LMFDB - Embedded newform 370.2.o.b.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 25 x^{15} + 132 x^{14} - 135 x^{13} + 666 x^{12} - 297 x^{11} + 1845 x^{10} + \cdots + 9 $ x^18 - 3x^17 + 18x^16 - 25x^15 + 132x^14 - 135x^13 + 666x^12 - 297x^11 + 1845x^10 - 382x^9 + 3810x^8 - 63x^7 + 3325x^6 - 1329x^5 + 1332x^4 - 192x^3 + 117x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			201.3
Root			$0.959958 + 1.66270i$ of defining polynomial
Character	$\chi$	$=$	370.201
Dual form			370.2.o.b.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(1.80413 - 0.656650i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{5} +1.91992 q^{6} +(0.523752 - 2.97035i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.525568 - 0.441004i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(1.80413 - 0.656650i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{5} +1.91992 q^{6} +(0.523752 - 2.97035i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.525568 - 0.441004i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.0362713 - 0.0628237i) q^{11} +(1.80413 + 0.656650i) q^{12} +(1.38935 + 1.16580i) q^{13} +(1.50808 - 2.61208i) q^{14} +(0.333390 + 1.89075i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.95162 - 2.47670i) q^{17} +(0.644705 - 0.234653i) q^{18} +(-4.22689 + 1.53846i) q^{19} +(-0.766044 + 0.642788i) q^{20} +(-1.00556 - 5.70282i) q^{21} +(-0.0125969 - 0.0714405i) q^{22} +(-2.29082 + 3.96781i) q^{23} +(1.47074 + 1.23410i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(0.906834 + 1.57068i) q^{26} +(-2.22127 + 3.84735i) q^{27} +(2.31052 - 1.93876i) q^{28} +(-0.789286 - 1.36708i) q^{29} +(-0.333390 + 1.89075i) q^{30} -7.06550 q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.106691 - 0.0895247i) q^{33} +(3.62069 - 1.31782i) q^{34} +(2.83427 + 1.03159i) q^{35} +0.686081 q^{36} +(4.63389 - 3.94044i) q^{37} -4.49816 q^{38} +(3.27210 + 1.19095i) q^{39} +(-0.939693 + 0.342020i) q^{40} +(0.737121 + 0.618518i) q^{41} +(1.00556 - 5.70282i) q^{42} -12.0058 q^{43} +(0.0125969 - 0.0714405i) q^{44} +(0.343040 + 0.594163i) q^{45} +(-3.50974 + 2.94502i) q^{46} +(4.71107 - 8.15981i) q^{47} +(0.959958 + 1.66270i) q^{48} +(-1.97080 - 0.717312i) q^{49} +(-0.766044 - 0.642788i) q^{50} +(3.69878 - 6.40647i) q^{51} +(0.314940 + 1.78611i) q^{52} +(0.660914 + 3.74823i) q^{53} +(-3.40318 + 2.85560i) q^{54} +(0.0681677 - 0.0248110i) q^{55} +(2.83427 - 1.03159i) q^{56} +(-6.61563 + 5.55117i) q^{57} +(-0.274116 - 1.55459i) q^{58} +(1.10423 + 6.26238i) q^{59} +(-0.959958 + 1.66270i) q^{60} +(-7.74792 - 6.50128i) q^{61} +(-6.63940 - 2.41655i) q^{62} +(-1.03467 - 1.79210i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.38935 + 1.16580i) q^{65} +(-0.0696378 - 0.120616i) q^{66} +(-0.207073 + 1.17437i) q^{67} +3.85306 q^{68} +(-1.52747 + 8.66272i) q^{69} +(2.31052 + 1.93876i) q^{70} +(10.1312 - 3.68746i) q^{71} +(0.644705 + 0.234653i) q^{72} +7.23307 q^{73} +(5.70214 - 2.11791i) q^{74} -1.91992 q^{75} +(-4.22689 - 1.53846i) q^{76} +(-0.205605 + 0.0748342i) q^{77} +(2.66744 + 2.23825i) q^{78} +(-0.426172 + 2.41694i) q^{79} -1.00000 q^{80} +(-1.83851 + 10.4267i) q^{81} +(0.481122 + 0.833327i) q^{82} +(-6.19118 + 5.19502i) q^{83} +(2.89540 - 5.01498i) q^{84} +(1.92653 + 3.33685i) q^{85} +(-11.2817 - 4.10622i) q^{86} +(-2.32167 - 1.94811i) q^{87} +(0.0362713 - 0.0628237i) q^{88} +(-0.212676 - 1.20614i) q^{89} +(0.119137 + 0.675658i) q^{90} +(4.19052 - 3.51626i) q^{91} +(-4.30533 + 1.56701i) q^{92} +(-12.7471 + 4.63957i) q^{93} +(7.21777 - 6.05643i) q^{94} +(-0.781097 - 4.42982i) q^{95} +(0.333390 + 1.89075i) q^{96} +(-3.99518 + 6.91985i) q^{97} +(-1.60661 - 1.34810i) q^{98} +(-0.0467685 - 0.0170224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	1.80413	−	0.656650i	1.04162	−	0.379117i	0.236123	−	0.971723i	$-0.424123\pi$
$3$	1.80413	−	0.656650i	1.04162	−	0.379117i	0.805493	+	0.592606i	$0.201901\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$6$	1.91992			0.783803
$7$	0.523752	−	2.97035i	0.197960	−	1.12269i	−0.710180	−	0.704020i	$-0.751387\pi$
$7$	0.523752	−	2.97035i	0.197960	−	1.12269i	0.908140	−	0.418666i	$-0.137502\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.525568	−	0.441004i	0.175189	−	0.147001i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−0.0362713	−	0.0628237i	−0.0109362	−	0.0189421i	0.860506	−	0.509441i	$-0.170148\pi$
$11$	−0.0362713	−	0.0628237i	−0.0109362	−	0.0189421i	−0.871442	+	0.490499i	$0.836815\pi$
$12$	1.80413	+	0.656650i	0.520808	+	0.189559i
$13$	1.38935	+	1.16580i	0.385337	+	0.323336i	0.814793	−	0.579752i	$-0.196850\pi$
$13$	1.38935	+	1.16580i	0.385337	+	0.323336i	−0.429457	+	0.903087i	$0.641295\pi$
$14$	1.50808	−	2.61208i	0.403053	−	0.698108i
$15$	0.333390	+	1.89075i	0.0860809	+	0.488189i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	2.95162	−	2.47670i	0.715872	−	0.600688i	−0.210368	−	0.977622i	$-0.567466\pi$
$17$	2.95162	−	2.47670i	0.715872	−	0.600688i	0.926240	+	0.376934i	$0.123022\pi$
$18$	0.644705	−	0.234653i	0.151958	−	0.0553083i
$19$	−4.22689	+	1.53846i	−0.969714	+	0.352947i	−0.777833	−	0.628471i	$-0.783681\pi$
$19$	−4.22689	+	1.53846i	−0.969714	+	0.352947i	−0.191881	+	0.981418i	$0.561459\pi$
$20$	−0.766044	+	0.642788i	−0.171293	+	0.143732i
$21$	−1.00556	−	5.70282i	−0.219431	−	1.24446i
$22$	−0.0125969	−	0.0714405i	−0.00268566	−	0.0152312i
$23$	−2.29082	+	3.96781i	−0.477669	+	0.827346i	−0.999672	−	0.0255970i	$-0.991851\pi$
$23$	−2.29082	+	3.96781i	−0.477669	+	0.827346i	0.522004	+	0.852943i	$0.325185\pi$
$24$	1.47074	+	1.23410i	0.300214	+	0.251909i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	0.906834	+	1.57068i	0.177845	+	0.308036i
$27$	−2.22127	+	3.84735i	−0.427483	+	0.740422i
$28$	2.31052	−	1.93876i	0.436647	−	0.366391i
$29$	−0.789286	−	1.36708i	−0.146567	−	0.253861i	0.783390	−	0.621531i	$-0.213489\pi$
$29$	−0.789286	−	1.36708i	−0.146567	−	0.253861i	−0.929956	+	0.367670i	$0.880156\pi$
$30$	−0.333390	+	1.89075i	−0.0608684	+	0.345202i
$31$	−7.06550			−1.26900			−0.634501	−	0.772922i	$-0.718794\pi$
$31$	−7.06550			−1.26900			−0.634501	+	0.772922i	$0.718794\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−0.106691	−	0.0895247i	−0.0185726	−	0.0155842i
$34$	3.62069	−	1.31782i	0.620944	−	0.226005i
$35$	2.83427	+	1.03159i	0.479079	+	0.174371i
$36$	0.686081			0.114347
$37$	4.63389	−	3.94044i	0.761807	−	0.647804i
$37$	4.63389	−	3.94044i	0.761807	−	0.647804i
$38$	−4.49816			−0.729697
$39$	3.27210	+	1.19095i	0.523955	+	0.190704i
$40$	−0.939693	+	0.342020i	−0.148578	+	0.0540781i
$41$	0.737121	+	0.618518i	0.115119	+	0.0965963i	0.698530	−	0.715581i	$-0.253838\pi$
$41$	0.737121	+	0.618518i	0.115119	+	0.0965963i	−0.583411	+	0.812177i	$0.698282\pi$
$42$	1.00556	−	5.70282i	0.155161	−	0.879964i
$43$	−12.0058			−1.83087			−0.915433	−	0.402472i	$-0.868151\pi$
$43$	−12.0058			−1.83087			−0.915433	+	0.402472i	$0.868151\pi$
$44$	0.0125969	−	0.0714405i	0.00189905	−	0.0107701i
$45$	0.343040	+	0.594163i	0.0511374	+	0.0885726i
$46$	−3.50974	+	2.94502i	−0.517482	+	0.434219i
$47$	4.71107	−	8.15981i	0.687180	−	1.19023i	−0.285567	−	0.958359i	$-0.592182\pi$
$47$	4.71107	−	8.15981i	0.687180	−	1.19023i	0.972746	−	0.231871i	$-0.0744848\pi$
$48$	0.959958	+	1.66270i	0.138558	+	0.239990i
$49$	−1.97080	−	0.717312i	−0.281542	−	0.102473i
$50$	−0.766044	−	0.642788i	−0.108335	−	0.0909039i
$51$	3.69878	−	6.40647i	0.517933	−	0.897086i
$52$	0.314940	+	1.78611i	0.0436744	+	0.247690i
$53$	0.660914	+	3.74823i	0.0907835	+	0.514859i	0.995958	+	0.0898190i	$0.0286289\pi$
$53$	0.660914	+	3.74823i	0.0907835	+	0.514859i	−0.905175	+	0.425040i	$0.860260\pi$
$54$	−3.40318	+	2.85560i	−0.463114	+	0.388599i
$55$	0.0681677	−	0.0248110i	0.00919173	−	0.00334552i
$56$	2.83427	−	1.03159i	0.378746	−	0.137852i
$57$	−6.61563	+	5.55117i	−0.876261	+	0.735270i
$58$	−0.274116	−	1.55459i	−0.0359932	−	0.204128i
$59$	1.10423	+	6.26238i	0.143758	+	0.815293i	0.968356	+	0.249573i	$0.0802904\pi$
$59$	1.10423	+	6.26238i	0.143758	+	0.815293i	−0.824598	+	0.565719i	$0.808599\pi$
$60$	−0.959958	+	1.66270i	−0.123930	+	0.214653i
$61$	−7.74792	−	6.50128i	−0.992020	−	0.832403i	−0.00616074	−	0.999981i	$-0.501961\pi$
$61$	−7.74792	−	6.50128i	−0.992020	−	0.832403i	−0.985859	+	0.167578i	$0.946405\pi$
$62$	−6.63940	−	2.41655i	−0.843205	−	0.306902i
$63$	−1.03467	−	1.79210i	−0.130356	−	0.225783i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.38935	+	1.16580i	−0.172328	+	0.144600i
$66$	−0.0696378	−	0.120616i	−0.00857182	−	0.0148468i
$67$	−0.207073	+	1.17437i	−0.0252980	+	0.143472i	−0.994841	−	0.101451i	$-0.967652\pi$
$67$	−0.207073	+	1.17437i	−0.0252980	+	0.143472i	0.969543	+	0.244923i	$0.0787627\pi$
$68$	3.85306			0.467252
$69$	−1.52747	+	8.66272i	−0.183886	+	1.04287i
$70$	2.31052	+	1.93876i	0.276160	+	0.231726i
$71$	10.1312	−	3.68746i	1.20235	−	0.437620i	0.338308	−	0.941036i	$-0.390146\pi$
$71$	10.1312	−	3.68746i	1.20235	−	0.437620i	0.864045	+	0.503415i	$0.167923\pi$
$72$	0.644705	+	0.234653i	0.0759792	+	0.0276542i
$73$	7.23307			0.846566			0.423283	−	0.905997i	$-0.360878\pi$
$73$	7.23307			0.846566			0.423283	+	0.905997i	$0.360878\pi$
$74$	5.70214	−	2.11791i	0.662861	−	0.246202i
$75$	−1.91992			−0.221693
$76$	−4.22689	−	1.53846i	−0.484857	−	0.176474i
$77$	−0.205605	+	0.0748342i	−0.0234309	+	0.00852815i
$78$	2.66744	+	2.23825i	0.302028	+	0.253431i
$79$	−0.426172	+	2.41694i	−0.0479481	+	0.271927i	−0.999351	−	0.0360216i	$-0.988532\pi$
$79$	−0.426172	+	2.41694i	−0.0479481	+	0.271927i	0.951403	+	0.307949i	$0.0996426\pi$
$80$	−1.00000			−0.111803
$81$	−1.83851	+	10.4267i	−0.204278	+	1.15852i
$82$	0.481122	+	0.833327i	0.0531310	+	0.0920256i
$83$	−6.19118	+	5.19502i	−0.679570	+	0.570227i	−0.915881	−	0.401450i	$-0.868506\pi$
$83$	−6.19118	+	5.19502i	−0.679570	+	0.570227i	0.236311	+	0.971678i	$0.424062\pi$
$84$	2.89540	−	5.01498i	0.315914	−	0.547179i
$85$	1.92653	+	3.33685i	0.208962	+	0.361932i
$86$	−11.2817	−	4.10622i	−1.21654	−	0.442785i
$87$	−2.32167	−	1.94811i	−0.248909	−	0.208860i
$88$	0.0362713	−	0.0628237i	0.00386653	−	0.00669703i
$89$	−0.212676	−	1.20614i	−0.0225436	−	0.127851i	0.971459	−	0.237207i	$-0.0762321\pi$
$89$	−0.212676	−	1.20614i	−0.0225436	−	0.127851i	−0.994003	+	0.109356i	$0.965121\pi$
$90$	0.119137	+	0.675658i	0.0125581	+	0.0712206i
$91$	4.19052	−	3.51626i	0.439286	−	0.368604i
$92$	−4.30533	+	1.56701i	−0.448862	+	0.163372i
$93$	−12.7471	+	4.63957i	−1.32181	+	0.481101i
$94$	7.21777	−	6.05643i	0.744456	−	0.624673i
$95$	−0.781097	−	4.42982i	−0.0801388	−	0.454490i
$96$	0.333390	+	1.89075i	0.0340265	+	0.192974i
$97$	−3.99518	+	6.91985i	−0.405649	+	0.702605i	−0.994397	−	0.105712i	$-0.966288\pi$
$97$	−3.99518	+	6.91985i	−0.405649	+	0.702605i	0.588748	+	0.808317i	$0.299621\pi$
$98$	−1.60661	−	1.34810i	−0.162292	−	0.136179i
$99$	−0.0467685	−	0.0170224i	−0.00470042	−	0.00171081i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.33351	−	9.23790i	0.530704	−	0.919206i	−0.468654	−	0.883382i	$-0.655261\pi$
$101$	5.33351	−	9.23790i	0.530704	−	0.919206i	0.999358	−	0.0358241i	$-0.0114056\pi$
$102$	5.66686	−	4.75506i	0.561102	−	0.470821i
$103$	0.0988979	+	0.171296i	0.00974470	+	0.0168783i	0.870857	−	0.491537i	$-0.163565\pi$
$103$	0.0988979	+	0.171296i	0.00974470	+	0.0168783i	−0.861112	+	0.508415i	$0.830231\pi$
$104$	−0.314940	+	1.78611i	−0.0308824	+	0.175143i
$105$	5.79079			0.565124
$106$	−0.660914	+	3.74823i	−0.0641937	+	0.364060i
$107$	−14.9638	−	12.5561i	−1.44661	−	1.21385i	−0.935010	−	0.354620i	$-0.884610\pi$
$107$	−14.9638	−	12.5561i	−1.44661	−	1.21385i	−0.511596	−	0.859226i	$-0.670945\pi$
$108$	−4.17462	+	1.51944i	−0.401703	+	0.146208i
$109$	0.221869	+	0.0807537i	0.0212512	+	0.00773480i	0.352624	−	0.935765i	$-0.385290\pi$
$109$	0.221869	+	0.0807537i	0.0212512	+	0.00773480i	−0.331373	+	0.943500i	$0.607512\pi$
$110$	0.0725425			0.00691666
$111$	5.77267	−	10.1519i	0.547917	−	0.963577i
$112$	3.01617			0.285001
$113$	5.43148	+	1.97690i	0.510951	+	0.185971i	0.584613	−	0.811312i	$-0.301246\pi$
$113$	5.43148	+	1.97690i	0.510951	+	0.185971i	−0.0736619	+	0.997283i	$0.523469\pi$
$114$	−8.11527	+	2.95372i	−0.760064	+	0.276641i
$115$	−3.50974	−	2.94502i	−0.327285	−	0.274624i
$116$	0.274116	−	1.55459i	0.0254510	−	0.144340i
$117$	1.24432			0.115038
$118$	−1.10423	+	6.26238i	−0.101652	+	0.576499i
$119$	−5.81074	−	10.0645i	−0.532670	−	0.922611i
$120$	−1.47074	+	1.23410i	−0.134260	+	0.112657i
$121$	5.49737	−	9.52172i	0.499761	−	0.865611i
$122$	−5.05710	−	8.75915i	−0.457848	−	0.793016i
$123$	1.73601	+	0.631857i	0.156531	+	0.0569726i
$124$	−5.41249	−	4.54162i	−0.486056	−	0.407849i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	−0.359336	−	2.03790i	−0.0320122	−	0.181550i
$127$	1.17874	+	6.68494i	0.104596	+	0.593193i	0.991381	+	0.131011i	$0.0418222\pi$
$127$	1.17874	+	6.68494i	0.104596	+	0.593193i	−0.886785	+	0.462182i	$0.847067\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−21.6600	+	7.88360i	−1.90706	+	0.694112i
$130$	−1.70429	+	0.620311i	−0.149476	+	0.0544049i
$131$	8.59193	−	7.20949i	0.750681	−	0.629896i	−0.185002	−	0.982738i	$-0.559229\pi$
$131$	8.59193	−	7.20949i	0.750681	−	0.629896i	0.935683	+	0.352842i	$0.114785\pi$
$132$	−0.0241850	−	0.137160i	−0.00210503	−	0.0119382i
$133$	2.35592	+	13.3611i	0.204284	+	1.15855i
$134$	−0.596244	+	1.03272i	−0.0515076	+	0.0892138i
$135$	−3.40318	−	2.85560i	−0.292899	−	0.245771i
$136$	3.62069	+	1.31782i	0.310472	+	0.113003i
$137$	9.04516	+	15.6667i	0.772781	+	1.33850i	0.936033	+	0.351911i	$0.114468\pi$
$137$	9.04516	+	15.6667i	0.772781	+	1.33850i	−0.163253	+	0.986584i	$0.552199\pi$
$138$	−4.39818	+	7.61787i	−0.374398	+	0.648476i
$139$	2.10630	−	1.76739i	0.178654	−	0.149908i	−0.549076	−	0.835773i	$-0.685020\pi$
$139$	2.10630	−	1.76739i	0.178654	−	0.149908i	0.727729	+	0.685864i	$0.240576\pi$
$140$	1.50808	+	2.61208i	0.127456	+	0.220761i
$141$	3.14125	−	17.8149i	0.264541	−	1.50028i
$142$	10.7814			0.904755
$143$	0.0228466	−	0.129569i	0.00191053	−	0.0108351i
$144$	0.525568	+	0.441004i	0.0437974	+	0.0367503i
$145$	1.48337	−	0.539903i	0.123187	−	0.0448365i
$146$	6.79686	+	2.47385i	0.562512	+	0.204738i
$147$	−4.02660			−0.332108
$148$	6.08263	−	0.0399398i	0.499989	−	0.00328304i
$149$	0.832346			0.0681885			0.0340942	−	0.999419i	$-0.489145\pi$
$149$	0.832346			0.0681885			0.0340942	+	0.999419i	$0.489145\pi$
$150$	−1.80413	−	0.656650i	−0.147307	−	0.0536153i
$151$	−1.86366	+	0.678318i	−0.151663	+	0.0552008i	−0.416736	−	0.909028i	$-0.636826\pi$
$151$	−1.86366	+	0.678318i	−0.151663	+	0.0552008i	0.265073	+	0.964228i	$0.414604\pi$
$152$	−3.44579	−	2.89136i	−0.279490	−	0.234520i
$153$	0.459041	−	2.60335i	0.0371113	−	0.210468i
$154$	−0.218801			−0.0176315
$155$	1.22691	−	6.95816i	0.0985479	−	0.558893i
$156$	1.74105	+	3.01558i	0.139395	+	0.241440i
$157$	0.690555	−	0.579444i	0.0551123	−	0.0462447i	−0.614815	−	0.788671i	$-0.710770\pi$
$157$	0.690555	−	0.579444i	0.0551123	−	0.0462447i	0.669928	+	0.742426i	$0.266325\pi$
$158$	−1.22711	+	2.12542i	−0.0976240	+	0.169090i
$159$	3.65365	+	6.32831i	0.289754	+	0.501868i
$160$	−0.939693	−	0.342020i	−0.0742892	−	0.0270391i
$161$	10.5860	+	8.88268i	0.834291	+	0.700053i
$162$	−5.29377	+	9.16907i	−0.415918	+	0.720391i
$163$	3.37925	+	19.1647i	0.264684	+	1.50109i	0.769935	+	0.638123i	$0.220289\pi$
$163$	3.37925	+	19.1647i	0.264684	+	1.50109i	−0.505251	+	0.862972i	$0.668600\pi$
$164$	0.167092	+	0.947624i	0.0130477	+	0.0739970i
$165$	0.106691	−	0.0895247i	0.00830591	−	0.00696949i
$166$	−7.59461	+	2.76421i	−0.589456	+	0.214544i
$167$	15.0722	−	5.48583i	1.16632	−	0.424506i	0.314969	−	0.949102i	$-0.398006\pi$
$167$	15.0722	−	5.48583i	1.16632	−	0.424506i	0.851351	+	0.524596i	$0.175784\pi$
$168$	4.43601	−	3.72225i	0.342245	−	0.287178i
$169$	−1.68623	−	9.56308i	−0.129710	−	0.735622i
$170$	0.669077	+	3.79452i	0.0513159	+	0.291027i
$171$	−1.54305	+	2.67264i	−0.118000	+	0.204382i
$172$	−9.19696	−	7.71717i	−0.701262	−	0.588429i
$173$	19.7208	+	7.17780i	1.49935	+	0.545718i	0.955891	−	0.293720i	$-0.0948934\pi$
$173$	19.7208	+	7.17780i	1.49935	+	0.545718i	0.543456	+	0.839438i	$0.317116\pi$
$174$	−1.51536	−	2.62469i	−0.114879	−	0.198977i
$175$	−1.50808	+	2.61208i	−0.114000	+	0.197455i
$176$	0.0555708	−	0.0466295i	0.00418881	−	0.00351483i
$177$	6.10437	+	10.5731i	0.458832	+	0.794721i
$178$	0.212676	−	1.20614i	0.0159407	−	0.0904043i
$179$	15.4891			1.15771			0.578854	−	0.815431i	$-0.303500\pi$
$179$	15.4891			1.15771			0.578854	+	0.815431i	$0.303500\pi$
$180$	−0.119137	+	0.675658i	−0.00887992	+	0.0503605i
$181$	5.69804	+	4.78122i	0.423532	+	0.355385i	0.829505	−	0.558500i	$-0.188623\pi$
$181$	5.69804	+	4.78122i	0.423532	+	0.355385i	−0.405973	+	0.913885i	$0.633067\pi$
$182$	5.14043	−	1.87096i	0.381034	−	0.138685i
$183$	−18.2473	−	6.64149i	−1.34888	−	0.490953i
$184$	−4.58164			−0.337763
$185$	3.07590	+	5.24774i	0.226145	+	0.385822i
$186$	−13.5652			−0.994647
$187$	−0.262654	−	0.0955983i	−0.0192072	−	0.00699084i
$188$	8.85391	−	3.22256i	0.645738	−	0.235029i
$189$	10.2646	+	8.61299i	0.746637	+	0.626503i
$190$	0.781097	−	4.42982i	0.0566667	−	0.321373i
$191$	7.78055			0.562981			0.281490	−	0.959564i	$-0.409171\pi$
$191$	7.78055			0.562981			0.281490	+	0.959564i	$0.409171\pi$
$192$	−0.333390	+	1.89075i	−0.0240604	+	0.136453i
$193$	9.16086	+	15.8671i	0.659413	+	1.14214i	0.980768	+	0.195178i	$0.0625286\pi$
$193$	9.16086	+	15.8671i	0.659413	+	1.14214i	−0.321355	+	0.946959i	$0.604138\pi$
$194$	−6.12097	+	5.13610i	−0.439460	+	0.368751i
$195$	−1.74105	+	3.01558i	−0.124679	+	0.215950i
$196$	−1.04864	−	1.81630i	−0.0749028	−	0.129735i
$197$	−12.8040	−	4.66028i	−0.912249	−	0.332031i	−0.157098	−	0.987583i	$-0.550214\pi$
$197$	−12.8040	−	4.66028i	−0.912249	−	0.332031i	−0.755151	+	0.655551i	$0.772436\pi$
$198$	−0.0381261	−	0.0319916i	−0.00270950	−	0.00227354i
$199$	9.40801	−	16.2951i	0.666916	−	1.15513i	−0.311846	−	0.950133i	$-0.600947\pi$
$199$	9.40801	−	16.2951i	0.666916	−	1.15513i	0.978762	−	0.205000i	$-0.0657193\pi$
$200$	−0.173648	−	0.984808i	−0.0122788	−	0.0696364i
$201$	0.397563	+	2.25469i	0.0280420	+	0.159034i
$202$	8.17140	−	6.85662i	0.574938	−	0.482430i
$203$	−4.47410	+	1.62844i	−0.314020	+	0.114294i
$204$	6.95143	−	2.53011i	0.486697	−	0.177143i
$205$	−0.737121	+	0.618518i	−0.0514828	+	0.0431992i
$206$	0.0343469	+	0.194791i	0.00239306	+	0.0135717i
$207$	0.545841	+	3.09562i	0.0379386	+	0.215160i
$208$	−0.906834	+	1.57068i	−0.0628776	+	0.108907i
$209$	0.249966	+	0.209747i	0.0172905	+	0.0145085i
$210$	5.44157	+	1.98057i	0.375504	+	0.136672i
$211$	−6.59683	−	11.4260i	−0.454145	−	0.786602i	0.544494	−	0.838765i	$-0.316722\pi$
$211$	−6.59683	−	11.4260i	−0.454145	−	0.786602i	−0.998639	+	0.0521632i	$0.983388\pi$
$212$	−1.90303	+	3.29614i	−0.130700	+	0.226380i
$213$	15.8567	−	13.3053i	1.08648	−	0.911665i
$214$	−9.76693	−	16.9168i	−0.667654	−	1.15641i
$215$	2.08478	−	11.8234i	0.142181	−	0.806348i
$216$	−4.44253			−0.302276
$217$	−3.70057	+	20.9870i	−0.251211	+	1.42469i
$218$	0.180869	+	0.151767i	0.0122500	+	0.0102790i
$219$	13.0494	−	4.74959i	0.881797	−	0.320948i
$220$	0.0681677	+	0.0248110i	0.00459587	+	0.00167276i
$221$	6.98818			0.470076
$222$	8.89669	−	7.56531i	0.597107	−	0.507750i
$223$	−7.58430			−0.507882			−0.253941	−	0.967220i	$-0.581727\pi$
$223$	−7.58430			−0.507882			−0.253941	+	0.967220i	$0.581727\pi$
$224$	2.83427	+	1.03159i	0.189373	+	0.0689261i
$225$	−0.644705	+	0.234653i	−0.0429803	+	0.0156436i
$226$	4.42779	+	3.71535i	0.294532	+	0.247142i
$227$	−3.40608	+	19.3169i	−0.226070	+	1.28210i	0.634560	+	0.772874i	$0.281181\pi$
$227$	−3.40608	+	19.3169i	−0.226070	+	1.28210i	−0.860630	+	0.509231i	$0.829930\pi$
$228$	−8.63609			−0.571939
$229$	−0.729381	+	4.13653i	−0.0481989	+	0.273349i	−0.999377	−	0.0352931i	$-0.988764\pi$
$229$	−0.729381	+	4.13653i	−0.0481989	+	0.273349i	0.951178	+	0.308642i	$0.0998746\pi$
$230$	−2.29082	−	3.96781i	−0.151052	−	0.261630i
$231$	−0.321799	+	0.270022i	−0.0211728	+	0.0177661i
$232$	0.789286	−	1.36708i	0.0518191	−	0.0897534i
$233$	−3.61938	−	6.26894i	−0.237113	−	0.410692i	0.722772	−	0.691087i	$-0.242868\pi$
$233$	−3.61938	−	6.26894i	−0.237113	−	0.410692i	−0.959885	+	0.280395i	$0.909535\pi$
$234$	1.16928	+	0.425584i	0.0764383	+	0.0278213i
$235$	7.21777	+	6.05643i	0.470836	+	0.395078i
$236$	−3.17950	+	5.50705i	−0.206968	+	0.358478i
$237$	0.818216	+	4.64033i	0.0531488	+	0.301422i
$238$	−2.01805	−	11.4449i	−0.130811	−	0.741865i
$239$	13.7270	−	11.5183i	0.887927	−	0.745059i	−0.0798662	−	0.996806i	$-0.525449\pi$
$239$	13.7270	−	11.5183i	0.887927	−	0.745059i	0.967793	+	0.251746i	$0.0810049\pi$
$240$	−1.80413	+	0.656650i	−0.116456	+	0.0423866i
$241$	−5.64874	+	2.05597i	−0.363868	+	0.132437i	−0.517482	−	0.855694i	$-0.673131\pi$
$241$	−5.64874	+	2.05597i	−0.363868	+	0.132437i	0.153615	+	0.988131i	$0.450908\pi$
$242$	8.42246	−	7.06728i	0.541416	−	0.454302i
$243$	1.21547	+	6.89325i	0.0779722	+	0.442202i
$244$	−1.75631	−	9.96053i	−0.112436	−	0.637658i
$245$	1.04864	−	1.81630i	0.0669951	−	0.116039i
$246$	1.41521	+	1.18750i	0.0902306	+	0.0757124i
$247$	−7.66617	−	2.79026i	−0.487787	−	0.177540i
$248$	−3.53275	−	6.11891i	−0.224330	−	0.388551i
$249$	−7.75839	+	13.4379i	−0.491668	+	0.851594i
$250$	0.766044	−	0.642788i	0.0484489	−	0.0406535i
$251$	7.52954	+	13.0415i	0.475260	+	0.823175i	0.999598	−	0.0283349i	$-0.00902049\pi$
$251$	7.52954	+	13.0415i	0.475260	+	0.823175i	−0.524338	+	0.851510i	$0.675687\pi$
$252$	0.359336	−	2.03790i	0.0226361	−	0.128376i
$253$	0.332364			0.0208955
$254$	−1.17874	+	6.68494i	−0.0739605	+	0.419451i
$255$	5.66686	+	4.75506i	0.354872	+	0.297773i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−3.72728	−	1.35662i	−0.232502	−	0.0846237i	0.223142	−	0.974786i	$-0.428369\pi$
$257$	−3.72728	−	1.35662i	−0.232502	−	0.0846237i	−0.455644	+	0.890162i	$0.650591\pi$
$258$	−23.0501			−1.43504
$259$	−9.27745	−	15.8281i	−0.576473	−	0.983509i
$260$	−1.81367			−0.112479
$261$	−1.01771	−	0.370417i	−0.0629948	−	0.0229282i
$262$	10.5396	−	3.83609i	0.651137	−	0.236994i
$263$	−12.9633	−	10.8775i	−0.799353	−	0.670737i	0.148688	−	0.988884i	$-0.452495\pi$
$263$	−12.9633	−	10.8775i	−0.799353	−	0.670737i	−0.948041	+	0.318147i	$0.896939\pi$
$264$	0.0241850	−	0.137160i	0.00148848	−	0.00844160i
$265$	−3.80605			−0.233804
$266$	−2.35592	+	13.3611i	−0.144451	+	0.819221i
$267$	−1.17571	−	2.03639i	−0.0719523	−	0.124625i
$268$	−0.913498	+	0.766516i	−0.0558008	+	0.0468224i
$269$	6.39745	−	11.0807i	0.390059	−	0.675602i	−0.602398	−	0.798196i	$-0.705788\pi$
$269$	6.39745	−	11.0807i	0.390059	−	0.675602i	0.992457	+	0.122594i	$0.0391212\pi$
$270$	−2.22127	−	3.84735i	−0.135182	−	0.234142i
$271$	−13.6487	−	4.96771i	−0.829098	−	0.301767i	−0.107609	−	0.994193i	$-0.534320\pi$
$271$	−13.6487	−	4.96771i	−0.829098	−	0.301767i	−0.721489	+	0.692426i	$0.756542\pi$
$272$	2.95162	+	2.47670i	0.178968	+	0.150172i
$273$	5.25129	−	9.09550i	0.317823	−	0.550485i
$274$	3.14135	+	17.8155i	0.189776	+	1.07627i
$275$	0.0125969	+	0.0714405i	0.000759621	+	0.00430802i
$276$	−6.73840	+	5.65419i	−0.405604	+	0.340342i
$277$	−3.72999	+	1.35761i	−0.224113	+	0.0815706i	−0.451636	−	0.892202i	$-0.649160\pi$
$277$	−3.72999	+	1.35761i	−0.224113	+	0.0815706i	0.227523	+	0.973773i	$0.426937\pi$
$278$	2.58376	−	0.940410i	0.154963	−	0.0564020i
$279$	−3.71341	+	3.11592i	−0.222316	+	0.186545i
$280$	0.523752	+	2.97035i	0.0313002	+	0.177512i
$281$	2.65688	+	15.0679i	0.158496	+	0.898877i	0.955519	+	0.294928i	$0.0952957\pi$
$281$	2.65688	+	15.0679i	0.158496	+	0.898877i	−0.797023	+	0.603949i	$0.793593\pi$
$282$	9.04486	−	15.6662i	0.538613	−	0.932906i
$283$	−13.1056	−	10.9969i	−0.779048	−	0.653699i	0.163961	−	0.986467i	$-0.447573\pi$
$283$	−13.1056	−	10.9969i	−0.779048	−	0.653699i	−0.943009	+	0.332768i	$0.892017\pi$
$284$	10.1312	+	3.68746i	0.601176	+	0.218810i
$285$	−4.31804	−	7.47907i	−0.255779	−	0.443022i
$286$	0.0657841	−	0.113941i	0.00388989	−	0.00673749i
$287$	2.22328	−	1.86556i	0.131236	−	0.110120i
$288$	0.343040	+	0.594163i	0.0202138	+	0.0350114i
$289$	−0.374025	+	2.12120i	−0.0220014	+	0.124776i
$290$	1.57857			0.0926969
$291$	−2.66391	+	15.1078i	−0.156161	+	0.885633i
$292$	5.54085	+	4.64933i	0.324254	+	0.272081i
$293$	32.0304	−	11.6581i	1.87123	−	0.681074i	0.903798	−	0.427960i	$-0.140768\pi$
$293$	32.0304	−	11.6581i	1.87123	−	0.681074i	0.967437	−	0.253113i	$-0.0814546\pi$
$294$	−3.78377	−	1.37718i	−0.220674	−	0.0803187i
$295$	−6.35899			−0.370235
$296$	5.72946	+	2.04285i	0.333018	+	0.118738i
$297$	0.322273			0.0187002
$298$	0.782150	+	0.284679i	0.0453087	+	0.0164910i
$299$	−7.80844	+	2.84204i	−0.451574	+	0.164359i
$300$	−1.47074	−	1.23410i	−0.0849133	−	0.0712507i
$301$	−6.28806	+	35.6613i	−0.362438	+	2.05549i
$302$	−1.98327			−0.114124
$303$	3.55628	−	20.1686i	0.204303	−	1.15866i
$304$	−2.24908	−	3.89552i	−0.128994	−	0.223423i
$305$	7.74792	−	6.50128i	0.443645	−	0.372262i
$306$	1.32176	−	2.28935i	0.0755597	−	0.130873i
$307$	7.71779	+	13.3676i	0.440478	+	0.762930i	0.997725	−	0.0674169i	$-0.0214758\pi$
$307$	7.71779	+	13.3676i	0.440478	+	0.762930i	−0.557247	+	0.830347i	$0.688142\pi$
$308$	−0.205605	−	0.0748342i	−0.0117155	−	0.00426408i
$309$	0.290907	+	0.244100i	0.0165491	+	0.0138863i
$310$	3.53275	−	6.11891i	0.200647	−	0.347531i
$311$	−0.386719	−	2.19319i	−0.0219288	−	0.124365i	0.971878	−	0.235484i	$-0.0756675\pi$
$311$	−0.386719	−	2.19319i	−0.0219288	−	0.124365i	−0.993807	+	0.111119i	$0.964556\pi$
$312$	0.604659	+	3.42919i	0.0342321	+	0.194140i
$313$	23.2118	−	19.4770i	1.31201	−	1.10091i	0.324075	−	0.946031i	$-0.394947\pi$
$313$	23.2118	−	19.4770i	1.31201	−	1.10091i	0.987934	−	0.154875i	$-0.0494974\pi$
$314$	0.847091	−	0.308316i	0.0478041	−	0.0173993i
$315$	1.94454	−	0.707755i	0.109562	−	0.0398774i
$316$	−1.88005	+	1.57755i	−0.105761	+	0.0887440i
$317$	−4.77729	−	27.0933i	−0.268319	−	1.52171i	−0.759414	−	0.650607i	$-0.774514\pi$
$317$	−4.77729	−	27.0933i	−0.268319	−	1.52171i	0.491095	−	0.871106i	$-0.336597\pi$
$318$	1.26890	+	7.19629i	0.0711564	+	0.403548i
$319$	−0.0572568	+	0.0991717i	−0.00320576	+	0.00555255i
$320$	−0.766044	−	0.642788i	−0.0428232	−	0.0359329i
$321$	−35.2417	−	12.8269i	−1.96700	−	0.715929i
$322$	6.90949	+	11.9676i	0.385051	+	0.666928i
$323$	−8.66584	+	15.0097i	−0.482180	+	0.835160i
$324$	−8.11052	+	6.80554i	−0.450585	+	0.378085i
$325$	−0.906834	−	1.57068i	−0.0503021	−	0.0871258i
$326$	−3.37925	+	19.1647i	−0.187160	+	1.06143i
$327$	0.453308			0.0250680
$328$	−0.167092	+	0.947624i	−0.00922610	+	0.0523238i
$329$	−21.7700	−	18.2672i	−1.20022	−	1.00710i
$330$	0.130876	−	0.0476351i	0.00720450	−	0.00262222i
$331$	−28.6624	−	10.4323i	−1.57543	−	0.573409i	−0.601224	−	0.799081i	$-0.705320\pi$
$331$	−28.6624	−	10.4323i	−1.57543	−	0.573409i	−0.974203	+	0.225672i	$0.927542\pi$
$332$	−8.08201			−0.443558
$333$	0.697679	−	4.11453i	0.0382326	−	0.225475i
$334$	16.0395			0.877641
$335$	−1.12057	−	0.407855i	−0.0612233	−	0.0222835i
$336$	5.44157	−	1.98057i	0.296862	−	0.108049i
$337$	−4.31933	−	3.62435i	−0.235289	−	0.197431i	0.517518	−	0.855672i	$-0.326856\pi$
$337$	−4.31933	−	3.62435i	−0.235289	−	0.197431i	−0.752807	+	0.658242i	$0.771301\pi$
$338$	1.68623	−	9.56308i	0.0917188	−	0.520163i
$339$	11.0972			0.602720
$340$	−0.669077	+	3.79452i	−0.0362858	+	0.205787i
$341$	0.256275	+	0.443881i	0.0138781	+	0.0240375i
$342$	−2.36409	+	1.98371i	−0.127835	+	0.107267i
$343$	7.39372	−	12.8063i	0.399223	−	0.691475i
$344$	−6.00289	−	10.3973i	−0.323654	−	0.560586i
$345$	−8.26587	−	3.00853i	−0.445020	−	0.161974i
$346$	16.0766	+	13.4898i	0.864282	+	0.725218i
$347$	0.179334	−	0.310615i	0.00962713	−	0.0166747i	−0.861172	−	0.508314i	$-0.830269\pi$
$347$	0.179334	−	0.310615i	0.00962713	−	0.0166747i	0.870799	+	0.491639i	$0.163602\pi$
$348$	−0.526280	−	2.98468i	−0.0282116	−	0.159996i
$349$	1.58957	+	9.01490i	0.0850877	+	0.482556i	0.997338	+	0.0729223i	$0.0232325\pi$
$349$	1.58957	+	9.01490i	0.0850877	+	0.482556i	−0.912250	+	0.409634i	$0.865656\pi$
$350$	−2.31052	+	1.93876i	−0.123502	+	0.103631i
$351$	−7.57137	+	2.75575i	−0.404130	+	0.147091i
$352$	0.0681677	−	0.0248110i	0.00363335	−	0.00132243i
$353$	−20.1210	+	16.8836i	−1.07093	+	0.898621i	−0.995137	−	0.0985023i	$-0.968595\pi$
$353$	−20.1210	+	16.8836i	−1.07093	+	0.898621i	−0.0757979	+	0.997123i	$0.524150\pi$
$354$	2.12002	+	12.0233i	0.112678	+	0.639029i
$355$	1.87217	+	10.6176i	0.0993645	+	0.563524i
$356$	0.612376	−	1.06067i	0.0324558	−	0.0562152i
$357$	−17.0922	−	14.3421i	−0.904615	−	0.759062i
$358$	14.5550	+	5.29758i	0.769254	+	0.279986i
$359$	−10.2805	−	17.8064i	−0.542585	−	0.939785i	−0.998755	−	0.0498920i	$-0.984112\pi$
$359$	−10.2805	−	17.8064i	−0.542585	−	0.939785i	0.456170	−	0.889893i	$-0.349221\pi$
$360$	−0.343040	+	0.594163i	−0.0180798	+	0.0313152i
$361$	0.944853	−	0.792826i	0.0497291	−	0.0417277i
$362$	3.71913	+	6.44172i	0.195473	+	0.338569i
$363$	3.66554	−	20.7883i	0.192391	−	1.09110i
$364$	5.47033			0.286723
$365$	−1.25601	+	7.12318i	−0.0657425	+	0.372844i
$366$	−14.8754	−	12.4819i	−0.777548	−	0.652440i
$367$	−12.3611	+	4.49906i	−0.645243	+	0.234849i	−0.643852	−	0.765150i	$-0.722665\pi$
$367$	−12.3611	+	4.49906i	−0.645243	+	0.234849i	−0.00139041	+	0.999999i	$0.500443\pi$
$368$	−4.30533	−	1.56701i	−0.224431	−	0.0816861i
$369$	0.660176			0.0343674
$370$	1.09557	+	5.98329i	0.0569560	+	0.311056i
$371$	11.4797			0.595996
$372$	−12.7471	−	4.63957i	−0.660906	−	0.240550i
$373$	−20.0144	+	7.28465i	−1.03631	+	0.377185i	−0.803479	−	0.595333i	$-0.797020\pi$
$373$	−20.0144	+	7.28465i	−1.03631	+	0.377185i	−0.232828	+	0.972518i	$0.574798\pi$
$374$	−0.214118	−	0.179666i	−0.0110718	−	0.00929031i
$375$	0.333390	−	1.89075i	0.0172162	−	0.0976379i
$376$	9.42213			0.485909
$377$	0.497156	−	2.81951i	0.0256048	−	0.145212i
$378$	6.69972	+	11.6042i	0.344596	+	0.596858i
$379$	−27.4821	+	23.0602i	−1.41166	+	1.18452i	−0.456027	+	0.889966i	$0.650728\pi$
$379$	−27.4821	+	23.0602i	−1.41166	+	1.18452i	−0.955634	+	0.294558i	$0.904827\pi$
$380$	2.24908	−	3.89552i	0.115375	−	0.199836i
$381$	6.51626	+	11.2865i	0.333838	+	0.578225i
$382$	7.31133	+	2.66110i	0.374080	+	0.136154i
$383$	5.63939	+	4.73201i	0.288160	+	0.241795i	0.775396	−	0.631476i	$-0.217550\pi$
$383$	5.63939	+	4.73201i	0.288160	+	0.241795i	−0.487236	+	0.873270i	$0.661995\pi$
$384$	−0.959958	+	1.66270i	−0.0489877	+	0.0848491i
$385$	−0.0379943	−	0.215477i	−0.00193637	−	0.0109817i
$386$	3.18153	+	18.0434i	0.161936	+	0.918384i
$387$	−6.30986	+	5.29460i	−0.320748	+	0.269140i
$388$	−7.50848	+	2.73286i	−0.381185	+	0.138740i
$389$	−13.2763	+	4.83219i	−0.673137	+	0.245002i	−0.655898	−	0.754850i	$-0.727710\pi$
$389$	−13.2763	+	4.83219i	−0.673137	+	0.245002i	−0.0172390	+	0.999851i	$0.505488\pi$
$390$	−2.66744	+	2.23825i	−0.135071	+	0.113338i
$391$	3.06547	+	17.3851i	0.155027	+	0.879204i
$392$	−0.364189	−	2.06542i	−0.0183943	−	0.104319i
$393$	10.7669	−	18.6488i	0.543117	−	0.940706i
$394$	−10.4379	−	8.75847i	−0.525856	−	0.441245i
$395$	−2.30622	−	0.839396i	−0.116039	−	0.0422346i
$396$	−0.0248850	−	0.0431021i	−0.00125052	−	0.00216596i
$397$	−13.8801	+	24.0411i	−0.696623	+	1.20659i	0.273008	+	0.962012i	$0.411982\pi$
$397$	−13.8801	+	24.0411i	−0.696623	+	1.20659i	−0.969631	+	0.244574i	$0.921352\pi$
$398$	14.4139	−	12.0947i	0.722504	−	0.606252i
$399$	13.0240	+	22.5581i	0.652013	+	1.12932i
$400$	0.173648	−	0.984808i	0.00868241	−	0.0492404i
$401$	−33.9959			−1.69768			−0.848838	−	0.528653i	$-0.822697\pi$
$401$	−33.9959			−1.69768			−0.848838	+	0.528653i	$0.822697\pi$
$402$	−0.397563	+	2.25469i	−0.0198287	+	0.112454i
$403$	−9.81646	−	8.23699i	−0.488993	−	0.410314i
$404$	10.0237	−	3.64833i	0.498698	−	0.181511i
$405$	−9.94903	−	3.62115i	−0.494371	−	0.179936i
$406$	−4.76124			−0.236296
$407$	−0.415630	−	0.148194i	−0.0206020	−	0.00734569i
$408$	7.39756			0.366234
$409$	−21.0798	−	7.67243i	−1.04233	−	0.379377i	−0.236567	−	0.971615i	$-0.576022\pi$
$409$	−21.0798	−	7.67243i	−1.04233	−	0.379377i	−0.805763	+	0.592238i	$0.798244\pi$
$410$	−0.904213	+	0.329107i	−0.0446559	+	0.0162534i
$411$	26.6062	+	22.3253i	1.31239	+	1.10122i
$412$	−0.0343469	+	0.194791i	−0.00169215	+	0.00959666i
$413$	19.1798			0.943776
$414$	−0.545841	+	3.09562i	−0.0268266	+	0.152141i
$415$	−4.04101	−	6.99923i	−0.198365	−	0.343579i
$416$	−1.38935	+	1.16580i	−0.0681185	+	0.0571582i
$417$	2.63948	−	4.57171i	0.129256	−	0.223878i
$418$	0.163154	+	0.282591i	0.00798012	+	0.0138220i
$419$	25.6289	+	9.32816i	1.25205	+	0.455710i	0.881095	−	0.472939i	$-0.156807\pi$
$419$	25.6289	+	9.32816i	1.25205	+	0.455710i	0.370959	+	0.928649i	$0.379029\pi$
$420$	4.43601	+	3.72225i	0.216455	+	0.181627i
$421$	5.73948	−	9.94108i	0.279725	−	0.484499i	−0.691591	−	0.722289i	$-0.743090\pi$
$421$	5.73948	−	9.94108i	0.279725	−	0.484499i	0.971316	+	0.237791i	$0.0764232\pi$
$422$	−2.29106	−	12.9932i	−0.111527	−	0.632500i
$423$	−1.12252	−	6.36614i	−0.0545789	−	0.309532i
$424$	−2.91561	+	2.44648i	−0.141594	+	0.118812i
$425$	−3.62069	+	1.31782i	−0.175629	+	0.0639239i
$426$	19.4511	−	7.07961i	0.942407	−	0.343008i
$427$	−23.3690	+	19.6090i	−1.13091	+	0.948944i
$428$	−3.39202	−	19.2371i	−0.163959	−	0.929860i
$429$	−0.0438635	−	0.248762i	−0.00211775	−	0.0120104i
$430$	6.00289	−	10.3973i	0.289485	−	0.501403i
$431$	−2.46860	−	2.07140i	−0.118908	−	0.0997761i	0.581394	−	0.813622i	$-0.302507\pi$
$431$	−2.46860	−	2.07140i	−0.118908	−	0.0997761i	−0.700303	+	0.713846i	$0.746952\pi$
$432$	−4.17462	−	1.51944i	−0.200851	−	0.0731039i
$433$	−17.4071	−	30.1499i	−0.836530	−	1.44891i	−0.892779	−	0.450496i	$-0.851247\pi$
$433$	−17.4071	−	30.1499i	−0.836530	−	1.44891i	0.0562485	−	0.998417i	$-0.482086\pi$
$434$	−10.6554	+	18.4557i	−0.511475	+	0.885900i
$435$	2.32167	−	1.94811i	0.111316	−	0.0934049i
$436$	0.118054	+	0.204476i	0.00565376	+	0.00979260i
$437$	3.57870	−	20.2958i	0.171192	−	0.970881i
$438$	13.8869			0.663541
$439$	3.72905	−	21.1485i	0.177978	−	1.00936i	−0.756673	−	0.653794i	$-0.773176\pi$
$439$	3.72905	−	21.1485i	0.177978	−	1.00936i	0.934651	−	0.355568i	$-0.115712\pi$
$440$	0.0555708	+	0.0466295i	0.00264923	+	0.00222297i
$441$	−1.35213	+	0.492134i	−0.0643870	+	0.0234349i
$442$	6.56674	+	2.39010i	0.312348	+	0.113685i
$443$	−31.2314			−1.48385			−0.741923	−	0.670485i	$-0.766086\pi$
$443$	−31.2314			−1.48385			−0.741923	+	0.670485i	$0.766086\pi$
$444$	10.9476	−	4.06622i	0.519552	−	0.192974i
$445$	1.22475			0.0580588
$446$	−7.12691	−	2.59398i	−0.337469	−	0.122829i
$447$	1.50166	−	0.546560i	0.0710262	−	0.0258514i
$448$	2.31052	+	1.93876i	0.109162	+	0.0915976i
$449$	−0.0871484	+	0.494243i	−0.00411279	+	0.0233248i	−0.986795	−	0.161974i	$-0.948214\pi$
$449$	−0.0871484	+	0.494243i	−0.00411279	+	0.0233248i	0.982682	+	0.185298i	$0.0593252\pi$
$450$	−0.686081			−0.0323422
$451$	0.0121213	−	0.0687431i	0.000570768	−	0.00323699i
$452$	2.89003	+	5.00568i	0.135936	+	0.235448i
$453$	−2.91688	+	2.44755i	−0.137047	+	0.114996i
$454$	−9.80742	+	16.9870i	−0.460285	+	0.797237i
$455$	2.73517	+	4.73745i	0.128227	+	0.222095i
$456$	−8.11527	−	2.95372i	−0.380032	−	0.138320i
$457$	14.6298	+	12.2759i	0.684354	+	0.574241i	0.917275	−	0.398254i	$-0.130384\pi$
$457$	14.6298	+	12.2759i	0.684354	+	0.574241i	−0.232921	+	0.972496i	$0.574828\pi$
$458$	−2.10017	+	3.63760i	−0.0981345	+	0.169974i
$459$	2.97240	+	16.8573i	0.138740	+	0.786831i
$460$	−0.795593	−	4.51203i	−0.0370947	−	0.210374i
$461$	2.28359	−	1.91616i	0.106357	−	0.0892444i	−0.588058	−	0.808819i	$-0.700107\pi$
$461$	2.28359	−	1.91616i	0.106357	−	0.0892444i	0.694416	+	0.719574i	$0.255663\pi$
$462$	−0.394745	+	0.143675i	−0.0183652	+	0.00668439i
$463$	−21.7370	+	7.91162i	−1.01020	+	0.367684i	−0.793511	−	0.608555i	$-0.791749\pi$
$463$	−21.7370	+	7.91162i	−1.01020	+	0.367684i	−0.216693	+	0.976240i	$0.569527\pi$
$464$	1.20926	−	1.01469i	0.0561383	−	0.0471056i
$465$	−2.35557	−	13.3591i	−0.109237	−	0.619513i
$466$	−1.25700	−	7.12878i	−0.0582292	−	0.330234i
$467$	19.0700	−	33.0302i	0.882453	−	1.52845i	0.0338485	−	0.999427i	$-0.489224\pi$
$467$	19.0700	−	33.0302i	0.882453	−	1.52845i	0.848605	−	0.529027i	$-0.177443\pi$
$468$	0.953207	+	0.799835i	0.0440620	+	0.0369724i
$469$	3.37983	+	1.23016i	0.156066	+	0.0568034i
$470$	4.71107	+	8.15981i	0.217305	+	0.376384i
$471$	0.865360	−	1.49885i	0.0398737	−	0.0690632i
$472$	−4.87127	+	4.08748i	−0.224218	+	0.188142i
$473$	0.435465	+	0.754248i	0.0200227	+	0.0346803i
$474$	−0.818216	+	4.64033i	−0.0375819	+	0.213137i
$475$	4.49816			0.206390
$476$	2.01805	−	11.4449i	0.0924972	−	0.524577i
$477$	2.00034	+	1.67849i	0.0915893	+	0.0768526i
$478$	16.8387	−	6.12878i	0.770183	−	0.280324i
$479$	5.88643	+	2.14249i	0.268958	+	0.0978927i	0.472979	−	0.881074i	$-0.343179\pi$
$479$	5.88643	+	2.14249i	0.268958	+	0.0978927i	−0.204021	+	0.978967i	$0.565401\pi$
$480$	−1.91992			−0.0876318
$481$	11.0319	−	0.0724376i	0.503010	−	0.00330287i
$482$	−6.01127			−0.273806
$483$	24.9313	+	9.07424i	1.13441	+	0.412892i
$484$	10.3317	−	3.76042i	0.469622	−	0.170928i
$485$	−6.12097	−	5.13610i	−0.277939	−	0.233218i
$486$	−1.21547	+	6.89325i	−0.0551347	+	0.312684i
$487$	42.2462			1.91436			0.957178	−	0.289500i	$-0.0934890\pi$
$487$	42.2462			1.91436			0.957178	+	0.289500i	$0.0934890\pi$
$488$	1.75631	−	9.96053i	0.0795045	−	0.450892i
$489$	18.6811	+	32.3566i	0.844789	+	1.46322i
$490$	1.60661	−	1.34810i	0.0725792	−	0.0609012i
$491$	−10.6611	+	18.4655i	−0.481128	+	0.833338i	−0.999765	−	0.0216561i	$-0.993106\pi$
$491$	−10.6611	+	18.4655i	−0.481128	+	0.833338i	0.518637	+	0.854994i	$0.326439\pi$
$492$	0.923713	+	1.59992i	0.0416442	+	0.0721299i
$493$	−5.71552	−	2.08028i	−0.257414	−	0.0936911i
$494$	−6.24952	−	5.24397i	−0.281179	−	0.235937i
$495$	0.0248850	−	0.0431021i	0.00111850	−	0.00193730i
$496$	−1.22691	−	6.95816i	−0.0550900	−	0.312431i
$497$	−5.64678	−	32.0245i	−0.253293	−	1.43650i
$498$	−11.8865	+	9.97400i	−0.532649	+	0.446946i
$499$	−20.1627	+	7.33860i	−0.902604	+	0.328521i	−0.751296	−	0.659966i	$-0.770571\pi$
$499$	−20.1627	+	7.33860i	−0.902604	+	0.328521i	−0.151308	+	0.988487i	$0.548349\pi$
$500$	0.939693	−	0.342020i	0.0420243	−	0.0152956i
$501$	23.5899	−	19.7943i	1.05392	−	0.884344i
$502$	2.61498	+	14.8303i	0.116712	+	0.661909i
$503$	1.92939	+	10.9421i	0.0860272	+	0.487884i	0.997130	+	0.0757057i	$0.0241210\pi$
$503$	1.92939	+	10.9421i	0.0860272	+	0.487884i	−0.911103	+	0.412179i	$0.864768\pi$
$504$	1.03467	−	1.79210i	0.0460878	−	0.0798264i
$505$	8.17140	+	6.85662i	0.363623	+	0.305116i
$506$	0.312320	+	0.113675i	0.0138843	+	0.00505347i
$507$	−9.32178	−	16.1458i	−0.413995	−	0.717060i
$508$	−3.39403	+	5.87864i	−0.150586	+	0.260822i
$509$	−22.7105	+	19.0564i	−1.00663	+	0.844660i	−0.987889	−	0.155165i	$-0.950409\pi$
$509$	−22.7105	+	19.0564i	−1.00663	+	0.844660i	−0.0187377	+	0.999824i	$0.505965\pi$
$510$	3.69878	+	6.40647i	0.163785	+	0.283683i
$511$	3.78834	−	21.4847i	0.167586	−	0.950428i
$512$	−1.00000			−0.0441942
$513$	3.47005	−	19.6796i	0.153206	−	0.868876i
$514$	−3.03851	−	2.54961i	−0.134023	−	0.112459i
$515$	−0.185867	+	0.0676502i	−0.00819029	+	0.00298102i
$516$	−21.6600	−	7.88360i	−0.953529	−	0.347056i
$517$	−0.683506			−0.0300605
$518$	−3.30443	−	18.0466i	−0.145188	−	0.792922i
$519$	40.2923			1.76863
$520$	−1.70429	−	0.620311i	−0.0747381	−	0.0272024i
$521$	−17.0500	+	6.20569i	−0.746974	+	0.271876i	−0.687332	−	0.726344i	$-0.741218\pi$
$521$	−17.0500	+	6.20569i	−0.746974	+	0.271876i	−0.0596421	+	0.998220i	$0.518996\pi$
$522$	−0.829647	−	0.696156i	−0.0363127	−	0.0304699i
$523$	5.51399	−	31.2714i	0.241110	−	1.36740i	−0.588246	−	0.808682i	$-0.700181\pi$
$523$	5.51399	−	31.2714i	0.241110	−	1.36740i	0.829356	−	0.558720i	$-0.188707\pi$
$524$	11.2160			0.489972
$525$	−1.00556	+	5.70282i	−0.0438863	+	0.248891i
$526$	−8.46121	−	14.6552i	−0.368926	−	0.638999i
$527$	−20.8547	+	17.4991i	−0.908443	+	0.762274i
$528$	0.0696378	−	0.120616i	0.00303060	−	0.00524915i
$529$	1.00431	+	1.73951i	0.0436656	+	0.0756310i
$530$	−3.57652	−	1.30175i	−0.155354	−	0.0565443i
$531$	3.34208	+	2.80434i	0.145034	+	0.121698i
$532$	−6.78360	+	11.7495i	−0.294106	+	0.509407i
$533$	0.303049	+	1.71868i	0.0131265	+	0.0744442i
$534$	−0.408320	−	2.31570i	−0.0176697	−	0.100210i
$535$	14.9638	−	12.5561i	0.646942	−	0.542849i
$536$	−1.12057	+	0.407855i	−0.0484013	+	0.0176166i
$537$	27.9443	−	10.1709i	1.20589	−	0.438907i
$538$	9.80146	−	8.22440i	0.422571	−	0.354579i
$539$	0.0264192	+	0.149831i	0.00113795	+	0.00645366i
$540$	−0.771438	−	4.37504i	−0.0331974	−	0.188272i
$541$	16.3510	−	28.3208i	0.702986	−	1.21761i	−0.264427	−	0.964406i	$-0.585183\pi$
$541$	16.3510	−	28.3208i	0.702986	−	1.21761i	0.967413	−	0.253202i	$-0.0814838\pi$
$542$	−11.1265	−	9.33624i	−0.477924	−	0.401026i
$543$	13.4196	+	4.88434i	0.575890	+	0.209607i
$544$	1.92653	+	3.33685i	0.0825993	+	0.143066i
$545$	−0.118054	+	0.204476i	−0.00505688	+	0.00875877i
$546$	8.04544	−	6.75093i	0.344313	−	0.288913i
$547$	20.2361	+	35.0500i	0.865235	+	1.49863i	0.866814	+	0.498632i	$0.166164\pi$
$547$	20.2361	+	35.0500i	0.865235	+	1.49863i	−0.00157915	+	0.999999i	$0.500503\pi$
$548$	−3.14135	+	17.8155i	−0.134192	+	0.761040i
$549$	−6.93915			−0.296156
$550$	−0.0125969	+	0.0714405i	−0.000537133	+	0.00304623i
$551$	5.43942	+	4.56422i	0.231727	+	0.194442i
$552$	−8.26587	+	3.00853i	−0.351819	+	0.128052i
$553$	6.95595	+	2.53176i	0.295797	+	0.107661i
$554$	−3.96937			−0.168643
$555$	8.99527	+	7.44783i	0.381828	+	0.316143i
$556$	2.74957			0.116608
$557$	−19.4772	−	7.08913i	−0.825277	−	0.300376i	−0.105358	−	0.994434i	$-0.533599\pi$
$557$	−19.4772	−	7.08913i	−0.825277	−	0.300376i	−0.719919	+	0.694058i	$0.755821\pi$
$558$	−4.55517	+	1.65794i	−0.192836	+	0.0701864i
$559$	−16.6802	−	13.9964i	−0.705499	−	0.591984i
$560$	−0.523752	+	2.97035i	−0.0221326	+	0.125520i
$561$	−0.536638			−0.0226569
$562$	−2.65688	+	15.0679i	−0.112074	+	0.635602i
$563$	7.57486	+	13.1200i	0.319242	+	0.552944i	0.980330	−	0.197365i	$-0.0632383\pi$
$563$	7.57486	+	13.1200i	0.319242	+	0.552944i	−0.661088	+	0.750308i	$0.729905\pi$
$564$	13.8575	−	11.6278i	0.583507	−	0.489621i
$565$	−2.89003	+	5.00568i	−0.121585	+	0.210591i
$566$	−8.55408	−	14.8161i	−0.359555	−	0.622767i
$567$	30.0080	+	10.9220i	1.26022	+	0.458681i
$568$	8.25903	+	6.93015i	0.346541	+	0.290783i
$569$	−3.47940	+	6.02650i	−0.145864	+	0.252644i	−0.929695	−	0.368330i	$-0.879930\pi$
$569$	−3.47940	+	6.02650i	−0.145864	+	0.252644i	0.783831	+	0.620974i	$0.213263\pi$
$570$	−1.49964	−	8.50489i	−0.0628130	−	0.356230i
$571$	7.17077	+	40.6675i	0.300087	+	1.70188i	0.645772	+	0.763530i	$0.276535\pi$
$571$	7.17077	+	40.6675i	0.300087	+	1.70188i	−0.345685	+	0.938351i	$0.612353\pi$
$572$	0.100787	−	0.0845704i	0.00421412	−	0.00353606i
$573$	14.0371	−	5.10910i	0.586410	−	0.213436i
$574$	2.72726	−	0.992641i	0.113834	−	0.0414320i
$575$	3.50974	−	2.94502i	0.146366	−	0.122816i
$576$	0.119137	+	0.675658i	0.00496403	+	0.0281524i
$577$	2.95069	+	16.7342i	0.122839	+	0.696654i	0.982568	+	0.185904i	$0.0595213\pi$
$577$	2.95069	+	16.7342i	0.122839	+	0.696654i	−0.859729	+	0.510750i	$0.829368\pi$
$578$	−1.07696	+	1.86535i	−0.0447957	+	0.0775884i
$579$	26.9465	+	22.6108i	1.11986	+	0.939673i
$580$	1.48337	+	0.539903i	0.0615937	+	0.0224183i
$581$	12.1884	+	21.1109i	0.505658	+	0.875826i
$582$	−7.67041	+	13.2855i	−0.317949	+	0.550704i
$583$	0.211505	−	0.177474i	0.00875966	−	0.00735023i
$584$	3.61653	+	6.26402i	0.149653	+	0.259207i
$585$	−0.216074	+	1.22542i	−0.00893358	+	0.0506648i
$586$	34.0860			1.40808
$587$	−7.48504	+	42.4498i	−0.308941	+	1.75209i	0.295410	+	0.955371i	$0.404544\pi$
$587$	−7.48504	+	42.4498i	−0.308941	+	1.75209i	−0.604350	+	0.796719i	$0.706567\pi$
$588$	−3.08456	−	2.58825i	−0.127205	−	0.106738i
$589$	29.8651	−	10.8700i	1.23057	−	0.447891i
$590$	−5.97550	−	2.17490i	−0.246007	−	0.0895393i
$591$	−26.1603			−1.07609
$592$	4.68524	+	3.87924i	0.192562	+	0.159436i
$593$	14.0231			0.575858			0.287929	−	0.957652i	$-0.407033\pi$
$593$	14.0231			0.575858			0.287929	+	0.957652i	$0.407033\pi$
$594$	0.302837	+	0.110224i	0.0124256	+	0.00452253i
$595$	10.9206	−	3.97478i	0.447702	−	0.162950i
$596$	0.637614	+	0.535022i	0.0261177	+	0.0219153i
$597$	6.27307	−	35.5764i	0.256740	−	1.45604i
$598$	−8.30957			−0.339804
$599$	−4.54861	+	25.7965i	−0.185851	+	1.05402i	0.739005	+	0.673700i	$0.235296\pi$
$599$	−4.54861	+	25.7965i	−0.185851	+	1.05402i	−0.924857	+	0.380316i	$0.875815\pi$
$600$	−0.959958	−	1.66270i	−0.0391901	−	0.0678793i
$601$	29.3363	−	24.6161i	1.19665	−	1.00411i	0.196934	−	0.980417i	$-0.436901\pi$
$601$	29.3363	−	24.6161i	1.19665	−	1.00411i	0.999719	−	0.0236949i	$-0.00754303\pi$
$602$	−18.1057	+	31.3601i	−0.737935	+	1.27814i
$603$	0.409071	+	0.708532i	0.0166587	+	0.0288537i
$604$	−1.86366	−	0.678318i	−0.0758314	−	0.0276004i
$605$	8.42246	+	7.06728i	0.342422	+	0.287326i
$606$	10.2399	−	17.7360i	0.415967	−	0.720476i
$607$	4.47367	+	25.3715i	0.181581	+	1.02980i	0.930270	+	0.366875i	$0.119572\pi$
$607$	4.47367	+	25.3715i	0.181581	+	1.02980i	−0.748689	+	0.662921i	$0.769317\pi$
$608$	−0.781097	−	4.42982i	−0.0316777	−	0.179653i
$609$	−7.00255	+	5.87584i	−0.283758	+	0.238101i
$610$	9.50423	−	3.45926i	0.384815	−	0.140061i
$611$	16.0581	−	5.84465i	0.649639	−	0.236449i
$612$	2.02505	−	1.69922i	0.0818577	−	0.0686867i
$613$	−2.74917	−	15.5913i	−0.111038	−	0.629727i	−0.988636	−	0.150330i	$-0.951966\pi$
$613$	−2.74917	−	15.5913i	−0.111038	−	0.629727i	0.877598	−	0.479397i	$-0.159145\pi$
$614$	2.68036	+	15.2011i	0.108171	+	0.613466i
$615$	−0.923713	+	1.59992i	−0.0372477	+	0.0645149i
$616$	−0.167611	−	0.140642i	−0.00675324	−	0.00566664i
$617$	−17.2572	−	6.28112i	−0.694750	−	0.252868i	−0.0295822	−	0.999562i	$-0.509418\pi$
$617$	−17.2572	−	6.28112i	−0.694750	−	0.252868i	−0.665168	+	0.746694i	$0.731640\pi$
$618$	0.189876	+	0.328875i	0.00763792	+	0.0132293i
$619$	19.2518	−	33.3451i	0.773796	−	1.34025i	−0.161673	−	0.986844i	$-0.551689\pi$
$619$	19.2518	−	33.3451i	0.773796	−	1.34025i	0.935469	−	0.353409i	$-0.114978\pi$
$620$	5.41249	−	4.54162i	0.217371	−	0.182396i
$621$	−10.1770	−	17.6271i	−0.408390	−	0.707353i
$622$	0.386719	−	2.19319i	0.0155060	−	0.0879391i
$623$	−3.69406			−0.147999
$624$	−0.604659	+	3.42919i	−0.0242057	+	0.137278i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	28.4735	−	10.3635i	1.13803	−	0.414209i
$627$	0.588702	+	0.214270i	0.0235105	+	0.00855712i
$628$	0.901455			0.0359720
$629$	3.91820	−	23.1074i	0.156229	−	0.921353i
$630$	2.06934			0.0824443
$631$	−36.8402	−	13.4087i	−1.46659	−	0.533794i	−0.519415	−	0.854522i	$-0.673850\pi$
$631$	−36.8402	−	13.4087i	−1.46659	−	0.533794i	−0.947171	+	0.320728i	$0.896072\pi$
$632$	−2.30622	+	0.839396i	−0.0917365	+	0.0333894i
$633$	−19.4045	−	16.2823i	−0.771258	−	0.647163i
$634$	4.77729	−	27.0933i	0.189730	−	1.07601i
$635$	−6.78807			−0.269376
$636$	−1.26890	+	7.19629i	−0.0503152	+	0.285352i
$637$	−1.90188	−	3.29416i	−0.0753554	−	0.130519i
$638$	−0.0877225	+	0.0736079i	−0.00347297	+	0.00291416i
$639$	3.69846	−	6.40591i	0.146309	−	0.253414i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	31.8845	+	11.6050i	1.25936	+	0.458371i	0.883555	−	0.468327i	$-0.155143\pi$
$641$	31.8845	+	11.6050i	1.25936	+	0.458371i	0.375808	+	0.926698i	$0.377365\pi$
$642$	−28.7293	−	24.1067i	−1.13385	−	0.951416i
$643$	−0.171424	+	0.296915i	−0.00676030	+	0.0117092i	−0.869386	−	0.494134i	$-0.835485\pi$
$643$	−0.171424	+	0.296915i	−0.00676030	+	0.0117092i	0.862625	+	0.505843i	$0.168819\pi$
$644$	2.39964	+	13.6090i	0.0945592	+	0.536272i
$645$	−4.00261	−	22.6999i	−0.157603	−	0.893809i
$646$	−13.2768	+	11.1406i	−0.522370	+	0.438320i
$647$	36.4913	−	13.2817i	1.43462	−	0.522159i	0.496369	−	0.868112i	$-0.334666\pi$
$647$	36.4913	−	13.2817i	1.43462	−	0.522159i	0.938252	+	0.345952i	$0.112444\pi$
$648$	−9.94903	+	3.62115i	−0.390835	+	0.142252i
$649$	0.353374	−	0.296516i	0.0138712	−	0.0116393i
$650$	−0.314940	−	1.78611i	−0.0123530	−	0.0700572i
$651$	7.10480	+	40.2933i	0.278459	+	1.57922i
$652$	−9.73017	+	16.8532i	−0.381063	+	0.660020i
$653$	3.81462	+	3.20085i	0.149278	+	0.125259i	0.714368	−	0.699770i	$-0.246714\pi$
$653$	3.81462	+	3.20085i	0.149278	+	0.125259i	−0.565090	+	0.825029i	$0.691159\pi$
$654$	0.425970	+	0.155040i	0.0166567	+	0.00606256i
$655$	5.60799	+	9.71332i	0.219122	+	0.379531i
$656$	−0.481122	+	0.833327i	−0.0187846	+	0.0325360i
$657$	3.80147	−	3.18981i	0.148309	−	0.124446i
$658$	−14.2094	−	24.6114i	−0.553939	−	0.959451i
$659$	3.88305	−	22.0219i	0.151262	−	0.857850i	−0.810862	−	0.585237i	$-0.801001\pi$
$659$	3.88305	−	22.0219i	0.151262	−	0.857850i	0.962124	−	0.272612i	$-0.0878876\pi$
$660$	0.139276			0.00542130
$661$	0.383702	−	2.17608i	0.0149243	−	0.0846398i	−0.976436	−	0.215808i	$-0.930762\pi$
$661$	0.383702	−	2.17608i	0.0149243	−	0.0846398i	0.991360	+	0.131168i	$0.0418727\pi$
$662$	−23.3658	−	19.6062i	−0.908137	−	0.762018i
$663$	12.6076	−	4.58879i	0.489638	−	0.178214i
$664$	−7.59461	−	2.76421i	−0.294728	−	0.107272i
$665$	−13.5672			−0.526114
$666$	2.06286	−	3.62778i	0.0799341	−	0.140574i
$667$	7.23244			0.280041
$668$	15.0722	+	5.48583i	0.583160	+	0.212253i
$669$	−13.6831	+	4.98023i	−0.529018	+	0.192547i
$670$	−0.913498	−	0.766516i	−0.0352915	−	0.0296131i
$671$	−0.127407	+	0.722563i	−0.00491850	+	0.0278942i
$672$	5.79079			0.223385
$673$	−0.255515	+	1.44910i	−0.00984938	+	0.0558586i	−0.989336	−	0.145649i	$-0.953473\pi$
$673$	−0.255515	+	1.44910i	−0.00984938	+	0.0558586i	0.979487	+	0.201508i	$0.0645841\pi$
$674$	−2.81924	−	4.88307i	−0.108593	−	0.188089i
$675$	3.40318	−	2.85560i	0.130988	−	0.109912i
$676$	4.85530	−	8.40963i	0.186742	−	0.323447i
$677$	19.0938	+	33.0714i	0.733833	+	1.27104i	0.955234	+	0.295852i	$0.0956037\pi$
$677$	19.0938	+	33.0714i	0.733833	+	1.27104i	−0.221401	+	0.975183i	$0.571063\pi$
$678$	10.4280	+	3.79548i	0.400485	+	0.145765i
$679$	18.4619	+	15.4914i	0.708502	+	0.594504i
$680$	−1.92653	+	3.33685i	−0.0738791	+	0.127962i
$681$	6.53940	+	37.0868i	0.250590	+	1.42117i
$682$	0.0890033	+	0.504763i	0.00340811	+	0.0193284i
$683$	−34.9550	+	29.3307i	−1.33752	+	1.12231i	−0.355260	+	0.934767i	$0.615608\pi$
$683$	−34.9550	+	29.3307i	−1.33752	+	1.12231i	−0.982256	+	0.187542i	$0.939948\pi$
$684$	−2.89998	+	1.05551i	−0.110884	+	0.0403584i
$685$	−16.9993	+	6.18726i	−0.649512	+	0.236403i
$686$	11.3278	−	9.50518i	0.432499	−	0.362910i
$687$	1.40035	+	7.94179i	0.0534267	+	0.302998i
$688$	−2.08478	−	11.8234i	−0.0794816	−	0.450763i
$689$	−3.45146	+	5.97810i	−0.131490	+	0.227748i
$690$	−6.73840	−	5.65419i	−0.256527	−	0.215251i
$691$	14.2719	+	5.19455i	0.542929	+	0.197610i	0.598902	−	0.800822i	$-0.295604\pi$
$691$	14.2719	+	5.19455i	0.542929	+	0.197610i	−0.0559732	+	0.998432i	$0.517826\pi$
$692$	10.4932	+	18.1748i	0.398893	+	0.690903i
$693$	−0.0750574	+	0.130003i	−0.00285120	+	0.00493842i
$694$	0.274755	−	0.230547i	0.0104296	−	0.00875144i
$695$	1.37479	+	2.38120i	0.0521487	+	0.0903241i
$696$	0.526280	−	2.98468i	0.0199486	−	0.113134i
$697$	3.70758			0.140435
$698$	−1.58957	+	9.01490i	−0.0601661	+	0.341219i
$699$	−10.6463	−	8.93333i	−0.402681	−	0.337890i
$700$	−2.83427	+	1.03159i	−0.107125	+	0.0389905i
$701$	−44.4192	−	16.1673i	−1.67769	−	0.610629i	−0.684699	−	0.728826i	$-0.740066\pi$
$701$	−44.4192	−	16.1673i	−1.67769	−	0.610629i	−0.992990	+	0.118197i	$0.962289\pi$
$702$	−8.05728			−0.304103
$703$	−13.5247	+	23.7848i	−0.510095	+	0.897062i
$704$	0.0725425			0.00273405
$705$	16.9988	+	6.18705i	0.640211	+	0.233018i
$706$	−24.6821	+	8.98355i	−0.928923	+	0.338100i
$707$	−24.6463	−	20.6807i	−0.926921	−	0.777779i
$708$	−2.12002	+	12.0233i	−0.0796754	+	0.451862i
$709$	−18.5782			−0.697718			−0.348859	−	0.937175i	$-0.613431\pi$
$709$	−18.5782			−0.697718			−0.348859	+	0.937175i	$0.613431\pi$
$710$	−1.87217	+	10.6176i	−0.0702613	+	0.398472i
$711$	0.841900	+	1.45821i	0.0315737	+	0.0546873i
$712$	0.938214	−	0.787255i	0.0351610	−	0.0295036i
$713$	16.1858	−	28.0346i	0.606162	−	1.04990i
$714$	−11.1561	−	19.3230i	−0.417508	−	0.723145i
$715$	0.123634	+	0.0449990i	0.00462363	+	0.00168287i
$716$	11.8653	+	9.95619i	0.443428	+	0.372080i
$717$	17.2018	−	29.7944i	0.642414	−	1.11269i
$718$	−3.57039	−	20.2487i	−0.133246	−	0.755674i
$719$	2.00006	+	11.3429i	0.0745898	+	0.423020i	0.999121	+	0.0419140i	$0.0133456\pi$
$719$	2.00006	+	11.3429i	0.0745898	+	0.423020i	−0.924531	+	0.381106i	$0.875543\pi$
$720$	−0.525568	+	0.441004i	−0.0195868	+	0.0164353i
$721$	0.560607	−	0.204044i	0.0208781	−	0.00759901i
$722$	1.15903	−	0.421854i	0.0431348	−	0.0156998i
$723$	−8.84102	+	7.41850i	−0.328801	+	0.275897i
$724$	1.29164	+	7.32526i	0.0480034	+	0.272241i
$725$	0.274116	+	1.55459i	0.0101804	+	0.0577360i
$726$	10.5545	−	18.2809i	0.391714	−	0.678468i
$727$	−35.7672	−	30.0123i	−1.32653	−	1.11309i	−0.984874	−	0.173270i	$-0.944567\pi$
$727$	−35.7672	−	30.0123i	−1.32653	−	1.11309i	−0.341659	−	0.939824i	$-0.610989\pi$
$728$	5.14043	+	1.87096i	0.190517	+	0.0693425i
$729$	−9.16199	−	15.8690i	−0.339333	−	0.587742i
$730$	−3.61653	+	6.26402i	−0.133854	+	0.231842i
$731$	−35.4365	+	29.7347i	−1.31067	+	1.09978i
$732$	−9.70920	−	16.8168i	−0.358863	−	0.621568i
$733$	−6.78776	+	38.4953i	−0.250712	+	1.42186i	0.556133	+	0.831093i	$0.312284\pi$
$733$	−6.78776	+	38.4953i	−0.250712	+	1.42186i	−0.806845	+	0.590763i	$0.798827\pi$
$734$	−13.1544			−0.485537
$735$	0.699212	−	3.96543i	0.0257908	−	0.146267i
$736$	−3.50974	−	2.94502i	−0.129371	−	0.108555i
$737$	0.0812891	−	0.0295868i	0.00299432	−	0.00108984i
$738$	0.620363	+	0.225794i	0.0228359	+	0.00831158i
$739$	−10.9808			−0.403934			−0.201967	−	0.979392i	$-0.564733\pi$
$739$	−10.9808			−0.403934			−0.201967	+	0.979392i	$0.564733\pi$
$740$	−1.01690	+	5.99716i	−0.0373822	+	0.220460i
$741$	−15.6630			−0.575395
$742$	10.7874	+	3.92629i	0.396018	+	0.144139i
$743$	−29.5252	+	10.7463i	−1.08318	+	0.394244i	−0.821089	−	0.570800i	$-0.806633\pi$
$743$	−29.5252	+	10.7463i	−1.08318	+	0.394244i	−0.262087	+	0.965044i	$0.584411\pi$
$744$	−10.3915	−	8.71953i	−0.380972	−	0.319674i
$745$	−0.144535	+	0.819701i	−0.00529537	+	0.0300315i
$746$	−21.2989			−0.779808
$747$	−0.962864	+	5.46067i	−0.0352293	+	0.199796i
$748$	−0.139755	−	0.242063i	−0.00510996	−	0.00885072i
$749$	−45.1334	+	37.8714i	−1.64914	+	1.38379i
$750$	0.959958	−	1.66270i	0.0350527	−	0.0607131i
$751$	−23.1335	−	40.0684i	−0.844153	−	1.46212i	−0.886355	−	0.463007i	$-0.846771\pi$
$751$	−23.1335	−	40.0684i	−0.844153	−	1.46212i	0.0422016	−	0.999109i	$-0.486563\pi$
$752$	8.85391	+	3.22256i	0.322869	+	0.117515i
$753$	22.1480	+	18.5844i	0.807119	+	0.677253i
$754$	1.43150	−	2.47943i	0.0521322	−	0.0902957i
$755$	−0.344391	−	1.95314i	−0.0125337	−	0.0710820i
$756$	2.32679	+	13.1959i	0.0846244	+	0.479929i
$757$	0.600653	−	0.504008i	0.0218311	−	0.0183185i	−0.631807	−	0.775126i	$-0.717686\pi$
$757$	0.600653	−	0.504008i	0.0218311	−	0.0183185i	0.653638	+	0.756807i	$0.273242\pi$
$758$	−33.7118	+	12.2701i	−1.22447	+	0.445670i
$759$	0.599628	−	0.218247i	0.0217651	−	0.00792185i
$760$	3.44579	−	2.89136i	0.124992	−	0.104881i
$761$	−6.54278	−	37.1060i	−0.237176	−	1.34509i	−0.837983	−	0.545696i	$-0.816265\pi$
$761$	−6.54278	−	37.1060i	−0.237176	−	1.34509i	0.600807	−	0.799394i	$-0.294846\pi$
$762$	2.26307	+	12.8345i	0.0819825	+	0.464946i
$763$	0.356071	−	0.616733i	0.0128906	−	0.0223272i
$764$	5.96025	+	5.00124i	0.215634	+	0.180939i
$765$	2.48409	+	0.904134i	0.0898124	+	0.0326890i
$766$	3.68085	+	6.37542i	0.132995	+	0.230353i
$767$	−5.76655	+	9.98796i	−0.208218	+	0.360644i
$768$	−1.47074	+	1.23410i	−0.0530708	+	0.0445317i
$769$	−19.6250	−	33.9915i	−0.707696	−	1.22577i	−0.965710	−	0.259625i	$-0.916401\pi$
$769$	−19.6250	−	33.9915i	−0.707696	−	1.22577i	0.258013	−	0.966141i	$-0.416932\pi$
$770$	0.0379943	−	0.215477i	0.00136922	−	0.00776524i
$771$	−7.61534			−0.274260
$772$	−3.18153	+	18.0434i	−0.114506	+	0.649395i
$773$	36.1298	+	30.3165i	1.29950	+	1.09041i	0.990231	+	0.139433i	$0.0445281\pi$
$773$	36.1298	+	30.3165i	1.29950	+	1.09041i	0.309267	+	0.950975i	$0.399916\pi$
$774$	−7.74019	+	2.81720i	−0.278215	+	0.101262i
$775$	6.63940	+	2.41655i	0.238494	+	0.0868049i
$776$	−7.99036			−0.286837
$777$	−27.1313	−	22.4639i	−0.973328	−	0.805888i
$778$	−14.1284			−0.506527
$779$	−4.06729	−	1.48037i	−0.145726	−	0.0530399i
$780$	−3.27210	+	1.19095i	−0.117160	+	0.0426427i
$781$	−0.599131	−	0.502731i	−0.0214386	−	0.0179891i
$782$	−3.06547	+	17.3851i	−0.109621	+	0.621691i
$783$	7.01285			0.250619
$784$	0.364189	−	2.06542i	0.0130067	−	0.0737649i
$785$	0.450728	+	0.780683i	0.0160872	+	0.0278638i
$786$	16.4958	−	13.8416i	0.588386	−	0.493714i
$787$	24.7243	−	42.8238i	0.881327	−	1.52650i	0.0314598	−	0.999505i	$-0.489984\pi$
$787$	24.7243	−	42.8238i	0.881327	−	1.52650i	0.849867	−	0.526998i	$-0.176682\pi$
$788$	−6.81288	−	11.8003i	−0.242699	−	0.420367i
$789$	−30.5303	−	11.1121i	−1.08691	−	0.395602i
$790$	−1.88005	−	1.57755i	−0.0668891	−	0.0561266i
$791$	8.71683	−	15.0980i	0.309935	−	0.536823i
$792$	−0.00864248	−	0.0490139i	−0.000307097	−	0.00174163i
$793$	−3.18537	−	18.0651i	−0.113116	−	0.641511i
$794$	−21.2656	+	17.8439i	−0.754687	+	0.633257i
$795$	−6.86662	+	2.49925i	−0.243534	+	0.0886391i
$796$	17.6813	−	6.43545i	0.626696	−	0.228099i
$797$	−37.0082	+	31.0536i	−1.31090	+	1.09997i	−0.322749	+	0.946485i	$0.604607\pi$
$797$	−37.0082	+	31.0536i	−1.31090	+	1.09997i	−0.988150	+	0.153490i	$0.950949\pi$
$798$	4.52317	+	25.6522i	0.160119	+	0.908077i
$799$	−6.30413	−	35.7525i	−0.223024	−	1.26483i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−0.643690	−	0.540120i	−0.0227437	−	0.0190842i
$802$	−31.9457	−	11.6273i	−1.12804	−	0.410574i
$803$	−0.262353	−	0.454408i	−0.00925822	−	0.0160357i
$804$	−1.14474	+	1.98274i	−0.0403718	+	0.0699260i
$805$	−10.5860	+	8.88268i	−0.373106	+	0.313073i
$806$	−6.40724	−	11.0977i	−0.225685	−	0.390899i
$807$	4.26569	−	24.1919i	0.150159	−	0.851596i
$808$	10.6670			0.375264
$809$	8.06617	−	45.7455i	0.283591	−	1.60833i	−0.426683	−	0.904401i	$-0.640318\pi$
$809$	8.06617	−	45.7455i	0.283591	−	1.60833i	0.710274	−	0.703925i	$-0.248571\pi$
$810$	−8.11052	−	6.80554i	−0.284975	−	0.239122i
$811$	−16.9101	+	6.15477i	−0.593794	+	0.216123i	−0.621397	−	0.783496i	$-0.713435\pi$
$811$	−16.9101	+	6.15477i	−0.593794	+	0.216123i	0.0276033	+	0.999619i	$0.491212\pi$
$812$	−4.47410	−	1.62844i	−0.157010	−	0.0571470i
$813$	−27.8861			−0.978007
$814$	−0.339879	−	0.281410i	−0.0119128	−	0.00986342i
$815$	−19.4603			−0.681666
$816$	6.95143	+	2.53011i	0.243349	+	0.0885717i
$817$	50.7471	−	18.4704i	1.77542	−	0.646198i
$818$	−17.1844	−	14.4194i	−0.600839	−	0.504164i
$819$	0.651717	−	3.69607i	0.0227728	−	0.129151i
$820$	−0.962243			−0.0336030
$821$	−7.42182	+	42.0912i	−0.259023	+	1.46899i	0.526507	+	0.850171i	$0.323501\pi$
$821$	−7.42182	+	42.0912i	−0.259023	+	1.46899i	−0.785531	+	0.618823i	$0.787610\pi$
$822$	17.3660	+	30.0787i	0.605708	+	1.04912i
$823$	25.7726	−	21.6258i	0.898375	−	0.753826i	−0.0714968	−	0.997441i	$-0.522778\pi$
$823$	25.7726	−	21.6258i	0.898375	−	0.753826i	0.969872	+	0.243614i	$0.0783331\pi$
$824$	−0.0988979	+	0.171296i	−0.00344527	+	0.00596739i
$825$	0.0696378	+	0.120616i	0.00242448	+	0.00419932i
$826$	18.0231	+	6.55988i	0.627104	+	0.228247i
$827$	−0.426486	−	0.357864i	−0.0148304	−	0.0124442i	0.635342	−	0.772231i	$-0.280859\pi$
$827$	−0.426486	−	0.357864i	−0.0148304	−	0.0124442i	−0.650173	+	0.759786i	$0.725303\pi$
$828$	−1.57169	+	2.72224i	−0.0546199	+	0.0946044i
$829$	5.30864	+	30.1068i	0.184377	+	1.04565i	0.926754	+	0.375670i	$0.122587\pi$
$829$	5.30864	+	30.1068i	0.184377	+	1.04565i	−0.742377	+	0.669983i	$0.766302\pi$
$830$	−1.40343	−	7.95923i	−0.0487136	−	0.276269i
$831$	−5.83792	+	4.89860i	−0.202515	+	0.169931i
$832$	−1.70429	+	0.620311i	−0.0590857	+	0.0215054i
$833$	−7.59360	+	2.76385i	−0.263103	+	0.0957616i
$834$	4.04391	−	3.39325i	0.140029	−	0.117499i
$835$	2.78523	+	15.7958i	0.0963867	+	0.546636i
$836$	0.0566628	+	0.321350i	0.00195972	+	0.0111141i
$837$	15.6944	−	27.1834i	0.542477	−	0.939597i
$838$	20.8929	+	17.5312i	0.721732	+	0.605605i
$839$	−3.28834	−	1.19686i	−0.113526	−	0.0413202i	0.284632	−	0.958637i	$-0.408128\pi$
$839$	−3.28834	−	1.19686i	−0.113526	−	0.0413202i	−0.398159	+	0.917317i	$0.630351\pi$
$840$	2.89540	+	5.01498i	0.0999007	+	0.173033i
$841$	13.2541	−	22.9567i	0.457036	−	0.791610i
$842$	8.79340	−	7.37854i	0.303041	−	0.254281i
$843$	14.6877	+	25.4399i	0.505872	+	0.876196i
$844$	2.29106	−	12.9932i	0.0788614	−	0.447245i
$845$	9.71061			0.334055
$846$	1.12252	−	6.36614i	0.0385931	−	0.218872i
$847$	−25.4036	−	21.3161i	−0.872877	−	0.732430i
$848$	−3.57652	+	1.30175i	−0.122818	+	0.0447022i
$849$	−30.8654	−	11.2341i	−1.05930	−	0.385552i
$850$	−3.85306			−0.132159
$851$	5.01951	+	27.4132i	0.172066	+	0.939714i
$852$	20.6994			0.709149
$853$	−20.4655	−	7.44881i	−0.700724	−	0.255043i	−0.0330038	−	0.999455i	$-0.510507\pi$
$853$	−20.4655	−	7.44881i	−0.700724	−	0.255043i	−0.667720	+	0.744413i	$0.732730\pi$
$854$	−28.6664	+	10.4337i	−0.980943	+	0.357034i
$855$	−2.36409	−	1.98371i	−0.0808501	−	0.0678413i
$856$	3.39202	−	19.2371i	0.115937	−	0.657511i
$857$	32.2598			1.10197			0.550987	−	0.834514i	$-0.314251\pi$
$857$	32.2598			1.10197			0.550987	+	0.834514i	$0.314251\pi$
$858$	0.0438635	−	0.248762i	0.00149748	−	0.00849261i
$859$	15.9040	+	27.5465i	0.542638	+	0.939876i	0.998751	+	0.0499546i	$0.0159077\pi$
$859$	15.9040	+	27.5465i	0.542638	+	0.939876i	−0.456114	+	0.889921i	$0.650759\pi$
$860$	9.19696	−	7.71717i	0.313614	−	0.263153i
$861$	2.78608	−	4.82563i	0.0949492	−	0.164457i
$862$	−1.61127	−	2.79080i	−0.0548800	−	0.0950549i
$863$	28.9989	+	10.5547i	0.987133	+	0.359287i	0.784609	−	0.619991i	$-0.212864\pi$
$863$	28.9989	+	10.5547i	0.987133	+	0.359287i	0.202523	+	0.979277i	$0.435086\pi$
$864$	−3.40318	−	2.85560i	−0.115778	−	0.0971497i
$865$	−10.4932	+	18.1748i	−0.356781	+	0.617962i
$866$	−6.04541	−	34.2852i	−0.205431	−	1.16506i
$867$	0.718096	+	4.07253i	0.0243878	+	0.138310i
$868$	−16.3250	+	13.6983i	−0.554106	+	0.464950i
$869$	0.167299	−	0.0608919i	0.00567523	−	0.00206562i
$870$	2.84795	−	1.03657i	0.0965546	−	0.0351430i
$871$	−1.65678	+	1.39021i	−0.0561379	+	0.0471053i
$872$	0.0409997	+	0.232521i	0.00138843	+	0.00787416i
$873$	0.951945	+	5.39875i	0.0322184	+	0.182720i
$874$	10.3045	−	17.8478i	0.348553	−	0.603712i
$875$	−2.31052	−	1.93876i	−0.0781098	−	0.0655419i
$876$	13.0494	+	4.74959i	0.440898	+	0.160474i
$877$	13.5311	+	23.4366i	0.456913	+	0.791396i	0.998796	−	0.0490575i	$-0.0156217\pi$
$877$	13.5311	+	23.4366i	0.456913	+	0.791396i	−0.541883	+	0.840454i	$0.682288\pi$
$878$	10.7374	−	18.5977i	0.362368	−	0.627640i
$879$	50.1317	−	42.0655i	1.69090	−	1.41883i
$880$	0.0362713	+	0.0628237i	0.00122270	+	0.00211779i
$881$	−0.0953767	+	0.540908i	−0.00321332	+	0.0182237i	−0.986372	−	0.164529i	$-0.947390\pi$
$881$	−0.0953767	+	0.540908i	−0.00321332	+	0.0182237i	0.983159	+	0.182753i	$0.0585007\pi$
$882$	−1.43890			−0.0484504
$883$	−4.26880	+	24.2096i	−0.143657	+	0.814717i	0.824779	+	0.565455i	$0.191299\pi$
$883$	−4.26880	+	24.2096i	−0.143657	+	0.814717i	−0.968436	+	0.249263i	$0.919812\pi$
$884$	5.35325	+	4.49191i	0.180049	+	0.151079i
$885$	−11.4725	+	4.17563i	−0.385642	+	0.140362i
$886$	−29.3479	−	10.6818i	−0.985961	−	0.358861i
$887$	−5.58146			−0.187407			−0.0937035	−	0.995600i	$-0.529871\pi$
$887$	−5.58146			−0.187407			−0.0937035	+	0.995600i	$0.529871\pi$
$888$	11.6781	−	0.0766812i	0.391893	−	0.00257325i
$889$	20.4740			0.686675
$890$	1.15089	+	0.418890i	0.0385779	+	0.0140412i
$891$	0.721728	−	0.262687i	0.0241788	−	0.00880036i
$892$	−5.80991	−	4.87509i	−0.194530	−	0.163230i
$893$	−7.35960	+	41.7384i	−0.246280	+	1.39672i
$894$	1.59804			0.0534463
$895$	−2.68965	+	15.2538i	−0.0899051	+	0.509877i
$896$	1.50808	+	2.61208i	0.0503816	+	0.0872634i
$897$	−12.2212	+	10.2548i	−0.408055	+	0.342399i
$898$	−0.250934	+	0.434630i	−0.00837377	+	0.0145038i
$899$	5.57670	+	9.65913i	0.185993	+	0.322150i
$900$	−0.644705	−	0.234653i	−0.0214902	−	0.00782178i
$901$	11.2340	+	9.42645i	0.374259	+	0.314041i
$902$	0.0349018	−	0.0604517i	0.00116210	−	0.00201282i
$903$	12.0725	+	68.4668i	0.401749	+	2.27843i
$904$	1.00370	+	5.69225i	0.0333825	+	0.189322i
$905$	−5.69804	+	4.78122i	−0.189409	+	0.158933i
$906$	−3.57808	+	1.30231i	−0.118874	+	0.0432665i
$907$	29.1422	−	10.6069i	0.967650	−	0.352196i	0.190623	−	0.981663i	$-0.438949\pi$
$907$	29.1422	−	10.6069i	0.967650	−	0.352196i	0.777027	+	0.629467i	$0.216727\pi$
$908$	−15.0258	+	12.6082i	−0.498650	+	0.418417i
$909$	−1.27083	−	7.20725i	−0.0421508	−	0.239049i
$910$	0.949913	+	5.38723i	0.0314893	+	0.178585i
$911$	−1.36976	+	2.37249i	−0.0453821	+	0.0786041i	−0.887824	−	0.460183i	$-0.847784\pi$
$911$	−1.36976	+	2.37249i	−0.0453821	+	0.0786041i	0.842442	+	0.538787i	$0.181117\pi$
$912$	−6.61563	−	5.55117i	−0.219065	−	0.183818i
$913$	0.550932	+	0.200523i	0.0182332	+	0.00663634i
$914$	9.54894	+	16.5392i	0.315851	+	0.547070i
$915$	9.70920	−	16.8168i	0.320976	−	0.555947i
$916$	−3.21765	+	2.69993i	−0.106314	+	0.0892080i
$917$	−16.9146	−	29.2970i	−0.558571	−	0.967473i
$918$	−2.97240	+	16.8573i	−0.0981037	+	0.556374i
$919$	−28.4037			−0.936951			−0.468475	−	0.883477i	$-0.655197\pi$
$919$	−28.4037			−0.936951			−0.468475	+	0.883477i	$0.655197\pi$
$920$	0.795593	−	4.51203i	0.0262299	−	0.148757i
$921$	22.7018	+	19.0490i	0.748048	+	0.627687i
$922$	2.80124	−	1.01957i	0.0922538	−	0.0335776i
$923$	18.3746	+	6.68782i	0.604809	+	0.220132i
$924$	−0.420079			−0.0138196
$925$	−5.70214	+	2.11791i	−0.187485	+	0.0696366i
$926$	−23.1320			−0.760166
$927$	0.127520	+	0.0464135i	0.00418831	+	0.00152442i
$928$	1.48337	−	0.539903i	0.0486941	−	0.0177232i
$929$	21.9387	+	18.4087i	0.719784	+	0.603971i	0.927326	−	0.374255i	$-0.122102\pi$
$929$	21.9387	+	18.4087i	0.719784	+	0.603971i	−0.207541	+	0.978226i	$0.566546\pi$
$930$	2.35557	−	13.3591i	0.0772422	−	0.438062i
$931$	9.43389			0.309183
$932$	1.25700	−	7.12878i	0.0411743	−	0.233511i
$933$	−2.13785	−	3.70287i	−0.0699902	−	0.121227i
$934$	29.2169	−	24.5159i	0.956006	−	0.802185i
$935$	0.139755	−	0.242063i	0.00457049	−	0.00791632i
$936$	0.622162	+	1.07762i	0.0203360	+	0.0352230i
$937$	52.7647	+	19.2048i	1.72375	+	0.627393i	0.998154	−	0.0607302i	$-0.0193429\pi$
$937$	52.7647	+	19.2048i	1.72375	+	0.627393i	0.725594	+	0.688123i	$0.241565\pi$
$938$	2.75527	+	2.31194i	0.0899626	+	0.0754876i
$939$	29.0876	−	50.3811i	0.949237	−	1.64413i
$940$	1.63614	+	9.27899i	0.0533649	+	0.302647i
$941$	0.992102	+	5.62649i	0.0323416	+	0.183418i	0.996699	−	0.0811844i	$-0.0258703\pi$
$941$	0.992102	+	5.62649i	0.0323416	+	0.183418i	−0.964357	+	0.264603i	$0.914759\pi$
$942$	1.32581	−	1.11248i	0.0431972	−	0.0362467i
$943$	−4.14277	+	1.50785i	−0.134907	+	0.0491022i
$944$	−5.97550	+	2.17490i	−0.194486	+	0.0707871i
$945$	−10.2646	+	8.61299i	−0.333906	+	0.280181i
$946$	0.151235	+	0.857699i	0.00491709	+	0.0278862i
$947$	−6.61836	−	37.5346i	−0.215068	−	1.21971i	−0.880789	−	0.473509i	$-0.842987\pi$
$947$	−6.61836	−	37.5346i	−0.215068	−	1.21971i	0.665721	−	0.746201i	$-0.268124\pi$
$948$	−2.35596	+	4.08064i	−0.0765180	+	0.132533i
$949$	10.0493	+	8.43233i	0.326213	+	0.273725i
$950$	4.22689	+	1.53846i	0.137138	+	0.0499142i
$951$	−26.4097	−	45.7429i	−0.856393	−	1.48332i
$952$	5.81074	−	10.0645i	0.188327	−	0.326192i
$953$	−29.0268	+	24.3563i	−0.940269	+	0.788979i	−0.977632	−	0.210322i	$-0.932549\pi$
$953$	−29.0268	+	24.3563i	−0.940269	+	0.788979i	0.0373632	+	0.999302i	$0.488104\pi$
$954$	1.30563	+	2.26142i	0.0422713	+	0.0732161i
$955$	−1.35108	+	7.66235i	−0.0437199	+	0.247948i
$956$	17.9194			0.579553
$957$	−0.0381777	+	0.216516i	−0.00123411	+	0.00699898i
$958$	4.79866	+	4.02656i	0.155038	+	0.130092i
$959$	51.2729	−	18.6618i	1.65569	−	0.602621i
$960$	−1.80413	−	0.656650i	−0.0582281	−	0.0211933i
$961$	18.9214			0.610366
$962$	10.3913	+	3.70506i	0.335031	+	0.119456i
$963$	−13.4018			−0.431867
$964$	−5.64874	−	2.05597i	−0.181934	−	0.0662185i
$965$	−17.2168	+	6.26640i	−0.554228	+	0.201723i
$966$	20.3242	+	17.0540i	0.653919	+	0.548703i
$967$	4.36416	−	24.7504i	0.140342	−	0.795919i	−0.830648	−	0.556798i	$-0.812030\pi$
$967$	4.36416	−	24.7504i	0.140342	−	0.795919i	0.970990	−	0.239121i	$-0.0768592\pi$
$968$	10.9947			0.353384
$969$	−5.77821	+	32.7698i	−0.185623	+	1.05272i
$970$	−3.99518	−	6.91985i	−0.128277	−	0.222183i
$971$	−4.22943	+	3.54892i	−0.135729	+	0.113890i	−0.708125	−	0.706087i	$-0.750459\pi$
$971$	−4.22943	+	3.54892i	−0.135729	+	0.113890i	0.572396	+	0.819978i	$0.306014\pi$
$972$	−3.49979	+	6.06182i	−0.112256	+	0.194433i
$973$	−4.14659	−	7.18211i	−0.132934	−	0.230248i
$974$	39.6984	+	14.4490i	1.27202	+	0.462977i
$975$	−2.66744	−	2.23825i	−0.0854264	−	0.0716812i
$976$	5.05710	−	8.75915i	0.161874	−	0.280373i
$977$	−1.60348	−	9.09376i	−0.0512997	−	0.290935i	0.948355	−	0.317211i	$-0.102746\pi$
$977$	−1.60348	−	9.09376i	−0.0512997	−	0.290935i	−0.999655	+	0.0262758i	$0.991635\pi$
$978$	6.48788	+	36.7946i	0.207460	+	1.17656i
$979$	−0.0680604	+	0.0571095i	−0.00217522	+	0.00182523i
$980$	1.97080	−	0.717312i	0.0629548	−	0.0229137i
$981$	0.152220	−	0.0554036i	0.00486001	−	0.00176890i
$982$	−16.3337	+	13.7056i	−0.521230	+	0.437364i
$983$	2.70413	+	15.3359i	0.0862484	+	0.489139i	0.997080	+	0.0763613i	$0.0243302\pi$
$983$	2.70413	+	15.3359i	0.0862484	+	0.489139i	−0.910832	+	0.412778i	$0.864559\pi$
$984$	0.320802	+	1.81936i	0.0102268	+	0.0579991i
$985$	6.81288	−	11.8003i	0.217076	−	0.375987i
$986$	−4.65934	−	3.90965i	−0.148383	−	0.124509i
$987$	−51.2712	−	18.6612i	−1.63198	−	0.593992i
$988$	−4.07908	−	7.06518i	−0.129773	−	0.224773i
$989$	27.5031	−	47.6367i	0.874547	−	1.51476i
$990$	0.0381261	−	0.0319916i	0.00121173	−	0.00101676i
$991$	−11.2791	−	19.5359i	−0.358292	−	0.620579i	0.629384	−	0.777094i	$-0.283307\pi$
$991$	−11.2791	−	19.5359i	−0.358292	−	0.620579i	−0.987676	+	0.156515i	$0.949974\pi$
$992$	1.22691	−	6.95816i	0.0389545	−	0.220922i
$993$	−58.5611			−1.85838
$994$	5.64678	−	32.0245i	0.179105	−	1.01576i
$995$	14.4139	+	12.0947i	0.456951	+	0.383428i
$996$	−14.5810	+	5.30705i	−0.462017	+	0.168160i
$997$	58.8744	+	21.4285i	1.86457	+	0.678648i	0.975145	+	0.221568i	$0.0711176\pi$
$997$	58.8744	+	21.4285i	1.86457	+	0.678648i	0.889426	+	0.457080i	$0.151105\pi$
$998$	−21.4566			−0.679198
$999$	4.86711	+	26.5809i	0.153989	+	0.840984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.b.201.3	yes	18
37.7	even	9	inner	370.2.o.b.81.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.81.3	✓	18	37.7	even	9	inner
370.2.o.b.201.3	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.80413 - 0.656650i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{5} +1.91992 q^{6} +(0.523752 - 2.97035i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.525568 - 0.441004i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.80413 - 0.656650i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.173648 + 0.984808i) q^{5} +1.91992 q^{6} +(0.523752 - 2.97035i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.525568 - 0.441004i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.0362713 - 0.0628237i) q^{11} +(1.80413 + 0.656650i) q^{12} +(1.38935 + 1.16580i) q^{13} +(1.50808 - 2.61208i) q^{14} +(0.333390 + 1.89075i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.95162 - 2.47670i) q^{17} +(0.644705 - 0.234653i) q^{18} +(-4.22689 + 1.53846i) q^{19} +(-0.766044 + 0.642788i) q^{20} +(-1.00556 - 5.70282i) q^{21} +(-0.0125969 - 0.0714405i) q^{22} +(-2.29082 + 3.96781i) q^{23} +(1.47074 + 1.23410i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(0.906834 + 1.57068i) q^{26} +(-2.22127 + 3.84735i) q^{27} +(2.31052 - 1.93876i) q^{28} +(-0.789286 - 1.36708i) q^{29} +(-0.333390 + 1.89075i) q^{30} -7.06550 q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.106691 - 0.0895247i) q^{33} +(3.62069 - 1.31782i) q^{34} +(2.83427 + 1.03159i) q^{35} +0.686081 q^{36} +(4.63389 - 3.94044i) q^{37} -4.49816 q^{38} +(3.27210 + 1.19095i) q^{39} +(-0.939693 + 0.342020i) q^{40} +(0.737121 + 0.618518i) q^{41} +(1.00556 - 5.70282i) q^{42} -12.0058 q^{43} +(0.0125969 - 0.0714405i) q^{44} +(0.343040 + 0.594163i) q^{45} +(-3.50974 + 2.94502i) q^{46} +(4.71107 - 8.15981i) q^{47} +(0.959958 + 1.66270i) q^{48} +(-1.97080 - 0.717312i) q^{49} +(-0.766044 - 0.642788i) q^{50} +(3.69878 - 6.40647i) q^{51} +(0.314940 + 1.78611i) q^{52} +(0.660914 + 3.74823i) q^{53} +(-3.40318 + 2.85560i) q^{54} +(0.0681677 - 0.0248110i) q^{55} +(2.83427 - 1.03159i) q^{56} +(-6.61563 + 5.55117i) q^{57} +(-0.274116 - 1.55459i) q^{58} +(1.10423 + 6.26238i) q^{59} +(-0.959958 + 1.66270i) q^{60} +(-7.74792 - 6.50128i) q^{61} +(-6.63940 - 2.41655i) q^{62} +(-1.03467 - 1.79210i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.38935 + 1.16580i) q^{65} +(-0.0696378 - 0.120616i) q^{66} +(-0.207073 + 1.17437i) q^{67} +3.85306 q^{68} +(-1.52747 + 8.66272i) q^{69} +(2.31052 + 1.93876i) q^{70} +(10.1312 - 3.68746i) q^{71} +(0.644705 + 0.234653i) q^{72} +7.23307 q^{73} +(5.70214 - 2.11791i) q^{74} -1.91992 q^{75} +(-4.22689 - 1.53846i) q^{76} +(-0.205605 + 0.0748342i) q^{77} +(2.66744 + 2.23825i) q^{78} +(-0.426172 + 2.41694i) q^{79} -1.00000 q^{80} +(-1.83851 + 10.4267i) q^{81} +(0.481122 + 0.833327i) q^{82} +(-6.19118 + 5.19502i) q^{83} +(2.89540 - 5.01498i) q^{84} +(1.92653 + 3.33685i) q^{85} +(-11.2817 - 4.10622i) q^{86} +(-2.32167 - 1.94811i) q^{87} +(0.0362713 - 0.0628237i) q^{88} +(-0.212676 - 1.20614i) q^{89} +(0.119137 + 0.675658i) q^{90} +(4.19052 - 3.51626i) q^{91} +(-4.30533 + 1.56701i) q^{92} +(-12.7471 + 4.63957i) q^{93} +(7.21777 - 6.05643i) q^{94} +(-0.781097 - 4.42982i) q^{95} +(0.333390 + 1.89075i) q^{96} +(-3.99518 + 6.91985i) q^{97} +(-1.60661 - 1.34810i) q^{98} +(-0.0467685 - 0.0170224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Introduction

L-functions

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