LMFDB - Embedded newform 690.3.k.a.277.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.20
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(1.06006 + 4.88634i) q^{5} +2.44949 q^{6} +(6.77823 + 6.77823i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(1.06006 + 4.88634i) q^{5} +2.44949 q^{6} +(6.77823 + 6.77823i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-3.82628 + 5.94639i) q^{10} +6.48073 q^{11} +(2.44949 + 2.44949i) q^{12} +(7.70435 - 7.70435i) q^{13} +13.5565i q^{14} +(7.28281 + 4.68622i) q^{15} -4.00000 q^{16} +(0.781759 + 0.781759i) q^{17} +(3.00000 - 3.00000i) q^{18} -0.529087i q^{19} +(-9.77267 + 2.12011i) q^{20} +16.6032 q^{21} +(6.48073 + 6.48073i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(-22.7526 + 10.3596i) q^{25} +15.4087 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-13.5565 + 13.5565i) q^{28} +22.8105i q^{29} +(2.59660 + 11.9690i) q^{30} -24.3355 q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.93724 - 7.93724i) q^{33} +1.56352i q^{34} +(-25.9354 + 40.3060i) q^{35} +6.00000 q^{36} +(6.38099 + 6.38099i) q^{37} +(0.529087 - 0.529087i) q^{38} -18.8717i q^{39} +(-11.8928 - 7.65256i) q^{40} +16.5189 q^{41} +(16.6032 + 16.6032i) q^{42} +(11.3582 - 11.3582i) q^{43} +12.9615i q^{44} +(14.6590 - 3.18017i) q^{45} -6.78233 q^{46} +(-19.1854 - 19.1854i) q^{47} +(-4.89898 + 4.89898i) q^{48} +42.8889i q^{49} +(-33.1121 - 12.3930i) q^{50} +1.91491 q^{51} +(15.4087 + 15.4087i) q^{52} +(-7.76688 + 7.76688i) q^{53} -7.34847i q^{54} +(6.86994 + 31.6670i) q^{55} -27.1129 q^{56} +(-0.647996 - 0.647996i) q^{57} +(-22.8105 + 22.8105i) q^{58} +62.7613i q^{59} +(-9.37243 + 14.5656i) q^{60} +37.8465 q^{61} +(-24.3355 - 24.3355i) q^{62} +(20.3347 - 20.3347i) q^{63} -8.00000i q^{64} +(45.8131 + 29.4790i) q^{65} +15.8745 q^{66} +(-23.8308 - 23.8308i) q^{67} +(-1.56352 + 1.56352i) q^{68} +8.30662i q^{69} +(-66.2415 + 14.3706i) q^{70} +82.9169 q^{71} +(6.00000 + 6.00000i) q^{72} +(32.9265 - 32.9265i) q^{73} +12.7620i q^{74} +(-15.1782 + 40.5539i) q^{75} +1.05817 q^{76} +(43.9279 + 43.9279i) q^{77} +(18.8717 - 18.8717i) q^{78} -55.5424i q^{79} +(-4.24022 - 19.5453i) q^{80} -9.00000 q^{81} +(16.5189 + 16.5189i) q^{82} +(-53.8067 + 53.8067i) q^{83} +33.2064i q^{84} +(-2.99123 + 4.64864i) q^{85} +22.7164 q^{86} +(27.9371 + 27.9371i) q^{87} +(-12.9615 + 12.9615i) q^{88} +9.20780i q^{89} +(17.8392 + 11.4788i) q^{90} +104.444 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-29.8048 + 29.8048i) q^{93} -38.3707i q^{94} +(2.58529 - 0.560862i) q^{95} -9.79796 q^{96} +(79.6850 + 79.6850i) q^{97} +(-42.8889 + 42.8889i) q^{98} -19.4422i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$	1.06006	+	4.88634i	0.212011	+	0.977267i
$5$	1.06006	+	4.88634i	0.212011	+	0.977267i
$6$	2.44949			0.408248
$7$	6.77823	+	6.77823i	0.968319	+	0.968319i	0.999513	−	0.0311941i	$-0.00993100\pi$
$7$	6.77823	+	6.77823i	0.968319	+	0.968319i	−0.0311941	+	0.999513i	$0.509931\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−3.82628	+	5.94639i	−0.382628	+	0.594639i
$11$	6.48073			0.589157			0.294579	−	0.955627i	$-0.404821\pi$
$11$	6.48073			0.589157			0.294579	+	0.955627i	$0.404821\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	7.70435	−	7.70435i	0.592642	−	0.592642i	−0.345702	−	0.938344i	$-0.612359\pi$
$13$	7.70435	−	7.70435i	0.592642	−	0.592642i	0.938344	+	0.345702i	$0.112359\pi$
$14$			13.5565i			0.968319i
$15$	7.28281	+	4.68622i	0.485521	+	0.312414i
$16$	−4.00000			−0.250000
$17$	0.781759	+	0.781759i	0.0459858	+	0.0459858i	0.729726	−	0.683740i	$-0.239648\pi$
$17$	0.781759	+	0.781759i	0.0459858	+	0.0459858i	−0.683740	+	0.729726i	$0.739648\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	0.529087i		−	0.0278467i	−0.999903	−	0.0139233i	$-0.995568\pi$
$19$		−	0.529087i		−	0.0278467i	0.999903	−	0.0139233i	$-0.00443208\pi$
$20$	−9.77267	+	2.12011i	−0.488634	+	0.106006i
$21$	16.6032			0.790629
$22$	6.48073	+	6.48073i	0.294579	+	0.294579i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			4.89898i			0.204124i
$25$	−22.7526	+	10.3596i	−0.910102	+	0.414383i
$26$	15.4087			0.592642
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−13.5565	+	13.5565i	−0.484160	+	0.484160i
$29$			22.8105i			0.786570i	0.919417	+	0.393285i	$0.128662\pi$
$29$			22.8105i			0.786570i	−0.919417	+	0.393285i	$0.871338\pi$
$30$	2.59660	+	11.9690i	0.0865532	+	0.398968i
$31$	−24.3355			−0.785017			−0.392508	−	0.919748i	$-0.628393\pi$
$31$	−24.3355			−0.785017			−0.392508	+	0.919748i	$0.628393\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	7.93724	−	7.93724i	0.240522	−	0.240522i
$34$			1.56352i			0.0459858i
$35$	−25.9354	+	40.3060i	−0.741012	+	1.15160i
$36$	6.00000			0.166667
$37$	6.38099	+	6.38099i	0.172459	+	0.172459i	0.788059	−	0.615600i	$-0.211086\pi$
$37$	6.38099	+	6.38099i	0.172459	+	0.172459i	−0.615600	+	0.788059i	$0.711086\pi$
$38$	0.529087	−	0.529087i	0.0139233	−	0.0139233i
$39$		−	18.8717i		−	0.483890i
$40$	−11.8928	−	7.65256i	−0.297320	−	0.191314i
$41$	16.5189			0.402899			0.201450	−	0.979499i	$-0.435435\pi$
$41$	16.5189			0.402899			0.201450	+	0.979499i	$0.435435\pi$
$42$	16.6032	+	16.6032i	0.395315	+	0.395315i
$43$	11.3582	−	11.3582i	0.264144	−	0.264144i	−0.562591	−	0.826735i	$-0.690195\pi$
$43$	11.3582	−	11.3582i	0.264144	−	0.264144i	0.826735	+	0.562591i	$0.190195\pi$
$44$			12.9615i			0.294579i
$45$	14.6590	−	3.18017i	0.325756	−	0.0706704i
$46$	−6.78233			−0.147442
$47$	−19.1854	−	19.1854i	−0.408199	−	0.408199i	0.472911	−	0.881110i	$-0.343203\pi$
$47$	−19.1854	−	19.1854i	−0.408199	−	0.408199i	−0.881110	+	0.472911i	$0.843203\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			42.8889i			0.875284i
$50$	−33.1121	−	12.3930i	−0.662243	−	0.247860i
$51$	1.91491			0.0375473
$52$	15.4087	+	15.4087i	0.296321	+	0.296321i
$53$	−7.76688	+	7.76688i	−0.146545	+	0.146545i	−0.776573	−	0.630028i	$-0.783043\pi$
$53$	−7.76688	+	7.76688i	−0.146545	+	0.146545i	0.630028	+	0.776573i	$0.283043\pi$
$54$		−	7.34847i		−	0.136083i
$55$	6.86994	+	31.6670i	0.124908	+	0.575764i
$56$	−27.1129			−0.484160
$57$	−0.647996	−	0.647996i	−0.0113684	−	0.0113684i
$58$	−22.8105	+	22.8105i	−0.393285	+	0.393285i
$59$			62.7613i			1.06375i	0.846822	+	0.531876i	$0.178513\pi$
$59$			62.7613i			1.06375i	−0.846822	+	0.531876i	$0.821487\pi$
$60$	−9.37243	+	14.5656i	−0.156207	+	0.242760i
$61$	37.8465			0.620435			0.310218	−	0.950666i	$-0.399598\pi$
$61$	37.8465			0.620435			0.310218	+	0.950666i	$0.399598\pi$
$62$	−24.3355	−	24.3355i	−0.392508	−	0.392508i
$63$	20.3347	−	20.3347i	0.322773	−	0.322773i
$64$		−	8.00000i		−	0.125000i
$65$	45.8131	+	29.4790i	0.704817	+	0.453523i
$66$	15.8745			0.240522
$67$	−23.8308	−	23.8308i	−0.355683	−	0.355683i	0.506536	−	0.862219i	$-0.330926\pi$
$67$	−23.8308	−	23.8308i	−0.355683	−	0.355683i	−0.862219	+	0.506536i	$0.830926\pi$
$68$	−1.56352	+	1.56352i	−0.0229929	+	0.0229929i
$69$			8.30662i			0.120386i
$70$	−66.2415	+	14.3706i	−0.946307	+	0.205295i
$71$	82.9169			1.16784			0.583922	−	0.811810i	$-0.301517\pi$
$71$	82.9169			1.16784			0.583922	+	0.811810i	$0.301517\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	32.9265	−	32.9265i	0.451048	−	0.451048i	−0.444654	−	0.895702i	$-0.646674\pi$
$73$	32.9265	−	32.9265i	0.451048	−	0.451048i	0.895702	+	0.444654i	$0.146674\pi$
$74$			12.7620i			0.172459i
$75$	−15.1782	+	40.5539i	−0.202377	+	0.540719i
$76$	1.05817			0.0139233
$77$	43.9279	+	43.9279i	0.570492	+	0.570492i
$78$	18.8717	−	18.8717i	0.241945	−	0.241945i
$79$		−	55.5424i		−	0.703069i	−0.936175	−	0.351534i	$-0.885660\pi$
$79$		−	55.5424i		−	0.703069i	0.936175	−	0.351534i	$-0.114340\pi$
$80$	−4.24022	−	19.5453i	−0.0530028	−	0.244317i
$81$	−9.00000			−0.111111
$82$	16.5189	+	16.5189i	0.201450	+	0.201450i
$83$	−53.8067	+	53.8067i	−0.648274	+	0.648274i	−0.952576	−	0.304302i	$-0.901577\pi$
$83$	−53.8067	+	53.8067i	−0.648274	+	0.648274i	0.304302	+	0.952576i	$0.401577\pi$
$84$			33.2064i			0.395315i
$85$	−2.99123	+	4.64864i	−0.0351909	+	0.0546899i
$86$	22.7164			0.264144
$87$	27.9371	+	27.9371i	0.321116	+	0.321116i
$88$	−12.9615	+	12.9615i	−0.147289	+	0.147289i
$89$			9.20780i			0.103458i	0.998661	+	0.0517292i	$0.0164733\pi$
$89$			9.20780i			0.103458i	−0.998661	+	0.0517292i	$0.983527\pi$
$90$	17.8392	+	11.4788i	0.198213	+	0.127543i
$91$	104.444			1.14773
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	−29.8048	+	29.8048i	−0.320482	+	0.320482i
$94$		−	38.3707i		−	0.408199i
$95$	2.58529	−	0.560862i	0.0272136	−	0.00590381i
$96$	−9.79796			−0.102062
$97$	79.6850	+	79.6850i	0.821495	+	0.821495i	0.986322	−	0.164828i	$-0.0527068\pi$
$97$	79.6850	+	79.6850i	0.821495	+	0.821495i	−0.164828	+	0.986322i	$0.552707\pi$
$98$	−42.8889	+	42.8889i	−0.437642	+	0.437642i
$99$		−	19.4422i		−	0.196386i
$100$	−20.7192	−	45.5051i	−0.207192	−	0.455051i
$101$	−139.733			−1.38350			−0.691749	−	0.722138i	$-0.743160\pi$
$101$	−139.733			−1.38350			−0.691749	+	0.722138i	$0.743160\pi$
$102$	1.91491	+	1.91491i	0.0187736	+	0.0187736i
$103$	98.3312	−	98.3312i	0.954672	−	0.954672i	−0.0443444	−	0.999016i	$-0.514120\pi$
$103$	98.3312	−	98.3312i	0.954672	−	0.954672i	0.999016	+	0.0443444i	$0.0141199\pi$
$104$			30.8174i			0.296321i
$105$	17.6003	+	81.1289i	0.167622	+	0.772656i
$106$	−15.5338			−0.146545
$107$	−11.4279	−	11.4279i	−0.106803	−	0.106803i	0.651686	−	0.758489i	$-0.274062\pi$
$107$	−11.4279	−	11.4279i	−0.106803	−	0.106803i	−0.758489	+	0.651686i	$0.774062\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	79.8261i		−	0.732350i	−0.930546	−	0.366175i	$-0.880667\pi$
$109$		−	79.8261i		−	0.732350i	0.930546	−	0.366175i	$-0.119333\pi$
$110$	−24.7971	+	38.5370i	−0.225428	+	0.350336i
$111$	15.6302			0.140812
$112$	−27.1129	−	27.1129i	−0.242080	−	0.242080i
$113$	80.7359	−	80.7359i	0.714477	−	0.714477i	−0.252992	−	0.967468i	$-0.581415\pi$
$113$	80.7359	−	80.7359i	0.714477	−	0.714477i	0.967468	+	0.252992i	$0.0814145\pi$
$114$		−	1.29599i		−	0.0113684i
$115$	−20.1652	−	12.9755i	−0.175350	−	0.112831i
$116$	−45.6211			−0.393285
$117$	−23.1130	−	23.1130i	−0.197547	−	0.197547i
$118$	−62.7613	+	62.7613i	−0.531876	+	0.531876i
$119$			10.5979i			0.0890579i
$120$	−23.9381	+	5.19319i	−0.199484	+	0.0432766i
$121$	−79.0002			−0.652894
$122$	37.8465	+	37.8465i	0.310218	+	0.310218i
$123$	20.2314	−	20.2314i	0.164483	−	0.164483i
$124$		−	48.6710i		−	0.392508i
$125$	−74.7394	−	100.195i	−0.597915	−	0.801559i
$126$	40.6694			0.322773
$127$	−130.755	−	130.755i	−1.02957	−	1.02957i	−0.999549	−	0.0300209i	$-0.990443\pi$
$127$	−130.755	−	130.755i	−1.02957	−	1.02957i	−0.0300209	−	0.999549i	$-0.509557\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	27.8218i		−	0.215673i
$130$	16.3341	+	75.2921i	0.125647	+	0.579170i
$131$	38.3122			0.292459			0.146230	−	0.989251i	$-0.453286\pi$
$131$	38.3122			0.292459			0.146230	+	0.989251i	$0.453286\pi$
$132$	15.8745	+	15.8745i	0.120261	+	0.120261i
$133$	3.58627	−	3.58627i	0.0269645	−	0.0269645i
$134$		−	47.6616i		−	0.355683i
$135$	14.0587	−	21.8484i	0.104138	−	0.161840i
$136$	−3.12703			−0.0229929
$137$	−43.2358	−	43.2358i	−0.315589	−	0.315589i	0.531481	−	0.847070i	$-0.321636\pi$
$137$	−43.2358	−	43.2358i	−0.315589	−	0.315589i	−0.847070	+	0.531481i	$0.821636\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$		−	113.502i		−	0.816562i	−0.912856	−	0.408281i	$-0.866128\pi$
$139$		−	113.502i		−	0.816562i	0.912856	−	0.408281i	$-0.133872\pi$
$140$	−80.6121	−	51.8708i	−0.575801	−	0.370506i
$141$	−46.9944			−0.333293
$142$	82.9169	+	82.9169i	0.583922	+	0.583922i
$143$	49.9298	−	49.9298i	0.349159	−	0.349159i
$144$			12.0000i			0.0833333i
$145$	−111.460	+	24.1805i	−0.768690	+	0.166762i
$146$	65.8530			0.451048
$147$	52.5280	+	52.5280i	0.357333	+	0.357333i
$148$	−12.7620	+	12.7620i	−0.0862295	+	0.0862295i
$149$		−	80.8820i		−	0.542832i	−0.962462	−	0.271416i	$-0.912508\pi$
$149$		−	80.8820i		−	0.542832i	0.962462	−	0.271416i	$-0.0874920\pi$
$150$	−55.7322	+	25.3757i	−0.371548	+	0.169171i
$151$	−54.8655			−0.363348			−0.181674	−	0.983359i	$-0.558152\pi$
$151$	−54.8655			−0.363348			−0.181674	+	0.983359i	$0.558152\pi$
$152$	1.05817	+	1.05817i	0.00696167	+	0.00696167i
$153$	2.34528	−	2.34528i	0.0153286	−	0.0153286i
$154$			87.8558i			0.570492i
$155$	−25.7970	−	118.912i	−0.166432	−	0.767171i
$156$	37.7434			0.241945
$157$	−143.794	−	143.794i	−0.915885	−	0.915885i	0.0808422	−	0.996727i	$-0.474239\pi$
$157$	−143.794	−	143.794i	−0.915885	−	0.915885i	−0.996727	+	0.0808422i	$0.974239\pi$
$158$	55.5424	−	55.5424i	0.351534	−	0.351534i
$159$			19.0249i			0.119653i
$160$	15.3051	−	23.7856i	0.0956570	−	0.148660i
$161$	−45.9722			−0.285542
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	108.194	−	108.194i	0.663769	−	0.663769i	−0.292497	−	0.956266i	$-0.594486\pi$
$163$	108.194	−	108.194i	0.663769	−	0.663769i	0.956266	+	0.292497i	$0.0944862\pi$
$164$			33.0377i			0.201450i
$165$	47.1979	+	30.3701i	0.286048	+	0.184061i
$166$	−107.613			−0.648274
$167$	178.168	+	178.168i	1.06688	+	1.06688i	0.997597	+	0.0692787i	$0.0220698\pi$
$167$	178.168	+	178.168i	1.06688	+	1.06688i	0.0692787	+	0.997597i	$0.477930\pi$
$168$	−33.2064	+	33.2064i	−0.197657	+	0.197657i
$169$			50.2860i			0.297550i
$170$	−7.63987	+	1.65742i	−0.0449404	+	0.00974951i
$171$	−1.58726			−0.00928222
$172$	22.7164	+	22.7164i	0.132072	+	0.132072i
$173$	−12.0550	+	12.0550i	−0.0696822	+	0.0696822i	−0.741089	−	0.671407i	$-0.765690\pi$
$173$	−12.0550	+	12.0550i	−0.0696822	+	0.0696822i	0.671407	+	0.741089i	$0.265690\pi$
$174$			55.8742i			0.321116i
$175$	−224.442	−	84.0025i	−1.28253	−	0.480014i
$176$	−25.9229			−0.147289
$177$	76.8666	+	76.8666i	0.434275	+	0.434275i
$178$	−9.20780	+	9.20780i	−0.0517292	+	0.0517292i
$179$			47.2728i			0.264094i	0.991243	+	0.132047i	$0.0421550\pi$
$179$			47.2728i			0.264094i	−0.991243	+	0.132047i	$0.957845\pi$
$180$	6.36034	+	29.3180i	0.0353352	+	0.162878i
$181$	−47.4383			−0.262090			−0.131045	−	0.991376i	$-0.541833\pi$
$181$	−47.4383			−0.262090			−0.131045	+	0.991376i	$0.541833\pi$
$182$	104.444	+	104.444i	0.573867	+	0.573867i
$183$	46.3524	−	46.3524i	0.253292	−	0.253292i
$184$		−	13.5647i		−	0.0737210i
$185$	−24.4154	+	37.9438i	−0.131975	+	0.205102i
$186$	−59.6096			−0.320482
$187$	5.06637	+	5.06637i	0.0270929	+	0.0270929i
$188$	38.3707	−	38.3707i	0.204100	−	0.204100i
$189$		−	49.8097i		−	0.263543i
$190$	3.14616	+	2.02443i	0.0165587	+	0.0106549i
$191$	126.903			0.664416			0.332208	−	0.943206i	$-0.392206\pi$
$191$	126.903			0.664416			0.332208	+	0.943206i	$0.392206\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−148.959	+	148.959i	−0.771811	+	0.771811i	−0.978423	−	0.206612i	$-0.933756\pi$
$193$	−148.959	+	148.959i	−0.771811	+	0.771811i	0.206612	+	0.978423i	$0.433756\pi$
$194$			159.370i			0.821495i
$195$	92.2136	−	20.0051i	0.472890	−	0.102590i
$196$	−85.7779			−0.437642
$197$	10.2081	+	10.2081i	0.0518175	+	0.0518175i	0.732541	−	0.680723i	$-0.238334\pi$
$197$	10.2081	+	10.2081i	0.0518175	+	0.0518175i	−0.680723	+	0.732541i	$0.738334\pi$
$198$	19.4422	−	19.4422i	0.0981929	−	0.0981929i
$199$		−	365.840i		−	1.83839i	−0.393803	−	0.919195i	$-0.628841\pi$
$199$		−	365.840i		−	1.83839i	0.393803	−	0.919195i	$-0.371159\pi$
$200$	24.7860	−	66.2243i	0.123930	−	0.331121i
$201$	−58.3732			−0.290414
$202$	−139.733	−	139.733i	−0.691749	−	0.691749i
$203$	−154.615	+	154.615i	−0.761651	+	0.761651i
$204$			3.82982i			0.0187736i
$205$	17.5109	+	80.7167i	0.0854192	+	0.393740i
$206$	196.662			0.954672
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	−30.8174	+	30.8174i	−0.148161	+	0.148161i
$209$		−	3.42887i		−	0.0164061i
$210$	−63.5286	+	98.7292i	−0.302517	+	0.470139i
$211$	52.5021			0.248825			0.124413	−	0.992231i	$-0.460295\pi$
$211$	52.5021			0.248825			0.124413	+	0.992231i	$0.460295\pi$
$212$	−15.5338	−	15.5338i	−0.0732724	−	0.0732724i
$213$	101.552	−	101.552i	0.476770	−	0.476770i
$214$		−	22.8558i		−	0.106803i
$215$	67.5403	+	43.4596i	0.314141	+	0.202138i
$216$	14.6969			0.0680414
$217$	−164.952	−	164.952i	−0.760147	−	0.760147i
$218$	79.8261	−	79.8261i	0.366175	−	0.366175i
$219$		−	80.6531i		−	0.368279i
$220$	−63.3340	+	13.7399i	−0.287882	+	0.0624540i
$221$	12.0459			0.0545063
$222$	15.6302	+	15.6302i	0.0704061	+	0.0704061i
$223$	−20.5666	+	20.5666i	−0.0922271	+	0.0922271i	−0.751715	−	0.659488i	$-0.770773\pi$
$223$	−20.5666	+	20.5666i	−0.0922271	+	0.0922271i	0.659488	+	0.751715i	$0.270773\pi$
$224$		−	54.2259i		−	0.242080i
$225$	31.0787	+	68.2577i	0.138128	+	0.303367i
$226$	161.472			0.714477
$227$	233.250	+	233.250i	1.02753	+	1.02753i	0.999610	+	0.0279229i	$0.00888930\pi$
$227$	233.250	+	233.250i	1.02753	+	1.02753i	0.0279229	+	0.999610i	$0.491111\pi$
$228$	1.29599	−	1.29599i	0.00568418	−	0.00568418i
$229$		−	407.228i		−	1.77829i	−0.457629	−	0.889143i	$-0.651301\pi$
$229$		−	407.228i		−	1.77829i	0.457629	−	0.889143i	$-0.348699\pi$
$230$	−7.18965	−	33.1407i	−0.0312594	−	0.144090i
$231$	107.601			0.465805
$232$	−45.6211	−	45.6211i	−0.196643	−	0.196643i
$233$	67.8138	−	67.8138i	0.291046	−	0.291046i	−0.546447	−	0.837494i	$-0.684020\pi$
$233$	67.8138	−	67.8138i	0.291046	−	0.291046i	0.837494	+	0.546447i	$0.184020\pi$
$234$		−	46.2261i		−	0.197547i
$235$	73.4086	−	114.084i	0.312377	−	0.485463i
$236$	−125.523			−0.531876
$237$	−68.0253	−	68.0253i	−0.287027	−	0.287027i
$238$	−10.5979	+	10.5979i	−0.0445289	+	0.0445289i
$239$		−	126.104i		−	0.527630i	−0.964573	−	0.263815i	$-0.915019\pi$
$239$		−	126.104i		−	0.527630i	0.964573	−	0.263815i	$-0.0849808\pi$
$240$	−29.1313	−	18.7449i	−0.121380	−	0.0781036i
$241$	169.295			0.702467			0.351234	−	0.936288i	$-0.385762\pi$
$241$	169.295			0.702467			0.351234	+	0.936288i	$0.385762\pi$
$242$	−79.0002	−	79.0002i	−0.326447	−	0.326447i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			75.6931i			0.310218i
$245$	−209.570	+	45.4647i	−0.855387	+	0.185570i
$246$	40.4628			0.164483
$247$	−4.07627	−	4.07627i	−0.0165031	−	0.0165031i
$248$	48.6710	−	48.6710i	0.196254	−	0.196254i
$249$			131.799i			0.529313i
$250$	25.4555	−	174.934i	0.101822	−	0.699737i
$251$	352.257			1.40341			0.701707	−	0.712466i	$-0.252422\pi$
$251$	352.257			1.40341			0.701707	+	0.712466i	$0.252422\pi$
$252$	40.6694	+	40.6694i	0.161387	+	0.161387i
$253$	−21.9772	+	21.9772i	−0.0868665	+	0.0868665i
$254$		−	261.511i		−	1.02957i
$255$	2.02991	+	9.35689i	0.00796044	+	0.0366937i
$256$	16.0000			0.0625000
$257$	36.1183	+	36.1183i	0.140538	+	0.140538i	0.773876	−	0.633338i	$-0.218316\pi$
$257$	36.1183	+	36.1183i	0.140538	+	0.140538i	−0.633338	+	0.773876i	$0.718316\pi$
$258$	27.8218	−	27.8218i	0.107836	−	0.107836i
$259$			86.5037i			0.333991i
$260$	−58.9580	+	91.6262i	−0.226762	+	0.352408i
$261$	68.4316			0.262190
$262$	38.3122	+	38.3122i	0.146230	+	0.146230i
$263$	−217.636	+	217.636i	−0.827513	+	0.827513i	−0.987172	−	0.159660i	$-0.948960\pi$
$263$	−217.636	+	217.636i	−0.827513	+	0.827513i	0.159660	+	0.987172i	$0.448960\pi$
$264$			31.7490i			0.120261i
$265$	−46.1849	−	29.7182i	−0.174283	−	0.112144i
$266$	7.17255			0.0269645
$267$	11.2772	+	11.2772i	0.0422367	+	0.0422367i
$268$	47.6616	−	47.6616i	0.177842	−	0.177842i
$269$		−	525.831i		−	1.95476i	−0.211488	−	0.977381i	$-0.567831\pi$
$269$		−	525.831i		−	1.95476i	0.211488	−	0.977381i	$-0.432169\pi$
$270$	35.9071	−	7.78979i	0.132989	−	0.0288511i
$271$	518.661			1.91388			0.956939	−	0.290289i	$-0.0937514\pi$
$271$	518.661			1.91388			0.956939	+	0.290289i	$0.0937514\pi$
$272$	−3.12703	−	3.12703i	−0.0114965	−	0.0114965i
$273$	127.917	−	127.917i	0.468560	−	0.468560i
$274$		−	86.4715i		−	0.315589i
$275$	−147.453	+	67.1376i	−0.536193	+	0.244137i
$276$	−16.6132			−0.0601929
$277$	−223.617	−	223.617i	−0.807281	−	0.807281i	0.176940	−	0.984222i	$-0.443380\pi$
$277$	−223.617	−	223.617i	−0.807281	−	0.807281i	−0.984222	+	0.176940i	$0.943380\pi$
$278$	113.502	−	113.502i	0.408281	−	0.408281i
$279$			73.0066i			0.261672i
$280$	−28.7412	−	132.483i	−0.102647	−	0.473153i
$281$	425.954			1.51585			0.757926	−	0.652341i	$-0.226213\pi$
$281$	425.954			1.51585			0.757926	+	0.652341i	$0.226213\pi$
$282$	−46.9944	−	46.9944i	−0.166647	−	0.166647i
$283$	30.5658	−	30.5658i	0.108006	−	0.108006i	−0.651038	−	0.759045i	$-0.725666\pi$
$283$	30.5658	−	30.5658i	0.108006	−	0.108006i	0.759045	+	0.651038i	$0.225666\pi$
$284$			165.834i			0.583922i
$285$	2.47941	−	3.85324i	0.00869970	−	0.0135201i
$286$	99.8596			0.349159
$287$	111.969	+	111.969i	0.390135	+	0.390135i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	287.778i		−	0.995771i
$290$	−135.640	−	87.2795i	−0.467726	−	0.300964i
$291$	195.188			0.670748
$292$	65.8530	+	65.8530i	0.225524	+	0.225524i
$293$	−237.549	+	237.549i	−0.810749	+	0.810749i	−0.984746	−	0.173997i	$-0.944332\pi$
$293$	−237.549	+	237.549i	−0.810749	+	0.810749i	0.173997	+	0.984746i	$0.444332\pi$
$294$			105.056i			0.357333i
$295$	−306.673	+	66.5305i	−1.03957	+	0.225527i
$296$	−25.5239			−0.0862295
$297$	−23.8117	−	23.8117i	−0.0801741	−	0.0801741i
$298$	80.8820	−	80.8820i	0.271416	−	0.271416i
$299$			52.2534i			0.174761i
$300$	−81.1079	−	30.3565i	−0.270360	−	0.101188i
$301$	153.977			0.511552
$302$	−54.8655	−	54.8655i	−0.181674	−	0.181674i
$303$	−171.138	+	171.138i	−0.564811	+	0.564811i
$304$			2.11635i			0.00696167i
$305$	40.1195	+	184.931i	0.131539	+	0.606331i
$306$	4.69055			0.0153286
$307$	−237.912	−	237.912i	−0.774959	−	0.774959i	0.204010	−	0.978969i	$-0.434602\pi$
$307$	−237.912	−	237.912i	−0.774959	−	0.774959i	−0.978969	+	0.204010i	$0.934602\pi$
$308$	−87.8558	+	87.8558i	−0.285246	+	0.285246i
$309$		−	240.861i		−	0.779486i
$310$	93.1145	−	144.709i	0.300369	−	0.466802i
$311$	−81.3114			−0.261452			−0.130726	−	0.991419i	$-0.541731\pi$
$311$	−81.3114			−0.261452			−0.130726	+	0.991419i	$0.541731\pi$
$312$	37.7434	+	37.7434i	0.120973	+	0.120973i
$313$	−327.200	+	327.200i	−1.04537	+	1.04537i	−0.0464467	+	0.998921i	$0.514790\pi$
$313$	−327.200	+	327.200i	−1.04537	+	1.04537i	−0.998921	+	0.0464467i	$0.985210\pi$
$314$		−	287.588i		−	0.915885i
$315$	120.918	+	77.8063i	0.383867	+	0.247004i
$316$	111.085			0.351534
$317$	274.470	+	274.470i	0.865837	+	0.865837i	0.992008	−	0.126171i	$-0.0402690\pi$
$317$	274.470	+	274.470i	0.865837	+	0.865837i	−0.126171	+	0.992008i	$0.540269\pi$
$318$	−19.0249	+	19.0249i	−0.0598267	+	0.0598267i
$319$			147.829i			0.463414i
$320$	39.0907	−	8.48045i	0.122158	−	0.0265014i
$321$	−27.9925			−0.0872040
$322$	−45.9722	−	45.9722i	−0.142771	−	0.142771i
$323$	0.413618	−	0.413618i	0.00128055	−	0.00128055i
$324$		−	18.0000i		−	0.0555556i
$325$	−95.4798	+	255.108i	−0.293784	+	0.784946i
$326$	216.389			0.663769
$327$	−97.7666	−	97.7666i	−0.298981	−	0.298981i
$328$	−33.0377	+	33.0377i	−0.100725	+	0.100725i
$329$		−	260.086i		−	0.790535i
$330$	16.8278	+	77.5680i	0.0509934	+	0.235055i
$331$	209.454			0.632791			0.316396	−	0.948627i	$-0.397527\pi$
$331$	209.454			0.632791			0.316396	+	0.948627i	$0.397527\pi$
$332$	−107.613	−	107.613i	−0.324137	−	0.324137i
$333$	19.1430	−	19.1430i	0.0574864	−	0.0574864i
$334$			356.337i			1.06688i
$335$	91.1832	−	141.707i	0.272189	−	0.423006i
$336$	−66.4129			−0.197657
$337$	−267.075	−	267.075i	−0.792506	−	0.792506i	0.189395	−	0.981901i	$-0.439347\pi$
$337$	−267.075	−	267.075i	−0.792506	−	0.792506i	−0.981901	+	0.189395i	$0.939347\pi$
$338$	−50.2860	+	50.2860i	−0.148775	+	0.148775i
$339$		−	197.762i		−	0.583368i
$340$	−9.29729	−	5.98246i	−0.0273450	−	0.0175955i
$341$	−157.712			−0.462498
$342$	−1.58726	−	1.58726i	−0.00464111	−	0.00464111i
$343$	41.4222	−	41.4222i	0.120765	−	0.120765i
$344$			45.4328i			0.132072i
$345$	−40.5890	+	8.80549i	−0.117649	+	0.0255232i
$346$	−24.1100			−0.0696822
$347$	302.377	+	302.377i	0.871403	+	0.871403i	0.992625	−	0.121222i	$-0.0386813\pi$
$347$	302.377	+	302.377i	0.871403	+	0.871403i	−0.121222	+	0.992625i	$0.538681\pi$
$348$	−55.8742	+	55.8742i	−0.160558	+	0.160558i
$349$		−	38.7883i		−	0.111141i	−0.998455	−	0.0555706i	$-0.982302\pi$
$349$		−	38.7883i		−	0.111141i	0.998455	−	0.0555706i	$-0.0176978\pi$
$350$	−140.439	−	308.444i	−0.401255	−	0.881270i
$351$	−56.6152			−0.161297
$352$	−25.9229	−	25.9229i	−0.0736446	−	0.0736446i
$353$	228.425	−	228.425i	0.647096	−	0.647096i	−0.305194	−	0.952290i	$-0.598721\pi$
$353$	228.425	−	228.425i	0.647096	−	0.647096i	0.952290	+	0.305194i	$0.0987213\pi$
$354$			153.733i			0.434275i
$355$	87.8966	+	405.160i	0.247596	+	1.14130i
$356$	−18.4156			−0.0517292
$357$	12.9797	+	12.9797i	0.0363577	+	0.0363577i
$358$	−47.2728	+	47.2728i	−0.132047	+	0.132047i
$359$			572.493i			1.59469i	0.603525	+	0.797344i	$0.293762\pi$
$359$			572.493i			1.59469i	−0.603525	+	0.797344i	$0.706238\pi$
$360$	−22.9577	+	35.6784i	−0.0637713	+	0.0991065i
$361$	360.720			0.999225
$362$	−47.4383	−	47.4383i	−0.131045	−	0.131045i
$363$	−96.7550	+	96.7550i	−0.266543	+	0.266543i
$364$			208.888i			0.573867i
$365$	195.794	+	125.986i	0.536421	+	0.345167i
$366$	92.7047			0.253292
$367$	−156.250	−	156.250i	−0.425750	−	0.425750i	0.461428	−	0.887178i	$-0.347337\pi$
$367$	−156.250	−	156.250i	−0.425750	−	0.425750i	−0.887178	+	0.461428i	$0.847337\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$		−	49.5566i		−	0.134300i
$370$	−62.3593	+	13.5284i	−0.168539	+	0.0365633i
$371$	−105.291			−0.283804
$372$	−59.6096	−	59.6096i	−0.160241	−	0.160241i
$373$	14.7884	−	14.7884i	0.0396472	−	0.0396472i	−0.687005	−	0.726652i	$-0.741075\pi$
$373$	14.7884	−	14.7884i	0.0396472	−	0.0396472i	0.726652	+	0.687005i	$0.241075\pi$
$374$			10.1327i			0.0270929i
$375$	−214.250	−	31.1765i	−0.571333	−	0.0831374i
$376$	76.7415			0.204100
$377$	175.740	+	175.740i	0.466155	+	0.466155i
$378$	49.8097	−	49.8097i	0.131772	−	0.131772i
$379$			39.4302i			0.104038i	0.998646	+	0.0520188i	$0.0165656\pi$
$379$			39.4302i			0.104038i	−0.998646	+	0.0520188i	$0.983434\pi$
$380$	1.12172	+	5.17059i	0.00295190	+	0.0136068i
$381$	−320.284			−0.840640
$382$	126.903	+	126.903i	0.332208	+	0.332208i
$383$	−262.977	+	262.977i	−0.686624	+	0.686624i	−0.961484	−	0.274860i	$-0.911368\pi$
$383$	−262.977	+	262.977i	−0.686624	+	0.686624i	0.274860	+	0.961484i	$0.411368\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−168.080	+	261.213i	−0.436573	+	0.678474i
$386$	−297.919			−0.771811
$387$	−34.0746	−	34.0746i	−0.0880480	−	0.0880480i
$388$	−159.370	+	159.370i	−0.410747	+	0.410747i
$389$		−	412.312i		−	1.05993i	−0.848021	−	0.529963i	$-0.822206\pi$
$389$		−	412.312i		−	1.05993i	0.848021	−	0.529963i	$-0.177794\pi$
$390$	112.219	+	72.2085i	0.287740	+	0.185150i
$391$	−5.30215			−0.0135605
$392$	−85.7779	−	85.7779i	−0.218821	−	0.218821i
$393$	46.9226	−	46.9226i	0.119396	−	0.119396i
$394$			20.4161i			0.0518175i
$395$	271.399	−	58.8781i	0.687086	−	0.149058i
$396$	38.8844			0.0981929
$397$	79.4123	+	79.4123i	0.200031	+	0.200031i	0.800013	−	0.599982i	$-0.204826\pi$
$397$	79.4123	+	79.4123i	0.200031	+	0.200031i	−0.599982	+	0.800013i	$0.704826\pi$
$398$	365.840	−	365.840i	0.919195	−	0.919195i
$399$		−	8.78454i		−	0.0220164i
$400$	91.0102	−	41.4383i	0.227526	−	0.103596i
$401$	−604.333			−1.50706			−0.753532	−	0.657411i	$-0.771651\pi$
$401$	−604.333			−1.50706			−0.753532	+	0.657411i	$0.771651\pi$
$402$	−58.3732	−	58.3732i	−0.145207	−	0.145207i
$403$	−187.489	+	187.489i	−0.465234	+	0.465234i
$404$		−	279.467i		−	0.691749i
$405$	−9.54051	−	43.9770i	−0.0235568	−	0.108585i
$406$	−309.230			−0.761651
$407$	41.3534	+	41.3534i	0.101606	+	0.101606i
$408$	−3.82982	+	3.82982i	−0.00938681	+	0.00938681i
$409$		−	31.8712i		−	0.0779247i	−0.999241	−	0.0389624i	$-0.987595\pi$
$409$		−	31.8712i		−	0.0779247i	0.999241	−	0.0389624i	$-0.0124052\pi$
$410$	−63.2058	+	98.2277i	−0.154161	+	0.239580i
$411$	−105.906			−0.257678
$412$	196.662	+	196.662i	0.477336	+	0.477336i
$413$	−425.411	+	425.411i	−1.03005	+	1.03005i
$414$			20.3470i			0.0491473i
$415$	−319.956	−	205.880i	−0.770978	−	0.496095i
$416$	−61.6348			−0.148161
$417$	−139.011	−	139.011i	−0.333360	−	0.333360i
$418$	3.42887	−	3.42887i	0.00820303	−	0.00820303i
$419$		−	542.434i		−	1.29459i	−0.762239	−	0.647296i	$-0.775900\pi$
$419$		−	542.434i		−	1.29459i	0.762239	−	0.647296i	$-0.224100\pi$
$420$	−162.258	+	35.2007i	−0.386328	+	0.0838112i
$421$	−377.783			−0.897347			−0.448673	−	0.893696i	$-0.648103\pi$
$421$	−377.783			−0.897347			−0.448673	+	0.893696i	$0.648103\pi$
$422$	52.5021	+	52.5021i	0.124413	+	0.124413i
$423$	−57.5561	+	57.5561i	−0.136066	+	0.136066i
$424$		−	31.0675i		−	0.0732724i
$425$	−25.8857	−	9.68832i	−0.0609075	−	0.0227960i
$426$	203.104			0.476770
$427$	256.533	+	256.533i	0.600779	+	0.600779i
$428$	22.8558	−	22.8558i	0.0534013	−	0.0534013i
$429$		−	122.303i		−	0.285087i
$430$	24.0807	+	111.000i	0.0560015	+	0.258139i
$431$	−380.401			−0.882600			−0.441300	−	0.897360i	$-0.645483\pi$
$431$	−380.401			−0.882600			−0.441300	+	0.897360i	$0.645483\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−520.972	+	520.972i	−1.20317	+	1.20317i	−0.229972	+	0.973197i	$0.573863\pi$
$433$	−520.972	+	520.972i	−1.20317	+	1.20317i	−0.973197	+	0.229972i	$0.926137\pi$
$434$		−	329.904i		−	0.760147i
$435$	−106.895	+	166.125i	−0.245736	+	0.381896i
$436$	159.652			0.366175
$437$	1.79422	+	1.79422i	0.00410577	+	0.00410577i
$438$	80.6531	−	80.6531i	0.184139	−	0.184139i
$439$		−	62.4039i		−	0.142150i	−0.997471	−	0.0710750i	$-0.977357\pi$
$439$		−	62.4039i		−	0.142150i	0.997471	−	0.0710750i	$-0.0226430\pi$
$440$	−77.0739	−	49.5942i	−0.175168	−	0.112714i
$441$	128.667			0.291761
$442$	12.0459	+	12.0459i	0.0272531	+	0.0272531i
$443$	3.05050	−	3.05050i	0.00688601	−	0.00688601i	−0.703655	−	0.710541i	$-0.748450\pi$
$443$	3.05050	−	3.05050i	0.00688601	−	0.00688601i	0.710541	+	0.703655i	$0.248450\pi$
$444$			31.2603i			0.0704061i
$445$	−44.9924	+	9.76079i	−0.101107	+	0.0219344i
$446$	−41.1333			−0.0922271
$447$	−99.0598	−	99.0598i	−0.221610	−	0.221610i
$448$	54.2259	−	54.2259i	0.121040	−	0.121040i
$449$			122.374i			0.272547i	0.990671	+	0.136274i	$0.0435127\pi$
$449$			122.374i			0.272547i	−0.990671	+	0.136274i	$0.956487\pi$
$450$	−37.1789	+	99.3364i	−0.0826199	+	0.220748i
$451$	107.054			0.237371
$452$	161.472	+	161.472i	0.357238	+	0.357238i
$453$	−67.1963	+	67.1963i	−0.148336	+	0.148336i
$454$			466.500i			1.02753i
$455$	110.716	+	510.347i	0.243332	+	1.12164i
$456$	2.59198			0.00568418
$457$	191.581	+	191.581i	0.419213	+	0.419213i	0.884933	−	0.465719i	$-0.154204\pi$
$457$	191.581	+	191.581i	0.419213	+	0.419213i	−0.465719	+	0.884933i	$0.654204\pi$
$458$	407.228	−	407.228i	0.889143	−	0.889143i
$459$		−	5.74473i		−	0.0125158i
$460$	25.9511	−	40.3304i	0.0564154	−	0.0876748i
$461$	−69.9790			−0.151798			−0.0758992	−	0.997115i	$-0.524183\pi$
$461$	−69.9790			−0.151798			−0.0758992	+	0.997115i	$0.524183\pi$
$462$	107.601	+	107.601i	0.232902	+	0.232902i
$463$	−506.603	+	506.603i	−1.09417	+	1.09417i	−0.0990971	+	0.995078i	$0.531595\pi$
$463$	−506.603	+	506.603i	−1.09417	+	1.09417i	−0.995078	+	0.0990971i	$0.968405\pi$
$464$		−	91.2422i		−	0.196643i
$465$	−177.231	−	114.042i	−0.381142	−	0.245251i
$466$	135.628			0.291046
$467$	361.691	+	361.691i	0.774498	+	0.774498i	0.978889	−	0.204391i	$-0.0655215\pi$
$467$	361.691	+	361.691i	0.774498	+	0.774498i	−0.204391	+	0.978889i	$0.565521\pi$
$468$	46.2261	−	46.2261i	0.0987737	−	0.0987737i
$469$		−	323.061i		−	0.688830i
$470$	187.492	−	40.6751i	0.398920	−	0.0865429i
$471$	−352.222			−0.747817
$472$	−125.523	−	125.523i	−0.265938	−	0.265938i
$473$	73.6094	−	73.6094i	0.155622	−	0.155622i
$474$		−	136.051i		−	0.287027i
$475$	5.48112	+	12.0381i	0.0115392	+	0.0253433i
$476$	−21.1958			−0.0445289
$477$	23.3006	+	23.3006i	0.0488483	+	0.0488483i
$478$	126.104	−	126.104i	0.263815	−	0.263815i
$479$			472.746i			0.986945i	0.869762	+	0.493472i	$0.164273\pi$
$479$			472.746i			0.986945i	−0.869762	+	0.493472i	$0.835727\pi$
$480$	−10.3864	−	47.8761i	−0.0216383	−	0.0997419i
$481$	98.3227			0.204413
$482$	169.295	+	169.295i	0.351234	+	0.351234i
$483$	−56.3042	+	56.3042i	−0.116572	+	0.116572i
$484$		−	158.000i		−	0.326447i
$485$	−304.897	+	473.838i	−0.628654	+	0.976986i
$486$	−22.0454			−0.0453609
$487$	−245.070	−	245.070i	−0.503224	−	0.503224i	0.409214	−	0.912438i	$-0.365803\pi$
$487$	−245.070	−	245.070i	−0.503224	−	0.503224i	−0.912438	+	0.409214i	$0.865803\pi$
$488$	−75.6931	+	75.6931i	−0.155109	+	0.155109i
$489$		−	265.021i		−	0.541965i
$490$	−255.034	−	164.105i	−0.520478	−	0.334908i
$491$	−89.9842			−0.183267			−0.0916336	−	0.995793i	$-0.529209\pi$
$491$	−89.9842			−0.183267			−0.0916336	+	0.995793i	$0.529209\pi$
$492$	40.4628	+	40.4628i	0.0822415	+	0.0822415i
$493$	−17.8323	+	17.8323i	−0.0361711	+	0.0361711i
$494$		−	8.15254i		−	0.0165031i
$495$	95.0011	−	20.6098i	0.191921	−	0.0416360i
$496$	97.3421			0.196254
$497$	562.030	+	562.030i	1.13085	+	1.13085i
$498$	−131.799	+	131.799i	−0.264657	+	0.264657i
$499$			823.542i			1.65038i	0.564852	+	0.825192i	$0.308933\pi$
$499$			823.542i			1.65038i	−0.564852	+	0.825192i	$0.691067\pi$
$500$	200.390	−	149.479i	0.400780	−	0.298958i
$501$	436.421			0.871101
$502$	352.257	+	352.257i	0.701707	+	0.701707i
$503$	−141.332	+	141.332i	−0.280978	+	0.280978i	−0.833499	−	0.552521i	$-0.813666\pi$
$503$	−141.332	+	141.332i	−0.280978	+	0.280978i	0.552521	+	0.833499i	$0.313666\pi$
$504$			81.3388i			0.161387i
$505$	−148.125	−	682.784i	−0.293317	−	1.35205i
$506$	−43.9544			−0.0868665
$507$	61.5875	+	61.5875i	0.121474	+	0.121474i
$508$	261.511	−	261.511i	0.514785	−	0.514785i
$509$		−	565.134i		−	1.11028i	−0.831756	−	0.555141i	$-0.812664\pi$
$509$		−	565.134i		−	1.11028i	0.831756	−	0.555141i	$-0.187336\pi$
$510$	−7.32698	+	11.3868i	−0.0143666	+	0.0223271i
$511$	446.367			0.873517
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−1.94399	+	1.94399i	−0.00378945	+	0.00378945i
$514$			72.2366i			0.140538i
$515$	584.716	+	376.243i	1.13537	+	0.730568i
$516$	55.6436			0.107836
$517$	−124.335	−	124.335i	−0.240494	−	0.240494i
$518$	−86.5037	+	86.5037i	−0.166995	+	0.166995i
$519$			29.5286i			0.0568953i
$520$	−150.584	+	32.6682i	−0.289585	+	0.0628234i
$521$	−355.537			−0.682413			−0.341206	−	0.939988i	$-0.610835\pi$
$521$	−355.537			−0.682413			−0.341206	+	0.939988i	$0.610835\pi$
$522$	68.4316	+	68.4316i	0.131095	+	0.131095i
$523$	−325.412	+	325.412i	−0.622204	+	0.622204i	−0.946094	−	0.323891i	$-0.895009\pi$
$523$	−325.412	+	325.412i	−0.622204	+	0.622204i	0.323891	+	0.946094i	$0.395009\pi$
$524$			76.6244i			0.146230i
$525$	−377.766	+	172.002i	−0.719554	+	0.327624i
$526$	−435.272			−0.827513
$527$	−19.0245	−	19.0245i	−0.0360996	−	0.0360996i
$528$	−31.7490	+	31.7490i	−0.0601306	+	0.0601306i
$529$		−	23.0000i		−	0.0434783i
$530$	−16.4666	−	75.9031i	−0.0310691	−	0.143213i
$531$	188.284			0.354584
$532$	7.17255	+	7.17255i	0.0134822	+	0.0134822i
$533$	127.267	−	127.267i	0.238775	−	0.238775i
$534$			22.5544i			0.0422367i
$535$	43.7263	−	67.9546i	0.0817313	−	0.127018i
$536$	95.3231			0.177842
$537$	57.8971	+	57.8971i	0.107816	+	0.107816i
$538$	525.831	−	525.831i	0.977381	−	0.977381i
$539$			277.952i			0.515680i
$540$	43.6969	+	28.1173i	0.0809202	+	0.0520691i
$541$	862.324			1.59394			0.796972	−	0.604016i	$-0.206434\pi$
$541$	862.324			1.59394			0.796972	+	0.604016i	$0.206434\pi$
$542$	518.661	+	518.661i	0.956939	+	0.956939i
$543$	−58.0998	+	58.0998i	−0.106998	+	0.106998i
$544$		−	6.25407i		−	0.0114965i
$545$	390.057	−	84.6202i	0.715701	−	0.155266i
$546$	255.834			0.468560
$547$	530.824	+	530.824i	0.970429	+	0.970429i	0.999575	−	0.0291465i	$-0.00927895\pi$
$547$	530.824	+	530.824i	0.970429	+	0.970429i	−0.0291465	+	0.999575i	$0.509279\pi$
$548$	86.4715	−	86.4715i	0.157795	−	0.157795i
$549$		−	113.540i		−	0.206812i
$550$	−214.591	−	80.3155i	−0.390165	−	0.146028i
$551$	12.0688			0.0219034
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	376.480	−	376.480i	0.680795	−	0.680795i
$554$		−	447.234i		−	0.807281i
$555$	16.5688	+	76.3742i	0.0298538	+	0.137611i
$556$	227.004			0.408281
$557$	82.0074	+	82.0074i	0.147230	+	0.147230i	0.776880	−	0.629649i	$-0.216801\pi$
$557$	82.0074	+	82.0074i	0.147230	+	0.147230i	−0.629649	+	0.776880i	$0.716801\pi$
$558$	−73.0066	+	73.0066i	−0.130836	+	0.130836i
$559$		−	175.015i		−	0.313086i
$560$	103.742	−	161.224i	0.185253	−	0.287900i
$561$	12.4100			0.0221212
$562$	425.954	+	425.954i	0.757926	+	0.757926i
$563$	−467.229	+	467.229i	−0.829892	+	0.829892i	−0.987501	−	0.157610i	$-0.949621\pi$
$563$	−467.229	+	467.229i	−0.829892	+	0.829892i	0.157610	+	0.987501i	$0.449621\pi$
$564$		−	93.9887i		−	0.166647i
$565$	480.087	+	308.918i	0.849712	+	0.546758i
$566$	61.1315			0.108006
$567$	−61.0041	−	61.0041i	−0.107591	−	0.107591i
$568$	−165.834	+	165.834i	−0.291961	+	0.291961i
$569$		−	571.773i		−	1.00487i	−0.864614	−	0.502437i	$-0.832437\pi$
$569$		−	571.773i		−	1.00487i	0.864614	−	0.502437i	$-0.167563\pi$
$570$	6.33265	−	1.37382i	0.0111099	−	0.00241022i
$571$	303.885			0.532197			0.266099	−	0.963946i	$-0.414265\pi$
$571$	303.885			0.532197			0.266099	+	0.963946i	$0.414265\pi$
$572$	99.8596	+	99.8596i	0.174580	+	0.174580i
$573$	155.424	−	155.424i	0.271247	−	0.271247i
$574$			223.938i			0.390135i
$575$	42.0266	−	112.289i	0.0730898	−	0.195285i
$576$	−24.0000			−0.0416667
$577$	334.483	+	334.483i	0.579693	+	0.579693i	0.934819	−	0.355126i	$-0.115562\pi$
$577$	334.483	+	334.483i	0.579693	+	0.579693i	−0.355126	+	0.934819i	$0.615562\pi$
$578$	287.778	−	287.778i	0.497885	−	0.497885i
$579$			364.875i			0.630181i
$580$	−48.3609	−	222.920i	−0.0833809	−	0.384345i
$581$	−729.429			−1.25547
$582$	195.188	+	195.188i	0.335374	+	0.335374i
$583$	−50.3350	+	50.3350i	−0.0863379	+	0.0863379i
$584$			131.706i			0.225524i
$585$	88.4370	−	137.439i	0.151174	−	0.234939i
$586$	−475.099			−0.810749
$587$	102.989	+	102.989i	0.175450	+	0.175450i	0.789369	−	0.613919i	$-0.210408\pi$
$587$	102.989	+	102.989i	0.175450	+	0.175450i	−0.613919	+	0.789369i	$0.710408\pi$
$588$	−105.056	+	105.056i	−0.178667	+	0.178667i
$589$			12.8756i			0.0218601i
$590$	−373.204	−	240.142i	−0.632548	−	0.407021i
$591$	25.0045			0.0423088
$592$	−25.5239	−	25.5239i	−0.0431148	−	0.0431148i
$593$	−798.294	+	798.294i	−1.34620	+	1.34620i	−0.456444	+	0.889752i	$0.650877\pi$
$593$	−798.294	+	798.294i	−1.34620	+	1.34620i	−0.889752	+	0.456444i	$0.849123\pi$
$594$		−	47.6234i		−	0.0801741i
$595$	−51.7848	+	11.2344i	−0.0870333	+	0.0188813i
$596$	161.764			0.271416
$597$	−448.060	−	448.060i	−0.750520	−	0.750520i
$598$	−52.2534	+	52.2534i	−0.0873803	+	0.0873803i
$599$			176.987i			0.295471i	0.989027	+	0.147736i	$0.0471984\pi$
$599$			176.987i			0.295471i	−0.989027	+	0.147736i	$0.952802\pi$
$600$	−50.7514	−	111.464i	−0.0845856	−	0.185774i
$601$	−879.913			−1.46408			−0.732041	−	0.681261i	$-0.761432\pi$
$601$	−879.913			−1.46408			−0.732041	+	0.681261i	$0.761432\pi$
$602$	153.977	+	153.977i	0.255776	+	0.255776i
$603$	−71.4923	+	71.4923i	−0.118561	+	0.118561i
$604$		−	109.731i		−	0.181674i
$605$	−83.7446	−	386.021i	−0.138421	−	0.638052i
$606$	−342.275			−0.564811
$607$	80.2035	+	80.2035i	0.132131	+	0.132131i	0.770079	−	0.637948i	$-0.220217\pi$
$607$	80.2035	+	80.2035i	0.132131	+	0.132131i	−0.637948	+	0.770079i	$0.720217\pi$
$608$	−2.11635	+	2.11635i	−0.00348083	+	0.00348083i
$609$			378.728i			0.621886i
$610$	−144.811	+	225.050i	−0.237396	+	0.368935i
$611$	−295.622			−0.483832
$612$	4.69055	+	4.69055i	0.00766430	+	0.00766430i
$613$	−619.641	+	619.641i	−1.01083	+	1.01083i	−0.0108925	+	0.999941i	$0.503467\pi$
$613$	−619.641	+	619.641i	−1.01083	+	1.01083i	−0.999941	+	0.0108925i	$0.996533\pi$
$614$		−	475.825i		−	0.774959i
$615$	120.304	+	77.4110i	0.195616	+	0.125872i
$616$	−175.712			−0.285246
$617$	−29.7434	−	29.7434i	−0.0482065	−	0.0482065i	0.682593	−	0.730799i	$-0.260852\pi$
$617$	−29.7434	−	29.7434i	−0.0482065	−	0.0482065i	−0.730799	+	0.682593i	$0.760852\pi$
$618$	240.861	−	240.861i	0.389743	−	0.389743i
$619$			220.508i			0.356233i	0.984009	+	0.178116i	$0.0570004\pi$
$619$			220.508i			0.356233i	−0.984009	+	0.178116i	$0.943000\pi$
$620$	237.823	−	51.5940i	0.383586	−	0.0832162i
$621$	24.9199			0.0401286
$622$	−81.3114	−	81.3114i	−0.130726	−	0.130726i
$623$	−62.4127	+	62.4127i	−0.100181	+	0.100181i
$624$			75.4869i			0.120973i
$625$	410.358	−	471.414i	0.656573	−	0.754262i
$626$	−654.400			−1.04537
$627$	−4.19949	−	4.19949i	−0.00669775	−	0.00669775i
$628$	287.588	−	287.588i	0.457942	−	0.457942i
$629$			9.97678i			0.0158613i
$630$	43.1119	+	198.724i	0.0684315	+	0.315436i
$631$	716.316			1.13521			0.567604	−	0.823302i	$-0.307871\pi$
$631$	716.316			1.13521			0.567604	+	0.823302i	$0.307871\pi$
$632$	111.085	+	111.085i	0.175767	+	0.175767i
$633$	64.3017	−	64.3017i	0.101582	−	0.101582i
$634$			548.941i			0.865837i
$635$	500.307	−	777.523i	0.787885	−	1.22445i
$636$	−38.0498			−0.0598267
$637$	330.431	+	330.431i	0.518730	+	0.518730i
$638$	−147.829	+	147.829i	−0.231707	+	0.231707i
$639$		−	248.751i		−	0.389281i
$640$	47.5711	+	30.6102i	0.0743299	+	0.0478285i
$641$	−969.601			−1.51264			−0.756319	−	0.654203i	$-0.773004\pi$
$641$	−969.601			−1.51264			−0.756319	+	0.654203i	$0.773004\pi$
$642$	−27.9925	−	27.9925i	−0.0436020	−	0.0436020i
$643$	373.341	−	373.341i	0.580623	−	0.580623i	−0.354451	−	0.935075i	$-0.615332\pi$
$643$	373.341	−	373.341i	0.580623	−	0.580623i	0.935075	+	0.354451i	$0.115332\pi$
$644$		−	91.9445i		−	0.142771i
$645$	135.947	−	29.4927i	0.210770	−	0.0457250i
$646$	0.827236			0.00128055
$647$	−695.075	−	695.075i	−1.07430	−	1.07430i	−0.997008	−	0.0772961i	$-0.975371\pi$
$647$	−695.075	−	695.075i	−1.07430	−	1.07430i	−0.0772961	−	0.997008i	$-0.524629\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			406.739i			0.626717i
$650$	−350.587	+	159.628i	−0.539365	+	0.245581i
$651$	−404.048			−0.620657
$652$	216.389	+	216.389i	0.331885	+	0.331885i
$653$	42.2499	−	42.2499i	0.0647012	−	0.0647012i	−0.674016	−	0.738717i	$-0.735432\pi$
$653$	42.2499	−	42.2499i	0.0647012	−	0.0647012i	0.738717	+	0.674016i	$0.235432\pi$
$654$		−	195.533i		−	0.298981i
$655$	40.6131	+	187.206i	0.0620047	+	0.285811i
$656$	−66.0755			−0.100725
$657$	−98.7795	−	98.7795i	−0.150349	−	0.150349i
$658$	260.086	−	260.086i	0.395267	−	0.395267i
$659$		−	961.226i		−	1.45861i	−0.684187	−	0.729307i	$-0.739843\pi$
$659$		−	961.226i		−	1.45861i	0.684187	−	0.729307i	$-0.260157\pi$
$660$	−60.7402	+	94.3959i	−0.0920306	+	0.143024i
$661$	163.994			0.248100			0.124050	−	0.992276i	$-0.460412\pi$
$661$	163.994			0.248100			0.124050	+	0.992276i	$0.460412\pi$
$662$	209.454	+	209.454i	0.316396	+	0.316396i
$663$	14.7531	−	14.7531i	0.0222521	−	0.0222521i
$664$		−	215.227i		−	0.324137i
$665$	21.3254	+	13.7221i	0.0320683	+	0.0206347i
$666$	38.2859			0.0574864
$667$	−77.3543	−	77.3543i	−0.115973	−	0.115973i
$668$	−356.337	+	356.337i	−0.533438	+	0.533438i
$669$			50.3778i			0.0753031i
$670$	232.890	−	50.5239i	0.347598	−	0.0754088i
$671$	245.273			0.365534
$672$	−66.4129	−	66.4129i	−0.0988287	−	0.0988287i
$673$	171.550	−	171.550i	0.254904	−	0.254904i	−0.568074	−	0.822978i	$-0.692311\pi$
$673$	171.550	−	171.550i	0.254904	−	0.254904i	0.822978	+	0.568074i	$0.192311\pi$
$674$		−	534.149i		−	0.792506i
$675$	121.662	+	45.5347i	0.180240	+	0.0674588i
$676$	−100.572			−0.148775
$677$	−164.860	−	164.860i	−0.243516	−	0.243516i	0.574787	−	0.818303i	$-0.305085\pi$
$677$	−164.860	−	164.860i	−0.243516	−	0.243516i	−0.818303	+	0.574787i	$0.805085\pi$
$678$	197.762	−	197.762i	0.291684	−	0.291684i
$679$			1080.25i			1.59094i
$680$	−3.31483	−	15.2797i	−0.00487475	−	0.0224702i
$681$	571.343			0.838977
$682$	−157.712	−	157.712i	−0.231249	−	0.231249i
$683$	16.9389	−	16.9389i	0.0248007	−	0.0248007i	−0.694598	−	0.719398i	$-0.744418\pi$
$683$	16.9389	−	16.9389i	0.0248007	−	0.0248007i	0.719398	+	0.694598i	$0.244418\pi$
$684$		−	3.17452i		−	0.00464111i
$685$	165.432	−	257.097i	0.241507	−	0.375324i
$686$	82.8445			0.120765
$687$	−498.750	−	498.750i	−0.725982	−	0.725982i
$688$	−45.4328	+	45.4328i	−0.0660360	+	0.0660360i
$689$			119.677i			0.173697i
$690$	−49.3944	−	31.7835i	−0.0715862	−	0.0460630i
$691$	1270.25			1.83828			0.919141	−	0.393928i	$-0.128884\pi$
$691$	1270.25			1.83828			0.919141	+	0.393928i	$0.128884\pi$
$692$	−24.1100	−	24.1100i	−0.0348411	−	0.0348411i
$693$	131.784	−	131.784i	0.190164	−	0.190164i
$694$			604.754i			0.871403i
$695$	554.609	−	120.319i	0.797999	−	0.173120i
$696$	−111.748			−0.160558
$697$	12.9138	+	12.9138i	0.0185276	+	0.0185276i
$698$	38.7883	−	38.7883i	0.0555706	−	0.0555706i
$699$		−	166.109i		−	0.237638i
$700$	168.005	−	448.884i	0.240007	−	0.641263i
$701$	−1394.68			−1.98956			−0.994781	−	0.102031i	$-0.967466\pi$
$701$	−1394.68			−1.98956			−0.994781	+	0.102031i	$0.967466\pi$
$702$	−56.6152	−	56.6152i	−0.0806484	−	0.0806484i
$703$	3.37609	−	3.37609i	0.00480241	−	0.00480241i
$704$		−	51.8458i		−	0.0736446i
$705$	−49.8167	−	229.630i	−0.0706620	−	0.325717i
$706$	456.850			0.647096
$707$	−947.145	−	947.145i	−1.33967	−	1.33967i
$708$	−153.733	+	153.733i	−0.217137	+	0.217137i
$709$		−	842.555i		−	1.18837i	−0.804328	−	0.594185i	$-0.797475\pi$
$709$		−	842.555i		−	1.18837i	0.804328	−	0.594185i	$-0.202525\pi$
$710$	−317.263	+	493.057i	−0.446850	+	0.694446i
$711$	−166.627			−0.234356
$712$	−18.4156	−	18.4156i	−0.0258646	−	0.0258646i
$713$	82.5258	−	82.5258i	0.115744	−	0.115744i
$714$			25.9594i			0.0363577i
$715$	296.902	+	191.045i	0.415248	+	0.267196i
$716$	−94.5456			−0.132047
$717$	−154.445	−	154.445i	−0.215404	−	0.215404i
$718$	−572.493	+	572.493i	−0.797344	+	0.797344i
$719$			685.162i			0.952937i	0.879191	+	0.476469i	$0.158083\pi$
$719$			685.162i			0.952937i	−0.879191	+	0.476469i	$0.841917\pi$
$720$	−58.6360	+	12.7207i	−0.0814389	+	0.0176676i
$721$	1333.02			1.84885
$722$	360.720	+	360.720i	0.499612	+	0.499612i
$723$	207.343	−	207.343i	0.286781	−	0.286781i
$724$		−	94.8765i		−	0.131045i
$725$	−236.308	−	518.998i	−0.325942	−	0.715860i
$726$	−193.510			−0.266543
$727$	752.841	+	752.841i	1.03554	+	1.03554i	0.999345	+	0.0361997i	$0.0115252\pi$
$727$	752.841	+	752.841i	1.03554	+	1.03554i	0.0361997	+	0.999345i	$0.488475\pi$
$728$	−208.888	+	208.888i	−0.286933	+	0.286933i
$729$			27.0000i			0.0370370i
$730$	69.8079	+	321.780i	0.0956272	+	0.440794i
$731$	17.7587			0.0242938
$732$	92.7047	+	92.7047i	0.126646	+	0.126646i
$733$	−232.917	+	232.917i	−0.317758	+	0.317758i	−0.847905	−	0.530148i	$-0.822137\pi$
$733$	−232.917	+	232.917i	−0.317758	+	0.317758i	0.530148	+	0.847905i	$0.322137\pi$
$734$		−	312.501i		−	0.425750i
$735$	−200.987	+	312.352i	−0.273451	+	0.424969i
$736$	27.1293			0.0368605
$737$	−154.441	−	154.441i	−0.209553	−	0.209553i
$738$	49.5566	−	49.5566i	0.0671499	−	0.0671499i
$739$		−	135.488i		−	0.183339i	−0.995789	−	0.0916696i	$-0.970780\pi$
$739$		−	135.488i		−	0.183339i	0.995789	−	0.0916696i	$-0.0292204\pi$
$740$	−75.8877	−	48.8309i	−0.102551	−	0.0659877i
$741$	−9.98478			−0.0134747
$742$	−105.291	−	105.291i	−0.141902	−	0.141902i
$743$	726.590	−	726.590i	0.977914	−	0.977914i	−0.0218472	−	0.999761i	$-0.506955\pi$
$743$	726.590	−	726.590i	0.977914	−	0.977914i	0.999761	+	0.0218472i	$0.00695474\pi$
$744$		−	119.219i		−	0.160241i
$745$	395.217	−	85.7395i	0.530492	−	0.115087i
$746$	29.5768			0.0396472
$747$	161.420	+	161.420i	0.216091	+	0.216091i
$748$	−10.1327	+	10.1327i	−0.0135464	+	0.0135464i
$749$		−	154.922i		−	0.206838i
$750$	−183.073	−	245.426i	−0.244098	−	0.327235i
$751$	−1008.88			−1.34339			−0.671694	−	0.740829i	$-0.734433\pi$
$751$	−1008.88			−1.34339			−0.671694	+	0.740829i	$0.734433\pi$
$752$	76.7415	+	76.7415i	0.102050	+	0.102050i
$753$	431.425	−	431.425i	0.572941	−	0.572941i
$754$			351.481i			0.466155i
$755$	−58.1605	−	268.091i	−0.0770338	−	0.355088i
$756$	99.6193			0.131772
$757$	570.746	+	570.746i	0.753958	+	0.753958i	0.975215	−	0.221257i	$-0.0710161\pi$
$757$	570.746	+	570.746i	0.753958	+	0.753958i	−0.221257	+	0.975215i	$0.571016\pi$
$758$	−39.4302	+	39.4302i	−0.0520188	+	0.0520188i
$759$			53.8330i			0.0709262i
$760$	−4.04887	+	6.29231i	−0.00532746	+	0.00827936i
$761$	−1183.62			−1.55535			−0.777675	−	0.628667i	$-0.783601\pi$
$761$	−1183.62			−1.55535			−0.777675	+	0.628667i	$0.783601\pi$
$762$	−320.284	−	320.284i	−0.420320	−	0.420320i
$763$	541.080	−	541.080i	0.709148	−	0.709148i
$764$			253.807i			0.332208i
$765$	13.9459	+	8.97368i	0.0182300	+	0.0117303i
$766$	−525.954			−0.686624
$767$	483.535	+	483.535i	0.630424	+	0.630424i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	363.068i		−	0.472130i	−0.971737	−	0.236065i	$-0.924142\pi$
$769$		−	363.068i		−	0.472130i	0.971737	−	0.236065i	$-0.0758578\pi$
$770$	−429.293	+	93.1321i	−0.557523	+	0.120951i
$771$	88.4714			0.114749
$772$	−297.919	−	297.919i	−0.385905	−	0.385905i
$773$	−1014.90	+	1014.90i	−1.31293	+	1.31293i	−0.393693	+	0.919242i	$0.628803\pi$
$773$	−1014.90	+	1014.90i	−1.31293	+	1.31293i	−0.919242	+	0.393693i	$0.871197\pi$
$774$		−	68.1492i		−	0.0880480i
$775$	553.695	−	252.106i	0.714446	−	0.325298i
$776$	−318.740			−0.410747
$777$	105.945	+	105.945i	0.136351	+	0.136351i
$778$	412.312	−	412.312i	0.529963	−	0.529963i
$779$		−	8.73991i		−	0.0112194i
$780$	40.0102	+	184.427i	0.0512951	+	0.236445i
$781$	537.362			0.688044
$782$	−5.30215	−	5.30215i	−0.00678024	−	0.00678024i
$783$	83.8113	−	83.8113i	0.107039	−	0.107039i
$784$		−	171.556i		−	0.218821i
$785$	550.196	−	855.055i	0.700886	−	1.08924i
$786$	93.8453			0.119396
$787$	−225.596	−	225.596i	−0.286653	−	0.286653i	0.549102	−	0.835755i	$-0.314970\pi$
$787$	−225.596	−	225.596i	−0.286653	−	0.286653i	−0.835755	+	0.549102i	$0.814970\pi$
$788$	−20.4161	+	20.4161i	−0.0259088	+	0.0259088i
$789$			533.097i			0.675661i
$790$	330.277	+	212.521i	0.418072	+	0.269014i
$791$	1094.49			1.38368
$792$	38.8844	+	38.8844i	0.0490964	+	0.0490964i
$793$	291.583	−	291.583i	0.367696	−	0.367696i
$794$			158.825i			0.200031i
$795$	−92.9620	+	20.1674i	−0.116933	+	0.0253679i
$796$	731.679			0.919195
$797$	−991.681	−	991.681i	−1.24427	−	1.24427i	−0.958213	−	0.286054i	$-0.907656\pi$
$797$	−991.681	−	991.681i	−1.24427	−	1.24427i	−0.286054	−	0.958213i	$-0.592344\pi$
$798$	8.78454	−	8.78454i	0.0110082	−	0.0110082i
$799$		−	29.9967i		−	0.0375428i
$800$	132.449	+	49.5719i	0.165561	+	0.0619649i
$801$	27.6234			0.0344862
$802$	−604.333	−	604.333i	−0.753532	−	0.753532i
$803$	213.388	−	213.388i	0.265738	−	0.265738i
$804$		−	116.746i		−	0.145207i
$805$	−48.7331	−	224.636i	−0.0605381	−	0.279051i
$806$	−374.979			−0.465234
$807$	−644.009	−	644.009i	−0.798028	−	0.798028i
$808$	279.467	−	279.467i	0.345875	−	0.345875i
$809$			846.880i			1.04682i	0.852080	+	0.523412i	$0.175341\pi$
$809$			846.880i			1.04682i	−0.852080	+	0.523412i	$0.824659\pi$
$810$	34.4365	−	53.5175i	0.0425142	−	0.0660710i
$811$	−703.466			−0.867405			−0.433703	−	0.901056i	$-0.642793\pi$
$811$	−703.466			−0.867405			−0.433703	+	0.901056i	$0.642793\pi$
$812$	−309.230	−	309.230i	−0.380826	−	0.380826i
$813$	635.227	−	635.227i	0.781337	−	0.781337i
$814$			82.7069i			0.101606i
$815$	643.366	+	413.982i	0.789406	+	0.507953i
$816$	−7.65964			−0.00938681
$817$	−6.00947	−	6.00947i	−0.00735553	−	0.00735553i
$818$	31.8712	−	31.8712i	0.0389624	−	0.0389624i
$819$		−	313.331i		−	0.382578i
$820$	−161.433	+	35.0219i	−0.196870	+	0.0427096i
$821$	−252.059			−0.307015			−0.153507	−	0.988147i	$-0.549057\pi$
$821$	−252.059			−0.307015			−0.153507	+	0.988147i	$0.549057\pi$
$822$	−105.906	−	105.906i	−0.128839	−	0.128839i
$823$	511.780	−	511.780i	0.621847	−	0.621847i	−0.324156	−	0.946003i	$-0.605080\pi$
$823$	511.780	−	511.780i	0.621847	−	0.621847i	0.946003	+	0.324156i	$0.105080\pi$
$824$			393.325i			0.477336i
$825$	−98.3660	+	262.819i	−0.119232	+	0.318568i
$826$	−850.822			−1.03005
$827$	169.581	+	169.581i	0.205055	+	0.205055i	0.802162	−	0.597107i	$-0.203683\pi$
$827$	169.581	+	169.581i	0.205055	+	0.205055i	−0.597107	+	0.802162i	$0.703683\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$		−	772.576i		−	0.931938i	−0.884801	−	0.465969i	$-0.845706\pi$
$829$		−	772.576i		−	0.931938i	0.884801	−	0.465969i	$-0.154294\pi$
$830$	−114.076	−	525.835i	−0.137441	−	0.633537i
$831$	−547.747			−0.659142
$832$	−61.6348	−	61.6348i	−0.0740803	−	0.0740803i
$833$	−33.5288	+	33.5288i	−0.0402507	+	0.0402507i
$834$		−	278.022i		−	0.333360i
$835$	−681.722	+	1059.46i	−0.816433	+	1.26881i
$836$	6.85773			0.00820303
$837$	89.4144	+	89.4144i	0.106827	+	0.106827i
$838$	542.434	−	542.434i	0.647296	−	0.647296i
$839$			252.116i			0.300496i	0.988648	+	0.150248i	$0.0480072\pi$
$839$			252.116i			0.300496i	−0.988648	+	0.150248i	$0.951993\pi$
$840$	−197.458	−	127.057i	−0.235070	−	0.151258i
$841$	320.679			0.381307
$842$	−377.783	−	377.783i	−0.448673	−	0.448673i
$843$	521.685	−	521.685i	0.618844	−	0.618844i
$844$			105.004i			0.124413i
$845$	−245.714	+	53.3060i	−0.290786	+	0.0630840i
$846$	−115.112			−0.136066
$847$	−535.482	−	535.482i	−0.632210	−	0.632210i
$848$	31.0675	−	31.0675i	0.0366362	−	0.0366362i
$849$		−	74.8705i		−	0.0881867i
$850$	−16.1974	−	35.5740i	−0.0190557	−	0.0418518i
$851$	−43.2780			−0.0508554
$852$	203.104	+	203.104i	0.238385	+	0.238385i
$853$	−758.628	+	758.628i	−0.889365	+	0.889365i	−0.994462	−	0.105097i	$-0.966485\pi$
$853$	−758.628	+	758.628i	−0.889365	+	0.889365i	0.105097	+	0.994462i	$0.466485\pi$
$854$			513.066i			0.600779i
$855$	−1.68258	−	7.75588i	−0.00196794	−	0.00907121i
$856$	45.7115			0.0534013
$857$	−303.385	−	303.385i	−0.354008	−	0.354008i	0.507591	−	0.861598i	$-0.330536\pi$
$857$	−303.385	−	303.385i	−0.354008	−	0.354008i	−0.861598	+	0.507591i	$0.830536\pi$
$858$	122.303	−	122.303i	0.142544	−	0.142544i
$859$			1629.59i			1.89707i	0.316668	+	0.948536i	$0.397436\pi$
$859$			1629.59i			1.89707i	−0.316668	+	0.948536i	$0.602564\pi$
$860$	−86.9193	+	135.081i	−0.101069	+	0.157070i
$861$	274.266			0.318544
$862$	−380.401	−	380.401i	−0.441300	−	0.441300i
$863$	−545.327	+	545.327i	−0.631896	+	0.631896i	−0.948543	−	0.316647i	$-0.897443\pi$
$863$	−545.327	+	545.327i	−0.631896	+	0.631896i	0.316647	+	0.948543i	$0.397443\pi$
$864$			29.3939i			0.0340207i
$865$	−71.6839	−	46.1259i	−0.0828715	−	0.0533247i
$866$	−1041.94			−1.20317
$867$	−352.454	−	352.454i	−0.406522	−	0.406522i
$868$	329.904	−	329.904i	0.380073	−	0.380073i
$869$		−	359.955i		−	0.414218i
$870$	−273.020	+	59.2298i	−0.313816	+	0.0680802i
$871$	−367.201			−0.421586
$872$	159.652	+	159.652i	0.183087	+	0.183087i
$873$	239.055	−	239.055i	0.273832	−	0.273832i
$874$			3.58844i			0.00410577i
$875$	172.544	−	1185.75i	0.197193	−	1.35514i
$876$	161.306			0.184139
$877$	−229.151	−	229.151i	−0.261290	−	0.261290i	0.564288	−	0.825578i	$-0.309151\pi$
$877$	−229.151	−	229.151i	−0.261290	−	0.261290i	−0.825578	+	0.564288i	$0.809151\pi$
$878$	62.4039	−	62.4039i	0.0710750	−	0.0710750i
$879$			581.875i			0.661974i
$880$	−27.4797	−	126.668i	−0.0312270	−	0.143941i
$881$	−1029.46			−1.16851			−0.584254	−	0.811571i	$-0.698613\pi$
$881$	−1029.46			−1.16851			−0.584254	+	0.811571i	$0.698613\pi$
$882$	128.667	+	128.667i	0.145881	+	0.145881i
$883$	1211.81	−	1211.81i	1.37238	−	1.37238i	0.515473	−	0.856906i	$-0.327616\pi$
$883$	1211.81	−	1211.81i	1.37238	−	1.37238i	0.856906	−	0.515473i	$-0.172384\pi$
$884$			24.0918i			0.0272531i
$885$	−294.113	+	457.079i	−0.332331	+	0.516474i
$886$	6.10101			0.00688601
$887$	653.892	+	653.892i	0.737196	+	0.737196i	0.972034	−	0.234839i	$-0.0754562\pi$
$887$	653.892	+	653.892i	0.737196	+	0.737196i	−0.234839	+	0.972034i	$0.575456\pi$
$888$	−31.2603	+	31.2603i	−0.0352031	+	0.0352031i
$889$		−	1772.58i		−	1.99391i
$890$	−54.7532	−	35.2316i	−0.0615205	−	0.0395861i
$891$	−58.3266			−0.0654619
$892$	−41.1333	−	41.1333i	−0.0461136	−	0.0461136i
$893$	−10.1507	+	10.1507i	−0.0113670	+	0.0113670i
$894$		−	198.120i		−	0.221610i
$895$	−230.991	+	50.1118i	−0.258090	+	0.0559909i
$896$	108.452			0.121040
$897$	63.9971	+	63.9971i	0.0713457	+	0.0713457i
$898$	−122.374	+	122.374i	−0.136274	+	0.136274i
$899$		−	555.106i		−	0.617471i
$900$	−136.515	+	62.1575i	−0.151684	+	0.0690639i
$901$	−12.1436			−0.0134780
$902$	107.054	+	107.054i	0.118685	+	0.118685i
$903$	188.583	−	188.583i	0.208840	−	0.208840i
$904$			322.943i			0.357238i
$905$	−50.2872	−	231.799i	−0.0555660	−	0.256132i
$906$	−134.393			−0.148336
$907$	−494.427	−	494.427i	−0.545123	−	0.545123i	0.379903	−	0.925026i	$-0.375957\pi$
$907$	−494.427	−	494.427i	−0.545123	−	0.545123i	−0.925026	+	0.379903i	$0.875957\pi$
$908$	−466.500	+	466.500i	−0.513767	+	0.513767i
$909$			419.200i			0.461166i
$910$	−399.631	+	621.064i	−0.439155	+	0.682488i
$911$	1357.22			1.48982			0.744909	−	0.667167i	$-0.232493\pi$
$911$	1357.22			1.48982			0.744909	+	0.667167i	$0.232493\pi$
$912$	2.59198	+	2.59198i	0.00284209	+	0.00284209i
$913$	−348.707	+	348.707i	−0.381935	+	0.381935i
$914$			383.161i			0.419213i
$915$	275.629	+	177.357i	0.301234	+	0.193833i
$916$	814.455			0.889143
$917$	259.689	+	259.689i	0.283194	+	0.283194i
$918$	5.74473	−	5.74473i	0.00625788	−	0.00625788i
$919$		−	34.5757i		−	0.0376232i	−0.999823	−	0.0188116i	$-0.994012\pi$
$919$		−	34.5757i		−	0.0376232i	0.999823	−	0.0188116i	$-0.00598828\pi$
$920$	66.2815	−	14.3793i	0.0720451	−	0.0156297i
$921$	−582.764			−0.632751
$922$	−69.9790	−	69.9790i	−0.0758992	−	0.0758992i
$923$	638.821	−	638.821i	0.692114	−	0.692114i
$924$			215.202i			0.232902i
$925$	−211.288	−	79.0794i	−0.228420	−	0.0854913i
$926$	−1013.21			−1.09417
$927$	−294.994	−	294.994i	−0.318224	−	0.318224i
$928$	91.2422	−	91.2422i	0.0983213	−	0.0983213i
$929$		−	317.252i		−	0.341499i	−0.985314	−	0.170749i	$-0.945381\pi$
$929$		−	317.252i		−	0.341499i	0.985314	−	0.170749i	$-0.0546189\pi$
$930$	−63.1895	−	291.273i	−0.0679457	−	0.313196i
$931$	22.6920			0.0243737
$932$	135.628	+	135.628i	0.145523	+	0.145523i
$933$	−99.5858	+	99.5858i	−0.106737	+	0.106737i
$934$			723.381i			0.774498i
$935$	−19.3853	+	30.1266i	−0.0207330	+	0.0322210i
$936$	92.4522			0.0987737
$937$	−1061.58	−	1061.58i	−1.13296	−	1.13296i	−0.989682	−	0.143279i	$-0.954235\pi$
$937$	−1061.58	−	1061.58i	−1.13296	−	1.13296i	−0.143279	−	0.989682i	$-0.545765\pi$
$938$	323.061	−	323.061i	0.344415	−	0.344415i
$939$			801.473i			0.853539i
$940$	228.168	+	146.817i	0.242731	+	0.156189i
$941$	615.031			0.653593			0.326797	−	0.945095i	$-0.394031\pi$
$941$	615.031			0.653593			0.326797	+	0.945095i	$0.394031\pi$
$942$	−352.222	−	352.222i	−0.373908	−	0.373908i
$943$	−56.0182	+	56.0182i	−0.0594042	+	0.0594042i
$944$		−	251.045i		−	0.265938i
$945$	243.387	−	52.8010i	0.257552	−	0.0558741i
$946$	147.219			0.155622
$947$	−560.762	−	560.762i	−0.592146	−	0.592146i	0.346065	−	0.938211i	$-0.387518\pi$
$947$	−560.762	−	560.762i	−0.592146	−	0.592146i	−0.938211	+	0.346065i	$0.887518\pi$
$948$	136.051	−	136.051i	0.143513	−	0.143513i
$949$		−	507.354i		−	0.534620i
$950$	−6.55696	+	17.5192i	−0.00690206	+	0.0184413i
$951$	672.312			0.706953
$952$	−21.1958	−	21.1958i	−0.0222645	−	0.0222645i
$953$	576.041	−	576.041i	0.604450	−	0.604450i	−0.337040	−	0.941490i	$-0.609426\pi$
$953$	576.041	−	576.041i	0.604450	−	0.604450i	0.941490	+	0.337040i	$0.109426\pi$
$954$			46.6013i			0.0488483i
$955$	134.525	+	620.093i	0.140864	+	0.649312i
$956$	252.207			0.263815
$957$	181.053	+	181.053i	0.189188	+	0.189188i
$958$	−472.746	+	472.746i	−0.493472	+	0.493472i
$959$		−	586.124i		−	0.611183i
$960$	37.4897	−	58.2625i	0.0390518	−	0.0606901i
$961$	−368.782			−0.383749
$962$	98.3227	+	98.3227i	0.102207	+	0.102207i
$963$	−34.2836	+	34.2836i	−0.0356009	+	0.0356009i
$964$			338.589i			0.351234i
$965$	−885.772	−	569.961i	−0.917898	−	0.590633i
$966$	−112.608			−0.116572
$967$	−1250.23	−	1250.23i	−1.29290	−	1.29290i	−0.932987	−	0.359910i	$-0.882807\pi$
$967$	−1250.23	−	1250.23i	−1.29290	−	1.29290i	−0.359910	−	0.932987i	$-0.617193\pi$
$968$	158.000	−	158.000i	0.163223	−	0.163223i
$969$		−	1.01315i		−	0.00104557i
$970$	−778.735	+	168.941i	−0.802820	+	0.174166i
$971$	1207.50			1.24357			0.621784	−	0.783189i	$-0.286408\pi$
$971$	1207.50			1.24357			0.621784	+	0.783189i	$0.286408\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	769.344	−	769.344i	0.790692	−	0.790692i
$974$		−	490.141i		−	0.503224i
$975$	195.503	+	429.380i	0.200516	+	0.440390i
$976$	−151.386			−0.155109
$977$	−873.381	−	873.381i	−0.893942	−	0.893942i	0.100950	−	0.994892i	$-0.467812\pi$
$977$	−873.381	−	873.381i	−0.893942	−	0.893942i	−0.994892	+	0.100950i	$0.967812\pi$
$978$	265.021	−	265.021i	0.270983	−	0.270983i
$979$			59.6733i			0.0609533i
$980$	−90.9294	−	419.140i	−0.0927851	−	0.427693i
$981$	−239.478			−0.244117
$982$	−89.9842	−	89.9842i	−0.0916336	−	0.0916336i
$983$	1034.87	−	1034.87i	1.05277	−	1.05277i	0.0542382	−	0.998528i	$-0.482727\pi$
$983$	1034.87	−	1034.87i	1.05277	−	1.05277i	0.998528	−	0.0542382i	$-0.0172730\pi$
$984$			80.9256i			0.0822415i
$985$	−39.0589	+	60.7011i	−0.0396537	+	0.0616255i
$986$	−35.6647			−0.0361711
$987$	−318.539	−	318.539i	−0.322734	−	0.322734i
$988$	8.15254	−	8.15254i	0.00825155	−	0.00825155i
$989$			77.0350i			0.0778918i
$990$	115.611	+	74.3912i	0.116779	+	0.0751427i
$991$	−665.229			−0.671270			−0.335635	−	0.941992i	$-0.608951\pi$
$991$	−665.229			−0.671270			−0.335635	+	0.941992i	$0.608951\pi$
$992$	97.3421	+	97.3421i	0.0981271	+	0.0981271i
$993$	256.528	−	256.528i	0.258336	−	0.258336i
$994$			1124.06i			1.13085i
$995$	1787.62	−	387.811i	1.79660	−	0.389759i
$996$	−263.598			−0.264657
$997$	802.959	+	802.959i	0.805375	+	0.805375i	0.983930	−	0.178555i	$-0.0571423\pi$
$997$	802.959	+	802.959i	0.805375	+	0.805375i	−0.178555	+	0.983930i	$0.557142\pi$
$998$	−823.542	+	823.542i	−0.825192	+	0.825192i
$999$		−	46.8905i		−	0.0469374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.277.20	✓	40
5.3	odd	4	inner	690.3.k.a.553.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.20	✓	40	1.1	even	1	trivial
690.3.k.a.553.20	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(1.06006 + 4.88634i) q^{5} +2.44949 q^{6} +(6.77823 + 6.77823i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(1.06006 + 4.88634i) q^{5} +2.44949 q^{6} +(6.77823 + 6.77823i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-3.82628 + 5.94639i) q^{10} +6.48073 q^{11} +(2.44949 + 2.44949i) q^{12} +(7.70435 - 7.70435i) q^{13} +13.5565i q^{14} +(7.28281 + 4.68622i) q^{15} -4.00000 q^{16} +(0.781759 + 0.781759i) q^{17} +(3.00000 - 3.00000i) q^{18} -0.529087i q^{19} +(-9.77267 + 2.12011i) q^{20} +16.6032 q^{21} +(6.48073 + 6.48073i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(-22.7526 + 10.3596i) q^{25} +15.4087 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-13.5565 + 13.5565i) q^{28} +22.8105i q^{29} +(2.59660 + 11.9690i) q^{30} -24.3355 q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.93724 - 7.93724i) q^{33} +1.56352i q^{34} +(-25.9354 + 40.3060i) q^{35} +6.00000 q^{36} +(6.38099 + 6.38099i) q^{37} +(0.529087 - 0.529087i) q^{38} -18.8717i q^{39} +(-11.8928 - 7.65256i) q^{40} +16.5189 q^{41} +(16.6032 + 16.6032i) q^{42} +(11.3582 - 11.3582i) q^{43} +12.9615i q^{44} +(14.6590 - 3.18017i) q^{45} -6.78233 q^{46} +(-19.1854 - 19.1854i) q^{47} +(-4.89898 + 4.89898i) q^{48} +42.8889i q^{49} +(-33.1121 - 12.3930i) q^{50} +1.91491 q^{51} +(15.4087 + 15.4087i) q^{52} +(-7.76688 + 7.76688i) q^{53} -7.34847i q^{54} +(6.86994 + 31.6670i) q^{55} -27.1129 q^{56} +(-0.647996 - 0.647996i) q^{57} +(-22.8105 + 22.8105i) q^{58} +62.7613i q^{59} +(-9.37243 + 14.5656i) q^{60} +37.8465 q^{61} +(-24.3355 - 24.3355i) q^{62} +(20.3347 - 20.3347i) q^{63} -8.00000i q^{64} +(45.8131 + 29.4790i) q^{65} +15.8745 q^{66} +(-23.8308 - 23.8308i) q^{67} +(-1.56352 + 1.56352i) q^{68} +8.30662i q^{69} +(-66.2415 + 14.3706i) q^{70} +82.9169 q^{71} +(6.00000 + 6.00000i) q^{72} +(32.9265 - 32.9265i) q^{73} +12.7620i q^{74} +(-15.1782 + 40.5539i) q^{75} +1.05817 q^{76} +(43.9279 + 43.9279i) q^{77} +(18.8717 - 18.8717i) q^{78} -55.5424i q^{79} +(-4.24022 - 19.5453i) q^{80} -9.00000 q^{81} +(16.5189 + 16.5189i) q^{82} +(-53.8067 + 53.8067i) q^{83} +33.2064i q^{84} +(-2.99123 + 4.64864i) q^{85} +22.7164 q^{86} +(27.9371 + 27.9371i) q^{87} +(-12.9615 + 12.9615i) q^{88} +9.20780i q^{89} +(17.8392 + 11.4788i) q^{90} +104.444 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-29.8048 + 29.8048i) q^{93} -38.3707i q^{94} +(2.58529 - 0.560862i) q^{95} -9.79796 q^{96} +(79.6850 + 79.6850i) q^{97} +(-42.8889 + 42.8889i) q^{98} -19.4422i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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