LMFDB - Embedded newform 315.2.bs.a.52.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(52,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3, 2]))

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

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

chi := DirichletCharacter("315.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bs (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			52.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.52
Dual form			315.2.bs.a.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +1.73205i q^{4} +(-1.23205 - 1.86603i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +1.73205i q^{4} +(-1.23205 - 1.86603i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 + 4.23205i) q^{10} +(1.00000 + 1.73205i) q^{11} +(2.59808 + 1.50000i) q^{12} +(-1.36603 + 5.09808i) q^{13} +(4.59808 + 2.23205i) q^{14} +(-3.86603 + 0.232051i) q^{15} +4.46410 q^{16} +(-2.00000 - 7.46410i) q^{17} +(-1.50000 + 5.59808i) q^{18} +(-1.36603 - 2.36603i) q^{19} +(3.23205 - 2.13397i) q^{20} +(-0.866025 + 4.50000i) q^{21} +(1.00000 - 3.73205i) q^{22} +(-0.901924 - 3.36603i) q^{23} +(0.232051 + 0.866025i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(8.83013 - 5.09808i) q^{26} -5.19615 q^{27} +(-1.50000 - 4.33013i) q^{28} +(3.40192 + 1.96410i) q^{29} +(5.59808 + 4.96410i) q^{30} -1.46410i q^{31} +(-5.36603 - 5.36603i) q^{32} +3.46410 q^{33} +(-7.46410 + 12.9282i) q^{34} +(4.69615 + 3.59808i) q^{35} +(4.50000 - 2.59808i) q^{36} +(0.169873 - 0.633975i) q^{37} +(-1.36603 + 5.09808i) q^{38} +(6.46410 + 6.46410i) q^{39} +(1.13397 + 0.232051i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(7.33013 - 4.96410i) q^{42} +(-0.866025 - 3.23205i) q^{43} +(-3.00000 + 1.73205i) q^{44} +(-3.00000 + 6.00000i) q^{45} +(-3.36603 + 5.83013i) q^{46} +(-5.36603 + 5.36603i) q^{47} +(3.86603 - 6.69615i) q^{48} +(5.50000 - 4.33013i) q^{49} +(8.96410 - 3.59808i) q^{50} +(-12.9282 - 3.46410i) q^{51} +(-8.83013 - 2.36603i) q^{52} +(-1.00000 - 3.73205i) q^{53} +(7.09808 + 7.09808i) q^{54} +(2.00000 - 4.00000i) q^{55} +(0.598076 - 1.23205i) q^{56} -4.73205 q^{57} +(-1.96410 - 7.33013i) q^{58} -15.1244 q^{59} +(-0.401924 - 6.69615i) q^{60} -2.92820i q^{61} +(-2.00000 + 2.00000i) q^{62} +(6.00000 + 5.19615i) q^{63} +5.73205i q^{64} +(11.1962 - 3.73205i) q^{65} +(-4.73205 - 4.73205i) q^{66} +(-4.46410 - 4.46410i) q^{67} +(12.9282 - 3.46410i) q^{68} +(-5.83013 - 1.56218i) q^{69} +(-1.50000 - 11.3301i) q^{70} +4.73205 q^{71} +(1.50000 + 0.401924i) q^{72} +(3.46410 - 0.928203i) q^{73} +(-1.09808 + 0.633975i) q^{74} +(5.19615 + 6.92820i) q^{75} +(4.09808 - 2.36603i) q^{76} +(-4.00000 - 3.46410i) q^{77} -17.6603i q^{78} -4.53590i q^{79} +(-5.50000 - 8.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(5.59808 + 1.50000i) q^{82} +(11.3301 - 3.03590i) q^{83} +(-7.79423 - 1.50000i) q^{84} +(-11.4641 + 12.9282i) q^{85} +(-3.23205 + 5.59808i) q^{86} +(5.89230 - 3.40192i) q^{87} +(-1.00000 - 0.267949i) q^{88} +(-7.46410 - 12.9282i) q^{89} +(12.2942 - 4.09808i) q^{90} +(-1.00000 - 13.9282i) q^{91} +(5.83013 - 1.56218i) q^{92} +(-2.19615 - 1.26795i) q^{93} +14.6603 q^{94} +(-2.73205 + 5.46410i) q^{95} +(-12.6962 + 3.40192i) q^{96} +(-3.90192 - 14.5622i) q^{97} +(-13.4282 - 1.59808i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 2 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 2 q^{8} - 6 q^{9} + 4 q^{11} - 2 q^{13} + 8 q^{14} - 12 q^{15} + 4 q^{16} - 8 q^{17} - 6 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{22} - 14 q^{23} - 6 q^{24} + 6 q^{25} + 18 q^{26} - 6 q^{28} + 24 q^{29} + 12 q^{30} - 18 q^{32} - 16 q^{34} - 2 q^{35} + 18 q^{36} + 18 q^{37} - 2 q^{38} + 12 q^{39} + 8 q^{40} + 12 q^{42} - 12 q^{44} - 12 q^{45} - 10 q^{46} - 18 q^{47} + 12 q^{48} + 22 q^{49} + 22 q^{50} - 24 q^{51} - 18 q^{52} - 4 q^{53} + 18 q^{54} + 8 q^{55} - 8 q^{56} - 12 q^{57} + 6 q^{58} - 12 q^{59} - 12 q^{60} - 8 q^{62} + 24 q^{63} + 24 q^{65} - 12 q^{66} - 4 q^{67} + 24 q^{68} - 6 q^{69} - 6 q^{70} + 12 q^{71} + 6 q^{72} + 6 q^{74} + 6 q^{76} - 16 q^{77} - 22 q^{80} - 18 q^{81} + 12 q^{82} + 28 q^{83} - 32 q^{85} - 6 q^{86} - 18 q^{87} - 4 q^{88} - 16 q^{89} + 18 q^{90} - 4 q^{91} + 6 q^{92} + 12 q^{93} + 24 q^{94} - 4 q^{95} - 30 q^{96} - 26 q^{97} - 26 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 2 * q^8 - 6 * q^9 + 4 * q^11 - 2 * q^13 + 8 * q^14 - 12 * q^15 + 4 * q^16 - 8 * q^17 - 6 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^22 - 14 * q^23 - 6 * q^24 + 6 * q^25 + 18 * q^26 - 6 * q^28 + 24 * q^29 + 12 * q^30 - 18 * q^32 - 16 * q^34 - 2 * q^35 + 18 * q^36 + 18 * q^37 - 2 * q^38 + 12 * q^39 + 8 * q^40 + 12 * q^42 - 12 * q^44 - 12 * q^45 - 10 * q^46 - 18 * q^47 + 12 * q^48 + 22 * q^49 + 22 * q^50 - 24 * q^51 - 18 * q^52 - 4 * q^53 + 18 * q^54 + 8 * q^55 - 8 * q^56 - 12 * q^57 + 6 * q^58 - 12 * q^59 - 12 * q^60 - 8 * q^62 + 24 * q^63 + 24 * q^65 - 12 * q^66 - 4 * q^67 + 24 * q^68 - 6 * q^69 - 6 * q^70 + 12 * q^71 + 6 * q^72 + 6 * q^74 + 6 * q^76 - 16 * q^77 - 22 * q^80 - 18 * q^81 + 12 * q^82 + 28 * q^83 - 32 * q^85 - 6 * q^86 - 18 * q^87 - 4 * q^88 - 16 * q^89 + 18 * q^90 - 4 * q^91 + 6 * q^92 + 12 * q^93 + 24 * q^94 - 4 * q^95 - 30 * q^96 - 26 * q^97 - 26 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.36603	−	1.36603i	−0.965926	−	0.965926i	0.0335125	−	0.999438i	$-0.489331\pi$
$2$	−1.36603	−	1.36603i	−0.965926	−	0.965926i	−0.999438	+	0.0335125i	$0.989331\pi$
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$			1.73205i			0.866025i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$6$	−3.23205	+	0.866025i	−1.31948	+	0.353553i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−0.366025	+	0.366025i	−0.129410	+	0.129410i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−0.866025	+	4.23205i	−0.273861	+	1.33829i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	2.59808	+	1.50000i	0.750000	+	0.433013i
$13$	−1.36603	+	5.09808i	−0.378867	+	1.41395i	0.468744	+	0.883334i	$0.344707\pi$
$13$	−1.36603	+	5.09808i	−0.378867	+	1.41395i	−0.847611	+	0.530618i	$0.821960\pi$
$14$	4.59808	+	2.23205i	1.22889	+	0.596541i
$15$	−3.86603	+	0.232051i	−0.998203	+	0.0599153i
$16$	4.46410			1.11603
$17$	−2.00000	−	7.46410i	−0.485071	−	1.81031i	−0.579740	−	0.814802i	$-0.696846\pi$
$17$	−2.00000	−	7.46410i	−0.485071	−	1.81031i	0.0946685	−	0.995509i	$-0.469821\pi$
$18$	−1.50000	+	5.59808i	−0.353553	+	1.31948i
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	0.665706	−	0.746214i	$-0.268131\pi$
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	−0.979093	+	0.203411i	$0.934797\pi$
$20$	3.23205	−	2.13397i	0.722709	−	0.477171i
$21$	−0.866025	+	4.50000i	−0.188982	+	0.981981i
$22$	1.00000	−	3.73205i	0.213201	−	0.795676i
$23$	−0.901924	−	3.36603i	−0.188064	−	0.701865i	−0.993954	−	0.109799i	$-0.964979\pi$
$23$	−0.901924	−	3.36603i	−0.188064	−	0.701865i	0.805890	−	0.592066i	$-0.201687\pi$
$24$	0.232051	+	0.866025i	0.0473672	+	0.176777i
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	8.83013	−	5.09808i	1.73173	−	0.999815i
$27$	−5.19615			−1.00000
$28$	−1.50000	−	4.33013i	−0.283473	−	0.818317i
$29$	3.40192	+	1.96410i	0.631721	+	0.364725i	0.781418	−	0.624007i	$-0.214497\pi$
$29$	3.40192	+	1.96410i	0.631721	+	0.364725i	−0.149697	+	0.988732i	$0.547830\pi$
$30$	5.59808	+	4.96410i	1.02206	+	0.906317i
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	−5.36603	−	5.36603i	−0.948588	−	0.948588i
$33$	3.46410			0.603023
$34$	−7.46410	+	12.9282i	−1.28008	+	2.21717i
$35$	4.69615	+	3.59808i	0.793795	+	0.608186i
$36$	4.50000	−	2.59808i	0.750000	−	0.433013i
$37$	0.169873	−	0.633975i	0.0279269	−	0.104225i	−0.950556	−	0.310554i	$-0.899485\pi$
$37$	0.169873	−	0.633975i	0.0279269	−	0.104225i	0.978483	+	0.206330i	$0.0661519\pi$
$38$	−1.36603	+	5.09808i	−0.221599	+	0.827017i
$39$	6.46410	+	6.46410i	1.03508	+	1.03508i
$40$	1.13397	+	0.232051i	0.179297	+	0.0366905i
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	−0.688963	−	0.724797i	$-0.741934\pi$
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	0.283211	+	0.959058i	$0.408600\pi$
$42$	7.33013	−	4.96410i	1.13106	−	0.765978i
$43$	−0.866025	−	3.23205i	−0.132068	−	0.492883i	0.867925	−	0.496695i	$-0.165453\pi$
$43$	−0.866025	−	3.23205i	−0.132068	−	0.492883i	−0.999993	+	0.00381197i	$0.998787\pi$
$44$	−3.00000	+	1.73205i	−0.452267	+	0.261116i
$45$	−3.00000	+	6.00000i	−0.447214	+	0.894427i
$46$	−3.36603	+	5.83013i	−0.496293	+	0.859605i
$47$	−5.36603	+	5.36603i	−0.782715	+	0.782715i	−0.980288	−	0.197573i	$-0.936694\pi$
$47$	−5.36603	+	5.36603i	−0.782715	+	0.782715i	0.197573	+	0.980288i	$0.436694\pi$
$48$	3.86603	−	6.69615i	0.558013	−	0.966506i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	8.96410	−	3.59808i	1.26772	−	0.508845i
$51$	−12.9282	−	3.46410i	−1.81031	−	0.485071i
$52$	−8.83013	−	2.36603i	−1.22452	−	0.328109i
$53$	−1.00000	−	3.73205i	−0.137361	−	0.512637i	−0.999977	−	0.00677809i	$-0.997842\pi$
$53$	−1.00000	−	3.73205i	−0.137361	−	0.512637i	0.862616	−	0.505859i	$-0.168824\pi$
$54$	7.09808	+	7.09808i	0.965926	+	0.965926i
$55$	2.00000	−	4.00000i	0.269680	−	0.539360i
$56$	0.598076	−	1.23205i	0.0799213	−	0.164640i
$57$	−4.73205			−0.626775
$58$	−1.96410	−	7.33013i	−0.257899	−	0.962493i
$59$	−15.1244			−1.96902			−0.984512	−	0.175319i	$-0.943904\pi$
$59$	−15.1244			−1.96902			−0.984512	+	0.175319i	$0.943904\pi$
$60$	−0.401924	−	6.69615i	−0.0518881	−	0.864470i
$61$		−	2.92820i		−	0.374918i	−0.982272	−	0.187459i	$-0.939975\pi$
$61$		−	2.92820i		−	0.374918i	0.982272	−	0.187459i	$-0.0600252\pi$
$62$	−2.00000	+	2.00000i	−0.254000	+	0.254000i
$63$	6.00000	+	5.19615i	0.755929	+	0.654654i
$64$			5.73205i			0.716506i
$65$	11.1962	−	3.73205i	1.38871	−	0.462904i
$66$	−4.73205	−	4.73205i	−0.582475	−	0.582475i
$67$	−4.46410	−	4.46410i	−0.545377	−	0.545377i	0.379723	−	0.925100i	$-0.376019\pi$
$67$	−4.46410	−	4.46410i	−0.545377	−	0.545377i	−0.925100	+	0.379723i	$0.876019\pi$
$68$	12.9282	−	3.46410i	1.56777	−	0.420084i
$69$	−5.83013	−	1.56218i	−0.701865	−	0.188064i
$70$	−1.50000	−	11.3301i	−0.179284	−	1.35421i
$71$	4.73205			0.561591			0.280796	−	0.959768i	$-0.409402\pi$
$71$	4.73205			0.561591			0.280796	+	0.959768i	$0.409402\pi$
$72$	1.50000	+	0.401924i	0.176777	+	0.0473672i
$73$	3.46410	−	0.928203i	0.405442	−	0.108638i	−0.0503336	−	0.998732i	$-0.516028\pi$
$73$	3.46410	−	0.928203i	0.405442	−	0.108638i	0.455776	+	0.890094i	$0.349362\pi$
$74$	−1.09808	+	0.633975i	−0.127649	+	0.0736980i
$75$	5.19615	+	6.92820i	0.600000	+	0.800000i
$76$	4.09808	−	2.36603i	0.470082	−	0.271402i
$77$	−4.00000	−	3.46410i	−0.455842	−	0.394771i
$78$		−	17.6603i		−	1.99963i
$79$		−	4.53590i		−	0.510328i	−0.966898	−	0.255164i	$-0.917870\pi$
$79$		−	4.53590i		−	0.510328i	0.966898	−	0.255164i	$-0.0821295\pi$
$80$	−5.50000	−	8.33013i	−0.614919	−	0.931337i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	5.59808	+	1.50000i	0.618204	+	0.165647i
$83$	11.3301	−	3.03590i	1.24364	−	0.333233i	0.423765	−	0.905772i	$-0.360708\pi$
$83$	11.3301	−	3.03590i	1.24364	−	0.333233i	0.819878	+	0.572539i	$0.194041\pi$
$84$	−7.79423	−	1.50000i	−0.850420	−	0.163663i
$85$	−11.4641	+	12.9282i	−1.24346	+	1.40226i
$86$	−3.23205	+	5.59808i	−0.348521	+	0.603656i
$87$	5.89230	−	3.40192i	0.631721	−	0.364725i
$88$	−1.00000	−	0.267949i	−0.106600	−	0.0285635i
$89$	−7.46410	−	12.9282i	−0.791193	−	1.37039i	−0.925229	−	0.379410i	$-0.876127\pi$
$89$	−7.46410	−	12.9282i	−0.791193	−	1.37039i	0.134035	−	0.990977i	$-0.457206\pi$
$90$	12.2942	−	4.09808i	1.29593	−	0.431975i
$91$	−1.00000	−	13.9282i	−0.104828	−	1.46007i
$92$	5.83013	−	1.56218i	0.607833	−	0.162868i
$93$	−2.19615	−	1.26795i	−0.227730	−	0.131480i
$94$	14.6603			1.51209
$95$	−2.73205	+	5.46410i	−0.280302	+	0.560605i
$96$	−12.6962	+	3.40192i	−1.29580	+	0.347207i
$97$	−3.90192	−	14.5622i	−0.396180	−	1.47857i	−0.819760	−	0.572707i	$-0.805893\pi$
$97$	−3.90192	−	14.5622i	−0.396180	−	1.47857i	0.423580	−	0.905859i	$-0.360773\pi$
$98$	−13.4282	−	1.59808i	−1.35645	−	0.161430i
$99$	3.00000	−	5.19615i	0.301511	−	0.522233i
$100$	−7.96410	−	3.40192i	−0.796410	−	0.340192i
$101$	3.23205	−	1.86603i	0.321601	−	0.185676i	−0.330505	−	0.943804i	$-0.607219\pi$
$101$	3.23205	−	1.86603i	0.321601	−	0.185676i	0.652106	+	0.758128i	$0.273886\pi$
$102$	12.9282	+	22.3923i	1.28008	+	2.21717i
$103$	8.69615	−	2.33013i	0.856857	−	0.229594i	0.196461	−	0.980512i	$-0.437055\pi$
$103$	8.69615	−	2.33013i	0.856857	−	0.229594i	0.660396	+	0.750917i	$0.270388\pi$
$104$	−1.36603	−	2.36603i	−0.133950	−	0.232008i
$105$	9.46410	−	3.92820i	0.923602	−	0.383353i
$106$	−3.73205	+	6.46410i	−0.362489	+	0.627849i
$107$	−3.06218	+	11.4282i	−0.296032	+	1.10481i	0.644362	+	0.764720i	$0.277123\pi$
$107$	−3.06218	+	11.4282i	−0.296032	+	1.10481i	−0.940394	+	0.340086i	$0.889544\pi$
$108$		−	9.00000i		−	0.866025i
$109$	−5.42820	−	3.13397i	−0.519928	−	0.300180i	0.216977	−	0.976177i	$-0.430380\pi$
$109$	−5.42820	−	3.13397i	−0.519928	−	0.300180i	−0.736905	+	0.675996i	$0.763714\pi$
$110$	−8.19615	+	2.73205i	−0.781472	+	0.260491i
$111$	−0.803848	−	0.803848i	−0.0762978	−	0.0762978i
$112$	−11.1603	+	3.86603i	−1.05454	+	0.365305i
$113$	−9.46410	−	2.53590i	−0.890308	−	0.238557i	−0.215459	−	0.976513i	$-0.569125\pi$
$113$	−9.46410	−	2.53590i	−0.890308	−	0.238557i	−0.674849	+	0.737956i	$0.735791\pi$
$114$	6.46410	+	6.46410i	0.605419	+	0.605419i
$115$	−5.16987	+	5.83013i	−0.482093	+	0.543662i
$116$	−3.40192	+	5.89230i	−0.315861	+	0.547087i
$117$	15.2942	−	4.09808i	1.41395	−	0.378867i
$118$	20.6603	+	20.6603i	1.90193	+	1.90193i
$119$	11.4641	+	16.9282i	1.05091	+	1.55181i
$120$	1.33013	−	1.50000i	0.121423	−	0.136931i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−4.00000	+	4.00000i	−0.362143	+	0.362143i
$123$			5.19615i			0.468521i
$124$	2.53590			0.227730
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	−1.09808	−	15.2942i	−0.0978244	−	1.36252i
$127$	9.63397	+	9.63397i	0.854877	+	0.854877i	0.990729	−	0.135852i	$-0.0433772\pi$
$127$	9.63397	+	9.63397i	0.854877	+	0.854877i	−0.135852	+	0.990729i	$0.543377\pi$
$128$	−2.90192	+	2.90192i	−0.256496	+	0.256496i
$129$	−5.59808	−	1.50000i	−0.492883	−	0.132068i
$130$	−20.3923	−	10.1962i	−1.78852	−	0.894262i
$131$	−4.39230	−	2.53590i	−0.383757	−	0.221562i	0.295694	−	0.955283i	$-0.404449\pi$
$131$	−4.39230	−	2.53590i	−0.383757	−	0.221562i	−0.679452	+	0.733720i	$0.737782\pi$
$132$			6.00000i			0.522233i
$133$	5.46410	+	4.73205i	0.473798	+	0.410321i
$134$			12.1962i			1.05359i
$135$	6.40192	+	9.69615i	0.550990	+	0.834512i
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	0.366025	−	1.36603i	0.0312717	−	0.116707i	−0.948526	−	0.316700i	$-0.897425\pi$
$137$	0.366025	−	1.36603i	0.0312717	−	0.116707i	0.979797	+	0.199993i	$0.0640918\pi$
$138$	5.83013	+	10.0981i	0.496293	+	0.859605i
$139$	6.29423	+	10.9019i	0.533870	+	0.924689i	0.999217	+	0.0395611i	$0.0125960\pi$
$139$	6.29423	+	10.9019i	0.533870	+	0.924689i	−0.465348	+	0.885128i	$0.654071\pi$
$140$	−6.23205	+	8.13397i	−0.526704	+	0.687446i
$141$	3.40192	+	12.6962i	0.286494	+	1.06921i
$142$	−6.46410	−	6.46410i	−0.542455	−	0.542455i
$143$	−10.1962	+	2.73205i	−0.852645	+	0.228466i
$144$	−6.69615	−	11.5981i	−0.558013	−	0.966506i
$145$	−0.526279	−	8.76795i	−0.0437051	−	0.728139i
$146$	−6.00000	−	3.46410i	−0.496564	−	0.286691i
$147$	−1.73205	−	12.0000i	−0.142857	−	0.989743i
$148$	1.09808	+	0.294229i	0.0902613	+	0.0241854i
$149$	13.3923	+	7.73205i	1.09714	+	0.633434i	0.935468	−	0.353410i	$-0.114978\pi$
$149$	13.3923	+	7.73205i	1.09714	+	0.633434i	0.161672	+	0.986845i	$0.448311\pi$
$150$	2.36603	−	16.5622i	0.193185	−	1.35230i
$151$	8.83013	+	15.2942i	0.718586	+	1.24463i	0.961560	+	0.274594i	$0.0885435\pi$
$151$	8.83013	+	15.2942i	0.718586	+	1.24463i	−0.242975	+	0.970033i	$0.578123\pi$
$152$	1.36603	+	0.366025i	0.110799	+	0.0296886i
$153$	−16.3923	+	16.3923i	−1.32524	+	1.32524i
$154$	0.732051	+	10.1962i	0.0589903	+	0.821629i
$155$	−2.73205	+	1.80385i	−0.219444	+	0.144889i
$156$	−11.1962	+	11.1962i	−0.896410	+	0.896410i
$157$	7.19615	−	7.19615i	0.574315	−	0.574315i	−0.359016	−	0.933331i	$-0.616888\pi$
$157$	7.19615	−	7.19615i	0.574315	−	0.574315i	0.933331	+	0.359016i	$0.116888\pi$
$158$	−6.19615	+	6.19615i	−0.492939	+	0.492939i
$159$	−6.46410	−	1.73205i	−0.512637	−	0.137361i
$160$	−3.40192	+	16.6244i	−0.268946	+	1.31427i
$161$	5.16987	+	7.63397i	0.407443	+	0.601641i
$162$	16.7942	−	4.50000i	1.31948	−	0.353553i
$163$	9.29423	+	2.49038i	0.727980	+	0.195062i	0.603730	−	0.797189i	$-0.293681\pi$
$163$	9.29423	+	2.49038i	0.727980	+	0.195062i	0.124251	+	0.992251i	$0.460347\pi$
$164$	−2.59808	−	4.50000i	−0.202876	−	0.351391i
$165$	−4.26795	−	6.46410i	−0.332259	−	0.503230i
$166$	−19.6244	−	11.3301i	−1.52315	−	0.879388i
$167$	3.36603	+	0.901924i	0.260471	+	0.0697930i	0.386691	−	0.922209i	$-0.373618\pi$
$167$	3.36603	+	0.901924i	0.260471	+	0.0697930i	−0.126220	+	0.992002i	$0.540285\pi$
$168$	−1.33013	−	1.96410i	−0.102622	−	0.151534i
$169$	−12.8660	−	7.42820i	−0.989694	−	0.571400i
$170$	33.3205	−	2.00000i	2.55557	−	0.153393i
$171$	−4.09808	+	7.09808i	−0.313388	+	0.542803i
$172$	5.59808	−	1.50000i	0.426849	−	0.114374i
$173$	−16.0000	−	16.0000i	−1.21646	−	1.21646i	−0.968864	−	0.247593i	$-0.920360\pi$
$173$	−16.0000	−	16.0000i	−1.21646	−	1.21646i	−0.247593	−	0.968864i	$-0.579640\pi$
$174$	−12.6962	−	3.40192i	−0.962493	−	0.257899i
$175$	0.928203	−	13.1962i	0.0701656	−	0.997535i
$176$	4.46410	+	7.73205i	0.336494	+	0.582825i
$177$	−13.0981	+	22.6865i	−0.984512	+	1.70522i
$178$	−7.46410	+	27.8564i	−0.559458	+	2.08793i
$179$	1.09808	+	0.633975i	0.0820741	+	0.0473855i	0.540475	−	0.841360i	$-0.318244\pi$
$179$	1.09808	+	0.633975i	0.0820741	+	0.0473855i	−0.458401	+	0.888745i	$0.651578\pi$
$180$	−10.3923	−	5.19615i	−0.774597	−	0.387298i
$181$		−	20.1244i		−	1.49583i	−0.663794	−	0.747916i	$-0.731055\pi$
$181$		−	20.1244i		−	1.49583i	0.663794	−	0.747916i	$-0.268945\pi$
$182$	−17.6603	+	20.3923i	−1.30907	+	1.51158i
$183$	−4.39230	−	2.53590i	−0.324689	−	0.187459i
$184$	1.56218	+	0.901924i	0.115165	+	0.0664907i
$185$	−1.39230	+	0.464102i	−0.102364	+	0.0341214i
$186$	1.26795	+	4.73205i	0.0929705	+	0.346971i
$187$	10.9282	−	10.9282i	0.799149	−	0.799149i
$188$	−9.29423	−	9.29423i	−0.677851	−	0.677851i
$189$	12.9904	−	4.50000i	0.944911	−	0.327327i
$190$	11.1962	−	3.73205i	0.812254	−	0.270751i
$191$	−9.80385			−0.709382			−0.354691	−	0.934984i	$-0.615414\pi$
$191$	−9.80385			−0.709382			−0.354691	+	0.934984i	$0.615414\pi$
$192$	8.59808	+	4.96410i	0.620513	+	0.358253i
$193$	0.196152	−	0.196152i	0.0141194	−	0.0141194i	−0.700012	−	0.714131i	$-0.746822\pi$
$193$	0.196152	−	0.196152i	0.0141194	−	0.0141194i	0.714131	+	0.700012i	$0.246822\pi$
$194$	−14.5622	+	25.2224i	−1.04550	+	1.81087i
$195$	4.09808	−	20.0263i	0.293469	−	1.43411i
$196$	7.50000	+	9.52628i	0.535714	+	0.680449i
$197$	4.00000	+	4.00000i	0.284988	+	0.284988i	0.835095	−	0.550106i	$-0.185413\pi$
$197$	4.00000	+	4.00000i	0.284988	+	0.284988i	−0.550106	+	0.835095i	$0.685413\pi$
$198$	−11.1962	+	3.00000i	−0.795676	+	0.213201i
$199$	2.19615	−	3.80385i	0.155681	−	0.269648i	−0.777626	−	0.628727i	$-0.783576\pi$
$199$	2.19615	−	3.80385i	0.155681	−	0.269648i	0.933307	+	0.359080i	$0.116909\pi$
$200$	−0.964102	−	2.40192i	−0.0681723	−	0.169842i
$201$	−10.5622	+	2.83013i	−0.744999	+	0.199622i
$202$	−6.96410	−	1.86603i	−0.489992	−	0.131293i
$203$	−10.2058	−	1.96410i	−0.716305	−	0.137853i
$204$	6.00000	−	22.3923i	0.420084	−	1.56777i
$205$	6.00000	+	3.00000i	0.419058	+	0.209529i
$206$	−15.0622	−	8.69615i	−1.04943	−	0.605890i
$207$	−7.39230	+	7.39230i	−0.513801	+	0.513801i
$208$	−6.09808	+	22.7583i	−0.422826	+	1.57801i
$209$	2.73205	−	4.73205i	0.188980	−	0.327323i
$210$	−18.2942	−	7.56218i	−1.26242	−	0.521840i
$211$	−6.53590	−	11.3205i	−0.449950	−	0.779336i	0.548432	−	0.836195i	$-0.315225\pi$
$211$	−6.53590	−	11.3205i	−0.449950	−	0.779336i	−0.998382	+	0.0568590i	$0.981891\pi$
$212$	6.46410	−	1.73205i	0.443956	−	0.118958i
$213$	4.09808	−	7.09808i	0.280796	−	0.486352i
$214$	19.7942	−	11.4282i	1.35311	−	0.781216i
$215$	−4.96410	+	5.59808i	−0.338549	+	0.381786i
$216$	1.90192	−	1.90192i	0.129410	−	0.129410i
$217$	1.26795	+	3.66025i	0.0860740	+	0.248474i
$218$	3.13397	+	11.6962i	0.212260	+	0.792163i
$219$	1.60770	−	6.00000i	0.108638	−	0.405442i
$220$	6.92820	+	3.46410i	0.467099	+	0.233550i
$221$	40.7846			2.74347
$222$			2.19615i			0.147396i
$223$	−7.33013	+	1.96410i	−0.490862	+	0.131526i	−0.495756	−	0.868462i	$-0.665109\pi$
$223$	−7.33013	+	1.96410i	−0.490862	+	0.131526i	0.00489404	+	0.999988i	$0.498442\pi$
$224$	18.0622	+	8.76795i	1.20683	+	0.585833i
$225$	14.8923	−	1.79423i	0.992820	−	0.119615i
$226$	9.46410	+	16.3923i	0.629543	+	1.09040i
$227$	18.5622	+	4.97372i	1.23202	+	0.330117i	0.815364	−	0.578949i	$-0.196537\pi$
$227$	18.5622	+	4.97372i	1.23202	+	0.330117i	0.416651	+	0.909066i	$0.363204\pi$
$228$		−	8.19615i		−	0.542803i
$229$	−2.66987	+	4.62436i	−0.176430	+	0.305586i	−0.940655	−	0.339364i	$-0.889788\pi$
$229$	−2.66987	+	4.62436i	−0.176430	+	0.305586i	0.764225	+	0.644950i	$0.223122\pi$
$230$	15.0263	−	0.901924i	0.990804	−	0.0594711i
$231$	−8.66025	+	3.00000i	−0.569803	+	0.197386i
$232$	−1.96410	+	0.526279i	−0.128950	+	0.0345519i
$233$	12.4641	+	3.33975i	0.816550	+	0.218794i	0.642838	−	0.766002i	$-0.277757\pi$
$233$	12.4641	+	3.33975i	0.816550	+	0.218794i	0.173713	+	0.984796i	$0.444424\pi$
$234$	−26.4904	−	15.2942i	−1.73173	−	0.999815i
$235$	16.6244	+	3.40192i	1.08445	+	0.221917i
$236$		−	26.1962i		−	1.70522i
$237$	−6.80385	−	3.92820i	−0.441957	−	0.255164i
$238$	7.46410	−	38.7846i	0.483826	−	2.51403i
$239$	1.73205	−	1.00000i	0.112037	−	0.0646846i	−0.442934	−	0.896554i	$-0.646063\pi$
$239$	1.73205	−	1.00000i	0.112037	−	0.0646846i	0.554971	+	0.831869i	$0.312729\pi$
$240$	−17.2583	+	1.03590i	−1.11402	+	0.0668670i
$241$	19.4545	−	11.2321i	1.25317	−	0.723520i	0.281435	−	0.959580i	$-0.409190\pi$
$241$	19.4545	−	11.2321i	1.25317	−	0.723520i	0.971738	+	0.236060i	$0.0758563\pi$
$242$	−13.0622	+	3.50000i	−0.839669	+	0.224989i
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$	5.07180			0.324689
$245$	−14.8564	−	4.92820i	−0.949141	−	0.314851i
$246$	7.09808	−	7.09808i	0.452557	−	0.452557i
$247$	13.9282	−	3.73205i	0.886230	−	0.237465i
$248$	0.535898	+	0.535898i	0.0340296	+	0.0340296i
$249$	5.25833	−	19.6244i	0.333233	−	1.24364i
$250$	−17.7583	−	12.2942i	−1.12314	−	0.777555i
$251$			3.66025i			0.231033i	0.993306	+	0.115517i	$0.0368523\pi$
$251$			3.66025i			0.231033i	−0.993306	+	0.115517i	$0.963148\pi$
$252$	−9.00000	+	10.3923i	−0.566947	+	0.654654i
$253$	4.92820	−	4.92820i	0.309833	−	0.309833i
$254$		−	26.3205i		−	1.65150i
$255$	9.46410	+	28.3923i	0.592665	+	1.77800i
$256$	19.3923			1.21202
$257$	−0.0717968	−	0.267949i	−0.00447856	−	0.0167142i	0.963650	−	0.267166i	$-0.0860874\pi$
$257$	−0.0717968	−	0.267949i	−0.00447856	−	0.0167142i	−0.968129	+	0.250452i	$0.919421\pi$
$258$	5.59808	+	9.69615i	0.348521	+	0.603656i
$259$	0.124356	+	1.73205i	0.00772708	+	0.107624i
$260$	6.46410	+	19.3923i	0.400887	+	1.20266i
$261$		−	11.7846i		−	0.729449i
$262$	2.53590	+	9.46410i	0.156668	+	0.584694i
$263$	−5.33013	−	1.42820i	−0.328670	−	0.0880668i	0.0907109	−	0.995877i	$-0.471086\pi$
$263$	−5.33013	−	1.42820i	−0.328670	−	0.0880668i	−0.419381	+	0.907810i	$0.637753\pi$
$264$	−1.26795	+	1.26795i	−0.0780369	+	0.0780369i
$265$	−5.73205	+	6.46410i	−0.352117	+	0.397087i
$266$	−1.00000	−	13.9282i	−0.0613139	−	0.853993i
$267$	−25.8564			−1.58239
$268$	7.73205	−	7.73205i	0.472310	−	0.472310i
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	−0.000940662	−	1.00000i	$-0.500299\pi$
$269$	14.1962	−	24.5885i	0.865555	−	1.49918i	0.866495	−	0.499185i	$-0.166367\pi$
$270$	4.50000	−	21.9904i	0.273861	−	1.33829i
$271$	−28.2224	+	16.2942i	−1.71439	+	0.989804i	−0.785977	+	0.618256i	$0.787840\pi$
$271$	−28.2224	+	16.2942i	−1.71439	+	0.989804i	−0.928414	+	0.371548i	$0.878827\pi$
$272$	−8.92820	−	33.3205i	−0.541352	−	2.02035i
$273$	−21.7583	−	10.5622i	−1.31687	−	0.639252i
$274$	−2.36603	+	1.36603i	−0.142937	+	0.0825246i
$275$	−9.92820	+	1.19615i	−0.598693	+	0.0721307i
$276$	2.70577	−	10.0981i	0.162868	−	0.607833i
$277$	−3.00000	+	11.1962i	−0.180253	+	0.672712i	0.815345	+	0.578976i	$0.196548\pi$
$277$	−3.00000	+	11.1962i	−0.180253	+	0.672712i	−0.995597	+	0.0937356i	$0.970119\pi$
$278$	6.29423	−	23.4904i	0.377503	−	1.40886i
$279$	−3.80385	+	2.19615i	−0.227730	+	0.131480i
$280$	−3.03590	+	0.401924i	−0.181430	+	0.0240195i
$281$	−11.1340	+	19.2846i	−0.664197	+	1.15042i	0.315305	+	0.948990i	$0.397893\pi$
$281$	−11.1340	+	19.2846i	−0.664197	+	1.15042i	−0.979502	+	0.201433i	$0.935440\pi$
$282$	12.6962	−	21.9904i	0.756045	−	1.30951i
$283$	9.63397	+	9.63397i	0.572680	+	0.572680i	0.932877	−	0.360196i	$-0.117290\pi$
$283$	9.63397	+	9.63397i	0.572680	+	0.572680i	−0.360196	+	0.932877i	$0.617290\pi$
$284$			8.19615i			0.486352i
$285$	5.83013	+	8.83013i	0.345347	+	0.523052i
$286$	17.6603	+	10.1962i	1.04427	+	0.602911i
$287$	5.19615	−	6.00000i	0.306719	−	0.354169i
$288$	−5.89230	+	21.9904i	−0.347207	+	1.29580i
$289$	−36.9904	+	21.3564i	−2.17590	+	1.25626i
$290$	−11.2583	+	12.6962i	−0.661112	+	0.745544i
$291$	−25.2224	−	6.75833i	−1.47857	−	0.396180i
$292$	1.60770	+	6.00000i	0.0940832	+	0.351123i
$293$	1.80385	−	6.73205i	0.105382	−	0.393291i	−0.893006	−	0.450044i	$-0.851408\pi$
$293$	1.80385	−	6.73205i	0.105382	−	0.393291i	0.998388	+	0.0567535i	$0.0180749\pi$
$294$	−14.0263	+	18.7583i	−0.818029	+	1.09401i
$295$	18.6340	+	28.2224i	1.08491	+	1.64317i
$296$	0.169873	+	0.294229i	0.00987367	+	0.0171017i
$297$	−5.19615	−	9.00000i	−0.301511	−	0.522233i
$298$	−7.73205	−	28.8564i	−0.447906	−	1.67161i
$299$	18.3923			1.06365
$300$	−12.0000	+	9.00000i	−0.692820	+	0.519615i
$301$	4.96410	+	7.33013i	0.286126	+	0.422501i
$302$	8.83013	−	32.9545i	0.508117	−	1.89632i
$303$		−	6.46410i		−	0.371353i
$304$	−6.09808	−	10.5622i	−0.349749	−	0.605782i
$305$	−5.46410	+	3.60770i	−0.312874	+	0.206576i
$306$	44.7846			2.56017
$307$	−5.36603	+	5.36603i	−0.306255	+	0.306255i	−0.843455	−	0.537200i	$-0.819482\pi$
$307$	−5.36603	+	5.36603i	−0.306255	+	0.306255i	0.537200	+	0.843455i	$0.319482\pi$
$308$	6.00000	−	6.92820i	0.341882	−	0.394771i
$309$	4.03590	−	15.0622i	0.229594	−	0.856857i
$310$	6.19615	+	1.26795i	0.351918	+	0.0720147i
$311$		−	7.12436i		−	0.403985i	−0.979387	−	0.201993i	$-0.935258\pi$
$311$		−	7.12436i		−	0.403985i	0.979387	−	0.201993i	$-0.0647417\pi$
$312$	−4.73205			−0.267900
$313$	1.60770	+	1.60770i	0.0908723	+	0.0908723i	0.751082	−	0.660209i	$-0.229532\pi$
$313$	1.60770	+	1.60770i	0.0908723	+	0.0908723i	−0.660209	+	0.751082i	$0.729532\pi$
$314$	−19.6603			−1.10949
$315$	2.30385	−	17.5981i	0.129807	−	0.991539i
$316$	7.85641			0.441957
$317$	8.46410	+	8.46410i	0.475391	+	0.475391i	0.903654	−	0.428263i	$-0.140874\pi$
$317$	8.46410	+	8.46410i	0.475391	+	0.475391i	−0.428263	+	0.903654i	$0.640874\pi$
$318$	6.46410	+	11.1962i	0.362489	+	0.627849i
$319$			7.85641i			0.439874i
$320$	10.6962	−	7.06218i	0.597933	−	0.394788i
$321$	14.4904	+	14.4904i	0.808774	+	0.808774i
$322$	3.36603	−	17.4904i	0.187581	−	0.974701i
$323$	−14.9282	+	14.9282i	−0.830627	+	0.830627i
$324$	−13.5000	−	7.79423i	−0.750000	−	0.433013i
$325$	−20.7583	−	16.2942i	−1.15146	−	0.903841i
$326$	−9.29423	−	16.0981i	−0.514760	−	0.891590i
$327$	−9.40192	+	5.42820i	−0.519928	+	0.300180i
$328$	0.401924	−	1.50000i	0.0221925	−	0.0828236i
$329$	8.76795	−	18.0622i	0.483393	−	0.995800i
$330$	−3.00000	+	14.6603i	−0.165145	+	0.807020i
$331$	−6.00000			−0.329790			−0.164895	−	0.986311i	$-0.552728\pi$
$331$	−6.00000			−0.329790			−0.164895	+	0.986311i	$0.552728\pi$
$332$	5.25833	+	19.6244i	0.288588	+	1.07703i
$333$	−1.90192	+	0.509619i	−0.104225	+	0.0279269i
$334$	−3.36603	−	5.83013i	−0.184181	−	0.319010i
$335$	−2.83013	+	13.8301i	−0.154626	+	0.755621i
$336$	−3.86603	+	20.0885i	−0.210909	+	1.09592i
$337$	1.97372	−	7.36603i	0.107515	−	0.401253i	−0.891103	−	0.453801i	$-0.850068\pi$
$337$	1.97372	−	7.36603i	0.107515	−	0.401253i	0.998618	+	0.0525482i	$0.0167343\pi$
$338$	7.42820	+	27.7224i	0.404041	+	1.50790i
$339$	−12.0000	+	12.0000i	−0.651751	+	0.651751i
$340$	−22.3923	−	19.8564i	−1.21439	−	1.07686i
$341$	2.53590	−	1.46410i	0.137327	−	0.0792855i
$342$	15.2942	−	4.09808i	0.827017	−	0.221599i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	1.50000	+	0.866025i	0.0808746	+	0.0466930i
$345$	4.26795	+	12.8038i	0.229779	+	0.689336i
$346$			43.7128i			2.35002i
$347$	6.63397	+	6.63397i	0.356130	+	0.356130i	0.862384	−	0.506254i	$-0.168970\pi$
$347$	6.63397	+	6.63397i	0.356130	+	0.356130i	−0.506254	+	0.862384i	$0.668970\pi$
$348$	5.89230	+	10.2058i	0.315861	+	0.547087i
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$	−19.2942	+	16.7583i	−1.03132	+	0.895770i
$351$	7.09808	−	26.4904i	0.378867	−	1.41395i
$352$	3.92820	−	14.6603i	0.209374	−	0.781394i
$353$	−4.56218	+	17.0263i	−0.242820	+	0.906217i	0.731646	+	0.681684i	$0.238752\pi$
$353$	−4.56218	+	17.0263i	−0.242820	+	0.906217i	−0.974467	+	0.224533i	$0.927914\pi$
$354$	48.8827	−	13.0981i	2.59809	−	0.696155i
$355$	−5.83013	−	8.83013i	−0.309431	−	0.468654i
$356$	22.3923	−	12.9282i	1.18679	−	0.685193i
$357$	35.3205	−	2.53590i	1.86936	−	0.134214i
$358$	−0.633975	−	2.36603i	−0.0335066	−	0.125048i
$359$	9.46410	−	5.46410i	0.499496	−	0.288384i	−0.229009	−	0.973424i	$-0.573549\pi$
$359$	9.46410	−	5.46410i	0.499496	−	0.288384i	0.728505	+	0.685040i	$0.240215\pi$
$360$	−1.09808	−	3.29423i	−0.0578737	−	0.173621i
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$	−27.4904	+	27.4904i	−1.44486	+	1.44486i
$363$	−6.06218	−	10.5000i	−0.318182	−	0.551107i
$364$	24.1244	−	1.73205i	1.26446	−	0.0907841i
$365$	−6.00000	−	5.32051i	−0.314054	−	0.278488i
$366$	2.53590	+	9.46410i	0.132554	+	0.494697i
$367$	−5.33013	−	1.42820i	−0.278230	−	0.0745516i	0.117006	−	0.993131i	$-0.462670\pi$
$367$	−5.33013	−	1.42820i	−0.278230	−	0.0745516i	−0.395236	+	0.918580i	$0.629337\pi$
$368$	−4.02628	−	15.0263i	−0.209884	−	0.783299i
$369$	7.79423	+	4.50000i	0.405751	+	0.234261i
$370$	2.53590	+	1.26795i	0.131835	+	0.0659175i
$371$	5.73205	+	8.46410i	0.297593	+	0.439434i
$372$	2.19615	−	3.80385i	0.113865	−	0.197220i
$373$	−2.02628	−	7.56218i	−0.104917	−	0.391555i	0.893419	−	0.449224i	$-0.148300\pi$
$373$	−2.02628	−	7.56218i	−0.104917	−	0.391555i	−0.998336	+	0.0576697i	$0.981633\pi$
$374$	−29.8564			−1.54384
$375$	6.52628	−	18.2321i	0.337016	−	0.941499i
$376$		−	3.92820i		−	0.202582i
$377$	−14.6603	+	14.6603i	−0.755041	+	0.755041i
$378$	−23.8923	−	11.5981i	−1.22889	−	0.596541i
$379$		−	17.5167i		−	0.899770i	−0.893086	−	0.449885i	$-0.851465\pi$
$379$		−	17.5167i		−	0.899770i	0.893086	−	0.449885i	$-0.148535\pi$
$380$	−9.46410	−	4.73205i	−0.485498	−	0.242749i
$381$	22.7942	−	6.10770i	1.16778	−	0.312907i
$382$	13.3923	+	13.3923i	0.685210	+	0.685210i
$383$	10.5981	−	2.83975i	0.541536	−	0.145104i	0.0223261	−	0.999751i	$-0.492893\pi$
$383$	10.5981	−	2.83975i	0.541536	−	0.145104i	0.519210	+	0.854647i	$0.326226\pi$
$384$	1.83975	+	6.86603i	0.0938841	+	0.350380i
$385$	−1.53590	+	11.7321i	−0.0782766	+	0.597921i
$386$	−0.535898			−0.0272765
$387$	−7.09808	+	7.09808i	−0.360815	+	0.360815i
$388$	25.2224	−	6.75833i	1.28047	−	0.343102i
$389$	−7.83975	+	4.52628i	−0.397491	+	0.229491i	−0.685401	−	0.728166i	$-0.740373\pi$
$389$	−7.83975	+	4.52628i	−0.397491	+	0.229491i	0.287910	+	0.957658i	$0.407040\pi$
$390$	−32.9545	+	21.7583i	−1.66872	+	1.10178i
$391$	−23.3205	+	13.4641i	−1.17937	+	0.680909i
$392$	−0.428203	+	3.59808i	−0.0216275	+	0.181730i
$393$	−7.60770	+	4.39230i	−0.383757	+	0.221562i
$394$		−	10.9282i		−	0.550555i
$395$	−8.46410	+	5.58846i	−0.425875	+	0.281186i
$396$	9.00000	+	5.19615i	0.452267	+	0.261116i
$397$	29.3205	+	7.85641i	1.47155	+	0.394302i	0.903464	−	0.428664i	$-0.141016\pi$
$397$	29.3205	+	7.85641i	1.47155	+	0.394302i	0.568090	+	0.822966i	$0.307682\pi$
$398$	−8.19615	+	2.19615i	−0.410836	+	0.110083i
$399$	11.8301	−	4.09808i	0.592247	−	0.205160i
$400$	−8.76795	+	20.5263i	−0.438397	+	1.02631i
$401$	4.69615	−	8.13397i	0.234515	−	0.406191i	−0.724617	−	0.689152i	$-0.757983\pi$
$401$	4.69615	−	8.13397i	0.234515	−	0.406191i	0.959132	+	0.282961i	$0.0913166\pi$
$402$	18.2942	+	10.5622i	0.912433	+	0.526794i
$403$	7.46410	+	2.00000i	0.371813	+	0.0996271i
$404$	3.23205	+	5.59808i	0.160801	+	0.278515i
$405$	20.0885	−	1.20577i	0.998203	−	0.0599153i
$406$	11.2583	+	16.6244i	0.558742	+	0.825053i
$407$	1.26795	−	0.339746i	0.0628499	−	0.0168406i
$408$	6.00000	−	3.46410i	0.297044	−	0.171499i
$409$	−22.3205			−1.10368			−0.551839	−	0.833951i	$-0.686074\pi$
$409$	−22.3205			−1.10368			−0.551839	+	0.833951i	$0.686074\pi$
$410$	−4.09808	−	12.2942i	−0.202390	−	0.607169i
$411$	−1.73205	−	1.73205i	−0.0854358	−	0.0854358i
$412$	4.03590	+	15.0622i	0.198834	+	0.742060i
$413$	37.8109	−	13.0981i	1.86055	−	0.644514i
$414$	20.1962			0.992587
$415$	−19.6244	−	17.4019i	−0.963322	−	0.854227i
$416$	34.6865	−	20.0263i	1.70065	−	0.981869i
$417$	21.8038			1.06774
$418$	−10.1962	+	2.73205i	−0.498710	+	0.133629i
$419$	−1.16987	−	2.02628i	−0.0571520	−	0.0989902i	0.836034	−	0.548678i	$-0.184869\pi$
$419$	−1.16987	−	2.02628i	−0.0571520	−	0.0989902i	−0.893186	+	0.449688i	$0.851535\pi$
$420$	6.80385	+	16.3923i	0.331994	+	0.799863i
$421$	−2.40192	+	4.16025i	−0.117063	+	0.202758i	−0.918602	−	0.395183i	$-0.870681\pi$
$421$	−2.40192	+	4.16025i	−0.117063	+	0.202758i	0.801540	+	0.597941i	$0.204014\pi$
$422$	−6.53590	+	24.3923i	−0.318163	+	1.18740i
$423$	21.9904	+	5.89230i	1.06921	+	0.286494i
$424$	1.73205	+	1.00000i	0.0841158	+	0.0485643i
$425$	38.2487	+	5.46410i	1.85534	+	0.265048i
$426$	−15.2942	+	4.09808i	−0.741008	+	0.198552i
$427$	2.53590	+	7.32051i	0.122721	+	0.354264i
$428$	−19.7942	−	5.30385i	−0.956790	−	0.256371i
$429$	−4.73205	+	17.6603i	−0.228466	+	0.852645i
$430$	14.4282	−	0.866025i	0.695790	−	0.0417635i
$431$	−10.2942	+	17.8301i	−0.495856	+	0.858847i	−0.999989	−	0.00477901i	$-0.998479\pi$
$431$	−10.2942	+	17.8301i	−0.495856	+	0.858847i	0.504133	+	0.863626i	$0.331812\pi$
$432$	−23.1962			−1.11603
$433$	−0.124356	−	0.124356i	−0.00597615	−	0.00597615i	0.704112	−	0.710089i	$-0.251345\pi$
$433$	−0.124356	−	0.124356i	−0.00597615	−	0.00597615i	−0.710089	+	0.704112i	$0.751345\pi$
$434$	3.26795	−	6.73205i	0.156867	−	0.323149i
$435$	−13.6077	−	6.80385i	−0.652439	−	0.326220i
$436$	5.42820	−	9.40192i	0.259964	−	0.450270i
$437$	−6.73205	+	6.73205i	−0.322038	+	0.322038i
$438$	−10.3923	+	6.00000i	−0.496564	+	0.286691i
$439$	−35.8564			−1.71133			−0.855666	−	0.517528i	$-0.826852\pi$
$439$	−35.8564			−1.71133			−0.855666	+	0.517528i	$0.826852\pi$
$440$	0.732051	+	2.19615i	0.0348992	+	0.104697i
$441$	−19.5000	−	7.79423i	−0.928571	−	0.371154i
$442$	−55.7128	−	55.7128i	−2.64999	−	2.64999i
$443$	8.63397	−	8.63397i	0.410213	−	0.410213i	−0.471600	−	0.881813i	$-0.656323\pi$
$443$	8.63397	−	8.63397i	0.410213	−	0.410213i	0.881813	+	0.471600i	$0.156323\pi$
$444$	1.39230	−	1.39230i	0.0660759	−	0.0660759i
$445$	−14.9282	+	29.8564i	−0.707665	+	1.41533i
$446$	12.6962	+	7.33013i	0.601180	+	0.347092i
$447$	23.1962	−	13.3923i	1.09714	−	0.633434i
$448$	−4.96410	−	14.3301i	−0.234532	−	0.677035i
$449$		−	7.33975i		−	0.346384i	−0.984888	−	0.173192i	$-0.944592\pi$
$449$		−	7.33975i		−	0.346384i	0.984888	−	0.173192i	$-0.0554081\pi$
$450$	−22.7942	−	17.8923i	−1.07453	−	0.843451i
$451$	−5.19615	−	3.00000i	−0.244677	−	0.141264i
$452$	4.39230	−	16.3923i	0.206597	−	0.771029i
$453$	30.5885			1.43717
$454$	−18.5622	−	32.1506i	−0.871166	−	1.50890i
$455$	−24.7583	+	19.0263i	−1.16069	+	0.891966i
$456$	1.73205	−	1.73205i	0.0811107	−	0.0811107i
$457$	−23.0526	−	23.0526i	−1.07835	−	1.07835i	−0.996657	−	0.0816959i	$-0.973966\pi$
$457$	−23.0526	−	23.0526i	−1.07835	−	1.07835i	−0.0816959	−	0.996657i	$-0.526034\pi$
$458$	9.96410	−	2.66987i	0.465592	−	0.124755i
$459$	10.3923	+	38.7846i	0.485071	+	1.81031i
$460$	−10.0981	−	8.95448i	−0.470825	−	0.417505i
$461$	−20.7679	−	11.9904i	−0.967260	−	0.558448i	−0.0688601	−	0.997626i	$-0.521936\pi$
$461$	−20.7679	−	11.9904i	−0.967260	−	0.558448i	−0.898400	+	0.439179i	$0.855270\pi$
$462$	15.9282	+	7.73205i	0.741047	+	0.359728i
$463$	−14.3301	−	3.83975i	−0.665977	−	0.178448i	−0.0900353	−	0.995939i	$-0.528698\pi$
$463$	−14.3301	−	3.83975i	−0.665977	−	0.178448i	−0.575942	+	0.817490i	$0.695365\pi$
$464$	15.1865	+	8.76795i	0.705017	+	0.407042i
$465$	0.339746	+	5.66025i	0.0157553	+	0.262488i
$466$	−12.4641	−	21.5885i	−0.577388	−	1.00007i
$467$	−2.50000	−	0.669873i	−0.115686	−	0.0309980i	0.200511	−	0.979691i	$-0.435740\pi$
$467$	−2.50000	−	0.669873i	−0.115686	−	0.0309980i	−0.316198	+	0.948693i	$0.602406\pi$
$468$	7.09808	+	26.4904i	0.328109	+	1.22452i
$469$	15.0263	+	7.29423i	0.693849	+	0.336816i
$470$	−18.0622	−	27.3564i	−0.833146	−	1.26186i
$471$	−4.56218	−	17.0263i	−0.210214	−	0.784530i
$472$	5.53590	−	5.53590i	0.254810	−	0.254810i
$473$	4.73205	−	4.73205i	0.217580	−	0.217580i
$474$	3.92820	+	14.6603i	0.180428	+	0.673368i
$475$	13.5622	−	1.63397i	0.622275	−	0.0749719i
$476$	−29.3205	+	19.8564i	−1.34390	+	0.910117i
$477$	−8.19615	+	8.19615i	−0.375276	+	0.375276i
$478$	−3.73205	−	1.00000i	−0.170700	−	0.0457389i
$479$	8.63397	+	14.9545i	0.394496	+	0.683288i	0.993037	−	0.117805i	$-0.0375857\pi$
$479$	8.63397	+	14.9545i	0.394496	+	0.683288i	−0.598540	+	0.801093i	$0.704252\pi$
$480$	21.9904	+	19.5000i	1.00372	+	0.890049i
$481$	3.00000	+	1.73205i	0.136788	+	0.0789747i
$482$	−41.9186	−	11.2321i	−1.90934	−	0.511606i
$483$	15.9282	−	1.14359i	0.724758	−	0.0520353i
$484$	10.5000	+	6.06218i	0.477273	+	0.275554i
$485$	−22.3660	+	25.2224i	−1.01559	+	1.14529i
$486$	7.79423	−	29.0885i	0.353553	−	1.31948i
$487$	−29.7583	+	7.97372i	−1.34848	+	0.361324i	−0.859573	−	0.511013i	$-0.829270\pi$
$487$	−29.7583	+	7.97372i	−1.34848	+	0.361324i	−0.488906	+	0.872337i	$0.662604\pi$
$488$	1.07180	+	1.07180i	0.0485180	+	0.0485180i
$489$	11.7846	−	11.7846i	0.532918	−	0.532918i
$490$	13.5622	+	27.0263i	0.612677	+	1.22092i
$491$	8.29423	+	14.3660i	0.374313	+	0.648330i	0.990224	−	0.139486i	$-0.0445451\pi$
$491$	8.29423	+	14.3660i	0.374313	+	0.648330i	−0.615911	+	0.787816i	$0.711212\pi$
$492$	−9.00000			−0.405751
$493$	7.85641	−	29.3205i	0.353835	−	1.32053i
$494$	−24.1244	−	13.9282i	−1.08541	−	0.626659i
$495$	−13.3923	+	0.803848i	−0.601939	+	0.0361303i
$496$		−	6.53590i		−	0.293471i
$497$	−11.8301	+	4.09808i	−0.530654	+	0.183824i
$498$	−33.9904	+	19.6244i	−1.52315	+	0.879388i
$499$	−15.2487	−	8.80385i	−0.682626	−	0.394114i	0.118218	−	0.992988i	$-0.462282\pi$
$499$	−15.2487	−	8.80385i	−0.682626	−	0.394114i	−0.800844	+	0.598873i	$0.795615\pi$
$500$	3.46410	+	19.0526i	0.154919	+	0.852056i
$501$	4.26795	−	4.26795i	0.190678	−	0.190678i
$502$	5.00000	−	5.00000i	0.223161	−	0.223161i
$503$	4.36603	+	4.36603i	0.194671	+	0.194671i	0.797711	−	0.603040i	$-0.206044\pi$
$503$	4.36603	+	4.36603i	0.194671	+	0.194671i	−0.603040	+	0.797711i	$0.706044\pi$
$504$	−4.09808	+	0.294229i	−0.182543	+	0.0131060i
$505$	−7.46410	−	3.73205i	−0.332148	−	0.166074i
$506$	−13.4641			−0.598552
$507$	−22.2846	+	12.8660i	−0.989694	+	0.571400i
$508$	−16.6865	+	16.6865i	−0.740345	+	0.740345i
$509$	16.4545	−	28.5000i	0.729332	−	1.26324i	−0.227834	−	0.973700i	$-0.573164\pi$
$509$	16.4545	−	28.5000i	0.729332	−	1.26324i	0.957166	−	0.289540i	$-0.0935024\pi$
$510$	25.8564	−	51.7128i	1.14494	−	2.28988i
$511$	−7.85641	+	5.32051i	−0.347547	+	0.235365i
$512$	−20.6865	−	20.6865i	−0.914224	−	0.914224i
$513$	7.09808	+	12.2942i	0.313388	+	0.542803i
$514$	−0.267949	+	0.464102i	−0.0118187	+	0.0204706i
$515$	−15.0622	−	13.3564i	−0.663719	−	0.588554i
$516$	2.59808	−	9.69615i	0.114374	−	0.426849i
$517$	−14.6603	−	3.92820i	−0.644757	−	0.172762i
$518$	2.19615	−	2.53590i	0.0964934	−	0.111421i
$519$	−37.8564	+	10.1436i	−1.66171	+	0.445254i
$520$	−2.73205	+	5.46410i	−0.119808	+	0.239617i
$521$	−6.35641	−	3.66987i	−0.278479	−	0.160780i	0.354256	−	0.935149i	$-0.384734\pi$
$521$	−6.35641	−	3.66987i	−0.278479	−	0.160780i	−0.632735	+	0.774369i	$0.718068\pi$
$522$	−16.0981	+	16.0981i	−0.704594	+	0.704594i
$523$	6.23205	−	23.2583i	0.272509	−	1.01702i	−0.684984	−	0.728558i	$-0.740191\pi$
$523$	6.23205	−	23.2583i	0.272509	−	1.01702i	0.957493	−	0.288458i	$-0.0931425\pi$
$524$	4.39230	−	7.60770i	0.191879	−	0.332344i
$525$	−18.9904	−	12.8205i	−0.828808	−	0.559533i
$526$	5.33013	+	9.23205i	0.232405	+	0.402537i
$527$	−10.9282	+	2.92820i	−0.476040	+	0.127555i
$528$	15.4641			0.672989
$529$	9.40192	−	5.42820i	0.408779	−	0.236009i
$530$	16.6603	−	1.00000i	0.723675	−	0.0434372i
$531$	22.6865	+	39.2942i	0.984512	+	1.70522i
$532$	−8.19615	+	9.46410i	−0.355348	+	0.410321i
$533$	−4.09808	−	15.2942i	−0.177507	−	0.662467i
$534$	35.3205	+	35.3205i	1.52847	+	1.52847i
$535$	25.0981	−	8.36603i	1.08508	−	0.361695i
$536$	3.26795			0.141154
$537$	1.90192	−	1.09808i	0.0820741	−	0.0473855i
$538$	−52.9808	+	14.1962i	−2.28416	+	0.612040i
$539$	13.0000	+	5.19615i	0.559950	+	0.223814i
$540$	−16.7942	+	11.0885i	−0.722709	+	0.477171i
$541$	3.46410	+	6.00000i	0.148933	+	0.257960i	0.930834	−	0.365444i	$-0.119083\pi$
$541$	3.46410	+	6.00000i	0.148933	+	0.257960i	−0.781900	+	0.623404i	$0.785749\pi$
$542$	60.8109	+	16.2942i	2.61205	+	0.699897i
$543$	−30.1865	−	17.4282i	−1.29543	−	0.747916i
$544$	−29.3205	+	50.7846i	−1.25711	+	2.17737i
$545$	0.839746	+	13.9904i	0.0359708	+	0.599282i
$546$	15.2942	+	44.1506i	0.654533	+	1.88947i
$547$	38.8205	−	10.4019i	1.65985	−	0.444754i	0.697500	−	0.716585i	$-0.254296\pi$
$547$	38.8205	−	10.4019i	1.65985	−	0.444754i	0.962345	+	0.271831i	$0.0876291\pi$
$548$	2.36603	+	0.633975i	0.101072	+	0.0270821i
$549$	−7.60770	+	4.39230i	−0.324689	+	0.187459i
$550$	15.1962	+	11.9282i	0.647966	+	0.508620i
$551$		−	10.7321i		−	0.457201i
$552$	2.70577	−	1.56218i	0.115165	−	0.0664907i
$553$	3.92820	+	11.3397i	0.167044	+	0.482215i
$554$	19.3923	−	11.1962i	0.823900	−	0.475679i
$555$	−0.509619	+	2.49038i	−0.0216321	+	0.105711i
$556$	−18.8827	+	10.9019i	−0.800804	+	0.462345i
$557$	41.3205	−	11.0718i	1.75081	−	0.469127i	0.766008	−	0.642831i	$-0.222240\pi$
$557$	41.3205	−	11.0718i	1.75081	−	0.469127i	0.984798	+	0.173704i	$0.0555735\pi$
$558$	8.19615	+	2.19615i	0.346971	+	0.0929705i
$559$	17.6603			0.746949
$560$	20.9641	+	16.0622i	0.885895	+	0.678751i
$561$	−6.92820	−	25.8564i	−0.292509	−	1.09166i
$562$	41.5526	−	11.1340i	1.75279	−	0.469658i
$563$	−3.00000	−	3.00000i	−0.126435	−	0.126435i	0.641058	−	0.767493i	$-0.278496\pi$
$563$	−3.00000	−	3.00000i	−0.126435	−	0.126435i	−0.767493	+	0.641058i	$0.778496\pi$
$564$	−21.9904	+	5.89230i	−0.925962	+	0.248111i
$565$	6.92820	+	20.7846i	0.291472	+	0.874415i
$566$		−	26.3205i		−	1.10633i
$567$	4.50000	−	23.3827i	0.188982	−	0.981981i
$568$	−1.73205	+	1.73205i	−0.0726752	+	0.0726752i
$569$		−	10.9282i		−	0.458134i	−0.973411	−	0.229067i	$-0.926432\pi$
$569$		−	10.9282i		−	0.458134i	0.973411	−	0.229067i	$-0.0735675\pi$
$570$	4.09808	−	20.0263i	0.171650	−	0.838809i
$571$	6.19615			0.259301			0.129650	−	0.991560i	$-0.458614\pi$
$571$	6.19615			0.259301			0.129650	+	0.991560i	$0.458614\pi$
$572$	−4.73205	−	17.6603i	−0.197857	−	0.738412i
$573$	−8.49038	+	14.7058i	−0.354691	+	0.614342i
$574$	−15.2942	+	1.09808i	−0.638369	+	0.0458328i
$575$	17.2487	+	2.46410i	0.719321	+	0.102760i
$576$	14.8923	−	8.59808i	0.620513	−	0.358253i
$577$	8.80385	+	32.8564i	0.366509	+	1.36783i	0.865364	+	0.501144i	$0.167087\pi$
$577$	8.80385	+	32.8564i	0.366509	+	1.36783i	−0.498855	+	0.866686i	$0.666246\pi$
$578$	79.7032	+	21.3564i	3.31522	+	0.888309i
$579$	−0.124356	−	0.464102i	−0.00516804	−	0.0192874i
$580$	15.1865	−	0.911543i	0.630586	−	0.0378498i
$581$	−25.6962	+	17.4019i	−1.06606	+	0.721953i
$582$	25.2224	+	43.6865i	1.04550	+	1.81087i
$583$	5.46410	−	5.46410i	0.226300	−	0.226300i
$584$	−0.928203	+	1.60770i	−0.0384093	+	0.0665269i
$585$	−26.4904	−	23.4904i	−1.09524	−	0.971208i
$586$	−11.6603	+	6.73205i	−0.481681	+	0.278098i
$587$	7.00962	+	26.1603i	0.289318	+	1.07975i	0.945626	+	0.325256i	$0.105451\pi$
$587$	7.00962	+	26.1603i	0.289318	+	1.07975i	−0.656308	+	0.754493i	$0.727883\pi$
$588$	20.7846	−	3.00000i	0.857143	−	0.123718i
$589$	−3.46410	+	2.00000i	−0.142736	+	0.0824086i
$590$	13.0981	−	64.0070i	0.539239	−	2.63513i
$591$	9.46410	−	2.53590i	0.389301	−	0.104313i
$592$	0.758330	−	2.83013i	0.0311672	−	0.116318i
$593$	7.75833	−	28.9545i	0.318596	−	1.18902i	−0.601998	−	0.798498i	$-0.705628\pi$
$593$	7.75833	−	28.9545i	0.318596	−	1.18902i	0.920594	−	0.390520i	$-0.127705\pi$
$594$	−5.19615	+	19.3923i	−0.213201	+	0.795676i
$595$	17.4641	−	42.2487i	0.715958	−	1.73203i
$596$	−13.3923	+	23.1962i	−0.548570	+	0.950151i
$597$	−3.80385	−	6.58846i	−0.155681	−	0.269648i
$598$	−25.1244	−	25.1244i	−1.02741	−	1.02741i
$599$			18.1436i			0.741327i	0.928767	+	0.370664i	$0.120870\pi$
$599$			18.1436i			0.741327i	−0.928767	+	0.370664i	$0.879130\pi$
$600$	−4.43782	−	0.633975i	−0.181173	−	0.0258819i
$601$	−29.3205	−	16.9282i	−1.19601	−	0.690516i	−0.236346	−	0.971669i	$-0.575950\pi$
$601$	−29.3205	−	16.9282i	−1.19601	−	0.690516i	−0.959663	+	0.281153i	$0.909283\pi$
$602$	3.23205	−	16.7942i	0.131729	−	0.684482i
$603$	−4.90192	+	18.2942i	−0.199622	+	0.744999i
$604$	−26.4904	+	15.2942i	−1.07788	+	0.622313i
$605$	−15.6244	+	0.937822i	−0.635220	+	0.0381279i
$606$	−8.83013	+	8.83013i	−0.358699	+	0.358699i
$607$	0.990381	+	3.69615i	0.0401983	+	0.150022i	0.983108	−	0.183026i	$-0.0585894\pi$
$607$	0.990381	+	3.69615i	0.0401983	+	0.150022i	−0.942910	+	0.333049i	$0.891923\pi$
$608$	−5.36603	+	20.0263i	−0.217621	+	0.812173i
$609$	−11.7846	+	13.6077i	−0.477536	+	0.551412i
$610$	12.3923	+	2.53590i	0.501750	+	0.102676i
$611$	−20.0263	−	34.6865i	−0.810177	−	1.40327i
$612$	−28.3923	−	28.3923i	−1.14769	−	1.14769i
$613$	6.09808	+	22.7583i	0.246299	+	0.919200i	0.972726	+	0.231957i	$0.0745128\pi$
$613$	6.09808	+	22.7583i	0.246299	+	0.919200i	−0.726427	+	0.687244i	$0.758821\pi$
$614$	14.6603			0.591640
$615$	9.69615	−	6.40192i	0.390987	−	0.258150i
$616$	2.73205	−	0.196152i	0.110077	−	0.00790321i
$617$	−3.32051	+	12.3923i	−0.133679	+	0.498895i	−1.00000		0.000591902i	$-0.999812\pi$
$617$	−3.32051	+	12.3923i	−0.133679	+	0.498895i	0.866321	+	0.499487i	$0.166478\pi$
$618$	−26.0885	+	15.0622i	−1.04943	+	0.605890i
$619$	20.3923	+	35.3205i	0.819636	+	1.41965i	0.905951	+	0.423383i	$0.139158\pi$
$619$	20.3923	+	35.3205i	0.819636	+	1.41965i	−0.0863148	+	0.996268i	$0.527509\pi$
$620$	−3.12436	−	4.73205i	−0.125477	−	0.190044i
$621$	4.68653	+	17.4904i	0.188064	+	0.701865i
$622$	−9.73205	+	9.73205i	−0.390220	+	0.390220i
$623$	29.8564	+	25.8564i	1.19617	+	1.03592i
$624$	28.8564	+	28.8564i	1.15518	+	1.15518i
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$		−	4.39230i		−	0.175552i
$627$	−4.73205	−	8.19615i	−0.188980	−	0.327323i
$628$	12.4641	+	12.4641i	0.497372	+	0.497372i
$629$	−5.07180			−0.202226
$630$	−27.1865	+	20.8923i	−1.08314	+	0.832369i
$631$	15.8564			0.631234			0.315617	−	0.948887i	$-0.397789\pi$
$631$	15.8564			0.631234			0.315617	+	0.948887i	$0.397789\pi$
$632$	1.66025	+	1.66025i	0.0660414	+	0.0660414i
$633$	−22.6410			−0.899900
$634$		−	23.1244i		−	0.918385i
$635$	6.10770	−	29.8468i	0.242376	−	1.18443i
$636$	3.00000	−	11.1962i	0.118958	−	0.443956i
$637$	14.5622	+	33.9545i	0.576974	+	1.34533i
$638$	10.7321	−	10.7321i	0.424886	−	0.424886i
$639$	−7.09808	−	12.2942i	−0.280796	−	0.486352i
$640$	8.99038	+	1.83975i	0.355376	+	0.0727223i
$641$	−19.1962	−	33.2487i	−0.758202	−	1.31325i	−0.943766	−	0.330613i	$-0.892745\pi$
$641$	−19.1962	−	33.2487i	−0.758202	−	1.31325i	0.185564	−	0.982632i	$-0.440589\pi$
$642$		−	39.5885i		−	1.56243i
$643$	9.82051	−	36.6506i	0.387283	−	1.44536i	−0.447253	−	0.894407i	$-0.647598\pi$
$643$	9.82051	−	36.6506i	0.387283	−	1.44536i	0.834536	−	0.550953i	$-0.185736\pi$
$644$	−13.2224	+	8.95448i	−0.521037	+	0.352856i
$645$	4.09808	+	12.2942i	0.161362	+	0.484085i
$646$	40.7846			1.60465
$647$	−7.40192	−	27.6244i	−0.291000	−	1.08603i	−0.944343	−	0.328963i	$-0.893301\pi$
$647$	−7.40192	−	27.6244i	−0.291000	−	1.08603i	0.653343	−	0.757062i	$-0.273366\pi$
$648$	−1.20577	−	4.50000i	−0.0473672	−	0.176777i
$649$	−15.1244	−	26.1962i	−0.593683	−	1.02829i
$650$	6.09808	+	50.6147i	0.239186	+	1.98527i
$651$	6.58846	+	1.26795i	0.258222	+	0.0496948i
$652$	−4.31347	+	16.0981i	−0.168928	+	0.630449i
$653$	4.12436	+	15.3923i	0.161399	+	0.602347i	0.998472	+	0.0552572i	$0.0175979\pi$
$653$	4.12436	+	15.3923i	0.161399	+	0.602347i	−0.837074	+	0.547090i	$0.815735\pi$
$654$	20.2583	+	5.42820i	0.792163	+	0.212260i
$655$	0.679492	+	11.3205i	0.0265499	+	0.442329i
$656$	−11.5981	+	6.69615i	−0.452829	+	0.261441i
$657$	−7.60770	−	7.60770i	−0.296804	−	0.296804i
$658$	−36.6506	+	12.6962i	−1.42879	+	0.494948i
$659$	−34.3468	−	19.8301i	−1.33796	−	0.772472i	−0.351456	−	0.936204i	$-0.614313\pi$
$659$	−34.3468	−	19.8301i	−1.33796	−	0.772472i	−0.986505	+	0.163732i	$0.947647\pi$
$660$	11.1962	−	7.39230i	0.435810	−	0.287745i
$661$			23.3923i			0.909855i	0.890528	+	0.454928i	$0.150335\pi$
$661$			23.3923i			0.909855i	−0.890528	+	0.454928i	$0.849665\pi$
$662$	8.19615	+	8.19615i	0.318553	+	0.318553i
$663$	35.3205	−	61.1769i	1.37173	−	2.37591i
$664$	−3.03590	+	5.25833i	−0.117816	+	0.204063i
$665$	2.09808	−	16.0263i	0.0813599	−	0.621472i
$666$	3.29423	+	1.90192i	0.127649	+	0.0736980i
$667$	3.54294	−	13.2224i	0.137183	−	0.511975i
$668$	−1.56218	+	5.83013i	−0.0604425	+	0.225574i
$669$	−3.40192	+	12.6962i	−0.131526	+	0.490862i
$670$	22.7583	−	15.0263i	0.879231	−	0.580516i
$671$	5.07180	−	2.92820i	0.195795	−	0.113042i
$672$	28.7942	−	19.5000i	1.11076	−	0.752229i
$673$	3.63397	+	13.5622i	0.140079	+	0.522784i	0.999925	+	0.0122297i	$0.00389293\pi$
$673$	3.63397	+	13.5622i	0.140079	+	0.522784i	−0.859846	+	0.510554i	$0.829440\pi$
$674$	−12.7583	+	7.36603i	−0.491433	+	0.283729i
$675$	10.2058	−	23.8923i	0.392820	−	0.919615i
$676$	12.8660	−	22.2846i	0.494847	−	0.857100i
$677$	−34.5167	+	34.5167i	−1.32658	+	1.32658i	−0.418252	+	0.908331i	$0.637357\pi$
$677$	−34.5167	+	34.5167i	−1.32658	+	1.32658i	−0.908331	+	0.418252i	$0.862643\pi$
$678$	32.7846			1.25909
$679$	22.3660	+	33.0263i	0.858329	+	1.26743i
$680$	−0.535898	−	8.92820i	−0.0205508	−	0.342381i
$681$	23.5359	−	23.5359i	0.901898	−	0.901898i
$682$	−5.46410	−	1.46410i	−0.209231	−	0.0560633i
$683$	−3.08142	−	11.5000i	−0.117907	−	0.440035i	0.881581	−	0.472033i	$-0.156480\pi$
$683$	−3.08142	−	11.5000i	−0.117907	−	0.440035i	−0.999488	+	0.0319978i	$0.989813\pi$
$684$	−12.2942	−	7.09808i	−0.470082	−	0.271402i
$685$	−3.00000	+	1.00000i	−0.114624	+	0.0382080i
$686$	34.9545	−	7.63397i	1.33457	−	0.291467i
$687$	4.62436	+	8.00962i	0.176430	+	0.305586i
$688$	−3.86603	−	14.4282i	−0.147391	−	0.550070i
$689$	20.3923			0.776885
$690$	11.6603	−	23.3205i	0.443898	−	0.887797i
$691$		−	12.5359i		−	0.476888i	−0.971156	−	0.238444i	$-0.923363\pi$
$691$		−	12.5359i		−	0.476888i	0.971156	−	0.238444i	$-0.0766374\pi$
$692$	27.7128	−	27.7128i	1.05348	−	1.05348i
$693$	−3.00000	+	15.5885i	−0.113961	+	0.592157i
$694$		−	18.1244i		−	0.687991i
$695$	12.5885	−	25.1769i	0.477507	−	0.955015i
$696$	−0.911543	+	3.40192i	−0.0345519	+	0.128950i
$697$	16.3923	+	16.3923i	0.620903	+	0.620903i
$698$	−18.6603	+	5.00000i	−0.706301	+	0.189253i
$699$	15.8038	−	15.8038i	0.597756	−	0.597756i
$700$	22.8564	+	1.60770i	0.863891	+	0.0607652i
$701$	−27.0526			−1.02176			−0.510881	−	0.859652i	$-0.670681\pi$
$701$	−27.0526			−1.02176			−0.510881	+	0.859652i	$0.670681\pi$
$702$	−45.8827	+	26.4904i	−1.73173	+	0.999815i
$703$	−1.73205	+	0.464102i	−0.0653255	+	0.0175039i
$704$	−9.92820	+	5.73205i	−0.374183	+	0.216035i
$705$	19.5000	−	21.9904i	0.734412	−	0.828206i
$706$	29.4904	−	17.0263i	1.10989	−	0.640792i
$707$	−6.46410	+	7.46410i	−0.243108	+	0.280716i
$708$	−39.2942	−	22.6865i	−1.47677	−	0.852612i
$709$		−	28.6410i		−	1.07564i	−0.843061	−	0.537818i	$-0.819249\pi$
$709$		−	28.6410i		−	1.07564i	0.843061	−	0.537818i	$-0.180751\pi$
$710$	−4.09808	+	20.0263i	−0.153798	+	0.751573i
$711$	−11.7846	+	6.80385i	−0.441957	+	0.255164i
$712$	7.46410	+	2.00000i	0.279729	+	0.0749532i
$713$	−4.92820	+	1.32051i	−0.184563	+	0.0494534i
$714$	−51.7128	−	44.7846i	−1.93530	−	1.67602i
$715$	17.6603	+	15.6603i	0.660456	+	0.585660i
$716$	−1.09808	+	1.90192i	−0.0410370	+	0.0710782i
$717$		−	3.46410i		−	0.129369i
$718$	−20.3923	−	5.46410i	−0.761034	−	0.203918i
$719$	4.53590	+	7.85641i	0.169160	+	0.292995i	0.938125	−	0.346297i	$-0.112561\pi$
$719$	4.53590	+	7.85641i	0.169160	+	0.292995i	−0.768964	+	0.639292i	$0.779228\pi$
$720$	−13.3923	+	26.7846i	−0.499102	+	0.998203i
$721$	−19.7224	+	13.3564i	−0.734502	+	0.497419i
$722$	−21.5263	+	5.76795i	−0.801125	+	0.214661i
$723$		−	38.9090i		−	1.44704i
$724$	34.8564			1.29543
$725$	−15.7128	+	11.7846i	−0.583559	+	0.437669i
$726$	−6.06218	+	22.6244i	−0.224989	+	0.839669i
$727$	4.22243	+	15.7583i	0.156601	+	0.584444i	0.998963	+	0.0455314i	$0.0144981\pi$
$727$	4.22243	+	15.7583i	0.156601	+	0.584444i	−0.842362	+	0.538913i	$0.818835\pi$
$728$	5.46410	+	4.73205i	0.202513	+	0.175381i
$729$	27.0000			1.00000
$730$	0.928203	+	15.4641i	0.0343543	+	0.572352i
$731$	−22.3923	+	12.9282i	−0.828209	+	0.478167i
$732$	4.39230	−	7.60770i	0.162344	−	0.281189i
$733$	−41.4186	+	11.0981i	−1.52983	+	0.409917i	−0.922964	−	0.384887i	$-0.874240\pi$
$733$	−41.4186	+	11.0981i	−1.52983	+	0.409917i	−0.606867	+	0.794804i	$0.707574\pi$
$734$	5.33013	+	9.23205i	0.196739	+	0.340761i
$735$	−20.2583	+	18.0167i	−0.747240	+	0.664555i
$736$	−13.2224	+	22.9019i	−0.487385	+	0.844176i
$737$	3.26795	−	12.1962i	0.120376	−	0.449251i
$738$	−4.50000	−	16.7942i	−0.165647	−	0.618204i
$739$	−35.3205	−	20.3923i	−1.29929	−	0.750143i	−0.319005	−	0.947753i	$-0.603349\pi$
$739$	−35.3205	−	20.3923i	−1.29929	−	0.750143i	−0.980281	+	0.197610i	$0.936682\pi$
$740$	−0.803848	−	2.41154i	−0.0295500	−	0.0886501i
$741$	6.46410	−	24.1244i	0.237465	−	0.886230i
$742$	3.73205	−	19.3923i	0.137008	−	0.711914i
$743$	−18.3564	−	4.91858i	−0.673431	−	0.180445i	−0.0941313	−	0.995560i	$-0.530007\pi$
$743$	−18.3564	−	4.91858i	−0.673431	−	0.180445i	−0.579300	+	0.815114i	$0.696674\pi$
$744$	1.26795	−	0.339746i	0.0464853	−	0.0124557i
$745$	−2.07180	−	34.5167i	−0.0759048	−	1.26459i
$746$	−7.56218	+	13.0981i	−0.276871	+	0.479555i
$747$	−24.8827	−	24.8827i	−0.910410	−	0.910410i
$748$	18.9282	+	18.9282i	0.692084	+	0.692084i
$749$	−2.24167	−	31.2224i	−0.0819088	−	1.14084i
$750$	−33.8205	+	15.9904i	−1.23495	+	0.583886i
$751$	−24.5622	+	42.5429i	−0.896287	+	1.55241i	−0.0640824	+	0.997945i	$0.520412\pi$
$751$	−24.5622	+	42.5429i	−0.896287	+	1.55241i	−0.832204	+	0.554469i	$0.812921\pi$
$752$	−23.9545	+	23.9545i	−0.873530	+	0.873530i
$753$	5.49038	+	3.16987i	0.200081	+	0.115517i
$754$	40.0526			1.45863
$755$	17.6603	−	35.3205i	0.642722	−	1.28544i
$756$	7.79423	+	22.5000i	0.283473	+	0.818317i
$757$	6.39230	+	6.39230i	0.232332	+	0.232332i	0.813666	−	0.581333i	$-0.197469\pi$
$757$	6.39230	+	6.39230i	0.232332	+	0.232332i	−0.581333	+	0.813666i	$0.697469\pi$
$758$	−23.9282	+	23.9282i	−0.869111	+	0.869111i
$759$	−3.12436	−	11.6603i	−0.113407	−	0.423240i
$760$	−1.00000	−	3.00000i	−0.0362738	−	0.108821i
$761$	−1.03590	−	0.598076i	−0.0375513	−	0.0216802i	0.481107	−	0.876662i	$-0.340235\pi$
$761$	−1.03590	−	0.598076i	−0.0375513	−	0.0216802i	−0.518658	+	0.854982i	$0.673568\pi$
$762$	−39.4808	−	22.7942i	−1.43024	−	0.825748i
$763$	16.2846	+	3.13397i	0.589542	+	0.113457i
$764$		−	16.9808i		−	0.614342i
$765$	50.7846	+	10.3923i	1.83612	+	0.375735i
$766$	−18.3564	−	10.5981i	−0.663244	−	0.382924i
$767$	20.6603	−	77.1051i	0.745999	−	2.78410i
$768$	16.7942	−	29.0885i	0.606010	−	1.04964i
$769$	−7.40192	−	12.8205i	−0.266920	−	0.462319i	0.701145	−	0.713019i	$-0.252673\pi$
$769$	−7.40192	−	12.8205i	−0.266920	−	0.462319i	−0.968065	+	0.250700i	$0.919339\pi$
$770$	18.1244	−	13.9282i	0.653156	−	0.501938i
$771$	−0.464102	−	0.124356i	−0.0167142	−	0.00447856i
$772$	0.339746	+	0.339746i	0.0122277	+	0.0122277i
$773$	−44.4186	+	11.9019i	−1.59763	+	0.428082i	−0.944324	−	0.329016i	$-0.893283\pi$
$773$	−44.4186	+	11.9019i	−1.59763	+	0.428082i	−0.653301	+	0.757098i	$0.726616\pi$
$774$	19.3923			0.697042
$775$	6.73205	+	2.87564i	0.241822	+	0.103296i
$776$	6.75833	+	3.90192i	0.242610	+	0.140071i
$777$	2.70577	+	1.31347i	0.0970690	+	0.0471203i
$778$	16.8923	+	4.52628i	0.605618	+	0.162275i
$779$	7.09808	+	4.09808i	0.254315	+	0.146829i
$780$	34.6865	+	7.09808i	1.24198	+	0.254152i
$781$	4.73205	+	8.19615i	0.169326	+	0.293281i
$782$	50.2487	+	13.4641i	1.79689	+	0.481475i
$783$	−17.6769	−	10.2058i	−0.631721	−	0.364725i
$784$	24.5526	−	19.3301i	0.876877	−	0.690362i
$785$	−22.2942	−	4.56218i	−0.795715	−	0.162831i
$786$	16.3923	+	4.39230i	0.584694	+	0.156668i
$787$	−37.8301	+	37.8301i	−1.34850	+	1.34850i	−0.461205	+	0.887294i	$0.652583\pi$
$787$	−37.8301	+	37.8301i	−1.34850	+	1.34850i	−0.887294	+	0.461205i	$0.847417\pi$
$788$	−6.92820	+	6.92820i	−0.246807	+	0.246807i
$789$	−6.75833	+	6.75833i	−0.240603	+	0.240603i
$790$	19.1962	+	3.92820i	0.682968	+	0.139759i
$791$	25.8564	−	1.85641i	0.919348	−	0.0660062i
$792$	0.803848	+	3.00000i	0.0285635	+	0.106600i
$793$	14.9282	+	4.00000i	0.530116	+	0.142044i
$794$	−29.3205	−	50.7846i	−1.04055	−	1.80228i
$795$	4.73205	+	14.1962i	0.167829	+	0.503486i
$796$	6.58846	+	3.80385i	0.233522	+	0.134824i
$797$	44.3468	+	11.8827i	1.57084	+	0.420906i	0.936076	−	0.351797i	$-0.114429\pi$
$797$	44.3468	+	11.8827i	1.57084	+	0.420906i	0.634767	+	0.772703i	$0.281096\pi$
$798$	−21.7583	−	10.5622i	−0.770237	−	0.373897i
$799$	50.7846	+	29.3205i	1.79663	+	1.03729i
$800$	35.2128	−	14.1340i	1.24496	−	0.499711i
$801$	−22.3923	+	38.7846i	−0.791193	+	1.37039i
$802$	−17.5263	+	4.69615i	−0.618874	+	0.165827i
$803$	5.07180	+	5.07180i	0.178980	+	0.178980i
$804$	−4.90192	−	18.2942i	−0.172878	−	0.645188i
$805$	7.87564	−	19.0526i	0.277580	−	0.671514i
$806$	−7.46410	−	12.9282i	−0.262912	−	0.455377i
$807$	−24.5885	−	42.5885i	−0.865555	−	1.49918i
$808$	−0.500000	+	1.86603i	−0.0175899	+	0.0656465i
$809$	−8.38269	−	4.83975i	−0.294720	−	0.170156i	0.345349	−	0.938474i	$-0.387761\pi$
$809$	−8.38269	−	4.83975i	−0.294720	−	0.170156i	−0.640068	+	0.768318i	$0.721094\pi$
$810$	−29.0885	−	25.7942i	−1.02206	−	0.906317i
$811$		−	24.5885i		−	0.863418i	−0.902013	−	0.431709i	$-0.857911\pi$
$811$		−	24.5885i		−	0.863418i	0.902013	−	0.431709i	$-0.142089\pi$
$812$	3.40192	−	17.6769i	0.119384	−	0.620338i
$813$			56.4449i			1.97961i
$814$	−2.19615	−	1.26795i	−0.0769751	−	0.0444416i
$815$	−6.80385	−	20.4115i	−0.238328	−	0.714985i
$816$	−57.7128	−	15.4641i	−2.02035	−	0.541352i
$817$	−6.46410	+	6.46410i	−0.226150	+	0.226150i
$818$	30.4904	+	30.4904i	1.06607	+	1.06607i
$819$	−34.6865	+	23.4904i	−1.21205	+	0.820820i
$820$	−5.19615	+	10.3923i	−0.181458	+	0.362915i
$821$	10.4115			0.363365			0.181683	−	0.983357i	$-0.441846\pi$
$821$	10.4115			0.363365			0.181683	+	0.983357i	$0.441846\pi$
$822$			4.73205i			0.165049i
$823$	19.5622	−	19.5622i	0.681895	−	0.681895i	−0.278532	−	0.960427i	$-0.589848\pi$
$823$	19.5622	−	19.5622i	0.681895	−	0.681895i	0.960427	+	0.278532i	$0.0898479\pi$
$824$	−2.33013	+	4.03590i	−0.0811738	+	0.140597i
$825$	−6.80385	+	15.9282i	−0.236880	+	0.554549i
$826$	−69.5429	−	33.7583i	−2.41971	−	1.17460i
$827$	22.8301	+	22.8301i	0.793881	+	0.793881i	0.982123	−	0.188241i	$-0.0602788\pi$
$827$	22.8301	+	22.8301i	0.793881	+	0.793881i	−0.188241	+	0.982123i	$0.560279\pi$
$828$	−12.8038	−	12.8038i	−0.444964	−	0.444964i
$829$	−4.83975	+	8.38269i	−0.168091	+	0.291143i	−0.937749	−	0.347314i	$-0.887094\pi$
$829$	−4.83975	+	8.38269i	−0.168091	+	0.291143i	0.769657	+	0.638457i	$0.220427\pi$
$830$	3.03590	+	50.5788i	0.105378	+	1.75562i
$831$	14.1962	+	14.1962i	0.492459	+	0.492459i
$832$	−29.2224	−	7.83013i	−1.01311	−	0.271461i
$833$	−43.3205	−	32.3923i	−1.50097	−	1.12233i
$834$	−29.7846	−	29.7846i	−1.03136	−	1.03136i
$835$	−2.46410	−	7.39230i	−0.0852738	−	0.255821i
$836$	8.19615	+	4.73205i	0.283470	+	0.163661i
$837$			7.60770i			0.262960i
$838$	−1.16987	+	4.36603i	−0.0404126	+	0.150822i
$839$	−27.6147	+	47.8301i	−0.953367	+	1.65128i	−0.215304	+	0.976547i	$0.569074\pi$
$839$	−27.6147	+	47.8301i	−0.953367	+	1.65128i	−0.738063	+	0.674732i	$0.764259\pi$
$840$	−2.02628	+	4.90192i	−0.0699133	+	0.169132i
$841$	−6.78461	−	11.7513i	−0.233952	−	0.405217i
$842$	8.96410	−	2.40192i	0.308923	−	0.0827758i
$843$	19.2846	+	33.4019i	0.664197	+	1.15042i
$844$	19.6077	−	11.3205i	0.674925	−	0.389668i
$845$	1.99038	+	33.1603i	0.0684712	+	1.14075i
$846$	−21.9904	−	38.0885i	−0.756045	−	1.30951i
$847$	−3.50000	+	18.1865i	−0.120261	+	0.624897i
$848$	−4.46410	−	16.6603i	−0.153298	−	0.572115i
$849$	22.7942	−	6.10770i	0.782296	−	0.209616i
$850$	−44.7846	−	59.7128i	−1.53610	−	2.04813i
$851$	−2.28719			−0.0784038
$852$	12.2942	+	7.09808i	0.421193	+	0.243176i
$853$	−0.464102	+	0.124356i	−0.0158905	+	0.00425786i	−0.266756	−	0.963764i	$-0.585952\pi$
$853$	−0.464102	+	0.124356i	−0.0158905	+	0.00425786i	0.250865	+	0.968022i	$0.419285\pi$
$854$	6.53590	−	13.4641i	0.223654	−	0.460732i
$855$	18.2942	−	1.09808i	0.625649	−	0.0375534i
$856$	−3.06218	−	5.30385i	−0.104663	−	0.181282i
$857$	−6.73205	−	1.80385i	−0.229962	−	0.0616183i	0.141998	−	0.989867i	$-0.454647\pi$
$857$	−6.73205	−	1.80385i	−0.229962	−	0.0616183i	−0.371960	+	0.928249i	$0.621314\pi$
$858$	30.5885	−	17.6603i	1.04427	−	0.602911i
$859$	−5.16987	+	8.95448i	−0.176394	+	0.305523i	−0.940643	−	0.339398i	$-0.889777\pi$
$859$	−5.16987	+	8.95448i	−0.176394	+	0.305523i	0.764249	+	0.644921i	$0.223110\pi$
$860$	−9.69615	−	8.59808i	−0.330636	−	0.293192i
$861$	−4.50000	−	12.9904i	−0.153360	−	0.442711i
$862$	38.4186	−	10.2942i	1.30854	−	0.350623i
$863$	−37.6147	−	10.0788i	−1.28042	−	0.343088i	−0.446406	−	0.894830i	$-0.647296\pi$
$863$	−37.6147	−	10.0788i	−1.28042	−	0.343088i	−0.834014	+	0.551743i	$0.813963\pi$
$864$	27.8827	+	27.8827i	0.948588	+	0.948588i
$865$	−10.1436	+	49.5692i	−0.344893	+	1.68540i
$866$			0.339746i			0.0115450i
$867$			73.9808i			2.51252i
$868$	−6.33975	+	2.19615i	−0.215185	+	0.0745423i
$869$	7.85641	−	4.53590i	0.266510	−	0.153870i
$870$	9.29423	+	27.8827i	0.315104	+	0.945312i
$871$	28.8564	−	16.6603i	0.977762	−	0.564511i
$872$	3.13397	−	0.839746i	0.106130	−	0.0284374i
$873$	−31.9808	+	31.9808i	−1.08238	+	1.08238i
$874$	18.3923			0.622129
$875$	−25.7679	+	14.5263i	−0.871116	+	0.491078i
$876$	10.3923	+	2.78461i	0.351123	+	0.0940832i
$877$	12.5622	−	3.36603i	0.424195	−	0.113663i	−0.0404052	−	0.999183i	$-0.512865\pi$
$877$	12.5622	−	3.36603i	0.424195	−	0.113663i	0.464600	+	0.885521i	$0.346198\pi$
$878$	48.9808	+	48.9808i	1.65302	+	1.65302i
$879$	−8.53590	−	8.53590i	−0.287909	−	0.287909i
$880$	8.92820	−	17.8564i	0.300970	−	0.601939i
$881$			51.0333i			1.71936i	0.510836	+	0.859678i	$0.329336\pi$
$881$			51.0333i			1.71936i	−0.510836	+	0.859678i	$0.670664\pi$
$882$	15.9904	+	37.2846i	0.538424	+	1.25544i
$883$	19.4378	−	19.4378i	0.654135	−	0.654135i	−0.299851	−	0.953986i	$-0.596937\pi$
$883$	19.4378	−	19.4378i	0.654135	−	0.654135i	0.953986	+	0.299851i	$0.0969370\pi$
$884$			70.6410i			2.37591i
$885$	58.4711	−	3.50962i	1.96549	−	0.117975i
$886$	−23.5885			−0.792470
$887$	−2.37564	−	8.86603i	−0.0797663	−	0.297692i	0.914505	−	0.404574i	$-0.132580\pi$
$887$	−2.37564	−	8.86603i	−0.0797663	−	0.297692i	−0.994272	+	0.106882i	$0.965913\pi$
$888$	0.588457			0.0197473
$889$	−32.4282	−	15.7417i	−1.08761	−	0.527959i
$890$	61.1769	−	20.3923i	2.05065	−	0.683552i
$891$	−18.0000			−0.603023
$892$	−3.40192	−	12.6962i	−0.113905	−	0.425099i
$893$	20.0263	+	5.36603i	0.670154	+	0.179567i
$894$	−49.9808	−	13.3923i	−1.67161	−	0.447906i
$895$	−0.169873	−	2.83013i	−0.00567823	−	0.0946007i
$896$	4.74167	−	9.76795i	0.158408	−	0.326324i
$897$	15.9282	−	27.5885i	0.531827	−	0.921152i
$898$	−10.0263	+	10.0263i	−0.334581	+	0.334581i
$899$	2.87564	−	4.98076i	0.0959081	−	0.166118i
$900$	3.10770	+	25.7942i	0.103590	+	0.859808i
$901$	−25.8564	+	14.9282i	−0.861402	+	0.497331i
$902$	3.00000	+	11.1962i	0.0998891	+	0.372791i
$903$	15.2942	−	1.09808i	0.508960	−	0.0365417i
$904$	4.39230	−	2.53590i	0.146086	−	0.0843427i
$905$	−37.5526	+	24.7942i	−1.24829	+	0.824188i
$906$	−41.7846	−	41.7846i	−1.38820	−	1.38820i
$907$	3.42820	−	12.7942i	0.113832	−	0.424825i	−0.885365	−	0.464896i	$-0.846092\pi$
$907$	3.42820	−	12.7942i	0.113832	−	0.424825i	0.999197	+	0.0400707i	$0.0127583\pi$
$908$	−8.61474	+	32.1506i	−0.285890	+	1.06696i
$909$	−9.69615	−	5.59808i	−0.321601	−	0.185676i
$910$	59.8109	+	7.83013i	1.98271	+	0.259566i
$911$	−0.633975	+	1.09808i	−0.0210045	+	0.0363809i	−0.876337	−	0.481699i	$-0.840020\pi$
$911$	−0.633975	+	1.09808i	−0.0210045	+	0.0363809i	0.855332	+	0.518080i	$0.173353\pi$
$912$	−21.1244			−0.699497
$913$	16.5885	+	16.5885i	0.548998	+	0.548998i
$914$			62.9808i			2.08322i
$915$	0.679492	+	11.3205i	0.0224633	+	0.374244i
$916$	−8.00962	−	4.62436i	−0.264645	−	0.152793i
$917$	13.1769	+	2.53590i	0.435140	+	0.0837427i
$918$	38.7846	−	67.1769i	1.28008	−	2.21717i
$919$	16.0981	−	9.29423i	0.531027	−	0.306588i	−0.210408	−	0.977614i	$-0.567479\pi$
$919$	16.0981	−	9.29423i	0.531027	−	0.306588i	0.741434	+	0.671025i	$0.234146\pi$
$920$	−0.241670	−	4.02628i	−0.00796762	−	0.132743i
$921$	3.40192	+	12.6962i	0.112097	+	0.418352i
$922$	11.9904	+	44.7487i	0.394882	+	1.47372i
$923$	−6.46410	+	24.1244i	−0.212768	+	0.794063i
$924$	−5.19615	−	15.0000i	−0.170941	−	0.493464i
$925$	2.58142	+	2.02628i	0.0848764	+	0.0666237i
$926$	14.3301	+	24.8205i	0.470917	+	0.815653i
$927$	−19.0981	−	19.0981i	−0.627263	−	0.627263i
$928$	−7.71539	−	28.7942i	−0.253270	−	0.945217i
$929$	31.7846			1.04282			0.521410	−	0.853307i	$-0.325406\pi$
$929$	31.7846			1.04282			0.521410	+	0.853307i	$0.325406\pi$
$930$	7.26795	−	8.19615i	0.238325	−	0.268762i
$931$	−17.7583	−	7.09808i	−0.582006	−	0.232630i
$932$	−5.78461	+	21.5885i	−0.189481	+	0.707153i
$933$	−10.6865	−	6.16987i	−0.349861	−	0.201993i
$934$	2.50000	+	4.33013i	0.0818025	+	0.141686i
$935$	−33.8564	−	6.92820i	−1.10722	−	0.226576i
$936$	−4.09808	+	7.09808i	−0.133950	+	0.232008i
$937$	5.53590	−	5.53590i	0.180850	−	0.180850i	−0.610876	−	0.791726i	$-0.709183\pi$
$937$	5.53590	−	5.53590i	0.180850	−	0.180850i	0.791726	+	0.610876i	$0.209183\pi$
$938$	−10.5622	−	30.4904i	−0.344867	−	0.995546i
$939$	3.80385	−	1.01924i	0.124134	−	0.0332616i
$940$	−5.89230	+	28.7942i	−0.192186	+	0.939164i
$941$		−	7.05256i		−	0.229907i	−0.993371	−	0.114953i	$-0.963328\pi$
$941$		−	7.05256i		−	0.229907i	0.993371	−	0.114953i	$-0.0366719\pi$
$942$	−17.0263	+	29.4904i	−0.554746	+	0.960849i
$943$	7.39230	+	7.39230i	0.240727	+	0.240727i
$944$	−67.5167			−2.19748
$945$	−24.4019	−	18.6962i	−0.793795	−	0.608186i
$946$	−12.9282			−0.420332
$947$	5.00000	+	5.00000i	0.162478	+	0.162478i	0.783664	−	0.621185i	$-0.213349\pi$
$947$	5.00000	+	5.00000i	0.162478	+	0.162478i	−0.621185	+	0.783664i	$0.713349\pi$
$948$	6.80385	−	11.7846i	0.220979	−	0.382746i
$949$			18.9282i			0.614435i
$950$	−20.7583	−	16.2942i	−0.673489	−	0.528655i
$951$	20.0263	−	5.36603i	0.649397	−	0.174005i
$952$	−10.3923	−	2.00000i	−0.336817	−	0.0648204i
$953$	22.0526	−	22.0526i	0.714352	−	0.714352i	−0.253090	−	0.967443i	$-0.581447\pi$
$953$	22.0526	−	22.0526i	0.714352	−	0.714352i	0.967443	+	0.253090i	$0.0814470\pi$
$954$	22.3923			0.724978
$955$	12.0788	+	18.2942i	0.390862	+	0.591987i
$956$	1.73205	+	3.00000i	0.0560185	+	0.0970269i
$957$	11.7846	+	6.80385i	0.380942	+	0.219937i
$958$	8.63397	−	32.2224i	0.278951	−	1.04106i
$959$	0.267949	+	3.73205i	0.00865253	+	0.120514i
$960$	−1.33013	−	22.1603i	−0.0429297	−	0.715219i
$961$	28.8564			0.930852
$962$	−1.73205	−	6.46410i	−0.0558436	−	0.208411i
$963$	34.2846	−	9.18653i	1.10481	−	0.296032i
$964$	19.4545	+	33.6962i	0.626587	+	1.08528i
$965$	−0.607695	−	0.124356i	−0.0195624	−	0.00400315i
$966$	−23.3205	−	20.1962i	−0.750325	−	0.649801i
$967$	13.6865	−	51.0788i	0.440129	−	1.64258i	−0.288356	−	0.957523i	$-0.593109\pi$
$967$	13.6865	−	51.0788i	0.440129	−	1.64258i	0.728485	−	0.685061i	$-0.240225\pi$
$968$	0.937822	+	3.50000i	0.0301427	+	0.112494i
$969$	9.46410	+	35.3205i	0.304031	+	1.13466i
$970$	65.0070	−	3.90192i	2.08725	−	0.125283i
$971$	−13.2224	+	7.63397i	−0.424328	+	0.244986i	−0.696927	−	0.717142i	$-0.745450\pi$
$971$	−13.2224	+	7.63397i	−0.424328	+	0.244986i	0.272599	+	0.962128i	$0.412117\pi$
$972$	−23.3827	+	13.5000i	−0.750000	+	0.433013i
$973$	−25.1769	−	21.8038i	−0.807135	−	0.698999i
$974$	51.5429	+	29.7583i	1.65154	+	0.953518i
$975$	−42.4186	+	17.0263i	−1.35848	+	0.545277i
$976$		−	13.0718i		−	0.418418i
$977$	−28.1962	−	28.1962i	−0.902075	−	0.902075i	0.0935406	−	0.995615i	$-0.470182\pi$
$977$	−28.1962	−	28.1962i	−0.902075	−	0.902075i	−0.995615	+	0.0935406i	$0.970182\pi$
$978$	−32.1962			−1.02952
$979$	14.9282	−	25.8564i	0.477107	−	0.826374i
$980$	8.53590	−	25.7321i	0.272669	−	0.821980i
$981$			18.8038i			0.600361i
$982$	8.29423	−	30.9545i	0.264679	−	0.987797i
$983$	7.67691	−	28.6506i	0.244856	−	0.913813i	−0.728600	−	0.684939i	$-0.759829\pi$
$983$	7.67691	−	28.6506i	0.244856	−	0.913813i	0.973456	−	0.228874i	$-0.0735045\pi$
$984$	−1.90192	−	1.90192i	−0.0606311	−	0.0606311i
$985$	2.53590	−	12.3923i	0.0808004	−	0.394852i
$986$	−50.7846	+	29.3205i	−1.61731	+	0.933755i
$987$	−19.5000	−	28.7942i	−0.620692	−	0.916530i
$988$	6.46410	+	24.1244i	0.205650	+	0.767498i
$989$	−10.0981	+	5.83013i	−0.321100	+	0.185387i
$990$	19.3923	+	17.1962i	0.616328	+	0.546530i
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	−7.85641	+	7.85641i	−0.249441	+	0.249441i
$993$	−5.19615	+	9.00000i	−0.164895	+	0.285606i
$994$	21.7583	+	10.5622i	0.690132	+	0.335012i
$995$	−9.80385	+	0.588457i	−0.310803	+	0.0186553i
$996$	33.9904	+	9.10770i	1.07703	+	0.288588i
$997$	−48.0788	−	12.8827i	−1.52267	−	0.407999i	−0.602052	−	0.798457i	$-0.705650\pi$
$997$	−48.0788	−	12.8827i	−1.52267	−	0.407999i	−0.920621	+	0.390458i	$0.872317\pi$
$998$	8.80385	+	32.8564i	0.278681	+	1.04005i
$999$	−0.882686	+	3.29423i	−0.0279269	+	0.104225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bs.a.52.1	✓	4
3.2	odd	2		945.2.bv.b.262.1		4
5.3	odd	4		315.2.bs.d.178.1	yes	4
7.5	odd	6		315.2.cg.b.187.1	yes	4
9.4	even	3		315.2.cg.d.157.1	yes	4
9.5	odd	6		945.2.cj.b.577.1		4
15.8	even	4		945.2.bv.c.73.1		4
21.5	even	6		945.2.cj.c.397.1		4
35.33	even	12		315.2.cg.d.313.1	yes	4
45.13	odd	12		315.2.cg.b.283.1	yes	4
45.23	even	12		945.2.cj.c.388.1		4
63.5	even	6		945.2.bv.c.712.1		4
63.40	odd	6		315.2.bs.d.292.1	yes	4
105.68	odd	12		945.2.cj.b.208.1		4
315.68	odd	12		945.2.bv.b.523.1		4
315.103	even	12	inner	315.2.bs.a.103.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.a.52.1	✓	4	1.1	even	1	trivial
315.2.bs.a.103.1	yes	4	315.103	even	12	inner
315.2.bs.d.178.1	yes	4	5.3	odd	4
315.2.bs.d.292.1	yes	4	63.40	odd	6
315.2.cg.b.187.1	yes	4	7.5	odd	6
315.2.cg.b.283.1	yes	4	45.13	odd	12
315.2.cg.d.157.1	yes	4	9.4	even	3
315.2.cg.d.313.1	yes	4	35.33	even	12
945.2.bv.b.262.1		4	3.2	odd	2
945.2.bv.b.523.1		4	315.68	odd	12
945.2.bv.c.73.1		4	15.8	even	4
945.2.bv.c.712.1		4	63.5	even	6
945.2.cj.b.208.1		4	105.68	odd	12
945.2.cj.b.577.1		4	9.5	odd	6
945.2.cj.c.388.1		4	45.23	even	12
945.2.cj.c.397.1		4	21.5	even	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +1.73205i q^{4} +(-1.23205 - 1.86603i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.36603 - 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +1.73205i q^{4} +(-1.23205 - 1.86603i) q^{5} +(-3.23205 + 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-0.866025 + 4.23205i) q^{10} +(1.00000 + 1.73205i) q^{11} +(2.59808 + 1.50000i) q^{12} +(-1.36603 + 5.09808i) q^{13} +(4.59808 + 2.23205i) q^{14} +(-3.86603 + 0.232051i) q^{15} +4.46410 q^{16} +(-2.00000 - 7.46410i) q^{17} +(-1.50000 + 5.59808i) q^{18} +(-1.36603 - 2.36603i) q^{19} +(3.23205 - 2.13397i) q^{20} +(-0.866025 + 4.50000i) q^{21} +(1.00000 - 3.73205i) q^{22} +(-0.901924 - 3.36603i) q^{23} +(0.232051 + 0.866025i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(8.83013 - 5.09808i) q^{26} -5.19615 q^{27} +(-1.50000 - 4.33013i) q^{28} +(3.40192 + 1.96410i) q^{29} +(5.59808 + 4.96410i) q^{30} -1.46410i q^{31} +(-5.36603 - 5.36603i) q^{32} +3.46410 q^{33} +(-7.46410 + 12.9282i) q^{34} +(4.69615 + 3.59808i) q^{35} +(4.50000 - 2.59808i) q^{36} +(0.169873 - 0.633975i) q^{37} +(-1.36603 + 5.09808i) q^{38} +(6.46410 + 6.46410i) q^{39} +(1.13397 + 0.232051i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(7.33013 - 4.96410i) q^{42} +(-0.866025 - 3.23205i) q^{43} +(-3.00000 + 1.73205i) q^{44} +(-3.00000 + 6.00000i) q^{45} +(-3.36603 + 5.83013i) q^{46} +(-5.36603 + 5.36603i) q^{47} +(3.86603 - 6.69615i) q^{48} +(5.50000 - 4.33013i) q^{49} +(8.96410 - 3.59808i) q^{50} +(-12.9282 - 3.46410i) q^{51} +(-8.83013 - 2.36603i) q^{52} +(-1.00000 - 3.73205i) q^{53} +(7.09808 + 7.09808i) q^{54} +(2.00000 - 4.00000i) q^{55} +(0.598076 - 1.23205i) q^{56} -4.73205 q^{57} +(-1.96410 - 7.33013i) q^{58} -15.1244 q^{59} +(-0.401924 - 6.69615i) q^{60} -2.92820i q^{61} +(-2.00000 + 2.00000i) q^{62} +(6.00000 + 5.19615i) q^{63} +5.73205i q^{64} +(11.1962 - 3.73205i) q^{65} +(-4.73205 - 4.73205i) q^{66} +(-4.46410 - 4.46410i) q^{67} +(12.9282 - 3.46410i) q^{68} +(-5.83013 - 1.56218i) q^{69} +(-1.50000 - 11.3301i) q^{70} +4.73205 q^{71} +(1.50000 + 0.401924i) q^{72} +(3.46410 - 0.928203i) q^{73} +(-1.09808 + 0.633975i) q^{74} +(5.19615 + 6.92820i) q^{75} +(4.09808 - 2.36603i) q^{76} +(-4.00000 - 3.46410i) q^{77} -17.6603i q^{78} -4.53590i q^{79} +(-5.50000 - 8.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(5.59808 + 1.50000i) q^{82} +(11.3301 - 3.03590i) q^{83} +(-7.79423 - 1.50000i) q^{84} +(-11.4641 + 12.9282i) q^{85} +(-3.23205 + 5.59808i) q^{86} +(5.89230 - 3.40192i) q^{87} +(-1.00000 - 0.267949i) q^{88} +(-7.46410 - 12.9282i) q^{89} +(12.2942 - 4.09808i) q^{90} +(-1.00000 - 13.9282i) q^{91} +(5.83013 - 1.56218i) q^{92} +(-2.19615 - 1.26795i) q^{93} +14.6603 q^{94} +(-2.73205 + 5.46410i) q^{95} +(-12.6962 + 3.40192i) q^{96} +(-3.90192 - 14.5622i) q^{97} +(-13.4282 - 1.59808i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 2 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 2 q^{8} - 6 q^{9} + 4 q^{11} - 2 q^{13} + 8 q^{14} - 12 q^{15} + 4 q^{16} - 8 q^{17} - 6 q^{18} - 2 q^{19} + 6 q^{20} + 4 q^{22} - 14 q^{23} - 6 q^{24} + 6 q^{25} + 18 q^{26} - 6 q^{28} + 24 q^{29} + 12 q^{30} - 18 q^{32} - 16 q^{34} - 2 q^{35} + 18 q^{36} + 18 q^{37} - 2 q^{38} + 12 q^{39} + 8 q^{40} + 12 q^{42} - 12 q^{44} - 12 q^{45} - 10 q^{46} - 18 q^{47} + 12 q^{48} + 22 q^{49} + 22 q^{50} - 24 q^{51} - 18 q^{52} - 4 q^{53} + 18 q^{54} + 8 q^{55} - 8 q^{56} - 12 q^{57} + 6 q^{58} - 12 q^{59} - 12 q^{60} - 8 q^{62} + 24 q^{63} + 24 q^{65} - 12 q^{66} - 4 q^{67} + 24 q^{68} - 6 q^{69} - 6 q^{70} + 12 q^{71} + 6 q^{72} + 6 q^{74} + 6 q^{76} - 16 q^{77} - 22 q^{80} - 18 q^{81} + 12 q^{82} + 28 q^{83} - 32 q^{85} - 6 q^{86} - 18 q^{87} - 4 q^{88} - 16 q^{89} + 18 q^{90} - 4 q^{91} + 6 q^{92} + 12 q^{93} + 24 q^{94} - 4 q^{95} - 30 q^{96} - 26 q^{97} - 26 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 2 * q^8 - 6 * q^9 + 4 * q^11 - 2 * q^13 + 8 * q^14 - 12 * q^15 + 4 * q^16 - 8 * q^17 - 6 * q^18 - 2 * q^19 + 6 * q^20 + 4 * q^22 - 14 * q^23 - 6 * q^24 + 6 * q^25 + 18 * q^26 - 6 * q^28 + 24 * q^29 + 12 * q^30 - 18 * q^32 - 16 * q^34 - 2 * q^35 + 18 * q^36 + 18 * q^37 - 2 * q^38 + 12 * q^39 + 8 * q^40 + 12 * q^42 - 12 * q^44 - 12 * q^45 - 10 * q^46 - 18 * q^47 + 12 * q^48 + 22 * q^49 + 22 * q^50 - 24 * q^51 - 18 * q^52 - 4 * q^53 + 18 * q^54 + 8 * q^55 - 8 * q^56 - 12 * q^57 + 6 * q^58 - 12 * q^59 - 12 * q^60 - 8 * q^62 + 24 * q^63 + 24 * q^65 - 12 * q^66 - 4 * q^67 + 24 * q^68 - 6 * q^69 - 6 * q^70 + 12 * q^71 + 6 * q^72 + 6 * q^74 + 6 * q^76 - 16 * q^77 - 22 * q^80 - 18 * q^81 + 12 * q^82 + 28 * q^83 - 32 * q^85 - 6 * q^86 - 18 * q^87 - 4 * q^88 - 16 * q^89 + 18 * q^90 - 4 * q^91 + 6 * q^92 + 12 * q^93 + 24 * q^94 - 4 * q^95 - 30 * q^96 - 26 * q^97 - 26 * q^98 + 12 * q^99

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