LMFDB - Embedded newform 416.2.bg.a.77.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(77,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 4]))

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

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

chi := DirichletCharacter("416.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$416 = 2^{5} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	416.bg (of order $8$ , degree $4$ , 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.14
Character	$\chi$	$=$	416.77
Dual form			416.2.bg.a.389.14

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01393 - 0.985874i) q^{2} +(0.225020 - 0.543247i) q^{3} +(0.0561057 + 1.99921i) q^{4} +(-0.861807 - 2.08059i) q^{5} +(-0.763728 + 0.328973i) q^{6} +(1.89986 + 1.89986i) q^{7} +(1.91408 - 2.08237i) q^{8} +(1.87684 + 1.87684i) q^{9} +(-1.17738 + 2.95920i) q^{10} +(0.272084 - 0.112701i) q^{11} +(1.09869 + 0.419384i) q^{12} +(3.52742 + 0.746523i) q^{13} +(-0.0533016 - 3.79934i) q^{14} -1.32420 q^{15} +(-3.99370 + 0.224335i) q^{16} +1.54597i q^{17} +(-0.0526558 - 3.75330i) q^{18} +(1.03779 - 2.50544i) q^{19} +(4.11118 - 1.83967i) q^{20} +(1.45960 - 0.604585i) q^{21} +(-0.386983 - 0.153970i) q^{22} +(-2.39305 - 2.39305i) q^{23} +(-0.700536 - 1.50840i) q^{24} +(-0.0505958 + 0.0505958i) q^{25} +(-2.84058 - 4.23451i) q^{26} +(3.07165 - 1.27232i) q^{27} +(-3.69162 + 3.90481i) q^{28} +(3.18608 - 7.69189i) q^{29} +(1.34264 + 1.30549i) q^{30} +3.40252i q^{31} +(4.27050 + 3.70983i) q^{32} -0.173169i q^{33} +(1.52413 - 1.56750i) q^{34} +(2.31550 - 5.59012i) q^{35} +(-3.64690 + 3.85750i) q^{36} +(-0.622028 - 1.50171i) q^{37} +(-3.52229 + 1.51721i) q^{38} +(1.19929 - 1.74828i) q^{39} +(-5.98213 - 2.18781i) q^{40} +(1.66466 - 1.66466i) q^{41} +(-2.07597 - 0.825972i) q^{42} +(3.33749 + 8.05742i) q^{43} +(0.240578 + 0.537630i) q^{44} +(2.28745 - 5.52239i) q^{45} +(0.0671385 + 4.78563i) q^{46} -4.15187 q^{47} +(-0.776795 + 2.22005i) q^{48} +0.218899i q^{49} +(0.101182 - 0.00141950i) q^{50} +(0.839842 + 0.347874i) q^{51} +(-1.29455 + 7.09395i) q^{52} +(-3.70845 - 8.95298i) q^{53} +(-4.36879 - 1.73822i) q^{54} +(-0.468968 - 0.468968i) q^{55} +(7.59269 - 0.319726i) q^{56} +(-1.12755 - 1.12755i) q^{57} +(-10.8137 + 4.65795i) q^{58} +(2.12024 + 5.11871i) q^{59} +(-0.0742950 - 2.64735i) q^{60} +(2.10134 - 5.07310i) q^{61} +(3.35445 - 3.44991i) q^{62} +7.13144i q^{63} +(-0.672562 - 7.97168i) q^{64} +(-1.48675 - 7.98247i) q^{65} +(-0.170723 + 0.175581i) q^{66} +(-3.13250 - 1.29753i) q^{67} +(-3.09072 + 0.0867377i) q^{68} +(-1.83850 + 0.761533i) q^{69} +(-7.85891 + 3.38519i) q^{70} +(2.17999 + 2.17999i) q^{71} +(7.50070 - 0.315852i) q^{72} +(-2.66459 + 2.66459i) q^{73} +(-0.849803 + 2.13587i) q^{74} +(0.0161009 + 0.0388711i) q^{75} +(5.06713 + 1.93419i) q^{76} +(0.731035 + 0.302805i) q^{77} +(-2.93958 + 0.590284i) q^{78} +1.27845i q^{79} +(3.90855 + 8.11592i) q^{80} +6.00778i q^{81} +(-3.32900 + 0.0467032i) q^{82} +(-6.55193 + 15.8177i) q^{83} +(1.29059 + 2.88412i) q^{84} +(3.21652 - 1.33233i) q^{85} +(4.55962 - 11.4600i) q^{86} +(-3.46166 - 3.46166i) q^{87} +(0.286106 - 0.782299i) q^{88} +(9.11213 + 9.11213i) q^{89} +(-7.76370 + 3.34418i) q^{90} +(5.28330 + 8.11988i) q^{91} +(4.64995 - 4.91848i) q^{92} +(1.84841 + 0.765635i) q^{93} +(4.20970 + 4.09322i) q^{94} -6.10715 q^{95} +(2.97630 - 1.48515i) q^{96} -13.3207i q^{97} +(0.215806 - 0.221948i) q^{98} +(0.722178 + 0.299136i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100})$ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$ .

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−1.01393	−	0.985874i	−0.716956	−	0.697118i
$2$	−1.01393	−	0.985874i	−0.716956	−	0.697118i
$3$	0.225020	−	0.543247i	0.129916	−	0.313644i	−0.845515	−	0.533952i	$-0.820706\pi$
$3$	0.225020	−	0.543247i	0.129916	−	0.313644i	0.975430	+	0.220308i	$0.0707063\pi$
$4$	0.0561057	+	1.99921i	0.0280529	+	0.999606i
$5$	−0.861807	−	2.08059i	−0.385412	−	0.930467i	−0.990898	−	0.134611i	$-0.957021\pi$
$5$	−0.861807	−	2.08059i	−0.385412	−	0.930467i	0.605487	−	0.795856i	$-0.292979\pi$
$6$	−0.763728	+	0.328973i	−0.311791	+	0.134302i
$7$	1.89986	+	1.89986i	0.718078	+	0.718078i	0.968211	−	0.250134i	$-0.0804745\pi$
$7$	1.89986	+	1.89986i	0.718078	+	0.718078i	−0.250134	+	0.968211i	$0.580475\pi$
$8$	1.91408	−	2.08237i	0.676731	−	0.736230i
$9$	1.87684	+	1.87684i	0.625612	+	0.625612i
$10$	−1.17738	+	2.95920i	−0.372322	+	0.935782i
$11$	0.272084	−	0.112701i	0.0820364	−	0.0339806i	−0.341288	−	0.939959i	$-0.610863\pi$
$11$	0.272084	−	0.112701i	0.0820364	−	0.0339806i	0.423324	+	0.905978i	$0.360863\pi$
$12$	1.09869	+	0.419384i	0.317165	+	0.121066i
$13$	3.52742	+	0.746523i	0.978331	+	0.207048i
$13$	3.52742	+	0.746523i	0.978331	+	0.207048i
$14$	−0.0533016	−	3.79934i	−0.0142455	−	1.01542i
$15$	−1.32420			−0.341906
$16$	−3.99370	+	0.224335i	−0.998426	+	0.0560837i
$17$			1.54597i			0.374952i	0.982269	+	0.187476i	$0.0600307\pi$
$17$			1.54597i			0.374952i	−0.982269	+	0.187476i	$0.939969\pi$
$18$	−0.0526558	−	3.75330i	−0.0124111	−	0.884662i
$19$	1.03779	−	2.50544i	0.238084	−	0.574787i	−0.759000	−	0.651090i	$-0.774312\pi$
$19$	1.03779	−	2.50544i	0.238084	−	0.574787i	0.997085	+	0.0763038i	$0.0243119\pi$
$20$	4.11118	−	1.83967i	0.919289	−	0.411363i
$21$	1.45960	−	0.604585i	0.318510	−	0.131931i
$22$	−0.386983	−	0.153970i	−0.0825050	−	0.0328264i
$23$	−2.39305	−	2.39305i	−0.498985	−	0.498985i	0.412137	−	0.911122i	$-0.364783\pi$
$23$	−2.39305	−	2.39305i	−0.498985	−	0.498985i	−0.911122	+	0.412137i	$0.864783\pi$
$24$	−0.700536	−	1.50840i	−0.142996	−	0.307900i
$25$	−0.0505958	+	0.0505958i	−0.0101192	+	0.0101192i
$26$	−2.84058	−	4.23451i	−0.557083	−	0.830457i
$27$	3.07165	−	1.27232i	0.591140	−	0.244858i
$28$	−3.69162	+	3.90481i	−0.697651	+	0.737939i
$29$	3.18608	−	7.69189i	0.591641	−	1.42835i	−0.290276	−	0.956943i	$-0.593747\pi$
$29$	3.18608	−	7.69189i	0.591641	−	1.42835i	0.881917	−	0.471405i	$-0.156253\pi$
$30$	1.34264	+	1.30549i	0.245132	+	0.238349i
$31$			3.40252i			0.611110i	0.952174	+	0.305555i	$0.0988420\pi$
$31$			3.40252i			0.611110i	−0.952174	+	0.305555i	$0.901158\pi$
$32$	4.27050	+	3.70983i	0.754925	+	0.655811i
$33$		−	0.173169i		−	0.0301448i
$34$	1.52413	−	1.56750i	0.261386	−	0.268824i
$35$	2.31550	−	5.59012i	0.391392	−	0.944903i
$36$	−3.64690	+	3.85750i	−0.607816	+	0.642916i
$37$	−0.622028	−	1.50171i	−0.102261	−	0.246879i	0.864466	−	0.502692i	$-0.167657\pi$
$37$	−0.622028	−	1.50171i	−0.102261	−	0.246879i	−0.966726	+	0.255813i	$0.917657\pi$
$38$	−3.52229	+	1.51721i	−0.571390	+	0.246124i
$39$	1.19929	−	1.74828i	0.192040	−	0.279949i
$40$	−5.98213	−	2.18781i	−0.945858	−	0.345924i
$41$	1.66466	−	1.66466i	0.259977	−	0.259977i	−0.565068	−	0.825045i	$-0.691150\pi$
$41$	1.66466	−	1.66466i	0.259977	−	0.259977i	0.825045	+	0.565068i	$0.191150\pi$
$42$	−2.07597	−	0.825972i	−0.320329	−	0.127450i
$43$	3.33749	+	8.05742i	0.508963	+	1.22875i	0.944481	+	0.328565i	$0.106565\pi$
$43$	3.33749	+	8.05742i	0.508963	+	1.22875i	−0.435518	+	0.900180i	$0.643435\pi$
$44$	0.240578	+	0.537630i	0.0362686	+	0.0810508i
$45$	2.28745	−	5.52239i	0.340993	−	0.823230i
$46$	0.0671385	+	4.78563i	0.00989904	+	0.705603i
$47$	−4.15187			−0.605612			−0.302806	−	0.953052i	$-0.597923\pi$
$47$	−4.15187			−0.605612			−0.302806	+	0.953052i	$0.597923\pi$
$48$	−0.776795	+	2.22005i	−0.112121	+	0.320436i
$49$			0.218899i			0.0312712i
$50$	0.101182	−	0.00141950i	0.0143092	−	0.000200747i
$51$	0.839842	+	0.347874i	0.117601	+	0.0487121i
$52$	−1.29455	+	7.09395i	−0.179522	+	0.983754i
$53$	−3.70845	−	8.95298i	−0.509394	−	1.22979i	−0.944233	−	0.329278i	$-0.893195\pi$
$53$	−3.70845	−	8.95298i	−0.509394	−	1.22979i	0.434839	−	0.900508i	$-0.356805\pi$
$54$	−4.36879	−	1.73822i	−0.594517	−	0.236542i
$55$	−0.468968	−	0.468968i	−0.0632356	−	0.0632356i
$56$	7.59269	−	0.319726i	1.01462	−	0.0427252i
$57$	−1.12755	−	1.12755i	−0.149347	−	0.149347i
$58$	−10.8137	+	4.65795i	−1.41991	+	0.611619i
$59$	2.12024	+	5.11871i	0.276032	+	0.666399i	0.999718	−	0.0237292i	$-0.00755394\pi$
$59$	2.12024	+	5.11871i	0.276032	+	0.666399i	−0.723687	+	0.690129i	$0.757554\pi$
$60$	−0.0742950	−	2.64735i	−0.00959145	−	0.341772i
$61$	2.10134	−	5.07310i	0.269050	−	0.649543i	−0.730390	−	0.683031i	$-0.760661\pi$
$61$	2.10134	−	5.07310i	0.269050	−	0.649543i	0.999439	+	0.0334876i	$0.0106614\pi$
$62$	3.35445	−	3.44991i	0.426016	−	0.438139i
$63$			7.13144i			0.898477i
$64$	−0.672562	−	7.97168i	−0.0840703	−	0.996460i
$65$	−1.48675	−	7.98247i	−0.184409	−	0.990103i
$66$	−0.170723	+	0.175581i	−0.0210145	+	0.0216125i
$67$	−3.13250	−	1.29753i	−0.382696	−	0.158518i	0.183038	−	0.983106i	$-0.441407\pi$
$67$	−3.13250	−	1.29753i	−0.382696	−	0.158518i	−0.565734	+	0.824588i	$0.691407\pi$
$68$	−3.09072	+	0.0867377i	−0.374805	+	0.0105185i
$69$	−1.83850	+	0.761533i	−0.221330	+	0.0916777i
$70$	−7.85891	+	3.38519i	−0.939320	+	0.404608i
$71$	2.17999	+	2.17999i	0.258717	+	0.258717i	0.824532	−	0.565815i	$-0.191438\pi$
$71$	2.17999	+	2.17999i	0.258717	+	0.258717i	−0.565815	+	0.824532i	$0.691438\pi$
$72$	7.50070	−	0.315852i	0.883966	−	0.0372235i
$73$	−2.66459	+	2.66459i	−0.311867	+	0.311867i	−0.845632	−	0.533766i	$-0.820776\pi$
$73$	−2.66459	+	2.66459i	−0.311867	+	0.311867i	0.533766	+	0.845632i	$0.320776\pi$
$74$	−0.849803	+	2.13587i	−0.0987876	+	0.248290i
$75$	0.0161009	+	0.0388711i	0.00185918	+	0.00448845i
$76$	5.06713	+	1.93419i	0.581239	+	0.221866i
$77$	0.731035	+	0.302805i	0.0833092	+	0.0345078i
$78$	−2.93958	+	0.590284i	−0.332841	+	0.0668366i
$79$			1.27845i			0.143837i	0.997411	+	0.0719186i	$0.0229122\pi$
$79$			1.27845i			0.143837i	−0.997411	+	0.0719186i	$0.977088\pi$
$80$	3.90855	+	8.11592i	0.436989	+	0.907387i
$81$			6.00778i			0.667531i
$82$	−3.32900	+	0.0467032i	−0.367627	+	0.00515751i
$83$	−6.55193	+	15.8177i	−0.719167	+	1.73622i	−0.0434582	+	0.999055i	$0.513838\pi$
$83$	−6.55193	+	15.8177i	−0.719167	+	1.73622i	−0.675709	+	0.737168i	$0.736162\pi$
$84$	1.29059	+	2.88412i	0.140814	+	0.314684i
$85$	3.21652	−	1.33233i	0.348881	−	0.144511i
$86$	4.55962	−	11.4600i	0.491676	−	1.23576i
$87$	−3.46166	−	3.46166i	−0.371129	−	0.371129i
$88$	0.286106	−	0.782299i	0.0304990	−	0.0833934i
$89$	9.11213	+	9.11213i	0.965884	+	0.965884i	0.999437	−	0.0335530i	$-0.0106823\pi$
$89$	9.11213	+	9.11213i	0.965884	+	0.965884i	−0.0335530	+	0.999437i	$0.510682\pi$
$90$	−7.76370	+	3.34418i	−0.818366	+	0.352508i
$91$	5.28330	+	8.11988i	0.553841	+	0.851194i
$92$	4.64995	−	4.91848i	0.484791	−	0.512787i
$93$	1.84841	+	0.765635i	0.191671	+	0.0793927i
$94$	4.20970	+	4.09322i	0.434197	+	0.422183i
$95$	−6.10715			−0.626580
$96$	2.97630	−	1.48515i	0.303768	−	0.151577i
$97$		−	13.3207i		−	1.35251i	−0.736669	−	0.676254i	$-0.763602\pi$
$97$		−	13.3207i		−	1.35251i	0.736669	−	0.676254i	$-0.236398\pi$
$98$	0.215806	−	0.221948i	0.0217997	−	0.0224201i
$99$	0.722178	+	0.299136i	0.0725816	+	0.0300643i
$100$	−0.103990	−	0.0983130i	−0.0103990	−	0.00983130i
$101$	0.776313	−	0.321559i	0.0772460	−	0.0319963i	−0.343726	−	0.939070i	$-0.611689\pi$
$101$	0.776313	−	0.321559i	0.0772460	−	0.0319963i	0.420972	+	0.907074i	$0.361689\pi$
$102$	−0.508581	−	1.18070i	−0.0503570	−	0.116907i
$103$	0.180206	−	0.180206i	0.0177562	−	0.0177562i	−0.698173	−	0.715929i	$-0.746003\pi$
$103$	0.180206	−	0.180206i	0.0177562	−	0.0177562i	0.715929	+	0.698173i	$0.246003\pi$
$104$	8.30632	−	5.91650i	0.814502	−	0.580161i
$105$	−2.51578	−	2.51578i	−0.245515	−	0.245515i
$106$	−5.06641	+	12.7337i	−0.492093	+	1.23681i
$107$	4.37571	+	10.5639i	0.423016	+	1.02125i	0.981453	+	0.191703i	$0.0614011\pi$
$107$	4.37571	+	10.5639i	0.423016	+	1.02125i	−0.558437	+	0.829547i	$0.688599\pi$
$108$	2.71598	+	6.06950i	0.261345	+	0.584038i
$109$	−5.92089	+	14.2943i	−0.567118	+	1.36914i	0.336856	+	0.941556i	$0.390636\pi$
$109$	−5.92089	+	14.2943i	−0.567118	+	1.36914i	−0.903974	+	0.427588i	$0.859364\pi$
$110$	0.0131572	+	0.937843i	0.00125449	+	0.0894198i
$111$	−0.955768			−0.0907175
$112$	−8.01366	−	7.16126i	−0.757220	−	0.676675i
$113$			11.2161i			1.05512i	0.849518	+	0.527559i	$0.176893\pi$
$113$			11.2161i			1.05512i	−0.849518	+	0.527559i	$0.823107\pi$
$114$	0.0316341	+	2.25487i	0.00296280	+	0.211188i
$115$	−2.91660	+	7.04130i	−0.271974	+	0.656604i
$116$	15.5565	+	5.93810i	1.44438	+	0.551339i
$117$	5.21929	+	8.02150i	0.482524	+	0.741588i
$118$	2.89663	−	7.28030i	0.266656	−	0.670206i
$119$	−2.93712	+	2.93712i	−0.269245	+	0.269245i
$120$	−2.53462	+	2.75747i	−0.231378	+	0.251722i
$121$	−7.71685	+	7.71685i	−0.701531	+	0.701531i
$122$	−7.13205	+	3.07210i	−0.645705	+	0.278135i
$123$	−0.529741	−	1.27891i	−0.0477651	−	0.115315i
$124$	−6.80235	+	0.190901i	−0.610870	+	0.0171434i
$125$	−10.2541	−	4.24737i	−0.917151	−	0.379896i
$126$	7.03070	−	7.23077i	0.626344	−	0.644169i
$127$	−6.34275			−0.562828			−0.281414	−	0.959586i	$-0.590803\pi$
$127$	−6.34275			−0.562828			−0.281414	+	0.959586i	$0.590803\pi$
$128$	−7.17714	+	8.74578i	−0.634375	+	0.773025i
$129$	5.12817			0.451510
$130$	−6.36224	+	9.55941i	−0.558006	+	0.838415i
$131$	−2.43098	+	5.86891i	−0.212396	+	0.512769i	−0.993790	−	0.111268i	$-0.964509\pi$
$131$	−2.43098	+	5.86891i	−0.212396	+	0.512769i	0.781395	+	0.624037i	$0.214509\pi$
$132$	0.346201	−	0.00971576i	0.0301329	−	0.000845648i
$133$	6.73161	−	2.78832i	0.583705	−	0.241778i
$134$	1.89694	+	4.40385i	0.163871	+	0.380435i
$135$	−5.29435	−	5.29435i	−0.455665	−	0.455665i
$136$	3.21928	+	2.95911i	0.276051	+	0.253742i
$137$	1.40408	−	1.40408i	0.119959	−	0.119959i	−0.644579	−	0.764538i	$-0.722967\pi$
$137$	1.40408	−	1.40408i	0.119959	−	0.119959i	0.764538	+	0.644579i	$0.222967\pi$
$138$	2.61489	+	1.04039i	0.222594	+	0.0885640i
$139$	−5.32075	−	12.8454i	−0.451300	−	1.08953i	−0.971828	−	0.235690i	$-0.924265\pi$
$139$	−5.32075	−	12.8454i	−0.451300	−	1.08953i	0.520528	−	0.853844i	$-0.325735\pi$
$140$	11.3058	+	4.31555i	0.955511	+	0.364730i
$141$	−0.934254	+	2.25549i	−0.0786784	+	0.189946i
$142$	−0.0611610	−	4.35956i	−0.00513252	−	0.365846i
$143$	1.04389	−	0.194426i	0.0872943	−	0.0162588i
$144$	−7.91657	−	7.07449i	−0.659714	−	0.589541i
$145$	−18.7494			−1.55706
$146$	5.32866	−	0.0747568i	0.441003	−	0.00618692i
$147$	0.118916	+	0.0492566i	0.00980803	+	0.00406262i
$148$	2.96734	−	1.32782i	0.243914	−	0.109146i
$149$	21.4079	−	8.86744i	1.75380	−	0.726449i	0.756426	−	0.654080i	$-0.226944\pi$
$149$	21.4079	−	8.86744i	1.75380	−	0.726449i	0.997378	−	0.0723693i	$-0.0230560\pi$
$150$	0.0219968	−	0.0552860i	0.00179603	−	0.00451408i
$151$	12.3805	−	12.3805i	1.00751	−	1.00751i	0.00753666	−	0.999972i	$-0.497601\pi$
$151$	12.3805	−	12.3805i	1.00751	−	1.00751i	0.999972	−	0.00753666i	$-0.00239902\pi$
$152$	−3.23085	−	6.95668i	−0.262056	−	0.564261i
$153$	−2.90153	+	2.90153i	−0.234575	+	0.234575i
$154$	−0.442691	−	1.02773i	−0.0356730	−	0.0828169i
$155$	7.07923	−	2.93231i	0.568618	−	0.235529i
$156$	3.56247	+	2.29954i	0.285226	+	0.184111i
$157$	0.725039	−	1.75040i	0.0578644	−	0.139697i	−0.892303	−	0.451437i	$-0.850912\pi$
$157$	0.725039	−	1.75040i	0.0578644	−	0.139697i	0.950168	+	0.311740i	$0.100912\pi$
$158$	1.26039	−	1.29626i	0.100271	−	0.103125i
$159$	−5.69815			−0.451893
$160$	4.03827	−	12.0823i	0.319254	−	0.955190i
$161$		−	9.09290i		−	0.716621i
$162$	5.92291	−	6.09147i	0.465348	−	0.478591i
$163$	−16.6154	−	6.88231i	−1.30142	−	0.539064i	−0.379049	−	0.925377i	$-0.623749\pi$
$163$	−16.6154	−	6.88231i	−1.30142	−	0.539064i	−0.922368	+	0.386312i	$0.873749\pi$
$164$	3.42142	+	3.23462i	0.267168	+	0.252582i
$165$	−0.360293	+	0.149238i	−0.0280487	+	0.0116182i
$166$	22.2375	−	9.57871i	1.72596	−	0.743452i
$167$	−11.2426	−	11.2426i	−0.869982	−	0.869982i	0.122488	−	0.992470i	$-0.460913\pi$
$167$	−11.2426	−	11.2426i	−0.869982	−	0.869982i	−0.992470	+	0.122488i	$0.960913\pi$
$168$	1.53482	−	4.19665i	0.118414	−	0.323779i
$169$	11.8854	+	5.26660i	0.914262	+	0.405123i
$170$	−4.57483	−	1.82020i	−0.350873	−	0.139603i
$171$	6.65005	−	2.75454i	0.508542	−	0.210645i
$172$	−15.9212	+	7.12443i	−1.21398	+	0.543232i
$173$	−10.2262	−	4.23582i	−0.777481	−	0.322043i	−0.0415826	−	0.999135i	$-0.513240\pi$
$173$	−10.2262	−	4.23582i	−0.777481	−	0.322043i	−0.735899	+	0.677092i	$0.763240\pi$
$174$	0.0971191	+	6.92264i	0.00736258	+	0.524804i
$175$	−0.192249			−0.0145327
$176$	−1.06134	+	0.511132i	−0.0800015	+	0.0385280i
$177$	3.25782			0.244873
$178$	−0.255647	−	18.2225i	−0.0191615	−	1.36583i
$179$	−8.94016	−	3.70313i	−0.668219	−	0.276785i	0.0226737	−	0.999743i	$-0.492782\pi$
$179$	−8.94016	−	3.70313i	−0.668219	−	0.276785i	−0.690892	+	0.722958i	$0.742782\pi$
$180$	11.1688	+	4.26326i	0.832472	+	0.317765i
$181$	−4.18085	−	10.0935i	−0.310760	−	0.750241i	−0.999677	−	0.0254009i	$-0.991914\pi$
$181$	−4.18085	−	10.0935i	−0.310760	−	0.750241i	0.688917	−	0.724840i	$-0.258086\pi$
$182$	2.64827	−	13.4417i	0.196303	−	0.996362i
$183$	−2.28310	−	2.28310i	−0.168771	−	0.168771i
$184$	−9.56373	+	0.402725i	−0.705047	+	0.0296893i
$185$	−2.58837	+	2.58837i	−0.190301	+	0.190301i
$186$	−1.11933	−	2.59860i	−0.0820736	−	0.190538i
$187$	0.174232	+	0.420633i	0.0127411	+	0.0307597i
$188$	−0.232943	−	8.30046i	−0.0169892	−	0.605374i
$189$	8.25292	+	3.41847i	0.600312	+	0.248657i
$190$	6.19222	+	6.02088i	0.449231	+	0.436800i
$191$	−24.4152			−1.76662			−0.883311	−	0.468787i	$-0.844691\pi$
$191$	−24.4152			−1.76662			−0.883311	+	0.468787i	$0.844691\pi$
$192$	−4.48193	−	1.42842i	−0.323455	−	0.103087i
$193$		−	0.547736i		−	0.0394269i	−0.999806	−	0.0197134i	$-0.993725\pi$
$193$		−	0.547736i		−	0.0394269i	0.999806	−	0.0197134i	$-0.00627539\pi$
$194$	−13.1325	+	13.5062i	−0.942857	+	0.969689i
$195$	−4.67100	−	0.988543i	−0.334497	−	0.0707911i
$196$	−0.437625	+	0.0122815i	−0.0312589	+	0.000877248i
$197$	−3.16563	−	7.64251i	−0.225542	−	0.544506i	0.770083	−	0.637943i	$-0.220215\pi$
$197$	−3.16563	−	7.64251i	−0.225542	−	0.544506i	−0.995625	+	0.0934370i	$0.970215\pi$
$198$	−0.437327	−	1.01528i	−0.0310795	−	0.0721528i
$199$	−14.8646	+	14.8646i	−1.05373	+	1.05373i	−0.0552539	+	0.998472i	$0.517597\pi$
$199$	−14.8646	+	14.8646i	−1.05373	+	1.05373i	−0.998472	+	0.0552539i	$0.982403\pi$
$200$	0.00851474	+	0.202204i	0.000602083	+	0.0142980i
$201$	−1.40975	+	1.40975i	−0.0994363	+	0.0994363i
$202$	−1.10414	−	0.439308i	−0.0776872	−	0.0309096i
$203$	20.6666	−	8.56037i	1.45051	−	0.600820i
$204$	−0.648354	+	1.69854i	−0.0453939	+	0.118922i
$205$	−4.89810	−	2.02886i	−0.342098	−	0.141702i
$206$	−0.360376	+	0.00505578i	−0.0251086	+	0.000352253i
$207$		−	8.98273i		−	0.624343i
$208$	−14.2549	−	2.19007i	−0.988403	−	0.151854i
$209$		−	0.798648i		−	0.0552437i
$210$	0.0705818	+	5.03107i	0.00487061	+	0.347177i
$211$	25.8157	+	10.6932i	1.77722	+	0.736150i	0.993337	+	0.115245i	$0.0367652\pi$
$211$	25.8157	+	10.6932i	1.77722	+	0.736150i	0.783886	+	0.620905i	$0.213235\pi$
$212$	17.6908	−	7.91628i	1.21501	−	0.543693i
$213$	1.67482	−	0.693732i	0.114757	−	0.0475337i
$214$	5.97801	−	15.0249i	0.408648	−	1.02708i
$215$	13.8879	−	13.8879i	0.947146	−	0.947146i
$216$	3.22996	−	8.83166i	0.219771	−	0.600918i
$217$	−6.46429	+	6.46429i	−0.438824	+	0.438824i
$218$	20.0957	−	8.65615i	1.36105	−	0.586268i
$219$	0.847944	+	2.04712i	0.0572988	+	0.138331i
$220$	0.911255	−	0.963878i	0.0614368	−	0.0649847i
$221$	−1.15410	+	5.45328i	−0.0776332	+	0.366827i
$222$	0.969081	+	0.942266i	0.0650405	+	0.0632408i
$223$			20.4305i			1.36813i	0.729422	+	0.684064i	$0.239789\pi$
$223$			20.4305i			1.36813i	−0.729422	+	0.684064i	$0.760211\pi$
$224$	1.06519	+	15.1615i	0.0711712	+	1.01302i
$225$	−0.189920			−0.0126613
$226$	11.0576	−	11.3723i	0.735542	−	0.756474i
$227$	−11.8137	−	4.89339i	−0.784102	−	0.324786i	−0.0455321	−	0.998963i	$-0.514498\pi$
$227$	−11.8137	−	4.89339i	−0.784102	−	0.324786i	−0.738569	+	0.674177i	$0.764498\pi$
$228$	2.19095	−	2.31747i	0.145099	−	0.153478i
$229$	1.59286	+	3.84550i	0.105259	+	0.254118i	0.967730	−	0.251988i	$-0.0810844\pi$
$229$	1.59286	+	3.84550i	0.105259	+	0.254118i	−0.862471	+	0.506106i	$0.831084\pi$
$230$	9.89906	−	4.26398i	0.652725	−	0.281158i
$231$	0.328995	−	0.328995i	0.0216463	−	0.0216463i
$232$	−9.91895	−	21.3575i	−0.651211	−	1.40219i
$233$	−3.69919	−	3.69919i	−0.242342	−	0.242342i	0.575476	−	0.817818i	$-0.304817\pi$
$233$	−3.69919	−	3.69919i	−0.242342	−	0.242342i	−0.817818	+	0.575476i	$0.804817\pi$
$234$	2.61619	−	13.2788i	0.171026	−	0.868062i
$235$	3.57811	+	8.63832i	0.233410	+	0.563502i
$236$	−10.1144	+	4.52600i	−0.658394	+	0.294617i
$237$	0.694515	+	0.287678i	0.0451136	+	0.0186867i
$238$	5.87365	−	0.0824026i	0.380732	−	0.00534137i
$239$	15.8866			1.02762			0.513810	−	0.857904i	$-0.328234\pi$
$239$	15.8866			1.02762			0.513810	+	0.857904i	$0.328234\pi$
$240$	5.28845	−	0.297063i	0.341368	−	0.0191753i
$241$	−18.5743			−1.19648			−0.598238	−	0.801319i	$-0.704132\pi$
$241$	−18.5743			−1.19648			−0.598238	+	0.801319i	$0.704132\pi$
$242$	15.4322	−	0.216501i	0.992018	−	0.0139172i
$243$	12.4787	+	5.16883i	0.800507	+	0.331581i
$244$	10.2601	+	3.91641i	0.656835	+	0.250722i
$245$	0.455438	−	0.188648i	0.0290968	−	0.0120523i
$246$	−0.723722	+	1.81898i	−0.0461428	+	0.115974i
$247$	5.53107	−	8.06300i	0.351934	−	0.513036i
$248$	7.08531	+	6.51270i	0.449918	+	0.413557i
$249$	7.11863	+	7.11863i	0.451125	+	0.451125i
$250$	6.20952	+	14.4157i	0.392725	+	0.911732i
$251$	0.271506	−	0.112462i	0.0171373	−	0.00709852i	−0.374098	−	0.927389i	$-0.622048\pi$
$251$	0.271506	−	0.112462i	0.0171373	−	0.00709852i	0.391236	+	0.920291i	$0.372048\pi$
$252$	−14.2573	+	0.400115i	−0.898123	+	0.0252048i
$253$	−0.920809	−	0.381412i	−0.0578908	−	0.0239791i
$254$	6.43110	+	6.25315i	0.403523	+	0.392358i
$255$		−	2.04717i		−	0.128198i
$256$	15.8993	−	1.79185i	0.993709	−	0.111991i
$257$	−22.7896			−1.42158			−0.710788	−	0.703406i	$-0.751662\pi$
$257$	−22.7896			−1.42158			−0.710788	+	0.703406i	$0.751662\pi$
$258$	−5.19961	−	5.05573i	−0.323713	−	0.314756i
$259$	1.67127	−	4.03479i	0.103847	−	0.250710i
$260$	15.8752	−	3.42020i	0.984540	−	0.212111i
$261$	20.4162	−	8.45666i	1.26373	−	0.523454i
$262$	8.25085	−	3.55402i	0.509739	−	0.219568i
$263$	−8.22104	+	8.22104i	−0.506931	+	0.506931i	−0.913583	−	0.406652i	$-0.866696\pi$
$263$	−8.22104	+	8.22104i	−0.506931	+	0.506931i	0.406652	+	0.913583i	$0.366696\pi$
$264$	−0.360602	−	0.331460i	−0.0221935	−	0.0203999i
$265$	−15.4315	+	15.4315i	−0.947949	+	0.947949i
$266$	−9.57431	−	3.80935i	−0.587039	−	0.233566i
$267$	7.00055	−	2.89972i	0.428427	−	0.177460i
$268$	2.41828	−	6.33534i	0.147720	−	0.386992i
$269$	−14.2598	−	5.90661i	−0.869437	−	0.360133i	−0.0970461	−	0.995280i	$-0.530939\pi$
$269$	−14.2598	−	5.90661i	−0.869437	−	0.360133i	−0.772391	+	0.635147i	$0.780939\pi$
$270$	0.148536	+	10.5877i	0.00903963	+	0.644344i
$271$	−19.0391			−1.15655			−0.578273	−	0.815843i	$-0.696273\pi$
$271$	−19.0391			−1.15655			−0.578273	+	0.815843i	$0.696273\pi$
$272$	−0.346814	−	6.17414i	−0.0210287	−	0.374362i
$273$	5.59995	−	1.04300i	0.338924	−	0.0631254i
$274$	−2.80789	+	0.0393924i	−0.169631	+	0.00237978i
$275$	−0.00806411	+	0.0194685i	−0.000486284	+	0.00117399i
$276$	−1.62562	−	3.63283i	−0.0978506	−	0.218671i
$277$	−2.68301	−	6.47737i	−0.161207	−	0.389187i	0.822550	−	0.568692i	$-0.192550\pi$
$277$	−2.68301	−	6.47737i	−0.161207	−	0.389187i	−0.983757	+	0.179505i	$0.942550\pi$
$278$	−7.26910	+	18.2699i	−0.435972	+	1.09576i
$279$	−6.38597	+	6.38597i	−0.382318	+	0.382318i
$280$	−7.20865	−	15.5217i	−0.430799	−	0.927600i
$281$	14.6376	+	14.6376i	0.873204	+	0.873204i	0.992820	−	0.119616i	$-0.0381664\pi$
$281$	14.6376	+	14.6376i	0.873204	+	0.873204i	−0.119616	+	0.992820i	$0.538166\pi$
$282$	3.17089	−	1.36585i	0.188824	−	0.0813352i
$283$	−1.49263	+	0.618269i	−0.0887278	+	0.0367522i	−0.426606	−	0.904438i	$-0.640291\pi$
$283$	−1.49263	+	0.618269i	−0.0887278	+	0.0367522i	0.337878	+	0.941190i	$0.390291\pi$
$284$	−4.23596	+	4.48058i	−0.251358	+	0.265873i
$285$	−1.37423	+	3.31769i	−0.0814025	+	0.196523i
$286$	−1.25011	−	0.832007i	−0.0739205	−	0.0491976i
$287$	6.32524			0.373367
$288$	1.05229	+	14.9778i	0.0620067	+	0.882574i
$289$	14.6100			0.859411
$290$	19.0106	+	18.4846i	1.11634	+	1.08545i
$291$	−7.23640	−	2.99742i	−0.424205	−	0.175712i
$292$	−5.47659	−	5.17759i	−0.320493	−	0.302995i
$293$	−0.486278	−	1.17398i	−0.0284087	−	0.0685846i	0.909039	−	0.416712i	$-0.136818\pi$
$293$	−0.486278	−	1.17398i	−0.0284087	−	0.0685846i	−0.937447	+	0.348127i	$0.886818\pi$
$294$	−0.0720116	−	0.167179i	−0.00419980	−	0.00975007i
$295$	8.82269	−	8.82269i	0.513677	−	0.513677i
$296$	−4.31773	−	1.57910i	−0.250963	−	0.0917835i
$297$	0.692356	−	0.692356i	0.0401746	−	0.0401746i
$298$	−30.4483	−	12.1145i	−1.76382	−	0.701776i
$299$	−6.65483	−	10.2278i	−0.384859	−	0.591487i
$300$	−0.0768082	+	0.0343701i	−0.00443452	+	0.00198436i
$301$	−8.96718	+	21.6487i	−0.516860	+	1.24781i
$302$	−24.7585	+	0.347342i	−1.42469	+	0.0199873i
$303$		−	0.494087i		−	0.0283846i
$304$	−3.58255	+	10.2388i	−0.205474	+	0.587235i
$305$	−12.3660			−0.708073
$306$	5.80249	−	0.0814043i	0.331706	−	0.00465357i
$307$	11.2089	−	27.0607i	0.639727	−	1.54444i	−0.187316	−	0.982300i	$-0.559979\pi$
$307$	11.2089	−	27.0607i	0.639727	−	1.54444i	0.827043	−	0.562138i	$-0.190021\pi$
$308$	−0.564356	+	1.47848i	−0.0321572	+	0.0842445i
$309$	−0.0573462	−	0.138446i	−0.00326231	−	0.00787592i
$310$	−10.0687	−	4.00607i	−0.571866	−	0.227529i
$311$	13.9931	+	13.9931i	0.793475	+	0.793475i	0.982057	−	0.188582i	$-0.0603891\pi$
$311$	13.9931	+	13.9931i	0.793475	+	0.793475i	−0.188582	+	0.982057i	$0.560389\pi$
$312$	−1.34503	−	5.84372i	−0.0761474	−	0.330835i
$313$	−11.2722	+	11.2722i	−0.637143	+	0.637143i	−0.949850	−	0.312707i	$-0.898764\pi$
$313$	−11.2722	+	11.2722i	−0.637143	+	0.637143i	0.312707	+	0.949850i	$0.398764\pi$
$314$	−2.46081	+	1.05998i	−0.138872	+	0.0598184i
$315$	14.8376	−	6.14592i	0.836003	−	0.346284i
$316$	−2.55590	+	0.0717285i	−0.143781	+	0.00403504i
$317$	−11.0380	−	4.57207i	−0.619953	−	0.256793i	0.0505243	−	0.998723i	$-0.483911\pi$
$317$	−11.0380	−	4.57207i	−0.619953	−	0.256793i	−0.670478	+	0.741930i	$0.733911\pi$
$318$	5.77753	+	5.61766i	0.323988	+	0.315023i
$319$		−	2.45191i		−	0.137281i
$320$	−16.0062	+	8.26938i	−0.894771	+	0.462272i
$321$	6.72342			0.375265
$322$	−8.96445	+	9.21956i	−0.499569	+	0.513786i
$323$	3.87332	+	1.60438i	0.215518	+	0.0892703i
$324$	−12.0108	+	0.337071i	−0.667269	+	0.0187262i
$325$	−0.216244	+	0.140702i	−0.0119950	+	0.00780473i
$326$	10.0617	+	23.3588i	0.557267	+	1.29373i
$327$	6.43301	+	6.43301i	0.355746	+	0.355746i
$328$	−0.280146	−	6.65276i	−0.0154685	−	0.367337i
$329$	−7.88794	−	7.88794i	−0.434876	−	0.434876i
$330$	0.512441	+	0.203886i	0.0282090	+	0.0112236i
$331$	0.547817	−	0.226913i	0.0301107	−	0.0124723i	−0.367577	−	0.929993i	$-0.619813\pi$
$331$	0.547817	−	0.226913i	0.0301107	−	0.0124723i	0.397688	+	0.917521i	$0.369813\pi$
$332$	−31.9906	−	12.2112i	−1.75572	−	0.670178i
$333$	1.65102	−	3.98591i	0.0904752	−	0.218426i
$334$	0.315419	+	22.4831i	0.0172590	+	1.23022i
$335$			7.63566i			0.417181i
$336$	−5.69357	+	2.74197i	−0.310610	+	0.149587i
$337$		−	17.1228i		−	0.932736i	−0.884591	−	0.466368i	$-0.845562\pi$
$337$		−	17.1228i		−	0.932736i	0.884591	−	0.466368i	$-0.154438\pi$
$338$	−6.85876	−	17.0575i	−0.373067	−	0.927804i
$339$	6.09309	+	2.52384i	0.330931	+	0.137076i
$340$	2.84407	+	6.35576i	0.154241	+	0.344689i
$341$	0.383466	+	0.925770i	0.0207659	+	0.0501333i
$342$	−9.45831	−	3.76320i	−0.511447	−	0.203491i
$343$	12.8831	−	12.8831i	0.695623	−	0.695623i
$344$	23.1668	+	8.47267i	1.24907	+	0.456816i
$345$	3.16887	+	3.16887i	0.170606	+	0.170606i
$346$	6.19263	+	14.3765i	0.332918	+	0.772887i
$347$	−25.5814	+	10.5962i	−1.37328	+	0.568832i	−0.942676	−	0.333709i	$-0.891700\pi$
$347$	−25.5814	+	10.5962i	−1.37328	+	0.568832i	−0.430605	+	0.902540i	$0.641700\pi$
$348$	6.72638	−	7.11482i	0.360572	−	0.381394i
$349$	−26.9904	−	11.1798i	−1.44476	−	0.598440i	−0.483815	−	0.875170i	$-0.660749\pi$
$349$	−26.9904	−	11.1798i	−1.44476	−	0.598440i	−0.960948	+	0.276730i	$0.910749\pi$
$350$	0.194927	+	0.189534i	0.0104193	+	0.0101310i
$351$	11.7848	−	2.19495i	0.629028	−	0.117158i
$352$	1.58004	+	0.528096i	0.0842162	+	0.0281476i
$353$			15.9332i			0.848038i	0.905653	+	0.424019i	$0.139381\pi$
$353$			15.9332i			0.848038i	−0.905653	+	0.424019i	$0.860619\pi$
$354$	−3.30320	−	3.21180i	−0.175563	−	0.170705i
$355$	2.65693	−	6.41440i	0.141015	−	0.340441i
$356$	−17.7058	+	18.7283i	−0.938408	+	0.992600i
$357$	0.934669	+	2.25649i	0.0494679	+	0.119426i
$358$	5.41386	+	12.5686i	0.286132	+	0.664270i
$359$	−12.8643	−	12.8643i	−0.678951	−	0.678951i	0.280812	−	0.959763i	$-0.409396\pi$
$359$	−12.8643	−	12.8643i	−0.678951	−	0.678951i	−0.959763	+	0.280812i	$0.909396\pi$
$360$	−7.12132	−	15.3337i	−0.375326	−	0.808155i
$361$	8.23482	+	8.23482i	0.433411	+	0.433411i
$362$	−5.71179	+	14.3558i	−0.300205	+	0.754526i
$363$	2.45571	+	5.92860i	0.128891	+	0.311171i
$364$	−15.9369	+	11.0180i	−0.835322	+	0.577501i
$365$	7.84028	+	3.24755i	0.410379	+	0.169985i
$366$	0.0640538	+	4.56575i	0.00334814	+	0.238655i
$367$		−	20.7490i		−	1.08309i	−0.840672	−	0.541545i	$-0.817840\pi$
$367$		−	20.7490i		−	1.08309i	0.840672	−	0.541545i	$-0.182160\pi$
$368$	10.0940	+	9.02029i	0.526185	+	0.470215i
$369$	6.24861			0.325290
$370$	5.17623	−	0.0726183i	0.269099	−	0.00377524i
$371$	9.96385	−	24.0549i	0.517298	−	1.24887i
$372$	−1.42696	+	3.73832i	−0.0739845	+	0.193823i
$373$	11.6919	+	28.2266i	0.605381	+	1.46152i	0.867972	+	0.496613i	$0.165423\pi$
$373$	11.6919	+	28.2266i	0.605381	+	1.46152i	−0.262591	+	0.964907i	$0.584577\pi$
$374$	0.238032	−	0.598263i	0.0123084	−	0.0309354i
$375$	−4.61474	+	4.61474i	−0.238304	+	0.238304i
$376$	−7.94702	+	8.64574i	−0.409836	+	0.445870i
$377$	16.9808	−	24.7540i	0.874557	−	1.27490i
$378$	−4.99770	−	11.6024i	−0.257054	−	0.596765i
$379$	3.88328	+	9.37508i	0.199471	+	0.481565i	0.991687	−	0.128676i	$-0.0410726\pi$
$379$	3.88328	+	9.37508i	0.199471	+	0.481565i	−0.792216	+	0.610241i	$0.791073\pi$
$380$	−0.342646	−	12.2095i	−0.0175774	−	0.626334i
$381$	−1.42725	+	3.44568i	−0.0731201	+	0.176528i
$382$	24.7553	+	24.0703i	1.26659	+	1.23154i
$383$			18.7905i			0.960151i	0.877227	+	0.480076i	$0.159391\pi$
$383$			18.7905i			0.960151i	−0.877227	+	0.480076i	$0.840609\pi$
$384$	3.13612	+	5.86694i	0.160039	+	0.299396i
$385$		−	1.78194i		−	0.0908162i
$386$	−0.539998	+	0.555365i	−0.0274852	+	0.0282673i
$387$	−8.85854	+	21.3864i	−0.450305	+	1.08713i
$388$	26.6308	−	0.747365i	1.35197	−	0.0379417i
$389$	4.93429	−	2.04385i	0.250178	−	0.103627i	−0.254070	−	0.967186i	$-0.581769\pi$
$389$	4.93429	−	2.04385i	0.250178	−	0.103627i	0.504249	+	0.863558i	$0.331769\pi$
$390$	3.76149	+	5.60733i	0.190470	+	0.283938i
$391$	3.69958	−	3.69958i	0.187096	−	0.187096i
$392$	0.455829	+	0.418990i	0.0230228	+	0.0211622i
$393$	2.64125	+	2.64125i	0.133233	+	0.133233i
$394$	−4.32482	+	10.8699i	−0.217881	+	0.547617i
$395$	2.65993	−	1.10178i	0.133836	−	0.0554365i
$396$	−0.557518	+	1.46057i	−0.0280163	+	0.0733965i
$397$	−12.9545	+	31.2750i	−0.650170	+	1.56965i	0.162362	+	0.986731i	$0.448089\pi$
$397$	−12.9545	+	31.2750i	−0.650170	+	1.56965i	−0.812532	+	0.582917i	$0.801911\pi$
$398$	29.7264	−	0.417037i	1.49005	−	0.0209042i
$399$		−	4.28436i		−	0.214486i
$400$	0.190714	−	0.213415i	0.00953571	−	0.0106707i
$401$	29.6479			1.48055			0.740273	−	0.672307i	$-0.234696\pi$
$401$	29.6479			1.48055			0.740273	+	0.672307i	$0.234696\pi$
$402$	2.81923	−	0.0395515i	0.140610	−	0.00197265i
$403$	−2.54006	+	12.0021i	−0.126529	+	0.597868i
$404$	0.686421	+	1.53397i	0.0341507	+	0.0763180i
$405$	12.4997	−	5.17755i	0.621116	−	0.257275i
$406$	−29.3939	−	11.6950i	−1.45879	−	0.580414i
$407$	−0.338488	−	0.338488i	−0.0167782	−	0.0167782i
$408$	2.33193	−	1.08301i	0.115448	−	0.0536168i
$409$	13.4190	+	13.4190i	0.663526	+	0.663526i	0.956209	−	0.292683i	$-0.0945482\pi$
$409$	13.4190	+	13.4190i	0.663526	+	0.663526i	−0.292683	+	0.956209i	$0.594548\pi$
$410$	2.96613	+	6.88603i	0.146487	+	0.340077i
$411$	−0.446817	−	1.07871i	−0.0220398	−	0.0532089i
$412$	0.370380	+	0.350159i	0.0182473	+	0.0172511i
$413$	−5.69666	+	13.7530i	−0.280314	+	0.676739i
$414$	−8.85584	+	9.10786i	−0.435241	+	0.447627i
$415$	38.5567			1.89267
$416$	12.2944	+	16.2742i	0.602782	+	0.797906i
$417$	−8.17551			−0.400357
$418$	−0.787366	+	0.809773i	−0.0385114	+	0.0396073i
$419$	12.8161	−	30.9408i	0.626108	−	1.51156i	−0.218313	−	0.975879i	$-0.570055\pi$
$419$	12.8161	−	30.9408i	0.626108	−	1.51156i	0.844421	−	0.535680i	$-0.179945\pi$
$420$	4.88843	−	5.17073i	0.238531	−	0.252306i
$421$	15.4113	+	37.2063i	0.751103	+	1.81332i	0.553086	+	0.833124i	$0.313450\pi$
$421$	15.4113	+	37.2063i	0.751103	+	1.81332i	0.198017	+	0.980199i	$0.436550\pi$
$422$	−15.6331	−	36.2931i	−0.761008	−	1.76672i
$423$	−7.79238	−	7.79238i	−0.378878	−	0.378878i
$424$	−25.7417	−	9.41439i	−1.25013	−	0.457203i
$425$	−0.0782194	−	0.0782194i	−0.00379420	−	0.00379420i
$426$	−2.38208	−	0.947763i	−0.115412	−	0.0459193i
$427$	13.6304	−	5.64589i	0.659621	−	0.273224i
$428$	−20.8740	+	9.34066i	−1.00898	+	0.451498i
$429$	0.129274	−	0.610839i	0.00624143	−	0.0294916i
$430$	−27.7730	+	0.389633i	−1.33934	+	0.0187898i
$431$	−27.0271			−1.30185			−0.650924	−	0.759143i	$-0.725618\pi$
$431$	−27.0271			−1.30185			−0.650924	+	0.759143i	$0.725618\pi$
$432$	−11.9819	+	5.77035i	−0.576477	+	0.277626i
$433$		−	15.9742i		−	0.767673i	−0.923401	−	0.383836i	$-0.874603\pi$
$433$		−	15.9742i		−	0.767673i	0.923401	−	0.383836i	$-0.125397\pi$
$434$	12.9273	−	0.181360i	0.620530	−	0.00870554i
$435$	−4.21900	+	10.1856i	−0.202286	+	0.488361i
$436$	−28.9095	−	11.0351i	−1.38451	−	0.528486i
$437$	−8.47911	+	3.51216i	−0.405611	+	0.168010i
$438$	1.15844	−	2.91160i	0.0553526	−	0.139122i
$439$	−20.8177	−	20.8177i	−0.993573	−	0.993573i	0.00640633	−	0.999979i	$-0.497961\pi$
$439$	−20.8177	−	20.8177i	−0.993573	−	0.993573i	−0.999979	+	0.00640633i	$0.997961\pi$
$440$	−1.87421	+	0.0789224i	−0.0893495	+	0.00376248i
$441$	−0.410837	+	0.410837i	−0.0195637	+	0.0195637i
$442$	6.54642	−	4.39144i	0.311382	−	0.208880i
$443$	−0.714464	+	0.295941i	−0.0339452	+	0.0140606i	−0.399591	−	0.916693i	$-0.630848\pi$
$443$	−0.714464	+	0.295941i	−0.0339452	+	0.0140606i	0.365646	+	0.930754i	$0.380848\pi$
$444$	−0.0536241	−	1.91078i	−0.00254489	−	0.0906818i
$445$	11.1057	−	26.8115i	0.526460	−	1.27099i
$446$	20.1419	−	20.7151i	0.953747	−	0.980888i
$447$		−	13.6251i		−	0.644447i
$448$	13.8673	−	16.4228i	0.655167	−	0.775905i
$449$			7.88902i			0.372306i	0.982521	+	0.186153i	$0.0596020\pi$
$449$			7.88902i			0.372306i	−0.982521	+	0.186153i	$0.940398\pi$
$450$	0.192566	+	0.187237i	0.00907763	+	0.00882645i
$451$	0.265319	−	0.640538i	0.0124934	−	0.0301617i
$452$	−22.4233	+	0.629286i	−1.05470	+	0.0295991i
$453$	−3.93980	−	9.51151i	−0.185108	−	0.446890i
$454$	7.15398	+	16.6083i	0.335753	+	0.779468i
$455$	12.3409	−	17.9901i	0.578551	−	0.843391i
$456$	−4.50620	+	0.189755i	−0.211022	+	0.00888607i
$457$	−13.9052	+	13.9052i	−0.650458	+	0.650458i	−0.953103	−	0.302645i	$-0.902130\pi$
$457$	−13.9052	+	13.9052i	−0.650458	+	0.650458i	0.302645	+	0.953103i	$0.402130\pi$
$458$	2.17613	−	5.46943i	0.101684	−	0.255570i
$459$	1.96697	+	4.74868i	0.0918101	+	0.221649i
$460$	−14.2407	−	5.43585i	−0.663976	−	0.253448i
$461$	−5.42528	+	13.0978i	−0.252681	+	0.610025i	−0.998419	−	0.0562142i	$-0.982097\pi$
$461$	−5.42528	+	13.0978i	−0.252681	+	0.610025i	0.745738	+	0.666239i	$0.232097\pi$
$462$	−0.657926	+	0.00923018i	−0.0306095	+	0.000429427i
$463$	35.4260			1.64638			0.823192	−	0.567762i	$-0.192191\pi$
$463$	35.4260			1.64638			0.823192	+	0.567762i	$0.192191\pi$
$464$	−10.9987	+	31.4339i	−0.510603	+	1.45928i
$465$		−	4.50560i		−	0.208942i
$466$	0.103783	+	7.39766i	0.00480766	+	0.342690i
$467$	−25.8129	−	10.6921i	−1.19448	−	0.494769i	−0.305268	−	0.952267i	$-0.598746\pi$
$467$	−25.8129	−	10.6921i	−1.19448	−	0.494769i	−0.889211	+	0.457497i	$0.848746\pi$
$468$	−15.7439	+	10.8845i	−0.727760	+	0.503138i
$469$	−3.48619	−	8.41641i	−0.160977	−	0.388634i
$470$	4.88834	−	12.2862i	0.225482	−	0.566720i
$471$	−0.787751	−	0.787751i	−0.0362976	−	0.0362976i
$472$	14.7174	+	5.38251i	0.677423	+	0.247750i
$473$	1.81616	+	1.81616i	0.0835070	+	0.0835070i
$474$	−0.420576	−	0.976389i	−0.0193177	−	0.0448470i
$475$	0.0742569	+	0.179272i	0.00340714	+	0.00822557i
$476$	−6.03671	−	5.70713i	−0.276692	−	0.261586i
$477$	9.84314	−	23.7634i	0.450686	−	1.08805i
$478$	−16.1079	−	15.6622i	−0.736759	−	0.716372i
$479$			15.4184i			0.704487i	0.935908	+	0.352243i	$0.114581\pi$
$479$			15.4184i			0.704487i	−0.935908	+	0.352243i	$0.885419\pi$
$480$	−5.65498	−	4.91254i	−0.258113	−	0.224226i
$481$	−1.07310	−	5.76152i	−0.0489289	−	0.262703i
$482$	18.8330	+	18.3119i	0.857821	+	0.834085i
$483$	−4.93969	−	2.04609i	−0.224764	−	0.0931002i
$484$	−15.8606	−	14.9947i	−0.720935	−	0.681575i
$485$	−27.7148	+	11.4798i	−1.25846	+	0.521272i
$486$	−7.55667	−	17.5432i	−0.342778	−	0.795777i
$487$	3.03613	+	3.03613i	0.137580	+	0.137580i	0.772543	−	0.634963i	$-0.218985\pi$
$487$	3.03613	+	3.03613i	0.137580	+	0.137580i	−0.634963	+	0.772543i	$0.718985\pi$
$488$	−6.54193	−	14.0861i	−0.296139	−	0.637649i
$489$	−7.47759	+	7.47759i	−0.338148	+	0.338148i
$490$	−0.647765	−	0.257728i	−0.0292630	−	0.0116430i
$491$	−5.89307	−	14.2271i	−0.265950	−	0.642061i	0.733335	−	0.679868i	$-0.237963\pi$
$491$	−5.89307	−	14.2271i	−0.265950	−	0.642061i	−0.999285	+	0.0378068i	$0.987963\pi$
$492$	2.52709	−	1.13082i	0.113930	−	0.0509812i
$493$	11.8914	+	4.92558i	0.535562	+	0.221837i
$494$	−13.5572	+	2.72237i	−0.609968	+	0.122485i
$495$		−	1.76035i		−	0.0791219i
$496$	−0.763302	−	13.5886i	−0.0342733	−	0.610148i
$497$			8.28334i			0.371558i
$498$	−0.199718	−	14.2359i	−0.00894956	−	0.637924i
$499$	−0.627777	+	1.51559i	−0.0281032	+	0.0678471i	−0.937308	−	0.348502i	$-0.886691\pi$
$499$	−0.627777	+	1.51559i	−0.0281032	+	0.0678471i	0.909205	+	0.416349i	$0.136691\pi$
$500$	7.91609	−	20.7384i	0.354018	−	0.927447i
$501$	−8.63736	+	3.57771i	−0.385889	+	0.159840i
$502$	−0.386161	−	0.153643i	−0.0172352	−	0.00685742i
$503$	28.8253	+	28.8253i	1.28526	+	1.28526i	0.937636	+	0.347620i	$0.113010\pi$
$503$	28.8253	+	28.8253i	1.28526	+	1.28526i	0.347620	+	0.937636i	$0.386990\pi$
$504$	14.8503	+	13.6502i	0.661486	+	0.608027i
$505$	−1.33806	−	1.33806i	−0.0595431	−	0.0595431i
$506$	0.557612	+	1.29453i	0.0247889	+	0.0575487i
$507$	5.53552	−	5.27162i	0.245841	−	0.234121i
$508$	−0.355865	−	12.6805i	−0.0157889	−	0.562607i
$509$	1.48284	+	0.614212i	0.0657257	+	0.0272245i	0.415304	−	0.909683i	$-0.363675\pi$
$509$	1.48284	+	0.614212i	0.0657257	+	0.0272245i	−0.349578	+	0.936907i	$0.613675\pi$
$510$	−2.01825	+	2.07568i	−0.0893695	+	0.0919127i
$511$	−10.1247			−0.447889
$512$	−17.8874	−	13.8579i	−0.790517	−	0.612440i
$513$		−	9.01623i		−	0.398076i
$514$	23.1070	+	22.4677i	1.01921	+	0.991006i
$515$	−0.530236	−	0.219631i	−0.0233650	−	0.00967809i
$516$	0.287720	+	10.2523i	0.0126662	+	0.451333i
$517$	−1.12966	+	0.467919i	−0.0496822	+	0.0205790i
$518$	−5.67234	+	2.44334i	−0.249228	+	0.107354i
$519$	−4.60219	+	4.60219i	−0.202014	+	0.202014i
$520$	−19.4682	−	12.1831i	−0.853739	−	0.534266i
$521$	6.76691	+	6.76691i	0.296464	+	0.296464i	0.839627	−	0.543163i	$-0.182774\pi$
$521$	6.76691	+	6.76691i	0.296464	+	0.296464i	−0.543163	+	0.839627i	$0.682774\pi$
$522$	−29.0378	−	11.5533i	−1.27095	−	0.505675i
$523$	2.95594	+	7.13628i	0.129254	+	0.312048i	0.975237	−	0.221163i	$-0.0709853\pi$
$523$	2.95594	+	7.13628i	0.129254	+	0.312048i	−0.845983	+	0.533211i	$0.820985\pi$
$524$	−11.8696	−	4.53077i	−0.518525	−	0.197928i
$525$	−0.0432600	+	0.104439i	−0.00188802	+	0.00455808i
$526$	16.4405	−	0.230647i	0.716839	−	0.0100567i
$527$	−5.26018			−0.229137
$528$	0.0388477	+	0.691585i	0.00169063	+	0.0300974i
$529$		−	11.5466i		−	0.502027i
$530$	30.8599	−	0.432940i	1.34047	−	0.0188057i
$531$	−5.62764	+	13.5863i	−0.244219	+	0.589597i
$532$	5.95214	+	13.3015i	0.258058	+	0.576692i
$533$	7.11469	−	4.62926i	0.308171	−	0.200516i
$534$	−9.95683	−	3.96155i	−0.430874	−	0.171433i
$535$	18.2081	−	18.2081i	0.787204	−	0.787204i
$536$	−8.69781	+	4.03947i	−0.375688	+	0.174478i
$537$	−4.02343	+	4.02343i	−0.173624	+	0.173624i
$538$	8.63528	+	20.0473i	0.372294	+	0.864300i
$539$	0.0246701	+	0.0595588i	0.00106261	+	0.00256538i
$540$	10.2875	−	10.8816i	0.442703	−	0.468268i
$541$	−10.8918	−	4.51155i	−0.468277	−	0.193967i	0.136052	−	0.990702i	$-0.456559\pi$
$541$	−10.8918	−	4.51155i	−0.468277	−	0.193967i	−0.604329	+	0.796735i	$0.706559\pi$
$542$	19.3043	+	18.7702i	0.829193	+	0.806249i
$543$	−6.42402			−0.275681
$544$	−5.73528	+	6.60206i	−0.245898	+	0.283061i
$545$	34.8432			1.49252
$546$	−6.70622	−	4.46331i	−0.287000	−	0.191012i
$547$	2.22656	−	5.37540i	0.0952010	−	0.229836i	−0.869104	−	0.494629i	$-0.835304\pi$
$547$	2.22656	−	5.37540i	0.0952010	−	0.229836i	0.964305	+	0.264794i	$0.0853039\pi$
$548$	2.88584	+	2.72828i	0.123277	+	0.116547i
$549$	13.4653	−	5.57749i	0.574683	−	0.238042i
$550$	0.0273699	−	0.0117895i	0.00116706	−	0.000502705i
$551$	−15.9651	−	15.9651i	−0.680135	−	0.680135i
$552$	−1.93325	+	5.28609i	−0.0822847	+	0.224991i
$553$	−2.42887	+	2.42887i	−0.103286	+	0.103286i
$554$	−3.66548	+	9.21271i	−0.155731	+	0.391410i
$555$	0.823688	+	1.98856i	0.0349636	+	0.0844096i
$556$	25.3822	−	11.3580i	1.07645	−	0.481687i
$557$	9.00421	−	21.7381i	0.381521	−	0.921072i	−0.610152	−	0.792285i	$-0.708891\pi$
$557$	9.00421	−	21.7381i	0.381521	−	0.921072i	0.991672	−	0.128787i	$-0.0411085\pi$
$558$	12.7707	−	0.179162i	0.540626	−	0.00758455i
$559$	5.75769	+	30.9134i	0.243525	+	1.30750i
$560$	−7.99338	+	22.8447i	−0.337782	+	0.965367i
$561$	0.267713			0.0113029
$562$	−0.410666	−	29.2723i	−0.0173229	−	1.23478i
$563$	−32.0070	−	13.2577i	−1.34893	−	0.558746i	−0.412938	−	0.910759i	$-0.635497\pi$
$563$	−32.0070	−	13.2577i	−1.34893	−	0.558746i	−0.935995	+	0.352013i	$0.885497\pi$
$564$	−4.56162	−	1.74123i	−0.192079	−	0.0733189i
$565$	23.3360	−	9.66609i	0.981753	−	0.406655i
$566$	2.12296	+	0.844666i	0.0892346	+	0.0355040i
$567$	−11.4139	+	11.4139i	−0.479339	+	0.479339i
$568$	8.71225	−	0.366870i	0.365558	−	0.0153935i
$569$	15.8237	−	15.8237i	0.663362	−	0.663362i	−0.292809	−	0.956171i	$-0.594590\pi$
$569$	15.8237	−	15.8237i	0.663362	−	0.663362i	0.956171	+	0.292809i	$0.0945900\pi$
$570$	4.66420	−	2.00908i	0.195362	−	0.0841513i
$571$	−0.470039	+	0.194697i	−0.0196705	+	0.00814780i	−0.392497	−	0.919753i	$-0.628389\pi$
$571$	−0.470039	+	0.194697i	−0.0196705	+	0.00814780i	0.372826	+	0.927901i	$0.378389\pi$
$572$	0.447268	+	2.07605i	0.0187012	+	0.0868039i
$573$	−5.49392	+	13.2635i	−0.229512	+	0.554090i
$574$	−6.41335	−	6.23589i	−0.267688	−	0.260281i
$575$	0.242156			0.0100986
$576$	13.6993	−	16.2238i	0.570802	−	0.675993i
$577$		−	12.7285i		−	0.529896i	−0.964263	−	0.264948i	$-0.914645\pi$
$577$		−	12.7285i		−	0.529896i	0.964263	−	0.264948i	$-0.0853548\pi$
$578$	−14.8135	−	14.4036i	−0.616160	−	0.599111i
$579$	−0.297556	−	0.123252i	−0.0123660	−	0.00512216i
$580$	−1.05195	−	37.4841i	−0.0436799	−	1.55644i
$581$	−42.4991	+	17.6037i	−1.76316	+	0.730325i
$582$	4.38213	+	10.1733i	0.181645	+	0.421699i
$583$	−2.01802	−	2.01802i	−0.0835777	−	0.0835777i
$584$	0.448423	+	10.6489i	0.0185559	+	0.440656i
$585$	12.1914	−	17.7722i	0.504052	−	0.734789i
$586$	−0.664343	+	1.66974i	−0.0274438	+	0.0689763i
$587$	−25.1616	+	10.4223i	−1.03853	+	0.430174i	−0.835785	−	0.549057i	$-0.814987\pi$
$587$	−25.1616	+	10.4223i	−1.03853	+	0.430174i	−0.202747	+	0.979231i	$0.564987\pi$
$588$	−0.0918026	+	0.240502i	−0.00378588	+	0.00991814i
$589$	8.52479	+	3.53108i	0.351258	+	0.145496i
$590$	−17.6436	+	0.247526i	−0.726377	+	0.0101905i
$591$	−4.86410			−0.200082
$592$	2.82108	+	5.85784i	0.115946	+	0.240756i
$593$	−35.5406			−1.45948			−0.729738	−	0.683727i	$-0.760358\pi$
$593$	−35.5406			−1.45948			−0.729738	+	0.683727i	$0.760358\pi$
$594$	−1.38458	+	0.0194245i	−0.0568098	+	0.000796996i
$595$	8.64215	+	3.57970i	0.354294	+	0.146753i
$596$	18.9290	+	42.3014i	0.775362	+	1.73273i
$597$	4.73033	+	11.4200i	0.193599	+	0.467390i
$598$	−3.33576	+	16.9311i	−0.136409	+	0.692362i
$599$	−4.68757	−	4.68757i	−0.191529	−	0.191529i	0.604828	−	0.796356i	$-0.293242\pi$
$599$	−4.68757	−	4.68757i	−0.191529	−	0.191529i	−0.796356	+	0.604828i	$0.793242\pi$
$600$	0.111763	+	0.0408744i	0.00456269	+	0.00166869i
$601$	−4.34417	+	4.34417i	−0.177202	+	0.177202i	−0.790135	−	0.612933i	$-0.789990\pi$
$601$	−4.34417	+	4.34417i	−0.177202	+	0.177202i	0.612933	+	0.790135i	$0.289990\pi$
$602$	30.4350	−	13.1097i	1.24044	−	0.534313i
$603$	−3.44395	−	8.31444i	−0.140249	−	0.338590i
$604$	25.4458	+	24.0566i	1.03538	+	0.978848i
$605$	22.7060	+	9.40513i	0.923130	+	0.382373i
$606$	−0.487107	+	0.500969i	−0.0197874	+	0.0203505i
$607$	24.5703			0.997279			0.498640	−	0.866809i	$-0.333833\pi$
$607$	24.5703			0.997279			0.498640	+	0.866809i	$0.333833\pi$
$608$	13.7266	−	6.84946i	0.556687	−	0.277782i
$609$		−	13.1533i		−	0.532999i
$610$	12.5382	+	12.1913i	0.507658	+	0.493611i
$611$	−14.6454	−	3.09946i	−0.592489	−	0.125391i
$612$	−5.96357	−	5.63798i	−0.241063	−	0.227902i
$613$	−11.7668	−	28.4075i	−0.475256	−	1.14737i	−0.961810	−	0.273718i	$-0.911746\pi$
$613$	−11.7668	−	28.4075i	−0.475256	−	1.14737i	0.486554	−	0.873650i	$-0.338254\pi$
$614$	−38.0435	+	16.3871i	−1.53531	+	0.661329i
$615$	−2.20434	+	2.20434i	−0.0888877	+	0.0888877i
$616$	2.02982	−	0.942695i	0.0817836	−	0.0379823i
$617$	24.1582	−	24.1582i	0.972574	−	0.972574i	−0.0270602	−	0.999634i	$-0.508615\pi$
$617$	24.1582	−	24.1582i	0.972574	−	0.972574i	0.999634	+	0.0270602i	$0.00861458\pi$
$618$	−0.0783453	+	0.196911i	−0.00315151	+	0.00792091i
$619$	30.9152	−	12.8055i	1.24259	−	0.514697i	0.338066	−	0.941122i	$-0.390227\pi$
$619$	30.9152	−	12.8055i	1.24259	−	0.514697i	0.904523	+	0.426425i	$0.140227\pi$
$620$	6.25950	+	13.9884i	0.251388	+	0.561786i
$621$	−10.3953	−	4.30589i	−0.417151	−	0.172790i
$622$	−0.392585	−	27.9834i	−0.0157412	−	1.12203i
$623$			34.6235i			1.38716i
$624$	−4.39740	+	7.25115i	−0.176037	+	0.290278i
$625$			25.3526i			1.01411i
$626$	22.5422	−	0.316249i	0.900967	−	0.0126398i
$627$	−0.433863	−	0.179712i	−0.0173268	−	0.00717701i
$628$	3.54010	+	1.35130i	0.141265	+	0.0539228i
$629$	2.32159	−	0.961636i	0.0925680	−	0.0383429i
$630$	−21.1034	−	8.39644i	−0.840778	−	0.334522i
$631$	20.9769	−	20.9769i	0.835076	−	0.835076i	−0.153130	−	0.988206i	$-0.548935\pi$
$631$	20.9769	−	20.9769i	0.835076	−	0.835076i	0.988206	+	0.153130i	$0.0489354\pi$
$632$	2.66222	+	2.44707i	0.105897	+	0.0973390i
$633$	11.6181	−	11.6181i	0.461778	−	0.461778i
$634$	6.68422	+	15.5178i	0.265464	+	0.616290i
$635$	5.46623	+	13.1966i	0.216921	+	0.523693i
$636$	−0.319699	−	11.3918i	−0.0126769	−	0.451715i
$637$	−0.163413	+	0.772148i	−0.00647465	+	0.0305936i
$638$	−2.41728	+	2.48607i	−0.0957009	+	0.0984243i
$639$			8.18298i			0.323714i
$640$	24.3817	+	7.39548i	0.963770	+	0.292332i
$641$	3.06007			0.120865			0.0604327	−	0.998172i	$-0.480752\pi$
$641$	3.06007			0.120865			0.0604327	+	0.998172i	$0.480752\pi$
$642$	−6.81708	−	6.62845i	−0.269049	−	0.261604i
$643$	7.47701	+	3.09708i	0.294864	+	0.122137i	0.525212	−	0.850972i	$-0.323986\pi$
$643$	7.47701	+	3.09708i	0.294864	+	0.122137i	−0.230347	+	0.973109i	$0.573986\pi$
$644$	18.1786	−	0.510164i	0.716339	−	0.0201033i
$645$	−4.41950	−	10.6696i	−0.174018	−	0.420115i
$646$	−2.34556	−	5.44534i	−0.0922848	−	0.214244i
$647$	14.4723	−	14.4723i	0.568963	−	0.568963i	−0.362875	−	0.931838i	$-0.618205\pi$
$647$	14.4723	−	14.4723i	0.568963	−	0.568963i	0.931838	+	0.362875i	$0.118205\pi$
$648$	12.5104	+	11.4994i	0.491457	+	0.451739i
$649$	1.15377	+	1.15377i	0.0452893	+	0.0452893i
$650$	0.357970	+	0.0705272i	0.0140407	+	0.00276631i
$651$	2.05711	+	4.96630i	0.0806245	+	0.194645i
$652$	12.8270	−	33.6038i	0.502344	−	1.31603i
$653$	20.3866	+	8.44440i	0.797789	+	0.330455i	0.744071	−	0.668101i	$-0.232893\pi$
$653$	20.3866	+	8.44440i	0.797789	+	0.330455i	0.0537185	+	0.998556i	$0.482893\pi$
$654$	−0.180482	−	12.8647i	−0.00705741	−	0.503051i
$655$	14.3058			0.558974
$656$	−6.27474	+	7.02162i	−0.244987	+	0.274148i
$657$	−10.0020			−0.390216
$658$	0.221301	+	15.7743i	0.00862722	+	0.614948i
$659$	−17.2370	−	7.13980i	−0.671458	−	0.278127i	0.0207928	−	0.999784i	$-0.493381\pi$
$659$	−17.2370	−	7.13980i	−0.671458	−	0.278127i	−0.692251	+	0.721657i	$0.743381\pi$
$660$	−0.318573	−	0.711928i	−0.0124004	−	0.0277118i
$661$	22.4009	−	9.27875i	0.871293	−	0.360901i	0.0981793	−	0.995169i	$-0.468698\pi$
$661$	22.4009	−	9.27875i	0.871293	−	0.360901i	0.773114	+	0.634267i	$0.218698\pi$
$662$	−0.779156	−	0.310004i	−0.0302827	−	0.0120487i
$663$	2.70278	+	1.85406i	0.104967	+	0.0720057i
$664$	20.3975	+	43.9201i	0.791578	+	1.70443i
$665$	−11.6027	−	11.6027i	−0.449933	−	0.449933i
$666$	−5.60362	+	2.41374i	−0.217136	+	0.0935303i
$667$	−26.0315	+	10.7826i	−1.00795	+	0.417505i
$668$	21.8457	−	23.1072i	0.845234	−	0.894045i
$669$	11.0988	+	4.59728i	0.429105	+	0.177741i
$670$	7.52780	−	7.74202i	0.290824	−	0.299100i
$671$		−	1.61713i		−	0.0624286i
$672$	8.47611	+	2.83297i	0.326973	+	0.109284i
$673$	−31.8284			−1.22690			−0.613448	−	0.789735i	$-0.710218\pi$
$673$	−31.8284			−1.22690			−0.613448	+	0.789735i	$0.710218\pi$
$674$	−16.8809	+	17.3613i	−0.650227	+	0.668731i
$675$	−0.0910387	+	0.219787i	−0.00350408	+	0.00845960i
$676$	−9.86222	+	24.0569i	−0.379316	+	0.925267i
$677$	−5.59582	+	2.31786i	−0.215065	+	0.0890827i	−0.487615	−	0.873059i	$-0.662133\pi$
$677$	−5.59582	+	2.31786i	−0.215065	+	0.0890827i	0.272550	+	0.962142i	$0.412133\pi$
$678$	−3.68978	−	8.56602i	−0.141705	−	0.328976i
$679$	25.3073	−	25.3073i	0.971205	−	0.971205i
$680$	3.38229	−	9.24818i	0.129705	−	0.354652i
$681$	−5.31664	+	5.31664i	−0.203734	+	0.203734i
$682$	0.523884	−	1.31671i	0.0200606	−	0.0504196i
$683$	−8.82829	+	3.65680i	−0.337805	+	0.139923i	−0.545136	−	0.838347i	$-0.683522\pi$
$683$	−8.82829	+	3.65680i	−0.337805	+	0.139923i	0.207331	+	0.978271i	$0.433522\pi$
$684$	5.88002	+	13.1403i	0.224828	+	0.502433i
$685$	−4.13137	−	1.71127i	−0.157851	−	0.0653842i
$686$	−25.7637	+	0.361444i	−0.983662	+	0.0138000i
$687$	2.44748			0.0933773
$688$	−15.1365	−	31.4302i	−0.577074	−	1.19827i
$689$	−6.39764	−	34.3494i	−0.243731	−	1.30861i
$690$	−0.0889046	−	6.33711i	−0.00338454	−	0.241250i
$691$	13.1413	−	31.7259i	0.499919	−	1.20691i	−0.449608	−	0.893226i	$-0.648436\pi$
$691$	13.1413	−	31.7259i	0.499919	−	1.20691i	0.949527	−	0.313686i	$-0.101564\pi$
$692$	7.89455	−	20.6819i	0.300106	−	0.786209i
$693$	0.803719	+	1.94035i	0.0305308	+	0.0737078i
$694$	36.3842	+	14.4763i	1.38113	+	0.549512i
$695$	−22.1406	+	22.1406i	−0.839839	+	0.839839i
$696$	−13.8344	+	0.582562i	−0.524391	+	0.0220819i
$697$	2.57352	+	2.57352i	0.0974790	+	0.0974790i
$698$	16.3445	+	37.9446i	0.618648	+	1.43623i
$699$	−2.84197	+	1.17718i	−0.107493	+	0.0445251i
$700$	−0.0107863	−	0.384347i	−0.000407683	−	0.0145270i
$701$	−16.6497	+	40.1959i	−0.628850	+	1.51818i	0.212202	+	0.977226i	$0.431936\pi$
$701$	−16.6497	+	40.1959i	−0.628850	+	1.51818i	−0.841053	+	0.540953i	$0.818064\pi$
$702$	−14.1129	−	9.39283i	−0.532658	−	0.354510i
$703$	−4.40797			−0.166250
$704$	−1.08141	−	2.09317i	−0.0407571	−	0.0788892i
$705$	5.49789			0.207062
$706$	15.7081	−	16.1551i	0.591182	−	0.608006i
$707$	2.08580	+	0.863966i	0.0784445	+	0.0324928i
$708$	0.182782	+	6.51308i	0.00686939	+	0.244776i
$709$	5.60922	+	13.5419i	0.210659	+	0.508575i	0.993525	−	0.113615i	$-0.0362430\pi$
$709$	5.60922	+	13.5419i	0.210659	+	0.508575i	−0.782866	+	0.622190i	$0.786243\pi$
$710$	−9.01772	+	3.88435i	−0.338429	+	0.145777i
$711$	−2.39945	+	2.39945i	−0.0899863	+	0.0899863i
$712$	36.4162	−	1.53348i	1.36476	−	0.0574695i
$713$	8.14239	−	8.14239i	0.304935	−	0.304935i
$714$	1.27693	−	3.20939i	0.0477877	−	0.120108i
$715$	−1.30415	−	2.00434i	−0.0487725	−	0.0749582i
$716$	6.90176	−	18.0810i	0.257931	−	0.675720i
$717$	3.57481	−	8.63036i	0.133504	−	0.322307i
$718$	0.360915	+	25.7260i	0.0134692	+	0.960087i
$719$		−	43.5840i		−	1.62541i	−0.582676	−	0.812704i	$-0.697995\pi$
$719$		−	43.5840i		−	1.62541i	0.582676	−	0.812704i	$-0.302005\pi$
$720$	−7.89654	+	22.5680i	−0.294287	+	0.841058i
$721$	0.684729			0.0255006
$722$	−0.231033	−	16.4680i	−0.00859815	−	0.612876i
$723$	−4.17959	+	10.0904i	−0.155441	+	0.375267i
$724$	19.9444	−	8.92470i	0.741228	−	0.331684i
$725$	0.227975	+	0.550379i	0.00846677	+	0.0204406i
$726$	3.35494	−	8.43220i	0.124513	−	0.312948i
$727$	21.7543	+	21.7543i	0.806821	+	0.806821i	0.984151	−	0.177330i	$-0.0567461\pi$
$727$	21.7543	+	21.7543i	0.806821	+	0.806821i	−0.177330	+	0.984151i	$0.556746\pi$
$728$	27.0213	+	4.54031i	1.00148	+	0.168275i
$729$	−7.12852	+	7.12852i	−0.264019	+	0.264019i
$730$	−4.74782	−	11.0223i	−0.175725	−	0.407954i
$731$	−12.4565	+	5.15966i	−0.460721	+	0.190837i
$732$	4.43631	−	4.69249i	0.163971	−	0.173440i
$733$	−17.5779	−	7.28102i	−0.649256	−	0.268931i	0.0336537	−	0.999434i	$-0.489286\pi$
$733$	−17.5779	−	7.28102i	−0.649256	−	0.268931i	−0.682909	+	0.730503i	$0.739286\pi$
$734$	−20.4559	+	21.0380i	−0.755041	+	0.776528i
$735$		−	0.289865i		−	0.0106918i
$736$	−1.34171	−	19.0973i	−0.0494562	−	0.703937i
$737$	−0.998536			−0.0367815
$738$	−6.33565	−	6.16034i	−0.233218	−	0.226765i
$739$	−20.2495	−	8.38763i	−0.744891	−	0.308544i	−0.0222358	−	0.999753i	$-0.507078\pi$
$739$	−20.2495	−	8.38763i	−0.744891	−	0.308544i	−0.722655	+	0.691209i	$0.757078\pi$
$740$	−5.31992	−	5.02948i	−0.195564	−	0.184887i
$741$	−3.13560	−	4.81908i	−0.115189	−	0.177033i
$742$	−33.8177	+	14.5668i	−1.24149	+	0.534765i
$743$	26.0929	+	26.0929i	0.957254	+	0.957254i	0.999123	−	0.0418687i	$-0.0133311\pi$
$743$	26.0929	+	26.0929i	0.957254	+	0.957254i	−0.0418687	+	0.999123i	$0.513331\pi$
$744$	5.13235	−	2.38358i	0.188161	−	0.0873864i
$745$	−36.8990	−	36.8990i	−1.35187	−	1.35187i
$746$	15.9732	−	40.1465i	0.584820	−	1.46987i
$747$	−41.9842	+	17.3904i	−1.53612	+	0.636283i
$748$	−0.831159	+	0.371927i	−0.0303902	+	0.0135990i
$749$	−11.7567	+	28.3831i	−0.429579	+	1.03709i
$750$	9.22858	−	0.129470i	0.336980	−	0.00472756i
$751$			31.9743i			1.16676i	0.812200	+	0.583380i	$0.198270\pi$
$751$			31.9743i			1.16676i	−0.812200	+	0.583380i	$0.801730\pi$
$752$	16.5813	−	0.931407i	0.604659	−	0.0339649i
$753$		−	0.172801i		−	0.00629723i
$754$	−41.6217	+	8.35790i	−1.51577	+	0.304377i
$755$	−36.4282	−	15.0891i	−1.32576	−	0.549147i
$756$	−6.37122	+	16.6911i	−0.231719	+	0.607051i
$757$	10.6311	+	25.6658i	0.386394	+	0.932838i	0.990697	+	0.136084i	$0.0434516\pi$
$757$	10.6311	+	25.6658i	0.386394	+	0.932838i	−0.604303	+	0.796755i	$0.706548\pi$
$758$	5.30527	−	13.3341i	0.192696	−	0.484316i
$759$	−0.414401	+	0.414401i	−0.0150418	+	0.0150418i
$760$	−11.6896	+	12.7174i	−0.424026	+	0.461307i
$761$	0.617516	+	0.617516i	0.0223849	+	0.0223849i	0.718211	−	0.695826i	$-0.244961\pi$
$761$	0.617516	+	0.617516i	0.0223849	+	0.0223849i	−0.695826	+	0.718211i	$0.744961\pi$
$762$	4.84413	−	2.08659i	0.175484	−	0.0755892i
$763$	−38.4059	+	15.9082i	−1.39039	+	0.575917i
$764$	−1.36983	−	48.8112i	−0.0495588	−	1.76593i
$765$	8.53745	+	3.53633i	0.308672	+	0.127856i
$766$	18.5251	−	19.0523i	0.669339	−	0.688387i
$767$	3.65774	+	19.6387i	0.132073	+	0.709111i
$768$	2.60426	−	9.04048i	0.0939730	−	0.326220i
$769$		−	21.5765i		−	0.778069i	−0.921223	−	0.389035i	$-0.872809\pi$
$769$		−	21.5765i		−	0.778069i	0.921223	−	0.389035i	$-0.127191\pi$
$770$	−1.75677	+	1.80676i	−0.0633096	+	0.0651112i
$771$	−5.12812	+	12.3804i	−0.184685	+	0.445869i
$772$	1.09504	−	0.0307311i	0.0394114	−	0.00110604i
$773$	−16.2570	−	39.2478i	−0.584723	−	1.41165i	−0.888488	−	0.458899i	$-0.848244\pi$
$773$	−16.2570	−	39.2478i	−0.584723	−	1.41165i	0.303765	−	0.952747i	$-0.401756\pi$
$774$	30.0662	−	12.9509i	1.08071	−	0.465510i
$775$	−0.172153	−	0.172153i	−0.00618392	−	0.00618392i
$776$	−27.7386	−	25.4968i	−0.995757	−	0.915284i
$777$	−1.81582	−	1.81582i	−0.0651422	−	0.0651422i
$778$	−7.01800	−	2.79227i	−0.251607	−	0.100108i
$779$	−2.44315	−	5.89828i	−0.0875348	−	0.211328i
$780$	1.71424	−	9.39379i	0.0613796	−	0.336351i
$781$	0.838828	+	0.347454i	0.0300156	+	0.0124329i
$782$	−7.39843	+	0.103794i	−0.264567	+	0.00371167i
$783$		−	27.6805i		−	0.989222i
$784$	−0.0491065	−	0.874216i	−0.00175380	−	0.0312220i
$785$	−4.26670			−0.152285
$786$	−0.0741018	−	5.28197i	−0.00264312	−	0.188402i
$787$	1.24639	−	3.00906i	0.0444291	−	0.107261i	−0.900107	−	0.435669i	$-0.856512\pi$
$787$	1.24639	−	3.00906i	0.0444291	−	0.107261i	0.944536	+	0.328408i	$0.106512\pi$
$788$	15.1014	−	6.75756i	0.537965	−	0.240728i
$789$	2.61616	+	6.31596i	0.0931376	+	0.224854i
$790$	−3.78320	−	1.50523i	−0.134600	−	0.0535537i
$791$	−21.3089	+	21.3089i	−0.757657	+	0.757657i
$792$	2.00522	−	0.931274i	0.0712525	−	0.0330914i
$793$	11.1995	−	16.3262i	0.397706	−	0.579762i
$794$	43.9682	−	18.9391i	1.56037	−	0.672124i
$795$	4.91071	+	11.8555i	0.174165	+	0.420471i
$796$	−30.5516	−	28.8836i	−1.08287	−	1.02375i
$797$	−16.2400	+	39.2068i	−0.575250	+	1.38878i	0.321783	+	0.946814i	$0.395718\pi$
$797$	−16.2400	+	39.2068i	−0.575250	+	1.38878i	−0.897033	+	0.441964i	$0.854282\pi$
$798$	−4.22383	+	4.34403i	−0.149522	+	0.153777i
$799$		−	6.41865i		−	0.227076i
$800$	−0.403771	+	0.0283676i	−0.0142755	+	0.00100295i
$801$			34.2040i			1.20854i
$802$	−30.0609	−	29.2291i	−1.06149	−	1.03211i
$803$	−0.424691	+	1.02529i	−0.0149870	+	0.0361818i
$804$	−2.89749	−	2.73930i	−0.102187	−	0.0966077i
$805$	−18.9186	+	7.83633i	−0.666792	+	0.276194i
$806$	14.4080	−	9.66512i	0.507500	−	0.340439i
$807$	−6.41750	+	6.41750i	−0.225907	+	0.225907i
$808$	0.816321	−	2.23206i	0.0287181	−	0.0785238i
$809$	−11.0692	−	11.0692i	−0.389173	−	0.389173i	0.485219	−	0.874393i	$-0.338740\pi$
$809$	−11.0692	−	11.0692i	−0.389173	−	0.389173i	−0.874393	+	0.485219i	$0.838740\pi$
$810$	−17.7782	−	7.07347i	−0.624663	−	0.248536i
$811$	14.7544	−	6.11147i	0.518097	−	0.214603i	−0.108284	−	0.994120i	$-0.534536\pi$
$811$	14.7544	−	6.11147i	0.518097	−	0.214603i	0.626381	+	0.779517i	$0.284536\pi$
$812$	18.2735	+	40.8366i	0.641275	+	1.43308i
$813$	−4.28419	+	10.3430i	−0.150253	+	0.362743i
$814$	0.00949649	+	0.676909i	0.000332852	+	0.0237256i
$815$			40.5010i			1.41869i
$816$	−3.43212	−	1.20090i	−0.120148	−	0.0420399i
$817$	23.6510			0.827442
$818$	−0.376478	−	26.8353i	−0.0131632	−	0.938275i
$819$	−5.32378	+	25.1556i	−0.186028	+	0.879007i
$820$	3.78131	−	9.90617i	0.132049	−	0.345939i
$821$	0.790558	−	0.327460i	0.0275907	−	0.0114284i	−0.368845	−	0.929491i	$-0.620247\pi$
$821$	0.790558	−	0.327460i	0.0275907	−	0.0114284i	0.396436	+	0.918062i	$0.370247\pi$
$822$	−0.610432	+	1.53424i	−0.0212913	+	0.0535128i
$823$	−1.70085	−	1.70085i	−0.0592879	−	0.0592879i	0.676841	−	0.736129i	$-0.263348\pi$
$823$	−1.70085	−	1.70085i	−0.0592879	−	0.0592879i	−0.736129	+	0.676841i	$0.763348\pi$
$824$	−0.0303267	−	0.720184i	−0.00105648	−	0.0250888i
$825$	0.00876161	+	0.00876161i	0.000305040	+	0.000305040i
$826$	19.3347	−	8.32834i	0.672740	−	0.289780i
$827$	−7.46627	−	18.0252i	−0.259628	−	0.626797i	0.739286	−	0.673391i	$-0.235163\pi$
$827$	−7.46627	−	18.0252i	−0.259628	−	0.626797i	−0.998914	+	0.0465946i	$0.985163\pi$
$828$	17.9584	−	0.503983i	0.624097	−	0.0175146i
$829$	−0.458416	+	1.10671i	−0.0159215	+	0.0384378i	−0.931640	−	0.363382i	$-0.881622\pi$
$829$	−0.458416	+	1.10671i	−0.0159215	+	0.0384378i	0.915719	+	0.401820i	$0.131622\pi$
$830$	−39.0938	−	38.0120i	−1.35696	−	1.31942i
$831$	−4.12254			−0.143009
$832$	3.57863	−	28.6216i	0.124067	−	0.992274i
$833$	−0.338410			−0.0117252
$834$	8.28939	+	8.06002i	0.287038	+	0.279096i
$835$	−13.7023	+	33.0803i	−0.474188	+	1.14479i
$836$	1.59667	−	0.0448088i	0.0552219	−	0.00154974i
$837$	4.32909	+	10.4514i	0.149635	+	0.361252i
$838$	−43.4984	+	18.7368i	−1.50263	+	0.647250i
$839$	24.5929	+	24.5929i	0.849041	+	0.849041i	0.990014	−	0.140972i	$-0.0450228\pi$
$839$	24.5929	+	24.5929i	0.849041	+	0.849041i	−0.140972	+	0.990014i	$0.545023\pi$
$840$	−10.0542	+	0.423380i	−0.346903	+	0.0146080i
$841$	−28.5079	−	28.5079i	−0.983031	−	0.983031i
$842$	21.0547	−	52.9182i	0.725592	−	1.82368i
$843$	11.2456	−	4.65807i	0.387318	−	0.160432i
$844$	−19.9296	+	52.2109i	−0.686004	+	1.79717i
$845$	0.714695	−	29.2674i	0.0245863	−	1.00683i
$846$	0.218620	+	15.5832i	0.00751631	+	0.535762i
$847$	−29.3218			−1.00751
$848$	16.8189	+	34.9236i	0.577563	+	1.19928i
$849$			0.949991i			0.0326036i
$850$	0.00219450	+	0.156424i	7.52706e−5	+	0.00536528i
$851$	−2.10512	+	5.08221i	−0.0721626	+	0.174216i
$852$	1.48088	+	3.30939i	0.0507343	+	0.113378i
$853$	−28.5129	+	11.8104i	−0.976263	+	0.404381i	−0.813040	−	0.582208i	$-0.802189\pi$
$853$	−28.5129	+	11.8104i	−0.976263	+	0.404381i	−0.163223	+	0.986589i	$0.552189\pi$
$854$	−19.3864	−	7.71331i	−0.663389	−	0.263944i
$855$	−11.4621	−	11.4621i	−0.391996	−	0.391996i
$856$	30.3734	+	11.1083i	1.03814	+	0.379675i
$857$	32.9468	−	32.9468i	1.12544	−	1.12544i	0.134532	−	0.990909i	$-0.457047\pi$
$857$	32.9468	−	32.9468i	1.12544	−	1.12544i	0.990909	−	0.134532i	$-0.0429530\pi$
$858$	−0.733285	+	0.491899i	−0.0250340	+	0.0167932i
$859$	36.5772	−	15.1508i	1.24800	−	0.516937i	0.341791	−	0.939776i	$-0.388966\pi$
$859$	36.5772	−	15.1508i	1.24800	−	0.516937i	0.906205	+	0.422839i	$0.138966\pi$
$860$	28.5440	+	26.9857i	0.973344	+	0.920203i
$861$	1.42331	−	3.43617i	0.0485062	−	0.117104i
$862$	27.4035	+	26.6453i	0.933368	+	0.907542i
$863$			15.6056i			0.531221i	0.964080	+	0.265611i	$0.0855735\pi$
$863$			15.6056i			0.531221i	−0.964080	+	0.265611i	$0.914426\pi$
$864$	17.8376	+	5.96186i	0.606847	+	0.202827i
$865$			24.9269i			0.847540i
$866$	−15.7486	+	16.1967i	−0.535158	+	0.550388i
$867$	3.28754	−	7.93683i	0.111651	−	0.269549i
$868$	−13.2862	−	12.5608i	−0.450962	−	0.426342i
$869$	0.144083	+	0.347846i	0.00488767	+	0.0117999i
$870$	14.3195	−	6.16805i	0.485475	−	0.209116i
$871$	−10.0810	−	6.91540i	−0.341582	−	0.234319i
$872$	18.4330	+	39.6900i	0.624219	+	1.34407i
$873$	25.0007	−	25.0007i	0.846145	−	0.846145i
$874$	12.0598	+	4.79825i	0.407928	+	0.162303i
$875$	−11.4118	−	27.5506i	−0.385791	−	0.931381i
$876$	−4.04505	+	1.81008i	−0.136670	+	0.0611568i
$877$	15.3997	−	37.1782i	0.520012	−	1.25542i	−0.417884	−	0.908500i	$-0.637228\pi$
$877$	15.3997	−	37.1782i	0.520012	−	1.25542i	0.937895	−	0.346918i	$-0.112772\pi$
$878$	0.584053	+	41.6312i	0.0197108	+	1.40499i
$879$	−0.747183			−0.0252018
$880$	1.97812	+	1.76771i	0.0666826	+	0.0595896i
$881$			27.6941i			0.933037i	0.884511	+	0.466519i	$0.154492\pi$
$881$			27.6941i			0.933037i	−0.884511	+	0.466519i	$0.845508\pi$
$882$	0.821593	−	0.0115263i	0.0276645	−	0.000388110i
$883$	−35.2261	−	14.5911i	−1.18545	−	0.491031i	−0.299181	−	0.954196i	$-0.596713\pi$
$883$	−35.2261	−	14.5911i	−1.18545	−	0.491031i	−0.886272	+	0.463166i	$0.846713\pi$
$884$	−10.9670	−	2.00133i	−0.368861	−	0.0673121i
$885$	−2.80761	−	6.77818i	−0.0943769	−	0.227846i
$886$	1.01618	+	0.404308i	0.0341391	+	0.0135830i
$887$	6.26722	+	6.26722i	0.210433	+	0.210433i	0.804451	−	0.594019i	$-0.202459\pi$
$887$	6.26722	+	6.26722i	0.210433	+	0.210433i	−0.594019	+	0.804451i	$0.702459\pi$
$888$	−1.82942	+	1.99027i	−0.0613913	+	0.0667890i
$889$	−12.0503	−	12.0503i	−0.404154	−	0.404154i
$890$	−37.6931	+	16.2362i	−1.26348	+	0.544237i
$891$	0.677082	+	1.63462i	0.0226831	+	0.0547618i
$892$	−40.8449	+	1.14627i	−1.36759	+	0.0383799i
$893$	−4.30875	+	10.4022i	−0.144187	+	0.348098i
$894$	−13.4327	+	13.8149i	−0.449255	+	0.462040i
$895$			21.7922i			0.728431i
$896$	−30.2512	+	2.98019i	−1.01062	+	0.0995613i
$897$	−7.05367	+	1.31376i	−0.235515	+	0.0438652i
$898$	7.77758	−	7.99891i	0.259541	−	0.266927i
$899$	26.1718	+	10.8407i	0.872878	+	0.361558i
$900$	−0.0106556	−	0.379691i	−0.000355187	−	0.0126564i
$901$	13.8410	−	5.73314i	0.461111	−	0.190999i
$902$	−0.900504	+	0.387889i	−0.0299835	+	0.0129153i
$903$	9.74279	+	9.74279i	0.324220	+	0.324220i
$904$	23.3560	+	21.4685i	0.776810	+	0.714032i
$905$	−17.3972	+	17.3972i	−0.578303	+	0.578303i
$906$	−5.38247	+	13.5281i	−0.178821	+	0.449442i
$907$	5.98441	+	14.4476i	0.198709	+	0.479726i	0.991554	−	0.129698i	$-0.0414008\pi$
$907$	5.98441	+	14.4476i	0.198709	+	0.479726i	−0.792845	+	0.609424i	$0.791401\pi$
$908$	9.12011	−	23.8926i	0.302661	−	0.792904i
$909$	2.06053	+	0.853498i	0.0683434	+	0.0283087i
$910$	−30.2488	+	6.07415i	−1.00274	+	0.201356i
$911$		−	3.04000i		−	0.100720i	−0.998731	−	0.0503599i	$-0.983963\pi$
$911$		−	3.04000i		−	0.100720i	0.998731	−	0.0503599i	$-0.0160368\pi$
$912$	4.75604	+	4.25015i	0.157488	+	0.140736i
$913$			5.04216i			0.166871i
$914$	27.8077	−	0.390119i	0.919796	−	0.0129040i
$915$	−2.78259	+	6.71778i	−0.0919897	+	0.222083i
$916$	−7.59861	+	3.40022i	−0.251065	+	0.112346i
$917$	−15.7686	+	6.53156i	−0.520725	+	0.215691i
$918$	2.68723	−	6.75401i	0.0886919	−	0.222915i
$919$	33.5627	+	33.5627i	1.10713	+	1.10713i	0.993526	+	0.113604i	$0.0362394\pi$
$919$	33.5627	+	33.5627i	1.10713	+	1.10713i	0.113604	+	0.993526i	$0.463761\pi$
$920$	9.07999	+	19.5511i	0.299359	+	0.644580i
$921$	−12.1784	−	12.1784i	−0.401293	−	0.401293i
$922$	18.4136	−	7.93159i	0.606421	−	0.261213i
$923$	6.06234	+	9.31717i	0.199544	+	0.306678i
$924$	0.676191	+	0.639273i	0.0222450	+	0.0210306i
$925$	0.107452	+	0.0445081i	0.00353300	+	0.00146342i
$926$	−35.9194	−	34.9255i	−1.18039	−	1.14772i
$927$	0.676433			0.0222170
$928$	42.1418	−	21.0284i	1.38337	−	0.690290i
$929$		−	21.5345i		−	0.706525i	−0.935524	−	0.353262i	$-0.885072\pi$
$929$		−	21.5345i		−	0.706525i	0.935524	−	0.353262i	$-0.114928\pi$
$930$	−4.44195	+	4.56836i	−0.145657	+	0.149802i
$931$	0.548437	+	0.227170i	0.0179743	+	0.00744519i
$932$	7.18793	−	7.60302i	0.235448	−	0.249045i
$933$	10.7504	−	4.45298i	0.351953	−	0.145784i
$934$	15.6314	+	36.2893i	0.511477	+	1.18742i
$935$	0.725009	−	0.725009i	0.0237103	−	0.0237103i
$936$	26.6939	+	4.48530i	0.872518	+	0.146607i
$937$	30.1985	+	30.1985i	0.986543	+	0.986543i	0.999911	−	0.0133676i	$-0.00425517\pi$
$937$	30.1985	+	30.1985i	0.986543	+	0.986543i	−0.0133676	+	0.999911i	$0.504255\pi$
$938$	−4.76277	+	11.9706i	−0.155510	+	0.390854i
$939$	3.58712	+	8.66006i	0.117061	+	0.282611i
$940$	−17.0691	+	7.63806i	−0.556732	+	0.249126i
$941$	6.63828	−	16.0262i	0.216402	−	0.522440i	−0.777980	−	0.628288i	$-0.783756\pi$
$941$	6.63828	−	16.0262i	0.216402	−	0.522440i	0.994382	+	0.105848i	$0.0337558\pi$
$942$	0.0221008	+	1.57535i	0.000720085	+	0.0513276i
$943$	−7.96725			−0.259449
$944$	−9.61591	−	19.9670i	−0.312971	−	0.649870i
$945$		−	20.1170i		−	0.654406i
$946$	−0.0509534	−	3.63196i	−0.00165664	−	0.118085i
$947$	−5.67821	+	13.7084i	−0.184517	+	0.445464i	−0.988888	−	0.148664i	$-0.952503\pi$
$947$	−5.67821	+	13.7084i	−0.184517	+	0.445464i	0.804371	+	0.594128i	$0.202503\pi$
$948$	−0.536163	+	1.40462i	−0.0174138	+	0.0456201i
$949$	−11.3883	+	7.40996i	−0.369680	+	0.240537i
$950$	0.101448	−	0.254977i	0.00329142	−	0.00827255i
$951$	−4.96753	+	4.96753i	−0.161083	+	0.161083i
$952$	0.494286	+	11.7381i	0.0160199	+	0.380433i
$953$	−9.76835	+	9.76835i	−0.316428	+	0.316428i	−0.847393	−	0.530965i	$-0.821829\pi$
$953$	−9.76835	+	9.76835i	−0.316428	+	0.316428i	0.530965	+	0.847393i	$0.321829\pi$
$954$	−33.4080	+	14.3904i	−1.08162	+	0.465905i
$955$	21.0412	+	50.7980i	0.680877	+	1.64378i
$956$	0.891330	+	31.7607i	0.0288277	+	1.02722i
$957$	−1.33199	−	0.551730i	−0.0430573	−	0.0178349i
$958$	15.2006	−	15.6332i	0.491111	−	0.505086i
$959$	5.33511			0.172280
$960$	0.890605	+	10.5561i	0.0287441	+	0.340696i
$961$	19.4229			0.626545
$962$	−4.59209	+	6.89971i	−0.148055	+	0.222456i
$963$	−11.6142	+	28.0392i	−0.374263	+	0.903550i
$964$	−1.04212	−	37.1340i	−0.0335646	−	1.19600i
$965$	−1.13961	+	0.472043i	−0.0366854	+	0.0151956i
$966$	2.99131	+	6.94450i	0.0962439	+	0.223436i
$967$	14.7331	+	14.7331i	0.473786	+	0.473786i	0.903137	−	0.429352i	$-0.141258\pi$
$967$	14.7331	+	14.7331i	0.473786	+	0.473786i	−0.429352	+	0.903137i	$0.641258\pi$
$968$	1.29867	+	30.8401i	0.0417407	+	0.991237i
$969$	1.74315	−	1.74315i	0.0559982	−	0.0559982i
$970$	39.4185	+	15.6835i	1.26565	+	0.503568i
$971$	−12.5401	−	30.2746i	−0.402432	−	0.971557i	−0.987074	−	0.160265i	$-0.948765\pi$
$971$	−12.5401	−	30.2746i	−0.402432	−	0.971557i	0.584642	−	0.811291i	$-0.301235\pi$
$972$	−9.63348	+	25.2375i	−0.308994	+	0.809494i
$973$	14.2958	−	34.5131i	0.458302	−	1.10644i
$974$	−0.0851806	−	6.07166i	−0.00272936	−	0.194549i
$975$	0.0277766	+	0.149134i	0.000889563	+	0.00477612i
$976$	−7.25408	+	20.7318i	−0.232197	+	0.663610i
$977$	53.9729			1.72675			0.863373	−	0.504566i	$-0.168347\pi$
$977$	53.9729			1.72675			0.863373	+	0.504566i	$0.168347\pi$
$978$	14.9537	−	0.209789i	0.478167	−	0.00670830i
$979$	3.50621	+	1.45232i	0.112059	+	0.0464163i
$980$	0.402701	+	0.899932i	0.0128638	+	0.0287473i
$981$	−37.9406	+	15.7155i	−1.21135	+	0.501757i
$982$	−8.05099	+	20.2351i	−0.256917	+	0.645728i
$983$	−17.0008	+	17.0008i	−0.542242	+	0.542242i	−0.924186	−	0.381944i	$-0.875255\pi$
$983$	−17.0008	+	17.0008i	−0.542242	+	0.542242i	0.381944	+	0.924186i	$0.375255\pi$
$984$	−3.67713	−	1.34482i	−0.117223	−	0.0428712i
$985$	−13.1727	+	13.1727i	−0.419718	+	0.419718i
$986$	−7.20105	−	16.7176i	−0.229328	−	0.532398i
$987$	−6.06005	+	2.51015i	−0.192893	+	0.0798991i
$988$	16.4300	+	10.6054i	0.522707	+	0.337403i
$989$	11.2950	−	27.2686i	0.359161	−	0.867091i
$990$	−1.73549	+	1.78487i	−0.0551573	+	0.0567270i
$991$	−47.1637			−1.49820			−0.749102	−	0.662455i	$-0.769515\pi$
$991$	−47.1637			−1.49820			−0.749102	+	0.662455i	$0.769515\pi$
$992$	−12.6228	+	14.5304i	−0.400773	+	0.461342i
$993$		−	0.348660i		−	0.0110644i
$994$	8.16633	−	8.39872i	0.259020	−	0.266391i
$995$	43.7376	+	18.1167i	1.38658	+	0.574339i
$996$	−13.8323	+	14.6311i	−0.438292	+	0.463603i
$997$	−3.94594	+	1.63446i	−0.124969	+	0.0517639i	−0.444292	−	0.895882i	$-0.646545\pi$
$997$	−3.94594	+	1.63446i	−0.124969	+	0.0517639i	0.319323	+	0.947646i	$0.396545\pi$
$998$	2.13070	−	0.917791i	0.0674462	−	0.0290522i
$999$	−3.82131	−	3.82131i	−0.120901	−	0.120901i

Display

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p

up to: 50 250 1000 (See

a_n

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a_n

instead) (See

a_n

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a_n

with

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up to: 50 250 1000 (See only

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a_p

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bg.a.77.14	✓	216
13.12	even	2	inner	416.2.bg.a.77.41	yes	216
32.5	even	8	inner	416.2.bg.a.389.41	yes	216
416.389	even	8	inner	416.2.bg.a.389.14	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bg.a.77.14	✓	216	1.1	even	1	trivial
416.2.bg.a.77.41	yes	216	13.12	even	2	inner
416.2.bg.a.389.14	yes	216	416.389	even	8	inner
416.2.bg.a.389.41	yes	216	32.5	even	8	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	416.2.bg.a.77.14

Level	$416$
Weight	$2$
Character	416.77
Analytic conductor	$3.322$
Analytic rank	$0$
Dimension	$216$
Inner twists	$4$