LMFDB - Embedded newform 370.2.o.b.81.3

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			81.3
Root			$0.959958 - 1.66270i$ of defining polynomial
Character	$\chi$	$=$	370.81
Dual form			370.2.o.b.201.3

$q$-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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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	0.805493	−	0.592606i	$-0.201901\pi$
$3$	1.80413	+	0.656650i	1.04162	+	0.379117i	0.236123	+	0.971723i	$0.424123\pi$
$4$	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	0.908140	+	0.418666i	$0.137502\pi$
$7$	0.523752	+	2.97035i	0.197960	+	1.12269i	−0.710180	+	0.704020i	$0.751387\pi$
$8$	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	−0.871442	−	0.490499i	$-0.836815\pi$
$11$	−0.0362713	+	0.0628237i	−0.0109362	+	0.0189421i	0.860506	+	0.509441i	$0.170148\pi$
$12$	1.80413	−	0.656650i	0.520808	−	0.189559i
$13$	1.38935	−	1.16580i	0.385337	−	0.323336i	−0.429457	−	0.903087i	$-0.641295\pi$
$13$	1.38935	−	1.16580i	0.385337	−	0.323336i	0.814793	+	0.579752i	$0.196850\pi$
$14$	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	0.926240	−	0.376934i	$-0.123022\pi$
$17$	2.95162	+	2.47670i	0.715872	+	0.600688i	−0.210368	+	0.977622i	$0.567466\pi$
$18$	0.644705	+	0.234653i	0.151958	+	0.0553083i
$19$	−4.22689	−	1.53846i	−0.969714	−	0.352947i	−0.191881	−	0.981418i	$-0.561459\pi$
$19$	−4.22689	−	1.53846i	−0.969714	−	0.352947i	−0.777833	+	0.628471i	$0.783681\pi$
$20$	−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	0.522004	−	0.852943i	$-0.325185\pi$
$23$	−2.29082	−	3.96781i	−0.477669	−	0.827346i	−0.999672	+	0.0255970i	$0.991851\pi$
$24$	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	−0.929956	−	0.367670i	$-0.880156\pi$
$29$	−0.789286	+	1.36708i	−0.146567	+	0.253861i	0.783390	+	0.621531i	$0.213489\pi$
$30$	−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	−0.583411	−	0.812177i	$-0.698282\pi$
$41$	0.737121	−	0.618518i	0.115119	−	0.0965963i	0.698530	+	0.715581i	$0.253838\pi$
$42$	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	0.972746	+	0.231871i	$0.0744848\pi$
$47$	4.71107	+	8.15981i	0.687180	+	1.19023i	−0.285567	+	0.958359i	$0.592182\pi$
$48$	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	−0.905175	−	0.425040i	$-0.860260\pi$
$53$	0.660914	−	3.74823i	0.0907835	−	0.514859i	0.995958	−	0.0898190i	$-0.0286289\pi$
$54$	−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	−0.824598	−	0.565719i	$-0.808599\pi$
$59$	1.10423	−	6.26238i	0.143758	−	0.815293i	0.968356	−	0.249573i	$-0.0802904\pi$
$60$	−0.959958	−	1.66270i	−0.123930	−	0.214653i
$61$	−7.74792	+	6.50128i	−0.992020	+	0.832403i	−0.985859	−	0.167578i	$-0.946405\pi$
$61$	−7.74792	+	6.50128i	−0.992020	+	0.832403i	−0.00616074	+	0.999981i	$0.501961\pi$
$62$	−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	0.969543	−	0.244923i	$-0.0787627\pi$
$67$	−0.207073	−	1.17437i	−0.0252980	−	0.143472i	−0.994841	+	0.101451i	$0.967652\pi$
$68$	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	0.864045	−	0.503415i	$-0.167923\pi$
$71$	10.1312	+	3.68746i	1.20235	+	0.437620i	0.338308	+	0.941036i	$0.390146\pi$
$72$	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	0.951403	−	0.307949i	$-0.0996426\pi$
$79$	−0.426172	−	2.41694i	−0.0479481	−	0.271927i	−0.999351	+	0.0360216i	$0.988532\pi$
$80$	−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	0.236311	−	0.971678i	$-0.424062\pi$
$83$	−6.19118	−	5.19502i	−0.679570	−	0.570227i	−0.915881	+	0.401450i	$0.868506\pi$
$84$	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	−0.994003	−	0.109356i	$-0.965121\pi$
$89$	−0.212676	+	1.20614i	−0.0225436	+	0.127851i	0.971459	+	0.237207i	$0.0762321\pi$
$90$	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	0.588748	−	0.808317i	$-0.299621\pi$
$97$	−3.99518	−	6.91985i	−0.405649	−	0.702605i	−0.994397	+	0.105712i	$0.966288\pi$
$98$	−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	0.999358	+	0.0358241i	$0.0114056\pi$
$101$	5.33351	+	9.23790i	0.530704	+	0.919206i	−0.468654	+	0.883382i	$0.655261\pi$
$102$	5.66686	+	4.75506i	0.561102	+	0.470821i
$103$	0.0988979	−	0.171296i	0.00974470	−	0.0168783i	−0.861112	−	0.508415i	$-0.830231\pi$
$103$	0.0988979	−	0.171296i	0.00974470	−	0.0168783i	0.870857	+	0.491537i	$0.163565\pi$
$104$	−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	−0.511596	+	0.859226i	$0.670945\pi$
$107$	−14.9638	+	12.5561i	−1.44661	+	1.21385i	−0.935010	+	0.354620i	$0.884610\pi$
$108$	−4.17462	−	1.51944i	−0.401703	−	0.146208i
$109$	0.221869	−	0.0807537i	0.0212512	−	0.00773480i	−0.331373	−	0.943500i	$-0.607512\pi$
$109$	0.221869	−	0.0807537i	0.0212512	−	0.00773480i	0.352624	+	0.935765i	$0.385290\pi$
$110$	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	−0.0736619	−	0.997283i	$-0.523469\pi$
$113$	5.43148	−	1.97690i	0.510951	−	0.185971i	0.584613	+	0.811312i	$0.301246\pi$
$114$	−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	−0.886785	−	0.462182i	$-0.847067\pi$
$127$	1.17874	−	6.68494i	0.104596	−	0.593193i	0.991381	−	0.131011i	$-0.0418222\pi$
$128$	−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	0.935683	−	0.352842i	$-0.114785\pi$
$131$	8.59193	+	7.20949i	0.750681	+	0.629896i	−0.185002	+	0.982738i	$0.559229\pi$
$132$	−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	−0.163253	−	0.986584i	$-0.552199\pi$
$137$	9.04516	−	15.6667i	0.772781	−	1.33850i	0.936033	−	0.351911i	$-0.114468\pi$
$138$	−4.39818	−	7.61787i	−0.374398	−	0.648476i
$139$	2.10630	+	1.76739i	0.178654	+	0.149908i	0.727729	−	0.685864i	$-0.240576\pi$
$139$	2.10630	+	1.76739i	0.178654	+	0.149908i	−0.549076	+	0.835773i	$0.685020\pi$
$140$	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	0.265073	−	0.964228i	$-0.414604\pi$
$151$	−1.86366	−	0.678318i	−0.151663	−	0.0552008i	−0.416736	+	0.909028i	$0.636826\pi$
$152$	−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	0.669928	−	0.742426i	$-0.266325\pi$
$157$	0.690555	+	0.579444i	0.0551123	+	0.0462447i	−0.614815	+	0.788671i	$0.710770\pi$
$158$	−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	−0.505251	−	0.862972i	$-0.668600\pi$
$163$	3.37925	−	19.1647i	0.264684	−	1.50109i	0.769935	−	0.638123i	$-0.220289\pi$
$164$	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	0.851351	−	0.524596i	$-0.175784\pi$
$167$	15.0722	+	5.48583i	1.16632	+	0.424506i	0.314969	+	0.949102i	$0.398006\pi$
$168$	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	0.543456	−	0.839438i	$-0.317116\pi$
$173$	19.7208	−	7.17780i	1.49935	−	0.545718i	0.955891	+	0.293720i	$0.0948934\pi$
$174$	−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	−0.405973	−	0.913885i	$-0.633067\pi$
$181$	5.69804	−	4.78122i	0.423532	−	0.355385i	0.829505	+	0.558500i	$0.188623\pi$
$182$	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	−0.321355	−	0.946959i	$-0.604138\pi$
$193$	9.16086	−	15.8671i	0.659413	−	1.14214i	0.980768	−	0.195178i	$-0.0625286\pi$
$194$	−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	−0.755151	−	0.655551i	$-0.772436\pi$
$197$	−12.8040	+	4.66028i	−0.912249	+	0.332031i	−0.157098	+	0.987583i	$0.550214\pi$
$198$	−0.0381261	+	0.0319916i	−0.00270950	+	0.00227354i
$199$	9.40801	+	16.2951i	0.666916	+	1.15513i	0.978762	+	0.205000i	$0.0657193\pi$
$199$	9.40801	+	16.2951i	0.666916	+	1.15513i	−0.311846	+	0.950133i	$0.600947\pi$
$200$	−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	−0.998639	−	0.0521632i	$-0.983388\pi$
$211$	−6.59683	+	11.4260i	−0.454145	+	0.786602i	0.544494	+	0.838765i	$0.316722\pi$
$212$	−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	−0.860630	−	0.509231i	$-0.829930\pi$
$227$	−3.40608	−	19.3169i	−0.226070	−	1.28210i	0.634560	−	0.772874i	$-0.281181\pi$
$228$	−8.63609			−0.571939
$229$	−0.729381	−	4.13653i	−0.0481989	−	0.273349i	0.951178	−	0.308642i	$-0.0998746\pi$
$229$	−0.729381	−	4.13653i	−0.0481989	−	0.273349i	−0.999377	+	0.0352931i	$0.988764\pi$
$230$	−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	−0.959885	−	0.280395i	$-0.909535\pi$
$233$	−3.61938	+	6.26894i	−0.237113	+	0.410692i	0.722772	+	0.691087i	$0.242868\pi$
$234$	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	0.967793	−	0.251746i	$-0.0810049\pi$
$239$	13.7270	+	11.5183i	0.887927	+	0.745059i	−0.0798662	+	0.996806i	$0.525449\pi$
$240$	−1.80413	−	0.656650i	−0.116456	−	0.0423866i
$241$	−5.64874	−	2.05597i	−0.363868	−	0.132437i	0.153615	−	0.988131i	$-0.450908\pi$
$241$	−5.64874	−	2.05597i	−0.363868	−	0.132437i	−0.517482	+	0.855694i	$0.673131\pi$
$242$	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	−0.524338	−	0.851510i	$-0.675687\pi$
$251$	7.52954	−	13.0415i	0.475260	−	0.823175i	0.999598	+	0.0283349i	$0.00902049\pi$
$252$	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	−0.455644	−	0.890162i	$-0.650591\pi$
$257$	−3.72728	+	1.35662i	−0.232502	+	0.0846237i	0.223142	+	0.974786i	$0.428369\pi$
$258$	−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	−0.948041	−	0.318147i	$-0.896939\pi$
$263$	−12.9633	+	10.8775i	−0.799353	+	0.670737i	0.148688	+	0.988884i	$0.452495\pi$
$264$	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	0.992457	−	0.122594i	$-0.0391212\pi$
$269$	6.39745	+	11.0807i	0.390059	+	0.675602i	−0.602398	+	0.798196i	$0.705788\pi$
$270$	−2.22127	+	3.84735i	−0.135182	+	0.234142i
$271$	−13.6487	+	4.96771i	−0.829098	+	0.301767i	−0.721489	−	0.692426i	$-0.756542\pi$
$271$	−13.6487	+	4.96771i	−0.829098	+	0.301767i	−0.107609	+	0.994193i	$0.534320\pi$
$272$	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	0.227523	−	0.973773i	$-0.426937\pi$
$277$	−3.72999	−	1.35761i	−0.224113	−	0.0815706i	−0.451636	+	0.892202i	$0.649160\pi$
$278$	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	−0.797023	−	0.603949i	$-0.793593\pi$
$281$	2.65688	−	15.0679i	0.158496	−	0.898877i	0.955519	−	0.294928i	$-0.0952957\pi$
$282$	9.04486	+	15.6662i	0.538613	+	0.932906i
$283$	−13.1056	+	10.9969i	−0.779048	+	0.653699i	−0.943009	−	0.332768i	$-0.892017\pi$
$283$	−13.1056	+	10.9969i	−0.779048	+	0.653699i	0.163961	+	0.986467i	$0.447573\pi$
$284$	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	0.967437	+	0.253113i	$0.0814546\pi$
$293$	32.0304	+	11.6581i	1.87123	+	0.681074i	0.903798	+	0.427960i	$0.140768\pi$
$294$	−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	−0.557247	−	0.830347i	$-0.688142\pi$
$307$	7.71779	−	13.3676i	0.440478	−	0.762930i	0.997725	+	0.0674169i	$0.0214758\pi$
$308$	−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	−0.993807	−	0.111119i	$-0.964556\pi$
$311$	−0.386719	+	2.19319i	−0.0219288	+	0.124365i	0.971878	+	0.235484i	$0.0756675\pi$
$312$	0.604659	−	3.42919i	0.0342321	−	0.194140i
$313$	23.2118	+	19.4770i	1.31201	+	1.10091i	0.987934	+	0.154875i	$0.0494974\pi$
$313$	23.2118	+	19.4770i	1.31201	+	1.10091i	0.324075	+	0.946031i	$0.394947\pi$
$314$	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	0.491095	+	0.871106i	$0.336597\pi$
$317$	−4.77729	+	27.0933i	−0.268319	+	1.52171i	−0.759414	+	0.650607i	$0.774514\pi$
$318$	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	−0.974203	−	0.225672i	$-0.927542\pi$
$331$	−28.6624	+	10.4323i	−1.57543	+	0.573409i	−0.601224	+	0.799081i	$0.705320\pi$
$332$	−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	−0.752807	−	0.658242i	$-0.771301\pi$
$337$	−4.31933	+	3.62435i	−0.235289	+	0.197431i	0.517518	+	0.855672i	$0.326856\pi$
$338$	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	0.870799	−	0.491639i	$-0.163602\pi$
$347$	0.179334	+	0.310615i	0.00962713	+	0.0166747i	−0.861172	+	0.508314i	$0.830269\pi$
$348$	−0.526280	+	2.98468i	−0.0282116	+	0.159996i
$349$	1.58957	−	9.01490i	0.0850877	−	0.482556i	−0.912250	−	0.409634i	$-0.865656\pi$
$349$	1.58957	−	9.01490i	0.0850877	−	0.482556i	0.997338	−	0.0729223i	$-0.0232325\pi$
$350$	−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	−0.0757979	−	0.997123i	$-0.524150\pi$
$353$	−20.1210	−	16.8836i	−1.07093	−	0.898621i	−0.995137	+	0.0985023i	$0.968595\pi$
$354$	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	0.456170	+	0.889893i	$0.349221\pi$
$359$	−10.2805	+	17.8064i	−0.542585	+	0.939785i	−0.998755	+	0.0498920i	$0.984112\pi$
$360$	−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	−0.00139041	−	0.999999i	$-0.500443\pi$
$367$	−12.3611	−	4.49906i	−0.645243	−	0.234849i	−0.643852	+	0.765150i	$0.722665\pi$
$368$	−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	−0.232828	−	0.972518i	$-0.574798\pi$
$373$	−20.0144	−	7.28465i	−1.03631	−	0.377185i	−0.803479	+	0.595333i	$0.797020\pi$
$374$	−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	−0.955634	−	0.294558i	$-0.904827\pi$
$379$	−27.4821	−	23.0602i	−1.41166	−	1.18452i	−0.456027	−	0.889966i	$-0.650728\pi$
$380$	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	−0.487236	−	0.873270i	$-0.661995\pi$
$383$	5.63939	−	4.73201i	0.288160	−	0.241795i	0.775396	+	0.631476i	$0.217550\pi$
$384$	−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	−0.0172390	−	0.999851i	$-0.505488\pi$
$389$	−13.2763	−	4.83219i	−0.673137	−	0.245002i	−0.655898	+	0.754850i	$0.727710\pi$
$390$	−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	−0.969631	−	0.244574i	$-0.921352\pi$
$397$	−13.8801	−	24.0411i	−0.696623	−	1.20659i	0.273008	−	0.962012i	$-0.411982\pi$
$398$	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	−0.805763	−	0.592238i	$-0.798244\pi$
$409$	−21.0798	+	7.67243i	−1.04233	+	0.379377i	−0.236567	+	0.971615i	$0.576022\pi$
$410$	−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	0.370959	−	0.928649i	$-0.379029\pi$
$419$	25.6289	−	9.32816i	1.25205	−	0.455710i	0.881095	+	0.472939i	$0.156807\pi$
$420$	4.43601	−	3.72225i	0.216455	−	0.181627i
$421$	5.73948	+	9.94108i	0.279725	+	0.484499i	0.971316	−	0.237791i	$-0.0764232\pi$
$421$	5.73948	+	9.94108i	0.279725	+	0.484499i	−0.691591	+	0.722289i	$0.743090\pi$
$422$	−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	−0.700303	−	0.713846i	$-0.746952\pi$
$431$	−2.46860	+	2.07140i	−0.118908	+	0.0997761i	0.581394	+	0.813622i	$0.302507\pi$
$432$	−4.17462	+	1.51944i	−0.200851	+	0.0731039i
$433$	−17.4071	+	30.1499i	−0.836530	+	1.44891i	0.0562485	+	0.998417i	$0.482086\pi$
$433$	−17.4071	+	30.1499i	−0.836530	+	1.44891i	−0.892779	+	0.450496i	$0.851247\pi$
$434$	−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	0.934651	+	0.355568i	$0.115712\pi$
$439$	3.72905	+	21.1485i	0.177978	+	1.00936i	−0.756673	+	0.653794i	$0.773176\pi$
$440$	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	0.982682	−	0.185298i	$-0.0593252\pi$
$449$	−0.0871484	−	0.494243i	−0.00411279	−	0.0233248i	−0.986795	+	0.161974i	$0.948214\pi$
$450$	−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	−0.232921	−	0.972496i	$-0.574828\pi$
$457$	14.6298	−	12.2759i	0.684354	−	0.574241i	0.917275	+	0.398254i	$0.130384\pi$
$458$	−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	0.694416	−	0.719574i	$-0.255663\pi$
$461$	2.28359	+	1.91616i	0.106357	+	0.0892444i	−0.588058	+	0.808819i	$0.700107\pi$
$462$	−0.394745	−	0.143675i	−0.0183652	−	0.00668439i
$463$	−21.7370	−	7.91162i	−1.01020	−	0.367684i	−0.216693	−	0.976240i	$-0.569527\pi$
$463$	−21.7370	−	7.91162i	−1.01020	−	0.367684i	−0.793511	+	0.608555i	$0.791749\pi$
$464$	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	0.848605	+	0.529027i	$0.177443\pi$
$467$	19.0700	+	33.0302i	0.882453	+	1.52845i	0.0338485	+	0.999427i	$0.489224\pi$
$468$	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	−0.204021	−	0.978967i	$-0.565401\pi$
$479$	5.88643	−	2.14249i	0.268958	−	0.0978927i	0.472979	+	0.881074i	$0.343179\pi$
$480$	−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	0.518637	−	0.854994i	$-0.326439\pi$
$491$	−10.6611	−	18.4655i	−0.481128	−	0.833338i	−0.999765	+	0.0216561i	$0.993106\pi$
$492$	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	−0.151308	−	0.988487i	$-0.548349\pi$
$499$	−20.1627	−	7.33860i	−0.902604	−	0.328521i	−0.751296	+	0.659966i	$0.770571\pi$
$500$	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	−0.911103	−	0.412179i	$-0.864768\pi$
$503$	1.92939	−	10.9421i	0.0860272	−	0.487884i	0.997130	−	0.0757057i	$-0.0241210\pi$
$504$	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	−0.0187377	−	0.999824i	$-0.505965\pi$
$509$	−22.7105	−	19.0564i	−1.00663	−	0.844660i	−0.987889	+	0.155165i	$0.950409\pi$
$510$	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	−0.0596421	−	0.998220i	$-0.518996\pi$
$521$	−17.0500	−	6.20569i	−0.746974	−	0.271876i	−0.687332	+	0.726344i	$0.741218\pi$
$522$	−0.829647	+	0.696156i	−0.0363127	+	0.0304699i
$523$	5.51399	+	31.2714i	0.241110	+	1.36740i	0.829356	+	0.558720i	$0.188707\pi$
$523$	5.51399	+	31.2714i	0.241110	+	1.36740i	−0.588246	+	0.808682i	$0.700181\pi$
$524$	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	0.967413	+	0.253202i	$0.0814838\pi$
$541$	16.3510	+	28.3208i	0.702986	+	1.21761i	−0.264427	+	0.964406i	$0.585183\pi$
$542$	−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	−0.00157915	−	0.999999i	$-0.500503\pi$
$547$	20.2361	−	35.0500i	0.865235	−	1.49863i	0.866814	−	0.498632i	$-0.166164\pi$
$548$	−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	−0.719919	−	0.694058i	$-0.755821\pi$
$557$	−19.4772	+	7.08913i	−0.825277	+	0.300376i	−0.105358	+	0.994434i	$0.533599\pi$
$558$	−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	−0.661088	−	0.750308i	$-0.729905\pi$
$563$	7.57486	−	13.1200i	0.319242	−	0.552944i	0.980330	+	0.197365i	$0.0632383\pi$
$564$	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	0.783831	−	0.620974i	$-0.213263\pi$
$569$	−3.47940	−	6.02650i	−0.145864	−	0.252644i	−0.929695	+	0.368330i	$0.879930\pi$
$570$	−1.49964	+	8.50489i	−0.0628130	+	0.356230i
$571$	7.17077	−	40.6675i	0.300087	−	1.70188i	−0.345685	−	0.938351i	$-0.612353\pi$
$571$	7.17077	−	40.6675i	0.300087	−	1.70188i	0.645772	−	0.763530i	$-0.276535\pi$
$572$	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	−0.859729	−	0.510750i	$-0.829368\pi$
$577$	2.95069	−	16.7342i	0.122839	−	0.696654i	0.982568	−	0.185904i	$-0.0595213\pi$
$578$	−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	−0.604350	−	0.796719i	$-0.706567\pi$
$587$	−7.48504	−	42.4498i	−0.308941	−	1.75209i	0.295410	−	0.955371i	$-0.404544\pi$
$588$	−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	−0.924857	−	0.380316i	$-0.875815\pi$
$599$	−4.54861	−	25.7965i	−0.185851	−	1.05402i	0.739005	−	0.673700i	$-0.235296\pi$
$600$	−0.959958	+	1.66270i	−0.0391901	+	0.0678793i
$601$	29.3363	+	24.6161i	1.19665	+	1.00411i	0.999719	+	0.0236949i	$0.00754303\pi$
$601$	29.3363	+	24.6161i	1.19665	+	1.00411i	0.196934	+	0.980417i	$0.436901\pi$
$602$	−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	−0.748689	−	0.662921i	$-0.769317\pi$
$607$	4.47367	−	25.3715i	0.181581	−	1.02980i	0.930270	−	0.366875i	$-0.119572\pi$
$608$	−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	0.877598	+	0.479397i	$0.159145\pi$
$613$	−2.74917	+	15.5913i	−0.111038	+	0.629727i	−0.988636	+	0.150330i	$0.951966\pi$
$614$	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	−0.665168	−	0.746694i	$-0.731640\pi$
$617$	−17.2572	+	6.28112i	−0.694750	+	0.252868i	−0.0295822	+	0.999562i	$0.509418\pi$
$618$	0.189876	−	0.328875i	0.00763792	−	0.0132293i
$619$	19.2518	+	33.3451i	0.773796	+	1.34025i	0.935469	+	0.353409i	$0.114978\pi$
$619$	19.2518	+	33.3451i	0.773796	+	1.34025i	−0.161673	+	0.986844i	$0.551689\pi$
$620$	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	−0.947171	−	0.320728i	$-0.896072\pi$
$631$	−36.8402	+	13.4087i	−1.46659	+	0.533794i	−0.519415	+	0.854522i	$0.673850\pi$
$632$	−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	0.375808	−	0.926698i	$-0.377365\pi$
$641$	31.8845	−	11.6050i	1.25936	−	0.458371i	0.883555	+	0.468327i	$0.155143\pi$
$642$	−28.7293	+	24.1067i	−1.13385	+	0.951416i
$643$	−0.171424	−	0.296915i	−0.00676030	−	0.0117092i	0.862625	−	0.505843i	$-0.168819\pi$
$643$	−0.171424	−	0.296915i	−0.00676030	−	0.0117092i	−0.869386	+	0.494134i	$0.835485\pi$
$644$	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	0.938252	−	0.345952i	$-0.112444\pi$
$647$	36.4913	+	13.2817i	1.43462	+	0.522159i	0.496369	+	0.868112i	$0.334666\pi$
$648$	−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	−0.565090	−	0.825029i	$-0.691159\pi$
$653$	3.81462	−	3.20085i	0.149278	−	0.125259i	0.714368	+	0.699770i	$0.246714\pi$
$654$	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	0.962124	+	0.272612i	$0.0878876\pi$
$659$	3.88305	+	22.0219i	0.151262	+	0.857850i	−0.810862	+	0.585237i	$0.801001\pi$
$660$	0.139276			0.00542130
$661$	0.383702	+	2.17608i	0.0149243	+	0.0846398i	0.991360	−	0.131168i	$-0.0418727\pi$
$661$	0.383702	+	2.17608i	0.0149243	+	0.0846398i	−0.976436	+	0.215808i	$0.930762\pi$
$662$	−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	0.979487	−	0.201508i	$-0.0645841\pi$
$673$	−0.255515	−	1.44910i	−0.00984938	−	0.0558586i	−0.989336	+	0.145649i	$0.953473\pi$
$674$	−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	−0.221401	−	0.975183i	$-0.571063\pi$
$677$	19.0938	−	33.0714i	0.733833	−	1.27104i	0.955234	−	0.295852i	$-0.0956037\pi$
$678$	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	−0.982256	−	0.187542i	$-0.939948\pi$
$683$	−34.9550	−	29.3307i	−1.33752	−	1.12231i	−0.355260	−	0.934767i	$-0.615608\pi$
$684$	−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	−0.0559732	−	0.998432i	$-0.517826\pi$
$691$	14.2719	−	5.19455i	0.542929	−	0.197610i	0.598902	+	0.800822i	$0.295604\pi$
$692$	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	−0.992990	−	0.118197i	$-0.962289\pi$
$701$	−44.4192	+	16.1673i	−1.67769	+	0.610629i	−0.684699	+	0.728826i	$0.740066\pi$
$702$	−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	−0.924531	−	0.381106i	$-0.875543\pi$
$719$	2.00006	−	11.3429i	0.0745898	−	0.423020i	0.999121	−	0.0419140i	$-0.0133456\pi$
$720$	−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	−0.341659	+	0.939824i	$0.610989\pi$
$727$	−35.7672	+	30.0123i	−1.32653	+	1.11309i	−0.984874	+	0.173270i	$0.944567\pi$
$728$	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	−0.806845	−	0.590763i	$-0.798827\pi$
$733$	−6.78776	−	38.4953i	−0.250712	−	1.42186i	0.556133	−	0.831093i	$-0.312284\pi$
$734$	−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	−0.262087	−	0.965044i	$-0.584411\pi$
$743$	−29.5252	−	10.7463i	−1.08318	−	0.394244i	−0.821089	+	0.570800i	$0.806633\pi$
$744$	−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	0.0422016	+	0.999109i	$0.486563\pi$
$751$	−23.1335	+	40.0684i	−0.844153	+	1.46212i	−0.886355	+	0.463007i	$0.846771\pi$
$752$	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	0.653638	−	0.756807i	$-0.273242\pi$
$757$	0.600653	+	0.504008i	0.0218311	+	0.0183185i	−0.631807	+	0.775126i	$0.717686\pi$
$758$	−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	0.600807	+	0.799394i	$0.294846\pi$
$761$	−6.54278	+	37.1060i	−0.237176	+	1.34509i	−0.837983	+	0.545696i	$0.816265\pi$
$762$	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	0.258013	+	0.966141i	$0.416932\pi$
$769$	−19.6250	+	33.9915i	−0.707696	+	1.22577i	−0.965710	+	0.259625i	$0.916401\pi$
$770$	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	0.309267	−	0.950975i	$-0.399916\pi$
$773$	36.1298	−	30.3165i	1.29950	−	1.09041i	0.990231	−	0.139433i	$-0.0445281\pi$
$774$	−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	0.849867	+	0.526998i	$0.176682\pi$
$787$	24.7243	+	42.8238i	0.881327	+	1.52650i	0.0314598	+	0.999505i	$0.489984\pi$
$788$	−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	−0.988150	−	0.153490i	$-0.950949\pi$
$797$	−37.0082	−	31.0536i	−1.31090	−	1.09997i	−0.322749	−	0.946485i	$-0.604607\pi$
$798$	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	0.710274	+	0.703925i	$0.248571\pi$
$809$	8.06617	+	45.7455i	0.283591	+	1.60833i	−0.426683	+	0.904401i	$0.640318\pi$
$810$	−8.11052	+	6.80554i	−0.284975	+	0.239122i
$811$	−16.9101	−	6.15477i	−0.593794	−	0.216123i	0.0276033	−	0.999619i	$-0.491212\pi$
$811$	−16.9101	−	6.15477i	−0.593794	−	0.216123i	−0.621397	+	0.783496i	$0.713435\pi$
$812$	−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	−0.785531	−	0.618823i	$-0.787610\pi$
$821$	−7.42182	−	42.0912i	−0.259023	−	1.46899i	0.526507	−	0.850171i	$-0.323501\pi$
$822$	17.3660	−	30.0787i	0.605708	−	1.04912i
$823$	25.7726	+	21.6258i	0.898375	+	0.753826i	0.969872	−	0.243614i	$-0.0783331\pi$
$823$	25.7726	+	21.6258i	0.898375	+	0.753826i	−0.0714968	+	0.997441i	$0.522778\pi$
$824$	−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	−0.650173	−	0.759786i	$-0.725303\pi$
$827$	−0.426486	+	0.357864i	−0.0148304	+	0.0124442i	0.635342	+	0.772231i	$0.280859\pi$
$828$	−1.57169	−	2.72224i	−0.0546199	−	0.0946044i
$829$	5.30864	−	30.1068i	0.184377	−	1.04565i	−0.742377	−	0.669983i	$-0.766302\pi$
$829$	5.30864	−	30.1068i	0.184377	−	1.04565i	0.926754	−	0.375670i	$-0.122587\pi$
$830$	−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	−0.398159	−	0.917317i	$-0.630351\pi$
$839$	−3.28834	+	1.19686i	−0.113526	+	0.0413202i	0.284632	+	0.958637i	$0.408128\pi$
$840$	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	−0.667720	−	0.744413i	$-0.732730\pi$
$853$	−20.4655	+	7.44881i	−0.700724	+	0.255043i	−0.0330038	+	0.999455i	$0.510507\pi$
$854$	−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	−0.456114	−	0.889921i	$-0.650759\pi$
$859$	15.9040	−	27.5465i	0.542638	−	0.939876i	0.998751	−	0.0499546i	$-0.0159077\pi$
$860$	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	0.202523	−	0.979277i	$-0.435086\pi$
$863$	28.9989	−	10.5547i	0.987133	−	0.359287i	0.784609	+	0.619991i	$0.212864\pi$
$864$	−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	−0.541883	−	0.840454i	$-0.682288\pi$
$877$	13.5311	−	23.4366i	0.456913	−	0.791396i	0.998796	+	0.0490575i	$0.0156217\pi$
$878$	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	0.983159	−	0.182753i	$-0.0585007\pi$
$881$	−0.0953767	−	0.540908i	−0.00321332	−	0.0182237i	−0.986372	+	0.164529i	$0.947390\pi$
$882$	−1.43890			−0.0484504
$883$	−4.26880	−	24.2096i	−0.143657	−	0.814717i	−0.968436	−	0.249263i	$-0.919812\pi$
$883$	−4.26880	−	24.2096i	−0.143657	−	0.814717i	0.824779	−	0.565455i	$-0.191299\pi$
$884$	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	0.777027	−	0.629467i	$-0.216727\pi$
$907$	29.1422	+	10.6069i	0.967650	+	0.352196i	0.190623	+	0.981663i	$0.438949\pi$
$908$	−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	0.842442	−	0.538787i	$-0.181117\pi$
$911$	−1.36976	−	2.37249i	−0.0453821	−	0.0786041i	−0.887824	+	0.460183i	$0.847784\pi$
$912$	−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	−0.207541	−	0.978226i	$-0.566546\pi$
$929$	21.9387	−	18.4087i	0.719784	−	0.603971i	0.927326	+	0.374255i	$0.122102\pi$
$930$	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	0.725594	−	0.688123i	$-0.241565\pi$
$937$	52.7647	−	19.2048i	1.72375	−	0.627393i	0.998154	+	0.0607302i	$0.0193429\pi$
$938$	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	−0.964357	−	0.264603i	$-0.914759\pi$
$941$	0.992102	−	5.62649i	0.0323416	−	0.183418i	0.996699	+	0.0811844i	$0.0258703\pi$
$942$	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	0.665721	+	0.746201i	$0.268124\pi$
$947$	−6.61836	+	37.5346i	−0.215068	+	1.21971i	−0.880789	+	0.473509i	$0.842987\pi$
$948$	−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	0.0373632	−	0.999302i	$-0.488104\pi$
$953$	−29.0268	−	24.3563i	−0.940269	−	0.788979i	−0.977632	+	0.210322i	$0.932549\pi$
$954$	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	0.970990	+	0.239121i	$0.0768592\pi$
$967$	4.36416	+	24.7504i	0.140342	+	0.795919i	−0.830648	+	0.556798i	$0.812030\pi$
$968$	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	0.572396	−	0.819978i	$-0.306014\pi$
$971$	−4.22943	−	3.54892i	−0.135729	−	0.113890i	−0.708125	+	0.706087i	$0.750459\pi$
$972$	−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	−0.999655	−	0.0262758i	$-0.991635\pi$
$977$	−1.60348	+	9.09376i	−0.0512997	+	0.290935i	0.948355	+	0.317211i	$0.102746\pi$
$978$	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	−0.910832	−	0.412778i	$-0.864559\pi$
$983$	2.70413	−	15.3359i	0.0862484	−	0.489139i	0.997080	−	0.0763613i	$-0.0243302\pi$
$984$	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	−0.987676	−	0.156515i	$-0.949974\pi$
$991$	−11.2791	+	19.5359i	−0.358292	+	0.620579i	0.629384	+	0.777094i	$0.283307\pi$
$992$	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	0.889426	−	0.457080i	$-0.151105\pi$
$997$	58.8744	−	21.4285i	1.86457	−	0.678648i	0.975145	−	0.221568i	$-0.0711176\pi$
$998$	−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.81.3	✓	18
37.16	even	9	inner	370.2.o.b.201.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.81.3	✓	18	1.1	even	1	trivial
370.2.o.b.201.3	yes	18	37.16	even	9	inner

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

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