LMFDB - Embedded newform 67.2.e.b.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,2,Mod(9,67)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("67.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.e (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:	$0.534997693543$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
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			22.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	67.22
Dual form			67.2.e.b.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.459493 + 0.134919i) q^{2} +(0.260554 + 1.81219i) q^{3} +(-1.48958 + 0.957293i) q^{4} +(-0.345139 + 0.755750i) q^{5} +(-0.364223 - 0.797537i) q^{6} +(1.04408 - 0.306569i) q^{7} +(1.18251 - 1.36469i) q^{8} +(-0.337683 + 0.0991526i) q^{9} +O(q^{10})$	\(q+(-0.459493 + 0.134919i) q^{2} +(0.260554 + 1.81219i) q^{3} +(-1.48958 + 0.957293i) q^{4} +(-0.345139 + 0.755750i) q^{5} +(-0.364223 - 0.797537i) q^{6} +(1.04408 - 0.306569i) q^{7} +(1.18251 - 1.36469i) q^{8} +(-0.337683 + 0.0991526i) q^{9} +(0.0566239 - 0.393828i) q^{10} +(1.19505 - 2.61680i) q^{11} +(-2.12292 - 2.44998i) q^{12} +(2.87491 + 3.31782i) q^{13} +(-0.438384 + 0.281733i) q^{14} +(-1.45949 - 0.428546i) q^{15} +(1.11189 - 2.43470i) q^{16} +(-2.76321 - 1.77580i) q^{17} +(0.141785 - 0.0911198i) q^{18} +(-3.40746 - 1.00052i) q^{19} +(-0.209362 - 1.45615i) q^{20} +(0.827602 + 1.81219i) q^{21} +(-0.196061 + 1.36364i) q^{22} +(-0.912860 - 6.34908i) q^{23} +(2.78118 + 1.78736i) q^{24} +(2.82227 + 3.25707i) q^{25} +(-1.76864 - 1.13663i) q^{26} +(2.01399 + 4.41003i) q^{27} +(-1.26176 + 1.45615i) q^{28} -1.97270 q^{29} +0.728446 q^{30} +(-1.76031 + 2.03151i) q^{31} +(-0.696384 + 4.84346i) q^{32} +(5.05353 + 1.48385i) q^{33} +(1.50926 + 0.443160i) q^{34} +(-0.128663 + 0.894870i) q^{35} +(0.408086 - 0.470956i) q^{36} +8.07686 q^{37} +1.70069 q^{38} +(-5.26347 + 6.07437i) q^{39} +(0.623231 + 1.36469i) q^{40} +(-2.28074 - 1.46575i) q^{41} +(-0.624777 - 0.721031i) q^{42} +(-6.51473 - 4.18676i) q^{43} +(0.724922 + 5.04194i) q^{44} +(0.0416130 - 0.289425i) q^{45} +(1.27607 + 2.79420i) q^{46} +(-1.56014 - 10.8510i) q^{47} +(4.70185 + 1.38059i) q^{48} +(-4.89266 + 3.14432i) q^{49} +(-1.73625 - 1.11582i) q^{50} +(2.49814 - 5.47016i) q^{51} +(-7.45852 - 2.19002i) q^{52} +(6.30856 - 4.05427i) q^{53} +(-1.52041 - 1.75465i) q^{54} +(1.56519 + 1.80632i) q^{55} +(0.816259 - 1.78736i) q^{56} +(0.925309 - 6.43566i) q^{57} +(0.906440 - 0.266155i) q^{58} +(-6.97706 + 8.05195i) q^{59} +(2.58427 - 0.758810i) q^{60} +(-3.84302 - 8.41503i) q^{61} +(0.534760 - 1.17096i) q^{62} +(-0.322170 + 0.207046i) q^{63} +(0.428340 + 2.97917i) q^{64} +(-3.49969 + 1.02760i) q^{65} -2.52226 q^{66} +(7.85223 + 2.31139i) q^{67} +5.81597 q^{68} +(11.2679 - 3.30856i) q^{69} +(-0.0616156 - 0.428546i) q^{70} +(-1.45889 + 0.937571i) q^{71} +(-0.264000 + 0.578079i) q^{72} +(-0.608158 - 1.33168i) q^{73} +(-3.71126 + 1.08972i) q^{74} +(-5.16709 + 5.96314i) q^{75} +(6.03346 - 1.77158i) q^{76} +(0.445499 - 3.09851i) q^{77} +(1.59898 - 3.50127i) q^{78} +(-10.1410 - 11.7033i) q^{79} +(1.45626 + 1.68062i) q^{80} +(-8.35529 + 5.36962i) q^{81} +(1.24574 + 0.365783i) q^{82} +(-3.35960 + 7.35650i) q^{83} +(-2.96758 - 1.90715i) q^{84} +(2.29575 - 1.47539i) q^{85} +(3.55835 + 1.04483i) q^{86} +(-0.513994 - 3.57491i) q^{87} +(-2.15795 - 4.72526i) q^{88} +(-2.19746 + 15.2836i) q^{89} +(0.0199281 + 0.138603i) q^{90} +(4.01877 + 2.58271i) q^{91} +(7.43771 + 8.58357i) q^{92} +(-4.14014 - 2.66071i) q^{93} +(2.18089 + 4.77548i) q^{94} +(1.93219 - 2.22987i) q^{95} -8.95874 q^{96} +1.03304 q^{97} +(1.82391 - 2.10491i) q^{98} +(-0.144086 + 1.00214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 3 q^{3} - 14 q^{4} - 9 q^{5} + 10 q^{6} + 7 q^{7} - 7 q^{8} - 6 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 3 * q^3 - 14 * q^4 - 9 * q^5 + 10 * q^6 + 7 * q^7 - 7 * q^8 - 6 * q^9	\( 10 q + 4 q^{2} + 3 q^{3} - 14 q^{4} - 9 q^{5} + 10 q^{6} + 7 q^{7} - 7 q^{8} - 6 q^{9} - 8 q^{10} - 12 q^{11} - 13 q^{12} + 15 q^{13} + 5 q^{14} - 6 q^{15} + 12 q^{16} + q^{17} + 24 q^{18} - 13 q^{19} + 6 q^{20} + q^{21} - 7 q^{22} - 7 q^{23} - 23 q^{24} + 12 q^{25} + 28 q^{26} + 9 q^{27} + 10 q^{28} - 24 q^{29} - 20 q^{30} - q^{31} - q^{32} + 3 q^{33} - 15 q^{34} - 3 q^{35} + 37 q^{36} + 2 q^{37} - 36 q^{38} - 23 q^{39} + 25 q^{40} - 7 q^{41} + 7 q^{42} - 2 q^{43} + 41 q^{44} + 12 q^{45} + 6 q^{46} + 33 q^{47} + 8 q^{48} + 2 q^{49} - 4 q^{50} + 30 q^{51} - 21 q^{52} + 21 q^{53} - 14 q^{54} + 13 q^{55} - 17 q^{56} + 28 q^{57} - 3 q^{58} - 38 q^{59} + 4 q^{60} - 50 q^{61} + 4 q^{62} - 13 q^{63} - 31 q^{64} - 8 q^{65} - 78 q^{66} + 32 q^{67} - 30 q^{68} + 21 q^{69} - 10 q^{70} - 16 q^{71} - 53 q^{72} + 3 q^{73} - 8 q^{74} - 14 q^{75} + 5 q^{76} + 7 q^{77} + 70 q^{78} - 19 q^{79} + 9 q^{80} - 9 q^{81} - 16 q^{82} + 5 q^{83} + 25 q^{84} - 13 q^{85} + 19 q^{86} + 6 q^{87} + 48 q^{88} + 7 q^{89} - 15 q^{90} - 6 q^{91} + 45 q^{92} - 19 q^{93} + 22 q^{94} + 15 q^{95} + 14 q^{96} + 54 q^{97} + 47 q^{98} + 16 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 3 * q^3 - 14 * q^4 - 9 * q^5 + 10 * q^6 + 7 * q^7 - 7 * q^8 - 6 * q^9 - 8 * q^10 - 12 * q^11 - 13 * q^12 + 15 * q^13 + 5 * q^14 - 6 * q^15 + 12 * q^16 + q^17 + 24 * q^18 - 13 * q^19 + 6 * q^20 + q^21 - 7 * q^22 - 7 * q^23 - 23 * q^24 + 12 * q^25 + 28 * q^26 + 9 * q^27 + 10 * q^28 - 24 * q^29 - 20 * q^30 - q^31 - q^32 + 3 * q^33 - 15 * q^34 - 3 * q^35 + 37 * q^36 + 2 * q^37 - 36 * q^38 - 23 * q^39 + 25 * q^40 - 7 * q^41 + 7 * q^42 - 2 * q^43 + 41 * q^44 + 12 * q^45 + 6 * q^46 + 33 * q^47 + 8 * q^48 + 2 * q^49 - 4 * q^50 + 30 * q^51 - 21 * q^52 + 21 * q^53 - 14 * q^54 + 13 * q^55 - 17 * q^56 + 28 * q^57 - 3 * q^58 - 38 * q^59 + 4 * q^60 - 50 * q^61 + 4 * q^62 - 13 * q^63 - 31 * q^64 - 8 * q^65 - 78 * q^66 + 32 * q^67 - 30 * q^68 + 21 * q^69 - 10 * q^70 - 16 * q^71 - 53 * q^72 + 3 * q^73 - 8 * q^74 - 14 * q^75 + 5 * q^76 + 7 * q^77 + 70 * q^78 - 19 * q^79 + 9 * q^80 - 9 * q^81 - 16 * q^82 + 5 * q^83 + 25 * q^84 - 13 * q^85 + 19 * q^86 + 6 * q^87 + 48 * q^88 + 7 * q^89 - 15 * q^90 - 6 * q^91 + 45 * q^92 - 19 * q^93 + 22 * q^94 + 15 * q^95 + 14 * q^96 + 54 * q^97 + 47 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−0.459493	+	0.134919i	−0.324911	+	0.0954024i	−0.440120	−	0.897939i	$-0.645064\pi$
$2$	−0.459493	+	0.134919i	−0.324911	+	0.0954024i	0.115210	+	0.993341i	$0.463246\pi$
$3$	0.260554	+	1.81219i	0.150431	+	1.04627i	0.915499	+	0.402321i	$0.131796\pi$
$3$	0.260554	+	1.81219i	0.150431	+	1.04627i	−0.765068	+	0.643950i	$0.777294\pi$
$4$	−1.48958	+	0.957293i	−0.744788	+	0.478646i
$5$	−0.345139	+	0.755750i	−0.154351	+	0.337981i	−0.970972	−	0.239193i	$-0.923117\pi$
$5$	−0.345139	+	0.755750i	−0.154351	+	0.337981i	0.816621	+	0.577174i	$0.195845\pi$
$6$	−0.364223	−	0.797537i	−0.148693	−	0.325593i
$7$	1.04408	−	0.306569i	0.394624	−	0.115872i	−0.0783990	−	0.996922i	$-0.524981\pi$
$7$	1.04408	−	0.306569i	0.394624	−	0.115872i	0.473023	+	0.881050i	$0.343163\pi$
$8$	1.18251	−	1.36469i	0.418079	−	0.482489i
$9$	−0.337683	+	0.0991526i	−0.112561	+	0.0330509i
$10$	0.0566239	−	0.393828i	0.0179060	−	0.124539i
$11$	1.19505	−	2.61680i	0.360322	−	0.788995i	−0.639474	−	0.768812i	$-0.720848\pi$
$11$	1.19505	−	2.61680i	0.360322	−	0.788995i	0.999796	−	0.0201827i	$-0.00642479\pi$
$12$	−2.12292	−	2.44998i	−0.612833	−	0.707247i
$13$	2.87491	+	3.31782i	0.797356	+	0.920198i	0.998233	−	0.0594185i	$-0.0189247\pi$
$13$	2.87491	+	3.31782i	0.797356	+	0.920198i	−0.200877	+	0.979616i	$0.564379\pi$
$14$	−0.438384	+	0.281733i	−0.117163	+	0.0752962i
$15$	−1.45949	−	0.428546i	−0.376839	−	0.110650i
$16$	1.11189	−	2.43470i	0.277972	−	0.608674i
$17$	−2.76321	−	1.77580i	−0.670176	−	0.430696i	0.160813	−	0.986985i	$-0.448588\pi$
$17$	−2.76321	−	1.77580i	−0.670176	−	0.430696i	−0.830989	+	0.556289i	$0.812225\pi$
$18$	0.141785	−	0.0911198i	0.0334191	−	0.0214771i
$19$	−3.40746	−	1.00052i	−0.781724	−	0.229535i	−0.133565	−	0.991040i	$-0.542643\pi$
$19$	−3.40746	−	1.00052i	−0.781724	−	0.229535i	−0.648159	+	0.761505i	$0.724461\pi$
$20$	−0.209362	−	1.45615i	−0.0468148	−	0.325604i
$21$	0.827602	+	1.81219i	0.180597	+	0.395453i
$22$	−0.196061	+	1.36364i	−0.0418004	+	0.290728i
$23$	−0.912860	−	6.34908i	−0.190345	−	1.32388i	−0.831097	−	0.556128i	$-0.812286\pi$
$23$	−0.912860	−	6.34908i	−0.190345	−	1.32388i	0.640752	−	0.767748i	$-0.278623\pi$
$24$	2.78118	+	1.78736i	0.567707	+	0.364843i
$25$	2.82227	+	3.25707i	0.564453	+	0.651414i
$26$	−1.76864	−	1.13663i	−0.346858	−	0.222912i
$27$	2.01399	+	4.41003i	0.387593	+	0.848711i
$28$	−1.26176	+	1.45615i	−0.238450	+	0.275186i
$29$	−1.97270			−0.366320			−0.183160	−	0.983083i	$-0.558633\pi$
$29$	−1.97270			−0.366320			−0.183160	+	0.983083i	$0.558633\pi$
$30$	0.728446			0.132995
$31$	−1.76031	+	2.03151i	−0.316161	+	0.364869i	−0.891480	−	0.453060i	$-0.850332\pi$
$31$	−1.76031	+	2.03151i	−0.316161	+	0.364869i	0.575319	+	0.817929i	$0.304878\pi$
$32$	−0.696384	+	4.84346i	−0.123104	+	0.856211i
$33$	5.05353	+	1.48385i	0.879707	+	0.258305i
$34$	1.50926	+	0.443160i	0.258837	+	0.0760013i
$35$	−0.128663	+	0.894870i	−0.0217480	+	0.151261i
$36$	0.408086	−	0.470956i	0.0680143	−	0.0784927i
$37$	8.07686			1.32783			0.663914	−	0.747809i	$-0.268894\pi$
$37$	8.07686			1.32783			0.663914	+	0.747809i	$0.268894\pi$
$38$	1.70069			0.275889
$39$	−5.26347	+	6.07437i	−0.842829	+	0.972677i
$40$	0.623231	+	1.36469i	0.0985415	+	0.215776i
$41$	−2.28074	−	1.46575i	−0.356192	−	0.228911i	0.350290	−	0.936641i	$-0.386083\pi$
$41$	−2.28074	−	1.46575i	−0.356192	−	0.228911i	−0.706483	+	0.707730i	$0.749719\pi$
$42$	−0.624777	−	0.721031i	−0.0964052	−	0.111258i
$43$	−6.51473	−	4.18676i	−0.993487	−	0.638476i	−0.0604184	−	0.998173i	$-0.519244\pi$
$43$	−6.51473	−	4.18676i	−0.993487	−	0.638476i	−0.933069	+	0.359698i	$0.882880\pi$
$44$	0.724922	+	5.04194i	0.109286	+	0.760101i
$45$	0.0416130	−	0.289425i	0.00620330	−	0.0431449i
$46$	1.27607	+	2.79420i	0.188146	+	0.411982i
$47$	−1.56014	−	10.8510i	−0.227570	−	1.58278i	−0.708297	−	0.705914i	$-0.750536\pi$
$47$	−1.56014	−	10.8510i	−0.227570	−	1.58278i	0.480727	−	0.876870i	$-0.340373\pi$
$48$	4.70185	+	1.38059i	0.678654	+	0.199271i
$49$	−4.89266	+	3.14432i	−0.698951	+	0.449189i
$50$	−1.73625	−	1.11582i	−0.245543	−	0.157801i
$51$	2.49814	−	5.47016i	0.349809	−	0.765976i
$52$	−7.45852	−	2.19002i	−1.03431	−	0.303701i
$53$	6.30856	−	4.05427i	0.866548	−	0.556896i	−0.0301473	−	0.999545i	$-0.509598\pi$
$53$	6.30856	−	4.05427i	0.866548	−	0.556896i	0.896695	+	0.442649i	$0.145961\pi$
$54$	−1.52041	−	1.75465i	−0.206902	−	0.238778i
$55$	1.56519	+	1.80632i	0.211050	+	0.243564i
$56$	0.816259	−	1.78736i	0.109077	−	0.238846i
$57$	0.925309	−	6.43566i	0.122560	−	0.852425i
$58$	0.906440	−	0.266155i	0.119021	−	0.0349478i
$59$	−6.97706	+	8.05195i	−0.908336	+	1.04828i	0.0902927	+	0.995915i	$0.471220\pi$
$59$	−6.97706	+	8.05195i	−0.908336	+	1.04828i	−0.998628	+	0.0523599i	$0.983326\pi$
$60$	2.58427	−	0.758810i	0.333628	−	0.0979620i
$61$	−3.84302	−	8.41503i	−0.492048	−	1.07743i	−0.978973	−	0.203991i	$-0.934609\pi$
$61$	−3.84302	−	8.41503i	−0.492048	−	1.07743i	0.486925	−	0.873444i	$-0.338119\pi$
$62$	0.534760	−	1.17096i	0.0679146	−	0.148712i
$63$	−0.322170	+	0.207046i	−0.0405896	+	0.0260853i
$64$	0.428340	+	2.97917i	0.0535425	+	0.372396i
$65$	−3.49969	+	1.02760i	−0.434083	+	0.127458i
$66$	−2.52226			−0.310469
$67$	7.85223	+	2.31139i	0.959302	+	0.282381i
$67$	7.85223	+	2.31139i	0.959302	+	0.282381i
$68$	5.81597			0.705290
$69$	11.2679	−	3.30856i	1.35650	−	0.398304i
$70$	−0.0616156	−	0.428546i	−0.00736447	−	0.0512210i
$71$	−1.45889	+	0.937571i	−0.173138	+	0.111269i	−0.624340	−	0.781153i	$-0.714632\pi$
$71$	−1.45889	+	0.937571i	−0.173138	+	0.111269i	0.451202	+	0.892422i	$0.350996\pi$
$72$	−0.264000	+	0.578079i	−0.0311127	+	0.0681273i
$73$	−0.608158	−	1.33168i	−0.0711796	−	0.155862i	0.870698	−	0.491818i	$-0.163668\pi$
$73$	−0.608158	−	1.33168i	−0.0711796	−	0.155862i	−0.941877	+	0.335957i	$0.890940\pi$
$74$	−3.71126	+	1.08972i	−0.431425	+	0.126678i
$75$	−5.16709	+	5.96314i	−0.596644	+	0.688564i
$76$	6.03346	−	1.77158i	0.692085	−	0.203214i
$77$	0.445499	−	3.09851i	0.0507693	−	0.353108i
$78$	1.59898	−	3.50127i	0.181049	−	0.396441i
$79$	−10.1410	−	11.7033i	−1.14095	−	1.31672i	−0.941577	−	0.336799i	$-0.890656\pi$
$79$	−10.1410	−	11.7033i	−1.14095	−	1.31672i	−0.199370	−	0.979924i	$-0.563890\pi$
$80$	1.45626	+	1.68062i	0.162815	+	0.187899i
$81$	−8.35529	+	5.36962i	−0.928366	+	0.596624i
$82$	1.24574	+	0.365783i	0.137569	+	0.0403940i
$83$	−3.35960	+	7.35650i	−0.368764	+	0.807480i	0.630740	+	0.775994i	$0.282751\pi$
$83$	−3.35960	+	7.35650i	−0.368764	+	0.807480i	−0.999504	+	0.0314863i	$0.989976\pi$
$84$	−2.96758	−	1.90715i	−0.323789	−	0.208087i
$85$	2.29575	−	1.47539i	0.249010	−	0.160029i
$86$	3.55835	+	1.04483i	0.383707	+	0.112666i
$87$	−0.513994	−	3.57491i	−0.0551060	−	0.383271i
$88$	−2.15795	−	4.72526i	−0.230039	−	0.503714i
$89$	−2.19746	+	15.2836i	−0.232930	+	1.62006i	0.452389	+	0.891821i	$0.350572\pi$
$89$	−2.19746	+	15.2836i	−0.232930	+	1.62006i	−0.685319	+	0.728243i	$0.740337\pi$
$90$	0.0199281	+	0.138603i	0.00210061	+	0.0146101i
$91$	4.01877	+	2.58271i	0.421281	+	0.270741i
$92$	7.43771	+	8.58357i	0.775435	+	0.894899i
$93$	−4.14014	−	2.66071i	−0.429312	−	0.275902i
$94$	2.18089	+	4.77548i	0.224941	+	0.492553i
$95$	1.93219	−	2.22987i	0.198238	−	0.228779i
$96$	−8.95874			−0.914347
$97$	1.03304			0.104890			0.0524448	−	0.998624i	$-0.483299\pi$
$97$	1.03304			0.104890			0.0524448	+	0.998624i	$0.483299\pi$
$98$	1.82391	−	2.10491i	0.184243	−	0.212628i
$99$	−0.144086	+	1.00214i	−0.0144812	+	0.100719i
$100$	−7.32195	−	2.14992i	−0.732195	−	0.214992i
$101$	14.7982	+	4.34515i	1.47248	+	0.432359i	0.916904	−	0.399108i	$-0.130680\pi$
$101$	14.7982	+	4.34515i	1.47248	+	0.432359i	0.555575	+	0.831466i	$0.312498\pi$
$102$	−0.409847	+	2.85055i	−0.0405809	+	0.282246i
$103$	2.64709	−	3.05490i	0.260825	−	0.301009i	−0.610199	−	0.792248i	$-0.708911\pi$
$103$	2.64709	−	3.05490i	0.260825	−	0.301009i	0.871025	+	0.491239i	$0.163456\pi$
$104$	7.92738			0.777344
$105$	−1.65520			−0.161531
$106$	−2.35174	+	2.71405i	−0.228421	+	0.263612i
$107$	4.27363	+	9.35794i	0.413147	+	0.904667i	0.995766	+	0.0919211i	$0.0293008\pi$
$107$	4.27363	+	9.35794i	0.413147	+	0.904667i	−0.582619	+	0.812745i	$0.697972\pi$
$108$	−7.22169	−	4.64110i	−0.694908	−	0.446590i
$109$	5.18000	+	5.97804i	0.496154	+	0.572592i	0.947500	−	0.319757i	$-0.103601\pi$
$109$	5.18000	+	5.97804i	0.496154	+	0.572592i	−0.451346	+	0.892349i	$0.649056\pi$
$110$	−0.962900	−	0.618818i	−0.0918089	−	0.0590020i
$111$	2.10446	+	14.6368i	0.199746	+	1.38927i
$112$	0.414496	−	2.88288i	0.0391662	−	0.272407i
$113$	−5.47815	−	11.9955i	−0.515341	−	1.12844i	−0.971173	−	0.238374i	$-0.923386\pi$
$113$	−5.47815	−	11.9955i	−0.515341	−	1.12844i	0.455832	−	0.890066i	$-0.349342\pi$
$114$	0.443122	+	3.08198i	0.0415022	+	0.288654i
$115$	5.11338	+	1.50142i	0.476825	+	0.140009i
$116$	2.93848	−	1.88845i	0.272831	−	0.175338i
$117$	−1.29978	−	0.835316i	−0.120164	−	0.0772250i
$118$	2.11955	−	4.64116i	0.195120	−	0.427253i
$119$	−3.42941	−	1.00697i	−0.314373	−	0.0923084i
$120$	−2.31069	+	1.48499i	−0.210936	+	0.135561i
$121$	1.78397	+	2.05881i	0.162179	+	0.187165i
$122$	2.90119	+	3.34815i	0.262661	+	0.303127i
$123$	2.06196	−	4.51506i	0.185921	−	0.407109i
$124$	0.677370	−	4.71121i	0.0608296	−	0.423079i
$125$	−7.42148	+	2.17914i	−0.663798	+	0.194909i
$126$	0.120100	−	0.138603i	0.0106994	−	0.0123477i
$127$	−1.08241	+	0.317824i	−0.0960483	+	0.0282023i	−0.329404	−	0.944189i	$-0.606848\pi$
$127$	−1.08241	+	0.317824i	−0.0960483	+	0.0282023i	0.233355	+	0.972392i	$0.425029\pi$
$128$	−4.66424	−	10.2133i	−0.412264	−	0.902733i
$129$	5.88979	−	12.8968i	0.518567	−	1.13550i
$130$	1.46944	−	0.944350i	0.128878	−	0.0828250i
$131$	−0.304226	−	2.11594i	−0.0265803	−	0.184870i	0.972206	−	0.234128i	$-0.0752235\pi$
$131$	−0.304226	−	2.11594i	−0.0265803	−	0.184870i	−0.998786	+	0.0492579i	$0.984314\pi$
$132$	−8.94810	+	2.62740i	−0.778832	+	0.228686i
$133$	−3.86438			−0.335084
$134$	−3.91989	−	0.00264966i	−0.338627	−	0.000228895i
$135$	−4.02799			−0.346674
$136$	−5.69093	+	1.67101i	−0.487993	+	0.143288i
$137$	1.51982	+	10.5706i	0.129847	+	0.903107i	0.945745	+	0.324910i	$0.105334\pi$
$137$	1.51982	+	10.5706i	0.129847	+	0.903107i	−0.815898	+	0.578196i	$0.803757\pi$
$138$	−4.73114	+	3.04052i	−0.402742	+	0.258826i
$139$	0.348882	−	0.763945i	0.0295918	−	0.0647970i	−0.894259	−	0.447550i	$-0.852297\pi$
$139$	0.348882	−	0.763945i	0.0295918	−	0.0647970i	0.923851	+	0.382753i	$0.125024\pi$
$140$	−0.665000	−	1.45615i	−0.0562027	−	0.123067i
$141$	19.2577	−	5.65456i	1.62179	−	0.476200i
$142$	0.543853	−	0.627640i	0.0456391	−	0.0526703i
$143$	12.1177	−	3.55809i	1.01334	−	0.297542i
$144$	−0.134059	+	0.932401i	−0.0111716	+	0.0777001i
$145$	0.680855	−	1.49086i	0.0565419	−	0.123810i
$146$	0.459114	+	0.529846i	0.0379966	+	0.0438504i
$147$	−6.97293	−	8.04719i	−0.575117	−	0.663721i
$148$	−12.0311	+	7.73192i	−0.988950	+	0.635560i
$149$	−11.8242	−	3.47190i	−0.968676	−	0.284429i	−0.241134	−	0.970492i	$-0.577519\pi$
$149$	−11.8242	−	3.47190i	−0.968676	−	0.284429i	−0.727542	+	0.686063i	$0.759337\pi$
$150$	1.56970	−	3.43716i	0.128165	−	0.280643i
$151$	−9.27257	−	5.95912i	−0.754591	−	0.484946i	0.105922	−	0.994374i	$-0.466221\pi$
$151$	−9.27257	−	5.95912i	−0.754591	−	0.484946i	−0.860513	+	0.509428i	$0.829857\pi$
$152$	−5.39474	+	3.46699i	−0.437571	+	0.281210i
$153$	1.10916	+	0.325679i	0.0896705	+	0.0263296i
$154$	0.213345	+	1.48385i	0.0171919	+	0.119572i
$155$	−0.927757	−	2.03151i	−0.0745193	−	0.163174i
$156$	2.02539	−	14.0869i	0.162161	−	1.12786i
$157$	−1.18301	−	8.22804i	−0.0944148	−	0.656669i	−0.980986	−	0.194077i	$-0.937829\pi$
$157$	−1.18301	−	8.22804i	−0.0944148	−	0.656669i	0.886571	−	0.462592i	$-0.153080\pi$
$158$	6.23870	+	4.00937i	0.496324	+	0.318968i
$159$	8.99084	+	10.3760i	0.713020	+	0.822869i
$160$	−3.42009	−	2.19796i	−0.270382	−	0.173764i
$161$	−2.89953	−	6.34908i	−0.228515	−	0.500378i
$162$	3.11473	−	3.59459i	0.244717	−	0.282418i
$163$	6.95133			0.544470			0.272235	−	0.962231i	$-0.412237\pi$
$163$	6.95133			0.544470			0.272235	+	0.962231i	$0.412237\pi$
$164$	4.80049			0.374855
$165$	−2.86559	+	3.30707i	−0.223086	+	0.257455i
$166$	0.551179	−	3.83353i	0.0427798	−	0.297540i
$167$	18.2260	+	5.35164i	1.41037	+	0.414122i	0.896232	−	0.443585i	$-0.146294\pi$
$167$	18.2260	+	5.35164i	1.41037	+	0.414122i	0.514138	+	0.857707i	$0.328112\pi$
$168$	3.45172	+	1.01352i	0.266306	+	0.0781945i
$169$	−0.892745	+	6.20918i	−0.0686727	+	0.477629i
$170$	−0.855824	+	0.987674i	−0.0656387	+	0.0757511i
$171$	1.24984			0.0955779
$172$	13.7122			1.04554
$173$	−6.43299	+	7.42406i	−0.489091	+	0.564441i	−0.945622	−	0.325266i	$-0.894546\pi$
$173$	−6.43299	+	7.42406i	−0.489091	+	0.564441i	0.456532	+	0.889707i	$0.349092\pi$
$174$	0.718501	+	1.57330i	0.0544694	+	0.119271i
$175$	3.94518	+	2.53542i	0.298228	+	0.191659i
$176$	−5.04235	−	5.81918i	−0.380082	−	0.438637i
$177$	−16.4096	−	10.5458i	−1.23342	−	0.792672i
$178$	−1.05234	−	7.31921i	−0.0788765	−	0.548598i
$179$	3.09043	−	21.4944i	0.230990	−	1.60657i	−0.462849	−	0.886437i	$-0.653173\pi$
$179$	3.09043	−	21.4944i	0.230990	−	1.60657i	0.693839	−	0.720130i	$-0.255918\pi$
$180$	0.215079	+	0.470956i	0.0160310	+	0.0351030i
$181$	3.66805	+	25.5118i	0.272644	+	1.89628i	0.420537	+	0.907275i	$0.361842\pi$
$181$	3.66805	+	25.5118i	0.272644	+	1.89628i	−0.147894	+	0.989003i	$0.547249\pi$
$182$	−2.19505	−	0.644526i	−0.162708	−	0.0477754i
$183$	14.2484	−	9.15687i	1.05327	−	0.676895i
$184$	−9.74397	−	6.26207i	−0.718335	−	0.461646i
$185$	−2.78764	+	6.10408i	−0.204951	+	0.448781i
$186$	2.26135	+	0.663991i	0.165810	+	0.0486862i
$187$	−7.94911	+	5.10858i	−0.581296	+	0.373576i
$188$	12.7116	+	14.6699i	0.927085	+	1.06991i
$189$	3.45475	+	3.98699i	0.251296	+	0.290011i
$190$	−0.586975	+	1.28530i	−0.0425837	+	0.0932452i
$191$	−2.29093	+	15.9338i	−0.165766	+	1.15293i	0.721751	+	0.692153i	$0.243338\pi$
$191$	−2.29093	+	15.9338i	−0.165766	+	1.15293i	−0.887517	+	0.460775i	$0.847572\pi$
$192$	−5.28723	+	1.55247i	−0.381573	+	0.112040i
$193$	−16.3152	+	18.8288i	−1.17440	+	1.35533i	−0.252639	+	0.967561i	$0.581299\pi$
$193$	−16.3152	+	18.8288i	−1.17440	+	1.35533i	−0.921758	+	0.387766i	$0.873247\pi$
$194$	−0.474676	+	0.139377i	−0.0340797	+	0.0100067i
$195$	−2.77407	−	6.07437i	−0.198655	−	0.434994i
$196$	4.27796	−	9.36742i	0.305568	−	0.669101i
$197$	−10.1617	+	6.53055i	−0.723993	+	0.465282i	−0.850024	−	0.526744i	$-0.823413\pi$
$197$	−10.1617	+	6.53055i	−0.723993	+	0.465282i	0.126031	+	0.992026i	$0.459776\pi$
$198$	−0.0690016	−	0.479917i	−0.00490373	−	0.0341062i
$199$	2.26261	−	0.664361i	0.160392	−	0.0470953i	−0.200551	−	0.979683i	$-0.564273\pi$
$199$	2.26261	−	0.664361i	0.160392	−	0.0470953i	0.360943	+	0.932588i	$0.382455\pi$
$200$	7.78223			0.550287
$201$	−2.14275	+	14.8320i	−0.151138	+	1.04617i
$202$	−7.38593			−0.519672
$203$	−2.05965	+	0.604767i	−0.144559	+	0.0424464i
$204$	1.51538	+	10.5397i	0.106098	+	0.737925i
$205$	1.89491	−	1.21779i	0.132346	−	0.0850538i
$206$	−0.804153	+	1.76085i	−0.0560280	+	0.122684i
$207$	0.937785	+	2.05346i	0.0651806	+	0.142726i
$208$	11.2745	−	3.31048i	0.781744	−	0.229541i
$209$	−6.69025	+	7.72096i	−0.462774	+	0.534070i
$210$	0.760554	−	0.223319i	0.0524832	−	0.0154105i
$211$	0.100070	−	0.696002i	0.00688910	−	0.0479147i	−0.986087	−	0.166231i	$-0.946840\pi$
$211$	0.100070	−	0.696002i	0.00688910	−	0.0479147i	0.992976	+	0.118316i	$0.0377495\pi$
$212$	−5.51597	+	12.0783i	−0.378838	+	0.829540i
$213$	−2.07918	−	2.39950i	−0.142463	−	0.164411i
$214$	−3.22627	−	3.72331i	−0.220543	−	0.254521i
$215$	5.41264	−	3.47849i	0.369139	−	0.237231i
$216$	8.39987	+	2.46642i	0.571539	+	0.167819i
$217$	−1.21510	+	2.66071i	−0.0824866	+	0.180620i
$218$	−3.18673	−	2.04798i	−0.215832	−	0.138707i
$219$	2.25481	−	1.44908i	0.152366	−	0.0979195i
$220$	−4.06064	−	1.19231i	−0.273769	−	0.0803857i
$221$	−2.05216	−	14.2731i	−0.138043	−	0.960113i
$222$	−2.94178	−	6.44159i	−0.197439	−	0.432331i
$223$	−1.08766	+	7.56487i	−0.0728354	+	0.506581i	0.920447	+	0.390867i	$0.127825\pi$
$223$	−1.08766	+	7.56487i	−0.0728354	+	0.506581i	−0.993283	+	0.115714i	$0.963084\pi$
$224$	0.757775	+	5.27044i	0.0506309	+	0.352146i
$225$	−1.27598	−	0.820021i	−0.0850652	−	0.0546681i
$226$	4.13559	+	4.77273i	0.275096	+	0.317477i
$227$	9.19211	+	5.90741i	0.610102	+	0.392089i	0.808895	−	0.587953i	$-0.200066\pi$
$227$	9.19211	+	5.90741i	0.610102	+	0.392089i	−0.198793	+	0.980041i	$0.563702\pi$
$228$	4.78250	+	10.4722i	0.316729	+	0.693539i
$229$	17.4133	−	20.0960i	1.15070	−	1.32798i	0.214415	−	0.976743i	$-0.431215\pi$
$229$	17.4133	−	20.0960i	1.15070	−	1.32798i	0.936286	−	0.351238i	$-0.114239\pi$
$230$	−2.55213			−0.168283
$231$	5.73118			0.377084
$232$	−2.33273	+	2.69211i	−0.153151	+	0.176746i
$233$	0.351538	−	2.44500i	0.0230301	−	0.160178i	−0.975061	−	0.221937i	$-0.928762\pi$
$233$	0.351538	−	2.44500i	0.0230301	−	0.160178i	0.998091	+	0.0617595i	$0.0196712\pi$
$234$	0.709939	+	0.208457i	0.0464101	+	0.0136272i
$235$	8.73912	+	2.56604i	0.570077	+	0.167390i
$236$	2.68478	−	18.6731i	0.174765	−	1.21551i
$237$	18.5664	−	21.4267i	1.20602	−	1.39182i
$238$	1.71165			0.110950
$239$	−15.7639			−1.01968			−0.509839	−	0.860270i	$-0.670295\pi$
$239$	−15.7639			−1.01968			−0.509839	+	0.860270i	$0.670295\pi$
$240$	−2.66617	+	3.07693i	−0.172101	+	0.198615i
$241$	−7.72379	−	16.9127i	−0.497533	−	1.08945i	−0.977263	−	0.212029i	$-0.931993\pi$
$241$	−7.72379	−	16.9127i	−0.497533	−	1.08945i	0.479730	−	0.877416i	$-0.340734\pi$
$242$	−1.09750	−	0.705318i	−0.0705497	−	0.0453396i
$243$	−2.38322	−	2.75038i	−0.152883	−	0.176437i
$244$	13.7801	+	8.85594i	0.882182	+	0.566944i
$245$	−0.687671	−	4.78286i	−0.0439337	−	0.305565i
$246$	−0.338287	+	2.35284i	−0.0215684	+	0.150011i
$247$	−6.47658	−	14.1817i	−0.412095	−	0.902362i
$248$	0.690788	+	4.80454i	0.0438651	+	0.305088i
$249$	−14.2068	−	4.17148i	−0.900317	−	0.264357i
$250$	3.11611	−	2.00260i	0.197080	−	0.126656i
$251$	−11.4684	−	7.37030i	−0.723879	−	0.465209i	0.126105	−	0.992017i	$-0.459752\pi$
$251$	−11.4684	−	7.37030i	−0.723879	−	0.465209i	−0.849984	+	0.526808i	$0.823389\pi$
$252$	0.281693	−	0.616822i	0.0177450	−	0.0388561i
$253$	−17.7052	−	5.19872i	−1.11312	−	0.326841i
$254$	0.454479	−	0.292076i	0.0285165	−	0.0183265i
$255$	3.27187	+	3.77594i	0.204892	+	0.236458i
$256$	−0.420855	−	0.485693i	−0.0263035	−	0.0303558i
$257$	−2.01878	+	4.42052i	−0.125928	+	0.275744i	−0.962087	−	0.272743i	$-0.912069\pi$
$257$	−2.01878	+	4.42052i	−0.125928	+	0.275744i	0.836159	+	0.548488i	$0.184796\pi$
$258$	−0.966284	+	6.72066i	−0.0601582	+	0.418410i
$259$	8.43287	−	2.47611i	0.523993	−	0.153858i
$260$	4.22933	−	4.88091i	0.262292	−	0.302701i
$261$	0.666145	−	0.195598i	0.0412334	−	0.0121072i
$262$	0.425270	+	0.931212i	0.0262733	+	0.0575304i
$263$	5.18826	−	11.3607i	0.319922	−	0.700530i	−0.679530	−	0.733648i	$-0.737816\pi$
$263$	5.18826	−	11.3607i	0.319922	−	0.700530i	0.999451	+	0.0331174i	$0.0105435\pi$
$264$	8.00082	−	5.14182i	0.492417	−	0.316457i
$265$	0.886678	+	6.16698i	0.0544682	+	0.378835i
$266$	1.77565	−	0.521379i	0.108872	−	0.0319678i
$267$	−28.2695			−1.73007
$268$	−13.9092	+	4.07389i	−0.849638	+	0.248852i
$269$	−10.3046			−0.628282			−0.314141	−	0.949376i	$-0.601716\pi$
$269$	−10.3046			−0.628282			−0.314141	+	0.949376i	$0.601716\pi$
$270$	1.85083	−	0.543453i	0.112638	−	0.0330735i
$271$	0.613771	+	4.26887i	0.0372839	+	0.259315i	0.999935	−	0.0114309i	$-0.00363865\pi$
$271$	0.613771	+	4.26887i	0.0372839	+	0.259315i	−0.962651	+	0.270746i	$0.912730\pi$
$272$	−7.39592	+	4.75307i	−0.448444	+	0.288197i
$273$	−3.63326	+	7.95573i	−0.219895	+	0.481503i
$274$	−2.12452	−	4.65206i	−0.128347	−	0.281041i
$275$	11.8959	−	3.49294i	0.717348	−	0.210632i
$276$	−13.6172	+	15.7151i	−0.819658	+	0.945935i
$277$	15.7476	−	4.62392i	0.946183	−	0.277824i	0.227986	−	0.973664i	$-0.426786\pi$
$277$	15.7476	−	4.62392i	0.946183	−	0.277824i	0.718197	+	0.695840i	$0.244968\pi$
$278$	−0.0572379	+	0.398098i	−0.00343290	+	0.0238764i
$279$	0.392997	−	0.860543i	0.0235281	−	0.0515194i
$280$	1.06907	+	1.23378i	0.0638893	+	0.0737322i
$281$	−15.7848	−	18.2166i	−0.941642	−	1.08671i	−0.996103	−	0.0881964i	$-0.971890\pi$
$281$	−15.7848	−	18.2166i	−0.941642	−	1.08671i	0.0544616	−	0.998516i	$-0.482656\pi$
$282$	−8.08585	+	5.19646i	−0.481506	+	0.309445i
$283$	25.1857	+	7.39518i	1.49713	+	0.439598i	0.924810	−	0.380430i	$-0.124224\pi$
$283$	25.1857	+	7.39518i	1.49713	+	0.439598i	0.572323	+	0.820028i	$0.306042\pi$
$284$	1.27560	−	2.79317i	0.0756927	−	0.165744i
$285$	4.54439	+	2.92050i	0.269186	+	0.172996i
$286$	−5.08796	+	3.26984i	−0.300858	+	0.193349i
$287$	−2.83063	−	0.831147i	−0.167087	−	0.0490611i
$288$	−0.245084	−	1.70460i	−0.0144417	−	0.100445i
$289$	−2.58023	−	5.64991i	−0.151778	−	0.332348i
$290$	−0.111702	+	0.776902i	−0.00655935	+	0.0456213i
$291$	0.269164	+	1.87207i	0.0157787	+	0.109743i
$292$	2.18071	+	1.40146i	0.127616	+	0.0820140i
$293$	−11.2167	−	12.9447i	−0.655284	−	0.756238i	0.326715	−	0.945123i	$-0.394058\pi$
$293$	−11.2167	−	12.9447i	−0.655284	−	0.756238i	−0.981999	+	0.188885i	$0.939513\pi$
$294$	4.28973	+	2.75684i	0.250182	+	0.160782i
$295$	−3.67720	−	8.05195i	−0.214095	−	0.468803i
$296$	9.55094	−	11.0224i	0.555137	−	0.640662i
$297$	13.9470			0.809287
$298$	5.90156			0.341868
$299$	18.4407	−	21.2817i	1.06646	−	1.23075i
$300$	1.98831	−	13.8290i	0.114795	−	0.798416i
$301$	−8.08542	−	2.37409i	−0.466036	−	0.136840i
$302$	5.06468	+	1.48712i	0.291440	+	0.0855744i
$303$	−4.01852	+	27.9494i	−0.230858	+	1.60565i
$304$	−6.22467	+	7.18366i	−0.357010	+	0.412011i
$305$	7.68603			0.440101
$306$	−0.553593			−0.0316468
$307$	−5.78540	+	6.67671i	−0.330190	+	0.381060i	−0.896433	−	0.443178i	$-0.853851\pi$
$307$	−5.78540	+	6.67671i	−0.330190	+	0.381060i	0.566243	+	0.824238i	$0.308396\pi$
$308$	2.30258	+	5.04194i	0.131202	+	0.287291i
$309$	6.22579	+	4.00107i	0.354173	+	0.227613i
$310$	0.700387	+	0.808290i	0.0397793	+	0.0459078i
$311$	17.9884	+	11.5604i	1.02003	+	0.655531i	0.939969	−	0.341259i	$-0.110853\pi$
$311$	17.9884	+	11.5604i	1.02003	+	0.655531i	0.0800571	+	0.996790i	$0.474490\pi$
$312$	2.06551	+	14.3660i	0.116937	+	0.813312i
$313$	−0.415962	+	2.89308i	−0.0235115	+	0.163526i	−0.998194	−	0.0600653i	$-0.980869\pi$
$313$	−0.415962	+	2.89308i	−0.0235115	+	0.163526i	0.974683	+	0.223592i	$0.0717782\pi$
$314$	1.65371	+	3.62112i	0.0933241	+	0.204351i
$315$	−0.0452815	−	0.314939i	−0.00255132	−	0.0177448i
$316$	26.3092	+	7.72508i	1.48001	+	0.434570i
$317$	−6.54402	+	4.20559i	−0.367549	+	0.236209i	−0.711357	−	0.702830i	$-0.751919\pi$
$317$	−6.54402	+	4.20559i	−0.367549	+	0.236209i	0.343808	+	0.939040i	$0.388283\pi$
$318$	−5.53115	−	3.55465i	−0.310172	−	0.199335i
$319$	−2.35748	+	5.16215i	−0.131993	+	0.289025i
$320$	−2.39934	−	0.704511i	−0.134127	−	0.0393833i
$321$	−15.8449	+	10.1829i	−0.884376	+	0.568354i
$322$	2.18893	+	2.52616i	0.121984	+	0.140777i
$323$	7.63878	+	8.81562i	0.425033	+	0.490514i
$324$	7.30555	−	15.9969i	0.405864	−	0.888718i
$325$	−2.69262	+	18.7276i	−0.149359	+	1.03882i
$326$	−3.19409	+	0.937868i	−0.176904	+	0.0519437i
$327$	−9.48370	+	10.9448i	−0.524450	+	0.605247i
$328$	−4.69728	+	1.37925i	−0.259364	+	0.0761561i
$329$	−4.95550	−	10.8510i	−0.273205	−	0.598236i
$330$	0.870531	−	1.90620i	0.0479212	−	0.104933i
$331$	−27.7329	+	17.8228i	−1.52434	+	0.979632i	−0.533318	+	0.845915i	$0.679055\pi$
$331$	−27.7329	+	17.8228i	−1.52434	+	0.979632i	−0.991020	+	0.133717i	$0.957309\pi$
$332$	−2.03794	−	14.1742i	−0.111846	−	0.777909i
$333$	−2.72741	+	0.800841i	−0.149461	+	0.0438858i
$334$	−9.09676			−0.497752
$335$	−4.45694	+	5.13657i	−0.243509	+	0.280641i
$336$	5.33235			0.290903
$337$	26.4246	−	7.75896i	1.43944	−	0.422658i	0.533404	−	0.845860i	$-0.320912\pi$
$337$	26.4246	−	7.75896i	1.43944	−	0.422658i	0.906035	+	0.423203i	$0.139094\pi$
$338$	−0.427528	−	2.97352i	−0.0232545	−	0.161738i
$339$	20.3108	−	13.0529i	1.10313	−	0.708939i
$340$	−2.00732	+	4.39542i	−0.108862	+	0.238375i
$341$	3.21238	+	7.03414i	0.173960	+	0.380920i
$342$	−0.574294	+	0.168628i	−0.0310543	+	0.00911835i
$343$	−9.13250	+	10.5395i	−0.493109	+	0.569078i
$344$	−13.4173	+	3.93969i	−0.723414	+	0.212414i
$345$	−1.38856	+	9.65765i	−0.0747576	+	0.519950i
$346$	1.95426	−	4.27924i	0.105062	−	0.230053i
$347$	−5.54126	−	6.39495i	−0.297470	−	0.343299i	0.587263	−	0.809396i	$-0.300205\pi$
$347$	−5.54126	−	6.39495i	−0.297470	−	0.343299i	−0.884734	+	0.466097i	$0.845660\pi$
$348$	4.18787	+	4.83306i	0.224493	+	0.259079i
$349$	24.1955	−	15.5495i	1.29516	−	0.832347i	0.302481	−	0.953155i	$-0.402185\pi$
$349$	24.1955	−	15.5495i	1.29516	−	0.832347i	0.992676	+	0.120808i	$0.0385486\pi$
$350$	−2.15486	−	0.632724i	−0.115182	−	0.0338205i
$351$	−8.84165	+	19.3605i	−0.471932	+	1.03339i
$352$	11.8422	+	7.61049i	0.631189	+	0.405640i
$353$	−18.6338	+	11.9752i	−0.991778	+	0.637377i	−0.932616	−	0.360871i	$-0.882479\pi$
$353$	−18.6338	+	11.9752i	−0.991778	+	0.637377i	−0.0591626	+	0.998248i	$0.518843\pi$
$354$	8.96294	+	2.63176i	0.476375	+	0.139876i
$355$	−0.205049	−	1.42615i	−0.0108829	−	0.0756920i
$356$	−11.3576	−	24.8698i	−0.601954	−	1.31810i
$357$	0.931270	−	6.47713i	0.0492881	−	0.342806i
$358$	1.47998	+	10.2935i	0.0782194	+	0.544028i
$359$	7.06702	+	4.54170i	0.372983	+	0.239702i	0.713681	−	0.700471i	$-0.247027\pi$
$359$	7.06702	+	4.54170i	0.372983	+	0.239702i	−0.340697	+	0.940173i	$0.610663\pi$
$360$	−0.345766	−	0.399036i	−0.0182235	−	0.0210310i
$361$	−5.37410	−	3.45372i	−0.282847	−	0.181775i
$362$	−5.12748	−	11.2276i	−0.269494	−	0.590110i
$363$	−3.26615	+	3.76934i	−0.171428	+	0.197839i
$364$	−8.45867			−0.443355
$365$	1.21632			0.0636649
$366$	−5.31159	+	6.12990i	−0.277641	+	0.320415i
$367$	0.527829	−	3.67113i	0.0275524	−	0.191631i	−0.971397	−	0.237462i	$-0.923684\pi$
$367$	0.527829	−	3.67113i	0.0275524	−	0.191631i	0.998949	+	0.0458308i	$0.0145935\pi$
$368$	−16.4731	−	4.83694i	−0.858719	−	0.252143i
$369$	0.915500	+	0.268815i	0.0476590	+	0.0139940i
$370$	0.457343	−	3.18089i	0.0237761	−	0.165367i
$371$	5.34372	−	6.16698i	0.277432	−	0.320174i
$372$	8.71413			0.451807
$373$	11.2150			0.580689			0.290345	−	0.956922i	$-0.406230\pi$
$373$	11.2150			0.580689			0.290345	+	0.956922i	$0.406230\pi$
$374$	2.96331	−	3.41984i	0.153229	−	0.176836i
$375$	−5.88273	−	12.8814i	−0.303783	−	0.665192i
$376$	−16.6531	−	10.7023i	−0.858819	−	0.551929i
$377$	−5.67132	−	6.54505i	−0.292088	−	0.337087i
$378$	−2.12535	−	1.36588i	−0.109316	−	0.0702534i
$379$	−0.847495	−	5.89446i	−0.0435329	−	0.302778i	−0.999942	−	0.0107485i	$-0.996579\pi$
$379$	−0.847495	−	5.89446i	−0.0435329	−	0.302778i	0.956409	−	0.292029i	$-0.0943305\pi$
$380$	−0.743510	+	5.17123i	−0.0381413	+	0.265278i
$381$	−0.857985	−	1.87873i	−0.0439559	−	0.0962501i
$382$	−1.09711	−	7.63055i	−0.0561329	−	0.390413i
$383$	13.6416	+	4.00554i	0.697054	+	0.204674i	0.611016	−	0.791618i	$-0.290761\pi$
$383$	13.6416	+	4.00554i	0.697054	+	0.204674i	0.0860383	+	0.996292i	$0.472579\pi$
$384$	17.2931	−	11.1136i	0.882486	−	0.567139i
$385$	2.18794	+	1.40610i	0.111508	+	0.0716616i
$386$	4.95637	−	10.8529i	0.252273	−	0.552400i
$387$	2.61504	+	0.767845i	0.132930	+	0.0390318i
$388$	−1.53880	+	0.988924i	−0.0781205	+	0.0502050i
$389$	9.26185	+	10.6887i	0.469594	+	0.541941i	0.940299	−	0.340350i	$-0.110546\pi$
$389$	9.26185	+	10.6887i	0.469594	+	0.541941i	−0.470704	+	0.882291i	$0.656000\pi$
$390$	2.09421	+	2.41685i	0.106045	+	0.122382i
$391$	−8.75231	+	19.1649i	−0.442623	+	0.969210i
$392$	−1.49459	+	10.3951i	−0.0754884	+	0.525033i
$393$	3.75522	−	1.10263i	0.189426	−	0.0556204i
$394$	3.78815	−	4.37175i	0.190844	−	0.220246i
$395$	12.3448	−	3.62476i	0.621134	−	0.182381i
$396$	−0.744715	−	1.63070i	−0.0374233	−	0.0819456i
$397$	−0.131292	+	0.287489i	−0.00658935	+	0.0144287i	−0.912898	−	0.408188i	$-0.866161\pi$
$397$	−0.131292	+	0.287489i	−0.00658935	+	0.0144287i	0.906309	+	0.422616i	$0.138888\pi$
$398$	−0.950017	+	0.610539i	−0.0476200	+	0.0306035i
$399$	−1.00688	−	7.00301i	−0.0504071	−	0.350589i
$400$	11.0680	−	3.24987i	0.553401	−	0.162493i
$401$	30.4915			1.52267			0.761336	−	0.648358i	$-0.224544\pi$
$401$	30.4915			1.52267			0.761336	+	0.648358i	$0.224544\pi$
$402$	−1.01654	−	7.10430i	−0.0507006	−	0.354330i
$403$	−11.8009			−0.587845
$404$	−26.2027	+	7.69380i	−1.30363	+	0.382781i
$405$	−1.17435	−	8.16778i	−0.0583539	−	0.405860i
$406$	0.864799	−	0.555773i	0.0429193	−	0.0275825i
$407$	9.65227	−	21.1355i	0.478445	−	1.04765i
$408$	−4.51099	−	9.87768i	−0.223327	−	0.489018i
$409$	10.2810	−	3.01878i	0.508363	−	0.149269i	−0.0174854	−	0.999847i	$-0.505566\pi$
$409$	10.2810	−	3.01878i	0.508363	−	0.149269i	0.525849	+	0.850578i	$0.323748\pi$
$410$	−0.706395	+	0.815224i	−0.0348864	+	0.0402610i
$411$	−18.7600	+	5.50843i	−0.925361	+	0.271711i
$412$	−1.01860	+	7.08455i	−0.0501831	+	0.349031i
$413$	−4.81611	+	10.5458i	−0.236985	+	0.518926i
$414$	−0.707957	−	0.817026i	−0.0347942	−	0.0401547i
$415$	−4.40014	−	5.07803i	−0.215994	−	0.249271i
$416$	−18.0718	+	11.6140i	−0.886041	+	0.569424i
$417$	1.47532	+	0.433193i	0.0722468	+	0.0212136i
$418$	2.03242	−	4.45037i	0.0994087	−	0.217675i
$419$	−3.70553	−	2.38140i	−0.181027	−	0.116339i	0.446989	−	0.894540i	$-0.352496\pi$
$419$	−3.70553	−	2.38140i	−0.181027	−	0.116339i	−0.628016	+	0.778201i	$0.716133\pi$
$420$	2.46555	−	1.58451i	0.120307	−	0.0773164i
$421$	2.55888	+	0.751355i	0.124712	+	0.0366188i	0.343493	−	0.939155i	$-0.388390\pi$
$421$	2.55888	+	0.751355i	0.124712	+	0.0366188i	−0.218781	+	0.975774i	$0.570208\pi$
$422$	0.0479227	+	0.333309i	0.00233284	+	0.0162252i
$423$	1.60274	+	3.50951i	0.0779279	+	0.170638i
$424$	1.92712	−	13.4034i	0.0935892	−	0.650927i
$425$	−2.01459	−	14.0118i	−0.0977218	−	0.679670i
$426$	1.27911	+	0.822033i	0.0619730	+	0.0398276i
$427$	−6.59220	−	7.60780i	−0.319019	−	0.368167i
$428$	−15.3242	−	9.84826i	−0.740723	−	0.476034i
$429$	9.60528	+	21.0326i	0.463747	+	1.01547i
$430$	−2.01775	+	2.32861i	−0.0973047	+	0.112296i
$431$	−10.2150			−0.492037			−0.246019	−	0.969265i	$-0.579122\pi$
$431$	−10.2150			−0.492037			−0.246019	+	0.969265i	$0.579122\pi$
$432$	12.9764			0.624329
$433$	0.136279	−	0.157275i	0.00654917	−	0.00755815i	−0.752466	−	0.658632i	$-0.771136\pi$
$433$	0.136279	−	0.157275i	0.00654917	−	0.00755815i	0.759015	+	0.651073i	$0.225681\pi$
$434$	0.199351	−	1.38652i	0.00956915	−	0.0665549i
$435$	2.87914	+	0.845391i	0.138044	+	0.0405334i
$436$	−13.4387	−	3.94597i	−0.643599	−	0.188978i
$437$	−3.24185	+	22.5476i	−0.155079	+	1.07860i
$438$	−0.840560	+	0.970058i	−0.0401635	+	0.0463512i
$439$	−4.44240			−0.212024			−0.106012	−	0.994365i	$-0.533808\pi$
$439$	−4.44240			−0.212024			−0.106012	+	0.994365i	$0.533808\pi$
$440$	4.31591			0.205753
$441$	1.34040	−	1.54690i	0.0638285	−	0.0736620i
$442$	2.86867	+	6.28151i	0.136449	+	0.298781i
$443$	23.5711	+	15.1482i	1.11990	+	0.719713i	0.963427	−	0.267970i	$-0.0863528\pi$
$443$	23.5711	+	15.1482i	1.11990	+	0.719713i	0.156468	+	0.987683i	$0.449989\pi$
$444$	−17.1465	−	19.7881i	−0.813737	−	0.939102i
$445$	−10.7922	−	6.93571i	−0.511598	−	0.328784i
$446$	−0.520873	−	3.62275i	−0.0246641	−	0.171542i
$447$	3.21091	−	22.3324i	0.151871	−	1.05628i
$448$	1.36054	+	2.97917i	0.0642795	+	0.140752i
$449$	−0.0420093	−	0.292181i	−0.00198254	−	0.0137889i	0.988806	−	0.149206i	$-0.0476717\pi$
$449$	−0.0420093	−	0.292181i	−0.00198254	−	0.0137889i	−0.990789	+	0.135417i	$0.956763\pi$
$450$	0.696939	+	0.204640i	0.0328540	+	0.00964681i
$451$	−6.56117	+	4.21661i	−0.308954	+	0.198552i
$452$	19.6433	+	12.6240i	0.923943	+	0.593782i
$453$	8.38307	−	18.3564i	0.393871	−	0.862458i
$454$	−5.02073	−	1.47422i	−0.235635	−	0.0691886i
$455$	−3.33891	+	2.14579i	−0.156531	+	0.100596i
$456$	−7.68848	−	8.87297i	−0.360046	−	0.415515i
$457$	−11.6201	−	13.4103i	−0.543565	−	0.627308i	0.415806	−	0.909453i	$-0.363499\pi$
$457$	−11.6201	−	13.4103i	−0.543565	−	0.627308i	−0.959372	+	0.282145i	$0.908954\pi$
$458$	−5.28994	+	11.5834i	−0.247183	+	0.541255i
$459$	2.26628	−	15.7623i	0.105781	−	0.735721i
$460$	−9.05408	+	2.65852i	−0.422148	+	0.123954i
$461$	14.7043	−	16.9697i	0.684849	−	0.790357i	−0.301774	−	0.953380i	$-0.597579\pi$
$461$	14.7043	−	16.9697i	0.684849	−	0.790357i	0.986622	+	0.163022i	$0.0521242\pi$
$462$	−2.63344	+	0.773247i	−0.122519	+	0.0359747i
$463$	8.22023	+	17.9998i	0.382027	+	0.836522i	0.998781	+	0.0493657i	$0.0157200\pi$
$463$	8.22023	+	17.9998i	0.382027	+	0.836522i	−0.616754	+	0.787156i	$0.711553\pi$
$464$	−2.19342	+	4.80292i	−0.101827	+	0.222970i
$465$	3.43975	−	2.21059i	0.159515	−	0.102514i
$466$	0.168349	+	1.17089i	0.00779861	+	0.0542405i
$467$	−21.2742	+	6.24668i	−0.984455	+	0.289062i	−0.734062	−	0.679082i	$-0.762378\pi$
$467$	−21.2742	+	6.24668i	−0.984455	+	0.289062i	−0.250393	+	0.968144i	$0.580560\pi$
$468$	2.73576			0.126460
$469$	8.90694	+	0.00602065i	0.411284	+	0.000278008i
$470$	−4.36177			−0.201194
$471$	14.6026	−	4.28770i	0.672851	−	0.197567i
$472$	2.73797	+	19.0430i	0.126025	+	0.876524i
$473$	−18.7414	+	12.0444i	−0.861730	+	0.553800i
$474$	−5.64024	+	12.3504i	−0.259065	+	0.567272i
$475$	−6.35799	−	13.9221i	−0.291725	−	0.638788i
$476$	6.07233	−	1.78300i	0.278325	−	0.0817235i
$477$	−1.72830	+	1.99457i	−0.0791335	+	0.0913249i
$478$	7.24338	−	2.12685i	0.331304	−	0.0972798i
$479$	0.555874	−	3.86619i	0.0253985	−	0.176651i	−0.973174	−	0.230072i	$-0.926104\pi$
$479$	0.555874	−	3.86619i	0.0253985	−	0.176651i	0.998572	+	0.0534218i	$0.0170128\pi$
$480$	3.09201	−	6.77056i	0.141130	−	0.309032i
$481$	23.2202	+	26.7976i	1.05875	+	1.22186i
$482$	5.83088	+	6.72920i	0.265589	+	0.306506i
$483$	10.7503	−	6.90879i	0.489155	−	0.314361i
$484$	−4.62825	−	1.35898i	−0.210375	−	0.0617717i
$485$	−0.356544	+	0.780721i	−0.0161898	+	0.0354507i
$486$	1.46615	+	0.942237i	0.0665059	+	0.0427407i
$487$	22.5654	−	14.5019i	1.02253	−	0.657143i	0.0819269	−	0.996638i	$-0.473893\pi$
$487$	22.5654	−	14.5019i	1.02253	−	0.657143i	0.940608	+	0.339495i	$0.110256\pi$
$488$	−16.0283	−	4.70633i	−0.725566	−	0.213045i
$489$	1.81120	+	12.5972i	0.0819052	+	0.569663i
$490$	0.961279	+	2.10491i	0.0434262	+	0.0950901i
$491$	−5.24247	+	36.4622i	−0.236589	+	1.64551i	0.431993	+	0.901877i	$0.357810\pi$
$491$	−5.24247	+	36.4622i	−0.236589	+	1.64551i	−0.668582	+	0.743638i	$0.733099\pi$
$492$	1.25079	+	8.69942i	0.0563899	+	0.392200i
$493$	5.45097	+	3.50312i	0.245499	+	0.157773i
$494$	4.88933	+	5.64259i	0.219981	+	0.253872i
$495$	−0.707638	−	0.454771i	−0.0318059	−	0.0204404i
$496$	2.98883	+	6.54463i	0.134202	+	0.293862i
$497$	−1.23576	+	1.42615i	−0.0554316	+	0.0639714i
$498$	7.09072			0.317743
$499$	3.06877			0.137377			0.0686885	−	0.997638i	$-0.478119\pi$
$499$	3.06877			0.137377			0.0686885	+	0.997638i	$0.478119\pi$
$500$	8.96879	−	10.3505i	0.401096	−	0.462890i
$501$	−4.94935	+	34.4235i	−0.221120	+	1.53793i
$502$	6.26405	+	1.83929i	0.279578	+	0.0820915i
$503$	−3.52345	−	1.03458i	−0.157103	−	0.0461295i	0.202235	−	0.979337i	$-0.435179\pi$
$503$	−3.52345	−	1.03458i	−0.157103	−	0.0461295i	−0.359338	+	0.933207i	$0.616998\pi$
$504$	−0.0984154	+	0.684494i	−0.00438377	+	0.0304898i
$505$	−8.39130	+	9.68407i	−0.373408	+	0.430936i
$506$	8.83683			0.392845
$507$	−11.4849			−0.510060
$508$	1.30808	−	1.50961i	0.0580367	−	0.0669779i
$509$	6.43959	+	14.1007i	0.285430	+	0.625004i	0.996982	−	0.0776289i	$-0.0247349\pi$
$509$	6.43959	+	14.1007i	0.285430	+	0.625004i	−0.711553	+	0.702633i	$0.752008\pi$
$510$	−2.01285	−	1.29358i	−0.0891303	−	0.0572806i
$511$	−1.04322	−	1.20394i	−0.0461492	−	0.0532590i
$512$	19.1499	+	12.3069i	0.846315	+	0.543894i
$513$	−2.45027	−	17.0420i	−0.108182	−	0.752424i
$514$	0.331203	−	2.30357i	0.0146088	−	0.101606i
$515$	1.39513	+	3.05490i	0.0614767	+	0.134615i
$516$	3.57276	+	24.8491i	0.157282	+	1.09392i
$517$	−30.2594	−	8.88497i	−1.33081	−	0.390760i
$518$	−3.54077	+	2.27551i	−0.155572	+	0.0999803i
$519$	−15.1300	−	9.72345i	−0.664133	−	0.426812i
$520$	−2.73605	+	5.99112i	−0.119984	+	0.262728i
$521$	10.6289	+	3.12094i	0.465662	+	0.136731i	0.506143	−	0.862449i	$-0.331071\pi$
$521$	10.6289	+	3.12094i	0.465662	+	0.136731i	−0.0404807	+	0.999180i	$0.512889\pi$
$522$	−0.279699	+	0.179752i	−0.0122421	+	0.00786752i
$523$	−12.6858	−	14.6402i	−0.554711	−	0.640170i	0.407263	−	0.913311i	$-0.366483\pi$
$523$	−12.6858	−	14.6402i	−0.554711	−	0.640170i	−0.961974	+	0.273140i	$0.911938\pi$
$524$	2.47874	+	2.86061i	0.108284	+	0.124967i
$525$	−3.56673	+	7.81005i	−0.155665	+	0.340859i
$526$	−0.851190	+	5.92015i	−0.0371136	+	0.258131i
$527$	8.47165	−	2.48750i	0.369031	−	0.108357i
$528$	9.23169	−	10.6539i	0.401758	−	0.463653i
$529$	−17.4092	+	5.11181i	−0.756922	+	0.222252i
$530$	−1.23947	−	2.71405i	−0.0538390	−	0.117891i
$531$	1.55766	−	3.41080i	0.0675967	−	0.148016i
$532$	5.75629	−	3.69934i	0.249567	−	0.160387i
$533$	−1.69385	−	11.7810i	−0.0733688	−	0.510291i
$534$	12.9896	−	3.81410i	0.562117	−	0.165052i
$535$	−8.54726			−0.369530
$536$	12.4396	−	7.98259i	0.537310	−	0.344795i
$537$	39.7573			1.71565
$538$	4.73489	−	1.39029i	0.204135	−	0.0599396i
$539$	2.38108	+	16.5607i	0.102560	+	0.713322i
$540$	6.00000	−	3.85596i	0.258199	−	0.165934i
$541$	−2.86340	+	6.26997i	−0.123107	+	0.269567i	−0.961144	−	0.276046i	$-0.910976\pi$
$541$	−2.86340	+	6.26997i	−0.123107	+	0.269567i	0.838037	+	0.545613i	$0.183703\pi$
$542$	−0.857976	−	1.87871i	−0.0368532	−	0.0806973i
$543$	−45.2767	+	13.2944i	−1.94301	+	0.570518i
$544$	10.5253	−	12.1468i	0.451268	−	0.520791i
$545$	−6.30572	+	1.85153i	−0.270107	+	0.0793107i
$546$	0.596076	−	4.14580i	0.0255097	−	0.177424i
$547$	4.02139	−	8.80562i	0.171942	−	0.376501i	−0.803968	−	0.594672i	$-0.797282\pi$
$547$	4.02139	−	8.80562i	0.171942	−	0.376501i	0.975911	+	0.218171i	$0.0700091\pi$
$548$	−12.3830	−	14.2908i	−0.528977	−	0.610472i
$549$	2.13209	+	2.46057i	0.0909955	+	0.105014i
$550$	−4.99480	+	3.20996i	−0.212979	+	0.136873i
$551$	6.72188	+	1.97372i	0.286362	+	0.0840833i
$552$	8.80926	−	19.2896i	0.374947	−	0.821019i
$553$	−14.1758	−	9.11024i	−0.602817	−	0.387407i
$554$	−6.61207	+	4.24932i	−0.280920	+	0.180536i
$555$	−11.7881	−	3.46130i	−0.500378	−	0.146924i
$556$	0.211633	+	1.47194i	0.00897522	+	0.0624240i
$557$	6.76438	+	14.8119i	0.286616	+	0.627602i	0.997099	−	0.0761124i	$-0.0242508\pi$
$557$	6.76438	+	14.8119i	0.286616	+	0.627602i	−0.710483	+	0.703714i	$0.751524\pi$
$558$	−0.0644754	+	0.448436i	−0.00272946	+	0.0189838i
$559$	−4.83832	−	33.6513i	−0.204639	−	1.42330i
$560$	2.03568	+	1.30825i	0.0860232	+	0.0552837i
$561$	−11.3289	−	13.0743i	−0.478307	−	0.551996i
$562$	9.71077	+	6.24073i	0.409624	+	0.263249i
$563$	−5.49481	−	12.0319i	−0.231578	−	0.507086i	0.757793	−	0.652495i	$-0.226278\pi$
$563$	−5.49481	−	12.0319i	−0.231578	−	0.507086i	−0.989372	+	0.145409i	$0.953550\pi$
$564$	−23.2727	+	26.8581i	−0.979957	+	1.13093i
$565$	10.9563			0.460935
$566$	−12.5704			−0.528373
$567$	−7.07742	+	8.16778i	−0.297224	+	0.343014i
$568$	−0.445657	+	3.09961i	−0.0186993	+	0.130057i
$569$	43.5275	+	12.7808i	1.82477	+	0.535800i	0.999578	−	0.0290558i	$-0.00925006\pi$
$569$	43.5275	+	12.7808i	1.82477	+	0.535800i	0.825190	+	0.564856i	$0.191068\pi$
$570$	−2.48215	−	0.728824i	−0.103966	−	0.0305271i
$571$	3.00470	−	20.8982i	0.125743	−	0.874561i	−0.825122	−	0.564955i	$-0.808894\pi$
$571$	3.00470	−	20.8982i	0.125743	−	0.874561i	0.950865	−	0.309606i	$-0.100197\pi$
$572$	−14.6442	+	16.9003i	−0.612304	+	0.706636i
$573$	−29.4720			−1.23121
$574$	1.41279			0.0589687
$575$	18.1031	−	20.8921i	0.754950	−	0.871259i
$576$	−0.440035	−	0.963542i	−0.0183348	−	0.0401476i
$577$	−20.1398	−	12.9431i	−0.838432	−	0.538827i	0.0495150	−	0.998773i	$-0.484232\pi$
$577$	−20.1398	−	12.9431i	−0.838432	−	0.538827i	−0.887947	+	0.459946i	$0.847869\pi$
$578$	1.94788	+	2.24797i	0.0810211	+	0.0935033i
$579$	−38.3725	−	24.6605i	−1.59470	−	1.02485i
$580$	0.413008	+	2.87253i	0.0171492	+	0.119275i
$581$	−1.25241	+	8.71070i	−0.0519587	+	0.361381i
$582$	−0.376258	−	0.823890i	−0.0155964	−	0.0341513i
$583$	−3.07014	−	21.3533i	−0.127152	−	0.884364i
$584$	−2.53648	−	0.744777i	−0.104960	−	0.0308191i
$585$	1.07989	−	0.694005i	0.0446481	−	0.0286936i
$586$	6.90046	+	4.43466i	0.285056	+	0.183194i
$587$	−15.8332	+	34.6699i	−0.653506	+	1.43098i	0.234946	+	0.972008i	$0.424509\pi$
$587$	−15.8332	+	34.6699i	−0.653506	+	1.43098i	−0.888452	+	0.458970i	$0.848219\pi$
$588$	18.0902	+	5.31177i	0.746028	+	0.219054i
$589$	8.03074	−	5.16104i	0.330901	−	0.212657i
$590$	2.77601	+	3.20369i	0.114287	+	0.131894i
$591$	−14.4823	−	16.7135i	−0.595722	−	0.687500i
$592$	8.98057	−	19.6647i	0.369099	−	0.808214i
$593$	3.00793	−	20.9206i	0.123521	−	0.859106i	−0.829997	−	0.557768i	$-0.811658\pi$
$593$	3.00793	−	20.9206i	0.123521	−	0.859106i	0.953518	−	0.301338i	$-0.0974331\pi$
$594$	−6.40855	+	1.88172i	−0.262946	+	0.0772079i
$595$	1.94464	−	2.24423i	0.0797224	−	0.0920045i
$596$	20.9367	−	6.14756i	0.857599	−	0.251814i
$597$	1.79348	+	3.92718i	0.0734024	+	0.160729i
$598$	−5.60207	+	12.2668i	−0.229086	+	0.501628i
$599$	9.77166	−	6.27987i	0.399259	−	0.256588i	−0.325568	−	0.945518i	$-0.605556\pi$
$599$	9.77166	−	6.27987i	0.399259	−	0.256588i	0.724828	+	0.688930i	$0.241919\pi$
$600$	2.02769	+	14.1029i	0.0827802	+	0.575749i
$601$	46.4950	−	13.6522i	1.89657	−	0.556883i	0.905349	−	0.424667i	$-0.139609\pi$
$601$	46.4950	−	13.6522i	1.89657	−	0.556883i	0.991221	−	0.132216i	$-0.0422092\pi$
$602$	4.03550			0.164475
$603$	−2.88074	−	0.00194724i	−0.117313	−	7.92977e-5i
$604$	19.5168			0.794128
$605$	−2.17167	+	0.637659i	−0.0882908	+	0.0259245i
$606$	−1.92444	−	13.3847i	−0.0781748	−	0.543718i
$607$	−18.5371	+	11.9131i	−0.752397	+	0.483536i	−0.859769	−	0.510683i	$-0.829393\pi$
$607$	−18.5371	+	11.9131i	−0.752397	+	0.483536i	0.107372	+	0.994219i	$0.465756\pi$
$608$	7.21887	−	15.8071i	0.292764	−	0.641064i
$609$	−1.63261	−	3.57491i	−0.0661566	−	0.144863i
$610$	−3.53168	+	1.03699i	−0.142993	+	0.0419867i
$611$	31.5165	−	36.3720i	1.27502	−	1.47145i
$612$	−1.96395	+	0.576669i	−0.0793881	+	0.0233104i
$613$	2.76264	−	19.2146i	0.111582	−	0.776071i	−0.854799	−	0.518959i	$-0.826320\pi$
$613$	2.76264	−	19.2146i	0.111582	−	0.776071i	0.966382	−	0.257112i	$-0.0827710\pi$
$614$	1.75753	−	3.84846i	0.0709283	−	0.155311i
$615$	2.70059	+	3.11665i	0.108898	+	0.125675i
$616$	−3.70169	−	4.27198i	−0.149145	−	0.172123i
$617$	6.46427	−	4.15433i	0.260242	−	0.167247i	−0.404014	−	0.914753i	$-0.632385\pi$
$617$	6.46427	−	4.15433i	0.260242	−	0.167247i	0.664255	+	0.747506i	$0.268749\pi$
$618$	−3.40053	−	0.998486i	−0.136789	−	0.0401650i
$619$	−11.6926	+	25.6033i	−0.469966	+	1.02908i	0.515135	+	0.857109i	$0.327742\pi$
$619$	−11.6926	+	25.6033i	−0.469966	+	1.02908i	−0.985102	+	0.171974i	$0.944986\pi$
$620$	3.32671	+	2.13795i	0.133604	+	0.0858620i
$621$	26.1612	−	16.8128i	1.04981	−	0.674673i
$622$	−9.82525	−	2.88495i	−0.393957	−	0.115676i
$623$	2.39118	+	16.6310i	0.0958004	+	0.666307i
$624$	8.93685	+	19.5690i	0.357760	+	0.783386i
$625$	−2.15213	+	14.9684i	−0.0860851	+	0.598735i
$626$	−0.199200	−	1.38547i	−0.00796165	−	0.0553745i
$627$	−15.7351	−	10.1123i	−0.628398	−	0.403847i
$628$	9.63883	+	11.1238i	0.384631	+	0.443888i
$629$	−22.3180	−	14.3429i	−0.889878	−	0.571890i
$630$	0.0632979	+	0.138603i	0.00252185	+	0.00552208i
$631$	−4.84651	+	5.59318i	−0.192937	+	0.222661i	−0.843973	−	0.536386i	$-0.819789\pi$
$631$	−4.84651	+	5.59318i	−0.192937	+	0.222661i	0.651036	+	0.759047i	$0.274335\pi$
$632$	−27.9631			−1.11231
$633$	1.28736			0.0511682
$634$	2.43952	−	2.81535i	0.0968856	−	0.111812i
$635$	0.133387	−	0.927724i	0.00529328	−	0.0368156i
$636$	−23.3254	−	6.84896i	−0.924913	−	0.271579i
$637$	−24.4982	−	7.19333i	−0.970656	−	0.285010i
$638$	0.386770	−	2.69004i	0.0153124	−	0.106500i
$639$	0.399679	−	0.461254i	0.0158111	−	0.0182469i
$640$	9.32848			0.368740
$641$	−6.58756			−0.260193			−0.130097	−	0.991501i	$-0.541529\pi$
$641$	−6.58756			−0.260193			−0.130097	+	0.991501i	$0.541529\pi$
$642$	5.90675	−	6.81676i	0.233121	−	0.269036i
$643$	0.143538	+	0.314305i	0.00566059	+	0.0123950i	0.912441	−	0.409208i	$-0.134195\pi$
$643$	0.143538	+	0.314305i	0.00566059	+	0.0123950i	−0.906781	+	0.421603i	$0.861468\pi$
$644$	10.3970	+	6.68175i	0.409699	+	0.263298i
$645$	7.71399	+	8.90241i	0.303738	+	0.350532i
$646$	−4.69936	−	3.02010i	−0.184894	−	0.118824i
$647$	1.12118	+	7.79799i	0.0440782	+	0.306571i	0.999920	+	0.0126873i	$0.00403860\pi$
$647$	1.12118	+	7.79799i	0.0440782	+	0.306571i	−0.955841	+	0.293883i	$0.905052\pi$
$648$	−2.55235	+	17.7520i	−0.100266	+	0.697363i
$649$	12.7324	+	27.8801i	0.499791	+	1.09439i
$650$	−1.28947	−	8.96847i	−0.0505772	−	0.351772i
$651$	−5.13832	−	1.50875i	−0.201387	−	0.0591324i
$652$	−10.3545	+	6.65445i	−0.405515	+	0.260609i
$653$	26.6118	+	17.1024i	1.04140	+	0.669267i	0.945333	−	0.326108i	$-0.105737\pi$
$653$	26.6118	+	17.1024i	1.04140	+	0.669267i	0.0960676	+	0.995375i	$0.469374\pi$
$654$	2.88103	−	6.30858i	0.112657	−	0.246685i
$655$	1.70412	+	0.500374i	0.0665854	+	0.0195512i
$656$	−6.10458	+	3.92317i	−0.238344	+	0.153174i
$657$	0.337404	+	0.389385i	0.0131634	+	0.0151914i
$658$	3.74103	+	4.31738i	0.145840	+	0.168309i
$659$	1.80243	−	3.94677i	0.0702127	−	0.153744i	−0.871272	−	0.490801i	$-0.836704\pi$
$659$	1.80243	−	3.94677i	0.0702127	−	0.153744i	0.941484	+	0.337057i	$0.109431\pi$
$660$	1.10268	−	7.66934i	0.0429219	−	0.298529i
$661$	8.20594	−	2.40948i	0.319174	−	0.0937180i	−0.118221	−	0.992987i	$-0.537719\pi$
$661$	8.20594	−	2.40948i	0.319174	−	0.0937180i	0.437395	+	0.899269i	$0.355901\pi$
$662$	10.3384	−	11.9312i	0.401814	−	0.463718i
$663$	25.3309	−	7.43783i	0.983772	−	0.288862i
$664$	6.06656	+	13.2839i	0.235428	+	0.515515i
$665$	1.33375	−	2.92050i	0.0517206	−	0.113252i
$666$	1.14518	−	0.735962i	0.0443748	−	0.0285179i
$667$	1.80080	+	12.5248i	0.0697271	+	0.484963i
$668$	−32.2721	+	9.47594i	−1.24865	+	0.366635i
$669$	−13.9924			−0.540978
$670$	1.35491	−	2.96154i	0.0523448	−	0.114414i
$671$	−26.6131			−1.02739
$672$	−9.35362	+	2.74647i	−0.360824	+	0.105947i
$673$	−5.21849	−	36.2954i	−0.201158	−	1.39909i	−0.800855	−	0.598858i	$-0.795621\pi$
$673$	−5.21849	−	36.2954i	−0.201158	−	1.39909i	0.599697	−	0.800227i	$-0.295288\pi$
$674$	−11.0951	+	7.13038i	−0.427367	+	0.274652i
$675$	−8.67976	+	19.0060i	−0.334084	+	0.731542i
$676$	−4.61419	−	10.1037i	−0.177469	−	0.388603i
$677$	−27.2962	+	8.01488i	−1.04908	+	0.308037i	−0.760444	−	0.649403i	$-0.775019\pi$
$677$	−27.2962	+	8.01488i	−1.04908	+	0.308037i	−0.288633	+	0.957440i	$0.593201\pi$
$678$	−7.57157	+	8.73806i	−0.290784	+	0.335583i
$679$	1.07858	−	0.316699i	0.0413920	−	0.0121538i
$680$	0.701300	−	4.87765i	0.0268936	−	0.187049i
$681$	−8.31033	+	18.1971i	−0.318453	+	0.697314i
$682$	−2.42511	−	2.79872i	−0.0928622	−	0.107169i
$683$	23.4493	+	27.0620i	0.897264	+	1.03550i	0.999171	+	0.0407041i	$0.0129601\pi$
$683$	23.4493	+	27.0620i	0.897264	+	1.03550i	−0.101907	+	0.994794i	$0.532494\pi$
$684$	−1.86174	+	1.19647i	−0.0711853	+	0.0457480i
$685$	−8.51327	−	2.49972i	−0.325275	−	0.0955095i
$686$	2.77434	−	6.07496i	0.105925	−	0.231943i
$687$	40.9549	+	26.3201i	1.56253	+	1.00418i
$688$	−17.4372	+	11.2062i	−0.664785	+	0.427232i
$689$	31.5879	+	9.27503i	1.20340	+	0.353351i
$690$	−0.664969	−	4.62496i	−0.0253150	−	0.176069i
$691$	9.21471	+	20.1774i	0.350544	+	0.767584i	0.999974	+	0.00716307i	$0.00228010\pi$
$691$	9.21471	+	20.1774i	0.350544	+	0.767584i	−0.649430	+	0.760421i	$0.724993\pi$
$692$	2.47543	−	17.2170i	0.0941015	−	0.654491i
$693$	0.156788	+	1.09049i	0.00595589	+	0.0414241i
$694$	3.40897	+	2.19081i	0.129403	+	0.0831621i
$695$	0.456938	+	0.527335i	0.0173327	+	0.0200030i
$696$	−5.48643	−	3.52592i	−0.207963	−	0.133649i
$697$	3.69929	+	8.10031i	0.140121	+	0.306821i
$698$	−9.01975	+	10.4093i	−0.341402	+	0.393999i
$699$	4.52242			0.171054
$700$	−8.30379			−0.313854
$701$	−8.11956	+	9.37047i	−0.306672	+	0.353918i	−0.888076	−	0.459697i	$-0.847958\pi$
$701$	−8.11956	+	9.37047i	−0.306672	+	0.353918i	0.581404	+	0.813615i	$0.302503\pi$
$702$	1.45057	−	10.0889i	0.0547482	−	0.380782i
$703$	−27.5215	−	8.08105i	−1.03799	−	0.304783i
$704$	8.30778	+	2.43938i	0.313111	+	0.0919378i
$705$	−2.37314	+	16.5056i	−0.0893778	+	0.621636i
$706$	6.94642	−	8.01660i	0.261432	−	0.301709i
$707$	16.7826			0.631174
$708$	34.5388			1.29805
$709$	−16.3609	+	18.8815i	−0.614445	+	0.709108i	−0.974642	−	0.223768i	$-0.928164\pi$
$709$	−16.3609	+	18.8815i	−0.614445	+	0.709108i	0.360197	+	0.932876i	$0.382710\pi$
$710$	0.286633	+	0.627640i	0.0107572	+	0.0235549i
$711$	4.58484	+	2.94650i	0.171945	+	0.110502i
$712$	18.2589	+	21.0719i	0.684280	+	0.789701i
$713$	14.5051	+	9.32187i	0.543221	+	0.349107i
$714$	0.445977	+	3.10184i	0.0166903	+	0.116083i
$715$	−1.49328	+	10.3860i	−0.0558456	+	0.388415i
$716$	15.9730	+	34.9760i	0.596939	+	1.30711i
$717$	−4.10734	−	28.5672i	−0.153391	−	1.06686i
$718$	−3.86001	−	1.13340i	−0.144054	−	0.0422982i
$719$	−37.9952	+	24.4180i	−1.41698	+	0.910638i	−0.416982	+	0.908915i	$0.636912\pi$
$719$	−37.9952	+	24.4180i	−1.41698	+	0.910638i	−0.999999	+	0.00172296i	$0.999452\pi$
$720$	−0.658393	−	0.423123i	−0.0245369	−	0.0157689i
$721$	1.82723	−	4.00107i	0.0680496	−	0.149008i
$722$	2.93533	+	0.861892i	0.109242	+	0.0320763i
$723$	28.6367	−	18.4037i	1.06501	−	0.684441i
$724$	−29.8861	−	34.4904i	−1.11071	−	1.28183i
$725$	−5.56748	−	6.42521i	−0.206771	−	0.238626i
$726$	0.992217	−	2.17265i	0.0368246	−	0.0806346i
$727$	5.29490	−	36.8268i	0.196377	−	1.36583i	−0.618312	−	0.785933i	$-0.712183\pi$
$727$	5.29490	−	36.8268i	0.196377	−	1.36583i	0.814689	−	0.579898i	$-0.196908\pi$
$728$	8.27680	−	2.43029i	0.306759	−	0.0900725i
$729$	−15.1489	+	17.4827i	−0.561070	+	0.647509i
$730$	−0.558889	+	0.164105i	−0.0206854	+	0.00607379i
$731$	10.5667	+	23.1378i	0.390823	+	0.855782i
$732$	−12.4582	+	27.2797i	−0.460469	+	1.00829i
$733$	18.5007	−	11.8897i	0.683339	−	0.439156i	−0.152373	−	0.988323i	$-0.548691\pi$
$733$	18.5007	−	11.8897i	0.683339	−	0.439156i	0.835712	+	0.549167i	$0.185055\pi$
$734$	0.252773	+	1.75807i	0.00933001	+	0.0648916i
$735$	8.48829	−	2.49239i	0.313095	−	0.0919331i
$736$	31.3872			1.15695
$737$	15.4323	−	17.7855i	0.568455	−	0.655137i
$738$	−0.456934			−0.0168200
$739$	−26.2427	+	7.70554i	−0.965352	+	0.283453i	−0.726165	−	0.687521i	$-0.758699\pi$
$739$	−26.2427	+	7.70554i	−0.965352	+	0.283453i	−0.239187	+	0.970973i	$0.576881\pi$
$740$	−1.69099	−	11.7611i	−0.0621620	−	0.432346i
$741$	24.0126	−	15.4319i	0.882123	−	0.566906i
$742$	−1.62336	+	3.55465i	−0.0595953	+	0.130495i
$743$	14.3874	+	31.5041i	0.527824	+	1.15577i	0.966392	+	0.257075i	$0.0827586\pi$
$743$	14.3874	+	31.5041i	0.527824	+	1.15577i	−0.438568	+	0.898698i	$0.644514\pi$
$744$	−8.52677	+	2.50369i	−0.312607	+	0.0917896i
$745$	6.70488	−	7.73784i	0.245648	−	0.283493i
$746$	−5.15320	+	1.51312i	−0.188672	+	0.0553991i
$747$	0.405063	−	2.81727i	0.0148205	−	0.103079i
$748$	6.95039	−	15.2192i	0.254132	−	0.556471i
$749$	7.33086	+	8.46026i	0.267864	+	0.309131i
$750$	4.44102	+	5.12521i	0.162163	+	0.187146i
$751$	17.1100	−	10.9959i	0.624353	−	0.401247i	−0.189862	−	0.981811i	$-0.560804\pi$
$751$	17.1100	−	10.9959i	0.624353	−	0.401247i	0.814215	+	0.580564i	$0.197168\pi$
$752$	−28.1537	−	8.26666i	−1.02666	−	0.301454i
$753$	10.3683	−	22.7033i	0.377841	−	0.827356i
$754$	3.48899	+	2.24223i	0.127061	+	0.0816574i
$755$	7.70393	−	4.95101i	0.280375	−	0.180186i
$756$	−8.96283	−	2.63172i	−0.325975	−	0.0957148i
$757$	0.149712	+	1.04127i	0.00544138	+	0.0378456i	0.992361	−	0.123366i	$-0.0393689\pi$
$757$	0.149712	+	1.04127i	0.00544138	+	0.0378456i	−0.986920	+	0.161212i	$0.948460\pi$
$758$	1.18469	+	2.59412i	0.0430300	+	0.0942226i
$759$	4.80792	−	33.4398i	0.174517	−	1.21379i
$760$	−0.758238	−	5.27366i	−0.0275042	−	0.191296i
$761$	−36.0458	−	23.1653i	−1.30666	−	0.839740i	−0.312740	−	0.949839i	$-0.601247\pi$
$761$	−36.0458	−	23.1653i	−1.30666	−	0.839740i	−0.993921	+	0.110099i	$0.964883\pi$
$762$	0.647715	+	0.747503i	0.0234642	+	0.0270792i
$763$	7.24101	+	4.65351i	0.262142	+	0.168468i
$764$	−11.8408	−	25.9277i	−0.428384	−	0.938030i
$765$	−0.628948	+	0.725844i	−0.0227396	+	0.0262430i
$766$	−6.80865			−0.246007
$767$	−46.7733			−1.68889
$768$	0.770515	−	0.889221i	0.0278036	−	0.0320870i
$769$	−2.84713	+	19.8023i	−0.102670	+	0.714087i	0.871848	+	0.489777i	$0.162922\pi$
$769$	−2.84713	+	19.8023i	−0.102670	+	0.714087i	−0.974518	+	0.224310i	$0.927987\pi$
$770$	−1.19505	−	0.350899i	−0.0430667	−	0.0126455i
$771$	−8.53684	−	2.50664i	−0.307447	−	0.0902745i
$772$	6.27814	−	43.6654i	0.225955	−	1.57155i
$773$	−4.37215	+	5.04573i	−0.157255	+	0.181482i	−0.828910	−	0.559382i	$-0.811038\pi$
$773$	−4.37215	+	5.04573i	−0.157255	+	0.181482i	0.671655	+	0.740864i	$0.265584\pi$
$774$	−1.30519			−0.0469141
$775$	−11.5848			−0.416139
$776$	1.22158	−	1.40978i	0.0438522	−	0.0506081i
$777$	6.68442	+	14.6368i	0.239802	+	0.525094i
$778$	−5.69787	−	3.66180i	−0.204279	−	0.131282i
$779$	6.30503	+	7.27639i	0.225901	+	0.260704i
$780$	9.94714	+	6.39264i	0.356165	+	0.228893i
$781$	0.709987	+	4.93807i	0.0254053	+	0.176698i
$782$	1.43591	−	9.98699i	0.0513481	−	0.357134i
$783$	−3.97300	−	8.69965i	−0.141983	−	0.310900i
$784$	2.21538	+	15.4083i	0.0791206	+	0.550296i
$785$	6.62664	+	1.94576i	0.236515	+	0.0694471i
$786$	−1.57673	+	1.01330i	−0.0562401	+	0.0361433i
$787$	15.4463	+	9.92675i	0.550602	+	0.353850i	0.786173	−	0.618007i	$-0.212060\pi$
$787$	15.4463	+	9.92675i	0.550602	+	0.353850i	−0.235571	+	0.971857i	$0.575696\pi$
$788$	8.88503	−	19.4555i	0.316516	−	0.693073i
$789$	21.9396	+	6.44205i	0.781071	+	0.229343i
$790$	−5.18330	+	3.33110i	−0.184413	+	0.118515i
$791$	−9.39706	−	10.8448i	−0.334121	−	0.385596i
$792$	1.19722	+	1.38167i	0.0425415	+	0.0490955i
$793$	16.8713	−	36.9429i	0.599116	−	1.31188i
$794$	0.0215399	−	0.149813i	0.000764421	−	0.00531667i
$795$	−10.9447	+	3.21367i	−0.388170	+	0.113977i
$796$	−2.73434	+	3.15559i	−0.0969160	+	0.111847i
$797$	−47.4382	+	13.9291i	−1.68035	+	0.493395i	−0.976239	−	0.216697i	$-0.930472\pi$
$797$	−47.4382	+	13.9291i	−1.68035	+	0.493395i	−0.704109	+	0.710092i	$0.748653\pi$
$798$	1.40750	+	3.08198i	0.0498248	+	0.109101i
$799$	−14.9583	+	32.7541i	−0.529187	+	1.15876i
$800$	−17.7409	+	11.4014i	−0.627234	+	0.403099i
$801$	−0.773370	−	5.37891i	−0.0273257	−	0.190054i
$802$	−14.0106	+	4.11389i	−0.494732	+	0.145266i
$803$	−4.21153			−0.148622
$804$	−11.0068	−	24.1447i	−0.388179	−	0.851516i
$805$	5.79906			0.204390
$806$	5.42243	−	1.59217i	0.190997	−	0.0560818i
$807$	−2.68491	−	18.6739i	−0.0945131	−	0.657353i
$808$	23.4288	−	15.0568i	0.824222	−	0.529695i
$809$	20.9457	−	45.8646i	0.736410	−	1.61251i	−0.0529599	−	0.998597i	$-0.516866\pi$
$809$	20.9457	−	45.8646i	0.736410	−	1.61251i	0.789370	−	0.613917i	$-0.210407\pi$
$810$	1.64160	+	3.59459i	0.0576798	+	0.126301i
$811$	−35.6538	+	10.4689i	−1.25197	+	0.367613i	−0.839502	−	0.543357i	$-0.817153\pi$
$811$	−35.6538	+	10.4689i	−1.25197	+	0.367613i	−0.412473	+	0.910970i	$0.635335\pi$
$812$	2.48906	−	2.87253i	0.0873491	−	0.100806i
$813$	−7.57610	+	2.22454i	−0.265706	+	0.0780182i
$814$	−1.58356	+	11.0139i	−0.0555038	+	0.386037i
$815$	−2.39918	+	5.25346i	−0.0840395	+	0.184021i
$816$	−10.5405	−	12.1644i	−0.368992	−	0.425840i
$817$	18.0097	+	20.7843i	0.630081	+	0.727152i
$818$	−4.31676	+	2.77421i	−0.150932	+	0.0969981i
$819$	−1.61315	−	0.473664i	−0.0563680	−	0.0165511i
$820$	−1.65684	+	3.62797i	−0.0578593	+	0.126694i
$821$	−29.7766	−	19.1363i	−1.03921	−	0.667860i	−0.0944193	−	0.995533i	$-0.530099\pi$
$821$	−29.7766	−	19.1363i	−1.03921	−	0.667860i	−0.944791	+	0.327672i	$0.893736\pi$
$822$	7.87688	−	5.06217i	0.274738	−	0.176563i
$823$	36.5105	+	10.7205i	1.27268	+	0.373692i	0.847198	−	0.531277i	$-0.178288\pi$
$823$	36.5105	+	10.7205i	1.27268	+	0.373692i	0.425479	+	0.904968i	$0.360106\pi$
$824$	−1.03878	−	7.22489i	−0.0361877	−	0.251691i
$825$	9.42941	+	20.6475i	0.328290	+	0.718854i
$826$	0.790136	−	5.49552i	0.0274923	−	0.191213i
$827$	7.53408	+	52.4007i	0.261986	+	1.82215i	0.517888	+	0.855448i	$0.326718\pi$
$827$	7.53408	+	52.4007i	0.261986	+	1.82215i	−0.255902	+	0.966703i	$0.582373\pi$
$828$	−3.36267	−	2.16106i	−0.116861	−	0.0751019i
$829$	−20.4030	−	23.5463i	−0.708626	−	0.817798i	0.281265	−	0.959630i	$-0.409246\pi$
$829$	−20.4030	−	23.5463i	−0.708626	−	0.817798i	−0.989891	+	0.141832i	$0.954701\pi$
$830$	2.70696	+	1.73966i	0.0939599	+	0.0603843i
$831$	12.4826	+	27.3330i	0.433015	+	0.948171i
$832$	−8.65291	+	9.98599i	−0.299986	+	0.346202i
$833$	19.1031			0.661884
$834$	−0.736346			−0.0254976
$835$	−10.3350	+	11.9272i	−0.357658	+	0.412759i
$836$	2.57442	−	17.9055i	0.0890382	−	0.619274i
$837$	−12.5043	−	3.67158i	−0.432210	−	0.126908i
$838$	2.02396	+	0.594289i	0.0699166	+	0.0205294i
$839$	4.56090	−	31.7217i	0.157460	−	1.09516i	−0.745834	−	0.666132i	$-0.767949\pi$
$839$	4.56090	−	31.7217i	0.157460	−	1.09516i	0.903293	−	0.429023i	$-0.141142\pi$
$840$	−1.95729	+	2.25883i	−0.0675329	+	0.0779371i
$841$	−25.1085			−0.865809
$842$	−1.27716			−0.0440138
$843$	28.8993	−	33.3515i	0.995344	−	1.14869i
$844$	0.517216	+	1.13254i	0.0178033	+	0.0389838i
$845$	−4.38446	−	2.81772i	−0.150830	−	0.0969326i
$846$	−1.20995	−	1.39635i	−0.0415989	−	0.0480077i
$847$	2.49377	+	1.60265i	0.0856871	+	0.0550678i
$848$	−2.85649	−	19.8673i	−0.0980923	−	0.682247i
$849$	−6.83927	+	47.5682i	−0.234723	+	1.63254i
$850$	2.81614	+	6.16650i	0.0965929	+	0.211509i
$851$	−7.37304	−	51.2806i	−0.252745	−	1.75788i
$852$	5.39413	+	1.58386i	0.184800	+	0.0542621i
$853$	−9.90519	+	6.36568i	−0.339147	+	0.217957i	−0.699117	−	0.715007i	$-0.746423\pi$
$853$	−9.90519	+	6.36568i	−0.339147	+	0.217957i	0.359970	+	0.932964i	$0.382787\pi$
$854$	4.05551	+	2.60632i	0.138777	+	0.0891863i
$855$	−0.431370	+	0.944568i	−0.0147525	+	0.0323035i
$856$	17.8243	+	5.23367i	0.609220	+	0.178883i
$857$	27.6259	−	17.7541i	0.943684	−	0.606469i	0.0242467	−	0.999706i	$-0.492281\pi$
$857$	27.6259	−	17.7541i	0.943684	−	0.606469i	0.919437	+	0.393237i	$0.128645\pi$
$858$	−7.25127	−	8.36841i	−0.247554	−	0.285693i
$859$	15.1582	+	17.4935i	0.517191	+	0.596871i	0.952925	−	0.303205i	$-0.0980566\pi$
$859$	15.1582	+	17.4935i	0.517191	+	0.596871i	−0.435734	+	0.900075i	$0.643511\pi$
$860$	−4.73260	+	10.3630i	−0.161380	+	0.353374i
$861$	0.768668	−	5.34621i	0.0261961	−	0.182198i
$862$	4.69370	−	1.37820i	0.159868	−	0.0469415i
$863$	13.9719	−	16.1245i	0.475610	−	0.548883i	−0.466354	−	0.884598i	$-0.654433\pi$
$863$	13.9719	−	16.1245i	0.475610	−	0.548883i	0.941963	+	0.335716i	$0.108978\pi$
$864$	−22.7623	+	6.68362i	−0.774390	+	0.227381i
$865$	−3.39046	−	7.42406i	−0.115279	−	0.252426i
$866$	−0.0414000	+	0.0906534i	−0.00140683	+	0.00308053i
$867$	9.56645	−	6.14799i	0.324894	−	0.208797i
$868$	−0.737084	−	5.12653i	−0.0250183	−	0.174006i
$869$	−42.7442	+	12.5508i	−1.45000	+	0.425757i
$870$	−1.43700			−0.0487189
$871$	14.9057	+	32.6973i	0.505059	+	1.10791i
$872$	14.2835			0.483701
$873$	−0.348840	+	0.102429i	−0.0118065	+	0.00346669i
$874$	−1.55249	−	10.7978i	−0.0525139	−	0.365242i
$875$	−7.08055	+	4.55039i	−0.239366	+	0.153831i
$876$	−1.97152	+	4.31702i	−0.0666114	+	0.145859i
$877$	−1.36599	−	2.99109i	−0.0461261	−	0.101002i	0.885166	−	0.465275i	$-0.154045\pi$
$877$	−1.36599	−	2.99109i	−0.0461261	−	0.101002i	−0.931292	+	0.364273i	$0.881317\pi$
$878$	2.04125	−	0.599366i	0.0688890	−	0.0202276i
$879$	20.5358	−	23.6996i	0.692655	−	0.799366i
$880$	6.13816	−	1.80233i	0.206917	−	0.0607564i
$881$	5.42224	−	37.7125i	0.182680	−	1.27057i	−0.667713	−	0.744419i	$-0.732727\pi$
$881$	5.42224	−	37.7125i	0.182680	−	1.27057i	0.850393	−	0.526148i	$-0.176364\pi$
$882$	−0.407197	+	0.891637i	−0.0137110	+	0.0300230i
$883$	26.8916	+	31.0346i	0.904976	+	1.04440i	0.998808	+	0.0488098i	$0.0155428\pi$
$883$	26.8916	+	31.0346i	0.904976	+	1.04440i	−0.0938322	+	0.995588i	$0.529912\pi$
$884$	16.7204	+	19.2964i	0.562367	+	0.649007i
$885$	13.6336	−	8.76178i	0.458288	−	0.294524i
$886$	−12.8745	−	3.78030i	−0.432528	−	0.127002i
$887$	15.8290	−	34.6606i	0.531485	−	1.16379i	−0.433420	−	0.901192i	$-0.642693\pi$
$887$	15.8290	−	34.6606i	0.531485	−	1.16379i	0.964905	−	0.262598i	$-0.0845793\pi$
$888$	22.4632	+	14.4362i	0.753817	+	0.484448i
$889$	−1.03268	+	0.663666i	−0.0346351	+	0.0222586i
$890$	5.89469	+	1.73084i	0.197591	+	0.0580178i
$891$	4.06621	+	28.2811i	0.136223	+	0.947453i
$892$	−5.62164	−	12.3097i	−0.188226	−	0.412158i
$893$	−5.54055	+	38.5353i	−0.185407	+	1.28954i
$894$	1.53768	+	10.6948i	0.0514276	+	0.357687i
$895$	15.1778	+	9.75415i	0.507337	+	0.326045i
$896$	−8.00089	−	9.23352i	−0.267291	−	0.308470i
$897$	43.3715	+	27.8732i	1.44813	+	0.930657i
$898$	0.0587239	+	0.128587i	0.00195964	+	0.00429102i
$899$	3.47256	−	4.00754i	0.115816	−	0.133659i
$900$	2.68567			0.0895222
$901$	−24.6314			−0.820592
$902$	2.44591	−	2.82273i	0.0814399	−	0.0939867i
$903$	2.19563	−	15.2709i	0.0730660	−	0.508185i
$904$	−22.8480	−	6.70878i	−0.759914	−	0.223131i
$905$	−20.5465	−	6.03301i	−0.682990	−	0.200544i
$906$	−1.37533	+	9.56566i	−0.0456924	+	0.317798i
$907$	−23.9745	+	27.6680i	−0.796060	+	0.918702i	−0.998158	−	0.0606632i	$-0.980678\pi$
$907$	−23.9745	+	27.6680i	−0.796060	+	0.918702i	0.202098	+	0.979365i	$0.435224\pi$
$908$	−19.3475			−0.642068
$909$	−5.42794			−0.180033
$910$	1.24470	−	1.43646i	0.0412614	−	0.0476182i
$911$	−17.9986	−	39.4115i	−0.596322	−	1.30576i	−0.931546	−	0.363624i	$-0.881539\pi$
$911$	−17.9986	−	39.4115i	−0.596322	−	1.30576i	0.335224	−	0.942138i	$-0.391188\pi$
$912$	−14.6401	−	9.40859i	−0.484781	−	0.311550i
$913$	15.2356	+	17.5828i	0.504224	+	0.581906i
$914$	7.14866	+	4.59417i	0.236457	+	0.151962i
$915$	2.00263	+	13.9286i	0.0662049	+	0.460465i
$916$	−6.70066	+	46.6041i	−0.221396	+	1.53984i
$917$	−0.966315	−	2.11594i	−0.0319105	−	0.0698743i
$918$	1.08530	+	7.54843i	0.0358202	+	0.249135i
$919$	−21.9739	−	6.45211i	−0.724851	−	0.212835i	−0.101564	−	0.994829i	$-0.532385\pi$
$919$	−21.9739	−	6.45211i	−0.724851	−	0.212835i	−0.623286	+	0.781994i	$0.714203\pi$
$920$	8.09558	−	5.20271i	0.266903	−	0.171528i
$921$	−13.6069	−	8.74463i	−0.448363	−	0.288145i
$922$	−4.46699	+	9.78135i	−0.147113	+	0.322132i
$923$	−7.30486	−	2.14490i	−0.240443	−	0.0706003i
$924$	−8.53703	+	5.48642i	−0.280848	+	0.180490i
$925$	22.7951	+	26.3069i	0.749497	+	0.864965i
$926$	−6.20566	−	7.16171i	−0.203931	−	0.235348i
$927$	−0.590974	+	1.29405i	−0.0194101	+	0.0425023i
$928$	1.37375	−	9.55467i	0.0450957	−	0.313647i
$929$	26.3881	−	7.74824i	0.865765	−	0.254212i	0.181452	−	0.983400i	$-0.441920\pi$
$929$	26.3881	−	7.74824i	0.865765	−	0.254212i	0.684313	+	0.729188i	$0.260102\pi$
$930$	−1.28229	+	1.47984i	−0.0420479	+	0.0485259i
$931$	19.8175	−	5.81894i	0.649492	−	0.190708i
$932$	1.81694	+	3.97855i	0.0595159	+	0.130322i
$933$	−16.2628	+	35.6105i	−0.532420	+	1.16584i
$934$	8.93257	−	5.74061i	0.292283	−	0.187839i
$935$	−1.11726	−	7.77070i	−0.0365383	−	0.254129i
$936$	−2.67694	+	0.786020i	−0.0874985	+	0.0256919i
$937$	4.58217			0.149693			0.0748464	−	0.997195i	$-0.476153\pi$
$937$	4.58217			0.149693			0.0748464	+	0.997195i	$0.476153\pi$
$938$	−4.09349	+	1.19895i	−0.133657	+	0.0391472i
$939$	−5.35120			−0.174630
$940$	−15.4740	+	4.54359i	−0.504708	+	0.148196i
$941$	−1.99987	−	13.9094i	−0.0651940	−	0.453434i	−0.996104	−	0.0881858i	$-0.971893\pi$
$941$	−1.99987	−	13.9094i	−0.0651940	−	0.453434i	0.930910	−	0.365249i	$-0.119016\pi$
$942$	−6.13129	+	3.94034i	−0.199768	+	0.128383i
$943$	−7.22414	+	15.8187i	−0.235250	+	0.515126i
$944$	11.8464	+	25.9399i	0.385566	+	0.844272i
$945$	−4.20553	+	1.23486i	−0.136806	+	0.0401699i
$946$	6.98652	−	8.06287i	0.227151	−	0.262146i
$947$	9.40132	−	2.76048i	0.305502	−	0.0897034i	−0.125389	−	0.992108i	$-0.540018\pi$
$947$	9.40132	−	2.76048i	0.305502	−	0.0897034i	0.430890	+	0.902404i	$0.358200\pi$
$948$	−7.14437	+	49.6902i	−0.232038	+	1.61386i
$949$	2.66988	−	5.84622i	0.0866680	−	0.189776i
$950$	4.79981	+	5.53927i	0.155726	+	0.179718i
$951$	−9.32642	−	10.7633i	−0.302430	−	0.349023i
$952$	−5.42949	+	3.48932i	−0.175971	+	0.113090i
$953$	−27.5145	−	8.07897i	−0.891281	−	0.261704i	−0.196139	−	0.980576i	$-0.562840\pi$
$953$	−27.5145	−	8.07897i	−0.891281	−	0.261704i	−0.695142	+	0.718873i	$0.744658\pi$
$954$	0.525037	−	1.14967i	0.0169987	−	0.0372219i
$955$	−11.2513	−	7.23074i	−0.364082	−	0.233981i
$956$	23.4815	−	15.0906i	0.759445	−	0.488066i
$957$	−9.96908	−	2.92719i	−0.322255	−	0.0946225i
$958$	0.266203	+	1.85148i	0.00860064	+	0.0598187i
$959$	4.82743	+	10.5706i	0.155886	+	0.341342i
$960$	0.651551	−	4.53164i	0.0210287	−	0.146258i
$961$	3.38344	+	23.5323i	0.109143	+	0.759107i
$962$	−14.2850	−	9.18044i	−0.460568	−	0.295989i
$963$	−2.37099	−	2.73627i	−0.0764042	−	0.0881752i
$964$	27.6956	+	17.7989i	0.892016	+	0.573264i
$965$	−8.59882	−	18.8288i	−0.276806	−	0.606120i
$966$	−4.00755	+	4.62496i	−0.128941	+	0.148806i
$967$	3.62365			0.116529			0.0582644	−	0.998301i	$-0.481443\pi$
$967$	3.62365			0.116529			0.0582644	+	0.998301i	$0.481443\pi$
$968$	4.91919			0.158109
$969$	−13.9853	+	16.1399i	−0.449273	+	0.518488i
$970$	0.0584948	−	0.406841i	0.00187816	−	0.0130629i
$971$	13.4807	+	3.95828i	0.432615	+	0.127027i	0.490787	−	0.871279i	$-0.336709\pi$
$971$	13.4807	+	3.95828i	0.432615	+	0.127027i	−0.0581725	+	0.998307i	$0.518527\pi$
$972$	6.18290	+	1.81546i	0.198317	+	0.0582310i
$973$	0.130058	−	0.904575i	0.00416948	−	0.0289993i
$974$	−8.41205	+	9.70802i	−0.269539	+	0.311065i
$975$	−34.6395			−1.10935
$976$	−24.7611			−0.792582
$977$	−8.59122	+	9.91480i	−0.274858	+	0.317203i	−0.876349	−	0.481677i	$-0.840028\pi$
$977$	−8.59122	+	9.91480i	−0.274858	+	0.317203i	0.601491	+	0.798879i	$0.294573\pi$
$978$	−2.53183	−	5.54394i	−0.0809591	−	0.177276i
$979$	37.3682	+	24.0151i	1.19429	+	0.767525i
$980$	5.60293	+	6.46613i	0.178979	+	0.206553i
$981$	−2.34193	−	1.50507i	−0.0747722	−	0.0480532i
$982$	−2.51057	−	17.4614i	−0.0801156	−	0.557216i
$983$	3.83285	−	26.6581i	0.122249	−	0.850260i	−0.832750	−	0.553650i	$-0.813235\pi$
$983$	3.83285	−	26.6581i	0.122249	−	0.850260i	0.954999	−	0.296611i	$-0.0958563\pi$
$984$	−3.72336	−	8.15301i	−0.118696	−	0.259909i
$985$	−1.42825	−	9.93367i	−0.0455077	−	0.316513i
$986$	−2.97732	−	0.874220i	−0.0948172	−	0.0278408i
$987$	18.3730	−	11.8076i	0.584819	−	0.375840i
$988$	23.2234	+	14.9248i	0.738836	+	0.474821i
$989$	−20.6351	+	45.1845i	−0.656157	+	1.43678i
$990$	0.386512	+	0.113490i	0.0122842	+	0.00360695i
$991$	27.4529	−	17.6429i	0.872069	−	0.560445i	−0.0263159	−	0.999654i	$-0.508378\pi$
$991$	27.4529	−	17.6429i	0.872069	−	0.560445i	0.898385	+	0.439209i	$0.144741\pi$
$992$	−8.61366	−	9.94069i	−0.273484	−	0.315617i
$993$	−39.5244	−	45.6136i	−1.25427	−	1.44750i
$994$	0.375410	−	0.822033i	0.0119073	−	0.0260733i
$995$	−0.278824	+	1.93926i	−0.00883931	+	0.0614787i
$996$	25.1554	−	7.38629i	0.797079	−	0.234043i
$997$	25.8805	−	29.8677i	0.819645	−	0.945921i	−0.179640	−	0.983732i	$-0.557493\pi$
$997$	25.8805	−	29.8677i	0.819645	−	0.945921i	0.999285	+	0.0378119i	$0.0120388\pi$
$998$	−1.41008	+	0.414036i	−0.0446352	+	0.0131061i
$999$	16.2667	+	35.6192i	0.514657	+	1.12694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.b.22.1	✓	10
3.2	odd	2		603.2.u.a.424.1		10
67.8	odd	22		4489.2.a.h.1.3		5
67.59	even	11		4489.2.a.i.1.3		5
67.64	even	11	inner	67.2.e.b.64.1	yes	10
201.131	odd	22		603.2.u.a.64.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.b.22.1	✓	10	1.1	even	1	trivial
67.2.e.b.64.1	yes	10	67.64	even	11	inner
603.2.u.a.64.1		10	201.131	odd	22
603.2.u.a.424.1		10	3.2	odd	2
4489.2.a.h.1.3		5	67.8	odd	22
4489.2.a.i.1.3		5	67.59	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:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.459493 + 0.134919i) q^{2} +(0.260554 + 1.81219i) q^{3} +(-1.48958 + 0.957293i) q^{4} +(-0.345139 + 0.755750i) q^{5} +(-0.364223 - 0.797537i) q^{6} +(1.04408 - 0.306569i) q^{7} +(1.18251 - 1.36469i) q^{8} +(-0.337683 + 0.0991526i) q^{9} +O(q^{10})\)	\(q+(-0.459493 + 0.134919i) q^{2} +(0.260554 + 1.81219i) q^{3} +(-1.48958 + 0.957293i) q^{4} +(-0.345139 + 0.755750i) q^{5} +(-0.364223 - 0.797537i) q^{6} +(1.04408 - 0.306569i) q^{7} +(1.18251 - 1.36469i) q^{8} +(-0.337683 + 0.0991526i) q^{9} +(0.0566239 - 0.393828i) q^{10} +(1.19505 - 2.61680i) q^{11} +(-2.12292 - 2.44998i) q^{12} +(2.87491 + 3.31782i) q^{13} +(-0.438384 + 0.281733i) q^{14} +(-1.45949 - 0.428546i) q^{15} +(1.11189 - 2.43470i) q^{16} +(-2.76321 - 1.77580i) q^{17} +(0.141785 - 0.0911198i) q^{18} +(-3.40746 - 1.00052i) q^{19} +(-0.209362 - 1.45615i) q^{20} +(0.827602 + 1.81219i) q^{21} +(-0.196061 + 1.36364i) q^{22} +(-0.912860 - 6.34908i) q^{23} +(2.78118 + 1.78736i) q^{24} +(2.82227 + 3.25707i) q^{25} +(-1.76864 - 1.13663i) q^{26} +(2.01399 + 4.41003i) q^{27} +(-1.26176 + 1.45615i) q^{28} -1.97270 q^{29} +0.728446 q^{30} +(-1.76031 + 2.03151i) q^{31} +(-0.696384 + 4.84346i) q^{32} +(5.05353 + 1.48385i) q^{33} +(1.50926 + 0.443160i) q^{34} +(-0.128663 + 0.894870i) q^{35} +(0.408086 - 0.470956i) q^{36} +8.07686 q^{37} +1.70069 q^{38} +(-5.26347 + 6.07437i) q^{39} +(0.623231 + 1.36469i) q^{40} +(-2.28074 - 1.46575i) q^{41} +(-0.624777 - 0.721031i) q^{42} +(-6.51473 - 4.18676i) q^{43} +(0.724922 + 5.04194i) q^{44} +(0.0416130 - 0.289425i) q^{45} +(1.27607 + 2.79420i) q^{46} +(-1.56014 - 10.8510i) q^{47} +(4.70185 + 1.38059i) q^{48} +(-4.89266 + 3.14432i) q^{49} +(-1.73625 - 1.11582i) q^{50} +(2.49814 - 5.47016i) q^{51} +(-7.45852 - 2.19002i) q^{52} +(6.30856 - 4.05427i) q^{53} +(-1.52041 - 1.75465i) q^{54} +(1.56519 + 1.80632i) q^{55} +(0.816259 - 1.78736i) q^{56} +(0.925309 - 6.43566i) q^{57} +(0.906440 - 0.266155i) q^{58} +(-6.97706 + 8.05195i) q^{59} +(2.58427 - 0.758810i) q^{60} +(-3.84302 - 8.41503i) q^{61} +(0.534760 - 1.17096i) q^{62} +(-0.322170 + 0.207046i) q^{63} +(0.428340 + 2.97917i) q^{64} +(-3.49969 + 1.02760i) q^{65} -2.52226 q^{66} +(7.85223 + 2.31139i) q^{67} +5.81597 q^{68} +(11.2679 - 3.30856i) q^{69} +(-0.0616156 - 0.428546i) q^{70} +(-1.45889 + 0.937571i) q^{71} +(-0.264000 + 0.578079i) q^{72} +(-0.608158 - 1.33168i) q^{73} +(-3.71126 + 1.08972i) q^{74} +(-5.16709 + 5.96314i) q^{75} +(6.03346 - 1.77158i) q^{76} +(0.445499 - 3.09851i) q^{77} +(1.59898 - 3.50127i) q^{78} +(-10.1410 - 11.7033i) q^{79} +(1.45626 + 1.68062i) q^{80} +(-8.35529 + 5.36962i) q^{81} +(1.24574 + 0.365783i) q^{82} +(-3.35960 + 7.35650i) q^{83} +(-2.96758 - 1.90715i) q^{84} +(2.29575 - 1.47539i) q^{85} +(3.55835 + 1.04483i) q^{86} +(-0.513994 - 3.57491i) q^{87} +(-2.15795 - 4.72526i) q^{88} +(-2.19746 + 15.2836i) q^{89} +(0.0199281 + 0.138603i) q^{90} +(4.01877 + 2.58271i) q^{91} +(7.43771 + 8.58357i) q^{92} +(-4.14014 - 2.66071i) q^{93} +(2.18089 + 4.77548i) q^{94} +(1.93219 - 2.22987i) q^{95} -8.95874 q^{96} +1.03304 q^{97} +(1.82391 - 2.10491i) q^{98} +(-0.144086 + 1.00214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 3 q^{3} - 14 q^{4} - 9 q^{5} + 10 q^{6} + 7 q^{7} - 7 q^{8} - 6 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 3 * q^3 - 14 * q^4 - 9 * q^5 + 10 * q^6 + 7 * q^7 - 7 * q^8 - 6 * q^9	\( 10 q + 4 q^{2} + 3 q^{3} - 14 q^{4} - 9 q^{5} + 10 q^{6} + 7 q^{7} - 7 q^{8} - 6 q^{9} - 8 q^{10} - 12 q^{11} - 13 q^{12} + 15 q^{13} + 5 q^{14} - 6 q^{15} + 12 q^{16} + q^{17} + 24 q^{18} - 13 q^{19} + 6 q^{20} + q^{21} - 7 q^{22} - 7 q^{23} - 23 q^{24} + 12 q^{25} + 28 q^{26} + 9 q^{27} + 10 q^{28} - 24 q^{29} - 20 q^{30} - q^{31} - q^{32} + 3 q^{33} - 15 q^{34} - 3 q^{35} + 37 q^{36} + 2 q^{37} - 36 q^{38} - 23 q^{39} + 25 q^{40} - 7 q^{41} + 7 q^{42} - 2 q^{43} + 41 q^{44} + 12 q^{45} + 6 q^{46} + 33 q^{47} + 8 q^{48} + 2 q^{49} - 4 q^{50} + 30 q^{51} - 21 q^{52} + 21 q^{53} - 14 q^{54} + 13 q^{55} - 17 q^{56} + 28 q^{57} - 3 q^{58} - 38 q^{59} + 4 q^{60} - 50 q^{61} + 4 q^{62} - 13 q^{63} - 31 q^{64} - 8 q^{65} - 78 q^{66} + 32 q^{67} - 30 q^{68} + 21 q^{69} - 10 q^{70} - 16 q^{71} - 53 q^{72} + 3 q^{73} - 8 q^{74} - 14 q^{75} + 5 q^{76} + 7 q^{77} + 70 q^{78} - 19 q^{79} + 9 q^{80} - 9 q^{81} - 16 q^{82} + 5 q^{83} + 25 q^{84} - 13 q^{85} + 19 q^{86} + 6 q^{87} + 48 q^{88} + 7 q^{89} - 15 q^{90} - 6 q^{91} + 45 q^{92} - 19 q^{93} + 22 q^{94} + 15 q^{95} + 14 q^{96} + 54 q^{97} + 47 q^{98} + 16 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 3 * q^3 - 14 * q^4 - 9 * q^5 + 10 * q^6 + 7 * q^7 - 7 * q^8 - 6 * q^9 - 8 * q^10 - 12 * q^11 - 13 * q^12 + 15 * q^13 + 5 * q^14 - 6 * q^15 + 12 * q^16 + q^17 + 24 * q^18 - 13 * q^19 + 6 * q^20 + q^21 - 7 * q^22 - 7 * q^23 - 23 * q^24 + 12 * q^25 + 28 * q^26 + 9 * q^27 + 10 * q^28 - 24 * q^29 - 20 * q^30 - q^31 - q^32 + 3 * q^33 - 15 * q^34 - 3 * q^35 + 37 * q^36 + 2 * q^37 - 36 * q^38 - 23 * q^39 + 25 * q^40 - 7 * q^41 + 7 * q^42 - 2 * q^43 + 41 * q^44 + 12 * q^45 + 6 * q^46 + 33 * q^47 + 8 * q^48 + 2 * q^49 - 4 * q^50 + 30 * q^51 - 21 * q^52 + 21 * q^53 - 14 * q^54 + 13 * q^55 - 17 * q^56 + 28 * q^57 - 3 * q^58 - 38 * q^59 + 4 * q^60 - 50 * q^61 + 4 * q^62 - 13 * q^63 - 31 * q^64 - 8 * q^65 - 78 * q^66 + 32 * q^67 - 30 * q^68 + 21 * q^69 - 10 * q^70 - 16 * q^71 - 53 * q^72 + 3 * q^73 - 8 * q^74 - 14 * q^75 + 5 * q^76 + 7 * q^77 + 70 * q^78 - 19 * q^79 + 9 * q^80 - 9 * q^81 - 16 * q^82 + 5 * q^83 + 25 * q^84 - 13 * q^85 + 19 * q^86 + 6 * q^87 + 48 * q^88 + 7 * q^89 - 15 * q^90 - 6 * q^91 + 45 * q^92 - 19 * q^93 + 22 * q^94 + 15 * q^95 + 14 * q^96 + 54 * q^97 + 47 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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