LMFDB - Embedded newform 930.2.s.c.439.4

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			439.4
Character	$\chi$	$=$	930.439
Dual form			930.2.s.c.769.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.875319 - 2.05762i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.765960 + 0.442227i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.875319 - 2.05762i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.765960 + 0.442227i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.05762 - 0.875319i) 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} +(-0.875319 + 2.05762i) q^{20} +(-0.442227 - 0.765960i) q^{21} +(-1.96663 + 1.13544i) q^{22} +7.05585i q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.46763 - 3.60216i) 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} +(2.05762 + 0.875319i) 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} +(2.21961 - 0.270763i) q^{45} +7.05585 q^{46} +10.1666i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.10887 - 5.38472i) q^{49} +(-3.60216 + 3.46763i) q^{50} +(1.02557 + 1.77634i) q^{51} +(-3.52906 + 2.03750i) q^{52} +(5.20023 - 3.00236i) q^{53} -1.00000 q^{54} +(-5.04046 + 0.614869i) 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} +(-1.10336 - 9.04495i) 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} +(1.20198 + 4.85337i) q^{75} +(-3.64074 + 6.30594i) q^{76} -2.00848i q^{77} +4.07501i q^{78} +(-8.18988 + 14.1853i) q^{79} +(0.875319 - 2.05762i) 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} +(-0.270763 - 2.21961i) 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
$5$	0.875319	−	2.05762i	0.391455	−	0.920197i
$5$	0.875319	−	2.05762i	0.391455	−	0.920197i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	0.765960	+	0.442227i	0.289506	+	0.167146i	0.637719	−	0.770269i	$-0.279878\pi$
$7$	0.765960	+	0.442227i	0.289506	+	0.167146i	−0.348213	+	0.937415i	$0.613211\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.05762	−	0.875319i	−0.650678	−	0.276800i
$11$	−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	0.0768822	−	0.997040i	$-0.475503\pi$
$13$	3.52906	−	2.03750i	0.978785	−	0.565102i	0.901903	+	0.431938i	$0.142170\pi$
$14$	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	0.268873	−	0.963176i	$-0.413349\pi$
$17$	−1.77634	−	1.02557i	−0.430825	−	0.248737i	−0.699698	+	0.714439i	$0.746682\pi$
$18$	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	$-0.148006\pi$
$20$	−0.875319	+	2.05762i	−0.195727	+	0.460099i
$21$	−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	$0.263110\pi$
$23$			7.05585i			1.47125i	−0.677391	+	0.735623i	$0.736890\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−3.46763	−	3.60216i	−0.693527	−	0.720431i
$26$	−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	0.664173	−	0.747579i	$-0.268784\pi$
$37$	2.12189	+	1.22508i	0.348837	+	0.201401i	−0.315336	+	0.948980i	$0.602117\pi$
$38$	−6.30594	−	3.64074i	−1.02296	−	0.590605i
$39$	−4.07501			−0.652524
$40$	2.05762	+	0.875319i	0.325339	+	0.138400i
$41$	−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	0.0969403	−	0.995290i	$-0.469094\pi$
$43$	−4.69864	−	2.71276i	−0.716536	−	0.413692i	−0.813476	+	0.581598i	$0.802428\pi$
$44$	1.13544	+	1.96663i	0.171173	+	0.296481i
$45$	2.21961	−	0.270763i	0.330881	−	0.0403630i
$46$	7.05585			1.04033
$47$			10.1666i			1.48295i	0.670980	+	0.741476i	$0.265874\pi$
$47$			10.1666i			1.48295i	−0.670980	+	0.741476i	$0.734126\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−3.10887	−	5.38472i	−0.444124	−	0.769246i
$50$	−3.60216	+	3.46763i	−0.509422	+	0.490397i
$51$	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	−0.0983468	−	0.995152i	$-0.531355\pi$
$53$	5.20023	−	3.00236i	0.714307	−	0.412405i	0.812654	+	0.582747i	$0.198022\pi$
$54$	−1.00000			−0.136083
$55$	−5.04046	+	0.614869i	−0.679656	+	0.0829089i
$56$	−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
$65$	−1.10336	−	9.04495i	−0.136855	−	1.12189i
$66$	2.27087			0.279525
$67$	−9.40561	+	5.43033i	−1.14908	+	0.663420i	−0.948662	−	0.316291i	$-0.897563\pi$
$67$	−9.40561	+	5.43033i	−1.14908	+	0.663420i	−0.200415	+	0.979711i	$0.564229\pi$
$68$	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	−0.322699	−	0.946502i	$-0.604590\pi$
$73$	2.86777	−	1.65570i	0.335647	−	0.193786i	0.658345	+	0.752716i	$0.271257\pi$
$74$	1.22508	−	2.12189i	0.142412	−	0.246665i
$75$	1.20198	+	4.85337i	0.138793	+	0.560419i
$76$	−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	$0.793686\pi$
$80$	0.875319	−	2.05762i	0.0978637	−	0.230049i
$81$	−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	−0.0580412	−	0.998314i	$-0.518485\pi$
$83$	7.08339	−	4.08960i	0.777504	−	0.448892i	0.835545	+	0.549422i	$0.185152\pi$
$84$	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	$0.716503\pi$
$90$	−0.270763	−	2.21961i	−0.0285410	−	0.233968i
$91$	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	$-0.727210\pi$
$97$		−	14.8891i		−	1.51176i	0.654713	−	0.755878i	$-0.272790\pi$
$98$	−5.38472	+	3.10887i	−0.543939	+	0.314043i
$99$	1.13544	−	1.96663i	0.114116	−	0.197654i
$100$	3.46763	+	3.60216i	0.346763	+	0.360216i
$101$	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	0.0551089	−	0.998480i	$-0.482449\pi$
$103$	9.61478	−	5.55110i	0.947373	−	0.546966i	0.892264	+	0.451514i	$0.149116\pi$
$104$	2.03750	+	3.52906i	0.199794	+	0.346053i
$105$	−1.96315	+	0.239478i	−0.191584	+	0.0233706i
$106$	−3.00236	−	5.20023i	−0.291615	−	0.505091i
$107$	−3.50773	−	2.02519i	−0.339105	−	0.195783i	0.320771	−	0.947157i	$-0.396058\pi$
$107$	−3.50773	−	2.02519i	−0.339105	−	0.195783i	−0.659876	+	0.751374i	$0.729391\pi$
$108$			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	$0.504476\pi$
$110$	0.614869	+	5.04046i	0.0586255	+	0.480589i
$111$	−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	−0.917898	−	0.396817i	$-0.870115\pi$
$113$	−10.9830	+	6.34103i	−1.03319	+	0.596514i	−0.115295	+	0.993331i	$0.536781\pi$
$114$	3.64074	+	6.30594i	0.340986	+	0.590605i
$115$	14.5183	+	6.17612i	1.35384	+	0.575926i
$116$	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	0.684613	−	0.728907i	$-0.259971\pi$
$127$	4.45894	+	2.57437i	0.395667	+	0.228438i	−0.288946	+	0.957346i	$0.593305\pi$
$128$			1.00000i			0.0883883i
$129$	2.71276	+	4.69864i	0.238845	+	0.413692i
$130$	−9.04495	+	1.10336i	−0.793294	+	0.0967713i
$131$	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
$135$	−2.05762	−	0.875319i	−0.177092	−	0.0753355i
$136$	1.02557	−	1.77634i	0.0879418	−	0.152320i
$137$	15.8965	−	9.17786i	1.35813	−	0.784118i	0.368760	−	0.929525i	$-0.379782\pi$
$137$	15.8965	−	9.17786i	1.35813	−	0.784118i	0.989372	+	0.145407i	$0.0464491\pi$
$138$	−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
$145$	−4.18478	+	9.83722i	−0.347527	+	0.816936i
$146$	−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	$0.0217443\pi$
$150$	4.85337	−	1.20198i	0.396276	−	0.0981413i
$151$	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
$155$	−11.6058	−	4.50622i	−0.932198	−	0.361948i
$156$	4.07501			0.326262
$157$			12.7875i			1.02055i	0.860011	+	0.510276i	$0.170457\pi$
$157$			12.7875i			1.02055i	−0.860011	+	0.510276i	$0.829543\pi$
$158$	14.1853	+	8.18988i	1.12852	+	0.651552i
$159$	−6.00471			−0.476205
$160$	−2.05762	−	0.875319i	−0.162669	−	0.0692001i
$161$	−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	$0.0323786\pi$
$163$			2.59288i			0.203090i	−0.994831	+	0.101545i	$0.967621\pi$
$164$	3.43154	+	5.94360i	0.267958	+	0.464117i
$165$	4.67260	+	1.98774i	0.363762	+	0.154745i
$166$	−4.08960	−	7.08339i	−0.317415	−	0.549778i
$167$	16.5678	+	9.56543i	1.28206	+	0.740195i	0.977224	−	0.212211i	$-0.0680665\pi$
$167$	16.5678	+	9.56543i	1.28206	+	0.740195i	0.304832	+	0.952406i	$0.401400\pi$
$168$	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	0.0268669	−	0.999639i	$-0.491447\pi$
$173$	11.9167	−	6.88013i	0.906013	−	0.523087i	0.879146	+	0.476552i	$0.158114\pi$
$174$	2.39043	−	4.14035i	0.181218	−	0.313879i
$175$	−1.06310	−	4.29259i	−0.0803626	−	0.324489i
$176$	−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	$0.182171\pi$
$180$	−2.21961	+	0.270763i	−0.165440	+	0.0201815i
$181$	−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	$0.0342456\pi$
$193$	22.0101	+	12.7075i	1.58432	+	0.914707i	0.590102	+	0.807329i	$0.299088\pi$
$194$	−14.8891			−1.06897
$195$	−3.56693	+	8.38484i	−0.255433	+	0.600451i
$196$	3.10887	+	5.38472i	0.222062	+	0.384623i
$197$	−2.57038	+	1.48401i	−0.183132	+	0.105732i	−0.588764	−	0.808305i	$-0.700385\pi$
$197$	−2.57038	+	1.48401i	−0.183132	+	0.105732i	0.405631	+	0.914037i	$0.367052\pi$
$198$	−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	$0.836555\pi$
$200$	3.60216	−	3.46763i	0.254711	−	0.245199i
$201$	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
$205$	−15.2334	+	1.85827i	−1.06395	+	0.129787i
$206$	−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
$210$	0.239478	+	1.96315i	0.0165255	+	0.135470i
$211$	−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
$220$	5.04046	−	0.614869i	0.339828	−	0.0414545i
$221$	−8.35840			−0.562247
$222$	−2.12189	+	1.22508i	−0.142412	+	0.0822217i
$223$	−7.89299	−	4.55702i	−0.528553	−	0.305160i	0.211874	−	0.977297i	$-0.432043\pi$
$223$	−7.89299	−	4.55702i	−0.528553	−	0.305160i	−0.740427	+	0.672137i	$0.765377\pi$
$224$	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	−0.00320461	−	0.999995i	$-0.501020\pi$
$227$	12.9755	−	7.49141i	0.861214	−	0.497222i	0.864419	+	0.502773i	$0.167687\pi$
$228$	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	$0.140203\pi$
$230$	6.17612	−	14.5183i	0.407241	−	0.957307i
$231$	−1.00424	+	1.73940i	−0.0660743	+	0.114444i
$232$		−	4.78086i		−	0.313879i
$233$		−	16.7264i		−	1.09578i	−0.836550	−	0.547891i	$-0.815431\pi$
$233$		−	16.7264i		−	1.09578i	0.836550	−	0.547891i	$-0.184569\pi$
$234$	2.03750	−	3.52906i	0.133196	−	0.230702i
$235$	20.9190	+	8.89902i	1.36461	+	0.580508i
$236$	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
$245$	−13.8010	+	1.68354i	−0.881713	+	0.107557i
$246$	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
$255$	4.55273	−	0.555373i	0.285103	−	0.0347788i
$256$	1.00000			0.0625000
$257$	3.05748	−	1.76523i	0.190720	−	0.110112i	−0.401600	−	0.915815i	$-0.631546\pi$
$257$	3.05748	−	1.76523i	0.190720	−	0.110112i	0.592320	+	0.805703i	$0.298212\pi$
$258$	4.69864	−	2.71276i	0.292525	−	0.168889i
$259$	1.08352	+	1.87672i	0.0673269	+	0.116614i
$260$	1.10336	+	9.04495i	0.0684277	+	0.560944i
$261$	−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	$0.264957\pi$
$263$			23.9867i			1.47908i	−0.673112	+	0.739541i	$0.735043\pi$
$264$	−2.27087			−0.139763
$265$	−1.62586	−	13.3281i	−0.0998755	−	0.818741i
$266$	−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	$0.777844\pi$
$270$	−0.875319	+	2.05762i	−0.0532702	+	0.125223i
$271$	−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	$0.115864\pi$
$277$			11.8505i			0.712027i	−0.934481	+	0.356013i	$0.884136\pi$
$278$		−	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	$0.0101534\pi$
$283$			1.07303i			0.0637852i	−0.999491	+	0.0318926i	$0.989847\pi$
$284$	7.51690	+	13.0196i	0.446046	+	0.772574i
$285$	1.97156	+	16.1621i	0.116785	+	0.957358i
$286$	−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
$290$	9.83722	+	4.18478i	0.577661	+	0.245739i
$291$	−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	−0.0265529	−	0.999647i	$-0.508453\pi$
$293$	−15.5005	−	8.94922i	−0.905549	−	0.522819i	−0.878996	+	0.476828i	$0.841786\pi$
$294$	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
$300$	−1.20198	−	4.85337i	−0.0693964	−	0.280210i
$301$	−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
$305$	9.86799	−	23.1968i	0.565039	−	1.32825i
$306$	−2.05114			−0.117256
$307$	0.351516	+	0.202948i	0.0200621	+	0.0115829i	0.509998	−	0.860176i	$-0.329646\pi$
$307$	0.351516	+	0.202948i	0.0200621	+	0.0115829i	−0.489935	+	0.871759i	$0.662980\pi$
$308$			2.00848i			0.114444i
$309$	−11.1022			−0.631582
$310$	−4.50622	+	11.6058i	−0.255936	+	0.659164i
$311$	−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	0.718747	−	0.695272i	$-0.244716\pi$
$313$	8.42126	+	4.86202i	0.475998	+	0.274817i	−0.242749	+	0.970089i	$0.578049\pi$
$314$	12.7875			0.721639
$315$	1.81987	+	0.774180i	0.102538	+	0.0436201i
$316$	8.18988	−	14.1853i	0.460717	−	0.797985i
$317$	−9.07485	−	5.23937i	−0.509694	−	0.294272i	0.223014	−	0.974815i	$-0.428411\pi$
$317$	−9.07485	−	5.23937i	−0.509694	−	0.294272i	−0.732708	+	0.680543i	$0.761744\pi$
$318$			6.00471i			0.336727i
$319$	5.42837	+	9.40220i	0.303930	+	0.526422i
$320$	−0.875319	+	2.05762i	−0.0489318	+	0.115025i
$321$	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
$330$	1.98774	−	4.67260i	0.109421	−	0.257218i
$331$	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
$335$	2.94067	+	24.1065i	0.160666	+	1.31708i
$336$	−0.442227	−	0.765960i	−0.0241255	−	0.0417865i
$337$			26.4138i			1.43885i	0.694569	+	0.719426i	$0.255595\pi$
$337$			26.4138i			1.43885i	−0.694569	+	0.719426i	$0.744405\pi$
$338$	−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	0.0803410	−	0.996767i	$-0.474399\pi$
$347$	−13.8352	−	7.98778i	−0.742714	−	0.428806i	−0.823055	+	0.567961i	$0.807732\pi$
$348$	−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	$0.635095\pi$
$350$	−4.29259	+	1.06310i	−0.229448	+	0.0568249i
$351$	−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	0.666402	−	0.745593i	$-0.267834\pi$
$353$	6.64918	+	3.83891i	0.353900	+	0.204324i	−0.312501	+	0.949917i	$0.601167\pi$
$354$	−7.14671	−	12.3785i	−0.379844	−	0.657908i
$355$	−33.3692	+	4.07060i	−1.77105	+	0.216045i
$356$	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	$0.691029\pi$
$360$	0.270763	+	2.21961i	0.0142705	+	0.116984i
$361$	−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
$365$	−0.896608	−	7.35005i	−0.0469306	−	0.384719i
$366$	−5.63679	+	9.76321i	−0.294640	+	0.510331i
$367$	−25.3805	+	14.6534i	−1.32485	+	0.764903i	−0.984498	−	0.175394i	$-0.943880\pi$
$367$	−25.3805	+	14.6534i	−1.32485	+	0.764903i	−0.340353	+	0.940298i	$0.610547\pi$
$368$			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	$-0.932966\pi$
$373$		−	8.07447i		−	0.418080i	0.977907	−	0.209040i	$-0.0670339\pi$
$374$	4.65787			0.240853
$375$	11.0385	+	1.77503i	0.570028	+	0.0916621i
$376$	−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	−0.588229	−	0.808694i	$-0.700175\pi$
$383$	−3.56168	+	2.05634i	−0.181993	+	0.105074i	0.406236	+	0.913768i	$0.366841\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−4.13270	−	1.75806i	−0.210622	−	0.0895992i
$386$	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	$0.110014\pi$
$390$	8.38484	+	3.56693i	0.424583	+	0.180619i
$391$	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	0.580730	−	0.814096i	$-0.302767\pi$
$397$	3.30888	+	1.91038i	0.166068	+	0.0958794i	−0.414663	+	0.909975i	$0.636100\pi$
$398$	−0.247303	+	0.142781i	−0.0123962	+	0.00715695i
$399$	−6.44013			−0.322410
$400$	−3.46763	−	3.60216i	−0.173382	−	0.180108i
$401$	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	$0.964362\pi$
$410$	1.85827	+	15.2334i	0.0917734	+	0.752323i
$411$	−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
$415$	−2.21463	−	18.1547i	−0.108712	−	0.891178i
$416$	−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	$0.555441\pi$
$420$	1.96315	−	0.239478i	0.0957918	−	0.0116853i
$421$	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
$425$	2.46543	+	9.95493i	0.119591	+	0.482885i
$426$	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	$0.0260075\pi$
$433$			3.39656i			0.163228i	−0.996664	+	0.0816141i	$0.973992\pi$
$434$	−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	$0.563229\pi$
$440$	−0.614869	−	5.04046i	−0.0293127	−	0.240295i
$441$	3.10887	−	5.38472i	0.148041	−	0.256415i
$442$			8.35840i			0.397569i
$443$	−31.4657	+	18.1668i	−1.49498	+	0.863129i	−0.999983	−	0.00576451i	$-0.998165\pi$
$443$	−31.4657	+	18.1668i	−1.49498	+	0.863129i	−0.494999	+	0.868893i	$0.664832\pi$
$444$	1.22508	+	2.12189i	0.0581395	+	0.100701i
$445$	−10.3869	+	24.4167i	−0.492389	+	1.15746i
$446$	−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
$455$	3.15479	−	7.41600i	0.147899	−	0.347668i
$456$	−3.64074	−	6.30594i	−0.170493	−	0.295303i
$457$			21.0166i			0.983117i	0.870844	+	0.491559i	$0.163573\pi$
$457$			21.0166i			0.983117i	−0.870844	+	0.491559i	$0.836427\pi$
$458$	−2.17660	−	1.25666i	−0.101706	−	0.0587198i
$459$	−1.02557	+	1.77634i	−0.0478694	+	0.0829123i
$460$	−14.5183	−	6.17612i	−0.676918	−	0.287963i
$461$	−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	$-0.687218\pi$
$463$		−	35.8033i		−	1.66392i	0.554835	−	0.831961i	$-0.312782\pi$
$464$	−4.78086			−0.221946
$465$	7.79779	+	9.70539i	0.361614	+	0.450077i
$466$	−16.7264			−0.774834
$467$			32.7979i			1.51770i	0.651263	+	0.758852i	$0.274240\pi$
$467$			32.7979i			1.51770i	−0.651263	+	0.758852i	$0.725760\pi$
$468$	−3.52906	−	2.03750i	−0.163131	−	0.0941837i
$469$	−9.60576			−0.443553
$470$	8.89902	−	20.9190i	0.410481	−	0.964924i
$471$	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
$475$	−35.3397	+	8.75219i	−1.62150	+	0.401578i
$476$	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
$485$	−30.6361	−	13.0327i	−1.39111	−	0.591784i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	18.2290	−	10.5245i	0.826034	−	0.476911i	−0.0264587	−	0.999650i	$-0.508423\pi$
$487$	18.2290	−	10.5245i	0.826034	−	0.476911i	0.852493	+	0.522739i	$0.175090\pi$
$488$			11.2736i			0.510331i
$489$	1.29644	−	2.24550i	0.0586271	−	0.101545i
$490$	1.68354	+	13.8010i	0.0760544	+	0.623465i
$491$	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	0.0709547	−	0.997480i	$-0.477395\pi$
$503$	−16.9869	−	9.80742i	−0.757411	−	0.437291i	−0.828365	+	0.560188i	$0.810729\pi$
$504$	−0.884454			−0.0393967
$505$	8.69335	−	20.4356i	0.386849	−	0.909371i
$506$	−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	$0.650785\pi$
$510$	−0.555373	−	4.55273i	−0.0245923	−	0.201598i
$511$	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
$515$	−3.00607	−	24.6426i	−0.132463	−	1.08588i
$516$	−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
$520$	9.04495	−	1.10336i	0.396647	−	0.0483857i
$521$	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	$-0.859529\pi$
$523$		−	19.5357i		−	0.854235i	0.904196	−	0.427117i	$-0.140471\pi$
$524$	−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
$530$	−13.3281	+	1.62586i	−0.578937	+	0.0706226i
$531$	−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
$540$	2.05762	+	0.875319i	0.0885460	+	0.0376677i
$541$	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
$545$	−0.256996	+	0.604123i	−0.0110085	+	0.0258778i
$546$	−1.80208	+	3.12129i	−0.0771219	+	0.133579i
$547$	−28.0710	+	16.2068i	−1.20023	+	0.692954i	−0.960607	−	0.277912i	$-0.910358\pi$
$547$	−28.0710	+	16.2068i	−1.20023	+	0.692954i	−0.239624	+	0.970866i	$0.577024\pi$
$548$	−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
$555$	−5.43839	+	0.663411i	−0.230847	+	0.0281602i
$556$	−18.5039			−0.784741
$557$			6.95561i			0.294719i	0.989083	+	0.147359i	$0.0470774\pi$
$557$			6.95561i			0.294719i	−0.989083	+	0.147359i	$0.952923\pi$
$558$	−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	−0.590221	−	0.807241i	$-0.700960\pi$
$563$	−4.41905	+	2.55134i	−0.186241	+	0.107526i	0.403981	+	0.914767i	$0.367626\pi$
$564$	−5.08330	+	8.80454i	−0.214046	+	0.370738i
$565$	3.43384	+	28.1493i	0.144463	+	1.18425i
$566$	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	$0.986108\pi$
$570$	16.1621	−	1.97156i	0.676954	−	0.0825794i
$571$	−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
$575$	25.4163	−	24.4671i	1.05993	−	1.02035i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−24.0859	−	13.9060i	−1.00271	−	0.578915i	−0.0936613	−	0.995604i	$-0.529857\pi$
$577$	−24.0859	−	13.9060i	−1.00271	−	0.578915i	−0.909049	+	0.416689i	$0.863190\pi$
$578$	−11.0789	+	6.39642i	−0.460822	+	0.266056i
$579$	−12.7075	−	22.0101i	−0.528107	−	0.914707i
$580$	4.18478	−	9.83722i	0.173764	−	0.408468i
$581$	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	$0.0706267\pi$
$587$			10.6635i			0.440128i	−0.975485	+	0.220064i	$0.929373\pi$
$588$		−	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	$0.134398\pi$
$593$			19.9581i			0.819581i	−0.912180	+	0.409790i	$0.865602\pi$
$594$	1.13544	+	1.96663i	0.0465875	+	0.0806920i
$595$	−4.02668	+	0.491202i	−0.165078	+	0.0201373i
$596$	−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	$0.784391\pi$
$600$	−4.85337	+	1.20198i	−0.198138	+	0.0490706i
$601$	−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	0.130271	−	0.991478i	$-0.458415\pi$
$607$	25.9691	−	14.9933i	1.05405	−	0.608558i	0.923781	+	0.382921i	$0.125082\pi$
$608$	−6.30594	−	3.64074i	−0.255740	−	0.147651i
$609$	2.11423	+	3.66195i	0.0856728	+	0.148390i
$610$	−23.1968	−	9.86799i	−0.939211	−	0.399543i
$611$	20.7145	+	35.8786i	0.838019	+	1.45149i
$612$			2.05114i			0.0829123i
$613$	27.5591	+	15.9113i	1.11310	+	0.642650i	0.939631	−	0.342189i	$-0.111168\pi$
$613$	27.5591	+	15.9113i	1.11310	+	0.642650i	0.173471	+	0.984839i	$0.444502\pi$
$614$	0.202948	−	0.351516i	0.00819032	−	0.0141860i
$615$	14.1216	+	6.00738i	0.569439	+	0.242241i
$616$	2.00848			0.0809241
$617$	9.09198	+	5.24926i	0.366029	+	0.211327i	0.671722	−	0.740803i	$-0.265555\pi$
$617$	9.09198	+	5.24926i	0.366029	+	0.211327i	−0.305693	+	0.952130i	$0.598888\pi$
$618$			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	$0.318249\pi$
$620$	11.6058	+	4.50622i	0.466099	+	0.180974i
$621$	7.05585			0.283141
$622$			20.8407i			0.835638i
$623$	−9.08924	−	5.24768i	−0.364153	−	0.210244i
$624$	−4.07501			−0.163131
$625$	−0.951048	+	24.9819i	−0.0380419	+	0.999276i
$626$	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
$630$	0.774180	−	1.81987i	0.0308441	−	0.0725055i
$631$	−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
$640$	2.05762	+	0.875319i	0.0813347	+	0.0346000i
$641$	−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	$-0.974653\pi$
$643$		−	4.03418i		−	0.159092i	0.996831	−	0.0795462i	$-0.0253471\pi$
$644$	3.12029	−	5.40450i	0.122957	−	0.212967i
$645$	12.0426	−	1.46903i	0.474176	−	0.0578431i
$646$	7.46765	+	12.9343i	0.293811	+	0.508895i
$647$		−	28.5420i		−	1.12210i	−0.827782	−	0.561050i	$-0.810397\pi$
$647$		−	28.5420i		−	1.12210i	0.827782	−	0.561050i	$-0.189603\pi$
$648$	−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	$-0.919336\pi$
$653$		−	12.8131i		−	0.501417i	0.968063	−	0.250708i	$-0.0806636\pi$
$654$	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	$0.466031\pi$
$660$	−4.67260	−	1.98774i	−0.181881	−	0.0773726i
$661$	−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
$665$	−1.74375	−	14.2946i	−0.0676198	−	0.554321i
$666$	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
$670$	24.1065	−	2.94067i	0.931314	−	0.113608i
$671$	−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	−0.755824	−	0.654775i	$-0.772763\pi$
$673$	−14.7010	+	8.48765i	−0.566683	+	0.327175i	0.189140	+	0.981950i	$0.439430\pi$
$674$	26.4138			1.01742
$675$	−3.60216	+	3.46763i	−0.138647	+	0.133469i
$676$	−1.80285	+	3.12262i	−0.0693403	+	0.120101i
$677$	−20.5575	+	11.8689i	−0.790091	+	0.456159i	−0.839994	−	0.542595i	$-0.817442\pi$
$677$	−20.5575	+	11.8689i	−0.790091	+	0.456159i	0.0499038	+	0.998754i	$0.484109\pi$
$678$		−	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	$0.0146505\pi$
$683$			2.40486i			0.0920195i	−0.998941	+	0.0460097i	$0.985349\pi$
$684$	−7.28147			−0.278414
$685$	−4.97006	−	40.7426i	−0.189896	−	1.55670i
$686$	−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
$695$	16.1968	−	38.0741i	0.614381	−	1.44423i
$696$	−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
$700$	1.06310	+	4.29259i	0.0401813	+	0.162245i
$701$	−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	$0.238226\pi$
$710$	4.07060	+	33.3692i	0.152767	+	1.25232i
$711$	−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	$0.270687\pi$
$720$	2.21961	−	0.270763i	0.0827201	−	0.0100908i
$721$	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
$725$	16.5783	+	17.2214i	0.615702	+	0.639587i
$726$	2.92157	+	5.06030i	0.108430	+	0.187805i
$727$	23.1985	+	13.3937i	0.860385	+	0.496744i	0.864141	−	0.503249i	$-0.167862\pi$
$727$	23.1985	+	13.3937i	0.860385	+	0.496744i	−0.00375614	+	0.999993i	$0.501196\pi$
$728$			3.60416i			0.133579i
$729$	−1.00000			−0.0370370
$730$	−7.35005	+	0.896608i	−0.272038	+	0.0331850i
$731$	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	−0.180380	−	0.983597i	$-0.557733\pi$
$733$	15.7367	−	9.08561i	0.581250	−	0.335585i	0.761630	+	0.648012i	$0.224399\pi$
$734$	14.6534	+	25.3805i	0.540868	+	0.936811i
$735$	12.7938	+	5.44251i	0.471905	+	0.200750i
$736$	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	$0.0736429\pi$
$743$			12.5004i			0.458595i	−0.973356	+	0.229298i	$0.926357\pi$
$744$	−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
$750$	1.77503	−	11.0385i	0.0648149	−	0.403070i
$751$	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
$755$	7.78720	−	18.3055i	0.283405	−	0.666204i
$756$	−0.442227	+	0.765960i	−0.0160836	+	0.0278577i
$757$	42.0183	−	24.2593i	1.52718	−	0.881718i	0.527701	−	0.849430i	$-0.323054\pi$
$757$	42.0183	−	24.2593i	1.52718	−	0.881718i	0.999479	−	0.0322879i	$-0.0102793\pi$
$758$	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
$765$	−4.22047	−	1.79540i	−0.152591	−	0.0649128i
$766$	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	$0.280836\pi$
$770$	−1.75806	+	4.13270i	−0.0633562	+	0.148932i
$771$	−3.53047			−0.127147
$772$	−22.0101	−	12.7075i	−0.792160	−	0.457354i
$773$			0.0438161i			0.00157596i	1.00000		0.000787979i	$0.000250821\pi$
$773$			0.0438161i			0.00157596i	−1.00000		0.000787979i	$0.999749\pi$
$774$	−5.42552			−0.195016
$775$	−19.4309	+	19.9359i	−0.697977	+	0.716120i
$776$	14.8891			0.534486
$777$		−	2.16705i		−	0.0777424i
$778$	−6.04800	−	3.49182i	−0.216831	−	0.125188i
$779$	−49.9733			−1.79048
$780$	3.56693	−	8.38484i	0.127717	−	0.300225i
$781$	−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
$785$	26.3118	+	11.1931i	0.939109	+	0.399500i
$786$	4.99879	+	8.65816i	0.178301	+	0.308826i
$787$	29.7276	+	17.1632i	1.05967	+	0.611802i	0.925342	−	0.379134i	$-0.123778\pi$
$787$	29.7276	+	17.1632i	1.05967	+	0.611802i	0.134331	+	0.990937i	$0.457111\pi$
$788$	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
$795$	−5.25604	+	12.3554i	−0.186412	+	0.438202i
$796$	0.142781	+	0.247303i	0.00506073	+	0.00876544i
$797$	25.9478	−	14.9810i	0.919119	−	0.530654i	0.0357650	−	0.999360i	$-0.488613\pi$
$797$	25.9478	−	14.9810i	0.919119	−	0.530654i	0.883354	+	0.468707i	$0.155280\pi$
$798$			6.44013i			0.227978i
$799$	10.4265	−	18.0593i	0.368865	−	0.638892i
$800$	−3.60216	+	3.46763i	−0.127355	+	0.122599i
$801$	−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
$815$	5.33518	+	2.26960i	0.186883	+	0.0795006i
$816$	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
$820$	15.2334	−	1.85827i	0.531973	−	0.0648936i
$821$	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	0.876450	−	0.481493i	$-0.159905\pi$
$823$	25.7529	+	14.8684i	0.897689	+	0.518281i	0.0212396	+	0.999774i	$0.493239\pi$
$824$	5.55110	+	9.61478i	0.193382	+	0.334947i
$825$	8.18004	−	7.87455i	0.284792	−	0.274157i
$826$	6.32094	+	10.9482i	0.219934	+	0.380936i
$827$	0.509073	−	0.293914i	0.0177022	−	0.0102204i	−0.491123	−	0.871090i	$-0.663413\pi$
$827$	0.509073	−	0.293914i	0.0177022	−	0.0102204i	0.508825	+	0.860870i	$0.330080\pi$
$828$	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	$0.508858\pi$
$830$	−18.1547	+	2.21463i	−0.630158	+	0.0768708i
$831$	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	$0.605580\pi$
$840$	−0.239478	−	1.96315i	−0.00826277	−	0.0677350i
$841$	−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
$850$	9.95493	−	2.46543i	0.341451	−	0.0845634i
$851$	−8.64395	+	14.9718i	−0.296311	+	0.513225i
$852$		−	15.0338i		−	0.515049i
$853$			11.5308i			0.394807i	0.980322	+	0.197403i	$0.0632508\pi$
$853$			11.5308i			0.394807i	−0.980322	+	0.197403i	$0.936749\pi$
$854$	4.98549	−	8.63512i	0.170600	−	0.295488i
$855$	6.37361	−	14.9825i	0.217973	−	0.512392i
$856$	2.02519	−	3.50773i	0.0692196	−	0.119892i
$857$	14.3541	−	8.28736i	0.490328	−	0.283091i	−0.234383	−	0.972144i	$-0.575307\pi$
$857$	14.3541	−	8.28736i	0.490328	−	0.283091i	0.724710	+	0.689054i	$0.241974\pi$
$858$	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	−0.772092	−	0.635510i	$-0.780790\pi$
$863$	−17.8544	+	10.3082i	−0.607770	+	0.350896i	0.164322	+	0.986407i	$0.447456\pi$
$864$	−1.00000			−0.0340207
$865$	−3.72578	−	30.5425i	−0.126680	−	1.03848i
$866$	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
$875$	−9.76308	−	1.56993i	−0.330052	−	0.0530734i
$876$	3.31141			0.111882
$877$	−43.8356	+	25.3085i	−1.48022	+	0.854606i	−0.999749	−	0.0224036i	$-0.992868\pi$
$877$	−43.8356	+	25.3085i	−1.48022	+	0.854606i	−0.480472	+	0.877010i	$0.659535\pi$
$878$	27.2298	−	15.7211i	0.918960	−	0.530562i
$879$	8.94922	+	15.5005i	0.301850	+	0.522819i
$880$	−5.04046	+	0.614869i	−0.169914	+	0.0207272i
$881$	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	$-0.761988\pi$
$883$		−	40.4118i		−	1.35996i	0.733229	−	0.679982i	$-0.238012\pi$
$884$	8.35840			0.281123
$885$	−3.87014	−	31.7259i	−0.130093	−	1.06645i
$886$	18.1668	+	31.4657i	0.610324	+	1.05711i
$887$	−24.2568	−	14.0047i	−0.814465	−	0.470232i	0.0340391	−	0.999421i	$-0.489163\pi$
$887$	−24.2568	−	14.0047i	−0.814465	−	0.470232i	−0.848504	+	0.529189i	$0.822496\pi$
$888$	2.12189	−	1.22508i	0.0712061	−	0.0411108i
$889$	2.27691	+	3.94373i	0.0763652	+	0.132268i
$890$	24.4167	+	10.3869i	0.818451	+	0.348171i
$891$	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
$905$	−4.60271	+	0.561470i	−0.152999	+	0.0186639i
$906$	−4.44820	+	7.70452i	−0.147782	+	0.255965i
$907$		−	20.5075i		−	0.680942i	−0.940255	−	0.340471i	$-0.889414\pi$
$907$		−	20.5075i		−	0.680942i	0.940255	−	0.340471i	$-0.110586\pi$
$908$	−12.9755	+	7.49141i	−0.430607	+	0.248611i
$909$	4.96582	+	8.60105i	0.164706	+	0.285279i
$910$	−7.41600	−	3.15479i	−0.245838	−	0.104580i
$911$	−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	$0.954438\pi$
$920$	−6.17612	+	14.5183i	−0.203621	+	0.478654i
$921$	−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
$925$	−2.94503	−	11.8915i	−0.0968321	−	0.390990i
$926$	−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	$0.497909\pi$
$930$	9.70539	−	7.79779i	0.318252	−	0.255699i
$931$	−45.2743			−1.48381
$932$			16.7264i			0.547891i
$933$	18.0486	+	10.4204i	0.590885	+	0.341148i
$934$	32.7979			1.07318
$935$	9.58415	+	4.07712i	0.313435	+	0.133336i
$936$	−2.03750	+	3.52906i	−0.0665979	+	0.115351i
$937$	5.18660	+	2.99448i	0.169439	+	0.0978255i	0.582321	−	0.812959i	$-0.302145\pi$
$937$	5.18660	+	2.99448i	0.169439	+	0.0978255i	−0.412882	+	0.910784i	$0.635478\pi$
$938$			9.60576i			0.313639i
$939$	−4.86202	−	8.42126i	−0.158666	−	0.274817i
$940$	−20.9190	−	8.89902i	−0.682304	−	0.290254i
$941$	−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	0.935968	−	0.352085i	$-0.114527\pi$
$947$	33.8211	+	19.5266i	1.09904	+	0.634529i	0.163069	+	0.986615i	$0.447861\pi$
$948$	−14.1853	+	8.18988i	−0.460717	+	0.265995i
$949$	6.74701	−	11.6862i	0.219017	−	0.379349i
$950$	8.75219	+	35.3397i	0.283958	+	1.14657i
$951$	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	$0.0821922\pi$
$953$			15.7659i			0.510709i	−0.966847	+	0.255355i	$0.917808\pi$
$954$	3.00236	−	5.20023i	0.0972048	−	0.168364i
$955$	47.4671	−	5.79035i	1.53600	−	0.187371i
$956$	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	0.396747	−	0.917928i	$-0.370139\pi$
$967$	−6.21397	−	3.58764i	−0.199828	−	0.115371i	−0.596575	+	0.802557i	$0.703472\pi$
$968$	5.06030	+	2.92157i	0.162644	+	0.0939027i
$969$	14.9353			0.479791
$970$	−13.0327	+	30.6361i	−0.418454	+	0.983666i
$971$	−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
$975$	14.1306	+	14.6788i	0.452542	+	0.470098i
$976$	11.2736			0.360859
$977$		−	25.1123i		−	0.803414i	−0.915768	−	0.401707i	$-0.868417\pi$
$977$		−	25.1123i		−	0.803414i	0.915768	−	0.401707i	$-0.131583\pi$
$978$	−2.24550	−	1.29644i	−0.0718032	−	0.0414556i
$979$	13.4736	+	23.3370i	0.430619	+	0.745854i
$980$	13.8010	−	1.68354i	0.440856	−	0.0537786i
$981$	−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	−0.491965	−	0.870615i	$-0.663721\pi$
$983$	0.502493	−	0.290114i	0.0160270	−	0.00925321i	0.507992	+	0.861362i	$0.330388\pi$
$984$	−6.86308			−0.218787
$985$	0.803632	+	6.58787i	0.0256059	+	0.209907i
$986$	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
$995$	−0.633836	+	0.0773196i	−0.0200940	+	0.00245119i
$996$	8.17920			0.259168
$997$	41.3509	−	23.8739i	1.30960	−	0.756095i	0.327567	−	0.944828i	$-0.393771\pi$
$997$	41.3509	−	23.8739i	1.30960	−	0.756095i	0.982029	+	0.188732i	$0.0604379\pi$
$998$	−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.439.4	✓	24
5.4	even	2	inner	930.2.s.c.439.7	yes	24
31.25	even	3	inner	930.2.s.c.769.1	yes	24
155.149	even	6	inner	930.2.s.c.769.10	yes	24

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.875319 - 2.05762i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.765960 + 0.442227i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(0.875319 - 2.05762i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.765960 + 0.442227i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.05762 - 0.875319i) 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} +(-0.875319 + 2.05762i) q^{20} +(-0.442227 - 0.765960i) q^{21} +(-1.96663 + 1.13544i) q^{22} +7.05585i q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.46763 - 3.60216i) 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} +(2.05762 + 0.875319i) 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} +(2.21961 - 0.270763i) q^{45} +7.05585 q^{46} +10.1666i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-3.10887 - 5.38472i) q^{49} +(-3.60216 + 3.46763i) q^{50} +(1.02557 + 1.77634i) q^{51} +(-3.52906 + 2.03750i) q^{52} +(5.20023 - 3.00236i) q^{53} -1.00000 q^{54} +(-5.04046 + 0.614869i) 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} +(-1.10336 - 9.04495i) 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} +(1.20198 + 4.85337i) q^{75} +(-3.64074 + 6.30594i) q^{76} -2.00848i q^{77} +4.07501i q^{78} +(-8.18988 + 14.1853i) q^{79} +(0.875319 - 2.05762i) 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} +(-0.270763 - 2.21961i) 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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