LMFDB - Embedded newform 93.2.m.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	93.49
Dual form			93.2.m.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08748 + 1.51664i) q^{2} +(0.913545 - 0.406737i) q^{3} +(1.43933 - 4.42980i) q^{4} +(-1.93212 - 3.34652i) q^{5} +(-1.29013 + 2.23457i) q^{6} +(-2.07563 - 2.30522i) q^{7} +(2.11916 + 6.52210i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-2.08748 + 1.51664i) q^{2} +(0.913545 - 0.406737i) q^{3} +(1.43933 - 4.42980i) q^{4} +(-1.93212 - 3.34652i) q^{5} +(-1.29013 + 2.23457i) q^{6} +(-2.07563 - 2.30522i) q^{7} +(2.11916 + 6.52210i) q^{8} +(0.669131 - 0.743145i) q^{9} +(9.10873 + 4.05547i) q^{10} +(1.06351 - 0.226056i) q^{11} +(-0.486869 - 4.63225i) q^{12} +(-0.249014 + 2.36921i) q^{13} +(7.82901 + 1.66411i) q^{14} +(-3.12623 - 2.27134i) q^{15} +(-6.77896 - 4.92520i) q^{16} +(1.60951 + 0.342112i) q^{17} +(-0.269711 + 2.56613i) q^{18} +(-0.0767990 - 0.730694i) q^{19} +(-17.6054 + 3.74214i) q^{20} +(-2.83380 - 1.26169i) q^{21} +(-1.87721 + 2.08485i) q^{22} +(-0.222870 - 0.685924i) q^{23} +(4.58873 + 5.09630i) q^{24} +(-4.96614 + 8.60161i) q^{25} +(-3.07343 - 5.32333i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-13.1992 + 5.87665i) q^{28} +(7.88779 - 5.73082i) q^{29} +9.97074 q^{30} +(3.03814 - 4.66580i) q^{31} +7.90522 q^{32} +(0.879620 - 0.639082i) q^{33} +(-3.87868 + 1.72690i) q^{34} +(-3.70411 + 11.4001i) q^{35} +(-2.32888 - 4.03374i) q^{36} +(1.16410 - 2.01628i) q^{37} +(1.26852 + 1.40883i) q^{38} +(0.736157 + 2.26566i) q^{39} +(17.7319 - 19.6933i) q^{40} +(3.77729 + 1.68176i) q^{41} +(7.82901 - 1.66411i) q^{42} +(0.791467 + 7.53030i) q^{43} +(0.529359 - 5.03651i) q^{44} +(-3.77979 - 0.803419i) q^{45} +(1.50554 + 1.09384i) q^{46} +(-1.30356 - 0.947094i) q^{47} +(-8.19615 - 1.74215i) q^{48} +(-0.274100 + 2.60789i) q^{49} +(-2.67885 - 25.4875i) q^{50} +(1.60951 - 0.342112i) q^{51} +(10.1367 + 4.51315i) q^{52} +(-2.07659 + 2.30629i) q^{53} +(0.797346 + 2.45398i) q^{54} +(-2.81133 - 3.12230i) q^{55} +(10.6363 - 18.4226i) q^{56} +(-0.367359 - 0.636285i) q^{57} +(-7.77400 + 23.9259i) q^{58} +(-9.44332 + 4.20444i) q^{59} +(-14.5612 + 10.5794i) q^{60} +13.5425 q^{61} +(0.734283 + 14.3475i) q^{62} -3.10198 q^{63} +(-2.94405 + 2.13898i) q^{64} +(8.40972 - 3.74425i) q^{65} +(-0.866930 + 2.66814i) q^{66} +(-1.32349 - 2.29235i) q^{67} +(3.83210 - 6.63740i) q^{68} +(-0.482593 - 0.535973i) q^{69} +(-9.55759 - 29.4152i) q^{70} +(-5.02644 + 5.58243i) q^{71} +(6.26486 + 2.78929i) q^{72} +(1.71580 - 0.364705i) q^{73} +(0.627942 + 5.97447i) q^{74} +(-1.03821 + 9.87788i) q^{75} +(-3.34737 - 0.711505i) q^{76} +(-2.72856 - 1.98242i) q^{77} +(-4.97291 - 3.61303i) q^{78} +(-10.7922 - 2.29395i) q^{79} +(-3.38457 + 32.2020i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-10.4356 + 2.21816i) q^{82} +(9.96558 + 4.43696i) q^{83} +(-9.66779 + 10.7372i) q^{84} +(-1.96488 - 6.04727i) q^{85} +(-13.0729 - 14.5190i) q^{86} +(4.87492 - 8.44362i) q^{87} +(3.72811 + 6.45728i) q^{88} +(1.89815 - 5.84191i) q^{89} +(9.10873 - 4.05547i) q^{90} +(5.97839 - 4.34356i) q^{91} -3.35929 q^{92} +(0.877732 - 5.49814i) q^{93} +4.15756 q^{94} +(-2.29690 + 1.66880i) q^{95} +(7.22178 - 3.21534i) q^{96} +(3.74552 - 11.5275i) q^{97} +(-3.38306 - 5.85963i) q^{98} +(0.543635 - 0.941604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{13}{15}\right)$

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 $

$2$	−2.08748	+	1.51664i	−1.47607	+	1.07243i	−0.497273	+	0.867594i	$0.665665\pi$
$2$	−2.08748	+	1.51664i	−1.47607	+	1.07243i	−0.978797	+	0.204834i	$0.934335\pi$
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$4$	1.43933	−	4.42980i	0.719665	−	2.21490i
$5$	−1.93212	−	3.34652i	−0.864068	−	1.49661i	−0.867969	−	0.496618i	$-0.834575\pi$
$5$	−1.93212	−	3.34652i	−0.864068	−	1.49661i	0.00390072	−	0.999992i	$-0.498758\pi$
$6$	−1.29013	+	2.23457i	−0.526694	+	0.912261i
$7$	−2.07563	−	2.30522i	−0.784513	−	0.871290i	0.209804	−	0.977743i	$-0.432717\pi$
$7$	−2.07563	−	2.30522i	−0.784513	−	0.871290i	−0.994318	+	0.106453i	$0.966051\pi$
$8$	2.11916	+	6.52210i	0.749236	+	2.30591i
$9$	0.669131	−	0.743145i	0.223044	−	0.247715i
$10$	9.10873	+	4.05547i	2.88043	+	1.28245i
$11$	1.06351	−	0.226056i	0.320661	−	0.0681585i	−0.0447693	−	0.998997i	$-0.514255\pi$
$11$	1.06351	−	0.226056i	0.320661	−	0.0681585i	0.365430	+	0.930839i	$0.380922\pi$
$12$	−0.486869	−	4.63225i	−0.140547	−	1.33722i
$13$	−0.249014	+	2.36921i	−0.0690639	+	0.657099i	0.904153	+	0.427209i	$0.140503\pi$
$13$	−0.249014	+	2.36921i	−0.0690639	+	0.657099i	−0.973217	+	0.229890i	$0.926163\pi$
$14$	7.82901	+	1.66411i	2.09239	+	0.444752i
$15$	−3.12623	−	2.27134i	−0.807189	−	0.586457i
$16$	−6.77896	−	4.92520i	−1.69474	−	1.23130i
$17$	1.60951	+	0.342112i	0.390364	+	0.0829744i	0.398912	−	0.916989i	$-0.369388\pi$
$17$	1.60951	+	0.342112i	0.390364	+	0.0829744i	−0.00854849	+	0.999963i	$0.502721\pi$
$18$	−0.269711	+	2.56613i	−0.0635715	+	0.604843i
$19$	−0.0767990	−	0.730694i	−0.0176189	−	0.167633i	0.982174	−	0.187973i	$-0.0601917\pi$
$19$	−0.0767990	−	0.730694i	−0.0176189	−	0.167633i	−0.999793	+	0.0203402i	$0.993525\pi$
$20$	−17.6054	+	3.74214i	−3.93668	+	0.836767i
$21$	−2.83380	−	1.26169i	−0.618385	−	0.275323i
$22$	−1.87721	+	2.08485i	−0.400222	+	0.444492i
$23$	−0.222870	−	0.685924i	−0.0464717	−	0.143025i	0.925128	−	0.379655i	$-0.123957\pi$
$23$	−0.222870	−	0.685924i	−0.0464717	−	0.143025i	−0.971600	+	0.236630i	$0.923957\pi$
$24$	4.58873	+	5.09630i	0.936670	+	1.04028i
$25$	−4.96614	+	8.60161i	−0.993229	+	1.72032i
$26$	−3.07343	−	5.32333i	−0.602748	−	1.04399i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−13.1992	+	5.87665i	−2.49441	+	1.11058i
$29$	7.88779	−	5.73082i	1.46473	−	1.06419i	0.482626	−	0.875826i	$-0.339683\pi$
$29$	7.88779	−	5.73082i	1.46473	−	1.06419i	0.982100	−	0.188360i	$-0.0603171\pi$
$30$	9.97074			1.82040
$31$	3.03814	−	4.66580i	0.545667	−	0.838002i
$31$	3.03814	−	4.66580i	0.545667	−	0.838002i
$32$	7.90522			1.39746
$33$	0.879620	−	0.639082i	0.153122	−	0.111250i
$34$	−3.87868	+	1.72690i	−0.665188	+	0.296161i
$35$	−3.70411	+	11.4001i	−0.626109	+	1.92697i
$36$	−2.32888	−	4.03374i	−0.388147	−	0.672291i
$37$	1.16410	−	2.01628i	0.191377	−	0.331475i	−0.754330	−	0.656496i	$-0.772038\pi$
$37$	1.16410	−	2.01628i	0.191377	−	0.331475i	0.945707	+	0.325021i	$0.105371\pi$
$38$	1.26852	+	1.40883i	0.205781	+	0.228543i
$39$	0.736157	+	2.26566i	0.117880	+	0.362796i
$40$	17.7319	−	19.6933i	2.80366	−	3.11378i
$41$	3.77729	+	1.68176i	0.589913	+	0.262646i	0.679910	−	0.733296i	$-0.262019\pi$
$41$	3.77729	+	1.68176i	0.589913	+	0.262646i	−0.0899964	+	0.995942i	$0.528686\pi$
$42$	7.82901	−	1.66411i	1.20804	−	0.256778i
$43$	0.791467	+	7.53030i	0.120698	+	1.14836i	0.872378	+	0.488833i	$0.162577\pi$
$43$	0.791467	+	7.53030i	0.120698	+	1.14836i	−0.751680	+	0.659528i	$0.770756\pi$
$44$	0.529359	−	5.03651i	0.0798038	−	0.759282i
$45$	−3.77979	−	0.803419i	−0.563458	−	0.119767i
$46$	1.50554	+	1.09384i	0.221979	+	0.161277i
$47$	−1.30356	−	0.947094i	−0.190144	−	0.138148i	0.488640	−	0.872485i	$-0.337493\pi$
$47$	−1.30356	−	0.947094i	−0.190144	−	0.138148i	−0.678785	+	0.734337i	$0.737493\pi$
$48$	−8.19615	−	1.74215i	−1.18301	−	0.251457i
$49$	−0.274100	+	2.60789i	−0.0391572	+	0.372556i
$50$	−2.67885	−	25.4875i	−0.378846	−	3.60448i
$51$	1.60951	−	0.342112i	0.225377	−	0.0479053i
$52$	10.1367	+	4.51315i	1.40571	+	0.625861i
$53$	−2.07659	+	2.30629i	−0.285241	+	0.316793i	−0.868689	−	0.495358i	$-0.835037\pi$
$53$	−2.07659	+	2.30629i	−0.285241	+	0.316793i	0.583447	+	0.812151i	$0.301703\pi$
$54$	0.797346	+	2.45398i	0.108505	+	0.333944i
$55$	−2.81133	−	3.12230i	−0.379080	−	0.421010i
$56$	10.6363	−	18.4226i	1.42133	−	2.46182i
$57$	−0.367359	−	0.636285i	−0.0486580	−	0.0842780i
$58$	−7.77400	+	23.9259i	−1.02078	+	3.14163i
$59$	−9.44332	+	4.20444i	−1.22942	+	0.547371i	−0.915591	−	0.402110i	$-0.868277\pi$
$59$	−9.44332	+	4.20444i	−1.22942	+	0.547371i	−0.313824	+	0.949481i	$0.601610\pi$
$60$	−14.5612	+	10.5794i	−1.87985	+	1.36579i
$61$	13.5425			1.73395			0.866973	−	0.498355i	$-0.166063\pi$
$61$	13.5425			1.73395			0.866973	+	0.498355i	$0.166063\pi$
$62$	0.734283	+	14.3475i	0.0932540	+	1.82214i
$63$	−3.10198			−0.390812
$64$	−2.94405	+	2.13898i	−0.368006	+	0.267372i
$65$	8.40972	−	3.74425i	1.04310	−	0.464417i
$66$	−0.866930	+	2.66814i	−0.106712	+	0.328425i
$67$	−1.32349	−	2.29235i	−0.161690	−	0.280055i	0.773785	−	0.633448i	$-0.218361\pi$
$67$	−1.32349	−	2.29235i	−0.161690	−	0.280055i	−0.935475	+	0.353393i	$0.885028\pi$
$68$	3.83210	−	6.63740i	0.464711	−	0.804903i
$69$	−0.482593	−	0.535973i	−0.0580973	−	0.0645236i
$70$	−9.55759	−	29.4152i	−1.14235	−	3.51579i
$71$	−5.02644	+	5.58243i	−0.596529	+	0.662513i	−0.963496	−	0.267721i	$-0.913729\pi$
$71$	−5.02644	+	5.58243i	−0.596529	+	0.662513i	0.366967	+	0.930234i	$0.380396\pi$
$72$	6.26486	+	2.78929i	0.738321	+	0.328722i
$73$	1.71580	−	0.364705i	0.200819	−	0.0426855i	−0.106404	−	0.994323i	$-0.533934\pi$
$73$	1.71580	−	0.364705i	0.200819	−	0.0426855i	0.307223	+	0.951638i	$0.400600\pi$
$74$	0.627942	+	5.97447i	0.0729968	+	0.694518i
$75$	−1.03821	+	9.87788i	−0.119882	+	1.14060i
$76$	−3.34737	−	0.711505i	−0.383969	−	0.0816152i
$77$	−2.72856	−	1.98242i	−0.310948	−	0.225917i
$78$	−4.97291	−	3.61303i	−0.563071	−	0.409095i
$79$	−10.7922	−	2.29395i	−1.21421	−	0.258089i	−0.444089	−	0.895983i	$-0.646473\pi$
$79$	−10.7922	−	2.29395i	−1.21421	−	0.258089i	−0.770125	+	0.637893i	$0.779806\pi$
$80$	−3.38457	+	32.2020i	−0.378406	+	3.60029i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	−10.4356	+	2.21816i	−1.15242	+	0.244955i
$83$	9.96558	+	4.43696i	1.09386	+	0.487020i	0.872720	−	0.488221i	$-0.162354\pi$
$83$	9.96558	+	4.43696i	1.09386	+	0.487020i	0.221145	+	0.975241i	$0.429021\pi$
$84$	−9.66779	+	10.7372i	−1.05484	+	1.17152i
$85$	−1.96488	−	6.04727i	−0.213121	−	0.655918i
$86$	−13.0729	−	14.5190i	−1.40969	−	1.56562i
$87$	4.87492	−	8.44362i	0.522647	−	0.905251i
$88$	3.72811	+	6.45728i	0.397418	+	0.688348i
$89$	1.89815	−	5.84191i	0.201204	−	0.619241i	−0.798644	−	0.601803i	$-0.794449\pi$
$89$	1.89815	−	5.84191i	0.201204	−	0.619241i	0.999848	−	0.0174376i	$-0.00555085\pi$
$90$	9.10873	−	4.05547i	0.960144	−	0.427484i
$91$	5.97839	−	4.34356i	0.626706	−	0.455328i
$92$	−3.35929			−0.350230
$93$	0.877732	−	5.49814i	0.0910166	−	0.570131i
$94$	4.15756			0.428820
$95$	−2.29690	+	1.66880i	−0.235657	+	0.171215i
$96$	7.22178	−	3.21534i	0.737070	−	0.328164i
$97$	3.74552	−	11.5275i	0.380300	−	1.17044i	−0.559532	−	0.828809i	$-0.689019\pi$
$97$	3.74552	−	11.5275i	0.380300	−	1.17044i	0.939833	−	0.341636i	$-0.110981\pi$
$98$	−3.38306	−	5.85963i	−0.341740	−	0.591912i
$99$	0.543635	−	0.941604i	0.0546374	−	0.0946348i
$100$	30.9555	+	34.3796i	3.09555	+	3.43796i
$101$	2.98732	+	9.19401i	0.297249	+	0.914838i	0.982457	+	0.186491i	$0.0597114\pi$
$101$	2.98732	+	9.19401i	0.297249	+	0.914838i	−0.685208	+	0.728348i	$0.740289\pi$
$102$	−2.84096	+	3.15520i	−0.281297	+	0.312412i
$103$	−5.10625	−	2.27345i	−0.503134	−	0.224010i	0.139444	−	0.990230i	$-0.455468\pi$
$103$	−5.10625	−	2.27345i	−0.503134	−	0.224010i	−0.642578	+	0.766220i	$0.722135\pi$
$104$	−15.9799	+	3.39663i	−1.56696	+	0.333067i
$105$	1.25296	+	11.9211i	0.122276	+	1.16338i
$106$	0.837025	−	7.96376i	0.0812991	−	0.773509i
$107$	4.09493	+	0.870403i	0.395871	+	0.0841451i	0.401546	−	0.915839i	$-0.368473\pi$
$107$	4.09493	+	0.870403i	0.395871	+	0.0841451i	−0.00567462	+	0.999984i	$0.501806\pi$
$108$	−3.76821	−	2.73777i	−0.362596	−	0.263442i
$109$	4.42032	+	3.21155i	0.423390	+	0.307611i	0.779000	−	0.627023i	$-0.215727\pi$
$109$	4.42032	+	3.21155i	0.423390	+	0.307611i	−0.355610	+	0.934634i	$0.615727\pi$
$110$	10.6040	+	2.25395i	1.01105	+	0.214906i
$111$	0.243363	−	2.31545i	0.0230990	−	0.219773i
$112$	2.71693	+	25.8499i	0.256726	+	2.44258i
$113$	14.3351	−	3.04703i	1.34854	−	0.286640i	0.523647	−	0.851935i	$-0.324571\pi$
$113$	14.3351	−	3.04703i	1.34854	−	0.286640i	0.824889	+	0.565295i	$0.191238\pi$
$114$	1.73187	+	0.771079i	0.162205	+	0.0722182i
$115$	−1.86485	+	2.07113i	−0.173898	+	0.193133i
$116$	−14.0332	−	43.1899i	−1.30295	−	4.01008i
$117$	1.59404	+	1.77036i	0.147369	+	0.163670i
$118$	13.3361	−	23.0988i	1.22769	−	2.12642i
$119$	−2.55210	−	4.42037i	−0.233951	−	0.405215i
$120$	8.18892	−	25.2029i	0.747543	−	2.30070i
$121$	−8.96905	+	3.99328i	−0.815368	+	0.363025i
$122$	−28.2698	+	20.5392i	−2.55942	+	1.85953i
$123$	4.13476			0.372819
$124$	−16.2957	−	20.1740i	−1.46339	−	1.81168i
$125$	19.0595			1.70473
$126$	6.47531	−	4.70459i	0.576866	−	0.419118i
$127$	−12.8112	+	5.70393i	−1.13681	+	0.506142i	−0.886824	−	0.462107i	$-0.847094\pi$
$127$	−12.8112	+	5.70393i	−1.13681	+	0.506142i	−0.249989	+	0.968249i	$0.580427\pi$
$128$	−1.98412	+	6.10649i	−0.175373	+	0.539742i
$129$	3.78589	+	6.55736i	0.333329	+	0.577343i
$130$	−11.8764	+	20.5706i	−1.04163	+	1.80416i
$131$	−9.25965	−	10.2839i	−0.809020	−	0.898507i	0.187466	−	0.982271i	$-0.439973\pi$
$131$	−9.25965	−	10.2839i	−0.809020	−	0.898507i	−0.996486	+	0.0837638i	$0.973306\pi$
$132$	−1.56494	−	4.81639i	−0.136211	−	0.419213i
$133$	−1.52500	+	1.69369i	−0.132234	+	0.146861i
$134$	6.23943	+	2.77797i	0.539005	+	0.239980i
$135$	−3.77979	+	0.803419i	−0.325312	+	0.0691473i
$136$	1.17952	+	11.2224i	0.101143	+	0.962312i
$137$	−0.591136	+	5.62428i	−0.0505041	+	0.480515i	0.939813	+	0.341690i	$0.110999\pi$
$137$	−0.591136	+	5.62428i	−0.0505041	+	0.480515i	−0.990317	+	0.138825i	$0.955667\pi$
$138$	1.82028	+	0.386913i	0.154953	+	0.0329362i
$139$	4.57543	+	3.32425i	0.388083	+	0.281959i	0.764670	−	0.644423i	$-0.222902\pi$
$139$	4.57543	+	3.32425i	0.388083	+	0.281959i	−0.376586	+	0.926382i	$0.622902\pi$
$140$	45.1686	+	32.8169i	3.81745	+	2.77354i
$141$	−1.57608	−	0.335006i	−0.132730	−	0.0282126i
$142$	2.02604	−	19.2765i	0.170022	−	1.61765i
$143$	0.270745	+	2.57597i	0.0226408	+	0.215413i
$144$	−8.19615	+	1.74215i	−0.683013	+	0.145179i
$145$	−34.4184	−	15.3241i	−2.85830	−	1.27260i
$146$	−3.02857	+	3.36357i	−0.250646	+	0.278371i
$147$	0.810321	+	2.49391i	0.0668342	+	0.205694i
$148$	−7.25620	−	8.05883i	−0.596456	−	0.662432i
$149$	−8.43564	+	14.6110i	−0.691075	+	1.19698i	0.280411	+	0.959880i	$0.409529\pi$
$149$	−8.43564	+	14.6110i	−0.691075	+	1.19698i	−0.971486	+	0.237097i	$0.923804\pi$
$150$	−12.8140	−	22.1944i	−1.04626	−	1.81217i
$151$	1.39505	−	4.29351i	0.113527	−	0.349401i	−0.878110	−	0.478459i	$-0.841195\pi$
$151$	1.39505	−	4.29351i	0.113527	−	0.349401i	0.991637	+	0.129058i	$0.0411954\pi$
$152$	4.60291	−	2.04935i	0.373345	−	0.166224i
$153$	1.33121	−	0.967182i	0.107622	−	0.0781921i
$154$	8.70243			0.701261
$155$	−21.4842	−	1.15236i	−1.72566	−	0.0925596i
$156$	11.0960			0.888390
$157$	6.36232	−	4.62249i	0.507768	−	0.368915i	−0.304208	−	0.952606i	$-0.598392\pi$
$157$	6.36232	−	4.62249i	0.507768	−	0.368915i	0.811976	+	0.583690i	$0.198392\pi$
$158$	26.0075	−	11.5793i	2.06905	−	0.921199i
$159$	−0.959007	+	2.95152i	−0.0760542	+	0.234071i
$160$	−15.2738	−	26.4550i	−1.20750	−	2.09145i
$161$	−1.11861	+	1.93749i	−0.0881587	+	0.152695i
$162$	1.72653	+	1.91751i	0.135649	+	0.150654i
$163$	4.02379	+	12.3839i	0.315167	+	0.969986i	0.975685	+	0.219175i	$0.0703367\pi$
$163$	4.02379	+	12.3839i	0.315167	+	0.969986i	−0.660518	+	0.750810i	$0.729663\pi$
$164$	12.8866	−	14.3120i	1.00628	−	1.11758i
$165$	−3.83823	−	1.70889i	−0.298806	−	0.133037i
$166$	−27.5322	+	5.85215i	−2.13691	+	0.454215i
$167$	−2.22382	−	21.1583i	−0.172085	−	1.63728i	−0.650760	−	0.759284i	$-0.725549\pi$
$167$	−2.22382	−	21.1583i	−0.172085	−	1.63728i	0.478675	−	0.877992i	$-0.341117\pi$
$168$	2.22359	−	21.1560i	0.171553	−	1.63222i
$169$	7.16479	+	1.52292i	0.551138	+	0.117148i
$170$	13.2732	+	9.64352i	1.01801	+	0.739625i
$171$	−0.594400	−	0.431857i	−0.0454549	−	0.0330249i
$172$	34.4969	+	7.33255i	2.63037	+	0.559101i
$173$	1.32757	−	12.6309i	0.100933	−	0.960313i	−0.820466	−	0.571695i	$-0.806286\pi$
$173$	1.32757	−	12.6309i	0.100933	−	0.960313i	0.921399	−	0.388618i	$-0.127047\pi$
$174$	2.62964	+	25.0194i	0.199353	+	1.89671i
$175$	30.1364	−	6.40570i	2.27810	−	0.484225i
$176$	−8.32287	−	3.70558i	−0.627360	−	0.279319i
$177$	−6.91680	+	7.68189i	−0.519899	+	0.577406i
$178$	4.89773	+	15.0737i	0.367100	+	1.12982i
$179$	10.2337	+	11.3656i	0.764900	+	0.849507i	0.992244	−	0.124307i	$-0.0396709\pi$
$179$	10.2337	+	11.3656i	0.764900	+	0.849507i	−0.227344	+	0.973814i	$0.573004\pi$
$180$	−8.99934	+	15.5873i	−0.670772	+	1.16181i
$181$	8.52389	+	14.7638i	0.633576	+	1.09739i	0.986815	+	0.161853i	$0.0517469\pi$
$181$	8.52389	+	14.7638i	0.633576	+	1.09739i	−0.353239	+	0.935533i	$0.614920\pi$
$182$	−5.89215	+	18.1342i	−0.436755	+	1.34419i
$183$	12.3717	−	5.50825i	0.914545	−	0.407182i
$184$	4.00137	−	2.90716i	0.294985	−	0.214319i
$185$	−8.99671			−0.661451
$186$	6.50647	+	12.8085i	0.477077	+	0.939162i
$187$	1.78907			0.130830
$188$	−6.07169	+	4.41134i	−0.442823	+	0.321730i
$189$	−2.83380	+	1.26169i	−0.206128	+	0.0917742i
$190$	2.26376	−	6.96715i	0.164231	−	0.505450i
$191$	4.80846	+	8.32850i	0.347928	+	0.602629i	0.985881	−	0.167446i	$-0.0535520\pi$
$191$	4.80846	+	8.32850i	0.347928	+	0.602629i	−0.637953	+	0.770075i	$0.720219\pi$
$192$	−1.81952	+	3.15150i	−0.131313	+	0.227440i
$193$	6.62768	+	7.36079i	0.477071	+	0.529841i	0.932856	−	0.360249i	$-0.117308\pi$
$193$	6.62768	+	7.36079i	0.477071	+	0.529841i	−0.455785	+	0.890090i	$0.650642\pi$
$194$	9.66444	+	29.7441i	0.693867	+	2.13550i
$195$	6.15974	−	6.84108i	0.441108	−	0.489900i
$196$	11.1579	+	4.96782i	0.796994	+	0.354844i
$197$	−22.0638	+	4.68980i	−1.57198	+	0.334134i	−0.909747	−	0.415164i	$-0.863724\pi$
$197$	−22.0638	+	4.68980i	−1.57198	+	0.334134i	−0.662232	+	0.749298i	$0.730391\pi$
$198$	0.293249	+	2.79008i	0.0208403	+	0.198282i
$199$	0.832137	−	7.91725i	0.0589886	−	0.561239i	−0.924616	−	0.380901i	$-0.875614\pi$
$199$	0.832137	−	7.91725i	0.0589886	−	0.561239i	0.983605	−	0.180339i	$-0.0577194\pi$
$200$	−66.6246	−	14.1615i	−4.71107	−	1.00137i
$201$	−2.14145	−	1.55586i	−0.151046	−	0.109742i
$202$	−20.1800	−	14.6616i	−1.41986	−	1.03159i
$203$	−29.5829	−	6.28804i	−2.07631	−	0.441334i
$204$	0.801128	−	7.62222i	0.0560902	−	0.533662i
$205$	−1.67012	−	15.8901i	−0.116646	−	1.10982i
$206$	14.1072	−	2.99858i	0.982895	−	0.208921i
$207$	−0.658870	−	0.293348i	−0.0457946	−	0.0203891i
$208$	13.3569	−	14.8343i	0.926132	−	1.02857i
$209$	−0.246855	−	0.759740i	−0.0170753	−	0.0525523i
$210$	−20.6955	−	22.9847i	−1.42813	−	1.58610i
$211$	−3.67864	+	6.37160i	−0.253248	+	0.438639i	−0.964418	−	0.264381i	$-0.914832\pi$
$211$	−3.67864	+	6.37160i	−0.253248	+	0.438639i	0.711170	+	0.703020i	$0.248166\pi$
$212$	7.22749	+	12.5184i	0.496386	+	0.859766i
$213$	−2.32130	+	7.14424i	−0.159053	+	0.489515i
$214$	−9.86816	+	4.39359i	−0.674573	+	0.300339i
$215$	23.6711	−	17.1981i	1.61436	−	1.17290i
$216$	6.85774			0.466610
$217$	−17.0617	+	2.68087i	−1.15823	+	0.181990i
$218$	−14.0981			−0.954844
$219$	1.41912	−	1.03105i	0.0958956	−	0.0696722i
$220$	−17.8776	+	7.95961i	−1.20531	+	0.536637i
$221$	−1.21132	+	3.72807i	−0.0814825	+	0.250777i
$222$	3.00369	+	5.20254i	0.201594	+	0.349172i
$223$	11.7266	−	20.3111i	0.785271	−	1.36013i	−0.143566	−	0.989641i	$-0.545857\pi$
$223$	11.7266	−	20.3111i	0.785271	−	1.36013i	0.928837	−	0.370489i	$-0.120810\pi$
$224$	−16.4083	−	18.2232i	−1.09632	−	1.21759i
$225$	3.06925	+	9.44617i	0.204616	+	0.629744i
$226$	−25.3030	+	28.1019i	−1.68313	+	1.86931i
$227$	2.64310	+	1.17678i	0.175429	+	0.0781059i	0.492572	−	0.870272i	$-0.336057\pi$
$227$	2.64310	+	1.17678i	0.175429	+	0.0781059i	−0.317143	+	0.948378i	$0.602724\pi$
$228$	−3.34737	+	0.711505i	−0.221685	+	0.0471206i
$229$	−0.632597	−	6.01876i	−0.0418032	−	0.397731i	−0.995338	−	0.0964479i	$-0.969252\pi$
$229$	−0.632597	−	6.01876i	−0.0418032	−	0.397731i	0.953535	−	0.301283i	$-0.0974148\pi$
$230$	0.751678	−	7.15174i	0.0495642	−	0.471572i
$231$	−3.29899	−	0.701221i	−0.217057	−	0.0461370i
$232$	54.0925	+	39.3005i	3.55134	+	2.58020i
$233$	−18.9279	−	13.7519i	−1.24001	−	0.900917i	−0.242407	−	0.970175i	$-0.577937\pi$
$233$	−18.9279	−	13.7519i	−1.24001	−	0.900917i	−0.997599	+	0.0692572i	$0.977937\pi$
$234$	−6.01253	−	1.27800i	−0.393051	−	0.0835456i
$235$	−0.650836	+	6.19230i	−0.0424559	+	0.403941i
$236$	5.03277	+	47.8836i	0.327605	+	3.11696i
$237$	−10.7922	+	2.29395i	−0.701027	+	0.149008i
$238$	12.0316	+	5.35680i	0.779891	+	0.347230i
$239$	−6.93759	+	7.70498i	−0.448755	+	0.498393i	−0.924496	−	0.381192i	$-0.875514\pi$
$239$	−6.93759	+	7.70498i	−0.448755	+	0.498393i	0.475740	+	0.879586i	$0.342180\pi$
$240$	10.0058	+	30.7946i	0.645870	+	1.98778i
$241$	5.54025	+	6.15307i	0.356879	+	0.396354i	0.894673	−	0.446722i	$-0.147409\pi$
$241$	5.54025	+	6.15307i	0.356879	+	0.396354i	−0.537794	+	0.843076i	$0.680742\pi$
$242$	12.6663	−	21.9387i	0.814222	−	1.41027i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	19.4922	−	59.9908i	1.24786	−	3.84052i
$245$	9.25696	−	4.12146i	0.591405	−	0.263311i
$246$	−8.63122	+	6.27095i	−0.550306	+	0.399821i
$247$	1.75029			0.111368
$248$	36.8691	+	9.92752i	2.34119	+	0.630398i
$249$	10.9087			0.691310
$250$	−39.7863	+	28.9064i	−2.51631	+	1.82820i
$251$	−6.31041	+	2.80958i	−0.398310	+	0.177339i	−0.596109	−	0.802904i	$-0.703287\pi$
$251$	−6.31041	+	2.80958i	−0.398310	+	0.177339i	0.197799	+	0.980243i	$0.436621\pi$
$252$	−4.46476	+	13.7411i	−0.281254	+	0.865610i
$253$	−0.392082	−	0.679107i	−0.0246500	−	0.0426951i
$254$	18.0924	−	31.3369i	1.13522	−	1.96625i
$255$	−4.25465	−	4.72527i	−0.266436	−	0.295908i
$256$	−7.36860	−	22.6782i	−0.460538	−	1.41739i
$257$	16.5146	−	18.3413i	1.03015	−	1.14410i	0.0407094	−	0.999171i	$-0.487038\pi$
$257$	16.5146	−	18.3413i	1.03015	−	1.14410i	0.989442	−	0.144928i	$-0.0462951\pi$
$258$	−17.8481	−	7.94650i	−1.11118	−	0.494727i
$259$	−7.06421	+	1.50154i	−0.438949	+	0.0933014i
$260$	−4.48192	−	42.6426i	−0.277957	−	2.64458i
$261$	1.01914	−	9.69644i	0.0630830	−	0.600194i
$262$	34.9263	+	7.42381i	2.15775	+	0.458645i
$263$	19.0727	+	13.8571i	1.17607	+	0.854467i	0.991723	−	0.128394i	$-0.0409823\pi$
$263$	19.0727	+	13.8571i	1.17607	+	0.854467i	0.184349	+	0.982861i	$0.440982\pi$
$264$	6.03221	+	4.38266i	0.371257	+	0.269734i
$265$	11.7302	+	2.49334i	0.720583	+	0.153165i
$266$	0.614693	−	5.84842i	0.0376893	−	0.358589i
$267$	−0.642071	−	6.10889i	−0.0392941	−	0.373858i
$268$	−12.0596	+	2.56335i	−0.736657	+	0.156581i
$269$	0.864697	+	0.384988i	0.0527215	+	0.0234731i	0.432928	−	0.901428i	$-0.357480\pi$
$269$	0.864697	+	0.384988i	0.0527215	+	0.0234731i	−0.380207	+	0.924902i	$0.624147\pi$
$270$	6.67173	−	7.40970i	0.406028	−	0.450940i
$271$	9.65333	+	29.7099i	0.586398	+	1.80475i	0.593582	+	0.804774i	$0.297713\pi$
$271$	9.65333	+	29.7099i	0.586398	+	1.80475i	−0.00718389	+	0.999974i	$0.502287\pi$
$272$	−9.22584	−	10.2463i	−0.559399	−	0.621275i
$273$	3.69485	−	6.39967i	0.223622	−	0.387326i
$274$	−7.29604	−	12.6371i	−0.440770	−	0.763436i
$275$	−3.33710	+	10.2705i	−0.201235	+	0.619337i
$276$	−3.06886	+	1.36635i	−0.184724	+	0.0822444i
$277$	−22.3794	+	16.2596i	−1.34465	+	0.976942i	−0.345387	+	0.938460i	$0.612252\pi$
$277$	−22.3794	+	16.2596i	−1.34465	+	0.976942i	−0.999259	+	0.0384820i	$0.987748\pi$
$278$	−14.5928			−0.875219
$279$	−1.43445	−	5.37981i	−0.0858782	−	0.322081i
$280$	−82.2021			−4.91251
$281$	6.69071	−	4.86109i	0.399134	−	0.289988i	−0.370054	−	0.929010i	$-0.620661\pi$
$281$	6.69071	−	4.86109i	0.399134	−	0.289988i	0.769188	+	0.639022i	$0.220661\pi$
$282$	3.79812	−	1.69103i	0.226175	−	0.100699i
$283$	0.254844	−	0.784328i	0.0151489	−	0.0466234i	−0.943196	−	0.332236i	$-0.892197\pi$
$283$	0.254844	−	0.784328i	0.0151489	−	0.0466234i	0.958345	+	0.285612i	$0.0921970\pi$
$284$	17.4943	+	30.3011i	1.03810	+	1.79804i
$285$	−1.41956	+	2.45875i	−0.0840876	+	0.145644i
$286$	−4.47199	−	4.96665i	−0.264435	−	0.293684i
$287$	−3.96343	−	12.1982i	−0.233954	−	0.720035i
$288$	5.28962	−	5.87472i	0.311694	−	0.346171i
$289$	−13.0568	−	5.81326i	−0.768046	−	0.341956i
$290$	95.0889	−	20.2118i	5.58381	−	1.18688i
$291$	−1.26697	−	12.0544i	−0.0742708	−	0.706640i
$292$	0.854034	−	8.12559i	0.0499786	−	0.475514i
$293$	3.44829	+	0.732958i	0.201452	+	0.0428198i	0.307532	−	0.951538i	$-0.400497\pi$
$293$	3.44829	+	0.732958i	0.201452	+	0.0428198i	−0.106081	+	0.994358i	$0.533830\pi$
$294$	−5.47390	−	3.97702i	−0.319244	−	0.231945i
$295$	32.3158	+	23.4788i	1.88150	+	1.36699i
$296$	15.6173	+	3.31956i	0.907738	+	0.192946i
$297$	0.113651	−	1.08131i	0.00659468	−	0.0627442i
$298$	−4.55037	−	43.2939i	−0.263596	−	2.50795i
$299$	1.68059	−	0.357221i	0.0971912	−	0.0206586i
$300$	42.2627	+	18.8166i	2.44004	+	1.08637i
$301$	15.7162	−	17.4546i	0.905867	−	1.00607i
$302$	3.59959	+	11.0784i	0.207133	+	0.637490i
$303$	6.46859	+	7.18410i	0.371611	+	0.412716i
$304$	−3.07820	+	5.33160i	−0.176547	+	0.305788i
$305$	−26.1658	−	45.3204i	−1.49825	−	2.59504i
$306$	−1.31201	+	4.03794i	−0.0750025	+	0.230834i
$307$	−8.13923	+	3.62382i	−0.464530	+	0.206822i	−0.625636	−	0.780115i	$-0.715161\pi$
$307$	−8.13923	+	3.62382i	−0.464530	+	0.206822i	0.161106	+	0.986937i	$0.448494\pi$
$308$	−12.7090	+	9.23363i	−0.724163	+	0.526135i
$309$	−5.58949			−0.317975
$310$	46.5956	−	30.1784i	2.64645	−	1.71402i
$311$	−26.1174			−1.48098			−0.740491	−	0.672066i	$-0.765407\pi$
$311$	−26.1174			−1.48098			−0.740491	+	0.672066i	$0.765407\pi$
$312$	−13.2168	+	9.60259i	−0.748255	+	0.543639i
$313$	−4.63794	+	2.06494i	−0.262152	+	0.116717i	−0.533604	−	0.845734i	$-0.679163\pi$
$313$	−4.63794	+	2.06494i	−0.262152	+	0.116717i	0.271452	+	0.962452i	$0.412496\pi$
$314$	−6.27053	+	19.2987i	−0.353867	+	1.08909i
$315$	5.99338	+	10.3808i	0.337689	+	0.584894i
$316$	−25.6952	+	44.5054i	−1.44547	+	2.50362i
$317$	3.73508	+	4.14823i	0.209783	+	0.232988i	0.838849	−	0.544364i	$-0.183229\pi$
$317$	3.73508	+	4.14823i	0.209783	+	0.232988i	−0.629066	+	0.777352i	$0.716562\pi$
$318$	−2.47449	−	7.61571i	−0.138763	−	0.427068i
$319$	7.09327	−	7.87787i	0.397147	−	0.441076i
$320$	12.8464	+	5.71957i	0.718134	+	0.319734i
$321$	4.09493	−	0.870403i	0.228556	−	0.0485812i
$322$	−0.603402	−	5.74099i	−0.0336263	−	0.319933i
$323$	0.126370	−	1.20233i	0.00703144	−	0.0668997i
$324$	−4.55598	−	0.968404i	−0.253110	−	0.0538002i
$325$	−19.1423	−	13.9077i	−1.06183	−	0.771462i
$326$	−27.1816	−	19.7486i	−1.50545	−	1.09377i
$327$	5.34442	+	1.13599i	0.295547	+	0.0628205i
$328$	−2.96392	+	28.1998i	−0.163655	+	1.55707i
$329$	0.522453	+	4.97081i	0.0288038	+	0.274049i
$330$	10.6040	−	2.25395i	0.583731	−	0.124076i
$331$	−3.37335	−	1.50191i	−0.185416	−	0.0825527i	0.311929	−	0.950106i	$-0.399025\pi$
$331$	−3.37335	−	1.50191i	−0.185416	−	0.0825527i	−0.497345	+	0.867553i	$0.665692\pi$
$332$	33.9986	−	37.7593i	1.86592	−	2.07231i
$333$	−0.719454	−	2.21425i	−0.0394258	−	0.121340i
$334$	36.7317	+	40.7947i	2.00987	+	2.23219i
$335$	−5.11427	+	8.85818i	−0.279422	+	0.483974i
$336$	12.9961	+	22.5100i	0.708997	+	1.22802i
$337$	−10.1823	+	31.3380i	−0.554668	+	1.70709i	0.142151	+	0.989845i	$0.454598\pi$
$337$	−10.1823	+	31.3380i	−0.554668	+	1.70709i	−0.696819	+	0.717247i	$0.745402\pi$
$338$	−17.2661	+	7.68735i	−0.939151	+	0.418137i
$339$	11.8565	−	8.61422i	0.643955	−	0.467860i
$340$	−29.6163			−1.60617
$341$	2.17637	−	5.64892i	0.117857	−	0.305906i
$342$	1.89577			0.102511
$343$	−10.9862	+	7.98192i	−0.593198	+	0.430983i
$344$	−47.4362	+	21.1199i	−2.55759	+	1.13871i
$345$	−0.861222	+	2.65057i	−0.0463666	+	0.142702i
$346$	16.3853	+	28.3803i	0.880882	+	1.52573i
$347$	3.85451	−	6.67621i	0.206921	−	0.358398i	−0.743822	−	0.668378i	$-0.766989\pi$
$347$	3.85451	−	6.67621i	0.206921	−	0.358398i	0.950743	+	0.309980i	$0.100322\pi$
$348$	−30.3869	−	33.7481i	−1.62891	−	1.80909i
$349$	7.90757	+	24.3370i	0.423283	+	1.30273i	0.904629	+	0.426199i	$0.140148\pi$
$349$	7.90757	+	24.3370i	0.423283	+	1.30273i	−0.481347	+	0.876530i	$0.659852\pi$
$350$	−53.1940	+	59.0779i	−2.84334	+	3.15785i
$351$	2.17630	+	0.968951i	0.116162	+	0.0517188i
$352$	8.40729	−	1.78702i	0.448110	−	0.0952487i
$353$	0.834879	+	7.94335i	0.0444362	+	0.422782i	0.994014	+	0.109251i	$0.0348452\pi$
$353$	0.834879	+	7.94335i	0.0444362	+	0.422782i	−0.949578	+	0.313531i	$0.898488\pi$
$354$	2.78800	−	26.5261i	0.148181	−	1.40985i
$355$	28.3934	+	6.03520i	1.50697	+	0.320315i
$356$	−23.1464	−	16.8169i	−1.22676	−	0.891291i
$357$	−4.12939	−	3.00018i	−0.218550	−	0.158786i
$358$	−38.6001	−	8.20471i	−2.04008	−	0.433632i
$359$	−0.493090	+	4.69143i	−0.0260243	+	0.247604i	0.973774	+	0.227518i	$0.0730609\pi$
$359$	−0.493090	+	4.69143i	−0.0260243	+	0.247604i	−0.999798	+	0.0200868i	$0.993606\pi$
$360$	−2.76999	−	26.3547i	−0.145992	−	1.38902i
$361$	18.0568	−	3.83809i	0.950357	−	0.202005i
$362$	−40.1849	−	17.8915i	−2.11207	−	0.940354i
$363$	−6.56942	+	7.29608i	−0.344805	+	0.382945i
$364$	−10.6362	−	32.7349i	−0.557489	−	1.71577i
$365$	−4.53562	−	5.03732i	−0.237405	−	0.263665i
$366$	−17.4717	+	30.2618i	−0.913259	+	1.58181i
$367$	−12.2456	−	21.2100i	−0.639217	−	1.10716i	−0.985605	−	0.169064i	$-0.945925\pi$
$367$	−12.2456	−	21.2100i	−0.639217	−	1.10716i	0.346389	−	0.938091i	$-0.387408\pi$
$368$	−1.86749	+	5.74753i	−0.0973495	+	0.299611i
$369$	3.77729	−	1.68176i	0.196638	−	0.0875488i
$370$	18.7804	−	13.6448i	0.976349	−	0.709359i
$371$	9.62671			0.499794
$372$	−23.0923	−	11.8018i	−1.19728	−	0.611896i
$373$	1.58686			0.0821647			0.0410824	−	0.999156i	$-0.486919\pi$
$373$	1.58686			0.0821647			0.0410824	+	0.999156i	$0.486919\pi$
$374$	−3.73464	+	2.71338i	−0.193114	+	0.140305i
$375$	17.4117	−	7.75220i	0.899137	−	0.400322i
$376$	3.41458	−	10.5090i	0.176094	−	0.541961i
$377$	11.6133	+	20.1149i	0.598116	+	1.03597i
$378$	4.00196	−	6.93160i	0.205839	−	0.356523i
$379$	5.13571	+	5.70379i	0.263804	+	0.292984i	0.860465	−	0.509509i	$-0.170173\pi$
$379$	5.13571	+	5.70379i	0.263804	+	0.292984i	−0.596661	+	0.802493i	$0.703506\pi$
$380$	4.08643	+	12.5768i	0.209630	+	0.645174i
$381$	−9.38365	+	10.4216i	−0.480739	+	0.533915i
$382$	−22.6689	−	10.0928i	−1.15984	−	0.516395i
$383$	11.4719	−	2.43842i	0.586185	−	0.124598i	0.0947341	−	0.995503i	$-0.469800\pi$
$383$	11.4719	−	2.43842i	0.586185	−	0.124598i	0.491451	+	0.870905i	$0.336467\pi$
$384$	0.671150	+	6.38557i	0.0342495	+	0.325862i
$385$	−1.36230	+	12.9614i	−0.0694294	+	0.660577i
$386$	−24.9988	−	5.31366i	−1.27241	−	0.270458i
$387$	6.12570	+	4.45058i	0.311387	+	0.226236i
$388$	−45.6736	−	33.1838i	−2.31873	−	1.68465i
$389$	4.50941	+	0.958505i	0.228636	+	0.0485981i	0.320805	−	0.947145i	$-0.396047\pi$
$389$	4.50941	+	0.958505i	0.228636	+	0.0485981i	−0.0921688	+	0.995743i	$0.529380\pi$
$390$	−2.48285	+	23.6227i	−0.125724	+	1.19618i
$391$	−0.124049	−	1.18025i	−0.00627344	−	0.0596878i
$392$	−17.5898	+	3.73882i	−0.888418	+	0.188839i
$393$	−12.6419	−	5.62856i	−0.637702	−	0.283923i
$394$	38.9449	−	43.2527i	1.96202	−	2.17904i
$395$	13.1750	+	40.5484i	0.662905	+	2.04021i
$396$	−3.38865	−	3.76347i	−0.170286	−	0.189122i
$397$	−16.0539	+	27.8062i	−0.805723	+	1.39555i	0.110079	+	0.993923i	$0.464890\pi$
$397$	−16.0539	+	27.8062i	−0.805723	+	1.39555i	−0.915802	+	0.401630i	$0.868444\pi$
$398$	10.2706	+	17.7891i	0.514817	+	0.891689i
$399$	−0.704275	+	2.16753i	−0.0352578	+	0.108512i
$400$	76.0300	−	33.8507i	3.80150	−	1.69254i
$401$	−1.99995	+	1.45305i	−0.0998725	+	0.0725616i	−0.636601	−	0.771194i	$-0.719660\pi$
$401$	−1.99995	+	1.45305i	−0.0998725	+	0.0725616i	0.536728	+	0.843755i	$0.319660\pi$
$402$	6.82991			0.340645
$403$	10.2977	+	8.35984i	0.512965	+	0.416433i
$404$	45.0274			2.24019
$405$	−3.12623	+	2.27134i	−0.155344	+	0.112864i
$406$	71.2904	−	31.7405i	3.53808	−	1.57526i
$407$	0.782241	−	2.40749i	0.0387743	−	0.119335i
$408$	5.64210	+	9.77240i	0.279326	+	0.483806i
$409$	−10.1579	+	17.5939i	−0.502274	+	0.869965i	0.497722	+	0.867336i	$0.334170\pi$
$409$	−10.1579	+	17.5939i	−0.502274	+	0.869965i	−0.999997	+	0.00262811i	$0.999163\pi$
$410$	27.5860	+	30.6373i	1.36237	+	1.51307i
$411$	1.74757	+	5.37847i	0.0862014	+	0.265301i
$412$	−17.4205	+	19.3474i	−0.858246	+	0.953179i
$413$	29.2929	+	13.0421i	1.44141	+	0.641758i
$414$	1.82028	−	0.386913i	0.0894619	−	0.0190157i
$415$	−4.40626	−	41.9228i	−0.216295	−	2.05791i
$416$	−1.96851	+	18.7291i	−0.0965140	+	0.918269i
$417$	5.53196	+	1.17585i	0.270901	+	0.0575818i
$418$	1.66756	+	1.21155i	0.0815629	+	0.0592589i
$419$	11.4035	+	8.28511i	0.557096	+	0.404754i	0.830395	−	0.557175i	$-0.188115\pi$
$419$	11.4035	+	8.28511i	0.557096	+	0.404754i	−0.273299	+	0.961929i	$0.588115\pi$
$420$	54.6115	+	11.6080i	2.66477	+	0.566413i
$421$	0.806922	−	7.67735i	0.0393270	−	0.374171i	−0.957103	−	0.289748i	$-0.906429\pi$
$421$	0.806922	−	7.67735i	0.0393270	−	0.374171i	0.996430	−	0.0844233i	$-0.0269048\pi$
$422$	−1.98434	−	18.8797i	−0.0965962	−	0.919052i
$423$	−1.57608	+	0.335006i	−0.0766317	+	0.0162886i
$424$	−19.4424	−	8.65633i	−0.944209	−	0.420389i
$425$	−10.9358	+	12.1454i	−0.530463	+	0.589139i
$426$	−5.98958	−	18.4340i	−0.290196	−	0.893132i
$427$	−28.1093	−	31.2185i	−1.36030	−	1.51077i
$428$	9.74966	−	16.8869i	0.471268	−	0.816259i
$429$	1.29508	+	2.24314i	0.0625270	+	0.108300i
$430$	−23.3296	+	71.8012i	−1.12505	+	3.46256i
$431$	23.9510	−	10.6637i	1.15368	−	0.513652i	0.261444	−	0.965219i	$-0.415801\pi$
$431$	23.9510	−	10.6637i	1.15368	−	0.513652i	0.892237	+	0.451567i	$0.149135\pi$
$432$	−6.77896	+	4.92520i	−0.326153	+	0.236964i
$433$	22.6643			1.08918			0.544589	−	0.838703i	$-0.316685\pi$
$433$	22.6643			1.08918			0.544589	+	0.838703i	$0.316685\pi$
$434$	31.5501	−	31.4728i	1.51445	−	1.51074i
$435$	−37.6757			−1.80641
$436$	20.5888	−	14.9587i	0.986027	−	0.716390i
$437$	−0.484084	+	0.215528i	−0.0231569	+	0.0103101i
$438$	−1.39865	+	4.30461i	−0.0668302	+	0.205682i
$439$	−11.0343	−	19.1119i	−0.526636	−	0.912161i	−0.999518	−	0.0310352i	$-0.990120\pi$
$439$	−11.0343	−	19.1119i	−0.526636	−	0.912161i	0.472882	−	0.881126i	$-0.343214\pi$
$440$	14.4063	−	24.9524i	0.686793	−	1.18956i
$441$	1.75463	+	1.94872i	0.0835539	+	0.0927960i
$442$	−3.12554	−	9.61941i	−0.148667	−	0.457549i
$443$	−2.84672	+	3.16160i	−0.135252	+	0.150212i	−0.806966	−	0.590598i	$-0.798892\pi$
$443$	−2.84672	+	3.16160i	−0.135252	+	0.150212i	0.671714	+	0.740811i	$0.265558\pi$
$444$	−9.90669	−	4.41074i	−0.470151	−	0.209325i
$445$	−23.2175	+	4.93504i	−1.10062	+	0.233943i
$446$	6.32559	+	60.1839i	0.299525	+	2.84979i
$447$	−1.76353	+	16.7789i	−0.0834121	+	0.793613i
$448$	11.0416	+	2.34695i	0.521664	+	0.110883i
$449$	−25.7852	−	18.7340i	−1.21688	−	0.884113i	−0.221040	−	0.975265i	$-0.570945\pi$
$449$	−25.7852	−	18.7340i	−1.21688	−	0.884113i	−0.995837	+	0.0911522i	$0.970945\pi$
$450$	−20.7334	−	15.0637i	−0.977383	−	0.710110i
$451$	4.39736	+	0.934688i	0.207064	+	0.0440127i
$452$	7.13526	−	67.8874i	0.335614	−	3.19316i
$453$	−0.471890	−	4.48974i	−0.0221713	−	0.210946i
$454$	−7.30217	+	1.55212i	−0.342708	+	0.0728448i
$455$	−26.0868	−	11.6146i	−1.22297	−	0.544500i
$456$	3.37142	−	3.74435i	0.157881	−	0.175345i
$457$	−2.55831	−	7.87366i	−0.119673	−	0.368314i	0.873220	−	0.487326i	$-0.162028\pi$
$457$	−2.55831	−	7.87366i	−0.119673	−	0.368314i	−0.992893	+	0.119011i	$0.962028\pi$
$458$	10.4488	+	11.6046i	0.488242	+	0.542247i
$459$	0.822734	−	1.42502i	0.0384020	−	0.0665141i
$460$	6.49054	+	11.2419i	0.302623	+	0.524158i
$461$	−3.47956	+	10.7090i	−0.162059	+	0.498767i	−0.998808	−	0.0488209i	$-0.984454\pi$
$461$	−3.47956	+	10.7090i	−0.162059	+	0.498767i	0.836748	+	0.547587i	$0.184454\pi$
$462$	7.95006	−	3.53960i	0.369870	−	0.164677i
$463$	16.5630	−	12.0337i	0.769746	−	0.559253i	−0.132138	−	0.991231i	$-0.542184\pi$
$463$	16.5630	−	12.0337i	0.769746	−	0.559253i	0.901884	+	0.431978i	$0.142184\pi$
$464$	−81.6965			−3.79266
$465$	−20.0955	+	7.68570i	−0.931909	+	0.356416i
$466$	60.3682			2.79650
$467$	19.3637	−	14.0685i	0.896045	−	0.651015i	−0.0414023	−	0.999143i	$-0.513183\pi$
$467$	19.3637	−	14.0685i	0.896045	−	0.651015i	0.937447	+	0.348128i	$0.113183\pi$
$468$	10.1367	−	4.51315i	0.468569	−	0.208620i
$469$	−2.53730	+	7.80900i	−0.117162	+	0.360586i
$470$	−8.03289	−	13.9134i	−0.370529	−	0.641776i
$471$	3.93213	−	6.81065i	0.181183	−	0.313818i
$472$	−47.4336	−	52.6804i	−2.18331	−	2.42481i
$473$	2.54401	+	7.82965i	0.116974	+	0.360007i
$474$	19.0493	−	21.1564i	0.874964	−	0.971746i
$475$	6.66654	+	2.96814i	0.305882	+	0.136187i
$476$	−23.2547	+	4.94293i	−1.06588	+	0.226559i
$477$	0.324395	+	3.08641i	0.0148530	+	0.141317i
$478$	2.79638	−	26.6058i	0.127904	−	1.21692i
$479$	−16.4014	−	3.48622i	−0.749399	−	0.159290i	−0.182647	−	0.983178i	$-0.558467\pi$
$479$	−16.4014	−	3.48622i	−0.749399	−	0.159290i	−0.566751	+	0.823889i	$0.691800\pi$
$480$	−24.7135	−	17.9554i	−1.12801	−	0.819549i
$481$	4.48711	+	3.26008i	0.204595	+	0.148647i
$482$	−20.8972	−	4.44183i	−0.951839	−	0.202320i
$483$	−0.233853	+	2.22496i	−0.0106407	+	0.101239i
$484$	4.78001	+	45.4787i	0.217273	+	2.06721i
$485$	−45.8140	+	9.73806i	−2.08030	+	0.442182i
$486$	2.35719	+	1.04949i	0.106924	+	0.0476058i
$487$	−2.46520	+	2.73788i	−0.111709	+	0.124065i	−0.796406	−	0.604763i	$-0.793268\pi$
$487$	−2.46520	+	2.73788i	−0.111709	+	0.124065i	0.684697	+	0.728828i	$0.259935\pi$
$488$	28.6988	+	88.3259i	1.29913	+	3.99832i
$489$	8.71292	+	9.67668i	0.394012	+	0.437594i
$490$	−13.0729	+	22.6430i	−0.590574	+	1.02290i
$491$	1.93176	+	3.34591i	0.0871791	+	0.150999i	0.906318	−	0.422597i	$-0.138881\pi$
$491$	1.93176	+	3.34591i	0.0871791	+	0.150999i	−0.819139	+	0.573596i	$0.805548\pi$
$492$	5.95128	−	18.3161i	0.268304	−	0.825756i
$493$	14.6561	−	6.52531i	0.660077	−	0.293885i
$494$	−3.65369	+	2.65456i	−0.164387	+	0.119434i
$495$	−4.20147			−0.188842
$496$	−43.5755	+	16.6658i	−1.95660	+	0.748316i
$497$	23.3017			1.04523
$498$	−22.7717	+	16.5446i	−1.02042	+	0.741380i
$499$	−24.9120	+	11.0915i	−1.11522	+	0.496526i	−0.879788	−	0.475366i	$-0.842316\pi$
$499$	−24.9120	+	11.0915i	−1.11522	+	0.496526i	−0.235427	+	0.971892i	$0.575649\pi$
$500$	27.4329	−	84.4297i	1.22684	−	3.77581i
$501$	−10.6374	−	18.4245i	−0.475244	−	0.823147i
$502$	8.91173	−	15.4356i	0.397750	−	0.688923i
$503$	−6.93122	−	7.69790i	−0.309048	−	0.343232i	0.568534	−	0.822660i	$-0.307511\pi$
$503$	−6.93122	−	7.69790i	−0.309048	−	0.343232i	−0.877581	+	0.479428i	$0.840844\pi$
$504$	−6.57358	−	20.2314i	−0.292811	−	0.901178i
$505$	24.9961	−	27.7610i	1.11231	−	1.23535i
$506$	1.84842	+	0.822972i	0.0821725	+	0.0365856i
$507$	7.16479	−	1.52292i	0.318200	−	0.0676354i
$508$	6.82768	+	64.9610i	0.302929	+	2.88218i
$509$	−2.99643	+	28.5091i	−0.132814	+	1.26364i	0.701626	+	0.712545i	$0.252458\pi$
$509$	−2.99643	+	28.5091i	−0.132814	+	1.26364i	−0.834440	+	0.551098i	$0.814209\pi$
$510$	16.0480	+	3.41111i	0.710618	+	0.151047i
$511$	−4.40209	−	3.19831i	−0.194737	−	0.141485i
$512$	39.3876	+	28.6167i	1.74070	+	1.26469i
$513$	−0.718664	−	0.152757i	−0.0317298	−	0.00674437i
$514$	−6.65665	+	63.3338i	−0.293612	+	2.79353i
$515$	2.25772	+	21.4808i	0.0994869	+	0.946555i
$516$	34.4969	−	7.33255i	1.51864	−	0.322797i
$517$	−1.60045	−	0.712566i	−0.0703877	−	0.0313386i
$518$	12.4691	−	13.8483i	0.547860	−	0.608460i
$519$	−3.92468	−	12.0789i	−0.172274	−	0.530205i
$520$	42.2419	+	46.9144i	1.85243	+	2.05733i
$521$	4.39356	−	7.60986i	0.192485	−	0.333394i	−0.753588	−	0.657347i	$-0.771679\pi$
$521$	4.39356	−	7.60986i	0.192485	−	0.333394i	0.946073	+	0.323953i	$0.105012\pi$
$522$	12.5786	+	21.7868i	0.550550	+	0.953581i
$523$	11.3608	−	34.9649i	0.496773	−	1.52891i	−0.317403	−	0.948291i	$-0.602811\pi$
$523$	11.3608	−	34.9649i	0.496773	−	1.52891i	0.814176	−	0.580618i	$-0.197189\pi$
$524$	−58.8832	+	26.2165i	−2.57233	+	1.14527i
$525$	24.9256	−	18.1095i	1.08784	−	0.790363i
$526$	−60.8301			−2.65232
$527$	6.48616	−	6.47027i	0.282541	−	0.281849i
$528$	−9.11052			−0.396484
$529$	18.1866	−	13.2133i	0.790720	−	0.574492i
$530$	−28.2681	+	12.5858i	−1.22789	+	0.546692i
$531$	−3.19431	+	9.83107i	−0.138621	+	0.426632i
$532$	5.30771	+	9.19323i	0.230119	+	0.398577i
$533$	−4.92502	+	8.53039i	−0.213327	+	0.369492i
$534$	10.6053	+	11.7784i	0.458937	+	0.509701i
$535$	−4.99905	−	15.3855i	−0.216128	−	0.665172i
$536$	12.1463	−	13.4898i	0.524639	−	0.582670i
$537$	13.9717	+	6.22061i	0.602925	+	0.268439i
$538$	−2.38892	+	0.507781i	−0.102994	+	0.0218920i
$539$	0.298021	+	2.83548i	0.0128367	+	0.122133i
$540$	−1.88138	+	17.9001i	−0.0809615	+	0.770297i
$541$	−5.92038	−	1.25842i	−0.254537	−	0.0541035i	0.0788758	−	0.996884i	$-0.474867\pi$
$541$	−5.92038	−	1.25842i	−0.254537	−	0.0541035i	−0.333413	+	0.942781i	$0.608200\pi$
$542$	−65.2104	−	47.3781i	−2.80103	−	2.03506i
$543$	13.7919	+	10.0204i	0.591869	+	0.430018i
$544$	12.7235	+	2.70447i	0.545517	+	0.115953i
$545$	2.20696	−	20.9978i	0.0945357	−	0.899447i
$546$	1.99308	+	18.9629i	0.0852961	+	0.811538i
$547$	3.80881	−	0.809587i	0.162853	−	0.0346155i	−0.125764	−	0.992060i	$-0.540138\pi$
$547$	3.80881	−	0.809587i	0.162853	−	0.0346155i	0.288617	+	0.957445i	$0.406805\pi$
$548$	24.0636	+	10.7138i	1.02795	+	0.457671i
$549$	9.06173	−	10.0641i	0.386745	−	0.429524i
$550$	−8.61060	−	26.5007i	−0.367157	−	1.12999i
$551$	−4.79325	−	5.32344i	−0.204199	−	0.226786i
$552$	2.47298	−	4.28333i	0.105257	−	0.182311i
$553$	17.1125	+	29.6397i	0.727696	+	1.26041i
$554$	22.0565	−	67.8830i	0.937091	−	2.88407i
$555$	−8.21891	+	3.65929i	−0.348873	+	0.155328i
$556$	21.3113	−	15.4836i	0.903801	−	0.656650i
$557$	36.1880			1.53334			0.766668	−	0.642044i	$-0.221913\pi$
$557$	36.1880			1.53334			0.766668	+	0.642044i	$0.221913\pi$
$558$	11.1536	+	9.05469i	0.472171	+	0.383316i
$559$	−18.0379			−0.762923
$560$	81.2577	−	59.0372i	3.43377	−	2.49478i
$561$	1.63440	−	0.727680i	0.0690043	−	0.0307227i
$562$	−6.59419	+	20.2948i	−0.278159	+	0.856085i
$563$	−5.47949	−	9.49076i	−0.230933	−	0.399988i	0.727150	−	0.686479i	$-0.240845\pi$
$563$	−5.47949	−	9.49076i	−0.230933	−	0.399988i	−0.958083	+	0.286491i	$0.907511\pi$
$564$	−3.75251	+	6.49954i	−0.158009	+	0.273680i
$565$	−37.8941	−	42.0856i	−1.59422	−	1.77056i
$566$	0.657564	+	2.02377i	0.0276395	+	0.0850655i
$567$	−2.07563	+	2.30522i	−0.0871681	+	0.0968100i
$568$	−47.0610	−	20.9529i	−1.97464	−	0.879164i
$569$	−5.61416	+	1.19333i	−0.235358	+	0.0500269i	−0.324081	−	0.946030i	$-0.605055\pi$
$569$	−5.61416	+	1.19333i	−0.235358	+	0.0500269i	0.0887226	+	0.996056i	$0.471722\pi$
$570$	−0.765743	−	7.28556i	−0.0320735	−	0.305159i
$571$	2.17507	−	20.6944i	0.0910238	−	0.866033i	−0.849793	−	0.527117i	$-0.823273\pi$
$571$	2.17507	−	20.6944i	0.0910238	−	0.866033i	0.940816	−	0.338916i	$-0.110060\pi$
$572$	11.8007	+	2.50832i	0.493412	+	0.104878i
$573$	7.78025	+	5.65269i	0.325025	+	0.236144i
$574$	26.7738	+	19.4523i	1.11752	+	0.811924i
$575$	7.00686	+	1.48935i	0.292206	+	0.0621103i
$576$	−0.380384	+	3.61911i	−0.0158493	+	0.150796i
$577$	−0.234062	−	2.22695i	−0.00974414	−	0.0927093i	0.988569	−	0.150770i	$-0.0481751\pi$
$577$	−0.234062	−	2.22695i	−0.00974414	−	0.0927093i	−0.998313	+	0.0580602i	$0.981508\pi$
$578$	36.0724	−	7.66742i	1.50041	−	0.318923i
$579$	9.04859	+	4.02869i	0.376047	+	0.167427i
$580$	−117.422	+	130.410i	−4.87569	+	5.41500i
$581$	−10.4567	−	32.1823i	−0.433816	−	1.33515i
$582$	20.9269	+	23.2417i	0.867449	+	0.963400i
$583$	−1.68712	+	2.92219i	−0.0698736	+	0.121025i
$584$	6.01470	+	10.4178i	0.248890	+	0.431090i
$585$	2.84468	−	8.75503i	0.117613	−	0.361976i
$586$	−8.30987	+	3.69979i	−0.343278	+	0.152837i
$587$	8.76402	−	6.36744i	0.361730	−	0.262812i	−0.392043	−	0.919947i	$-0.628232\pi$
$587$	8.76402	−	6.36744i	0.361730	−	0.262812i	0.753773	+	0.657135i	$0.228232\pi$
$588$	12.2139			0.503691
$589$	−3.64260	−	1.86163i	−0.150091	−	0.0767070i
$590$	−103.068			−4.24322
$591$	−18.2488	+	13.2585i	−0.750653	+	0.545382i
$592$	−17.8220	+	7.93486i	−0.732480	+	0.326121i
$593$	2.39504	−	7.37117i	0.0983524	−	0.302698i	−0.889760	−	0.456428i	$-0.849129\pi$
$593$	2.39504	−	7.37117i	0.0983524	−	0.302698i	0.988113	+	0.153730i	$0.0491287\pi$
$594$	1.40272	+	2.42959i	0.0575544	+	0.0996872i
$595$	−9.86191	+	17.0813i	−0.404299	+	0.700267i
$596$	52.5820	+	58.3982i	2.15384	+	2.39208i
$597$	−2.46004	−	7.57123i	−0.100683	−	0.309870i
$598$	−2.96642	+	3.29455i	−0.121306	+	0.134724i
$599$	−7.29277	−	3.24695i	−0.297974	−	0.132667i	0.252304	−	0.967648i	$-0.418812\pi$
$599$	−7.29277	−	3.24695i	−0.297974	−	0.132667i	−0.550278	+	0.834981i	$0.685478\pi$
$600$	−66.6246	+	14.1615i	−2.71994	+	0.578141i
$601$	−2.68517	−	25.5477i	−0.109531	−	1.04211i	−0.901863	−	0.432023i	$-0.857800\pi$
$601$	−2.68517	−	25.5477i	−0.109531	−	1.04211i	0.792332	−	0.610090i	$-0.208867\pi$
$602$	−6.33484	+	60.2719i	−0.258189	+	2.45650i
$603$	−2.58914	−	0.550338i	−0.105438	−	0.0224115i
$604$	−17.0115	−	12.3596i	−0.692187	−	0.502903i
$605$	30.6928	+	22.2996i	1.24784	+	0.906609i
$606$	−24.3987	−	5.18611i	−0.991131	−	0.210671i
$607$	1.84497	−	17.5537i	0.0748850	−	0.712483i	−0.891086	−	0.453834i	$-0.850056\pi$
$607$	1.84497	−	17.5537i	0.0748850	−	0.712483i	0.965971	−	0.258649i	$-0.0832774\pi$
$608$	−0.607113	−	5.77630i	−0.0246217	−	0.234260i
$609$	−29.5829	+	6.28804i	−1.19876	+	0.254804i
$610$	123.355	+	54.9213i	4.99451	+	2.22370i
$611$	2.56846	−	2.85257i	0.103909	−	0.115403i
$612$	−2.36837	−	7.28910i	−0.0957357	−	0.294644i
$613$	−28.3742	−	31.5127i	−1.14602	−	1.27279i	−0.956766	−	0.290859i	$-0.906059\pi$
$613$	−28.3742	−	31.5127i	−1.14602	−	1.27279i	−0.189256	−	0.981928i	$-0.560608\pi$
$614$	11.4944	−	19.9089i	0.463877	−	0.803459i
$615$	−7.98883	−	13.8371i	−0.322141	−	0.557964i
$616$	7.14726	−	21.9970i	0.287971	−	0.886285i
$617$	31.1398	−	13.8643i	1.25364	−	0.558157i	0.330932	−	0.943655i	$-0.392637\pi$
$617$	31.1398	−	13.8643i	1.25364	−	0.558157i	0.922709	+	0.385498i	$0.125970\pi$
$618$	11.6679	−	8.47725i	0.469353	−	0.341005i
$619$	−6.20601			−0.249441			−0.124720	−	0.992192i	$-0.539803\pi$
$619$	−6.20601			−0.249441			−0.124720	+	0.992192i	$0.539803\pi$
$620$	−36.0276	+	93.5123i	−1.44690	+	3.75554i
$621$	−0.721223			−0.0289417
$622$	54.5195	−	39.6107i	2.18603	−	1.58825i
$623$	−17.4067	+	7.74997i	−0.697385	+	0.310496i
$624$	6.16845	−	18.9845i	0.246936	−	0.759990i
$625$	−11.9944	−	20.7750i	−0.479777	−	0.830999i
$626$	6.54981	−	11.3446i	0.261783	−	0.453422i
$627$	−0.534527	−	0.593653i	−0.0213470	−	0.0237082i
$628$	−11.3193	−	34.8371i	−0.451687	−	1.39015i
$629$	2.56343	−	2.84698i	0.102211	−	0.113516i
$630$	−28.2550	−	12.5800i	−1.12571	−	0.501198i
$631$	−20.2648	+	4.30743i	−0.806731	+	0.171476i	−0.592776	−	0.805368i	$-0.701968\pi$
$631$	−20.2648	+	4.30743i	−0.806731	+	0.171476i	−0.213955	+	0.976843i	$0.568635\pi$
$632$	−7.90897	−	75.2488i	−0.314602	−	2.99324i
$633$	−0.769046	+	7.31698i	−0.0305668	+	0.290824i
$634$	−14.0883	−	2.99456i	−0.559517	−	0.118929i
$635$	43.8411	+	31.8524i	1.73978	+	1.26403i
$636$	11.6943	+	8.49642i	0.463710	+	0.336905i
$637$	−6.11037	−	1.29880i	−0.242102	−	0.0514603i
$638$	−2.85913	+	27.2028i	−0.113194	+	1.07697i
$639$	0.785207	+	7.47075i	0.0310623	+	0.295538i
$640$	24.2690	−	5.15854i	0.959318	−	0.203909i
$641$	−36.0859	−	16.0665i	−1.42531	−	0.634588i	−0.458176	−	0.888862i	$-0.651497\pi$
$641$	−36.0859	−	16.0665i	−1.42531	−	0.634588i	−0.967132	+	0.254274i	$0.918164\pi$
$642$	−7.22798	+	8.02748i	−0.285266	+	0.316820i
$643$	9.75533	+	30.0238i	0.384713	+	1.18402i	0.936689	+	0.350163i	$0.113874\pi$
$643$	9.75533	+	30.0238i	0.384713	+	1.18402i	−0.551976	+	0.833860i	$0.686126\pi$
$644$	6.97263	+	7.74389i	0.274760	+	0.305152i
$645$	14.6296	−	25.3391i	0.576038	−	0.997728i
$646$	1.55971	+	2.70151i	0.0613662	+	0.106289i
$647$	−8.38234	+	25.7982i	−0.329544	+	1.01423i	0.639804	+	0.768538i	$0.279016\pi$
$647$	−8.38234	+	25.7982i	−0.329544	+	1.01423i	−0.969348	+	0.245693i	$0.920984\pi$
$648$	6.26486	−	2.78929i	0.246107	−	0.109574i
$649$	−9.09263	+	6.60619i	−0.356917	+	0.259315i
$650$	61.0523			2.39467
$651$	−14.4963	+	9.38873i	−0.568153	+	0.367973i
$652$	60.6500			2.37524
$653$	0.429357	−	0.311946i	0.0168020	−	0.0122074i	−0.579353	−	0.815077i	$-0.696695\pi$
$653$	0.429357	−	0.311946i	0.0168020	−	0.0122074i	0.596155	+	0.802870i	$0.296695\pi$
$654$	−12.8793	+	5.73422i	−0.503619	+	0.224226i
$655$	−16.5245	+	50.8573i	−0.645667	+	1.98716i
$656$	−17.3231	−	30.0045i	−0.676353	−	1.17148i
$657$	0.877067	−	1.51913i	0.0342177	−	0.0592667i
$658$	−8.62954	−	9.58408i	−0.336415	−	0.373626i
$659$	−4.88814	−	15.0442i	−0.190415	−	0.586037i	0.809585	−	0.587003i	$-0.199692\pi$
$659$	−4.88814	−	15.0442i	−0.190415	−	0.586037i	−1.00000		0.000966277i	$0.999692\pi$
$660$	−13.0945	+	14.5429i	−0.509703	+	0.566083i
$661$	36.5859	+	16.2891i	1.42303	+	0.633573i	0.966624	−	0.256200i	$-0.0824707\pi$
$661$	36.5859	+	16.2891i	1.42303	+	0.633573i	0.456403	+	0.889773i	$0.349137\pi$
$662$	9.31967	−	1.98096i	0.362219	−	0.0769921i
$663$	0.409744	+	3.89845i	0.0159131	+	0.151403i
$664$	−7.81967	+	74.3992i	−0.303462	+	2.88725i
$665$	8.61444	+	1.83106i	0.334054	+	0.0710053i
$666$	4.86007	+	3.53105i	0.188324	+	0.136825i
$667$	−5.68886	−	4.13320i	−0.220274	−	0.160038i
$668$	−96.9277	−	20.6026i	−3.75025	−	0.797139i
$669$	2.45153	−	23.3247i	0.0947815	−	0.901786i
$670$	−2.75875	−	26.2478i	−0.106580	−	1.01404i
$671$	14.4026	−	3.06138i	0.556008	−	0.118183i
$672$	−22.4018	−	9.97391i	−0.864167	−	0.384752i
$673$	−9.68290	+	10.7539i	−0.373248	+	0.414534i	−0.900280	−	0.435312i	$-0.856638\pi$
$673$	−9.68290	+	10.7539i	−0.373248	+	0.414534i	0.527032	+	0.849846i	$0.323305\pi$
$674$	−26.2732	−	80.8605i	−1.01200	−	3.11463i
$675$	6.64600	+	7.38113i	0.255805	+	0.284100i
$676$	17.0587	−	29.5466i	0.656105	−	1.13641i
$677$	13.1537	+	22.7829i	0.505538	+	0.875618i	0.999979	+	0.00640672i	$0.00203934\pi$
$677$	13.1537	+	22.7829i	0.505538	+	0.875618i	−0.494441	+	0.869211i	$0.664627\pi$
$678$	−11.6854	+	35.9640i	−0.448776	+	1.38119i
$679$	−34.3478	+	15.2926i	−1.31815	+	0.586877i
$680$	35.2770	−	25.6302i	1.35281	−	0.982875i
$681$	2.89323			0.110869
$682$	4.02427	+	15.0928i	0.154097	+	0.577932i
$683$	4.22266			0.161575			0.0807877	−	0.996731i	$-0.474256\pi$
$683$	4.22266			0.161575			0.0807877	+	0.996731i	$0.474256\pi$
$684$	−2.76858	+	2.01149i	−0.105859	+	0.0769112i
$685$	19.9639	−	8.88852i	0.762783	−	0.339613i
$686$	10.8277	−	33.3242i	0.413403	−	1.27232i
$687$	−3.02595	−	5.24111i	−0.115447	−	0.199961i
$688$	31.7230	−	54.9458i	1.20943	−	2.09479i
$689$	−4.94696	−	5.49416i	−0.188464	−	0.209311i
$690$	−2.22218	−	6.83917i	−0.0845970	−	0.260363i
$691$	−23.4319	+	26.0237i	−0.891391	+	0.989990i	−0.999992	−	0.00409566i	$-0.998696\pi$
$691$	−23.4319	+	26.0237i	−0.891391	+	0.989990i	0.108601	+	0.994085i	$0.465363\pi$
$692$	−54.0417	−	24.0609i	−2.05436	−	0.914659i
$693$	−3.29899	+	0.701221i	−0.125318	+	0.0266372i
$694$	2.07921	+	19.7824i	0.0789257	+	0.750928i
$695$	2.28440	−	21.7346i	0.0866523	−	0.824441i
$696$	65.4009	+	13.9014i	2.47901	+	0.526931i
$697$	5.50424	+	3.99906i	0.208488	+	0.151475i
$698$	−53.4174	−	38.8100i	−2.02188	−	1.46898i
$699$	−22.8849	−	4.86433i	−0.865586	−	0.183986i
$700$	15.0003	−	142.718i	0.566958	−	5.39425i
$701$	1.63569	+	15.5626i	0.0617793	+	0.587791i	0.980995	+	0.194035i	$0.0621576\pi$
$701$	1.63569	+	15.5626i	0.0617793	+	0.587791i	−0.919215	+	0.393755i	$0.871176\pi$
$702$	−6.01253	+	1.27800i	−0.226928	+	0.0482351i
$703$	−1.56269	−	0.695753i	−0.0589379	−	0.0262408i
$704$	−2.64750	+	2.94035i	−0.0997814	+	0.110818i
$705$	1.92406	+	5.92166i	0.0724645	+	0.223023i
$706$	−13.7900	−	15.3154i	−0.518994	−	0.576401i
$707$	14.9936	−	25.9697i	0.563894	−	0.976693i
$708$	24.0737	+	41.6968i	0.904744	+	1.56706i
$709$	11.5303	−	35.4865i	0.433028	−	1.33272i	−0.462067	−	0.886845i	$-0.652892\pi$
$709$	11.5303	−	35.4865i	0.433028	−	1.33272i	0.895094	−	0.445877i	$-0.147108\pi$
$710$	−68.4238	+	30.4643i	−2.56790	+	1.14330i
$711$	−8.92610	+	6.48519i	−0.334755	+	0.243214i
$712$	42.1240			1.57866
$713$	−3.87750	−	1.04407i	−0.145213	−	0.0391007i
$714$	13.1702			0.492882
$715$	8.09742	−	5.88312i	0.302826	−	0.220016i
$716$	65.0771	−	28.9742i	2.43204	−	1.08282i
$717$	−3.20391	+	9.86062i	−0.119652	+	0.368252i
$718$	−6.08591	−	10.5411i	−0.227124	−	0.393391i
$719$	−17.7379	+	30.7229i	−0.661511	+	1.14577i	0.318708	+	0.947853i	$0.396751\pi$
$719$	−17.7379	+	30.7229i	−0.661511	+	1.14577i	−0.980219	+	0.197917i	$0.936582\pi$
$720$	21.6660	+	24.0626i	0.807446	+	0.896759i
$721$	5.35788	+	16.4899i	0.199538	+	0.614114i
$722$	−31.8721	+	35.3976i	−1.18616	+	1.31736i
$723$	7.56395	+	3.36769i	0.281306	+	0.125246i
$724$	77.6694	−	16.5091i	2.88656	−	0.613558i
$725$	10.1224	+	96.3078i	0.375935	+	3.57678i
$726$	2.64798	−	25.1939i	0.0982758	−	0.935032i
$727$	7.11776	+	1.51293i	0.263983	+	0.0561114i	0.338002	−	0.941146i	$-0.390249\pi$
$727$	7.11776	+	1.51293i	0.263983	+	0.0561114i	−0.0740185	+	0.997257i	$0.523582\pi$
$728$	40.9983	+	29.7870i	1.51950	+	1.10398i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	17.1078	+	3.63638i	0.633189	+	0.134588i
$731$	−1.30233	+	12.3909i	−0.0481686	+	0.458293i
$732$	−6.59345	−	62.7325i	−0.243701	−	2.31866i
$733$	−2.43273	+	0.517093i	−0.0898550	+	0.0190993i	−0.252620	−	0.967566i	$-0.581292\pi$
$733$	−2.43273	+	0.517093i	−0.0898550	+	0.0190993i	0.162765	+	0.986665i	$0.447959\pi$
$734$	57.7305	+	25.7033i	2.13087	+	0.948725i
$735$	6.78030	−	7.53029i	0.250095	−	0.277759i
$736$	−1.76184	−	5.42238i	−0.0649422	−	0.199872i
$737$	−1.92575	−	2.13876i	−0.0709358	−	0.0787822i
$738$	−5.33439	+	9.23943i	−0.196361	+	0.340108i
$739$	6.27959	+	10.8766i	0.230998	+	0.400101i	0.958102	−	0.286427i	$-0.0924675\pi$
$739$	6.27959	+	10.8766i	0.230998	+	0.400101i	−0.727104	+	0.686528i	$0.759134\pi$
$740$	−12.9492	+	39.8536i	−0.476023	+	1.46505i
$741$	1.59897	−	0.711906i	0.0587396	−	0.0261525i
$742$	−20.0956	+	14.6003i	−0.737731	+	0.535993i
$743$	−16.9054			−0.620198			−0.310099	−	0.950704i	$-0.600362\pi$
$743$	−16.9054			−0.620198			−0.310099	+	0.950704i	$0.600362\pi$
$744$	37.7195	−	5.92678i	1.38286	−	0.217286i
$745$	65.1946			2.38854
$746$	−3.31255	+	2.40671i	−0.121281	+	0.0881157i
$747$	9.96558	−	4.43696i	0.364622	−	0.162340i
$748$	2.57506	−	7.92522i	0.0941535	−	0.289775i
$749$	−6.49307	−	11.2463i	−0.237252	−	0.410932i
$750$	−24.5893	+	42.5899i	−0.897873	+	1.55516i
$751$	28.2436	+	31.3677i	1.03062	+	1.14462i	0.989362	+	0.145474i	$0.0464707\pi$
$751$	28.2436	+	31.3677i	1.03062	+	1.14462i	0.0412605	+	0.999148i	$0.486863\pi$
$752$	4.17217	+	12.8406i	0.152143	+	0.468249i
$753$	−4.62209	+	5.13335i	−0.168438	+	0.187070i
$754$	−54.7496	−	24.3761i	−1.99386	−	0.887724i
$755$	−17.0637	+	3.62701i	−0.621013	+	0.132000i
$756$	1.51026	+	14.3691i	0.0549275	+	0.522600i
$757$	−1.15362	+	10.9760i	−0.0419290	+	0.398928i	0.953350	+	0.301868i	$0.0976103\pi$
$757$	−1.15362	+	10.9760i	−0.0419290	+	0.398928i	−0.995279	+	0.0970593i	$0.969056\pi$
$758$	−19.3713	−	4.11749i	−0.703597	−	0.149554i
$759$	−0.634403	−	0.460921i	−0.0230274	−	0.0167304i
$760$	−15.7515	−	11.4442i	−0.571369	−	0.415124i
$761$	14.8990	+	3.16687i	0.540087	+	0.114799i	0.469875	−	0.882733i	$-0.344299\pi$
$761$	14.8990	+	3.16687i	0.540087	+	0.114799i	0.0702120	+	0.997532i	$0.477632\pi$
$762$	3.78233	−	35.9865i	0.137019	−	1.30365i
$763$	−1.77162	−	16.8558i	−0.0641368	−	0.610221i
$764$	43.8145	−	9.31307i	1.58515	−	0.336935i
$765$	−5.80875	−	2.58622i	−0.210016	−	0.0935051i
$766$	−20.2491	+	22.4889i	−0.731629	+	0.812556i
$767$	−7.60966	−	23.4201i	−0.274769	−	0.845652i
$768$	−15.9556	−	17.7205i	−0.575749	−	0.639434i
$769$	−7.88074	+	13.6498i	−0.284187	+	0.492226i	−0.972412	−	0.233271i	$-0.925057\pi$
$769$	−7.88074	+	13.6498i	−0.284187	+	0.492226i	0.688225	+	0.725498i	$0.258390\pi$
$770$	−16.8141	−	29.1229i	−0.605938	−	1.04952i
$771$	7.62674	−	23.4727i	0.274670	−	0.845349i
$772$	42.1462	−	18.7647i	1.51688	−	0.675357i
$773$	17.2180	−	12.5096i	0.619287	−	0.449939i	−0.233385	−	0.972384i	$-0.574980\pi$
$773$	17.2180	−	12.5096i	0.619287	−	0.449939i	0.852673	+	0.522446i	$0.174980\pi$
$774$	−19.5372			−0.702250
$775$	25.0455	+	49.3040i	0.899662	+	1.77105i
$776$	83.1211			2.98387
$777$	−5.84274	+	4.24500i	−0.209607	+	0.152289i
$778$	−10.8670	+	4.83830i	−0.389601	+	0.173461i
$779$	0.938758	−	2.88920i	0.0336345	−	0.103516i
$780$	−21.4387	−	37.1330i	−0.767630	−	1.32957i
$781$	−4.08373	+	7.07323i	−0.146127	+	0.253100i
$782$	2.04897	+	2.27561i	0.0732708	+	0.0813755i
$783$	−3.01287	−	9.27266i	−0.107671	−	0.331378i
$784$	14.7025	−	16.3288i	0.525090	−	0.583171i
$785$	−27.7620	−	12.3604i	−0.990869	−	0.441163i
$786$	34.9263	−	7.42381i	1.24578	−	0.264799i
$787$	−0.268859	−	2.55803i	−0.00958380	−	0.0911838i	0.988684	−	0.150010i	$-0.0479307\pi$
$787$	−0.268859	−	2.55803i	−0.00958380	−	0.0911838i	−0.998268	+	0.0588267i	$0.981264\pi$
$788$	−10.9822	+	104.488i	−0.391223	+	3.72224i
$789$	23.0600	+	4.90155i	0.820957	+	0.174500i
$790$	−88.9999	−	64.6622i	−3.16647	−	2.30058i
$791$	−36.7785	−	26.7211i	−1.30769	−	0.950093i
$792$	7.29328	+	1.55024i	0.259156	+	0.0550852i
$793$	−3.37228	+	32.0851i	−0.119753	+	1.13937i
$794$	−8.65984	−	82.3928i	−0.307326	−	2.92401i
$795$	11.7302	−	2.49334i	0.416029	−	0.0884297i
$796$	−33.8741	−	15.0817i	−1.20064	−	0.534558i
$797$	−21.6032	+	23.9928i	−0.765224	+	0.849867i	−0.992280	−	0.124015i	$-0.960423\pi$
$797$	−21.6032	+	23.9928i	−0.765224	+	0.849867i	0.227057	+	0.973882i	$0.427090\pi$
$798$	−1.81722	−	5.59281i	−0.0643287	−	0.197983i
$799$	−1.77409	−	1.97032i	−0.0627627	−	0.0697050i
$800$	−39.2584	+	67.9976i	−1.38800	+	2.40408i
$801$	−3.07127	−	5.31960i	−0.108518	−	0.187959i
$802$	1.97109	−	6.06640i	0.0696017	−	0.214212i
$803$	1.74233	−	0.775736i	0.0614855	−	0.0273751i
$804$	−9.97438	+	7.24681i	−0.351769	+	0.255575i
$805$	8.64513			0.304701
$806$	−34.1751	−	1.83306i	−1.20377	−	0.0645668i
$807$	0.946528			0.0333194
$808$	−53.6337	+	38.9671i	−1.88683	+	1.37086i
$809$	−8.45847	+	3.76596i	−0.297384	+	0.132404i	−0.550005	−	0.835161i	$-0.685374\pi$
$809$	−8.45847	+	3.76596i	−0.297384	+	0.132404i	0.252621	+	0.967565i	$0.418707\pi$
$810$	3.08113	−	9.48274i	0.108260	−	0.333189i
$811$	24.7603	+	42.8861i	0.869452	+	1.50593i	0.862558	+	0.505958i	$0.168861\pi$
$811$	24.7603	+	42.8861i	0.869452	+	1.50593i	0.00689343	+	0.999976i	$0.497806\pi$
$812$	−70.4343	+	121.996i	−2.47176	+	4.28121i
$813$	20.9029	+	23.2150i	0.733095	+	0.814185i
$814$	2.01839	+	6.21196i	0.0707445	+	0.217729i
$815$	33.6687	−	37.3929i	1.17936	−	1.30982i
$816$	−12.5958	−	5.60801i	−0.440941	−	0.196319i
$817$	5.44156	−	1.15664i	0.190376	−	0.0404657i
$818$	−5.47938	−	52.1328i	−0.191582	−	1.82278i
$819$	0.772434	−	7.34922i	0.0269910	−	0.256802i
$820$	−72.7940	−	15.4728i	−2.54208	−	0.540335i
$821$	11.1586	+	8.10722i	0.389439	+	0.282944i	0.765226	−	0.643762i	$-0.222627\pi$
$821$	11.1586	+	8.10722i	0.389439	+	0.282944i	−0.375787	+	0.926706i	$0.622627\pi$
$822$	−11.8052	−	8.57701i	−0.411755	−	0.299157i
$823$	−19.5004	−	4.14495i	−0.679742	−	0.144484i	−0.144914	−	0.989444i	$-0.546290\pi$
$823$	−19.5004	−	4.14495i	−0.679742	−	0.144484i	−0.534829	+	0.844961i	$0.679624\pi$
$824$	4.00671	−	38.1213i	0.139580	−	1.32802i
$825$	1.12881	+	10.7399i	0.0393002	+	0.373916i
$826$	−80.9285	+	17.2019i	−2.81586	+	0.598530i
$827$	28.0336	+	12.4814i	0.974825	+	0.434020i	0.831420	−	0.555644i	$-0.187528\pi$
$827$	28.0336	+	12.4814i	0.974825	+	0.434020i	0.143405	+	0.989664i	$0.454195\pi$
$828$	−2.24780	+	2.49644i	−0.0781166	+	0.0867572i
$829$	−8.61884	−	26.5261i	−0.299345	−	0.921289i	−0.981727	−	0.190293i	$-0.939056\pi$
$829$	−8.61884	−	26.5261i	−0.299345	−	0.921289i	0.682382	−	0.730995i	$-0.260944\pi$
$830$	72.7798	+	80.8302i	2.52622	+	2.80566i
$831$	−13.8312	+	23.9564i	−0.479799	+	0.831037i
$832$	−4.33457	−	7.50769i	−0.150274	−	0.260282i
$833$	−1.33336	+	4.10366i	−0.0461981	+	0.142183i
$834$	−13.3312	+	5.93543i	−0.461622	+	0.205527i
$835$	−66.5099	+	48.3223i	−2.30167	+	1.67226i
$836$	−3.72080			−0.128687
$837$	−3.49860	−	4.33126i	−0.120929	−	0.149710i
$838$	−36.3701			−1.25638
$839$	30.0289	−	21.8172i	1.03671	−	0.753215i	0.0670707	−	0.997748i	$-0.478635\pi$
$839$	30.0289	−	21.8172i	1.03671	−	0.753215i	0.969641	+	0.244533i	$0.0786347\pi$
$840$	−75.0953	+	33.4346i	−2.59103	+	1.15360i
$841$	20.4135	−	62.8264i	0.703915	−	2.16643i
$842$	9.95936	+	17.2501i	0.343222	+	0.594478i
$843$	4.13509	−	7.16218i	0.142420	−	0.246679i
$844$	22.9301	+	25.4665i	0.789287	+	0.876592i
$845$	−8.74671	−	26.9196i	−0.300896	−	0.926063i
$846$	2.78195	−	3.08967i	0.0956454	−	0.106225i
$847$	27.8218	+	12.3870i	0.955967	+	0.425624i
$848$	25.4360	−	5.40660i	0.873477	−	0.185663i
$849$	−0.0862037	−	0.820173i	−0.00295850	−	0.0281483i
$850$	4.40796	−	41.9389i	0.151192	−	1.43849i
$851$	−1.64246	−	0.349116i	−0.0563028	−	0.0119675i
$852$	28.3064	+	20.5658i	0.969763	+	0.704574i
$853$	14.9845	+	10.8868i	0.513058	+	0.372758i	0.813982	−	0.580890i	$-0.197295\pi$
$853$	14.9845	+	10.8868i	0.513058	+	0.372758i	−0.300924	+	0.953648i	$0.597295\pi$
$854$	106.025	+	22.5363i	3.62809	+	0.771175i
$855$	−0.296769	+	2.82357i	−0.0101493	+	0.0965641i
$856$	3.00094	+	28.5520i	0.102570	+	0.975889i
$857$	−54.2375	+	11.5285i	−1.85272	+	0.393807i	−0.993114	−	0.117152i	$-0.962623\pi$
$857$	−54.2375	+	11.5285i	−1.85272	+	0.393807i	−0.859605	+	0.510960i	$0.829290\pi$
$858$	−6.10549	−	2.71834i	−0.208438	−	0.0928026i
$859$	37.2700	−	41.3925i	1.27164	−	1.41230i	0.404259	−	0.914645i	$-0.367529\pi$
$859$	37.2700	−	41.3925i	1.27164	−	1.41230i	0.867378	−	0.497651i	$-0.165804\pi$
$860$	−42.1135	−	129.612i	−1.43606	−	4.41973i
$861$	−8.58222	−	9.53152i	−0.292481	−	0.324833i
$862$	−33.8243	+	58.5854i	−1.15206	+	1.99543i
$863$	21.4622	+	37.1736i	0.730581	+	1.26540i	0.956635	+	0.291289i	$0.0940841\pi$
$863$	21.4622	+	37.1736i	0.730581	+	1.26540i	−0.226054	+	0.974115i	$0.572583\pi$
$864$	2.44285	−	7.51831i	0.0831073	−	0.255778i
$865$	−44.8347	+	19.9617i	−1.52443	+	0.678719i
$866$	−47.3113	+	34.3737i	−1.60770	+	1.16807i
$867$	−14.2924			−0.485396
$868$	−12.6817	+	79.4387i	−0.430446	+	2.69633i
$869$	−11.9962			−0.406942
$870$	78.6472	−	57.1405i	2.66639	−	1.93724i
$871$	5.76062	−	2.56479i	0.195191	−	0.0869047i
$872$	−11.5787	+	35.6356i	−0.392104	+	1.20677i
$873$	−6.06039	−	10.4969i	−0.205113	−	0.355266i
$874$	0.683637	−	1.18409i	0.0231244	−	0.0400526i
$875$	−39.5604	−	43.9363i	−1.33739	−	1.48532i
$876$	−2.52478	−	7.77046i	−0.0853043	−	0.262540i
$877$	0.430758	−	0.478406i	0.0145457	−	0.0161546i	−0.735828	−	0.677168i	$-0.763207\pi$
$877$	0.430758	−	0.478406i	0.0145457	−	0.0161546i	0.750374	+	0.661014i	$0.229874\pi$
$878$	52.0197	+	23.1606i	1.75558	+	0.781634i
$879$	3.44829	−	0.732958i	0.116308	−	0.0247220i
$880$	3.67994	+	35.0123i	0.124051	+	1.18026i
$881$	−0.975867	+	9.28476i	−0.0328778	+	0.312811i	0.965707	+	0.259633i	$0.0836017\pi$
$881$	−0.975867	+	9.28476i	−0.0328778	+	0.312811i	−0.998585	+	0.0531780i	$0.983065\pi$
$882$	−6.61826	−	1.40675i	−0.222848	−	0.0473679i
$883$	−33.4000	−	24.2665i	−1.12400	−	0.816632i	−0.139188	−	0.990266i	$-0.544449\pi$
$883$	−33.4000	−	24.2665i	−1.12400	−	0.816632i	−0.984810	+	0.173634i	$0.944449\pi$
$884$	14.7711	+	10.7318i	0.496806	+	0.360951i
$885$	39.0717	+	8.30494i	1.31338	+	0.279168i
$886$	1.14745	−	10.9172i	0.0385492	−	0.366771i
$887$	3.21546	+	30.5931i	0.107965	+	1.02722i	0.905617	+	0.424097i	$0.139409\pi$
$887$	3.21546	+	30.5931i	0.107965	+	1.02722i	−0.797652	+	0.603118i	$0.793925\pi$
$888$	15.6173	−	3.31956i	0.524083	−	0.111397i
$889$	39.7401	+	17.6934i	1.33284	+	0.593419i
$890$	40.9814	−	45.5144i	1.37370	−	1.52565i
$891$	−0.335985	−	1.03406i	−0.0112559	−	0.0346422i
$892$	−73.0955	−	81.1808i	−2.44742	−	2.71813i
$893$	−0.591923	+	1.02524i	−0.0198080	+	0.0343084i
$894$	−21.7662	−	37.7002i	−0.727970	−	1.26088i
$895$	18.2627	−	56.2069i	0.610456	−	1.87879i
$896$	18.1951	−	8.10097i	0.607855	−	0.270634i
$897$	1.39000	−	1.00990i	0.0464108	−	0.0337195i
$898$	82.2387			2.74434
$899$	−2.77458	−	54.2139i	−0.0925374	−	1.80814i
$900$	46.2623			1.54208
$901$	−4.13130	+	3.00157i	−0.137634	+	0.0999967i
$902$	−10.5970	+	4.71808i	−0.352841	+	0.157095i
$903$	7.25803	−	22.3379i	0.241532	−	0.743360i
$904$	50.2514	+	87.0381i	1.67134	+	2.89484i
$905$	32.9383	−	57.0508i	1.09491	−	1.89643i
$906$	7.79438	+	8.65654i	0.258951	+	0.287594i
$907$	9.94174	+	30.5975i	0.330110	+	1.01597i	0.969081	+	0.246743i	$0.0793604\pi$
$907$	9.94174	+	30.5975i	0.330110	+	1.01597i	−0.638971	+	0.769231i	$0.720640\pi$
$908$	9.01721	−	10.0146i	0.299246	−	0.332347i
$909$	8.83139	+	3.93199i	0.292919	+	0.130416i
$910$	72.0707	−	15.3191i	2.38912	−	0.507823i
$911$	−1.81555	−	17.2738i	−0.0601518	−	0.572306i	−0.982541	−	0.186045i	$-0.940433\pi$
$911$	−1.81555	−	17.2738i	−0.0601518	−	0.572306i	0.922389	−	0.386261i	$-0.126234\pi$
$912$	−0.643519	+	6.12267i	−0.0213090	+	0.202742i
$913$	11.6015	+	2.46598i	0.383954	+	0.0816119i
$914$	17.2819	+	12.5561i	0.571636	+	0.415318i
$915$	−42.3371	−	30.7597i	−1.39962	−	1.01688i
$916$	−27.5724	−	5.86069i	−0.911018	−	0.193643i
$917$	−4.48701	+	42.6910i	−0.148174	+	1.40978i
$918$	0.443801	+	4.22249i	0.0146476	+	0.139363i
$919$	−46.9202	+	9.97320i	−1.54776	+	0.328986i	−0.901037	−	0.433743i	$-0.857193\pi$
$919$	−46.9202	+	9.97320i	−1.54776	+	0.328986i	−0.646719	+	0.762728i	$0.723859\pi$
$920$	−17.4600	−	7.77369i	−0.575639	−	0.256291i
$921$	−5.96161	+	6.62104i	−0.196442	+	0.218171i
$922$	−8.97818	−	27.6320i	−0.295680	−	0.910011i
$923$	−11.9743	−	13.2988i	−0.394138	−	0.437734i
$924$	−7.85460	+	13.6046i	−0.258397	+	0.447557i
$925$	11.5622	+	20.0263i	0.380162	+	0.658460i
$926$	−16.3240	+	50.2401i	−0.536440	+	1.65099i
$927$	−5.10625	+	2.27345i	−0.167711	+	0.0746699i
$928$	62.3547	−	45.3034i	2.04689	−	1.48716i
$929$	−36.7464			−1.20561			−0.602805	−	0.797888i	$-0.705950\pi$
$929$	−36.7464			−1.20561			−0.602805	+	0.797888i	$0.705950\pi$
$930$	30.2926	−	46.5215i	0.993332	−	1.52550i
$931$	1.92662			0.0631424
$932$	−88.1616	+	64.0532i	−2.88783	+	2.09813i
$933$	−23.8594	+	10.6229i	−0.781123	+	0.347778i
$934$	−19.0843	+	58.7356i	−0.624459	+	1.92189i
$935$	−3.45669	−	5.98716i	−0.113046	−	0.195801i
$936$	−8.16845	+	14.1482i	−0.266994	+	0.462447i
$937$	20.0011	+	22.2135i	0.653407	+	0.725682i	0.975249	−	0.221111i	$-0.0709684\pi$
$937$	20.0011	+	22.2135i	0.653407	+	0.725682i	−0.321841	+	0.946794i	$0.604302\pi$
$938$	−6.54690	−	20.1493i	−0.213764	−	0.657898i
$939$	−3.39708	+	3.77284i	−0.110859	+	0.123122i
$940$	26.4939	+	11.7958i	0.864134	+	0.384737i
$941$	11.8565	−	2.52017i	0.386510	−	0.0821553i	−0.0105582	−	0.999944i	$-0.503361\pi$
$941$	11.8565	−	2.52017i	0.386510	−	0.0821553i	0.397069	+	0.917789i	$0.370028\pi$
$942$	2.12108	+	20.1807i	0.0691085	+	0.657523i
$943$	0.311713	−	2.96575i	0.0101508	−	0.0965780i
$944$	84.7236	+	18.0086i	2.75752	+	0.586129i
$945$	9.69749	+	7.04564i	0.315459	+	0.229195i
$946$	−17.1853	−	12.4859i	−0.558743	−	0.405951i
$947$	20.9933	+	4.46226i	0.682191	+	0.145004i	0.535956	−	0.844246i	$-0.319951\pi$
$947$	20.9933	+	4.46226i	0.682191	+	0.145004i	0.146235	+	0.989250i	$0.453285\pi$
$948$	−5.37176	+	51.1089i	−0.174467	+	1.65994i
$949$	0.436803	+	4.15590i	0.0141792	+	0.134906i
$950$	−18.4179	+	3.91484i	−0.597554	+	0.127014i
$951$	5.09941	+	2.27040i	0.165360	+	0.0736228i
$952$	23.4218	−	26.0125i	0.759105	−	0.843071i
$953$	−0.178594	−	0.549655i	−0.00578522	−	0.0178051i	0.948122	−	0.317906i	$-0.102980\pi$
$953$	−0.178594	−	0.549655i	−0.00578522	−	0.0178051i	−0.953907	+	0.300101i	$0.902980\pi$
$954$	−5.35815	−	5.95083i	−0.173476	−	0.192665i
$955$	18.5810	−	32.1833i	0.601267	−	1.04143i
$956$	24.1460	+	41.8221i	0.780938	+	1.35262i
$957$	3.27580	−	10.0819i	0.105892	−	0.325901i
$958$	39.5249	−	17.5976i	1.27699	−	0.568553i
$959$	14.1922	−	10.3112i	0.458289	−	0.332967i
$960$	14.0621			0.453853
$961$	−12.5394	−	28.3507i	−0.404495	−	0.914540i
$962$	−14.3111			−0.461409
$963$	3.38688	−	2.46071i	0.109141	−	0.0792953i
$964$	35.2311	−	15.6859i	1.13472	−	0.505209i
$965$	11.8276	−	36.4016i	0.380744	−	1.17181i
$966$	−2.88631	−	4.99923i	−0.0928654	−	0.160848i
$967$	18.3533	−	31.7888i	0.590202	−	1.02226i	−0.404003	−	0.914758i	$-0.632381\pi$
$967$	18.3533	−	31.7888i	0.590202	−	1.02226i	0.994205	−	0.107502i	$-0.0342853\pi$
$968$	−45.0514	−	50.0346i	−1.44801	−	1.60817i
$969$	−0.373588	−	1.14979i	−0.0120014	−	0.0369365i
$970$	80.8665	−	89.8113i	2.59647	−	2.88367i
$971$	−25.0672	−	11.1606i	−0.804443	−	0.358161i	−0.0370301	−	0.999314i	$-0.511790\pi$
$971$	−25.0672	−	11.1606i	−0.804443	−	0.358161i	−0.767413	+	0.641153i	$0.778456\pi$
$972$	−4.55598	+	0.968404i	−0.146133	+	0.0310616i
$973$	−1.83378	−	17.4473i	−0.0587884	−	0.559334i
$974$	0.993666	−	9.45410i	0.0318391	−	0.302929i
$975$	−23.1442	−	4.91945i	−0.741207	−	0.157548i
$976$	−91.8044	−	66.6998i	−2.93859	−	2.13501i
$977$	−11.1842	−	8.12581i	−0.357815	−	0.259968i	0.394325	−	0.918971i	$-0.370978\pi$
$977$	−11.1842	−	8.12581i	−0.357815	−	0.259968i	−0.752140	+	0.659003i	$0.770978\pi$
$978$	−32.8641	−	6.98548i	−1.05088	−	0.223371i
$979$	0.698105	−	6.64202i	0.0223115	−	0.212280i
$980$	−4.93345	−	46.9386i	−0.157593	−	1.49940i
$981$	5.34442	−	1.13599i	0.170634	−	0.0362694i
$982$	−9.10705	−	4.05472i	−0.290618	−	0.129391i
$983$	−8.13914	+	9.03943i	−0.259598	+	0.288313i	−0.858828	−	0.512264i	$-0.828807\pi$
$983$	−8.13914	+	9.03943i	−0.259598	+	0.288313i	0.599230	+	0.800577i	$0.295474\pi$
$984$	8.76221	+	26.9673i	0.279329	+	0.859686i
$985$	58.3243	+	64.7757i	1.85837	+	2.06393i
$986$	−20.6977	+	35.8494i	−0.659149	+	1.14168i
$987$	2.49909	+	4.32856i	0.0795470	+	0.137780i
$988$	2.51924	−	7.75343i	0.0801477	−	0.246669i
$989$	4.98882	−	2.22117i	0.158635	−	0.0706290i
$990$	8.77047	−	6.37212i	0.278744	−	0.202519i
$991$	−49.0596			−1.55843			−0.779214	−	0.626758i	$-0.784382\pi$
$991$	−49.0596			−1.55843			−0.779214	+	0.626758i	$0.784382\pi$
$992$	24.0172	−	36.8842i	0.762547	−	1.17107i
$993$	−3.69260			−0.117181
$994$	−48.6419	+	35.3404i	−1.54283	+	1.12093i
$995$	−28.1031	+	12.5123i	−0.890927	+	0.396666i
$996$	15.7012	−	48.3233i	0.497511	−	1.53118i
$997$	−28.6217	−	49.5742i	−0.906459	−	1.57003i	−0.818947	−	0.573869i	$-0.805442\pi$
$997$	−28.6217	−	49.5742i	−0.906459	−	1.57003i	−0.0875112	−	0.996164i	$-0.527891\pi$
$998$	35.1814	−	60.9360i	1.11365	−	1.92889i
$999$	−1.55787	−	1.73019i	−0.0492889	−	0.0547408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.b.49.1	yes	24
3.2	odd	2		279.2.y.d.235.3		24
31.9	even	15		2883.2.a.t.1.11		12
31.19	even	15	inner	93.2.m.b.19.1	✓	24
31.22	odd	30		2883.2.a.s.1.11		12
93.50	odd	30		279.2.y.d.19.3		24
93.53	even	30		8649.2.a.bl.1.2		12
93.71	odd	30		8649.2.a.bk.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.19.1	✓	24	31.19	even	15	inner
93.2.m.b.49.1	yes	24	1.1	even	1	trivial
279.2.y.d.19.3		24	93.50	odd	30
279.2.y.d.235.3		24	3.2	odd	2
2883.2.a.s.1.11		12	31.22	odd	30
2883.2.a.t.1.11		12	31.9	even	15
8649.2.a.bk.1.2		12	93.71	odd	30
8649.2.a.bl.1.2		12	93.53	even	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08748 + 1.51664i) q^{2} +(0.913545 - 0.406737i) q^{3} +(1.43933 - 4.42980i) q^{4} +(-1.93212 - 3.34652i) q^{5} +(-1.29013 + 2.23457i) q^{6} +(-2.07563 - 2.30522i) q^{7} +(2.11916 + 6.52210i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-2.08748 + 1.51664i) q^{2} +(0.913545 - 0.406737i) q^{3} +(1.43933 - 4.42980i) q^{4} +(-1.93212 - 3.34652i) q^{5} +(-1.29013 + 2.23457i) q^{6} +(-2.07563 - 2.30522i) q^{7} +(2.11916 + 6.52210i) q^{8} +(0.669131 - 0.743145i) q^{9} +(9.10873 + 4.05547i) q^{10} +(1.06351 - 0.226056i) q^{11} +(-0.486869 - 4.63225i) q^{12} +(-0.249014 + 2.36921i) q^{13} +(7.82901 + 1.66411i) q^{14} +(-3.12623 - 2.27134i) q^{15} +(-6.77896 - 4.92520i) q^{16} +(1.60951 + 0.342112i) q^{17} +(-0.269711 + 2.56613i) q^{18} +(-0.0767990 - 0.730694i) q^{19} +(-17.6054 + 3.74214i) q^{20} +(-2.83380 - 1.26169i) q^{21} +(-1.87721 + 2.08485i) q^{22} +(-0.222870 - 0.685924i) q^{23} +(4.58873 + 5.09630i) q^{24} +(-4.96614 + 8.60161i) q^{25} +(-3.07343 - 5.32333i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-13.1992 + 5.87665i) q^{28} +(7.88779 - 5.73082i) q^{29} +9.97074 q^{30} +(3.03814 - 4.66580i) q^{31} +7.90522 q^{32} +(0.879620 - 0.639082i) q^{33} +(-3.87868 + 1.72690i) q^{34} +(-3.70411 + 11.4001i) q^{35} +(-2.32888 - 4.03374i) q^{36} +(1.16410 - 2.01628i) q^{37} +(1.26852 + 1.40883i) q^{38} +(0.736157 + 2.26566i) q^{39} +(17.7319 - 19.6933i) q^{40} +(3.77729 + 1.68176i) q^{41} +(7.82901 - 1.66411i) q^{42} +(0.791467 + 7.53030i) q^{43} +(0.529359 - 5.03651i) q^{44} +(-3.77979 - 0.803419i) q^{45} +(1.50554 + 1.09384i) q^{46} +(-1.30356 - 0.947094i) q^{47} +(-8.19615 - 1.74215i) q^{48} +(-0.274100 + 2.60789i) q^{49} +(-2.67885 - 25.4875i) q^{50} +(1.60951 - 0.342112i) q^{51} +(10.1367 + 4.51315i) q^{52} +(-2.07659 + 2.30629i) q^{53} +(0.797346 + 2.45398i) q^{54} +(-2.81133 - 3.12230i) q^{55} +(10.6363 - 18.4226i) q^{56} +(-0.367359 - 0.636285i) q^{57} +(-7.77400 + 23.9259i) q^{58} +(-9.44332 + 4.20444i) q^{59} +(-14.5612 + 10.5794i) q^{60} +13.5425 q^{61} +(0.734283 + 14.3475i) q^{62} -3.10198 q^{63} +(-2.94405 + 2.13898i) q^{64} +(8.40972 - 3.74425i) q^{65} +(-0.866930 + 2.66814i) q^{66} +(-1.32349 - 2.29235i) q^{67} +(3.83210 - 6.63740i) q^{68} +(-0.482593 - 0.535973i) q^{69} +(-9.55759 - 29.4152i) q^{70} +(-5.02644 + 5.58243i) q^{71} +(6.26486 + 2.78929i) q^{72} +(1.71580 - 0.364705i) q^{73} +(0.627942 + 5.97447i) q^{74} +(-1.03821 + 9.87788i) q^{75} +(-3.34737 - 0.711505i) q^{76} +(-2.72856 - 1.98242i) q^{77} +(-4.97291 - 3.61303i) q^{78} +(-10.7922 - 2.29395i) q^{79} +(-3.38457 + 32.2020i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-10.4356 + 2.21816i) q^{82} +(9.96558 + 4.43696i) q^{83} +(-9.66779 + 10.7372i) q^{84} +(-1.96488 - 6.04727i) q^{85} +(-13.0729 - 14.5190i) q^{86} +(4.87492 - 8.44362i) q^{87} +(3.72811 + 6.45728i) q^{88} +(1.89815 - 5.84191i) q^{89} +(9.10873 - 4.05547i) q^{90} +(5.97839 - 4.34356i) q^{91} -3.35929 q^{92} +(0.877732 - 5.49814i) q^{93} +4.15756 q^{94} +(-2.29690 + 1.66880i) q^{95} +(7.22178 - 3.21534i) q^{96} +(3.74552 - 11.5275i) q^{97} +(-3.38306 - 5.85963i) q^{98} +(0.543635 - 0.941604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

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