LMFDB - Embedded newform 930.2.s.c.439.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.7
Character	$\chi$	$=$	930.439
Dual form			930.2.s.c.769.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-2.21961 - 0.270763i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.765960 - 0.442227i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-2.21961 - 0.270763i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.765960 - 0.442227i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.270763 - 2.21961i) q^{10} +(-1.13544 - 1.96663i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-3.52906 + 2.03750i) q^{13} +(0.442227 - 0.765960i) q^{14} +(-1.78686 - 1.34430i) q^{15} +1.00000 q^{16} +(1.77634 + 1.02557i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.64074 - 6.30594i) q^{19} +(2.21961 + 0.270763i) q^{20} +(-0.442227 - 0.765960i) q^{21} +(1.96663 - 1.13544i) q^{22} -7.05585i q^{23} +(0.500000 - 0.866025i) q^{24} +(4.85337 + 1.20198i) q^{25} +(-2.03750 - 3.52906i) q^{26} +1.00000i q^{27} +(0.765960 + 0.442227i) q^{28} -4.78086 q^{29} +(1.34430 - 1.78686i) q^{30} +(-0.177331 - 5.56494i) q^{31} +1.00000i q^{32} -2.27087i q^{33} +(-1.02557 + 1.77634i) q^{34} +(1.58040 + 1.18897i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.12189 - 1.22508i) q^{37} +(6.30594 + 3.64074i) q^{38} -4.07501 q^{39} +(-0.270763 + 2.21961i) q^{40} +(-3.43154 - 5.94360i) q^{41} +(0.765960 - 0.442227i) q^{42} +(4.69864 + 2.71276i) q^{43} +(1.13544 + 1.96663i) q^{44} +(-0.875319 - 2.05762i) q^{45} +7.05585 q^{46} -10.1666i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.10887 - 5.38472i) q^{49} +(-1.20198 + 4.85337i) q^{50} +(1.02557 + 1.77634i) q^{51} +(3.52906 - 2.03750i) q^{52} +(-5.20023 + 3.00236i) q^{53} -1.00000 q^{54} +(1.98774 + 4.67260i) q^{55} +(-0.442227 + 0.765960i) q^{56} +(6.30594 - 3.64074i) q^{57} -4.78086i q^{58} +(-7.14671 + 12.3785i) q^{59} +(1.78686 + 1.34430i) q^{60} +11.2736 q^{61} +(5.56494 - 0.177331i) q^{62} -0.884454i q^{63} -1.00000 q^{64} +(8.38484 - 3.56693i) q^{65} +2.27087 q^{66} +(9.40561 - 5.43033i) q^{67} +(-1.77634 - 1.02557i) q^{68} +(3.52792 - 6.11054i) q^{69} +(-1.18897 + 1.58040i) q^{70} +(-7.51690 - 13.0196i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-2.86777 + 1.65570i) q^{73} +(1.22508 - 2.12189i) q^{74} +(3.60216 + 3.46763i) q^{75} +(-3.64074 + 6.30594i) q^{76} +2.00848i q^{77} -4.07501i q^{78} +(-8.18988 + 14.1853i) q^{79} +(-2.21961 - 0.270763i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.94360 - 3.43154i) q^{82} +(-7.08339 + 4.08960i) q^{83} +(0.442227 + 0.765960i) q^{84} +(-3.66510 - 2.75733i) q^{85} +(-2.71276 + 4.69864i) q^{86} +(-4.14035 - 2.39043i) q^{87} +(-1.96663 + 1.13544i) q^{88} -11.8665 q^{89} +(2.05762 - 0.875319i) q^{90} +3.60416 q^{91} +7.05585i q^{92} +(2.62890 - 4.90804i) q^{93} +10.1666 q^{94} +(-9.78845 + 13.0110i) q^{95} +(-0.500000 + 0.866025i) q^{96} +14.8891i q^{97} +(5.38472 - 3.10887i) q^{98} +(1.13544 - 1.96663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9	$ 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) $ 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9 - 4 * q^11 + 12 * q^14 + 24 * q^16 - 4 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^24 - 4 * q^25 + 16 * q^26 + 32 * q^29 - 8 * q^30 + 24 * q^31 - 20 * q^34 + 48 * q^35 - 12 * q^36 + 32 * q^39 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 56 * q^46 + 24 * q^49 - 16 * q^50 + 20 * q^51 - 24 * q^54 + 36 * q^55 - 12 * q^56 - 4 * q^59 - 40 * q^61 - 24 * q^64 - 4 * q^65 + 8 * q^66 + 28 * q^69 - 32 * q^70 - 56 * q^71 + 12 * q^74 + 16 * q^75 + 4 * q^76 - 72 * q^79 + 4 * q^80 - 12 * q^81 + 12 * q^84 + 40 * q^85 - 24 * q^86 + 128 * q^89 - 160 * q^91 + 56 * q^94 - 56 * q^95 - 12 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.00000			−0.500000
$5$	−2.21961	−	0.270763i	−0.992642	−	0.121089i
$5$	−2.21961	−	0.270763i	−0.992642	−	0.121089i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.765960	−	0.442227i	−0.289506	−	0.167146i	0.348213	−	0.937415i	$-0.386789\pi$
$7$	−0.765960	−	0.442227i	−0.289506	−	0.167146i	−0.637719	+	0.770269i	$0.720122\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.270763	−	2.21961i	0.0856229	−	0.701904i
$11$	−1.13544	−	1.96663i	−0.342347	−	0.592962i	0.642521	−	0.766268i	$-0.277889\pi$
$11$	−1.13544	−	1.96663i	−0.342347	−	0.592962i	−0.984868	+	0.173306i	$0.944555\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−3.52906	+	2.03750i	−0.978785	+	0.565102i	−0.901903	−	0.431938i	$-0.857830\pi$
$13$	−3.52906	+	2.03750i	−0.978785	+	0.565102i	−0.0768822	+	0.997040i	$0.524497\pi$
$14$	0.442227	−	0.765960i	0.118190	−	0.204711i
$15$	−1.78686	−	1.34430i	−0.461365	−	0.347095i
$16$	1.00000			0.250000
$17$	1.77634	+	1.02557i	0.430825	+	0.248737i	0.699698	−	0.714439i	$-0.253318\pi$
$17$	1.77634	+	1.02557i	0.430825	+	0.248737i	−0.268873	+	0.963176i	$0.586651\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	3.64074	−	6.30594i	0.835242	−	1.44668i	−0.0585909	−	0.998282i	$-0.518661\pi$
$19$	3.64074	−	6.30594i	0.835242	−	1.44668i	0.893833	−	0.448400i	$-0.148006\pi$
$20$	2.21961	+	0.270763i	0.496321	+	0.0605445i
$21$	−0.442227	−	0.765960i	−0.0965019	−	0.167146i
$22$	1.96663	−	1.13544i	0.419288	−	0.242076i
$23$		−	7.05585i		−	1.47125i	−0.677391	−	0.735623i	$-0.736890\pi$
$23$		−	7.05585i		−	1.47125i	0.677391	−	0.735623i	$-0.263110\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.85337	+	1.20198i	0.970675	+	0.240396i
$26$	−2.03750	−	3.52906i	−0.399587	−	0.692106i
$27$			1.00000i			0.192450i
$28$	0.765960	+	0.442227i	0.144753	+	0.0835731i
$29$	−4.78086			−0.887784			−0.443892	−	0.896080i	$-0.646403\pi$
$29$	−4.78086			−0.887784			−0.443892	+	0.896080i	$0.646403\pi$
$30$	1.34430	−	1.78686i	0.245434	−	0.326235i
$31$	−0.177331	−	5.56494i	−0.0318496	−	0.999493i
$31$	−0.177331	−	5.56494i	−0.0318496	−	0.999493i
$32$			1.00000i			0.176777i
$33$		−	2.27087i		−	0.395308i
$34$	−1.02557	+	1.77634i	−0.175884	+	0.304639i
$35$	1.58040	+	1.18897i	0.267136	+	0.200972i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−2.12189	−	1.22508i	−0.348837	−	0.201401i	0.315336	−	0.948980i	$-0.397883\pi$
$37$	−2.12189	−	1.22508i	−0.348837	−	0.201401i	−0.664173	+	0.747579i	$0.731216\pi$
$38$	6.30594	+	3.64074i	1.02296	+	0.590605i
$39$	−4.07501			−0.652524
$40$	−0.270763	+	2.21961i	−0.0428114	+	0.350952i
$41$	−3.43154	−	5.94360i	−0.535916	−	0.928234i	−0.999118	−	0.0419817i	$-0.986633\pi$
$41$	−3.43154	−	5.94360i	−0.535916	−	0.928234i	0.463202	−	0.886253i	$-0.346700\pi$
$42$	0.765960	−	0.442227i	0.118190	−	0.0682371i
$43$	4.69864	+	2.71276i	0.716536	+	0.413692i	0.813476	−	0.581598i	$-0.197572\pi$
$43$	4.69864	+	2.71276i	0.716536	+	0.413692i	−0.0969403	+	0.995290i	$0.530906\pi$
$44$	1.13544	+	1.96663i	0.171173	+	0.296481i
$45$	−0.875319	−	2.05762i	−0.130485	−	0.306732i
$46$	7.05585			1.04033
$47$		−	10.1666i		−	1.48295i	−0.670980	−	0.741476i	$-0.734126\pi$
$47$		−	10.1666i		−	1.48295i	0.670980	−	0.741476i	$-0.265874\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−3.10887	−	5.38472i	−0.444124	−	0.769246i
$50$	−1.20198	+	4.85337i	−0.169986	+	0.686371i
$51$	1.02557	+	1.77634i	0.143608	+	0.248737i
$52$	3.52906	−	2.03750i	0.489393	−	0.282551i
$53$	−5.20023	+	3.00236i	−0.714307	+	0.412405i	−0.812654	−	0.582747i	$-0.801978\pi$
$53$	−5.20023	+	3.00236i	−0.714307	+	0.412405i	0.0983468	+	0.995152i	$0.468645\pi$
$54$	−1.00000			−0.136083
$55$	1.98774	+	4.67260i	0.268027	+	0.630054i
$56$	−0.442227	+	0.765960i	−0.0590951	+	0.102356i
$57$	6.30594	−	3.64074i	0.835242	−	0.482227i
$58$		−	4.78086i		−	0.627758i
$59$	−7.14671	+	12.3785i	−0.930423	+	1.61154i	−0.147824	+	0.989014i	$0.547227\pi$
$59$	−7.14671	+	12.3785i	−0.930423	+	1.61154i	−0.782599	+	0.622526i	$0.786107\pi$
$60$	1.78686	+	1.34430i	0.230683	+	0.173548i
$61$	11.2736			1.44344			0.721718	−	0.692188i	$-0.243353\pi$
$61$	11.2736			1.44344			0.721718	+	0.692188i	$0.243353\pi$
$62$	5.56494	−	0.177331i	0.706748	−	0.0225210i
$63$		−	0.884454i		−	0.111431i
$64$	−1.00000			−0.125000
$65$	8.38484	−	3.56693i	1.04001	−	0.442424i
$66$	2.27087			0.279525
$67$	9.40561	−	5.43033i	1.14908	−	0.663420i	0.200415	−	0.979711i	$-0.435771\pi$
$67$	9.40561	−	5.43033i	1.14908	−	0.663420i	0.948662	+	0.316291i	$0.102437\pi$
$68$	−1.77634	−	1.02557i	−0.215412	−	0.124368i
$69$	3.52792	−	6.11054i	0.424712	−	0.735623i
$70$	−1.18897	+	1.58040i	−0.142109	+	0.188894i
$71$	−7.51690	−	13.0196i	−0.892092	−	1.54515i	−0.837363	−	0.546647i	$-0.815904\pi$
$71$	−7.51690	−	13.0196i	−0.892092	−	1.54515i	−0.0547283	−	0.998501i	$-0.517429\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−2.86777	+	1.65570i	−0.335647	+	0.193786i	−0.658345	−	0.752716i	$-0.728743\pi$
$73$	−2.86777	+	1.65570i	−0.335647	+	0.193786i	0.322699	+	0.946502i	$0.395410\pi$
$74$	1.22508	−	2.12189i	0.142412	−	0.246665i
$75$	3.60216	+	3.46763i	0.415941	+	0.400408i
$76$	−3.64074	+	6.30594i	−0.417621	+	0.723341i
$77$			2.00848i			0.228888i
$78$		−	4.07501i		−	0.461404i
$79$	−8.18988	+	14.1853i	−0.921433	+	1.59597i	−0.124234	+	0.992253i	$0.539647\pi$
$79$	−8.18988	+	14.1853i	−0.921433	+	1.59597i	−0.797199	+	0.603716i	$0.793686\pi$
$80$	−2.21961	−	0.270763i	−0.248160	−	0.0302723i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.94360	−	3.43154i	0.656361	−	0.378950i
$83$	−7.08339	+	4.08960i	−0.777504	+	0.448892i	−0.835545	−	0.549422i	$-0.814848\pi$
$83$	−7.08339	+	4.08960i	−0.777504	+	0.448892i	0.0580412	+	0.998314i	$0.481515\pi$
$84$	0.442227	+	0.765960i	0.0482509	+	0.0835731i
$85$	−3.66510	−	2.75733i	−0.397535	−	0.299075i
$86$	−2.71276	+	4.69864i	−0.292525	+	0.506668i
$87$	−4.14035	−	2.39043i	−0.443892	−	0.256281i
$88$	−1.96663	+	1.13544i	−0.209644	+	0.121038i
$89$	−11.8665			−1.25784			−0.628922	−	0.777469i	$-0.716503\pi$
$89$	−11.8665			−1.25784			−0.628922	+	0.777469i	$0.716503\pi$
$90$	2.05762	−	0.875319i	0.216893	−	0.0922667i
$91$	3.60416			0.377819
$92$			7.05585i			0.735623i
$93$	2.62890	−	4.90804i	0.272604	−	0.508941i
$94$	10.1666			1.04861
$95$	−9.78845	+	13.0110i	−1.00427	+	1.33490i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			14.8891i			1.51176i	0.654713	+	0.755878i	$0.272790\pi$
$97$			14.8891i			1.51176i	−0.654713	+	0.755878i	$0.727210\pi$
$98$	5.38472	−	3.10887i	0.543939	−	0.314043i
$99$	1.13544	−	1.96663i	0.114116	−	0.197654i
$100$	−4.85337	−	1.20198i	−0.485337	−	0.120198i
$101$	9.93163			0.988235			0.494117	−	0.869395i	$-0.335491\pi$
$101$	9.93163			0.988235			0.494117	+	0.869395i	$0.335491\pi$
$102$	−1.77634	+	1.02557i	−0.175884	+	0.101546i
$103$	−9.61478	+	5.55110i	−0.947373	+	0.546966i	−0.892264	−	0.451514i	$-0.850884\pi$
$103$	−9.61478	+	5.55110i	−0.947373	+	0.546966i	−0.0551089	+	0.998480i	$0.517551\pi$
$104$	2.03750	+	3.52906i	0.199794	+	0.346053i
$105$	0.774180	+	1.81987i	0.0755522	+	0.177602i
$106$	−3.00236	−	5.20023i	−0.291615	−	0.505091i
$107$	3.50773	+	2.02519i	0.339105	+	0.195783i	0.659876	−	0.751374i	$-0.270609\pi$
$107$	3.50773	+	2.02519i	0.339105	+	0.195783i	−0.320771	+	0.947157i	$0.603942\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−0.293602			−0.0281220			−0.0140610	−	0.999901i	$-0.504476\pi$
$109$	−0.293602			−0.0281220			−0.0140610	+	0.999901i	$0.504476\pi$
$110$	−4.67260	+	1.98774i	−0.445515	+	0.189523i
$111$	−1.22508	−	2.12189i	−0.116279	−	0.201401i
$112$	−0.765960	−	0.442227i	−0.0723764	−	0.0417865i
$113$	10.9830	−	6.34103i	1.03319	−	0.596514i	0.115295	−	0.993331i	$-0.463219\pi$
$113$	10.9830	−	6.34103i	1.03319	−	0.596514i	0.917898	+	0.396817i	$0.129885\pi$
$114$	3.64074	+	6.30594i	0.340986	+	0.590605i
$115$	−1.91046	+	15.6613i	−0.178152	+	1.46042i
$116$	4.78086			0.443892
$117$	−3.52906	−	2.03750i	−0.326262	−	0.188367i
$118$	−12.3785	−	7.14671i	−1.13953	−	0.657908i
$119$	−0.907068	−	1.57109i	−0.0831508	−	0.144021i
$120$	−1.34430	+	1.78686i	−0.122717	+	0.163117i
$121$	2.92157	−	5.06030i	0.265597	−	0.460028i
$122$			11.2736i			1.02066i
$123$		−	6.86308i		−	0.618823i
$124$	0.177331	+	5.56494i	0.0159248	+	0.499746i
$125$	−10.4472	−	3.98205i	−0.934423	−	0.356165i
$126$	0.884454			0.0787935
$127$	−4.45894	−	2.57437i	−0.395667	−	0.228438i	0.288946	−	0.957346i	$-0.406695\pi$
$127$	−4.45894	−	2.57437i	−0.395667	−	0.228438i	−0.684613	+	0.728907i	$0.740029\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.71276	+	4.69864i	0.238845	+	0.413692i
$130$	3.56693	+	8.38484i	0.312841	+	0.735399i
$131$	4.99879	−	8.65816i	0.436746	−	0.756467i	−0.560690	−	0.828026i	$-0.689464\pi$
$131$	4.99879	−	8.65816i	0.436746	−	0.756467i	0.997436	+	0.0715589i	$0.0227974\pi$
$132$			2.27087i			0.197654i
$133$	−5.57732	+	3.22007i	−0.483615	+	0.279215i
$134$	5.43033	+	9.40561i	0.469109	+	0.812521i
$135$	0.270763	−	2.21961i	0.0233036	−	0.191034i
$136$	1.02557	−	1.77634i	0.0879418	−	0.152320i
$137$	−15.8965	+	9.17786i	−1.35813	+	0.784118i	−0.989372	−	0.145407i	$-0.953551\pi$
$137$	−15.8965	+	9.17786i	−1.35813	+	0.784118i	−0.368760	+	0.929525i	$0.620218\pi$
$138$	6.11054	+	3.52792i	0.520164	+	0.300317i
$139$	18.5039			1.56948			0.784741	−	0.619824i	$-0.212796\pi$
$139$	18.5039			1.56948			0.784741	+	0.619824i	$0.212796\pi$
$140$	−1.58040	−	1.18897i	−0.133568	−	0.100486i
$141$	5.08330	−	8.80454i	0.428091	−	0.741476i
$142$	13.0196	−	7.51690i	1.09258	−	0.630804i
$143$	8.01405	+	4.62691i	0.670169	+	0.386922i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	10.6117	+	1.29448i	0.881251	+	0.107501i
$146$	−1.65570	−	2.86777i	−0.137027	−	0.237338i
$147$		−	6.21774i		−	0.512831i
$148$	2.12189	+	1.22508i	0.174419	+	0.100701i
$149$	5.36747	−	9.29673i	0.439720	−	0.761618i	−0.557947	−	0.829876i	$-0.688411\pi$
$149$	5.36747	−	9.29673i	0.439720	−	0.761618i	0.997668	+	0.0682586i	$0.0217443\pi$
$150$	−3.46763	+	3.60216i	−0.283131	+	0.294115i
$151$	8.89641			0.723979			0.361990	−	0.932182i	$-0.382098\pi$
$151$	8.89641			0.723979			0.361990	+	0.932182i	$0.382098\pi$
$152$	−6.30594	−	3.64074i	−0.511479	−	0.295303i
$153$			2.05114i			0.165825i
$154$	−2.00848			−0.161848
$155$	−1.11318	+	12.4000i	−0.0894124	+	0.995995i
$156$	4.07501			0.326262
$157$		−	12.7875i		−	1.02055i	−0.860011	−	0.510276i	$-0.829543\pi$
$157$		−	12.7875i		−	1.02055i	0.860011	−	0.510276i	$-0.170457\pi$
$158$	−14.1853	−	8.18988i	−1.12852	−	0.651552i
$159$	−6.00471			−0.476205
$160$	0.270763	−	2.21961i	0.0214057	−	0.175476i
$161$	−3.12029	+	5.40450i	−0.245913	+	0.425934i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$		−	2.59288i		−	0.203090i	−0.994831	−	0.101545i	$-0.967621\pi$
$163$		−	2.59288i		−	0.203090i	0.994831	−	0.101545i	$-0.0323786\pi$
$164$	3.43154	+	5.94360i	0.267958	+	0.464117i
$165$	−0.614869	+	5.04046i	−0.0478675	+	0.392399i
$166$	−4.08960	−	7.08339i	−0.317415	−	0.549778i
$167$	−16.5678	−	9.56543i	−1.28206	−	0.740195i	−0.304832	−	0.952406i	$-0.598600\pi$
$167$	−16.5678	−	9.56543i	−1.28206	−	0.740195i	−0.977224	+	0.212211i	$0.931934\pi$
$168$	−0.765960	+	0.442227i	−0.0590951	+	0.0341186i
$169$	1.80285	−	3.12262i	0.138681	−	0.240202i
$170$	2.75733	−	3.66510i	0.211478	−	0.281100i
$171$	7.28147			0.556828
$172$	−4.69864	−	2.71276i	−0.358268	−	0.206846i
$173$	−11.9167	+	6.88013i	−0.906013	+	0.523087i	−0.879146	−	0.476552i	$-0.841886\pi$
$173$	−11.9167	+	6.88013i	−0.906013	+	0.523087i	−0.0268669	+	0.999639i	$0.508553\pi$
$174$	2.39043	−	4.14035i	0.181218	−	0.313879i
$175$	−3.18594	−	3.06696i	−0.240835	−	0.231841i
$176$	−1.13544	−	1.96663i	−0.0855867	−	0.148241i
$177$	−12.3785	+	7.14671i	−0.930423	+	0.537180i
$178$		−	11.8665i		−	0.889430i
$179$	−0.651424	+	1.12830i	−0.0486897	+	0.0843331i	−0.889343	−	0.457240i	$-0.848838\pi$
$179$	−0.651424	+	1.12830i	−0.0486897	+	0.0843331i	0.840653	+	0.541574i	$0.182171\pi$
$180$	0.875319	+	2.05762i	0.0652424	+	0.153366i
$181$	−1.03683	−	1.79584i	−0.0770668	−	0.133484i	0.824916	−	0.565255i	$-0.191222\pi$
$181$	−1.03683	−	1.79584i	−0.0770668	−	0.133484i	−0.901983	+	0.431771i	$0.857889\pi$
$182$			3.60416i			0.267158i
$183$	9.76321	+	5.63679i	0.721718	+	0.416684i
$184$	−7.05585			−0.520164
$185$	4.37808	+	3.29373i	0.321883	+	0.242160i
$186$	4.90804	+	2.62890i	0.359875	+	0.192760i
$187$		−	4.65787i		−	0.340617i
$188$			10.1666i			0.741476i
$189$	0.442227	−	0.765960i	0.0321673	−	0.0557154i
$190$	−13.0110	−	9.78845i	−0.943915	−	0.710129i
$191$	10.6926	+	18.5202i	0.773692	+	1.34007i	0.935527	+	0.353257i	$0.114926\pi$
$191$	10.6926	+	18.5202i	0.773692	+	1.34007i	−0.161834	+	0.986818i	$0.551741\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−22.0101	−	12.7075i	−1.58432	−	0.914707i	−0.994218	−	0.107378i	$-0.965754\pi$
$193$	−22.0101	−	12.7075i	−1.58432	−	0.914707i	−0.590102	−	0.807329i	$-0.700912\pi$
$194$	−14.8891			−1.06897
$195$	9.04495	+	1.10336i	0.647722	+	0.0790135i
$196$	3.10887	+	5.38472i	0.222062	+	0.384623i
$197$	2.57038	−	1.48401i	0.183132	−	0.105732i	−0.405631	−	0.914037i	$-0.632948\pi$
$197$	2.57038	−	1.48401i	0.183132	−	0.105732i	0.588764	+	0.808305i	$0.299615\pi$
$198$	1.96663	+	1.13544i	0.139763	+	0.0806920i
$199$	−0.142781	−	0.247303i	−0.0101215	−	0.0175309i	0.860920	−	0.508740i	$-0.169888\pi$
$199$	−0.142781	−	0.247303i	−0.0101215	−	0.0175309i	−0.871042	+	0.491209i	$0.836555\pi$
$200$	1.20198	−	4.85337i	0.0849928	−	0.343185i
$201$	10.8607			0.766052
$202$			9.93163i			0.698787i
$203$	3.66195	+	2.11423i	0.257018	+	0.148390i
$204$	−1.02557	−	1.77634i	−0.0718041	−	0.124368i
$205$	6.00738	+	14.1216i	0.419574	+	0.986298i
$206$	−5.55110	−	9.61478i	−0.386763	−	0.669894i
$207$	6.11054	−	3.52792i	0.424712	−	0.245208i
$208$	−3.52906	+	2.03750i	−0.244696	+	0.141276i
$209$	−16.5353			−1.14377
$210$	−1.81987	+	0.774180i	−0.125583	+	0.0534235i
$211$	−1.43360	+	2.48306i	−0.0986928	+	0.170941i	−0.911144	−	0.412089i	$-0.864799\pi$
$211$	−1.43360	+	2.48306i	−0.0986928	+	0.170941i	0.812451	+	0.583029i	$0.198133\pi$
$212$	5.20023	−	3.00236i	0.357153	−	0.206203i
$213$		−	15.0338i		−	1.03010i
$214$	−2.02519	+	3.50773i	−0.138439	+	0.239784i
$215$	−9.69465	−	7.29350i	−0.661170	−	0.497413i
$216$	1.00000			0.0680414
$217$	−2.32514	+	4.34094i	−0.157841	+	0.294682i
$218$		−	0.293602i		−	0.0198853i
$219$	−3.31141			−0.223764
$220$	−1.98774	−	4.67260i	−0.134013	−	0.315027i
$221$	−8.35840			−0.562247
$222$	2.12189	−	1.22508i	0.142412	−	0.0822217i
$223$	7.89299	+	4.55702i	0.528553	+	0.305160i	0.740427	−	0.672137i	$-0.234623\pi$
$223$	7.89299	+	4.55702i	0.528553	+	0.305160i	−0.211874	+	0.977297i	$0.567957\pi$
$224$	0.442227	−	0.765960i	0.0295475	−	0.0511779i
$225$	1.38574	+	4.80414i	0.0923828	+	0.320276i
$226$	6.34103	+	10.9830i	0.421799	+	0.730577i
$227$	−12.9755	+	7.49141i	−0.861214	+	0.497222i	−0.864419	−	0.502773i	$-0.832313\pi$
$227$	−12.9755	+	7.49141i	−0.861214	+	0.497222i	0.00320461	+	0.999995i	$0.498980\pi$
$228$	−6.30594	+	3.64074i	−0.417621	+	0.241114i
$229$	1.25666	−	2.17660i	0.0830424	−	0.143834i	−0.821513	−	0.570190i	$-0.806870\pi$
$229$	1.25666	−	2.17660i	0.0830424	−	0.143834i	0.904555	+	0.426356i	$0.140203\pi$
$230$	−15.6613	−	1.91046i	−1.03267	−	0.125972i
$231$	−1.00424	+	1.73940i	−0.0660743	+	0.114444i
$232$			4.78086i			0.313879i
$233$			16.7264i			1.09578i	0.836550	+	0.547891i	$0.184569\pi$
$233$			16.7264i			1.09578i	−0.836550	+	0.547891i	$0.815431\pi$
$234$	2.03750	−	3.52906i	0.133196	−	0.230702i
$235$	−2.75274	+	22.5659i	−0.179569	+	1.47204i
$236$	7.14671	−	12.3785i	0.465211	−	0.805770i
$237$	−14.1853	+	8.18988i	−0.921433	+	0.531990i
$238$	1.57109	−	0.907068i	0.101839	−	0.0587965i
$239$	−0.373086	−	0.646204i	−0.0241329	−	0.0417995i	0.853707	−	0.520754i	$-0.174349\pi$
$239$	−0.373086	−	0.646204i	−0.0241329	−	0.0417995i	−0.877840	+	0.478955i	$0.841016\pi$
$240$	−1.78686	−	1.34430i	−0.115341	−	0.0867739i
$241$	8.72913	−	15.1193i	0.562292	−	0.973919i	−0.435003	−	0.900429i	$-0.643253\pi$
$241$	8.72913	−	15.1193i	0.562292	−	0.973919i	0.997296	−	0.0734904i	$-0.0234138\pi$
$242$	5.06030	+	2.92157i	0.325289	+	0.187805i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−11.2736			−0.721718
$245$	5.44251	+	12.7938i	0.347709	+	0.817364i
$246$	6.86308			0.437574
$247$			29.6721i			1.88799i
$248$	−5.56494	+	0.177331i	−0.353374	+	0.0112605i
$249$	−8.17920			−0.518336
$250$	3.98205	−	10.4472i	0.251847	−	0.660737i
$251$	6.85998	−	11.8818i	0.432998	−	0.749975i	−0.564132	−	0.825685i	$-0.690789\pi$
$251$	6.85998	−	11.8818i	0.432998	−	0.749975i	0.997130	+	0.0757099i	$0.0241223\pi$
$252$			0.884454i			0.0557154i
$253$	−13.8763	+	8.01147i	−0.872393	+	0.503677i
$254$	2.57437	−	4.45894i	0.161530	−	0.279779i
$255$	−1.79540	−	4.22047i	−0.112432	−	0.264296i
$256$	1.00000			0.0625000
$257$	−3.05748	+	1.76523i	−0.190720	+	0.110112i	−0.592320	−	0.805703i	$-0.701788\pi$
$257$	−3.05748	+	1.76523i	−0.190720	+	0.110112i	0.401600	+	0.915815i	$0.368454\pi$
$258$	−4.69864	+	2.71276i	−0.292525	+	0.168889i
$259$	1.08352	+	1.87672i	0.0673269	+	0.116614i
$260$	−8.38484	+	3.56693i	−0.520005	+	0.221212i
$261$	−2.39043	−	4.14035i	−0.147964	−	0.256281i
$262$	8.65816	+	4.99879i	0.534903	+	0.308826i
$263$		−	23.9867i		−	1.47908i	−0.673112	−	0.739541i	$-0.735043\pi$
$263$		−	23.9867i		−	1.47908i	0.673112	−	0.739541i	$-0.264957\pi$
$264$	−2.27087			−0.139763
$265$	12.3554	−	5.25604i	0.758988	−	0.322876i
$266$	−3.22007	−	5.57732i	−0.197435	−	0.341967i
$267$	−10.2767	−	5.93324i	−0.628922	−	0.363108i
$268$	−9.40561	+	5.43033i	−0.574539	+	0.331710i
$269$	2.84467	+	4.92712i	0.173443	+	0.300412i	0.939621	−	0.342216i	$-0.111178\pi$
$269$	2.84467	+	4.92712i	0.173443	+	0.300412i	−0.766179	+	0.642628i	$0.777844\pi$
$270$	2.21961	+	0.270763i	0.135081	+	0.0164781i
$271$	−9.25028			−0.561914			−0.280957	−	0.959720i	$-0.590652\pi$
$271$	−9.25028			−0.561914			−0.280957	+	0.959720i	$0.590652\pi$
$272$	1.77634	+	1.02557i	0.107706	+	0.0621842i
$273$	3.12129	+	1.80208i	0.188909	+	0.109067i
$274$	−9.17786	−	15.8965i	−0.554455	−	0.960344i
$275$	−3.14684	−	10.9096i	−0.189762	−	0.657873i
$276$	−3.52792	+	6.11054i	−0.212356	+	0.367811i
$277$		−	11.8505i		−	0.712027i	−0.934481	−	0.356013i	$-0.884136\pi$
$277$		−	11.8505i		−	0.712027i	0.934481	−	0.356013i	$-0.115864\pi$
$278$			18.5039i			1.10979i
$279$	4.73071	−	2.93604i	0.283220	−	0.175776i
$280$	1.18897	−	1.58040i	0.0710544	−	0.0944468i
$281$	21.3731			1.27501			0.637505	−	0.770446i	$-0.279966\pi$
$281$	21.3731			1.27501			0.637505	+	0.770446i	$0.279966\pi$
$282$	8.80454	+	5.08330i	0.524303	+	0.302706i
$283$		−	1.07303i		−	0.0637852i	−0.999491	−	0.0318926i	$-0.989847\pi$
$283$		−	1.07303i		−	0.0637852i	0.999491	−	0.0318926i	$-0.0101534\pi$
$284$	7.51690	+	13.0196i	0.446046	+	0.772574i
$285$	−14.9825	+	6.37361i	−0.887489	+	0.377540i
$286$	−4.62691	+	8.01405i	−0.273595	+	0.473881i
$287$			6.07008i			0.358305i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−6.39642	−	11.0789i	−0.376260	−	0.651701i
$290$	−1.29448	+	10.6117i	−0.0760146	+	0.623139i
$291$	−7.44453	+	12.8943i	−0.436406	+	0.755878i
$292$	2.86777	−	1.65570i	0.167823	−	0.0968928i
$293$	15.5005	+	8.94922i	0.905549	+	0.522819i	0.878996	−	0.476828i	$-0.158214\pi$
$293$	15.5005	+	8.94922i	0.905549	+	0.522819i	0.0265529	+	0.999647i	$0.491547\pi$
$294$	6.21774			0.362626
$295$	19.2146	−	25.5404i	1.11872	−	1.48702i
$296$	−1.22508	+	2.12189i	−0.0712061	+	0.123333i
$297$	1.96663	−	1.13544i	0.114116	−	0.0658847i
$298$	9.29673	+	5.36747i	0.538545	+	0.310929i
$299$	14.3763	+	24.9005i	0.831404	+	1.44003i
$300$	−3.60216	−	3.46763i	−0.207971	−	0.200204i
$301$	−2.39931	−	4.15573i	−0.138294	−	0.239533i
$302$			8.89641i			0.511931i
$303$	8.60105	+	4.96582i	0.494117	+	0.285279i
$304$	3.64074	−	6.30594i	0.208811	−	0.361670i
$305$	−25.0230	−	3.05247i	−1.43281	−	0.174784i
$306$	−2.05114			−0.117256
$307$	−0.351516	−	0.202948i	−0.0200621	−	0.0115829i	0.489935	−	0.871759i	$-0.337020\pi$
$307$	−0.351516	−	0.202948i	−0.0200621	−	0.0115829i	−0.509998	+	0.860176i	$0.670354\pi$
$308$		−	2.00848i		−	0.114444i
$309$	−11.1022			−0.631582
$310$	−12.4000	−	1.11318i	−0.704275	−	0.0632241i
$311$	−20.8407			−1.18177			−0.590885	−	0.806756i	$-0.701221\pi$
$311$	−20.8407			−1.18177			−0.590885	+	0.806756i	$0.701221\pi$
$312$			4.07501i			0.230702i
$313$	−8.42126	−	4.86202i	−0.475998	−	0.274817i	0.242749	−	0.970089i	$-0.421951\pi$
$313$	−8.42126	−	4.86202i	−0.475998	−	0.274817i	−0.718747	+	0.695272i	$0.755284\pi$
$314$	12.7875			0.721639
$315$	−0.239478	+	1.96315i	−0.0134930	+	0.110611i
$316$	8.18988	−	14.1853i	0.460717	−	0.797985i
$317$	9.07485	+	5.23937i	0.509694	+	0.294272i	0.732708	−	0.680543i	$-0.238256\pi$
$317$	9.07485	+	5.23937i	0.509694	+	0.294272i	−0.223014	+	0.974815i	$0.571589\pi$
$318$		−	6.00471i		−	0.336727i
$319$	5.42837	+	9.40220i	0.303930	+	0.526422i
$320$	2.21961	+	0.270763i	0.124080	+	0.0151361i
$321$	2.02519	+	3.50773i	0.113035	+	0.195783i
$322$	−5.40450	−	3.12029i	−0.301181	−	0.173887i
$323$	12.9343	−	7.46765i	0.719686	−	0.415511i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−19.5769	+	5.64691i	−1.08593	+	0.313234i
$326$	2.59288			0.143606
$327$	−0.254267	−	0.146801i	−0.0140610	−	0.00811812i
$328$	−5.94360	+	3.43154i	−0.328180	+	0.189475i
$329$	−4.49595	+	7.78721i	−0.247870	+	0.429323i
$330$	−5.04046	−	0.614869i	−0.277468	−	0.0338474i
$331$	10.2399	+	17.7361i	0.562837	+	0.974863i	0.997247	+	0.0741478i	$0.0236236\pi$
$331$	10.2399	+	17.7361i	0.562837	+	0.974863i	−0.434410	+	0.900715i	$0.643043\pi$
$332$	7.08339	−	4.08960i	0.388752	−	0.224446i
$333$		−	2.45015i		−	0.134267i
$334$	9.56543	−	16.5678i	0.523397	−	0.906550i
$335$	−22.3472	+	9.50654i	−1.22096	+	0.519398i
$336$	−0.442227	−	0.765960i	−0.0241255	−	0.0417865i
$337$		−	26.4138i		−	1.43885i	−0.694569	−	0.719426i	$-0.744405\pi$
$337$		−	26.4138i		−	1.43885i	0.694569	−	0.719426i	$-0.255595\pi$
$338$	3.12262	+	1.80285i	0.169848	+	0.0980620i
$339$	12.6821			0.688795
$340$	3.66510	+	2.75733i	0.198768	+	0.149537i
$341$	−10.7429	+	6.66738i	−0.581758	+	0.361059i
$342$			7.28147i			0.393737i
$343$			11.6905i			0.631227i
$344$	2.71276	−	4.69864i	0.146262	−	0.253334i
$345$	−9.48514	+	12.6078i	−0.510663	+	0.678782i
$346$	−6.88013	−	11.9167i	−0.369878	−	0.640648i
$347$	13.8352	+	7.98778i	0.742714	+	0.428806i	0.823055	−	0.567961i	$-0.192268\pi$
$347$	13.8352	+	7.98778i	0.742714	+	0.428806i	−0.0803410	+	0.996767i	$0.525601\pi$
$348$	4.14035	+	2.39043i	0.221946	+	0.128141i
$349$	−15.3856			−0.823570			−0.411785	−	0.911281i	$-0.635095\pi$
$349$	−15.3856			−0.823570			−0.411785	+	0.911281i	$0.635095\pi$
$350$	3.06696	−	3.18594i	0.163936	−	0.170296i
$351$	−2.03750	−	3.52906i	−0.108754	−	0.188367i
$352$	1.96663	−	1.13544i	0.104822	−	0.0605190i
$353$	−6.64918	−	3.83891i	−0.353900	−	0.204324i	0.312501	−	0.949917i	$-0.398833\pi$
$353$	−6.64918	−	3.83891i	−0.353900	−	0.204324i	−0.666402	+	0.745593i	$0.732166\pi$
$354$	−7.14671	−	12.3785i	−0.379844	−	0.657908i
$355$	13.1594	+	30.9339i	0.698427	+	1.64180i
$356$	11.8665			0.628922
$357$		−	1.81414i		−	0.0960143i
$358$	−1.12830	−	0.651424i	−0.0596325	−	0.0344288i
$359$	8.19127	+	14.1877i	0.432319	+	0.748798i	0.997073	−	0.0764612i	$-0.0243621\pi$
$359$	8.19127	+	14.1877i	0.432319	+	0.748798i	−0.564754	+	0.825260i	$0.691029\pi$
$360$	−2.05762	+	0.875319i	−0.108446	+	0.0461334i
$361$	−17.0099	−	29.4621i	−0.895259	−	1.55063i
$362$	1.79584	−	1.03683i	0.0943871	−	0.0544944i
$363$	5.06030	−	2.92157i	0.265597	−	0.153343i
$364$	−3.60416			−0.188909
$365$	6.81364	−	2.89854i	0.356642	−	0.151717i
$366$	−5.63679	+	9.76321i	−0.294640	+	0.510331i
$367$	25.3805	−	14.6534i	1.32485	−	0.764903i	0.340353	−	0.940298i	$-0.389453\pi$
$367$	25.3805	−	14.6534i	1.32485	−	0.764903i	0.984498	+	0.175394i	$0.0561200\pi$
$368$		−	7.05585i		−	0.367811i
$369$	3.43154	−	5.94360i	0.178639	−	0.309411i
$370$	−3.29373	+	4.37808i	−0.171233	+	0.227605i
$371$	5.31089			0.275728
$372$	−2.62890	+	4.90804i	−0.136302	+	0.254470i
$373$			8.07447i			0.418080i	0.977907	+	0.209040i	$0.0670339\pi$
$373$			8.07447i			0.418080i	−0.977907	+	0.209040i	$0.932966\pi$
$374$	4.65787			0.240853
$375$	−7.05649	−	8.67214i	−0.364395	−	0.447827i
$376$	−10.1666			−0.524303
$377$	16.8720	−	9.74103i	0.868950	−	0.501688i
$378$	0.765960	+	0.442227i	0.0393967	+	0.0227457i
$379$	−0.0607779	+	0.105270i	−0.00312195	+	0.00540738i	−0.867582	−	0.497294i	$-0.834327\pi$
$379$	−0.0607779	+	0.105270i	−0.00312195	+	0.00540738i	0.864460	+	0.502701i	$0.167660\pi$
$380$	9.78845	−	13.0110i	0.502137	−	0.667449i
$381$	−2.57437	−	4.45894i	−0.131889	−	0.228438i
$382$	−18.5202	+	10.6926i	−0.947576	+	0.547083i
$383$	3.56168	−	2.05634i	0.181993	−	0.105074i	−0.406236	−	0.913768i	$-0.633159\pi$
$383$	3.56168	−	2.05634i	0.181993	−	0.105074i	0.588229	+	0.808694i	$0.299825\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	0.543824	−	4.45806i	0.0277158	−	0.227204i
$386$	12.7075	−	22.0101i	0.646796	−	1.12028i
$387$			5.42552i			0.275795i
$388$		−	14.8891i		−	0.755878i
$389$	3.49182	−	6.04800i	0.177042	−	0.306646i	−0.763824	−	0.645425i	$-0.776680\pi$
$389$	3.49182	−	6.04800i	0.177042	−	0.306646i	0.940866	+	0.338779i	$0.110014\pi$
$390$	−1.10336	+	9.04495i	−0.0558710	+	0.458009i
$391$	7.23625	−	12.5336i	0.365953	−	0.633849i
$392$	−5.38472	+	3.10887i	−0.271969	+	0.157022i
$393$	8.65816	−	4.99879i	0.436746	−	0.252156i
$394$	1.48401	+	2.57038i	0.0747635	+	0.129494i
$395$	22.0192	−	29.2683i	1.10791	−	1.47265i
$396$	−1.13544	+	1.96663i	−0.0570578	+	0.0988271i
$397$	−3.30888	−	1.91038i	−0.166068	−	0.0958794i	0.414663	−	0.909975i	$-0.363900\pi$
$397$	−3.30888	−	1.91038i	−0.166068	−	0.0958794i	−0.580730	+	0.814096i	$0.697233\pi$
$398$	0.247303	−	0.142781i	0.0123962	−	0.00715695i
$399$	−6.44013			−0.322410
$400$	4.85337	+	1.20198i	0.242669	+	0.0600990i
$401$	7.44481			0.371776			0.185888	−	0.982571i	$-0.440484\pi$
$401$	7.44481			0.371776			0.185888	+	0.982571i	$0.440484\pi$
$402$			10.8607i			0.541680i
$403$	11.9644	+	19.2777i	0.595989	+	0.960291i
$404$	−9.93163			−0.494117
$405$	1.34430	−	1.78686i	0.0667986	−	0.0887898i
$406$	−2.11423	+	3.66195i	−0.104927	+	0.181739i
$407$			5.56398i			0.275796i
$408$	1.77634	−	1.02557i	0.0879418	−	0.0507732i
$409$	−12.0054	+	20.7939i	−0.593627	+	1.02819i	0.400112	+	0.916466i	$0.368971\pi$
$409$	−12.0054	+	20.7939i	−0.593627	+	1.02819i	−0.993739	+	0.111725i	$0.964362\pi$
$410$	−14.1216	+	6.00738i	−0.697418	+	0.296684i
$411$	−18.3557			−0.905421
$412$	9.61478	−	5.55110i	0.473686	−	0.273483i
$413$	10.9482	−	6.32094i	0.538725	−	0.311033i
$414$	3.52792	+	6.11054i	0.173388	+	0.300317i
$415$	16.8297	−	7.15941i	0.826138	−	0.351442i
$416$	−2.03750	−	3.52906i	−0.0998969	−	0.173026i
$417$	16.0249	+	9.25196i	0.784741	+	0.453071i
$418$		−	16.5353i		−	0.808768i
$419$	−7.09447			−0.346587			−0.173294	−	0.984870i	$-0.555441\pi$
$419$	−7.09447			−0.346587			−0.173294	+	0.984870i	$0.555441\pi$
$420$	−0.774180	−	1.81987i	−0.0377761	−	0.0888008i
$421$	6.96292	+	12.0601i	0.339352	+	0.587774i	0.984311	−	0.176443i	$-0.0564590\pi$
$421$	6.96292	+	12.0601i	0.339352	+	0.587774i	−0.644959	+	0.764217i	$0.723126\pi$
$422$	−2.48306	−	1.43360i	−0.120873	−	0.0697863i
$423$	8.80454	−	5.08330i	0.428091	−	0.247159i
$424$	3.00236	+	5.20023i	0.145807	+	0.252546i
$425$	7.38851	+	7.11259i	0.358396	+	0.345011i
$426$	15.0338			0.728390
$427$	−8.63512	−	4.98549i	−0.417883	−	0.241265i
$428$	−3.50773	−	2.02519i	−0.169553	−	0.0978913i
$429$	4.62691	+	8.01405i	0.223390	+	0.386922i
$430$	7.29350	−	9.69465i	0.351724	−	0.467518i
$431$	14.6790	−	25.4248i	0.707063	−	1.22467i	−0.258879	−	0.965910i	$-0.583353\pi$
$431$	14.6790	−	25.4248i	0.707063	−	1.22467i	0.965942	−	0.258759i	$-0.0833136\pi$
$432$			1.00000i			0.0481125i
$433$		−	3.39656i		−	0.163228i	−0.996664	−	0.0816141i	$-0.973992\pi$
$433$		−	3.39656i		−	0.163228i	0.996664	−	0.0816141i	$-0.0260075\pi$
$434$	−4.34094	−	2.32514i	−0.208372	−	0.111610i
$435$	8.54273	+	6.42689i	0.409593	+	0.308146i
$436$	0.293602			0.0140610
$437$	−44.4938	−	25.6885i	−2.12842	−	1.22885i
$438$		−	3.31141i		−	0.158225i
$439$	15.7211	+	27.2298i	0.750328	+	1.29961i	0.947664	+	0.319270i	$0.103438\pi$
$439$	15.7211	+	27.2298i	0.750328	+	1.29961i	−0.197336	+	0.980336i	$0.563229\pi$
$440$	4.67260	−	1.98774i	0.222758	−	0.0947617i
$441$	3.10887	−	5.38472i	0.148041	−	0.256415i
$442$		−	8.35840i		−	0.397569i
$443$	31.4657	−	18.1668i	1.49498	−	0.863129i	0.494999	−	0.868893i	$-0.335168\pi$
$443$	31.4657	−	18.1668i	1.49498	−	0.863129i	0.999983	+	0.00576451i	$0.00183491\pi$
$444$	1.22508	+	2.12189i	0.0581395	+	0.100701i
$445$	26.3390	+	3.21300i	1.24859	+	0.152311i
$446$	−4.55702	+	7.89299i	−0.215781	+	0.373744i
$447$	9.29673	−	5.36747i	0.439720	−	0.253873i
$448$	0.765960	+	0.442227i	0.0361882	+	0.0208933i
$449$	38.6289			1.82301			0.911505	−	0.411289i	$-0.134921\pi$
$449$	38.6289			1.82301			0.911505	+	0.411289i	$0.134921\pi$
$450$	−4.80414	+	1.38574i	−0.226469	+	0.0653245i
$451$	−7.79259	+	13.4972i	−0.366939	+	0.635557i
$452$	−10.9830	+	6.34103i	−0.516596	+	0.298257i
$453$	7.70452	+	4.44820i	0.361990	+	0.208995i
$454$	−7.49141	−	12.9755i	−0.351589	−	0.608970i
$455$	−7.99984	−	0.975874i	−0.375038	−	0.0457497i
$456$	−3.64074	−	6.30594i	−0.170493	−	0.295303i
$457$		−	21.0166i		−	0.983117i	−0.870844	−	0.491559i	$-0.836427\pi$
$457$		−	21.0166i		−	0.983117i	0.870844	−	0.491559i	$-0.163573\pi$
$458$	2.17660	+	1.25666i	0.101706	+	0.0587198i
$459$	−1.02557	+	1.77634i	−0.0478694	+	0.0829123i
$460$	1.91046	−	15.6613i	0.0890759	−	0.730210i
$461$	−8.71999			−0.406130			−0.203065	−	0.979165i	$-0.565090\pi$
$461$	−8.71999			−0.406130			−0.203065	+	0.979165i	$0.565090\pi$
$462$	−1.73940	−	1.00424i	−0.0809241	−	0.0467216i
$463$			35.8033i			1.66392i	0.554835	+	0.831961i	$0.312782\pi$
$463$			35.8033i			1.66392i	−0.554835	+	0.831961i	$0.687218\pi$
$464$	−4.78086			−0.221946
$465$	−7.16406	+	10.1822i	−0.332225	+	0.472186i
$466$	−16.7264			−0.774834
$467$		−	32.7979i		−	1.51770i	−0.651263	−	0.758852i	$-0.725760\pi$
$467$		−	32.7979i		−	1.51770i	0.651263	−	0.758852i	$-0.274240\pi$
$468$	3.52906	+	2.03750i	0.163131	+	0.0941837i
$469$	−9.60576			−0.443553
$470$	−22.5659	−	2.75274i	−1.04089	−	0.126975i
$471$	6.39374	−	11.0743i	0.294608	−	0.510276i
$472$	12.3785	+	7.14671i	0.569765	+	0.328954i
$473$		−	12.3207i		−	0.566505i
$474$	−8.18988	−	14.1853i	−0.376174	−	0.651552i
$475$	25.2495	−	26.2290i	1.15853	−	1.20347i
$476$	0.907068	+	1.57109i	0.0415754	+	0.0720107i
$477$	−5.20023	−	3.00236i	−0.238102	−	0.137468i
$478$	0.646204	−	0.373086i	0.0295567	−	0.0170646i
$479$	20.3485	−	35.2446i	0.929747	−	1.61037i	0.146003	−	0.989284i	$-0.453359\pi$
$479$	20.3485	−	35.2446i	0.929747	−	1.61037i	0.783744	−	0.621084i	$-0.213308\pi$
$480$	1.34430	−	1.78686i	0.0613584	−	0.0815587i
$481$	9.98439			0.455249
$482$	15.1193	+	8.72913i	0.688665	+	0.397601i
$483$	−5.40450	+	3.12029i	−0.245913	+	0.141978i
$484$	−2.92157	+	5.06030i	−0.132799	+	0.230014i
$485$	4.03141	−	33.0480i	0.183057	−	1.50063i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−18.2290	+	10.5245i	−0.826034	+	0.476911i	−0.852493	−	0.522739i	$-0.824910\pi$
$487$	−18.2290	+	10.5245i	−0.826034	+	0.476911i	0.0264587	+	0.999650i	$0.491577\pi$
$488$		−	11.2736i		−	0.510331i
$489$	1.29644	−	2.24550i	0.0586271	−	0.101545i
$490$	−12.7938	+	5.44251i	−0.577964	+	0.245867i
$491$	18.4176	+	31.9002i	0.831174	+	1.43964i	0.897108	+	0.441812i	$0.145664\pi$
$491$	18.4176	+	31.9002i	0.831174	+	1.43964i	−0.0659338	+	0.997824i	$0.521003\pi$
$492$			6.86308i			0.309411i
$493$	−8.49242	−	4.90310i	−0.382479	−	0.220825i
$494$	−29.6721			−1.33501
$495$	−3.05272	+	4.05773i	−0.137210	+	0.182382i
$496$	−0.177331	−	5.56494i	−0.00796239	−	0.249873i
$497$			13.2967i			0.596439i
$498$		−	8.17920i		−	0.366519i
$499$	12.4901	−	21.6335i	0.559135	−	0.968449i	−0.438434	−	0.898763i	$-0.644467\pi$
$499$	12.4901	−	21.6335i	0.559135	−	0.968449i	0.997569	−	0.0696863i	$-0.0221998\pi$
$500$	10.4472	+	3.98205i	0.467212	+	0.178083i
$501$	−9.56543	−	16.5678i	−0.427352	−	0.740195i
$502$	11.8818	+	6.85998i	0.530312	+	0.306176i
$503$	16.9869	+	9.80742i	0.757411	+	0.437291i	0.828365	−	0.560188i	$-0.189271\pi$
$503$	16.9869	+	9.80742i	0.757411	+	0.437291i	−0.0709547	+	0.997480i	$0.522605\pi$
$504$	−0.884454			−0.0393967
$505$	−22.0444	−	2.68912i	−0.980963	−	0.119664i
$506$	−8.01147	−	13.8763i	−0.356153	−	0.616875i
$507$	3.12262	−	1.80285i	0.138681	−	0.0800673i
$508$	4.45894	+	2.57437i	0.197834	+	0.114219i
$509$	12.2409	+	21.2019i	0.542569	+	0.939757i	0.998756	+	0.0498729i	$0.0158816\pi$
$509$	12.2409	+	21.2019i	0.542569	+	0.939757i	−0.456187	+	0.889884i	$0.650785\pi$
$510$	4.22047	−	1.79540i	0.186885	−	0.0795016i
$511$	2.92879			0.129562
$512$			1.00000i			0.0441942i
$513$	6.30594	+	3.64074i	0.278414	+	0.160742i
$514$	−1.76523	−	3.05748i	−0.0778612	−	0.134860i
$515$	22.8441	−	9.71796i	1.00663	−	0.428225i
$516$	−2.71276	−	4.69864i	−0.119423	−	0.206846i
$517$	−19.9940	+	11.5435i	−0.879335	+	0.507684i
$518$	−1.87672	+	1.08352i	−0.0824582	+	0.0476073i
$519$	−13.7603			−0.604009
$520$	−3.56693	−	8.38484i	−0.156420	−	0.367699i
$521$	4.73612	−	8.20319i	0.207493	−	0.359388i	−0.743431	−	0.668812i	$-0.766803\pi$
$521$	4.73612	−	8.20319i	0.207493	−	0.359388i	0.950924	+	0.309424i	$0.100136\pi$
$522$	4.14035	−	2.39043i	0.181218	−	0.104626i
$523$			19.5357i			0.854235i	0.904196	+	0.427117i	$0.140471\pi$
$523$			19.5357i			0.854235i	−0.904196	+	0.427117i	$0.859529\pi$
$524$	−4.99879	+	8.65816i	−0.218373	+	0.378233i
$525$	−1.22563	−	4.24904i	−0.0534907	−	0.185443i
$526$	23.9867			1.04587
$527$	5.39223	−	10.0671i	0.234889	−	0.438528i
$528$		−	2.27087i		−	0.0988271i
$529$	−26.7850			−1.16456
$530$	5.25604	+	12.3554i	0.228308	+	0.536686i
$531$	−14.2934			−0.620282
$532$	5.57732	−	3.22007i	0.241807	−	0.139608i
$533$	24.2202	+	13.9836i	1.04909	+	0.605695i
$534$	5.93324	−	10.2767i	0.256756	−	0.444715i
$535$	−7.23747	−	5.44491i	−0.312903	−	0.235404i
$536$	−5.43033	−	9.40561i	−0.234555	−	0.406260i
$537$	−1.12830	+	0.651424i	−0.0486897	+	0.0281110i
$538$	−4.92712	+	2.84467i	−0.212423	+	0.122643i
$539$	−7.05985	+	12.2280i	−0.304089	+	0.526698i
$540$	−0.270763	+	2.21961i	−0.0116518	+	0.0955170i
$541$	13.9176	−	24.1060i	0.598364	−	1.03640i	−0.394699	−	0.918811i	$-0.629151\pi$
$541$	13.9176	−	24.1060i	0.598364	−	1.03640i	0.993063	−	0.117586i	$-0.0375156\pi$
$542$		−	9.25028i		−	0.397334i
$543$		−	2.07365i		−	0.0889891i
$544$	−1.02557	+	1.77634i	−0.0439709	+	0.0761598i
$545$	0.651684	+	0.0794967i	0.0279151	+	0.00340527i
$546$	−1.80208	+	3.12129i	−0.0771219	+	0.133579i
$547$	28.0710	−	16.2068i	1.20023	−	0.692954i	0.239624	−	0.970866i	$-0.422976\pi$
$547$	28.0710	−	16.2068i	1.20023	−	0.692954i	0.960607	+	0.277912i	$0.0896423\pi$
$548$	15.8965	−	9.17786i	0.679066	−	0.392059i
$549$	5.63679	+	9.76321i	0.240573	+	0.416684i
$550$	10.9096	−	3.14684i	0.465186	−	0.134182i
$551$	−17.4059	+	30.1478i	−0.741515	+	1.28434i
$552$	−6.11054	−	3.52792i	−0.260082	−	0.150158i
$553$	12.5462	−	7.24357i	0.533520	−	0.308028i
$554$	11.8505			0.503479
$555$	2.14466	+	5.04149i	0.0910359	+	0.213999i
$556$	−18.5039			−0.784741
$557$		−	6.95561i		−	0.294719i	−0.989083	−	0.147359i	$-0.952923\pi$
$557$		−	6.95561i		−	0.294719i	0.989083	−	0.147359i	$-0.0470774\pi$
$558$	2.93604	+	4.73071i	0.124293	+	0.200267i
$559$	−22.1091			−0.935113
$560$	1.58040	+	1.18897i	0.0667839	+	0.0502431i
$561$	2.32894	−	4.03383i	0.0983277	−	0.170309i
$562$			21.3731i			0.901568i
$563$	4.41905	−	2.55134i	0.186241	−	0.107526i	−0.403981	−	0.914767i	$-0.632374\pi$
$563$	4.41905	−	2.55134i	0.186241	−	0.107526i	0.590221	+	0.807241i	$0.299040\pi$
$564$	−5.08330	+	8.80454i	−0.214046	+	0.370738i
$565$	−26.0949	+	11.1008i	−1.09782	+	0.467016i
$566$	1.07303			0.0451029
$567$	0.765960	−	0.442227i	0.0321673	−	0.0185718i
$568$	−13.0196	+	7.51690i	−0.546292	+	0.315402i
$569$	−11.0142	−	19.0772i	−0.461741	−	0.799758i	0.537307	−	0.843387i	$-0.319442\pi$
$569$	−11.0142	−	19.0772i	−0.461741	−	0.799758i	−0.999048	+	0.0436284i	$0.986108\pi$
$570$	−6.37361	−	14.9825i	−0.266961	−	0.627549i
$571$	−3.07363	−	5.32368i	−0.128627	−	0.222789i	0.794518	−	0.607241i	$-0.207724\pi$
$571$	−3.07363	−	5.32368i	−0.128627	−	0.222789i	−0.923145	+	0.384452i	$0.874390\pi$
$572$	−8.01405	−	4.62691i	−0.335084	−	0.193461i
$573$			21.3853i			0.893383i
$574$	−6.07008			−0.253360
$575$	8.48099	−	34.2447i	0.353682	−	1.42810i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	24.0859	+	13.9060i	1.00271	+	0.578915i	0.909049	−	0.416689i	$-0.136810\pi$
$577$	24.0859	+	13.9060i	1.00271	+	0.578915i	0.0936613	+	0.995604i	$0.470143\pi$
$578$	11.0789	−	6.39642i	0.460822	−	0.266056i
$579$	−12.7075	−	22.0101i	−0.528107	−	0.914707i
$580$	−10.6117	−	1.29448i	−0.440626	−	0.0537504i
$581$	7.23413			0.300122
$582$	−12.8943	−	7.44453i	−0.534486	−	0.308586i
$583$	11.8091	+	6.81797i	0.489082	+	0.282371i
$584$	1.65570	+	2.86777i	0.0685136	+	0.118669i
$585$	7.28147	+	5.47801i	0.301052	+	0.226488i
$586$	−8.94922	+	15.5005i	−0.369689	+	0.640320i
$587$		−	10.6635i		−	0.440128i	−0.975485	−	0.220064i	$-0.929373\pi$
$587$		−	10.6635i		−	0.440128i	0.975485	−	0.220064i	$-0.0706267\pi$
$588$			6.21774i			0.256415i
$589$	−35.7378	−	19.1422i	−1.47255	−	0.788742i
$590$	25.5404	+	19.2146i	1.05148	+	0.791052i
$591$	2.96802			0.122088
$592$	−2.12189	−	1.22508i	−0.0872093	−	0.0503503i
$593$		−	19.9581i		−	0.819581i	−0.912180	−	0.409790i	$-0.865602\pi$
$593$		−	19.9581i		−	0.819581i	0.912180	−	0.409790i	$-0.134398\pi$
$594$	1.13544	+	1.96663i	0.0465875	+	0.0806920i
$595$	1.58795	+	3.73281i	0.0650995	+	0.153030i
$596$	−5.36747	+	9.29673i	−0.219860	+	0.380809i
$597$		−	0.285561i		−	0.0116873i
$598$	−24.9005	+	14.3763i	−1.01826	+	0.587891i
$599$	3.74829	+	6.49223i	0.153151	+	0.265265i	0.932384	−	0.361469i	$-0.117725\pi$
$599$	3.74829	+	6.49223i	0.153151	+	0.265265i	−0.779233	+	0.626734i	$0.784391\pi$
$600$	3.46763	−	3.60216i	0.141566	−	0.147057i
$601$	−18.0079	+	31.1905i	−0.734556	+	1.27229i	0.220362	+	0.975418i	$0.429276\pi$
$601$	−18.0079	+	31.1905i	−0.734556	+	1.27229i	−0.954918	+	0.296870i	$0.904057\pi$
$602$	4.15573	−	2.39931i	0.169375	−	0.0977887i
$603$	9.40561	+	5.43033i	0.383026	+	0.221140i
$604$	−8.89641			−0.361990
$605$	−7.85490	+	10.4409i	−0.319347	+	0.424482i
$606$	−4.96582	+	8.60105i	−0.201723	+	0.349394i
$607$	−25.9691	+	14.9933i	−1.05405	+	0.608558i	−0.923781	−	0.382921i	$-0.874918\pi$
$607$	−25.9691	+	14.9933i	−1.05405	+	0.608558i	−0.130271	+	0.991478i	$0.541585\pi$
$608$	6.30594	+	3.64074i	0.255740	+	0.147651i
$609$	2.11423	+	3.66195i	0.0856728	+	0.148390i
$610$	3.05247	−	25.0230i	0.123591	−	1.01315i
$611$	20.7145	+	35.8786i	0.838019	+	1.45149i
$612$		−	2.05114i		−	0.0829123i
$613$	−27.5591	−	15.9113i	−1.11310	−	0.642650i	−0.173471	−	0.984839i	$-0.555498\pi$
$613$	−27.5591	−	15.9113i	−1.11310	−	0.642650i	−0.939631	+	0.342189i	$0.888832\pi$
$614$	0.202948	−	0.351516i	0.00819032	−	0.0141860i
$615$	−1.85827	+	15.2334i	−0.0749327	+	0.614269i
$616$	2.00848			0.0809241
$617$	−9.09198	−	5.24926i	−0.366029	−	0.211327i	0.305693	−	0.952130i	$-0.401112\pi$
$617$	−9.09198	−	5.24926i	−0.366029	−	0.211327i	−0.671722	+	0.740803i	$0.734445\pi$
$618$		−	11.1022i		−	0.446596i
$619$	26.8932			1.08093			0.540464	−	0.841367i	$-0.318249\pi$
$619$	26.8932			1.08093			0.540464	+	0.841367i	$0.318249\pi$
$620$	1.11318	−	12.4000i	0.0447062	−	0.497997i
$621$	7.05585			0.283141
$622$		−	20.8407i		−	0.835638i
$623$	9.08924	+	5.24768i	0.364153	+	0.210244i
$624$	−4.07501			−0.163131
$625$	22.1105	+	11.6673i	0.884419	+	0.466693i
$626$	4.86202	−	8.42126i	0.194325	−	0.336581i
$627$	−14.3200	−	8.26765i	−0.571885	−	0.330178i
$628$			12.7875i			0.510276i
$629$	−2.51280	−	4.35229i	−0.100192	−	0.173537i
$630$	−1.96315	−	0.239478i	−0.0782137	−	0.00954102i
$631$	−3.55927	−	6.16484i	−0.141692	−	0.245418i	0.786442	−	0.617665i	$-0.211921\pi$
$631$	−3.55927	−	6.16484i	−0.141692	−	0.245418i	−0.928134	+	0.372246i	$0.878588\pi$
$632$	14.1853	+	8.18988i	0.564260	+	0.325776i
$633$	−2.48306	+	1.43360i	−0.0986928	+	0.0569803i
$634$	−5.23937	+	9.07485i	−0.208082	+	0.360408i
$635$	9.20008	+	6.92143i	0.365094	+	0.274668i
$636$	6.00471			0.238102
$637$	21.9428	+	12.6687i	0.869405	+	0.501951i
$638$	−9.40220	+	5.42837i	−0.372237	+	0.214911i
$639$	7.51690	−	13.0196i	0.297364	−	0.515049i
$640$	−0.270763	+	2.21961i	−0.0107029	+	0.0877380i
$641$	−3.70122	−	6.41070i	−0.146189	−	0.253207i	0.783627	−	0.621232i	$-0.213368\pi$
$641$	−3.70122	−	6.41070i	−0.146189	−	0.253207i	−0.929816	+	0.368025i	$0.880034\pi$
$642$	−3.50773	+	2.02519i	−0.138439	+	0.0799279i
$643$			4.03418i			0.159092i	0.996831	+	0.0795462i	$0.0253471\pi$
$643$			4.03418i			0.159092i	−0.996831	+	0.0795462i	$0.974653\pi$
$644$	3.12029	−	5.40450i	0.122957	−	0.212967i
$645$	−4.74906	−	11.1637i	−0.186994	−	0.439570i
$646$	7.46765	+	12.9343i	0.293811	+	0.508895i
$647$			28.5420i			1.12210i	0.827782	+	0.561050i	$0.189603\pi$
$647$			28.5420i			1.12210i	−0.827782	+	0.561050i	$0.810397\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	32.4586			1.27411
$650$	−5.64691	−	19.5769i	−0.221490	−	0.767869i
$651$	−4.18410	+	2.59680i	−0.163988	+	0.101776i
$652$			2.59288i			0.101545i
$653$			12.8131i			0.501417i	0.968063	+	0.250708i	$0.0806636\pi$
$653$			12.8131i			0.501417i	−0.968063	+	0.250708i	$0.919336\pi$
$654$	0.146801	−	0.254267i	0.00574038	−	0.00994263i
$655$	−13.4397	+	17.8643i	−0.525132	+	0.698015i
$656$	−3.43154	−	5.94360i	−0.133979	−	0.232059i
$657$	−2.86777	−	1.65570i	−0.111882	−	0.0645952i
$658$	−7.78721	−	4.49595i	−0.303577	−	0.175270i
$659$	5.46864			0.213028			0.106514	−	0.994311i	$-0.466031\pi$
$659$	5.46864			0.213028			0.106514	+	0.994311i	$0.466031\pi$
$660$	0.614869	−	5.04046i	0.0239337	−	0.196200i
$661$	−1.47049	−	2.54696i	−0.0571954	−	0.0990654i	0.836010	−	0.548714i	$-0.184882\pi$
$661$	−1.47049	−	2.54696i	−0.0571954	−	0.0990654i	−0.893205	+	0.449649i	$0.851549\pi$
$662$	−17.7361	+	10.2399i	−0.689332	+	0.397986i
$663$	−7.23859	−	4.17920i	−0.281123	−	0.162307i
$664$	4.08960	+	7.08339i	0.158707	+	0.274889i
$665$	13.2514	−	5.63717i	0.513866	−	0.218600i
$666$	2.45015			0.0949414
$667$			33.7330i			1.30615i
$668$	16.5678	+	9.56543i	0.641028	+	0.370098i
$669$	4.55702	+	7.89299i	0.176184	+	0.305160i
$670$	−9.50654	−	22.3472i	−0.367270	−	0.863346i
$671$	−12.8004	−	22.1710i	−0.494156	−	0.855903i
$672$	0.765960	−	0.442227i	0.0295475	−	0.0170593i
$673$	14.7010	−	8.48765i	0.566683	−	0.327175i	−0.189140	−	0.981950i	$-0.560570\pi$
$673$	14.7010	−	8.48765i	0.566683	−	0.327175i	0.755824	+	0.654775i	$0.227237\pi$
$674$	26.4138			1.01742
$675$	−1.20198	+	4.85337i	−0.0462642	+	0.186806i
$676$	−1.80285	+	3.12262i	−0.0693403	+	0.120101i
$677$	20.5575	−	11.8689i	0.790091	−	0.456159i	−0.0499038	−	0.998754i	$-0.515891\pi$
$677$	20.5575	−	11.8689i	0.790091	−	0.456159i	0.839994	+	0.542595i	$0.182558\pi$
$678$			12.6821i			0.487052i
$679$	6.58435	−	11.4044i	0.252684	−	0.437662i
$680$	−2.75733	+	3.66510i	−0.105739	+	0.140550i
$681$	−14.9828			−0.574143
$682$	−6.66738	−	10.7429i	−0.255307	−	0.411365i
$683$		−	2.40486i		−	0.0920195i	−0.998941	−	0.0460097i	$-0.985349\pi$
$683$		−	2.40486i		−	0.0920195i	0.998941	−	0.0460097i	$-0.0146505\pi$
$684$	−7.28147			−0.278414
$685$	37.7692	−	16.0671i	1.44309	−	0.613893i
$686$	−11.6905			−0.446345
$687$	2.17660	−	1.25666i	0.0830424	−	0.0479446i
$688$	4.69864	+	2.71276i	0.179134	+	0.103423i
$689$	12.2346	−	21.1910i	0.466102	−	0.807312i
$690$	−12.6078	−	9.48514i	−0.479971	−	0.361093i
$691$	12.4899	+	21.6331i	0.475138	+	0.822962i	0.999595	−	0.0284746i	$-0.00906496\pi$
$691$	12.4899	+	21.6331i	0.475138	+	0.822962i	−0.524457	+	0.851437i	$0.675732\pi$
$692$	11.9167	−	6.88013i	0.453007	−	0.261543i
$693$	−1.73940	+	1.00424i	−0.0660743	+	0.0381480i
$694$	−7.98778	+	13.8352i	−0.303212	+	0.525178i
$695$	−41.0716	−	5.01018i	−1.55793	−	0.190047i
$696$	−2.39043	+	4.14035i	−0.0906091	+	0.156939i
$697$		−	14.0771i		−	0.533209i
$698$		−	15.3856i		−	0.582352i
$699$	−8.36319	+	14.4855i	−0.316325	+	0.547891i
$700$	3.18594	+	3.06696i	0.120417	+	0.115920i
$701$	−15.3779	+	26.6353i	−0.580816	+	1.00600i	0.414567	+	0.910019i	$0.363933\pi$
$701$	−15.3779	+	26.6353i	−0.580816	+	1.00600i	−0.995383	+	0.0959837i	$0.969400\pi$
$702$	3.52906	−	2.03750i	0.133196	−	0.0769006i
$703$	−15.4505	+	8.92035i	−0.582727	+	0.336438i
$704$	1.13544	+	1.96663i	0.0427934	+	0.0741203i
$705$	−13.6669	+	18.1663i	−0.514726	+	0.684183i
$706$	3.83891	−	6.64918i	0.144479	−	0.250245i
$707$	−7.60723	−	4.39204i	−0.286099	−	0.165180i
$708$	12.3785	−	7.14671i	0.465211	−	0.268590i
$709$	39.0231			1.46554			0.732771	−	0.680475i	$-0.238226\pi$
$709$	39.0231			1.46554			0.732771	+	0.680475i	$0.238226\pi$
$710$	−30.9339	+	13.1594i	−1.16093	+	0.493862i
$711$	−16.3798			−0.614289
$712$			11.8665i			0.444715i
$713$	−39.2654	+	1.25122i	−1.47050	+	0.0468585i
$714$	1.81414			0.0678924
$715$	−16.5353	−	12.4399i	−0.618385	−	0.465225i
$716$	0.651424	−	1.12830i	0.0243449	−	0.0421665i
$717$		−	0.746172i		−	0.0278663i
$718$	−14.1877	+	8.19127i	−0.529480	+	0.305696i
$719$	−8.60747	+	14.9086i	−0.321005	+	0.555996i	−0.980696	−	0.195541i	$-0.937354\pi$
$719$	−8.60747	+	14.9086i	−0.321005	+	0.555996i	0.659691	+	0.751537i	$0.270687\pi$
$720$	−0.875319	−	2.05762i	−0.0326212	−	0.0766831i
$721$	9.81938			0.365693
$722$	29.4621	−	17.0099i	1.09646	−	0.633044i
$723$	15.1193	−	8.72913i	0.562292	−	0.324640i
$724$	1.03683	+	1.79584i	0.0385334	+	0.0667418i
$725$	−23.2033	−	5.74650i	−0.861749	−	0.213420i
$726$	2.92157	+	5.06030i	0.108430	+	0.187805i
$727$	−23.1985	−	13.3937i	−0.860385	−	0.496744i	0.00375614	−	0.999993i	$-0.498804\pi$
$727$	−23.1985	−	13.3937i	−0.860385	−	0.496744i	−0.864141	+	0.503249i	$0.832138\pi$
$728$		−	3.60416i		−	0.133579i
$729$	−1.00000			−0.0370370
$730$	2.89854	+	6.81364i	0.107280	+	0.252184i
$731$	5.56424	+	9.63755i	0.205801	+	0.356458i
$732$	−9.76321	−	5.63679i	−0.360859	−	0.208342i
$733$	−15.7367	+	9.08561i	−0.581250	+	0.335585i	−0.761630	−	0.648012i	$-0.775601\pi$
$733$	−15.7367	+	9.08561i	−0.581250	+	0.335585i	0.180380	+	0.983597i	$0.442267\pi$
$734$	14.6534	+	25.3805i	0.540868	+	0.936811i
$735$	−1.68354	+	13.8010i	−0.0620982	+	0.509057i
$736$	7.05585			0.260082
$737$	−21.3589	−	12.3316i	−0.786767	−	0.454240i
$738$	5.94360	+	3.43154i	0.218787	+	0.126317i
$739$	−11.6418	−	20.1642i	−0.428251	−	0.741753i	0.568467	−	0.822706i	$-0.307537\pi$
$739$	−11.6418	−	20.1642i	−0.428251	−	0.741753i	−0.996718	+	0.0809535i	$0.974203\pi$
$740$	−4.37808	−	3.29373i	−0.160941	−	0.121080i
$741$	−14.8360	+	25.6968i	−0.545015	+	0.943994i
$742$			5.31089i			0.194969i
$743$		−	12.5004i		−	0.458595i	−0.973356	−	0.229298i	$-0.926357\pi$
$743$		−	12.5004i		−	0.458595i	0.973356	−	0.229298i	$-0.0736429\pi$
$744$	−4.90804	−	2.62890i	−0.179938	−	0.0963800i
$745$	−14.4309	+	19.1818i	−0.528708	+	0.702768i
$746$	−8.07447			−0.295627
$747$	−7.08339	−	4.08960i	−0.259168	−	0.149631i
$748$			4.65787i			0.170309i
$749$	−1.79119	−	3.10243i	−0.0654486	−	0.113360i
$750$	8.67214	−	7.05649i	0.316662	−	0.257667i
$751$	13.8275	−	23.9499i	0.504572	−	0.873945i	−0.495414	−	0.868657i	$-0.664984\pi$
$751$	13.8275	−	23.9499i	0.504572	−	0.873945i	0.999986	−	0.00528775i	$-0.00168315\pi$
$752$		−	10.1666i		−	0.370738i
$753$	11.8818	−	6.85998i	0.432998	−	0.249992i
$754$	9.74103	+	16.8720i	0.354747	+	0.614440i
$755$	−19.7466	−	2.40882i	−0.718652	−	0.0876660i
$756$	−0.442227	+	0.765960i	−0.0160836	+	0.0278577i
$757$	−42.0183	+	24.2593i	−1.52718	+	0.881718i	−0.527701	+	0.849430i	$0.676946\pi$
$757$	−42.0183	+	24.2593i	−1.52718	+	0.881718i	−0.999479	+	0.0322879i	$0.989721\pi$
$758$	−0.105270	−	0.0607779i	−0.00382360	−	0.00220755i
$759$	−16.0229			−0.581596
$760$	13.0110	+	9.78845i	0.471958	+	0.355064i
$761$	5.64455	−	9.77665i	0.204615	−	0.354403i	−0.745395	−	0.666623i	$-0.767739\pi$
$761$	5.64455	−	9.77665i	0.204615	−	0.354403i	0.950010	+	0.312220i	$0.101073\pi$
$762$	4.45894	−	2.57437i	0.161530	−	0.0932596i
$763$	0.224888	+	0.129839i	0.00814148	+	0.00470048i
$764$	−10.6926	−	18.5202i	−0.386846	−	0.670037i
$765$	0.555373	−	4.55273i	0.0200795	−	0.164604i
$766$	2.05634	+	3.56168i	0.0742985	+	0.128689i
$767$		−	58.2458i		−	2.10314i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−9.73442	+	16.8605i	−0.351032	+	0.608005i	−0.986431	−	0.164179i	$-0.947503\pi$
$769$	−9.73442	+	16.8605i	−0.351032	+	0.608005i	0.635399	+	0.772184i	$0.280836\pi$
$770$	4.45806	+	0.543824i	0.160657	+	0.0195980i
$771$	−3.53047			−0.127147
$772$	22.0101	+	12.7075i	0.792160	+	0.457354i
$773$		−	0.0438161i		−	0.00157596i	−1.00000		0.000787979i	$-0.999749\pi$
$773$		−	0.0438161i		−	0.00157596i	1.00000		0.000787979i	$-0.000250821\pi$
$774$	−5.42552			−0.195016
$775$	5.82829	−	27.2219i	0.209359	−	0.977839i
$776$	14.8891			0.534486
$777$			2.16705i			0.0777424i
$778$	6.04800	+	3.49182i	0.216831	+	0.125188i
$779$	−49.9733			−1.79048
$780$	−9.04495	−	1.10336i	−0.323861	−	0.0395067i
$781$	−17.0699	+	29.5660i	−0.610810	+	1.05795i
$782$	12.5336	+	7.23625i	0.448199	+	0.258768i
$783$		−	4.78086i		−	0.170854i
$784$	−3.10887	−	5.38472i	−0.111031	−	0.192311i
$785$	−3.46238	+	28.3833i	−0.123578	+	1.01304i
$786$	4.99879	+	8.65816i	0.178301	+	0.308826i
$787$	−29.7276	−	17.1632i	−1.05967	−	0.611802i	−0.134331	−	0.990937i	$-0.542889\pi$
$787$	−29.7276	−	17.1632i	−1.05967	−	0.611802i	−0.925342	+	0.379134i	$0.876222\pi$
$788$	−2.57038	+	1.48401i	−0.0915662	+	0.0528658i
$789$	11.9933	−	20.7731i	0.426974	−	0.739541i
$790$	29.2683	+	22.0192i	1.04132	+	0.783409i
$791$	−11.2167			−0.398820
$792$	−1.96663	−	1.13544i	−0.0698813	−	0.0403460i
$793$	−39.7852	+	22.9700i	−1.41281	+	0.815688i
$794$	1.91038	−	3.30888i	0.0677969	−	0.117428i
$795$	13.3281	+	1.62586i	0.472700	+	0.0576631i
$796$	0.142781	+	0.247303i	0.00506073	+	0.00876544i
$797$	−25.9478	+	14.9810i	−0.919119	+	0.530654i	−0.883354	−	0.468707i	$-0.844720\pi$
$797$	−25.9478	+	14.9810i	−0.919119	+	0.530654i	−0.0357650	+	0.999360i	$0.511387\pi$
$798$		−	6.44013i		−	0.227978i
$799$	10.4265	−	18.0593i	0.368865	−	0.638892i
$800$	−1.20198	+	4.85337i	−0.0424964	+	0.171593i
$801$	−5.93324	−	10.2767i	−0.209641	−	0.363108i
$802$			7.44481i			0.262885i
$803$	6.51233	+	3.75990i	0.229815	+	0.132684i
$804$	−10.8607			−0.383026
$805$	8.38917	−	11.1510i	0.295680	−	0.393022i
$806$	−19.2777	+	11.9644i	−0.679028	+	0.421428i
$807$			5.68935i			0.200274i
$808$		−	9.93163i		−	0.349394i
$809$	3.41705	−	5.91850i	0.120137	−	0.208083i	−0.799685	−	0.600420i	$-0.795000\pi$
$809$	3.41705	−	5.91850i	0.120137	−	0.208083i	0.919822	+	0.392337i	$0.128333\pi$
$810$	1.78686	+	1.34430i	0.0627839	+	0.0472337i
$811$	−17.2427	−	29.8653i	−0.605475	−	1.04871i	−0.991976	−	0.126424i	$-0.959650\pi$
$811$	−17.2427	−	29.8653i	−0.605475	−	1.04871i	0.386502	−	0.922289i	$-0.373683\pi$
$812$	−3.66195	−	2.11423i	−0.128509	−	0.0741948i
$813$	−8.01098	−	4.62514i	−0.280957	−	0.162211i
$814$	−5.56398			−0.195017
$815$	−0.702058	+	5.75520i	−0.0245920	+	0.201596i
$816$	1.02557	+	1.77634i	0.0359021	+	0.0621842i
$817$	34.2130	−	19.7529i	1.19696	−	0.691067i
$818$	−20.7939	−	12.0054i	−0.727041	−	0.419757i
$819$	1.80208	+	3.12129i	0.0629698	+	0.109067i
$820$	−6.00738	−	14.1216i	−0.209787	−	0.493149i
$821$	37.0321			1.29243			0.646215	−	0.763156i	$-0.276351\pi$
$821$	37.0321			1.29243			0.646215	+	0.763156i	$0.276351\pi$
$822$		−	18.3557i		−	0.640229i
$823$	−25.7529	−	14.8684i	−0.897689	−	0.518281i	−0.0212396	−	0.999774i	$-0.506761\pi$
$823$	−25.7529	−	14.8684i	−0.897689	−	0.518281i	−0.876450	+	0.481493i	$0.840095\pi$
$824$	5.55110	+	9.61478i	0.193382	+	0.334947i
$825$	2.72954	−	11.0214i	0.0950305	−	0.383716i
$826$	6.32094	+	10.9482i	0.219934	+	0.380936i
$827$	−0.509073	+	0.293914i	−0.0177022	+	0.0102204i	−0.508825	−	0.860870i	$-0.669920\pi$
$827$	−0.509073	+	0.293914i	−0.0177022	+	0.0102204i	0.491123	+	0.871090i	$0.336587\pi$
$828$	−6.11054	+	3.52792i	−0.212356	+	0.122604i
$829$	−1.60233			−0.0556512			−0.0278256	−	0.999613i	$-0.508858\pi$
$829$	−1.60233			−0.0556512			−0.0278256	+	0.999613i	$0.508858\pi$
$830$	7.15941	+	16.8297i	0.248507	+	0.584168i
$831$	5.92524	−	10.2628i	0.205544	−	0.356013i
$832$	3.52906	−	2.03750i	0.122348	−	0.0706378i
$833$		−	12.7534i		−	0.441880i
$834$	−9.25196	+	16.0249i	−0.320369	+	0.554896i
$835$	34.1842	+	25.7175i	1.18299	+	0.889991i
$836$	16.5353			0.571885
$837$	5.56494	−	0.177331i	0.192352	−	0.00612945i
$838$		−	7.09447i		−	0.245074i
$839$	−18.8647			−0.651283			−0.325642	−	0.945493i	$-0.605580\pi$
$839$	−18.8647			−0.651283			−0.325642	+	0.945493i	$0.605580\pi$
$840$	1.81987	−	0.774180i	0.0627916	−	0.0267117i
$841$	−6.14336			−0.211840
$842$	−12.0601	+	6.96292i	−0.415619	+	0.239958i
$843$	18.5096	+	10.6865i	0.637505	+	0.368064i
$844$	1.43360	−	2.48306i	0.0493464	−	0.0854705i
$845$	−4.84712	+	6.44288i	−0.166746	+	0.221642i
$846$	5.08330	+	8.80454i	0.174768	+	0.302706i
$847$	−4.47561	+	2.58399i	−0.153784	+	0.0887871i
$848$	−5.20023	+	3.00236i	−0.178577	+	0.103101i
$849$	0.536516	−	0.929274i	0.0184132	−	0.0318926i
$850$	−7.11259	+	7.38851i	−0.243960	+	0.253424i
$851$	−8.64395	+	14.9718i	−0.296311	+	0.513225i
$852$			15.0338i			0.515049i
$853$		−	11.5308i		−	0.394807i	−0.980322	−	0.197403i	$-0.936749\pi$
$853$		−	11.5308i		−	0.394807i	0.980322	−	0.197403i	$-0.0632508\pi$
$854$	4.98549	−	8.63512i	0.170600	−	0.295488i
$855$	−16.1621	−	1.97156i	−0.552731	−	0.0674258i
$856$	2.02519	−	3.50773i	0.0692196	−	0.119892i
$857$	−14.3541	+	8.28736i	−0.490328	+	0.283091i	−0.724710	−	0.689054i	$-0.758026\pi$
$857$	−14.3541	+	8.28736i	−0.490328	+	0.283091i	0.234383	+	0.972144i	$0.424693\pi$
$858$	−8.01405	+	4.62691i	−0.273595	+	0.157960i
$859$	6.30252	+	10.9163i	0.215039	+	0.372459i	0.953285	−	0.302073i	$-0.0976788\pi$
$859$	6.30252	+	10.9163i	0.215039	+	0.372459i	−0.738246	+	0.674532i	$0.764345\pi$
$860$	9.69465	+	7.29350i	0.330585	+	0.248706i
$861$	−3.03504	+	5.25684i	−0.103434	+	0.179153i
$862$	25.4248	+	14.6790i	0.865972	+	0.499969i
$863$	17.8544	−	10.3082i	0.607770	−	0.350896i	−0.164322	−	0.986407i	$-0.552544\pi$
$863$	17.8544	−	10.3082i	0.607770	−	0.350896i	0.772092	+	0.635510i	$0.219210\pi$
$864$	−1.00000			−0.0340207
$865$	28.3135	−	12.0446i	0.962686	−	0.409530i
$866$	3.39656			0.115420
$867$		−	12.7928i		−	0.434468i
$868$	2.32514	−	4.34094i	0.0789204	−	0.147341i
$869$	37.1963			1.26180
$870$	−6.42689	+	8.54273i	−0.217892	+	0.289626i
$871$	−22.1286	+	38.3279i	−0.749800	+	1.29869i
$872$			0.293602i			0.00994263i
$873$	−12.8943	+	7.44453i	−0.436406	+	0.251959i
$874$	25.6885	−	44.4938i	0.868926	−	1.50502i
$875$	6.24114	+	7.67011i	0.210989	+	0.259297i
$876$	3.31141			0.111882
$877$	43.8356	−	25.3085i	1.48022	−	0.854606i	0.480472	−	0.877010i	$-0.340465\pi$
$877$	43.8356	−	25.3085i	1.48022	−	0.854606i	0.999749	+	0.0224036i	$0.00713188\pi$
$878$	−27.2298	+	15.7211i	−0.918960	+	0.530562i
$879$	8.94922	+	15.5005i	0.301850	+	0.522819i
$880$	1.98774	+	4.67260i	0.0670067	+	0.157513i
$881$	18.1940	+	31.5129i	0.612970	+	1.06170i	0.990737	+	0.135795i	$0.0433587\pi$
$881$	18.1940	+	31.5129i	0.612970	+	1.06170i	−0.377767	+	0.925901i	$0.623308\pi$
$882$	5.38472	+	3.10887i	0.181313	+	0.104681i
$883$			40.4118i			1.35996i	0.733229	+	0.679982i	$0.238012\pi$
$883$			40.4118i			1.35996i	−0.733229	+	0.679982i	$0.761988\pi$
$884$	8.35840			0.281123
$885$	29.4105	−	12.5113i	0.988623	−	0.420563i
$886$	18.1668	+	31.4657i	0.610324	+	1.05711i
$887$	24.2568	+	14.0047i	0.814465	+	0.470232i	0.848504	−	0.529189i	$-0.177504\pi$
$887$	24.2568	+	14.0047i	0.814465	+	0.470232i	−0.0340391	+	0.999421i	$0.510837\pi$
$888$	−2.12189	+	1.22508i	−0.0712061	+	0.0411108i
$889$	2.27691	+	3.94373i	0.0763652	+	0.132268i
$890$	−3.21300	+	26.3390i	−0.107700	+	0.882885i
$891$	2.27087			0.0760771
$892$	−7.89299	−	4.55702i	−0.264277	−	0.152580i
$893$	−64.1100	−	37.0139i	−2.14536	−	1.23862i
$894$	5.36747	+	9.29673i	0.179515	+	0.310929i
$895$	1.75141	−	2.32801i	0.0585433	−	0.0778167i
$896$	−0.442227	+	0.765960i	−0.0147738	+	0.0255889i
$897$			28.7526i			0.960023i
$898$			38.6289i			1.28906i
$899$	0.847794	+	26.6052i	0.0282755	+	0.887333i
$900$	−1.38574	−	4.80414i	−0.0461914	−	0.160138i
$901$	−12.3165			−0.410321
$902$	−13.4972	−	7.79259i	−0.449406	−	0.259465i
$903$		−	4.79863i		−	0.159688i
$904$	−6.34103	−	10.9830i	−0.210900	−	0.365289i
$905$	1.81511	+	4.26680i	0.0603363	+	0.141833i
$906$	−4.44820	+	7.70452i	−0.147782	+	0.255965i
$907$			20.5075i			0.680942i	0.940255	+	0.340471i	$0.110586\pi$
$907$			20.5075i			0.680942i	−0.940255	+	0.340471i	$0.889414\pi$
$908$	12.9755	−	7.49141i	0.430607	−	0.248611i
$909$	4.96582	+	8.60105i	0.164706	+	0.285279i
$910$	0.975874	−	7.99984i	0.0323499	−	0.265192i
$911$	−11.1352	+	19.2868i	−0.368926	+	0.638999i	−0.989398	−	0.145230i	$-0.953608\pi$
$911$	−11.1352	+	19.2868i	−0.368926	+	0.638999i	0.620472	+	0.784229i	$0.286941\pi$
$912$	6.30594	−	3.64074i	0.208811	−	0.120557i
$913$	16.0855	+	9.28696i	0.532352	+	0.307354i
$914$	21.0166			0.695169
$915$	−20.1443	−	15.1550i	−0.665951	−	0.501010i
$916$	−1.25666	+	2.17660i	−0.0415212	+	0.0719168i
$917$	−7.65775	+	4.42120i	−0.252881	+	0.146001i
$918$	−1.77634	−	1.02557i	−0.0586278	−	0.0338488i
$919$	−11.2575	−	19.4985i	−0.371350	−	0.643197i	0.618424	−	0.785845i	$-0.287772\pi$
$919$	−11.2575	−	19.4985i	−0.371350	−	0.643197i	−0.989773	+	0.142648i	$0.954438\pi$
$920$	15.6613	+	1.91046i	0.516336	+	0.0629862i
$921$	−0.202948	−	0.351516i	−0.00668737	−	0.0115829i
$922$		−	8.71999i		−	0.287177i
$923$	53.0552	+	30.6314i	1.74633	+	1.00825i
$924$	1.00424	−	1.73940i	0.0330371	−	0.0572220i
$925$	−8.82582	−	8.49622i	−0.290191	−	0.279354i
$926$	−35.8033			−1.17657
$927$	−9.61478	−	5.55110i	−0.315791	−	0.182322i
$928$		−	4.78086i		−	0.156939i
$929$	0.400366			0.0131356			0.00656780	−	0.999978i	$-0.497909\pi$
$929$	0.400366			0.0131356			0.00656780	+	0.999978i	$0.497909\pi$
$930$	−10.1822	−	7.16406i	−0.333886	−	0.234919i
$931$	−45.2743			−1.48381
$932$		−	16.7264i		−	0.547891i
$933$	−18.0486	−	10.4204i	−0.590885	−	0.341148i
$934$	32.7979			1.07318
$935$	−1.26118	+	10.3387i	−0.0412450	+	0.338111i
$936$	−2.03750	+	3.52906i	−0.0665979	+	0.115351i
$937$	−5.18660	−	2.99448i	−0.169439	−	0.0978255i	0.412882	−	0.910784i	$-0.364522\pi$
$937$	−5.18660	−	2.99448i	−0.169439	−	0.0978255i	−0.582321	+	0.812959i	$0.697855\pi$
$938$		−	9.60576i		−	0.313639i
$939$	−4.86202	−	8.42126i	−0.158666	−	0.274817i
$940$	2.75274	−	22.5659i	0.0897846	−	0.736020i
$941$	−0.00627605	−	0.0108704i	−0.000204593	−	0.000354366i	0.865923	−	0.500177i	$-0.166732\pi$
$941$	−0.00627605	−	0.0108704i	−0.000204593	−	0.000354366i	−0.866128	+	0.499823i	$0.833398\pi$
$942$	11.0743	+	6.39374i	0.360819	+	0.208319i
$943$	−41.9371	+	24.2124i	−1.36566	+	0.788465i
$944$	−7.14671	+	12.3785i	−0.232606	+	0.402885i
$945$	−1.18897	+	1.58040i	−0.0386771	+	0.0514103i
$946$	12.3207			0.400580
$947$	−33.8211	−	19.5266i	−1.09904	−	0.634529i	−0.163069	−	0.986615i	$-0.552139\pi$
$947$	−33.8211	−	19.5266i	−1.09904	−	0.634529i	−0.935968	+	0.352085i	$0.885473\pi$
$948$	14.1853	−	8.18988i	0.460717	−	0.265995i
$949$	6.74701	−	11.6862i	0.219017	−	0.379349i
$950$	26.2290	+	25.2495i	0.850981	+	0.819201i
$951$	5.23937	+	9.07485i	0.169898	+	0.294272i
$952$	−1.57109	+	0.907068i	−0.0509193	+	0.0293983i
$953$		−	15.7659i		−	0.510709i	−0.966847	−	0.255355i	$-0.917808\pi$
$953$		−	15.7659i		−	0.510709i	0.966847	−	0.255355i	$-0.0821922\pi$
$954$	3.00236	−	5.20023i	0.0972048	−	0.168364i
$955$	−18.7189	−	44.0029i	−0.605731	−	1.42390i
$956$	0.373086	+	0.646204i	0.0120665	+	0.0208997i
$957$			10.8567i			0.350948i
$958$	35.2446	+	20.3485i	1.13870	+	0.657430i
$959$	16.2348			0.524249
$960$	1.78686	+	1.34430i	0.0576707	+	0.0433869i
$961$	−30.9371	+	1.97367i	−0.997971	+	0.0636668i
$962$			9.98439i			0.321910i
$963$			4.05038i			0.130522i
$964$	−8.72913	+	15.1193i	−0.281146	+	0.486960i
$965$	45.4131	+	34.1653i	1.46190	+	1.09982i
$966$	−3.12029	−	5.40450i	−0.100394	−	0.173887i
$967$	6.21397	+	3.58764i	0.199828	+	0.115371i	0.596575	−	0.802557i	$-0.296528\pi$
$967$	6.21397	+	3.58764i	0.199828	+	0.115371i	−0.396747	+	0.917928i	$0.629861\pi$
$968$	−5.06030	−	2.92157i	−0.162644	−	0.0939027i
$969$	14.9353			0.479791
$970$	33.0480	+	4.03141i	1.06111	+	0.129441i
$971$	−18.5512	−	32.1316i	−0.595336	−	1.03115i	−0.993499	−	0.113838i	$-0.963686\pi$
$971$	−18.5512	−	32.1316i	−0.595336	−	1.03115i	0.398163	−	0.917315i	$-0.369648\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	−14.1733	−	8.18294i	−0.454374	−	0.262333i
$974$	−10.5245	−	18.2290i	−0.337227	−	0.584094i
$975$	−19.7775	−	4.89808i	−0.633388	−	0.156864i
$976$	11.2736			0.360859
$977$			25.1123i			0.803414i	0.915768	+	0.401707i	$0.131583\pi$
$977$			25.1123i			0.803414i	−0.915768	+	0.401707i	$0.868417\pi$
$978$	2.24550	+	1.29644i	0.0718032	+	0.0414556i
$979$	13.4736	+	23.3370i	0.430619	+	0.745854i
$980$	−5.44251	−	12.7938i	−0.173855	−	0.408682i
$981$	−0.146801	−	0.254267i	−0.00468700	−	0.00811812i
$982$	−31.9002	+	18.4176i	−1.01798	+	0.587729i
$983$	−0.502493	+	0.290114i	−0.0160270	+	0.00925321i	−0.507992	−	0.861362i	$-0.669612\pi$
$983$	−0.502493	+	0.290114i	−0.0160270	+	0.00925321i	0.491965	+	0.870615i	$0.336279\pi$
$984$	−6.86308			−0.218787
$985$	−6.10708	+	2.59797i	−0.194588	+	0.0827782i
$986$	4.90310	−	8.49242i	0.156147	−	0.270454i
$987$	−7.78721	+	4.49595i	−0.247870	+	0.143108i
$988$		−	29.6721i		−	0.943994i
$989$	19.1408	−	33.1529i	0.608643	−	1.05420i
$990$	−4.05773	−	3.05272i	−0.128963	−	0.0970219i
$991$	45.1857			1.43537			0.717685	−	0.696368i	$-0.245202\pi$
$991$	45.1857			1.43537			0.717685	+	0.696368i	$0.245202\pi$
$992$	5.56494	−	0.177331i	0.176687	−	0.00563026i
$993$			20.4799i			0.649909i
$994$	−13.2967			−0.421746
$995$	0.249957	+	0.587578i	0.00792418	+	0.0186275i
$996$	8.17920			0.259168
$997$	−41.3509	+	23.8739i	−1.30960	+	0.756095i	−0.982029	−	0.188732i	$-0.939562\pi$
$997$	−41.3509	+	23.8739i	−1.30960	+	0.756095i	−0.327567	+	0.944828i	$0.606229\pi$
$998$	21.6335	+	12.4901i	0.684797	+	0.395368i
$999$	1.22508	−	2.12189i	0.0387597	−	0.0671337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.c.439.7	yes	24
5.4	even	2	inner	930.2.s.c.439.4	✓	24
31.25	even	3	inner	930.2.s.c.769.10	yes	24
155.149	even	6	inner	930.2.s.c.769.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.c.439.4	✓	24	5.4	even	2	inner
930.2.s.c.439.7	yes	24	1.1	even	1	trivial
930.2.s.c.769.1	yes	24	155.149	even	6	inner
930.2.s.c.769.10	yes	24	31.25	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-2.21961 - 0.270763i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.765960 - 0.442227i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-2.21961 - 0.270763i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.765960 - 0.442227i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.270763 - 2.21961i) q^{10} +(-1.13544 - 1.96663i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-3.52906 + 2.03750i) q^{13} +(0.442227 - 0.765960i) q^{14} +(-1.78686 - 1.34430i) q^{15} +1.00000 q^{16} +(1.77634 + 1.02557i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.64074 - 6.30594i) q^{19} +(2.21961 + 0.270763i) q^{20} +(-0.442227 - 0.765960i) q^{21} +(1.96663 - 1.13544i) q^{22} -7.05585i q^{23} +(0.500000 - 0.866025i) q^{24} +(4.85337 + 1.20198i) q^{25} +(-2.03750 - 3.52906i) q^{26} +1.00000i q^{27} +(0.765960 + 0.442227i) q^{28} -4.78086 q^{29} +(1.34430 - 1.78686i) q^{30} +(-0.177331 - 5.56494i) q^{31} +1.00000i q^{32} -2.27087i q^{33} +(-1.02557 + 1.77634i) q^{34} +(1.58040 + 1.18897i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.12189 - 1.22508i) q^{37} +(6.30594 + 3.64074i) q^{38} -4.07501 q^{39} +(-0.270763 + 2.21961i) q^{40} +(-3.43154 - 5.94360i) q^{41} +(0.765960 - 0.442227i) q^{42} +(4.69864 + 2.71276i) q^{43} +(1.13544 + 1.96663i) q^{44} +(-0.875319 - 2.05762i) q^{45} +7.05585 q^{46} -10.1666i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.10887 - 5.38472i) q^{49} +(-1.20198 + 4.85337i) q^{50} +(1.02557 + 1.77634i) q^{51} +(3.52906 - 2.03750i) q^{52} +(-5.20023 + 3.00236i) q^{53} -1.00000 q^{54} +(1.98774 + 4.67260i) q^{55} +(-0.442227 + 0.765960i) q^{56} +(6.30594 - 3.64074i) q^{57} -4.78086i q^{58} +(-7.14671 + 12.3785i) q^{59} +(1.78686 + 1.34430i) q^{60} +11.2736 q^{61} +(5.56494 - 0.177331i) q^{62} -0.884454i q^{63} -1.00000 q^{64} +(8.38484 - 3.56693i) q^{65} +2.27087 q^{66} +(9.40561 - 5.43033i) q^{67} +(-1.77634 - 1.02557i) q^{68} +(3.52792 - 6.11054i) q^{69} +(-1.18897 + 1.58040i) q^{70} +(-7.51690 - 13.0196i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-2.86777 + 1.65570i) q^{73} +(1.22508 - 2.12189i) q^{74} +(3.60216 + 3.46763i) q^{75} +(-3.64074 + 6.30594i) q^{76} +2.00848i q^{77} -4.07501i q^{78} +(-8.18988 + 14.1853i) q^{79} +(-2.21961 - 0.270763i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.94360 - 3.43154i) q^{82} +(-7.08339 + 4.08960i) q^{83} +(0.442227 + 0.765960i) q^{84} +(-3.66510 - 2.75733i) q^{85} +(-2.71276 + 4.69864i) q^{86} +(-4.14035 - 2.39043i) q^{87} +(-1.96663 + 1.13544i) q^{88} -11.8665 q^{89} +(2.05762 - 0.875319i) q^{90} +3.60416 q^{91} +7.05585i q^{92} +(2.62890 - 4.90804i) q^{93} +10.1666 q^{94} +(-9.78845 + 13.0110i) q^{95} +(-0.500000 + 0.866025i) q^{96} +14.8891i q^{97} +(5.38472 - 3.10887i) q^{98} +(1.13544 - 1.96663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9	\( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) \) 24 * q - 24 * q^4 + 4 * q^5 - 12 * q^6 + 12 * q^9 - 4 * q^11 + 12 * q^14 + 24 * q^16 - 4 * q^19 - 4 * q^20 - 12 * q^21 + 12 * q^24 - 4 * q^25 + 16 * q^26 + 32 * q^29 - 8 * q^30 + 24 * q^31 - 20 * q^34 + 48 * q^35 - 12 * q^36 + 32 * q^39 - 12 * q^41 + 4 * q^44 - 4 * q^45 + 56 * q^46 + 24 * q^49 - 16 * q^50 + 20 * q^51 - 24 * q^54 + 36 * q^55 - 12 * q^56 - 4 * q^59 - 40 * q^61 - 24 * q^64 - 4 * q^65 + 8 * q^66 + 28 * q^69 - 32 * q^70 - 56 * q^71 + 12 * q^74 + 16 * q^75 + 4 * q^76 - 72 * q^79 + 4 * q^80 - 12 * q^81 + 12 * q^84 + 40 * q^85 - 24 * q^86 + 128 * q^89 - 160 * q^91 + 56 * q^94 - 56 * q^95 - 12 * q^96 + 4 * q^99

Introduction

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