LMFDB - Embedded newform 1110.2.u.f.191.19

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			191.19
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.f.401.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.72452 - 0.161390i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.33354 + 1.10530i) q^{6} +0.212791 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.94791 - 0.556641i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.72452 - 0.161390i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.33354 + 1.10530i) q^{6} +0.212791 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.94791 - 0.556641i) q^{9} -1.00000 q^{10} +4.71272 q^{11} +(0.161390 + 1.72452i) q^{12} +(1.41003 + 1.41003i) q^{13} +(0.150466 + 0.150466i) q^{14} +(-1.10530 + 1.33354i) q^{15} -1.00000 q^{16} +(-2.20409 + 2.20409i) q^{17} +(2.47809 + 1.69088i) q^{18} +(-1.02880 - 1.02880i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(0.366962 - 0.0343425i) q^{21} +(3.33240 + 3.33240i) q^{22} +(-1.60069 + 1.60069i) q^{23} +(-1.10530 + 1.33354i) q^{24} -1.00000i q^{25} +1.99409i q^{26} +(4.99387 - 1.43570i) q^{27} +0.212791i q^{28} +(-3.47408 - 3.47408i) q^{29} +(-1.72452 + 0.161390i) q^{30} +(0.648056 - 0.648056i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.12716 - 0.760588i) q^{33} -3.11705 q^{34} +(-0.150466 + 0.150466i) q^{35} +(0.556641 + 2.94791i) q^{36} +(5.76392 - 1.94352i) q^{37} -1.45494i q^{38} +(2.65919 + 2.20406i) q^{39} -1.00000i q^{40} +1.68887 q^{41} +(0.283765 + 0.235197i) q^{42} +(2.65864 + 2.65864i) q^{43} +4.71272i q^{44} +(-1.69088 + 2.47809i) q^{45} -2.26372 q^{46} +12.0822i q^{47} +(-1.72452 + 0.161390i) q^{48} -6.95472 q^{49} +(0.707107 - 0.707107i) q^{50} +(-3.44527 + 4.15670i) q^{51} +(-1.41003 + 1.41003i) q^{52} +6.21062i q^{53} +(4.54639 + 2.51601i) q^{54} +(-3.33240 + 3.33240i) q^{55} +(-0.150466 + 0.150466i) q^{56} +(-1.94022 - 1.60814i) q^{57} -4.91308i q^{58} +(5.08490 - 5.08490i) q^{59} +(-1.33354 - 1.10530i) q^{60} +(-0.209223 + 0.209223i) q^{61} +0.916490 q^{62} +(0.627289 - 0.118448i) q^{63} -1.00000i q^{64} -1.99409 q^{65} +(6.28459 + 5.20895i) q^{66} -6.62596i q^{67} +(-2.20409 - 2.20409i) q^{68} +(-2.50208 + 3.01876i) q^{69} -0.212791 q^{70} +9.09313i q^{71} +(-1.69088 + 2.47809i) q^{72} -7.72992i q^{73} +(5.44998 + 2.70143i) q^{74} +(-0.161390 - 1.72452i) q^{75} +(1.02880 - 1.02880i) q^{76} +1.00283 q^{77} +(0.321827 + 3.43883i) q^{78} +(-12.0740 - 12.0740i) q^{79} +(0.707107 - 0.707107i) q^{80} +(8.38030 - 3.28185i) q^{81} +(1.19421 + 1.19421i) q^{82} +1.76283i q^{83} +(0.0343425 + 0.366962i) q^{84} -3.11705i q^{85} +3.75989i q^{86} +(-6.55178 - 5.43041i) q^{87} +(-3.33240 + 3.33240i) q^{88} +(6.73631 + 6.73631i) q^{89} +(-2.94791 + 0.556641i) q^{90} +(0.300042 + 0.300042i) q^{91} +(-1.60069 - 1.60069i) q^{92} +(1.01299 - 1.22217i) q^{93} +(-8.54344 + 8.54344i) q^{94} +1.45494 q^{95} +(-1.33354 - 1.10530i) q^{96} +(-10.7615 - 10.7615i) q^{97} +(-4.91773 - 4.91773i) q^{98} +(13.8927 - 2.62329i) 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
$3$	1.72452	−	0.161390i	0.995649	−	0.0931788i
$3$	1.72452	−	0.161390i	0.995649	−	0.0931788i
$4$			1.00000i			0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	1.33354	+	1.10530i	0.544414	+	0.451235i
$7$	0.212791			0.0804275			0.0402138	−	0.999191i	$-0.487196\pi$
$7$	0.212791			0.0804275			0.0402138	+	0.999191i	$0.487196\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.94791	−	0.556641i	0.982635	−	0.185547i
$10$	−1.00000			−0.316228
$11$	4.71272			1.42094			0.710469	−	0.703728i	$-0.248483\pi$
$11$	4.71272			1.42094			0.710469	+	0.703728i	$0.248483\pi$
$12$	0.161390	+	1.72452i	0.0465894	+	0.497825i
$13$	1.41003	+	1.41003i	0.391073	+	0.391073i	0.875070	−	0.483997i	$-0.160815\pi$
$13$	1.41003	+	1.41003i	0.391073	+	0.391073i	−0.483997	+	0.875070i	$0.660815\pi$
$14$	0.150466	+	0.150466i	0.0402138	+	0.0402138i
$15$	−1.10530	+	1.33354i	−0.285386	+	0.344318i
$16$	−1.00000			−0.250000
$17$	−2.20409	+	2.20409i	−0.534570	+	0.534570i	−0.921929	−	0.387359i	$-0.873387\pi$
$17$	−2.20409	+	2.20409i	−0.534570	+	0.534570i	0.387359	+	0.921929i	$0.373387\pi$
$18$	2.47809	+	1.69088i	0.584091	+	0.398544i
$19$	−1.02880	−	1.02880i	−0.236023	−	0.236023i	0.579178	−	0.815201i	$-0.303374\pi$
$19$	−1.02880	−	1.02880i	−0.236023	−	0.236023i	−0.815201	+	0.579178i	$0.803374\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	0.366962	−	0.0343425i	0.0800776	−	0.00749414i
$22$	3.33240	+	3.33240i	0.710469	+	0.710469i
$23$	−1.60069	+	1.60069i	−0.333768	+	0.333768i	−0.854015	−	0.520248i	$-0.825840\pi$
$23$	−1.60069	+	1.60069i	−0.333768	+	0.333768i	0.520248	+	0.854015i	$0.325840\pi$
$24$	−1.10530	+	1.33354i	−0.225618	+	0.272207i
$25$		−	1.00000i		−	0.200000i
$26$			1.99409i			0.391073i
$27$	4.99387	−	1.43570i	0.961071	−	0.276300i
$28$			0.212791i			0.0402138i
$29$	−3.47408	−	3.47408i	−0.645120	−	0.645120i	0.306690	−	0.951810i	$-0.400779\pi$
$29$	−3.47408	−	3.47408i	−0.645120	−	0.645120i	−0.951810	+	0.306690i	$0.900779\pi$
$30$	−1.72452	+	0.161390i	−0.314852	+	0.0294657i
$31$	0.648056	−	0.648056i	0.116394	−	0.116394i	−0.646511	−	0.762905i	$-0.723772\pi$
$31$	0.648056	−	0.648056i	0.116394	−	0.116394i	0.762905	+	0.646511i	$0.223772\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	8.12716	−	0.760588i	1.41476	−	0.132401i
$34$	−3.11705			−0.534570
$35$	−0.150466	+	0.150466i	−0.0254334	+	0.0254334i
$36$	0.556641	+	2.94791i	0.0927734	+	0.491318i
$37$	5.76392	−	1.94352i	0.947582	−	0.319513i
$37$	5.76392	−	1.94352i	0.947582	−	0.319513i
$38$		−	1.45494i		−	0.236023i
$39$	2.65919	+	2.20406i	0.425811	+	0.352931i
$40$		−	1.00000i		−	0.158114i
$41$	1.68887			0.263758			0.131879	−	0.991266i	$-0.457899\pi$
$41$	1.68887			0.263758			0.131879	+	0.991266i	$0.457899\pi$
$42$	0.283765	+	0.235197i	0.0437859	+	0.0362917i
$43$	2.65864	+	2.65864i	0.405439	+	0.405439i	0.880145	−	0.474706i	$-0.157445\pi$
$43$	2.65864	+	2.65864i	0.405439	+	0.405439i	−0.474706	+	0.880145i	$0.657445\pi$
$44$			4.71272i			0.710469i
$45$	−1.69088	+	2.47809i	−0.252062	+	0.369412i
$46$	−2.26372			−0.333768
$47$			12.0822i			1.76238i	0.472765	+	0.881189i	$0.343256\pi$
$47$			12.0822i			1.76238i	−0.472765	+	0.881189i	$0.656744\pi$
$48$	−1.72452	+	0.161390i	−0.248912	+	0.0232947i
$49$	−6.95472			−0.993531
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	−3.44527	+	4.15670i	−0.482434	+	0.582055i
$52$	−1.41003	+	1.41003i	−0.195536	+	0.195536i
$53$			6.21062i			0.853094i	0.904465	+	0.426547i	$0.140270\pi$
$53$			6.21062i			0.853094i	−0.904465	+	0.426547i	$0.859730\pi$
$54$	4.54639	+	2.51601i	0.618686	+	0.342385i
$55$	−3.33240	+	3.33240i	−0.449340	+	0.449340i
$56$	−0.150466	+	0.150466i	−0.0201069	+	0.0201069i
$57$	−1.94022	−	1.60814i	−0.256989	−	0.213004i
$58$		−	4.91308i		−	0.645120i
$59$	5.08490	−	5.08490i	0.661997	−	0.661997i	−0.293853	−	0.955851i	$-0.594938\pi$
$59$	5.08490	−	5.08490i	0.661997	−	0.661997i	0.955851	+	0.293853i	$0.0949377\pi$
$60$	−1.33354	−	1.10530i	−0.172159	−	0.142693i
$61$	−0.209223	+	0.209223i	−0.0267883	+	0.0267883i	−0.720374	−	0.693586i	$-0.756030\pi$
$61$	−0.209223	+	0.209223i	−0.0267883	+	0.0267883i	0.693586	+	0.720374i	$0.256030\pi$
$62$	0.916490			0.116394
$63$	0.627289	−	0.118448i	0.0790309	−	0.0149231i
$64$		−	1.00000i		−	0.125000i
$65$	−1.99409			−0.247336
$66$	6.28459	+	5.20895i	0.773579	+	0.641178i
$67$		−	6.62596i		−	0.809489i	−0.914430	−	0.404745i	$-0.867360\pi$
$67$		−	6.62596i		−	0.809489i	0.914430	−	0.404745i	$-0.132640\pi$
$68$	−2.20409	−	2.20409i	−0.267285	−	0.267285i
$69$	−2.50208	+	3.01876i	−0.301216	+	0.363416i
$70$	−0.212791			−0.0254334
$71$			9.09313i			1.07916i	0.841936	+	0.539578i	$0.181416\pi$
$71$			9.09313i			1.07916i	−0.841936	+	0.539578i	$0.818584\pi$
$72$	−1.69088	+	2.47809i	−0.199272	+	0.292046i
$73$		−	7.72992i		−	0.904718i	−0.891836	−	0.452359i	$-0.850583\pi$
$73$		−	7.72992i		−	0.904718i	0.891836	−	0.452359i	$-0.149417\pi$
$74$	5.44998	+	2.70143i	0.633547	+	0.314034i
$75$	−0.161390	−	1.72452i	−0.0186358	−	0.199130i
$76$	1.02880	−	1.02880i	0.118012	−	0.118012i
$77$	1.00283			0.114283
$78$	0.321827	+	3.43883i	0.0364397	+	0.389371i
$79$	−12.0740	−	12.0740i	−1.35843	−	1.35843i	−0.875854	−	0.482576i	$-0.839701\pi$
$79$	−12.0740	−	12.0740i	−1.35843	−	1.35843i	−0.482576	−	0.875854i	$-0.660299\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	8.38030	−	3.28185i	0.931145	−	0.364650i
$82$	1.19421	+	1.19421i	0.131879	+	0.131879i
$83$			1.76283i			0.193496i	0.995309	+	0.0967479i	$0.0308440\pi$
$83$			1.76283i			0.193496i	−0.995309	+	0.0967479i	$0.969156\pi$
$84$	0.0343425	+	0.366962i	0.00374707	+	0.0400388i
$85$		−	3.11705i		−	0.338092i
$86$			3.75989i			0.405439i
$87$	−6.55178	−	5.43041i	−0.702424	−	0.582201i
$88$	−3.33240	+	3.33240i	−0.355235	+	0.355235i
$89$	6.73631	+	6.73631i	0.714048	+	0.714048i	0.967379	−	0.253332i	$-0.0815264\pi$
$89$	6.73631	+	6.73631i	0.714048	+	0.714048i	−0.253332	+	0.967379i	$0.581526\pi$
$90$	−2.94791	+	0.556641i	−0.310737	+	0.0586751i
$91$	0.300042	+	0.300042i	0.0314530	+	0.0314530i
$92$	−1.60069	−	1.60069i	−0.166884	−	0.166884i
$93$	1.01299	−	1.22217i	0.105042	−	0.126733i
$94$	−8.54344	+	8.54344i	−0.881189	+	0.881189i
$95$	1.45494			0.149274
$96$	−1.33354	−	1.10530i	−0.136104	−	0.112809i
$97$	−10.7615	−	10.7615i	−1.09266	−	1.09266i	−0.995244	−	0.0974174i	$-0.968942\pi$
$97$	−10.7615	−	10.7615i	−1.09266	−	1.09266i	−0.0974174	−	0.995244i	$-0.531058\pi$
$98$	−4.91773	−	4.91773i	−0.496766	−	0.496766i
$99$	13.8927	−	2.62329i	1.39626	−	0.263651i
$100$	1.00000			0.100000
$101$	2.17380			0.216301			0.108151	−	0.994135i	$-0.465507\pi$
$101$	2.17380			0.216301			0.108151	+	0.994135i	$0.465507\pi$
$102$	−5.37541	+	0.503063i	−0.532244	+	0.0498106i
$103$	7.15412	−	7.15412i	0.704916	−	0.704916i	−0.260545	−	0.965462i	$-0.583902\pi$
$103$	7.15412	−	7.15412i	0.704916	−	0.704916i	0.965462	+	0.260545i	$0.0839023\pi$
$104$	−1.99409			−0.195536
$105$	−0.235197	+	0.283765i	−0.0229529	+	0.0276926i
$106$	−4.39157	+	4.39157i	−0.426547	+	0.426547i
$107$		−	7.17188i		−	0.693332i	−0.937989	−	0.346666i	$-0.887314\pi$
$107$		−	7.17188i		−	0.693332i	0.937989	−	0.346666i	$-0.112686\pi$
$108$	1.43570	+	4.99387i	0.138150	+	0.480536i
$109$	−12.2708	−	12.2708i	−1.17533	−	1.17533i	−0.980921	−	0.194406i	$-0.937722\pi$
$109$	−12.2708	−	12.2708i	−1.17533	−	1.17533i	−0.194406	−	0.980921i	$-0.562278\pi$
$110$	−4.71272			−0.449340
$111$	9.62630	−	4.28187i	0.913688	−	0.406417i
$112$	−0.212791			−0.0201069
$113$	−11.9771	−	11.9771i	−1.12671	−	1.12671i	−0.990709	−	0.135999i	$-0.956576\pi$
$113$	−11.9771	−	11.9771i	−1.12671	−	1.12671i	−0.135999	−	0.990709i	$-0.543424\pi$
$114$	−0.234814	−	2.50907i	−0.0219924	−	0.234996i
$115$		−	2.26372i		−	0.211093i
$116$	3.47408	−	3.47408i	0.322560	−	0.322560i
$117$	4.94152	+	3.37176i	0.456844	+	0.311719i
$118$	7.19113			0.661997
$119$	−0.469011	+	0.469011i	−0.0429942	+	0.0429942i
$120$	−0.161390	−	1.72452i	−0.0147329	−	0.157426i
$121$	11.2097			1.01907
$122$	−0.295886			−0.0267883
$123$	2.91249	−	0.272568i	0.262610	−	0.0245767i
$124$	0.648056	+	0.648056i	0.0581972	+	0.0581972i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	0.527316	+	0.359804i	0.0469770	+	0.0320539i
$127$	−5.62416			−0.499064			−0.249532	−	0.968367i	$-0.580277\pi$
$127$	−5.62416			−0.499064			−0.249532	+	0.968367i	$0.580277\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	5.01395	+	4.15579i	0.441454	+	0.365897i
$130$	−1.41003	−	1.41003i	−0.123668	−	0.123668i
$131$	−8.26356	−	8.26356i	−0.721990	−	0.721990i	0.247020	−	0.969010i	$-0.420549\pi$
$131$	−8.26356	−	8.26356i	−0.721990	−	0.721990i	−0.969010	+	0.247020i	$0.920549\pi$
$132$	0.760588	+	8.12716i	0.0662007	+	0.707379i
$133$	−0.218920	−	0.218920i	−0.0189828	−	0.0189828i
$134$	4.68526	−	4.68526i	0.404745	−	0.404745i
$135$	−2.51601	+	4.54639i	−0.216544	+	0.391291i
$136$		−	3.11705i		−	0.267285i
$137$			6.03021i			0.515195i	0.966252	+	0.257598i	$0.0829309\pi$
$137$			6.03021i			0.515195i	−0.966252	+	0.257598i	$0.917069\pi$
$138$	−3.90382	+	0.365343i	−0.332316	+	0.0311001i
$139$		−	2.97812i		−	0.252601i	−0.991992	−	0.126301i	$-0.959690\pi$
$139$		−	2.97812i		−	0.252601i	0.991992	−	0.126301i	$-0.0403104\pi$
$140$	−0.150466	−	0.150466i	−0.0127167	−	0.0127167i
$141$	1.94996	+	20.8360i	0.164216	+	1.75471i
$142$	−6.42981	+	6.42981i	−0.539578	+	0.539578i
$143$	6.64509	+	6.64509i	0.555690	+	0.555690i
$144$	−2.94791	+	0.556641i	−0.245659	+	0.0463867i
$145$	4.91308			0.408009
$146$	5.46588	−	5.46588i	0.452359	−	0.452359i
$147$	−11.9935	+	1.12243i	−0.989209	+	0.0925761i
$148$	1.94352	+	5.76392i	0.159756	+	0.473791i
$149$		−	12.2264i		−	1.00162i	−0.865557	−	0.500811i	$-0.833035\pi$
$149$		−	12.2264i		−	1.00162i	0.865557	−	0.500811i	$-0.166965\pi$
$150$	1.10530	−	1.33354i	0.0902471	−	0.108883i
$151$		−	3.92504i		−	0.319416i	−0.987164	−	0.159708i	$-0.948945\pi$
$151$		−	3.92504i		−	0.319416i	0.987164	−	0.159708i	$-0.0510552\pi$
$152$	1.45494			0.118012
$153$	−5.27056	+	7.72433i	−0.426100	+	0.624475i
$154$	0.709105	+	0.709105i	0.0571413	+	0.0571413i
$155$			0.916490i			0.0736142i
$156$	−2.20406	+	2.65919i	−0.176466	+	0.212905i
$157$	3.99434			0.318783			0.159391	−	0.987215i	$-0.449047\pi$
$157$	3.99434			0.318783			0.159391	+	0.987215i	$0.449047\pi$
$158$		−	17.0752i		−	1.35843i
$159$	1.00233	+	10.7103i	0.0794903	+	0.849382i
$160$	1.00000			0.0790569
$161$	−0.340614	+	0.340614i	−0.0268441	+	0.0268441i
$162$	8.24639	+	3.60515i	0.647897	+	0.283247i
$163$	0.442429	−	0.442429i	0.0346537	−	0.0346537i	−0.689568	−	0.724221i	$-0.742199\pi$
$163$	0.442429	−	0.442429i	0.0346537	−	0.0346537i	0.724221	+	0.689568i	$0.242199\pi$
$164$			1.68887i			0.131879i
$165$	−5.20895	+	6.28459i	−0.405516	+	0.489254i
$166$	−1.24651	+	1.24651i	−0.0967479	+	0.0967479i
$167$	4.70495	−	4.70495i	0.364080	−	0.364080i	−0.501233	−	0.865313i	$-0.667120\pi$
$167$	4.70495	−	4.70495i	0.364080	−	0.364080i	0.865313	+	0.501233i	$0.167120\pi$
$168$	−0.235197	+	0.283765i	−0.0181459	+	0.0218929i
$169$		−	9.02362i		−	0.694124i
$170$	2.20409	−	2.20409i	0.169046	−	0.169046i
$171$	−3.60548	−	2.46014i	−0.275718	−	0.188131i
$172$	−2.65864	+	2.65864i	−0.202720	+	0.202720i
$173$	−7.18735			−0.546444			−0.273222	−	0.961951i	$-0.588089\pi$
$173$	−7.18735			−0.546444			−0.273222	+	0.961951i	$0.588089\pi$
$174$	−0.792925	−	8.47269i	−0.0601115	−	0.642313i
$175$		−	0.212791i		−	0.0160855i
$176$	−4.71272			−0.355235
$177$	7.94833	−	9.58964i	0.597433	−	0.720801i
$178$			9.52659i			0.714048i
$179$	−10.3857	−	10.3857i	−0.776265	−	0.776265i	0.202929	−	0.979194i	$-0.434954\pi$
$179$	−10.3857	−	10.3857i	−0.776265	−	0.776265i	−0.979194	+	0.202929i	$0.934954\pi$
$180$	−2.47809	−	1.69088i	−0.184706	−	0.126031i
$181$	12.2446			0.910134			0.455067	−	0.890457i	$-0.349615\pi$
$181$	12.2446			0.910134			0.455067	+	0.890457i	$0.349615\pi$
$182$			0.424324i			0.0314530i
$183$	−0.327042	+	0.394575i	−0.0241756	+	0.0291679i
$184$		−	2.26372i		−	0.166884i
$185$	−2.70143	+	5.44998i	−0.198613	+	0.400691i
$186$	1.58050	−	0.147913i	0.115888	−	0.0108455i
$187$	−10.3873	+	10.3873i	−0.759592	+	0.759592i
$188$	−12.0822			−0.881189
$189$	1.06265	−	0.305504i	0.0772966	−	0.0222222i
$190$	1.02880	+	1.02880i	0.0746371	+	0.0746371i
$191$	−16.9400	+	16.9400i	−1.22573	+	1.22573i	−0.260170	+	0.965563i	$0.583779\pi$
$191$	−16.9400	+	16.9400i	−1.22573	+	1.22573i	−0.965563	+	0.260170i	$0.916221\pi$
$192$	−0.161390	−	1.72452i	−0.0116474	−	0.124456i
$193$	−4.52736	−	4.52736i	−0.325886	−	0.325886i	0.525133	−	0.851020i	$-0.324015\pi$
$193$	−4.52736	−	4.52736i	−0.325886	−	0.325886i	−0.851020	+	0.525133i	$0.824015\pi$
$194$		−	15.2190i		−	1.09266i
$195$	−3.43883	+	0.321827i	−0.246260	+	0.0230465i
$196$		−	6.95472i		−	0.496766i
$197$			9.73635i			0.693686i	0.937923	+	0.346843i	$0.112746\pi$
$197$			9.73635i			0.693686i	−0.937923	+	0.346843i	$0.887254\pi$
$198$	11.6785	+	7.96865i	0.829958	+	0.566307i
$199$	−9.81131	+	9.81131i	−0.695506	+	0.695506i	−0.963438	−	0.267932i	$-0.913660\pi$
$199$	−9.81131	+	9.81131i	−0.695506	+	0.695506i	0.267932	+	0.963438i	$0.413660\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	−1.06937	−	11.4266i	−0.0754273	−	0.805968i
$202$	1.53711	+	1.53711i	0.108151	+	0.108151i
$203$	−0.739253	−	0.739253i	−0.0518854	−	0.0518854i
$204$	−4.15670	−	3.44527i	−0.291028	−	0.241217i
$205$	−1.19421	+	1.19421i	−0.0834076	+	0.0834076i
$206$	10.1175			0.704916
$207$	−3.82768	+	5.60971i	−0.266042	+	0.389901i
$208$	−1.41003	−	1.41003i	−0.0977681	−	0.0977681i
$209$	−4.84845	−	4.84845i	−0.335374	−	0.335374i
$210$	−0.366962	+	0.0343425i	−0.0253228	+	0.00236986i
$211$	17.1979			1.18395			0.591975	−	0.805956i	$-0.298348\pi$
$211$	17.1979			1.18395			0.591975	+	0.805956i	$0.298348\pi$
$212$	−6.21062			−0.426547
$213$	1.46754	+	15.6812i	0.100554	+	1.07446i
$214$	5.07128	−	5.07128i	0.346666	−	0.346666i
$215$	−3.75989			−0.256422
$216$	−2.51601	+	4.54639i	−0.171193	+	0.309343i
$217$	0.137901	−	0.137901i	0.00936131	−	0.00936131i
$218$		−	17.3535i		−	1.17533i
$219$	−1.24753	−	13.3304i	−0.0843006	−	0.900782i
$220$	−3.33240	−	3.33240i	−0.224670	−	0.224670i
$221$	−6.21567			−0.418111
$222$	9.83456	+	3.77908i	0.660052	+	0.253635i
$223$	14.2436			0.953822			0.476911	−	0.878952i	$-0.341756\pi$
$223$	14.2436			0.953822			0.476911	+	0.878952i	$0.341756\pi$
$224$	−0.150466	−	0.150466i	−0.0100534	−	0.0100534i
$225$	−0.556641	−	2.94791i	−0.0371094	−	0.196527i
$226$		−	16.9381i		−	1.12671i
$227$	7.34361	−	7.34361i	0.487413	−	0.487413i	−0.420076	−	0.907489i	$-0.637997\pi$
$227$	7.34361	−	7.34361i	0.487413	−	0.487413i	0.907489	+	0.420076i	$0.137997\pi$
$228$	1.60814	−	1.94022i	0.106502	−	0.128494i
$229$	−7.18264			−0.474642			−0.237321	−	0.971431i	$-0.576269\pi$
$229$	−7.18264			−0.474642			−0.237321	+	0.971431i	$0.576269\pi$
$230$	1.60069	−	1.60069i	0.105547	−	0.105547i
$231$	1.72939	−	0.161847i	0.113785	−	0.0106487i
$232$	4.91308			0.322560
$233$	13.6955			0.897222			0.448611	−	0.893727i	$-0.351919\pi$
$233$	13.6955			0.897222			0.448611	+	0.893727i	$0.351919\pi$
$234$	1.10999	+	5.87838i	0.0725623	+	0.384282i
$235$	−8.54344	−	8.54344i	−0.557313	−	0.557313i
$236$	5.08490	+	5.08490i	0.330999	+	0.330999i
$237$	−22.7704	−	18.8732i	−1.47910	−	1.22594i
$238$	−0.663281			−0.0429942
$239$	−18.3219	+	18.3219i	−1.18514	+	1.18514i	−0.206751	+	0.978394i	$0.566289\pi$
$239$	−18.3219	+	18.3219i	−1.18514	+	1.18514i	−0.978394	+	0.206751i	$0.933711\pi$
$240$	1.10530	−	1.33354i	0.0713466	−	0.0860794i
$241$	10.3781	+	10.3781i	0.668513	+	0.668513i	0.957372	−	0.288859i	$-0.0932758\pi$
$241$	10.3781	+	10.3781i	0.668513	+	0.668513i	−0.288859	+	0.957372i	$0.593276\pi$
$242$	7.92649	+	7.92649i	0.509534	+	0.509534i
$243$	13.9223	−	7.01210i	0.893116	−	0.449826i
$244$	−0.209223	−	0.209223i	−0.0133941	−	0.0133941i
$245$	4.91773	−	4.91773i	0.314182	−	0.314182i
$246$	2.25218	+	1.86671i	0.143594	+	0.119017i
$247$		−	2.90128i		−	0.184604i
$248$			0.916490i			0.0581972i
$249$	0.284504	+	3.04003i	0.0180297	+	0.192654i
$250$			1.00000i			0.0632456i
$251$	0.243445	+	0.243445i	0.0153661	+	0.0153661i	0.714748	−	0.699382i	$-0.246541\pi$
$251$	0.243445	+	0.243445i	0.0153661	+	0.0153661i	−0.699382	+	0.714748i	$0.746541\pi$
$252$	0.118448	+	0.627289i	0.00746154	+	0.0395155i
$253$	−7.54362	+	7.54362i	−0.474264	+	0.474264i
$254$	−3.97688	−	3.97688i	−0.249532	−	0.249532i
$255$	−0.503063	−	5.37541i	−0.0315030	−	0.336621i
$256$	1.00000			0.0625000
$257$	−5.22108	+	5.22108i	−0.325682	+	0.325682i	−0.850942	−	0.525260i	$-0.823968\pi$
$257$	−5.22108	+	5.22108i	−0.325682	+	0.325682i	0.525260	+	0.850942i	$0.323968\pi$
$258$	0.606810	+	6.48399i	0.0377783	+	0.403675i
$259$	1.22651	−	0.413564i	0.0762117	−	0.0256976i
$260$		−	1.99409i		−	0.123668i
$261$	−12.1751	−	8.30744i	−0.753617	−	0.514217i
$262$		−	11.6864i		−	0.721990i
$263$	17.2011			1.06067			0.530333	−	0.847789i	$-0.322067\pi$
$263$	17.2011			1.06067			0.530333	+	0.847789i	$0.322067\pi$
$264$	−5.20895	+	6.28459i	−0.320589	+	0.386790i
$265$	−4.39157	−	4.39157i	−0.269772	−	0.269772i
$266$		−	0.309599i		−	0.0189828i
$267$	12.7041	+	10.5297i	0.777475	+	0.644407i
$268$	6.62596			0.404745
$269$		−	0.804854i		−	0.0490728i	−0.999699	−	0.0245364i	$-0.992189\pi$
$269$		−	0.804854i		−	0.0490728i	0.999699	−	0.0245364i	$-0.00781097\pi$
$270$	−4.99387	+	1.43570i	−0.303917	+	0.0873739i
$271$	−3.45379			−0.209803			−0.104901	−	0.994483i	$-0.533453\pi$
$271$	−3.45379			−0.209803			−0.104901	+	0.994483i	$0.533453\pi$
$272$	2.20409	−	2.20409i	0.133643	−	0.133643i
$273$	0.565852	+	0.469004i	0.0342469	+	0.0283854i
$274$	−4.26400	+	4.26400i	−0.257598	+	0.257598i
$275$		−	4.71272i		−	0.284188i
$276$	−3.01876	−	2.50208i	−0.181708	−	0.150608i
$277$	8.54695	−	8.54695i	0.513537	−	0.513537i	−0.402072	−	0.915608i	$-0.631710\pi$
$277$	8.54695	−	8.54695i	0.513537	−	0.513537i	0.915608	+	0.402072i	$0.131710\pi$
$278$	2.10585	−	2.10585i	0.126301	−	0.126301i
$279$	1.54967	−	2.27114i	0.0927766	−	0.135970i
$280$		−	0.212791i		−	0.0127167i
$281$	15.3513	−	15.3513i	0.915780	−	0.915780i	−0.0809388	−	0.996719i	$-0.525792\pi$
$281$	15.3513	−	15.3513i	0.915780	−	0.915780i	0.996719	+	0.0809388i	$0.0257918\pi$
$282$	−13.3545	+	16.1121i	−0.795247	+	0.959463i
$283$	1.29497	−	1.29497i	0.0769783	−	0.0769783i	−0.667569	−	0.744548i	$-0.732665\pi$
$283$	1.29497	−	1.29497i	0.0769783	−	0.0769783i	0.744548	+	0.667569i	$0.232665\pi$
$284$	−9.09313			−0.539578
$285$	2.50907	−	0.234814i	0.148625	−	0.0139092i
$286$			9.39757i			0.555690i
$287$	0.359378			0.0212134
$288$	−2.47809	−	1.69088i	−0.146023	−	0.0996361i
$289$			7.28398i			0.428469i
$290$	3.47408	+	3.47408i	0.204005	+	0.204005i
$291$	−20.2951	−	16.8215i	−1.18972	−	0.986094i
$292$	7.72992			0.452359
$293$			21.5240i			1.25745i	0.777629	+	0.628723i	$0.216422\pi$
$293$			21.5240i			1.25745i	−0.777629	+	0.628723i	$0.783578\pi$
$294$	−9.27437	−	7.68703i	−0.540893	−	0.448316i
$295$			7.19113i			0.418684i
$296$	−2.70143	+	5.44998i	−0.157017	+	0.316774i
$297$	23.5347	−	6.76605i	1.36562	−	0.392606i
$298$	8.64534	−	8.64534i	0.500811	−	0.500811i
$299$	−4.51406			−0.261055
$300$	1.72452	−	0.161390i	0.0995649	−	0.00931788i
$301$	0.565736	+	0.565736i	0.0326085	+	0.0326085i
$302$	2.77543	−	2.77543i	0.159708	−	0.159708i
$303$	3.74875	−	0.350831i	0.215360	−	0.0201547i
$304$	1.02880	+	1.02880i	0.0590058	+	0.0590058i
$305$		−	0.295886i		−	0.0169424i
$306$	−9.18878	+	1.73508i	−0.525288	+	0.0991878i
$307$			9.39455i			0.536175i	0.963394	+	0.268088i	$0.0863917\pi$
$307$			9.39455i			0.536175i	−0.963394	+	0.268088i	$0.913608\pi$
$308$			1.00283i			0.0571413i
$309$	11.1828	−	13.4920i	0.636166	−	0.767533i
$310$	−0.648056	+	0.648056i	−0.0368071	+	0.0368071i
$311$	−12.9009	−	12.9009i	−0.731542	−	0.731542i	0.239384	−	0.970925i	$-0.423055\pi$
$311$	−12.9009	−	12.9009i	−0.731542	−	0.731542i	−0.970925	+	0.239384i	$0.923055\pi$
$312$	−3.43883	+	0.321827i	−0.194686	+	0.0182198i
$313$	20.5528	+	20.5528i	1.16171	+	1.16171i	0.984101	+	0.177611i	$0.0568368\pi$
$313$	20.5528	+	20.5528i	1.16171	+	1.16171i	0.177611	+	0.984101i	$0.443163\pi$
$314$	2.82442	+	2.82442i	0.159391	+	0.159391i
$315$	−0.359804	+	0.527316i	−0.0202727	+	0.0297109i
$316$	12.0740	−	12.0740i	0.679215	−	0.679215i
$317$	−17.1597			−0.963782			−0.481891	−	0.876231i	$-0.660050\pi$
$317$	−17.1597			−0.963782			−0.481891	+	0.876231i	$0.660050\pi$
$318$	−6.86457	+	8.28209i	−0.384946	+	0.464436i
$319$	−16.3724	−	16.3724i	−0.916676	−	0.916676i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	−1.15747	−	12.3680i	−0.0646038	−	0.690315i
$322$	−0.481700			−0.0268441
$323$	4.53514			0.252342
$324$	3.28185	+	8.38030i	0.182325	+	0.465572i
$325$	1.41003	−	1.41003i	0.0782145	−	0.0782145i
$326$	0.625689			0.0346537
$327$	−23.1415	−	19.1807i	−1.27973	−	1.06070i
$328$	−1.19421	+	1.19421i	−0.0659395	+	0.0659395i
$329$			2.57100i			0.141744i
$330$	−8.12716	+	0.760588i	−0.447385	+	0.0418690i
$331$	−0.00989836	−	0.00989836i	−0.000544063	−	0.000544063i	0.706835	−	0.707379i	$-0.250122\pi$
$331$	−0.00989836	−	0.00989836i	−0.000544063	−	0.000544063i	−0.707379	+	0.706835i	$0.750122\pi$
$332$	−1.76283			−0.0967479
$333$	15.9096	−	8.93775i	0.871843	−	0.489786i
$334$	6.65380			0.364080
$335$	4.68526	+	4.68526i	0.255983	+	0.255983i
$336$	−0.366962	+	0.0343425i	−0.0200194	+	0.00187354i
$337$		−	0.449564i		−	0.0244893i	−0.999925	−	0.0122447i	$-0.996102\pi$
$337$		−	0.449564i		−	0.0244893i	0.999925	−	0.0122447i	$-0.00389769\pi$
$338$	6.38066	−	6.38066i	0.347062	−	0.347062i
$339$	−22.5876	−	18.7217i	−1.22679	−	1.01682i
$340$	3.11705			0.169046
$341$	3.05411	−	3.05411i	0.165389	−	0.165389i
$342$	−0.809881	−	4.28904i	−0.0437933	−	0.231925i
$343$	−2.96944			−0.160335
$344$	−3.75989			−0.202720
$345$	−0.365343	−	3.90382i	−0.0196694	−	0.210175i
$346$	−5.08223	−	5.08223i	−0.273222	−	0.273222i
$347$	3.08033	+	3.08033i	0.165361	+	0.165361i	0.784937	−	0.619576i	$-0.212695\pi$
$347$	3.08033	+	3.08033i	0.165361	+	0.165361i	−0.619576	+	0.784937i	$0.712695\pi$
$348$	5.43041	−	6.55178i	0.291101	−	0.351212i
$349$	23.9040			1.27955			0.639777	−	0.768561i	$-0.279027\pi$
$349$	23.9040			1.27955			0.639777	+	0.768561i	$0.279027\pi$
$350$	0.150466	−	0.150466i	0.00804275	−	0.00804275i
$351$	9.06590	+	5.01714i	0.483902	+	0.267795i
$352$	−3.33240	−	3.33240i	−0.177617	−	0.177617i
$353$	22.3814	+	22.3814i	1.19124	+	1.19124i	0.976719	+	0.214523i	$0.0688196\pi$
$353$	22.3814	+	22.3814i	1.19124	+	1.19124i	0.214523	+	0.976719i	$0.431180\pi$
$354$	12.4012	−	1.16058i	0.659117	−	0.0616841i
$355$	−6.42981	−	6.42981i	−0.341259	−	0.341259i
$356$	−6.73631	+	6.73631i	−0.357024	+	0.357024i
$357$	−0.733123	+	0.884510i	−0.0388010	+	0.0468132i
$358$		−	14.6876i		−	0.776265i
$359$		−	16.5691i		−	0.874485i	−0.899344	−	0.437243i	$-0.855955\pi$
$359$		−	16.5691i		−	0.874485i	0.899344	−	0.437243i	$-0.144045\pi$
$360$	−0.556641	−	2.94791i	−0.0293375	−	0.155368i
$361$		−	16.8831i		−	0.888586i
$362$	8.65824	+	8.65824i	0.455067	+	0.455067i
$363$	19.3314	−	1.80915i	1.01463	−	0.0949555i
$364$	−0.300042	+	0.300042i	−0.0157265	+	0.0157265i
$365$	5.46588	+	5.46588i	0.286097	+	0.286097i
$366$	−0.510261	+	0.0477532i	−0.0266718	+	0.00249610i
$367$	−32.7024			−1.70705			−0.853526	−	0.521050i	$-0.825541\pi$
$367$	−32.7024			−1.70705			−0.853526	+	0.521050i	$0.825541\pi$
$368$	1.60069	−	1.60069i	0.0834419	−	0.0834419i
$369$	4.97864	−	0.940096i	0.259178	−	0.0489395i
$370$	−5.76392	+	1.94352i	−0.299652	+	0.101039i
$371$			1.32156i			0.0686122i
$372$	1.22217	+	1.01299i	0.0633667	+	0.0525212i
$373$			25.5737i			1.32416i	0.749434	+	0.662079i	$0.230326\pi$
$373$			25.5737i			1.32416i	−0.749434	+	0.662079i	$0.769674\pi$
$374$	−14.6898			−0.759592
$375$	1.33354	+	1.10530i	0.0688635	+	0.0570772i
$376$	−8.54344	−	8.54344i	−0.440594	−	0.440594i
$377$		−	9.79712i		−	0.504577i
$378$	0.967433	+	0.535385i	0.0497594	+	0.0275372i
$379$	−35.8134			−1.83961			−0.919806	−	0.392373i	$-0.871654\pi$
$379$	−35.8134			−1.83961			−0.919806	+	0.392373i	$0.871654\pi$
$380$			1.45494i			0.0746371i
$381$	−9.69895	+	0.907686i	−0.496892	+	0.0465022i
$382$	−23.9567			−1.22573
$383$	10.9976	−	10.9976i	0.561949	−	0.561949i	−0.367912	−	0.929861i	$-0.619927\pi$
$383$	10.9976	−	10.9976i	0.561949	−	0.561949i	0.929861	+	0.367912i	$0.119927\pi$
$384$	1.10530	−	1.33354i	0.0564044	−	0.0680518i
$385$	−0.709105	+	0.709105i	−0.0361393	+	0.0361393i
$386$		−	6.40265i		−	0.325886i
$387$	9.31734	+	6.35752i	0.473627	+	0.323171i
$388$	10.7615	−	10.7615i	0.546331	−	0.546331i
$389$	−7.47270	+	7.47270i	−0.378881	+	0.378881i	−0.870698	−	0.491817i	$-0.836333\pi$
$389$	−7.47270	+	7.47270i	−0.378881	+	0.378881i	0.491817	+	0.870698i	$0.336333\pi$
$390$	−2.65919	−	2.20406i	−0.134653	−	0.111607i
$391$		−	7.05614i		−	0.356844i
$392$	4.91773	−	4.91773i	0.248383	−	0.248383i
$393$	−15.5843	−	12.9170i	−0.786124	−	0.651575i
$394$	−6.88464	+	6.88464i	−0.346843	+	0.346843i
$395$	17.0752			0.859147
$396$	2.62329	+	13.8927i	0.131825	+	0.698132i
$397$		−	3.58713i		−	0.180033i	−0.995940	−	0.0900165i	$-0.971308\pi$
$397$		−	3.58713i		−	0.180033i	0.995940	−	0.0900165i	$-0.0286920\pi$
$398$	−13.8753			−0.695506
$399$	−0.412862	−	0.342199i	−0.0206690	−	0.0171314i
$400$			1.00000i			0.0500000i
$401$	−13.6374	−	13.6374i	−0.681018	−	0.681018i	0.279212	−	0.960230i	$-0.409927\pi$
$401$	−13.6374	−	13.6374i	−0.681018	−	0.681018i	−0.960230	+	0.279212i	$0.909927\pi$
$402$	7.32364	−	8.83596i	0.365270	−	0.440697i
$403$	1.82756			0.0910373
$404$			2.17380i			0.108151i
$405$	−3.60515	+	8.24639i	−0.179141	+	0.409766i
$406$		−	1.04546i		−	0.0518854i
$407$	27.1637	−	9.15927i	1.34646	−	0.454008i
$408$	−0.503063	−	5.37541i	−0.0249053	−	0.266122i
$409$	7.37453	−	7.37453i	0.364647	−	0.364647i	−0.500874	−	0.865520i	$-0.666988\pi$
$409$	7.37453	−	7.37453i	0.364647	−	0.364647i	0.865520	+	0.500874i	$0.166988\pi$
$410$	−1.68887			−0.0834076
$411$	0.973218	+	10.3992i	0.0480053	+	0.512954i
$412$	7.15412	+	7.15412i	0.352458	+	0.352458i
$413$	1.08202	−	1.08202i	0.0532428	−	0.0532428i
$414$	−6.67324	+	1.26008i	−0.327972	+	0.0619296i
$415$	−1.24651	−	1.24651i	−0.0611887	−	0.0611887i
$416$		−	1.99409i		−	0.0977681i
$417$	−0.480641	−	5.13582i	−0.0235371	−	0.251502i
$418$		−	6.85675i		−	0.335374i
$419$			20.6670i			1.00965i	0.863222	+	0.504825i	$0.168443\pi$
$419$			20.6670i			1.00965i	−0.863222	+	0.504825i	$0.831557\pi$
$420$	−0.283765	−	0.235197i	−0.0138463	−	0.0114765i
$421$	−10.2138	+	10.2138i	−0.497789	+	0.497789i	−0.910749	−	0.412960i	$-0.864495\pi$
$421$	−10.2138	+	10.2138i	−0.497789	+	0.497789i	0.412960	+	0.910749i	$0.364495\pi$
$422$	12.1607	+	12.1607i	0.591975	+	0.591975i
$423$	6.72547	+	35.6173i	0.327004	+	1.73177i
$424$	−4.39157	−	4.39157i	−0.213273	−	0.213273i
$425$	2.20409	+	2.20409i	0.106914	+	0.106914i
$426$	−10.0506	+	12.1260i	−0.486953	+	0.587508i
$427$	−0.0445209	+	0.0445209i	−0.00215452	+	0.00215452i
$428$	7.17188			0.346666
$429$	12.5320	+	10.3871i	0.605051	+	0.501494i
$430$	−2.65864	−	2.65864i	−0.128211	−	0.128211i
$431$	−15.8544	−	15.8544i	−0.763678	−	0.763678i	0.213307	−	0.976985i	$-0.431577\pi$
$431$	−15.8544	−	15.8544i	−0.763678	−	0.763678i	−0.976985	+	0.213307i	$0.931577\pi$
$432$	−4.99387	+	1.43570i	−0.240268	+	0.0690751i
$433$	7.69201			0.369655			0.184827	−	0.982771i	$-0.440827\pi$
$433$	7.69201			0.369655			0.184827	+	0.982771i	$0.440827\pi$
$434$	0.195021			0.00936131
$435$	8.47269	−	0.792925i	0.406234	−	0.0380178i
$436$	12.2708	−	12.2708i	0.587663	−	0.587663i
$437$	3.29359			0.157554
$438$	8.54385	−	10.3081i	0.408241	−	0.492541i
$439$	−15.7691	+	15.7691i	−0.752617	+	0.752617i	−0.974967	−	0.222350i	$-0.928627\pi$
$439$	−15.7691	+	15.7691i	−0.752617	+	0.752617i	0.222350	+	0.974967i	$0.428627\pi$
$440$		−	4.71272i		−	0.224670i
$441$	−20.5019	+	3.87128i	−0.976279	+	0.184347i
$442$	−4.39514	−	4.39514i	−0.209056	−	0.209056i
$443$	−30.0415			−1.42732			−0.713658	−	0.700495i	$-0.752963\pi$
$443$	−30.0415			−1.42732			−0.713658	+	0.700495i	$0.752963\pi$
$444$	4.28187	+	9.62630i	0.203209	+	0.456844i
$445$	−9.52659			−0.451604
$446$	10.0717	+	10.0717i	0.476911	+	0.476911i
$447$	−1.97322	−	21.0845i	−0.0933300	−	0.997265i
$448$		−	0.212791i		−	0.0100534i
$449$	5.32424	−	5.32424i	0.251266	−	0.251266i	−0.570223	−	0.821490i	$-0.693143\pi$
$449$	5.32424	−	5.32424i	0.251266	−	0.251266i	0.821490	+	0.570223i	$0.193143\pi$
$450$	1.69088	−	2.47809i	0.0797089	−	0.116818i
$451$	7.95920			0.374784
$452$	11.9771	−	11.9771i	0.563354	−	0.563354i
$453$	−0.633465	−	6.76880i	−0.0297628	−	0.318026i
$454$	10.3854			0.487413
$455$	−0.424324			−0.0198926
$456$	2.50907	−	0.234814i	0.117498	−	0.0109962i
$457$	20.0929	+	20.0929i	0.939908	+	0.939908i	0.998294	−	0.0583858i	$-0.0185954\pi$
$457$	20.0929	+	20.0929i	0.939908	+	0.939908i	−0.0583858	+	0.998294i	$0.518595\pi$
$458$	−5.07889	−	5.07889i	−0.237321	−	0.237321i
$459$	−7.84253	+	14.1714i	−0.366058	+	0.661462i
$460$	2.26372			0.105547
$461$	−19.6493	+	19.6493i	−0.915159	+	0.915159i	−0.996672	−	0.0815134i	$-0.974025\pi$
$461$	−19.6493	+	19.6493i	−0.915159	+	0.915159i	0.0815134	+	0.996672i	$0.474025\pi$
$462$	1.33731	+	1.10842i	0.0622171	+	0.0515683i
$463$	22.7884	+	22.7884i	1.05906	+	1.05906i	0.998143	+	0.0609219i	$0.0194041\pi$
$463$	22.7884	+	22.7884i	1.05906	+	1.05906i	0.0609219	+	0.998143i	$0.480596\pi$
$464$	3.47408	+	3.47408i	0.161280	+	0.161280i
$465$	0.147913	+	1.58050i	0.00685929	+	0.0732940i
$466$	9.68419	+	9.68419i	0.448611	+	0.448611i
$467$	19.4943	−	19.4943i	0.902087	−	0.902087i	−0.0935295	−	0.995617i	$-0.529815\pi$
$467$	19.4943	−	19.4943i	0.902087	−	0.902087i	0.995617	+	0.0935295i	$0.0298150\pi$
$468$	−3.37176	+	4.94152i	−0.155860	+	0.228422i
$469$		−	1.40995i		−	0.0651052i
$470$		−	12.0822i		−	0.557313i
$471$	6.88830	−	0.644648i	0.317396	−	0.0297038i
$472$			7.19113i			0.330999i
$473$	12.5294	+	12.5294i	0.576104	+	0.576104i
$474$	−2.75577	−	29.4464i	−0.126577	−	1.35252i
$475$	−1.02880	+	1.02880i	−0.0472046	+	0.0472046i
$476$	−0.469011	−	0.469011i	−0.0214971	−	0.0214971i
$477$	3.45708	+	18.3083i	0.158289	+	0.838280i
$478$	−25.9111			−1.18514
$479$	−3.44266	+	3.44266i	−0.157299	+	0.157299i	−0.781369	−	0.624069i	$-0.785478\pi$
$479$	−3.44266	+	3.44266i	−0.157299	+	0.157299i	0.624069	+	0.781369i	$0.285478\pi$
$480$	1.72452	−	0.161390i	0.0787130	−	0.00736643i
$481$	10.8677	+	5.38688i	0.495526	+	0.245621i
$482$			14.6769i			0.668513i
$483$	−0.532422	+	0.642365i	−0.0242260	+	0.0292286i
$484$			11.2097i			0.509534i
$485$	15.2190			0.691060
$486$	14.8029	+	4.88625i	0.671471	+	0.221645i
$487$	−15.7230	−	15.7230i	−0.712475	−	0.712475i	0.254577	−	0.967052i	$-0.418064\pi$
$487$	−15.7230	−	15.7230i	−0.712475	−	0.712475i	−0.967052	+	0.254577i	$0.918064\pi$
$488$		−	0.295886i		−	0.0133941i
$489$	0.691572	−	0.834379i	0.0312740	−	0.0377319i
$490$	6.95472			0.314182
$491$		−	9.15640i		−	0.413222i	−0.978423	−	0.206611i	$-0.933756\pi$
$491$		−	9.15640i		−	0.413222i	0.978423	−	0.206611i	$-0.0662435\pi$
$492$	0.272568	+	2.91249i	0.0122883	+	0.131305i
$493$	15.3143			0.689723
$494$	2.05152	−	2.05152i	0.0923022	−	0.0923022i
$495$	−7.96865	+	11.6785i	−0.358164	+	0.524911i
$496$	−0.648056	+	0.648056i	−0.0290986	+	0.0290986i
$497$			1.93494i			0.0867938i
$498$	−1.94845	+	2.35080i	−0.0873121	+	0.105342i
$499$	−18.5063	+	18.5063i	−0.828454	+	0.828454i	−0.987303	−	0.158849i	$-0.949222\pi$
$499$	−18.5063	+	18.5063i	−0.828454	+	0.828454i	0.158849	+	0.987303i	$0.449222\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	7.35442	−	8.87309i	0.328571	−	0.396420i
$502$			0.344283i			0.0153661i
$503$	−28.9276	+	28.9276i	−1.28982	+	1.28982i	−0.354922	+	0.934896i	$0.615493\pi$
$503$	−28.9276	+	28.9276i	−1.28982	+	1.28982i	−0.934896	+	0.354922i	$0.884507\pi$
$504$	−0.359804	+	0.527316i	−0.0160270	+	0.0234885i
$505$	−1.53711	+	1.53711i	−0.0684004	+	0.0684004i
$506$	−10.6683			−0.474264
$507$	−1.45633	−	15.5614i	−0.0646777	−	0.691105i
$508$		−	5.62416i		−	0.249532i
$509$	0.543910			0.0241084			0.0120542	−	0.999927i	$-0.496163\pi$
$509$	0.543910			0.0241084			0.0120542	+	0.999927i	$0.496163\pi$
$510$	3.44527	−	4.15670i	0.152559	−	0.184062i
$511$		−	1.64486i		−	0.0727642i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−6.61475	−	3.66065i	−0.292048	−	0.161622i
$514$	−7.38372			−0.325682
$515$			10.1175i			0.445828i
$516$	−4.15579	+	5.01395i	−0.182948	+	0.220727i
$517$			56.9403i			2.50423i
$518$	1.15971	+	0.574840i	0.0509546	+	0.0252570i
$519$	−12.3947	+	1.15997i	−0.544067	+	0.0509170i
$520$	1.41003	−	1.41003i	0.0618340	−	0.0618340i
$521$	27.5450			1.20677			0.603383	−	0.797451i	$-0.293819\pi$
$521$	27.5450			1.20677			0.603383	+	0.797451i	$0.293819\pi$
$522$	−2.73482	−	14.4833i	−0.119700	−	0.633917i
$523$	−15.6798	−	15.6798i	−0.685629	−	0.685629i	0.275634	−	0.961263i	$-0.411112\pi$
$523$	−15.6798	−	15.6798i	−0.685629	−	0.685629i	−0.961263	+	0.275634i	$0.911112\pi$
$524$	8.26356	−	8.26356i	0.360995	−	0.360995i
$525$	−0.0343425	−	0.366962i	−0.00149883	−	0.0160155i
$526$	12.1630	+	12.1630i	0.530333	+	0.530333i
$527$			2.85675i			0.124442i
$528$	−8.12716	+	0.760588i	−0.353689	+	0.0331004i
$529$			17.8756i			0.777198i
$530$		−	6.21062i		−	0.269772i
$531$	12.1593	−	17.8203i	0.527670	−	0.773334i
$532$	0.218920	−	0.218920i	0.00949138	−	0.00949138i
$533$	2.38137	+	2.38137i	0.103148	+	0.103148i
$534$	1.53750	+	16.4287i	0.0665341	+	0.710941i
$535$	5.07128	+	5.07128i	0.219251	+	0.219251i
$536$	4.68526	+	4.68526i	0.202372	+	0.202372i
$537$	−19.5865	−	16.2342i	−0.845219	−	0.700556i
$538$	0.569118	−	0.569118i	0.0245364	−	0.0245364i
$539$	−32.7757			−1.41175
$540$	−4.54639	−	2.51601i	−0.195646	−	0.108272i
$541$	4.31448	+	4.31448i	0.185494	+	0.185494i	0.793745	−	0.608251i	$-0.208128\pi$
$541$	4.31448	+	4.31448i	0.185494	+	0.185494i	−0.608251	+	0.793745i	$0.708128\pi$
$542$	−2.44220	−	2.44220i	−0.104901	−	0.104901i
$543$	21.1160	−	1.97616i	0.906174	−	0.0848052i
$544$	3.11705			0.133643
$545$	17.3535			0.743342
$546$	0.0684819	+	0.731753i	0.00293075	+	0.0313162i
$547$	−20.1620	+	20.1620i	−0.862066	+	0.862066i	−0.991578	−	0.129512i	$-0.958659\pi$
$547$	−20.1620	+	20.1620i	−0.862066	+	0.862066i	0.129512	+	0.991578i	$0.458659\pi$
$548$	−6.03021			−0.257598
$549$	−0.500308	+	0.733233i	−0.0213526	+	0.0312936i
$550$	3.33240	−	3.33240i	0.142094	−	0.142094i
$551$			7.14826i			0.304526i
$552$	−0.365343	−	3.90382i	−0.0155500	−	0.166158i
$553$	−2.56924	−	2.56924i	−0.109255	−	0.109255i
$554$	12.0872			0.513537
$555$	−3.77908	+	9.83456i	−0.160413	+	0.417454i
$556$	2.97812			0.126301
$557$	24.9409	+	24.9409i	1.05678	+	1.05678i	0.998288	+	0.0584905i	$0.0186287\pi$
$557$	24.9409	+	24.9409i	1.05678	+	1.05678i	0.0584905	+	0.998288i	$0.481371\pi$
$558$	2.70173	−	0.510156i	0.114373	−	0.0215966i
$559$			7.49754i			0.317112i
$560$	0.150466	−	0.150466i	0.00635835	−	0.00635835i
$561$	−16.2366	+	19.5894i	−0.685509	+	0.827065i
$562$	21.7100			0.915780
$563$	2.53096	−	2.53096i	0.106667	−	0.106667i	−0.651759	−	0.758426i	$-0.725969\pi$
$563$	2.53096	−	2.53096i	0.106667	−	0.106667i	0.758426	+	0.651759i	$0.225969\pi$
$564$	−20.8360	+	1.94996i	−0.877355	+	0.0821081i
$565$	16.9381			0.712593
$566$	1.83137			0.0769783
$567$	1.78325	−	0.698349i	0.0748897	−	0.0293279i
$568$	−6.42981	−	6.42981i	−0.269789	−	0.269789i
$569$	19.1817	+	19.1817i	0.804140	+	0.804140i	0.983740	−	0.179600i	$-0.0574803\pi$
$569$	19.1817	+	19.1817i	0.804140	+	0.804140i	−0.179600	+	0.983740i	$0.557480\pi$
$570$	1.94022	+	1.60814i	0.0812669	+	0.0673577i
$571$	21.2645			0.889894			0.444947	−	0.895557i	$-0.353223\pi$
$571$	21.2645			0.889894			0.444947	+	0.895557i	$0.353223\pi$
$572$	−6.64509	+	6.64509i	−0.277845	+	0.277845i
$573$	−26.4793	+	31.9472i	−1.10619	+	1.33461i
$574$	0.254118	+	0.254118i	0.0106067	+	0.0106067i
$575$	1.60069	+	1.60069i	0.0667535	+	0.0667535i
$576$	−0.556641	−	2.94791i	−0.0231934	−	0.122829i
$577$	4.89468	+	4.89468i	0.203768	+	0.203768i	0.801612	−	0.597844i	$-0.203976\pi$
$577$	4.89468	+	4.89468i	0.203768	+	0.203768i	−0.597844	+	0.801612i	$0.703976\pi$
$578$	−5.15055	+	5.15055i	−0.214235	+	0.214235i
$579$	−8.53817	−	7.07683i	−0.354834	−	0.294103i
$580$			4.91308i			0.204005i
$581$			0.375115i			0.0155624i
$582$	−2.45620	−	26.2454i	−0.101813	−	1.08791i
$583$			29.2689i			1.21219i
$584$	5.46588	+	5.46588i	0.226180	+	0.226180i
$585$	−5.87838	+	1.10999i	−0.243041	+	0.0458924i
$586$	−15.2198	+	15.2198i	−0.628723	+	0.628723i
$587$	13.8700	+	13.8700i	0.572476	+	0.572476i	0.932820	−	0.360344i	$-0.117341\pi$
$587$	13.8700	+	13.8700i	0.572476	+	0.572476i	−0.360344	+	0.932820i	$0.617341\pi$
$588$	−1.12243	−	11.9935i	−0.0462880	−	0.494604i
$589$	−1.33344			−0.0549435
$590$	−5.08490	+	5.08490i	−0.209342	+	0.209342i
$591$	1.57135	+	16.7905i	0.0646369	+	0.690669i
$592$	−5.76392	+	1.94352i	−0.236895	+	0.0798782i
$593$		−	10.7721i		−	0.442356i	−0.975233	−	0.221178i	$-0.929010\pi$
$593$		−	10.7721i		−	0.442356i	0.975233	−	0.221178i	$-0.0709901\pi$
$594$	21.4259	+	11.8572i	0.879115	+	0.486509i
$595$		−	0.663281i		−	0.0271919i
$596$	12.2264			0.500811
$597$	−15.3363	+	18.5032i	−0.627673	+	0.757286i
$598$	−3.19192	−	3.19192i	−0.130527	−	0.130527i
$599$		−	23.5093i		−	0.960566i	−0.877114	−	0.480283i	$-0.840534\pi$
$599$		−	23.5093i		−	0.960566i	0.877114	−	0.480283i	$-0.159466\pi$
$600$	1.33354	+	1.10530i	0.0544414	+	0.0451235i
$601$	−29.5104			−1.20375			−0.601877	−	0.798589i	$-0.705580\pi$
$601$	−29.5104			−1.20375			−0.601877	+	0.798589i	$0.705580\pi$
$602$			0.800071i			0.0326085i
$603$	−3.68828	−	19.5327i	−0.150198	−	0.795433i
$604$	3.92504			0.159708
$605$	−7.92649	+	7.92649i	−0.322257	+	0.322257i
$606$	2.89884	+	2.40269i	0.117757	+	0.0976027i
$607$	26.5263	−	26.5263i	1.07667	−	1.07667i	0.0798642	−	0.996806i	$-0.474551\pi$
$607$	26.5263	−	26.5263i	1.07667	−	1.07667i	0.996806	−	0.0798642i	$-0.0254487\pi$
$608$			1.45494i			0.0590058i
$609$	−1.39416	−	1.15554i	−0.0564943	−	0.0468250i
$610$	0.209223	−	0.209223i	0.00847120	−	0.00847120i
$611$	−17.0364	+	17.0364i	−0.689217	+	0.689217i
$612$	−7.72433	−	5.27056i	−0.312238	−	0.213050i
$613$			1.60465i			0.0648114i	0.999475	+	0.0324057i	$0.0103169\pi$
$613$			1.60465i			0.0648114i	−0.999475	+	0.0324057i	$0.989683\pi$
$614$	−6.64295	+	6.64295i	−0.268088	+	0.268088i
$615$	−1.86671	+	2.25218i	−0.0752729	+	0.0908165i
$616$	−0.709105	+	0.709105i	−0.0285707	+	0.0285707i
$617$	−8.63939			−0.347809			−0.173904	−	0.984763i	$-0.555638\pi$
$617$	−8.63939			−0.347809			−0.173904	+	0.984763i	$0.555638\pi$
$618$	17.4477	−	1.63286i	0.701850	−	0.0656833i
$619$			8.50961i			0.342030i	0.985268	+	0.171015i	$0.0547046\pi$
$619$			8.50961i			0.342030i	−0.985268	+	0.171015i	$0.945295\pi$
$620$	−0.916490			−0.0368071
$621$	−5.69555	+	10.2918i	−0.228554	+	0.412995i
$622$		−	18.2446i		−	0.731542i
$623$	1.43343	+	1.43343i	0.0574291	+	0.0574291i
$624$	−2.65919	−	2.20406i	−0.106453	−	0.0882329i
$625$	−1.00000			−0.0400000
$626$			29.0660i			1.16171i
$627$	−9.14372	−	7.57874i	−0.365165	−	0.302666i
$628$			3.99434i			0.159391i
$629$	−8.42049	+	16.9879i	−0.335747	+	0.677351i
$630$	−0.627289	+	0.118448i	−0.0249918	+	0.00471909i
$631$	1.50414	−	1.50414i	0.0598789	−	0.0598789i	−0.676533	−	0.736412i	$-0.736518\pi$
$631$	1.50414	−	1.50414i	0.0598789	−	0.0598789i	0.736412	+	0.676533i	$0.236518\pi$
$632$	17.0752			0.679215
$633$	29.6580	−	2.77557i	1.17880	−	0.110319i
$634$	−12.1337	−	12.1337i	−0.481891	−	0.481891i
$635$	3.97688	−	3.97688i	0.157818	−	0.157818i
$636$	−10.7103	+	1.00233i	−0.424691	+	0.0397451i
$637$	−9.80638	−	9.80638i	−0.388543	−	0.388543i
$638$		−	23.1540i		−	0.916676i
$639$	5.06161	+	26.8057i	0.200234	+	1.06042i
$640$			1.00000i			0.0395285i
$641$			18.9364i			0.747942i	0.927440	+	0.373971i	$0.122004\pi$
$641$			18.9364i			0.747942i	−0.927440	+	0.373971i	$0.877996\pi$
$642$	7.92705	−	9.56396i	0.312856	−	0.377459i
$643$	−4.61814	+	4.61814i	−0.182122	+	0.182122i	−0.792280	−	0.610158i	$-0.791106\pi$
$643$	−4.61814	+	4.61814i	−0.182122	+	0.182122i	0.610158	+	0.792280i	$0.291106\pi$
$644$	−0.340614	−	0.340614i	−0.0134221	−	0.0134221i
$645$	−6.48399	+	0.606810i	−0.255307	+	0.0238931i
$646$	3.20683	+	3.20683i	0.126171	+	0.126171i
$647$	−2.59508	−	2.59508i	−0.102023	−	0.102023i	0.654253	−	0.756276i	$-0.272983\pi$
$647$	−2.59508	−	2.59508i	−0.102023	−	0.102023i	−0.756276	+	0.654253i	$0.772983\pi$
$648$	−3.60515	+	8.24639i	−0.141624	+	0.323949i
$649$	23.9637	−	23.9637i	0.940658	−	0.940658i
$650$	1.99409			0.0782145
$651$	0.215556	−	0.260068i	0.00844831	−	0.0101929i
$652$	0.442429	+	0.442429i	0.0173269	+	0.0173269i
$653$	23.4457	+	23.4457i	0.917500	+	0.917500i	0.996847	−	0.0793470i	$-0.0252835\pi$
$653$	23.4457	+	23.4457i	0.917500	+	0.917500i	−0.0793470	+	0.996847i	$0.525284\pi$
$654$	−2.80069	−	29.9264i	−0.109516	−	1.17021i
$655$	11.6864			0.456627
$656$	−1.68887			−0.0659395
$657$	−4.30279	−	22.7871i	−0.167868	−	0.889008i
$658$	−1.81797	+	1.81797i	−0.0708718	+	0.0708718i
$659$	−39.2785			−1.53007			−0.765037	−	0.643987i	$-0.777279\pi$
$659$	−39.2785			−1.53007			−0.765037	+	0.643987i	$0.777279\pi$
$660$	−6.28459	−	5.20895i	−0.244627	−	0.202758i
$661$	2.24363	−	2.24363i	0.0872673	−	0.0872673i	−0.662126	−	0.749393i	$-0.730345\pi$
$661$	2.24363	−	2.24363i	0.0872673	−	0.0872673i	0.749393	+	0.662126i	$0.230345\pi$
$662$		−	0.0139984i		−	0.000544063i
$663$	−10.7190	+	1.00315i	−0.416292	+	0.0389591i
$664$	−1.24651	−	1.24651i	−0.0483739	−	0.0483739i
$665$	0.309599			0.0120057
$666$	17.5698	+	4.92987i	0.680814	+	0.191029i
$667$	11.1219			0.430640
$668$	4.70495	+	4.70495i	0.182040	+	0.182040i
$669$	24.5633	−	2.29878i	0.949672	−	0.0888760i
$670$			6.62596i			0.255983i
$671$	−0.986011	+	0.986011i	−0.0380645	+	0.0380645i
$672$	−0.283765	−	0.235197i	−0.0109465	−	0.00907293i
$673$	19.2825			0.743286			0.371643	−	0.928376i	$-0.378795\pi$
$673$	19.2825			0.743286			0.371643	+	0.928376i	$0.378795\pi$
$674$	0.317890	−	0.317890i	0.0122447	−	0.0122447i
$675$	−1.43570	−	4.99387i	−0.0552601	−	0.192214i
$676$	9.02362			0.347062
$677$	33.8373			1.30047			0.650237	−	0.759732i	$-0.274670\pi$
$677$	33.8373			1.30047			0.650237	+	0.759732i	$0.274670\pi$
$678$	−2.73365	−	29.2101i	−0.104985	−	1.12181i
$679$	−2.28994	−	2.28994i	−0.0878800	−	0.0878800i
$680$	2.20409	+	2.20409i	0.0845230	+	0.0845230i
$681$	11.4790	−	13.8494i	0.439876	−	0.530709i
$682$	4.31916			0.165389
$683$	−29.5525	+	29.5525i	−1.13079	+	1.13079i	−0.140750	+	0.990045i	$0.544951\pi$
$683$	−29.5525	+	29.5525i	−1.13079	+	1.13079i	−0.990045	+	0.140750i	$0.955049\pi$
$684$	2.46014	−	3.60548i	0.0940656	−	0.137859i
$685$	−4.26400	−	4.26400i	−0.162919	−	0.162919i
$686$	−2.09971	−	2.09971i	−0.0801674	−	0.0801674i
$687$	−12.3866	+	1.15921i	−0.472577	+	0.0442266i
$688$	−2.65864	−	2.65864i	−0.101360	−	0.101360i
$689$	−8.75717	+	8.75717i	−0.333622	+	0.333622i
$690$	2.50208	−	3.01876i	0.0952527	−	0.114922i
$691$		−	50.1252i		−	1.90685i	−0.301624	−	0.953427i	$-0.597529\pi$
$691$		−	50.1252i		−	1.90685i	0.301624	−	0.953427i	$-0.402471\pi$
$692$		−	7.18735i		−	0.273222i
$693$	2.95624	−	0.558214i	0.112298	−	0.0212048i
$694$			4.35624i			0.165361i
$695$	2.10585	+	2.10585i	0.0798795	+	0.0798795i
$696$	8.47269	−	0.792925i	0.321156	−	0.0300557i
$697$	−3.72243	+	3.72243i	−0.140997	+	0.140997i
$698$	16.9027	+	16.9027i	0.639777	+	0.639777i
$699$	23.6181	−	2.21032i	0.893319	−	0.0836021i
$700$	0.212791			0.00804275
$701$	23.6130	−	23.6130i	0.891851	−	0.891851i	−0.102846	−	0.994697i	$-0.532795\pi$
$701$	23.6130	−	23.6130i	0.891851	−	0.891851i	0.994697	+	0.102846i	$0.0327950\pi$
$702$	2.86291	+	9.95822i	0.108054	+	0.375849i
$703$	−7.92942	−	3.93042i	−0.299064	−	0.148239i
$704$		−	4.71272i		−	0.177617i
$705$	−16.1121	−	13.3545i	−0.606818	−	0.502958i
$706$			31.6521i			1.19124i
$707$	0.462566			0.0173966
$708$	9.58964	+	7.94833i	0.360401	+	0.298717i
$709$	12.5716	+	12.5716i	0.472135	+	0.472135i	0.902605	−	0.430470i	$-0.141652\pi$
$709$	12.5716	+	12.5716i	0.472135	+	0.472135i	−0.430470	+	0.902605i	$0.641652\pi$
$710$		−	9.09313i		−	0.341259i
$711$	−42.3139	−	28.8721i	−1.58689	−	1.08279i
$712$	−9.52659			−0.357024
$713$			2.07468i			0.0776973i
$714$	−1.14384	+	0.107047i	−0.0428071	+	0.00400614i
$715$	−9.39757			−0.351449
$716$	10.3857	−	10.3857i	0.388132	−	0.388132i
$717$	−28.6394	+	34.5534i	−1.06956	+	1.29042i
$718$	11.7161	−	11.7161i	0.437243	−	0.437243i
$719$			18.5408i			0.691454i	0.938335	+	0.345727i	$0.112368\pi$
$719$			18.5408i			0.691454i	−0.938335	+	0.345727i	$0.887632\pi$
$720$	1.69088	−	2.47809i	0.0630154	−	0.0923529i
$721$	1.52233	−	1.52233i	0.0566947	−	0.0566947i
$722$	11.9382	−	11.9382i	0.444293	−	0.444293i
$723$	19.5721	+	16.2223i	0.727896	+	0.603313i
$724$			12.2446i			0.455067i
$725$	−3.47408	+	3.47408i	−0.129024	+	0.129024i
$726$	14.9486	+	12.3901i	0.554795	+	0.459839i
$727$	−1.75699	+	1.75699i	−0.0651631	+	0.0651631i	−0.738937	−	0.673774i	$-0.764672\pi$
$727$	−1.75699	+	1.75699i	−0.0651631	+	0.0651631i	0.673774	+	0.738937i	$0.264672\pi$
$728$	−0.424324			−0.0157265
$729$	22.8775	−	14.3394i	0.847316	−	0.531089i
$730$			7.72992i			0.286097i
$731$	−11.7198			−0.433471
$732$	−0.394575	−	0.327042i	−0.0145839	−	0.0120878i
$733$		−	17.0851i		−	0.631054i	−0.948917	−	0.315527i	$-0.897819\pi$
$733$		−	17.0851i		−	0.631054i	0.948917	−	0.315527i	$-0.102181\pi$
$734$	−23.1241	−	23.1241i	−0.853526	−	0.853526i
$735$	7.68703	−	9.27437i	0.283540	−	0.342090i
$736$	2.26372			0.0834419
$737$		−	31.2263i		−	1.15024i
$738$	4.18518	+	2.85568i	0.154059	+	0.105119i
$739$			16.2842i			0.599025i	0.954092	+	0.299513i	$0.0968241\pi$
$739$			16.2842i			0.599025i	−0.954092	+	0.299513i	$0.903176\pi$
$740$	−5.44998	−	2.70143i	−0.200345	−	0.0993064i
$741$	−0.468240	−	5.00331i	−0.0172012	−	0.183801i
$742$	−0.934487	+	0.934487i	−0.0343061	+	0.0343061i
$743$	−35.0227			−1.28486			−0.642430	−	0.766344i	$-0.722074\pi$
$743$	−35.0227			−1.28486			−0.642430	+	0.766344i	$0.722074\pi$
$744$	0.147913	+	1.58050i	0.00542274	+	0.0579440i
$745$	8.64534	+	8.64534i	0.316741	+	0.316741i
$746$	−18.0834	+	18.0834i	−0.662079	+	0.662079i
$747$	0.981263	+	5.19666i	0.0359025	+	0.190136i
$748$	−10.3873	−	10.3873i	−0.379796	−	0.379796i
$749$		−	1.52611i		−	0.0557629i
$750$	0.161390	+	1.72452i	0.00589315	+	0.0629704i
$751$			39.6480i			1.44678i	0.690441	+	0.723389i	$0.257416\pi$
$751$			39.6480i			1.44678i	−0.690441	+	0.723389i	$0.742584\pi$
$752$		−	12.0822i		−	0.440594i
$753$	0.459114	+	0.380535i	0.0167310	+	0.0138675i
$754$	6.92761	−	6.92761i	0.252289	−	0.252289i
$755$	2.77543	+	2.77543i	0.101008	+	0.101008i
$756$	0.305504	+	1.06265i	0.0111111	+	0.0386483i
$757$	11.2015	+	11.2015i	0.407125	+	0.407125i	0.880735	−	0.473610i	$-0.157049\pi$
$757$	11.2015	+	11.2015i	0.407125	+	0.407125i	−0.473610	+	0.880735i	$0.657049\pi$
$758$	−25.3239	−	25.3239i	−0.919806	−	0.919806i
$759$	−11.7916	+	14.2266i	−0.428009	+	0.516391i
$760$	−1.02880	+	1.02880i	−0.0373185	+	0.0373185i
$761$	−32.6590			−1.18389			−0.591944	−	0.805979i	$-0.701639\pi$
$761$	−32.6590			−1.18389			−0.591944	+	0.805979i	$0.701639\pi$
$762$	−7.50003	−	6.21636i	−0.271697	−	0.225195i
$763$	−2.61111	−	2.61111i	−0.0945286	−	0.0945286i
$764$	−16.9400	−	16.9400i	−0.612867	−	0.612867i
$765$	−1.73508	−	9.18878i	−0.0627319	−	0.332221i
$766$	15.5529			0.561949
$767$	14.3397			0.517778
$768$	1.72452	−	0.161390i	0.0622281	−	0.00582368i
$769$	22.1721	−	22.1721i	0.799546	−	0.799546i	−0.183478	−	0.983024i	$-0.558736\pi$
$769$	22.1721	−	22.1721i	0.799546	−	0.799546i	0.983024	+	0.183478i	$0.0587356\pi$
$770$	−1.00283			−0.0361393
$771$	−8.16120	+	9.84646i	−0.293918	+	0.354612i
$772$	4.52736	−	4.52736i	0.162943	−	0.162943i
$773$			1.63331i			0.0587463i	0.999569	+	0.0293731i	$0.00935110\pi$
$773$			1.63331i			0.0587463i	−0.999569	+	0.0293731i	$0.990649\pi$
$774$	2.09291	+	11.0838i	0.0752280	+	0.398399i
$775$	−0.648056	−	0.648056i	−0.0232789	−	0.0232789i
$776$	15.2190			0.546331
$777$	2.04839	−	0.911145i	0.0734856	−	0.0326871i
$778$	−10.5680			−0.378881
$779$	−1.73752	−	1.73752i	−0.0622530	−	0.0622530i
$780$	−0.321827	−	3.43883i	−0.0115232	−	0.123130i
$781$			42.8534i			1.53341i
$782$	4.98945	−	4.98945i	0.178422	−	0.178422i
$783$	−22.3368	−	12.3614i	−0.798253	−	0.441759i
$784$	6.95472			0.248383
$785$	−2.82442	+	2.82442i	−0.100808	+	0.100808i
$786$	−1.88608	−	20.1534i	−0.0672742	−	0.718849i
$787$	29.8554			1.06423			0.532114	−	0.846672i	$-0.321398\pi$
$787$	29.8554			1.06423			0.532114	+	0.846672i	$0.321398\pi$
$788$	−9.73635			−0.346843
$789$	29.6636	−	2.77610i	1.05605	−	0.0988317i
$790$	12.0740	+	12.0740i	0.429573	+	0.429573i
$791$	−2.54862	−	2.54862i	−0.0906183	−	0.0906183i
$792$	−7.96865	+	11.6785i	−0.283154	+	0.414979i
$793$	−0.590023			−0.0209523
$794$	2.53648	−	2.53648i	0.0900165	−	0.0900165i
$795$	−8.28209	−	6.86457i	−0.293735	−	0.243461i
$796$	−9.81131	−	9.81131i	−0.347753	−	0.347753i
$797$	22.9206	+	22.9206i	0.811889	+	0.811889i	0.984917	−	0.173028i	$-0.0553552\pi$
$797$	22.9206	+	22.9206i	0.811889	+	0.811889i	−0.173028	+	0.984917i	$0.555355\pi$
$798$	−0.0499664	−	0.533909i	−0.00176879	−	0.0189002i
$799$	−26.6304	−	26.6304i	−0.942114	−	0.942114i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	23.6077	+	16.1083i	0.834138	+	0.569159i
$802$		−	19.2862i		−	0.681018i
$803$		−	36.4289i		−	1.28555i
$804$	11.4266	−	1.06937i	0.402984	−	0.0377136i
$805$		−	0.481700i		−	0.0169777i
$806$	1.29228	+	1.29228i	0.0455186	+	0.0455186i
$807$	−0.129896	−	1.38798i	−0.00457255	−	0.0488593i
$808$	−1.53711	+	1.53711i	−0.0540753	+	0.0540753i
$809$	8.44776	+	8.44776i	0.297007	+	0.297007i	0.839841	−	0.542833i	$-0.182648\pi$
$809$	8.44776	+	8.44776i	0.297007	+	0.297007i	−0.542833	+	0.839841i	$0.682648\pi$
$810$	−8.38030	+	3.28185i	−0.294454	+	0.115312i
$811$	−24.0634			−0.844979			−0.422489	−	0.906368i	$-0.638844\pi$
$811$	−24.0634			−0.844979			−0.422489	+	0.906368i	$0.638844\pi$
$812$	0.739253	−	0.739253i	0.0259427	−	0.0259427i
$813$	−5.95611	+	0.557409i	−0.208890	+	0.0195492i
$814$	25.6842	+	12.7311i	0.900232	+	0.446224i
$815$			0.625689i			0.0219169i
$816$	3.44527	−	4.15670i	0.120608	−	0.145514i
$817$		−	5.47043i		−	0.191386i
$818$	10.4292			0.364647
$819$	1.05151	+	0.717481i	0.0367428	+	0.0250708i
$820$	−1.19421	−	1.19421i	−0.0417038	−	0.0417038i
$821$		−	43.3221i		−	1.51195i	−0.654600	−	0.755975i	$-0.727163\pi$
$821$		−	43.3221i		−	1.51195i	0.654600	−	0.755975i	$-0.272837\pi$
$822$	−6.66516	+	8.04150i	−0.232474	+	0.280480i
$823$	−27.3077			−0.951888			−0.475944	−	0.879476i	$-0.657894\pi$
$823$	−27.3077			−0.951888			−0.475944	+	0.879476i	$0.657894\pi$
$824$			10.1175i			0.352458i
$825$	−0.760588	−	8.12716i	−0.0264803	−	0.282951i
$826$	1.53021			0.0532428
$827$	24.2150	−	24.2150i	0.842039	−	0.842039i	−0.147085	−	0.989124i	$-0.546989\pi$
$827$	24.2150	−	24.2150i	0.842039	−	0.842039i	0.989124	+	0.147085i	$0.0469891\pi$
$828$	−5.60971	−	3.82768i	−0.194951	−	0.133021i
$829$	15.5768	−	15.5768i	0.541003	−	0.541003i	−0.382820	−	0.923823i	$-0.625047\pi$
$829$	15.5768	−	15.5768i	0.541003	−	0.541003i	0.923823	+	0.382820i	$0.125047\pi$
$830$		−	1.76283i		−	0.0611887i
$831$	13.3600	−	16.1187i	0.463452	−	0.559153i
$832$	1.41003	−	1.41003i	0.0488841	−	0.0488841i
$833$	15.3288	−	15.3288i	0.531112	−	0.531112i
$834$	3.29171	−	3.97144i	0.113983	−	0.137520i
$835$			6.65380i			0.230264i
$836$	4.84845	−	4.84845i	0.167687	−	0.167687i
$837$	2.30590	−	4.16672i	0.0797034	−	0.144023i
$838$	−14.6138	+	14.6138i	−0.504825	+	0.504825i
$839$	−21.6471			−0.747340			−0.373670	−	0.927562i	$-0.621901\pi$
$839$	−21.6471			−0.747340			−0.373670	+	0.927562i	$0.621901\pi$
$840$	−0.0343425	−	0.366962i	−0.00118493	−	0.0126614i
$841$		−	4.86160i		−	0.167641i
$842$	−14.4445			−0.497789
$843$	23.9960	−	28.9511i	0.826465	−	0.997127i
$844$			17.1979i			0.591975i
$845$	6.38066	+	6.38066i	0.219501	+	0.219501i
$846$	−20.4296	+	29.9409i	−0.702385	+	1.02939i
$847$	2.38533			0.0819611
$848$		−	6.21062i		−	0.213273i
$849$	2.02421	−	2.44220i	0.0694706	−	0.0838161i
$850$			3.11705i			0.106914i
$851$	−6.11528	+	12.3372i	−0.209629	+	0.422915i
$852$	−15.6812	+	1.46754i	−0.537231	+	0.0502772i
$853$	−25.9018	+	25.9018i	−0.886861	+	0.886861i	−0.994220	−	0.107359i	$-0.965761\pi$
$853$	−25.9018	+	25.9018i	−0.886861	+	0.886861i	0.107359	+	0.994220i	$0.465761\pi$
$854$	−0.0629620			−0.00215452
$855$	4.28904	−	0.809881i	0.146682	−	0.0276973i
$856$	5.07128	+	5.07128i	0.173333	+	0.173333i
$857$	−28.2689	+	28.2689i	−0.965648	+	0.965648i	−0.999429	−	0.0337813i	$-0.989245\pi$
$857$	−28.2689	+	28.2689i	−0.965648	+	0.965648i	0.0337813	+	0.999429i	$0.489245\pi$
$858$	1.51668	+	16.2063i	0.0517786	+	0.553273i
$859$	−1.06751	−	1.06751i	−0.0364231	−	0.0364231i	0.688661	−	0.725084i	$-0.258199\pi$
$859$	−1.06751	−	1.06751i	−0.0364231	−	0.0364231i	−0.725084	+	0.688661i	$0.758199\pi$
$860$		−	3.75989i		−	0.128211i
$861$	0.619752	−	0.0580001i	0.0211211	−	0.00197664i
$862$		−	22.4215i		−	0.763678i
$863$		−	6.12565i		−	0.208520i	−0.994550	−	0.104260i	$-0.966753\pi$
$863$		−	6.12565i		−	0.208520i	0.994550	−	0.104260i	$-0.0332474\pi$
$864$	−4.54639	−	2.51601i	−0.154671	−	0.0855964i
$865$	5.08223	−	5.08223i	0.172801	−	0.172801i
$866$	5.43907	+	5.43907i	0.184827	+	0.184827i
$867$	1.17557	+	12.5613i	0.0399243	+	0.426605i
$868$	0.137901	+	0.137901i	0.00468065	+	0.00468065i
$869$	−56.9014	−	56.9014i	−1.93025	−	1.93025i
$870$	6.55178	+	5.43041i	0.222126	+	0.184108i
$871$	9.34281	−	9.34281i	0.316569	−	0.316569i
$872$	17.3535			0.587663
$873$	−37.7141	−	25.7335i	−1.27643	−	0.870948i
$874$	2.32892	+	2.32892i	0.0787769	+	0.0787769i
$875$	0.150466	+	0.150466i	0.00508668	+	0.00508668i
$876$	13.3304	−	1.24753i	0.450391	−	0.0421503i
$877$	13.5779			0.458493			0.229246	−	0.973368i	$-0.426374\pi$
$877$	13.5779			0.458493			0.229246	+	0.973368i	$0.426374\pi$
$878$	−22.3009			−0.752617
$879$	3.47377	+	37.1185i	0.117167	+	1.25198i
$880$	3.33240	−	3.33240i	0.112335	−	0.112335i
$881$	56.3184			1.89742			0.948708	−	0.316153i	$-0.102391\pi$
$881$	56.3184			1.89742			0.948708	+	0.316153i	$0.102391\pi$
$882$	−17.2344	−	11.7596i	−0.580313	−	0.395966i
$883$	−1.46839	+	1.46839i	−0.0494152	+	0.0494152i	−0.731383	−	0.681967i	$-0.761125\pi$
$883$	−1.46839	+	1.46839i	−0.0494152	+	0.0494152i	0.681967	+	0.731383i	$0.261125\pi$
$884$		−	6.21567i		−	0.209056i
$885$	1.16058	+	12.4012i	0.0390125	+	0.416862i
$886$	−21.2426	−	21.2426i	−0.713658	−	0.713658i
$887$	31.9028			1.07119			0.535596	−	0.844474i	$-0.320087\pi$
$887$	31.9028			1.07119			0.535596	+	0.844474i	$0.320087\pi$
$888$	−3.77908	+	9.83456i	−0.126818	+	0.330026i
$889$	−1.19677			−0.0401384
$890$	−6.73631	−	6.73631i	−0.225802	−	0.225802i
$891$	39.4940	−	15.4664i	1.32310	−	0.518145i
$892$			14.2436i			0.476911i
$893$	12.4302	−	12.4302i	0.415962	−	0.415962i
$894$	13.5137	−	16.3043i	0.451967	−	0.545297i
$895$	14.6876			0.490953
$896$	0.150466	−	0.150466i	0.00502672	−	0.00502672i
$897$	−7.78456	+	0.728526i	−0.259919	+	0.0243248i
$898$	7.52961			0.251266
$899$	−4.50279			−0.150177
$900$	2.94791	−	0.556641i	0.0982635	−	0.0185547i
$901$	−13.6888	−	13.6888i	−0.456039	−	0.456039i
$902$	5.62800	+	5.62800i	0.187392	+	0.187392i
$903$	1.06692	+	0.884316i	0.0355050	+	0.0294282i
$904$	16.9381			0.563354
$905$	−8.65824	+	8.65824i	−0.287810	+	0.287810i
$906$	4.33834	−	5.23419i	0.144132	−	0.173894i
$907$	37.3736	+	37.3736i	1.24097	+	1.24097i	0.959600	+	0.281369i	$0.0907886\pi$
$907$	37.3736	+	37.3736i	1.24097	+	1.24097i	0.281369	+	0.959600i	$0.409211\pi$
$908$	7.34361	+	7.34361i	0.243706	+	0.243706i
$909$	6.40816	−	1.21003i	0.212545	−	0.0401340i
$910$	−0.300042	−	0.300042i	−0.00994631	−	0.00994631i
$911$	−1.14991	+	1.14991i	−0.0380983	+	0.0380983i	−0.725899	−	0.687801i	$-0.758576\pi$
$911$	−1.14991	+	1.14991i	−0.0380983	+	0.0380983i	0.687801	+	0.725899i	$0.258576\pi$
$912$	1.94022	+	1.60814i	0.0642471	+	0.0532510i
$913$			8.30773i			0.274946i
$914$			28.4157i			0.939908i
$915$	−0.0477532	−	0.510261i	−0.00157867	−	0.0168687i
$916$		−	7.18264i		−	0.237321i
$917$	−1.75841	−	1.75841i	−0.0580679	−	0.0580679i
$918$	−15.5662	+	4.47515i	−0.513760	+	0.147702i
$919$	37.5481	−	37.5481i	1.23860	−	1.23860i	0.278024	−	0.960574i	$-0.410320\pi$
$919$	37.5481	−	37.5481i	1.23860	−	1.23860i	0.960574	−	0.278024i	$-0.0896796\pi$
$920$	1.60069	+	1.60069i	0.0527733	+	0.0527733i
$921$	1.51619	+	16.2011i	0.0499602	+	0.533843i
$922$	−27.7883			−0.915159
$923$	−12.8216	+	12.8216i	−0.422028	+	0.422028i
$924$	0.161847	+	1.72939i	0.00532436	+	0.0568927i
$925$	−1.94352	−	5.76392i	−0.0639026	−	0.189516i
$926$			32.2276i			1.05906i
$927$	17.1074	−	25.0719i	0.561881	−	0.823471i
$928$			4.91308i			0.161280i
$929$	51.4288			1.68732			0.843662	−	0.536875i	$-0.180395\pi$
$929$	51.4288			1.68732			0.843662	+	0.536875i	$0.180395\pi$
$930$	−1.01299	+	1.22217i	−0.0332173	+	0.0400766i
$931$	7.15502	+	7.15502i	0.234496	+	0.234496i
$932$			13.6955i			0.448611i
$933$	−24.3298	−	20.1657i	−0.796523	−	0.660195i
$934$	27.5691			0.902087
$935$		−	14.6898i		−	0.480408i
$936$	−5.87838	+	1.10999i	−0.192141	+	0.0362811i
$937$	−9.59465			−0.313443			−0.156722	−	0.987643i	$-0.550093\pi$
$937$	−9.59465			−0.313443			−0.156722	+	0.987643i	$0.550093\pi$
$938$	0.996982	−	0.996982i	0.0325526	−	0.0325526i
$939$	38.7606	+	32.1266i	1.26490	+	1.04841i
$940$	8.54344	−	8.54344i	0.278656	−	0.278656i
$941$		−	36.1166i		−	1.17737i	−0.808364	−	0.588683i	$-0.799647\pi$
$941$		−	36.1166i		−	1.17737i	0.808364	−	0.588683i	$-0.200353\pi$
$942$	5.32660	+	4.41493i	0.173550	+	0.143846i
$943$	−2.70337	+	2.70337i	−0.0880339	+	0.0880339i
$944$	−5.08490	+	5.08490i	−0.165499	+	0.165499i
$945$	−0.535385	+	0.967433i	−0.0174161	+	0.0314706i
$946$			17.7193i			0.576104i
$947$	−7.30219	+	7.30219i	−0.237289	+	0.237289i	−0.815727	−	0.578437i	$-0.803663\pi$
$947$	−7.30219	+	7.30219i	−0.237289	+	0.237289i	0.578437	+	0.815727i	$0.303663\pi$
$948$	18.8732	−	22.7704i	0.612972	−	0.739548i
$949$	10.8994	−	10.8994i	0.353810	−	0.353810i
$950$	−1.45494			−0.0472046
$951$	−29.5921	+	2.76940i	−0.959589	+	0.0898041i
$952$		−	0.663281i		−	0.0214971i
$953$	−52.6512			−1.70554			−0.852769	−	0.522288i	$-0.825079\pi$
$953$	−52.6512			−1.70554			−0.852769	+	0.522288i	$0.825079\pi$
$954$	−10.5014	+	15.3905i	−0.339996	+	0.498285i
$955$		−	23.9567i		−	0.775222i
$956$	−18.3219	−	18.3219i	−0.592572	−	0.592572i
$957$	−30.8767	−	25.5920i	−0.998102	−	0.827273i
$958$	−4.86866			−0.157299
$959$			1.28318i			0.0414359i
$960$	1.33354	+	1.10530i	0.0430397	+	0.0356733i
$961$			30.1600i			0.972905i
$962$	3.87555	+	11.4937i	0.124953	+	0.370573i
$963$	−3.99216	−	21.1420i	−0.128646	−	0.681292i
$964$	−10.3781	+	10.3781i	−0.334256	+	0.334256i
$965$	6.40265			0.206109
$966$	−0.830700	+	0.0777418i	−0.0267273	+	0.00250130i
$967$	35.1799	+	35.1799i	1.13131	+	1.13131i	0.989960	+	0.141349i	$0.0451438\pi$
$967$	35.1799	+	35.1799i	1.13131	+	1.13131i	0.141349	+	0.989960i	$0.454856\pi$
$968$	−7.92649	+	7.92649i	−0.254767	+	0.254767i
$969$	7.82091	−	0.731928i	0.251244	−	0.0235129i
$970$	10.7615	+	10.7615i	0.345530	+	0.345530i
$971$		−	43.2285i		−	1.38727i	−0.720328	−	0.693634i	$-0.756009\pi$
$971$		−	43.2285i		−	1.38727i	0.720328	−	0.693634i	$-0.243991\pi$
$972$	7.01210	+	13.9223i	0.224913	+	0.446558i
$973$		−	0.633719i		−	0.0203161i
$974$		−	22.2356i		−	0.712475i
$975$	2.20406	−	2.65919i	0.0705863	−	0.0851622i
$976$	0.209223	−	0.209223i	0.00669707	−	0.00669707i
$977$	−3.14452	−	3.14452i	−0.100602	−	0.100602i	0.655014	−	0.755616i	$-0.272663\pi$
$977$	−3.14452	−	3.14452i	−0.100602	−	0.100602i	−0.755616	+	0.655014i	$0.772663\pi$
$978$	1.07901	−	0.100980i	0.0345030	−	0.00322899i
$979$	31.7464	+	31.7464i	1.01462	+	1.01462i
$980$	4.91773	+	4.91773i	0.157091	+	0.157091i
$981$	−43.0035	−	29.3427i	−1.37300	−	0.936840i
$982$	6.47455	−	6.47455i	0.206611	−	0.206611i
$983$	−51.5373			−1.64378			−0.821892	−	0.569644i	$-0.807081\pi$
$983$	−51.5373			−1.64378			−0.821892	+	0.569644i	$0.807081\pi$
$984$	−1.86671	+	2.25218i	−0.0595084	+	0.0717968i
$985$	−6.88464	−	6.88464i	−0.219363	−	0.219363i
$986$	10.8289	+	10.8289i	0.344862	+	0.344862i
$987$	0.414934	+	4.43372i	0.0132075	+	0.141127i
$988$	2.90128			0.0923022
$989$	−8.51134			−0.270645
$990$	−13.8927	+	2.62329i	−0.441538	+	0.0833737i
$991$	6.91897	−	6.91897i	0.219788	−	0.219788i	−0.588621	−	0.808409i	$-0.700329\pi$
$991$	6.91897	−	6.91897i	0.219788	−	0.219788i	0.808409	+	0.588621i	$0.200329\pi$
$992$	−0.916490			−0.0290986
$993$	−0.0186674	−	0.0154724i	−0.000592391	−	0.000491001i
$994$	−1.36821	+	1.36821i	−0.0433969	+	0.0433969i
$995$		−	13.8753i		−	0.439876i
$996$	−3.04003	+	0.284504i	−0.0963269	+	0.00901485i
$997$	6.96900	+	6.96900i	0.220710	+	0.220710i	0.808798	−	0.588087i	$-0.200119\pi$
$997$	6.96900	+	6.96900i	0.220710	+	0.220710i	−0.588087	+	0.808798i	$0.700119\pi$
$998$	−26.1718			−0.828454
$999$	25.9940	−	17.9809i	0.822412	−	0.568892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.191.19	yes	40
3.2	odd	2	inner	1110.2.u.f.191.8	✓	40
37.31	odd	4	inner	1110.2.u.f.401.8	yes	40
111.68	even	4	inner	1110.2.u.f.401.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.8	✓	40	3.2	odd	2	inner
1110.2.u.f.191.19	yes	40	1.1	even	1	trivial
1110.2.u.f.401.8	yes	40	37.31	odd	4	inner
1110.2.u.f.401.19	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.72452 - 0.161390i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.33354 + 1.10530i) q^{6} +0.212791 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.94791 - 0.556641i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.72452 - 0.161390i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.33354 + 1.10530i) q^{6} +0.212791 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.94791 - 0.556641i) q^{9} -1.00000 q^{10} +4.71272 q^{11} +(0.161390 + 1.72452i) q^{12} +(1.41003 + 1.41003i) q^{13} +(0.150466 + 0.150466i) q^{14} +(-1.10530 + 1.33354i) q^{15} -1.00000 q^{16} +(-2.20409 + 2.20409i) q^{17} +(2.47809 + 1.69088i) q^{18} +(-1.02880 - 1.02880i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(0.366962 - 0.0343425i) q^{21} +(3.33240 + 3.33240i) q^{22} +(-1.60069 + 1.60069i) q^{23} +(-1.10530 + 1.33354i) q^{24} -1.00000i q^{25} +1.99409i q^{26} +(4.99387 - 1.43570i) q^{27} +0.212791i q^{28} +(-3.47408 - 3.47408i) q^{29} +(-1.72452 + 0.161390i) q^{30} +(0.648056 - 0.648056i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.12716 - 0.760588i) q^{33} -3.11705 q^{34} +(-0.150466 + 0.150466i) q^{35} +(0.556641 + 2.94791i) q^{36} +(5.76392 - 1.94352i) q^{37} -1.45494i q^{38} +(2.65919 + 2.20406i) q^{39} -1.00000i q^{40} +1.68887 q^{41} +(0.283765 + 0.235197i) q^{42} +(2.65864 + 2.65864i) q^{43} +4.71272i q^{44} +(-1.69088 + 2.47809i) q^{45} -2.26372 q^{46} +12.0822i q^{47} +(-1.72452 + 0.161390i) q^{48} -6.95472 q^{49} +(0.707107 - 0.707107i) q^{50} +(-3.44527 + 4.15670i) q^{51} +(-1.41003 + 1.41003i) q^{52} +6.21062i q^{53} +(4.54639 + 2.51601i) q^{54} +(-3.33240 + 3.33240i) q^{55} +(-0.150466 + 0.150466i) q^{56} +(-1.94022 - 1.60814i) q^{57} -4.91308i q^{58} +(5.08490 - 5.08490i) q^{59} +(-1.33354 - 1.10530i) q^{60} +(-0.209223 + 0.209223i) q^{61} +0.916490 q^{62} +(0.627289 - 0.118448i) q^{63} -1.00000i q^{64} -1.99409 q^{65} +(6.28459 + 5.20895i) q^{66} -6.62596i q^{67} +(-2.20409 - 2.20409i) q^{68} +(-2.50208 + 3.01876i) q^{69} -0.212791 q^{70} +9.09313i q^{71} +(-1.69088 + 2.47809i) q^{72} -7.72992i q^{73} +(5.44998 + 2.70143i) q^{74} +(-0.161390 - 1.72452i) q^{75} +(1.02880 - 1.02880i) q^{76} +1.00283 q^{77} +(0.321827 + 3.43883i) q^{78} +(-12.0740 - 12.0740i) q^{79} +(0.707107 - 0.707107i) q^{80} +(8.38030 - 3.28185i) q^{81} +(1.19421 + 1.19421i) q^{82} +1.76283i q^{83} +(0.0343425 + 0.366962i) q^{84} -3.11705i q^{85} +3.75989i q^{86} +(-6.55178 - 5.43041i) q^{87} +(-3.33240 + 3.33240i) q^{88} +(6.73631 + 6.73631i) q^{89} +(-2.94791 + 0.556641i) q^{90} +(0.300042 + 0.300042i) q^{91} +(-1.60069 - 1.60069i) q^{92} +(1.01299 - 1.22217i) q^{93} +(-8.54344 + 8.54344i) q^{94} +1.45494 q^{95} +(-1.33354 - 1.10530i) q^{96} +(-10.7615 - 10.7615i) q^{97} +(-4.91773 - 4.91773i) q^{98} +(13.8927 - 2.62329i) 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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