LMFDB - Embedded newform 231.2.p.a.10.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(10,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("231.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.p (of order $6$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.8
Character	$\chi$	$=$	231.10
Dual form			231.2.p.a.208.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.360631 + 0.208210i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.913297 + 1.58188i) q^{4} +(0.414204 - 0.239141i) q^{5} +0.416420 q^{6} +(-2.50100 - 0.863126i) q^{7} -1.59347i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.360631 + 0.208210i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.913297 + 1.58188i) q^{4} +(0.414204 - 0.239141i) q^{5} +0.416420 q^{6} +(-2.50100 - 0.863126i) q^{7} -1.59347i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0995832 + 0.172483i) q^{10} +(-2.41111 + 2.27739i) q^{11} +(1.58188 - 0.913297i) q^{12} -5.34126 q^{13} +(1.08165 - 0.209464i) q^{14} -0.478282 q^{15} +(-1.49482 - 2.58910i) q^{16} +(-0.123176 + 0.213346i) q^{17} +(-0.360631 - 0.208210i) q^{18} +(-2.02073 - 3.50000i) q^{19} +0.873627i q^{20} +(1.73437 + 1.99799i) q^{21} +(0.395345 - 1.32332i) q^{22} +(-0.540408 - 0.936015i) q^{23} +(-0.796736 + 1.37999i) q^{24} +(-2.38562 + 4.13202i) q^{25} +(1.92622 - 1.11210i) q^{26} -1.00000i q^{27} +(3.64952 - 3.16799i) q^{28} +9.25276i q^{29} +(0.172483 - 0.0995832i) q^{30} +(-1.00565 - 0.580613i) q^{31} +(3.83813 + 2.21594i) q^{32} +(3.22678 - 0.766724i) q^{33} -0.102586i q^{34} +(-1.24234 + 0.240582i) q^{35} -1.82659 q^{36} +(-2.23464 - 3.87051i) q^{37} +(1.45747 + 0.841471i) q^{38} +(4.62566 + 2.67063i) q^{39} +(-0.381064 - 0.660023i) q^{40} +9.10753 q^{41} +(-1.04147 - 0.359423i) q^{42} -2.69865i q^{43} +(-1.40049 - 5.89402i) q^{44} +(0.414204 + 0.239141i) q^{45} +(0.389776 + 0.225037i) q^{46} +(6.81265 - 3.93329i) q^{47} +2.98963i q^{48} +(5.51003 + 4.31736i) q^{49} -1.98684i q^{50} +(0.213346 - 0.123176i) q^{51} +(4.87815 - 8.44921i) q^{52} +(0.242753 - 0.420460i) q^{53} +(0.208210 + 0.360631i) q^{54} +(-0.454076 + 1.51990i) q^{55} +(-1.37537 + 3.98528i) q^{56} +4.04145i q^{57} +(-1.92652 - 3.33683i) q^{58} +(-0.959337 - 0.553874i) q^{59} +(0.436814 - 0.756583i) q^{60} +(2.66954 + 4.62377i) q^{61} +0.483558 q^{62} +(-0.503012 - 2.59749i) q^{63} +4.13374 q^{64} +(-2.21237 + 1.27731i) q^{65} +(-1.00404 + 0.948354i) q^{66} +(-1.52930 + 2.64883i) q^{67} +(-0.224992 - 0.389697i) q^{68} +1.08082i q^{69} +(0.397933 - 0.345428i) q^{70} -11.9831 q^{71} +(1.37999 - 0.796736i) q^{72} +(-3.94325 + 6.82991i) q^{73} +(1.61176 + 0.930549i) q^{74} +(4.13202 - 2.38562i) q^{75} +7.38209 q^{76} +(7.99588 - 3.61467i) q^{77} -2.22421 q^{78} +(-12.3656 + 7.13929i) q^{79} +(-1.23832 - 0.714944i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.28445 + 1.89628i) q^{82} -13.3453 q^{83} +(-4.74457 + 0.918798i) q^{84} +0.117825i q^{85} +(0.561886 + 0.973215i) q^{86} +(4.62638 - 8.01313i) q^{87} +(3.62896 + 3.84204i) q^{88} +(11.9859 - 6.92007i) q^{89} -0.199166 q^{90} +(13.3585 + 4.61018i) q^{91} +1.97421 q^{92} +(0.580613 + 1.00565i) q^{93} +(-1.63790 + 2.83693i) q^{94} +(-1.67399 - 0.966477i) q^{95} +(-2.21594 - 3.83813i) q^{96} -8.20328i q^{97} +(-2.88600 - 0.409730i) q^{98} +(-3.17784 - 0.949389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.360631	+	0.208210i	−0.255004	+	0.147227i	−0.622054	−	0.782975i	$-0.713701\pi$
$2$	−0.360631	+	0.208210i	−0.255004	+	0.147227i	0.367049	+	0.930202i	$0.380368\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.913297	+	1.58188i	−0.456649	+	0.790938i
$5$	0.414204	−	0.239141i	0.185238	−	0.106947i	−0.404513	−	0.914532i	$-0.632559\pi$
$5$	0.414204	−	0.239141i	0.185238	−	0.106947i	0.589751	+	0.807585i	$0.299226\pi$
$6$	0.416420			0.170003
$7$	−2.50100	−	0.863126i	−0.945290	−	0.326231i
$7$	−2.50100	−	0.863126i	−0.945290	−	0.326231i
$8$		−	1.59347i		−	0.563377i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.0995832	+	0.172483i	−0.0314910	+	0.0545440i
$11$	−2.41111	+	2.27739i	−0.726978	+	0.686660i
$11$	−2.41111	+	2.27739i	−0.726978	+	0.686660i
$12$	1.58188	−	0.913297i	0.456649	−	0.263646i
$13$	−5.34126			−1.48140			−0.740699	−	0.671837i	$-0.765505\pi$
$13$	−5.34126			−1.48140			−0.740699	+	0.671837i	$0.765505\pi$
$14$	1.08165	−	0.209464i	0.289083	−	0.0559817i
$15$	−0.478282			−0.123492
$16$	−1.49482	−	2.58910i	−0.373704	−	0.647275i
$17$	−0.123176	+	0.213346i	−0.0298745	+	0.0517441i	−0.880576	−	0.473905i	$-0.842844\pi$
$17$	−0.123176	+	0.213346i	−0.0298745	+	0.0517441i	0.850702	+	0.525649i	$0.176177\pi$
$18$	−0.360631	−	0.208210i	−0.0850015	−	0.0490756i
$19$	−2.02073	−	3.50000i	−0.463586	−	0.802955i	0.535550	−	0.844503i	$-0.320104\pi$
$19$	−2.02073	−	3.50000i	−0.463586	−	0.802955i	−0.999136	+	0.0415484i	$0.986771\pi$
$20$			0.873627i			0.195349i
$21$	1.73437	+	1.99799i	0.378470	+	0.435997i
$22$	0.395345	−	1.32332i	0.0842879	−	0.282132i
$23$	−0.540408	−	0.936015i	−0.112683	−	0.195173i	0.804168	−	0.594402i	$-0.202611\pi$
$23$	−0.540408	−	0.936015i	−0.112683	−	0.195173i	−0.916851	+	0.399229i	$0.869278\pi$
$24$	−0.796736	+	1.37999i	−0.162633	+	0.281689i
$25$	−2.38562	+	4.13202i	−0.477125	+	0.826404i
$26$	1.92622	−	1.11210i	0.377763	−	0.218102i
$27$		−	1.00000i		−	0.192450i
$28$	3.64952	−	3.16799i	0.689694	−	0.598693i
$29$			9.25276i			1.71819i	0.511812	+	0.859097i	$0.328974\pi$
$29$			9.25276i			1.71819i	−0.511812	+	0.859097i	$0.671026\pi$
$30$	0.172483	−	0.0995832i	0.0314910	−	0.0181813i
$31$	−1.00565	−	0.580613i	−0.180620	−	0.104281i	0.406964	−	0.913444i	$-0.366587\pi$
$31$	−1.00565	−	0.580613i	−0.180620	−	0.104281i	−0.587584	+	0.809163i	$0.699921\pi$
$32$	3.83813	+	2.21594i	0.678492	+	0.391727i
$33$	3.22678	−	0.766724i	0.561711	−	0.133470i
$34$		−	0.102586i		−	0.0175933i
$35$	−1.24234	+	0.240582i	−0.209993	+	0.0406657i
$36$	−1.82659			−0.304432
$37$	−2.23464	−	3.87051i	−0.367372	−	0.636307i	0.621782	−	0.783191i	$-0.286409\pi$
$37$	−2.23464	−	3.87051i	−0.367372	−	0.636307i	−0.989154	+	0.146883i	$0.953076\pi$
$38$	1.45747	+	0.841471i	0.236433	+	0.136505i
$39$	4.62566	+	2.67063i	0.740699	+	0.427643i
$40$	−0.381064	−	0.660023i	−0.0602516	−	0.104359i
$41$	9.10753			1.42236			0.711179	−	0.703011i	$-0.248162\pi$
$41$	9.10753			1.42236			0.711179	+	0.703011i	$0.248162\pi$
$42$	−1.04147	−	0.359423i	−0.160702	−	0.0554602i
$43$		−	2.69865i		−	0.411540i	−0.978600	−	0.205770i	$-0.934030\pi$
$43$		−	2.69865i		−	0.411540i	0.978600	−	0.205770i	$-0.0659699\pi$
$44$	−1.40049	−	5.89402i	−0.211132	−	0.888558i
$45$	0.414204	+	0.239141i	0.0617459	+	0.0356490i
$46$	0.389776	+	0.225037i	0.0574693	+	0.0331799i
$47$	6.81265	−	3.93329i	0.993728	−	0.573729i	0.0873413	−	0.996178i	$-0.472163\pi$
$47$	6.81265	−	3.93329i	0.993728	−	0.573729i	0.906386	+	0.422449i	$0.138830\pi$
$48$			2.98963i			0.431516i
$49$	5.51003	+	4.31736i	0.787147	+	0.616766i
$50$		−	1.98684i		−	0.280982i
$51$	0.213346	−	0.123176i	0.0298745	−	0.0172480i
$52$	4.87815	−	8.44921i	0.676478	−	1.17169i
$53$	0.242753	−	0.420460i	0.0333446	−	0.0577546i	−0.848872	−	0.528599i	$-0.822717\pi$
$53$	0.242753	−	0.420460i	0.0333446	−	0.0577546i	0.882216	+	0.470845i	$0.156051\pi$
$54$	0.208210	+	0.360631i	0.0283338	+	0.0490756i
$55$	−0.454076	+	1.51990i	−0.0612276	+	0.204944i
$56$	−1.37537	+	3.98528i	−0.183791	+	0.532555i
$57$			4.04145i			0.535303i
$58$	−1.92652	−	3.33683i	−0.252964	−	0.438147i
$59$	−0.959337	−	0.553874i	−0.124895	−	0.0721082i	0.436251	−	0.899825i	$-0.356306\pi$
$59$	−0.959337	−	0.553874i	−0.124895	−	0.0721082i	−0.561146	+	0.827717i	$0.689639\pi$
$60$	0.436814	−	0.756583i	0.0563924	−	0.0976745i
$61$	2.66954	+	4.62377i	0.341799	+	0.592014i	0.984767	−	0.173880i	$-0.0556304\pi$
$61$	2.66954	+	4.62377i	0.341799	+	0.592014i	−0.642968	+	0.765893i	$0.722297\pi$
$62$	0.483558			0.0614119
$63$	−0.503012	−	2.59749i	−0.0633735	−	0.327254i
$64$	4.13374			0.516717
$65$	−2.21237	+	1.27731i	−0.274411	+	0.158431i
$66$	−1.00404	+	0.948354i	−0.123588	+	0.116734i
$67$	−1.52930	+	2.64883i	−0.186834	+	0.323606i	−0.944193	−	0.329393i	$-0.893156\pi$
$67$	−1.52930	+	2.64883i	−0.186834	+	0.323606i	0.757359	+	0.652999i	$0.226489\pi$
$68$	−0.224992	−	0.389697i	−0.0272843	−	0.0472577i
$69$			1.08082i			0.130115i
$70$	0.397933	−	0.345428i	0.0475620	−	0.0412865i
$71$	−11.9831			−1.42213			−0.711065	−	0.703126i	$-0.751787\pi$
$71$	−11.9831			−1.42213			−0.711065	+	0.703126i	$0.751787\pi$
$72$	1.37999	−	0.796736i	0.162633	−	0.0938962i
$73$	−3.94325	+	6.82991i	−0.461522	+	0.799380i	−0.999037	−	0.0438742i	$-0.986030\pi$
$73$	−3.94325	+	6.82991i	−0.461522	+	0.799380i	0.537515	+	0.843254i	$0.319363\pi$
$74$	1.61176	+	0.930549i	0.187363	+	0.108174i
$75$	4.13202	−	2.38562i	0.477125	−	0.275468i
$76$	7.38209			0.846784
$77$	7.99588	−	3.61467i	0.911215	−	0.411930i
$78$	−2.22421			−0.251842
$79$	−12.3656	+	7.13929i	−1.39124	+	0.803232i	−0.993453	−	0.114246i	$-0.963555\pi$
$79$	−12.3656	+	7.13929i	−1.39124	+	0.803232i	−0.397787	+	0.917478i	$0.630222\pi$
$80$	−1.23832	−	0.714944i	−0.138448	−	0.0799332i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.28445	+	1.89628i	−0.362707	+	0.209409i
$83$	−13.3453			−1.46484			−0.732419	−	0.680854i	$-0.761609\pi$
$83$	−13.3453			−1.46484			−0.732419	+	0.680854i	$0.761609\pi$
$84$	−4.74457	+	0.918798i	−0.517675	+	0.100249i
$85$			0.117825i			0.0127800i
$86$	0.561886	+	0.973215i	0.0605897	+	0.104944i
$87$	4.62638	−	8.01313i	0.496000	−	0.859097i
$88$	3.62896	+	3.84204i	0.386849	+	0.409563i
$89$	11.9859	−	6.92007i	1.27050	−	0.733526i	0.295422	−	0.955367i	$-0.404540\pi$
$89$	11.9859	−	6.92007i	1.27050	−	0.733526i	0.975083	+	0.221841i	$0.0712066\pi$
$90$	−0.199166			−0.0209940
$91$	13.3585	+	4.61018i	1.40035	+	0.483278i
$92$	1.97421			0.205826
$93$	0.580613	+	1.00565i	0.0602067	+	0.104281i
$94$	−1.63790	+	2.83693i	−0.168937	+	0.292607i
$95$	−1.67399	−	0.966477i	−0.171747	−	0.0991584i
$96$	−2.21594	−	3.83813i	−0.226164	−	0.391727i
$97$		−	8.20328i		−	0.832917i	−0.909155	−	0.416459i	$-0.863271\pi$
$97$		−	8.20328i		−	0.832917i	0.909155	−	0.416459i	$-0.136729\pi$
$98$	−2.88600	−	0.409730i	−0.291530	−	0.0413889i
$99$	−3.17784	−	0.949389i	−0.319385	−	0.0954172i
$100$	−4.35757	−	7.54752i	−0.435757	−	0.754752i
$101$	−5.00468	+	8.66837i	−0.497985	+	0.862535i	−0.999997	−	0.00232558i	$-0.999260\pi$
$101$	−5.00468	+	8.66837i	−0.497985	+	0.862535i	0.502013	+	0.864860i	$0.332593\pi$
$102$	−0.0512928	+	0.0888418i	−0.00507875	+	0.00879665i
$103$	−8.90299	+	5.14014i	−0.877237	+	0.506473i	−0.869747	−	0.493499i	$-0.835718\pi$
$103$	−8.90299	+	5.14014i	−0.877237	+	0.506473i	−0.00749085	+	0.999972i	$0.502384\pi$
$104$			8.51114i			0.834586i
$105$	1.19618	+	0.412818i	0.116736	+	0.0402869i
$106$			0.202174i			0.0196369i
$107$	14.4037	−	8.31597i	1.39246	−	0.803935i	0.398870	−	0.917008i	$-0.369403\pi$
$107$	14.4037	−	8.31597i	1.39246	−	0.803935i	0.993587	+	0.113073i	$0.0360693\pi$
$108$	1.58188	+	0.913297i	0.152216	+	0.0878820i
$109$	−5.48806	−	3.16853i	−0.525661	−	0.303490i	0.213587	−	0.976924i	$-0.431485\pi$
$109$	−5.48806	−	3.16853i	−0.525661	−	0.303490i	−0.739248	+	0.673434i	$0.764819\pi$
$110$	−0.152706	−	0.642667i	−0.0145599	−	0.0612759i
$111$			4.46928i			0.424205i
$112$	1.50382	+	7.76556i	0.142098	+	0.733776i
$113$	−13.7254			−1.29118			−0.645590	−	0.763684i	$-0.723389\pi$
$113$	−13.7254			−1.29118			−0.645590	+	0.763684i	$0.723389\pi$
$114$	−0.841471	−	1.45747i	−0.0788110	−	0.136505i
$115$	−0.447679	−	0.258468i	−0.0417463	−	0.0241022i
$116$	−14.6367	−	8.45052i	−1.35899	−	0.784611i
$117$	−2.67063	−	4.62566i	−0.246900	−	0.427643i
$118$	0.461289			0.0424651
$119$	0.492208	−	0.427264i	0.0451206	−	0.0391672i
$120$			0.762129i			0.0695725i
$121$	0.626948	−	10.9821i	0.0569952	−	0.998374i
$122$	−1.92543	−	1.11165i	−0.174321	−	0.100644i
$123$	−7.88735	−	4.55376i	−0.711179	−	0.410599i
$124$	1.83691	−	1.06054i	0.164960	−	0.0952396i
$125$			4.67341i			0.418003i
$126$	0.722226	+	0.832004i	0.0643410	+	0.0741208i
$127$		−	0.464814i		−	0.0412456i	−0.999787	−	0.0206228i	$-0.993435\pi$
$127$		−	0.464814i		−	0.0412456i	0.999787	−	0.0206228i	$-0.00656490\pi$
$128$	−9.16701	+	5.29258i	−0.810257	+	0.467802i
$129$	−1.34932	+	2.33710i	−0.118801	+	0.205770i
$130$	0.531899	−	0.921277i	0.0466507	−	0.0808013i
$131$	−7.16202	−	12.4050i	−0.625749	−	1.08383i	−0.988396	−	0.151902i	$-0.951460\pi$
$131$	−7.16202	−	12.4050i	−0.625749	−	1.08383i	0.362647	−	0.931927i	$-0.381873\pi$
$132$	−1.73415	+	5.80462i	−0.150938	+	0.505227i
$133$	2.03290	+	10.4976i	0.176275	+	0.910262i
$134$		−	1.27367i		−	0.110028i
$135$	−0.239141	−	0.414204i	−0.0205820	−	0.0356490i
$136$	0.339962	+	0.196277i	0.0291515	+	0.0168306i
$137$	1.61419	−	2.79585i	0.137909	−	0.238866i	−0.788796	−	0.614655i	$-0.789295\pi$
$137$	1.61419	−	2.79585i	0.137909	−	0.238866i	0.926705	+	0.375790i	$0.122628\pi$
$138$	−0.225037	−	0.389776i	−0.0191564	−	0.0331799i
$139$	−6.06911			−0.514775			−0.257388	−	0.966308i	$-0.582862\pi$
$139$	−6.06911			−0.514775			−0.257388	+	0.966308i	$0.582862\pi$
$140$	0.754051	−	2.18494i	0.0637289	−	0.184661i
$141$	−7.86658			−0.662485
$142$	4.32147	−	2.49500i	0.362649	−	0.209376i
$143$	12.8784	−	12.1641i	1.07694	−	1.01722i
$144$	1.49482	−	2.58910i	0.124568	−	0.215758i
$145$	2.21272	+	3.83253i	0.183756	+	0.318275i
$146$		−	3.28410i		−	0.271794i
$147$	−2.61314	−	6.49396i	−0.215528	−	0.535613i
$148$	8.16355			0.671040
$149$	−13.9948	+	8.07987i	−1.14649	+	0.661929i	−0.948031	−	0.318179i	$-0.896929\pi$
$149$	−13.9948	+	8.07987i	−1.14649	+	0.661929i	−0.198464	+	0.980108i	$0.563595\pi$
$150$	−0.993422	+	1.72066i	−0.0811126	+	0.140491i
$151$	8.90147	+	5.13927i	0.724391	+	0.418228i	0.816367	−	0.577534i	$-0.195985\pi$
$151$	8.90147	+	5.13927i	0.724391	+	0.418228i	−0.0919755	+	0.995761i	$0.529318\pi$
$152$	−5.57715	+	3.21997i	−0.452367	+	0.261174i
$153$	−0.246351			−0.0199163
$154$	−2.13095	+	2.96839i	−0.171717	+	0.239199i
$155$	−0.555393			−0.0446102
$156$	−8.44921	+	4.87815i	−0.676478	+	0.390565i
$157$	−3.10135	−	1.79057i	−0.247515	−	0.142903i	0.371111	−	0.928589i	$-0.378977\pi$
$157$	−3.10135	−	1.79057i	−0.247515	−	0.142903i	−0.618626	+	0.785686i	$0.712310\pi$
$158$	2.97294	−	5.14929i	0.236515	−	0.409656i
$159$	−0.420460	+	0.242753i	−0.0333446	+	0.0192515i
$160$	2.11969			0.167576
$161$	0.543664	+	2.80742i	0.0428467	+	0.221255i
$162$		−	0.416420i		−	0.0327171i
$163$	7.50093	+	12.9920i	0.587518	+	1.01761i	0.994556	+	0.104200i	$0.0332282\pi$
$163$	7.50093	+	12.9920i	0.587518	+	1.01761i	−0.407038	+	0.913411i	$0.633439\pi$
$164$	−8.31788	+	14.4070i	−0.649517	+	1.12500i
$165$	1.15319	−	1.08924i	0.0897759	−	0.0847970i
$166$	4.81273	−	2.77863i	0.373540	−	0.215664i
$167$	12.7582			0.987257			0.493629	−	0.869673i	$-0.335670\pi$
$167$	12.7582			0.987257			0.493629	+	0.869673i	$0.335670\pi$
$168$	3.18374	−	2.76367i	0.245631	−	0.213222i
$169$	15.5290			1.19454
$170$	−0.0245324	−	0.0424914i	−0.00188155	−	0.00325895i
$171$	2.02073	−	3.50000i	0.154529	−	0.267652i
$172$	4.26893	+	2.46467i	0.325503	+	0.187929i
$173$	5.01935	+	8.69377i	0.381614	+	0.660975i	0.991293	−	0.131674i	$-0.0420351\pi$
$173$	5.01935	+	8.69377i	0.381614	+	0.660975i	−0.609679	+	0.792648i	$0.708702\pi$
$174$			3.85304i			0.292098i
$175$	9.53290	−	8.27510i	0.720620	−	0.625539i
$176$	9.50057	+	2.83833i	0.716133	+	0.213947i
$177$	0.553874	+	0.959337i	0.0416317	+	0.0721082i
$178$	−2.88166	+	4.99118i	−0.215989	+	0.374105i
$179$	−9.79630	+	16.9677i	−0.732210	+	1.26822i	0.223727	+	0.974652i	$0.428178\pi$
$179$	−9.79630	+	16.9677i	−0.732210	+	1.26822i	−0.955937	+	0.293573i	$0.905156\pi$
$180$	−0.756583	+	0.436814i	−0.0563924	+	0.0325582i
$181$		−	20.3798i		−	1.51482i	−0.652941	−	0.757408i	$-0.726465\pi$
$181$		−	20.3798i		−	1.51482i	0.652941	−	0.757408i	$-0.273535\pi$
$182$	−5.77737	+	1.11880i	−0.428247	+	0.0829312i
$183$		−	5.33908i		−	0.394676i
$184$	−1.49151	+	0.861126i	−0.109956	+	0.0634830i
$185$	−1.85119	−	1.06879i	−0.136102	−	0.0785788i
$186$	−0.418773	−	0.241779i	−0.0307060	−	0.0177281i
$187$	−0.188883	−	0.794922i	−0.0138125	−	0.0581305i
$188$			14.3690i			1.04797i
$189$	−0.863126	+	2.50100i	−0.0627832	+	0.181921i
$190$	0.804921			0.0583951
$191$	3.24975	+	5.62872i	0.235143	+	0.407280i	0.959314	−	0.282340i	$-0.0911107\pi$
$191$	3.24975	+	5.62872i	0.235143	+	0.407280i	−0.724171	+	0.689620i	$0.757777\pi$
$192$	−3.57992	−	2.06687i	−0.258359	−	0.149163i
$193$	11.7283	+	6.77133i	0.844220	+	0.487411i	0.858697	−	0.512484i	$-0.171275\pi$
$193$	11.7283	+	6.77133i	0.844220	+	0.487411i	−0.0144762	+	0.999895i	$0.504608\pi$
$194$	1.70801	+	2.95835i	0.122628	+	0.212398i
$195$	2.55463			0.182941
$196$	−11.8618	+	4.77315i	−0.847273	+	0.340939i
$197$		−	16.9234i		−	1.20574i	−0.797839	−	0.602871i	$-0.794023\pi$
$197$		−	16.9234i		−	1.20574i	0.797839	−	0.602871i	$-0.205977\pi$
$198$	1.34370	−	0.319280i	0.0954925	−	0.0226902i
$199$	−22.7003	−	13.1060i	−1.60918	−	0.929060i	−0.989554	−	0.144161i	$-0.953952\pi$
$199$	−22.7003	−	13.1060i	−1.60918	−	0.929060i	−0.619624	−	0.784899i	$-0.712715\pi$
$200$	6.58426	+	3.80142i	0.465577	+	0.268801i
$201$	2.64883	−	1.52930i	0.186834	−	0.107869i
$202$		−	4.16811i		−	0.293267i
$203$	7.98630	−	23.1412i	0.560529	−	1.62419i
$204$			0.449984i			0.0315052i
$205$	3.77238	−	2.17798i	0.263474	−	0.152117i
$206$	2.14046	−	3.70739i	0.149133	−	0.258306i
$207$	0.540408	−	0.936015i	0.0375610	−	0.0650575i
$208$	7.98420	+	13.8290i	0.553605	+	0.958871i
$209$	12.8431	+	3.83691i	0.888375	+	0.265405i
$210$	−0.517334	+	0.100183i	−0.0356994	+	0.00691329i
$211$			7.93121i			0.546007i	0.962013	+	0.273004i	$0.0880171\pi$
$211$			7.93121i			0.546007i	−0.962013	+	0.273004i	$0.911983\pi$
$212$	0.443410	+	0.768009i	0.0304535	+	0.0527471i
$213$	10.3777	+	5.99154i	0.711065	+	0.410534i
$214$	−3.46294	+	5.99799i	−0.236722	+	0.410014i
$215$	−0.645357	−	1.11779i	−0.0440130	−	0.0762328i
$216$	−1.59347			−0.108422
$217$	2.01399	+	2.32012i	0.136719	+	0.157500i
$218$	2.63888			0.178728
$219$	6.82991	−	3.94325i	0.461522	−	0.266460i
$220$	−1.98959	−	2.10642i	−0.134138	−	0.142014i
$221$	0.657912	−	1.13954i	0.0442560	−	0.0766536i
$222$	−0.930549	−	1.61176i	−0.0624544	−	0.108174i
$223$		−	20.0220i		−	1.34077i	−0.742013	−	0.670386i	$-0.766129\pi$
$223$		−	20.0220i		−	1.34077i	0.742013	−	0.670386i	$-0.233871\pi$
$224$	−7.68653	−	8.85487i	−0.513578	−	0.591641i
$225$	−4.77125			−0.318083
$226$	4.94982	−	2.85778i	0.329257	−	0.190097i
$227$	1.28457	−	2.22494i	0.0852600	−	0.147675i	−0.820242	−	0.572017i	$-0.806161\pi$
$227$	1.28457	−	2.22494i	0.0852600	−	0.147675i	0.905502	+	0.424342i	$0.139495\pi$
$228$	−6.39308	−	3.69105i	−0.423392	−	0.244445i
$229$	−7.72938	+	4.46256i	−0.510772	+	0.294894i	−0.733151	−	0.680066i	$-0.761951\pi$
$229$	−7.72938	+	4.46256i	−0.510772	+	0.294894i	0.222379	+	0.974960i	$0.428618\pi$
$230$	0.215262			0.0141940
$231$	−8.73197	−	0.867543i	−0.574522	−	0.0570801i
$232$	14.7440			0.967992
$233$	13.4382	−	7.75856i	0.880367	−	0.508280i	0.00958736	−	0.999954i	$-0.496948\pi$
$233$	13.4382	−	7.75856i	0.880367	−	0.508280i	0.870779	+	0.491674i	$0.163615\pi$
$234$	1.92622	+	1.11210i	0.125921	+	0.0727005i
$235$	1.88122	−	3.25837i	0.122717	−	0.212553i
$236$	1.75232	−	1.01170i	0.114066	−	0.0658562i
$237$	14.2786			0.927493
$238$	−0.0885444	+	0.256567i	−0.00573948	+	0.0166308i
$239$		−	6.69266i		−	0.432912i	−0.976292	−	0.216456i	$-0.930550\pi$
$239$		−	6.69266i		−	0.432912i	0.976292	−	0.216456i	$-0.0694498\pi$
$240$	0.714944	+	1.23832i	0.0461494	+	0.0799332i
$241$	5.82218	−	10.0843i	0.375040	−	0.649588i	−0.615293	−	0.788298i	$-0.710962\pi$
$241$	5.82218	−	10.0843i	0.375040	−	0.649588i	0.990333	+	0.138711i	$0.0442958\pi$
$242$	2.06049	+	4.09103i	0.132453	+	0.262981i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−9.75232			−0.624328
$245$	3.31474	+	0.470597i	0.211771	+	0.0300654i
$246$	3.79256			0.241805
$247$	10.7932	+	18.6944i	0.686756	+	1.18950i
$248$	−0.925190	+	1.60248i	−0.0587496	+	0.101757i
$249$	11.5574	+	6.67266i	0.732419	+	0.422862i
$250$	−0.973052	−	1.68538i	−0.0615412	−	0.106593i
$251$		−	12.4098i		−	0.783298i	−0.920115	−	0.391649i	$-0.871905\pi$
$251$		−	12.4098i		−	0.783298i	0.920115	−	0.391649i	$-0.128095\pi$
$252$	4.56832	+	1.57658i	0.287777	+	0.0993153i
$253$	3.43466	+	1.02612i	0.215935	+	0.0645113i
$254$	0.0967790	+	0.167626i	0.00607245	+	0.0105178i
$255$	0.0589127	−	0.102040i	0.00368926	−	0.00638998i
$256$	−1.92980	+	3.34252i	−0.120613	+	0.208907i
$257$	−16.0619	+	9.27334i	−1.00191	+	0.578455i	−0.908814	−	0.417202i	$-0.863011\pi$
$257$	−16.0619	+	9.27334i	−1.00191	+	0.578455i	−0.0930997	+	0.995657i	$0.529678\pi$
$258$		−	1.12377i		−	0.0699630i
$259$	2.24810	+	11.6089i	0.139690	+	0.721343i
$260$		−	4.66627i		−	0.289389i
$261$	−8.01313	+	4.62638i	−0.496000	+	0.286366i
$262$	5.16569	+	2.98241i	0.319137	+	0.184254i
$263$	1.30559	+	0.753780i	0.0805059	+	0.0464801i	0.539713	−	0.841849i	$-0.318533\pi$
$263$	1.30559	+	0.753780i	0.0805059	+	0.0464801i	−0.459207	+	0.888329i	$0.651866\pi$
$264$	−1.22175	−	5.14179i	−0.0751937	−	0.316455i
$265$		−	0.232208i		−	0.0142644i
$266$	−2.91884	−	3.36250i	−0.178966	−	0.206168i
$267$	−13.8401			−0.847003
$268$	−2.79342	−	4.83834i	−0.170635	−	0.295549i
$269$	15.8064	+	9.12584i	0.963734	+	0.556412i	0.897320	−	0.441380i	$-0.145511\pi$
$269$	15.8064	+	9.12584i	0.963734	+	0.556412i	0.0664138	+	0.997792i	$0.478844\pi$
$270$	0.172483	+	0.0995832i	0.0104970	+	0.00606044i
$271$	0.726863	+	1.25896i	0.0441538	+	0.0764766i	0.887258	−	0.461274i	$-0.152608\pi$
$271$	0.726863	+	1.25896i	0.0441538	+	0.0764766i	−0.843104	+	0.537751i	$0.819274\pi$
$272$	0.736500			0.0446569
$273$	−9.26370	−	10.6718i	−0.560665	−	0.645885i
$274$			1.34436i			0.0812157i
$275$	−3.65823	−	15.3958i	−0.220600	−	0.928400i
$276$	−1.70972	−	0.987107i	−0.102913	−	0.0594168i
$277$	−16.9386	−	9.77949i	−1.01774	−	0.587593i	−0.104292	−	0.994547i	$-0.533258\pi$
$277$	−16.9386	−	9.77949i	−1.01774	−	0.587593i	−0.913449	+	0.406954i	$0.866591\pi$
$278$	2.18871	−	1.26365i	0.131270	−	0.0757887i
$279$		−	1.16123i		−	0.0695207i
$280$	0.383360	+	1.97963i	0.0229101	+	0.118305i
$281$			31.8002i			1.89704i	0.316719	+	0.948520i	$0.397419\pi$
$281$			31.8002i			1.89704i	−0.316719	+	0.948520i	$0.602581\pi$
$282$	2.83693	−	1.63790i	0.168937	−	0.0975356i
$283$	−10.9990	+	19.0508i	−0.653821	+	1.13245i	0.328367	+	0.944550i	$0.393502\pi$
$283$	−10.9990	+	19.0508i	−0.653821	+	1.13245i	−0.982188	+	0.187901i	$0.939831\pi$
$284$	10.9441	−	18.9558i	0.649413	−	1.12482i
$285$	0.966477	+	1.67399i	0.0572491	+	0.0991584i
$286$	−2.11164	+	7.06817i	−0.124864	+	0.417950i
$287$	−22.7780	−	7.86095i	−1.34454	−	0.464017i
$288$			4.43189i			0.261152i
$289$	8.46966	+	14.6699i	0.498215	+	0.862934i
$290$	−1.59595	−	0.921420i	−0.0937172	−	0.0541076i
$291$	−4.10164	+	7.10425i	−0.240442	+	0.416459i
$292$	−7.20271	−	12.4755i	−0.421507	−	0.730071i
$293$	−17.8824			−1.04470			−0.522351	−	0.852731i	$-0.674945\pi$
$293$	−17.8824			−1.04470			−0.522351	+	0.852731i	$0.674945\pi$
$294$	2.29449	+	1.79784i	0.133817	+	0.104852i
$295$	−0.529816			−0.0308471
$296$	−6.16754	+	3.56083i	−0.358481	+	0.206969i
$297$	2.27739	+	2.41111i	0.132148	+	0.139907i
$298$	3.36462	−	5.82770i	0.194907	−	0.337590i
$299$	2.88646	+	4.99949i	0.166928	+	0.289128i
$300$			8.71513i			0.503168i
$301$	−2.32927	+	6.74932i	−0.134257	+	0.389025i
$302$	−4.28019			−0.246297
$303$	8.66837	−	5.00468i	0.497985	−	0.287512i
$304$	−6.04123	+	10.4637i	−0.346488	+	0.600135i
$305$	2.21147	+	1.27679i	0.126628	+	0.0731089i
$306$	0.0888418	−	0.0512928i	0.00507875	−	0.00293222i
$307$	−1.73541			−0.0990450			−0.0495225	−	0.998773i	$-0.515770\pi$
$307$	−1.73541			−0.0990450			−0.0495225	+	0.998773i	$0.515770\pi$
$308$	−1.58465	+	15.9498i	−0.0902937	+	0.908823i
$309$	10.2803			0.584825
$310$	0.200292	−	0.115639i	0.0113758	−	0.00656783i
$311$	16.6034	+	9.58600i	0.941494	+	0.543572i	0.890428	−	0.455123i	$-0.150405\pi$
$311$	16.6034	+	9.58600i	0.941494	+	0.543572i	0.0510660	+	0.998695i	$0.483738\pi$
$312$	4.25557	−	7.37086i	0.240924	−	0.417293i
$313$	−21.9640	+	12.6809i	−1.24148	+	0.716767i	−0.969395	−	0.245508i	$-0.921045\pi$
$313$	−21.9640	+	12.6809i	−1.24148	+	0.716767i	−0.272082	+	0.962274i	$0.587712\pi$
$314$	1.49126			0.0841565
$315$	−0.829517	−	0.955603i	−0.0467380	−	0.0538421i
$316$		−	26.0812i		−	1.46718i
$317$	12.1785	+	21.0938i	0.684015	+	1.18475i	0.973745	+	0.227640i	$0.0731010\pi$
$317$	12.1785	+	21.0938i	0.684015	+	1.18475i	−0.289730	+	0.957108i	$0.593566\pi$
$318$	0.101087	−	0.175088i	0.00566868	−	0.00981845i
$319$	−21.0722	−	22.3095i	−1.17982	−	1.24909i
$320$	1.71221	−	0.988546i	0.0957156	−	0.0552614i
$321$	−16.6319			−0.928304
$322$	−0.780594	−	0.899244i	−0.0435008	−	0.0501129i
$323$	0.995617			0.0553976
$324$	−0.913297	−	1.58188i	−0.0507387	−	0.0878820i
$325$	12.7422	−	22.0702i	0.706811	−	1.22423i
$326$	−5.41013	−	3.12354i	−0.299639	−	0.172997i
$327$	3.16853	+	5.48806i	0.175220	+	0.303490i
$328$		−	14.5126i		−	0.801324i
$329$	−20.4334	+	3.95698i	−1.12653	+	0.218155i
$330$	−0.189086	+	0.632919i	−0.0104089	+	0.0348410i
$331$	2.76620	+	4.79119i	0.152044	+	0.263348i	0.931979	−	0.362513i	$-0.118081\pi$
$331$	2.76620	+	4.79119i	0.152044	+	0.263348i	−0.779935	+	0.625861i	$0.784748\pi$
$332$	12.1882	−	21.1106i	0.668916	−	1.15860i
$333$	2.23464	−	3.87051i	0.122457	−	0.212102i
$334$	−4.60099	+	2.65638i	−0.251755	+	0.145351i
$335$			1.46288i			0.0799255i
$336$	2.58043	−	7.47708i	0.140774	−	0.407908i
$337$		−	20.8649i		−	1.13658i	−0.822828	−	0.568291i	$-0.807605\pi$
$337$		−	20.8649i		−	1.13658i	0.822828	−	0.568291i	$-0.192395\pi$
$338$	−5.60024	+	3.23330i	−0.304613	+	0.175868i
$339$	11.8866	+	6.86272i	0.645590	+	0.372732i
$340$	−0.186385	−	0.107610i	−0.0101082	−	0.00583595i
$341$	3.74702	−	0.890339i	0.202913	−	0.0482146i
$342$			1.68294i			0.0910031i
$343$	−10.0542	−	15.5536i	−0.542874	−	0.839814i
$344$	−4.30022			−0.231852
$345$	0.258468	+	0.447679i	0.0139154	+	0.0241022i
$346$	−3.62026	−	2.09016i	−0.194626	−	0.112368i
$347$	−12.2856	−	7.09312i	−0.659528	−	0.380778i	0.132569	−	0.991174i	$-0.457677\pi$
$347$	−12.2856	−	7.09312i	−0.659528	−	0.380778i	−0.792097	+	0.610395i	$0.791011\pi$
$348$	8.45052	+	14.6367i	0.452995	+	0.784611i
$349$	−21.0581			−1.12721			−0.563606	−	0.826044i	$-0.690586\pi$
$349$	−21.0581			−1.12721			−0.563606	+	0.826044i	$0.690586\pi$
$350$	−1.71490	+	4.96910i	−0.0916651	+	0.265610i
$351$			5.34126i			0.285095i
$352$	−14.3007	+	3.39804i	−0.762232	+	0.181116i
$353$	0.882279	+	0.509384i	0.0469590	+	0.0271118i	0.523296	−	0.852151i	$-0.324702\pi$
$353$	0.882279	+	0.509384i	0.0469590	+	0.0271118i	−0.476337	+	0.879263i	$0.658036\pi$
$354$	−0.399488	−	0.230644i	−0.0212325	−	0.0122586i
$355$	−4.96344	+	2.86565i	−0.263432	+	0.152093i
$356$			25.2803i			1.33985i
$357$	−0.639896	+	0.123918i	−0.0338669	+	0.00655842i
$358$		−	8.15876i		−	0.431204i
$359$	5.80814	−	3.35333i	0.306542	−	0.176982i	−0.338836	−	0.940845i	$-0.610033\pi$
$359$	5.80814	−	3.35333i	0.306542	−	0.176982i	0.645378	+	0.763863i	$0.276700\pi$
$360$	0.381064	−	0.660023i	0.0200839	−	0.0347863i
$361$	1.33333	−	2.30940i	0.0701755	−	0.121548i
$362$	4.24328	+	7.34957i	0.223022	+	0.386285i
$363$	−6.03401	+	9.19732i	−0.316703	+	0.482734i
$364$	−19.4930	+	16.9210i	−1.02171	+	0.886903i
$365$			3.77197i			0.197434i
$366$	1.11165	+	1.92543i	0.0581069	+	0.100644i
$367$	4.75834	+	2.74723i	0.248383	+	0.143404i	0.619024	−	0.785372i	$-0.287528\pi$
$367$	4.75834	+	2.74723i	0.248383	+	0.143404i	−0.370641	+	0.928776i	$0.620862\pi$
$368$	−1.61562	+	2.79834i	−0.0842202	+	0.145874i
$369$	4.55376	+	7.88735i	0.237060	+	0.410599i
$370$	0.890130			0.0462756
$371$	−0.970034	+	0.842045i	−0.0503617	+	0.0437168i
$372$	−2.12109			−0.109973
$373$	0.0436937	−	0.0252266i	0.00226238	−	0.00130618i	−0.498868	−	0.866678i	$-0.666251\pi$
$373$	0.0436937	−	0.0252266i	0.00226238	−	0.00130618i	0.501131	+	0.865372i	$0.332918\pi$
$374$	0.233628	+	0.247346i	0.0120806	+	0.0127900i
$375$	2.33671	−	4.04729i	0.120667	−	0.209001i
$376$	−6.26758	−	10.8558i	−0.323226	−	0.559844i
$377$		−	49.4214i		−	2.54533i
$378$	−0.209464	−	1.08165i	−0.0107737	−	0.0556341i
$379$	1.32955			0.0682942			0.0341471	−	0.999417i	$-0.489129\pi$
$379$	1.32955			0.0682942			0.0341471	+	0.999417i	$0.489129\pi$
$380$	3.05769	−	1.76536i	0.156856	−	0.0905611i
$381$	−0.232407	+	0.402541i	−0.0119066	+	0.0206228i
$382$	−2.34392	−	1.35326i	−0.119925	−	0.0692388i
$383$	−18.9152	+	10.9207i	−0.966522	+	0.558022i	−0.898174	−	0.439640i	$-0.855106\pi$
$383$	−18.9152	+	10.9207i	−0.966522	+	0.558022i	−0.0683477	+	0.997662i	$0.521773\pi$
$384$	10.5852			0.540171
$385$	2.44751	−	3.40936i	0.124737	−	0.173757i
$386$	−5.63944			−0.287040
$387$	2.33710	−	1.34932i	0.118801	−	0.0685900i
$388$	12.9766	+	7.49203i	0.658786	+	0.380350i
$389$	15.3576	−	26.6002i	0.778664	−	1.34868i	−0.154049	−	0.988063i	$-0.549231\pi$
$389$	15.3576	−	26.6002i	0.778664	−	1.34868i	0.932712	−	0.360622i	$-0.117435\pi$
$390$	−0.921277	+	0.531899i	−0.0466507	+	0.0269338i
$391$	0.266261			0.0134654
$392$	6.87960	−	8.78007i	0.347472	−	0.443461i
$393$			14.3240i			0.722552i
$394$	3.52362	+	6.10310i	0.177518	+	0.307470i
$395$	−3.41459	+	5.91425i	−0.171807	+	0.297578i
$396$	4.40413	−	4.15988i	0.221316	−	0.209042i
$397$	−14.2958	+	8.25368i	−0.717485	+	0.414240i	−0.813826	−	0.581108i	$-0.802619\pi$
$397$	−14.2958	+	8.25368i	−0.717485	+	0.414240i	0.0963413	+	0.995348i	$0.469286\pi$
$398$	10.9152			0.547130
$399$	3.48828	−	10.1077i	0.174633	−	0.506017i
$400$	14.2643			0.713214
$401$	5.89092	+	10.2034i	0.294179	+	0.509532i	0.974793	−	0.223109i	$-0.0716206\pi$
$401$	5.89092	+	10.2034i	0.294179	+	0.509532i	−0.680615	+	0.732641i	$0.738287\pi$
$402$	−0.636833	+	1.10303i	−0.0317624	+	0.0550140i
$403$	5.37144	+	3.10120i	0.267570	+	0.154482i
$404$	−9.14153	−	15.8336i	−0.454808	−	0.787750i
$405$			0.478282i			0.0237660i
$406$	1.93812	+	10.0082i	0.0961875	+	0.496701i
$407$	14.2026	+	4.24308i	0.703999	+	0.210322i
$408$	−0.196277	−	0.339962i	−0.00971716	−	0.0168306i
$409$	7.25158	−	12.5601i	0.358567	−	0.621057i	−0.629154	−	0.777280i	$-0.716599\pi$
$409$	7.25158	−	12.5601i	0.358567	−	0.621057i	0.987722	+	0.156223i	$0.0499320\pi$
$410$	−0.906957	+	1.57090i	−0.0447914	+	0.0775810i
$411$	−2.79585	+	1.61419i	−0.137909	+	0.0796219i
$412$		−	18.7779i		−	0.925121i
$413$	1.92124	+	2.21327i	0.0945381	+	0.108908i
$414$			0.450074i			0.0221199i
$415$	−5.52769	+	3.19141i	−0.271343	+	0.156660i
$416$	−20.5004	−	11.8359i	−1.00512	−	0.580304i
$417$	5.25600	+	3.03456i	0.257388	+	0.148603i
$418$	−5.43049	+	1.29035i	−0.265614	+	0.0631132i
$419$			26.3346i			1.28653i	0.765643	+	0.643266i	$0.222421\pi$
$419$			26.3346i			1.28653i	−0.765643	+	0.643266i	$0.777579\pi$
$420$	−1.74550	+	1.51519i	−0.0851716	+	0.0739338i
$421$	−31.5201			−1.53619			−0.768097	−	0.640334i	$-0.778796\pi$
$421$	−31.5201			−1.53619			−0.768097	+	0.640334i	$0.778796\pi$
$422$	−1.65136	−	2.86024i	−0.0803869	−	0.139234i
$423$	6.81265	+	3.93329i	0.331243	+	0.191243i
$424$	−0.669991	−	0.386819i	−0.0325376	−	0.0187856i
$425$	−0.587701	−	1.01793i	−0.0285077	−	0.0493768i
$426$	−4.99000			−0.241766
$427$	−2.68562	−	13.8682i	−0.129966	−	0.671130i
$428$			30.3798i			1.46846i
$429$	−17.2351	+	4.09527i	−0.832117	+	0.197721i
$430$	0.465471	+	0.268740i	0.0224470	+	0.0129598i
$431$	23.0159	+	13.2882i	1.10864	+	0.640072i	0.938476	−	0.345345i	$-0.112238\pi$
$431$	23.0159	+	13.2882i	1.10864	+	0.640072i	0.170161	+	0.985416i	$0.445571\pi$
$432$	−2.58910	+	1.49482i	−0.124568	+	0.0719194i
$433$		−	2.09473i		−	0.100667i	−0.998732	−	0.0503333i	$-0.983972\pi$
$433$		−	2.09473i		−	0.100667i	0.998732	−	0.0503333i	$-0.0160283\pi$
$434$	−1.20938	−	0.417372i	−0.0580521	−	0.0200345i
$435$		−	4.42543i		−	0.212183i
$436$	10.0245	−	5.78762i	0.480084	−	0.277177i
$437$	−2.18403	+	3.78286i	−0.104477	+	0.180959i
$438$	−1.64205	+	2.84411i	−0.0784601	+	0.135897i
$439$	−0.677162	−	1.17288i	−0.0323192	−	0.0559785i	0.849413	−	0.527728i	$-0.176956\pi$
$439$	−0.677162	−	1.17288i	−0.0323192	−	0.0559785i	−0.881733	+	0.471750i	$0.843623\pi$
$440$	2.42192	+	0.723557i	0.115461	+	0.0344942i
$441$	−0.983932	+	6.93050i	−0.0468539	+	0.330024i
$442$			0.547936i			0.0260627i
$443$	9.11902	+	15.7946i	0.433257	+	0.750424i	0.997152	−	0.0754231i	$-0.0240307\pi$
$443$	9.11902	+	15.7946i	0.433257	+	0.750424i	−0.563894	+	0.825847i	$0.690697\pi$
$444$	−7.06985	−	4.08178i	−0.335520	−	0.193713i
$445$	3.30975	−	5.73265i	0.156897	−	0.271754i
$446$	4.16878	+	7.22054i	0.197398	+	0.341903i
$447$	16.1597			0.764330
$448$	−10.3385	−	3.56794i	−0.488448	−	0.168569i
$449$	9.75521			0.460377			0.230188	−	0.973146i	$-0.426066\pi$
$449$	9.75521			0.460377			0.230188	+	0.973146i	$0.426066\pi$
$450$	1.72066	−	0.993422i	0.0811126	−	0.0468304i
$451$	−21.9593	+	20.7414i	−1.03402	+	0.976676i
$452$	12.5354	−	21.7120i	0.589616	−	1.02124i
$453$	−5.13927	−	8.90147i	−0.241464	−	0.418228i
$454$			1.06984i			0.0502102i
$455$	6.63563	−	1.28501i	0.311083	−	0.0602421i
$456$	6.43994			0.301578
$457$	9.81669	−	5.66767i	0.459205	−	0.265122i	−0.252505	−	0.967596i	$-0.581254\pi$
$457$	9.81669	−	5.66767i	0.459205	−	0.265122i	0.711710	+	0.702473i	$0.247921\pi$
$458$	1.85830	−	3.21867i	0.0868327	−	0.150399i
$459$	0.213346	+	0.123176i	0.00995816	+	0.00574935i
$460$	0.817728	−	0.472115i	0.0381268	−	0.0220125i
$461$	−38.1954			−1.77894			−0.889468	−	0.456997i	$-0.848925\pi$
$461$	−38.1954			−1.77894			−0.889468	+	0.456997i	$0.848925\pi$
$462$	3.32965	−	1.50522i	0.154909	−	0.0700293i
$463$	28.5362			1.32619			0.663094	−	0.748536i	$-0.269243\pi$
$463$	28.5362			1.32619			0.663094	+	0.748536i	$0.269243\pi$
$464$	23.9563	−	13.8312i	1.11214	−	0.642097i
$465$	0.480984	+	0.277697i	0.0223051	+	0.0128779i
$466$	−3.23082	+	5.59595i	−0.149665	+	0.259227i
$467$	2.27213	−	1.31181i	0.105141	−	0.0607034i	−0.446507	−	0.894780i	$-0.647332\pi$
$467$	2.27213	−	1.31181i	0.105141	−	0.0607034i	0.551649	+	0.834077i	$0.313999\pi$
$468$	9.75630			0.450985
$469$	6.11107	−	5.30475i	0.282183	−	0.244951i
$470$			1.56676i			0.0722691i
$471$	1.79057	+	3.10135i	0.0825049	+	0.142903i
$472$	−0.882582	+	1.52868i	−0.0406241	+	0.0703631i
$473$	6.14589	+	6.50675i	0.282588	+	0.299181i
$474$	−5.14929	+	2.97294i	−0.236515	+	0.136552i
$475$	19.2828			0.884754
$476$	0.226347	+	1.16883i	0.0103746	+	0.0535733i
$477$	0.485505			0.0222297
$478$	1.39348	+	2.41358i	0.0637363	+	0.110394i
$479$	−8.59356	+	14.8845i	−0.392650	+	0.680089i	−0.992798	−	0.119799i	$-0.961775\pi$
$479$	−8.59356	+	14.8845i	−0.392650	+	0.680089i	0.600148	+	0.799889i	$0.295108\pi$
$480$	−1.83571	−	1.05985i	−0.0837882	−	0.0483751i
$481$	11.9358	+	20.6734i	0.544224	+	0.942624i
$482$			4.84895i			0.220864i
$483$	0.932881	−	2.70313i	0.0424476	−	0.122996i
$484$	16.7998	+	11.0217i	0.763626	+	0.500986i
$485$	−1.96174	−	3.39784i	−0.0890781	−	0.154288i
$486$	−0.208210	+	0.360631i	−0.00944461	+	0.0163585i
$487$	−1.42058	+	2.46052i	−0.0643726	+	0.111497i	−0.896416	−	0.443215i	$-0.853838\pi$
$487$	−1.42058	+	2.46052i	−0.0643726	+	0.111497i	0.832043	+	0.554711i	$0.187171\pi$
$488$	7.36786	−	4.25383i	0.333527	−	0.192562i
$489$		−	15.0019i		−	0.678407i
$490$	−1.29338	+	0.520450i	−0.0584289	+	0.0235115i
$491$		−	27.5167i		−	1.24181i	−0.783885	−	0.620906i	$-0.786765\pi$
$491$		−	27.5167i		−	1.24181i	0.783885	−	0.620906i	$-0.213235\pi$
$492$	14.4070	−	8.31788i	0.649517	−	0.374999i
$493$	−1.97404	−	1.13971i	−0.0889065	−	0.0513302i
$494$	−7.78473	−	4.49451i	−0.350251	−	0.202218i
$495$	−1.54331	+	0.366710i	−0.0693667	+	0.0164824i
$496$			3.47164i			0.155881i
$497$	29.9697	+	10.3429i	1.34433	+	0.463943i
$498$	−5.55726			−0.249027
$499$	−8.31850	−	14.4081i	−0.372387	−	0.644994i	0.617545	−	0.786536i	$-0.288127\pi$
$499$	−8.31850	−	14.4081i	−0.372387	−	0.644994i	−0.989932	+	0.141542i	$0.954794\pi$
$500$	−7.39276	−	4.26821i	−0.330614	−	0.190880i
$501$	−11.0489	−	6.37909i	−0.493629	−	0.284997i
$502$	2.58384	+	4.47534i	0.115322	+	0.199744i
$503$	0.132815			0.00592194			0.00296097	−	0.999996i	$-0.499057\pi$
$503$	0.132815			0.00592194			0.00296097	+	0.999996i	$0.499057\pi$
$504$	−4.13903	+	0.801535i	−0.184367	+	0.0357032i
$505$			4.78730i			0.213032i
$506$	−1.45229	+	0.345083i	−0.0645623	+	0.0153408i
$507$	−13.4485	−	7.76450i	−0.597269	−	0.344834i
$508$	0.735278	+	0.424513i	0.0326227	+	0.0188347i
$509$	−23.4923	+	13.5633i	−1.04128	+	0.601183i	−0.920195	−	0.391460i	$-0.871970\pi$
$509$	−23.4923	+	13.5633i	−1.04128	+	0.601183i	−0.121084	+	0.992642i	$0.538637\pi$
$510$			0.0490649i			0.00217263i
$511$	15.7571	−	13.6781i	0.697055	−	0.605083i
$512$		−	22.7775i		−	1.00663i
$513$	−3.50000	+	2.02073i	−0.154529	+	0.0892172i
$514$	3.86161	−	6.68850i	0.170328	−	0.295017i
$515$	−2.45844	+	4.25814i	−0.108332	+	0.187636i
$516$	−2.46467	−	4.26893i	−0.108501	−	0.187929i
$517$	−7.46844	+	24.9987i	−0.328462	+	1.09944i
$518$	−3.22783	−	3.71846i	−0.141823	−	0.163380i
$519$		−	10.0387i		−	0.440650i
$520$	2.03536	+	3.52535i	0.0892566	+	0.154597i
$521$	5.10877	+	2.94955i	0.223819	+	0.129222i	0.607718	−	0.794153i	$-0.292085\pi$
$521$	5.10877	+	2.94955i	0.223819	+	0.129222i	−0.383898	+	0.923375i	$0.625419\pi$
$522$	1.92652	−	3.33683i	0.0843215	−	0.146049i
$523$	2.74522	+	4.75486i	0.120040	+	0.207915i	0.919783	−	0.392427i	$-0.128364\pi$
$523$	2.74522	+	4.75486i	0.120040	+	0.207915i	−0.799743	+	0.600342i	$0.795031\pi$
$524$	26.1642			1.14299
$525$	−12.3933	+	2.39999i	−0.540887	+	0.104744i
$526$	−0.627779			−0.0273725
$527$	0.247743	−	0.143035i	0.0107919	−	0.00623069i
$528$	−6.80858	−	7.20835i	−0.296305	−	0.313703i
$529$	10.9159	−	18.9069i	0.474605	−	0.822040i
$530$	0.0483481	+	0.0837414i	0.00210011	+	0.00363750i
$531$		−	1.10775i		−	0.0480721i
$532$	−18.4626	−	6.37168i	−0.800456	−	0.276247i
$533$	−48.6456			−2.10708
$534$	4.99118	−	2.88166i	0.215989	−	0.124702i
$535$	3.97738	−	6.88902i	0.171957	−	0.297838i
$536$	4.22084	+	2.43690i	0.182312	+	0.105258i
$537$	16.9677	−	9.79630i	0.732210	−	0.422742i
$538$	−7.60037			−0.327675
$539$	−23.1176	+	2.13885i	−0.995747	+	0.0921267i
$540$	0.873627			0.0375949
$541$	16.8840	−	9.74796i	0.725898	−	0.419098i	−0.0910214	−	0.995849i	$-0.529013\pi$
$541$	16.8840	−	9.74796i	0.725898	−	0.419098i	0.816920	+	0.576751i	$0.195680\pi$
$542$	−0.524258	−	0.302681i	−0.0225188	−	0.0130013i
$543$	−10.1899	+	17.6494i	−0.437290	+	0.757408i
$544$	−0.945528	+	0.545901i	−0.0405392	+	0.0234053i
$545$	−3.03090			−0.129830
$546$	5.56275	+	1.91977i	0.238064	+	0.0821587i
$547$			42.3716i			1.81168i	0.423620	+	0.905840i	$0.360759\pi$
$547$			42.3716i			1.81168i	−0.423620	+	0.905840i	$0.639241\pi$
$548$	2.94846	+	5.10688i	0.125952	+	0.218155i
$549$	−2.66954	+	4.62377i	−0.113933	+	0.197338i
$550$	4.52483	+	4.79051i	0.192939	+	0.204268i
$551$	32.3847	−	18.6973i	1.37963	−	0.796532i
$552$	1.72225			0.0733039
$553$	37.0885	−	7.18229i	1.57716	−	0.305422i
$554$	8.14476			0.346038
$555$	1.06879	+	1.85119i	0.0453675	+	0.0785788i
$556$	5.54290	−	9.60058i	0.235071	−	0.407155i
$557$	2.05241	+	1.18496i	0.0869635	+	0.0502084i	0.542851	−	0.839829i	$-0.317345\pi$
$557$	2.05241	+	1.18496i	0.0869635	+	0.0502084i	−0.455888	+	0.890037i	$0.650678\pi$
$558$	0.241779	+	0.418773i	0.0102353	+	0.0177281i
$559$			14.4142i			0.609654i
$560$	2.47995	+	2.85690i	0.104797	+	0.120726i
$561$	−0.233883	+	0.782865i	−0.00987456	+	0.0330526i
$562$	−6.62112	−	11.4681i	−0.279295	−	0.483753i
$563$	11.6285	−	20.1411i	0.490082	−	0.848847i	−0.509853	−	0.860262i	$-0.670300\pi$
$563$	11.6285	−	20.1411i	0.490082	−	0.848847i	0.999935	+	0.0114144i	$0.00363339\pi$
$564$	7.18452	−	12.4440i	0.302523	−	0.523985i
$565$	−5.68514	+	3.28232i	−0.239176	+	0.138088i
$566$		−	9.16040i		−	0.385040i
$567$	1.99799	−	1.73437i	0.0839077	−	0.0728366i
$568$			19.0947i			0.801196i
$569$	−7.23342	+	4.17622i	−0.303241	+	0.175076i	−0.643898	−	0.765111i	$-0.722684\pi$
$569$	−7.23342	+	4.17622i	−0.303241	+	0.175076i	0.340657	+	0.940188i	$0.389350\pi$
$570$	−0.697082	−	0.402461i	−0.0291976	−	0.0168572i
$571$	26.7548	+	15.4469i	1.11966	+	0.646433i	0.941313	−	0.337535i	$-0.109593\pi$
$571$	26.7548	+	15.4469i	1.11966	+	0.646433i	0.178343	+	0.983968i	$0.442926\pi$
$572$	7.48040	+	31.4815i	0.312771	+	1.31631i
$573$		−	6.49949i		−	0.271520i
$574$	9.85116	−	1.90770i	0.411179	−	0.0796260i
$575$	5.15684			0.215055
$576$	2.06687	+	3.57992i	0.0861196	+	0.149163i
$577$	16.3092	+	9.41610i	0.678960	+	0.391998i	0.799463	−	0.600715i	$-0.205118\pi$
$577$	16.3092	+	9.41610i	0.678960	+	0.391998i	−0.120503	+	0.992713i	$0.538451\pi$
$578$	−6.10884	−	3.52694i	−0.254094	−	0.146701i
$579$	−6.77133	−	11.7283i	−0.281407	−	0.487411i
$580$	−8.08346			−0.335648
$581$	33.3767	+	11.5187i	1.38470	+	0.477876i
$582$		−	3.41601i		−	0.141598i
$583$	0.372248	+	1.56662i	0.0154170	+	0.0648828i
$584$	10.8833	+	6.28346i	0.450353	+	0.260011i
$585$	−2.21237	−	1.27731i	−0.0914703	−	0.0528104i
$586$	6.44894	−	3.72330i	0.266403	−	0.153808i
$587$			13.9495i			0.575758i	0.957667	+	0.287879i	$0.0929501\pi$
$587$			13.9495i			0.575758i	−0.957667	+	0.287879i	$0.907050\pi$
$588$	12.6592	+	1.79725i	0.522057	+	0.0741171i
$589$			4.69303i			0.193373i
$590$	0.191068	−	0.110313i	0.00786613	−	0.00454151i
$591$	−8.46170	+	14.6561i	−0.348068	+	0.602871i
$592$	−6.68075	+	11.5714i	−0.274577	+	0.475582i
$593$	−4.84778	−	8.39660i	−0.199074	−	0.344807i	0.749154	−	0.662396i	$-0.230460\pi$
$593$	−4.84778	−	8.39660i	−0.199074	−	0.344807i	−0.948229	+	0.317589i	$0.897127\pi$
$594$	−1.32332	−	0.395345i	−0.0542964	−	0.0162212i
$595$	0.101698	−	0.294682i	0.00416922	−	0.0120808i
$596$		−	29.5173i		−	1.20908i
$597$	13.1060	+	22.7003i	0.536393	+	0.929060i
$598$	−2.08189	−	1.20198i	−0.0851349	−	0.0491526i
$599$	−1.13166	+	1.96010i	−0.0462385	+	0.0800874i	−0.888218	−	0.459422i	$-0.848057\pi$
$599$	−1.13166	+	1.96010i	−0.0462385	+	0.0800874i	0.841980	+	0.539509i	$0.181390\pi$
$600$	−3.80142	−	6.58426i	−0.155192	−	0.268801i
$601$	46.5193			1.89756			0.948781	−	0.315935i	$-0.102318\pi$
$601$	46.5193			1.89756			0.948781	+	0.315935i	$0.102318\pi$
$602$	−0.565271	−	2.91899i	−0.0230387	−	0.118969i
$603$	−3.05861			−0.124556
$604$	−16.2594	+	9.38735i	−0.661584	+	0.381966i
$605$	−2.36659	−	4.69877i	−0.0962156	−	0.191032i
$606$	−2.08405	+	3.60968i	−0.0846588	+	0.146633i
$607$	14.7827	+	25.6043i	0.600010	+	1.03925i	0.992819	+	0.119628i	$0.0381702\pi$
$607$	14.7827	+	25.6043i	0.600010	+	1.03925i	−0.392808	+	0.919620i	$0.628496\pi$
$608$		−	17.9113i		−	0.726398i
$609$	−18.4869	+	16.0477i	−0.749128	+	0.650286i
$610$	−1.06336			−0.0430544
$611$	−36.3881	+	21.0087i	−1.47211	+	0.849921i
$612$	0.224992	−	0.389697i	0.00909476	−	0.0157526i
$613$	−4.07108	−	2.35044i	−0.164429	−	0.0949333i	0.415527	−	0.909581i	$-0.363597\pi$
$613$	−4.07108	−	2.35044i	−0.164429	−	0.0949333i	−0.579956	+	0.814647i	$0.696930\pi$
$614$	0.625841	−	0.361330i	0.0252569	−	0.0145821i
$615$	−4.35597			−0.175650
$616$	−5.75988	−	12.7412i	−0.232072	−	0.513358i
$617$	19.2863			0.776436			0.388218	−	0.921568i	$-0.373091\pi$
$617$	19.2863			0.776436			0.388218	+	0.921568i	$0.373091\pi$
$618$	−3.70739	+	2.14046i	−0.149133	+	0.0861019i
$619$	−19.9922	−	11.5425i	−0.803555	−	0.463933i	0.0411577	−	0.999153i	$-0.486895\pi$
$619$	−19.9922	−	11.5425i	−0.803555	−	0.463933i	−0.844713	+	0.535220i	$0.820229\pi$
$620$	0.507239	−	0.878563i	0.0203712	−	0.0352840i
$621$	−0.936015	+	0.540408i	−0.0375610	+	0.0216858i
$622$	−7.98361			−0.320114
$623$	−35.9497	+	6.96176i	−1.44029	+	0.278917i
$624$		−	15.9684i		−	0.639247i
$625$	−10.8105	−	18.7244i	−0.432420	−	0.748974i
$626$	5.28058	−	9.14624i	0.211055	−	0.365557i
$627$	−9.20398	−	9.74440i	−0.367572	−	0.389154i
$628$	5.66491	−	3.27064i	0.226054	−	0.130513i
$629$	1.10101			0.0439002
$630$	0.498116	+	0.171906i	0.0198454	+	0.00684889i
$631$	−5.79691			−0.230771			−0.115386	−	0.993321i	$-0.536810\pi$
$631$	−5.79691			−0.230771			−0.115386	+	0.993321i	$0.536810\pi$
$632$	11.3763	+	19.7042i	0.452523	+	0.783793i
$633$	3.96561	−	6.86863i	0.157619	−	0.273004i
$634$	−8.78391	−	5.07139i	−0.348854	−	0.201411i
$635$	−0.111156	−	0.192528i	−0.00441109	−	0.00764024i
$636$		−	0.886821i		−	0.0351647i
$637$	−29.4305	−	23.0601i	−1.16608	−	0.913676i
$638$	12.2443	+	3.65803i	0.484758	+	0.144823i
$639$	−5.99154	−	10.3777i	−0.237022	−	0.410534i
$640$	−2.53134	+	4.38442i	−0.100060	+	0.173309i
$641$	−16.2898	+	28.2148i	−0.643409	+	1.11442i	0.341258	+	0.939970i	$0.389147\pi$
$641$	−16.2898	+	28.2148i	−0.643409	+	1.11442i	−0.984667	+	0.174447i	$0.944186\pi$
$642$	5.99799	−	3.46294i	0.236722	−	0.136671i
$643$		−	11.3454i		−	0.447418i	−0.974656	−	0.223709i	$-0.928183\pi$
$643$		−	11.3454i		−	0.447418i	0.974656	−	0.223709i	$-0.0718166\pi$
$644$	−4.93751	−	1.70400i	−0.194565	−	0.0671468i
$645$			1.29071i			0.0508218i
$646$	−0.359050	+	0.207298i	−0.0141266	+	0.00815601i
$647$	−32.7961	−	18.9348i	−1.28935	−	0.744405i	−0.310810	−	0.950472i	$-0.600600\pi$
$647$	−32.7961	−	18.9348i	−1.28935	−	0.744405i	−0.978538	+	0.206067i	$0.933933\pi$
$648$	1.37999	+	0.796736i	0.0542110	+	0.0312987i
$649$	3.57446	−	0.849337i	0.140310	−	0.0333394i
$650$			10.6122i			0.416246i
$651$	−0.584110	−	3.01628i	−0.0228931	−	0.118217i
$652$	−27.4023			−1.07316
$653$	−14.7082	−	25.4753i	−0.575574	−	0.996924i	−0.995979	−	0.0895874i	$-0.971445\pi$
$653$	−14.7082	−	25.4753i	−0.575574	−	0.996924i	0.420405	−	0.907337i	$-0.361888\pi$
$654$	−2.28534	−	1.31944i	−0.0893639	−	0.0515943i
$655$	−5.93308	−	3.42547i	−0.231825	−	0.133844i
$656$	−13.6141	−	23.5803i	−0.531541	−	0.920656i
$657$	−7.88650			−0.307682
$658$	6.54502	−	5.68145i	0.255152	−	0.221486i
$659$			1.05149i			0.0409601i	0.999790	+	0.0204800i	$0.00651945\pi$
$659$			1.05149i			0.0409601i	−0.999790	+	0.0204800i	$0.993481\pi$
$660$	0.669831	+	2.81901i	0.0260731	+	0.109730i
$661$	−1.77054	−	1.02222i	−0.0688660	−	0.0397598i	0.465172	−	0.885221i	$-0.345993\pi$
$661$	−1.77054	−	1.02222i	−0.0688660	−	0.0397598i	−0.534038	+	0.845461i	$0.679326\pi$
$662$	−1.99515	−	1.15190i	−0.0775437	−	0.0447699i
$663$	−1.13954	+	0.657912i	−0.0442560	+	0.0255512i
$664$			21.2654i			0.825257i
$665$	3.35245	+	3.86202i	0.130003	+	0.149763i
$666$			1.86110i			0.0721161i
$667$	8.66072	−	5.00027i	0.335345	−	0.193611i
$668$	−11.6520	+	20.1819i	−0.450830	+	0.780860i
$669$	−10.0110	+	17.3395i	−0.387047	+	0.670386i
$670$	−0.304586	−	0.527558i	−0.0117672	−	0.0203814i
$671$	−16.9667	−	5.06886i	−0.654993	−	0.195681i
$672$	2.22929	+	11.5118i	0.0859968	+	0.444078i
$673$		−	35.1938i		−	1.35662i	−0.734775	−	0.678311i	$-0.762712\pi$
$673$		−	35.1938i		−	1.35662i	0.734775	−	0.678311i	$-0.237288\pi$
$674$	4.34428	+	7.52451i	0.167335	+	0.289833i
$675$	4.13202	+	2.38562i	0.159042	+	0.0918227i
$676$	−14.1826	+	24.5650i	−0.545484	+	0.944807i
$677$	−12.1377	−	21.0231i	−0.466489	−	0.807982i	0.532779	−	0.846255i	$-0.321148\pi$
$677$	−12.1377	−	21.0231i	−0.466489	−	0.807982i	−0.999267	+	0.0382725i	$0.987815\pi$
$678$	−5.71555			−0.219505
$679$	−7.08047	+	20.5164i	−0.271723	+	0.787348i
$680$	0.187751			0.00719994
$681$	−2.22494	+	1.28457i	−0.0852600	+	0.0492249i
$682$	−1.16591	+	1.10125i	−0.0446451	+	0.0421691i
$683$	−13.0258	+	22.5613i	−0.498417	+	0.863283i	−0.999998	−	0.00182735i	$-0.999418\pi$
$683$	−13.0258	+	22.5613i	−0.498417	+	0.863283i	0.501582	+	0.865110i	$0.332752\pi$
$684$	3.69105	+	6.39308i	0.141131	+	0.244445i
$685$		−	1.54407i		−	0.0589959i
$686$	6.86425	+	3.51572i	0.262078	+	0.134231i
$687$	8.92512			0.340514
$688$	−6.98707	+	4.03398i	−0.266379	+	0.153794i
$689$	−1.29660	+	2.24578i	−0.0493966	+	0.0855575i
$690$	−0.186423	−	0.107631i	−0.00709699	−	0.00409745i
$691$	36.2518	−	20.9300i	1.37908	−	0.796214i	0.387034	−	0.922065i	$-0.373500\pi$
$691$	36.2518	−	20.9300i	1.37908	−	0.796214i	0.992049	+	0.125851i	$0.0401663\pi$
$692$	−18.3366			−0.697054
$693$	7.12834	+	5.11730i	0.270783	+	0.194390i
$694$	5.90744			0.224243
$695$	−2.51385	+	1.45137i	−0.0953558	+	0.0550537i
$696$	−12.7687	−	7.37201i	−0.483996	−	0.279435i
$697$	−1.12183	+	1.94306i	−0.0424922	+	0.0735986i
$698$	7.59418	−	4.38450i	0.287444	−	0.165956i
$699$	−15.5171			−0.586911
$700$	4.38381	+	22.6375i	0.165693	+	0.855617i
$701$			12.0257i			0.454205i	0.973871	+	0.227103i	$0.0729253\pi$
$701$			12.0257i			0.454205i	−0.973871	+	0.227103i	$0.927075\pi$
$702$	−1.11210	−	1.92622i	−0.0419737	−	0.0727005i
$703$	−9.03118	+	15.6425i	−0.340618	+	0.589967i
$704$	−9.96692	+	9.41415i	−0.375642	+	0.354809i
$705$	−3.25837	+	1.88122i	−0.122717	+	0.0708509i
$706$	−0.424236			−0.0159663
$707$	19.9986	−	17.3599i	0.752126	−	0.652887i
$708$	−2.02340			−0.0760442
$709$	−9.94327	−	17.2222i	−0.373427	−	0.646795i	0.616663	−	0.787227i	$-0.288484\pi$
$709$	−9.94327	−	17.2222i	−0.373427	−	0.646795i	−0.990090	+	0.140432i	$0.955151\pi$
$710$	1.19331	−	2.06688i	0.0447843	−	0.0775686i
$711$	−12.3656	−	7.13929i	−0.463746	−	0.267744i
$712$	−11.0269	−	19.0992i	−0.413252	−	0.715773i
$713$			1.25507i			0.0470028i
$714$	0.204965	−	0.177921i	0.00767063	−	0.00665854i
$715$	2.42533	−	8.11819i	0.0907024	−	0.303603i
$716$	−17.8939	−	30.9931i	−0.668725	−	1.15827i
$717$	−3.34633	+	5.79601i	−0.124971	+	0.216456i
$718$	−1.39640	+	2.41863i	−0.0521130	+	0.0902624i
$719$	0.428020	−	0.247117i	0.0159624	−	0.00921592i	−0.491998	−	0.870597i	$-0.663733\pi$
$719$	0.428020	−	0.247117i	0.0159624	−	0.00921592i	0.507960	+	0.861381i	$0.330400\pi$
$720$		−	1.42989i		−	0.0532888i
$721$	26.7030	−	5.17110i	0.994471	−	0.192582i
$722$			1.11046i			0.0413269i
$723$	−10.0843	+	5.82218i	−0.375040	+	0.216529i
$724$	32.2383	+	18.6128i	1.19813	+	0.691739i
$725$	−38.2326	−	22.0736i	−1.41992	−	0.819793i
$726$	0.261074	−	4.57318i	0.00968936	−	0.169727i
$727$			46.9030i			1.73953i	0.493462	+	0.869767i	$0.335731\pi$
$727$			46.9030i			1.73953i	−0.493462	+	0.869767i	$0.664269\pi$
$728$	7.34619	−	21.2864i	0.272268	−	0.788926i
$729$	−1.00000			−0.0370370
$730$	−0.785363	−	1.36029i	−0.0290676	−	0.0503465i
$731$	0.575747	+	0.332408i	0.0212948	+	0.0122945i
$732$	8.44576	+	4.87616i	0.312164	+	0.180228i
$733$	−23.0439	−	39.9132i	−0.851146	−	1.47423i	−0.880175	−	0.474650i	$-0.842575\pi$
$733$	−23.0439	−	39.9132i	−0.851146	−	1.47423i	0.0290282	−	0.999579i	$-0.490759\pi$
$734$	−2.28800			−0.0844517
$735$	−2.63535	−	2.06492i	−0.0972062	−	0.0761656i
$736$		−	4.79006i		−	0.176564i
$737$	−2.34511	−	9.86947i	−0.0863832	−	0.363546i
$738$	−3.28445	−	1.89628i	−0.120902	−	0.0698031i
$739$	22.0396	+	12.7246i	0.810740	+	0.468081i	0.847213	−	0.531254i	$-0.178279\pi$
$739$	22.0396	+	12.7246i	0.810740	+	0.468081i	−0.0364730	+	0.999335i	$0.511612\pi$
$740$	3.38138	−	1.95224i	0.124302	−	0.0717658i
$741$		−	21.5864i		−	0.792997i
$742$	0.174502	−	0.505638i	0.00640617	−	0.0185626i
$743$		−	9.19015i		−	0.337154i	−0.985688	−	0.168577i	$-0.946083\pi$
$743$		−	9.19015i		−	0.337154i	0.985688	−	0.168577i	$-0.0539172\pi$
$744$	1.60248	−	0.925190i	0.0587496	−	0.0339191i
$745$	−3.86446	+	6.69344i	−0.141583	+	0.245229i
$746$	−0.0105049	+	0.0181950i	−0.000384610	+	0.000666165i
$747$	−6.67266	−	11.5574i	−0.244140	−	0.422862i
$748$	1.42998	+	0.427210i	0.0522851	+	0.0156203i
$749$	−43.2014	+	8.36606i	−1.57854	+	0.305689i
$750$			1.94610i			0.0710617i
$751$	17.1921	+	29.7777i	0.627350	+	1.08660i	0.988081	+	0.153932i	$0.0491938\pi$
$751$	17.1921	+	29.7777i	0.627350	+	1.08660i	−0.360731	+	0.932670i	$0.617473\pi$
$752$	−20.3673	−	11.7591i	−0.742721	−	0.428810i
$753$	−6.20488	+	10.7472i	−0.226119	+	0.391649i
$754$	10.2900	+	17.8229i	0.374741	+	0.649070i
$755$	4.91604			0.178913
$756$	−3.16799	−	3.64952i	−0.115219	−	0.132732i
$757$	−25.7961			−0.937576			−0.468788	−	0.883311i	$-0.655309\pi$
$757$	−25.7961			−0.937576			−0.468788	+	0.883311i	$0.655309\pi$
$758$	−0.479475	+	0.276825i	−0.0174153	+	0.0100547i
$759$	−2.46145	−	2.60597i	−0.0893448	−	0.0945908i
$760$	−1.54005	+	2.66745i	−0.0558636	+	0.0967586i
$761$	−1.99063	−	3.44787i	−0.0721603	−	0.124985i	0.827688	−	0.561189i	$-0.189656\pi$
$761$	−1.99063	−	3.44787i	−0.0721603	−	0.124985i	−0.899848	+	0.436204i	$0.856323\pi$
$762$		−	0.193558i		−	0.00701187i
$763$	10.9908	+	12.6614i	0.397894	+	0.458373i
$764$	−11.8719			−0.429511
$765$	−0.102040	+	0.0589127i	−0.00368926	+	0.00212999i
$766$	4.54760	−	7.87668i	0.164312	−	0.284596i
$767$	5.12406	+	2.95838i	0.185019	+	0.106821i
$768$	3.34252	−	1.92980i	0.120613	−	0.0696357i
$769$	37.7698			1.36201			0.681006	−	0.732277i	$-0.261543\pi$
$769$	37.7698			1.36201			0.681006	+	0.732277i	$0.261543\pi$
$770$	−0.172785	+	1.73912i	−0.00622675	+	0.0626734i
$771$	18.5467			0.667942
$772$	−21.4228	+	12.3685i	−0.771024	+	0.445151i
$773$	36.4030	+	21.0173i	1.30932	+	0.755938i	0.981983	−	0.188968i	$-0.0605143\pi$
$773$	36.4030	+	21.0173i	1.30932	+	0.755938i	0.327340	+	0.944906i	$0.393848\pi$
$774$	−0.561886	+	0.973215i	−0.0201966	+	0.0349815i
$775$	4.79821	−	2.77025i	0.172357	−	0.0995101i
$776$	−13.0717			−0.469247
$777$	3.85755	−	11.1777i	0.138389	−	0.400997i
$778$			12.7905i			0.458561i
$779$	−18.4038	−	31.8764i	−0.659385	−	1.14209i
$780$	−2.33313	+	4.04110i	−0.0835395	+	0.144695i
$781$	28.8926	−	27.2902i	1.03386	−	0.976520i
$782$	−0.0960217	+	0.0554382i	−0.00343373	+	0.00198246i
$783$	9.25276			0.330667
$784$	2.94160	−	20.7197i	0.105057	−	0.739988i
$785$	−1.71279			−0.0611321
$786$	−2.98241	−	5.16569i	−0.106379	−	0.184254i
$787$	−13.5587	+	23.4844i	−0.483316	+	0.837128i	−0.999816	−	0.0191591i	$-0.993901\pi$
$787$	−13.5587	+	23.4844i	−0.483316	+	0.837128i	0.516501	+	0.856287i	$0.327234\pi$
$788$	26.7707	+	15.4561i	0.953668	+	0.550600i
$789$	−0.753780	−	1.30559i	−0.0268353	−	0.0464801i
$790$		−	2.84381i		−	0.101178i
$791$	34.3274	+	11.8468i	1.22054	+	0.421223i
$792$	−1.51283	+	5.06380i	−0.0537559	+	0.179934i
$793$	−14.2587	−	24.6968i	−0.506341	−	0.877008i
$794$	3.43700	−	5.95306i	0.121975	−	0.211266i
$795$	−0.116104	+	0.201098i	−0.00411779	+	0.00713222i
$796$	41.4641	−	23.9393i	1.46966	−	0.848507i
$797$			8.03224i			0.284517i	0.989830	+	0.142258i	$0.0454364\pi$
$797$			8.03224i			0.284517i	−0.989830	+	0.142258i	$0.954564\pi$
$798$	0.846540	+	4.37144i	0.0299672	+	0.154747i
$799$			1.93794i			0.0685594i
$800$	−18.3127	+	10.5728i	−0.647450	+	0.373805i
$801$	11.9859	+	6.92007i	0.423501	+	0.244509i
$802$	−4.24889	−	2.45310i	−0.150034	−	0.0866220i
$803$	−6.04677	−	25.4480i	−0.213386	−	0.898041i
$804$			5.58683i			0.197032i
$805$	0.896556	+	1.03283i	0.0315994	+	0.0364025i
$806$	−2.58281			−0.0909754
$807$	−9.12584	−	15.8064i	−0.321245	−	0.556412i
$808$	13.8128	+	7.97482i	0.485933	+	0.280553i
$809$	37.7150	+	21.7748i	1.32599	+	0.765560i	0.984677	−	0.174390i	$-0.0557952\pi$
$809$	37.7150	+	21.7748i	1.32599	+	0.765560i	0.341312	+	0.939950i	$0.389129\pi$
$810$	−0.0995832	−	0.172483i	−0.00349900	−	0.00606044i
$811$	32.9735			1.15786			0.578929	−	0.815378i	$-0.303471\pi$
$811$	32.9735			1.15786			0.578929	+	0.815378i	$0.303471\pi$
$812$	29.3126	+	33.7681i	1.02867	+	1.18503i
$813$		−	1.45373i		−	0.0509844i
$814$	−6.00536	+	1.42695i	−0.210488	+	0.0500145i
$815$	6.21383	+	3.58756i	0.217661	+	0.125667i
$816$	−0.637828	−	0.368250i	−0.0223284	−	0.0128913i
$817$	−9.44527	+	5.45323i	−0.330448	+	0.190784i
$818$			6.03941i			0.211163i
$819$	2.68671	+	13.8739i	0.0938814	+	0.484793i
$820$			7.95658i			0.277856i
$821$	20.2658	−	11.7005i	0.707282	−	0.408349i	−0.102772	−	0.994705i	$-0.532771\pi$
$821$	20.2658	−	11.7005i	0.707282	−	0.408349i	0.810054	+	0.586356i	$0.199438\pi$
$822$	0.672180	−	1.16425i	0.0234450	−	0.0406079i
$823$	−13.8658	+	24.0162i	−0.483330	+	0.837153i	−0.999817	−	0.0191427i	$-0.993906\pi$
$823$	−13.8658	+	24.0162i	−0.483330	+	0.837153i	0.516486	+	0.856295i	$0.327240\pi$
$824$	8.19067	+	14.1867i	0.285336	+	0.494216i
$825$	−4.52977	+	15.1623i	−0.157706	+	0.527882i
$826$	−1.15368	−	0.398150i	−0.0401418	−	0.0138534i
$827$			37.2562i			1.29553i	0.761842	+	0.647763i	$0.224295\pi$
$827$			37.2562i			1.29553i	−0.761842	+	0.647763i	$0.775705\pi$
$828$	0.987107	+	1.70972i	0.0343043	+	0.0594168i
$829$	6.16417	+	3.55889i	0.214090	+	0.123605i	0.603211	−	0.797582i	$-0.293888\pi$
$829$	6.16417	+	3.55889i	0.214090	+	0.123605i	−0.389120	+	0.921187i	$0.627221\pi$
$830$	1.32897	−	2.30184i	0.0461292	−	0.0798981i
$831$	9.77949	+	16.9386i	0.339247	+	0.587593i
$832$	−22.0794			−0.765464
$833$	−1.59979	+	0.643751i	−0.0554296	+	0.0223046i
$834$	−2.52730			−0.0875133
$835$	5.28449	−	3.05100i	0.182877	−	0.105584i
$836$	−17.7991	+	16.8119i	−0.615594	+	0.581453i
$837$	−0.580613	+	1.00565i	−0.0200689	+	0.0347604i
$838$	−5.48314	−	9.49708i	−0.189412	−	0.328071i
$839$		−	49.7475i		−	1.71748i	−0.512415	−	0.858738i	$-0.671249\pi$
$839$		−	49.7475i		−	1.71748i	0.512415	−	0.858738i	$-0.328751\pi$
$840$	0.657814	−	1.90609i	0.0226967	−	0.0657662i
$841$	−56.6136			−1.95219
$842$	11.3671	−	6.56280i	0.391736	−	0.226169i
$843$	15.9001	−	27.5398i	0.547628	−	0.948520i
$844$	−12.5462	−	7.24355i	−0.431858	−	0.249333i
$845$	6.43218	−	3.71362i	0.221274	−	0.127752i
$846$	−3.27580			−0.112624
$847$	−11.0470	+	26.9252i	−0.379578	+	0.925160i
$848$	−1.45148			−0.0498441
$849$	19.0508	−	10.9990i	0.653821	−	0.377484i
$850$	0.423886	+	0.244731i	0.0145392	+	0.00839420i
$851$	−2.41523	+	4.18331i	−0.0827932	+	0.143402i
$852$	−18.9558	+	10.9441i	−0.649413	+	0.374939i
$853$	23.3841			0.800658			0.400329	−	0.916372i	$-0.368896\pi$
$853$	23.3841			0.800658			0.400329	+	0.916372i	$0.368896\pi$
$854$	3.85602	+	4.44213i	0.131950	+	0.152007i
$855$		−	1.93295i		−	0.0661056i
$856$	−13.2513	−	22.9519i	−0.452919	−	0.784478i
$857$	11.8103	−	20.4561i	0.403432	−	0.698765i	−0.590705	−	0.806887i	$-0.701150\pi$
$857$	11.8103	−	20.4561i	0.403432	−	0.698765i	0.994138	+	0.108122i	$0.0344837\pi$
$858$	5.36282	−	5.06540i	0.183084	−	0.172930i
$859$	17.7047	−	10.2218i	0.604075	−	0.348763i	−0.166568	−	0.986030i	$-0.553268\pi$
$859$	17.7047	−	10.2218i	0.604075	−	0.348763i	0.770643	+	0.637267i	$0.219935\pi$
$860$	2.35761			0.0803939
$861$	15.7958	+	18.1968i	0.538320	+	0.620144i
$862$	−11.0670			−0.376943
$863$	10.5700	+	18.3079i	0.359809	+	0.623207i	0.987929	−	0.154910i	$-0.0495087\pi$
$863$	10.5700	+	18.3079i	0.359809	+	0.623207i	−0.628120	+	0.778116i	$0.716175\pi$
$864$	2.21594	−	3.83813i	0.0753880	−	0.130576i
$865$	4.15807	+	2.40066i	0.141379	+	0.0816250i
$866$	0.436145	+	0.755426i	0.0148208	+	0.0256704i
$867$		−	16.9393i		−	0.575289i
$868$	−5.50951	+	1.06693i	−0.187005	+	0.0362140i
$869$	13.5559	−	45.3750i	0.459853	−	1.53924i
$870$	0.921420	+	1.59595i	0.0312391	+	0.0541076i
$871$	8.16840	−	14.1481i	0.276776	−	0.479390i
$872$	−5.04897	+	8.74507i	−0.170980	+	0.296145i
$873$	7.10425	−	4.10164i	0.240442	−	0.138820i
$874$		−	1.81895i		−	0.0615270i
$875$	4.03374	−	11.6882i	0.136365	−	0.395134i
$876$			14.4054i			0.486714i
$877$	−25.8776	+	14.9404i	−0.873824	+	0.504503i	−0.868617	−	0.495484i	$-0.834991\pi$
$877$	−25.8776	+	14.9404i	−0.873824	+	0.504503i	−0.00520722	+	0.999986i	$0.501658\pi$
$878$	0.488411	+	0.281984i	0.0164831	+	0.00951650i
$879$	15.4866	+	8.94120i	0.522351	+	0.301579i
$880$	4.61394	−	1.09633i	0.155536	−	0.0369573i
$881$		−	4.29272i		−	0.144626i	−0.997382	−	0.0723128i	$-0.976962\pi$
$881$		−	4.29272i		−	0.144626i	0.997382	−	0.0723128i	$-0.0230380\pi$
$882$	−1.08817	−	2.70422i	−0.0366404	−	0.0910557i
$883$	−44.7617			−1.50635			−0.753176	−	0.657820i	$-0.771479\pi$
$883$	−44.7617			−1.50635			−0.753176	+	0.657820i	$0.771479\pi$
$884$	1.20174	+	2.08147i	0.0404189	+	0.0700075i
$885$	0.458834	+	0.264908i	0.0154235	+	0.00890478i
$886$	−6.57719	−	3.79734i	−0.220965	−	0.127574i
$887$	16.7552	+	29.0208i	0.562583	+	0.974423i	0.997270	+	0.0738413i	$0.0235258\pi$
$887$	16.7552	+	29.0208i	0.562583	+	0.974423i	−0.434687	+	0.900582i	$0.643141\pi$
$888$	7.12167			0.238987
$889$	−0.401193	+	1.16250i	−0.0134556	+	0.0389890i
$890$			2.75649i			0.0923978i
$891$	−0.766724	−	3.22678i	−0.0256862	−	0.108101i
$892$	31.6723	+	18.2860i	1.06047	+	0.612261i
$893$	−27.5330	−	15.8962i	−0.921357	−	0.531946i
$894$	−5.82770	+	3.36462i	−0.194907	+	0.112530i
$895$			9.37079i			0.313231i
$896$	27.4949	−	5.32446i	0.918539	−	0.177878i
$897$		−	5.77292i		−	0.192752i
$898$	−3.51803	+	2.03113i	−0.117398	+	0.0677798i
$899$	5.37227	−	9.30504i	0.179175	−	0.310341i
$900$	4.35757	−	7.54752i	0.145252	−	0.251584i
$901$	0.0598024	+	0.103581i	0.00199231	+	0.00345078i
$902$	3.60062	−	12.0521i	0.119887	−	0.401293i
$903$	5.39187	−	4.68045i	0.179430	−	0.155756i
$904$			21.8711i			0.727422i
$905$	−4.87364	−	8.44139i	−0.162005	−	0.280601i
$906$	3.70675	+	2.14010i	0.123149	+	0.0710999i
$907$	−4.94342	+	8.56225i	−0.164143	+	0.284305i	−0.936351	−	0.351066i	$-0.885819\pi$
$907$	−4.94342	+	8.56225i	−0.164143	+	0.284305i	0.772207	+	0.635371i	$0.219153\pi$
$908$	2.34639	+	4.06407i	0.0778677	+	0.134871i
$909$	−10.0094			−0.331990
$910$	−2.12546	+	1.84502i	−0.0704583	+	0.0611618i
$911$	1.59373			0.0528028			0.0264014	−	0.999651i	$-0.491595\pi$
$911$	1.59373			0.0528028			0.0264014	+	0.999651i	$0.491595\pi$
$912$	10.4637	−	6.04123i	0.346488	−	0.200045i
$913$	32.1771	−	30.3925i	1.06491	−	1.00585i
$914$	−2.36013	+	4.08787i	−0.0780662	+	0.135215i
$915$	−1.27679	−	2.21147i	−0.0422094	−	0.0731089i
$916$		−	16.3026i		−	0.538652i
$917$	7.20516	+	37.2066i	0.237935	+	1.22867i
$918$	−0.102586			−0.00338583
$919$	7.81497	−	4.51197i	0.257792	−	0.148836i	−0.365535	−	0.930798i	$-0.619114\pi$
$919$	7.81497	−	4.51197i	0.257792	−	0.148836i	0.623327	+	0.781961i	$0.285781\pi$
$920$	−0.411861	+	0.713364i	−0.0135787	+	0.0235189i
$921$	1.50291	+	0.867704i	0.0495225	+	0.0285918i
$922$	13.7744	−	7.95267i	0.453637	−	0.261907i
$923$	64.0047			2.10674
$924$	9.34723	−	13.0206i	0.307501	−	0.428346i
$925$	21.3240			0.701129
$926$	−10.2910	+	5.94153i	−0.338184	+	0.195251i
$927$	−8.90299	−	5.14014i	−0.292412	−	0.168824i
$928$	−20.5036	+	35.5133i	−0.673064	+	1.16578i
$929$	41.9539	−	24.2221i	1.37646	−	0.794700i	0.384730	−	0.923029i	$-0.374295\pi$
$929$	41.9539	−	24.2221i	1.37646	−	0.794700i	0.991732	+	0.128329i	$0.0409613\pi$
$930$	−0.231277			−0.00758387
$931$	3.97652	−	28.0093i	0.130325	−	0.917968i
$932$			28.3435i			0.928421i
$933$	−9.58600	−	16.6034i	−0.313831	−	0.543572i
$934$	−0.546266	+	0.946160i	−0.0178744	+	0.0309593i
$935$	−0.268335	−	0.284091i	−0.00877549	−	0.00929075i
$936$	−7.37086	+	4.25557i	−0.240924	+	0.139098i
$937$	−34.8830			−1.13958			−0.569789	−	0.821791i	$-0.692975\pi$
$937$	−34.8830			−1.13958			−0.569789	+	0.821791i	$0.692975\pi$
$938$	−1.09934	+	3.18544i	−0.0358946	+	0.104008i
$939$	25.3618			0.827651
$940$	3.43623	+	5.95172i	0.112077	+	0.194124i
$941$	0.960946	−	1.66441i	0.0313259	−	0.0542581i	−0.849937	−	0.526884i	$-0.823360\pi$
$941$	0.960946	−	1.66441i	0.0313259	−	0.0542581i	0.881263	+	0.472626i	$0.156694\pi$
$942$	−1.29147	−	0.745628i	−0.0420782	−	0.0242939i
$943$	−4.92179	−	8.52478i	−0.160275	−	0.277605i
$944$			3.31176i			0.107789i
$945$	0.240582	+	1.24234i	0.00782612	+	0.0404132i
$946$	−3.57117	−	1.06690i	−0.116109	−	0.0346878i
$947$	−6.60448	−	11.4393i	−0.214617	−	0.371727i	0.738537	−	0.674213i	$-0.235517\pi$
$947$	−6.60448	−	11.4393i	−0.214617	−	0.371727i	−0.953154	+	0.302486i	$0.902184\pi$
$948$	−13.0406	+	22.5869i	−0.423538	+	0.733590i
$949$	21.0619	−	36.4803i	0.683698	−	1.18420i
$950$	−6.95395	+	4.01487i	−0.225616	+	0.130260i
$951$		−	24.3571i		−	0.789832i
$952$	−0.680833	−	0.784319i	−0.0220659	−	0.0254199i
$953$			19.9131i			0.645050i	0.946561	+	0.322525i	$0.104532\pi$
$953$			19.9131i			0.645050i	−0.946561	+	0.322525i	$0.895468\pi$
$954$	−0.175088	+	0.101087i	−0.00566868	+	0.00327282i
$955$	2.69212	+	1.55429i	0.0871149	+	0.0502958i
$956$	10.5870	+	6.11238i	0.342407	+	0.197689i
$957$	7.09432	+	29.8567i	0.229327	+	0.965129i
$958$		−	7.15707i		−	0.231234i
$959$	−6.45025	+	5.59918i	−0.208290	+	0.180807i
$960$	−1.97709			−0.0638104
$961$	−14.8258	−	25.6790i	−0.478251	−	0.828355i
$962$	−8.60881	−	4.97030i	−0.277559	−	0.160249i
$963$	14.4037	+	8.31597i	0.464152	+	0.267978i
$964$	10.6348	+	18.4199i	0.342522	+	0.593266i
$965$	6.47721			0.208509
$966$	0.226393	+	1.16907i	0.00728406	+	0.0376141i
$967$		−	10.1831i		−	0.327466i	−0.986505	−	0.163733i	$-0.947646\pi$
$967$		−	10.1831i		−	0.327466i	0.986505	−	0.163733i	$-0.0523535\pi$
$968$	−17.4997	−	0.999023i	−0.562462	−	0.0321098i
$969$	−0.862229	−	0.497808i	−0.0276988	−	0.0159919i
$970$	1.41493	+	0.816909i	0.0454306	+	0.0262294i
$971$	−5.07550	+	2.93034i	−0.162881	+	0.0940392i	−0.579225	−	0.815168i	$-0.696645\pi$
$971$	−5.07550	+	2.93034i	−0.162881	+	0.0940392i	0.416344	+	0.909207i	$0.363311\pi$
$972$			1.82659i			0.0585880i
$973$	15.1789	+	5.23841i	0.486612	+	0.167936i
$974$		−	1.18312i		−	0.0379095i
$975$	−22.0702	+	12.7422i	−0.706811	+	0.408078i
$976$	7.98094	−	13.8234i	0.255464	−	0.442476i
$977$	10.4758	−	18.1445i	0.335149	−	0.580495i	−0.648364	−	0.761330i	$-0.724547\pi$
$977$	10.4758	−	18.1445i	0.335149	−	0.580495i	0.983513	+	0.180835i	$0.0578800\pi$
$978$	3.12354	+	5.41013i	0.0998798	+	0.172997i
$979$	−13.1397	+	43.9817i	−0.419946	+	1.40566i
$980$	−3.77176	+	4.81371i	−0.120485	+	0.153768i
$981$		−	6.33706i		−	0.202327i
$982$	5.72926	+	9.92337i	0.182828	+	0.316667i
$983$	−47.0795	−	27.1813i	−1.50160	−	0.866950i	−0.999998	−	0.00185231i	$-0.999410\pi$
$983$	−47.0795	−	27.1813i	−1.50160	−	0.866950i	−0.501603	−	0.865098i	$-0.667256\pi$
$984$	−7.25630	+	12.5683i	−0.231322	+	0.400662i
$985$	−4.04708	−	7.00974i	−0.128951	−	0.223349i
$986$	0.949201			0.0302287
$987$	19.6743	+	6.78985i	0.626241	+	0.216123i
$988$	−39.4296			−1.25442
$989$	−2.52597	+	1.45837i	−0.0803213	+	0.0463735i
$990$	0.480213	−	0.453580i	0.0152622	−	0.0144157i
$991$	4.35988	−	7.55154i	0.138496	−	0.239883i	−0.788431	−	0.615123i	$-0.789106\pi$
$991$	4.35988	−	7.55154i	0.138496	−	0.239883i	0.926928	+	0.375240i	$0.122440\pi$
$992$	−2.57321	−	4.45693i	−0.0816995	−	0.141508i
$993$		−	5.53239i		−	0.175565i
$994$	−12.9615	+	2.51003i	−0.411114	+	0.0796133i
$995$	−12.5367			−0.397441
$996$	−21.1106	+	12.1882i	−0.668916	+	0.386199i
$997$	−1.94647	+	3.37139i	−0.0616454	+	0.106773i	−0.895201	−	0.445663i	$-0.852968\pi$
$997$	−1.94647	+	3.37139i	−0.0616454	+	0.106773i	0.833556	+	0.552436i	$0.186301\pi$
$998$	5.99982	+	3.46400i	0.189921	+	0.109651i
$999$	−3.87051	+	2.23464i	−0.122457	+	0.0707008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.p.a.10.8	✓	32
3.2	odd	2		693.2.bg.b.10.9		32
7.3	odd	6		1617.2.c.a.538.15		32
7.4	even	3		1617.2.c.a.538.16		32
7.5	odd	6	inner	231.2.p.a.208.9	yes	32
11.10	odd	2	inner	231.2.p.a.10.9	yes	32
21.5	even	6		693.2.bg.b.208.8		32
33.32	even	2		693.2.bg.b.10.8		32
77.10	even	6		1617.2.c.a.538.17		32
77.32	odd	6		1617.2.c.a.538.18		32
77.54	even	6	inner	231.2.p.a.208.8	yes	32
231.131	odd	6		693.2.bg.b.208.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.8	✓	32	1.1	even	1	trivial
231.2.p.a.10.9	yes	32	11.10	odd	2	inner
231.2.p.a.208.8	yes	32	77.54	even	6	inner
231.2.p.a.208.9	yes	32	7.5	odd	6	inner
693.2.bg.b.10.8		32	33.32	even	2
693.2.bg.b.10.9		32	3.2	odd	2
693.2.bg.b.208.8		32	21.5	even	6
693.2.bg.b.208.9		32	231.131	odd	6
1617.2.c.a.538.15		32	7.3	odd	6
1617.2.c.a.538.16		32	7.4	even	3
1617.2.c.a.538.17		32	77.10	even	6
1617.2.c.a.538.18		32	77.32	odd	6

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.360631 + 0.208210i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.913297 + 1.58188i) q^{4} +(0.414204 - 0.239141i) q^{5} +0.416420 q^{6} +(-2.50100 - 0.863126i) q^{7} -1.59347i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.360631 + 0.208210i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.913297 + 1.58188i) q^{4} +(0.414204 - 0.239141i) q^{5} +0.416420 q^{6} +(-2.50100 - 0.863126i) q^{7} -1.59347i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0995832 + 0.172483i) q^{10} +(-2.41111 + 2.27739i) q^{11} +(1.58188 - 0.913297i) q^{12} -5.34126 q^{13} +(1.08165 - 0.209464i) q^{14} -0.478282 q^{15} +(-1.49482 - 2.58910i) q^{16} +(-0.123176 + 0.213346i) q^{17} +(-0.360631 - 0.208210i) q^{18} +(-2.02073 - 3.50000i) q^{19} +0.873627i q^{20} +(1.73437 + 1.99799i) q^{21} +(0.395345 - 1.32332i) q^{22} +(-0.540408 - 0.936015i) q^{23} +(-0.796736 + 1.37999i) q^{24} +(-2.38562 + 4.13202i) q^{25} +(1.92622 - 1.11210i) q^{26} -1.00000i q^{27} +(3.64952 - 3.16799i) q^{28} +9.25276i q^{29} +(0.172483 - 0.0995832i) q^{30} +(-1.00565 - 0.580613i) q^{31} +(3.83813 + 2.21594i) q^{32} +(3.22678 - 0.766724i) q^{33} -0.102586i q^{34} +(-1.24234 + 0.240582i) q^{35} -1.82659 q^{36} +(-2.23464 - 3.87051i) q^{37} +(1.45747 + 0.841471i) q^{38} +(4.62566 + 2.67063i) q^{39} +(-0.381064 - 0.660023i) q^{40} +9.10753 q^{41} +(-1.04147 - 0.359423i) q^{42} -2.69865i q^{43} +(-1.40049 - 5.89402i) q^{44} +(0.414204 + 0.239141i) q^{45} +(0.389776 + 0.225037i) q^{46} +(6.81265 - 3.93329i) q^{47} +2.98963i q^{48} +(5.51003 + 4.31736i) q^{49} -1.98684i q^{50} +(0.213346 - 0.123176i) q^{51} +(4.87815 - 8.44921i) q^{52} +(0.242753 - 0.420460i) q^{53} +(0.208210 + 0.360631i) q^{54} +(-0.454076 + 1.51990i) q^{55} +(-1.37537 + 3.98528i) q^{56} +4.04145i q^{57} +(-1.92652 - 3.33683i) q^{58} +(-0.959337 - 0.553874i) q^{59} +(0.436814 - 0.756583i) q^{60} +(2.66954 + 4.62377i) q^{61} +0.483558 q^{62} +(-0.503012 - 2.59749i) q^{63} +4.13374 q^{64} +(-2.21237 + 1.27731i) q^{65} +(-1.00404 + 0.948354i) q^{66} +(-1.52930 + 2.64883i) q^{67} +(-0.224992 - 0.389697i) q^{68} +1.08082i q^{69} +(0.397933 - 0.345428i) q^{70} -11.9831 q^{71} +(1.37999 - 0.796736i) q^{72} +(-3.94325 + 6.82991i) q^{73} +(1.61176 + 0.930549i) q^{74} +(4.13202 - 2.38562i) q^{75} +7.38209 q^{76} +(7.99588 - 3.61467i) q^{77} -2.22421 q^{78} +(-12.3656 + 7.13929i) q^{79} +(-1.23832 - 0.714944i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.28445 + 1.89628i) q^{82} -13.3453 q^{83} +(-4.74457 + 0.918798i) q^{84} +0.117825i q^{85} +(0.561886 + 0.973215i) q^{86} +(4.62638 - 8.01313i) q^{87} +(3.62896 + 3.84204i) q^{88} +(11.9859 - 6.92007i) q^{89} -0.199166 q^{90} +(13.3585 + 4.61018i) q^{91} +1.97421 q^{92} +(0.580613 + 1.00565i) q^{93} +(-1.63790 + 2.83693i) q^{94} +(-1.67399 - 0.966477i) q^{95} +(-2.21594 - 3.83813i) q^{96} -8.20328i q^{97} +(-2.88600 - 0.409730i) q^{98} +(-3.17784 - 0.949389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

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