$-0.350246\pi$
$557$	−10.3385	−	10.3385i	−0.438055	−	0.438055i	−0.891357	+	0.453302i	$0.850246\pi$
$558$	7.17641	+	14.4261i	0.303802	+	0.610704i
$559$		−	13.2150i		−	0.558933i
$560$	−1.97890	+	1.97890i	−0.0836237	+	0.0836237i
$561$	−13.1030	−	55.7585i	−0.553208	−	2.35413i
$562$	−26.9090			−1.13509
$563$	−27.7261	+	27.7261i	−1.16852	+	1.16852i	−0.185959	+	0.982558i	$0.559539\pi$
$563$	−27.7261	+	27.7261i	−1.16852	+	1.16852i	−0.982558	+	0.185959i	$0.940461\pi$
$564$	2.20167	−	3.55429i	0.0927069	−	0.149663i
$565$	−16.9795			−0.714334
$566$	−25.9296			−1.08990
$567$	15.1942	−	20.0882i	0.638095	−	0.843624i
$568$	9.15610	+	9.15610i	0.384181	+	0.384181i
$569$	−24.9520	−	24.9520i	−1.04604	−	1.04604i	−0.998888	−	0.0471533i	$-0.984985\pi$
$569$	−24.9520	−	24.9520i	−1.04604	−	1.04604i	−0.0471533	−	0.998888i	$-0.515015\pi$
$570$	−1.15738	+	0.271978i	−0.0484773	+	0.0113919i
$571$	−33.1993			−1.38935			−0.694675	−	0.719324i	$-0.744452\pi$
$571$	−33.1993			−1.38935			−0.694675	+	0.719324i	$0.744452\pi$
$572$	7.56319	−	7.56319i	0.316233	−	0.316233i
$573$	1.28639	+	5.47412i	0.0537397	+	0.228684i
$574$	15.6040	+	15.6040i	0.651298	+	0.651298i
$575$	1.36769	+	1.36769i	0.0570367	+	0.0570367i
$576$	−2.68600	+	1.33618i	−0.111917	+	0.0556743i
$577$	−20.4920	−	20.4920i	−0.853092	−	0.853092i	0.137421	−	0.990513i	$-0.456119\pi$
$577$	−20.4920	−	20.4920i	−0.853092	−	0.853092i	−0.990513	+	0.137421i	$0.956119\pi$
$578$	30.5825	−	30.5825i	1.27206	−	1.27206i
$579$	45.7150	−	10.7428i	1.89985	−	0.446456i
$580$		−	9.93910i		−	0.412699i
$581$		−	35.2736i		−	1.46340i
$582$	7.95917	+	4.93022i	0.329918	+	0.204364i
$583$		−	9.92193i		−	0.410924i
$584$	5.82944	+	5.82944i	0.241224	+	0.241224i
$585$	3.35461	+	6.74347i	0.138696	+	0.278808i
$586$	−0.553288	+	0.553288i	−0.0228561	+	0.0228561i
$587$	−3.35864	−	3.35864i	−0.138626	−	0.138626i	0.634388	−	0.773014i	$-0.281252\pi$
$587$	−3.35864	−	3.35864i	−0.138626	−	0.138626i	−0.773014	+	0.634388i	$0.781252\pi$
$588$	1.22517	+	0.758920i	0.0505252	+	0.0312973i
$589$	−3.68662			−0.151905
$590$	−4.84986	+	4.84986i	−0.199666	+	0.199666i
$591$	−24.7187	−	15.3118i	−1.01679	−	0.629841i
$592$	−2.97703	+	5.30446i	−0.122355	+	0.218012i
$593$			29.3236i			1.20417i	0.798430	+	0.602087i	$0.205664\pi$
$593$			29.3236i			1.20417i	−0.798430	+	0.602087i	$0.794336\pi$
$594$	14.1325	+	17.0392i	0.579865	+	0.699125i
$595$			21.7229i			0.890551i
$596$	−2.23999			−0.0917534
$597$	3.17056	+	13.4921i	0.129763	+	0.552193i
$598$	−3.43372	−	3.43372i	−0.140415	−	0.140415i
$599$		−	39.8668i		−	1.62891i	−0.580225	−	0.814456i	$-0.697035\pi$
$599$		−	39.8668i		−	1.62891i	0.580225	−	0.814456i	$-0.302965\pi$
$600$	1.68612	−	0.396230i	0.0688356	−	0.0161760i
$601$	0.173361			0.00707156			0.00353578	−	0.999994i	$-0.498875\pi$
$601$	0.173361			0.00707156			0.00353578	+	0.999994i	$0.498875\pi$
$602$			14.7308i			0.600383i
$603$	1.69750	−	0.844442i	0.0691277	−	0.0343883i
$604$	−3.40280			−0.138458
$605$	−5.05611	+	5.05611i	−0.205560	+	0.205560i
$606$	−21.1318	+	4.96586i	−0.858419	+	0.201724i
$607$	−8.00701	+	8.00701i	−0.324995	+	0.324995i	−0.850679	−	0.525685i	$-0.823809\pi$
$607$	−8.00701	+	8.00701i	−0.324995	+	0.324995i	0.525685	+	0.850679i	$0.323809\pi$
$608$		−	0.686416i		−	0.0278378i
$609$	−46.9001	+	11.0213i	−1.90049	+	0.446605i
$610$	−3.08764	+	3.08764i	−0.125015	+	0.125015i
$611$	4.28525	−	4.28525i	0.173363	−	0.173363i
$612$	−7.40867	+	22.0763i	−0.299478	+	0.892382i
$613$		−	23.8974i		−	0.965205i	−0.875839	−	0.482603i	$-0.839692\pi$
$613$		−	23.8974i		−	0.965205i	0.875839	−	0.482603i	$-0.160308\pi$
$614$	−6.27552	+	6.27552i	−0.253259	+	0.253259i
$615$	−3.12435	−	13.2954i	−0.125986	−	0.536122i
$616$	−8.43076	+	8.43076i	−0.339685	+	0.339685i
$617$	−2.77943			−0.111896			−0.0559478	−	0.998434i	$-0.517818\pi$
$617$	−2.77943			−0.111896			−0.0559478	+	0.998434i	$0.517818\pi$
$618$	−4.80306	+	7.75387i	−0.193207	+	0.311907i
$619$			0.897258i			0.0360638i	0.999837	+	0.0180319i	$0.00574005\pi$
$619$			0.897258i			0.0360638i	−0.999837	+	0.0180319i	$0.994260\pi$
$620$	5.37083			0.215698
$621$	7.73585	−	6.41623i	0.310429	−	0.257475i
$622$		−	3.86086i		−	0.154806i
$623$	−3.17105	−	3.17105i	−0.127045	−	0.127045i
$624$	−4.23317	+	0.994773i	−0.169462	+	0.0398228i
$625$	−1.00000			−0.0400000
$626$		−	6.38966i		−	0.255382i
$627$	−4.93082	+	1.15872i	−0.196918	+	0.0462747i
$628$		−	14.8138i		−	0.591134i
$629$	12.7744	+	45.4541i	0.509349	+	1.81237i
$630$	−3.73942	−	7.51700i	−0.148982	−	0.299485i
$631$	4.89754	−	4.89754i	0.194968	−	0.194968i	−0.602871	−	0.797839i	$-0.705977\pi$
$631$	4.89754	−	4.89754i	0.194968	−	0.194968i	0.797839	+	0.602871i	$0.205977\pi$
$632$	5.90595			0.234926
$633$	12.6991	−	20.5009i	0.504744	−	0.814839i
$634$	−1.63079	−	1.63079i	−0.0647670	−	0.0647670i
$635$	9.85843	−	9.85843i	0.391220	−	0.391220i
$636$	−2.12418	+	3.42919i	−0.0842290	+	0.135976i
$637$	1.47713	+	1.47713i	0.0585262	+	0.0585262i
$638$		−	42.3439i		−	1.67641i
$639$	−34.7802	+	17.3018i	−1.37588	+	0.684448i
$640$			1.00000i			0.0395285i
$641$			38.4671i			1.51936i	0.650298	+	0.759679i	$0.274644\pi$
$641$			38.4671i			1.51936i	−0.650298	+	0.759679i	$0.725356\pi$
$642$	5.59548	+	23.8111i	0.220836	+	0.939748i
$643$	−16.9600	+	16.9600i	−0.668837	+	0.668837i	−0.957447	−	0.288610i	$-0.906807\pi$
$643$	−16.9600	+	16.9600i	−0.668837	+	0.668837i	0.288610	+	0.957447i	$0.406807\pi$
$644$	3.82760	+	3.82760i	0.150829	+	0.150829i
$645$	4.80094	−	7.75046i	0.189037	−	0.305174i
$646$	−3.76748	−	3.76748i	−0.148230	−	0.148230i
$647$	22.8453	+	22.8453i	0.898142	+	0.898142i	0.995272	−	0.0971299i	$-0.0309662\pi$
$647$	22.8453	+	22.8453i	0.898142	+	0.898142i	−0.0971299	+	0.995272i	$0.530966\pi$
$648$	−1.23655	−	8.91465i	−0.0485764	−	0.350200i
$649$	−20.6620	+	20.6620i	−0.811055	+	0.811055i
$650$	2.51060			0.0984737
$651$	−5.95562	−	25.3436i	−0.233419	−	0.993293i
$652$	7.65234	+	7.65234i	0.299689	+	0.299689i
$653$	−33.5975	−	33.5975i	−1.31477	−	1.31477i	−0.917854	−	0.396917i	$-0.870080\pi$
$653$	−33.5975	−	33.5975i	−1.31477	−	1.31477i	−0.396917	−	0.917854i	$-0.629920\pi$
$654$	5.79257	+	3.58815i	0.226508	+	0.140308i
$655$	−2.77732			−0.108519
$656$	7.88519			0.307865
$657$	−22.1436	+	11.0156i	−0.863904	+	0.429759i
$658$	−4.77680	+	4.77680i	−0.186219	+	0.186219i
$659$	−18.7953			−0.732162			−0.366081	−	0.930583i	$-0.619301\pi$
$659$	−18.7953			−0.732162			−0.366081	+	0.930583i	$0.619301\pi$
$660$	7.18343	−	1.68807i	0.279615	−	0.0657081i
$661$	12.8955	−	12.8955i	0.501575	−	0.501575i	−0.410352	−	0.911927i	$-0.634594\pi$
$661$	12.8955	−	12.8955i	0.501575	−	0.501575i	0.911927	+	0.410352i	$0.134594\pi$
$662$			13.1328i			0.510422i
$663$	−17.7744	+	28.6943i	−0.690299	+	1.11439i
$664$	−8.91245	−	8.91245i	−0.345870	−	0.345870i
$665$	1.92099			0.0744928
$666$	−12.2450	−	13.5300i	−0.474485	−	0.524275i
$667$	−19.2243			−0.744368
$668$	−11.7216	−	11.7216i	−0.453522	−	0.453522i
$669$	−6.87070	+	11.0918i	−0.265637	+	0.428834i
$670$		−	0.631981i		−	0.0244156i
$671$	−13.1544	+	13.1544i	−0.507819	+	0.507819i
$672$	4.71875	−	1.10888i	0.182030	−	0.0427761i
$673$	18.9774			0.731524			0.365762	−	0.930708i	$-0.380808\pi$
$673$	18.9774			0.731524			0.365762	+	0.930708i	$0.380808\pi$
$674$	−23.0844	+	23.0844i	−0.889179	+	0.889179i
$675$	−0.482424	+	5.17371i	−0.0185685	+	0.199136i
$676$	6.69691			0.257573
$677$	13.4356			0.516374			0.258187	−	0.966095i	$-0.416875\pi$
$677$	13.4356			0.516374			0.258187	+	0.966095i	$0.416875\pi$
$678$	25.0014	+	15.4869i	0.960172	+	0.594769i
$679$	−10.6968	−	10.6968i	−0.410504	−	0.410504i
$680$	5.48863	+	5.48863i	0.210479	+	0.210479i
$681$	−0.491563	−	2.09180i	−0.0188368	−	0.0801581i
$682$	22.8815			0.876178
$683$	−35.2795	+	35.2795i	−1.34993	+	1.34993i	−0.464204	+	0.885728i	$0.653660\pi$
$683$	−35.2795	+	35.2795i	−1.34993	+	1.34993i	−0.885728	+	0.464204i	$0.846340\pi$
$684$	1.95224	+	0.655162i	0.0746460	+	0.0250507i
$685$	−4.77085	−	4.77085i	−0.182285	−	0.182285i
$686$	12.2057	+	12.2057i	0.466016	+	0.466016i
$687$	20.3643	−	32.8754i	0.776948	−	1.25428i
$688$	3.72198	+	3.72198i	0.141899	+	0.141899i
$689$	−4.13442	+	4.13442i	−0.157509	+	0.157509i
$690$	−0.766391	−	3.26131i	−0.0291760	−	0.124156i
$691$			45.3698i			1.72595i	0.505249	+	0.862974i	$0.331401\pi$
$691$			45.3698i			1.72595i	−0.505249	+	0.862974i	$0.668599\pi$
$692$			4.86504i			0.184941i
$693$	−15.9312	−	32.0249i	−0.605175	−	1.21653i
$694$			2.27401i			0.0863203i
$695$	12.5739	+	12.5739i	0.476957	+	0.476957i
$696$	−9.06536	+	14.6348i	−0.343622	+	0.554730i
$697$	43.2789	−	43.2789i	1.63931	−	1.63931i
$698$	−18.7815	−	18.7815i	−0.710892	−	0.710892i
$699$	−8.93318	+	14.4214i	−0.337884	+	0.545467i
$700$	−2.79858			−0.105776
$701$	9.83366	−	9.83366i	0.371412	−	0.371412i	−0.496579	−	0.867991i	$-0.665411\pi$
$701$	9.83366	−	9.83366i	0.371412	−	0.371412i	0.867991	+	0.496579i	$0.165411\pi$
$702$	1.21117	−	12.9891i	0.0457128	−	0.490242i
$703$	4.01958	−	1.12966i	0.151601	−	0.0426060i
$704$			4.26033i			0.160567i
$705$	4.07008	−	0.956448i	0.153288	−	0.0360219i
$706$			19.4316i			0.731319i
$707$	35.0740			1.31909
$708$	11.5647	−	2.71764i	0.434627	−	0.102135i
$709$	20.5292	+	20.5292i	0.770992	+	0.770992i	0.978280	−	0.207288i	$-0.0664638\pi$
$709$	20.5292	+	20.5292i	0.770992	+	0.770992i	−0.207288	+	0.978280i	$0.566464\pi$
$710$			12.9487i			0.485955i
$711$	−5.63704	+	16.7972i	−0.211406	+	0.629945i
$712$	−1.60243			−0.0600537
$713$		−	10.3883i		−	0.389045i
$714$	19.8132	−	31.9857i	0.741491	−	1.19704i
$715$	10.6960			0.400007
$716$	9.23529	−	9.23529i	0.345139	−	0.345139i
$717$	−1.61296	−	6.86378i	−0.0602369	−	0.256333i
$718$	19.4896	−	19.4896i	0.727347	−	0.727347i
$719$			40.7293i			1.51894i	0.650539	+	0.759472i	$0.274543\pi$
$719$			40.7293i			1.51894i	−0.650539	+	0.759472i	$0.725457\pi$
$720$	−2.84412	−	0.954468i	−0.105994	−	0.0355709i
$721$	10.4209	−	10.4209i	0.388093	−	0.388093i
$722$	13.1019	−	13.1019i	0.487601	−	0.487601i
$723$	18.8021	−	4.41840i	0.699258	−	0.164322i
$724$			19.4997i			0.724699i
$725$	7.02801	−	7.02801i	0.261014	−	0.261014i
$726$	12.0565	−	2.83321i	0.447458	−	0.105150i
$727$	−26.8295	+	26.8295i	−0.995051	+	0.995051i	−0.999988	−	0.00493697i	$-0.998429\pi$
$727$	−26.8295	+	26.8295i	−0.995051	+	0.995051i	0.00493697	+	0.999988i	$0.498429\pi$
$728$	7.02611			0.260405
$729$	26.5345	+	4.99184i	0.982761	+	0.184883i
$730$			8.24407i			0.305127i
$731$	40.8571			1.51116
$732$	7.36258	−	1.73017i	0.272129	−	0.0639489i
$733$			30.8995i			1.14130i	0.821194	+	0.570649i	$0.193308\pi$
$733$			30.8995i			1.14130i	−0.821194	+	0.570649i	$0.806692\pi$
$734$	7.18855	+	7.18855i	0.265334	+	0.265334i
$735$	0.329690	+	1.40296i	0.0121608	+	0.0517491i
$736$	1.93421			0.0712959
$737$		−	2.69245i		−	0.0991776i
$738$	−7.52616	+	22.4264i	−0.277042	+	0.825527i
$739$			29.0826i			1.06982i	0.844909	+	0.534910i	$0.179655\pi$
$739$			29.0826i			1.06982i	−0.844909	+	0.534910i	$0.820345\pi$
$740$	−5.85590	+	1.64574i	−0.215267	+	0.0604986i
$741$	2.53748	+	1.57182i	0.0932167	+	0.0577421i
$742$	4.60867	−	4.60867i	0.169190	−	0.169190i
$743$	47.5193			1.74331			0.871657	−	0.490117i	$-0.163046\pi$
$743$	47.5193			1.74331			0.871657	+	0.490117i	$0.163046\pi$
$744$	−7.90824	−	4.89868i	−0.289930	−	0.179594i
$745$	−1.58391	−	1.58391i	−0.0580299	−	0.0580299i
$746$	−21.0826	+	21.0826i	−0.771887	+	0.771887i
$747$	33.8547	−	16.8414i	1.23868	−	0.616194i
$748$	23.3834	+	23.3834i	0.854982	+	0.854982i
$749$		−	39.5210i		−	1.44407i
$750$	1.47244	+	0.912090i	0.0537661	+	0.0333048i
$751$		−	26.5041i		−	0.967149i	−0.875303	−	0.483574i	$-0.839338\pi$
$751$		−	26.5041i		−	0.967149i	0.875303	−	0.483574i	$-0.160662\pi$
$752$			2.41387i			0.0880248i
$753$	45.3490	−	10.6568i	1.65261	−	0.388355i
$754$	−17.6445	+	17.6445i	−0.642574	+	0.642574i
$755$	−2.40614	−	2.40614i	−0.0875685	−	0.0875685i
$756$	−1.35010	+	14.4791i	−0.0491028	+	0.526598i
$757$	−5.02571	−	5.02571i	−0.182662	−	0.182662i	0.609852	−	0.792515i	$-0.291229\pi$
$757$	−5.02571	−	5.02571i	−0.182662	−	0.182662i	−0.792515	+	0.609852i	$0.791229\pi$
$758$	8.39311	+	8.39311i	0.304851	+	0.304851i
$759$	−3.26508	−	13.8943i	−0.118515	−	0.504330i
$760$	0.485369	−	0.485369i	0.0176062	−	0.0176062i
$761$	38.7905			1.40616			0.703078	−	0.711113i	$-0.251809\pi$
$761$	38.7905			1.40616			0.703078	+	0.711113i	$0.251809\pi$
$762$	−23.5078	+	5.52420i	−0.851596	+	0.200121i
$763$	−7.78495	−	7.78495i	−0.281834	−	0.281834i
$764$	−2.29567	−	2.29567i	−0.0830546	−	0.0830546i
$765$	−20.8490	+	10.3716i	−0.753798	+	0.374985i
$766$	2.95950			0.106931
$767$	17.2195			0.621761
$768$	0.912090	−	1.47244i	0.0329122	−	0.0531322i
$769$	3.86885	−	3.86885i	0.139514	−	0.139514i	−0.633900	−	0.773415i	$-0.718547\pi$
$769$	3.86885	−	3.86885i	0.139514	−	0.139514i	0.773415	+	0.633900i	$0.218547\pi$
$770$	−11.9229			−0.429671
$771$	−1.00653	−	4.28322i	−0.0362495	−	0.154256i
$772$	−19.1715	+	19.1715i	−0.689997	+	0.689997i
$773$		−	20.4737i		−	0.736387i	−0.929749	−	0.368194i	$-0.879976\pi$
$773$		−	20.4737i		−	0.736387i	0.929749	−	0.368194i	$-0.120024\pi$
$774$	−14.1382	+	7.03323i	−0.508189	+	0.252804i
$775$	3.79775	+	3.79775i	0.136419	+	0.136419i
$776$	−5.40541			−0.194043
$777$	14.2593	+	25.8076i	0.511551	+	0.925842i
$778$	−9.37084			−0.335961
$779$	−3.82723	−	3.82723i	−0.137125	−	0.137125i
$780$	−3.69671	−	2.28989i	−0.132364	−	0.0819912i
$781$			55.1656i			1.97398i
$782$	10.6162	−	10.6162i	0.379633	−	0.379633i
$783$	−32.9704	−	39.7514i	−1.17827	−	1.42060i
$784$	−0.832067			−0.0297167
$785$	10.4749	−	10.4749i	0.373866	−	0.373866i
$786$	4.08944	+	2.53316i	0.145866	+	0.0903549i
$787$	21.8523			0.778949			0.389475	−	0.921037i	$-0.372657\pi$
$787$	21.8523			0.778949			0.389475	+	0.921037i	$0.372657\pi$
$788$	16.7875			0.598031
$789$	−23.3831	+	37.7488i	−0.832461	+	1.34389i
$790$	4.17614	+	4.17614i	0.148580	+	0.148580i
$791$	−33.6007	−	33.6007i	−1.19470	−	1.19470i
$792$	−12.1169	−	4.06635i	−0.430554	−	0.144491i
$793$	10.9627			0.389298
$794$	−0.313756	+	0.313756i	−0.0111348	+	0.0111348i
$795$	−3.92682	+	0.922783i	−0.139270	+	0.0327278i
$796$	−5.65815	−	5.65815i	−0.200548	−	0.200548i
$797$	−4.06692	−	4.06692i	−0.144058	−	0.144058i	0.631400	−	0.775458i	$-0.282481\pi$
$797$	−4.06692	−	4.06692i	−0.144058	−	0.144058i	−0.775458	+	0.631400i	$0.782481\pi$
$798$	−2.82855	−	1.75212i	−0.100130	−	0.0620243i
$799$	13.2489	+	13.2489i	0.468711	+	0.468711i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	1.52947	−	4.55750i	0.0540412	−	0.161031i
$802$		−	24.6138i		−	0.869144i
$803$			35.1225i			1.23944i
$804$	−0.576424	+	0.930557i	−0.0203289	+	0.0328182i
$805$			5.41304i			0.190785i
$806$	−9.53461	−	9.53461i	−0.335842	−	0.335842i
$807$	30.5036	+	18.8952i	1.07378	+	0.665141i
$808$	8.86201	−	8.86201i	0.311764	−	0.311764i
$809$	−2.15527	−	2.15527i	−0.0757753	−	0.0757753i	0.668203	−	0.743979i	$-0.267064\pi$
$809$	−2.15527	−	2.15527i	−0.0757753	−	0.0757753i	−0.743979	+	0.668203i	$0.767064\pi$
$810$	5.42923	−	7.17798i	0.190764	−	0.252209i
$811$	−14.4881			−0.508744			−0.254372	−	0.967106i	$-0.581869\pi$
$811$	−14.4881			−0.508744			−0.254372	+	0.967106i	$0.581869\pi$
$812$	19.6685	−	19.6685i	0.690228	−	0.690228i
$813$	6.49679	−	10.4882i	0.227852	−	0.367836i
$814$	−24.9481	+	7.01140i	−0.874429	+	0.245749i
$815$			10.8220i			0.379080i
$816$	−3.07558	−	13.0878i	−0.107667	−	0.458166i
$817$		−	3.61307i		−	0.126405i
$818$	−36.6163			−1.28026
$819$	−6.70620	+	19.9831i	−0.234334	+	0.698265i
$820$	5.57567	+	5.57567i	0.194711	+	0.194711i
$821$		−	34.2164i		−	1.19416i	−0.802181	−	0.597081i	$-0.796327\pi$
$821$		−	34.2164i		−	1.19416i	0.802181	−	0.597081i	$-0.203673\pi$
$822$	2.67337	+	11.3763i	0.0932443	+	0.396793i
$823$	36.1760			1.26102			0.630508	−	0.776182i	$-0.282846\pi$
$823$	36.1760			1.26102			0.630508	+	0.776182i	$0.282846\pi$
$824$		−	5.26599i		−	0.183449i
$825$	6.27310	+	3.88581i	0.218401	+	0.135286i
$826$	−19.1948			−0.667871
$827$	12.5541	−	12.5541i	0.436548	−	0.436548i	−0.454301	−	0.890848i	$-0.650111\pi$
$827$	12.5541	−	12.5541i	0.436548	−	0.436548i	0.890848	+	0.454301i	$0.150111\pi$
$828$	−1.84614	+	5.50111i	−0.0641578	+	0.191177i
$829$	−21.0679	+	21.0679i	−0.731720	+	0.731720i	−0.970960	−	0.239240i	$-0.923102\pi$
$829$	−21.0679	+	21.0679i	−0.731720	+	0.731720i	0.239240	+	0.970960i	$0.423102\pi$
$830$		−	12.6041i		−	0.437495i
$831$	5.24609	+	22.3242i	0.181985	+	0.774419i
$832$	1.77526	−	1.77526i	0.0615461	−	0.0615461i
$833$	−4.56691	+	4.56691i	−0.158234	+	0.158234i
$834$	−7.04585	−	29.9830i	−0.243978	−	1.03823i
$835$		−	16.5768i		−	0.573665i
$836$	2.06783	−	2.06783i	0.0715175	−	0.0715175i
$837$	21.4806	−	17.8163i	0.742477	−	0.615822i
$838$	28.1250	−	28.1250i	0.971561	−	0.971561i
$839$	−39.3937			−1.36002			−0.680010	−	0.733203i	$-0.738025\pi$
$839$	−39.3937			−1.36002			−0.680010	+	0.733203i	$0.738025\pi$
$840$	4.12076	+	2.55256i	0.142180	+	0.0880717i
$841$			69.7858i			2.40641i
$842$	−12.9517			−0.446345
$843$	10.6621	+	45.3718i	0.367224	+	1.56269i
$844$			13.9231i			0.479252i
$845$	4.73543	+	4.73543i	0.162904	+	0.162904i
$846$	−6.86533	−	2.30396i	−0.236035	−	0.0792118i
$847$	−20.0111			−0.687588
$848$		−	2.32891i		−	0.0799751i
$849$	10.2741	+	43.7204i	0.352605	+	1.50048i
$850$			7.76210i			0.266238i
$851$	3.18320	+	11.3265i	0.109119	+	0.388268i
$852$	11.8104	−	19.0662i	0.404616	−	0.653197i
$853$	−26.3657	+	26.3657i	−0.902744	+	0.902744i	−0.995673	−	0.0929292i	$-0.970377\pi$
$853$	−26.3657	+	26.3657i	−0.902744	+	0.902744i	0.0929292	+	0.995673i	$0.470377\pi$
$854$	−12.2202			−0.418168
$855$	0.917176	+	1.84371i	0.0313668	+	0.0630537i
$856$	−9.98563	−	9.98563i	−0.341302	−	0.341302i
$857$	−12.9356	+	12.9356i	−0.441872	+	0.441872i	−0.892641	−	0.450769i	$-0.851150\pi$
$857$	−12.9356	+	12.9356i	−0.441872	+	0.441872i	0.450769	+	0.892641i	$0.351150\pi$
$858$	−15.7492	−	9.75569i	−0.537669	−	0.333054i
$859$	−0.276702	−	0.276702i	−0.00944096	−	0.00944096i	0.702371	−	0.711812i	$-0.252125\pi$
$859$	−0.276702	−	0.276702i	−0.00944096	−	0.00944096i	−0.711812	+	0.702371i	$0.752125\pi$
$860$			5.26367i			0.179490i
$861$	20.1274	−	32.4930i	0.685941	−	1.10736i
$862$			31.7416i			1.08112i
$863$		−	11.7729i		−	0.400755i	−0.979719	−	0.200377i	$-0.935783\pi$
$863$		−	11.7729i		−	0.400755i	0.979719	−	0.200377i	$-0.0642168\pi$
$864$	3.31724	+	3.99949i	0.112855	+	0.136065i
$865$	−3.44010	+	3.44010i	−0.116967	+	0.116967i
$866$	−18.3533	−	18.3533i	−0.623671	−	0.623671i
$867$	−63.6835	−	39.4481i	−2.16280	−	1.33973i
$868$	10.6283	+	10.6283i	0.360749	+	0.360749i
$869$	17.7917	+	17.7917i	0.603543	+	0.603543i
$870$	−16.7585	+	3.93817i	−0.568167	+	0.133516i
$871$	−1.12193	+	1.12193i	−0.0380152	+	0.0380152i
$872$	−3.93399			−0.133222
$873$	5.15929	−	15.3736i	0.174616	−	0.520318i
$874$	−0.938805	−	0.938805i	−0.0317556	−	0.0317556i
$875$	−1.97890	−	1.97890i	−0.0668989	−	0.0668989i
$876$	7.51934	−	12.1389i	0.254055	−	0.410136i
$877$	13.9101			0.469712			0.234856	−	0.972030i	$-0.424538\pi$
$877$	13.9101			0.469712			0.234856	+	0.972030i	$0.424538\pi$
$878$	20.5772			0.694446
$879$	1.15214	+	0.713680i	0.0388607	+	0.0240718i
$880$	−3.01251	+	3.01251i	−0.101552	+	0.101552i
$881$	−10.8210			−0.364570			−0.182285	−	0.983246i	$-0.558349\pi$
$881$	−10.8210			−0.364570			−0.182285	+	0.983246i	$0.558349\pi$
$882$	0.794181	−	2.36649i	0.0267415	−	0.0796840i
$883$	17.6013	−	17.6013i	0.592332	−	0.592332i	−0.345929	−	0.938261i	$-0.612436\pi$
$883$	17.6013	−	17.6013i	0.592332	−	0.592332i	0.938261	+	0.345929i	$0.112436\pi$
$884$		−	19.4875i		−	0.655436i
$885$	10.0991	+	6.25579i	0.339478	+	0.210286i
$886$	−10.6085	−	10.6085i	−0.356399	−	0.356399i
$887$	−26.4867			−0.889337			−0.444669	−	0.895695i	$-0.646679\pi$
$887$	−26.4867			−0.889337			−0.444669	+	0.895695i	$0.646679\pi$
$888$	10.1235	+	2.91785i	0.339724	+	0.0979166i
$889$	39.0176			1.30861
$890$	−1.13309	−	1.13309i	−0.0379813	−	0.0379813i
$891$	23.1303	−	30.5806i	0.774895	−	1.02449i
$892$		−	7.53292i		−	0.252221i
$893$	1.17162	−	1.17162i	0.0392067	−	0.0392067i
$894$	0.887549	+	3.77689i	0.0296841	+	0.126318i
$895$	13.0607			0.436570
$896$	−1.97890	+	1.97890i	−0.0661103	+	0.0661103i
$897$	−4.42913	+	7.15021i	−0.147884	+	0.238739i
$898$	28.0761			0.936912
$899$	−53.3812			−1.78036
$900$	−1.33618	−	2.68600i	−0.0445394	−	0.0895335i
$901$	−12.7825	−	12.7825i	−0.425848	−	0.425848i
$902$	23.7542	+	23.7542i	0.790929	+	0.790929i
$903$	24.8379	−	5.83679i	0.826555	−	0.194236i
$904$	−16.9795			−0.564730
$905$	−13.7883	+	13.7883i	−0.458340	+	0.458340i
$906$	1.34829	+	5.73753i	0.0447940	+	0.190617i
$907$	6.82860	+	6.82860i	0.226740	+	0.226740i	0.811329	−	0.584589i	$-0.198744\pi$
$907$	6.82860	+	6.82860i	0.226740	+	0.226740i	−0.584589	+	0.811329i	$0.698744\pi$
$908$	0.877238	+	0.877238i	0.0291122	+	0.0291122i
$909$	16.7461	+	33.6631i	0.555432	+	1.11653i
$910$	4.96821	+	4.96821i	0.164695	+	0.164695i
$911$	9.63018	−	9.63018i	0.319062	−	0.319062i	−0.529345	−	0.848407i	$-0.677562\pi$
$911$	9.63018	−	9.63018i	0.319062	−	0.319062i	0.848407	+	0.529345i	$0.177562\pi$
$912$	−1.15738	+	0.271978i	−0.0383247	+	0.00900610i
$913$		−	53.6977i		−	1.77713i
$914$			27.3135i			0.903451i
$915$	6.42955	+	3.98272i	0.212554	+	0.131665i
$916$			22.3271i			0.737708i
$917$	−5.49602	−	5.49602i	−0.181495	−	0.181495i
$918$	40.1588	+	3.74462i	1.32544	+	0.123591i
$919$	29.4281	−	29.4281i	0.970743	−	0.970743i	−0.0288412	−	0.999584i	$-0.509182\pi$
$919$	29.4281	−	29.4281i	0.970743	−	0.970743i	0.999584	+	0.0288412i	$0.00918173\pi$
$920$	1.36769	+	1.36769i	0.0450915	+	0.0450915i
$921$	13.0678	+	8.09473i	0.430599	+	0.266730i
$922$	−13.7990			−0.454447
$923$	22.9873	−	22.9873i	0.756635	−	0.756635i
$924$	17.5558	+	10.8748i	0.577543	+	0.357753i
$925$	−5.30446	−	2.97703i	−0.174410	−	0.0978842i
$926$		−	18.8000i		−	0.617806i
$927$	14.9771	+	5.02622i	0.491912	+	0.165083i
$928$		−	9.93910i		−	0.326267i
$929$	16.9816			0.557150			0.278575	−	0.960415i	$-0.410138\pi$
$929$	16.9816			0.557150			0.278575	+	0.960415i	$0.410138\pi$
$930$	−2.12808	−	9.05586i	−0.0697826	−	0.296953i
$931$	0.403859	+	0.403859i	0.0132360	+	0.0132360i
$932$		−	9.79418i		−	0.320819i
$933$	−6.50987	+	1.52979i	−0.213124	+	0.0500830i
$934$	23.8341			0.779876
$935$			33.0691i			1.08148i
$936$	3.35461	+	6.74347i	0.109649	+	0.220417i
$937$	−5.98915			−0.195657			−0.0978285	−	0.995203i	$-0.531190\pi$
$937$	−5.98915			−0.195657			−0.0978285	+	0.995203i	$0.531190\pi$
$938$	1.25063	−	1.25063i	0.0408344	−	0.0408344i
$939$	−10.7737	+	2.53177i	−0.351587	+	0.0826213i
$940$	−1.70686	+	1.70686i	−0.0556718	+	0.0556718i
$941$		−	18.8149i		−	0.613347i	−0.951815	−	0.306674i	$-0.900784\pi$
$941$		−	18.8149i		−	0.613347i	0.951815	−	0.306674i	$-0.0992160\pi$
$942$	−24.9778	+	5.86966i	−0.813821	+	0.191244i
$943$	10.7845	−	10.7845i	0.351192	−	0.351192i
$944$	−4.84986	+	4.84986i	−0.157850	+	0.157850i
$945$	−11.1929	+	9.28357i	−0.364105	+	0.301995i
$946$			22.4250i			0.729099i
$947$	−33.8673	+	33.8673i	−1.10054	+	1.10054i	−0.106195	+	0.994345i	$0.533867\pi$
$947$	−33.8673	+	33.8673i	−1.10054	+	1.10054i	−0.994345	+	0.106195i	$0.966133\pi$
$948$	−2.34011	−	9.95815i	−0.0760034	−	0.323426i
$949$	14.6354	−	14.6354i	0.475084	−	0.475084i
$950$	0.686416			0.0222703
$951$	−2.10354	+	3.39588i	−0.0682121	+	0.110119i
$952$			21.7229i			0.704043i
$953$	−58.5974			−1.89816			−0.949079	−	0.315039i	$-0.897982\pi$
$953$	−58.5974			−1.89816			−0.949079	+	0.315039i	$0.897982\pi$
$954$	6.62369	+	2.22287i	0.214450	+	0.0719680i
$955$		−	3.24657i		−	0.105057i
$956$	2.87846	+	2.87846i	0.0930960	+	0.0930960i
$957$	−71.3969	+	16.7779i	−2.30793	+	0.542353i
$958$	2.53407			0.0818722
$959$		−	18.8821i		−	0.609734i
$960$	1.68612	−	0.396230i	0.0544193	−	0.0127883i
$961$			2.15420i			0.0694905i
$962$	13.3174	+	7.47412i	0.429369	+	0.240975i
$963$	37.9312	−	18.8693i	1.22232	−	0.608055i
$964$	−7.88502	+	7.88502i	−0.253960	+	0.253960i
$965$	−27.1126			−0.872784
$966$	4.93719	−	7.97040i	0.158851	−	0.256444i
$967$	−18.9184	−	18.9184i	−0.608373	−	0.608373i	0.334148	−	0.942521i	$-0.391552\pi$
$967$	−18.9184	−	18.9184i	−0.608373	−	0.608373i	−0.942521	+	0.334148i	$0.891552\pi$
$968$	−5.05611	+	5.05611i	−0.162510	+	0.162510i
$969$	−4.85964	+	7.84522i	−0.156114	+	0.252025i
$970$	−3.82220	−	3.82220i	−0.122724	−	0.122724i
$971$		−	53.0598i		−	1.70277i	−0.524541	−	0.851385i	$-0.675763\pi$
$971$		−	53.0598i		−	1.70277i	0.524541	−	0.851385i	$-0.324237\pi$
$972$	−14.5412	+	5.61723i	−0.466410	+	0.180173i
$973$			49.7651i			1.59539i
$974$		−	12.3037i		−	0.394237i
$975$	−0.994773	−	4.23317i	−0.0318582	−	0.135570i
$976$	−3.08764	+	3.08764i	−0.0988329	+	0.0988329i
$977$	19.6380	+	19.6380i	0.628276	+	0.628276i	0.947634	−	0.319358i	$-0.103467\pi$
$977$	19.6380	+	19.6380i	0.628276	+	0.628276i	−0.319358	+	0.947634i	$0.603467\pi$
$978$	9.87069	−	15.9349i	0.315630	−	0.509541i
$979$	−4.82734	−	4.82734i	−0.154282	−	0.154282i
$980$	−0.588360	−	0.588360i	−0.0187945	−	0.0187945i
$981$	3.75486	−	11.1887i	0.119884	−	0.357228i
$982$	−0.883287	+	0.883287i	−0.0281868	+	0.0281868i
$983$	18.0079			0.574363			0.287182	−	0.957876i	$-0.407282\pi$
$983$	18.0079			0.574363			0.287182	+	0.957876i	$0.407282\pi$
$984$	−3.12435	−	13.2954i	−0.0996006	−	0.423841i
$985$	11.8706	+	11.8706i	0.378228	+	0.378228i
$986$	−54.5521	−	54.5521i	−1.73729	−	1.73729i
$987$	9.94697	+	6.16155i	0.316616	+	0.196124i
$988$	−1.72331			−0.0548259
$989$	10.1810			0.323738
$990$	−5.69258	−	11.4433i	−0.180922	−	0.363691i
$991$	−29.7464	+	29.7464i	−0.944925	+	0.944925i	−0.998561	−	0.0536360i	$-0.982919\pi$
$991$	−29.7464	+	29.7464i	−0.944925	+	0.944925i	0.0536360	+	0.998561i	$0.482919\pi$
$992$	5.37083			0.170524
$993$	22.1435	−	5.20362i	0.702704	−	0.165132i
$994$	−25.6241	+	25.6241i	−0.812747	+	0.812747i
$995$		−	8.00183i		−	0.253675i
$996$	−11.4961	+	18.5588i	−0.364267	+	0.588059i
$997$	−30.3800	−	30.3800i	−0.962143	−	0.962143i	0.0371662	−	0.999309i	$-0.488167\pi$
$997$	−30.3800	−	30.3800i	−0.962143	−	0.962143i	−0.999309	+	0.0371662i	$0.988167\pi$
$998$	36.9537			1.16975
$999$	−17.9613	+	26.0075i	−0.568270	+	0.822842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.191.12	yes	40
3.2	odd	2	inner	1110.2.u.f.191.4	✓	40
37.31	odd	4	inner	1110.2.u.f.401.4	yes	40
111.68	even	4	inner	1110.2.u.f.401.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.4	✓	40	3.2	odd	2	inner
1110.2.u.f.191.12	yes	40	1.1	even	1	trivial
1110.2.u.f.401.4	yes	40	37.31	odd	4	inner
1110.2.u.f.401.12	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.912090 - 1.47244i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.68612 - 0.396230i) q^{6} -2.79858 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33618 - 2.68600i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.912090 - 1.47244i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.68612 - 0.396230i) q^{6} -2.79858 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.33618 - 2.68600i) q^{9} -1.00000 q^{10} -4.26033 q^{11} +(1.47244 + 0.912090i) q^{12} +(1.77526 + 1.77526i) q^{13} +(-1.97890 - 1.97890i) q^{14} +(0.396230 + 1.68612i) q^{15} -1.00000 q^{16} +(-5.48863 + 5.48863i) q^{17} +(0.954468 - 2.84412i) q^{18} +(0.485369 + 0.485369i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-2.55256 + 4.12076i) q^{21} +(-3.01251 - 3.01251i) q^{22} +(-1.36769 + 1.36769i) q^{23} +(0.396230 + 1.68612i) q^{24} -1.00000i q^{25} +2.51060i q^{26} +(-5.17371 - 0.482424i) q^{27} -2.79858i q^{28} +(7.02801 + 7.02801i) q^{29} +(-0.912090 + 1.47244i) q^{30} +(-3.79775 + 3.79775i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.88581 + 6.27310i) q^{33} -7.76210 q^{34} +(1.97890 - 1.97890i) q^{35} +(2.68600 - 1.33618i) q^{36} +(2.97703 - 5.30446i) q^{37} +0.686416i q^{38} +(4.23317 - 0.994773i) q^{39} -1.00000i q^{40} -7.88519 q^{41} +(-4.71875 + 1.10888i) q^{42} +(-3.72198 - 3.72198i) q^{43} -4.26033i q^{44} +(2.84412 + 0.954468i) q^{45} -1.93421 q^{46} -2.41387i q^{47} +(-0.912090 + 1.47244i) q^{48} +0.832067 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.07558 + 13.0878i) q^{51} +(-1.77526 + 1.77526i) q^{52} +2.32891i q^{53} +(-3.31724 - 3.99949i) q^{54} +(3.01251 - 3.01251i) q^{55} +(1.97890 - 1.97890i) q^{56} +(1.15738 - 0.271978i) q^{57} +9.93910i q^{58} +(4.84986 - 4.84986i) q^{59} +(-1.68612 + 0.396230i) q^{60} +(3.08764 - 3.08764i) q^{61} -5.37083 q^{62} +(3.73942 + 7.51700i) q^{63} -1.00000i q^{64} -2.51060 q^{65} +(-7.18343 + 1.68807i) q^{66} +0.631981i q^{67} +(-5.48863 - 5.48863i) q^{68} +(0.766391 + 3.26131i) q^{69} +2.79858 q^{70} -12.9487i q^{71} +(2.84412 + 0.954468i) q^{72} -8.24407i q^{73} +(5.85590 - 1.64574i) q^{74} +(-1.47244 - 0.912090i) q^{75} +(-0.485369 + 0.485369i) q^{76} +11.9229 q^{77} +(3.69671 + 2.28989i) q^{78} +(-4.17614 - 4.17614i) q^{79} +(0.707107 - 0.707107i) q^{80} +(-5.42923 + 7.17798i) q^{81} +(-5.57567 - 5.57567i) q^{82} +12.6041i q^{83} +(-4.12076 - 2.55256i) q^{84} -7.76210i q^{85} -5.26367i q^{86} +(16.7585 - 3.93817i) q^{87} +(3.01251 - 3.01251i) q^{88} +(1.13309 + 1.13309i) q^{89} +(1.33618 + 2.68600i) q^{90} +(-4.96821 - 4.96821i) q^{91} +(-1.36769 - 1.36769i) q^{92} +(2.12808 + 9.05586i) q^{93} +(1.70686 - 1.70686i) q^{94} -0.686416 q^{95} +(-1.68612 + 0.396230i) q^{96} +(3.82220 + 3.82220i) q^{97} +(0.588360 + 0.588360i) q^{98} +(5.69258 + 11.4433i) 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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