LMFDB - Embedded newform 231.2.u.a.20.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(20,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6]))

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

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

chi := DirichletCharacter("231.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.10
Character	$\chi$	$=$	231.20
Dual form			231.2.u.a.104.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17237 - 0.380926i) q^{2} +(1.03573 - 1.38826i) q^{3} +(-0.388687 - 0.282397i) q^{4} +(0.966595 + 2.97487i) q^{5} +(-1.74309 + 1.23301i) q^{6} +(2.62308 - 0.345622i) q^{7} +(1.79724 + 2.47369i) q^{8} +(-0.854517 - 2.87573i) q^{9} +O(q^{10})$	\(q+(-1.17237 - 0.380926i) q^{2} +(1.03573 - 1.38826i) q^{3} +(-0.388687 - 0.282397i) q^{4} +(0.966595 + 2.97487i) q^{5} +(-1.74309 + 1.23301i) q^{6} +(2.62308 - 0.345622i) q^{7} +(1.79724 + 2.47369i) q^{8} +(-0.854517 - 2.87573i) q^{9} -3.85585i q^{10} +(2.35123 + 2.33917i) q^{11} +(-0.794615 + 0.247109i) q^{12} +(1.83070 + 0.594831i) q^{13} +(-3.20688 - 0.594002i) q^{14} +(5.13102 + 1.73929i) q^{15} +(-0.867809 - 2.67084i) q^{16} +(-1.78185 - 5.48398i) q^{17} +(-0.0936286 + 3.69692i) q^{18} +(-3.31616 - 4.56430i) q^{19} +(0.464394 - 1.42926i) q^{20} +(2.23700 - 3.99948i) q^{21} +(-1.86545 - 3.63802i) q^{22} +5.79074i q^{23} +(5.29558 + 0.0670474i) q^{24} +(-3.87048 + 2.81207i) q^{25} +(-1.91967 - 1.39472i) q^{26} +(-4.87730 - 1.79219i) q^{27} +(-1.11716 - 0.606412i) q^{28} +(2.41572 - 3.32496i) q^{29} +(-5.35292 - 3.99363i) q^{30} +(3.87003 + 1.25745i) q^{31} -2.65351i q^{32} +(5.68262 - 0.841349i) q^{33} +7.10801i q^{34} +(3.56364 + 7.46925i) q^{35} +(-0.479958 + 1.35907i) q^{36} +(7.22445 + 5.24887i) q^{37} +(2.14910 + 6.61426i) q^{38} +(2.72190 - 1.92540i) q^{39} +(-5.62171 + 7.73762i) q^{40} +(-2.54229 + 1.84708i) q^{41} +(-4.14609 + 3.83674i) q^{42} -6.95014 q^{43} +(-0.253313 - 1.57319i) q^{44} +(7.72895 - 5.32174i) q^{45} +(2.20584 - 6.78889i) q^{46} +(-4.70535 + 3.41864i) q^{47} +(-4.60663 - 1.56153i) q^{48} +(6.76109 - 1.81319i) q^{49} +(5.60883 - 1.82242i) q^{50} +(-9.45870 - 3.20626i) q^{51} +(-0.543591 - 0.748188i) q^{52} +(-5.95831 - 1.93597i) q^{53} +(5.03531 + 3.95900i) q^{54} +(-4.68606 + 9.25563i) q^{55} +(5.56927 + 5.86752i) q^{56} +(-9.77108 - 0.123712i) q^{57} +(-4.09869 + 2.97787i) q^{58} +(-1.83841 - 1.33568i) q^{59} +(-1.50319 - 2.12503i) q^{60} +(-5.18467 + 1.68460i) q^{61} +(-4.05811 - 2.94839i) q^{62} +(-3.23538 - 7.24792i) q^{63} +(-2.74641 + 8.45258i) q^{64} +6.02107i q^{65} +(-6.98262 - 1.17829i) q^{66} +3.70934 q^{67} +(-0.856079 + 2.63474i) q^{68} +(8.03904 + 5.99766i) q^{69} +(-1.33267 - 10.1142i) q^{70} +(-12.6990 + 4.12615i) q^{71} +(5.57788 - 7.28219i) q^{72} +(4.72522 - 6.50371i) q^{73} +(-6.47030 - 8.90560i) q^{74} +(-0.104906 + 8.28577i) q^{75} +2.71056i q^{76} +(6.97592 + 5.32320i) q^{77} +(-3.92451 + 1.22044i) q^{78} +(-2.21664 + 6.82211i) q^{79} +(7.10659 - 5.16324i) q^{80} +(-7.53960 + 4.91472i) q^{81} +(3.68410 - 1.19704i) q^{82} +(-1.93982 - 5.97015i) q^{83} +(-1.99893 + 0.922823i) q^{84} +(14.5918 - 10.6016i) q^{85} +(8.14814 + 2.64749i) q^{86} +(-2.11386 - 6.79741i) q^{87} +(-1.56067 + 10.0203i) q^{88} -2.91353 q^{89} +(-11.0884 + 3.29489i) q^{90} +(5.00766 + 0.927558i) q^{91} +(1.63529 - 2.25078i) q^{92} +(5.75397 - 4.07021i) q^{93} +(6.81866 - 2.21552i) q^{94} +(10.3728 - 14.2770i) q^{95} +(-3.68376 - 2.74833i) q^{96} +(-10.0014 - 3.24966i) q^{97} +(-8.61719 - 0.449747i) q^{98} +(4.71766 - 8.76035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.17237	−	0.380926i	−0.828991	−	0.269356i	−0.136371	−	0.990658i	$-0.543544\pi$
$2$	−1.17237	−	0.380926i	−0.828991	−	0.269356i	−0.692620	+	0.721302i	$0.743544\pi$
$3$	1.03573	−	1.38826i	0.597980	−	0.801511i
$3$	1.03573	−	1.38826i	0.597980	−	0.801511i
$4$	−0.388687	−	0.282397i	−0.194343	−	0.141199i
$5$	0.966595	+	2.97487i	0.432274	+	1.33040i	0.895854	+	0.444348i	$0.146565\pi$
$5$	0.966595	+	2.97487i	0.432274	+	1.33040i	−0.463580	+	0.886055i	$0.653435\pi$
$6$	−1.74309	+	1.23301i	−0.711612	+	0.503376i
$7$	2.62308	−	0.345622i	0.991431	−	0.130633i
$7$	2.62308	−	0.345622i	0.991431	−	0.130633i
$8$	1.79724	+	2.47369i	0.635421	+	0.874582i
$9$	−0.854517	−	2.87573i	−0.284839	−	0.958575i
$10$		−	3.85585i		−	1.21933i
$11$	2.35123	+	2.33917i	0.708921	+	0.705288i
$11$	2.35123	+	2.33917i	0.708921	+	0.705288i
$12$	−0.794615	+	0.247109i	−0.229386	+	0.0713342i
$13$	1.83070	+	0.594831i	0.507745	+	0.164976i	0.551677	−	0.834058i	$-0.313988\pi$
$13$	1.83070	+	0.594831i	0.507745	+	0.164976i	−0.0439312	+	0.999035i	$0.513988\pi$
$14$	−3.20688	−	0.594002i	−0.857074	−	0.158754i
$15$	5.13102	+	1.73929i	1.32482	+	0.449083i
$16$	−0.867809	−	2.67084i	−0.216952	−	0.667710i
$17$	−1.78185	−	5.48398i	−0.432163	−	1.33006i	−0.895966	−	0.444122i	$-0.853516\pi$
$17$	−1.78185	−	5.48398i	−0.432163	−	1.33006i	0.463803	−	0.885938i	$-0.346484\pi$
$18$	−0.0936286	+	3.69692i	−0.0220685	+	0.871373i
$19$	−3.31616	−	4.56430i	−0.760779	−	1.04712i	−0.997149	−	0.0754593i	$-0.975958\pi$
$19$	−3.31616	−	4.56430i	−0.760779	−	1.04712i	0.236370	−	0.971663i	$-0.424042\pi$
$20$	0.464394	−	1.42926i	0.103842	−	0.319592i
$21$	2.23700	−	3.99948i	0.488152	−	0.872758i
$22$	−1.86545	−	3.63802i	−0.397716	−	0.775629i
$23$			5.79074i			1.20745i	0.797192	+	0.603726i	$0.206318\pi$
$23$			5.79074i			1.20745i	−0.797192	+	0.603726i	$0.793682\pi$
$24$	5.29558	+	0.0670474i	1.08096	+	0.0136860i
$25$	−3.87048	+	2.81207i	−0.774096	+	0.562414i
$26$	−1.91967	−	1.39472i	−0.376479	−	0.273528i
$27$	−4.87730	−	1.79219i	−0.938637	−	0.344908i
$28$	−1.11716	−	0.606412i	−0.211123	−	0.114601i
$29$	2.41572	−	3.32496i	0.448589	−	0.617429i	−0.523505	−	0.852023i	$-0.675376\pi$
$29$	2.41572	−	3.32496i	0.448589	−	0.617429i	0.972094	+	0.234593i	$0.0753758\pi$
$30$	−5.35292	−	3.99363i	−0.977305	−	0.729134i
$31$	3.87003	+	1.25745i	0.695077	+	0.225844i	0.635184	−	0.772361i	$-0.280924\pi$
$31$	3.87003	+	1.25745i	0.695077	+	0.225844i	0.0598928	+	0.998205i	$0.480924\pi$
$32$		−	2.65351i		−	0.469079i
$33$	5.68262	−	0.841349i	0.989217	−	0.146460i
$34$			7.10801i			1.21901i
$35$	3.56364	+	7.46925i	0.602365	+	1.26253i
$36$	−0.479958	+	1.35907i	−0.0799930	+	0.226512i
$37$	7.22445	+	5.24887i	1.18769	+	0.862909i	0.993018	−	0.117959i	$-0.0376351\pi$
$37$	7.22445	+	5.24887i	1.18769	+	0.862909i	0.194674	+	0.980868i	$0.437635\pi$
$38$	2.14910	+	6.61426i	0.348631	+	1.07298i
$39$	2.72190	−	1.92540i	0.435852	−	0.308311i
$40$	−5.62171	+	7.73762i	−0.888871	+	1.22343i
$41$	−2.54229	+	1.84708i	−0.397038	+	0.288465i	−0.768334	−	0.640050i	$-0.778914\pi$
$41$	−2.54229	+	1.84708i	−0.397038	+	0.288465i	0.371295	+	0.928515i	$0.378914\pi$
$42$	−4.14609	+	3.83674i	−0.639756	+	0.592022i
$43$	−6.95014			−1.05989			−0.529943	−	0.848033i	$-0.677787\pi$
$43$	−6.95014			−1.05989			−0.529943	+	0.848033i	$0.677787\pi$
$44$	−0.253313	−	1.57319i	−0.0381884	−	0.237167i
$45$	7.72895	−	5.32174i	1.15216	−	0.793319i
$46$	2.20584	−	6.78889i	0.325234	−	1.00097i
$47$	−4.70535	+	3.41864i	−0.686346	+	0.498659i	−0.875457	−	0.483296i	$-0.839439\pi$
$47$	−4.70535	+	3.41864i	−0.686346	+	0.498659i	0.189111	+	0.981956i	$0.439439\pi$
$48$	−4.60663	−	1.56153i	−0.664910	−	0.225388i
$49$	6.76109	−	1.81319i	0.965870	−	0.259027i
$50$	5.60883	−	1.82242i	0.793208	−	0.257729i
$51$	−9.45870	−	3.20626i	−1.32448	−	0.448967i
$52$	−0.543591	−	0.748188i	−0.0753824	−	0.103755i
$53$	−5.95831	−	1.93597i	−0.818436	−	0.265926i	−0.130270	−	0.991479i	$-0.541584\pi$
$53$	−5.95831	−	1.93597i	−0.818436	−	0.265926i	−0.688167	+	0.725553i	$0.741584\pi$
$54$	5.03531	+	3.95900i	0.685219	+	0.538752i
$55$	−4.68606	+	9.25563i	−0.631869	+	1.24803i
$56$	5.56927	+	5.86752i	0.744225	+	0.784080i
$57$	−9.77108	−	0.123712i	−1.29421	−	0.0163860i
$58$	−4.09869	+	2.97787i	−0.538184	+	0.391014i
$59$	−1.83841	−	1.33568i	−0.239341	−	0.173891i	0.461649	−	0.887063i	$-0.347258\pi$
$59$	−1.83841	−	1.33568i	−0.239341	−	0.173891i	−0.700989	+	0.713172i	$0.747258\pi$
$60$	−1.50319	−	2.12503i	−0.194061	−	0.274340i
$61$	−5.18467	+	1.68460i	−0.663829	+	0.215691i	−0.621502	−	0.783413i	$-0.713477\pi$
$61$	−5.18467	+	1.68460i	−0.663829	+	0.215691i	−0.0423269	+	0.999104i	$0.513477\pi$
$62$	−4.05811	−	2.94839i	−0.515380	−	0.374446i
$63$	−3.23538	−	7.24792i	−0.407620	−	0.913152i
$64$	−2.74641	+	8.45258i	−0.343301	+	1.05657i
$65$			6.02107i			0.746821i
$66$	−6.98262	−	1.17829i	−0.859501	−	0.145037i
$67$	3.70934			0.453168			0.226584	−	0.973992i	$-0.427244\pi$
$67$	3.70934			0.453168			0.226584	+	0.973992i	$0.427244\pi$
$68$	−0.856079	+	2.63474i	−0.103815	+	0.319509i
$69$	8.03904	+	5.99766i	0.967786	+	0.722033i
$70$	−1.33267	−	10.1142i	−0.159284	−	1.20888i
$71$	−12.6990	+	4.12615i	−1.50709	+	0.489684i	−0.942077	−	0.335396i	$-0.891130\pi$
$71$	−12.6990	+	4.12615i	−1.50709	+	0.489684i	−0.565015	+	0.825080i	$0.691130\pi$
$72$	5.57788	−	7.28219i	0.657360	−	0.858214i
$73$	4.72522	−	6.50371i	0.553045	−	0.761201i	−0.437376	−	0.899279i	$-0.644092\pi$
$73$	4.72522	−	6.50371i	0.553045	−	0.761201i	0.990421	+	0.138077i	$0.0440922\pi$
$74$	−6.47030	−	8.90560i	−0.752157	−	1.03526i
$75$	−0.104906	+	8.28577i	−0.0121135	+	0.956759i
$76$			2.71056i			0.310922i
$77$	6.97592	+	5.32320i	0.794980	+	0.606635i
$78$	−3.92451	+	1.22044i	−0.444363	+	0.138188i
$79$	−2.21664	+	6.82211i	−0.249391	+	0.767548i	0.745492	+	0.666515i	$0.232215\pi$
$79$	−2.21664	+	6.82211i	−0.249391	+	0.767548i	−0.994883	+	0.101033i	$0.967785\pi$
$80$	7.10659	−	5.16324i	0.794541	−	0.577268i
$81$	−7.53960	+	4.91472i	−0.837733	+	0.546080i
$82$	3.68410	−	1.19704i	0.406841	−	0.132191i
$83$	−1.93982	−	5.97015i	−0.212923	−	0.655309i	−0.999295	−	0.0375553i	$-0.988043\pi$
$83$	−1.93982	−	5.97015i	−0.212923	−	0.655309i	0.786372	−	0.617753i	$-0.211957\pi$
$84$	−1.99893	+	0.922823i	−0.218101	+	0.100688i
$85$	14.5918	−	10.6016i	1.58270	−	1.14990i
$86$	8.14814	+	2.64749i	0.878637	+	0.285486i
$87$	−2.11386	−	6.79741i	−0.226629	−	0.728759i
$88$	−1.56067	+	10.0203i	−0.166368	+	1.06816i
$89$	−2.91353			−0.308833			−0.154417	−	0.988006i	$-0.549350\pi$
$89$	−2.91353			−0.308833			−0.154417	+	0.988006i	$0.549350\pi$
$90$	−11.0884	+	3.29489i	−1.16882	+	0.347312i
$91$	5.00766	+	0.927558i	0.524946	+	0.0972345i
$92$	1.63529	−	2.25078i	0.170491	−	0.234660i
$93$	5.75397	−	4.07021i	0.596659	−	0.422061i
$94$	6.81866	−	2.21552i	0.703291	−	0.228513i
$95$	10.3728	−	14.2770i	1.06423	−	1.46479i
$96$	−3.68376	−	2.74833i	−0.375972	−	0.280500i
$97$	−10.0014	−	3.24966i	−1.01549	−	0.329953i	−0.246453	−	0.969155i	$-0.579265\pi$
$97$	−10.0014	−	3.24966i	−1.01549	−	0.329953i	−0.769039	+	0.639202i	$0.779265\pi$
$98$	−8.61719	−	0.449747i	−0.870468	−	0.0454313i
$99$	4.71766	−	8.76035i	0.474143	−	0.880448i
$100$	2.29852			0.229852
$101$	−0.316750	+	0.974858i	−0.0315179	+	0.0970020i	−0.965578	−	0.260114i	$-0.916240\pi$
$101$	−0.316750	+	0.974858i	−0.0315179	+	0.0970020i	0.934060	+	0.357116i	$0.116240\pi$
$102$	9.86775	+	7.36199i	0.977053	+	0.728946i
$103$	−0.633933	+	0.872534i	−0.0624633	+	0.0859734i	−0.839106	−	0.543968i	$-0.816921\pi$
$103$	−0.633933	+	0.872534i	−0.0624633	+	0.0859734i	0.776643	+	0.629942i	$0.216921\pi$
$104$	1.81879	+	5.59765i	0.178347	+	0.548894i
$105$	14.0602	+	2.78890i	1.37214	+	0.272169i
$106$	6.24788	+	4.53935i	0.606848	+	0.440901i
$107$	1.19592	+	1.64605i	0.115614	+	0.159129i	0.862902	−	0.505371i	$-0.168644\pi$
$107$	1.19592	+	1.64605i	0.115614	+	0.159129i	−0.747288	+	0.664500i	$0.768644\pi$
$108$	1.38963	+	2.07394i	0.133717	+	0.199565i
$109$	9.24914			0.885907			0.442954	−	0.896545i	$-0.353931\pi$
$109$	9.24914			0.885907			0.442954	+	0.896545i	$0.353931\pi$
$110$	9.01952	−	9.06599i	0.859977	−	0.864408i
$111$	14.7694	−	4.59297i	1.40185	−	0.435946i
$112$	−3.19943	−	6.70589i	−0.302318	−	0.633647i
$113$	−2.13147	−	2.93372i	−0.200512	−	0.275981i	0.696906	−	0.717162i	$-0.254559\pi$
$113$	−2.13147	−	2.93372i	−0.200512	−	0.275981i	−0.897418	+	0.441182i	$0.854559\pi$
$114$	11.4082	+	3.86710i	1.06848	+	0.362187i
$115$	−17.2267	+	5.59730i	−1.60640	+	0.521951i
$116$	−1.87792	+	0.610173i	−0.174360	+	0.0566531i
$117$	0.146205	−	5.77289i	0.0135166	−	0.533704i
$118$	1.64650	+	2.26621i	0.151573	+	0.208622i
$119$	−6.56933	−	13.7691i	−0.602209	−	1.26221i
$120$	4.91922	+	15.8185i	0.449062	+	1.44402i
$121$	0.0565275	+	10.9999i	0.00513886	+	0.999987i
$122$	6.72006			0.608406
$123$	−0.0689066	+	5.44243i	−0.00621310	+	0.490727i
$124$	−1.14913	−	1.58164i	−0.103195	−	0.142035i
$125$	0.546159	+	0.396808i	0.0488500	+	0.0354916i
$126$	1.03214	+	9.72969i	0.0919507	+	0.866789i
$127$	−4.96592	−	15.2835i	−0.440654	−	1.35619i	−0.887180	−	0.461424i	$-0.847339\pi$
$127$	−4.96592	−	15.2835i	−0.440654	−	1.35619i	0.446526	−	0.894771i	$-0.352661\pi$
$128$	3.32023	−	4.56990i	0.293470	−	0.403926i
$129$	−7.19849	+	9.64859i	−0.633791	+	0.849511i
$130$	2.29358	−	7.05892i	0.201160	−	0.619108i
$131$	4.69154			0.409902			0.204951	−	0.978772i	$-0.434296\pi$
$131$	4.69154			0.409902			0.204951	+	0.978772i	$0.434296\pi$
$132$	−2.44635	−	1.27773i	−0.212928	−	0.111213i
$133$	−10.2761	−	10.8264i	−0.891048	−	0.938767i
$134$	−4.34872	−	1.41298i	−0.375672	−	0.122063i
$135$	0.617172	−	16.2417i	0.0531177	−	1.39786i
$136$	10.3632	−	14.2638i	0.888641	−	1.22311i
$137$	−3.12324	+	1.01480i	−0.266836	+	0.0867004i	−0.439379	−	0.898302i	$-0.644802\pi$
$137$	−3.12324	+	1.01480i	−0.266836	+	0.0867004i	0.172543	+	0.985002i	$0.444802\pi$
$138$	−7.14007	−	10.0938i	−0.607803	−	0.859237i
$139$	−1.74369	+	2.39999i	−0.147898	+	0.203564i	−0.876538	−	0.481333i	$-0.840153\pi$
$139$	−1.74369	+	2.39999i	−0.147898	+	0.203564i	0.728640	+	0.684897i	$0.240153\pi$
$140$	0.724158	−	3.90956i	0.0612026	−	0.330418i
$141$	−0.127535	+	10.0730i	−0.0107404	+	0.848302i
$142$	16.4597			1.38127
$143$	2.91298	+	5.68091i	0.243596	+	0.475062i
$144$	−6.93905	+	4.77786i	−0.578254	+	0.398155i
$145$	12.2264	+	3.97258i	1.01534	+	0.329905i
$146$	−8.01714	+	5.82479i	−0.663503	+	0.482063i
$147$	4.48551	−	11.2641i	0.369958	−	0.929048i
$148$	−1.32578	−	4.08033i	−0.108978	−	0.335401i
$149$	3.73287	−	1.21288i	0.305809	−	0.0993633i	−0.152093	−	0.988366i	$-0.548601\pi$
$149$	3.73287	−	1.21288i	0.305809	−	0.0993633i	0.457901	+	0.889003i	$0.348601\pi$
$150$	3.27926	−	9.67403i	0.267750	−	0.789881i
$151$	−12.1170	+	8.80351i	−0.986067	+	0.716419i	−0.959056	−	0.283216i	$-0.908599\pi$
$151$	−12.1170	+	8.80351i	−0.986067	+	0.716419i	−0.0270105	+	0.999635i	$0.508599\pi$
$152$	5.33073	−	16.4063i	0.432379	−	1.33073i
$153$	−14.2478	+	9.81028i	−1.15187	+	0.793114i
$154$	−6.15062	−	8.89808i	−0.495631	−	0.717028i
$155$			12.7283i			1.02236i
$156$	−1.60169	−	0.0202790i	−0.128238	−	0.00162362i
$157$	−7.06712	−	9.72705i	−0.564017	−	0.776303i	0.427813	−	0.903867i	$-0.359284\pi$
$157$	−7.06712	−	9.72705i	−0.564017	−	0.776303i	−0.991830	+	0.127564i	$0.959284\pi$
$158$	5.19744	−	7.15367i	0.413486	−	0.569115i
$159$	−8.85884	+	6.26652i	−0.702551	+	0.496967i
$160$	7.89387	−	2.56487i	0.624065	−	0.202771i
$161$	2.00141	+	15.1896i	0.157733	+	1.19711i
$162$	10.7113	−	2.88984i	0.841563	−	0.227047i
$163$	3.84778	−	11.8422i	0.301381	−	0.927556i	−0.679622	−	0.733563i	$-0.737856\pi$
$163$	3.84778	−	11.8422i	0.301381	−	0.927556i	0.981003	−	0.193993i	$-0.0621440\pi$
$164$	1.50976			0.117893
$165$	7.99569	+	16.0918i	0.622464	+	1.25275i
$166$			7.73815i			0.600597i
$167$	0.988524	−	3.04236i	0.0764943	−	0.235425i	−0.905497	−	0.424354i	$-0.860501\pi$
$167$	0.988524	−	3.04236i	0.0764943	−	0.235425i	0.981991	+	0.188928i	$0.0605014\pi$
$168$	13.9139	−	1.65440i	1.07348	−	0.127640i
$169$	−7.51957	−	5.46329i	−0.578429	−	0.420253i
$170$	−21.1454	+	6.87057i	−1.62178	+	0.526948i
$171$	−10.2920	+	13.4366i	−0.787046	+	1.02753i
$172$	2.70143	+	1.96270i	0.205982	+	0.149655i
$173$	−10.9084	+	7.92540i	−0.829349	+	0.602557i	−0.919375	−	0.393382i	$-0.871305\pi$
$173$	−10.9084	+	7.92540i	−0.829349	+	0.602557i	0.0900261	+	0.995939i	$0.471305\pi$
$174$	−0.111092	+	8.77431i	−0.00842183	+	0.665179i
$175$	−9.18066	+	8.71400i	−0.693993	+	0.658717i
$176$	4.20715	−	8.30971i	0.317126	−	0.626368i
$177$	−3.75837	+	1.16878i	−0.282497	+	0.0878506i
$178$	3.41573	+	1.10984i	0.256020	+	0.0831860i
$179$	4.81451	+	6.62661i	0.359854	+	0.495296i	0.950108	−	0.311921i	$-0.100973\pi$
$179$	4.81451	+	6.62661i	0.359854	+	0.495296i	−0.590254	+	0.807217i	$0.700973\pi$
$180$	−4.50698	−	0.114144i	−0.335931	−	0.00850781i
$181$	−3.94617	+	1.28219i	−0.293317	+	0.0953043i	−0.451979	−	0.892029i	$-0.649282\pi$
$181$	−3.94617	+	1.28219i	−0.293317	+	0.0953043i	0.158662	+	0.987333i	$0.449282\pi$
$182$	−5.51751	−	2.99499i	−0.408985	−	0.222004i
$183$	−3.03127	+	8.94245i	−0.224078	+	0.661045i
$184$	−14.3245	+	10.4074i	−1.05602	+	0.767241i
$185$	−8.63161	+	26.5654i	−0.634608	+	1.95312i
$186$	−8.29624	+	2.57996i	−0.608310	+	0.189172i
$187$	8.63844	−	17.0621i	0.631706	−	1.24771i
$188$	2.79432			0.203797
$189$	−13.4130	−	3.01536i	−0.975650	−	0.219335i
$190$	−17.5993	+	12.7866i	−1.27679	+	0.927639i
$191$	4.45001	−	6.12491i	0.321991	−	0.443183i	−0.617082	−	0.786899i	$-0.711685\pi$
$191$	4.45001	−	6.12491i	0.321991	−	0.443183i	0.939074	+	0.343715i	$0.111685\pi$
$192$	8.88981	+	12.5673i	0.641567	+	0.906969i
$193$	4.62029	+	14.2198i	0.332576	+	1.02356i	0.967904	+	0.251321i	$0.0808651\pi$
$193$	4.62029	+	14.2198i	0.332576	+	1.02356i	−0.635328	+	0.772243i	$0.719135\pi$
$194$	10.4875	+	7.61962i	0.752959	+	0.547057i
$195$	8.35879	+	6.23621i	0.598585	+	0.446585i
$196$	−3.13998	−	1.20455i	−0.224285	−	0.0860394i
$197$		−	18.2597i		−	1.30095i	−0.759526	−	0.650476i	$-0.774569\pi$
$197$		−	18.2597i		−	1.30095i	0.759526	−	0.650476i	$-0.225431\pi$
$198$	−8.86789	+	8.47329i	−0.630214	+	0.602171i
$199$			25.7556i			1.82577i	0.408220	+	0.912883i	$0.366149\pi$
$199$			25.7556i			1.82577i	−0.408220	+	0.912883i	$0.633851\pi$
$200$	−13.9124	−	4.52040i	−0.983753	−	0.319641i
$201$	3.84188	−	5.14952i	0.270985	−	0.363219i
$202$	0.742698	−	1.02224i	0.0522560	−	0.0719243i
$203$	5.18746	−	9.55656i	0.364088	−	0.670739i
$204$	2.77103	+	3.91734i	0.194011	+	0.274269i
$205$	−7.95219	−	5.77760i	−0.555405	−	0.403525i
$206$	1.07558	−	0.781452i	0.0749389	−	0.0544463i
$207$	16.6526	−	4.94829i	1.15743	−	0.343930i
$208$		−	5.40571i		−	0.374819i
$209$	2.87966	−	18.4888i	0.199190	−	1.27890i
$210$	−15.4214	−	8.62553i	−1.06418	−	0.595218i
$211$	1.10921	−	3.41380i	0.0763613	−	0.235016i	−0.905589	−	0.424157i	$-0.860570\pi$
$211$	1.10921	−	3.41380i	0.0763613	−	0.235016i	0.981950	+	0.189141i	$0.0605704\pi$
$212$	1.76920	+	2.43510i	0.121509	+	0.167243i
$213$	−7.42459	+	21.9030i	−0.508725	+	1.50077i
$214$	−0.775043	−	2.38534i	−0.0529808	−	0.163058i
$215$	−6.71797	−	20.6758i	−0.458162	−	1.41008i
$216$	−4.33236	−	15.2859i	−0.294779	−	1.04008i
$217$	10.5860	+	1.96082i	0.718624	+	0.133109i
$218$	−10.8434	−	3.52324i	−0.734409	−	0.238624i
$219$	−4.13476	−	13.2959i	−0.279401	−	0.898455i
$220$	4.43518	−	2.27421i	0.299019	−	0.153327i
$221$		−	11.0994i		−	0.746629i
$222$	−19.0648	−	0.241379i	−1.27954	−	0.0162003i
$223$	−7.35053	−	10.1171i	−0.492228	−	0.677493i	0.488569	−	0.872525i	$-0.337519\pi$
$223$	−7.35053	−	10.1171i	−0.492228	−	0.677493i	−0.980797	+	0.195032i	$0.937519\pi$
$224$	−0.917114	−	6.96038i	−0.0612772	−	0.465060i
$225$	11.3941	+	8.72748i	0.759609	+	0.581832i
$226$	1.38134	+	4.25133i	0.0918855	+	0.282795i
$227$	−18.8958	−	13.7286i	−1.25416	−	0.911202i	−0.255706	−	0.966755i	$-0.582308\pi$
$227$	−18.8958	−	13.7286i	−1.25416	−	0.911202i	−0.998456	+	0.0555530i	$0.982308\pi$
$228$	3.76295	+	2.80741i	0.249207	+	0.185925i
$229$	22.9123	+	7.44464i	1.51408	+	0.491956i	0.944089	−	0.329692i	$-0.106945\pi$
$229$	22.9123	+	7.44464i	1.51408	+	0.491956i	0.569996	+	0.821648i	$0.306945\pi$
$230$	22.3283			1.47228
$231$	14.6152	−	4.17096i	0.961607	−	0.274429i
$232$	12.5666			0.825035
$233$	3.07237	+	0.998274i	0.201278	+	0.0653991i	0.407921	−	0.913017i	$-0.366254\pi$
$233$	3.07237	+	0.998274i	0.201278	+	0.0653991i	−0.206643	+	0.978416i	$0.566254\pi$
$234$	−2.37045	+	6.71227i	−0.154961	+	0.438795i
$235$	−14.7182	−	10.6934i	−0.960108	−	0.697559i
$236$	0.337372	+	1.03832i	0.0219610	+	0.0675891i
$237$	7.17500	+	10.1431i	0.466067	+	0.658868i
$238$	2.45669	+	18.6449i	0.159243	+	1.20857i
$239$	1.62258	+	2.23329i	0.104956	+	0.144460i	0.858264	−	0.513208i	$-0.171543\pi$
$239$	1.62258	+	2.23329i	0.104956	+	0.144460i	−0.753308	+	0.657668i	$0.771543\pi$
$240$	0.192618	−	15.2135i	0.0124335	−	0.982028i
$241$			15.9400i			1.02678i	0.858154	+	0.513392i	$0.171611\pi$
$241$			15.9400i			1.02678i	−0.858154	+	0.513392i	$0.828389\pi$
$242$	4.12386	−	12.9174i	0.265092	−	0.830364i
$243$	−0.986116	+	15.5572i	−0.0632594	+	0.997997i
$244$	2.49094	+	0.809354i	0.159466	+	0.0518136i
$245$	11.9292	+	18.3608i	0.762131	+	1.17303i
$246$	2.15395	−	6.35429i	0.137331	−	0.405135i
$247$	−3.35591	−	10.3284i	−0.213531	−	0.657182i
$248$	3.84483	+	11.8332i	0.244147	+	0.751408i
$249$	−10.2972	−	3.49051i	−0.652561	−	0.221202i
$250$	−0.489147	−	0.673252i	−0.0309363	−	0.0425802i
$251$	−2.17901	+	6.70629i	−0.137538	+	0.423297i	−0.995976	−	0.0896192i	$-0.971435\pi$
$251$	−2.17901	+	6.70629i	−0.137538	+	0.423297i	0.858438	+	0.512917i	$0.171435\pi$
$252$	−0.789243	+	3.73083i	−0.0497176	+	0.235020i
$253$	−13.5456	+	13.6153i	−0.851601	+	0.855989i
$254$			19.8096i			1.24297i
$255$	0.395499	−	31.2376i	0.0247671	−	1.95617i
$256$	8.74706	−	6.35511i	0.546691	−	0.397194i
$257$	9.08063	+	6.59746i	0.566434	+	0.411538i	0.833808	−	0.552054i	$-0.186156\pi$
$257$	9.08063	+	6.59746i	0.566434	+	0.411538i	−0.267374	+	0.963593i	$0.586156\pi$
$258$	12.1147	−	8.56962i	0.754228	−	0.533521i
$259$	20.7644	+	11.2713i	1.29024	+	0.700363i
$260$	1.70033	−	2.34031i	0.105450	−	0.145140i
$261$	−11.6259	−	4.10572i	−0.719628	−	0.254138i
$262$	−5.50023	−	1.78713i	−0.339805	−	0.110409i
$263$		−	8.45856i		−	0.521577i	−0.965396	−	0.260789i	$-0.916017\pi$
$263$		−	8.45856i		−	0.521577i	0.965396	−	0.260789i	$-0.0839825\pi$
$264$	12.2943	+	12.5449i	0.756660	+	0.772087i
$265$		−	19.5965i		−	1.20380i
$266$	7.92331	+	16.6070i	0.485809	+	1.01824i
$267$	−3.01764	+	4.04473i	−0.184676	+	0.247533i
$268$	−1.44177	−	1.04751i	−0.0880701	−	0.0639867i
$269$	−6.36071	−	19.5763i	−0.387819	−	1.19359i	−0.934414	−	0.356188i	$-0.884076\pi$
$269$	−6.36071	−	19.5763i	−0.387819	−	1.19359i	0.546595	−	0.837397i	$-0.315924\pi$
$270$	−6.91043	+	18.8062i	−0.420555	+	1.14451i
$271$	−12.3298	+	16.9706i	−0.748984	+	1.03089i	0.249067	+	0.968486i	$0.419876\pi$
$271$	−12.3298	+	16.9706i	−0.748984	+	1.03089i	−0.998051	+	0.0624022i	$0.980124\pi$
$272$	−13.1005	+	9.51809i	−0.794336	+	0.577119i
$273$	6.47429	−	5.99122i	0.391842	−	0.362605i
$274$	4.04816			0.244558
$275$	−15.6783	−	2.44192i	−0.945436	−	0.147253i
$276$	−1.43094	−	4.60141i	−0.0861327	−	0.276972i
$277$	5.06840	−	15.5989i	0.304531	−	0.937249i	−0.675321	−	0.737524i	$-0.735995\pi$
$277$	5.06840	−	15.5989i	0.304531	−	0.937249i	0.979852	−	0.199725i	$-0.0640049\pi$
$278$	2.95847	−	2.14945i	0.177437	−	0.128916i
$279$	0.309070	−	12.2036i	0.0185036	−	0.730613i
$280$	−12.0719	+	22.2394i	−0.721434	+	1.32906i
$281$	14.2425	−	4.62767i	0.849636	−	0.276063i	0.148342	−	0.988936i	$-0.452606\pi$
$281$	14.2425	−	4.62767i	0.849636	−	0.276063i	0.701293	+	0.712873i	$0.252606\pi$
$282$	3.98660	−	11.7607i	0.237398	−	0.700342i
$283$	−5.76795	−	7.93890i	−0.342869	−	0.471918i	0.602408	−	0.798188i	$-0.294208\pi$
$283$	−5.76795	−	7.93890i	−0.342869	−	0.471918i	−0.945277	+	0.326270i	$0.894208\pi$
$284$	6.10114	+	1.98238i	0.362036	+	0.117633i
$285$	−9.07665	−	29.1873i	−0.537654	−	1.72891i
$286$	−1.25108	−	7.76977i	−0.0739781	−	0.459436i
$287$	−6.03023	+	5.72371i	−0.355953	+	0.337860i
$288$	−7.63078	+	2.26747i	−0.449648	+	0.133612i
$289$	−13.1457	+	9.55094i	−0.773279	+	0.561820i
$290$	−12.8206	−	9.31468i	−0.752849	−	0.546977i
$291$	−14.8702	+	10.5188i	−0.871705	+	0.616622i
$292$	−3.67326	+	1.19351i	−0.214961	+	0.0698451i
$293$	12.6768	+	9.21022i	0.740585	+	0.538067i	0.892894	−	0.450266i	$-0.148671\pi$
$293$	12.6768	+	9.21022i	0.740585	+	0.538067i	−0.152309	+	0.988333i	$0.548671\pi$
$294$	−9.54947	+	11.4971i	−0.556936	+	0.670522i
$295$	2.19649	−	6.76010i	0.127885	−	0.393588i
$296$			27.3045i			1.58704i
$297$	−7.27538	−	15.6227i	−0.422161	−	0.906521i
$298$	−4.83833			−0.280277
$299$	−3.44451	+	10.6011i	−0.199201	+	0.613079i
$300$	2.38066	−	3.19094i	0.137447	−	0.184229i
$301$	−18.2308	+	2.40212i	−1.05080	+	0.138456i
$302$	17.5591	−	5.70529i	1.01041	−	0.328303i
$303$	1.02528	+	1.44942i	0.0589011	+	0.0832672i
$304$	−9.31273	+	12.8179i	−0.534122	+	0.735156i
$305$	−10.0229	−	13.7954i	−0.573912	−	0.789922i
$306$	20.4407	−	6.07392i	1.16852	−	0.347223i
$307$			4.77487i			0.272516i	0.990673	+	0.136258i	$0.0435077\pi$
$307$			4.77487i			0.272516i	−0.990673	+	0.136258i	$0.956492\pi$
$308$	−1.20819	−	4.03904i	−0.0688430	−	0.230146i
$309$	0.554717	+	1.78377i	0.0315568	+	0.101475i
$310$	4.84854	−	14.9223i	0.275378	−	0.847527i
$311$	7.45330	−	5.41514i	0.422638	−	0.307064i	−0.356060	−	0.934463i	$-0.615880\pi$
$311$	7.45330	−	5.41514i	0.422638	−	0.307064i	0.778698	+	0.627399i	$0.215880\pi$
$312$	9.65475	+	3.27272i	0.546592	+	0.185281i
$313$	25.7541	−	8.36800i	1.45571	−	0.472987i	0.528950	−	0.848653i	$-0.322586\pi$
$313$	25.7541	−	8.36800i	1.45571	−	0.472987i	0.926755	+	0.375666i	$0.122586\pi$
$314$	4.57999	+	14.0958i	0.258464	+	0.795470i
$315$	18.4343	−	16.6307i	1.03866	−	0.937031i
$316$	2.78812	−	2.02569i	0.156844	−	0.113954i
$317$	0.772203	+	0.250904i	0.0433712	+	0.0140922i	0.330622	−	0.943763i	$-0.392741\pi$
$317$	0.772203	+	0.250904i	0.0433712	+	0.0140922i	−0.287251	+	0.957855i	$0.592741\pi$
$318$	12.7729	−	3.97211i	0.716270	−	0.222745i
$319$	13.4576	−	2.16693i	0.753479	−	0.121325i
$320$	−27.8000			−1.55407
$321$	3.52379	+	0.0446148i	0.196679	+	0.00249015i
$322$	3.43971	−	18.5702i	0.191688	−	1.03488i
$323$	−19.1216	+	26.3187i	−1.06396	+	1.46441i
$324$	4.31844	+	0.218879i	0.239914	+	0.0121599i
$325$	−8.75840	+	2.84578i	−0.485829	+	0.157855i
$326$	−9.02204	+	12.4178i	−0.499685	+	0.687757i
$327$	9.57963	−	12.8402i	0.529755	−	0.710064i
$328$	−9.13820	−	2.96918i	−0.504573	−	0.163946i
$329$	−11.1609	+	10.5936i	−0.615323	+	0.584046i
$330$	−3.24412	−	21.9113i	−0.178583	−	1.20618i
$331$	22.3929			1.23083			0.615413	−	0.788205i	$-0.288989\pi$
$331$	22.3929			1.23083			0.615413	+	0.788205i	$0.288989\pi$
$332$	−0.931972	+	2.86832i	−0.0511486	+	0.157419i
$333$	8.92090	−	25.2608i	0.488862	−	1.38428i
$334$	−2.31783	+	3.19022i	−0.126826	+	0.174561i
$335$	3.58543	+	11.0348i	0.195893	+	0.602896i
$336$	−12.6233	−	2.50387i	−0.688656	−	0.136597i
$337$	19.5755	+	14.2224i	1.06634	+	0.774744i	0.975251	−	0.221099i	$-0.0709643\pi$
$337$	19.5755	+	14.2224i	1.06634	+	0.774744i	0.0910919	+	0.995842i	$0.470964\pi$
$338$	6.73462	+	9.26940i	0.366315	+	0.504189i
$339$	−6.28039	−	0.0795160i	−0.341104	−	0.00431872i
$340$	−8.66550			−0.469953
$341$	6.15792	+	12.0092i	0.333470	+	0.650335i
$342$	17.1844	−	11.8322i	0.929224	−	0.639814i
$343$	17.1082	−	7.09292i	0.923756	−	0.382982i
$344$	−12.4911	−	17.1925i	−0.673474	−	0.926958i
$345$	−10.0718	+	29.7124i	−0.542246	+	1.59966i
$346$	15.8077	−	5.13622i	0.849825	−	0.276125i
$347$	−20.4624	+	6.64864i	−1.09848	+	0.356918i	−0.801517	−	0.597972i	$-0.795974\pi$
$347$	−20.4624	+	6.64864i	−1.09848	+	0.356918i	−0.296962	+	0.954889i	$0.595974\pi$
$348$	−1.09794	+	3.23901i	−0.0588560	+	0.173629i
$349$	−1.69693	−	2.33563i	−0.0908348	−	0.125023i	0.761181	−	0.648540i	$-0.224620\pi$
$349$	−1.69693	−	2.33563i	−0.0908348	−	0.125023i	−0.852016	+	0.523516i	$0.824620\pi$
$350$	14.0825	−	6.71888i	0.752743	−	0.359139i
$351$	−7.86283	−	6.18214i	−0.419687	−	0.329978i
$352$	6.20703	−	6.23901i	0.330836	−	0.332540i
$353$	33.3905			1.77720			0.888598	−	0.458687i	$-0.151680\pi$
$353$	33.3905			1.77720			0.888598	+	0.458687i	$0.151680\pi$
$354$	4.85142	+	0.0614239i	0.257850	+	0.00326464i
$355$	−24.5496	−	33.7896i	−1.30295	−	1.79336i
$356$	1.13245	+	0.822773i	0.0600197	+	0.0436069i
$357$	−25.9191	−	5.14115i	−1.37178	−	0.272098i
$358$	−3.12014	−	9.60282i	−0.164905	−	0.507525i
$359$	−3.09333	+	4.25760i	−0.163260	+	0.224708i	−0.882807	−	0.469736i	$-0.844349\pi$
$359$	−3.09333	+	4.25760i	−0.163260	+	0.224708i	0.719548	+	0.694443i	$0.244349\pi$
$360$	27.0551	+	9.55457i	1.42593	+	0.503570i
$361$	−3.96461	+	12.2018i	−0.208664	+	0.642201i
$362$	5.11479			0.268828
$363$	15.3292	+	11.3144i	0.804573	+	0.593854i
$364$	−1.68447	−	1.77468i	−0.0882903	−	0.0930185i
$365$	23.9151	+	7.77048i	1.25177	+	0.406725i
$366$	6.96018	−	9.32917i	0.363815	−	0.487644i
$367$	−7.14408	+	9.83298i	−0.372918	+	0.513277i	−0.953691	−	0.300788i	$-0.902750\pi$
$367$	−7.14408	+	9.83298i	−0.372918	+	0.513277i	0.580773	+	0.814065i	$0.302750\pi$
$368$	15.4661	−	5.02526i	0.806229	−	0.261960i
$369$	7.48412	+	5.73256i	0.389608	+	0.298425i
$370$	20.2389	−	27.8564i	1.05217	−	1.44819i
$371$	−16.2982	−	3.01888i	−0.846162	−	0.156733i
$372$	−3.38591	−	0.0428690i	−0.175551	−	0.00222266i
$373$	1.61637			0.0836924			0.0418462	−	0.999124i	$-0.486676\pi$
$373$	1.61637			0.0836924			0.0418462	+	0.999124i	$0.486676\pi$
$374$	−16.6269	+	16.7125i	−0.859755	+	0.864185i
$375$	1.11655	−	0.347223i	0.0576582	−	0.0179305i
$376$	−16.9133	−	5.49546i	−0.872237	−	0.283407i
$377$	6.40026	−	4.65006i	0.329630	−	0.239490i
$378$	14.5763	+	8.64447i	0.749726	+	0.444623i
$379$	2.96126	+	9.11383i	0.152110	+	0.468146i	0.997857	−	0.0654384i	$-0.0208446\pi$
$379$	2.96126	+	9.11383i	0.152110	+	0.468146i	−0.845747	+	0.533585i	$0.820845\pi$
$380$	−8.06356	+	2.62001i	−0.413652	+	0.134404i
$381$	−26.3609	−	8.93567i	−1.35051	−	0.457788i
$382$	−7.55020	+	5.48554i	−0.386302	+	0.280665i
$383$	−3.63546	+	11.1888i	−0.185763	+	0.571721i	−0.999961	−	0.00886739i	$-0.997177\pi$
$383$	−3.63546	+	11.1888i	−0.185763	+	0.571721i	0.814197	+	0.580588i	$0.197177\pi$
$384$	−2.90533	−	9.34253i	−0.148262	−	0.476759i
$385$	−9.09296	+	25.8979i	−0.463420	+	1.31988i
$386$		−	18.4309i		−	0.938107i
$387$	5.93902	+	19.9867i	0.301897	+	1.01598i
$388$	2.96973	+	4.08748i	0.150765	+	0.207510i
$389$	11.4618	−	15.7758i	0.581134	−	0.799862i	−0.412685	−	0.910874i	$-0.635409\pi$
$389$	11.4618	−	15.7758i	0.581134	−	0.799862i	0.993819	+	0.111011i	$0.0354090\pi$
$390$	−7.42406	−	10.4952i	−0.375932	−	0.531447i
$391$	31.7563	−	10.3182i	1.60599	−	0.521816i
$392$	16.6366	+	13.4661i	0.840274	+	0.680141i
$393$	4.85918	−	6.51307i	0.245113	−	0.328541i
$394$	−6.95561	+	21.4072i	−0.350419	+	1.07848i
$395$	−22.4375			−1.12895
$396$	−4.30759	+	2.07277i	−0.216465	+	0.104161i
$397$			10.3361i			0.518756i	0.965776	+	0.259378i	$0.0835175\pi$
$397$			10.3361i			0.518756i	−0.965776	+	0.259378i	$0.916482\pi$
$398$	9.81099	−	30.1951i	0.491780	−	1.51354i
$399$	−25.6731	+	3.05260i	−1.28526	+	0.152821i
$400$	10.8694	+	7.89710i	0.543471	+	0.394855i
$401$	33.9387	−	11.0274i	1.69482	−	0.550680i	0.707125	−	0.707088i	$-0.249992\pi$
$401$	33.9387	−	11.0274i	1.69482	−	0.550680i	0.987692	+	0.156409i	$0.0499917\pi$
$402$	−6.46569	+	4.57367i	−0.322480	+	0.228114i
$403$	6.33690	+	4.60402i	0.315663	+	0.229343i
$404$	0.398414	−	0.289465i	0.0198218	−	0.0144014i
$405$	−21.9084	−	17.6788i	−1.08864	−	0.878467i
$406$	−9.72196	+	9.22779i	−0.482493	+	0.457967i
$407$	4.70829	+	29.2405i	0.233381	+	1.44940i
$408$	−9.06826	−	29.1603i	−0.448946	−	1.44365i
$409$	10.0010	+	3.24953i	0.494519	+	0.160679i	0.545650	−	0.838013i	$-0.316283\pi$
$409$	10.0010	+	3.24953i	0.494519	+	0.160679i	−0.0511311	+	0.998692i	$0.516283\pi$
$410$	7.12207	+	9.80268i	0.351734	+	0.484120i
$411$	−1.82603	+	5.38693i	−0.0900716	+	0.265717i
$412$	0.492803	−	0.160121i	0.0242786	−	0.00788861i
$413$	−5.28394	−	2.86821i	−0.260006	−	0.141135i
$414$	−21.4079	−	0.542179i	−1.05214	−	0.0266466i
$415$	15.8854	−	11.5414i	0.779784	−	0.566546i
$416$	1.57839	−	4.85779i	0.0773871	−	0.238173i
$417$	1.52580	+	4.90644i	0.0747188	+	0.240269i
$418$	−10.4189	+	20.5788i	−0.509604	+	1.00654i
$419$	−33.4067			−1.63203			−0.816013	−	0.578034i	$-0.803820\pi$
$419$	−33.4067			−1.63203			−0.816013	+	0.578034i	$0.803820\pi$
$420$	−4.67744	−	5.05457i	−0.228236	−	0.246638i
$421$	9.76280	−	7.09309i	0.475810	−	0.345696i	−0.323891	−	0.946094i	$-0.604991\pi$
$421$	9.76280	−	7.09309i	0.475810	−	0.345696i	0.799701	+	0.600398i	$0.204991\pi$
$422$	−2.60081	+	3.57971i	−0.126606	+	0.174258i
$423$	13.8519	+	10.6100i	0.673501	+	0.515876i
$424$	−5.91952	−	18.2184i	−0.287477	−	0.884764i
$425$	22.3179	+	16.2149i	1.08258	+	0.786540i
$426$	17.0478	−	22.8503i	0.825969	−	1.10710i
$427$	−13.0176	+	6.21078i	−0.629964	+	0.300561i
$428$		−	0.977522i		−	0.0472503i
$429$	10.9036	+	1.83994i	0.526433	+	0.0888331i
$430$			26.7987i			1.29235i
$431$	25.7987	+	8.38249i	1.24268	+	0.403771i	0.855292	−	0.518147i	$-0.173378\pi$
$431$	25.7987	+	8.38249i	1.24268	+	0.403771i	0.387386	+	0.921917i	$0.373378\pi$
$432$	−0.554097	+	14.5818i	−0.0266590	+	0.701566i
$433$	14.1845	−	19.5233i	0.681664	−	0.938230i	−0.318288	−	0.947994i	$-0.603108\pi$
$433$	14.1845	−	19.5233i	0.681664	−	0.938230i	0.999952	+	0.00976391i	$0.00310800\pi$
$434$	−11.6638	−	6.33128i	−0.559879	−	0.303911i
$435$	18.1782	−	12.8588i	0.871578	−	0.616532i
$436$	−3.59502	−	2.61193i	−0.172170	−	0.125089i
$437$	26.4307	−	19.2030i	1.26435	−	0.918605i
$438$	−0.217298	+	17.1628i	−0.0103829	+	0.820069i
$439$		−	26.1523i		−	1.24818i	−0.781353	−	0.624090i	$-0.785470\pi$
$439$		−	26.1523i		−	1.24818i	0.781353	−	0.624090i	$-0.214530\pi$
$440$	−31.3176	+	5.04274i	−1.49301	+	0.240403i
$441$	−10.9917	−	17.8936i	−0.523415	−	0.852078i
$442$	−4.22807	+	13.0126i	−0.201109	+	0.618949i
$443$	6.06024	+	8.34121i	0.287931	+	0.396303i	0.928341	−	0.371731i	$-0.121235\pi$
$443$	6.06024	+	8.34121i	0.287931	+	0.396303i	−0.640410	+	0.768033i	$0.721235\pi$
$444$	−7.03770	−	2.38561i	−0.333995	−	0.113216i
$445$	−2.81620	−	8.66738i	−0.133501	−	0.410873i
$446$	4.76366	+	14.6610i	0.225566	+	0.694220i
$447$	2.18246	−	6.43841i	0.103227	−	0.304526i
$448$	−4.28265	+	23.1210i	−0.202336	+	1.09237i
$449$	−20.3426	−	6.60972i	−0.960028	−	0.311932i	−0.213244	−	0.976999i	$-0.568403\pi$
$449$	−20.3426	−	6.60972i	−0.960028	−	0.311932i	−0.746784	+	0.665067i	$0.768403\pi$
$450$	−10.0336	−	14.5722i	−0.472989	−	0.686938i
$451$	−10.2981	−	1.60395i	−0.484920	−	0.0755271i
$452$			1.74222i			0.0819470i
$453$	−0.328421	+	25.9396i	−0.0154306	+	1.21875i
$454$	16.9233	+	23.2930i	0.794251	+	1.09319i
$455$	2.08102	+	15.7937i	0.0975595	+	0.740422i
$456$	−17.2550	−	24.3930i	−0.808038	−	1.14231i
$457$	−4.11115	−	12.6528i	−0.192311	−	0.591874i	−0.999997	−	0.00226099i	$-0.999280\pi$
$457$	−4.11115	−	12.6528i	−0.192311	−	0.591874i	0.807686	−	0.589613i	$-0.200720\pi$
$458$	−24.0258	−	17.4558i	−1.12265	−	0.815654i
$459$	−1.13771	+	29.9404i	−0.0531040	+	1.39750i
$460$	8.27646	+	2.68918i	0.385892	+	0.125384i
$461$	−1.89461			−0.0882406			−0.0441203	−	0.999026i	$-0.514048\pi$
$461$	−1.89461			−0.0882406			−0.0441203	+	0.999026i	$0.514048\pi$
$462$	−18.7232	−	0.677385i	−0.871083	−	0.0315148i
$463$	−5.58207			−0.259421			−0.129710	−	0.991552i	$-0.541405\pi$
$463$	−5.58207			−0.259421			−0.129710	+	0.991552i	$0.541405\pi$
$464$	−10.9768	−	3.56659i	−0.509586	−	0.165575i
$465$	17.6701	+	13.1831i	0.819433	+	0.611351i
$466$	−3.22169	−	2.34069i	−0.149242	−	0.108430i
$467$	−9.05072	−	27.8552i	−0.418817	−	1.28899i	−0.908792	−	0.417250i	$-0.862994\pi$
$467$	−9.05072	−	27.8552i	−0.418817	−	1.28899i	0.489974	−	0.871737i	$-0.337006\pi$
$468$	−1.68708	+	2.20256i	−0.0779851	+	0.101813i
$469$	9.72989	−	1.28203i	0.449285	−	0.0591987i
$470$	13.1818	+	18.1431i	0.608029	+	0.836881i
$471$	−20.8233	−	0.263644i	−0.959487	−	0.0121481i
$472$		−	6.94820i		−	0.319817i
$473$	−16.3414	−	16.2576i	−0.751376	−	0.747525i
$474$	−4.54797	−	14.6247i	−0.208895	−	0.671733i
$475$	25.6703	+	8.34077i	1.17783	+	0.382701i
$476$	−1.33494	+	7.20701i	−0.0611868	+	0.330333i
$477$	−0.475846	+	18.7888i	−0.0217875	+	0.860279i
$478$	−1.05155	−	3.23633i	−0.0480967	−	0.148026i
$479$	4.45113	+	13.6992i	0.203377	+	0.625931i	0.999776	+	0.0211595i	$0.00673576\pi$
$479$	4.45113	+	13.6992i	0.203377	+	0.625931i	−0.796399	+	0.604772i	$0.793264\pi$
$480$	4.61523	−	13.6152i	0.210655	−	0.621448i
$481$	10.1036	+	13.9064i	0.460686	+	0.634079i
$482$	6.07195	−	18.6875i	0.276570	−	0.851194i
$483$	23.1600	+	12.9539i	1.05381	+	0.589421i
$484$	3.08436	−	4.29146i	0.140198	−	0.195066i
$485$		−	32.8941i		−	1.49364i
$486$	7.08225	−	17.8632i	0.321257	−	0.810291i
$487$	−21.8845	+	15.9000i	−0.991681	+	0.720498i	−0.960289	−	0.279009i	$-0.909994\pi$
$487$	−21.8845	+	15.9000i	−0.991681	+	0.720498i	−0.0313924	+	0.999507i	$0.509994\pi$
$488$	−13.4853	−	9.79763i	−0.610450	−	0.443518i
$489$	−12.4548	−	17.6071i	−0.563226	−	0.796221i
$490$	−6.99140	−	26.0698i	−0.315839	−	1.17771i
$491$	12.5047	−	17.2112i	0.564328	−	0.776731i	−0.427541	−	0.903996i	$-0.640620\pi$
$491$	12.5047	−	17.2112i	0.564328	−	0.776731i	0.991869	+	0.127265i	$0.0406199\pi$
$492$	1.56371	−	2.09594i	0.0704975	−	0.0944922i
$493$	−22.5385	−	7.32319i	−1.01508	−	0.329820i
$494$			13.3871i			0.602314i
$495$	30.6210	+	5.56674i	1.37631	+	0.250206i
$496$		−	11.4274i		−	0.513108i
$497$	−31.8844	+	15.2123i	−1.43021	+	0.682364i
$498$	10.7425	+	8.01465i	0.481385	+	0.359145i
$499$	−30.9021	−	22.4517i	−1.38337	−	1.00508i	−0.996556	−	0.0829165i	$-0.973577\pi$
$499$	−30.9021	−	22.4517i	−1.38337	−	1.00508i	−0.386811	−	0.922159i	$-0.626423\pi$
$500$	−0.100227	−	0.308468i	−0.00448230	−	0.0137951i
$501$	−3.19974	−	4.52340i	−0.142954	−	0.202091i
$502$	5.10920	−	7.03222i	0.228035	−	0.313863i
$503$	6.59860	−	4.79417i	0.294217	−	0.213761i	−0.430878	−	0.902410i	$-0.641796\pi$
$503$	6.59860	−	4.79417i	0.294217	−	0.213761i	0.725095	+	0.688649i	$0.241796\pi$
$504$	12.1143	−	21.0296i	0.539616	−	0.936732i
$505$	−3.20625			−0.142676
$506$	21.0668	−	10.8024i	0.936535	−	0.480224i
$507$	−15.3727	+	4.78060i	−0.682726	+	0.212314i
$508$	−2.38584	+	7.34287i	−0.105855	+	0.325787i
$509$	−10.4037	+	7.55873i	−0.461136	+	0.335035i	−0.793977	−	0.607948i	$-0.791993\pi$
$509$	−10.4037	+	7.55873i	−0.461136	+	0.335035i	0.332841	+	0.942983i	$0.391993\pi$
$510$	−12.3629	+	36.4714i	−0.547438	+	1.61498i
$511$	10.1468	−	18.6929i	0.448868	−	0.826924i
$512$	−23.4201	+	7.60965i	−1.03503	+	0.336302i
$513$	7.99379	+	28.2047i	0.352935	+	1.24527i
$514$	−8.13271	−	11.1937i	−0.358719	−	0.493734i
$515$	−3.20844	−	1.04248i	−0.141381	−	0.0459373i
$516$	5.52269	−	1.71744i	0.243123	−	0.0756062i
$517$	−19.0601	−	2.96864i	−0.838263	−	0.130561i
$518$	−20.0501	−	21.1238i	−0.880950	−	0.928128i
$519$	−0.295663	+	23.3522i	−0.0129782	+	1.02505i
$520$	−14.8943	+	10.8213i	−0.653156	+	0.474546i
$521$	7.99606	+	5.80948i	0.350314	+	0.254518i	0.749001	−	0.662569i	$-0.230534\pi$
$521$	7.99606	+	5.80948i	0.350314	+	0.254518i	−0.398687	+	0.917087i	$0.630534\pi$
$522$	12.0659	+	9.24206i	0.528112	+	0.404514i
$523$	−26.6518	+	8.65971i	−1.16540	+	0.378663i	−0.826926	−	0.562311i	$-0.809912\pi$
$523$	−26.6518	+	8.65971i	−1.16540	+	0.378663i	−0.338478	+	0.940974i	$0.609912\pi$
$524$	−1.82354	−	1.32488i	−0.0796617	−	0.0578776i
$525$	2.58857	+	21.7705i	0.112974	+	0.950142i
$526$	−3.22209	+	9.91656i	−0.140490	+	0.432383i
$527$		−	23.4637i		−	1.02210i
$528$	−7.17853	−	14.4472i	−0.312406	−	0.628735i
$529$	−10.5327			−0.457942
$530$	−7.46482	+	22.9744i	−0.324251	+	0.997942i
$531$	−2.27011	+	6.42813i	−0.0985142	+	0.278957i
$532$	0.936829	+	7.11000i	0.0406167	+	0.308258i
$533$	−5.75287	+	1.86922i	−0.249184	+	0.0809649i
$534$	5.07853	−	3.59242i	0.219769	−	0.155459i
$535$	−3.74081	+	5.14878i	−0.161729	+	0.222601i
$536$	6.66658	+	9.17576i	0.287952	+	0.396332i
$537$	14.1860	+	0.179609i	0.612171	+	0.00775070i
$538$			25.3736i			1.09393i
$539$	20.1382	+	11.5522i	0.867414	+	0.497586i
$540$	−4.82649	+	6.13863i	−0.207699	+	0.264165i
$541$	1.43316	−	4.41081i	0.0616163	−	0.189635i	−0.915510	−	0.402295i	$-0.868213\pi$
$541$	1.43316	−	4.41081i	0.0616163	−	0.189635i	0.977126	+	0.212660i	$0.0682126\pi$
$542$	20.9197	−	15.1990i	0.898577	−	0.652854i
$543$	−2.30717	+	6.80631i	−0.0990101	+	0.292087i
$544$	−14.5518	+	4.72817i	−0.623904	+	0.202719i
$545$	8.94017	+	27.5150i	0.382955	+	1.17861i
$546$	−9.87248	+	4.55771i	−0.422503	+	0.195052i
$547$	−15.3131	+	11.1256i	−0.654739	+	0.475696i	−0.864882	−	0.501975i	$-0.832607\pi$
$547$	−15.3131	+	11.1256i	−0.654739	+	0.475696i	0.210143	+	0.977671i	$0.432607\pi$
$548$	1.50054	+	0.487555i	0.0640998	+	0.0208273i
$549$	9.27484	+	13.4702i	0.395840	+	0.574892i
$550$	17.4506	+	8.83511i	0.744095	+	0.376730i
$551$	−23.1870			−0.987801
$552$	−0.388254	+	30.6653i	−0.0165252	+	1.30520i
$553$	−3.45654	+	18.6611i	−0.146987	+	0.793549i
$554$	−11.8841	+	16.3570i	−0.504906	+	0.694944i
$555$	27.9395	+	39.4975i	1.18597	+	1.67658i
$556$	1.35550	−	0.440428i	0.0574860	−	0.0186783i
$557$	−19.7648	+	27.2039i	−0.837460	+	1.15266i	0.149028	+	0.988833i	$0.452385\pi$
$557$	−19.7648	+	27.2039i	−0.837460	+	1.15266i	−0.986488	+	0.163832i	$0.947615\pi$
$558$	−5.01103	+	14.1895i	−0.212134	+	0.600688i
$559$	−12.7236	−	4.13416i	−0.538153	−	0.174856i
$560$	16.8566	−	15.9998i	0.712323	−	0.676115i
$561$	−14.7395	−	29.6642i	−0.622303	−	1.25242i
$562$	−18.4603			−0.778700
$563$	14.2357	−	43.8130i	0.599964	−	1.84650i	0.0716850	−	0.997427i	$-0.477162\pi$
$563$	14.2357	−	43.8130i	0.599964	−	1.84650i	0.528279	−	0.849071i	$-0.322838\pi$
$564$	2.89417	−	3.87923i	0.121866	−	0.163345i
$565$	6.66717	−	9.17657i	0.280490	−	0.386061i
$566$	3.73803	+	11.5045i	0.157121	+	0.483570i
$567$	−18.0783	+	15.4975i	−0.759219	+	0.650836i
$568$	−33.0300	−	23.9977i	−1.38591	−	1.00692i
$569$	7.84790	+	10.8017i	0.329001	+	0.452831i	0.941189	−	0.337882i	$-0.109710\pi$
$569$	7.84790	+	10.8017i	0.329001	+	0.452831i	−0.612188	+	0.790712i	$0.709710\pi$
$570$	−0.477014	+	37.6759i	−0.0199799	+	1.57807i
$571$	26.4899			1.10857			0.554284	−	0.832328i	$-0.312992\pi$
$571$	26.4899			1.10857			0.554284	+	0.832328i	$0.312992\pi$
$572$	0.472038	−	3.03071i	0.0197369	−	0.126720i
$573$	−3.89394	−	12.5215i	−0.162672	−	0.523095i
$574$	9.24997	−	4.41323i	0.386086	−	0.184205i
$575$	−16.2840	−	22.4129i	−0.679088	−	0.934684i
$576$	26.6542	+	0.675046i	1.11059	+	0.0281269i
$577$	8.97599	−	2.91648i	0.373675	−	0.121414i	−0.116158	−	0.993231i	$-0.537058\pi$
$577$	8.97599	−	2.91648i	0.373675	−	0.121414i	0.489833	+	0.871816i	$0.337058\pi$
$578$	19.0499	−	6.18968i	0.792371	−	0.257457i
$579$	24.5261	+	8.31375i	1.01927	+	0.345508i
$580$	−3.63037	−	4.99678i	−0.150743	−	0.207480i
$581$	−7.15171	−	14.9897i	−0.296703	−	0.621879i
$582$	21.4402	−	6.66747i	0.888726	−	0.276376i
$583$	−9.48075	−	18.4894i	−0.392653	−	0.765754i
$584$	24.5805			1.01715
$585$	17.3149	−	5.14511i	0.715885	−	0.212724i
$586$	−11.3535	−	15.6267i	−0.469007	−	0.645533i
$587$	34.5165	+	25.0777i	1.42465	+	1.03507i	0.990982	+	0.133995i	$0.0427807\pi$
$587$	34.5165	+	25.0777i	1.42465	+	1.03507i	0.433667	+	0.901073i	$0.357219\pi$
$588$	−4.92441	+	3.11151i	−0.203079	+	0.128317i
$589$	−7.09425	−	21.8339i	−0.292314	−	0.899649i
$590$	−5.15020	+	7.08864i	−0.212030	+	0.291835i
$591$	−25.3492	−	18.9122i	−1.04273	−	0.777944i
$592$	7.74946	−	23.8504i	0.318501	−	0.980244i
$593$	20.9004			0.858275			0.429137	−	0.903239i	$-0.358818\pi$
$593$	20.9004			0.858275			0.429137	+	0.903239i	$0.358818\pi$
$594$	2.57835	+	21.0870i	0.105791	+	0.865209i
$595$	34.6113	−	32.8520i	1.41893	−	1.34680i
$596$	−1.79343	−	0.582721i	−0.0734618	−	0.0238692i
$597$	35.7554	+	26.6759i	1.46337	+	1.09177i
$598$	8.07649	−	11.1163i	0.330272	−	0.454581i
$599$	19.9847	−	6.49343i	0.816554	−	0.265315i	0.129183	−	0.991621i	$-0.458765\pi$
$599$	19.9847	−	6.49343i	0.816554	−	0.265315i	0.687371	+	0.726306i	$0.258765\pi$
$600$	−20.6850	+	14.6320i	−0.844461	+	0.597350i
$601$	−25.0526	+	34.4819i	−1.02191	+	1.40655i	−0.111062	+	0.993813i	$0.535425\pi$
$601$	−25.0526	+	34.4819i	−1.02191	+	1.40655i	−0.910853	+	0.412732i	$0.864575\pi$
$602$	22.2883	+	4.12840i	0.908401	+	0.168261i
$603$	−3.16969	−	10.6670i	−0.129080	−	0.434396i
$604$	7.19580			0.292793
$605$	−32.6685	+	10.8006i	−1.32816	+	0.439105i
$606$	−0.649890	−	2.08982i	−0.0264000	−	0.0848931i
$607$	−2.68800	−	0.873384i	−0.109102	−	0.0354495i	0.253957	−	0.967216i	$-0.418268\pi$
$607$	−2.68800	−	0.873384i	−0.109102	−	0.0354495i	−0.363059	+	0.931766i	$0.618268\pi$
$608$	−12.1114	+	8.79947i	−0.491184	+	0.356866i
$609$	−7.89415	−	17.0996i	−0.319887	−	0.692909i
$610$	6.49557	+	19.9913i	0.262998	+	0.809425i
$611$	−10.6476	+	3.45962i	−0.430756	+	0.139961i
$612$	8.30832	+	0.210417i	0.335844	+	0.00850561i
$613$	12.6556	−	9.19486i	0.511156	−	0.371377i	−0.302106	−	0.953274i	$-0.597690\pi$
$613$	12.6556	−	9.19486i	0.511156	−	0.371377i	0.813262	+	0.581898i	$0.197690\pi$
$614$	1.81887	−	5.59792i	0.0734038	−	0.225914i
$615$	−16.2571	+	5.05563i	−0.655551	+	0.203863i
$616$	−0.630540	+	26.8234i	−0.0254052	+	1.08074i
$617$		−	12.1157i		−	0.487761i	−0.969805	−	0.243880i	$-0.921580\pi$
$617$		−	12.1157i		−	0.487761i	0.969805	−	0.243880i	$-0.0784205\pi$
$618$	0.0291526	−	2.30255i	0.00117269	−	0.0926222i
$619$	20.0531	+	27.6008i	0.806004	+	1.10937i	0.991928	+	0.126805i	$0.0404722\pi$
$619$	20.0531	+	27.6008i	0.806004	+	1.10937i	−0.185924	+	0.982564i	$0.559528\pi$
$620$	3.59443	−	4.94731i	0.144356	−	0.198689i
$621$	10.3781	−	28.2432i	0.416460	−	1.13336i
$622$	−10.8008	+	3.50939i	−0.433073	+	0.140714i
$623$	−7.64242	+	1.00698i	−0.306187	+	0.0403438i
$624$	−7.50452	−	5.59887i	−0.300421	−	0.224134i
$625$	−8.04450	+	24.7584i	−0.321780	+	0.990337i
$626$	−33.3809			−1.33417
$627$	−22.6846	−	23.1471i	−0.905937	−	0.924407i
$628$			5.77651i			0.230508i
$629$	15.9118	−	48.9715i	0.634445	−	1.95262i
$630$	−27.9469	+	12.4752i	−1.11343	+	0.497022i
$631$	35.9036	+	26.0855i	1.42930	+	1.03845i	0.990146	+	0.140036i	$0.0447217\pi$
$631$	35.9036	+	26.0855i	1.42930	+	1.03845i	0.439154	+	0.898412i	$0.355278\pi$
$632$	−20.8596	+	6.77771i	−0.829752	+	0.269603i
$633$	−3.59039	−	5.07566i	−0.142705	−	0.201739i
$634$	−0.809732	−	0.588304i	−0.0321586	−	0.0233646i
$635$	40.6666	−	29.5460i	1.61380	−	1.17250i
$636$	5.21296	+	0.0660013i	0.206707	+	0.00261712i
$637$	13.4561	+	0.702297i	0.533149	+	0.0278260i
$638$	−16.6027	−	2.58590i	−0.657307	−	0.102377i
$639$	22.7172	+	32.9929i	0.898678	+	1.30518i
$640$	16.8042	+	5.46001i	0.664244	+	0.215826i
$641$	−14.6480	−	20.1612i	−0.578561	−	0.796321i	0.414976	−	0.909832i	$-0.363790\pi$
$641$	−14.6480	−	20.1612i	−0.578561	−	0.796321i	−0.993537	+	0.113512i	$0.963790\pi$
$642$	−4.11420	−	1.39461i	−0.162374	−	0.0550409i
$643$	11.9536	−	3.88397i	0.471405	−	0.153169i	−0.0636739	−	0.997971i	$-0.520282\pi$
$643$	11.9536	−	3.88397i	0.471405	−	0.153169i	0.535079	+	0.844802i	$0.320282\pi$
$644$	3.51157	−	6.46917i	0.138375	−	0.254921i
$645$	−35.6613	−	12.0883i	−1.40416	−	0.475977i
$646$	32.4431	−	23.5713i	1.27646	−	0.927400i
$647$	−6.82359	+	21.0009i	−0.268263	+	0.825629i	0.722661	+	0.691203i	$0.242919\pi$
$647$	−6.82359	+	21.0009i	−0.268263	+	0.825629i	−0.990924	+	0.134426i	$0.957081\pi$
$648$	−25.7080	−	9.81771i	−1.00990	−	0.385676i
$649$	−1.19812	−	7.44086i	−0.0470304	−	0.292079i
$650$	11.3521			0.445267
$651$	13.6864	−	12.6652i	0.536411	−	0.496388i
$652$	−4.83980	+	3.51632i	−0.189541	+	0.137710i
$653$	−2.68737	+	3.69885i	−0.105165	+	0.144747i	−0.858356	−	0.513055i	$-0.828514\pi$
$653$	−2.68737	+	3.69885i	−0.105165	+	0.144747i	0.753191	+	0.657802i	$0.228514\pi$
$654$	−16.1220	+	11.4043i	−0.630422	+	0.445944i
$655$	4.53482	+	13.9567i	0.177190	+	0.545335i
$656$	7.13947	+	5.18713i	0.278750	+	0.202523i
$657$	−22.7407	−	8.03091i	−0.887198	−	0.313315i
$658$	17.1202	−	8.16816i	0.667413	−	0.318428i
$659$			3.09680i			0.120634i	0.998179	+	0.0603171i	$0.0192112\pi$
$659$			3.09680i			0.120634i	−0.998179	+	0.0603171i	$0.980789\pi$
$660$	1.43647	−	8.51264i	0.0559144	−	0.331354i
$661$		−	23.9352i		−	0.930970i	−0.885056	−	0.465485i	$-0.845880\pi$
$661$		−	23.9352i		−	0.930970i	0.885056	−	0.465485i	$-0.154120\pi$
$662$	−26.2528	−	8.53004i	−1.02034	−	0.331530i
$663$	−15.4089	−	11.4960i	−0.598431	−	0.446469i
$664$	11.2820	−	15.5283i	0.437826	−	0.602615i
$665$	22.2743	−	41.0347i	0.863761	−	1.59126i
$666$	−20.0811	+	26.2168i	−0.778126	+	1.01588i
$667$	19.2540	+	13.9888i	0.745517	+	0.541650i
$668$	−1.24338	+	0.903370i	−0.0481079	+	0.0349524i
$669$	−21.6584	−	0.274217i	−0.837361	−	0.0106018i
$670$		−	14.3027i		−	0.552560i
$671$	−16.1309	−	8.16696i	−0.622726	−	0.315282i
$672$	−10.6127	−	5.93590i	−0.409393	−	0.228982i
$673$	1.90522	−	5.86365i	0.0734407	−	0.226027i	−0.907598	−	0.419841i	$-0.862086\pi$
$673$	1.90522	−	5.86365i	0.0734407	−	0.226027i	0.981038	+	0.193814i	$0.0620858\pi$
$674$	−17.5320	−	24.1307i	−0.675308	−	0.929481i
$675$	23.9173	−	6.77865i	0.920576	−	0.260911i
$676$	1.37994	+	4.24702i	0.0530746	+	0.163347i
$677$	−15.3544	−	47.2560i	−0.590118	−	1.81620i	−0.577665	−	0.816274i	$-0.696036\pi$
$677$	−15.3544	−	47.2560i	−0.590118	−	1.81620i	−0.0124536	−	0.999922i	$-0.503964\pi$
$678$	7.33265	+	2.48559i	0.281609	+	0.0954583i
$679$	−27.3577	−	5.06740i	−1.04989	−	0.194469i
$680$	52.4500	+	17.0420i	2.01137	+	0.653533i
$681$	−38.6299	+	12.0131i	−1.48030	+	0.460343i
$682$	−2.64474	−	16.4250i	−0.101272	−	0.628944i
$683$		−	12.4987i		−	0.478250i	−0.970989	−	0.239125i	$-0.923139\pi$
$683$		−	12.4987i		−	0.478250i	0.970989	−	0.239125i	$-0.0768606\pi$
$684$	7.79482	−	2.31622i	0.298042	−	0.0885628i
$685$	−6.03782	−	8.31034i	−0.230693	−	0.317522i
$686$	−22.7590	+	1.79857i	−0.868944	+	0.0686698i
$687$	34.0660	−	24.0975i	1.29970	−	0.919375i
$688$	6.03139	+	18.5627i	0.229945	+	0.707697i
$689$	−9.75631	−	7.08837i	−0.371686	−	0.270045i
$690$	23.1261	−	30.9974i	0.880395	−	1.18005i
$691$	33.6956	+	10.9484i	1.28184	+	0.416496i	0.869228	−	0.494411i	$-0.164616\pi$
$691$	33.6956	+	10.9484i	1.28184	+	0.416496i	0.412613	+	0.910906i	$0.364616\pi$
$692$	6.47805			0.246259
$693$	9.34703	−	24.6096i	0.355064	−	0.934842i
$694$	26.5222			1.00677
$695$	−8.82510	−	2.86745i	−0.334755	−	0.108768i
$696$	13.0156	−	17.4456i	0.493355	−	0.661274i
$697$	14.6593	+	10.6506i	0.555261	+	0.403421i
$698$	1.09973	+	3.38463i	0.0416255	+	0.128110i
$699$	4.56801	−	3.23130i	0.172778	−	0.122219i
$700$	6.02921	−	0.794421i	0.227883	−	0.0300263i
$701$	10.1240	+	13.9345i	0.382379	+	0.526300i	0.956213	−	0.292672i	$-0.0945444\pi$
$701$	10.1240	+	13.9345i	0.382379	+	0.526300i	−0.573834	+	0.818972i	$0.694544\pi$
$702$	6.86321	+	10.2429i	0.259035	+	0.386594i
$703$		−	50.3807i		−	1.90014i
$704$	−26.2295	+	13.4496i	−0.988561	+	0.506901i
$705$	−30.0893	+	9.35714i	−1.13323	+	0.352410i
$706$	−39.1460	−	12.7193i	−1.47328	−	0.478697i
$707$	−0.493929	+	2.66661i	−0.0185761	+	0.100288i
$708$	1.79089	+	0.607067i	0.0673057	+	0.0228150i
$709$	−6.38878	−	19.6626i	−0.239936	−	0.738446i	−0.996428	−	0.0844436i	$-0.973089\pi$
$709$	−6.38878	−	19.6626i	−0.239936	−	0.738446i	0.756493	−	0.654002i	$-0.226911\pi$
$710$	15.9098	+	48.9654i	0.597086	+	1.83764i
$711$	21.5127	+	0.544832i	0.806789	+	0.0204328i
$712$	−5.23631	−	7.20717i	−0.196239	−	0.270100i
$713$	−7.28155	+	22.4103i	−0.272696	+	0.839273i
$714$	28.4284	+	15.9006i	1.06390	+	0.595064i
$715$	−14.0843	+	14.1569i	−0.526724	+	0.529438i
$716$		−	3.93528i		−	0.147068i
$717$	4.78095	+	0.0605316i	0.178548	+	0.00226059i
$718$	5.24836	−	3.81316i	0.195867	−	0.142306i
$719$	29.6020	+	21.5071i	1.10397	+	0.802081i	0.981703	−	0.190417i	$-0.0609839\pi$
$719$	29.6020	+	21.5071i	1.10397	+	0.802081i	0.122266	+	0.992497i	$0.460984\pi$
$720$	−20.9208	−	16.0245i	−0.779671	−	0.597199i
$721$	−1.36129	+	2.50783i	−0.0506971	+	0.0933964i
$722$	9.29599	−	12.7948i	0.345961	−	0.476174i
$723$	22.1288	+	16.5095i	0.822978	+	0.613996i
$724$	1.89591	+	0.616019i	0.0704609	+	0.0228941i
$725$			19.6624i			0.730242i
$726$	−13.6615	−	19.1040i	−0.507026	−	0.709015i
$727$			32.5843i			1.20848i	0.796801	+	0.604242i	$0.206524\pi$
$727$			32.5843i			1.20848i	−0.796801	+	0.604242i	$0.793476\pi$
$728$	6.70549	+	14.0545i	0.248522	+	0.520893i
$729$	20.5761	+	17.4821i	0.762078	+	0.647486i
$730$	−25.0773	−	18.2198i	−0.928154	−	0.674344i
$731$	12.3841	+	38.1144i	0.458044	+	1.40971i
$732$	3.70354	−	2.61979i	0.136887	−	0.0968301i
$733$	−16.7614	+	23.0701i	−0.619098	+	0.852115i	−0.997287	−	0.0736133i	$-0.976547\pi$
$733$	−16.7614	+	23.0701i	−0.619098	+	0.852115i	0.378189	+	0.925728i	$0.376547\pi$
$734$	12.1211	−	8.80653i	0.447400	−	0.325055i
$735$	37.8450	+	2.45598i	1.39593	+	0.0905900i
$736$	15.3658			0.566391
$737$	8.72149	+	8.67679i	0.321260	+	0.319614i
$738$	−6.59048	−	9.57158i	−0.242599	−	0.352335i
$739$	−5.41889	+	16.6776i	−0.199337	+	0.613496i	0.800561	+	0.599251i	$0.204535\pi$
$739$	−5.41889	+	16.6776i	−0.199337	+	0.613496i	−0.999899	+	0.0142458i	$0.995465\pi$
$740$	10.8570	−	7.88805i	0.399110	−	0.289971i
$741$	−17.8143	−	6.03862i	−0.654426	−	0.221834i
$742$	17.9576	+	9.74767i	0.659244	+	0.357848i
$743$	−6.36882	+	2.06935i	−0.233649	+	0.0759172i	−0.423501	−	0.905895i	$-0.639199\pi$
$743$	−6.36882	+	2.06935i	−0.233649	+	0.0759172i	0.189852	+	0.981813i	$0.439199\pi$
$744$	20.4097	+	6.91839i	0.748257	+	0.253641i
$745$	7.21635	+	9.93245i	0.264387	+	0.363897i
$746$	−1.89498	−	0.615717i	−0.0693802	−	0.0225430i
$747$	−15.5109	+	10.6800i	−0.567514	+	0.390760i
$748$	−8.17595	+	4.19235i	−0.298942	+	0.153288i
$749$	3.70591	+	3.90438i	0.135411	+	0.142663i
$750$	−1.44127	−	0.0182480i	−0.0526278	−	0.000666321i
$751$	−6.35762	+	4.61908i	−0.231993	+	0.168553i	−0.697709	−	0.716382i	$-0.745797\pi$
$751$	−6.35762	+	4.61908i	−0.231993	+	0.168553i	0.465716	+	0.884934i	$0.345797\pi$
$752$	13.2140	+	9.60052i	0.481864	+	0.350095i
$753$	7.05319	+	9.97094i	0.257033	+	0.363361i
$754$	−9.27480	+	3.01357i	−0.337768	+	0.109748i
$755$	−37.9015	−	27.5371i	−1.37938	−	1.00218i
$756$	4.36191	+	4.95981i	0.158641	+	0.180387i
$757$	13.7778	−	42.4038i	0.500764	−	1.54119i	−0.307014	−	0.951705i	$-0.599330\pi$
$757$	13.7778	−	42.4038i	0.500764	−	1.54119i	0.807777	−	0.589488i	$-0.200670\pi$
$758$		−	11.8128i		−	0.429061i
$759$	4.87203	+	32.9066i	0.176844	+	1.19443i
$760$	53.9593			1.95731
$761$	1.62328	−	4.99596i	0.0588440	−	0.181103i	−0.917314	−	0.398165i	$-0.869647\pi$
$761$	1.62328	−	4.99596i	0.0588440	−	0.181103i	0.976158	+	0.217062i	$0.0696472\pi$
$762$	27.5008	+	20.5175i	0.996251	+	0.743269i
$763$	24.2612	−	3.19671i	0.878316	−	0.115729i
$764$	−3.45932	+	1.12400i	−0.125154	+	0.0406649i
$765$	−42.9562	−	32.9028i	−1.55308	−	1.18960i
$766$	8.52421	−	11.7326i	0.307992	−	0.423915i
$767$	−2.57108	−	3.53878i	−0.0928362	−	0.127778i
$768$	0.237082	−	18.7254i	0.00855496	−	0.675693i
$769$			20.4914i			0.738937i	0.929243	+	0.369468i	$0.120460\pi$
$769$			20.4914i			0.738937i	−0.929243	+	0.369468i	$0.879540\pi$
$770$	20.5255	−	26.8981i	0.739688	−	0.969342i
$771$	18.5641	−	5.77304i	0.668569	−	0.207911i
$772$	2.21979	−	6.83181i	0.0798919	−	0.245882i
$773$	−14.4866	+	10.5251i	−0.521046	+	0.378562i	−0.816998	−	0.576641i	$-0.804363\pi$
$773$	−14.4866	+	10.5251i	−0.521046	+	0.378562i	0.295952	+	0.955203i	$0.404363\pi$
$774$	0.650732	−	25.6941i	0.0233901	−	0.923557i
$775$	−18.5149	+	6.01585i	−0.665074	+	0.216096i
$776$	−9.93633	−	30.5809i	−0.356694	−	1.09779i
$777$	37.1538	−	17.1524i	1.33289	−	0.615337i
$778$	−19.4468	+	14.1289i	−0.697202	+	0.506547i
$779$	16.8612	+	5.47855i	0.604117	+	0.196289i
$780$	−1.48786	−	4.78443i	−0.0532739	−	0.171310i
$781$	−39.5100	−	20.0036i	−1.41378	−	0.715786i
$782$	−41.1606			−1.47190
$783$	−17.7412	+	11.8874i	−0.634018	+	0.424820i
$784$	−10.7101	−	16.4843i	−0.382503	−	0.588725i
$785$	22.1057	−	30.4259i	0.788987	−	1.08595i
$786$	−8.17776	+	5.78474i	−0.291691	+	0.206335i
$787$	−27.7323	+	9.01078i	−0.988551	+	0.321200i	−0.758282	−	0.651927i	$-0.773961\pi$
$787$	−27.7323	+	9.01078i	−0.988551	+	0.321200i	−0.230270	+	0.973127i	$0.573961\pi$
$788$	−5.15650	+	7.09732i	−0.183693	+	0.252831i
$789$	−11.7427	−	8.76080i	−0.418050	−	0.311893i
$790$	26.3051	+	8.54704i	0.935893	+	0.304090i
$791$	−6.60497	−	6.95869i	−0.234846	−	0.247422i
$792$	30.1492	−	4.07443i	1.07130	−	0.144778i
$793$	−10.4936			−0.372640
$794$	3.93731	−	12.1178i	0.139730	−	0.430044i
$795$	−27.2050	−	20.2967i	−0.964862	−	0.719851i
$796$	7.27331	−	10.0109i	0.257796	−	0.354825i
$797$	6.06662	+	18.6711i	0.214891	+	0.661366i	0.999161	+	0.0409467i	$0.0130374\pi$
$797$	6.06662	+	18.6711i	0.214891	+	0.661366i	−0.784271	+	0.620419i	$0.786963\pi$
$798$	31.2612	+	6.20077i	1.10663	+	0.219505i
$799$	27.1320	+	19.7125i	0.959860	+	0.697379i
$800$	7.46186	+	10.2704i	0.263817	+	0.363112i
$801$	2.48966	+	8.37851i	0.0879678	+	0.296040i
$802$	−43.9893			−1.55332
$803$	26.3234	−	4.23857i	0.928931	−	0.149576i
$804$	−2.94750	+	0.916611i	−0.103950	+	0.0323264i
$805$	−43.2525	+	20.6361i	−1.52445	+	0.727327i
$806$	−5.67540	−	7.81151i	−0.199907	−	0.275149i
$807$	−33.7649	−	11.4455i	−1.18858	−	0.402899i
$808$	−2.98077	+	0.968512i	−0.104863	+	0.0340721i
$809$	15.1424	−	4.92008i	0.532380	−	0.172981i	−0.0304764	−	0.999535i	$-0.509702\pi$
$809$	15.1424	−	4.92008i	0.532380	−	0.172981i	0.562856	+	0.826555i	$0.309702\pi$
$810$	18.9504	+	29.0716i	0.665850	+	1.02147i
$811$	23.1351	+	31.8428i	0.812384	+	1.11815i	0.990951	+	0.134223i	$0.0428539\pi$
$811$	23.1351	+	31.8428i	0.812384	+	1.11815i	−0.178567	+	0.983928i	$0.557146\pi$
$812$	−4.71504	+	2.24958i	−0.165465	+	0.0789449i
$813$	10.7891	+	34.6940i	0.378390	+	1.21677i
$814$	5.61862	−	36.0742i	0.196933	−	1.26440i
$815$	38.9484			1.36430
$816$	−0.355079	+	28.0451i	−0.0124303	+	0.981775i
$817$	23.0478	+	31.7225i	0.806340	+	1.10983i
$818$	−10.4871	−	7.61931i	−0.366672	−	0.266403i
$819$	−1.61173	−	15.1933i	−0.0563185	−	0.530896i
$820$	1.45933	+	4.49135i	0.0509620	+	0.156845i
$821$	14.6595	−	20.1770i	0.511619	−	0.704183i	−0.472572	−	0.881292i	$-0.656674\pi$
$821$	14.6595	−	20.1770i	0.511619	−	0.704183i	0.984191	+	0.177109i	$0.0566744\pi$
$822$	4.19281	−	5.61989i	0.146241	−	0.196016i
$823$	−1.62188	+	4.99164i	−0.0565352	+	0.173998i	−0.975337	−	0.220723i	$-0.929158\pi$
$823$	−1.62188	+	4.99164i	−0.0565352	+	0.173998i	0.918801	+	0.394720i	$0.129158\pi$
$824$	−3.29771			−0.114881
$825$	−19.6285	+	19.2363i	−0.683377	+	0.669723i
$826$	5.10216	+	5.37539i	0.177527	+	0.187034i
$827$	−21.3099	−	6.92399i	−0.741016	−	0.240771i	−0.0859052	−	0.996303i	$-0.527378\pi$
$827$	−21.3099	−	6.92399i	−0.741016	−	0.240771i	−0.655111	+	0.755533i	$0.727378\pi$
$828$	−7.87002	−	2.77931i	−0.273502	−	0.0965877i
$829$	−7.27790	+	10.0172i	−0.252772	+	0.347911i	−0.916480	−	0.400081i	$-0.868982\pi$
$829$	−7.27790	+	10.0172i	−0.252772	+	0.347911i	0.663708	+	0.747992i	$0.268982\pi$
$830$	−23.0200	+	7.47966i	−0.799036	+	0.259623i
$831$	−16.4058	−	23.1926i	−0.569112	−	0.804541i
$832$	−10.0557	+	13.8405i	−0.348619	+	0.479833i
$833$	−21.9908	−	33.8468i	−0.761935	−	1.17272i
$834$	0.0801869	−	6.33338i	0.00277665	−	0.219307i
$835$	10.0062			0.346277
$836$	−6.34046	+	6.37313i	−0.219290	+	0.220419i
$837$	−16.6217	−	13.0688i	−0.574530	−	0.451723i
$838$	39.1651	+	12.7255i	1.35293	+	0.439595i
$839$	1.79187	−	1.30187i	0.0618624	−	0.0449457i	−0.556424	−	0.830898i	$-0.687827\pi$
$839$	1.79187	−	1.30187i	0.0618624	−	0.0449457i	0.618287	+	0.785953i	$0.287827\pi$
$840$	18.3707	+	39.7930i	0.633851	+	1.37299i
$841$	3.74186	+	11.5163i	0.129030	+	0.397113i
$842$	−14.1476	+	4.59682i	−0.487557	+	0.158417i
$843$	8.32702	−	24.5653i	0.286798	−	0.846073i
$844$	−1.39518	+	1.01366i	−0.0480242	+	0.0348916i
$845$	8.98421	−	27.6506i	0.309066	−	0.951209i
$846$	−12.1979	−	17.7154i	−0.419372	−	0.609068i
$847$	3.95007	+	28.8340i	0.135726	+	0.990746i
$848$			17.5937i			0.604172i
$849$	−16.9953	−	0.215177i	−0.583276	−	0.00738487i
$850$	−19.9882	−	27.5114i	−0.685590	−	0.943633i
$851$	−30.3948	+	41.8349i	−1.04192	+	1.43408i
$852$	9.07120	−	6.41674i	0.310774	−	0.219834i
$853$	−49.8461	+	16.1960i	−1.70670	+	0.554540i	−0.989778	−	0.142614i	$-0.954449\pi$
$853$	−49.8461	+	16.1960i	−1.70670	+	0.554540i	−0.716921	+	0.697154i	$0.754449\pi$
$854$	17.6272	−	2.32260i	0.603192	−	0.0794778i
$855$	−49.9205	−	17.6295i	−1.70724	−	0.602916i
$856$	−1.92245	+	5.91669i	−0.0657080	+	0.202228i
$857$	2.43184			0.0830702			0.0415351	−	0.999137i	$-0.486775\pi$
$857$	2.43184			0.0830702			0.0415351	+	0.999137i	$0.486775\pi$
$858$	−12.0822	−	6.31057i	−0.412480	−	0.215439i
$859$			7.77125i			0.265152i	0.991173	+	0.132576i	$0.0423248\pi$
$859$			7.77125i			0.265152i	−0.991173	+	0.132576i	$0.957675\pi$
$860$	−3.22760	+	9.93354i	−0.110060	+	0.338731i
$861$	1.70028	+	14.2997i	0.0579453	+	0.487334i
$862$	−27.0525	−	19.6548i	−0.921411	−	0.669444i
$863$	−34.3219	+	11.1519i	−1.16833	+	0.379614i	−0.828020	−	0.560699i	$-0.810533\pi$
$863$	−34.3219	+	11.1519i	−1.16833	+	0.379614i	−0.340312	+	0.940313i	$0.610533\pi$
$864$	−4.75561	+	12.9420i	−0.161789	+	0.440295i
$865$	−34.1211	−	24.7904i	−1.16015	−	0.842899i
$866$	−24.0664	+	17.4853i	−0.817811	+	0.594174i
$867$	−0.356305	+	28.1419i	−0.0121007	+	0.955749i
$868$	−3.56090	−	3.75160i	−0.120865	−	0.127338i
$869$	−21.1699	+	10.8552i	−0.718141	+	0.368238i
$870$	−26.2098	+	8.15072i	−0.888597	+	0.276335i
$871$	6.79069	+	2.20643i	0.230094	+	0.0747620i
$872$	16.6229	+	22.8795i	0.562924	+	0.774798i
$873$	−0.798741	+	31.5383i	−0.0270333	+	1.06741i
$874$	−38.3015	+	12.4449i	−1.29557	+	0.420955i
$875$	1.56977	+	0.852094i	0.0530677	+	0.0288060i
$876$	−2.14761	+	6.33559i	−0.0725609	+	0.214060i
$877$	1.66592	−	1.21036i	0.0562540	−	0.0408709i	−0.559303	−	0.828963i	$-0.688931\pi$
$877$	1.66592	−	1.21036i	0.0562540	−	0.0408709i	0.615557	+	0.788092i	$0.288931\pi$
$878$	−9.96208	+	30.6601i	−0.336204	+	1.03473i
$879$	25.9159	−	8.05931i	0.874122	−	0.271834i
$880$	28.7869	+	4.48361i	0.970407	+	0.151143i
$881$	22.2425			0.749368			0.374684	−	0.927153i	$-0.377751\pi$
$881$	22.2425			0.749368			0.374684	+	0.927153i	$0.377751\pi$
$882$	6.07019	+	25.1650i	0.204394	+	0.847350i
$883$	16.1682	−	11.7469i	0.544104	−	0.395315i	−0.281503	−	0.959560i	$-0.590833\pi$
$883$	16.1682	−	11.7469i	0.544104	−	0.395315i	0.825607	+	0.564246i	$0.190833\pi$
$884$	−3.13445	+	4.31420i	−0.105423	+	0.145102i
$885$	−7.10979	−	10.0510i	−0.238993	−	0.337859i
$886$	−3.92746	−	12.0875i	−0.131946	−	0.406087i
$887$	−17.7763	−	12.9152i	−0.596869	−	0.433651i	0.247897	−	0.968786i	$-0.420261\pi$
$887$	−17.7763	−	12.9152i	−0.596869	−	0.433651i	−0.844766	+	0.535135i	$0.820261\pi$
$888$	37.9057	+	28.2802i	1.27203	+	0.949021i
$889$	−18.3083	−	38.3736i	−0.614042	−	1.28701i
$890$			11.2341i			0.376569i
$891$	−29.2237	−	6.08083i	−0.979030	−	0.203716i
$892$			6.00816i			0.201168i
$893$	31.2074	+	10.1399i	1.04431	+	0.339318i
$894$	−5.01121	+	6.71684i	−0.167600	+	0.224645i
$895$	−15.0596	+	20.7278i	−0.503388	+	0.692855i
$896$	7.12976	−	13.1348i	0.238189	−	0.438802i
$897$	11.1495	+	15.7618i	0.372271	+	0.526271i
$898$	21.3313	+	15.4981i	0.711834	+	0.517178i
$899$	13.5299	−	9.83003i	0.451247	−	0.327850i
$900$	−1.96413	−	6.60992i	−0.0654709	−	0.220331i
$901$			36.1248i			1.20349i
$902$	11.4622	+	5.80325i	0.381651	+	0.193227i
$903$	−15.5474	+	27.7970i	−0.517386	+	0.925025i
$904$	3.42634	−	10.5452i	0.113958	−	0.350728i
$905$	−7.62870	−	10.5000i	−0.253586	−	0.349032i
$906$	10.2661	−	30.2857i	0.341068	−	1.00617i
$907$	−3.44050	−	10.5888i	−0.114240	−	0.351594i	0.877548	−	0.479489i	$-0.159178\pi$
$907$	−3.44050	−	10.5888i	−0.114240	−	0.351594i	−0.991788	+	0.127895i	$0.959178\pi$
$908$	3.46763	+	10.6723i	0.115077	+	0.354172i
$909$	3.07409	+	0.0778547i	0.101961	+	0.00258228i
$910$	3.57653	−	19.3088i	0.118561	−	0.640081i
$911$	56.4618	+	18.3456i	1.87066	+	0.607816i	0.991292	+	0.131681i	$0.0420374\pi$
$911$	56.4618	+	18.3456i	1.87066	+	0.607816i	0.879372	+	0.476135i	$0.157963\pi$
$912$	8.14901	+	26.2044i	0.269841	+	0.867713i
$913$	9.40426	−	18.5747i	0.311236	−	0.614734i
$914$			16.3998i			0.542458i
$915$	−29.5327	−	0.373913i	−0.976319	−	0.0123612i
$916$	−6.80334	−	9.36399i	−0.224789	−	0.309395i
$917$	12.3063	−	1.62150i	0.406389	−	0.0535467i
$918$	12.7389	−	34.6679i	0.420447	−	1.14421i
$919$	10.1870	+	31.3523i	0.336037	+	1.03422i	0.966209	+	0.257760i	$0.0829844\pi$
$919$	10.1870	+	31.3523i	0.336037	+	1.03422i	−0.630172	+	0.776456i	$0.717016\pi$
$920$	−44.8066	−	32.5539i	−1.47723	−	1.07327i
$921$	6.62875	+	4.94549i	0.218425	+	0.162959i
$922$	2.22118	+	0.721705i	0.0731507	+	0.0237681i
$923$	−25.7024			−0.846006
$924$	−6.85859	−	2.50609i	−0.225631	−	0.0824442i
$925$	−42.7223			−1.40470
$926$	6.54426	+	2.12636i	0.215058	+	0.0698764i
$927$	3.05088	+	1.07742i	0.100204	+	0.0353872i
$928$	−8.82282	−	6.41016i	−0.289623	−	0.210424i
$929$	2.81397	+	8.66050i	0.0923233	+	0.284142i	0.986547	−	0.163479i	$-0.0522715\pi$
$929$	2.81397	+	8.66050i	0.0923233	+	0.284142i	−0.894224	+	0.447621i	$0.852272\pi$
$930$	−15.6942	−	22.1865i	−0.514631	−	0.727523i
$931$	−30.6968	−	24.8468i	−1.00605	−	0.814322i
$932$	−0.912279	−	1.25564i	−0.0298827	−	0.0411300i
$933$	0.202016	−	15.9557i	0.00661370	−	0.522367i
$934$			36.1043i			1.18137i
$935$	59.1076	+	9.20610i	1.93302	+	0.301072i
$936$	14.5431	−	10.0136i	0.475356	−	0.327305i
$937$	13.9446	+	4.53088i	0.455551	+	0.148018i	0.527799	−	0.849369i	$-0.323017\pi$
$937$	13.9446	+	4.53088i	0.455551	+	0.148018i	−0.0722481	+	0.997387i	$0.523017\pi$
$938$	−11.8954	−	2.20336i	−0.388398	−	0.0719421i
$939$	15.0574	−	44.4203i	0.491379	−	1.44960i
$940$	2.70097	+	8.31275i	0.0880961	+	0.271132i
$941$	10.2176	+	31.4465i	0.333084	+	1.02513i	0.967658	+	0.252265i	$0.0811753\pi$
$941$	10.2176	+	31.4465i	0.333084	+	1.02513i	−0.634575	+	0.772862i	$0.718825\pi$
$942$	24.3122	+	8.24123i	0.792134	+	0.268514i
$943$	−10.6960	−	14.7217i	−0.348308	−	0.479405i
$944$	−1.97201	+	6.06922i	−0.0641834	+	0.197536i
$945$	−3.99459	−	42.8165i	−0.129944	−	1.39282i
$946$	12.9652	+	25.2848i	0.421534	+	0.822079i
$947$		−	59.6811i		−	1.93938i	−0.244347	−	0.969688i	$-0.578574\pi$
$947$		−	59.6811i		−	1.93938i	0.244347	−	0.969688i	$-0.421426\pi$
$948$	0.0755698	−	5.96871i	0.00245439	−	0.193855i
$949$	12.5191	−	9.09564i	0.406386	−	0.295257i
$950$	−26.9178	−	19.5569i	−0.873329	−	0.634511i
$951$	1.14811	−	0.812147i	0.0372302	−	0.0263357i
$952$	22.2537	−	40.9968i	0.721248	−	1.32871i
$953$	−18.2905	+	25.1747i	−0.592486	+	0.815487i	−0.994995	−	0.0999290i	$-0.968138\pi$
$953$	−18.2905	+	25.1747i	−0.592486	+	0.815487i	0.402508	+	0.915416i	$0.368138\pi$
$954$	7.71501	−	21.8461i	0.249783	−	0.707295i
$955$	22.5222	+	7.31791i	0.728801	+	0.236802i
$956$		−	1.32626i		−	0.0428944i
$957$	10.9302	−	20.9269i	0.353323	−	0.676472i
$958$		−	17.7561i		−	0.573672i
$959$	−7.84177	+	3.74137i	−0.253224	+	0.120815i
$960$	−28.7934	+	38.5936i	−0.929303	+	1.24560i
$961$	−11.6836	−	8.48863i	−0.376890	−	0.273827i
$962$	−6.54786	−	20.1522i	−0.211111	−	0.649734i
$963$	3.71164	−	4.84572i	0.119606	−	0.156151i
$964$	4.50140	−	6.19565i	0.144980	−	0.199548i
$965$	−37.8362	+	27.4896i	−1.21799	+	0.884921i
$966$	−22.2176	−	24.0090i	−0.714839	−	0.772475i
$967$	−35.2253			−1.13277			−0.566385	−	0.824141i	$-0.691658\pi$
$967$	−35.2253			−1.13277			−0.566385	+	0.824141i	$0.691658\pi$
$968$	−27.1086	+	19.9092i	−0.871305	+	0.639907i
$969$	16.7322	+	53.8048i	0.537515	+	1.72846i
$970$	−12.5302	+	38.5641i	−0.402321	+	1.23822i
$971$	−45.5422	+	33.0883i	−1.46152	+	1.06185i	−0.478553	+	0.878059i	$0.658839\pi$
$971$	−45.5422	+	33.0883i	−1.46152	+	1.06185i	−0.982964	+	0.183796i	$0.941161\pi$
$972$	4.77661	−	5.76841i	0.153210	−	0.185022i
$973$	−3.74435	+	6.89801i	−0.120038	+	0.221140i
$974$	31.7135	−	10.3043i	1.01616	−	0.330172i
$975$	−5.12069	+	15.1064i	−0.163993	+	0.483791i
$976$	8.99860	+	12.3855i	0.288038	+	0.396451i
$977$	−5.42072	−	1.76130i	−0.173424	−	0.0563490i	0.221018	−	0.975270i	$-0.429062\pi$
$977$	−5.42072	−	1.76130i	−0.173424	−	0.0563490i	−0.394442	+	0.918921i	$0.629062\pi$
$978$	7.89465	+	25.3864i	0.252443	+	0.811768i
$979$	−6.85036	−	6.81525i	−0.218939	−	0.217816i
$980$	0.548294	−	10.5054i	0.0175146	−	0.335582i
$981$	−7.90355	−	26.5980i	−0.252341	−	0.849209i
$982$	−21.2163	+	15.4146i	−0.677040	+	0.491898i
$983$	−28.4046	−	20.6371i	−0.905965	−	0.658222i	0.0340265	−	0.999421i	$-0.489167\pi$
$983$	−28.4046	−	20.6371i	−0.905965	−	0.658222i	−0.939991	+	0.341199i	$0.889167\pi$
$984$	−13.5867	+	9.61090i	−0.433129	+	0.306384i
$985$	54.3204	−	17.6498i	1.73079	−	0.562369i
$986$	23.6338	+	17.1710i	0.752655	+	0.546836i
$987$	3.14693	+	26.4664i	0.100168	+	0.842436i
$988$	−1.61232	+	4.96222i	−0.0512948	+	0.157869i
$989$		−	40.2465i		−	1.27976i
$990$	−33.7786	−	18.1906i	−1.07356	−	0.578136i
$991$	−52.8169			−1.67778			−0.838892	−	0.544298i	$-0.816796\pi$
$991$	−52.8169			−1.67778			−0.838892	+	0.544298i	$0.816796\pi$
$992$	3.33665	−	10.2692i	0.105939	−	0.326046i
$993$	23.1930	−	31.0871i	0.736009	−	0.986520i
$994$	43.1750	−	5.68883i	1.36943	−	0.180439i
$995$	−76.6197	+	24.8952i	−2.42901	+	0.789232i
$996$	3.01669	+	4.26462i	0.0955874	+	0.135130i
$997$	35.3849	−	48.7031i	1.12065	−	1.54244i	0.315936	−	0.948781i	$-0.397682\pi$
$997$	35.3849	−	48.7031i	1.12065	−	1.54244i	0.804715	−	0.593662i	$-0.202318\pi$
$998$	27.6763	+	38.0931i	0.876077	+	1.20582i
$999$	−25.8288	−	38.5479i	−0.817188	−	1.21960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.u.a.20.10	yes	112
3.2	odd	2	inner	231.2.u.a.20.19	yes	112
7.6	odd	2	inner	231.2.u.a.20.9	✓	112
11.5	even	5	inner	231.2.u.a.104.20	yes	112
21.20	even	2	inner	231.2.u.a.20.20	yes	112
33.5	odd	10	inner	231.2.u.a.104.9	yes	112
77.27	odd	10	inner	231.2.u.a.104.19	yes	112
231.104	even	10	inner	231.2.u.a.104.10	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.u.a.20.9	✓	112	7.6	odd	2	inner
231.2.u.a.20.10	yes	112	1.1	even	1	trivial
231.2.u.a.20.19	yes	112	3.2	odd	2	inner
231.2.u.a.20.20	yes	112	21.20	even	2	inner
231.2.u.a.104.9	yes	112	33.5	odd	10	inner
231.2.u.a.104.10	yes	112	231.104	even	10	inner
231.2.u.a.104.19	yes	112	77.27	odd	10	inner
231.2.u.a.104.20	yes	112	11.5	even	5	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17237 - 0.380926i) q^{2} +(1.03573 - 1.38826i) q^{3} +(-0.388687 - 0.282397i) q^{4} +(0.966595 + 2.97487i) q^{5} +(-1.74309 + 1.23301i) q^{6} +(2.62308 - 0.345622i) q^{7} +(1.79724 + 2.47369i) q^{8} +(-0.854517 - 2.87573i) q^{9} +O(q^{10})\)	\(q+(-1.17237 - 0.380926i) q^{2} +(1.03573 - 1.38826i) q^{3} +(-0.388687 - 0.282397i) q^{4} +(0.966595 + 2.97487i) q^{5} +(-1.74309 + 1.23301i) q^{6} +(2.62308 - 0.345622i) q^{7} +(1.79724 + 2.47369i) q^{8} +(-0.854517 - 2.87573i) q^{9} -3.85585i q^{10} +(2.35123 + 2.33917i) q^{11} +(-0.794615 + 0.247109i) q^{12} +(1.83070 + 0.594831i) q^{13} +(-3.20688 - 0.594002i) q^{14} +(5.13102 + 1.73929i) q^{15} +(-0.867809 - 2.67084i) q^{16} +(-1.78185 - 5.48398i) q^{17} +(-0.0936286 + 3.69692i) q^{18} +(-3.31616 - 4.56430i) q^{19} +(0.464394 - 1.42926i) q^{20} +(2.23700 - 3.99948i) q^{21} +(-1.86545 - 3.63802i) q^{22} +5.79074i q^{23} +(5.29558 + 0.0670474i) q^{24} +(-3.87048 + 2.81207i) q^{25} +(-1.91967 - 1.39472i) q^{26} +(-4.87730 - 1.79219i) q^{27} +(-1.11716 - 0.606412i) q^{28} +(2.41572 - 3.32496i) q^{29} +(-5.35292 - 3.99363i) q^{30} +(3.87003 + 1.25745i) q^{31} -2.65351i q^{32} +(5.68262 - 0.841349i) q^{33} +7.10801i q^{34} +(3.56364 + 7.46925i) q^{35} +(-0.479958 + 1.35907i) q^{36} +(7.22445 + 5.24887i) q^{37} +(2.14910 + 6.61426i) q^{38} +(2.72190 - 1.92540i) q^{39} +(-5.62171 + 7.73762i) q^{40} +(-2.54229 + 1.84708i) q^{41} +(-4.14609 + 3.83674i) q^{42} -6.95014 q^{43} +(-0.253313 - 1.57319i) q^{44} +(7.72895 - 5.32174i) q^{45} +(2.20584 - 6.78889i) q^{46} +(-4.70535 + 3.41864i) q^{47} +(-4.60663 - 1.56153i) q^{48} +(6.76109 - 1.81319i) q^{49} +(5.60883 - 1.82242i) q^{50} +(-9.45870 - 3.20626i) q^{51} +(-0.543591 - 0.748188i) q^{52} +(-5.95831 - 1.93597i) q^{53} +(5.03531 + 3.95900i) q^{54} +(-4.68606 + 9.25563i) q^{55} +(5.56927 + 5.86752i) q^{56} +(-9.77108 - 0.123712i) q^{57} +(-4.09869 + 2.97787i) q^{58} +(-1.83841 - 1.33568i) q^{59} +(-1.50319 - 2.12503i) q^{60} +(-5.18467 + 1.68460i) q^{61} +(-4.05811 - 2.94839i) q^{62} +(-3.23538 - 7.24792i) q^{63} +(-2.74641 + 8.45258i) q^{64} +6.02107i q^{65} +(-6.98262 - 1.17829i) q^{66} +3.70934 q^{67} +(-0.856079 + 2.63474i) q^{68} +(8.03904 + 5.99766i) q^{69} +(-1.33267 - 10.1142i) q^{70} +(-12.6990 + 4.12615i) q^{71} +(5.57788 - 7.28219i) q^{72} +(4.72522 - 6.50371i) q^{73} +(-6.47030 - 8.90560i) q^{74} +(-0.104906 + 8.28577i) q^{75} +2.71056i q^{76} +(6.97592 + 5.32320i) q^{77} +(-3.92451 + 1.22044i) q^{78} +(-2.21664 + 6.82211i) q^{79} +(7.10659 - 5.16324i) q^{80} +(-7.53960 + 4.91472i) q^{81} +(3.68410 - 1.19704i) q^{82} +(-1.93982 - 5.97015i) q^{83} +(-1.99893 + 0.922823i) q^{84} +(14.5918 - 10.6016i) q^{85} +(8.14814 + 2.64749i) q^{86} +(-2.11386 - 6.79741i) q^{87} +(-1.56067 + 10.0203i) q^{88} -2.91353 q^{89} +(-11.0884 + 3.29489i) q^{90} +(5.00766 + 0.927558i) q^{91} +(1.63529 - 2.25078i) q^{92} +(5.75397 - 4.07021i) q^{93} +(6.81866 - 2.21552i) q^{94} +(10.3728 - 14.2770i) q^{95} +(-3.68376 - 2.74833i) q^{96} +(-10.0014 - 3.24966i) q^{97} +(-8.61719 - 0.449747i) q^{98} +(4.71766 - 8.76035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

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