LMFDB - Embedded newform 231.2.y.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	231.16
Dual form			231.2.y.a.130.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27562 - 0.271142i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.273395 - 0.121723i) q^{4} +(-0.103450 - 0.114892i) q^{5} +(-0.402996 + 1.24029i) q^{6} +(1.44851 - 2.21401i) q^{7} +(2.42586 + 1.76249i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-1.27562 - 0.271142i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.273395 - 0.121723i) q^{4} +(-0.103450 - 0.114892i) q^{5} +(-0.402996 + 1.24029i) q^{6} +(1.44851 - 2.21401i) q^{7} +(2.42586 + 1.76249i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.100810 + 0.174609i) q^{10} +(-3.23677 - 0.723422i) q^{11} +(-0.149634 + 0.259174i) q^{12} +(-1.38817 - 4.27234i) q^{13} +(-2.44806 + 2.43149i) q^{14} +(-0.125076 + 0.0908734i) q^{15} +(-2.21609 - 2.46122i) q^{16} +(-3.45715 + 0.734839i) q^{17} +(1.19137 + 0.530434i) q^{18} +(-3.40147 + 1.51443i) q^{19} +(0.0142975 + 0.0440033i) q^{20} +(-2.05047 - 1.67200i) q^{21} +(3.93274 + 1.80044i) q^{22} +(-0.285690 + 0.494829i) q^{23} +(2.00640 - 2.22834i) q^{24} +(0.520144 - 4.94884i) q^{25} +(0.612368 + 5.82629i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.665512 + 0.428982i) q^{28} +(-1.95460 + 1.42010i) q^{29} +(0.184190 - 0.0820066i) q^{30} +(4.80076 - 5.33179i) q^{31} +(-0.838964 - 1.45313i) q^{32} +(-1.05779 + 3.14342i) q^{33} +4.60926 q^{34} +(-0.404220 + 0.0626156i) q^{35} +(0.242113 + 0.175906i) q^{36} +(0.500772 + 4.76453i) q^{37} +(4.74962 - 1.00956i) q^{38} +(-4.39404 + 0.933983i) q^{39} +(-0.0484574 - 0.461041i) q^{40} +(-4.14207 - 3.00939i) q^{41} +(2.16227 + 2.68881i) q^{42} +6.28052 q^{43} +(0.796860 + 0.591771i) q^{44} +(0.0773015 + 0.133890i) q^{45} +(0.498601 - 0.553752i) q^{46} +(6.97299 - 3.10458i) q^{47} +(-2.67938 + 1.94669i) q^{48} +(-2.80365 - 6.41401i) q^{49} +(-2.00535 + 6.17182i) q^{50} +(0.369444 + 3.51502i) q^{51} +(-0.140526 + 1.33701i) q^{52} +(4.11992 - 4.57564i) q^{53} +(0.652060 - 1.12940i) q^{54} +(0.251726 + 0.446718i) q^{55} +(7.41603 - 2.81789i) q^{56} +(1.15058 + 3.54114i) q^{57} +(2.87839 - 1.28154i) q^{58} +(8.60235 + 3.83001i) q^{59} +(0.0452568 - 0.00961962i) q^{60} +(4.71868 + 5.24063i) q^{61} +(-7.56963 + 5.49966i) q^{62} +(-1.87717 + 1.86446i) q^{63} +(2.72307 + 8.38073i) q^{64} +(-0.347254 + 0.601462i) q^{65} +(2.20166 - 3.72300i) q^{66} +(6.87041 + 11.8999i) q^{67} +(1.03462 + 0.219914i) q^{68} +(0.462255 + 0.335848i) q^{69} +(0.532610 + 0.0297272i) q^{70} +(1.82585 - 5.61938i) q^{71} +(-2.00640 - 2.22834i) q^{72} +(-6.73763 - 2.99979i) q^{73} +(0.653067 - 6.21352i) q^{74} +(-4.86736 - 1.03459i) q^{75} +1.11429 q^{76} +(-6.29014 + 6.11834i) q^{77} +5.85838 q^{78} +(-4.17114 - 0.886603i) q^{79} +(-0.0535217 + 0.509225i) q^{80} +(0.913545 + 0.406737i) q^{81} +(4.46775 + 4.96194i) q^{82} +(-1.10089 + 3.38819i) q^{83} +(0.357067 + 0.706707i) q^{84} +(0.442068 + 0.321181i) q^{85} +(-8.01157 - 1.70291i) q^{86} +(1.20801 + 2.09234i) q^{87} +(-6.57691 - 7.45968i) q^{88} +(5.82649 - 10.0918i) q^{89} +(-0.0623043 - 0.191753i) q^{90} +(-11.4698 - 3.11511i) q^{91} +(0.138338 - 0.100509i) q^{92} +(-4.80076 - 5.33179i) q^{93} +(-9.73669 + 2.06960i) q^{94} +(0.525877 + 0.234136i) q^{95} +(-1.53286 + 0.682475i) q^{96} +(-2.74944 - 8.46191i) q^{97} +(1.83730 + 8.94205i) q^{98} +(3.01563 + 1.38058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−1.27562	−	0.271142i	−0.902002	−	0.191726i	−0.266508	−	0.963833i	$-0.585870\pi$
$2$	−1.27562	−	0.271142i	−0.902002	−	0.191726i	−0.635493	+	0.772106i	$0.719203\pi$
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	−0.273395	−	0.121723i	−0.136698	−	0.0608617i
$5$	−0.103450	−	0.114892i	−0.0462641	−	0.0513814i	0.719569	−	0.694421i	$-0.244340\pi$
$5$	−0.103450	−	0.114892i	−0.0462641	−	0.0513814i	−0.765833	+	0.643040i	$0.777673\pi$
$6$	−0.402996	+	1.24029i	−0.164522	+	0.506347i
$7$	1.44851	−	2.21401i	0.547484	−	0.836816i
$7$	1.44851	−	2.21401i	0.547484	−	0.836816i
$8$	2.42586	+	1.76249i	0.857670	+	0.623134i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	0.100810	+	0.174609i	0.0318791	+	0.0552162i
$11$	−3.23677	−	0.723422i	−0.975922	−	0.218120i
$11$	−3.23677	−	0.723422i	−0.975922	−	0.218120i
$12$	−0.149634	+	0.259174i	−0.0431957	+	0.0748171i
$13$	−1.38817	−	4.27234i	−0.385009	−	1.18494i	−0.936474	−	0.350737i	$-0.885931\pi$
$13$	−1.38817	−	4.27234i	−0.385009	−	1.18494i	0.551465	−	0.834198i	$-0.314069\pi$
$14$	−2.44806	+	2.43149i	−0.654271	+	0.649842i
$15$	−0.125076	+	0.0908734i	−0.0322946	+	0.0234634i
$16$	−2.21609	−	2.46122i	−0.554024	−	0.615306i
$17$	−3.45715	+	0.734839i	−0.838481	+	0.178225i	−0.607087	−	0.794635i	$-0.707662\pi$
$17$	−3.45715	+	0.734839i	−0.838481	+	0.178225i	−0.231394	+	0.972860i	$0.574329\pi$
$18$	1.19137	+	0.530434i	0.280809	+	0.125024i
$19$	−3.40147	+	1.51443i	−0.780350	+	0.347434i	−0.757948	−	0.652315i	$-0.773798\pi$
$19$	−3.40147	+	1.51443i	−0.780350	+	0.347434i	−0.0224022	+	0.999749i	$0.507131\pi$
$20$	0.0142975	+	0.0440033i	0.00319703	+	0.00983944i
$21$	−2.05047	−	1.67200i	−0.447449	−	0.364860i
$22$	3.93274	+	1.80044i	0.838464	+	0.383855i
$23$	−0.285690	+	0.494829i	−0.0595704	+	0.103179i	−0.894273	−	0.447523i	$-0.852306\pi$
$23$	−0.285690	+	0.494829i	−0.0595704	+	0.103179i	0.834702	+	0.550702i	$0.185640\pi$
$24$	2.00640	−	2.22834i	0.409556	−	0.454858i
$25$	0.520144	−	4.94884i	0.104029	−	0.989768i
$26$	0.612368	+	5.82629i	0.120095	+	1.14263i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.665512	+	0.428982i	−0.125770	+	0.0810700i
$29$	−1.95460	+	1.42010i	−0.362961	+	0.263706i	−0.754286	−	0.656546i	$-0.772017\pi$
$29$	−1.95460	+	1.42010i	−0.362961	+	0.263706i	0.391325	+	0.920252i	$0.372017\pi$
$30$	0.184190	−	0.0820066i	0.0336283	−	0.0149723i
$31$	4.80076	−	5.33179i	0.862242	−	0.957617i	−0.137216	−	0.990541i	$-0.543815\pi$
$31$	4.80076	−	5.33179i	0.862242	−	0.957617i	0.999458	+	0.0329241i	$0.0104820\pi$
$32$	−0.838964	−	1.45313i	−0.148309	−	0.256879i
$33$	−1.05779	+	3.14342i	−0.184138	+	0.547199i
$34$	4.60926			0.790482
$35$	−0.404220	+	0.0626156i	−0.0683257	+	0.0105840i
$36$	0.242113	+	0.175906i	0.0403522	+	0.0293176i
$37$	0.500772	+	4.76453i	0.0823264	+	0.783283i	0.955324	+	0.295559i	$0.0955060\pi$
$37$	0.500772	+	4.76453i	0.0823264	+	0.783283i	−0.872998	+	0.487724i	$0.837827\pi$
$38$	4.74962	−	1.00956i	0.770490	−	0.163773i
$39$	−4.39404	+	0.933983i	−0.703610	+	0.149557i
$40$	−0.0484574	−	0.461041i	−0.00766179	−	0.0728970i
$41$	−4.14207	−	3.00939i	−0.646883	−	0.469988i	0.215325	−	0.976542i	$-0.430919\pi$
$41$	−4.14207	−	3.00939i	−0.646883	−	0.469988i	−0.862208	+	0.506554i	$0.830919\pi$
$42$	2.16227	+	2.68881i	0.333646	+	0.414892i
$43$	6.28052			0.957770			0.478885	−	0.877878i	$-0.341041\pi$
$43$	6.28052			0.957770			0.478885	+	0.877878i	$0.341041\pi$
$44$	0.796860	+	0.591771i	0.120131	+	0.0892128i
$45$	0.0773015	+	0.133890i	0.0115234	+	0.0199592i
$46$	0.498601	−	0.553752i	0.0735147	−	0.0816463i
$47$	6.97299	−	3.10458i	1.01712	−	0.452849i	0.170672	−	0.985328i	$-0.445406\pi$
$47$	6.97299	−	3.10458i	1.01712	−	0.452849i	0.846443	+	0.532479i	$0.178739\pi$
$48$	−2.67938	+	1.94669i	−0.386736	+	0.280980i
$49$	−2.80365	−	6.41401i	−0.400522	−	0.916287i
$50$	−2.00535	+	6.17182i	−0.283599	+	0.872827i
$51$	0.369444	+	3.51502i	0.0517324	+	0.492201i
$52$	−0.140526	+	1.33701i	−0.0194874	+	0.185410i
$53$	4.11992	−	4.57564i	0.565915	−	0.628512i	−0.390472	−	0.920615i	$-0.627688\pi$
$53$	4.11992	−	4.57564i	0.565915	−	0.628512i	0.956387	+	0.292103i	$0.0943549\pi$
$54$	0.652060	−	1.12940i	0.0887342	−	0.153692i
$55$	0.251726	+	0.446718i	0.0339428	+	0.0602354i
$56$	7.41603	−	2.81789i	0.991009	−	0.376556i
$57$	1.15058	+	3.54114i	0.152399	+	0.469035i
$58$	2.87839	−	1.28154i	0.377950	−	0.168274i
$59$	8.60235	+	3.83001i	1.11993	+	0.498625i	0.881334	−	0.472494i	$-0.156646\pi$
$59$	8.60235	+	3.83001i	1.11993	+	0.498625i	0.238597	+	0.971119i	$0.423313\pi$
$60$	0.0452568	−	0.00961962i	0.00584262	−	0.00124189i
$61$	4.71868	+	5.24063i	0.604166	+	0.670994i	0.965186	−	0.261564i	$-0.0842383\pi$
$61$	4.71868	+	5.24063i	0.604166	+	0.670994i	−0.361021	+	0.932558i	$0.617572\pi$
$62$	−7.56963	+	5.49966i	−0.961344	+	0.698458i
$63$	−1.87717	+	1.86446i	−0.236501	+	0.234900i
$64$	2.72307	+	8.38073i	0.340383	+	1.04759i
$65$	−0.347254	+	0.601462i	−0.0430716	+	0.0746022i
$66$	2.20166	−	3.72300i	0.271005	−	0.458270i
$67$	6.87041	+	11.8999i	0.839354	+	1.45380i	0.890436	+	0.455109i	$0.150400\pi$
$67$	6.87041	+	11.8999i	0.839354	+	1.45380i	−0.0510822	+	0.998694i	$0.516267\pi$
$68$	1.03462	+	0.219914i	0.125466	+	0.0266685i
$69$	0.462255	+	0.335848i	0.0556490	+	0.0404314i
$70$	0.532610	+	0.0297272i	0.0636591	+	0.00355307i
$71$	1.82585	−	5.61938i	0.216688	−	0.666898i	−0.782341	−	0.622850i	$-0.785975\pi$
$71$	1.82585	−	5.61938i	0.216688	−	0.666898i	0.999029	−	0.0440477i	$-0.0140254\pi$
$72$	−2.00640	−	2.22834i	−0.236457	−	0.262612i
$73$	−6.73763	−	2.99979i	−0.788580	−	0.351099i	−0.0273880	−	0.999625i	$-0.508719\pi$
$73$	−6.73763	−	2.99979i	−0.788580	−	0.351099i	−0.761192	+	0.648526i	$0.775386\pi$
$74$	0.653067	−	6.21352i	0.0759175	−	0.722307i
$75$	−4.86736	−	1.03459i	−0.562034	−	0.119464i
$76$	1.11429			0.127818
$77$	−6.29014	+	6.11834i	−0.716828	+	0.697250i
$78$	5.85838			0.663331
$79$	−4.17114	−	0.886603i	−0.469290	−	0.0997506i	−0.0328040	−	0.999462i	$-0.510444\pi$
$79$	−4.17114	−	0.886603i	−0.469290	−	0.0997506i	−0.436486	+	0.899711i	$0.643777\pi$
$80$	−0.0535217	+	0.509225i	−0.00598391	+	0.0569331i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	4.46775	+	4.96194i	0.493380	+	0.547954i
$83$	−1.10089	+	3.38819i	−0.120838	+	0.371902i	−0.993120	−	0.117102i	$-0.962640\pi$
$83$	−1.10089	+	3.38819i	−0.120838	+	0.371902i	0.872282	+	0.489004i	$0.162640\pi$
$84$	0.357067	+	0.706707i	0.0389592	+	0.0771081i
$85$	0.442068	+	0.321181i	0.0479490	+	0.0348370i
$86$	−8.01157	−	1.70291i	−0.863910	−	0.183630i
$87$	1.20801	+	2.09234i	0.129512	+	0.224322i
$88$	−6.57691	−	7.45968i	−0.701101	−	0.795205i
$89$	5.82649	−	10.0918i	0.617607	−	1.06973i	−0.372314	−	0.928107i	$-0.621436\pi$
$89$	5.82649	−	10.0918i	0.617607	−	1.06973i	0.989921	−	0.141620i	$-0.0452311\pi$
$90$	−0.0623043	−	0.191753i	−0.00656745	−	0.0202125i
$91$	−11.4698	−	3.11511i	−1.20236	−	0.326552i
$92$	0.138338	−	0.100509i	0.0144228	−	0.0104788i
$93$	−4.80076	−	5.33179i	−0.497816	−	0.552881i
$94$	−9.73669	+	2.06960i	−1.00426	+	0.213463i
$95$	0.525877	+	0.234136i	0.0539539	+	0.0240218i
$96$	−1.53286	+	0.682475i	−0.156447	+	0.0696548i
$97$	−2.74944	−	8.46191i	−0.279164	−	0.859177i	−0.988088	−	0.153892i	$-0.950819\pi$
$97$	−2.74944	−	8.46191i	−0.279164	−	0.859177i	0.708924	−	0.705285i	$-0.249181\pi$
$98$	1.83730	+	8.94205i	0.185595	+	0.903283i
$99$	3.01563	+	1.38058i	0.303082	+	0.138753i
$100$	−0.744595	+	1.28968i	−0.0744595	+	0.128968i
$101$	12.4641	−	13.8427i	1.24022	−	1.37740i	0.340909	−	0.940096i	$-0.389265\pi$
$101$	12.4641	−	13.8427i	1.24022	−	1.37740i	0.899312	−	0.437308i	$-0.144068\pi$
$102$	0.481799	−	4.58401i	0.0477052	−	0.453885i
$103$	−0.642508	−	6.11306i	−0.0633082	−	0.602337i	−0.979479	−	0.201548i	$-0.935403\pi$
$103$	−0.642508	−	6.11306i	−0.0633082	−	0.602337i	0.916170	−	0.400789i	$-0.131264\pi$
$104$	4.16246	−	12.8107i	0.408163	−	1.25620i
$105$	0.0200201	+	0.408551i	0.00195376	+	0.0398705i
$106$	−6.49611	+	4.71970i	−0.630958	+	0.458418i
$107$	−17.1511	+	7.63616i	−1.65806	+	0.738216i	−0.999893	−	0.0146562i	$-0.995335\pi$
$107$	−17.1511	+	7.63616i	−1.65806	+	0.738216i	−0.658167	+	0.752872i	$0.728668\pi$
$108$	0.200250	−	0.222400i	0.0192690	−	0.0214004i
$109$	−0.414639	−	0.718176i	−0.0397152	−	0.0687888i	0.845485	−	0.534000i	$-0.179312\pi$
$109$	−0.414639	−	0.718176i	−0.0397152	−	0.0687888i	−0.885200	+	0.465211i	$0.845978\pi$
$110$	−0.199984	−	0.638097i	−0.0190677	−	0.0608401i
$111$	4.79077			0.454720
$112$	−8.65919	+	1.34135i	−0.818217	+	0.126746i
$113$	−0.819785	−	0.595608i	−0.0771188	−	0.0560301i	0.548558	−	0.836113i	$-0.315177\pi$
$113$	−0.819785	−	0.595608i	−0.0771188	−	0.0560301i	−0.625677	+	0.780083i	$0.715177\pi$
$114$	−0.507562	−	4.82913i	−0.0475375	−	0.452289i
$115$	0.0864065	−	0.0183663i	0.00805745	−	0.00171266i
$116$	0.707239	−	0.150328i	0.0656655	−	0.0139576i
$117$	0.469564	+	4.46760i	0.0434112	+	0.413030i
$118$	−9.93488	−	7.21811i	−0.914580	−	0.664481i
$119$	−3.38076	+	8.71857i	−0.309914	+	0.799230i
$120$	−0.463581			−0.0423189
$121$	9.95332	+	4.68310i	0.904847	+	0.425736i
$122$	−4.59831	−	7.96450i	−0.416311	−	0.721072i
$123$	−3.42587	+	3.80481i	−0.308900	+	0.343069i
$124$	−1.96151	+	0.873321i	−0.176149	+	0.0784265i
$125$	−1.24777	+	0.906561i	−0.111604	+	0.0810853i
$126$	2.90010	−	1.86937i	0.258361	−	0.166537i
$127$	−6.50604	+	20.0235i	−0.577318	+	1.77680i	0.0508289	+	0.998707i	$0.483814\pi$
$127$	−6.50604	+	20.0235i	−0.577318	+	1.77680i	−0.628147	+	0.778095i	$0.716186\pi$
$128$	−0.850453	−	8.09152i	−0.0751701	−	0.715196i
$129$	0.656493	−	6.24611i	0.0578010	−	0.549940i
$130$	0.606047	−	0.673084i	0.0531539	−	0.0590334i
$131$	7.59250	−	13.1506i	0.663359	−	1.14897i	−0.316368	−	0.948637i	$-0.602463\pi$
$131$	7.59250	−	13.1506i	0.663359	−	1.14897i	0.979727	−	0.200336i	$-0.0642033\pi$
$132$	0.671824	−	0.730638i	0.0584747	−	0.0635938i
$133$	−1.57409	+	9.72454i	−0.136491	+	0.843225i
$134$	−5.53749	−	17.0426i	−0.478366	−	1.47226i
$135$	0.141237	−	0.0628827i	0.0121557	−	0.00541208i
$136$	−9.68169	−	4.31057i	−0.830198	−	0.369628i
$137$	−9.72865	+	2.06789i	−0.831175	+	0.176672i	−0.603800	−	0.797136i	$-0.706348\pi$
$137$	−9.72865	+	2.06789i	−0.831175	+	0.176672i	−0.227375	+	0.973807i	$0.573014\pi$
$138$	−0.498601	−	0.553752i	−0.0424437	−	0.0471385i
$139$	12.5939	−	9.14999i	1.06820	−	0.776092i	0.0926115	−	0.995702i	$-0.470479\pi$
$139$	12.5939	−	9.14999i	1.06820	−	0.776092i	0.975588	+	0.219610i	$0.0704785\pi$
$140$	0.118134	+	0.0320843i	0.00998412	+	0.00271161i
$141$	−2.35869	−	7.25931i	−0.198638	−	0.611344i
$142$	−3.85274	+	6.67315i	−0.323315	+	0.559998i
$143$	1.40247	+	14.8328i	0.117280	+	1.24038i
$144$	1.65595	+	2.86819i	0.137996	+	0.239016i
$145$	0.365362	+	0.0776600i	0.0303416	+	0.00644932i
$146$	7.78131	+	5.65345i	0.643986	+	0.467883i
$147$	−6.67194	+	2.11785i	−0.550292	+	0.174677i
$148$	0.443046	−	1.36356i	0.0364182	−	0.112084i
$149$	−5.72923	−	6.36296i	−0.469357	−	0.521274i	0.461262	−	0.887264i	$-0.347397\pi$
$149$	−5.72923	−	6.36296i	−0.469357	−	0.521274i	−0.930619	+	0.365990i	$0.880730\pi$
$150$	5.92839	+	2.63949i	0.484051	+	0.215513i
$151$	−0.380892	+	3.62395i	−0.0309966	+	0.294913i	0.968031	+	0.250830i	$0.0807034\pi$
$151$	−0.380892	+	3.62395i	−0.0309966	+	0.294913i	−0.999028	+	0.0440833i	$0.985963\pi$
$152$	−10.9206	−	2.32125i	−0.885781	−	0.188279i
$153$	3.53438			0.285738
$154$	9.68279	−	6.09917i	0.780261	−	0.491485i
$155$	−1.10922			−0.0890946
$156$	1.31500	+	0.279512i	0.105284	+	0.0223788i
$157$	−0.385718	+	3.66986i	−0.0307837	+	0.292887i	0.968289	+	0.249832i	$0.0803755\pi$
$157$	−0.385718	+	3.66986i	−0.0307837	+	0.292887i	−0.999073	+	0.0430544i	$0.986291\pi$
$158$	5.08040	+	2.26194i	0.404175	+	0.179950i
$159$	−4.11992	−	4.57564i	−0.326731	−	0.362872i
$160$	−0.0801630	+	0.246716i	−0.00633744	+	0.0195046i
$161$	0.681731	+	1.34928i	0.0537279	+	0.106338i
$162$	−1.05506	−	0.766543i	−0.0828930	−	0.0602253i
$163$	23.9824	+	5.09761i	1.87845	+	0.399276i	0.997291	−	0.0735539i	$-0.0234341\pi$
$163$	23.9824	+	5.09761i	1.87845	+	0.399276i	0.881154	+	0.472830i	$0.156767\pi$
$164$	0.766110	+	1.32694i	0.0598231	+	0.103617i
$165$	0.470583	−	0.203653i	0.0366348	−	0.0158543i
$166$	2.32300	−	4.02355i	0.180300	−	0.312288i
$167$	4.34417	+	13.3700i	0.336162	+	1.03460i	0.966147	+	0.257993i	$0.0830611\pi$
$167$	4.34417	+	13.3700i	0.336162	+	1.03460i	−0.629985	+	0.776608i	$0.716939\pi$
$168$	−2.02726	−	7.66996i	−0.156407	−	0.591750i
$169$	−5.80870	+	4.22027i	−0.446823	+	0.324636i
$170$	−0.476826	−	0.529569i	−0.0365709	−	0.0406161i
$171$	3.64201	−	0.774132i	0.278511	−	0.0591994i
$172$	−1.71707	−	0.764487i	−0.130925	−	0.0582916i
$173$	13.3077	−	5.92497i	1.01177	−	0.450467i	0.167203	−	0.985923i	$-0.446527\pi$
$173$	13.3077	−	5.92497i	1.01177	−	0.450467i	0.844564	+	0.535455i	$0.179860\pi$
$174$	−0.973646	−	2.99657i	−0.0738119	−	0.227170i
$175$	−10.2033	−	8.32003i	−0.771299	−	0.628935i
$176$	5.39248	+	9.56957i	0.406473	+	0.721334i
$177$	4.70822	−	8.15488i	0.353892	−	0.612958i
$178$	−10.1687	+	11.2935i	−0.762177	+	0.846484i
$179$	−2.65388	+	25.2500i	−0.198361	+	1.88728i	0.214861	+	0.976645i	$0.431070\pi$
$179$	−2.65388	+	25.2500i	−0.198361	+	1.88728i	−0.413222	+	0.910630i	$0.635597\pi$
$180$	−0.00483630	−	0.0460144i	−0.000360477	−	0.00342971i
$181$	−0.175056	+	0.538765i	−0.0130118	+	0.0400461i	−0.957352	−	0.288925i	$-0.906702\pi$
$181$	−0.175056	+	0.538765i	−0.0130118	+	0.0400461i	0.944340	+	0.328972i	$0.106702\pi$
$182$	13.7865	+	7.08364i	1.02192	+	0.525074i
$183$	5.70516	−	4.14504i	0.421737	−	0.306410i
$184$	−1.56517	+	0.696859i	−0.115386	+	0.0513732i
$185$	0.495603	−	0.550423i	0.0364375	−	0.0404679i
$186$	4.67829	+	8.10304i	0.343029	+	0.594143i
$187$	11.7216	+	0.122473i	0.857167	+	0.00895613i
$188$	−2.28428			−0.166599
$189$	1.65803	+	2.06178i	0.120604	+	0.149972i
$190$	−0.607337	−	0.441256i	−0.0440609	−	0.0320121i
$191$	−0.435838	−	4.14672i	−0.0315361	−	0.300046i	−0.998909	−	0.0466907i	$-0.985132\pi$
$191$	−0.435838	−	4.14672i	−0.0315361	−	0.300046i	0.967373	−	0.253355i	$-0.0815342\pi$
$192$	8.61946	−	1.83212i	0.622056	−	0.132222i
$193$	13.6912	−	2.91016i	0.985515	−	0.209478i	0.313155	−	0.949702i	$-0.398614\pi$
$193$	13.6912	−	2.91016i	0.985515	−	0.209478i	0.672360	+	0.740224i	$0.265281\pi$
$194$	1.21287	+	11.5397i	0.0870791	+	0.828502i
$195$	0.561870	+	0.408222i	0.0402363	+	0.0292334i
$196$	−0.0142299	+	2.09483i	−0.00101642	+	0.149631i
$197$	−13.6176			−0.970217			−0.485108	−	0.874454i	$-0.661220\pi$
$197$	−13.6176			−0.970217			−0.485108	+	0.874454i	$0.661220\pi$
$198$	−3.47247	−	2.57876i	−0.246778	−	0.183264i
$199$	−0.860980	−	1.49126i	−0.0610333	−	0.105713i	0.833894	−	0.551924i	$-0.186106\pi$
$199$	−0.860980	−	1.49126i	−0.0610333	−	0.105713i	−0.894928	+	0.446211i	$0.852773\pi$
$200$	9.98406	−	11.0884i	0.705980	−	0.784070i
$201$	12.5529	−	5.58889i	0.885410	−	0.394210i
$202$	−19.6528	+	14.2786i	−1.38277	+	1.00464i
$203$	0.312859	+	6.38453i	0.0219584	+	0.448106i
$204$	0.326856	−	1.00596i	0.0228845	−	0.0704313i
$205$	0.0827394	+	0.787213i	0.00577877	+	0.0549813i
$206$	−0.837908	+	7.97216i	−0.0583798	+	0.555447i
$207$	0.382327	−	0.424617i	0.0265736	−	0.0295129i
$208$	−7.43888	+	12.8845i	−0.515793	+	0.893380i
$209$	12.1053	−	2.44116i	0.837344	−	0.168859i
$210$	0.0852372	−	0.526585i	0.00588193	−	0.0363378i
$211$	−2.02805	−	6.24168i	−0.139616	−	0.429695i	0.856663	−	0.515876i	$-0.172534\pi$
$211$	−2.02805	−	6.24168i	−0.139616	−	0.429695i	−0.996279	+	0.0861812i	$0.972534\pi$
$212$	−1.68333	+	0.749467i	−0.115612	+	0.0514736i
$213$	−5.39774	−	2.40323i	−0.369847	−	0.164667i
$214$	23.9488	−	5.09048i	1.63711	−	0.347978i
$215$	−0.649717	−	0.721584i	−0.0443103	−	0.0492116i
$216$	−2.42586	+	1.76249i	−0.165059	+	0.119922i
$217$	−4.85067	−	18.3521i	−0.329285	−	1.24582i
$218$	0.334195	+	1.02855i	0.0226346	+	0.0696620i
$219$	−3.68763	+	6.38716i	−0.249187	+	0.431604i
$220$	−0.0144448	−	0.152772i	−0.000973871	−	0.0102999i
$221$	7.93859	+	13.7500i	0.534008	+	0.924928i
$222$	−6.11122	−	1.29898i	−0.410158	−	0.0871818i
$223$	12.1530	+	8.82965i	0.813823	+	0.591277i	0.914937	−	0.403598i	$-0.132240\pi$
$223$	12.1530	+	8.82965i	0.813823	+	0.591277i	−0.101113	+	0.994875i	$0.532240\pi$
$224$	−4.43248	−	0.247395i	−0.296158	−	0.0165298i
$225$	−1.53770	+	4.73255i	−0.102513	+	0.315503i
$226$	0.884241	+	0.982050i	0.0588189	+	0.0653250i
$227$	−12.9391	−	5.76088i	−0.858801	−	0.382363i	−0.0703959	−	0.997519i	$-0.522426\pi$
$227$	−12.9391	−	5.76088i	−0.858801	−	0.382363i	−0.788405	+	0.615156i	$0.789093\pi$
$228$	0.116475	−	1.10818i	0.00771373	−	0.0733913i
$229$	−11.9086	−	2.53125i	−0.786943	−	0.167270i	−0.203123	−	0.979153i	$-0.565109\pi$
$229$	−11.9086	−	2.53125i	−0.786943	−	0.167270i	−0.583820	+	0.811883i	$0.698443\pi$
$230$	−0.115202			−0.00759620
$231$	5.42733	+	6.89523i	0.357092	+	0.453673i
$232$	−7.24450			−0.475625
$233$	14.7443	+	3.13400i	0.965933	+	0.205315i	0.663766	−	0.747940i	$-0.268957\pi$
$233$	14.7443	+	3.13400i	0.965933	+	0.205315i	0.302166	+	0.953255i	$0.402290\pi$
$234$	0.612368	−	5.82629i	0.0400317	−	0.380877i
$235$	−1.07805	−	0.479977i	−0.0703239	−	0.0313102i
$236$	−1.88564	−	2.09422i	−0.122745	−	0.136322i
$237$	−1.31775	+	4.05561i	−0.0855969	+	0.263440i
$238$	6.67655	−	10.2049i	0.432776	−	0.661488i
$239$	−11.7175	−	8.51324i	−0.757940	−	0.550676i	0.140338	−	0.990104i	$-0.455181\pi$
$239$	−11.7175	−	8.51324i	−0.757940	−	0.550676i	−0.898278	+	0.439428i	$0.855181\pi$
$240$	0.500841	+	0.106457i	0.0323291	+	0.00687177i
$241$	−6.87041	−	11.8999i	−0.442562	−	0.766540i	0.555317	−	0.831639i	$-0.312597\pi$
$241$	−6.87041	−	11.8999i	−0.442562	−	0.766540i	−0.997879	+	0.0650991i	$0.979264\pi$
$242$	−11.4269	−	8.67263i	−0.734549	−	0.557498i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.652159	−	2.00714i	−0.0417502	−	0.128494i
$245$	−0.446884	+	0.985645i	−0.0285504	+	0.0629706i
$246$	5.40176	−	3.92461i	0.344404	−	0.250224i
$247$	11.1920	+	12.4300i	0.712129	+	0.790899i
$248$	21.0432	−	4.47286i	1.33624	−	0.284027i
$249$	3.25455	+	1.44902i	0.206249	+	0.0918279i
$250$	1.83750	−	0.818106i	0.116214	−	0.0517416i
$251$	−4.35998	−	13.4186i	−0.275200	−	0.846977i	−0.989167	−	0.146798i	$-0.953103\pi$
$251$	−4.35998	−	13.4186i	−0.275200	−	0.846977i	0.713967	−	0.700179i	$-0.246897\pi$
$252$	0.740159	−	0.281240i	0.0466257	−	0.0177165i
$253$	1.28268	−	1.39497i	0.0806414	−	0.0877011i
$254$	13.7285	−	23.7784i	0.861401	−	1.49199i
$255$	0.365630	−	0.406074i	0.0228967	−	0.0254293i
$256$	0.733121	−	6.97519i	0.0458201	−	0.435949i
$257$	−0.0244923	−	0.233029i	−0.00152779	−	0.0145359i	0.993731	−	0.111794i	$-0.0356596\pi$
$257$	−0.0244923	−	0.233029i	−0.00152779	−	0.0145359i	−0.995259	+	0.0972577i	$0.968993\pi$
$258$	−2.53102	+	7.78968i	−0.157574	+	0.484964i
$259$	11.2741	+	5.79274i	0.700536	+	0.359943i
$260$	0.168150	−	0.122168i	0.0104282	−	0.00757654i
$261$	2.20715	−	0.982685i	0.136619	−	0.0608267i
$262$	−13.2508	+	14.7165i	−0.818640	+	0.909191i
$263$	−6.62526	−	11.4753i	−0.408531	−	0.707597i	0.586194	−	0.810171i	$-0.300626\pi$
$263$	−6.62526	−	11.4753i	−0.408531	−	0.707597i	−0.994725	+	0.102574i	$0.967292\pi$
$264$	−8.10629	+	5.76113i	−0.498908	+	0.354573i
$265$	−0.951910			−0.0584754
$266$	4.64468	−	11.9780i	0.284783	−	0.734421i
$267$	−9.42746	−	6.84945i	−0.576951	−	0.419180i
$268$	−0.429841	−	4.08967i	−0.0262567	−	0.249816i
$269$	−0.706005	+	0.150066i	−0.0430459	+	0.00914969i	−0.229384	−	0.973336i	$-0.573671\pi$
$269$	−0.706005	+	0.150066i	−0.0430459	+	0.00914969i	0.186338	+	0.982486i	$0.440338\pi$
$270$	−0.197215	+	0.0419194i	−0.0120021	+	0.00255113i
$271$	1.07745	+	10.2512i	0.0654504	+	0.622719i	0.977251	+	0.212086i	$0.0680256\pi$
$271$	1.07745	+	10.2512i	0.0654504	+	0.622719i	−0.911801	+	0.410633i	$0.865308\pi$
$272$	9.46997	+	6.88033i	0.574201	+	0.417182i
$273$	−4.29696	+	11.0813i	−0.260064	+	0.670672i
$274$	12.9708			0.783594
$275$	−5.26368	+	15.6420i	−0.317412	+	0.943245i
$276$	−0.0854979	−	0.148087i	−0.00514637	−	0.00891377i
$277$	−20.6174	+	22.8979i	−1.23878	+	1.37580i	−0.338218	+	0.941068i	$0.609824\pi$
$277$	−20.6174	+	22.8979i	−1.23878	+	1.37580i	−0.900559	+	0.434733i	$0.856843\pi$
$278$	−18.5460	+	8.25721i	−1.11231	+	0.495234i
$279$	−5.80439	+	4.21714i	−0.347500	+	0.252474i
$280$	−1.09094	−	0.560537i	−0.0651961	−	0.0334985i
$281$	3.21099	−	9.88241i	0.191551	−	0.589535i	−0.808448	−	0.588568i	$-0.799692\pi$
$281$	3.21099	−	9.88241i	0.191551	−	0.589535i	1.00000		0.000967316i	$-0.000307906\pi$
$282$	1.04050	+	9.89968i	0.0619608	+	0.589517i
$283$	−0.172598	+	1.64216i	−0.0102599	+	0.0976163i	−0.998453	−	0.0555944i	$-0.982295\pi$
$283$	−0.172598	+	1.64216i	−0.0102599	+	0.0976163i	0.988194	+	0.153211i	$0.0489613\pi$
$284$	−1.18319	+	1.31406i	−0.0702093	+	0.0779754i
$285$	0.287822	−	0.498523i	0.0170491	−	0.0295299i
$286$	2.23278	−	19.3013i	0.132027	−	1.14131i
$287$	−12.6626	+	4.81145i	−0.747452	+	0.284011i
$288$	0.518509	+	1.59581i	0.0305534	+	0.0940337i
$289$	−4.11839	+	1.83363i	−0.242258	+	0.107860i
$290$	−0.445007	−	0.198130i	−0.0261317	−	0.0116346i
$291$	−8.70295	+	1.84987i	−0.510176	+	0.108441i
$292$	1.47689	+	1.64026i	0.0864287	+	0.0959887i
$293$	−21.5073	+	15.6260i	−1.25647	+	0.912881i	−0.998579	−	0.0532928i	$-0.983028\pi$
$293$	−21.5073	+	15.6260i	−1.25647	+	0.912881i	−0.257893	+	0.966173i	$0.583028\pi$
$294$	9.08511	−	0.892532i	0.529854	−	0.0520535i
$295$	−0.449870	−	1.38456i	−0.0261925	−	0.0806121i
$296$	−7.18262	+	12.4407i	−0.417481	+	0.723099i
$297$	1.68823	−	2.85480i	0.0979611	−	0.165652i
$298$	5.58308	+	9.67017i	0.323419	+	0.560178i
$299$	2.51066	+	0.533658i	0.145195	+	0.0308623i
$300$	1.20478	+	0.875324i	0.0695580	+	0.0505368i
$301$	9.09738	−	13.9051i	0.524364	−	0.801477i
$302$	1.46848	−	4.51952i	0.0845015	−	0.260069i
$303$	−12.4641	−	13.8427i	−0.716042	−	0.795245i
$304$	11.2653	+	5.01565i	0.646111	+	0.287667i
$305$	0.113963	−	1.08428i	0.00652548	−	0.0620858i
$306$	−4.50854	−	0.958319i	−0.257736	−	0.0547835i
$307$	25.7622			1.47033			0.735163	−	0.677891i	$-0.237106\pi$
$307$	25.7622			1.47033			0.735163	+	0.677891i	$0.237106\pi$
$308$	2.46444	−	0.907069i	0.140425	−	0.0516850i
$309$	−6.14673			−0.349675
$310$	1.41494	+	0.300756i	0.0803635	+	0.0170818i
$311$	−2.20500	+	20.9792i	−0.125034	+	1.18962i	0.734524	+	0.678583i	$0.237405\pi$
$311$	−2.20500	+	20.9792i	−0.125034	+	1.18962i	−0.859558	+	0.511038i	$0.829261\pi$
$312$	−12.3055	−	5.47874i	−0.696659	−	0.310173i
$313$	−17.5856	−	19.5308i	−0.993998	−	1.10395i	−0.994583	−	0.103947i	$-0.966853\pi$
$313$	−17.5856	−	19.5308i	−0.993998	−	1.10395i	0.000584510	−	1.00000i	$-0.499814\pi$
$314$	1.48708	−	4.57678i	0.0839210	−	0.258282i
$315$	0.408405	+	0.0227948i	0.0230110	+	0.00128434i
$316$	1.03245	+	0.750118i	0.0580798	+	0.0421975i
$317$	18.2066	+	3.86994i	1.02259	+	0.217357i	0.688539	−	0.725199i	$-0.258252\pi$
$317$	18.2066	+	3.86994i	1.02259	+	0.217357i	0.334047	+	0.942556i	$0.391586\pi$
$318$	4.01482	+	6.95387i	0.225140	+	0.389954i
$319$	7.35393	−	3.18254i	0.411741	−	0.178188i
$320$	0.681183	−	1.17984i	0.0380793	−	0.0659552i
$321$	5.80155	+	17.8553i	0.323811	+	0.996588i
$322$	−0.503785	−	1.90602i	−0.0280748	−	0.106218i
$323$	10.6465	−	7.73515i	0.592388	−	0.430395i
$324$	−0.200250	−	0.222400i	−0.0111250	−	0.0123555i
$325$	−21.8652	+	4.64759i	−1.21286	+	0.257802i
$326$	−29.2103	−	13.0053i	−1.61781	−	0.720295i
$327$	−0.757583	+	0.337298i	−0.0418945	+	0.0186526i
$328$	−4.74406	−	14.6007i	−0.261947	−	0.806189i
$329$	3.22688	−	19.9353i	0.177904	−	1.09907i
$330$	−0.655505	+	0.132189i	−0.0360844	+	0.00727678i
$331$	9.23885	−	16.0022i	0.507813	−	0.879558i	−0.492146	−	0.870513i	$-0.663787\pi$
$331$	9.23885	−	16.0022i	0.507813	−	0.879558i	0.999959	−	0.00904536i	$-0.00287927\pi$
$332$	0.713400	−	0.792311i	0.0391529	−	0.0434837i
$333$	0.500772	−	4.76453i	0.0274421	−	0.261094i
$334$	−1.91636	−	18.2329i	−0.104859	−	0.997662i
$335$	0.656467	−	2.02040i	0.0358666	−	0.110386i
$336$	0.428870	+	8.75197i	0.0233968	+	0.477459i
$337$	17.8136	−	12.9423i	0.970369	−	0.705014i	0.0148333	−	0.999890i	$-0.495278\pi$
$337$	17.8136	−	12.9423i	0.970369	−	0.705014i	0.955536	+	0.294876i	$0.0952783\pi$
$338$	8.55400	−	3.80849i	0.465276	−	0.207154i
$339$	−0.678036	+	0.753036i	−0.0368259	+	0.0408993i
$340$	−0.0817641	−	0.141620i	−0.00443428	−	0.00768040i
$341$	−19.3961	+	13.7848i	−1.05036	+	0.746487i
$342$	−4.85573			−0.262568
$343$	−18.2618	−	3.08344i	−0.986043	−	0.166490i
$344$	15.2356	+	11.0693i	0.821451	+	0.596819i
$345$	−0.00923372	−	0.0878530i	−0.000497127	−	0.00472985i
$346$	−18.5821	+	3.94975i	−0.998981	+	0.212340i
$347$	8.56955	−	1.82151i	0.460038	−	0.0977840i	0.0279376	−	0.999610i	$-0.491106\pi$
$347$	8.56955	−	1.82151i	0.460038	−	0.0977840i	0.432100	+	0.901826i	$0.357773\pi$
$348$	−0.0755782	−	0.719079i	−0.00405142	−	0.0385467i
$349$	−2.99184	−	2.17370i	−0.160150	−	0.116356i	0.504824	−	0.863222i	$-0.331557\pi$
$349$	−2.99184	−	2.17370i	−0.160150	−	0.116356i	−0.664974	+	0.746867i	$0.731557\pi$
$350$	10.7597	+	13.3798i	0.575130	+	0.715179i
$351$	4.49221			0.239776
$352$	1.66431	+	5.31037i	0.0887078	+	0.283043i
$353$	−4.30583	−	7.45792i	−0.229176	−	0.396945i	0.728388	−	0.685165i	$-0.240270\pi$
$353$	−4.30583	−	7.45792i	−0.229176	−	0.396945i	−0.957564	+	0.288220i	$0.906937\pi$
$354$	−8.21705	+	9.12595i	−0.436731	+	0.485039i
$355$	−0.834507	+	0.371547i	−0.0442910	+	0.0197196i
$356$	−2.82134	+	2.04983i	−0.149531	+	0.108641i
$357$	8.31742	+	4.27358i	0.440205	+	0.226182i
$358$	10.2317	−	31.4899i	0.540762	−	1.66429i
$359$	−1.36557	−	12.9925i	−0.0720719	−	0.685718i	−0.969589	−	0.244739i	$-0.921298\pi$
$359$	−1.36557	−	12.9925i	−0.0720719	−	0.685718i	0.897517	−	0.440979i	$-0.145369\pi$
$360$	−0.0484574	+	0.461041i	−0.00255393	+	0.0242990i
$361$	−3.43699	+	3.81717i	−0.180894	+	0.200904i
$362$	0.369387	−	0.639797i	0.0194145	−	0.0336270i
$363$	5.69785	−	9.40928i	0.299059	−	0.493859i
$364$	2.75660	+	2.24780i	0.144485	+	0.117817i
$365$	0.352353	+	1.08443i	0.0184430	+	0.0567616i
$366$	−8.40152	+	3.74060i	−0.439155	+	0.195524i
$367$	15.1388	+	6.74023i	0.790239	+	0.351837i	0.761845	−	0.647760i	$-0.224294\pi$
$367$	15.1388	+	6.74023i	0.790239	+	0.351837i	0.0283945	+	0.999597i	$0.490961\pi$
$368$	1.85100	−	0.393442i	0.0964900	−	0.0205096i
$369$	3.42587	+	3.80481i	0.178344	+	0.198071i
$370$	−0.781445	+	0.567753i	−0.0406254	+	0.0295161i
$371$	−4.16275	−	15.7494i	−0.216119	−	0.817667i
$372$	0.663503	+	2.04205i	0.0344010	+	0.105875i
$373$	−0.319637	+	0.553628i	−0.0165502	+	0.0286658i	−0.874182	−	0.485599i	$-0.838602\pi$
$373$	−0.319637	+	0.553628i	−0.0165502	+	0.0286658i	0.857632	+	0.514264i	$0.171935\pi$
$374$	−14.9191	−	3.33444i	−0.771449	−	0.172420i
$375$	0.771167	+	1.33570i	0.0398229	+	0.0689753i
$376$	22.3873	+	4.75856i	1.15453	+	0.245404i
$377$	8.78048	+	6.37940i	0.452218	+	0.328556i
$378$	−1.55599	−	3.07961i	−0.0800314	−	0.158398i
$379$	−2.10990	+	6.49361i	−0.108378	+	0.333554i	−0.990509	−	0.137451i	$-0.956109\pi$
$379$	−2.10990	+	6.49361i	−0.108378	+	0.333554i	0.882130	+	0.471006i	$0.156109\pi$
$380$	−0.115273	−	0.128023i	−0.00591336	−	0.00656745i
$381$	19.2338	+	8.56343i	0.985377	+	0.438718i
$382$	−0.568385	+	5.40782i	−0.0290811	+	0.276688i
$383$	−14.2733	−	3.03388i	−0.729332	−	0.155024i	−0.171743	−	0.985142i	$-0.554940\pi$
$383$	−14.2733	−	3.03388i	−0.729332	−	0.155024i	−0.557588	+	0.830118i	$0.688273\pi$
$384$	−8.13609			−0.415193
$385$	1.35366	+	0.0897497i	0.0689891	+	0.00457407i
$386$	−18.2539			−0.929098
$387$	−6.14327	−	1.30579i	−0.312280	−	0.0663772i
$388$	−0.278329	+	2.64812i	−0.0141300	+	0.134438i
$389$	29.1685	+	12.9866i	1.47890	+	0.658449i	0.978293	−	0.207226i	$-0.0664437\pi$
$389$	29.1685	+	12.9866i	1.47890	+	0.658449i	0.500607	+	0.865675i	$0.333110\pi$
$390$	−0.606047	−	0.673084i	−0.0306884	−	0.0340829i
$391$	0.624051	−	1.92063i	0.0315596	−	0.0971305i
$392$	4.50336	−	20.5009i	0.227454	−	1.03545i
$393$	−12.2849	−	8.92551i	−0.619692	−	0.450233i
$394$	17.3710	+	3.69231i	0.875137	+	0.186016i
$395$	0.329639	+	0.570951i	0.0165859	+	0.0287276i
$396$	−0.656410	−	0.744516i	−0.0329859	−	0.0374133i
$397$	−5.48354	+	9.49778i	−0.275211	+	0.476680i	−0.970188	−	0.242352i	$-0.922081\pi$
$397$	−5.48354	+	9.49778i	−0.275211	+	0.476680i	0.694977	+	0.719032i	$0.255414\pi$
$398$	0.693943	+	2.13574i	0.0347842	+	0.107055i
$399$	9.50673	+	2.58196i	0.475932	+	0.129260i
$400$	−13.3329	+	9.68690i	−0.666644	+	0.484345i
$401$	−3.83106	−	4.25482i	−0.191314	−	0.212476i	0.639855	−	0.768496i	$-0.278994\pi$
$401$	−3.83106	−	4.25482i	−0.191314	−	0.212476i	−0.831169	+	0.556020i	$0.812328\pi$
$402$	−17.5281	+	3.72571i	−0.874222	+	0.185822i
$403$	−29.4435	−	13.1091i	−1.46669	−	0.653010i
$404$	−5.09260	+	2.26737i	−0.253367	+	0.112806i
$405$	−0.0477749	−	0.147036i	−0.00237396	−	0.00730629i
$406$	1.33202	−	8.22908i	0.0661073	−	0.408403i
$407$	1.82588	−	15.7839i	0.0905056	−	0.782380i
$408$	−5.29897	+	9.17808i	−0.262338	+	0.454383i
$409$	−5.74475	+	6.38019i	−0.284060	+	0.315480i	−0.868241	−	0.496143i	$-0.834749\pi$
$409$	−5.74475	+	6.38019i	−0.284060	+	0.315480i	0.584181	+	0.811623i	$0.301416\pi$
$410$	0.107902	−	1.02662i	0.00532891	−	0.0507012i
$411$	1.03964	+	9.89151i	0.0512817	+	0.487912i
$412$	−0.568444	+	1.74949i	−0.0280052	+	0.0861912i
$413$	20.9402	−	13.4979i	1.03040	−	0.664186i
$414$	−0.602837	+	0.437987i	−0.0296278	+	0.0215259i
$415$	0.503163	−	0.224023i	0.0246993	−	0.0109968i
$416$	−5.04364	+	5.60153i	−0.247285	+	0.274638i
$417$	−7.78345	−	13.4813i	−0.381157	−	0.660183i
$418$	−16.1037	−	0.168260i	−0.787660	−	0.00822988i
$419$	−39.3947			−1.92455			−0.962277	−	0.272070i	$-0.912292\pi$
$419$	−39.3947			−1.92455			−0.962277	+	0.272070i	$0.912292\pi$
$420$	0.0442568	−	0.114133i	0.00215951	−	0.00556911i
$421$	−28.0607	−	20.3873i	−1.36760	−	0.993616i	−0.997921	−	0.0644546i	$-0.979469\pi$
$421$	−28.0607	−	20.3873i	−1.36760	−	0.993616i	−0.369674	−	0.929161i	$-0.620531\pi$
$422$	0.894639	+	8.51192i	0.0435503	+	0.414354i
$423$	−7.46609	+	1.58697i	−0.363014	+	0.0771610i
$424$	18.0589	−	3.83853i	0.877015	−	0.186415i
$425$	1.83839	+	17.4911i	0.0891749	+	0.848442i
$426$	6.23387	+	4.52917i	0.302032	+	0.219439i
$427$	18.4378	−	2.85611i	0.892270	−	0.138217i
$428$	5.61853			0.271582
$429$	14.8982	+	0.155664i	0.719290	+	0.00751552i
$430$	0.633142	+	1.09663i	0.0305328	+	0.0528844i
$431$	−11.3586	+	12.6150i	−0.547123	+	0.607642i	−0.951763	−	0.306834i	$-0.900730\pi$
$431$	−11.3586	+	12.6150i	−0.547123	+	0.607642i	0.404640	+	0.914476i	$0.367397\pi$
$432$	3.02557	−	1.34707i	0.145568	−	0.0648110i
$433$	19.2167	−	13.9617i	0.923494	−	0.670958i	−0.0208974	−	0.999782i	$-0.506652\pi$
$433$	19.2167	−	13.9617i	0.923494	−	0.670958i	0.944391	+	0.328824i	$0.106652\pi$
$434$	1.21162	+	24.7255i	0.0581594	+	1.18686i
$435$	0.115425	−	0.355243i	0.00553422	−	0.0170326i
$436$	0.0259416	+	0.246817i	0.00124238	+	0.0118204i
$437$	0.222380	−	2.11580i	0.0106379	−	0.101213i
$438$	6.43585	−	7.14774i	0.307517	−	0.341532i
$439$	−3.08551	+	5.34426i	−0.147263	+	0.255067i	−0.930215	−	0.367015i	$-0.880380\pi$
$439$	−3.08551	+	5.34426i	−0.147263	+	0.255067i	0.782952	+	0.622082i	$0.213713\pi$
$440$	−0.176682	+	1.52734i	−0.00842299	+	0.0728130i
$441$	1.40884	+	6.85676i	0.0670875	+	0.326512i
$442$	−6.39843	−	19.6924i	−0.304342	−	0.936670i
$443$	2.58495	−	1.15089i	0.122814	−	0.0546805i	−0.344409	−	0.938820i	$-0.611921\pi$
$443$	2.58495	−	1.15089i	0.122814	−	0.0546805i	0.467224	+	0.884139i	$0.345254\pi$
$444$	−1.30977	−	0.583149i	−0.0621592	−	0.0276750i
$445$	−1.76222	+	0.374571i	−0.0835371	+	0.0177564i
$446$	−13.1085	−	14.5585i	−0.620707	−	0.689364i
$447$	−6.92697	+	5.03274i	−0.327634	+	0.238040i
$448$	22.4994	+	6.11067i	1.06300	+	0.288702i
$449$	1.13543	+	3.49449i	0.0535842	+	0.164915i	0.974267	−	0.225396i	$-0.0723675\pi$
$449$	1.13543	+	3.49449i	0.0535842	+	0.164915i	−0.920683	+	0.390311i	$0.872368\pi$
$450$	3.24472	−	5.62001i	0.152957	−	0.264930i
$451$	11.2299	+	12.7372i	0.528794	+	0.599770i
$452$	0.151626	+	0.262624i	0.00713188	+	0.0123528i
$453$	3.56428	+	0.757612i	0.167465	+	0.0355957i
$454$	14.9435	+	10.8571i	0.701331	+	0.509547i
$455$	0.828641	+	1.64005i	0.0388473	+	0.0768866i
$456$	−3.45006	+	10.6182i	−0.161564	+	0.497242i
$457$	−16.8851	−	18.7529i	−0.789854	−	0.877222i	0.204977	−	0.978767i	$-0.434288\pi$
$457$	−16.8851	−	18.7529i	−0.789854	−	0.877222i	−0.994831	+	0.101545i	$0.967621\pi$
$458$	14.5046	+	6.45785i	0.677754	+	0.301756i
$459$	0.369444	−	3.51502i	0.0172441	−	0.164067i
$460$	−0.0258588	−	0.00549645i	−0.00120567	−	0.000256273i
$461$	−1.65417			−0.0770423			−0.0385212	−	0.999258i	$-0.512265\pi$
$461$	−1.65417			−0.0770423			−0.0385212	+	0.999258i	$0.512265\pi$
$462$	−5.05364	−	10.2673i	−0.235116	−	0.477677i
$463$	−23.8870			−1.11012			−0.555061	−	0.831810i	$-0.687305\pi$
$463$	−23.8870			−1.11012			−0.555061	+	0.831810i	$0.687305\pi$
$464$	7.82677	+	1.66363i	0.363349	+	0.0772322i
$465$	−0.115945	+	1.10314i	−0.00537682	+	0.0511570i
$466$	−17.9584	−	7.99561i	−0.831908	−	0.370389i
$467$	11.5860	+	12.8676i	0.536137	+	0.595440i	0.948970	−	0.315366i	$-0.102127\pi$
$467$	11.5860	+	12.8676i	0.536137	+	0.595440i	−0.412833	+	0.910807i	$0.635461\pi$
$468$	0.415435	−	1.27858i	0.0192035	−	0.0591023i
$469$	36.2983	+	2.02596i	1.67610	+	0.0935500i
$470$	1.24504	+	0.904573i	0.0574293	+	0.0417248i
$471$	3.60944	+	0.767210i	0.166314	+	0.0353512i
$472$	14.1177	+	24.4526i	0.649821	+	1.12552i
$473$	−20.3286	−	4.54347i	−0.934709	−	0.208909i
$474$	2.78060	−	4.81613i	0.127717	−	0.221212i
$475$	5.72542	+	17.6210i	0.262700	+	0.808509i
$476$	1.98554	−	1.97210i	0.0910071	−	0.0903910i
$477$	−4.98122	+	3.61907i	−0.228074	+	0.165706i
$478$	12.6388	+	14.0368i	0.578084	+	0.642028i
$479$	−8.47341	+	1.80108i	−0.387160	+	0.0822934i	−0.397379	−	0.917654i	$-0.630080\pi$
$479$	−8.47341	+	1.80108i	−0.387160	+	0.0822934i	0.0102194	+	0.999948i	$0.496747\pi$
$480$	0.236985	+	0.105513i	0.0108169	+	0.00481597i
$481$	19.6605	−	8.75344i	0.896443	−	0.399122i
$482$	5.53749	+	17.0426i	0.252226	+	0.776271i
$483$	1.41315	−	0.536958i	0.0643006	−	0.0244324i
$484$	−2.15115	−	2.49189i	−0.0977795	−	0.113268i
$485$	−0.687781	+	1.19127i	−0.0312305	+	0.0540928i
$486$	−0.872627	+	0.969151i	−0.0395832	+	0.0439616i
$487$	4.36782	−	41.5570i	0.197925	−	1.88313i	−0.221244	−	0.975219i	$-0.571012\pi$
$487$	4.36782	−	41.5570i	0.197925	−	1.88313i	0.419168	−	0.907909i	$-0.362322\pi$
$488$	2.21030	+	21.0296i	0.100056	+	0.951967i
$489$	7.57653	−	23.3182i	0.342622	−	1.05448i
$490$	0.837306	−	1.13614i	0.0378256	−	0.0513257i
$491$	26.8166	−	19.4834i	1.21022	−	0.879274i	0.214966	−	0.976621i	$-0.431036\pi$
$491$	26.8166	−	19.4834i	1.21022	−	0.879274i	0.995250	+	0.0973476i	$0.0310359\pi$
$492$	1.39975	−	0.623210i	0.0631057	−	0.0280965i
$493$	5.71380	−	6.34582i	0.257337	−	0.285801i
$494$	−10.9065	−	18.8906i	−0.490705	−	0.849926i
$495$	−0.153348	−	0.489293i	−0.00689247	−	0.0219921i
$496$	−23.7617			−1.06693
$497$	−9.79659	−	12.1822i	−0.439437	−	0.546444i
$498$	−3.75869	−	2.73085i	−0.168431	−	0.122372i
$499$	0.969880	+	9.22779i	0.0434178	+	0.413093i	0.994546	+	0.104297i	$0.0332593\pi$
$499$	0.969880	+	9.22779i	0.0434178	+	0.413093i	−0.951128	+	0.308796i	$0.900074\pi$
$500$	0.451486	−	0.0959663i	0.0201911	−	0.00429174i
$501$	13.7508	−	2.92283i	0.614342	−	0.130582i
$502$	1.92333	+	18.2993i	0.0858426	+	0.816738i
$503$	25.4389	+	18.4825i	1.13427	+	0.824093i	0.986310	−	0.164901i	$-0.0527304\pi$
$503$	25.4389	+	18.4825i	1.13427	+	0.824093i	0.147956	+	0.988994i	$0.452730\pi$
$504$	−7.83985	+	1.21443i	−0.349215	+	0.0540950i
$505$	−2.87983			−0.128151
$506$	−2.01445	+	1.43167i	−0.0895533	+	0.0636454i
$507$	3.58997	+	6.21801i	0.159436	+	0.276152i
$508$	4.21606	−	4.68241i	0.187057	−	0.207748i
$509$	−16.0319	+	7.13788i	−0.710603	+	0.316381i	−0.730015	−	0.683431i	$-0.760487\pi$
$509$	−16.0319	+	7.13788i	−0.710603	+	0.316381i	0.0194124	+	0.999812i	$0.493820\pi$
$510$	−0.576510	+	0.418859i	−0.0255283	+	0.0185474i
$511$	−16.4011	+	10.5720i	−0.725540	+	0.467676i
$512$	−7.85483	+	24.1747i	−0.347138	+	1.06838i
$513$	−0.389198	−	3.70297i	−0.0171835	−	0.163490i
$514$	−0.0319409	+	0.303897i	−0.00140885	+	0.0134043i
$515$	−0.635877	+	0.706212i	−0.0280201	+	0.0311194i
$516$	−0.939781	+	1.62775i	−0.0413715	+	0.0716576i
$517$	−24.8159	+	5.00437i	−1.09140	+	0.220092i
$518$	−12.8108	−	10.4462i	−0.562874	−	0.458981i
$519$	−4.50148	−	13.8541i	−0.197593	−	0.608129i
$520$	−1.90246	+	0.847030i	−0.0834284	+	0.0371447i
$521$	1.31250	+	0.584362i	0.0575016	+	0.0256014i	0.435286	−	0.900292i	$-0.356647\pi$
$521$	1.31250	+	0.584362i	0.0575016	+	0.0256014i	−0.377784	+	0.925894i	$0.623314\pi$
$522$	−3.08193	+	0.655085i	−0.134893	+	0.0286723i
$523$	−0.192790	−	0.214115i	−0.00843013	−	0.00936261i	0.738915	−	0.673799i	$-0.235338\pi$
$523$	−0.192790	−	0.214115i	−0.00843013	−	0.00936261i	−0.747345	+	0.664436i	$0.768672\pi$
$524$	−3.67649	+	2.67113i	−0.160608	+	0.116689i
$525$	−9.34099	+	9.27775i	−0.407674	+	0.404914i
$526$	5.33990	+	16.4345i	0.232831	+	0.716579i
$527$	−12.6789	+	21.9606i	−0.552303	+	0.956617i
$528$	10.0808	−	4.36265i	0.438711	−	0.189860i
$529$	11.3368	+	19.6358i	0.492903	+	0.853733i
$530$	1.21428	+	0.258103i	0.0527449	+	0.0112113i
$531$	−7.61806	−	5.53485i	−0.330596	−	0.240192i
$532$	1.61405	−	2.46704i	0.0699781	−	0.106960i
$533$	−7.10726	+	21.8739i	−0.307850	+	0.947464i
$534$	10.1687	+	11.2935i	0.440043	+	0.488717i
$535$	2.65161	+	1.18057i	0.114639	+	0.0510406i
$536$	−4.30680	+	40.9764i	−0.186025	+	1.76991i
$537$	24.8343	+	5.27869i	1.07168	+	0.227792i
$538$	0.941285			0.0405817
$539$	4.43473	+	22.7889i	0.191017	+	0.981587i
$540$	−0.0462678			−0.00199105
$541$	16.5753	+	3.52320i	0.712630	+	0.151474i	0.549941	−	0.835203i	$-0.314650\pi$
$541$	16.5753	+	3.52320i	0.712630	+	0.151474i	0.162688	+	0.986677i	$0.447983\pi$
$542$	1.40512	−	13.3689i	0.0603553	−	0.574242i
$543$	0.517516	+	0.230413i	0.0222087	+	0.00988796i
$544$	3.96824	+	4.40718i	0.170137	+	0.188956i
$545$	−0.0396187	+	0.121934i	−0.00169708	+	0.00522307i
$546$	8.48591	−	12.9705i	0.363164	−	0.555086i
$547$	31.4138	+	22.8235i	1.34316	+	0.975862i	0.999321	+	0.0368329i	$0.0117269\pi$
$547$	31.4138	+	22.8235i	1.34316	+	0.975862i	0.343837	+	0.939029i	$0.388273\pi$
$548$	2.91148	+	0.618854i	0.124372	+	0.0264361i
$549$	−3.52598	−	6.10718i	−0.150485	−	0.260648i
$550$	10.9557	−	18.5260i	0.467151	−	0.789952i
$551$	4.49787	−	7.79054i	0.191616	−	0.331888i
$552$	0.529437	+	1.62944i	0.0225343	+	0.0693535i
$553$	−8.00487	+	7.95068i	−0.340402	+	0.338097i
$554$	32.5086	−	23.6188i	1.38116	−	1.00347i
$555$	−0.495603	−	0.550423i	−0.0210372	−	0.0233642i
$556$	−4.55688	+	0.968595i	−0.193255	+	0.0410776i
$557$	4.60590	+	2.05068i	0.195158	+	0.0868901i	0.501989	−	0.864874i	$-0.332602\pi$
$557$	4.60590	+	2.05068i	0.195158	+	0.0868901i	−0.306831	+	0.951764i	$0.599268\pi$
$558$	8.54766	−	3.80566i	0.361851	−	0.161107i
$559$	−8.71842	−	26.8325i	−0.368750	−	1.13490i
$560$	1.04990	+	0.856113i	0.0443664	+	0.0361774i
$561$	1.34704	−	11.6446i	0.0568721	−	0.491634i
$562$	−6.77554	+	11.7356i	−0.285809	+	0.495036i
$563$	13.1487	−	14.6031i	0.554151	−	0.615447i	−0.399364	−	0.916792i	$-0.630769\pi$
$563$	13.1487	−	14.6031i	0.554151	−	0.615447i	0.953515	+	0.301345i	$0.0974357\pi$
$564$	−0.238773	+	2.27177i	−0.0100541	+	0.0956588i
$565$	0.0163755	+	0.155802i	0.000688922	+	0.00655466i
$566$	0.665428	−	2.04798i	0.0279700	−	0.0860829i
$567$	2.22380	−	1.43343i	0.0933906	−	0.0601986i
$568$	14.3333	−	10.4138i	0.601413	−	0.436952i
$569$	30.6204	−	13.6331i	1.28367	−	0.571528i	0.352400	−	0.935849i	$-0.385365\pi$
$569$	30.6204	−	13.6331i	1.28367	−	0.571528i	0.931274	+	0.364321i	$0.118699\pi$
$570$	−0.502323	+	0.557886i	−0.0210400	+	0.0233673i
$571$	−9.83114	−	17.0280i	−0.411420	−	0.712601i	0.583625	−	0.812023i	$-0.301634\pi$
$571$	−9.83114	−	17.0280i	−0.411420	−	0.712601i	−0.995045	+	0.0994224i	$0.968301\pi$
$572$	1.42207	−	4.22594i	0.0594599	−	0.176695i
$573$	−4.16956			−0.174186
$574$	17.4573	−	2.70422i	0.728655	−	0.112872i
$575$	2.30023	+	1.67121i	0.0959261	+	0.0696944i
$576$	−0.921107	−	8.76375i	−0.0383795	−	0.365156i
$577$	−20.1876	+	4.29101i	−0.840422	+	0.178637i	−0.607959	−	0.793968i	$-0.708012\pi$
$577$	−20.1876	+	4.29101i	−0.840422	+	0.178637i	−0.232463	+	0.972605i	$0.574678\pi$
$578$	5.75069	−	1.22235i	0.239197	−	0.0508429i
$579$	−1.46309	−	13.9204i	−0.0608041	−	0.578512i
$580$	−0.0904352	−	0.0657050i	−0.00375512	−	0.00272825i
$581$	5.90682	+	7.34519i	0.245056	+	0.304730i
$582$	11.6033			0.480971
$583$	−16.6453	+	11.8298i	−0.689380	+	0.489941i
$584$	−11.0574	−	19.1521i	−0.457560	−	0.792518i
$585$	0.464717	−	0.516121i	0.0192137	−	0.0213390i
$586$	31.6721	−	14.1013i	1.30836	−	0.582521i
$587$	26.1653	−	19.0102i	1.07996	−	0.784635i	0.102282	−	0.994755i	$-0.467386\pi$
$587$	26.1653	−	19.0102i	1.07996	−	0.784635i	0.977675	+	0.210121i	$0.0673857\pi$
$588$	2.08187	+	0.233122i	0.0858548	+	0.00961377i
$589$	−8.25502	+	25.4063i	−0.340142	+	1.04685i
$590$	0.198453	+	1.88815i	0.00817017	+	0.0777340i
$591$	−1.42343	+	13.5430i	−0.0585521	+	0.557086i
$592$	10.6168	−	11.7911i	0.436348	−	0.484613i
$593$	12.0475	−	20.8669i	0.494732	−	0.856901i	−0.505250	−	0.862973i	$-0.668600\pi$
$593$	12.0475	−	20.8669i	0.494732	−	0.856901i	0.999982	+	0.00607259i	$0.00193298\pi$
$594$	−2.92760	+	3.18390i	−0.120121	+	0.130637i
$595$	1.35144	−	0.513508i	0.0554035	−	0.0210518i
$596$	0.791825	+	2.43699i	0.0324344	+	0.0998228i
$597$	−1.57309	+	0.700385i	−0.0643823	+	0.0286648i
$598$	−3.05796	−	1.36149i	−0.125049	−	0.0556756i
$599$	34.9220	−	7.42290i	1.42687	−	0.303292i	0.571202	−	0.820809i	$-0.306477\pi$
$599$	34.9220	−	7.42290i	1.42687	−	0.303292i	0.855672	+	0.517518i	$0.173144\pi$
$600$	−9.98406	−	11.0884i	−0.407598	−	0.452683i
$601$	−32.6349	+	23.7106i	−1.33120	+	0.967176i	−0.331485	+	0.943460i	$0.607550\pi$
$601$	−32.6349	+	23.7106i	−1.33120	+	0.967176i	−0.999719	+	0.0237157i	$0.992450\pi$
$602$	−15.3751	+	15.2710i	−0.626642	+	0.622399i
$603$	−4.24614	−	13.0683i	−0.172916	−	0.532182i
$604$	0.545254	−	0.944407i	0.0221861	−	0.0384274i
$605$	−0.491615	−	1.62803i	−0.0199870	−	0.0661886i
$606$	12.1461	+	21.0376i	0.493401	+	0.854596i
$607$	15.6318	+	3.32264i	0.634475	+	0.134862i	0.513911	−	0.857844i	$-0.328196\pi$
$607$	15.6318	+	3.32264i	0.634475	+	0.134862i	0.120564	+	0.992706i	$0.461530\pi$
$608$	5.05438	+	3.67222i	0.204982	+	0.148928i
$609$	6.38226	+	0.356220i	0.258622	+	0.0144348i
$610$	−0.439368	+	1.35223i	−0.0177895	+	0.0547504i
$611$	−22.9435	−	25.4813i	−0.928195	−	1.03087i
$612$	−0.966284	−	0.430217i	−0.0390597	−	0.0173905i
$613$	−4.81685	+	45.8292i	−0.194551	+	1.85103i	0.266731	+	0.963771i	$0.414057\pi$
$613$	−4.81685	+	45.8292i	−0.194551	+	1.85103i	−0.461281	+	0.887254i	$0.652610\pi$
$614$	−32.8628	−	6.98521i	−1.32624	−	0.281900i
$615$	0.791549			0.0319183
$616$	−26.0425	+	3.75592i	−1.04928	+	0.151330i
$617$	−18.3023			−0.736824			−0.368412	−	0.929663i	$-0.620098\pi$
$617$	−18.3023			−0.736824			−0.368412	+	0.929663i	$0.620098\pi$
$618$	7.84091	+	1.66664i	0.315408	+	0.0670419i
$619$	2.19931	−	20.9251i	0.0883978	−	0.841049i	−0.857041	−	0.515249i	$-0.827700\pi$
$619$	2.19931	−	20.9251i	0.0883978	−	0.841049i	0.945439	−	0.325801i	$-0.105634\pi$
$620$	0.303255	+	0.135018i	0.0121790	+	0.00542245i
$621$	−0.382327	−	0.424617i	−0.0153423	−	0.0170393i
$622$	8.50109	−	26.1637i	0.340863	−	1.04907i
$623$	−13.9036	−	27.5179i	−0.557034	−	1.10248i
$624$	12.0364	+	8.74492i	0.481840	+	0.350077i
$625$	−24.1036	−	5.12337i	−0.964142	−	0.204935i
$626$	17.1370	+	29.6822i	0.684932	+	1.18634i
$627$	−1.16244	−	12.2942i	−0.0464233	−	0.490983i
$628$	0.552162	−	0.956373i	0.0220337	−	0.0381634i
$629$	−5.23240	−	16.1037i	−0.208630	−	0.642096i
$630$	−0.514791	−	0.139813i	−0.0205097	−	0.00557030i
$631$	−0.0702369	+	0.0510301i	−0.00279608	+	0.00203147i	−0.589182	−	0.808000i	$-0.700550\pi$
$631$	−0.0702369	+	0.0510301i	−0.00279608	+	0.00203147i	0.586386	+	0.810032i	$0.300550\pi$
$632$	−8.55596	−	9.50235i	−0.340338	−	0.377983i
$633$	−6.41948	+	1.36450i	−0.255151	+	0.0542341i
$634$	−22.1755	−	9.87317i	−0.880701	−	0.392114i
$635$	2.97360	−	1.32393i	0.118004	−	0.0525386i
$636$	0.569405	+	1.75245i	0.0225784	+	0.0694892i
$637$	−23.5109	+	20.8819i	−0.931537	+	0.827371i
$638$	−10.2438	+	2.06576i	−0.405554	+	0.0817841i
$639$	−2.95428	+	5.11697i	−0.116870	+	0.202424i
$640$	−0.841675	+	0.934775i	−0.0332701	+	0.0369502i
$641$	−2.11146	+	20.0892i	−0.0833977	+	0.793476i	0.870262	+	0.492589i	$0.163949\pi$
$641$	−2.11146	+	20.0892i	−0.0833977	+	0.793476i	−0.953660	+	0.300887i	$0.902717\pi$
$642$	−2.55926	−	24.3497i	−0.101006	−	0.961007i
$643$	−11.8403	+	36.4406i	−0.466935	+	1.43708i	0.389598	+	0.920985i	$0.372614\pi$
$643$	−11.8403	+	36.4406i	−0.466935	+	1.43708i	−0.856533	+	0.516093i	$0.827386\pi$
$644$	−0.0221428	−	0.451870i	−0.000872550	−	0.0178062i
$645$	−0.785545	+	0.570732i	−0.0309308	+	0.0224725i
$646$	−15.6783	+	6.98041i	−0.616853	+	0.274641i
$647$	26.5397	−	29.4753i	1.04338	−	1.15880i	0.0563289	−	0.998412i	$-0.482060\pi$
$647$	26.5397	−	29.4753i	1.04338	−	1.15880i	0.987055	−	0.160383i	$-0.0512729\pi$
$648$	1.49926	+	2.59680i	0.0588966	+	0.102012i
$649$	−25.0731	−	18.6200i	−0.984205	−	0.730899i
$650$	29.1519			1.14343
$651$	−18.7586	+	2.90579i	−0.735206	+	0.113887i
$652$	−5.93617	−	4.31288i	−0.232479	−	0.168906i
$653$	0.631030	+	6.00385i	0.0246941	+	0.234949i	0.999906	+	0.0136777i	$0.00435388\pi$
$653$	0.631030	+	6.00385i	0.0246941	+	0.234949i	−0.975212	+	0.221271i	$0.928979\pi$
$654$	1.05785	−	0.224852i	0.0413651	−	0.00879242i
$655$	−2.29634	+	0.488103i	−0.0897256	+	0.0190718i
$656$	1.77244	+	16.8637i	0.0692022	+	0.658415i
$657$	5.96671	+	4.33507i	0.232783	+	0.169127i
$658$	−9.52156	+	24.5549i	−0.371189	+	0.957250i
$659$	−16.5792			−0.645833			−0.322916	−	0.946427i	$-0.604663\pi$
$659$	−16.5792			−0.645833			−0.322916	+	0.946427i	$0.604663\pi$
$660$	−0.153445	−	0.00160327i	−0.00597282	−	6.24072e-5i
$661$	−9.56491	−	16.5669i	−0.372032	−	0.644378i	0.617846	−	0.786299i	$-0.288005\pi$
$661$	−9.56491	−	16.5669i	−0.372032	−	0.644378i	−0.989878	+	0.141921i	$0.954672\pi$
$662$	−16.1241	+	17.9077i	−0.626683	+	0.696002i
$663$	14.5045	−	6.45783i	0.563309	−	0.250801i
$664$	−8.64224	+	6.27895i	−0.335384	+	0.243671i
$665$	1.28011	−	0.825149i	0.0496407	−	0.0319979i
$666$	−1.93066	+	5.94196i	−0.0748115	+	0.230246i
$667$	−0.144298	−	1.37290i	−0.00558723	−	0.0531590i
$668$	0.439765	−	4.18408i	0.0170150	−	0.161887i
$669$	10.0516	−	11.1635i	0.388618	−	0.431604i
$670$	−1.38522	+	2.39927i	−0.0535156	+	0.0926918i
$671$	−11.4821	−	20.3763i	−0.443261	−	0.786618i
$672$	−0.709361	+	4.38234i	−0.0273642	+	0.169053i
$673$	4.37491	+	13.4646i	0.168640	+	0.519022i	0.999286	−	0.0377795i	$-0.0120285\pi$
$673$	4.37491	+	13.4646i	0.168640	+	0.519022i	−0.830646	+	0.556801i	$0.812028\pi$
$674$	−26.2327	+	11.6795i	−1.01044	+	0.449879i
$675$	4.54589	+	2.02396i	0.174971	+	0.0779023i
$676$	2.10178	−	0.446746i	0.0808376	−	0.0171826i
$677$	−16.4896	−	18.3135i	−0.633745	−	0.703845i	0.337661	−	0.941268i	$-0.390364\pi$
$677$	−16.4896	−	18.3135i	−0.633745	−	0.703845i	−0.971407	+	0.237422i	$0.923697\pi$
$678$	1.06910	−	0.776745i	0.0410585	−	0.0298307i
$679$	−22.7173	−	6.16986i	−0.871811	−	0.236777i
$680$	0.506316	+	1.55828i	0.0194163	+	0.0597573i
$681$	−7.08183	+	12.2661i	−0.271376	+	0.470037i
$682$	28.4797	−	12.3251i	1.09054	−	0.471952i
$683$	5.33531	+	9.24103i	0.204150	+	0.353598i	0.949862	−	0.312671i	$-0.101224\pi$
$683$	5.33531	+	9.24103i	0.204150	+	0.353598i	−0.745712	+	0.666269i	$0.767890\pi$
$684$	−1.08994	−	0.231673i	−0.0416748	−	0.00885826i
$685$	1.24401	+	0.903826i	0.0475312	+	0.0345334i
$686$	22.4591	+	8.88484i	0.857492	+	0.339225i
$687$	−3.76218	+	11.5788i	−0.143536	+	0.441758i
$688$	−13.9182	−	15.4578i	−0.530627	−	0.589321i
$689$	−25.2679	−	11.2500i	−0.962628	−	0.428590i
$690$	−0.0120419	+	0.114571i	−0.000458427	+	0.00436164i
$691$	−27.3890	−	5.82171i	−1.04193	−	0.221468i	−0.344994	−	0.938605i	$-0.612119\pi$
$691$	−27.3890	−	5.82171i	−1.04193	−	0.221468i	−0.696933	+	0.717136i	$0.745452\pi$
$692$	−4.35947			−0.165722
$693$	7.42476	−	4.67685i	0.282043	−	0.177659i
$694$	−11.4254			−0.433702
$695$	−2.35410	−	0.500379i	−0.0892960	−	0.0189804i
$696$	−0.757257	+	7.20481i	−0.0287037	+	0.273098i
$697$	16.5312	+	7.36015i	0.626163	+	0.278786i
$698$	3.22708	+	3.58404i	0.122147	+	0.135658i
$699$	4.65804	−	14.3360i	0.176183	−	0.542236i
$700$	1.77680	+	3.51664i	0.0671567	+	0.132917i
$701$	22.2889	+	16.1938i	0.841841	+	0.611633i	0.922884	−	0.385078i	$-0.125825\pi$
$701$	22.2889	+	16.1938i	0.841841	+	0.611633i	−0.0810436	+	0.996711i	$0.525825\pi$
$702$	−5.73036	−	1.21803i	−0.216279	−	0.0459715i
$703$	−8.91891	−	15.4480i	−0.336383	−	0.582632i
$704$	−2.75112	−	29.0964i	−0.103687	−	1.09661i
$705$	−0.590034	+	1.02197i	−0.0222220	+	0.0384896i
$706$	3.47046	+	10.6810i	0.130613	+	0.401984i
$707$	−12.5936	−	47.6468i	−0.473633	−	1.79194i
$708$	−2.27985	+	1.65641i	−0.0856819	+	0.0622515i
$709$	−16.4673	−	18.2888i	−0.618442	−	0.686850i	0.349811	−	0.936820i	$-0.386246\pi$
$709$	−16.4673	−	18.2888i	−0.618442	−	0.686850i	−0.968253	+	0.249971i	$0.919579\pi$
$710$	1.16526	−	0.247683i	0.0437314	−	0.00929539i
$711$	3.89565	+	1.73446i	0.146098	+	0.0650472i
$712$	31.9209	−	14.2121i	1.19629	−	0.532621i
$713$	1.26679	+	3.89879i	0.0474418	+	0.146011i
$714$	−9.45114	−	7.70668i	−0.353700	−	0.288415i
$715$	1.55909	−	1.69558i	0.0583068	−	0.0634112i
$716$	3.79908	−	6.58020i	0.141978	−	0.245914i
$717$	−9.69141	+	10.7634i	−0.361933	+	0.401967i
$718$	−1.78086	+	16.9438i	−0.0664613	+	0.632337i
$719$	0.379286	+	3.60866i	0.0141450	+	0.134580i	0.999315	−	0.0369987i	$-0.0117797\pi$
$719$	0.379286	+	3.60866i	0.0141450	+	0.134580i	−0.985170	+	0.171579i	$0.945113\pi$
$720$	0.158226	−	0.486969i	0.00589673	−	0.0181483i
$721$	−14.4650	−	7.43229i	−0.538706	−	0.276793i
$722$	5.41930	−	3.93735i	0.201686	−	0.146533i
$723$	−12.5529	+	5.58889i	−0.466846	+	0.207853i
$724$	0.113440	−	0.125988i	0.00421596	−	0.00468229i
$725$	6.01118	+	10.4117i	0.223250	+	0.386680i
$726$	−9.81956	+	10.4578i	−0.364438	+	0.388124i
$727$	26.0955			0.967830			0.483915	−	0.875115i	$-0.339214\pi$
$727$	26.0955			0.967830			0.483915	+	0.875115i	$0.339214\pi$
$728$	−22.3337	−	27.7721i	−0.827742	−	1.02930i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−0.155435	−	1.47886i	−0.00575289	−	0.0547351i
$731$	−21.7127	+	4.61517i	−0.803072	+	0.170698i
$732$	−2.06431	+	0.438783i	−0.0762992	+	0.0162179i
$733$	5.56759	+	52.9721i	0.205644	+	1.95657i	0.281805	+	0.959472i	$0.409067\pi$
$733$	5.56759	+	52.9721i	0.205644	+	1.95657i	−0.0761611	+	0.997096i	$0.524266\pi$
$734$	−17.4838	−	12.7028i	−0.645341	−	0.468867i
$735$	0.933534	+	0.547464i	0.0344339	+	0.0201935i
$736$	0.958733			0.0353394
$737$	−13.6293	−	43.4874i	−0.502040	−	1.60188i
$738$	−3.33847	−	5.78241i	−0.122891	−	0.212853i
$739$	−12.1074	+	13.4467i	−0.445379	+	0.494644i	−0.923472	−	0.383665i	$-0.874662\pi$
$739$	−12.1074	+	13.4467i	−0.445379	+	0.494644i	0.478093	+	0.878309i	$0.341328\pi$
$740$	−0.202495	+	0.0901566i	−0.00744387	+	0.00331422i
$741$	13.5317	−	9.83139i	0.497101	−	0.361165i
$742$	1.03979	+	21.2190i	0.0381717	+	0.778973i
$743$	−6.14504	+	18.9125i	−0.225440	+	0.693832i	0.772807	+	0.634641i	$0.218852\pi$
$743$	−6.14504	+	18.9125i	−0.225440	+	0.693832i	−0.998247	+	0.0591909i	$0.981148\pi$
$744$	−2.24875	−	21.3954i	−0.0824432	−	0.784395i
$745$	−0.138369	+	1.31649i	−0.00506944	+	0.0482325i
$746$	0.557848	−	0.619553i	0.0204243	−	0.0226835i
$747$	1.78128	−	3.08526i	0.0651735	−	0.112884i
$748$	−3.18972	−	1.46028i	−0.116628	−	0.0533930i
$749$	−7.93698	+	49.0337i	−0.290011	+	1.79165i
$750$	−0.621554	−	1.91295i	−0.0226959	−	0.0698509i
$751$	32.8941	−	14.6454i	1.20032	−	0.534419i	0.293513	−	0.955955i	$-0.405176\pi$
$751$	32.8941	−	14.6454i	1.20032	−	0.534419i	0.906812	+	0.421536i	$0.138509\pi$
$752$	−23.0939	−	10.2820i	−0.842146	−	0.374948i
$753$	−13.8009	+	2.93347i	−0.502932	+	0.106901i
$754$	−9.47086	−	10.5185i	−0.344909	−	0.383060i
$755$	0.455767	−	0.331134i	0.0165871	−	0.0120512i
$756$	−0.202332	−	0.765502i	−0.00735873	−	0.0278410i
$757$	3.76954	+	11.6014i	0.137006	+	0.421662i	0.995897	−	0.0904977i	$-0.0288458\pi$
$757$	3.76954	+	11.6014i	0.137006	+	0.421662i	−0.858891	+	0.512159i	$0.828846\pi$
$758$	4.45213	−	7.71131i	0.161709	−	0.280087i
$759$	−1.25325	−	1.42147i	−0.0454902	−	0.0515960i
$760$	0.863042	+	1.49483i	0.0313058	+	0.0542233i
$761$	38.4686	+	8.17675i	1.39449	+	0.296407i	0.843061	−	0.537818i	$-0.180751\pi$
$761$	38.4686	+	8.17675i	1.39449	+	0.296407i	0.551424	+	0.834225i	$0.314085\pi$
$762$	−22.2131	−	16.1388i	−0.804697	−	0.584647i
$763$	−2.19065	−	0.122269i	−0.0793070	−	0.00442645i
$764$	−0.385597	+	1.18675i	−0.0139504	+	0.0429350i
$765$	−0.365630	−	0.406074i	−0.0132194	−	0.0146816i
$766$	17.3847	+	7.74018i	0.628136	+	0.279664i
$767$	4.42162	−	42.0689i	0.159655	−	1.51902i
$768$	−6.86034	−	1.45821i	−0.247551	−	0.0526186i
$769$	3.32739			0.119989			0.0599943	−	0.998199i	$-0.480892\pi$
$769$	3.32739			0.119989			0.0599943	+	0.998199i	$0.480892\pi$
$770$	−1.70243	−	0.481522i	−0.0613513	−	0.0173528i
$771$	−0.234312			−0.00843854
$772$	−4.09735	−	0.870918i	−0.147467	−	0.0313450i
$773$	2.45407	−	23.3489i	0.0882667	−	0.839802i	−0.857397	−	0.514656i	$-0.827920\pi$
$773$	2.45407	−	23.3489i	0.0882667	−	0.839802i	0.945664	−	0.325146i	$-0.105414\pi$
$774$	7.48245	+	3.33140i	0.268951	+	0.119745i
$775$	−23.8891	−	26.5315i	−0.858120	−	0.953039i
$776$	8.24427	−	25.3732i	0.295952	−	0.910847i
$777$	6.93947	−	10.6068i	0.248952	−	0.380517i
$778$	−33.6867	−	24.4748i	−1.20773	−	0.877466i
$779$	18.6466	+	3.96347i	0.668085	+	0.142006i
$780$	−0.103922	−	0.179999i	−0.00372102	−	0.00644499i
$781$	−9.97503	+	16.8678i	−0.356935	+	0.603576i
$782$	−1.31682	+	2.28080i	−0.0470893	+	0.0815611i
$783$	−0.746592	−	2.29777i	−0.0266810	−	0.0821157i
$784$	−9.57315	+	21.1145i	−0.341898	+	0.754088i
$785$	0.461542	−	0.335330i	0.0164731	−	0.0119684i
$786$	13.2508	+	14.7165i	0.472642	+	0.524922i
$787$	−10.9725	+	2.33228i	−0.391128	+	0.0831369i	−0.399278	−	0.916830i	$-0.630739\pi$
$787$	−10.9725	+	2.33228i	−0.391128	+	0.0831369i	0.00814969	+	0.999967i	$0.497406\pi$
$788$	3.72300	+	1.65759i	0.132626	+	0.0590491i
$789$	−12.1050	+	5.38947i	−0.430948	+	0.191870i
$790$	−0.265686	−	0.817697i	−0.00945267	−	0.0290923i
$791$	−2.50614	+	0.952265i	−0.0891083	+	0.0338587i
$792$	4.88223	+	8.66409i	0.173483	+	0.307865i
$793$	15.8394	−	27.4347i	0.562475	−	0.974236i
$794$	9.57018	−	10.6288i	0.339633	−	0.377201i
$795$	−0.0995017	+	0.946696i	−0.00352896	+	0.0335758i
$796$	0.0538665	+	0.512506i	0.00190925	+	0.0181653i
$797$	0.271756	−	0.836380i	0.00962610	−	0.0296261i	−0.946128	−	0.323793i	$-0.895042\pi$
$797$	0.271756	−	0.836380i	0.00962610	−	0.0296261i	0.955754	+	0.294166i	$0.0950420\pi$
$798$	−11.4269	−	5.87128i	−0.404509	−	0.207841i
$799$	−21.8253	+	15.8570i	−0.772123	+	0.560981i
$800$	−7.62768	+	3.39606i	−0.269679	+	0.120069i
$801$	−7.79737	+	8.65986i	−0.275506	+	0.305981i
$802$	3.73333	+	6.46631i	0.131828	+	0.228333i
$803$	19.6380	+	14.5838i	0.693011	+	0.514650i
$804$	−4.11219			−0.145026
$805$	0.0844974	−	0.217908i	0.00297814	−	0.00768026i
$806$	34.0044	+	24.7056i	1.19775	+	0.870219i
$807$	0.0754463	+	0.717824i	0.00265584	+	0.0252686i
$808$	54.6337	−	11.6128i	1.92201	−	0.408535i
$809$	44.8156	−	9.52584i	1.57563	−	0.334911i	0.664584	−	0.747213i	$-0.268609\pi$
$809$	44.8156	−	9.52584i	1.57563	−	0.334911i	0.911047	+	0.412303i	$0.135275\pi$
$810$	0.0210751	+	0.200516i	0.000740505	+	0.00704543i
$811$	12.5481	+	9.11676i	0.440625	+	0.320133i	0.785883	−	0.618375i	$-0.212209\pi$
$811$	12.5481	+	9.11676i	0.440625	+	0.320133i	−0.345258	+	0.938508i	$0.612209\pi$
$812$	0.691613	−	1.78358i	0.0242709	−	0.0625915i
$813$	10.3077			0.361507
$814$	−6.60882	+	19.6393i	−0.231639	+	0.688356i
$815$	−1.89529	−	3.28274i	−0.0663891	−	0.114989i
$816$	7.83252	−	8.69890i	0.274193	−	0.304522i
$817$	−21.3630	+	9.51142i	−0.747396	+	0.332762i
$818$	9.05808	−	6.58108i	0.316708	−	0.230102i
$819$	10.5715	+	5.43174i	0.369397	+	0.189800i
$820$	0.0732017	−	0.225292i	0.00255632	−	0.00786753i
$821$	1.29110	+	12.2840i	0.0450597	+	0.428715i	0.993676	+	0.112286i	$0.0358172\pi$
$821$	1.29110	+	12.2840i	0.0450597	+	0.428715i	−0.948616	+	0.316429i	$0.897516\pi$
$822$	1.35582	−	12.8997i	0.0472895	−	0.449930i
$823$	−9.34995	+	10.3842i	−0.325919	+	0.361969i	−0.883729	−	0.467999i	$-0.844975\pi$
$823$	−9.34995	+	10.3842i	−0.325919	+	0.361969i	0.557810	+	0.829969i	$0.311642\pi$
$824$	9.21556	−	15.9618i	0.321039	−	0.556056i
$825$	15.0061	+	6.86988i	0.522444	+	0.239178i
$826$	−30.3717	+	11.5404i	−1.05677	+	0.401542i
$827$	4.65409	+	14.3238i	0.161839	+	0.498088i	0.998789	−	0.0491902i	$-0.0156641\pi$
$827$	4.65409	+	14.3238i	0.161839	+	0.498088i	−0.836951	+	0.547278i	$0.815664\pi$
$828$	−0.156212	+	0.0695503i	−0.00542876	+	0.00241704i
$829$	13.0353	+	5.80371i	0.452736	+	0.201571i	0.620420	−	0.784270i	$-0.286962\pi$
$829$	13.0353	+	5.80371i	0.452736	+	0.201571i	−0.167684	+	0.985841i	$0.553629\pi$
$830$	−0.702589	+	0.149340i	−0.0243872	+	0.00518366i
$831$	20.6174	+	22.8979i	0.715208	+	0.794319i
$832$	32.0253	−	23.2677i	1.11028	−	0.806664i
$833$	14.4059	+	20.1139i	0.499135	+	0.696907i
$834$	6.27339	+	19.3075i	0.217230	+	0.668564i
$835$	1.08671	−	1.88223i	0.0376070	−	0.0651373i
$836$	−3.60669	−	0.806101i	−0.124740	−	0.0278796i
$837$	3.58731	+	6.21341i	0.123996	+	0.214767i
$838$	50.2527	+	10.6815i	1.73595	+	0.368988i
$839$	8.87876	+	6.45080i	0.306529	+	0.222706i	0.730406	−	0.683014i	$-0.239331\pi$
$839$	8.87876	+	6.45080i	0.306529	+	0.222706i	−0.423877	+	0.905720i	$0.639331\pi$
$840$	−0.671500	+	1.02637i	−0.0231690	+	0.0354132i
$841$	−7.15771	+	22.0292i	−0.246818	+	0.759626i
$842$	30.2670	+	33.6149i	1.04307	+	1.15845i
$843$	−9.49263	−	4.22639i	−0.326943	−	0.145565i
$844$	−0.205301	+	1.95331i	−0.00706675	+	0.0672356i
$845$	1.08578	+	0.230790i	0.0373521	+	0.00793943i
$846$	9.95421			0.342233
$847$	24.7859	−	15.2532i	0.851653	−	0.524107i
$848$	−20.3918			−0.700257
$849$	1.61512	+	0.343305i	0.0554309	+	0.0117822i
$850$	2.39748	−	22.8105i	0.0822329	−	0.782393i
$851$	−2.50069	−	1.11338i	−0.0857225	−	0.0381661i
$852$	1.18319	+	1.31406i	0.0405354	+	0.0450191i
$853$	−13.0482	+	40.1581i	−0.446761	+	1.37499i	0.433781	+	0.901018i	$0.357179\pi$
$853$	−13.0482	+	40.1581i	−0.446761	+	1.37499i	−0.880541	+	0.473969i	$0.842821\pi$
$854$	−24.2941	−	1.35596i	−0.831328	−	0.0463999i
$855$	−0.465706	−	0.338355i	−0.0159268	−	0.0115715i
$856$	−55.0648	−	11.7044i	−1.88208	−	0.400047i
$857$	15.5761	+	26.9785i	0.532068	+	0.921569i	0.999299	+	0.0374336i	$0.0119183\pi$
$857$	15.5761	+	26.9785i	0.532068	+	0.921569i	−0.467231	+	0.884135i	$0.654748\pi$
$858$	−18.9622	−	4.23808i	−0.647360	−	0.144686i
$859$	26.8597	−	46.5224i	0.916441	−	1.58732i	0.111663	−	0.993746i	$-0.464382\pi$
$859$	26.8597	−	46.5224i	0.916441	−	1.58732i	0.804778	−	0.593576i	$-0.202284\pi$
$860$	0.0897960	+	0.276364i	0.00306202	+	0.00942392i
$861$	3.46149	+	13.0962i	0.117967	+	0.446317i
$862$	17.9097	−	13.0122i	0.610007	−	0.443196i
$863$	11.3713	+	12.6291i	0.387085	+	0.429901i	0.904922	−	0.425578i	$-0.139929\pi$
$863$	11.3713	+	12.6291i	0.387085	+	0.429901i	−0.517837	+	0.855479i	$0.673263\pi$
$864$	1.64126	−	0.348861i	0.0558369	−	0.0118685i
$865$	−2.05741	−	0.916018i	−0.0699541	−	0.0311456i
$866$	−28.2988	+	12.5994i	−0.961633	+	0.428147i
$867$	1.39309	+	4.28750i	0.0473119	+	0.145611i
$868$	−0.907724	+	5.60781i	−0.0308102	+	0.190341i
$869$	12.8596	+	5.88722i	0.436232	+	0.199710i
$870$	−0.243560	+	0.421859i	−0.00825747	+	0.0143024i
$871$	41.3032	−	45.8718i	1.39950	−	1.55431i
$872$	0.259922	−	2.47299i	0.00880206	−	0.0837460i
$873$	0.930030	+	8.84864i	0.0314767	+	0.299481i
$874$	−0.857355	+	2.63867i	−0.0290005	+	0.0892543i
$875$	0.199722	+	4.07574i	0.00675184	+	0.137785i
$876$	1.78565	−	1.29735i	0.0603315	−	0.0438334i
$877$	−14.2183	+	6.33040i	−0.480118	+	0.213762i	−0.632502	−	0.774559i	$-0.717972\pi$
$877$	−14.2183	+	6.33040i	−0.480118	+	0.213762i	0.152383	+	0.988321i	$0.451305\pi$
$878$	5.38500	−	5.98065i	0.181735	−	0.201837i
$879$	13.2923	+	23.0229i	0.448337	+	0.776543i
$880$	0.541622	−	1.60952i	0.0182581	−	0.0542570i
$881$	2.11673			0.0713145			0.0356572	−	0.999364i	$-0.488648\pi$
$881$	2.11673			0.0713145			0.0356572	+	0.999364i	$0.488648\pi$
$882$	0.0620097	−	9.12864i	0.00208798	−	0.307377i
$883$	0.998367	+	0.725356i	0.0335977	+	0.0244102i	0.604457	−	0.796637i	$-0.293390\pi$
$883$	0.998367	+	0.725356i	0.0335977	+	0.0244102i	−0.570860	+	0.821048i	$0.693390\pi$
$884$	−0.496671	−	4.72551i	−0.0167049	−	0.158936i
$885$	−1.42400	+	0.302680i	−0.0478672	+	0.0101745i
$886$	−3.60947	+	0.767217i	−0.121263	+	0.0257752i
$887$	−2.64621	−	25.1770i	−0.0888511	−	0.845361i	−0.944656	−	0.328063i	$-0.893604\pi$
$887$	−2.64621	−	25.1770i	−0.0888511	−	0.845361i	0.855805	−	0.517299i	$-0.173062\pi$
$888$	11.6217	+	8.44368i	0.389999	+	0.283351i
$889$	34.9082	+	43.4087i	1.17078	+	1.45588i
$890$	2.34949			0.0787550
$891$	−2.66269	−	1.97739i	−0.0892035	−	0.0662451i
$892$	−2.24779	−	3.89329i	−0.0752616	−	0.130357i
$893$	−19.0167	+	21.1202i	−0.636371	+	0.706762i
$894$	10.2008	−	4.54168i	0.341165	−	0.151897i
$895$	3.17558	−	2.30719i	0.106148	−	0.0771210i
$896$	−19.1466	−	9.83772i	−0.639642	−	0.328655i
$897$	0.793171	−	2.44113i	0.0264832	−	0.0815069i
$898$	−0.500875	−	4.76551i	−0.0167144	−	0.159027i
$899$	−1.81190	+	17.2391i	−0.0604303	+	0.574956i
$900$	0.996462	−	1.10668i	0.0332154	−	0.0368895i
$901$	−10.8808	+	18.8461i	−0.362493	+	0.627856i
$902$	−10.8715	−	19.2927i	−0.361981	−	0.642377i
$903$	−12.8780	−	10.5010i	−0.428553	−	0.349452i
$904$	−0.938927	−	2.88972i	−0.0312283	−	0.0961107i
$905$	0.0800095	−	0.0356225i	0.00265961	−	0.00118413i
$906$	−4.34126	−	1.93285i	−0.144229	−	0.0642147i
$907$	30.4288	−	6.46783i	1.01037	−	0.214761i	0.327149	−	0.944973i	$-0.393912\pi$
$907$	30.4288	−	6.46783i	1.01037	−	0.214761i	0.683221	+	0.730212i	$0.260579\pi$
$908$	2.83627	+	3.15000i	0.0941249	+	0.104536i
$909$	−15.0698	+	10.9488i	−0.499832	+	0.363150i
$910$	−0.612348	−	2.31676i	−0.0202991	−	0.0767999i
$911$	10.0692	+	30.9897i	0.333606	+	1.02673i	0.967405	+	0.253236i	$0.0814949\pi$
$911$	10.0692	+	30.9897i	0.333606	+	1.02673i	−0.633798	+	0.773498i	$0.718505\pi$
$912$	6.16572	−	10.6793i	0.204167	−	0.353628i
$913$	6.01441	−	10.1704i	0.199048	−	0.336590i
$914$	16.4544	+	28.4998i	0.544263	+	0.942691i
$915$	−1.06643	−	0.226677i	−0.0352551	−	0.00749370i
$916$	2.94765	+	2.14159i	0.0973930	+	0.0707602i
$917$	−18.1177	−	35.8586i	−0.598299	−	1.18415i
$918$	−1.42434	+	4.38367i	−0.0470102	+	0.144683i
$919$	−0.752066	−	0.835253i	−0.0248084	−	0.0275525i	0.730613	−	0.682792i	$-0.239234\pi$
$919$	−0.752066	−	0.835253i	−0.0248084	−	0.0275525i	−0.755421	+	0.655239i	$0.772568\pi$
$920$	0.241980	+	0.107737i	0.00797785	+	0.00355197i
$921$	2.69288	−	25.6210i	0.0887334	−	0.844242i
$922$	2.11010	+	0.448515i	0.0694923	+	0.0147710i
$923$	−26.5425			−0.873658
$924$	−0.644495	−	2.54576i	−0.0212023	−	0.0837492i
$925$	23.8393			0.783833
$926$	30.4708	+	6.47676i	1.00133	+	0.212840i
$927$	−0.642508	+	6.11306i	−0.0211027	+	0.200779i
$928$	3.70343	+	1.64887i	0.121571	+	0.0541270i
$929$	24.7429	+	27.4798i	0.811788	+	0.901582i	0.996700	−	0.0811731i	$-0.0258667\pi$
$929$	24.7429	+	27.4798i	0.811788	+	0.901582i	−0.184912	+	0.982755i	$0.559200\pi$
$930$	0.447010	−	1.37576i	0.0146580	−	0.0451128i
$931$	19.2501	+	17.5711i	0.630897	+	0.575870i
$932$	−3.64955	−	2.65155i	−0.119545	−	0.0868545i
$933$	20.6338	+	4.38584i	0.675519	+	0.143586i
$934$	−11.2904	−	19.5556i	−0.369435	−	0.639880i
$935$	−1.19852	−	1.35939i	−0.0391958	−	0.0444568i
$936$	−6.73500	+	11.6654i	−0.220140	+	0.381294i
$937$	−4.27983	−	13.1719i	−0.139816	−	0.430309i	0.856492	−	0.516160i	$-0.172639\pi$
$937$	−4.27983	−	13.1719i	−0.139816	−	0.430309i	−0.996308	+	0.0858512i	$0.972639\pi$
$938$	−45.7536	−	12.4263i	−1.49391	−	0.405734i
$939$	−21.2620	+	15.4478i	−0.693860	+	0.504119i
$940$	0.236308	+	0.262447i	0.00770752	+	0.00856007i
$941$	−1.83729	+	0.390528i	−0.0598940	+	0.0127309i	−0.237761	−	0.971324i	$-0.576414\pi$
$941$	−1.83729	+	0.390528i	−0.0598940	+	0.0127309i	0.177867	+	0.984054i	$0.443080\pi$
$942$	−4.39626	−	1.95734i	−0.143238	−	0.0637736i
$943$	2.67248	−	1.18986i	0.0870279	−	0.0387473i
$944$	−9.63711	−	29.6600i	−0.313661	−	0.965350i
$945$	0.0653599	−	0.403785i	0.00212616	−	0.0131351i
$946$	24.6997	+	11.3077i	0.803056	+	0.367644i
$947$	−24.9177	+	43.1587i	−0.809717	+	1.40247i	0.103343	+	0.994646i	$0.467046\pi$
$947$	−24.9177	+	43.1587i	−0.809717	+	1.40247i	−0.913060	+	0.407825i	$0.866287\pi$
$948$	0.853930	−	0.948385i	0.0277343	−	0.0308021i
$949$	−3.46315	+	32.9497i	−0.112419	+	1.06959i
$950$	−2.52568	−	24.0302i	−0.0819438	−	0.779643i
$951$	5.75185	−	17.7024i	0.186517	−	0.574039i
$952$	−23.5676	+	15.1914i	−0.763831	+	0.492358i
$953$	43.7611	−	31.7943i	1.41756	−	1.02992i	0.425393	−	0.905009i	$-0.360136\pi$
$953$	43.7611	−	31.7943i	1.41756	−	1.02992i	0.992168	−	0.124909i	$-0.0398640\pi$
$954$	7.33544	−	3.26595i	0.237494	−	0.105739i
$955$	−0.431339	+	0.479051i	−0.0139578	+	0.0155017i
$956$	2.16724	+	3.75377i	0.0700936	+	0.121406i
$957$	−2.39641	−	7.64631i	−0.0774649	−	0.247170i
$958$	11.2972			0.364997
$959$	−9.51371	+	24.5347i	−0.307214	+	0.792265i
$960$	−1.10218	−	0.800778i	−0.0355726	−	0.0258450i
$961$	−2.14025	−	20.3631i	−0.0690403	−	0.656874i
$962$	−27.4529	+	5.83529i	−0.885116	+	0.188137i
$963$	18.3640	−	3.90338i	0.591770	−	0.125785i
$964$	0.429841	+	4.08967i	0.0138443	+	0.131719i
$965$	−1.75070	−	1.27196i	−0.0563572	−	0.0409459i
$966$	−1.94824	+	0.301791i	−0.0626836	+	0.00970998i
$967$	36.6625			1.17899			0.589493	−	0.807774i	$-0.299328\pi$
$967$	36.6625			1.17899			0.589493	+	0.807774i	$0.299328\pi$
$968$	15.8914	+	28.9031i	0.510770	+	0.928982i
$969$	−6.57991	−	11.3967i	−0.211377	−	0.366116i
$970$	1.20035	−	1.33313i	0.0385410	−	0.0428041i
$971$	27.2704	−	12.1416i	0.875148	−	0.389641i	0.0805310	−	0.996752i	$-0.474338\pi$
$971$	27.2704	−	12.1416i	0.875148	−	0.389641i	0.794617	+	0.607111i	$0.207672\pi$
$972$	−0.242113	+	0.175906i	−0.00776579	+	0.00564218i
$973$	−2.01581	−	41.1368i	−0.0646239	−	1.31878i
$974$	−16.8395	+	51.8267i	−0.539573	+	1.66064i
$975$	2.33660	+	22.2312i	0.0748309	+	0.711969i
$976$	2.44130	−	23.2275i	0.0781442	−	0.743493i
$977$	28.3554	−	31.4918i	0.907169	−	1.00751i	−0.0927608	−	0.995688i	$-0.529569\pi$
$977$	28.3554	−	31.4918i	0.907169	−	1.00751i	0.999930	−	0.0118251i	$-0.00376414\pi$
$978$	−15.9873	+	27.6909i	−0.511218	+	0.885456i
$979$	−26.1596	+	28.4497i	−0.836065	+	0.909257i
$980$	0.242152	−	0.215075i	0.00773527	−	0.00687030i
$981$	0.256261	+	0.788691i	0.00818179	+	0.0251809i
$982$	−39.4906	+	17.5824i	−1.26020	+	0.561076i
$983$	2.88604	+	1.28495i	0.0920505	+	0.0409835i	0.452245	−	0.891894i	$-0.350623\pi$
$983$	2.88604	+	1.28495i	0.0920505	+	0.0409835i	−0.360195	+	0.932877i	$0.617290\pi$
$984$	−15.0166	+	3.19188i	−0.478712	+	0.101753i
$985$	1.40874	+	1.56456i	0.0448862	+	0.0498511i
$986$	−9.00928	+	6.54562i	−0.286914	+	0.208455i
$987$	−19.4887	−	5.29300i	−0.620334	−	0.168478i
$988$	−1.54682	−	4.76062i	−0.0492109	−	0.151456i
$989$	−1.79428	+	3.10778i	−0.0570547	+	0.0988217i
$990$	0.0629462	+	0.665732i	0.00200056	+	0.0211584i
$991$	−17.3315	−	30.0190i	−0.550552	−	0.953584i	−0.998235	−	0.0593913i	$-0.981084\pi$
$991$	−17.3315	−	30.0190i	−0.550552	−	0.953584i	0.447683	−	0.894192i	$-0.352249\pi$
$992$	−11.7754	−	2.50295i	−0.373871	−	0.0794687i
$993$	−14.9488	−	10.8609i	−0.474385	−	0.344661i
$994$	9.19366	+	18.1961i	0.291605	+	0.577145i
$995$	−0.0822666	+	0.253191i	−0.00260803	+	0.00802668i
$996$	−0.713400	−	0.792311i	−0.0226049	−	0.0251053i
$997$	38.5421	+	17.1600i	1.22064	+	0.543464i	0.912969	−	0.408029i	$-0.133784\pi$
$997$	38.5421	+	17.1600i	1.22064	+	0.543464i	0.307670	+	0.951493i	$0.400451\pi$
$998$	1.26484	−	12.0342i	0.0400379	−	0.380935i
$999$	−4.68608	−	0.996057i	−0.148261	−	0.0315139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.a.16.2	✓	64
3.2	odd	2		693.2.by.d.478.7		64
7.4	even	3	inner	231.2.y.a.214.7	yes	64
11.9	even	5	inner	231.2.y.a.163.7	yes	64
21.11	odd	6		693.2.by.d.676.2		64
33.20	odd	10		693.2.by.d.163.2		64
77.53	even	15	inner	231.2.y.a.130.2	yes	64
231.53	odd	30		693.2.by.d.361.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.16.2	✓	64	1.1	even	1	trivial
231.2.y.a.130.2	yes	64	77.53	even	15	inner
231.2.y.a.163.7	yes	64	11.9	even	5	inner
231.2.y.a.214.7	yes	64	7.4	even	3	inner
693.2.by.d.163.2		64	33.20	odd	10
693.2.by.d.361.7		64	231.53	odd	30
693.2.by.d.478.7		64	3.2	odd	2
693.2.by.d.676.2		64	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27562 - 0.271142i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.273395 - 0.121723i) q^{4} +(-0.103450 - 0.114892i) q^{5} +(-0.402996 + 1.24029i) q^{6} +(1.44851 - 2.21401i) q^{7} +(2.42586 + 1.76249i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-1.27562 - 0.271142i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.273395 - 0.121723i) q^{4} +(-0.103450 - 0.114892i) q^{5} +(-0.402996 + 1.24029i) q^{6} +(1.44851 - 2.21401i) q^{7} +(2.42586 + 1.76249i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.100810 + 0.174609i) q^{10} +(-3.23677 - 0.723422i) q^{11} +(-0.149634 + 0.259174i) q^{12} +(-1.38817 - 4.27234i) q^{13} +(-2.44806 + 2.43149i) q^{14} +(-0.125076 + 0.0908734i) q^{15} +(-2.21609 - 2.46122i) q^{16} +(-3.45715 + 0.734839i) q^{17} +(1.19137 + 0.530434i) q^{18} +(-3.40147 + 1.51443i) q^{19} +(0.0142975 + 0.0440033i) q^{20} +(-2.05047 - 1.67200i) q^{21} +(3.93274 + 1.80044i) q^{22} +(-0.285690 + 0.494829i) q^{23} +(2.00640 - 2.22834i) q^{24} +(0.520144 - 4.94884i) q^{25} +(0.612368 + 5.82629i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.665512 + 0.428982i) q^{28} +(-1.95460 + 1.42010i) q^{29} +(0.184190 - 0.0820066i) q^{30} +(4.80076 - 5.33179i) q^{31} +(-0.838964 - 1.45313i) q^{32} +(-1.05779 + 3.14342i) q^{33} +4.60926 q^{34} +(-0.404220 + 0.0626156i) q^{35} +(0.242113 + 0.175906i) q^{36} +(0.500772 + 4.76453i) q^{37} +(4.74962 - 1.00956i) q^{38} +(-4.39404 + 0.933983i) q^{39} +(-0.0484574 - 0.461041i) q^{40} +(-4.14207 - 3.00939i) q^{41} +(2.16227 + 2.68881i) q^{42} +6.28052 q^{43} +(0.796860 + 0.591771i) q^{44} +(0.0773015 + 0.133890i) q^{45} +(0.498601 - 0.553752i) q^{46} +(6.97299 - 3.10458i) q^{47} +(-2.67938 + 1.94669i) q^{48} +(-2.80365 - 6.41401i) q^{49} +(-2.00535 + 6.17182i) q^{50} +(0.369444 + 3.51502i) q^{51} +(-0.140526 + 1.33701i) q^{52} +(4.11992 - 4.57564i) q^{53} +(0.652060 - 1.12940i) q^{54} +(0.251726 + 0.446718i) q^{55} +(7.41603 - 2.81789i) q^{56} +(1.15058 + 3.54114i) q^{57} +(2.87839 - 1.28154i) q^{58} +(8.60235 + 3.83001i) q^{59} +(0.0452568 - 0.00961962i) q^{60} +(4.71868 + 5.24063i) q^{61} +(-7.56963 + 5.49966i) q^{62} +(-1.87717 + 1.86446i) q^{63} +(2.72307 + 8.38073i) q^{64} +(-0.347254 + 0.601462i) q^{65} +(2.20166 - 3.72300i) q^{66} +(6.87041 + 11.8999i) q^{67} +(1.03462 + 0.219914i) q^{68} +(0.462255 + 0.335848i) q^{69} +(0.532610 + 0.0297272i) q^{70} +(1.82585 - 5.61938i) q^{71} +(-2.00640 - 2.22834i) q^{72} +(-6.73763 - 2.99979i) q^{73} +(0.653067 - 6.21352i) q^{74} +(-4.86736 - 1.03459i) q^{75} +1.11429 q^{76} +(-6.29014 + 6.11834i) q^{77} +5.85838 q^{78} +(-4.17114 - 0.886603i) q^{79} +(-0.0535217 + 0.509225i) q^{80} +(0.913545 + 0.406737i) q^{81} +(4.46775 + 4.96194i) q^{82} +(-1.10089 + 3.38819i) q^{83} +(0.357067 + 0.706707i) q^{84} +(0.442068 + 0.321181i) q^{85} +(-8.01157 - 1.70291i) q^{86} +(1.20801 + 2.09234i) q^{87} +(-6.57691 - 7.45968i) q^{88} +(5.82649 - 10.0918i) q^{89} +(-0.0623043 - 0.191753i) q^{90} +(-11.4698 - 3.11511i) q^{91} +(0.138338 - 0.100509i) q^{92} +(-4.80076 - 5.33179i) q^{93} +(-9.73669 + 2.06960i) q^{94} +(0.525877 + 0.234136i) q^{95} +(-1.53286 + 0.682475i) q^{96} +(-2.74944 - 8.46191i) q^{97} +(1.83730 + 8.94205i) q^{98} +(3.01563 + 1.38058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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