LMFDB - Embedded newform 230.2.g.b.131.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} + \cdots + 529 $ x^20 - 5x^19 + 12x^18 + 16x^17 - 49x^16 + 59x^15 - 197x^14 + 42x^13 + 1625x^12 - 5910x^11 + 14651x^10 - 22501x^9 + 26003x^8 - 19607x^7 + 13040x^6 + 348x^5 + 7193x^4 + 10771x^3 + 8781x^2 + 3105*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			131.2
Root			$1.33237 + 0.856263i$ of defining polynomial
Character	$\chi$	$=$	230.131
Dual form			230.2.g.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(1.45499 - 0.935068i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.246141 - 1.71195i) q^{6} +(1.53819 - 0.451652i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.00358844 + 0.00785758i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(1.45499 - 0.935068i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.246141 - 1.71195i) q^{6} +(1.53819 - 0.451652i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.00358844 + 0.00785758i) q^{9} +(0.959493 + 0.281733i) q^{10} +(0.784179 + 0.904991i) q^{11} +(-1.13262 - 1.30711i) q^{12} +(-4.64122 - 1.36279i) q^{13} +(0.665961 - 1.45825i) q^{14} +(1.45499 + 0.935068i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.194319 - 1.35152i) q^{17} +(0.00358844 + 0.00785758i) q^{18} +(0.206375 + 1.43537i) q^{19} +(0.841254 - 0.540641i) q^{20} +(1.81573 - 2.09546i) q^{21} +1.19747 q^{22} +(-4.66972 + 1.09257i) q^{23} -1.72956 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-4.06928 + 2.61517i) q^{26} +(0.740550 + 5.15064i) q^{27} +(-0.665961 - 1.45825i) q^{28} +(-0.197630 + 1.37454i) q^{29} +(1.65950 - 0.487272i) q^{30} +(-0.564860 - 0.363013i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(1.98720 + 0.583496i) q^{33} +(-0.894159 - 1.03191i) q^{34} +(1.04982 + 1.21156i) q^{35} +(0.00828829 + 0.00243366i) q^{36} +(3.99119 - 8.73948i) q^{37} +(1.21993 + 0.784001i) q^{38} +(-8.02725 + 2.35701i) q^{39} +(0.142315 - 0.989821i) q^{40} +(3.41025 + 7.46742i) q^{41} +(-0.394595 - 2.74447i) q^{42} +(-3.73941 + 2.40317i) q^{43} +(0.784179 - 0.904991i) q^{44} -0.00863819 q^{45} +(-2.23231 + 4.24462i) q^{46} +12.2002 q^{47} +(-1.13262 + 1.30711i) q^{48} +(-3.72675 + 2.39504i) q^{49} +(0.142315 + 0.989821i) q^{50} +(-0.981031 - 2.14816i) q^{51} +(-0.688400 + 4.78793i) q^{52} +(5.54408 - 1.62789i) q^{53} +(4.37755 + 2.81328i) q^{54} +(-0.497449 + 1.08926i) q^{55} +(-1.53819 - 0.451652i) q^{56} +(1.64245 + 1.89548i) q^{57} +(0.909391 + 1.04949i) q^{58} +(-9.36953 - 2.75114i) q^{59} +(0.718483 - 1.57326i) q^{60} +(-0.954342 - 0.613319i) q^{61} +(-0.644252 + 0.189169i) q^{62} +(-0.00197079 + 0.0137071i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.688400 - 4.78793i) q^{65} +(1.74232 - 1.11972i) q^{66} +(-4.19871 + 4.84557i) q^{67} -1.36542 q^{68} +(-5.77279 + 5.95619i) q^{69} +1.60312 q^{70} +(0.918560 - 1.06007i) q^{71} +(0.00726691 - 0.00467016i) q^{72} +(-0.286320 - 1.99140i) q^{73} +(-3.99119 - 8.73948i) q^{74} +(-0.246141 + 1.71195i) q^{75} +(1.39139 - 0.408550i) q^{76} +(1.61495 + 1.03787i) q^{77} +(-3.47542 + 7.61011i) q^{78} +(-8.87855 - 2.60698i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(5.87673 + 6.78210i) q^{81} +(7.87674 + 2.31282i) q^{82} +(2.55571 - 5.59623i) q^{83} +(-2.33254 - 1.49903i) q^{84} +(1.31011 - 0.384683i) q^{85} +(-0.632596 + 4.39980i) q^{86} +(0.997742 + 2.18475i) q^{87} +(-0.170418 - 1.18529i) q^{88} +(0.855412 - 0.549740i) q^{89} +(-0.00565681 + 0.00652831i) q^{90} -7.75456 q^{91} +(1.74602 + 4.46670i) q^{92} -1.16131 q^{93} +(7.98943 - 9.22030i) q^{94} +(-1.21993 + 0.784001i) q^{95} +(0.246141 + 1.71195i) q^{96} +(-2.09646 - 4.59061i) q^{97} +(-0.630454 + 4.38491i) q^{98} +(-0.00992501 + 0.00291425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	1.45499	−	0.935068i	0.840042	−	0.539862i	−0.0484126	−	0.998827i	$-0.515416\pi$
$3$	1.45499	−	0.935068i	0.840042	−	0.539862i	0.888454	+	0.458966i	$0.151780\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$6$	0.246141	−	1.71195i	0.100487	−	0.698901i
$7$	1.53819	−	0.451652i	0.581379	−	0.170708i	0.0221978	−	0.999754i	$-0.492934\pi$
$7$	1.53819	−	0.451652i	0.581379	−	0.170708i	0.559182	+	0.829045i	$0.311115\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	−0.00358844	+	0.00785758i	−0.00119615	+	0.00261919i
$10$	0.959493	+	0.281733i	0.303418	+	0.0890917i
$11$	0.784179	+	0.904991i	0.236439	+	0.272865i	0.861552	−	0.507669i	$-0.169493\pi$
$11$	0.784179	+	0.904991i	0.236439	+	0.272865i	−0.625113	+	0.780534i	$0.714947\pi$
$12$	−1.13262	−	1.30711i	−0.326959	−	0.377330i
$13$	−4.64122	−	1.36279i	−1.28724	−	0.377969i	−0.434676	−	0.900587i	$-0.643137\pi$
$13$	−4.64122	−	1.36279i	−1.28724	−	0.377969i	−0.852567	+	0.522618i	$0.824955\pi$
$14$	0.665961	−	1.45825i	0.177986	−	0.389734i
$15$	1.45499	+	0.935068i	0.375678	+	0.241434i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.194319	−	1.35152i	0.0471294	−	0.327792i	−0.952593	−	0.304246i	$-0.901595\pi$
$17$	0.194319	−	1.35152i	0.0471294	−	0.327792i	0.999723	−	0.0235456i	$-0.00749550\pi$
$18$	0.00358844	+	0.00785758i	0.000845802	+	0.00185205i
$19$	0.206375	+	1.43537i	0.0473458	+	0.329297i	0.999704	+	0.0243164i	$0.00774092\pi$
$19$	0.206375	+	1.43537i	0.0473458	+	0.329297i	−0.952359	+	0.304981i	$0.901350\pi$
$20$	0.841254	−	0.540641i	0.188110	−	0.120891i
$21$	1.81573	−	2.09546i	0.396224	−	0.457267i
$22$	1.19747			0.255302
$23$	−4.66972	+	1.09257i	−0.973704	+	0.227817i
$23$	−4.66972	+	1.09257i	−0.973704	+	0.227817i
$24$	−1.72956			−0.353044
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	−4.06928	+	2.61517i	−0.798051	+	0.512876i
$27$	0.740550	+	5.15064i	0.142519	+	0.991241i
$28$	−0.665961	−	1.45825i	−0.125855	−	0.275584i
$29$	−0.197630	+	1.37454i	−0.0366989	+	0.255246i	−0.999909	−	0.0135037i	$-0.995701\pi$
$29$	−0.197630	+	1.37454i	−0.0366989	+	0.255246i	0.963210	+	0.268750i	$0.0866106\pi$
$30$	1.65950	−	0.487272i	0.302981	−	0.0889633i
$31$	−0.564860	−	0.363013i	−0.101452	−	0.0651991i	0.488931	−	0.872322i	$-0.337387\pi$
$31$	−0.564860	−	0.363013i	−0.101452	−	0.0651991i	−0.590383	+	0.807123i	$0.701023\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	1.98720	+	0.583496i	0.345928	+	0.101574i
$34$	−0.894159	−	1.03191i	−0.153347	−	0.176972i
$35$	1.04982	+	1.21156i	0.177452	+	0.204791i
$36$	0.00828829	+	0.00243366i	0.00138138	+	0.000405610i
$37$	3.99119	−	8.73948i	0.656147	−	1.43676i	−0.229922	−	0.973209i	$-0.573847\pi$
$37$	3.99119	−	8.73948i	0.656147	−	1.43676i	0.886069	−	0.463553i	$-0.153426\pi$
$38$	1.21993	+	0.784001i	0.197899	+	0.127182i
$39$	−8.02725	+	2.35701i	−1.28539	+	0.377424i
$40$	0.142315	−	0.989821i	0.0225020	−	0.156505i
$41$	3.41025	+	7.46742i	0.532592	+	1.16621i	0.964448	+	0.264272i	$0.0851316\pi$
$41$	3.41025	+	7.46742i	0.532592	+	1.16621i	−0.431856	+	0.901943i	$0.642141\pi$
$42$	−0.394595	−	2.74447i	−0.0608873	−	0.423481i
$43$	−3.73941	+	2.40317i	−0.570255	+	0.366481i	−0.793768	−	0.608220i	$-0.791884\pi$
$43$	−3.73941	+	2.40317i	−0.570255	+	0.366481i	0.223513	+	0.974701i	$0.428247\pi$
$44$	0.784179	−	0.904991i	0.118219	−	0.136432i
$45$	−0.00863819			−0.00128771
$46$	−2.23231	+	4.24462i	−0.329136	+	0.625835i
$47$	12.2002			1.77958			0.889791	−	0.456368i	$-0.150850\pi$
$47$	12.2002			1.77958			0.889791	+	0.456368i	$0.150850\pi$
$48$	−1.13262	+	1.30711i	−0.163479	+	0.188665i
$49$	−3.72675	+	2.39504i	−0.532393	+	0.342148i
$50$	0.142315	+	0.989821i	0.0201264	+	0.139982i
$51$	−0.981031	−	2.14816i	−0.137372	−	0.300802i
$52$	−0.688400	+	4.78793i	−0.0954639	+	0.663966i
$53$	5.54408	−	1.62789i	0.761538	−	0.223608i	0.122171	−	0.992509i	$-0.461014\pi$
$53$	5.54408	−	1.62789i	0.761538	−	0.223608i	0.639368	+	0.768901i	$0.279196\pi$
$54$	4.37755	+	2.81328i	0.595709	+	0.382839i
$55$	−0.497449	+	1.08926i	−0.0670760	+	0.146876i
$56$	−1.53819	−	0.451652i	−0.205549	−	0.0603545i
$57$	1.64245	+	1.89548i	0.217547	+	0.251063i
$58$	0.909391	+	1.04949i	0.119409	+	0.137805i
$59$	−9.36953	−	2.75114i	−1.21981	−	0.358168i	−0.392414	−	0.919789i	$-0.628360\pi$
$59$	−9.36953	−	2.75114i	−1.21981	−	0.358168i	−0.827395	+	0.561620i	$0.810178\pi$
$60$	0.718483	−	1.57326i	0.0927558	−	0.203107i
$61$	−0.954342	−	0.613319i	−0.122191	−	0.0785274i	0.478118	−	0.878296i	$-0.341319\pi$
$61$	−0.954342	−	0.613319i	−0.122191	−	0.0785274i	−0.600309	+	0.799768i	$0.704956\pi$
$62$	−0.644252	+	0.189169i	−0.0818200	+	0.0240245i
$63$	−0.00197079	+	0.0137071i	−0.000248296	+	0.00172694i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.688400	−	4.78793i	−0.0853855	−	0.593869i
$66$	1.74232	−	1.11972i	0.214465	−	0.137828i
$67$	−4.19871	+	4.84557i	−0.512955	+	0.591981i	−0.951853	−	0.306556i	$-0.900823\pi$
$67$	−4.19871	+	4.84557i	−0.512955	+	0.591981i	0.438898	+	0.898537i	$0.355369\pi$
$68$	−1.36542			−0.165581
$69$	−5.77279	+	5.95619i	−0.694962	+	0.717041i
$70$	1.60312			0.191610
$71$	0.918560	−	1.06007i	0.109013	−	0.125808i	−0.698621	−	0.715492i	$-0.746202\pi$
$71$	0.918560	−	1.06007i	0.109013	−	0.125808i	0.807634	+	0.589685i	$0.200748\pi$
$72$	0.00726691	−	0.00467016i	0.000856414	−	0.000550384i
$73$	−0.286320	−	1.99140i	−0.0335112	−	0.233076i	0.966182	−	0.257863i	$-0.0830183\pi$
$73$	−0.286320	−	1.99140i	−0.0335112	−	0.233076i	−0.999693	+	0.0247871i	$0.992109\pi$
$74$	−3.99119	−	8.73948i	−0.463966	−	1.01594i
$75$	−0.246141	+	1.71195i	−0.0284220	+	0.197679i
$76$	1.39139	−	0.408550i	0.159604	−	0.0468639i
$77$	1.61495	+	1.03787i	0.184041	+	0.118276i
$78$	−3.47542	+	7.61011i	−0.393514	+	0.861675i
$79$	−8.87855	−	2.60698i	−0.998915	−	0.293308i	−0.258904	−	0.965903i	$-0.583361\pi$
$79$	−8.87855	−	2.60698i	−0.998915	−	0.293308i	−0.740011	+	0.672595i	$0.765180\pi$
$80$	−0.654861	−	0.755750i	−0.0732157	−	0.0844954i
$81$	5.87673	+	6.78210i	0.652970	+	0.753567i
$82$	7.87674	+	2.31282i	0.869840	+	0.255408i
$83$	2.55571	−	5.59623i	0.280526	−	0.614266i	−0.715949	−	0.698152i	$-0.754006\pi$
$83$	2.55571	−	5.59623i	0.280526	−	0.614266i	0.996475	+	0.0838860i	$0.0267332\pi$
$84$	−2.33254	−	1.49903i	−0.254500	−	0.163558i
$85$	1.31011	−	0.384683i	0.142101	−	0.0417247i
$86$	−0.632596	+	4.39980i	−0.0682146	+	0.474443i
$87$	0.997742	+	2.18475i	0.106969	+	0.234230i
$88$	−0.170418	−	1.18529i	−0.0181667	−	0.126352i
$89$	0.855412	−	0.549740i	0.0906735	−	0.0582723i	−0.494518	−	0.869167i	$-0.664656\pi$
$89$	0.855412	−	0.549740i	0.0906735	−	0.0582723i	0.585192	+	0.810895i	$0.301019\pi$
$90$	−0.00565681	+	0.00652831i	−0.000596281	+	0.000688144i
$91$	−7.75456			−0.812899
$92$	1.74602	+	4.46670i	0.182035	+	0.465686i
$93$	−1.16131			−0.120422
$94$	7.98943	−	9.22030i	0.824047	−	0.951001i
$95$	−1.21993	+	0.784001i	−0.125162	+	0.0804368i
$96$	0.246141	+	1.71195i	0.0251217	+	0.174725i
$97$	−2.09646	−	4.59061i	−0.212863	−	0.466105i	0.772839	−	0.634602i	$-0.218836\pi$
$97$	−2.09646	−	4.59061i	−0.212863	−	0.466105i	−0.985702	+	0.168497i	$0.946109\pi$
$98$	−0.630454	+	4.38491i	−0.0636855	+	0.442942i
$99$	−0.00992501	+	0.00291425i	−0.000997501	+	0.000292893i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	2.82994	−	6.19670i	0.281590	−	0.616595i	−0.714999	−	0.699125i	$-0.753573\pi$
$101$	2.82994	−	6.19670i	0.281590	−	0.616595i	0.996589	+	0.0825304i	$0.0263001\pi$
$102$	−2.26591	−	0.665330i	−0.224358	−	0.0658775i
$103$	−3.09575	−	3.57269i	−0.305033	−	0.352027i	0.582450	−	0.812866i	$-0.302094\pi$
$103$	−3.09575	−	3.57269i	−0.305033	−	0.352027i	−0.887484	+	0.460839i	$0.847549\pi$
$104$	3.16767	+	3.65568i	0.310615	+	0.358469i
$105$	2.66038	+	0.781157i	0.259626	+	0.0762331i
$106$	2.40033	−	5.25598i	0.233140	−	0.510506i
$107$	8.19725	+	5.26805i	0.792458	+	0.509282i	0.873147	−	0.487458i	$-0.162076\pi$
$107$	8.19725	+	5.26805i	0.792458	+	0.509282i	−0.0806889	+	0.996739i	$0.525712\pi$
$108$	4.99282	−	1.46603i	0.480435	−	0.141068i
$109$	1.50258	−	10.4506i	0.143921	−	1.00099i	−0.782002	−	0.623276i	$-0.785801\pi$
$109$	1.50258	−	10.4506i	0.143921	−	1.00099i	0.925922	−	0.377714i	$-0.123290\pi$
$110$	0.497449	+	1.08926i	0.0474299	+	0.103857i
$111$	−2.36486	−	16.4479i	−0.224462	−	1.56117i
$112$	−1.34863	+	0.866714i	−0.127434	+	0.0818968i
$113$	11.6460	−	13.4402i	1.09556	−	1.26435i	0.133637	−	0.991030i	$-0.457334\pi$
$113$	11.6460	−	13.4402i	1.09556	−	1.26435i	0.961924	−	0.273316i	$-0.0881203\pi$
$114$	2.50809			0.234904
$115$	−2.93371	−	3.79386i	−0.273570	−	0.353779i
$116$	1.38868			0.128936
$117$	0.0273629	−	0.0315785i	0.00252970	−	0.00291943i
$118$	−8.21491	+	5.27940i	−0.756244	+	0.486009i
$119$	−0.311518	−	2.16665i	−0.0285568	−	0.198617i
$120$	−0.718483	−	1.57326i	−0.0655882	−	0.143618i
$121$	1.36139	−	9.46869i	0.123763	−	0.860790i
$122$	−1.08848	+	0.319606i	−0.0985461	+	0.0289357i
$123$	11.9444	+	7.67623i	1.07699	+	0.692142i
$124$	−0.278930	+	0.610772i	−0.0250487	+	0.0548490i
$125$	−0.959493	−	0.281733i	−0.0858197	−	0.0251989i
$126$	0.00906857	+	0.0104657i	0.000807892	+	0.000932357i
$127$	−7.25322	−	8.37066i	−0.643619	−	0.742776i	0.336391	−	0.941722i	$-0.390794\pi$
$127$	−7.25322	−	8.37066i	−0.643619	−	0.742776i	−0.980010	+	0.198946i	$0.936248\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	−3.19369	+	6.99321i	−0.281189	+	0.615718i
$130$	−4.06928	−	2.61517i	−0.356899	−	0.229365i
$131$	−15.3179	+	4.49775i	−1.33833	+	0.392970i	−0.871074	−	0.491151i	$-0.836576\pi$
$131$	−15.3179	+	4.49775i	−1.33833	+	0.392970i	−0.467258	+	0.884121i	$0.654758\pi$
$132$	0.294748	−	2.05002i	0.0256545	−	0.178431i
$133$	0.965733	+	2.11466i	0.0837396	+	0.183364i
$134$	0.912468	+	6.34635i	0.0788252	+	0.548241i
$135$	−4.37755	+	2.81328i	−0.376760	+	0.242129i
$136$	−0.894159	+	1.03191i	−0.0766735	+	0.0884860i
$137$	14.9658			1.27862			0.639308	−	0.768951i	$-0.279221\pi$
$137$	14.9658			1.27862			0.639308	+	0.768951i	$0.279221\pi$
$138$	0.721014	+	8.26326i	0.0613768	+	0.703415i
$139$	−0.583936			−0.0495288			−0.0247644	−	0.999693i	$-0.507884\pi$
$139$	−0.583936			−0.0495288			−0.0247644	+	0.999693i	$0.507884\pi$
$140$	1.04982	−	1.21156i	0.0887262	−	0.102395i
$141$	17.7512	−	11.4080i	1.49492	−	0.960729i
$142$	−0.199622	−	1.38840i	−0.0167519	−	0.116512i
$143$	−2.40624	−	5.26893i	−0.201220	−	0.440610i
$144$	0.00122934	−	0.00855027i	0.000102445	−	0.000712522i
$145$	−1.33243	+	0.391236i	−0.110652	+	0.0324904i
$146$	−1.69250	−	1.08770i	−0.140072	−	0.0900190i
$147$	−3.18288	+	6.96953i	−0.262519	+	0.574837i
$148$	−9.21853	−	2.70680i	−0.757759	−	0.222498i
$149$	1.19518	+	1.37931i	0.0979127	+	0.112997i	0.802591	−	0.596530i	$-0.203454\pi$
$149$	1.19518	+	1.37931i	0.0979127	+	0.112997i	−0.704678	+	0.709527i	$0.748909\pi$
$150$	1.13262	+	1.30711i	0.0924779	+	0.106725i
$151$	−11.4513	−	3.36239i	−0.931890	−	0.273628i	−0.219662	−	0.975576i	$-0.570495\pi$
$151$	−11.4513	−	3.36239i	−0.931890	−	0.273628i	−0.712228	+	0.701948i	$0.752314\pi$
$152$	0.602407	−	1.31909i	0.0488617	−	0.106992i
$153$	0.00992238	+	0.00637672i	0.000802177	+	0.000515528i
$154$	1.84194	−	0.540842i	0.148428	−	0.0435823i
$155$	0.0955573	−	0.664616i	0.00767535	−	0.0533832i
$156$	3.47542	+	7.61011i	0.278256	+	0.609296i
$157$	−3.14317	−	21.8612i	−0.250852	−	1.74472i	−0.593119	−	0.805115i	$-0.702104\pi$
$157$	−3.14317	−	21.8612i	−0.250852	−	1.74472i	0.342267	−	0.939603i	$-0.388805\pi$
$158$	−7.78443	+	5.00275i	−0.619296	+	0.397998i
$159$	6.54442	−	7.55267i	0.519006	−	0.598965i
$160$	−1.00000			−0.0790569
$161$	−6.68943	+	3.78966i	−0.527201	+	0.298667i
$162$	8.97401			0.705065
$163$	7.72896	−	8.91969i	0.605379	−	0.698644i	−0.367483	−	0.930030i	$-0.619781\pi$
$163$	7.72896	−	8.91969i	0.605379	−	0.698644i	0.972862	+	0.231386i	$0.0743260\pi$
$164$	6.90608	−	4.43827i	0.539274	−	0.346570i
$165$	0.294748	+	2.05002i	0.0229461	+	0.159594i
$166$	−2.55571	−	5.59623i	−0.198362	−	0.434352i
$167$	−2.19920	+	15.2957i	−0.170179	+	1.18362i	0.708326	+	0.705886i	$0.249451\pi$
$167$	−2.19920	+	15.2957i	−0.170179	+	1.18362i	−0.878504	+	0.477734i	$0.841458\pi$
$168$	−2.66038	+	0.781157i	−0.205253	+	0.0602676i
$169$	8.74746	+	5.62165i	0.672881	+	0.432435i
$170$	0.567215	−	1.24203i	0.0435034	−	0.0952592i
$171$	−0.0120191	−	0.00352913i	−0.000919125	−	0.000269879i
$172$	2.91089	+	3.35934i	0.221953	+	0.256148i
$173$	5.25661	+	6.06645i	0.399653	+	0.461224i	0.919532	−	0.393016i	$-0.128568\pi$
$173$	5.25661	+	6.06645i	0.399653	+	0.461224i	−0.519879	+	0.854240i	$0.674023\pi$
$174$	2.30451	+	0.676664i	0.174704	+	0.0512978i
$175$	−0.665961	+	1.45825i	−0.0503419	+	0.110233i
$176$	−1.00738	−	0.647403i	−0.0759341	−	0.0487999i
$177$	−16.2051	+	4.75825i	−1.21805	+	0.357652i
$178$	0.144710	−	1.00648i	0.0108465	−	0.0754389i
$179$	10.2605	+	22.4673i	0.766903	+	1.67928i	0.733355	+	0.679846i	$0.237953\pi$
$179$	10.2605	+	22.4673i	0.766903	+	1.67928i	0.0335480	+	0.999437i	$0.489319\pi$
$180$	0.00122934	+	0.00855027i	9.16298e−5	+	0.000637299i
$181$	−6.33654	+	4.07225i	−0.470991	+	0.302688i	−0.754521	−	0.656276i	$-0.772131\pi$
$181$	−6.33654	+	4.07225i	−0.470991	+	0.302688i	0.283530	+	0.958963i	$0.408494\pi$
$182$	−5.07816	+	5.86051i	−0.376418	+	0.434410i
$183$	−1.96206			−0.145039
$184$	4.51911	+	1.60551i	0.333153	+	0.118360i
$185$	9.60771			0.706373
$186$	−0.760496	+	0.877659i	−0.0557623	+	0.0643531i
$187$	1.37549	−	0.883977i	0.100586	−	0.0646428i
$188$	−1.73627	−	12.0760i	−0.126630	−	0.880734i
$189$	3.46540	+	7.58817i	0.252071	+	0.551958i
$190$	−0.206375	+	1.43537i	−0.0149720	+	0.104133i
$191$	9.81455	−	2.88181i	0.710156	−	0.208521i	0.0933473	−	0.995634i	$-0.470243\pi$
$191$	9.81455	−	2.88181i	0.710156	−	0.208521i	0.616809	+	0.787113i	$0.288425\pi$
$192$	1.45499	+	0.935068i	0.105005	+	0.0674827i
$193$	−9.39377	+	20.5695i	−0.676179	+	1.48062i	0.190463	+	0.981694i	$0.439001\pi$
$193$	−9.39377	+	20.5695i	−0.676179	+	1.48062i	−0.866642	+	0.498930i	$0.833726\pi$
$194$	−4.84224	−	1.42181i	−0.347652	−	0.102080i
$195$	−5.47865	−	6.32270i	−0.392335	−	0.452778i
$196$	2.90103	+	3.34797i	0.207216	+	0.239141i
$197$	−18.6794	−	5.48477i	−1.33085	−	0.390773i	−0.462455	−	0.886643i	$-0.653031\pi$
$197$	−18.6794	−	5.48477i	−1.33085	−	0.390773i	−0.868397	+	0.495869i	$0.834849\pi$
$198$	−0.00429706	+	0.00940925i	−0.000305379	+	0.000668686i
$199$	22.0130	+	14.1469i	1.56046	+	1.00285i	0.982385	+	0.186866i	$0.0598331\pi$
$199$	22.0130	+	14.1469i	1.56046	+	1.00285i	0.578077	+	0.815982i	$0.303803\pi$
$200$	0.959493	−	0.281733i	0.0678464	−	0.0199215i
$201$	−1.57816	+	10.9764i	−0.111315	+	0.774213i
$202$	−2.82994	−	6.19670i	−0.199114	−	0.435999i
$203$	0.316825	+	2.20356i	0.0222367	+	0.154660i
$204$	−1.98668	+	1.27676i	−0.139095	+	0.0893911i
$205$	−5.37593	+	6.20415i	−0.375471	+	0.433317i
$206$	−4.72734			−0.329370
$207$	0.00817204	−	0.0406133i	0.000567996	−	0.00282282i
$208$	4.83716			0.335397
$209$	−1.13716	+	1.31236i	−0.0786592	+	0.0907776i
$210$	2.33254	−	1.49903i	0.160960	−	0.103443i
$211$	0.0168460	+	0.117167i	0.00115973	+	0.00806608i	0.990393	−	0.138281i	$-0.0441576\pi$
$211$	0.0168460	+	0.117167i	0.00115973	+	0.00806608i	−0.989233	+	0.146347i	$0.953248\pi$
$212$	−2.40033	−	5.25598i	−0.164855	−	0.360982i
$213$	0.345258	−	2.40132i	0.0236567	−	0.164536i
$214$	9.34938	−	2.74523i	0.639111	−	0.187660i
$215$	−3.73941	−	2.40317i	−0.255026	−	0.163895i
$216$	2.16166	−	4.73337i	0.147082	−	0.322065i
$217$	−1.03281	−	0.303262i	−0.0701120	−	0.0205867i
$218$	−6.91409	−	7.97928i	−0.468281	−	0.540425i
$219$	−2.27869	−	2.62975i	−0.153980	−	0.177702i
$220$	1.14897	+	0.337367i	0.0774634	+	0.0227453i
$221$	−2.74371	+	6.00789i	−0.184562	+	0.404135i
$222$	−13.9792	−	8.98387i	−0.938220	−	0.602958i
$223$	−12.2080	+	3.58459i	−0.817508	+	0.240042i	−0.663643	−	0.748050i	$-0.730990\pi$
$223$	−12.2080	+	3.58459i	−0.817508	+	0.240042i	−0.153866	+	0.988092i	$0.549172\pi$
$224$	−0.228148	+	1.58681i	−0.0152438	+	0.106023i
$225$	−0.00358844	−	0.00785758i	−0.000239229	−	0.000523838i
$226$	−2.53091	−	17.6029i	−0.168354	−	1.17093i
$227$	−20.3549	+	13.0813i	−1.35100	+	0.868237i	−0.997734	−	0.0672849i	$-0.978566\pi$
$227$	−20.3549	+	13.0813i	−1.35100	+	0.868237i	−0.353269	+	0.935522i	$0.614930\pi$
$228$	1.64245	−	1.89548i	0.108774	−	0.125532i
$229$	6.74051			0.445426			0.222713	−	0.974884i	$-0.428509\pi$
$229$	6.74051			0.445426			0.222713	+	0.974884i	$0.428509\pi$
$230$	−4.78838	−	0.267299i	−0.315736	−	0.0176252i
$231$	3.32022			0.218455
$232$	0.909391	−	1.04949i	0.0597045	−	0.0689026i
$233$	20.0242	−	12.8688i	1.31183	−	0.843062i	0.317382	−	0.948298i	$-0.397196\pi$
$233$	20.0242	−	12.8688i	1.31183	−	0.843062i	0.994447	+	0.105236i	$0.0335597\pi$
$234$	−0.00594653	−	0.0413590i	−0.000388737	−	0.00270372i
$235$	5.06815	+	11.0977i	0.330609	+	0.723934i
$236$	−1.38972	+	9.66569i	−0.0904628	+	0.629183i
$237$	−15.3559	+	4.50891i	−0.997476	+	0.292885i
$238$	−1.84145	−	1.18343i	−0.119363	−	0.0767102i
$239$	−2.98478	+	6.53575i	−0.193069	+	0.422763i	−0.981265	−	0.192662i	$-0.938288\pi$
$239$	−2.98478	+	6.53575i	−0.193069	+	0.422763i	0.788196	+	0.615424i	$0.211015\pi$
$240$	−1.65950	−	0.487272i	−0.107120	−	0.0314533i
$241$	15.2568	+	17.6073i	0.982775	+	1.13418i	0.990952	+	0.134217i	$0.0428518\pi$
$241$	15.2568	+	17.6073i	0.982775	+	1.13418i	−0.00817680	+	0.999967i	$0.502603\pi$
$242$	−6.26443	−	7.22954i	−0.402693	−	0.464733i
$243$	−0.0861341	−	0.0252913i	−0.00552551	−	0.00162244i
$244$	−0.471259	+	1.03191i	−0.0301693	+	0.0660615i
$245$	−3.72675	−	2.39504i	−0.238093	−	0.153013i
$246$	13.6233	−	4.00015i	0.868587	−	0.255040i
$247$	0.998271	−	6.94313i	0.0635185	−	0.441781i
$248$	0.278930	+	0.610772i	0.0177121	+	0.0387841i
$249$	−1.51431	−	10.5323i	−0.0959654	−	0.667454i
$250$	−0.841254	+	0.540641i	−0.0532055	+	0.0341931i
$251$	−8.73522	+	10.0810i	−0.551362	+	0.636306i	−0.961200	−	0.275852i	$-0.911040\pi$
$251$	−8.73522	+	10.0810i	−0.551362	+	0.636306i	0.409838	+	0.912158i	$0.365585\pi$
$252$	0.0138481			0.000872347
$253$	−4.65066	−	3.36928i	−0.292385	−	0.211825i
$254$	−11.0760			−0.694968
$255$	1.54650	−	1.78475i	0.0968454	−	0.111766i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	0.899923	+	6.25910i	0.0561357	+	0.390432i	0.998448	+	0.0556965i	$0.0177379\pi$
$257$	0.899923	+	6.25910i	0.0561357	+	0.390432i	−0.942312	+	0.334736i	$0.891353\pi$
$258$	3.19369	+	6.99321i	0.198831	+	0.435378i
$259$	2.19198	−	15.2456i	0.136203	−	0.947314i
$260$	−4.64122	+	1.36279i	−0.287836	+	0.0845164i
$261$	−0.0100914	−	0.00648535i	−0.000624642	−	0.000401433i
$262$	−6.63193	+	14.5219i	−0.409722	+	0.897166i
$263$	15.6062	+	4.58240i	0.962320	+	0.282563i	0.724908	−	0.688846i	$-0.241882\pi$
$263$	15.6062	+	4.58240i	0.962320	+	0.282563i	0.237413	+	0.971409i	$0.423701\pi$
$264$	−1.35628	−	1.56523i	−0.0834733	−	0.0963333i
$265$	3.78388	+	4.36683i	0.232442	+	0.268252i
$266$	2.23057	+	0.654955i	0.136765	+	0.0401579i
$267$	0.730575	−	1.59974i	0.0447105	−	0.0979023i
$268$	5.39379	+	3.46638i	0.329478	+	0.211743i
$269$	−26.0443	+	7.64729i	−1.58795	+	0.466263i	−0.952160	−	0.305601i	$-0.901143\pi$
$269$	−26.0443	+	7.64729i	−1.58795	+	0.466263i	−0.635787	+	0.771864i	$0.719324\pi$
$270$	−0.740550	+	5.15064i	−0.0450685	+	0.313458i
$271$	−1.55821	−	3.41201i	−0.0946548	−	0.207265i	0.856382	−	0.516343i	$-0.172707\pi$
$271$	−1.55821	−	3.41201i	−0.0946548	−	0.207265i	−0.951037	+	0.309078i	$0.899980\pi$
$272$	0.194319	+	1.35152i	0.0117823	+	0.0819480i
$273$	−11.2828	+	7.25105i	−0.682869	+	0.438853i
$274$	9.80053	−	11.3104i	0.592072	−	0.683287i
$275$	−1.19747			−0.0722104
$276$	6.71712	+	4.86638i	0.404323	+	0.292922i
$277$	−14.3223			−0.860545			−0.430273	−	0.902699i	$-0.641583\pi$
$277$	−14.3223			−0.860545			−0.430273	+	0.902699i	$0.641583\pi$
$278$	−0.382397	+	0.441310i	−0.0229346	+	0.0264680i
$279$	0.00487937	−	0.00313578i	0.000292120	−	0.000187734i
$280$	−0.228148	−	1.58681i	−0.0136345	−	0.0948298i
$281$	6.15953	+	13.4875i	0.367447	+	0.804597i	0.999558	+	0.0297191i	$0.00946128\pi$
$281$	6.15953	+	13.4875i	0.367447	+	0.804597i	−0.632111	+	0.774878i	$0.717811\pi$
$282$	3.00297	−	20.8861i	0.178825	−	1.24375i
$283$	14.0215	−	4.11709i	0.833492	−	0.244735i	0.162976	−	0.986630i	$-0.447891\pi$
$283$	14.0215	−	4.11709i	0.833492	−	0.244735i	0.670516	+	0.741895i	$0.266073\pi$
$284$	−1.18001	−	0.758346i	−0.0700207	−	0.0449996i
$285$	−1.04190	+	2.28143i	−0.0617166	+	0.135141i
$286$	−5.55774	−	1.63190i	−0.328636	−	0.0964963i
$287$	8.61828	+	9.94602i	0.508721	+	0.587095i
$288$	−0.00565681	−	0.00652831i	−0.000333331	−	0.000384684i
$289$	14.5225	+	4.26420i	0.854267	+	0.250835i
$290$	−0.576878	+	1.26319i	−0.0338754	+	0.0741769i
$291$	−7.34287	−	4.71897i	−0.430446	−	0.276631i
$292$	−1.93038	+	0.566812i	−0.112967	+	0.0331701i
$293$	4.01735	−	27.9413i	0.234696	−	1.63235i	−0.442657	−	0.896691i	$-0.645964\pi$
$293$	4.01735	−	27.9413i	0.234696	−	1.63235i	0.677354	−	0.735657i	$-0.263127\pi$
$294$	3.18288	+	6.96953i	0.185629	+	0.406471i
$295$	−1.38972	−	9.66569i	−0.0809124	−	0.562758i
$296$	−8.08252	+	5.19432i	−0.469787	+	0.301914i
$297$	−4.08056	+	4.70921i	−0.236778	+	0.273256i
$298$	1.82509			0.105724
$299$	23.1621	+	1.29297i	1.33950	+	0.0747744i
$300$	1.72956			0.0998559
$301$	−4.66651	+	5.38544i	−0.268973	+	0.310412i
$302$	−10.0401	+	6.45238i	−0.577743	+	0.371293i
$303$	−1.67679	−	11.6624i	−0.0963293	−	0.669985i
$304$	−0.602407	−	1.31909i	−0.0345504	−	0.0756548i
$305$	0.161446	−	1.12288i	0.00924438	−	0.0642960i
$306$	0.0113170	−	0.00332297i	0.000646949	−	0.000189961i
$307$	23.6725	+	15.2134i	1.35106	+	0.868276i	0.997738	−	0.0672250i	$-0.0214145\pi$
$307$	23.6725	+	15.2134i	1.35106	+	0.868276i	0.353325	+	0.935501i	$0.385051\pi$
$308$	0.797472	−	1.74622i	0.0454402	−	0.0995001i
$309$	−7.84501	−	2.30350i	−0.446287	−	0.131042i
$310$	−0.439706	−	0.507448i	−0.0249736	−	0.0288211i
$311$	12.7463	+	14.7100i	0.722777	+	0.834129i	0.991638	−	0.129050i	$-0.0411928\pi$
$311$	12.7463	+	14.7100i	0.722777	+	0.834129i	−0.268861	+	0.963179i	$0.586647\pi$
$312$	8.02725	+	2.35701i	0.454454	+	0.133440i
$313$	−12.1519	+	26.6090i	−0.686869	+	1.50403i	0.168329	+	0.985731i	$0.446163\pi$
$313$	−12.1519	+	26.6090i	−0.686869	+	1.50403i	−0.855198	+	0.518302i	$0.826564\pi$
$314$	−18.5800	−	11.9406i	−1.04853	−	0.673848i
$315$	−0.0132871	+	0.00390146i	−0.000748646	+	0.000219822i
$316$	−1.31689	+	9.15919i	−0.0740810	+	0.515245i
$317$	−12.7698	−	27.9620i	−0.717225	−	1.57050i	−0.817753	−	0.575569i	$-0.804781\pi$
$317$	−12.7698	−	27.9620i	−0.717225	−	1.57050i	0.100529	−	0.994934i	$-0.467947\pi$
$318$	−1.42224	−	9.89189i	−0.0797552	−	0.554710i
$319$	−1.39893	+	0.899035i	−0.0783248	+	0.0503363i
$320$	−0.654861	+	0.755750i	−0.0366078	+	0.0422477i
$321$	16.8529			0.940639
$322$	−1.51661	+	7.53724i	−0.0845175	+	0.420034i
$323$	1.98004			0.110172
$324$	5.87673	−	6.78210i	0.326485	−	0.376784i
$325$	4.06928	−	2.61517i	0.225723	−	0.145063i
$326$	−1.67966	−	11.6823i	−0.0930279	−	0.647023i
$327$	−7.58582	−	16.6106i	−0.419497	−	0.918570i
$328$	1.16830	−	8.12571i	0.0645086	−	0.448667i
$329$	18.7662	−	5.51025i	1.03461	−	0.303790i
$330$	1.74232	+	1.11972i	0.0959115	+	0.0616386i
$331$	2.27139	−	4.97365i	0.124847	−	0.273376i	−0.836880	−	0.547386i	$-0.815623\pi$
$331$	2.27139	−	4.97365i	0.124847	−	0.273376i	0.961727	+	0.274010i	$0.0883501\pi$
$332$	−5.90299	−	1.73327i	−0.323968	−	0.0951257i
$333$	0.0543490	+	0.0627221i	0.00297831	+	0.00343715i
$334$	10.1196	+	11.6786i	0.553719	+	0.639026i
$335$	−6.15190	−	1.80636i	−0.336114	−	0.0986920i
$336$	−1.15182	+	2.52213i	−0.0628368	+	0.137593i
$337$	−27.2206	−	17.4936i	−1.48280	−	0.952939i	−0.996880	−	0.0789378i	$-0.974847\pi$
$337$	−27.2206	−	17.4936i	−1.48280	−	0.952939i	−0.485923	−	0.874002i	$-0.661516\pi$
$338$	9.97693	−	2.92949i	0.542673	−	0.159343i
$339$	4.37736	−	30.4452i	0.237745	−	1.65356i
$340$	−0.567215	−	1.24203i	−0.0307616	−	0.0673585i
$341$	−0.114427	−	0.795860i	−0.00619659	−	0.0430982i
$342$	−0.0105380	+	0.00677235i	−0.000569829	+	0.000366207i
$343$	−11.9995	+	13.8481i	−0.647910	+	0.747728i
$344$	4.44505			0.239661
$345$	−7.81605	−	2.77682i	−0.420802	−	0.149499i
$346$	8.02707			0.431538
$347$	13.8697	−	16.0065i	0.744565	−	0.859274i	−0.249465	−	0.968384i	$-0.580255\pi$
$347$	13.8697	−	16.0065i	0.744565	−	0.859274i	0.994030	+	0.109110i	$0.0348001\pi$
$348$	2.02052	−	1.29851i	0.108311	−	0.0696074i
$349$	−3.59175	−	24.9812i	−0.192262	−	1.33721i	−0.826002	−	0.563666i	$-0.809390\pi$
$349$	−3.59175	−	24.9812i	−0.192262	−	1.33721i	0.633740	−	0.773546i	$-0.281519\pi$
$350$	0.665961	+	1.45825i	0.0355971	+	0.0779468i
$351$	3.58216	−	24.9145i	0.191202	−	1.32984i
$352$	−1.14897	+	0.337367i	−0.0612402	+	0.0179817i
$353$	12.4243	+	7.98462i	0.661279	+	0.424978i	0.827772	−	0.561064i	$-0.189608\pi$
$353$	12.4243	+	7.98462i	0.661279	+	0.424978i	−0.166493	+	0.986043i	$0.553244\pi$
$354$	−7.01605	+	15.3630i	−0.372899	+	0.816535i
$355$	1.34586	+	0.395181i	0.0714309	+	0.0209740i
$356$	−0.665882	−	0.768469i	−0.0352917	−	0.0407288i
$357$	−2.47923	−	2.86118i	−0.131215	−	0.151430i
$358$	23.6988	+	6.95860i	1.25252	+	0.367773i
$359$	7.11318	−	15.5757i	0.375419	−	0.822054i	−0.623763	−	0.781614i	$-0.714397\pi$
$359$	7.11318	−	15.5757i	0.375419	−	0.822054i	0.999182	−	0.0404399i	$-0.0128759\pi$
$360$	0.00726691	+	0.00467016i	0.000383000	+	0.000246139i
$361$	16.2127	−	4.76047i	0.853298	−	0.250551i
$362$	−1.07195	+	7.45559i	−0.0563406	+	0.391857i
$363$	−6.87305	−	15.0499i	−0.360742	−	0.789914i
$364$	1.10359	+	7.67563i	0.0578438	+	0.402313i
$365$	1.69250	−	1.08770i	0.0885895	−	0.0569330i
$366$	−1.28487	+	1.48282i	−0.0671615	+	0.0775085i
$367$	37.3209			1.94813			0.974067	−	0.226261i	$-0.0726502\pi$
$367$	37.3209			1.94813			0.974067	+	0.226261i	$0.0726502\pi$
$368$	4.17275	−	2.36393i	0.217520	−	0.123228i
$369$	−0.0709133			−0.00369160
$370$	6.29171	−	7.26102i	0.327091	−	0.377483i
$371$	7.79259	−	5.00799i	0.404571	−	0.260002i
$372$	0.165272	+	1.14949i	0.00856894	+	0.0595983i
$373$	−0.234522	−	0.513533i	−0.0121431	−	0.0265897i	0.903463	−	0.428665i	$-0.141016\pi$
$373$	−0.234522	−	0.513533i	−0.0121431	−	0.0265897i	−0.915606	+	0.402076i	$0.868289\pi$
$374$	0.232692	−	1.61841i	0.0120322	−	0.0836861i
$375$	−1.65950	+	0.487272i	−0.0856960	+	0.0251626i
$376$	−10.2635	−	6.59593i	−0.529298	−	0.340159i
$377$	2.79045	−	6.11024i	0.143716	−	0.314693i
$378$	8.00411	+	2.35022i	0.411687	+	0.120882i
$379$	−8.98174	−	10.3655i	−0.461361	−	0.532439i	0.476627	−	0.879105i	$-0.341859\pi$
$379$	−8.98174	−	10.3655i	−0.461361	−	0.532439i	−0.937989	+	0.346666i	$0.887314\pi$
$380$	0.949635	+	1.09594i	0.0487153	+	0.0562204i
$381$	−18.3805	−	5.39701i	−0.941663	−	0.276497i
$382$	4.24924	−	9.30453i	0.217410	−	0.476061i
$383$	11.4054	+	7.32980i	0.582788	+	0.374535i	0.798566	−	0.601907i	$-0.205592\pi$
$383$	11.4054	+	7.32980i	0.582788	+	0.374535i	−0.215778	+	0.976443i	$0.569229\pi$
$384$	1.65950	−	0.487272i	0.0846858	−	0.0248660i
$385$	−0.273202	+	1.90016i	−0.0139236	+	0.0968411i
$386$	9.39377	+	20.5695i	0.478131	+	1.04696i
$387$	−0.00546449	−	0.0380064i	−0.000277776	−	0.00193197i
$388$	−4.24552	+	2.72843i	−0.215534	+	0.138515i
$389$	−8.30445	+	9.58384i	−0.421052	+	0.485920i	−0.926157	−	0.377138i	$-0.876908\pi$
$389$	−8.30445	+	9.58384i	−0.421052	+	0.485920i	0.505105	+	0.863058i	$0.331454\pi$
$390$	−8.36614			−0.423636
$391$	0.569214	+	6.52353i	0.0287864	+	0.329909i
$392$	4.43000			0.223749
$393$	−18.0818	+	20.8675i	−0.912105	+	1.05263i
$394$	−16.3775	+	10.5252i	−0.825087	+	0.530251i
$395$	−1.31689	−	9.15919i	−0.0662601	−	0.460849i
$396$	0.00429706	+	0.00940925i	0.000215935	+	0.000472832i
$397$	−3.17492	+	22.0820i	−0.159345	+	1.10827i	0.740500	+	0.672056i	$0.234589\pi$
$397$	−3.17492	+	22.0820i	−0.159345	+	1.10827i	−0.899845	+	0.436210i	$0.856321\pi$
$398$	25.1070	−	7.37208i	1.25850	−	0.369529i
$399$	3.38249	+	2.17379i	0.169336	+	0.108826i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	−24.7148	−	7.25693i	−1.23420	−	0.362394i	−0.401367	−	0.915917i	$-0.631465\pi$
$401$	−24.7148	−	7.25693i	−1.23420	−	0.362394i	−0.832834	+	0.553524i	$0.813283\pi$
$402$	7.26191	+	8.38069i	0.362191	+	0.417991i
$403$	2.12693	+	2.45461i	0.105950	+	0.122273i
$404$	−6.53637	−	1.91925i	−0.325197	−	0.0954864i
$405$	−3.72794	+	8.16305i	−0.185243	+	0.405625i
$406$	1.87282	+	1.20359i	0.0929464	+	0.0597330i
$407$	11.0390	−	3.24133i	0.547181	−	0.160667i
$408$	−0.336086	+	2.33753i	−0.0166387	+	0.115725i
$409$	0.684671	+	1.49922i	0.0338548	+	0.0741317i	0.925804	−	0.378004i	$-0.123389\pi$
$409$	0.684671	+	1.49922i	0.0338548	+	0.0741317i	−0.891949	+	0.452136i	$0.850662\pi$
$410$	1.16830	+	8.12571i	0.0576983	+	0.401300i
$411$	21.7752	−	13.9941i	1.07409	−	0.690276i
$412$	−3.09575	+	3.57269i	−0.152517	+	0.176014i
$413$	−15.6546			−0.770314
$414$	−0.0253419	−	0.0327721i	−0.00124549	−	0.00161066i
$415$	6.15219			0.301999
$416$	3.16767	−	3.65568i	0.155308	−	0.179235i
$417$	−0.849624	+	0.546020i	−0.0416063	+	0.0267387i
$418$	0.247129	+	1.71882i	0.0120875	+	0.0840703i
$419$	1.59841	+	3.50004i	0.0780876	+	0.170988i	0.944649	−	0.328082i	$-0.106402\pi$
$419$	1.59841	+	3.50004i	0.0780876	+	0.170988i	−0.866562	+	0.499070i	$0.833675\pi$
$420$	0.394595	−	2.74447i	0.0192543	−	0.133916i
$421$	34.7066	−	10.1908i	1.69150	−	0.496668i	0.712694	−	0.701475i	$-0.247475\pi$
$421$	34.7066	−	10.1908i	1.69150	−	0.496668i	0.978803	+	0.204806i	$0.0656564\pi$
$422$	0.0995804	+	0.0639964i	0.00484750	+	0.00311530i
$423$	−0.0437796	+	0.0958640i	−0.00212864	+	0.00466107i
$424$	−5.54408	−	1.62789i	−0.269244	−	0.0790573i
$425$	0.894159	+	1.03191i	0.0433731	+	0.0500552i
$426$	−1.58870	−	1.83346i	−0.0769728	−	0.0888313i
$427$	−1.74496	−	0.512367i	−0.0844446	−	0.0247952i
$428$	4.04784	−	8.86353i	0.195660	−	0.428435i
$429$	−8.42787	−	5.41627i	−0.406902	−	0.261500i
$430$	−4.26499	+	1.25231i	−0.205676	+	0.0603920i
$431$	−2.98280	+	20.7458i	−0.143676	+	0.999290i	0.782622	+	0.622498i	$0.213882\pi$
$431$	−2.98280	+	20.7458i	−0.143676	+	0.999290i	−0.926298	+	0.376792i	$0.877027\pi$
$432$	−2.16166	−	4.73337i	−0.104003	−	0.227734i
$433$	2.71201	+	18.8625i	0.130331	+	0.906473i	0.945122	+	0.326718i	$0.105943\pi$
$433$	2.71201	+	18.8625i	0.130331	+	0.906473i	−0.814791	+	0.579755i	$0.803148\pi$
$434$	−0.905540	+	0.581955i	−0.0434673	+	0.0279347i
$435$	−1.57284	+	1.81516i	−0.0754120	+	0.0870301i
$436$	−10.5581			−0.505642
$437$	−2.53196	−	6.47731i	−0.121120	−	0.309852i
$438$	−3.47965			−0.166264
$439$	−15.1265	+	17.4569i	−0.721949	+	0.833174i	−0.991540	−	0.129801i	$-0.958566\pi$
$439$	−15.1265	+	17.4569i	−0.721949	+	0.833174i	0.269591	+	0.962975i	$0.413112\pi$
$440$	1.00738	−	0.647403i	0.0480249	−	0.0308637i
$441$	−0.00544599	−	0.0378777i	−0.000259333	−	0.00180370i
$442$	2.74371	+	6.00789i	0.130505	+	0.285766i
$443$	1.35285	−	9.40927i	0.0642758	−	0.447048i	−0.932115	−	0.362163i	$-0.882038\pi$
$443$	1.35285	−	9.40927i	0.0642758	−	0.447048i	0.996391	−	0.0848854i	$-0.0270524\pi$
$444$	−15.9440	+	4.68157i	−0.756667	+	0.222177i
$445$	0.855412	+	0.549740i	0.0405504	+	0.0260602i
$446$	−5.28549	+	11.5736i	−0.250275	+	0.548026i
$447$	3.02872	+	0.889314i	0.143254	+	0.0420631i
$448$	1.04982	+	1.21156i	0.0495994	+	0.0572408i
$449$	−7.78566	−	8.98513i	−0.367428	−	0.424035i	0.541687	−	0.840580i	$-0.317786\pi$
$449$	−7.78566	−	8.98513i	−0.367428	−	0.424035i	−0.909115	+	0.416546i	$0.863240\pi$
$450$	−0.00828829	−	0.00243366i	−0.000390714	−	0.000114724i
$451$	−4.08369	+	8.94204i	−0.192294	+	0.421064i
$452$	−14.9608	−	9.61471i	−0.703696	−	0.452238i
$453$	−19.8056	+	5.81544i	−0.930547	+	0.273233i
$454$	−3.44344	+	23.9496i	−0.161609	+	1.12401i
$455$	−3.22136	−	7.05380i	−0.151020	−	0.330687i
$456$	−0.356938	−	2.48256i	−0.0167151	−	0.116256i
$457$	−2.66556	+	1.71305i	−0.124690	+	0.0801331i	−0.601499	−	0.798874i	$-0.705430\pi$
$457$	−2.66556	+	1.71305i	−0.124690	+	0.0801331i	0.476809	+	0.879007i	$0.341793\pi$
$458$	4.41410	−	5.09414i	0.206257	−	0.238034i
$459$	7.10510			0.331638
$460$	−3.33773	+	3.44377i	−0.155623	+	0.160567i
$461$	−15.1878			−0.707366			−0.353683	−	0.935365i	$-0.615071\pi$
$461$	−15.1878			−0.707366			−0.353683	+	0.935365i	$0.615071\pi$
$462$	2.17428	−	2.50926i	0.101157	−	0.116741i
$463$	−12.3653	+	7.94669i	−0.574664	+	0.369314i	−0.795460	−	0.606006i	$-0.792771\pi$
$463$	−12.3653	+	7.94669i	−0.574664	+	0.369314i	0.220796	+	0.975320i	$0.429134\pi$
$464$	−0.197630	−	1.37454i	−0.00917472	−	0.0638116i
$465$	−0.482426	−	1.05636i	−0.0223720	−	0.0489877i
$466$	3.38750	−	23.5605i	0.156923	−	1.09142i
$467$	−23.5519	+	6.91547i	−1.08985	+	0.320010i	−0.776814	−	0.629730i	$-0.783165\pi$
$467$	−23.5519	+	6.91547i	−1.08985	+	0.320010i	−0.313039	+	0.949740i	$0.601347\pi$
$468$	−0.0351512	−	0.0225903i	−0.00162487	−	0.00104424i
$469$	−4.26989	+	9.34975i	−0.197165	+	0.431731i
$470$	11.7060	+	3.43719i	0.539958	+	0.158546i
$471$	−25.0151	−	28.8689i	−1.15263	−	1.33021i
$472$	6.39477	+	7.37996i	0.294343	+	0.339690i
$473$	−5.10722	−	1.49961i	−0.234830	−	0.0689524i
$474$	−6.64840	+	14.5580i	−0.305371	+	0.668669i
$475$	−1.21993	−	0.784001i	−0.0559742	−	0.0359724i
$476$	−2.10027	+	0.616694i	−0.0962656	+	0.0282661i
$477$	−0.00710331	+	0.0494046i	−0.000325238	+	0.00226208i
$478$	2.98478	+	6.53575i	0.136521	+	0.298938i
$479$	1.30224	+	9.05729i	0.0595009	+	0.413838i	0.997702	+	0.0677485i	$0.0215816\pi$
$479$	1.30224	+	9.05729i	0.0595009	+	0.413838i	−0.938202	+	0.346089i	$0.887509\pi$
$480$	−1.45499	+	0.935068i	−0.0664111	+	0.0426798i
$481$	−30.4340	+	35.1227i	−1.38767	+	1.60146i
$482$	23.2977			1.06118
$483$	−6.18950	+	11.7690i	−0.281632	+	0.535509i
$484$	−9.56606			−0.434821
$485$	3.30486	−	3.81401i	0.150066	−	0.173185i
$486$	−0.0755197	+	0.0485336i	−0.00342564	+	0.00220153i
$487$	2.78760	+	19.3882i	0.126318	+	0.878563i	0.950164	+	0.311749i	$0.100915\pi$
$487$	2.78760	+	19.3882i	0.126318	+	0.878563i	−0.823846	+	0.566813i	$0.808176\pi$
$488$	0.471259	+	1.03191i	0.0213329	+	0.0467125i
$489$	2.90507	−	20.2052i	0.131372	−	0.913711i
$490$	−4.25055	+	1.24807i	−0.192020	+	0.0563822i
$491$	−21.4833	−	13.8065i	−0.969526	−	0.623077i	−0.0429076	−	0.999079i	$-0.513662\pi$
$491$	−21.4833	−	13.8065i	−0.969526	−	0.623077i	−0.926619	+	0.376002i	$0.877298\pi$
$492$	5.89822	−	12.9153i	0.265912	−	0.582267i
$493$	1.81932	+	0.534201i	0.0819381	+	0.0240592i
$494$	−4.59354	−	5.30123i	−0.206673	−	0.238513i
$495$	−0.00677389	−	0.00781748i	−0.000304464	−	0.000351370i
$496$	0.644252	+	0.189169i	0.0289277	+	0.00849395i
$497$	0.934131	−	2.04546i	0.0419015	−	0.0917515i
$498$	−8.95141	−	5.75272i	−0.401122	−	0.257786i
$499$	−3.36063	+	0.986771i	−0.150443	+	0.0441739i	−0.356087	−	0.934453i	$-0.615889\pi$
$499$	−3.36063	+	0.986771i	−0.150443	+	0.0441739i	0.205644	+	0.978627i	$0.434071\pi$
$500$	−0.142315	+	0.989821i	−0.00636451	+	0.0442662i
$501$	11.1027	+	24.3116i	0.496034	+	1.08616i
$502$	1.89835	+	13.2033i	0.0847273	+	0.589291i
$503$	−24.8723	+	15.9845i	−1.10900	+	0.712712i	−0.961075	−	0.276287i	$-0.910896\pi$
$503$	−24.8723	+	15.9845i	−1.10900	+	0.712712i	−0.147926	+	0.988998i	$0.547260\pi$
$504$	0.00906857	−	0.0104657i	0.000403946	−	0.000466179i
$505$	6.81232			0.303144
$506$	−5.59187	+	1.30832i	−0.248589	+	0.0581621i
$507$	17.9841			0.798703
$508$	−7.25322	+	8.37066i	−0.321810	+	0.371388i
$509$	−18.3777	+	11.8106i	−0.814575	+	0.523496i	−0.880342	−	0.474339i	$-0.842687\pi$
$509$	−18.3777	+	11.8106i	−0.814575	+	0.523496i	0.0657668	+	0.997835i	$0.479051\pi$
$510$	−0.336086	−	2.33753i	−0.0148821	−	0.103508i
$511$	−1.33983	−	2.93383i	−0.0592707	−	0.129785i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−7.24026	+	2.12593i	−0.319665	+	0.0938622i
$514$	5.31964	+	3.41872i	0.234639	+	0.150793i
$515$	1.96381	−	4.30014i	0.0865358	−	0.189487i
$516$	7.37654	+	2.16595i	0.324734	+	0.0953505i
$517$	9.56714	+	11.0411i	0.420762	+	0.485586i
$518$	−10.0864	−	11.6403i	−0.443171	−	0.511446i
$519$	13.3209	+	3.91137i	0.584722	+	0.171690i
$520$	−2.00943	+	4.40004i	−0.0881193	+	0.192954i
$521$	6.77290	+	4.35268i	0.296726	+	0.190694i	0.680530	−	0.732720i	$-0.261750\pi$
$521$	6.77290	+	4.35268i	0.296726	+	0.190694i	−0.383804	+	0.923415i	$0.625386\pi$
$522$	−0.0115098	+	0.00337957i	−0.000503769	+	0.000147920i
$523$	2.78218	−	19.3505i	0.121656	−	0.846138i	−0.834023	−	0.551729i	$-0.813968\pi$
$523$	2.78218	−	19.3505i	0.121656	−	0.846138i	0.955680	−	0.294409i	$-0.0951227\pi$
$524$	6.63193	+	14.5219i	0.289717	+	0.634392i
$525$	0.394595	+	2.74447i	0.0172215	+	0.119778i
$526$	13.6830	−	8.79356i	0.596609	−	0.383417i
$527$	−0.600383	+	0.692879i	−0.0261531	+	0.0301823i
$528$	−2.07110			−0.0901330
$529$	20.6126	−	10.2040i	0.896199	−	0.443652i
$530$	5.77814			0.250986
$531$	0.0552393	−	0.0637495i	0.00239718	−	0.00276649i
$532$	1.95570	−	1.25685i	0.0847902	−	0.0544914i
$533$	−5.65126	−	39.3054i	−0.244783	−	1.70250i
$534$	−0.730575	−	1.59974i	−0.0316151	−	0.0692274i
$535$	−1.38673	+	9.64491i	−0.0599535	+	0.416986i
$536$	6.15190	−	1.80636i	0.265722	−	0.0780229i
$537$	35.9374	+	23.0955i	1.55081	+	0.996646i
$538$	−11.2759	+	24.6908i	−0.486140	+	1.06450i
$539$	−5.08992	−	1.49454i	−0.219239	−	0.0643743i
$540$	3.40764	+	3.93262i	0.146641	+	0.169233i
$541$	4.37998	+	5.05477i	0.188310	+	0.217321i	0.842052	−	0.539396i	$-0.181347\pi$
$541$	4.37998	+	5.05477i	0.188310	+	0.217321i	−0.653742	+	0.756717i	$0.726802\pi$
$542$	−3.59904	−	1.05677i	−0.154592	−	0.0453923i
$543$	−5.41180	+	11.8502i	−0.232243	+	0.508541i
$544$	1.14866	+	0.738201i	0.0492485	+	0.0316501i
$545$	10.1304	−	2.97456i	0.433940	−	0.127416i
$546$	−1.90872	+	13.2754i	−0.0816856	+	0.568136i
$547$	−6.99978	−	15.3274i	−0.299289	−	0.655351i	0.698918	−	0.715201i	$-0.253665\pi$
$547$	−6.99978	−	15.3274i	−0.299289	−	0.655351i	−0.998207	+	0.0598501i	$0.980938\pi$
$548$	−2.12986	−	14.8135i	−0.0909830	−	0.632801i
$549$	0.00824380	−	0.00529797i	0.000351837	−	0.000226112i
$550$	−0.784179	+	0.904991i	−0.0334375	+	0.0385889i
$551$	−2.01377			−0.0857894
$552$	8.07654	−	1.88966i	0.343760	−	0.0804293i
$553$	−14.8343			−0.630819
$554$	−9.37913	+	10.8241i	−0.398481	+	0.459872i
$555$	13.9792	−	8.98387i	0.593383	−	0.381344i
$556$	0.0831028	+	0.577993i	0.00352434	+	0.0245123i
$557$	8.13505	+	17.8133i	0.344693	+	0.754773i	1.00000		0.000590300i	$-0.000187898\pi$
$557$	8.13505	+	17.8133i	0.344693	+	0.754773i	−0.655307	+	0.755363i	$0.727461\pi$
$558$	0.000825442	−	0.00574108i	3.49438e−5	−	0.000243039i
$559$	20.6305	−	6.05765i	0.872575	−	0.256211i
$560$	−1.34863	−	0.866714i	−0.0569901	−	0.0366253i
$561$	1.17476	−	2.57236i	0.0495984	−	0.108605i
$562$	14.2268	+	4.17737i	0.600122	+	0.176212i
$563$	9.60219	+	11.0815i	0.404684	+	0.467030i	0.921111	−	0.389301i	$-0.127283\pi$
$563$	9.60219	+	11.0815i	0.404684	+	0.467030i	−0.516426	+	0.856332i	$0.672738\pi$
$564$	−13.8182	−	15.9470i	−0.581850	−	0.671491i
$565$	17.0635	+	5.01031i	0.717868	+	0.210785i
$566$	6.07065	−	13.2929i	0.255168	−	0.558741i
$567$	12.1026	+	7.77790i	0.508263	+	0.326641i
$568$	−1.34586	+	0.395181i	−0.0564711	+	0.0165814i
$569$	5.57191	−	38.7535i	0.233587	−	1.62463i	−0.448795	−	0.893635i	$-0.648147\pi$
$569$	5.57191	−	38.7535i	0.233587	−	1.62463i	0.682382	−	0.730996i	$-0.260944\pi$
$570$	1.04190	+	2.28143i	0.0436402	+	0.0955588i
$571$	−2.93146	−	20.3887i	−0.122678	−	0.853242i	−0.954502	−	0.298204i	$-0.903613\pi$
$571$	−2.93146	−	20.3887i	−0.122678	−	0.853242i	0.831825	−	0.555039i	$-0.187297\pi$
$572$	−4.87286	+	3.13159i	−0.203744	+	0.130939i
$573$	11.5854	−	13.3703i	0.483988	−	0.558552i
$574$	13.1605			0.549307
$575$	2.23231	−	4.24462i	0.0930937	−	0.177013i
$576$	−0.00863819			−0.000359925
$577$	−14.6211	+	16.8736i	−0.608683	+	0.702458i	−0.973517	−	0.228615i	$-0.926580\pi$
$577$	−14.6211	+	16.8736i	−0.608683	+	0.702458i	0.364834	+	0.931073i	$0.381126\pi$
$578$	12.7329	−	8.18294i	0.529619	−	0.340365i
$579$	5.56599	+	38.7123i	0.231315	+	1.60883i
$580$	0.576878	+	1.26319i	0.0239536	+	0.0524510i
$581$	1.40361	−	9.76233i	0.0582316	−	0.405010i
$582$	−8.37492	+	2.45910i	−0.347151	+	0.101933i
$583$	5.82078	+	3.74079i	0.241072	+	0.154928i
$584$	−0.835764	+	1.83007i	−0.0345842	+	0.0757288i
$585$	0.0400918	+	0.0117720i	0.00165759	+	0.000486713i
$586$	−18.4858	−	21.3338i	−0.763642	−	0.881290i
$587$	3.36274	+	3.88081i	0.138795	+	0.160178i	0.820892	−	0.571084i	$-0.193477\pi$
$587$	3.36274	+	3.88081i	0.138795	+	0.160178i	−0.682096	+	0.731262i	$0.738932\pi$
$588$	7.35156	+	2.15861i	0.303173	+	0.0890197i
$589$	0.404486	−	0.885701i	0.0166666	−	0.0364947i
$590$	−8.21491	−	5.27940i	−0.338203	−	0.217350i
$591$	−32.3071	+	9.48621i	−1.32893	+	0.390210i
$592$	−1.36732	+	9.50992i	−0.0561965	+	0.390855i
$593$	−7.03324	−	15.4006i	−0.288820	−	0.632429i	0.708490	−	0.705721i	$-0.249377\pi$
$593$	−7.03324	−	15.4006i	−0.288820	−	0.632429i	−0.997311	+	0.0732922i	$0.976649\pi$
$594$	0.886790	+	6.16776i	0.0363854	+	0.253066i
$595$	1.84145	−	1.18343i	0.0754920	−	0.0485158i
$596$	1.19518	−	1.37931i	0.0489564	−	0.0564987i
$597$	45.2572			1.85225
$598$	16.1451	−	16.6581i	0.660224	−	0.681199i
$599$	7.97972			0.326042			0.163021	−	0.986623i	$-0.447876\pi$
$599$	7.97972			0.326042			0.163021	+	0.986623i	$0.447876\pi$
$600$	1.13262	−	1.30711i	0.0462389	−	0.0533626i
$601$	20.6784	−	13.2892i	0.843491	−	0.542079i	−0.0460471	−	0.998939i	$-0.514662\pi$
$601$	20.6784	−	13.2892i	0.843491	−	0.542079i	0.889538	+	0.456860i	$0.151026\pi$
$602$	1.01413	+	7.05343i	0.0413328	+	0.287476i
$603$	−0.0230077	−	0.0503797i	−0.000936944	−	0.00205162i
$604$	−1.69848	+	11.8132i	−0.0691103	+	0.480673i
$605$	9.17856	−	2.69507i	0.373162	−	0.109570i
$606$	−9.91189	−	6.36998i	−0.402643	−	0.258763i
$607$	13.6096	−	29.8010i	0.552398	−	1.20958i	−0.403254	−	0.915088i	$-0.632121\pi$
$607$	13.6096	−	29.8010i	0.552398	−	1.20958i	0.955653	−	0.294496i	$-0.0951517\pi$
$608$	−1.39139	−	0.408550i	−0.0564284	−	0.0165689i
$609$	2.52146	+	2.90992i	0.102175	+	0.117916i
$610$	−0.742893	−	0.857344i	−0.0300789	−	0.0347129i
$611$	−56.6238	−	16.6263i	−2.29076	−	0.672627i
$612$	0.00489972	−	0.0107289i	0.000198059	−	0.000433689i
$613$	−13.9895	−	8.99051i	−0.565031	−	0.363123i	0.226727	−	0.973958i	$-0.427197\pi$
$613$	−13.9895	−	8.99051i	−0.565031	−	0.363123i	−0.791758	+	0.610835i	$0.790834\pi$
$614$	26.9997	−	7.92784i	1.08962	−	0.319942i
$615$	−2.02064	+	14.0539i	−0.0814801	+	0.566707i
$616$	−0.797472	−	1.74622i	−0.0321310	−	0.0703572i
$617$	1.62076	+	11.2726i	0.0652492	+	0.453818i	0.996086	+	0.0883843i	$0.0281704\pi$
$617$	1.62076	+	11.2726i	0.0652492	+	0.453818i	−0.930837	+	0.365434i	$0.880921\pi$
$618$	−6.87826	+	4.42039i	−0.276684	+	0.177814i
$619$	−10.9143	+	12.5958i	−0.438685	+	0.506269i	−0.931438	−	0.363900i	$-0.881445\pi$
$619$	−10.9143	+	12.5958i	−0.438685	+	0.506269i	0.492753	+	0.870169i	$0.335990\pi$
$620$	−0.671450			−0.0269661
$621$	−9.08560	−	23.2430i	−0.364593	−	0.932708i
$622$	19.4642			0.780441
$623$	1.06749	−	1.23195i	0.0427681	−	0.0493570i
$624$	7.03804	−	4.52308i	0.281747	−	0.181068i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	12.1519	+	26.6090i	0.485689	+	1.06351i
$627$	−0.427424	+	2.97280i	−0.0170697	+	0.118722i
$628$	−21.1914	+	6.22236i	−0.845629	+	0.248299i
$629$	−11.0360	−	7.09242i	−0.440035	−	0.282793i
$630$	−0.00575270	+	0.0125967i	−0.000229193	+	0.000501863i
$631$	34.3339	+	10.0813i	1.36681	+	0.401332i	0.881159	−	0.472820i	$-0.156764\pi$
$631$	34.3339	+	10.0813i	1.36681	+	0.401332i	0.485652	+	0.874152i	$0.338582\pi$
$632$	6.05967	+	6.99323i	0.241041	+	0.278176i
$633$	0.134070	+	0.154725i	0.00532879	+	0.00614975i
$634$	−29.4947	−	8.66043i	−1.17139	−	0.343950i
$635$	4.60113	−	10.0751i	0.182590	−	0.399817i
$636$	−8.40716	−	5.40295i	−0.333366	−	0.214241i
$637$	20.5606	−	6.03714i	0.814640	−	0.239200i
$638$	−0.236656	+	1.64598i	−0.00936931	+	0.0651650i
$639$	0.00503343	+	0.0110217i	0.000199119	+	0.000436010i
$640$	0.142315	+	0.989821i	0.00562549	+	0.0391261i
$641$	36.8685	−	23.6940i	1.45622	−	0.935855i	0.457303	−	0.889311i	$-0.348815\pi$
$641$	36.8685	−	23.6940i	1.45622	−	0.935855i	0.998916	−	0.0465445i	$-0.0148209\pi$
$642$	11.0363	−	12.7366i	0.435569	−	0.502673i
$643$	−18.4253			−0.726623			−0.363311	−	0.931668i	$-0.618354\pi$
$643$	−18.4253			−0.726623			−0.363311	+	0.931668i	$0.618354\pi$
$644$	4.70310	+	6.08202i	0.185328	+	0.239665i
$645$	−7.68796			−0.302713
$646$	1.29665	−	1.49641i	0.0510160	−	0.0588756i
$647$	−23.1658	+	14.8878i	−0.910742	+	0.585299i	−0.909958	−	0.414701i	$-0.863886\pi$
$647$	−23.1658	+	14.8878i	−0.910742	+	0.585299i	−0.000784686		1.00000i	$0.500250\pi$
$648$	−1.27713	−	8.88267i	−0.0501706	−	0.348944i
$649$	−4.85763	−	10.6367i	−0.190679	−	0.417528i
$650$	0.688400	−	4.78793i	0.0270013	−	0.187798i
$651$	−1.78631	+	0.524508i	−0.0700110	+	0.0205571i
$652$	−9.92885	−	6.38088i	−0.388844	−	0.249895i
$653$	9.94883	−	21.7849i	0.389328	−	0.852509i	−0.608914	−	0.793236i	$-0.708395\pi$
$653$	9.94883	−	21.7849i	0.389328	−	0.852509i	0.998242	−	0.0592725i	$-0.0188781\pi$
$654$	−17.5211	−	5.14467i	−0.685131	−	0.201173i
$655$	−10.4546	−	12.0652i	−0.408495	−	0.471428i
$656$	−5.37593	−	6.20415i	−0.209895	−	0.242231i
$657$	0.0166750	+	0.00489623i	0.000650555	+	0.000191020i
$658$	8.12486	−	17.7910i	0.316740	−	0.693564i
$659$	12.2372	+	7.86438i	0.476694	+	0.306353i	0.756835	−	0.653606i	$-0.226745\pi$
$659$	12.2372	+	7.86438i	0.476694	+	0.306353i	−0.280141	+	0.959959i	$0.590381\pi$
$660$	1.98720	−	0.583496i	0.0773518	−	0.0227125i
$661$	−6.26531	+	43.5762i	−0.243692	+	1.69492i	0.389583	+	0.920991i	$0.372619\pi$
$661$	−6.26531	+	43.5762i	−0.243692	+	1.69492i	−0.633275	+	0.773927i	$0.718290\pi$
$662$	−2.27139	−	4.97365i	−0.0882800	−	0.193306i
$663$	1.62570	+	11.3070i	0.0631371	+	0.439128i
$664$	−5.17555	+	3.32613i	−0.200850	+	0.129079i
$665$	−1.52238	+	1.75692i	−0.0590354	+	0.0681305i
$666$	0.0829933			0.00321592
$667$	−0.578910	−	6.63466i	−0.0224155	−	0.256895i
$668$	15.4530			0.597896
$669$	−14.4107	+	16.6309i	−0.557151	+	0.642987i
$670$	−5.39379	+	3.46638i	−0.208380	+	0.133918i
$671$	−0.193328	−	1.34462i	−0.00746333	−	0.0519086i
$672$	1.15182	+	2.52213i	0.0444323	+	0.0972932i
$673$	−3.90234	+	27.1414i	−0.150424	+	1.04622i	0.765086	+	0.643928i	$0.222696\pi$
$673$	−3.90234	+	27.1414i	−0.150424	+	1.04622i	−0.915510	+	0.402295i	$0.868213\pi$
$674$	−31.0465	+	9.11609i	−1.19587	+	0.351139i
$675$	−4.37755	−	2.81328i	−0.168492	−	0.108283i
$676$	4.31954	−	9.45847i	0.166136	−	0.363787i
$677$	−5.01265	−	1.47185i	−0.192652	−	0.0565677i	0.183983	−	0.982929i	$-0.441101\pi$
$677$	−5.01265	−	1.47185i	−0.192652	−	0.0565677i	−0.376635	+	0.926362i	$0.622919\pi$
$678$	−20.1424	−	23.2455i	−0.773563	−	0.892739i
$679$	−5.29810	−	6.11433i	−0.203322	−	0.234647i
$680$	−1.31011	−	0.384683i	−0.0502404	−	0.0147519i
$681$	−17.3844	+	38.0665i	−0.666171	+	1.45871i
$682$	−0.676405	−	0.434699i	−0.0259009	−	0.0166455i
$683$	16.0361	−	4.70862i	0.613604	−	0.180170i	0.0398604	−	0.999205i	$-0.487309\pi$
$683$	16.0361	−	4.70862i	0.613604	−	0.180170i	0.573744	+	0.819035i	$0.305490\pi$
$684$	−0.00178271	+	0.0123990i	−6.81637e−5	+	0.000474089i
$685$	6.21703	+	13.6134i	0.237540	+	0.520141i
$686$	2.60773	+	18.1372i	0.0995637	+	0.692481i
$687$	9.80741	−	6.30284i	0.374176	−	0.240468i
$688$	2.91089	−	3.35934i	0.110977	−	0.128074i
$689$	−27.9498			−1.06480
$690$	−7.21701	+	4.08854i	−0.274747	+	0.155648i
$691$	−23.9800			−0.912241			−0.456121	−	0.889918i	$-0.650761\pi$
$691$	−23.9800			−0.912241			−0.456121	+	0.889918i	$0.650761\pi$
$692$	5.25661	−	6.06645i	0.199826	−	0.230612i
$693$	−0.0139503	+	0.00896530i	−0.000529927	+	0.000340564i
$694$	−3.01418	−	20.9641i	−0.114417	−	0.795785i
$695$	−0.242576	−	0.531167i	−0.00920143	−	0.0201483i
$696$	0.341811	−	2.37735i	0.0129563	−	0.0901132i
$697$	10.7550	−	3.15797i	0.407376	−	0.119617i
$698$	−21.2316	−	13.6447i	−0.803629	−	0.516461i
$699$	17.1019	−	37.4480i	0.646855	−	1.41641i
$700$	1.53819	+	0.451652i	0.0581379	+	0.0170708i
$701$	−3.30162	−	3.81027i	−0.124700	−	0.143912i	0.689966	−	0.723842i	$-0.257625\pi$
$701$	−3.30162	−	3.81027i	−0.124700	−	0.143912i	−0.814666	+	0.579930i	$0.803080\pi$
$702$	−16.4833	−	19.0227i	−0.622122	−	0.717967i
$703$	13.3681	+	3.92523i	0.504187	+	0.148043i
$704$	−0.497449	+	1.08926i	−0.0187483	+	0.0410531i
$705$	17.7512	+	11.4080i	0.668550	+	0.429651i
$706$	14.1706	−	4.16085i	0.533316	−	0.156596i
$707$	1.55422	−	10.8098i	0.0584524	−	0.406545i
$708$	7.01605	+	15.3630i	0.263679	+	0.577377i
$709$	−0.958393	−	6.66577i	−0.0359932	−	0.250338i	0.963879	−	0.266341i	$-0.0858149\pi$
$709$	−0.958393	−	6.66577i	−0.0359932	−	0.250338i	−0.999872	+	0.0160033i	$0.994906\pi$
$710$	1.18001	−	0.758346i	0.0442850	−	0.0284602i
$711$	0.0523446	−	0.0604089i	0.00196308	−	0.00226551i
$712$	−1.01683			−0.0381073
$713$	3.03435	+	1.07802i	0.113637	+	0.0403722i
$714$	−3.78588			−0.141683
$715$	3.79320	−	4.37758i	0.141858	−	0.163712i
$716$	20.7784	−	13.3535i	0.776524	−	0.499042i
$717$	1.76854	+	12.3005i	0.0660473	+	0.459369i
$718$	−7.11318	−	15.5757i	−0.265462	−	0.581280i
$719$	−2.96229	+	20.6032i	−0.110475	+	0.768368i	0.856985	+	0.515342i	$0.172335\pi$
$719$	−2.96229	+	20.6032i	−0.110475	+	0.768368i	−0.967459	+	0.253026i	$0.918574\pi$
$720$	0.00828829	−	0.00243366i	0.000308886	−	9.06972e-5i
$721$	−6.37545	−	4.09725i	−0.237434	−	0.152590i
$722$	7.01931	−	15.3702i	0.261232	−	0.572018i
$723$	38.6625	+	11.3523i	1.43787	+	0.422198i
$724$	4.93258	+	5.69250i	0.183318	+	0.211560i
$725$	−0.909391	−	1.04949i	−0.0337739	−	0.0389772i
$726$	−15.8748	−	4.66127i	−0.589170	−	0.172996i
$727$	6.42495	−	14.0687i	0.238288	−	0.521778i	−0.752273	−	0.658852i	$-0.771042\pi$
$727$	6.42495	−	14.0687i	0.238288	−	0.521778i	0.990561	+	0.137074i	$0.0437697\pi$
$728$	6.52355	+	4.19243i	0.241779	+	0.155382i
$729$	−25.9805	+	7.62856i	−0.962240	+	0.282539i
$730$	0.286320	−	1.99140i	0.0105972	−	0.0737050i
$731$	2.52130	+	5.52088i	0.0932537	+	0.204197i
$732$	0.279230	+	1.94209i	0.0103206	+	0.0717816i
$733$	22.3235	−	14.3464i	0.824536	−	0.529897i	−0.0590015	−	0.998258i	$-0.518792\pi$
$733$	22.3235	−	14.3464i	0.824536	−	0.529897i	0.883537	+	0.468361i	$0.155155\pi$
$734$	24.4400	−	28.2052i	0.902096	−	1.04107i
$735$	−7.66192			−0.282614
$736$	0.946036	−	4.70160i	0.0348713	−	0.173303i
$737$	−7.67774			−0.282813
$738$	−0.0464383	+	0.0535927i	−0.00170942	+	0.00197277i
$739$	−27.3775	+	17.5945i	−1.00710	+	0.647223i	−0.936641	−	0.350292i	$-0.886082\pi$
$739$	−27.3775	+	17.5945i	−1.00710	+	0.647223i	−0.0704581	+	0.997515i	$0.522446\pi$
$740$	−1.36732	−	9.50992i	−0.0502637	−	0.349592i
$741$	−5.03982	−	11.0357i	−0.185142	−	0.405405i
$742$	1.31827	−	9.16878i	0.0483953	−	0.336597i
$743$	−40.3165	+	11.8380i	−1.47907	+	0.434294i	−0.919035	−	0.394176i	$-0.871030\pi$
$743$	−40.3165	+	11.8380i	−1.47907	+	0.434294i	−0.560034	+	0.828470i	$0.689212\pi$
$744$	0.976956	+	0.627852i	0.0358169	+	0.0230182i
$745$	−0.758168	+	1.66016i	−0.0277771	+	0.0608234i
$746$	−0.541682	−	0.159052i	−0.0198324	−	0.00582331i
$747$	0.0348018	+	0.0401634i	0.00127333	+	0.00146950i
$748$	−1.07073	−	1.23569i	−0.0391499	−	0.0451813i
$749$	14.9882	+	4.40094i	0.547657	+	0.160807i
$750$	−0.718483	+	1.57326i	−0.0262353	+	0.0574473i
$751$	27.6487	+	17.7687i	1.00891	+	0.648390i	0.937112	−	0.349029i	$-0.113489\pi$
$751$	27.6487	+	17.7687i	1.00891	+	0.648390i	0.0718023	+	0.997419i	$0.477125\pi$
$752$	−11.7060	+	3.43719i	−0.426874	+	0.125342i
$753$	−3.28329	+	22.8358i	−0.119650	+	0.832183i
$754$	−2.79045	−	6.11024i	−0.101622	−	0.222522i
$755$	−1.69848	−	11.8132i	−0.0618142	−	0.429927i
$756$	7.01775	−	4.51004i	0.255233	−	0.164028i
$757$	14.7090	−	16.9750i	0.534606	−	0.616968i	−0.422621	−	0.906307i	$-0.638890\pi$
$757$	14.7090	−	16.9750i	0.534606	−	0.616968i	0.957227	+	0.289338i	$0.0934353\pi$
$758$	−13.7155			−0.498169
$759$	−9.91720	−	0.553603i	−0.359971	−	0.0200945i
$760$	1.45013			0.0526019
$761$	−7.22172	+	8.33431i	−0.261787	+	0.302119i	−0.871392	−	0.490587i	$-0.836783\pi$
$761$	−7.22172	+	8.33431i	−0.261787	+	0.302119i	0.609605	+	0.792705i	$0.291328\pi$
$762$	−16.1155	+	10.3568i	−0.583802	+	0.375187i
$763$	−2.40881	−	16.7537i	−0.0872049	−	0.606523i
$764$	−4.24924	−	9.30453i	−0.153732	−	0.336626i
$765$	−0.00167857	+	0.0116747i	−6.06888e−5	+	0.000422100i
$766$	13.0084	−	3.81962i	0.470014	−	0.138009i
$767$	39.7369	+	25.5373i	1.43481	+	0.922099i
$768$	0.718483	−	1.57326i	0.0259260	−	0.0567701i
$769$	11.5954	+	3.40472i	0.418141	+	0.122777i	0.484034	−	0.875049i	$-0.339171\pi$
$769$	11.5954	+	3.40472i	0.418141	+	0.122777i	−0.0658925	+	0.997827i	$0.520989\pi$
$770$	1.25714	+	1.45081i	0.0453040	+	0.0522836i
$771$	7.16207	+	8.26547i	0.257936	+	0.297674i
$772$	21.6970	+	6.37081i	0.780892	+	0.229291i
$773$	−5.28628	+	11.5753i	−0.190134	+	0.416336i	−0.980559	−	0.196223i	$-0.937132\pi$
$773$	−5.28628	+	11.5753i	−0.190134	+	0.416336i	0.790425	+	0.612559i	$0.209860\pi$
$774$	−0.0323018	−	0.0207591i	−0.00116106	−	0.000746170i
$775$	0.644252	−	0.189169i	0.0231422	−	0.00679516i
$776$	−0.718215	+	4.99529i	−0.0257824	+	0.179321i
$777$	−11.0663	−	24.2319i	−0.397002	−	0.869314i
$778$	1.80473	+	12.5522i	0.0647027	+	0.450017i
$779$	−10.0147	+	6.43608i	−0.358815	+	0.230596i
$780$	−5.47865	+	6.32270i	−0.196167	+	0.226389i
$781$	1.67967			0.0601034
$782$	5.30291	+	3.84182i	0.189632	+	0.137383i
$783$	−7.22614			−0.258241
$784$	2.90103	−	3.34797i	0.103608	−	0.119570i
$785$	18.5800	−	11.9406i	0.663147	−	0.426179i
$786$	3.92955	+	27.3306i	0.140162	+	0.974850i
$787$	−17.0915	−	37.4252i	−0.609248	−	1.33407i	−0.923087	−	0.384590i	$-0.874343\pi$
$787$	−17.0915	−	37.4252i	−0.609248	−	1.33407i	0.313840	−	0.949476i	$-0.398384\pi$
$788$	−2.77058	+	19.2698i	−0.0986980	+	0.686459i
$789$	26.9918	−	7.92551i	0.960934	−	0.282156i
$790$	−7.78443	−	5.00275i	−0.276958	−	0.177990i
$791$	11.8434	−	25.9334i	0.421103	−	0.922086i
$792$	0.00992501	+	0.00291425i	0.000352670	+	0.000103553i
$793$	3.59349	+	4.14711i	0.127609	+	0.147268i
$794$	14.6094	+	16.8601i	0.518467	+	0.598343i
$795$	9.58880	+	2.81553i	0.340080	+	0.0998564i
$796$	10.8701	−	23.8023i	0.385282	−	0.843650i
$797$	−21.1464	−	13.5900i	−0.749044	−	0.481381i	0.109586	−	0.993977i	$-0.465047\pi$
$797$	−21.1464	−	13.5900i	−0.749044	−	0.481381i	−0.858630	+	0.512596i	$0.828684\pi$
$798$	3.85790	−	1.13278i	0.136568	−	0.0401000i
$799$	2.37074	−	16.4888i	0.0838706	−	0.583333i
$800$	−0.415415	−	0.909632i	−0.0146871	−	0.0321603i
$801$	0.00125003	+	0.00869417i	4.41677e−5	+	0.000307193i
$802$	−21.6692	+	13.9260i	−0.765166	+	0.491742i
$803$	1.57767	−	1.82073i	0.0556748	−	0.0642522i
$804$	11.0892			0.391087
$805$	−6.22609	−	4.51064i	−0.219441	−	0.158979i
$806$	3.24791			0.114403
$807$	−30.7435	+	35.4799i	−1.08222	+	1.24895i
$808$	−5.73089	+	3.68302i	−0.201612	+	0.129568i
$809$	−0.108674	−	0.755846i	−0.00382078	−	0.0265741i	0.987822	−	0.155589i	$-0.0497276\pi$
$809$	−0.108674	−	0.755846i	−0.00382078	−	0.0265741i	−0.991643	+	0.129015i	$0.958818\pi$
$810$	3.72794	+	8.16305i	0.130986	+	0.286820i
$811$	−2.82102	+	19.6206i	−0.0990595	+	0.688974i	0.878412	+	0.477905i	$0.158604\pi$
$811$	−2.82102	+	19.6206i	−0.0990595	+	0.688974i	−0.977471	+	0.211069i	$0.932305\pi$
$812$	2.13605	−	0.627199i	0.0749605	−	0.0220104i
$813$	−5.45766	−	3.50742i	−0.191408	−	0.123011i
$814$	4.77934	−	10.4653i	0.167516	−	0.366809i
$815$	11.3244	+	3.32513i	0.396675	+	0.116474i
$816$	1.54650	+	1.78475i	0.0541383	+	0.0624789i
$817$	−4.22117	−	4.87149i	−0.147680	−	0.170432i
$818$	1.58140	+	0.464341i	0.0552924	+	0.0162353i
$819$	0.0278268	−	0.0609321i	0.000972345	−	0.00212914i
$820$	6.90608	+	4.43827i	0.241171	+	0.154991i
$821$	37.8092	−	11.1018i	1.31955	−	0.387455i	0.455221	−	0.890379i	$-0.349560\pi$
$821$	37.8092	−	11.1018i	1.31955	−	0.387455i	0.864331	+	0.502923i	$0.167742\pi$
$822$	3.68371	−	25.6207i	0.128484	−	0.893626i
$823$	16.5811	+	36.3077i	0.577983	+	1.26561i	0.942437	+	0.334384i	$0.108528\pi$
$823$	16.5811	+	36.3077i	0.577983	+	1.26561i	−0.364454	+	0.931221i	$0.618745\pi$
$824$	0.672771	+	4.67923i	0.0234371	+	0.163009i
$825$	−1.74232	+	1.11972i	−0.0606597	+	0.0389836i
$826$	−10.2516	+	11.8310i	−0.356699	+	0.411653i
$827$	−26.4271			−0.918960			−0.459480	−	0.888188i	$-0.651964\pi$
$827$	−26.4271			−0.918960			−0.459480	+	0.888188i	$0.651964\pi$
$828$	−0.0413629	−	0.00230898i	−0.00143746	−	8.02427e-5i
$829$	−46.1156			−1.60166			−0.800831	−	0.598890i	$-0.795608\pi$
$829$	−46.1156			−1.60166			−0.800831	+	0.598890i	$0.795608\pi$
$830$	4.02883	−	4.64952i	0.139843	−	0.161387i
$831$	−20.8389	+	13.3924i	−0.722894	+	0.464576i
$832$	−0.688400	−	4.78793i	−0.0238660	−	0.165991i
$833$	2.51276	+	5.50218i	0.0870621	+	0.190639i
$834$	−0.143731	+	0.999670i	−0.00497699	+	0.0346157i
$835$	−14.8271	+	4.35362i	−0.513112	+	0.150663i
$836$	1.46083	+	0.938821i	0.0505240	+	0.0324698i
$837$	1.45144	−	3.17822i	0.0501692	−	0.109855i
$838$	3.69189	+	1.08404i	0.127534	+	0.0374474i
$839$	8.14435	+	9.39908i	0.281174	+	0.324492i	0.878716	−	0.477346i	$-0.158401\pi$
$839$	8.14435	+	9.39908i	0.281174	+	0.324492i	−0.597541	+	0.801838i	$0.703856\pi$
$840$	−1.81573	−	2.09546i	−0.0626485	−	0.0723002i
$841$	25.9750	+	7.62694i	0.895689	+	0.262998i
$842$	15.0263	−	32.9031i	0.517841	−	1.13391i
$843$	21.5738	+	13.8647i	0.743042	+	0.477524i
$844$	0.113577	−	0.0333491i	0.00390947	−	0.00114792i
$845$	−1.47981	+	10.2923i	−0.0509069	+	0.354065i
$846$	0.0437796	+	0.0958640i	0.00150517	+	0.00329587i
$847$	−2.18248	−	15.1795i	−0.0749908	−	0.521573i
$848$	−4.86088	+	3.12390i	−0.166923	+	0.107275i
$849$	16.5515	−	19.1014i	0.568045	−	0.655558i
$850$	1.36542			0.0468335
$851$	−9.08924	+	45.1716i	−0.311575	+	1.54846i
$852$	−2.42601			−0.0831138
$853$	32.8069	−	37.8612i	1.12329	−	1.29634i	0.173018	−	0.984919i	$-0.444648\pi$
$853$	32.8069	−	37.8612i	1.12329	−	1.29634i	0.950271	−	0.311425i	$-0.100806\pi$
$854$	−1.52993	+	0.983225i	−0.0523531	+	0.0336453i
$855$	−0.00178271	−	0.0123990i	−6.09674e−5	−	0.000424038i
$856$	−4.04784	−	8.86353i	−0.138352	−	0.302949i
$857$	−6.20903	+	43.1848i	−0.212096	+	1.47516i	0.554043	+	0.832488i	$0.313084\pi$
$857$	−6.20903	+	43.1848i	−0.212096	+	1.47516i	−0.766139	+	0.642675i	$0.777825\pi$
$858$	−9.61242	+	2.82246i	−0.328163	+	0.0963573i
$859$	12.0765	+	7.76109i	0.412045	+	0.264805i	0.730200	−	0.683234i	$-0.239427\pi$
$859$	12.0765	+	7.76109i	0.412045	+	0.264805i	−0.318155	+	0.948039i	$0.603063\pi$
$860$	−1.84654	+	4.04336i	−0.0629665	+	0.137877i
$861$	21.8398	+	6.41273i	0.744297	+	0.218545i
$862$	13.7253	+	15.8399i	0.467486	+	0.539508i
$863$	4.08778	+	4.71755i	0.139150	+	0.160587i	0.821047	−	0.570861i	$-0.193390\pi$
$863$	4.08778	+	4.71755i	0.139150	+	0.160587i	−0.681897	+	0.731448i	$0.738845\pi$
$864$	−4.99282	−	1.46603i	−0.169859	−	0.0498752i
$865$	−3.33456	+	7.30168i	−0.113379	+	0.248264i
$866$	16.0313	+	10.3027i	0.544766	+	0.350100i
$867$	25.1175	−	7.37517i	0.853036	−	0.250474i
$868$	−0.153190	+	1.06546i	−0.00519961	+	0.0361641i
$869$	−4.60308	−	10.0793i	−0.156149	−	0.341918i
$870$	0.341811	+	2.37735i	0.0115885	+	0.0805997i
$871$	26.0906	−	16.7674i	0.884048	−	0.568143i
$872$	−6.91409	+	7.97928i	−0.234141	+	0.270213i
$873$	0.0435940			0.00147543
$874$	−6.55331	−	2.32821i	−0.221669	−	0.0787528i
$875$	−1.60312			−0.0541954
$876$	−2.27869	+	2.62975i	−0.0769898	+	0.0888509i
$877$	−36.9762	+	23.7632i	−1.24860	+	0.802426i	−0.986681	−	0.162664i	$-0.947991\pi$
$877$	−36.9762	+	23.7632i	−1.24860	+	0.802426i	−0.261917	+	0.965090i	$0.584355\pi$
$878$	3.28731	+	22.8637i	0.110941	+	0.771613i
$879$	−20.2818	−	44.4109i	−0.684088	−	1.49794i
$880$	0.170418	−	1.18529i	0.00574480	−	0.0399560i
$881$	−28.9763	+	8.50822i	−0.976237	+	0.286649i	−0.730670	−	0.682730i	$-0.760792\pi$
$881$	−28.9763	+	8.50822i	−0.976237	+	0.286649i	−0.245567	+	0.969380i	$0.578974\pi$
$882$	−0.0321924	−	0.0206888i	−0.00108397	−	0.000696628i
$883$	8.53106	−	18.6804i	0.287093	−	0.628646i	−0.710053	−	0.704149i	$-0.751329\pi$
$883$	8.53106	−	18.6804i	0.287093	−	0.628646i	0.997146	+	0.0755026i	$0.0240561\pi$
$884$	6.33721	+	1.86077i	0.213143	+	0.0625846i
$885$	−11.0601	−	12.7640i	−0.371782	−	0.429059i
$886$	−6.22513	−	7.18418i	−0.209137	−	0.241357i
$887$	−17.2277	−	5.05850i	−0.578449	−	0.169848i	−0.0205963	−	0.999788i	$-0.506556\pi$
$887$	−17.2277	−	5.05850i	−0.578449	−	0.169848i	−0.557853	+	0.829940i	$0.688375\pi$
$888$	−6.90298	+	15.1154i	−0.231649	+	0.507240i
$889$	−14.9374	−	9.59970i	−0.500985	−	0.321964i
$890$	0.975641	−	0.286474i	0.0327036	−	0.00960263i
$891$	−1.52934	+	10.6368i	−0.0512347	+	0.356345i
$892$	5.28549	+	11.5736i	0.176971	+	0.387513i
$893$	2.51782	+	17.5118i	0.0842557	+	0.586011i
$894$	2.65549	−	1.70658i	0.0888129	−	0.0570766i
$895$	−16.1746	+	18.6665i	−0.540657	+	0.623952i
$896$	1.60312			0.0535566
$897$	34.9098	−	19.7769i	1.16560	−	0.660332i
$898$	−11.8890			−0.396742
$899$	0.610611	−	0.704682i	0.0203650	−	0.0235025i
$900$	−0.00726691	+	0.00467016i	−0.000242230	+	0.000155672i
$901$	−1.12280	−	7.80927i	−0.0374060	−	0.260165i
$902$	4.08369	+	8.94204i	0.135972	+	0.297737i
$903$	−1.75399	+	12.1993i	−0.0583692	+	0.405967i
$904$	−17.0635	+	5.01031i	−0.567525	+	0.166640i
$905$	−6.33654	−	4.07225i	−0.210634	−	0.135366i
$906$	−8.57488	+	18.7764i	−0.284881	+	0.623803i
$907$	−30.7081	−	9.01670i	−1.01964	−	0.299395i	−0.271151	−	0.962537i	$-0.587404\pi$
$907$	−30.7081	−	9.01670i	−1.01964	−	0.299395i	−0.748493	+	0.663142i	$0.769222\pi$
$908$	15.8450	+	18.2861i	0.525834	+	0.606844i
$909$	0.0385360	+	0.0444729i	0.00127816	+	0.00147507i
$910$	−7.44045	−	2.18471i	−0.246648	−	0.0724225i
$911$	11.0208	−	24.1322i	0.365135	−	0.799534i	−0.634511	−	0.772914i	$-0.718798\pi$
$911$	11.0208	−	24.1322i	0.365135	−	0.799534i	0.999646	−	0.0266199i	$-0.00847439\pi$
$912$	−2.10994	−	1.35597i	−0.0698669	−	0.0449008i
$913$	7.06867	−	2.07555i	0.233939	−	0.0686907i
$914$	−0.450932	+	3.13630i	−0.0149155	+	0.103740i
$915$	−0.815068	−	1.78475i	−0.0269453	−	0.0590020i
$916$	−0.959275	−	6.67191i	−0.0316953	−	0.220446i
$917$	−21.5304	+	13.8367i	−0.710996	+	0.456929i
$918$	4.65285	−	5.36968i	0.153567	−	0.177226i
$919$	−52.7676			−1.74064			−0.870322	−	0.492483i	$-0.836089\pi$
$919$	−52.7676			−1.74064			−0.870322	+	0.492483i	$0.836089\pi$
$920$	0.416879	+	4.77768i	0.0137441	+	0.157515i
$921$	48.6690			1.60370
$922$	−9.94589	+	11.4782i	−0.327551	+	0.378013i
$923$	−5.70790	+	3.66824i	−0.187878	+	0.120742i
$924$	−0.472517	−	3.28643i	−0.0155447	−	0.108116i
$925$	3.99119	+	8.73948i	0.131229	+	0.287352i
$926$	−2.09184	+	14.5490i	−0.0687420	+	0.478111i
$927$	0.0391816	−	0.0115047i	0.00128689	−	0.000377865i
$928$	−1.16823	−	0.750776i	−0.0383491	−	0.0246454i
$929$	−0.697509	+	1.52733i	−0.0228845	+	0.0501101i	−0.920729	−	0.390202i	$-0.872405\pi$
$929$	−0.697509	+	1.52733i	−0.0228845	+	0.0501101i	0.897845	+	0.440312i	$0.145132\pi$
$930$	−1.11427	−	0.327179i	−0.0365383	−	0.0107286i
$931$	−4.20688	−	4.85500i	−0.137875	−	0.159116i
$932$	−15.5875	−	17.9890i	−0.510587	−	0.589249i
$933$	32.3007	+	9.48434i	1.05748	+	0.310503i
$934$	−10.1969	+	22.3280i	−0.333652	+	0.730595i
$935$	1.37549	+	0.883977i	0.0449835	+	0.0289091i
$936$	−0.0400918	+	0.0117720i	−0.00131044	+	0.000384780i
$937$	2.96201	−	20.6013i	0.0967648	−	0.673014i	−0.882483	−	0.470345i	$-0.844129\pi$
$937$	2.96201	−	20.6013i	0.0967648	−	0.673014i	0.979247	−	0.202669i	$-0.0649615\pi$
$938$	4.26989	+	9.34975i	0.139417	+	0.305280i
$939$	7.20026	+	50.0789i	0.234972	+	1.63426i
$940$	10.2635	−	6.59593i	0.334757	−	0.215135i
$941$	−33.5611	+	38.7315i	−1.09406	+	1.26261i	−0.131566	+	0.991307i	$0.542001\pi$
$941$	−33.5611	+	38.7315i	−1.09406	+	1.26261i	−0.962494	+	0.271305i	$0.912545\pi$
$942$	−38.1990			−1.24459
$943$	−24.0836	−	31.1448i	−0.784270	−	1.01421i
$944$	9.76509			0.317826
$945$	−5.46286	+	6.30448i	−0.177707	+	0.205085i
$946$	−4.47785	+	2.87774i	−0.145587	+	0.0935634i
$947$	6.50208	+	45.2230i	0.211289	+	1.46955i	0.768859	+	0.639419i	$0.220825\pi$
$947$	6.50208	+	45.2230i	0.211289	+	1.46955i	−0.557569	+	0.830130i	$0.688266\pi$
$948$	6.64840	+	14.5580i	0.215930	+	0.472820i
$949$	−1.38498	+	9.63272i	−0.0449582	+	0.312691i
$950$	−1.39139	+	0.408550i	−0.0451427	+	0.0132551i
$951$	−44.7264	−	28.7439i	−1.45035	−	0.932085i
$952$	−0.909316	+	1.99112i	−0.0294711	+	0.0645327i
$953$	−38.1907	−	11.2138i	−1.23712	−	0.363250i	−0.403185	−	0.915118i	$-0.632097\pi$
$953$	−38.1907	−	11.2138i	−1.23712	−	0.363250i	−0.833931	+	0.551868i	$0.813915\pi$
$954$	0.0326858	+	0.0377215i	0.00105824	+	0.00122128i
$955$	6.69850	+	7.73048i	0.216758	+	0.250153i
$956$	6.89401	+	2.02426i	0.222968	+	0.0654693i
$957$	−1.19477	+	2.61618i	−0.0386215	+	0.0845692i
$958$	7.69783	+	4.94709i	0.248706	+	0.159833i
$959$	23.0202	−	6.75934i	0.743361	−	0.218271i
$960$	−0.246141	+	1.71195i	−0.00794418	+	0.0552530i
$961$	−12.6906	−	27.7885i	−0.409373	−	0.896403i
$962$	6.61395	+	46.0010i	0.213242	+	1.48313i
$963$	−0.0708094	+	0.0455064i	−0.00228180	+	0.00146642i
$964$	15.2568	−	17.6073i	0.491388	−	0.567092i
$965$	−22.6130			−0.727938
$966$	4.84117	+	12.3848i	0.155762	+	0.398474i
$967$	−57.7041			−1.85564			−0.927819	−	0.373030i	$-0.878319\pi$
$967$	−57.7041			−1.85564			−0.927819	+	0.373030i	$0.878319\pi$
$968$	−6.26443	+	7.22954i	−0.201347	+	0.232366i
$969$	2.88095	−	1.85147i	0.0925493	−	0.0594778i
$970$	−0.718215	−	4.99529i	−0.0230605	−	0.160389i
$971$	16.0188	+	35.0762i	0.514067	+	1.12565i	0.971637	+	0.236476i	$0.0759924\pi$
$971$	16.0188	+	35.0762i	0.514067	+	1.12565i	−0.457571	+	0.889173i	$0.651280\pi$
$972$	−0.0127757	+	0.0888567i	−0.000409780	+	0.00285008i
$973$	−0.898202	+	0.263736i	−0.0287950	+	0.00845499i
$974$	16.4781	+	10.5898i	0.527993	+	0.339320i
$975$	3.47542	−	7.61011i	0.111302	−	0.243718i
$976$	1.08848	+	0.319606i	0.0348413	+	0.0102303i
$977$	−9.82162	−	11.3347i	−0.314221	−	0.362631i	0.576566	−	0.817050i	$-0.304392\pi$
$977$	−9.82162	−	11.3347i	−0.314221	−	0.362631i	−0.890788	+	0.454419i	$0.849847\pi$
$978$	−13.3677	−	15.4271i	−0.427451	−	0.493304i
$979$	1.16831	+	0.343045i	0.0373392	+	0.0109638i
$980$	−1.84029	+	4.02967i	−0.0587858	+	0.128723i
$981$	0.0767248	+	0.0493081i	0.00244964	+	0.00157428i
$982$	−24.5028	+	7.19466i	−0.781915	+	0.229591i
$983$	5.49496	−	38.2183i	0.175262	−	1.21897i	−0.692287	−	0.721622i	$-0.743397\pi$
$983$	5.49496	−	38.2183i	0.175262	−	1.21897i	0.867549	−	0.497351i	$-0.165694\pi$
$984$	−5.89822	−	12.9153i	−0.188029	−	0.411725i
$985$	−2.77058	−	19.2698i	−0.0882781	−	0.613988i
$986$	1.59512	−	1.02512i	0.0507991	−	0.0326466i
$987$	22.1522	−	25.5650i	0.705113	−	0.813744i
$988$	−7.01453			−0.223162
$989$	14.8364	−	15.3077i	0.471769	−	0.486757i
$990$	−0.0103440			−0.000328754
$991$	33.6221	−	38.8019i	1.06804	−	1.23258i	0.0965934	−	0.995324i	$-0.469205\pi$
$991$	33.6221	−	38.8019i	1.06804	−	1.23258i	0.971446	−	0.237260i	$-0.0762492\pi$
$992$	0.564860	−	0.363013i	0.0179343	−	0.0115257i
$993$	−1.34584	−	9.36053i	−0.0427090	−	0.297048i
$994$	−0.934131	−	2.04546i	−0.0296288	−	0.0648781i
$995$	−3.72394	+	25.9006i	−0.118057	+	0.821104i
$996$	−10.2095	+	2.99779i	−0.323502	+	0.0949887i
$997$	−33.2483	−	21.3674i	−1.05298	−	0.676712i	−0.104820	−	0.994491i	$-0.533426\pi$
$997$	−33.2483	−	21.3674i	−1.05298	−	0.676712i	−0.948165	+	0.317779i	$0.897063\pi$
$998$	−1.45500	+	3.18600i	−0.0460571	+	0.100851i
$999$	47.9696	+	14.0851i	1.51769	+	0.445634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.131.2	✓	20
23.6	even	11		5290.2.a.bj.1.8		10
23.13	even	11	inner	230.2.g.b.151.2	yes	20
23.17	odd	22		5290.2.a.bi.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.131.2	✓	20	1.1	even	1	trivial
230.2.g.b.151.2	yes	20	23.13	even	11	inner
5290.2.a.bi.1.8		10	23.17	odd	22
5290.2.a.bj.1.8		10	23.6	even	11

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(1.45499 - 0.935068i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.246141 - 1.71195i) q^{6} +(1.53819 - 0.451652i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.00358844 + 0.00785758i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(1.45499 - 0.935068i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.246141 - 1.71195i) q^{6} +(1.53819 - 0.451652i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.00358844 + 0.00785758i) q^{9} +(0.959493 + 0.281733i) q^{10} +(0.784179 + 0.904991i) q^{11} +(-1.13262 - 1.30711i) q^{12} +(-4.64122 - 1.36279i) q^{13} +(0.665961 - 1.45825i) q^{14} +(1.45499 + 0.935068i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.194319 - 1.35152i) q^{17} +(0.00358844 + 0.00785758i) q^{18} +(0.206375 + 1.43537i) q^{19} +(0.841254 - 0.540641i) q^{20} +(1.81573 - 2.09546i) q^{21} +1.19747 q^{22} +(-4.66972 + 1.09257i) q^{23} -1.72956 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-4.06928 + 2.61517i) q^{26} +(0.740550 + 5.15064i) q^{27} +(-0.665961 - 1.45825i) q^{28} +(-0.197630 + 1.37454i) q^{29} +(1.65950 - 0.487272i) q^{30} +(-0.564860 - 0.363013i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(1.98720 + 0.583496i) q^{33} +(-0.894159 - 1.03191i) q^{34} +(1.04982 + 1.21156i) q^{35} +(0.00828829 + 0.00243366i) q^{36} +(3.99119 - 8.73948i) q^{37} +(1.21993 + 0.784001i) q^{38} +(-8.02725 + 2.35701i) q^{39} +(0.142315 - 0.989821i) q^{40} +(3.41025 + 7.46742i) q^{41} +(-0.394595 - 2.74447i) q^{42} +(-3.73941 + 2.40317i) q^{43} +(0.784179 - 0.904991i) q^{44} -0.00863819 q^{45} +(-2.23231 + 4.24462i) q^{46} +12.2002 q^{47} +(-1.13262 + 1.30711i) q^{48} +(-3.72675 + 2.39504i) q^{49} +(0.142315 + 0.989821i) q^{50} +(-0.981031 - 2.14816i) q^{51} +(-0.688400 + 4.78793i) q^{52} +(5.54408 - 1.62789i) q^{53} +(4.37755 + 2.81328i) q^{54} +(-0.497449 + 1.08926i) q^{55} +(-1.53819 - 0.451652i) q^{56} +(1.64245 + 1.89548i) q^{57} +(0.909391 + 1.04949i) q^{58} +(-9.36953 - 2.75114i) q^{59} +(0.718483 - 1.57326i) q^{60} +(-0.954342 - 0.613319i) q^{61} +(-0.644252 + 0.189169i) q^{62} +(-0.00197079 + 0.0137071i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.688400 - 4.78793i) q^{65} +(1.74232 - 1.11972i) q^{66} +(-4.19871 + 4.84557i) q^{67} -1.36542 q^{68} +(-5.77279 + 5.95619i) q^{69} +1.60312 q^{70} +(0.918560 - 1.06007i) q^{71} +(0.00726691 - 0.00467016i) q^{72} +(-0.286320 - 1.99140i) q^{73} +(-3.99119 - 8.73948i) q^{74} +(-0.246141 + 1.71195i) q^{75} +(1.39139 - 0.408550i) q^{76} +(1.61495 + 1.03787i) q^{77} +(-3.47542 + 7.61011i) q^{78} +(-8.87855 - 2.60698i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(5.87673 + 6.78210i) q^{81} +(7.87674 + 2.31282i) q^{82} +(2.55571 - 5.59623i) q^{83} +(-2.33254 - 1.49903i) q^{84} +(1.31011 - 0.384683i) q^{85} +(-0.632596 + 4.39980i) q^{86} +(0.997742 + 2.18475i) q^{87} +(-0.170418 - 1.18529i) q^{88} +(0.855412 - 0.549740i) q^{89} +(-0.00565681 + 0.00652831i) q^{90} -7.75456 q^{91} +(1.74602 + 4.46670i) q^{92} -1.16131 q^{93} +(7.98943 - 9.22030i) q^{94} +(-1.21993 + 0.784001i) q^{95} +(0.246141 + 1.71195i) q^{96} +(-2.09646 - 4.59061i) q^{97} +(-0.630454 + 4.38491i) q^{98} +(-0.00992501 + 0.00291425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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