LMFDB - Embedded newform 210.3.v.b.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(37,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.v (of order $12$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			163.6
Character	$\chi$	$=$	210.163
Dual form			210.3.v.b.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(0.448288 - 1.67303i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.258026 + 4.99334i) q^{5} -2.44949 q^{6} +(6.75207 + 1.84650i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(0.448288 - 1.67303i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.258026 + 4.99334i) q^{5} -2.44949 q^{6} +(6.75207 + 1.84650i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(6.91547 - 1.47522i) q^{10} +(7.12207 + 12.3358i) q^{11} +(0.896575 + 3.34607i) q^{12} +(-2.75603 - 2.75603i) q^{13} +(0.0509352 - 9.89936i) q^{14} +(8.23835 + 2.67014i) q^{15} +(2.00000 - 3.46410i) q^{16} +(23.9506 + 6.41754i) q^{17} +(-1.09808 + 4.09808i) q^{18} +(-0.277055 - 0.159958i) q^{19} +(-4.54642 - 8.90674i) q^{20} +(6.11612 - 10.4687i) q^{21} +(14.2441 - 14.2441i) q^{22} +(13.6188 - 3.64915i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-24.8668 - 2.57682i) q^{25} +(-2.75603 + 4.77358i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-13.5414 + 3.55384i) q^{28} -24.2642i q^{29} +(0.632031 - 12.2311i) q^{30} +(-7.62013 - 13.1985i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(23.8309 - 6.38548i) q^{33} -35.0661i q^{34} +(-10.9624 + 33.2389i) q^{35} +6.00000 q^{36} +(0.611341 + 2.28156i) q^{37} +(-0.117097 + 0.437012i) q^{38} +(-5.84642 + 3.37543i) q^{39} +(-10.5027 + 9.47062i) q^{40} +29.0794 q^{41} +(-16.5391 - 4.52298i) q^{42} +(-11.7409 - 11.7409i) q^{43} +(-24.6716 - 14.2441i) q^{44} +(8.16038 - 12.5860i) q^{45} +(-9.96966 - 17.2680i) q^{46} +(21.9076 + 81.7602i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(42.1809 + 24.9354i) q^{49} +(5.58190 + 34.9119i) q^{50} +(21.4735 - 37.1932i) q^{51} +(7.52961 + 2.01755i) q^{52} +(-19.4580 + 72.6184i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-63.4344 + 32.3800i) q^{55} +(9.81114 + 17.1971i) q^{56} +(-0.391815 + 0.391815i) q^{57} +(-33.1456 + 8.88133i) q^{58} +(-31.7156 + 18.3110i) q^{59} +(-16.9394 + 3.61353i) q^{60} +(54.2209 - 93.9134i) q^{61} +(-15.2403 + 15.2403i) q^{62} +(-14.7726 - 14.9254i) q^{63} +8.00000i q^{64} +(14.4729 - 13.0507i) q^{65} +(-17.4454 - 30.2164i) q^{66} +(-66.0445 - 17.6966i) q^{67} +(-47.9012 + 12.8351i) q^{68} -24.4206i q^{69} +(49.4177 + 2.80863i) q^{70} -20.3365 q^{71} +(-2.19615 - 8.19615i) q^{72} +(-15.1623 + 56.5866i) q^{73} +(2.89290 - 1.67022i) q^{74} +(-15.4586 + 40.4479i) q^{75} +0.639831 q^{76} +(25.3107 + 96.4430i) q^{77} +(6.75087 + 6.75087i) q^{78} +(-44.5901 - 25.7441i) q^{79} +(16.7814 + 10.8805i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-10.6438 - 39.7232i) q^{82} +(-82.8590 - 82.8590i) q^{83} +(-0.124765 + 24.2484i) q^{84} +(-38.2248 + 117.937i) q^{85} +(-11.7409 + 20.3359i) q^{86} +(-40.5949 - 10.8774i) q^{87} +(-10.4274 + 38.9157i) q^{88} +(-95.6273 - 55.2104i) q^{89} +(-20.1797 - 6.54047i) q^{90} +(-13.5199 - 23.6979i) q^{91} +(-19.9393 + 19.9393i) q^{92} +(-25.4975 + 6.83202i) q^{93} +(103.668 - 59.8526i) q^{94} +(0.870210 - 1.34215i) q^{95} +(-4.89898 + 8.48528i) q^{96} +(68.2928 - 68.2928i) q^{97} +(18.6231 - 66.7471i) q^{98} -42.7324i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	0.448288	−	1.67303i	0.149429	−	0.557678i
$3$	0.448288	−	1.67303i	0.149429	−	0.557678i
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−0.258026	+	4.99334i	−0.0516051	+	0.998668i
$5$	−0.258026	+	4.99334i	−0.0516051	+	0.998668i
$6$	−2.44949			−0.408248
$7$	6.75207	+	1.84650i	0.964581	+	0.263786i
$7$	6.75207	+	1.84650i	0.964581	+	0.263786i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−2.59808	−	1.50000i	−0.288675	−	0.166667i
$10$	6.91547	−	1.47522i	0.691547	−	0.147522i
$11$	7.12207	+	12.3358i	0.647461	+	1.12144i	0.983727	+	0.179669i	$0.0575025\pi$
$11$	7.12207	+	12.3358i	0.647461	+	1.12144i	−0.336266	+	0.941767i	$0.609164\pi$
$12$	0.896575	+	3.34607i	0.0747146	+	0.278839i
$13$	−2.75603	−	2.75603i	−0.212002	−	0.212002i	0.593115	−	0.805118i	$-0.297898\pi$
$13$	−2.75603	−	2.75603i	−0.212002	−	0.212002i	−0.805118	+	0.593115i	$0.797898\pi$
$14$	0.0509352	−	9.89936i	0.00363823	−	0.707097i
$15$	8.23835	+	2.67014i	0.549223	+	0.178009i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	23.9506	+	6.41754i	1.40886	+	0.377502i	0.881517	−	0.472152i	$-0.156523\pi$
$17$	23.9506	+	6.41754i	1.40886	+	0.377502i	0.527341	+	0.849654i	$0.323189\pi$
$18$	−1.09808	+	4.09808i	−0.0610042	+	0.227671i
$19$	−0.277055	−	0.159958i	−0.0145818	−	0.00841882i	0.492691	−	0.870204i	$-0.336013\pi$
$19$	−0.277055	−	0.159958i	−0.0145818	−	0.00841882i	−0.507273	+	0.861785i	$0.669346\pi$
$20$	−4.54642	−	8.90674i	−0.227321	−	0.445337i
$21$	6.11612	−	10.4687i	0.291244	−	0.498508i
$22$	14.2441	−	14.2441i	0.647461	−	0.647461i
$23$	13.6188	−	3.64915i	0.592122	−	0.158659i	0.0496991	−	0.998764i	$-0.484174\pi$
$23$	13.6188	−	3.64915i	0.592122	−	0.158659i	0.542423	+	0.840106i	$0.317507\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$	−24.8668	−	2.57682i	−0.994674	−	0.103073i
$26$	−2.75603	+	4.77358i	−0.106001	+	0.183599i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−13.5414	+	3.55384i	−0.483622	+	0.126923i
$29$		−	24.2642i		−	0.836698i	−0.908286	−	0.418349i	$-0.862609\pi$
$29$		−	24.2642i		−	0.836698i	0.908286	−	0.418349i	$-0.137391\pi$
$30$	0.632031	−	12.2311i	0.0210677	−	0.407704i
$31$	−7.62013	−	13.1985i	−0.245811	−	0.425757i	0.716549	−	0.697537i	$-0.245721\pi$
$31$	−7.62013	−	13.1985i	−0.245811	−	0.425757i	−0.962359	+	0.271781i	$0.912387\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	23.8309	−	6.38548i	0.722149	−	0.193499i
$34$		−	35.0661i		−	1.03136i
$35$	−10.9624	+	33.2389i	−0.313211	+	0.949683i
$36$	6.00000			0.166667
$37$	0.611341	+	2.28156i	0.0165227	+	0.0616637i	0.973695	−	0.227855i	$-0.0731713\pi$
$37$	0.611341	+	2.28156i	0.0165227	+	0.0616637i	−0.957172	+	0.289519i	$0.906505\pi$
$38$	−0.117097	+	0.437012i	−0.00308150	+	0.0115003i
$39$	−5.84642	+	3.37543i	−0.149908	+	0.0865496i
$40$	−10.5027	+	9.47062i	−0.262568	+	0.236766i
$41$	29.0794			0.709254			0.354627	−	0.935008i	$-0.384608\pi$
$41$	29.0794			0.709254			0.354627	+	0.935008i	$0.384608\pi$
$42$	−16.5391	−	4.52298i	−0.393789	−	0.107690i
$43$	−11.7409	−	11.7409i	−0.273045	−	0.273045i	0.557280	−	0.830325i	$-0.311845\pi$
$43$	−11.7409	−	11.7409i	−0.273045	−	0.273045i	−0.830325	+	0.557280i	$0.811845\pi$
$44$	−24.6716	−	14.2441i	−0.560718	−	0.323731i
$45$	8.16038	−	12.5860i	0.181342	−	0.279690i
$46$	−9.96966	−	17.2680i	−0.216732	−	0.375390i
$47$	21.9076	+	81.7602i	0.466119	+	1.73958i	0.653154	+	0.757225i	$0.273445\pi$
$47$	21.9076	+	81.7602i	0.466119	+	1.73958i	−0.187035	+	0.982353i	$0.559888\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$	42.1809	+	24.9354i	0.860834	+	0.508885i
$50$	5.58190	+	34.9119i	0.111638	+	0.698238i
$51$	21.4735	−	37.1932i	0.421049	−	0.729279i
$52$	7.52961	+	2.01755i	0.144800	+	0.0387991i
$53$	−19.4580	+	72.6184i	−0.367133	+	1.37016i	0.497374	+	0.867536i	$0.334298\pi$
$53$	−19.4580	+	72.6184i	−0.367133	+	1.37016i	−0.864507	+	0.502622i	$0.832369\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$	−63.4344	+	32.3800i	−1.15335	+	0.588727i
$56$	9.81114	+	17.1971i	0.175199	+	0.307092i
$57$	−0.391815	+	0.391815i	−0.00687394	+	0.00687394i
$58$	−33.1456	+	8.88133i	−0.571475	+	0.153126i
$59$	−31.7156	+	18.3110i	−0.537553	+	0.310356i	−0.744087	−	0.668083i	$-0.767115\pi$
$59$	−31.7156	+	18.3110i	−0.537553	+	0.310356i	0.206534	+	0.978439i	$0.433782\pi$
$60$	−16.9394	+	3.61353i	−0.282323	+	0.0602256i
$61$	54.2209	−	93.9134i	0.888867	−	1.53956i	0.0476513	−	0.998864i	$-0.484826\pi$
$61$	54.2209	−	93.9134i	0.888867	−	1.53956i	0.841216	−	0.540699i	$-0.181840\pi$
$62$	−15.2403	+	15.2403i	−0.245811	+	0.245811i
$63$	−14.7726	−	14.9254i	−0.234486	−	0.236912i
$64$			8.00000i			0.125000i
$65$	14.4729	−	13.0507i	0.222660	−	0.200779i
$66$	−17.4454	−	30.2164i	−0.264325	−	0.457824i
$67$	−66.0445	−	17.6966i	−0.985739	−	0.264128i	−0.270279	−	0.962782i	$-0.587116\pi$
$67$	−66.0445	−	17.6966i	−0.985739	−	0.264128i	−0.715460	+	0.698654i	$0.753783\pi$
$68$	−47.9012	+	12.8351i	−0.704429	+	0.188751i
$69$		−	24.4206i		−	0.353921i
$70$	49.4177	+	2.80863i	0.705968	+	0.0401232i
$71$	−20.3365			−0.286429			−0.143215	−	0.989692i	$-0.545744\pi$
$71$	−20.3365			−0.286429			−0.143215	+	0.989692i	$0.545744\pi$
$72$	−2.19615	−	8.19615i	−0.0305021	−	0.113835i
$73$	−15.1623	+	56.5866i	−0.207703	+	0.775159i	0.780905	+	0.624649i	$0.214758\pi$
$73$	−15.1623	+	56.5866i	−0.207703	+	0.775159i	−0.988609	+	0.150510i	$0.951909\pi$
$74$	2.89290	−	1.67022i	0.0390932	−	0.0225705i
$75$	−15.4586	+	40.4479i	−0.206115	+	0.539305i
$76$	0.639831			0.00841882
$77$	25.3107	+	96.4430i	0.328710	+	1.25251i
$78$	6.75087	+	6.75087i	0.0865496	+	0.0865496i
$79$	−44.5901	−	25.7441i	−0.564431	−	0.325874i	0.190491	−	0.981689i	$-0.438992\pi$
$79$	−44.5901	−	25.7441i	−0.564431	−	0.325874i	−0.754922	+	0.655815i	$0.772325\pi$
$80$	16.7814	+	10.8805i	0.209767	+	0.136006i
$81$	4.50000	+	7.79423i	0.0555556	+	0.0962250i
$82$	−10.6438	−	39.7232i	−0.129802	−	0.484429i
$83$	−82.8590	−	82.8590i	−0.998301	−	0.998301i	0.00169722	−	0.999999i	$-0.499460\pi$
$83$	−82.8590	−	82.8590i	−0.998301	−	0.998301i	−0.999999	+	0.00169722i	$0.999460\pi$
$84$	−0.124765	+	24.2484i	−0.00148530	+	0.288671i
$85$	−38.2248	+	117.937i	−0.449704	+	1.38750i
$86$	−11.7409	+	20.3359i	−0.136522	+	0.236464i
$87$	−40.5949	−	10.8774i	−0.466608	−	0.125027i
$88$	−10.4274	+	38.9157i	−0.118494	+	0.442224i
$89$	−95.6273	−	55.2104i	−1.07446	−	0.620342i	−0.145066	−	0.989422i	$-0.546340\pi$
$89$	−95.6273	−	55.2104i	−1.07446	−	0.620342i	−0.929398	+	0.369080i	$0.879673\pi$
$90$	−20.1797	−	6.54047i	−0.224219	−	0.0726719i
$91$	−13.5199	−	23.6979i	−0.148570	−	0.260417i
$92$	−19.9393	+	19.9393i	−0.216732	+	0.216732i
$93$	−25.4975	+	6.83202i	−0.274166	+	0.0734626i
$94$	103.668	−	59.8526i	1.10285	−	0.636730i
$95$	0.870210	−	1.34215i	0.00916010	−	0.0141279i
$96$	−4.89898	+	8.48528i	−0.0510310	+	0.0883883i
$97$	68.2928	−	68.2928i	0.704050	−	0.704050i	−0.261228	−	0.965277i	$-0.584127\pi$
$97$	68.2928	−	68.2928i	0.704050	−	0.704050i	0.965277	+	0.261228i	$0.0841273\pi$
$98$	18.6231	−	66.7471i	0.190031	−	0.681093i
$99$		−	42.7324i		−	0.431641i
$100$	45.6475	−	20.4037i	0.456475	−	0.204037i
$101$	49.9666	+	86.5447i	0.494719	+	0.856878i	0.999981	−	0.00608738i	$-0.00193769\pi$
$101$	49.9666	+	86.5447i	0.494719	+	0.856878i	−0.505263	+	0.862966i	$0.668604\pi$
$102$	−58.6667	−	15.7197i	−0.575164	−	0.154115i
$103$	108.172	−	28.9847i	1.05022	−	0.281405i	0.307875	−	0.951427i	$-0.400382\pi$
$103$	108.172	−	28.9847i	1.05022	−	0.281405i	0.742341	+	0.670022i	$0.233715\pi$
$104$		−	11.0241i		−	0.106001i
$105$	50.6955	+	33.2411i	0.482814	+	0.316581i
$106$	106.321			1.00303
$107$	−28.8233	−	107.570i	−0.269377	−	1.00533i	−0.959517	−	0.281652i	$-0.909118\pi$
$107$	−28.8233	−	107.570i	−0.269377	−	1.00533i	0.690140	−	0.723676i	$-0.257549\pi$
$108$	2.68973	−	10.0382i	0.0249049	−	0.0929463i
$109$	−65.8933	+	38.0435i	−0.604526	+	0.349023i	−0.770820	−	0.637053i	$-0.780153\pi$
$109$	−65.8933	+	38.0435i	−0.604526	+	0.349023i	0.166294	+	0.986076i	$0.446820\pi$
$110$	67.4505	+	74.8012i	0.613186	+	0.680011i
$111$	4.09118			0.0368574
$112$	19.9006	−	19.6969i	0.177684	−	0.175865i
$113$	−76.5867	−	76.5867i	−0.677759	−	0.677759i	0.281734	−	0.959493i	$-0.409090\pi$
$113$	−76.5867	−	76.5867i	−0.677759	−	0.677759i	−0.959493	+	0.281734i	$0.909090\pi$
$114$	0.678643	+	0.391815i	0.00595301	+	0.00343697i
$115$	14.7074	+	68.9449i	0.127891	+	0.599521i
$116$	24.2642	+	42.0269i	0.209174	+	0.362301i
$117$	3.02633	+	11.2944i	0.0258661	+	0.0965335i
$118$	36.6220	+	36.6220i	0.310356	+	0.310356i
$119$	149.866	+	87.5564i	1.25938	+	0.735768i
$120$	11.1364	+	21.8170i	0.0928035	+	0.181808i
$121$	−40.9478	+	70.9237i	−0.338412	+	0.586146i
$122$	−148.134	−	39.6925i	−1.21422	−	0.325348i
$123$	13.0359	−	48.6508i	0.105983	−	0.395535i
$124$	26.3969	+	15.2403i	0.212878	+	0.122905i
$125$	19.2832	−	123.504i	0.154266	−	0.988029i
$126$	−14.9814	+	25.6429i	−0.118900	+	0.203515i
$127$	−85.3727	+	85.3727i	−0.672226	+	0.672226i	−0.958229	−	0.286003i	$-0.907673\pi$
$127$	−85.3727	+	85.3727i	−0.672226	+	0.672226i	0.286003	+	0.958229i	$0.407673\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$	−24.9063	+	14.3796i	−0.193072	+	0.111470i
$130$	−23.1250	−	14.9935i	−0.177885	−	0.115335i
$131$	109.573	−	189.787i	0.836438	−	1.44875i	−0.0564154	−	0.998407i	$-0.517967\pi$
$131$	109.573	−	189.787i	0.836438	−	1.44875i	0.892854	−	0.450347i	$-0.148700\pi$
$132$	−34.8909	+	34.8909i	−0.264325	+	0.264325i
$133$	−1.57533	−	1.59163i	−0.0118446	−	0.0119671i
$134$			96.6959i			0.721611i
$135$	−17.3986	−	19.2947i	−0.128879	−	0.142924i
$136$	35.0661	+	60.7362i	0.257839	+	0.446590i
$137$	199.663	+	53.4994i	1.45739	+	0.390507i	0.898588	−	0.438794i	$-0.144594\pi$
$137$	199.663	+	53.4994i	1.45739	+	0.390507i	0.558803	+	0.829300i	$0.311261\pi$
$138$	−33.3591	+	8.93855i	−0.241733	+	0.0647721i
$139$		−	217.562i		−	1.56519i	−0.622529	−	0.782597i	$-0.713895\pi$
$139$		−	217.562i		−	1.56519i	0.622529	−	0.782597i	$-0.286105\pi$
$140$	−14.2515	−	68.5339i	−0.101796	−	0.489528i
$141$	146.608			1.03978
$142$	7.44367	+	27.7802i	0.0524202	+	0.195635i
$143$	14.3692	−	53.6265i	0.100484	−	0.375010i
$144$	−10.3923	+	6.00000i	−0.0721688	+	0.0416667i
$145$	121.160	+	6.26079i	0.835583	+	0.0431779i
$146$	82.8485			0.567456
$147$	60.6269	−	59.3918i	0.412428	−	0.404026i
$148$	−3.34043	−	3.34043i	−0.0225705	−	0.0225705i
$149$	−202.765	−	117.066i	−1.36084	−	0.785680i	−0.371102	−	0.928592i	$-0.621020\pi$
$149$	−202.765	−	117.066i	−1.36084	−	0.785680i	−0.989735	+	0.142913i	$0.954353\pi$
$150$	60.9111	+	6.31189i	0.406074	+	0.0420793i
$151$	−113.664	−	196.871i	−0.752739	−	1.30378i	−0.946490	−	0.322732i	$-0.895399\pi$
$151$	−113.664	−	196.871i	−0.752739	−	1.30378i	0.193751	−	0.981051i	$-0.437935\pi$
$152$	−0.234194	−	0.874025i	−0.00154075	−	0.00575016i
$153$	−52.5991	−	52.5991i	−0.343785	−	0.343785i
$154$	122.479	−	69.8757i	0.795320	−	0.453738i
$155$	67.8705	−	34.6443i	0.437874	−	0.223512i
$156$	6.75087	−	11.6928i	0.0432748	−	0.0749541i
$157$	104.273	+	27.9400i	0.664162	+	0.177962i	0.575124	−	0.818066i	$-0.304954\pi$
$157$	104.273	+	27.9400i	0.664162	+	0.177962i	0.0890386	+	0.996028i	$0.471621\pi$
$158$	−18.8460	+	70.3341i	−0.119278	+	0.445153i
$159$	112.770	+	65.1078i	0.709246	+	0.409483i
$160$	8.72063	−	26.9063i	0.0545039	−	0.168165i
$161$	98.6933	+	0.507807i	0.613002	+	0.00315408i
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−291.300	+	78.0535i	−1.78711	+	0.478856i	−0.991850	−	0.127407i	$-0.959334\pi$
$163$	−291.300	+	78.0535i	−1.78711	+	0.478856i	−0.795264	+	0.606263i	$0.792668\pi$
$164$	−50.3670	+	29.0794i	−0.307116	+	0.177313i
$165$	25.7358	+	120.643i	0.155975	+	0.731172i
$166$	−82.8590	+	143.516i	−0.499151	+	0.864554i
$167$	55.7819	−	55.7819i	0.334023	−	0.334023i	−0.520089	−	0.854112i	$-0.674101\pi$
$167$	55.7819	−	55.7819i	0.334023	−	0.334023i	0.854112	+	0.520089i	$0.174101\pi$
$168$	33.1696	−	8.70509i	0.197438	−	0.0518160i
$169$		−	153.809i		−	0.910110i
$170$	175.097	+	9.04795i	1.02998	+	0.0532232i
$171$	0.479873	+	0.831164i	0.00280627	+	0.00486061i
$172$	32.0768	+	8.59496i	0.186493	+	0.0499707i
$173$	202.465	−	54.2505i	1.17032	−	0.313587i	0.379240	−	0.925298i	$-0.376185\pi$
$173$	202.465	−	54.2505i	1.17032	−	0.313587i	0.791081	+	0.611712i	$0.209519\pi$
$174$			59.4350i			0.341581i
$175$	−163.145	−	63.3155i	−0.932255	−	0.361803i
$176$	56.9766			0.323731
$177$	16.4172	+	61.2699i	0.0927526	+	0.346158i
$178$	−40.4168	+	150.838i	−0.227061	+	0.847403i
$179$	−130.023	+	75.0691i	−0.726388	+	0.419380i	−0.817099	−	0.576497i	$-0.804419\pi$
$179$	−130.023	+	75.0691i	−0.726388	+	0.419380i	0.0907112	+	0.995877i	$0.471086\pi$
$180$	−1.54815	+	29.9600i	−0.00860085	+	0.166445i
$181$	147.164			0.813063			0.406532	−	0.913637i	$-0.366738\pi$
$181$	147.164			0.813063			0.406532	+	0.913637i	$0.366738\pi$
$182$	−27.4233	+	27.1426i	−0.150678	+	0.149135i
$183$	−132.814	−	132.814i	−0.725757	−	0.725757i
$184$	34.5359	+	19.9393i	0.187695	+	0.108366i
$185$	−11.5503	+	2.46393i	−0.0624342	+	0.0133186i
$186$	18.6654	+	32.3295i	0.100352	+	0.173814i
$187$	91.4124	+	341.156i	0.488836	+	1.82436i
$188$	−119.705	−	119.705i	−0.636730	−	0.636730i
$189$	−31.5932	+	18.0242i	−0.167160	+	0.0953662i
$190$	−2.15194	−	0.697466i	−0.0113260	−	0.00367087i
$191$	−112.126	+	194.209i	−0.587049	+	1.01680i	0.407567	+	0.913175i	$0.366377\pi$
$191$	−112.126	+	194.209i	−0.587049	+	1.01680i	−0.994617	+	0.103624i	$0.966956\pi$
$192$	13.3843	+	3.58630i	0.0697097	+	0.0186787i
$193$	−4.23272	+	15.7967i	−0.0219312	+	0.0818483i	−0.976024	−	0.217663i	$-0.930157\pi$
$193$	−4.23272	+	15.7967i	−0.0219312	+	0.0818483i	0.954093	+	0.299511i	$0.0968235\pi$
$194$	−118.287	−	68.2928i	−0.609725	−	0.352025i
$195$	−15.3462	−	30.0641i	−0.0786982	−	0.154175i
$196$	−97.9948	−	1.00845i	−0.499974	−	0.00514517i
$197$	−199.522	+	199.522i	−1.01280	+	1.01280i	−0.0128826	+	0.999917i	$0.504101\pi$
$197$	−199.522	+	199.522i	−1.01280	+	1.01280i	−0.999917	+	0.0128826i	$0.995899\pi$
$198$	−58.3736	+	15.6412i	−0.294816	+	0.0789957i
$199$	−37.1474	+	21.4471i	−0.186670	+	0.107774i	−0.590423	−	0.807094i	$-0.701039\pi$
$199$	−37.1474	+	21.4471i	−0.186670	+	0.107774i	0.403753	+	0.914868i	$0.367706\pi$
$200$	−44.5801	−	54.8873i	−0.222900	−	0.274437i
$201$	−59.2139	+	102.561i	−0.294596	+	0.510256i
$202$	99.9332	−	99.9332i	0.494719	−	0.494719i
$203$	44.8039	−	163.834i	0.220709	−	0.807063i
$204$			85.8940i			0.421049i
$205$	−7.50323	+	145.203i	−0.0366011	+	0.708309i
$206$	−79.1876	−	137.157i	−0.384406	−	0.665811i
$207$	−40.8564	−	10.9474i	−0.197374	−	0.0528862i
$208$	−15.0592	+	4.03511i	−0.0724001	+	0.0193996i
$209$		−	4.55692i		−	0.0218034i
$210$	26.8523	−	81.4184i	0.127868	−	0.387707i
$211$	107.346			0.508747			0.254373	−	0.967106i	$-0.418131\pi$
$211$	107.346			0.508747			0.254373	+	0.967106i	$0.418131\pi$
$212$	−38.9161	−	145.237i	−0.183566	−	0.685079i
$213$	−9.11660	+	34.0236i	−0.0428009	+	0.159735i
$214$	−136.393	+	78.7467i	−0.637352	+	0.367975i
$215$	61.6559	−	55.5970i	0.286772	−	0.258591i
$216$	−14.6969			−0.0680414
$217$	−27.0807	−	103.187i	−0.124796	−	0.475518i
$218$	76.0871	+	76.0871i	0.349023	+	0.349023i
$219$	87.8741	+	50.7342i	0.401252	+	0.231663i
$220$	77.4917	−	119.518i	0.352235	−	0.543265i
$221$	−48.3216	−	83.6955i	−0.218650	−	0.378712i
$222$	−1.49747	−	5.58865i	−0.00674538	−	0.0251741i
$223$	152.586	+	152.586i	0.684241	+	0.684241i	0.960953	−	0.276712i	$-0.0892448\pi$
$223$	152.586	+	152.586i	0.684241	+	0.684241i	−0.276712	+	0.960953i	$0.589245\pi$
$224$	−34.1905	−	19.9752i	−0.152636	−	0.0891749i
$225$	60.7407	+	43.9950i	0.269959	+	0.195533i
$226$	−76.5867	+	132.652i	−0.338879	+	0.586956i
$227$	−311.447	−	83.4520i	−1.37201	−	0.367630i	−0.503800	−	0.863820i	$-0.668065\pi$
$227$	−311.447	−	83.4520i	−1.37201	−	0.367630i	−0.868214	+	0.496190i	$0.834732\pi$
$228$	0.286828	−	1.07046i	0.00125802	−	0.00469499i
$229$	80.3357	+	46.3818i	0.350811	+	0.202541i	0.665042	−	0.746806i	$-0.268413\pi$
$229$	80.3357	+	46.3818i	0.350811	+	0.202541i	−0.314232	+	0.949346i	$0.601747\pi$
$230$	88.7971	−	45.3263i	0.386075	−	0.197071i
$231$	172.699	+	0.888587i	0.747614	+	0.00384670i
$232$	48.5285	−	48.5285i	0.209174	−	0.209174i
$233$	367.086	−	98.3603i	1.57547	−	0.422147i	0.637953	−	0.770075i	$-0.279781\pi$
$233$	367.086	−	98.3603i	1.57547	−	0.422147i	0.937521	+	0.347928i	$0.113115\pi$
$234$	14.3208	−	8.26809i	0.0611998	−	0.0353337i
$235$	−413.909	+	88.2957i	−1.76131	+	0.375726i
$236$	36.6220	−	63.4312i	0.155178	−	0.268776i
$237$	−63.0599	+	63.0599i	−0.266075	+	0.266075i
$238$	64.7495	−	236.769i	0.272057	−	0.994826i
$239$			196.297i			0.821327i	0.911787	+	0.410664i	$0.134703\pi$
$239$			196.297i			0.821327i	−0.911787	+	0.410664i	$0.865297\pi$
$240$	25.7263	−	23.1982i	0.107193	−	0.0966592i
$241$	−188.179	−	325.936i	−0.780826	−	1.35243i	−0.931461	−	0.363841i	$-0.881465\pi$
$241$	−188.179	−	325.936i	−0.780826	−	1.35243i	0.150635	−	0.988589i	$-0.451868\pi$
$242$	111.872	+	29.9759i	0.462279	+	0.123867i
$243$	15.0573	−	4.03459i	0.0619642	−	0.0166032i
$244$			216.884i			0.888867i
$245$	−135.395	+	204.189i	−0.552631	+	0.833426i
$246$	−71.2297			−0.289552
$247$	0.322723	+	1.20442i	0.00130657	+	0.00487619i
$248$	11.1566	−	41.6372i	0.0449865	−	0.167892i
$249$	−175.771	+	101.481i	−0.705906	+	0.407555i
$250$	−175.767	+	18.8641i	−0.703069	+	0.0754566i
$251$	−193.073			−0.769215			−0.384607	−	0.923080i	$-0.625663\pi$
$251$	−193.073			−0.769215			−0.384607	+	0.923080i	$0.625663\pi$
$252$	40.5124	+	11.0790i	0.160764	+	0.0439643i
$253$	142.009	+	142.009i	0.561301	+	0.561301i
$254$	147.870	+	85.3727i	0.582164	+	0.336113i
$255$	180.178	+	116.821i	0.706579	+	0.458123i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−55.8673	−	208.500i	−0.217383	−	0.811283i	−0.985314	−	0.170751i	$-0.945381\pi$
$257$	−55.8673	−	208.500i	−0.217383	−	0.811283i	0.767932	−	0.640532i	$-0.221286\pi$
$258$	28.7593	+	28.7593i	0.111470	+	0.111470i
$259$	−0.0850728	+	16.5341i	−0.000328466	+	0.0638381i
$260$	−12.0172	+	37.0773i	−0.0462198	+	0.142605i
$261$	−36.3964	+	63.0403i	−0.139450	+	0.241534i
$262$	−299.360	−	80.2133i	−1.14260	−	0.306158i
$263$	116.022	−	433.000i	0.441148	−	1.64639i	−0.284761	−	0.958599i	$-0.591914\pi$
$263$	116.022	−	433.000i	0.441148	−	1.64639i	0.725910	−	0.687790i	$-0.241419\pi$
$264$	60.4328	+	34.8909i	0.228912	+	0.132162i
$265$	−357.587	−	115.898i	−1.34939	−	0.437351i
$266$	−1.59759	+	2.73452i	−0.00600598	+	0.0102801i
$267$	−135.237	+	135.237i	−0.506507	+	0.506507i
$268$	132.089	−	35.3931i	0.492869	−	0.132064i
$269$	−93.0558	+	53.7258i	−0.345932	+	0.199724i	−0.662892	−	0.748715i	$-0.730671\pi$
$269$	−93.0558	+	53.7258i	−0.345932	+	0.199724i	0.316960	+	0.948439i	$0.397338\pi$
$270$	−19.9888	+	30.8294i	−0.0740324	+	0.114183i
$271$	−98.0395	+	169.809i	−0.361769	+	0.626603i	−0.988252	−	0.152833i	$-0.951160\pi$
$271$	−98.0395	+	169.809i	−0.361769	+	0.626603i	0.626483	+	0.779435i	$0.284494\pi$
$272$	70.1322	−	70.1322i	0.257839	−	0.257839i
$273$	−45.7082	+	11.9957i	−0.167429	+	0.0439405i
$274$		−	292.326i		−	1.06688i
$275$	−145.316	−	325.104i	−0.528423	−	1.18220i
$276$	24.4206	+	42.2977i	0.0884803	+	0.153252i
$277$	359.876	+	96.4285i	1.29919	+	0.348117i	0.841145	−	0.540810i	$-0.181882\pi$
$277$	359.876	+	96.4285i	1.29919	+	0.348117i	0.458048	+	0.888928i	$0.348549\pi$
$278$	−297.195	+	79.6332i	−1.06905	+	0.286450i
$279$			45.7208i			0.163874i
$280$	−88.4026	+	44.5530i	−0.315724	+	0.159118i
$281$	−256.628			−0.913268			−0.456634	−	0.889655i	$-0.650945\pi$
$281$	−256.628			−0.913268			−0.456634	+	0.889655i	$0.650945\pi$
$282$	−53.6624	−	200.271i	−0.190292	−	0.710180i
$283$	−107.562	+	401.426i	−0.380076	+	1.41846i	0.465707	+	0.884939i	$0.345800\pi$
$283$	−107.562	+	401.426i	−0.380076	+	1.41846i	−0.845784	+	0.533526i	$0.820867\pi$
$284$	35.2238	−	20.3365i	0.124028	−	0.0716074i
$285$	−1.85536	−	2.05756i	−0.00651005	−	0.00721951i
$286$	−78.5146			−0.274526
$287$	196.346	+	53.6951i	0.684133	+	0.187091i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	282.164	+	162.908i	0.976347	+	0.563694i
$290$	−35.7951	−	167.799i	−0.123431	−	0.578616i
$291$	−83.6413	−	144.871i	−0.287427	−	0.497838i
$292$	−30.3247	−	113.173i	−0.103852	−	0.387579i
$293$	236.224	+	236.224i	0.806226	+	0.806226i	0.984060	−	0.177834i	$-0.0569091\pi$
$293$	236.224	+	236.224i	0.806226	+	0.806226i	−0.177834	+	0.984060i	$0.556909\pi$
$294$	−103.322	−	61.0789i	−0.351434	−	0.207752i
$295$	−83.2497	−	163.092i	−0.282202	−	0.552853i
$296$	−3.34043	+	5.78580i	−0.0112852	+	0.0195466i
$297$	−71.4928	−	19.1564i	−0.240716	−	0.0644998i
$298$	−85.6984	+	319.831i	−0.287579	+	1.07326i
$299$	−47.5910	−	27.4767i	−0.159167	−	0.0918952i
$300$	−13.6728	−	85.5164i	−0.0455760	−	0.285055i
$301$	−57.5960	−	100.955i	−0.191349	−	0.335399i
$302$	−227.327	+	227.327i	−0.752739	+	0.752739i
$303$	167.192	−	44.7988i	0.551787	−	0.147851i
$304$	−1.10822	+	0.639831i	−0.00364546	+	0.00210471i
$305$	454.951	+	294.975i	1.49164	+	0.967132i
$306$	−52.5991	+	91.1044i	−0.171893	+	0.297727i
$307$	−106.527	+	106.527i	−0.346995	+	0.346995i	−0.858989	−	0.511994i	$-0.828907\pi$
$307$	−106.527	+	106.527i	−0.346995	+	0.346995i	0.511994	+	0.858989i	$0.328907\pi$
$308$	−140.282	−	141.733i	−0.455462	−	0.460174i
$309$		−	193.969i		−	0.627732i
$310$	−72.1674	−	80.0322i	−0.232798	−	0.258168i
$311$	−102.511	−	177.554i	−0.329617	−	0.570914i	0.652819	−	0.757514i	$-0.273586\pi$
$311$	−102.511	−	177.554i	−0.329617	−	0.570914i	−0.982436	+	0.186601i	$0.940253\pi$
$312$	−18.4437	−	4.94198i	−0.0591145	−	0.0158397i
$313$	233.347	−	62.5250i	0.745516	−	0.199760i	0.133988	−	0.990983i	$-0.457222\pi$
$313$	233.347	−	62.5250i	0.745516	−	0.199760i	0.611528	+	0.791223i	$0.290555\pi$
$314$		−	152.667i		−	0.486201i
$315$	78.3395	−	69.9137i	0.248697	−	0.221948i
$316$	102.976			0.325874
$317$	−60.3297	−	225.154i	−0.190315	−	0.710263i	−0.993430	−	0.114440i	$-0.963493\pi$
$317$	−60.3297	−	225.154i	−0.190315	−	0.710263i	0.803116	−	0.595823i	$-0.203174\pi$
$318$	47.6623	−	177.878i	0.149881	−	0.559365i
$319$	299.319	−	172.812i	0.938303	−	0.541729i
$320$	−39.9467	−	2.06420i	−0.124833	−	0.00645064i
$321$	−192.889			−0.600901
$322$	−35.4306	−	135.003i	−0.110033	−	0.419265i
$323$	−5.60909	−	5.60909i	−0.0173656	−	0.0173656i
$324$	−15.5885	−	9.00000i	−0.0481125	−	0.0277778i
$325$	61.4320	+	75.6356i	0.189021	+	0.232725i
$326$	213.246	+	369.353i	0.654129	+	1.13299i
$327$	34.1089	+	127.296i	0.104309	+	0.389285i
$328$	58.1588	+	58.1588i	0.177313	+	0.177313i
$329$	−3.04861	+	592.503i	−0.00926628	+	1.80092i
$330$	155.382	−	79.3144i	0.470855	−	0.240347i
$331$	−182.812	+	316.640i	−0.552303	+	0.956617i	0.445805	+	0.895130i	$0.352917\pi$
$331$	−182.812	+	316.640i	−0.552303	+	0.956617i	−0.998108	+	0.0614865i	$0.980416\pi$
$332$	226.375	+	60.6570i	0.681852	+	0.182702i
$333$	1.83402	−	6.84467i	0.00550758	−	0.0205546i
$334$	−96.6171	−	55.7819i	−0.289273	−	0.167012i
$335$	105.406	−	325.216i	0.314645	−	0.970795i
$336$	−24.0323	−	42.1242i	−0.0715247	−	0.125370i
$337$	392.860	−	392.860i	1.16576	−	1.16576i	0.182562	−	0.983194i	$-0.441561\pi$
$337$	392.860	−	392.860i	1.16576	−	1.16576i	0.983194	−	0.182562i	$-0.0584389\pi$
$338$	−210.106	+	56.2979i	−0.621617	+	0.166562i
$339$	−162.465	+	93.7992i	−0.479248	+	0.276694i
$340$	−51.7302	−	242.498i	−0.152148	−	0.713231i
$341$	108.542	−	188.001i	0.318306	−	0.551322i
$342$	0.959746	−	0.959746i	0.00280627	−	0.00280627i
$343$	238.765	+	246.252i	0.696108	+	0.717937i
$344$		−	46.9637i		−	0.136522i
$345$	121.940	+	6.30113i	0.353450	+	0.0182642i
$346$	−148.215	−	256.716i	−0.428367	−	0.741954i
$347$	274.406	+	73.5268i	0.790795	+	0.211893i	0.631539	−	0.775344i	$-0.282424\pi$
$347$	274.406	+	73.5268i	0.790795	+	0.211893i	0.159256	+	0.987237i	$0.449090\pi$
$348$	81.1897	−	21.7547i	0.233304	−	0.0625136i
$349$		−	345.311i		−	0.989429i	−0.869055	−	0.494715i	$-0.835273\pi$
$349$		−	345.311i		−	0.989429i	0.869055	−	0.494715i	$-0.164727\pi$
$350$	−26.7755	+	246.035i	−0.0765013	+	0.702956i
$351$	20.2526			0.0576997
$352$	−20.8549	−	77.8315i	−0.0592468	−	0.221112i
$353$	−152.948	+	570.810i	−0.433281	+	1.61703i	0.311867	+	0.950126i	$0.399046\pi$
$353$	−152.948	+	570.810i	−0.433281	+	1.61703i	−0.745148	+	0.666900i	$0.767621\pi$
$354$	77.6871	−	44.8527i	0.219455	−	0.126702i
$355$	5.24733	−	101.547i	0.0147812	−	0.286048i
$356$	220.842			0.620342
$357$	213.668	−	211.480i	0.598509	−	0.592382i
$358$	150.138	+	150.138i	0.419380	+	0.419380i
$359$	358.501	+	206.981i	0.998611	+	0.576549i	0.907837	−	0.419323i	$-0.137733\pi$
$359$	358.501	+	206.981i	0.998611	+	0.576549i	0.0907742	+	0.995871i	$0.471066\pi$
$360$	41.4928	−	8.85131i	0.115258	−	0.0245870i
$361$	−180.449	−	312.547i	−0.499858	−	0.865780i
$362$	−53.8659	−	201.030i	−0.148801	−	0.555332i
$363$	100.301	+	100.301i	0.276312	+	0.276312i
$364$	47.1151	+	27.5261i	0.129437	+	0.0756211i
$365$	−278.644	−	90.3115i	−0.763408	−	0.247429i
$366$	−132.814	+	230.040i	−0.362879	+	0.628524i
$367$	411.646	+	110.300i	1.12165	+	0.300545i	0.771551	−	0.636167i	$-0.219481\pi$
$367$	411.646	+	110.300i	1.12165	+	0.300545i	0.350099	+	0.936713i	$0.386148\pi$
$368$	14.5966	−	54.4752i	0.0396647	−	0.148030i
$369$	−75.5505	−	43.6191i	−0.204744	−	0.118209i
$370$	7.59351	+	14.8762i	0.0205230	+	0.0402059i
$371$	−265.472	+	454.395i	−0.715557	+	1.22478i
$372$	37.3309	−	37.3309i	0.100352	−	0.100352i
$373$	155.797	−	41.7458i	0.417687	−	0.111919i	−0.0438534	−	0.999038i	$-0.513963\pi$
$373$	155.797	−	41.7458i	0.417687	−	0.111919i	0.461541	+	0.887119i	$0.347297\pi$
$374$	432.568	−	249.743i	1.15660	−	0.667763i
$375$	−197.981	−	87.6266i	−0.527950	−	0.233671i
$376$	−119.705	+	207.336i	−0.318365	+	0.551424i
$377$	−66.8730	+	66.8730i	−0.177382	+	0.177382i
$378$	36.1854	+	36.5597i	0.0957287	+	0.0967189i
$379$			230.272i			0.607577i	0.952740	+	0.303788i	$0.0982516\pi$
$379$			230.272i			0.607577i	−0.952740	+	0.303788i	$0.901748\pi$
$380$	−0.165093	+	3.19489i	−0.000434454	+	0.00840761i
$381$	104.560	+	181.103i	0.274435	+	0.475335i
$382$	306.335	+	82.0822i	0.801924	+	0.214875i
$383$	−140.358	+	37.6089i	−0.366471	+	0.0981956i	−0.437355	−	0.899289i	$-0.644085\pi$
$383$	−140.358	+	37.6089i	−0.366471	+	0.0981956i	0.0708839	+	0.997485i	$0.477418\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−488.103	+	101.500i	−1.26780	+	0.263637i
$386$	23.1280			0.0599171
$387$	12.8924	+	48.1152i	0.0333138	+	0.124329i
$388$	−49.9938	+	186.579i	−0.128850	+	0.480875i
$389$	414.884	−	239.533i	1.06654	−	0.615767i	0.139306	−	0.990249i	$-0.455513\pi$
$389$	414.884	−	239.533i	1.06654	−	0.615767i	0.927234	+	0.374483i	$0.122180\pi$
$390$	−35.4513	+	31.9675i	−0.0909007	+	0.0819679i
$391$	349.597			0.894110
$392$	34.4910	+	134.233i	0.0879873	+	0.342430i
$393$	−268.399	−	268.399i	−0.682949	−	0.682949i
$394$	345.581	+	199.522i	0.877110	+	0.506400i
$395$	140.054	−	216.011i	0.354568	−	0.546862i
$396$	42.7324	+	74.0147i	0.107910	+	0.186906i
$397$	−2.28439	−	8.52545i	−0.00575412	−	0.0214747i	0.962989	−	0.269540i	$-0.0868718\pi$
$397$	−2.28439	−	8.52545i	−0.00575412	−	0.0214747i	−0.968743	+	0.248066i	$0.920205\pi$
$398$	42.8941	+	42.8941i	0.107774	+	0.107774i
$399$	−3.36904	+	1.92207i	−0.00844372	+	0.00481723i
$400$	−58.6600	+	80.9876i	−0.146650	+	0.202469i
$401$	−396.991	+	687.608i	−0.990002	+	1.71473i	−0.372847	+	0.927893i	$0.621618\pi$
$401$	−396.991	+	687.608i	−0.990002	+	1.71473i	−0.617155	+	0.786841i	$0.711715\pi$
$402$	161.775	+	43.3476i	0.402426	+	0.107830i
$403$	−15.3740	+	57.3766i	−0.0381489	+	0.142374i
$404$	−173.089	−	99.9332i	−0.428439	−	0.247359i
$405$	−40.0803	+	20.4589i	−0.0989638	+	0.0505158i
$406$	−240.201	−	1.23590i	−0.591627	−	0.00304410i
$407$	−23.7908	+	23.7908i	−0.0584540	+	0.0584540i
$408$	117.333	−	31.4394i	0.287582	−	0.0770573i
$409$	521.846	−	301.288i	1.27591	−	0.736645i	0.299814	−	0.953998i	$-0.403075\pi$
$409$	521.846	−	301.288i	1.27591	−	0.736645i	0.976093	+	0.217352i	$0.0697421\pi$
$410$	201.098	−	42.8985i	0.490482	−	0.104630i
$411$	179.013	−	310.059i	0.435554	−	0.754401i
$412$	−158.375	+	158.375i	−0.384406	+	0.384406i
$413$	−247.957	+	65.0744i	−0.600381	+	0.157565i
$414$			59.8179i			0.144488i
$415$	435.123	−	392.363i	1.04849	−	0.945454i
$416$	11.0241	+	19.0943i	0.0265003	+	0.0458998i
$417$	−363.988	−	97.5303i	−0.872873	−	0.233886i
$418$	−6.22487	+	1.66795i	−0.0148920	+	0.00399031i
$419$			341.414i			0.814831i	0.913243	+	0.407415i	$0.133570\pi$
$419$			341.414i			0.814831i	−0.913243	+	0.407415i	$0.866430\pi$
$420$	−121.048	−	6.87970i	−0.288210	−	0.0163802i
$421$	94.3393			0.224084			0.112042	−	0.993703i	$-0.464261\pi$
$421$	94.3393			0.224084			0.112042	+	0.993703i	$0.464261\pi$
$422$	−39.2912	−	146.637i	−0.0931071	−	0.347481i
$423$	65.7227	−	245.281i	0.155373	−	0.579859i
$424$	−184.153	+	106.321i	−0.434323	+	0.250756i
$425$	−579.039	−	221.300i	−1.36244	−	0.520706i
$426$	49.8140			0.116934
$427$	539.514	−	533.991i	1.26350	−	1.25056i
$428$	157.493	+	157.493i	0.367975	+	0.367975i
$429$	−83.2773	−	48.0802i	−0.194120	−	0.112075i
$430$	−98.5145	−	63.8736i	−0.229103	−	0.148543i
$431$	149.099	+	258.247i	0.345937	+	0.599181i	0.985524	−	0.169538i	$-0.0542276\pi$
$431$	149.099	+	258.247i	0.345937	+	0.599181i	−0.639586	+	0.768719i	$0.720894\pi$
$432$	5.37945	+	20.0764i	0.0124524	+	0.0464731i
$433$	466.639	+	466.639i	1.07769	+	1.07769i	0.996716	+	0.0809720i	$0.0258024\pi$
$433$	466.639	+	466.639i	1.07769	+	1.07769i	0.0809720	+	0.996716i	$0.474198\pi$
$434$	−131.044	+	74.7622i	−0.301946	+	0.172263i
$435$	64.7889	−	199.897i	0.148940	−	0.459534i
$436$	76.0871	−	131.787i	0.174512	−	0.302263i
$437$	−4.35686	−	1.16742i	−0.00996994	−	0.00267144i
$438$	37.1400	−	138.608i	0.0847945	−	0.316457i
$439$	−66.2436	−	38.2457i	−0.150897	−	0.0871201i	0.422651	−	0.906293i	$-0.361100\pi$
$439$	−66.2436	−	38.2457i	−0.150897	−	0.0871201i	−0.573547	+	0.819173i	$0.694433\pi$
$440$	−191.629	−	62.1090i	−0.435520	−	0.141157i
$441$	−72.1861	−	128.055i	−0.163687	−	0.290375i
$442$	−96.6432	+	96.6432i	−0.218650	+	0.218650i
$443$	−204.019	+	54.6666i	−0.460538	+	0.123401i	−0.481626	−	0.876377i	$-0.659954\pi$
$443$	−204.019	+	54.6666i	−0.460538	+	0.123401i	0.0210878	+	0.999778i	$0.493287\pi$
$444$	−7.08612	+	4.09118i	−0.0159597	+	0.00921436i
$445$	300.359	−	463.254i	0.674963	−	1.04102i
$446$	152.586	−	264.286i	0.342120	−	0.592570i
$447$	−286.753	+	286.753i	−0.641505	+	0.641505i
$448$	−14.7720	+	54.0166i	−0.0329732	+	0.120573i
$449$		−	400.930i		−	0.892940i	−0.894799	−	0.446470i	$-0.852681\pi$
$449$		−	400.930i		−	0.892940i	0.894799	−	0.446470i	$-0.147319\pi$
$450$	37.8657	−	99.0767i	0.0841460	−	0.220170i
$451$	207.106	+	358.718i	0.459214	+	0.795383i
$452$	209.239	+	56.0654i	0.462918	+	0.124038i
$453$	−380.326	+	101.908i	−0.839572	+	0.224963i
$454$			455.990i			1.00438i
$455$	121.820	−	61.3948i	0.267737	−	0.134934i
$456$	−1.56726			−0.00343697
$457$	−189.476	−	707.134i	−0.414608	−	1.54734i	−0.785619	−	0.618711i	$-0.787655\pi$
$457$	−189.476	−	707.134i	−0.414608	−	1.54734i	0.371011	−	0.928629i	$-0.379011\pi$
$458$	33.9538	−	126.717i	0.0741350	−	0.276676i
$459$	−111.580	+	64.4205i	−0.243093	+	0.140350i
$460$	−94.4189	−	104.709i	−0.205258	−	0.227627i
$461$	−457.122			−0.991589			−0.495794	−	0.868440i	$-0.665123\pi$
$461$	−457.122			−0.991589			−0.495794	+	0.868440i	$0.665123\pi$
$462$	−61.9983	−	236.236i	−0.134195	−	0.511334i
$463$	−409.466	−	409.466i	−0.884376	−	0.884376i	0.109600	−	0.993976i	$-0.465043\pi$
$463$	−409.466	−	409.466i	−0.884376	−	0.884376i	−0.993976	+	0.109600i	$0.965043\pi$
$464$	−84.0538	−	48.5285i	−0.181150	−	0.104587i
$465$	−27.5356	−	129.080i	−0.0592163	−	0.277592i
$466$	−268.725	−	465.446i	−0.576664	−	0.998811i
$467$	−37.5596	−	140.174i	−0.0804275	−	0.300159i	0.913982	−	0.405756i	$-0.132992\pi$
$467$	−37.5596	−	140.174i	−0.0804275	−	0.300159i	−0.994409	+	0.105596i	$0.966325\pi$
$468$	−16.5362	−	16.5362i	−0.0353337	−	0.0353337i
$469$	−413.260	−	241.440i	−0.881152	−	0.514796i
$470$	272.115	+	533.092i	0.578969	+	1.13424i
$471$	93.4891	−	161.928i	0.198491	−	0.343796i
$472$	−100.053	−	26.8092i	−0.211977	−	0.0567992i
$473$	61.2139	−	228.453i	0.129416	−	0.482988i
$474$	109.223	+	63.0599i	0.230428	+	0.133038i
$475$	6.47730	+	4.69156i	0.0136364	+	0.00987697i
$476$	−347.132	−	1.78610i	−0.729269	−	0.00375231i
$477$	159.481	−	159.481i	0.334342	−	0.334342i
$478$	268.147	−	71.8498i	0.560977	−	0.150313i
$479$	−128.423	+	74.1449i	−0.268106	+	0.154791i	−0.628027	−	0.778192i	$-0.716137\pi$
$479$	−128.423	+	74.1449i	−0.268106	+	0.154791i	0.359921	+	0.932983i	$0.382804\pi$
$480$	−41.1058	−	26.6517i	−0.0856371	−	0.0555243i
$481$	4.60316	−	7.97291i	0.00956999	−	0.0165757i
$482$	−376.358	+	376.358i	−0.780826	+	0.780826i
$483$	45.0926	−	164.889i	0.0933593	−	0.341386i
$484$		−	163.791i		−	0.338412i
$485$	323.388	+	358.630i	0.666779	+	0.739444i
$486$	−11.0227	−	19.0919i	−0.0226805	−	0.0392837i
$487$	−322.819	−	86.4990i	−0.662872	−	0.177616i	−0.0883300	−	0.996091i	$-0.528153\pi$
$487$	−322.819	−	86.4990i	−0.662872	−	0.177616i	−0.574542	+	0.818475i	$0.694820\pi$
$488$	296.269	−	79.3849i	0.607108	−	0.162674i
$489$			522.344i			1.06819i
$490$	328.486	+	110.214i	0.670379	+	0.224926i
$491$	241.966			0.492801			0.246401	−	0.969168i	$-0.420752\pi$
$491$	241.966			0.492801			0.246401	+	0.969168i	$0.420752\pi$
$492$	26.0719	+	97.3016i	0.0529916	+	0.197767i
$493$	155.717	−	581.143i	0.315855	−	1.17879i
$494$	1.52714	−	0.881696i	0.00309138	−	0.00178481i
$495$	213.377	+	11.0261i	0.431066	+	0.0222749i
$496$	−60.9610			−0.122905
$497$	−137.313	−	37.5513i	−0.276284	−	0.0755559i
$498$	202.962	+	202.962i	0.407555	+	0.407555i
$499$	−578.512	−	334.004i	−1.15934	−	0.669346i	−0.208196	−	0.978087i	$-0.566759\pi$
$499$	−578.512	−	334.004i	−1.15934	−	0.669346i	−0.951146	+	0.308741i	$0.900092\pi$
$500$	90.1042	+	233.198i	0.180208	+	0.466396i
$501$	−68.3186	−	118.331i	−0.136364	−	0.236190i
$502$	70.6696	+	263.742i	0.140776	+	0.525383i
$503$	457.165	+	457.165i	0.908876	+	0.908876i	0.996182	−	0.0873055i	$-0.0278256\pi$
$503$	457.165	+	457.165i	0.908876	+	0.908876i	−0.0873055	+	0.996182i	$0.527826\pi$
$504$	0.305611	−	59.3962i	0.000606372	−	0.117850i
$505$	−445.040	+	227.169i	−0.881267	+	0.449840i
$506$	142.009	−	245.967i	0.280651	−	0.486101i
$507$	−257.327	−	68.9505i	−0.507548	−	0.135997i
$508$	62.4971	−	233.242i	0.123026	−	0.459139i
$509$	−438.332	−	253.071i	−0.861164	−	0.497193i	0.00323811	−	0.999995i	$-0.498969\pi$
$509$	−438.332	−	253.071i	−0.861164	−	0.497193i	−0.864402	+	0.502802i	$0.832303\pi$
$510$	93.6313	−	288.887i	0.183591	−	0.566444i
$511$	−206.864	+	354.079i	−0.404822	+	0.692915i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	1.60569	−	0.430242i	0.00312999	−	0.000838679i
$514$	−264.367	+	152.632i	−0.514333	+	0.296950i
$515$	116.819	+	547.620i	0.226833	+	1.06334i
$516$	28.7593	−	49.8125i	0.0557351	−	0.0965359i
$517$	−852.549	+	852.549i	−1.64903	+	1.64903i
$518$	22.6171	−	5.93568i	0.0436624	−	0.0114588i
$519$		−	363.051i		−	0.699521i
$520$	55.0472	+	2.84450i	0.105860	+	0.00547020i
$521$	63.4901	+	109.968i	0.121862	+	0.211071i	0.920502	−	0.390738i	$-0.127780\pi$
$521$	63.4901	+	109.968i	0.121862	+	0.211071i	−0.798640	+	0.601809i	$0.794447\pi$
$522$	99.4367	+	26.6440i	0.190492	+	0.0510421i
$523$	−372.899	+	99.9181i	−0.713001	+	0.191048i	−0.597046	−	0.802207i	$-0.703659\pi$
$523$	−372.899	+	99.9181i	−0.713001	+	0.191048i	−0.115954	+	0.993255i	$0.536993\pi$
$524$			438.294i			0.836438i
$525$	−179.065	+	244.563i	−0.341075	+	0.465834i
$526$	−633.956			−1.20524
$527$	−97.8050	−	365.013i	−0.185588	−	0.692625i
$528$	25.5419	−	95.3237i	0.0483748	−	0.180537i
$529$	−285.972	+	165.106i	−0.540590	+	0.312110i
$530$	−27.4335	+	530.895i	−0.0517612	+	1.00169i
$531$	109.866			0.206904
$532$	4.32018	+	1.18145i	0.00812064	+	0.00222076i
$533$	−80.1437	−	80.1437i	−0.150363	−	0.150363i
$534$	234.238	+	135.237i	0.438648	+	0.253254i
$535$	544.571	−	116.169i	1.01789	−	0.217138i
$536$	−96.6959	−	167.482i	−0.180403	−	0.312467i
$537$	67.3051	+	251.186i	0.125335	+	0.467758i
$538$	107.452	+	107.452i	0.199724	+	0.199724i
$539$	−7.18227	+	697.926i	−0.0133252	+	1.29485i
$540$	49.4301	+	16.0208i	0.0915372	+	0.0296682i
$541$	−85.0505	+	147.312i	−0.157210	+	0.272295i	−0.933861	−	0.357635i	$-0.883583\pi$
$541$	−85.0505	+	147.312i	−0.157210	+	0.272295i	0.776652	+	0.629930i	$0.216917\pi$
$542$	267.849	+	71.7699i	0.494186	+	0.132417i
$543$	65.9720	−	246.211i	0.121495	−	0.453427i
$544$	−121.472	−	70.1322i	−0.223295	−	0.128919i
$545$	−172.962	−	338.844i	−0.317362	−	0.621732i
$546$	33.1169	+	58.0478i	0.0606536	+	0.106315i
$547$	6.88719	−	6.88719i	0.0125908	−	0.0125908i	−0.700783	−	0.713374i	$-0.747166\pi$
$547$	6.88719	−	6.88719i	0.0125908	−	0.0125908i	0.713374	+	0.700783i	$0.247166\pi$
$548$	−399.325	+	106.999i	−0.728695	+	0.195253i
$549$	−281.740	+	162.663i	−0.513188	+	0.296289i
$550$	−390.912	+	317.502i	−0.710748	+	0.577277i
$551$	−3.88125	+	6.72252i	−0.00704401	+	0.0122006i
$552$	48.8411	−	48.8411i	0.0884803	−	0.0884803i
$553$	−253.539	−	256.161i	−0.458479	−	0.463221i
$554$		−	526.895i		−	0.951075i
$555$	−1.05563	+	20.4286i	−0.00190203	+	0.0368083i
$556$	217.562	+	376.828i	0.391298	+	0.677749i
$557$	−221.839	−	59.4417i	−0.398276	−	0.106718i	0.0541213	−	0.998534i	$-0.482764\pi$
$557$	−221.839	−	59.4417i	−0.398276	−	0.106718i	−0.452397	+	0.891817i	$0.649431\pi$
$558$	62.4558	−	16.7350i	0.111928	−	0.0299910i
$559$			64.7167i			0.115772i
$560$	93.2182	+	104.453i	0.166461	+	0.186523i
$561$	611.743			1.09045
$562$	93.9325	+	350.561i	0.167140	+	0.623774i
$563$	−95.1221	+	355.000i	−0.168956	+	0.630551i	0.828547	+	0.559920i	$0.189168\pi$
$563$	−95.1221	+	355.000i	−0.168956	+	0.630551i	−0.997502	+	0.0706314i	$0.977499\pi$
$564$	−253.933	+	146.608i	−0.450236	+	0.259944i
$565$	402.185	−	362.662i	0.711831	−	0.641880i
$566$	587.728			1.03839
$567$	15.9923	+	60.9364i	0.0282051	+	0.107472i
$568$	−40.6730	−	40.6730i	−0.0716074	−	0.0716074i
$569$	528.553	+	305.160i	0.928916	+	0.536310i	0.886468	−	0.462789i	$-0.153151\pi$
$569$	528.553	+	305.160i	0.928916	+	0.536310i	0.0424473	+	0.999099i	$0.486485\pi$
$570$	−2.13157	+	3.28759i	−0.00373960	+	0.00576771i
$571$	−52.9782	−	91.7610i	−0.0927815	−	0.160702i	0.815899	−	0.578194i	$-0.196242\pi$
$571$	−52.9782	−	91.7610i	−0.0927815	−	0.160702i	−0.908681	+	0.417492i	$0.862909\pi$
$572$	28.7383	+	107.253i	0.0502418	+	0.187505i
$573$	274.653	+	274.653i	0.479324	+	0.479324i
$574$	1.48117	−	287.868i	0.00258043	−	0.501512i
$575$	−348.060	+	55.6496i	−0.605322	+	0.0967819i
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	79.5502	+	21.3154i	0.137869	+	0.0369418i	0.327093	−	0.944992i	$-0.393931\pi$
$577$	79.5502	+	21.3154i	0.137869	+	0.0369418i	−0.189225	+	0.981934i	$0.560597\pi$
$578$	119.257	−	445.072i	0.206326	−	0.770021i
$579$	24.5309	+	14.1629i	0.0423678	+	0.0244610i
$580$	−216.115	+	110.316i	−0.372613	+	0.190199i
$581$	−406.471	−	712.469i	−0.699605	−	1.22628i
$582$	−167.283	+	167.283i	−0.287427	+	0.287427i
$583$	−1034.39	+	277.163i	−1.77425	+	0.475408i
$584$	−143.498	+	82.8485i	−0.245716	+	0.141864i
$585$	−57.1777	+	12.1972i	−0.0977397	+	0.0208500i
$586$	236.224	−	409.153i	0.403113	−	0.698212i
$587$	81.9493	−	81.9493i	0.139607	−	0.139607i	−0.633849	−	0.773456i	$-0.718526\pi$
$587$	81.9493	−	81.9493i	0.139607	−	0.139607i	0.773456	+	0.633849i	$0.218526\pi$
$588$	−45.6170	+	163.496i	−0.0775800	+	0.278055i
$589$			4.87559i			0.00827775i
$590$	−192.316	+	173.417i	−0.325959	+	0.293927i
$591$	244.363	+	423.249i	0.413474	+	0.716157i
$592$	9.12623	+	2.44537i	0.0154159	+	0.00413068i
$593$	390.869	−	104.733i	0.659139	−	0.176616i	0.0862815	−	0.996271i	$-0.472502\pi$
$593$	390.869	−	104.733i	0.659139	−	0.176616i	0.572857	+	0.819655i	$0.305835\pi$
$594$			104.673i			0.176217i
$595$	−475.868	+	725.740i	−0.799778	+	1.21973i
$596$	468.265			0.785680
$597$	19.2289	+	71.7633i	0.0322092	+	0.120206i
$598$	−20.1143	+	75.0677i	−0.0336360	+	0.125531i
$599$	688.462	−	397.484i	1.14935	−	0.663579i	0.200623	−	0.979669i	$-0.435703\pi$
$599$	688.462	−	397.484i	1.14935	−	0.663579i	0.948729	+	0.316090i	$0.102370\pi$
$600$	−111.813	+	49.9786i	−0.186355	+	0.0832976i
$601$	−225.975			−0.375999			−0.187999	−	0.982169i	$-0.560200\pi$
$601$	−225.975			−0.375999			−0.187999	+	0.982169i	$0.560200\pi$
$602$	−116.826	+	115.630i	−0.194063	+	0.192076i
$603$	145.044	+	145.044i	0.240537	+	0.240537i
$604$	393.742	+	227.327i	0.651891	+	0.376370i
$605$	−343.580	−	222.766i	−0.567902	−	0.368209i
$606$	−122.393	−	211.990i	−0.201968	−	0.349819i
$607$	206.256	+	769.756i	0.339795	+	1.26813i	0.898576	+	0.438817i	$0.144602\pi$
$607$	206.256	+	769.756i	0.339795	+	1.26813i	−0.558781	+	0.829315i	$0.688731\pi$
$608$	1.27966	+	1.27966i	0.00210471	+	0.00210471i
$609$	−254.014	−	148.403i	−0.417101	−	0.243683i
$610$	236.420	−	729.443i	0.387574	−	1.19581i
$611$	164.956	−	285.711i	0.269976	−	0.467613i
$612$	143.704	+	38.5052i	0.234810	+	0.0629171i
$613$	75.9279	−	283.367i	0.123863	−	0.462262i	−0.875934	−	0.482431i	$-0.839754\pi$
$613$	75.9279	−	283.367i	0.123863	−	0.462262i	0.999797	+	0.0201690i	$0.00642042\pi$
$614$	184.511	+	106.527i	0.300506	+	0.173497i
$615$	239.566	+	77.6460i	0.389539	+	0.126254i
$616$	−142.265	+	243.507i	−0.230949	+	0.395304i
$617$	−20.6583	+	20.6583i	−0.0334818	+	0.0334818i	−0.723649	−	0.690168i	$-0.757537\pi$
$617$	−20.6583	+	20.6583i	−0.0334818	+	0.0334818i	0.690168	+	0.723649i	$0.257537\pi$
$618$	−264.967	+	70.9977i	−0.428749	+	0.114883i
$619$	61.3713	−	35.4327i	0.0991458	−	0.0572419i	−0.449607	−	0.893226i	$-0.648436\pi$
$619$	61.3713	−	35.4327i	0.0991458	−	0.0572419i	0.548753	+	0.835984i	$0.315103\pi$
$620$	−82.9109	+	127.876i	−0.133727	+	0.206252i
$621$	−36.6309	+	63.4465i	−0.0589869	+	0.102168i
$622$	−205.022	+	205.022i	−0.329617	+	0.329617i
$623$	−543.736	−	549.360i	−0.872771	−	0.881798i
$624$			27.0035i			0.0432748i
$625$	611.720	+	128.155i	0.978752	+	0.205047i
$626$	−170.822	−	295.872i	−0.272878	−	0.472638i
$627$	−7.62387	−	2.04281i	−0.0121593	−	0.00325807i
$628$	−208.547	+	55.8800i	−0.332081	+	0.0889809i
$629$			58.5679i			0.0931128i
$630$	−124.178	−	81.4236i	−0.197108	−	0.129244i
$631$	711.319			1.12729			0.563644	−	0.826017i	$-0.309399\pi$
$631$	711.319			1.12729			0.563644	+	0.826017i	$0.309399\pi$
$632$	−37.6919	−	140.668i	−0.0596392	−	0.222576i
$633$	48.1217	−	179.593i	0.0760216	−	0.283717i
$634$	−285.483	+	164.824i	−0.450289	+	0.259974i
$635$	−404.266	−	448.323i	−0.636640	−	0.706020i
$636$	−260.431			−0.409483
$637$	−47.5291	−	184.974i	−0.0746140	−	0.290384i
$638$	−345.623	−	345.623i	−0.541729	−	0.541729i
$639$	52.8357	+	30.5047i	0.0826851	+	0.0477382i
$640$	11.8018	+	55.3238i	0.0184402	+	0.0864434i
$641$	−75.2839	−	130.395i	−0.117448	−	0.203425i	0.801308	−	0.598252i	$-0.204138\pi$
$641$	−75.2839	−	130.395i	−0.117448	−	0.203425i	−0.918755	+	0.394827i	$0.870805\pi$
$642$	70.6024	+	263.492i	0.109973	+	0.410423i
$643$	−569.798	−	569.798i	−0.886155	−	0.886155i	0.107996	−	0.994151i	$-0.465557\pi$
$643$	−569.798	−	569.798i	−0.886155	−	0.886155i	−0.994151	+	0.107996i	$0.965557\pi$
$644$	−171.450	+	97.8137i	−0.266226	+	0.151885i
$645$	−65.3760	−	128.076i	−0.101358	−	0.198567i
$646$	−5.60909	+	9.71523i	−0.00868280	+	0.0150390i
$647$	−371.507	−	99.5449i	−0.574199	−	0.153856i	−0.0399772	−	0.999201i	$-0.512729\pi$
$647$	−371.507	−	99.5449i	−0.574199	−	0.153856i	−0.534222	+	0.845345i	$0.679395\pi$
$648$	−6.58846	+	24.5885i	−0.0101674	+	0.0379452i
$649$	−451.762	−	260.825i	−0.696089	−	0.401887i
$650$	80.8344	−	111.602i	0.124361	−	0.171696i
$651$	−184.776	−	0.950728i	−0.283834	−	0.00146041i
$652$	426.492	−	426.492i	0.654129	−	0.654129i
$653$	−88.6589	+	23.7561i	−0.135772	+	0.0363799i	−0.326065	−	0.945347i	$-0.605723\pi$
$653$	−88.6589	+	23.7561i	−0.135772	+	0.0363799i	0.190293	+	0.981727i	$0.439056\pi$
$654$	161.405	−	93.1873i	0.246797	−	0.142488i
$655$	919.397	+	596.107i	1.40366	+	0.910087i
$656$	58.1588	−	100.734i	0.0886567	−	0.153558i
$657$	124.273	−	124.273i	0.189152	−	0.189152i
$658$	810.490	−	212.707i	1.23175	−	0.323262i
$659$			478.694i			0.726395i	0.931712	+	0.363197i	$0.118315\pi$
$659$			478.694i			0.726395i	−0.931712	+	0.363197i	$0.881685\pi$
$660$	−165.219	−	183.225i	−0.250332	−	0.277613i
$661$	28.9020	+	50.0598i	0.0437247	+	0.0757334i	0.887060	−	0.461655i	$-0.152744\pi$
$661$	28.9020	+	50.0598i	0.0437247	+	0.0757334i	−0.843335	+	0.537389i	$0.819411\pi$
$662$	499.452	+	133.828i	0.754460	+	0.202157i
$663$	−161.687	+	43.3240i	−0.243872	+	0.0653453i
$664$		−	331.436i		−	0.499151i
$665$	8.35400	−	7.45548i	0.0125624	−	0.0112112i
$666$	−10.0213			−0.0150470
$667$	−88.5438	−	330.450i	−0.132749	−	0.495427i
$668$	−40.8352	+	152.399i	−0.0611305	+	0.228142i
$669$	323.683	−	186.879i	0.483831	−	0.279340i
$670$	−482.835	−	24.9500i	−0.720649	−	0.0372388i
$671$	1544.66			2.30203
$672$	−48.7463	+	48.2473i	−0.0725392	+	0.0717965i
$673$	351.482	+	351.482i	0.522261	+	0.522261i	0.918254	−	0.395993i	$-0.129599\pi$
$673$	351.482	+	351.482i	0.522261	+	0.522261i	−0.395993	+	0.918254i	$0.629599\pi$
$674$	−680.453	−	392.860i	−1.00957	−	0.582878i
$675$	100.834	−	81.8988i	0.149384	−	0.121332i
$676$	153.809	+	266.404i	0.227528	+	0.394089i
$677$	−177.083	−	660.882i	−0.261570	−	0.976192i	−0.964317	−	0.264752i	$-0.914710\pi$
$677$	−177.083	−	660.882i	−0.261570	−	0.976192i	0.702747	−	0.711440i	$-0.251957\pi$
$678$	187.598	+	187.598i	0.276694	+	0.276694i
$679$	587.220	−	335.015i	0.864831	−	0.493395i
$680$	−312.325	+	159.425i	−0.459301	+	0.234449i
$681$	−279.236	+	483.651i	−0.410038	+	0.710207i
$682$	−296.543	−	79.4584i	−0.434814	−	0.116508i
$683$	110.918	−	413.953i	0.162399	−	0.606080i	−0.835959	−	0.548792i	$-0.815088\pi$
$683$	110.918	−	413.953i	0.162399	−	0.606080i	0.998358	−	0.0572882i	$-0.0182454\pi$
$684$	−1.66233	−	0.959746i	−0.00243030	−	0.00140314i
$685$	−318.659	+	983.178i	−0.465195	+	1.43530i
$686$	248.993	−	416.294i	0.362963	−	0.606842i
$687$	113.612	−	113.612i	0.165374	−	0.165374i
$688$	−64.1536	+	17.1899i	−0.0932466	+	0.0249853i
$689$	253.765	−	146.511i	0.368310	−	0.212644i
$690$	−36.0257	−	168.880i	−0.0522112	−	0.244753i
$691$	118.514	−	205.272i	0.171510	−	0.297065i	−0.767438	−	0.641124i	$-0.778469\pi$
$691$	118.514	−	205.272i	0.171510	−	0.297065i	0.938948	+	0.344059i	$0.111802\pi$
$692$	−296.430	+	296.430i	−0.428367	+	0.428367i
$693$	78.9054	−	288.532i	0.113861	−	0.416353i
$694$		−	401.758i		−	0.578902i
$695$	1086.36	+	56.1365i	1.56311	+	0.0807720i
$696$	−59.4350	−	102.944i	−0.0853951	−	0.147909i
$697$	696.469	+	186.618i	0.999238	+	0.267745i
$698$	−471.703	+	126.393i	−0.675793	+	0.181078i
$699$		−	658.240i		−	0.941688i
$700$	345.890	−	53.4790i	0.494129	−	0.0763986i
$701$	179.002			0.255352			0.127676	−	0.991816i	$-0.459248\pi$
$701$	179.002			0.255352			0.127676	+	0.991816i	$0.459248\pi$
$702$	−7.41297	−	27.6656i	−0.0105598	−	0.0394096i
$703$	0.195577	−	0.729905i	0.000278204	−	0.00103827i
$704$	−98.6863	+	56.9766i	−0.140179	+	0.0809326i
$705$	−37.8287	+	732.065i	−0.0536577	+	1.03839i
$706$	835.724			1.18374
$707$	177.573	+	676.619i	0.251165	+	0.957029i
$708$	−89.7053	−	89.7053i	−0.126702	−	0.126702i
$709$	614.815	+	354.963i	0.867158	+	0.500654i	0.866403	−	0.499346i	$-0.166426\pi$
$709$	614.815	+	354.963i	0.867158	+	0.500654i	0.000754991		1.00000i	$0.499760\pi$
$710$	−140.636	+	30.0008i	−0.198079	+	0.0422546i
$711$	77.2322	+	133.770i	0.108625	+	0.188144i
$712$	−80.8337	−	301.675i	−0.113530	−	0.423701i
$713$	−151.940	−	151.940i	−0.213100	−	0.213100i
$714$	−367.095	−	214.468i	−0.514139	−	0.300376i
$715$	264.067	+	85.5871i	0.369325	+	0.119702i
$716$	150.138	−	260.047i	0.209690	−	0.363194i
$717$	328.412	+	87.9976i	0.458036	+	0.122730i
$718$	151.521	−	565.482i	0.211031	−	0.787580i
$719$	281.298	+	162.407i	0.391235	+	0.225880i	0.682695	−	0.730703i	$-0.260808\pi$
$719$	281.298	+	162.407i	0.391235	+	0.225880i	−0.291460	+	0.956583i	$0.594141\pi$
$720$	−27.2785	−	53.4404i	−0.0378869	−	0.0742228i
$721$	783.907	+	4.03344i	1.08725	+	0.00559423i
$722$	−360.898	+	360.898i	−0.499858	+	0.499858i
$723$	−629.660	+	168.717i	−0.870898	+	0.233357i
$724$	−254.896	+	147.164i	−0.352067	+	0.203266i
$725$	−62.5245	+	603.375i	−0.0862407	+	0.832242i
$726$	100.301	−	173.727i	0.138156	−	0.239293i
$727$	32.6420	−	32.6420i	0.0448996	−	0.0448996i	−0.684301	−	0.729200i	$-0.739892\pi$
$727$	32.6420	−	32.6420i	0.0448996	−	0.0448996i	0.729200	+	0.684301i	$0.239892\pi$
$728$	20.3560	−	74.4356i	0.0279616	−	0.102247i
$729$		−	27.0000i		−	0.0370370i
$730$	−21.3770	+	413.691i	−0.0292836	+	0.566700i
$731$	−205.854	−	356.550i	−0.281606	−	0.487757i
$732$	362.853	+	97.2263i	0.495701	+	0.132823i
$733$	263.815	−	70.6890i	0.359911	−	0.0964379i	−0.0743321	−	0.997234i	$-0.523682\pi$
$733$	263.815	−	70.6890i	0.359911	−	0.0964379i	0.434243	+	0.900796i	$0.357016\pi$
$734$		−	602.691i		−	0.821105i
$735$	280.920	+	318.055i	0.382204	+	0.432728i
$736$	−79.7573			−0.108366
$737$	−252.072	−	940.747i	−0.342025	−	1.27645i
$738$	−31.9314	+	119.170i	−0.0432675	+	0.161476i
$739$	−852.048	+	491.930i	−1.15297	+	0.665670i	−0.949610	−	0.313434i	$-0.898521\pi$
$739$	−852.048	+	491.930i	−1.15297	+	0.665670i	−0.203364	+	0.979103i	$0.565187\pi$
$740$	17.5418	−	15.8180i	0.0237052	−	0.0213757i
$741$	2.15971			0.00291458
$742$	717.885	+	196.321i	0.967499	+	0.264584i
$743$	121.603	+	121.603i	0.163664	+	0.163664i	0.784188	−	0.620524i	$-0.213080\pi$
$743$	121.603	+	121.603i	0.163664	+	0.163664i	−0.620524	+	0.784188i	$0.713080\pi$
$744$	−64.6590	−	37.3309i	−0.0869072	−	0.0501759i
$745$	636.870	−	982.267i	0.854859	−	1.31848i
$746$	−114.052	−	197.543i	−0.152884	−	0.264803i
$747$	90.9855	+	339.563i	0.121801	+	0.454568i
$748$	−499.486	−	499.486i	−0.667763	−	0.667763i
$749$	4.01098	−	779.542i	0.00535512	−	1.04078i
$750$	−47.2340	+	302.521i	−0.0629787	+	0.403361i
$751$	340.967	−	590.571i	0.454017	−	0.786380i	−0.544614	−	0.838687i	$-0.683324\pi$
$751$	340.967	−	590.571i	0.454017	−	0.786380i	0.998631	+	0.0523066i	$0.0166573\pi$
$752$	327.041	+	87.6303i	0.434895	+	0.116530i
$753$	−86.5522	+	323.017i	−0.114943	+	0.428974i
$754$	115.827	+	66.8730i	0.153617	+	0.0886909i
$755$	1012.37	−	516.763i	1.34089	−	0.684455i
$756$	36.6967	−	62.8120i	0.0485407	−	0.0830847i
$757$	−734.889	+	734.889i	−0.970792	+	0.970792i	−0.999585	−	0.0287938i	$-0.990833\pi$
$757$	−734.889	+	734.889i	−0.970792	+	0.970792i	0.0287938	+	0.999585i	$0.490833\pi$
$758$	314.557	−	84.2852i	0.414983	−	0.111194i
$759$	301.247	−	173.925i	0.396900	−	0.229150i
$760$	4.42473	−	0.943890i	0.00582201	−	0.00124196i
$761$	−62.7638	+	108.710i	−0.0824755	+	0.142852i	−0.904313	−	0.426871i	$-0.859616\pi$
$761$	−62.7638	+	108.710i	−0.0824755	+	0.142852i	0.821837	+	0.569722i	$0.192949\pi$
$762$	209.119	−	209.119i	0.274435	−	0.274435i
$763$	−515.164	+	135.201i	−0.675182	+	0.177196i
$764$		−	448.506i		−	0.587049i
$765$	276.217	−	249.073i	0.361068	−	0.325586i
$766$	102.749	+	177.967i	0.134138	+	0.232333i
$767$	137.875	+	36.9435i	0.179759	+	0.0481662i
$768$	−26.7685	+	7.17260i	−0.0348548	+	0.00933933i
$769$		−	1052.67i		−	1.36888i	−0.729067	−	0.684442i	$-0.760046\pi$
$769$		−	1052.67i		−	1.36888i	0.729067	−	0.684442i	$-0.239954\pi$
$770$	317.310	+	629.610i	0.412091	+	0.817675i
$771$	−373.871			−0.484917
$772$	−8.46543	−	31.5934i	−0.0109656	−	0.0409241i
$773$	−163.653	+	610.760i	−0.211711	+	0.790116i	0.775588	+	0.631240i	$0.217454\pi$
$773$	−163.653	+	610.760i	−0.211711	+	0.790116i	−0.987299	+	0.158876i	$0.949213\pi$
$774$	61.0077	−	35.2228i	0.0788213	−	0.0455075i
$775$	155.479	+	347.840i	0.200618	+	0.448825i
$776$	273.171			0.352025
$777$	27.6239	+	7.55435i	0.0355520	+	0.00972246i
$778$	−479.067	−	479.067i	−0.615767	−	0.615767i
$779$	−8.05659	−	4.65147i	−0.0103422	−	0.00597108i
$780$	56.6444	+	36.7264i	0.0726211	+	0.0470851i
$781$	−144.838	−	250.867i	−0.185452	−	0.321212i
$782$	−127.961	−	477.558i	−0.163633	−	0.610688i
$783$	89.1525	+	89.1525i	0.113860	+	0.113860i
$784$	170.740	−	96.2481i	0.217781	−	0.122765i
$785$	−166.419	+	513.464i	−0.211999	+	0.654094i
$786$	−268.399	+	464.881i	−0.341475	+	0.591451i
$787$	−1108.94	−	297.140i	−1.40908	−	0.377561i	−0.527480	−	0.849567i	$-0.676863\pi$
$787$	−1108.94	−	297.140i	−1.40908	−	0.377561i	−0.881595	+	0.472007i	$0.843530\pi$
$788$	146.060	−	545.103i	0.185355	−	0.691755i
$789$	−672.412	−	388.217i	−0.852233	−	0.492037i
$790$	−346.339	−	112.252i	−0.438404	−	0.142092i
$791$	−375.702	−	658.536i	−0.474970	−	0.832536i
$792$	85.4649	−	85.4649i	0.107910	−	0.107910i
$793$	−408.262	+	109.394i	−0.514833	+	0.137949i
$794$	−10.8098	+	6.24106i	−0.0136144	+	0.00786028i
$795$	−354.203	+	546.300i	−0.445538	+	0.687169i
$796$	42.8941	−	74.2948i	0.0538871	−	0.0933352i
$797$	−862.362	+	862.362i	−1.08201	+	1.08201i	−0.0856885	+	0.996322i	$0.527309\pi$
$797$	−862.362	+	862.362i	−1.08201	+	1.08201i	−0.996322	+	0.0856885i	$0.972691\pi$
$798$	3.85876	+	3.89867i	0.00483554	+	0.00488555i
$799$			2098.80i			2.62678i
$800$	132.102	+	50.4876i	0.165128	+	0.0631095i
$801$	165.631	+	286.882i	0.206781	+	0.358155i
$802$	1084.60	+	290.618i	1.35237	+	0.362366i
$803$	−806.028	+	215.974i	−1.00377	+	0.268960i
$804$		−	236.855i		−	0.294596i
$805$	−28.0010	+	492.678i	−0.0347839	+	0.612022i
$806$	84.0052			0.104225
$807$	48.1692	+	179.770i	0.0596892	+	0.222763i
$808$	−73.1562	+	273.023i	−0.0905398	+	0.337899i
$809$	16.9629	−	9.79354i	0.0209677	−	0.0121057i	−0.489479	−	0.872015i	$-0.662813\pi$
$809$	16.9629	−	9.79354i	0.0209677	−	0.0121057i	0.510447	+	0.859909i	$0.329480\pi$
$810$	42.6178	+	47.2623i	0.0526146	+	0.0583485i
$811$	785.632			0.968721			0.484360	−	0.874869i	$-0.339052\pi$
$811$	785.632			0.968721			0.484360	+	0.874869i	$0.339052\pi$
$812$	86.2312	+	328.572i	0.106196	+	0.404646i
$813$	240.147	+	240.147i	0.295383	+	0.295383i
$814$	41.2069	+	23.7908i	0.0506227	+	0.0292270i
$815$	−314.585	−	1474.70i	−0.385994	−	1.80944i
$816$	−85.8940	−	148.773i	−0.105262	−	0.182320i
$817$	1.37483	+	5.13093i	0.00168278	+	0.00628021i
$818$	−602.576	−	602.576i	−0.736645	−	0.736645i
$819$	−0.421137	+	81.8488i	−0.000514209	+	0.0999375i
$820$	−132.207	−	259.003i	−0.161228	−	0.315857i
$821$	−689.847	+	1194.85i	−0.840252	+	1.45536i	0.0494290	+	0.998778i	$0.484260\pi$
$821$	−689.847	+	1194.85i	−0.840252	+	1.45536i	−0.889681	+	0.456582i	$0.849073\pi$
$822$	−489.071	−	131.046i	−0.594977	−	0.159424i
$823$	−156.383	+	583.631i	−0.190016	+	0.709151i	0.803484	+	0.595326i	$0.202977\pi$
$823$	−156.383	+	583.631i	−0.190016	+	0.709151i	−0.993501	+	0.113825i	$0.963690\pi$
$824$	274.314	+	158.375i	0.332905	+	0.192203i
$825$	−609.054	+	97.3787i	−0.738247	+	0.118035i
$826$	179.652	+	314.897i	0.217496	+	0.381231i
$827$	337.261	−	337.261i	0.407812	−	0.407812i	−0.473163	−	0.880975i	$-0.656888\pi$
$827$	337.261	−	337.261i	0.407812	−	0.407812i	0.880975	+	0.473163i	$0.156888\pi$
$828$	81.7128	−	21.8949i	0.0986870	−	0.0264431i
$829$	−594.040	+	342.969i	−0.716574	+	0.413714i	−0.813490	−	0.581578i	$-0.802435\pi$
$829$	−594.040	+	342.969i	−0.716574	+	0.413714i	0.0969163	+	0.995293i	$0.469102\pi$
$830$	−695.244	−	450.774i	−0.837644	−	0.543101i
$831$	322.656	−	558.857i	0.388275	−	0.672511i
$832$	22.0482	−	22.0482i	0.0265003	−	0.0265003i
$833$	850.233	+	867.914i	1.02069	+	1.04191i
$834$			532.916i			0.638988i
$835$	264.145	+	292.931i	0.316341	+	0.350816i
$836$	4.55692	+	7.89282i	0.00545086	+	0.00944117i
$837$	76.4924	+	20.4961i	0.0913887	+	0.0244875i
$838$	466.380	−	124.966i	0.556540	−	0.149124i
$839$		−	1160.13i		−	1.38275i	−0.722494	−	0.691377i	$-0.757004\pi$
$839$		−	1160.13i		−	1.38275i	0.722494	−	0.691377i	$-0.242996\pi$
$840$	34.9089	+	167.873i	0.0415582	+	0.199849i
$841$	252.247			0.299937
$842$	−34.5306	−	128.870i	−0.0410102	−	0.153052i
$843$	−115.043	+	429.348i	−0.136469	+	0.509309i
$844$	−185.928	+	107.346i	−0.220294	+	0.127187i
$845$	768.018	+	39.6866i	0.908897	+	0.0469663i
$846$	−359.116			−0.424487
$847$	−407.443	+	403.272i	−0.481043	+	0.476118i
$848$	212.641	+	212.641i	0.250756	+	0.250756i
$849$	623.379	+	359.908i	0.734251	+	0.423920i
$850$	−90.3589	+	871.983i	−0.106305	+	1.02586i
$851$	16.6515	+	28.8412i	0.0195670	+	0.0338910i
$852$	−18.2332	−	68.0472i	−0.0214005	−	0.0798676i
$853$	−62.9769	−	62.9769i	−0.0738299	−	0.0738299i	0.669228	−	0.743057i	$-0.266625\pi$
$853$	−62.9769	−	62.9769i	−0.0738299	−	0.0738299i	−0.743057	+	0.669228i	$0.766625\pi$
$854$	−926.921	−	541.536i	−1.08539	−	0.634117i
$855$	−4.27410	+	2.18171i	−0.00499895	+	0.00255170i
$856$	157.493	−	272.787i	0.183988	−	0.318676i
$857$	−98.2660	−	26.3303i	−0.114663	−	0.0307238i	0.201031	−	0.979585i	$-0.435571\pi$
$857$	−98.2660	−	26.3303i	−0.114663	−	0.0307238i	−0.315694	+	0.948861i	$0.602237\pi$
$858$	−35.1971	+	131.357i	−0.0410223	+	0.153097i
$859$	611.105	+	352.822i	0.711415	+	0.410735i	0.811585	−	0.584235i	$-0.198605\pi$
$859$	611.105	+	352.822i	0.711415	+	0.410735i	−0.100170	+	0.994970i	$0.531939\pi$
$860$	−51.1942	+	157.953i	−0.0595281	+	0.183666i
$861$	177.853	−	304.423i	0.206566	−	0.353569i
$862$	298.198	−	298.198i	0.345937	−	0.345937i
$863$	689.815	−	184.835i	0.799322	−	0.214178i	0.164036	−	0.986454i	$-0.447549\pi$
$863$	689.815	−	184.835i	0.799322	−	0.214178i	0.635286	+	0.772277i	$0.280882\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$	218.650	+	1024.98i	0.252774	+	1.18494i
$866$	466.639	−	808.243i	0.538844	−	0.933306i
$867$	399.041	−	399.041i	0.460254	−	0.460254i
$868$	150.093	+	151.645i	0.172918	+	0.174706i
$869$		−	733.405i		−	0.843964i
$870$	−296.779	−	15.3358i	−0.341125	−	0.0176273i
$871$	133.248	+	230.793i	0.152983	+	0.264975i
$872$	−207.874	−	55.6996i	−0.238387	−	0.0638757i
$873$	−279.869	+	74.9907i	−0.320583	+	0.0859000i
$874$			6.37889i			0.00729850i
$875$	358.251	−	798.299i	0.409430	−	0.912342i
$876$	−202.937			−0.231663
$877$	−254.444	−	949.597i	−0.290130	−	1.08278i	−0.945009	−	0.327045i	$-0.893947\pi$
$877$	−254.444	−	949.597i	−0.290130	−	1.08278i	0.654879	−	0.755733i	$-0.272719\pi$
$878$	−27.9978	+	104.489i	−0.0318882	+	0.119008i
$879$	501.107	−	289.315i	0.570088	−	0.329141i
$880$	−14.7014	+	284.503i	−0.0167062	+	0.323299i
$881$	−453.529			−0.514789			−0.257395	−	0.966306i	$-0.582864\pi$
$881$	−453.529			−0.514789			−0.257395	+	0.966306i	$0.582864\pi$
$882$	−148.505	+	145.480i	−0.168373	+	0.164943i
$883$	53.9427	+	53.9427i	0.0610903	+	0.0610903i	0.736992	−	0.675902i	$-0.236246\pi$
$883$	53.9427	+	53.9427i	0.0610903	+	0.0610903i	−0.675902	+	0.736992i	$0.736246\pi$
$884$	167.391	+	96.6432i	0.189356	+	0.109325i
$885$	−310.177	+	66.1675i	−0.350483	+	0.0747655i
$886$	149.352	+	258.685i	0.168569	+	0.291970i
$887$	399.489	+	1490.91i	0.450382	+	1.68085i	0.701321	+	0.712846i	$0.252594\pi$
$887$	399.489	+	1490.91i	0.450382	+	1.68085i	−0.250939	+	0.968003i	$0.580739\pi$
$888$	8.18235	+	8.18235i	0.00921436	+	0.00921436i
$889$	−734.083	+	418.802i	−0.825740	+	0.471093i
$890$	−742.755	−	240.735i	−0.834556	−	0.270489i
$891$	−64.0987	+	111.022i	−0.0719401	+	0.124604i
$892$	−416.872	−	111.700i	−0.467345	−	0.125225i
$893$	7.00857	−	26.1563i	0.00784834	−	0.0292904i
$894$	496.670	+	286.753i	0.555559	+	0.320752i
$895$	−341.296	−	668.621i	−0.381336	−	0.747063i
$896$	79.1949	+	0.407482i	0.0883872	+	0.000454779i
$897$	−67.3038	+	67.3038i	−0.0750321	+	0.0750321i
$898$	−547.681	+	146.751i	−0.609889	+	0.163419i
$899$	−320.250	+	184.897i	−0.356230	+	0.205669i
$900$	−149.201	−	15.4609i	−0.165779	−	0.0171788i
$901$	−932.063	+	1614.38i	−1.03448	+	1.79176i
$902$	414.211	−	414.211i	0.459214	−	0.459214i
$903$	−194.721	+	51.1030i	−0.215638	+	0.0565924i
$904$		−	306.347i		−	0.338879i
$905$	−37.9722	+	734.842i	−0.0419582	+	0.811980i
$906$	278.418	+	482.234i	0.307305	+	0.532267i
$907$	−1100.41	−	294.855i	−1.21324	−	0.325088i	−0.405210	−	0.914223i	$-0.632802\pi$
$907$	−1100.41	−	294.855i	−1.21324	−	0.325088i	−0.808034	+	0.589136i	$0.799468\pi$
$908$	622.894	−	166.904i	0.686007	−	0.183815i
$909$		−	299.800i		−	0.329813i
$910$	−128.456	−	143.937i	−0.141161	−	0.158173i
$911$	−848.410			−0.931296			−0.465648	−	0.884970i	$-0.654179\pi$
$911$	−848.410			−0.931296			−0.465648	+	0.884970i	$0.654179\pi$
$912$	0.573656	+	2.14091i	0.000629009	+	0.00234749i
$913$	432.004	−	1612.26i	0.473169	−	1.76589i
$914$	−896.610	+	517.658i	−0.980974	+	0.566366i
$915$	697.452	−	628.914i	0.762243	−	0.687337i
$916$	−185.527			−0.202541
$917$	1090.29	−	1079.13i	1.18897	−	1.17680i
$918$	128.841	+	128.841i	0.140350	+	0.140350i
$919$	−73.9472	−	42.6934i	−0.0804649	−	0.0464564i	0.459228	−	0.888319i	$-0.348126\pi$
$919$	−73.9472	−	42.6934i	−0.0804649	−	0.0464564i	−0.539693	+	0.841862i	$0.681460\pi$
$920$	−108.475	+	167.305i	−0.117907	+	0.181853i
$921$	130.469	+	225.979i	0.141660	+	0.245362i
$922$	167.318	+	624.441i	0.181473	+	0.677268i
$923$	56.0480	+	56.0480i	0.0607237	+	0.0607237i
$924$	−300.012	+	171.160i	−0.324688	+	0.185238i
$925$	−9.32297	−	58.3104i	−0.0100789	−	0.0630383i
$926$	−409.466	+	709.216i	−0.442188	+	0.765892i
$927$	−324.517	−	86.9541i	−0.350072	−	0.0938016i
$928$	−35.5253	+	132.582i	−0.0382816	+	0.142869i
$929$	−546.812	−	315.702i	−0.588603	−	0.339830i	0.175942	−	0.984401i	$-0.443703\pi$
$929$	−546.812	−	315.702i	−0.588603	−	0.339830i	−0.764545	+	0.644571i	$0.777036\pi$
$930$	−166.248	+	84.8610i	−0.178761	+	0.0912484i
$931$	−7.69781	−	13.6556i	−0.00826833	−	0.0146677i
$932$	−537.451	+	537.451i	−0.576664	+	0.576664i
$933$	−343.008	+	91.9088i	−0.367640	+	0.0985089i
$934$	−177.734	+	102.615i	−0.190293	+	0.109866i
$935$	−1727.09	+	368.426i	−1.84716	+	0.394038i
$936$	−16.5362	+	28.6415i	−0.0176669	+	0.0305999i
$937$	−481.721	+	481.721i	−0.514110	+	0.514110i	−0.915783	−	0.401673i	$-0.868429\pi$
$937$	−481.721	+	481.721i	−0.514110	+	0.514110i	0.401673	+	0.915783i	$0.368429\pi$
$938$	−178.549	+	652.897i	−0.190350	+	0.696052i
$939$		−	418.426i		−	0.445608i
$940$	628.616	−	566.842i	0.668740	−	0.603023i
$941$	458.205	+	793.634i	0.486934	+	0.843395i	0.999887	−	0.0150221i	$-0.00478185\pi$
$941$	458.205	+	793.634i	0.486934	+	0.843395i	−0.512953	+	0.858417i	$0.671449\pi$
$942$	−255.417	−	68.4387i	−0.271143	−	0.0726526i
$943$	396.027	−	106.115i	0.419965	−	0.112529i
$944$			146.488i			0.155178i
$945$	−81.8492	−	162.406i	−0.0866129	−	0.171858i
$946$	−334.479			−0.353572
$947$	−252.013	−	940.527i	−0.266118	−	0.993164i	−0.961563	−	0.274585i	$-0.911459\pi$
$947$	−252.013	−	940.527i	−0.266118	−	0.993164i	0.695445	−	0.718579i	$-0.255207\pi$
$948$	46.1630	−	172.283i	0.0486952	−	0.181733i
$949$	197.742	−	114.167i	0.208369	−	0.120302i
$950$	4.03794	−	10.5654i	0.00425046	−	0.0111215i
$951$	−403.734			−0.424536
$952$	124.619	+	474.845i	0.130903	+	0.498787i
$953$	451.156	+	451.156i	0.473407	+	0.473407i	0.903015	−	0.429609i	$-0.141348\pi$
$953$	451.156	+	451.156i	0.473407	+	0.473407i	−0.429609	+	0.903015i	$0.641348\pi$
$954$	−276.229	−	159.481i	−0.289548	−	0.167171i
$955$	−940.818	−	609.996i	−0.985150	−	0.638739i
$956$	−196.297	−	339.997i	−0.205332	−	0.355645i
$957$	−154.939	−	578.239i	−0.161900	−	0.604221i
$958$	148.290	+	148.290i	0.154791	+	0.154791i
$959$	1249.35	+	729.908i	1.30276	+	0.761114i
$960$	−21.3611	+	65.9068i	−0.0222511	+	0.0686529i
$961$	364.367	−	631.103i	0.379154	−	0.656714i
$962$	−12.5761	−	3.36975i	−0.0130728	−	0.00350286i
$963$	−86.4699	+	322.710i	−0.0897922	+	0.335109i
$964$	651.872	+	376.358i	0.676215	+	0.390413i
$965$	−77.7862	−	25.2113i	−0.0806074	−	0.0261257i
$966$	−241.748	−	1.24387i	−0.250257	−	0.00128765i
$967$	−1040.28	+	1040.28i	−1.07578	+	1.07578i	−0.0788960	+	0.996883i	$0.525139\pi$
$967$	−1040.28	+	1040.28i	−1.07578	+	1.07578i	−0.996883	+	0.0788960i	$0.974861\pi$
$968$	−223.743	+	59.9518i	−0.231140	+	0.0619337i
$969$	−11.8987	+	6.86970i	−0.0122793	+	0.00708948i
$970$	371.530	−	573.024i	0.383021	−	0.590746i
$971$	−295.722	+	512.205i	−0.304554	+	0.527503i	−0.977162	−	0.212496i	$-0.931841\pi$
$971$	−295.722	+	512.205i	−0.304554	+	0.527503i	0.672608	+	0.739999i	$0.265174\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	401.728	−	1468.99i	0.412875	−	1.50976i
$974$			472.639i			0.485256i
$975$	154.080	−	68.8712i	0.158031	−	0.0706371i
$976$	−216.884	−	375.653i	−0.222217	−	0.384891i
$977$	−53.8605	−	14.4319i	−0.0551284	−	0.0147716i	0.231149	−	0.972918i	$-0.425751\pi$
$977$	−53.8605	−	14.4319i	−0.0551284	−	0.0147716i	−0.286278	+	0.958147i	$0.592418\pi$
$978$	713.536	−	191.191i	0.729586	−	0.195492i
$979$		−	1572.85i		−	1.60659i
$980$	30.3207	−	489.061i	0.0309395	−	0.499042i
$981$	228.261			0.232682
$982$	−88.5655	−	330.531i	−0.0901889	−	0.336590i
$983$	−276.301	+	1031.17i	−0.281079	+	1.04900i	0.670578	+	0.741839i	$0.266046\pi$
$983$	−276.301	+	1031.17i	−0.281079	+	1.04900i	−0.951657	+	0.307162i	$0.900621\pi$
$984$	123.373	−	71.2297i	0.125380	−	0.0723879i
$985$	−944.797	−	1047.76i	−0.959184	−	1.06372i
$986$	−850.852			−0.862933
$987$	989.910	+	270.712i	1.00295	+	0.274278i
$988$	−1.76339	−	1.76339i	−0.00178481	−	0.00178481i
$989$	−202.742	−	117.053i	−0.204997	−	0.118355i
$990$	−63.0397	−	295.515i	−0.0636765	−	0.298500i
$991$	−924.731	−	1601.68i	−0.933130	−	1.61623i	−0.777936	−	0.628344i	$-0.783733\pi$
$991$	−924.731	−	1601.68i	−0.933130	−	1.61623i	−0.155194	−	0.987884i	$-0.549600\pi$
$992$	22.3133	+	83.2743i	0.0224932	+	0.0839459i
$993$	447.797	+	447.797i	0.450953	+	0.450953i
$994$	−1.03584	+	201.318i	−0.00104210	+	0.202534i
$995$	−97.5075	−	191.023i	−0.0979974	−	0.191983i
$996$	202.962	−	351.541i	0.203777	−	0.352953i
$997$	−444.584	−	119.126i	−0.445922	−	0.119484i	0.0288686	−	0.999583i	$-0.490810\pi$
$997$	−444.584	−	119.126i	−0.445922	−	0.119484i	−0.474791	+	0.880099i	$0.657476\pi$
$998$	−244.508	+	912.515i	−0.244998	+	0.914344i
$999$	−10.6292	−	6.13676i	−0.0106398	−	0.00614291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.v.b.163.6	yes	32
5.2	odd	4	inner	210.3.v.b.37.2	✓	32
7.4	even	3	inner	210.3.v.b.193.2	yes	32
35.32	odd	12	inner	210.3.v.b.67.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.v.b.37.2	✓	32	5.2	odd	4	inner
210.3.v.b.67.6	yes	32	35.32	odd	12	inner
210.3.v.b.163.6	yes	32	1.1	even	1	trivial
210.3.v.b.193.2	yes	32	7.4	even	3	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.448288 - 1.67303i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.258026 + 4.99334i) q^{5} -2.44949 q^{6} +(6.75207 + 1.84650i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.448288 - 1.67303i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.258026 + 4.99334i) q^{5} -2.44949 q^{6} +(6.75207 + 1.84650i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(6.91547 - 1.47522i) q^{10} +(7.12207 + 12.3358i) q^{11} +(0.896575 + 3.34607i) q^{12} +(-2.75603 - 2.75603i) q^{13} +(0.0509352 - 9.89936i) q^{14} +(8.23835 + 2.67014i) q^{15} +(2.00000 - 3.46410i) q^{16} +(23.9506 + 6.41754i) q^{17} +(-1.09808 + 4.09808i) q^{18} +(-0.277055 - 0.159958i) q^{19} +(-4.54642 - 8.90674i) q^{20} +(6.11612 - 10.4687i) q^{21} +(14.2441 - 14.2441i) q^{22} +(13.6188 - 3.64915i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-24.8668 - 2.57682i) q^{25} +(-2.75603 + 4.77358i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-13.5414 + 3.55384i) q^{28} -24.2642i q^{29} +(0.632031 - 12.2311i) q^{30} +(-7.62013 - 13.1985i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(23.8309 - 6.38548i) q^{33} -35.0661i q^{34} +(-10.9624 + 33.2389i) q^{35} +6.00000 q^{36} +(0.611341 + 2.28156i) q^{37} +(-0.117097 + 0.437012i) q^{38} +(-5.84642 + 3.37543i) q^{39} +(-10.5027 + 9.47062i) q^{40} +29.0794 q^{41} +(-16.5391 - 4.52298i) q^{42} +(-11.7409 - 11.7409i) q^{43} +(-24.6716 - 14.2441i) q^{44} +(8.16038 - 12.5860i) q^{45} +(-9.96966 - 17.2680i) q^{46} +(21.9076 + 81.7602i) q^{47} +(-4.89898 - 4.89898i) q^{48} +(42.1809 + 24.9354i) q^{49} +(5.58190 + 34.9119i) q^{50} +(21.4735 - 37.1932i) q^{51} +(7.52961 + 2.01755i) q^{52} +(-19.4580 + 72.6184i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-63.4344 + 32.3800i) q^{55} +(9.81114 + 17.1971i) q^{56} +(-0.391815 + 0.391815i) q^{57} +(-33.1456 + 8.88133i) q^{58} +(-31.7156 + 18.3110i) q^{59} +(-16.9394 + 3.61353i) q^{60} +(54.2209 - 93.9134i) q^{61} +(-15.2403 + 15.2403i) q^{62} +(-14.7726 - 14.9254i) q^{63} +8.00000i q^{64} +(14.4729 - 13.0507i) q^{65} +(-17.4454 - 30.2164i) q^{66} +(-66.0445 - 17.6966i) q^{67} +(-47.9012 + 12.8351i) q^{68} -24.4206i q^{69} +(49.4177 + 2.80863i) q^{70} -20.3365 q^{71} +(-2.19615 - 8.19615i) q^{72} +(-15.1623 + 56.5866i) q^{73} +(2.89290 - 1.67022i) q^{74} +(-15.4586 + 40.4479i) q^{75} +0.639831 q^{76} +(25.3107 + 96.4430i) q^{77} +(6.75087 + 6.75087i) q^{78} +(-44.5901 - 25.7441i) q^{79} +(16.7814 + 10.8805i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-10.6438 - 39.7232i) q^{82} +(-82.8590 - 82.8590i) q^{83} +(-0.124765 + 24.2484i) q^{84} +(-38.2248 + 117.937i) q^{85} +(-11.7409 + 20.3359i) q^{86} +(-40.5949 - 10.8774i) q^{87} +(-10.4274 + 38.9157i) q^{88} +(-95.6273 - 55.2104i) q^{89} +(-20.1797 - 6.54047i) q^{90} +(-13.5199 - 23.6979i) q^{91} +(-19.9393 + 19.9393i) q^{92} +(-25.4975 + 6.83202i) q^{93} +(103.668 - 59.8526i) q^{94} +(0.870210 - 1.34215i) q^{95} +(-4.89898 + 8.48528i) q^{96} +(68.2928 - 68.2928i) q^{97} +(18.6231 - 66.7471i) q^{98} -42.7324i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

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