LMFDB - Embedded newform 156.2.p.a.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(35,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("156.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.p (of order $6$, degree $2$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.2
Root			$1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	156.35
Dual form			156.2.p.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.23607i q^{5} +(-1.43649 + 1.98406i) q^{6} +(2.73861 - 1.58114i) q^{7} +2.82843 q^{8} +(2.93649 + 0.614017i) q^{9} +(2.73861 + 1.58114i) q^{10} +(-2.12132 + 3.67423i) q^{11} +(-1.41421 - 3.16228i) q^{12} +(-3.50000 - 0.866025i) q^{13} +4.47214i q^{14} +(0.398461 - 3.85243i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.93649 - 1.11803i) q^{17} +(-2.82843 + 3.16228i) q^{18} +(-5.47723 + 3.16228i) q^{19} +(-3.87298 + 2.23607i) q^{20} +(5.00000 - 2.23607i) q^{21} +(-3.00000 - 5.19615i) q^{22} +(-1.41421 + 2.44949i) q^{23} +(4.87298 + 0.504017i) q^{24} +(3.53553 - 3.67423i) q^{26} +(4.94975 + 1.58114i) q^{27} +(-5.47723 - 3.16228i) q^{28} +(5.80948 + 3.35410i) q^{29} +(4.43649 + 3.21209i) q^{30} -3.16228i q^{31} +(-2.82843 - 4.89898i) q^{32} +(-4.30948 + 5.95218i) q^{33} +3.16228i q^{34} +(-3.53553 - 6.12372i) q^{35} +(-1.87298 - 5.70017i) q^{36} +(-0.500000 + 0.866025i) q^{37} -8.94427i q^{38} +(-5.87569 - 2.11573i) q^{39} -6.32456i q^{40} +(-9.68246 - 5.59017i) q^{41} +(-0.796921 + 7.70486i) q^{42} +(-2.73861 + 1.58114i) q^{43} +8.48528 q^{44} +(1.37298 - 6.56619i) q^{45} +(-2.00000 - 3.46410i) q^{46} -2.82843 q^{47} +(-4.06301 + 5.61177i) q^{48} +(1.50000 - 2.59808i) q^{49} +(3.53553 - 1.58114i) q^{51} +(2.00000 + 6.92820i) q^{52} +2.23607i q^{53} +(-5.43649 + 4.94414i) q^{54} +(8.21584 + 4.74342i) q^{55} +(7.74597 - 4.47214i) q^{56} +(-10.0000 + 4.47214i) q^{57} +(-8.21584 + 4.74342i) q^{58} +(-7.07107 + 3.16228i) q^{60} +(-0.500000 - 0.866025i) q^{61} +(3.87298 + 2.23607i) q^{62} +(9.01276 - 2.96145i) q^{63} +8.00000 q^{64} +(-1.93649 + 7.82624i) q^{65} +(-4.24264 - 9.48683i) q^{66} +(5.47723 + 3.16228i) q^{67} +(-3.87298 - 2.23607i) q^{68} +(-2.87298 + 3.96812i) q^{69} +10.0000 q^{70} +(1.41421 + 2.44949i) q^{71} +(8.30565 + 1.73670i) q^{72} -3.00000 q^{73} +(-0.707107 - 1.22474i) q^{74} +(10.9545 + 6.32456i) q^{76} +13.4164i q^{77} +(6.74597 - 5.70017i) q^{78} -12.6491i q^{79} +(7.74597 + 4.47214i) q^{80} +(8.24597 + 3.60611i) q^{81} +(13.6931 - 7.90569i) q^{82} -9.89949 q^{83} +(-8.87298 - 6.42419i) q^{84} +(-2.50000 - 4.33013i) q^{85} -4.47214i q^{86} +(9.41122 + 6.81388i) q^{87} +(-6.00000 + 10.3923i) q^{88} +(-3.87298 - 2.23607i) q^{89} +(7.07107 + 6.32456i) q^{90} +(-10.9545 + 3.16228i) q^{91} +5.65685 q^{92} +(0.563508 - 5.44816i) q^{93} +(2.00000 - 3.46410i) q^{94} +(7.07107 + 12.2474i) q^{95} +(-4.00000 - 8.94427i) q^{96} +(8.00000 + 13.8564i) q^{97} +(2.12132 + 3.67423i) q^{98} +(-8.48528 + 9.48683i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{6} + 8 q^{9} - 28 q^{13} - 16 q^{16} + 40 q^{21} - 24 q^{22} + 8 q^{24} + 20 q^{30} + 12 q^{33} + 16 q^{36} - 4 q^{37} - 20 q^{45} - 16 q^{46} + 12 q^{49} + 16 q^{52} - 28 q^{54} - 80 q^{57}+ \cdots + 64 q^{97}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^6 + 8 * q^9 - 28 * q^13 - 16 * q^16 + 40 * q^21 - 24 * q^22 + 8 * q^24 + 20 * q^30 + 12 * q^33 + 16 * q^36 - 4 * q^37 - 20 * q^45 - 16 * q^46 + 12 * q^49 + 16 * q^52 - 28 * q^54 - 80 * q^57 - 4 * q^61 + 64 * q^64 + 8 * q^69 + 80 * q^70 - 24 * q^73 - 8 * q^78 + 4 * q^81 - 40 * q^84 - 20 * q^85 - 48 * q^88 + 20 * q^93 + 16 * q^94 - 32 * q^96 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i
$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$3$	1.72286	+	0.178197i	0.994694	+	0.102882i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$		−	2.23607i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$5$		−	2.23607i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$6$	−1.43649	+	1.98406i	−0.586445	+	0.809989i
$7$	2.73861	−	1.58114i	1.03510	−	0.597614i	0.116657	−	0.993172i	$-0.462782\pi$
$7$	2.73861	−	1.58114i	1.03510	−	0.597614i	0.918441	+	0.395558i	$0.129449\pi$
$8$	2.82843			1.00000
$9$	2.93649	+	0.614017i	0.978831	+	0.204672i
$10$	2.73861	+	1.58114i	0.866025	+	0.500000i
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	0.345918	+	0.938265i	$0.387568\pi$
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	−0.985520	+	0.169559i	$0.945766\pi$
$12$	−1.41421	−	3.16228i	−0.408248	−	0.912871i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$			4.47214i			1.19523i
$15$	0.398461	−	3.85243i	0.102882	−	0.994694i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	1.93649	−	1.11803i	0.469668	−	0.271163i	−0.246433	−	0.969160i	$-0.579258\pi$
$17$	1.93649	−	1.11803i	0.469668	−	0.271163i	0.716101	+	0.697997i	$0.245925\pi$
$18$	−2.82843	+	3.16228i	−0.666667	+	0.745356i
$19$	−5.47723	+	3.16228i	−1.25656	+	0.725476i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−5.47723	+	3.16228i	−1.25656	+	0.725476i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	−3.87298	+	2.23607i	−0.866025	+	0.500000i
$21$	5.00000	−	2.23607i	1.09109	−	0.487950i
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	−1.41421	+	2.44949i	−0.294884	+	0.510754i	−0.974958	−	0.222390i	$-0.928614\pi$
$23$	−1.41421	+	2.44949i	−0.294884	+	0.510754i	0.680074	+	0.733144i	$0.261948\pi$
$24$	4.87298	+	0.504017i	0.994694	+	0.102882i
$25$		0			0
$26$	3.53553	−	3.67423i	0.693375	−	0.720577i
$27$	4.94975	+	1.58114i	0.952579	+	0.304290i
$28$	−5.47723	−	3.16228i	−1.03510	−	0.597614i
$29$	5.80948	+	3.35410i	1.07879	+	0.622841i	0.930570	−	0.366113i	$-0.119312\pi$
$29$	5.80948	+	3.35410i	1.07879	+	0.622841i	0.148222	+	0.988954i	$0.452645\pi$
$30$	4.43649	+	3.21209i	0.809989	+	0.586445i
$31$		−	3.16228i		−	0.567962i	−0.958830	−	0.283981i	$-0.908345\pi$
$31$		−	3.16228i		−	0.567962i	0.958830	−	0.283981i	$-0.0916552\pi$
$32$	−2.82843	−	4.89898i	−0.500000	−	0.866025i
$33$	−4.30948	+	5.95218i	−0.750183	+	1.03614i
$34$			3.16228i			0.542326i
$35$	−3.53553	−	6.12372i	−0.597614	−	1.03510i
$36$	−1.87298	−	5.70017i	−0.312164	−	0.950028i
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$		−	8.94427i		−	1.45095i
$39$	−5.87569	−	2.11573i	−0.940863	−	0.338788i
$40$		−	6.32456i		−	1.00000i
$41$	−9.68246	−	5.59017i	−1.51215	−	0.873038i	−0.999899	−	0.0141996i	$-0.995480\pi$
$41$	−9.68246	−	5.59017i	−1.51215	−	0.873038i	−0.512247	−	0.858838i	$-0.671187\pi$
$42$	−0.796921	+	7.70486i	−0.122968	+	1.18889i
$43$	−2.73861	+	1.58114i	−0.417635	+	0.241121i	−0.694065	−	0.719913i	$-0.744182\pi$
$43$	−2.73861	+	1.58114i	−0.417635	+	0.241121i	0.276430	+	0.961034i	$0.410849\pi$
$44$	8.48528			1.27920
$45$	1.37298	−	6.56619i	0.204672	−	0.978831i
$46$	−2.00000	−	3.46410i	−0.294884	−	0.510754i
$47$	−2.82843			−0.412568			−0.206284	−	0.978492i	$-0.566137\pi$
$47$	−2.82843			−0.412568			−0.206284	+	0.978492i	$0.566137\pi$
$48$	−4.06301	+	5.61177i	−0.586445	+	0.809989i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	3.53553	−	1.58114i	0.495074	−	0.221404i
$52$	2.00000	+	6.92820i	0.277350	+	0.960769i
$53$			2.23607i			0.307148i	0.988137	+	0.153574i	$0.0490783\pi$
$53$			2.23607i			0.307148i	−0.988137	+	0.153574i	$0.950922\pi$
$54$	−5.43649	+	4.94414i	−0.739813	+	0.672813i
$55$	8.21584	+	4.74342i	1.10782	+	0.639602i
$56$	7.74597	−	4.47214i	1.03510	−	0.597614i
$57$	−10.0000	+	4.47214i	−1.32453	+	0.592349i
$58$	−8.21584	+	4.74342i	−1.07879	+	0.622841i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−7.07107	+	3.16228i	−0.912871	+	0.408248i
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	3.87298	+	2.23607i	0.491869	+	0.283981i
$63$	9.01276	−	2.96145i	1.13550	−	0.373107i
$64$	8.00000			1.00000
$65$	−1.93649	+	7.82624i	−0.240192	+	0.970725i
$66$	−4.24264	−	9.48683i	−0.522233	−	1.16775i
$67$	5.47723	+	3.16228i	0.669150	+	0.386334i	0.795754	−	0.605620i	$-0.207075\pi$
$67$	5.47723	+	3.16228i	0.669150	+	0.386334i	−0.126605	+	0.991953i	$0.540408\pi$
$68$	−3.87298	−	2.23607i	−0.469668	−	0.271163i
$69$	−2.87298	+	3.96812i	−0.345867	+	0.477705i
$70$	10.0000			1.19523
$71$	1.41421	+	2.44949i	0.167836	+	0.290701i	0.937659	−	0.347557i	$-0.112989\pi$
$71$	1.41421	+	2.44949i	0.167836	+	0.290701i	−0.769823	+	0.638258i	$0.779655\pi$
$72$	8.30565	+	1.73670i	0.978831	+	0.204672i
$73$	−3.00000			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$74$	−0.707107	−	1.22474i	−0.0821995	−	0.142374i
$75$		0			0
$76$	10.9545	+	6.32456i	1.25656	+	0.725476i
$77$			13.4164i			1.52894i
$78$	6.74597	−	5.70017i	0.763830	−	0.645417i
$79$		−	12.6491i		−	1.42314i	−0.702617	−	0.711568i	$-0.747985\pi$
$79$		−	12.6491i		−	1.42314i	0.702617	−	0.711568i	$-0.252015\pi$
$80$	7.74597	+	4.47214i	0.866025	+	0.500000i
$81$	8.24597	+	3.60611i	0.916219	+	0.400679i
$82$	13.6931	−	7.90569i	1.51215	−	0.873038i
$83$	−9.89949			−1.08661			−0.543305	−	0.839535i	$-0.682827\pi$
$83$	−9.89949			−1.08661			−0.543305	+	0.839535i	$0.682827\pi$
$84$	−8.87298	−	6.42419i	−0.968122	−	0.700936i
$85$	−2.50000	−	4.33013i	−0.271163	−	0.469668i
$86$		−	4.47214i		−	0.482243i
$87$	9.41122	+	6.81388i	1.00899	+	0.730524i
$88$	−6.00000	+	10.3923i	−0.639602	+	1.10782i
$89$	−3.87298	−	2.23607i	−0.410535	−	0.237023i	0.280484	−	0.959859i	$-0.409505\pi$
$89$	−3.87298	−	2.23607i	−0.410535	−	0.237023i	−0.691020	+	0.722836i	$0.742838\pi$
$90$	7.07107	+	6.32456i	0.745356	+	0.666667i
$91$	−10.9545	+	3.16228i	−1.14834	+	0.331497i
$92$	5.65685			0.589768
$93$	0.563508	−	5.44816i	0.0584331	−	0.564948i
$94$	2.00000	−	3.46410i	0.206284	−	0.357295i
$95$	7.07107	+	12.2474i	0.725476	+	1.25656i
$96$	−4.00000	−	8.94427i	−0.408248	−	0.912871i
$97$	8.00000	+	13.8564i	0.812277	+	1.40690i	0.911267	+	0.411816i	$0.135106\pi$
$97$	8.00000	+	13.8564i	0.812277	+	1.40690i	−0.0989899	+	0.995088i	$0.531561\pi$
$98$	2.12132	+	3.67423i	0.214286	+	0.371154i
$99$	−8.48528	+	9.48683i	−0.852803	+	0.953463i
$100$		0			0
$101$	−5.80948	−	3.35410i	−0.578064	−	0.333746i	0.182299	−	0.983243i	$-0.441646\pi$
$101$	−5.80948	−	3.35410i	−0.578064	−	0.333746i	−0.760364	+	0.649497i	$0.774979\pi$
$102$	−0.563508	+	5.44816i	−0.0557956	+	0.539448i
$103$		−	6.32456i		−	0.623177i	−0.950217	−	0.311588i	$-0.899139\pi$
$103$		−	6.32456i		−	0.623177i	0.950217	−	0.311588i	$-0.100861\pi$
$104$	−9.89949	−	2.44949i	−0.970725	−	0.240192i
$105$	−5.00000	−	11.1803i	−0.487950	−	1.09109i
$106$	−2.73861	−	1.58114i	−0.265998	−	0.153574i
$107$	−1.41421	+	2.44949i	−0.136717	+	0.236801i	−0.926252	−	0.376905i	$-0.876988\pi$
$107$	−1.41421	+	2.44949i	−0.136717	+	0.236801i	0.789535	+	0.613706i	$0.210322\pi$
$108$	−2.21113	−	10.1544i	−0.212767	−	0.977103i
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$	−11.6190	+	6.70820i	−1.10782	+	0.639602i
$111$	−1.01575	+	1.40294i	−0.0964110	+	0.133161i
$112$			12.6491i			1.19523i
$113$	5.80948	−	3.35410i	0.546509	−	0.315527i	−0.201204	−	0.979549i	$-0.564485\pi$
$113$	5.80948	−	3.35410i	0.546509	−	0.315527i	0.747713	+	0.664022i	$0.231152\pi$
$114$	1.59384	−	15.4097i	0.149277	−	1.44325i
$115$	5.47723	+	3.16228i	0.510754	+	0.294884i
$116$		−	13.4164i		−	1.24568i
$117$	−9.74597	−	4.69214i	−0.901015	−	0.433788i
$118$		0			0
$119$	3.53553	−	6.12372i	0.324102	−	0.561361i
$120$	1.12702	−	10.8963i	0.102882	−	0.994694i
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	1.41421			0.128037
$123$	−15.6854	−	11.3565i	−1.41430	−	1.02398i
$124$	−5.47723	+	3.16228i	−0.491869	+	0.283981i
$125$		−	11.1803i		−	1.00000i
$126$	−2.74597	+	13.1324i	−0.244630	+	1.16993i
$127$	−2.73861	−	1.58114i	−0.243013	−	0.140303i	0.373548	−	0.927611i	$-0.378141\pi$
$127$	−2.73861	−	1.58114i	−0.243013	−	0.140303i	−0.616561	+	0.787307i	$0.711474\pi$
$128$	−5.65685	+	9.79796i	−0.500000	+	0.866025i
$129$	−5.00000	+	2.23607i	−0.440225	+	0.196875i
$130$	−8.21584	−	7.90569i	−0.720577	−	0.693375i
$131$	7.07107			0.617802			0.308901	−	0.951094i	$-0.400039\pi$
$131$	7.07107			0.617802			0.308901	+	0.951094i	$0.400039\pi$
$132$	14.6190	+	1.51205i	1.27242	+	0.131607i
$133$	−10.0000	+	17.3205i	−0.867110	+	1.50188i
$134$	−7.74597	+	4.47214i	−0.669150	+	0.386334i
$135$	3.53553	−	11.0680i	0.304290	−	0.952579i
$136$	5.47723	−	3.16228i	0.469668	−	0.271163i
$137$	13.5554	−	7.82624i	1.15812	−	0.668641i	0.207267	−	0.978284i	$-0.433543\pi$
$137$	13.5554	−	7.82624i	1.15812	−	0.668641i	0.950853	+	0.309644i	$0.100210\pi$
$138$	−2.82843	−	6.32456i	−0.240772	−	0.538382i
$139$	−10.9545	+	6.32456i	−0.929144	+	0.536442i	−0.886541	−	0.462650i	$-0.846899\pi$
$139$	−10.9545	+	6.32456i	−0.929144	+	0.536442i	−0.0426035	+	0.999092i	$0.513565\pi$
$140$	−7.07107	+	12.2474i	−0.597614	+	1.03510i
$141$	−4.87298	−	0.504017i	−0.410379	−	0.0424459i
$142$	−4.00000			−0.335673
$143$	10.6066	−	11.0227i	0.886969	−	0.921765i
$144$	−8.00000	+	8.94427i	−0.666667	+	0.745356i
$145$	7.50000	−	12.9904i	0.622841	−	1.07879i
$146$	2.12132	−	3.67423i	0.175562	−	0.304082i
$147$	3.04726	−	4.20883i	0.251334	−	0.347138i
$148$	2.00000			0.164399
$149$	17.4284	−	10.0623i	1.42779	−	0.824336i	0.430846	−	0.902426i	$-0.358215\pi$
$149$	17.4284	−	10.0623i	1.42779	−	0.824336i	0.996946	+	0.0780893i	$0.0248819\pi$
$150$		0			0
$151$			6.32456i			0.514685i	0.966320	+	0.257343i	$0.0828469\pi$
$151$			6.32456i			0.514685i	−0.966320	+	0.257343i	$0.917153\pi$
$152$	−15.4919	+	8.94427i	−1.25656	+	0.725476i
$153$	6.37298	−	2.09406i	0.515225	−	0.169295i
$154$	−16.4317	−	9.48683i	−1.32410	−	0.764471i
$155$	−7.07107			−0.567962
$156$	2.21113	+	12.2927i	0.177032	+	0.984205i
$157$	11.0000			0.877896			0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000			0.877896			0.438948	+	0.898513i	$0.355351\pi$
$158$	15.4919	+	8.94427i	1.23247	+	0.711568i
$159$	−0.398461	+	3.85243i	−0.0316000	+	0.305518i
$160$	−10.9545	+	6.32456i	−0.866025	+	0.500000i
$161$			8.94427i			0.704907i
$162$	−10.2473	+	7.54930i	−0.805107	+	0.593129i
$163$	10.9545	−	6.32456i	0.858019	−	0.495377i	−0.00532951	−	0.999986i	$-0.501696\pi$
$163$	10.9545	−	6.32456i	0.858019	−	0.495377i	0.863348	+	0.504608i	$0.168363\pi$
$164$			22.3607i			1.74608i
$165$	13.3095	+	9.63628i	1.03614	+	0.750183i
$166$	7.00000	−	12.1244i	0.543305	−	0.941033i
$167$	−2.82843	+	4.89898i	−0.218870	+	0.379094i	−0.954463	−	0.298330i	$-0.903570\pi$
$167$	−2.82843	+	4.89898i	−0.218870	+	0.379094i	0.735593	+	0.677424i	$0.236904\pi$
$168$	14.1421	−	6.32456i	1.09109	−	0.487950i
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	7.07107			0.542326
$171$	−18.0255	+	5.92289i	−1.37845	+	0.452935i
$172$	5.47723	+	3.16228i	0.417635	+	0.241121i
$173$	−15.4919	+	8.94427i	−1.17783	+	0.680020i	−0.955512	−	0.294954i	$-0.904696\pi$
$173$	−15.4919	+	8.94427i	−1.17783	+	0.680020i	−0.222318	+	0.974974i	$0.571362\pi$
$174$	−15.0000	+	6.70820i	−1.13715	+	0.508548i
$175$		0			0
$176$	−8.48528	−	14.6969i	−0.639602	−	1.10782i
$177$		0			0
$178$	5.47723	−	3.16228i	0.410535	−	0.237023i
$179$	7.77817	−	13.4722i	0.581368	−	1.00696i	−0.413949	−	0.910300i	$-0.635851\pi$
$179$	7.77817	−	13.4722i	0.581368	−	1.00696i	0.995318	−	0.0966592i	$-0.0308157\pi$
$180$	−12.7460	+	4.18812i	−0.950028	+	0.312164i
$181$	−21.0000			−1.56092			−0.780459	−	0.625207i	$-0.785014\pi$
$181$	−21.0000			−1.56092			−0.780459	+	0.625207i	$0.785014\pi$
$182$	3.87298	−	15.6525i	0.287085	−	1.16024i
$183$	−0.707107	−	1.58114i	−0.0522708	−	0.116881i
$184$	−4.00000	+	6.92820i	−0.294884	+	0.510754i
$185$	1.93649	+	1.11803i	0.142374	+	0.0821995i
$186$	6.27415	+	4.54259i	0.460043	+	0.333079i
$187$			9.48683i			0.693746i
$188$	2.82843	+	4.89898i	0.206284	+	0.357295i
$189$	16.0554	−	3.49611i	1.16786	−	0.254305i
$190$	−20.0000			−1.45095
$191$	−9.19239	−	15.9217i	−0.665138	−	1.15205i	−0.979248	−	0.202666i	$-0.935039\pi$
$191$	−9.19239	−	15.9217i	−0.665138	−	1.15205i	0.314110	−	0.949387i	$-0.398294\pi$
$192$	13.7829	+	1.42558i	0.994694	+	0.102882i
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$	−22.6274			−1.62455
$195$	−4.73092	+	13.1384i	−0.338788	+	0.940863i
$196$	−6.00000			−0.428571
$197$	−7.74597	−	4.47214i	−0.551877	−	0.318626i	0.198002	−	0.980202i	$-0.436555\pi$
$197$	−7.74597	−	4.47214i	−0.551877	−	0.318626i	−0.749879	+	0.661575i	$0.769888\pi$
$198$	−5.61895	−	17.1005i	−0.399321	−	1.21528i
$199$	5.47723	−	3.16228i	0.388270	−	0.224168i	−0.293140	−	0.956069i	$-0.594700\pi$
$199$	5.47723	−	3.16228i	0.388270	−	0.224168i	0.681410	+	0.731902i	$0.261367\pi$
$200$		0			0
$201$	8.87298	+	6.42419i	0.625852	+	0.453127i
$202$	8.21584	−	4.74342i	0.578064	−	0.333746i
$203$	21.2132			1.48888
$204$	−6.27415	−	4.54259i	−0.439278	−	0.318045i
$205$	−12.5000	+	21.6506i	−0.873038	+	1.51215i
$206$	7.74597	+	4.47214i	0.539687	+	0.311588i
$207$	−5.65685	+	6.32456i	−0.393179	+	0.439587i
$208$	10.0000	−	10.3923i	0.693375	−	0.720577i
$209$		−	26.8328i		−	1.85606i
$210$	17.2286	+	1.78197i	1.18889	+	0.122968i
$211$	−2.73861	−	1.58114i	−0.188534	−	0.108850i	0.402762	−	0.915305i	$-0.368050\pi$
$211$	−2.73861	−	1.58114i	−0.188534	−	0.108850i	−0.591296	+	0.806455i	$0.701384\pi$
$212$	3.87298	−	2.23607i	0.265998	−	0.153574i
$213$	2.00000	+	4.47214i	0.137038	+	0.306426i
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$	3.53553	+	6.12372i	0.241121	+	0.417635i
$216$	14.0000	+	4.47214i	0.952579	+	0.304290i
$217$	−5.00000	−	8.66025i	−0.339422	−	0.587896i
$218$	−8.48528	+	14.6969i	−0.574696	+	0.995402i
$219$	−5.16858	−	0.534591i	−0.349260	−	0.0361243i
$220$		−	18.9737i		−	1.27920i
$221$	−7.74597	+	2.23607i	−0.521050	+	0.150414i
$222$	−1.00000	−	2.23607i	−0.0671156	−	0.150075i
$223$	−8.21584	−	4.74342i	−0.550173	−	0.317643i	0.199019	−	0.979996i	$-0.436225\pi$
$223$	−8.21584	−	4.74342i	−0.550173	−	0.317643i	−0.749192	+	0.662353i	$0.769558\pi$
$224$	−15.4919	−	8.94427i	−1.03510	−	0.597614i
$225$		0			0
$226$			9.48683i			0.631055i
$227$	9.89949	+	17.1464i	0.657053	+	1.13805i	0.981375	+	0.192102i	$0.0615304\pi$
$227$	9.89949	+	17.1464i	0.657053	+	1.13805i	−0.324322	+	0.945947i	$0.605136\pi$
$228$	17.7460	+	12.8484i	1.17526	+	0.850904i
$229$	−8.00000			−0.528655			−0.264327	−	0.964433i	$-0.585150\pi$
$229$	−8.00000			−0.528655			−0.264327	+	0.964433i	$0.585150\pi$
$230$	−7.74597	+	4.47214i	−0.510754	+	0.294884i
$231$	−2.39076	+	23.1146i	−0.157301	+	1.52083i
$232$	16.4317	+	9.48683i	1.07879	+	0.622841i
$233$			26.8328i			1.75788i	0.476936	+	0.878938i	$0.341747\pi$
$233$			26.8328i			1.75788i	−0.476936	+	0.878938i	$0.658253\pi$
$234$	12.6381	−	8.61848i	0.826179	−	0.563408i
$235$			6.32456i			0.412568i
$236$		0			0
$237$	2.25403	−	21.7926i	0.146415	−	1.41558i
$238$	5.00000	+	8.66025i	0.324102	+	0.561361i
$239$	15.5563			1.00626			0.503128	−	0.864212i	$-0.332182\pi$
$239$	15.5563			1.00626			0.503128	+	0.864212i	$0.332182\pi$
$240$	12.5483	+	9.08517i	0.809989	+	0.586445i
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	9.89949			0.636364
$243$	13.5640	+	7.68223i	0.870134	+	0.492815i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	−5.80948	−	3.35410i	−0.371154	−	0.214286i
$246$	25.0000	−	11.1803i	1.59394	−	0.712832i
$247$	21.9089	−	6.32456i	1.39403	−	0.402422i
$248$		−	8.94427i		−	0.567962i
$249$	−17.0554	−	1.76406i	−1.08084	−	0.111793i
$250$	13.6931	+	7.90569i	0.866025	+	0.500000i
$251$	−12.0208	−	20.8207i	−0.758747	−	1.31419i	−0.943490	−	0.331402i	$-0.892478\pi$
$251$	−12.0208	−	20.8207i	−0.758747	−	1.31419i	0.184743	−	0.982787i	$-0.440855\pi$
$252$	−14.1421	−	12.6491i	−0.890871	−	0.796819i
$253$	−6.00000	−	10.3923i	−0.377217	−	0.653359i
$254$	3.87298	−	2.23607i	0.243013	−	0.140303i
$255$	−3.53553	−	7.90569i	−0.221404	−	0.495074i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	9.68246	+	5.59017i	0.603975	+	0.348705i	0.770604	−	0.637315i	$-0.219955\pi$
$257$	9.68246	+	5.59017i	0.603975	+	0.348705i	−0.166629	+	0.986020i	$0.553288\pi$
$258$	0.796921	−	7.70486i	0.0496141	−	0.479684i
$259$			3.16228i			0.196494i
$260$	15.4919	−	4.47214i	0.960769	−	0.277350i
$261$	15.0000	+	13.4164i	0.928477	+	0.830455i
$262$	−5.00000	+	8.66025i	−0.308901	+	0.535032i
$263$	−2.12132	+	3.67423i	−0.130806	+	0.226563i	−0.923988	−	0.382422i	$-0.875090\pi$
$263$	−2.12132	+	3.67423i	−0.130806	+	0.226563i	0.793181	+	0.608985i	$0.208423\pi$
$264$	−12.1890	+	16.8353i	−0.750183	+	1.03614i
$265$	5.00000			0.307148
$266$	−14.1421	−	24.4949i	−0.867110	−	1.50188i
$267$	−6.27415	−	4.54259i	−0.383972	−	0.278002i
$268$		−	12.6491i		−	0.772667i
$269$	15.4919	−	8.94427i	0.944560	−	0.545342i	0.0531731	−	0.998585i	$-0.483067\pi$
$269$	15.4919	−	8.94427i	0.944560	−	0.545342i	0.891387	+	0.453243i	$0.149733\pi$
$270$	11.0554	+	12.1564i	0.672813	+	0.739813i
$271$	−10.9545	−	6.32456i	−0.665436	−	0.384189i	0.128909	−	0.991656i	$-0.458852\pi$
$271$	−10.9545	−	6.32456i	−0.665436	−	0.384189i	−0.794345	+	0.607467i	$0.792186\pi$
$272$			8.94427i			0.542326i
$273$	−19.4365	+	3.49611i	−1.17635	+	0.211594i
$274$			22.1359i			1.33728i
$275$		0			0
$276$	9.74597	+	1.00803i	0.586638	+	0.0606765i
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	0.652140	−	0.758099i	$-0.273872\pi$
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	−0.982603	+	0.185720i	$0.940538\pi$
$278$		−	17.8885i		−	1.07288i
$279$	1.94169	−	9.28600i	0.116246	−	0.555938i
$280$	−10.0000	−	17.3205i	−0.597614	−	1.03510i
$281$			15.6525i			0.933748i	0.884324	+	0.466874i	$0.154620\pi$
$281$			15.6525i			0.933748i	−0.884324	+	0.466874i	$0.845380\pi$
$282$	4.06301	−	5.61177i	0.241949	−	0.334176i
$283$	2.73861	+	1.58114i	0.162794	+	0.0939889i	0.579183	−	0.815197i	$-0.303371\pi$
$283$	2.73861	+	1.58114i	0.162794	+	0.0939889i	−0.416390	+	0.909186i	$0.636705\pi$
$284$	2.82843	−	4.89898i	0.167836	−	0.290701i
$285$	10.0000	+	22.3607i	0.592349	+	1.32453i
$286$	6.00000	+	20.7846i	0.354787	+	1.22902i
$287$	−35.3553			−2.08696
$288$	−5.29760	−	16.1225i	−0.312164	−	0.950028i
$289$	−6.00000	+	10.3923i	−0.352941	+	0.611312i
$290$	10.6066	+	18.3712i	0.622841	+	1.07879i
$291$	11.3137	+	25.2982i	0.663221	+	1.48301i
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	−17.4284	+	10.0623i	−1.01818	+	0.587846i	−0.913576	−	0.406668i	$-0.866691\pi$
$293$	−17.4284	+	10.0623i	−1.01818	+	0.587846i	−0.104603	+	0.994514i	$0.533357\pi$
$294$	3.00000	+	6.70820i	0.174964	+	0.391230i
$295$		0			0
$296$	−1.41421	+	2.44949i	−0.0821995	+	0.142374i
$297$	−16.3095	+	14.8324i	−0.946372	+	0.860665i
$298$			28.4605i			1.64867i
$299$	7.07107	−	7.34847i	0.408930	−	0.424973i
$300$		0			0
$301$	−5.00000	+	8.66025i	−0.288195	+	0.499169i
$302$	−7.74597	−	4.47214i	−0.445730	−	0.257343i
$303$	−9.41122	−	6.81388i	−0.540660	−	0.391447i
$304$		−	25.2982i		−	1.45095i
$305$	−1.93649	+	1.11803i	−0.110883	+	0.0640184i
$306$	−1.94169	+	9.28600i	−0.110999	+	0.530845i
$307$		−	18.9737i		−	1.08288i	−0.840738	−	0.541442i	$-0.817879\pi$
$307$		−	18.9737i		−	1.08288i	0.840738	−	0.541442i	$-0.182121\pi$
$308$	23.2379	−	13.4164i	1.32410	−	0.764471i
$309$	1.12702	−	10.8963i	0.0641137	−	0.619870i
$310$	5.00000	−	8.66025i	0.283981	−	0.491869i
$311$	31.1127			1.76424			0.882120	−	0.471025i	$-0.156116\pi$
$311$	31.1127			1.76424			0.882120	+	0.471025i	$0.156116\pi$
$312$	−16.6190	−	5.98419i	−0.940863	−	0.338788i
$313$	−8.00000			−0.452187			−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000			−0.452187			−0.226093	+	0.974106i	$0.572595\pi$
$314$	−7.77817	+	13.4722i	−0.438948	+	0.760280i
$315$	−6.62200	−	20.1531i	−0.373107	−	1.13550i
$316$	−21.9089	+	12.6491i	−1.23247	+	0.711568i
$317$			11.1803i			0.627950i	0.949431	+	0.313975i	$0.101661\pi$
$317$			11.1803i			0.627950i	−0.949431	+	0.313975i	$0.898339\pi$
$318$	−4.43649	−	3.21209i	−0.248786	−	0.180125i
$319$	−24.6475	+	14.2302i	−1.38000	+	0.796741i
$320$		−	17.8885i		−	1.00000i
$321$	−2.87298	+	3.96812i	−0.160354	+	0.221479i
$322$	−10.9545	−	6.32456i	−0.610468	−	0.352454i
$323$	−7.07107	+	12.2474i	−0.393445	+	0.681466i
$324$	−2.00000	−	17.8885i	−0.111111	−	0.993808i
$325$		0			0
$326$			17.8885i			0.990755i
$327$	20.6743	+	2.13836i	1.14329	+	0.118252i
$328$	−27.3861	−	15.8114i	−1.51215	−	0.873038i
$329$	−7.74597	+	4.47214i	−0.427049	+	0.246557i
$330$	−21.2132	+	9.48683i	−1.16775	+	0.522233i
$331$	10.9545	−	6.32456i	0.602111	−	0.347629i	−0.167761	−	0.985828i	$-0.553654\pi$
$331$	10.9545	−	6.32456i	0.602111	−	0.347629i	0.769872	+	0.638199i	$0.220320\pi$
$332$	9.89949	+	17.1464i	0.543305	+	0.941033i
$333$	−2.00000	+	2.23607i	−0.109599	+	0.122536i
$334$	−4.00000	−	6.92820i	−0.218870	−	0.379094i
$335$	7.07107	−	12.2474i	0.386334	−	0.669150i
$336$	−2.25403	+	21.7926i	−0.122968	+	1.18889i
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$	−15.5563	+	9.79796i	−0.846154	+	0.532939i
$339$	10.6066	−	4.74342i	0.576072	−	0.257627i
$340$	−5.00000	+	8.66025i	−0.271163	+	0.469668i
$341$	11.6190	+	6.70820i	0.629201	+	0.363270i
$342$	5.49193	−	26.2648i	0.296970	−	1.42024i
$343$			12.6491i			0.682988i
$344$	−7.74597	+	4.47214i	−0.417635	+	0.241121i
$345$	8.87298	+	6.42419i	0.477705	+	0.345867i
$346$		−	25.2982i		−	1.36004i
$347$	4.24264	+	7.34847i	0.227757	+	0.394486i	0.957143	−	0.289616i	$-0.0935275\pi$
$347$	4.24264	+	7.34847i	0.227757	+	0.394486i	−0.729386	+	0.684102i	$0.760194\pi$
$348$	2.39076	−	23.1146i	0.128158	−	1.23907i
$349$	6.00000	−	10.3923i	0.321173	−	0.556287i	−0.659558	−	0.751654i	$-0.729256\pi$
$349$	6.00000	−	10.3923i	0.321173	−	0.556287i	0.980730	+	0.195367i	$0.0625897\pi$
$350$		0			0
$351$	−15.9548	−	9.82059i	−0.851605	−	0.524184i
$352$	24.0000			1.27920
$353$	−5.80948	−	3.35410i	−0.309207	−	0.178521i	0.337364	−	0.941374i	$-0.390465\pi$
$353$	−5.80948	−	3.35410i	−0.309207	−	0.178521i	−0.646572	+	0.762853i	$0.723798\pi$
$354$		0			0
$355$	5.47723	−	3.16228i	0.290701	−	0.167836i
$356$			8.94427i			0.474045i
$357$	7.18246	−	9.92030i	0.380136	−	0.525038i
$358$	11.0000	+	19.0526i	0.581368	+	1.00696i
$359$	−21.2132			−1.11959			−0.559795	−	0.828631i	$-0.689120\pi$
$359$	−21.2132			−1.11959			−0.559795	+	0.828631i	$0.689120\pi$
$360$	3.88338	−	18.5720i	0.204672	−	0.978831i
$361$	10.5000	−	18.1865i	0.552632	−	0.957186i
$362$	14.8492	−	25.7196i	0.780459	−	1.35179i
$363$	−4.94975	−	11.0680i	−0.259794	−	0.580918i
$364$	16.4317	+	15.8114i	0.861254	+	0.828742i
$365$			6.70820i			0.351123i
$366$	2.43649	+	0.252009i	0.127357	+	0.0131727i
$367$	−16.4317	−	9.48683i	−0.857727	−	0.495209i	0.00552377	−	0.999985i	$-0.498242\pi$
$367$	−16.4317	−	9.48683i	−0.857727	−	0.495209i	−0.863250	+	0.504776i	$0.831575\pi$
$368$	−5.65685	−	9.79796i	−0.294884	−	0.510754i
$369$	−25.0000	−	22.3607i	−1.30145	−	1.16405i
$370$	−2.73861	+	1.58114i	−0.142374	+	0.0821995i
$371$	3.53553	+	6.12372i	0.183556	+	0.317928i
$372$	−10.0000	+	4.47214i	−0.518476	+	0.231869i
$373$	−1.50000	−	2.59808i	−0.0776671	−	0.134523i	0.824576	−	0.565751i	$-0.191414\pi$
$373$	−1.50000	−	2.59808i	−0.0776671	−	0.134523i	−0.902243	+	0.431228i	$0.858080\pi$
$374$	−11.6190	−	6.70820i	−0.600802	−	0.346873i
$375$	1.99230	−	19.2622i	0.102882	−	0.994694i
$376$	−8.00000			−0.412568
$377$	−17.4284	−	16.7705i	−0.897610	−	0.863725i
$378$	−7.07107	+	22.1359i	−0.363696	+	1.13855i
$379$	−2.73861	−	1.58114i	−0.140673	−	0.0812176i	0.428012	−	0.903773i	$-0.359214\pi$
$379$	−2.73861	−	1.58114i	−0.140673	−	0.0812176i	−0.568685	+	0.822556i	$0.692548\pi$
$380$	14.1421	−	24.4949i	0.725476	−	1.25656i
$381$	−4.43649	−	3.21209i	−0.227288	−	0.164561i
$382$	26.0000			1.33028
$383$	8.48528	+	14.6969i	0.433578	+	0.750978i	0.997178	−	0.0750689i	$-0.0239177\pi$
$383$	8.48528	+	14.6969i	0.433578	+	0.750978i	−0.563601	+	0.826047i	$0.690584\pi$
$384$	−11.4919	+	15.8725i	−0.586445	+	0.809989i
$385$	30.0000			1.52894
$386$	16.2635	+	28.1691i	0.827788	+	1.43377i
$387$	−9.01276	+	2.96145i	−0.458144	+	0.150539i
$388$	16.0000	−	27.7128i	0.812277	−	1.40690i
$389$		−	29.0689i		−	1.47385i	−0.675974	−	0.736925i	$-0.736277\pi$
$389$		−	29.0689i		−	1.47385i	0.675974	−	0.736925i	$-0.263723\pi$
$390$	−12.7460	−	15.0844i	−0.645417	−	0.763830i
$391$			6.32456i			0.319847i
$392$	4.24264	−	7.34847i	0.214286	−	0.371154i
$393$	12.1825	+	1.26004i	0.614524	+	0.0635608i
$394$	10.9545	−	6.32456i	0.551877	−	0.318626i
$395$	−28.2843			−1.42314
$396$	24.9170	+	5.21011i	1.25212	+	0.261818i
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	0.999998	+	0.00217869i	$0.000693499\pi$
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$398$			8.94427i			0.448336i
$399$	−20.3151	+	28.0588i	−1.01703	+	1.40470i
$400$		0			0
$401$	13.5554	+	7.82624i	0.676926	+	0.390824i	0.798696	−	0.601735i	$-0.205524\pi$
$401$	13.5554	+	7.82624i	0.676926	+	0.390824i	−0.121770	+	0.992558i	$0.538857\pi$
$402$	−14.1421	+	6.32456i	−0.705346	+	0.315440i
$403$	−2.73861	+	11.0680i	−0.136420	+	0.551335i
$404$			13.4164i			0.667491i
$405$	8.06351	−	18.4385i	0.400679	−	0.916219i
$406$	−15.0000	+	25.9808i	−0.744438	+	1.28940i
$407$	−2.12132	−	3.67423i	−0.105150	−	0.182125i
$408$	10.0000	−	4.47214i	0.495074	−	0.221404i
$409$	10.5000	+	18.1865i	0.519192	+	0.899266i	0.999751	+	0.0223042i	$0.00710022\pi$
$409$	10.5000	+	18.1865i	0.519192	+	0.899266i	−0.480560	+	0.876962i	$0.659566\pi$
$410$	−17.6777	−	30.6186i	−0.873038	−	1.51215i
$411$	24.7487	−	11.0680i	1.22077	−	0.545943i
$412$	−10.9545	+	6.32456i	−0.539687	+	0.311588i
$413$		0			0
$414$	−3.74597	−	11.4003i	−0.184104	−	0.560296i
$415$			22.1359i			1.08661i
$416$	5.65685	+	19.5959i	0.277350	+	0.960769i
$417$	−20.0000	+	8.94427i	−0.979404	+	0.438003i
$418$	32.8634	+	18.9737i	1.60740	+	0.928032i
$419$	−7.77817	+	13.4722i	−0.379989	+	0.658160i	−0.991060	−	0.133416i	$-0.957405\pi$
$419$	−7.77817	+	13.4722i	−0.379989	+	0.658160i	0.611071	+	0.791575i	$0.290739\pi$
$420$	−14.3649	+	19.8406i	−0.700936	+	0.968122i
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	3.87298	−	2.23607i	0.188534	−	0.108850i
$423$	−8.30565	−	1.73670i	−0.403835	−	0.0844413i
$424$			6.32456i			0.307148i
$425$		0			0
$426$	−6.89144	−	0.712788i	−0.333891	−	0.0345347i
$427$	−2.73861	−	1.58114i	−0.132531	−	0.0765167i
$428$	5.65685			0.273434
$429$	20.2379	−	17.1005i	0.977095	−	0.825620i
$430$	−10.0000			−0.482243
$431$	−12.0208	+	20.8207i	−0.579022	+	1.00290i	0.416570	+	0.909104i	$0.363232\pi$
$431$	−12.0208	+	20.8207i	−0.579022	+	1.00290i	−0.995592	+	0.0937922i	$0.970101\pi$
$432$	−15.3767	+	13.9842i	−0.739813	+	0.672813i
$433$	11.5000	+	19.9186i	0.552655	+	0.957226i	0.998082	+	0.0619079i	$0.0197185\pi$
$433$	11.5000	+	19.9186i	0.552655	+	0.957226i	−0.445427	+	0.895318i	$0.646948\pi$
$434$	14.1421			0.678844
$435$	15.2363	−	21.0441i	0.730524	−	1.00899i
$436$	−12.0000	−	20.7846i	−0.574696	−	0.995402i
$437$		−	17.8885i		−	0.855725i
$438$	4.30948	−	5.95218i	0.205915	−	0.284406i
$439$	8.21584	+	4.74342i	0.392121	+	0.226391i	0.683079	−	0.730345i	$-0.260641\pi$
$439$	8.21584	+	4.74342i	0.392121	+	0.226391i	−0.290958	+	0.956736i	$0.593974\pi$
$440$	23.2379	+	13.4164i	1.10782	+	0.639602i
$441$	6.00000	−	6.70820i	0.285714	−	0.319438i
$442$	2.73861	−	11.0680i	0.130263	−	0.526450i
$443$	−11.3137			−0.537531			−0.268765	−	0.963206i	$-0.586616\pi$
$443$	−11.3137			−0.537531			−0.268765	+	0.963206i	$0.586616\pi$
$444$	3.44572	+	0.356394i	0.163527	+	0.0169137i
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$	11.6190	−	6.70820i	0.550173	−	0.317643i
$447$	31.8198	−	14.2302i	1.50503	−	0.673068i
$448$	21.9089	−	12.6491i	1.03510	−	0.597614i
$449$	−7.74597	+	4.47214i	−0.365555	+	0.211053i	−0.671515	−	0.740991i	$-0.734356\pi$
$449$	−7.74597	+	4.47214i	−0.365555	+	0.211053i	0.305960	+	0.952044i	$0.401023\pi$
$450$		0			0
$451$	41.0792	−	23.7171i	1.93434	−	1.11679i
$452$	−11.6190	−	6.70820i	−0.546509	−	0.315527i
$453$	−1.12702	+	10.8963i	−0.0529519	+	0.511954i
$454$	−28.0000			−1.31411
$455$	7.07107	+	24.4949i	0.331497	+	1.14834i
$456$	−28.2843	+	12.6491i	−1.32453	+	0.592349i
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	−0.877483	−	0.479608i	$-0.840779\pi$
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	0.854094	+	0.520119i	$0.174112\pi$
$458$	5.65685	−	9.79796i	0.264327	−	0.457829i
$459$	11.3529	−	2.47212i	0.529909	−	0.115389i
$460$		−	12.6491i		−	0.589768i
$461$	9.68246	−	5.59017i	0.450957	−	0.260360i	−0.257277	−	0.966338i	$-0.582825\pi$
$461$	9.68246	−	5.59017i	0.450957	−	0.260360i	0.708234	+	0.705977i	$0.249492\pi$
$462$	−26.6190	−	19.2726i	−1.23843	−	0.896641i
$463$			22.1359i			1.02874i	0.857567	+	0.514372i	$0.171975\pi$
$463$			22.1359i			1.02874i	−0.857567	+	0.514372i	$0.828025\pi$
$464$	−23.2379	+	13.4164i	−1.07879	+	0.622841i
$465$	−12.1825	−	1.26004i	−0.564948	−	0.0584331i
$466$	−32.8634	−	18.9737i	−1.52237	−	0.878938i
$467$	−12.7279			−0.588978			−0.294489	−	0.955655i	$-0.595149\pi$
$467$	−12.7279			−0.588978			−0.294489	+	0.955655i	$0.595149\pi$
$468$	1.61895	+	21.5726i	0.0748360	+	0.997196i
$469$	20.0000			0.923514
$470$	−7.74597	−	4.47214i	−0.357295	−	0.206284i
$471$	18.9515	+	1.96017i	0.873237	+	0.0903197i
$472$		0			0
$473$		−	13.4164i		−	0.616887i
$474$	25.0966	+	18.1703i	1.15272	+	0.834591i
$475$		0			0
$476$	−14.1421			−0.648204
$477$	−1.37298	+	6.56619i	−0.0628646	+	0.300645i
$478$	−11.0000	+	19.0526i	−0.503128	+	0.871444i
$479$	10.6066	−	18.3712i	0.484628	−	0.839400i	−0.515216	−	0.857060i	$-0.672288\pi$
$479$	10.6066	−	18.3712i	0.484628	−	0.839400i	0.999844	+	0.0176600i	$0.00562165\pi$
$480$	−20.0000	+	8.94427i	−0.912871	+	0.408248i
$481$	2.50000	−	2.59808i	0.113990	−	0.118462i
$482$	9.89949			0.450910
$483$	−1.59384	+	15.4097i	−0.0725223	+	0.701167i
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$	30.9839	−	17.8885i	1.40690	−	0.812277i
$486$	−19.0000	+	11.1803i	−0.861858	+	0.507151i
$487$	19.1703	−	11.0680i	0.868689	−	0.501538i	0.00177647	−	0.999998i	$-0.499435\pi$
$487$	19.1703	−	11.0680i	0.868689	−	0.501538i	0.866912	+	0.498461i	$0.166101\pi$
$488$	−1.41421	−	2.44949i	−0.0640184	−	0.110883i
$489$	20.0000	−	8.94427i	0.904431	−	0.404474i
$490$	8.21584	−	4.74342i	0.371154	−	0.214286i
$491$	16.2635	−	28.1691i	0.733959	−	1.27126i	−0.221219	−	0.975224i	$-0.571004\pi$
$491$	16.2635	−	28.1691i	0.733959	−	1.27126i	0.955178	−	0.296031i	$-0.0956632\pi$
$492$	−3.98461	+	38.5243i	−0.179640	+	1.73681i
$493$	15.0000			0.675566
$494$	−7.74597	+	31.3050i	−0.348508	+	1.40848i
$495$	21.2132	+	18.9737i	0.953463	+	0.852803i
$496$	10.9545	+	6.32456i	0.491869	+	0.283981i
$497$	7.74597	+	4.47214i	0.347454	+	0.200603i
$498$	14.2205	−	19.6412i	0.637238	−	0.880143i
$499$		−	34.7851i		−	1.55719i	−0.627525	−	0.778596i	$-0.715932\pi$
$499$		−	34.7851i		−	1.55719i	0.627525	−	0.778596i	$-0.284068\pi$
$500$	−19.3649	+	11.1803i	−0.866025	+	0.500000i
$501$	−5.74597	+	7.93624i	−0.256711	+	0.354565i
$502$	34.0000			1.51749
$503$	−12.0208	−	20.8207i	−0.535982	−	0.928347i	−0.999115	−	0.0420589i	$-0.986608\pi$
$503$	−12.0208	−	20.8207i	−0.535982	−	0.928347i	0.463133	−	0.886289i	$-0.346725\pi$
$504$	25.4919	−	8.37624i	1.13550	−	0.373107i
$505$	−7.50000	+	12.9904i	−0.333746	+	0.578064i
$506$	16.9706			0.754434
$507$	18.7326	+	12.4935i	0.831945	+	0.554858i
$508$			6.32456i			0.280607i
$509$	9.68246	+	5.59017i	0.429167	+	0.247780i	0.698992	−	0.715130i	$-0.253632\pi$
$509$	9.68246	+	5.59017i	0.429167	+	0.247780i	−0.269824	+	0.962910i	$0.586966\pi$
$510$	12.1825	+	1.26004i	0.539448	+	0.0557956i
$511$	−8.21584	+	4.74342i	−0.363447	+	0.209836i
$512$	22.6274			1.00000
$513$	−32.1109	+	6.99222i	−1.41773	+	0.308714i
$514$	−13.6931	+	7.90569i	−0.603975	+	0.348705i
$515$	−14.1421			−0.623177
$516$	8.87298	+	6.42419i	0.390611	+	0.282809i
$517$	6.00000	−	10.3923i	0.263880	−	0.457053i
$518$	−3.87298	−	2.23607i	−0.170169	−	0.0982472i
$519$	−28.2843	+	12.6491i	−1.24154	+	0.555234i
$520$	−5.47723	+	22.1359i	−0.240192	+	0.970725i
$521$			6.70820i			0.293892i	0.989145	+	0.146946i	$0.0469443\pi$
$521$			6.70820i			0.293892i	−0.989145	+	0.146946i	$0.953056\pi$
$522$	−27.0383	+	8.88434i	−1.18343	+	0.388857i
$523$	−30.1247	−	17.3925i	−1.31726	−	0.760522i	−0.333975	−	0.942582i	$-0.608390\pi$
$523$	−30.1247	−	17.3925i	−1.31726	−	0.760522i	−0.983287	+	0.182060i	$0.941724\pi$
$524$	−7.07107	−	12.2474i	−0.308901	−	0.535032i
$525$		0			0
$526$	−3.00000	−	5.19615i	−0.130806	−	0.226563i
$527$	−3.53553	−	6.12372i	−0.154010	−	0.266754i
$528$	−12.0000	−	26.8328i	−0.522233	−	1.16775i
$529$	7.50000	+	12.9904i	0.326087	+	0.564799i
$530$	−3.53553	+	6.12372i	−0.153574	+	0.265998i
$531$		0			0
$532$	40.0000			1.73422
$533$	29.0474	+	27.9508i	1.25818	+	1.21069i
$534$	10.0000	−	4.47214i	0.432742	−	0.193528i
$535$	5.47723	+	3.16228i	0.236801	+	0.136717i
$536$	15.4919	+	8.94427i	0.669150	+	0.386334i
$537$	15.8014	−	21.8247i	0.681881	−	0.941803i
$538$			25.2982i			1.09068i
$539$	6.36396	+	11.0227i	0.274115	+	0.474781i
$540$	−22.7058	+	4.94425i	−0.977103	+	0.212767i
$541$	−39.0000			−1.67674			−0.838370	−	0.545101i	$-0.816491\pi$
$541$	−39.0000			−1.67674			−0.838370	+	0.545101i	$0.816491\pi$
$542$	15.4919	−	8.94427i	0.665436	−	0.384189i
$543$	−36.1801	−	3.74214i	−1.55263	−	0.160590i
$544$	−10.9545	−	6.32456i	−0.469668	−	0.271163i
$545$		−	26.8328i		−	1.14939i
$546$	9.46183	−	26.2769i	0.404929	−	1.12455i
$547$			44.2719i			1.89293i	0.322808	+	0.946465i	$0.395373\pi$
$547$			44.2719i			1.89293i	−0.322808	+	0.946465i	$0.604627\pi$
$548$	−27.1109	−	15.6525i	−1.15812	−	0.668641i
$549$	−0.936492	−	2.85008i	−0.0399685	−	0.121639i
$550$		0			0
$551$	−42.4264			−1.80743
$552$	−8.12602	+	11.2235i	−0.345867	+	0.477705i
$553$	−20.0000	−	34.6410i	−0.850487	−	1.47309i
$554$	15.5563			0.660926
$555$	3.13707	+	2.27129i	0.133161	+	0.0964110i
$556$	21.9089	+	12.6491i	0.929144	+	0.536442i
$557$	−25.1744	−	14.5344i	−1.06667	−	0.615844i	−0.139403	−	0.990236i	$-0.544518\pi$
$557$	−25.1744	−	14.5344i	−1.06667	−	0.615844i	−0.927271	+	0.374392i	$0.877852\pi$
$558$	10.0000	+	8.94427i	0.423334	+	0.378641i
$559$	10.9545	−	3.16228i	0.463324	−	0.133750i
$560$	28.2843			1.19523
$561$	−1.69052	+	16.3445i	−0.0713740	+	0.690065i
$562$	−19.1703	−	11.0680i	−0.808650	−	0.466874i
$563$	19.7990	+	34.2929i	0.834428	+	1.44527i	0.894495	+	0.447077i	$0.147535\pi$
$563$	19.7990	+	34.2929i	0.834428	+	1.44527i	−0.0600674	+	0.998194i	$0.519132\pi$
$564$	4.00000	+	8.94427i	0.168430	+	0.376622i
$565$	−7.50000	−	12.9904i	−0.315527	−	0.546509i
$566$	−3.87298	+	2.23607i	−0.162794	+	0.0939889i
$567$	28.2843	−	3.16228i	1.18783	−	0.132803i
$568$	4.00000	+	6.92820i	0.167836	+	0.290701i
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$	−34.4572	−	3.56394i	−1.44325	−	0.149277i
$571$		−	15.8114i		−	0.661686i	−0.943686	−	0.330843i	$-0.892667\pi$
$571$		−	15.8114i		−	0.661686i	0.943686	−	0.330843i	$-0.107333\pi$
$572$	−29.6985	−	7.34847i	−1.24176	−	0.307255i
$573$	−13.0000	−	29.0689i	−0.543083	−	1.21437i
$574$	25.0000	−	43.3013i	1.04348	−	1.80736i
$575$		0			0
$576$	23.4919	+	4.91213i	0.978831	+	0.204672i
$577$	39.0000			1.62359			0.811796	−	0.583942i	$-0.198490\pi$
$577$	39.0000			1.62359			0.811796	+	0.583942i	$0.198490\pi$
$578$	−8.48528	−	14.6969i	−0.352941	−	0.611312i
$579$	23.3623	−	32.2677i	0.970905	−	1.34100i
$580$	−30.0000			−1.24568
$581$	−27.1109	+	15.6525i	−1.12475	+	0.649374i
$582$	−38.9839	−	4.03214i	−1.61593	−	0.167137i
$583$	−8.21584	−	4.74342i	−0.340265	−	0.196452i
$584$	−8.48528			−0.351123
$585$	−10.4919	+	21.7926i	−0.433788	+	0.901015i
$586$		−	28.4605i		−	1.17569i
$587$	16.9706	−	29.3939i	0.700450	−	1.21322i	−0.267858	−	0.963458i	$-0.586316\pi$
$587$	16.9706	−	29.3939i	0.700450	−	1.21322i	0.968309	−	0.249757i	$-0.0803507\pi$
$588$	−10.3372	−	1.06918i	−0.426297	−	0.0440923i
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$	−12.5483	−	9.08517i	−0.516168	−	0.373714i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$		−	2.23607i		−	0.0918243i	−0.998945	−	0.0459122i	$-0.985381\pi$
$593$		−	2.23607i		−	0.0918243i	0.998945	−	0.0459122i	$-0.0146194\pi$
$594$	−6.63340	−	30.4631i	−0.272172	−	1.24991i
$595$	−13.6931	−	7.90569i	−0.561361	−	0.324102i
$596$	−34.8569	−	20.1246i	−1.42779	−	0.824336i
$597$	10.0000	−	4.47214i	0.409273	−	0.183032i
$598$	4.00000	+	13.8564i	0.163572	+	0.566631i
$599$	−15.5563			−0.635615			−0.317808	−	0.948155i	$-0.602947\pi$
$599$	−15.5563			−0.635615			−0.317808	+	0.948155i	$0.602947\pi$
$600$		0			0
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	−0.303986	−	0.952676i	$-0.598318\pi$
$601$	16.5000	−	28.5788i	0.673049	−	1.16576i	0.977035	−	0.213079i	$-0.0683491\pi$
$602$	−7.07107	−	12.2474i	−0.288195	−	0.499169i
$603$	14.1421	+	12.6491i	0.575912	+	0.515112i
$604$	10.9545	−	6.32456i	0.445730	−	0.257343i
$605$	−13.5554	+	7.82624i	−0.551107	+	0.318182i
$606$	15.0000	−	6.70820i	0.609333	−	0.272502i
$607$	−24.6475	+	14.2302i	−1.00041	+	0.577588i	−0.908370	−	0.418167i	$-0.862673\pi$
$607$	−24.6475	+	14.2302i	−1.00041	+	0.577588i	−0.0920417	+	0.995755i	$0.529339\pi$
$608$	30.9839	+	17.8885i	1.25656	+	0.725476i
$609$	36.5474	+	3.78013i	1.48097	+	0.153179i
$610$		−	3.16228i		−	0.128037i
$611$	9.89949	+	2.44949i	0.400491	+	0.0990957i
$612$	−10.0000	−	8.94427i	−0.404226	−	0.361551i
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	−0.912086	−	0.409998i	$-0.865529\pi$
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	0.811112	+	0.584891i	$0.198863\pi$
$614$	23.2379	+	13.4164i	0.937805	+	0.541442i
$615$	−25.3938	+	35.0735i	−1.02398	+	1.41430i
$616$			37.9473i			1.52894i
$617$	−21.3014	+	12.2984i	−0.857562	+	0.495114i	−0.863195	−	0.504870i	$-0.831540\pi$
$617$	−21.3014	+	12.2984i	−0.857562	+	0.495114i	0.00563284	+	0.999984i	$0.498207\pi$
$618$	12.5483	+	9.08517i	0.504766	+	0.365459i
$619$		−	25.2982i		−	1.01682i	−0.861115	−	0.508411i	$-0.830233\pi$
$619$		−	25.2982i		−	1.01682i	0.861115	−	0.508411i	$-0.169767\pi$
$620$	7.07107	+	12.2474i	0.283981	+	0.491869i
$621$	−10.8730	+	9.88829i	−0.436318	+	0.396803i
$622$	−22.0000	+	38.1051i	−0.882120	+	1.52788i
$623$	−14.1421			−0.566593
$624$	19.0805	−	16.1225i	0.763830	−	0.645417i
$625$	−25.0000			−1.00000
$626$	5.65685	−	9.79796i	0.226093	−	0.391605i
$627$	4.78153	−	46.2292i	0.190956	−	1.84622i
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$			2.23607i			0.0891579i
$630$	29.3649	+	6.14017i	1.16993	+	0.244630i
$631$	−21.9089	+	12.6491i	−0.872180	+	0.503553i	−0.868072	−	0.496438i	$-0.834641\pi$
$631$	−21.9089	+	12.6491i	−0.872180	+	0.503553i	−0.00410769	+	0.999992i	$0.501308\pi$
$632$		−	35.7771i		−	1.42314i
$633$	−4.43649	−	3.21209i	−0.176335	−	0.127669i
$634$	−13.6931	−	7.90569i	−0.543821	−	0.313975i
$635$	−3.53553	+	6.12372i	−0.140303	+	0.243013i
$636$	7.07107	−	3.16228i	0.280386	−	0.125392i
$637$	−7.50000	+	7.79423i	−0.297161	+	0.308819i
$638$		−	40.2492i		−	1.59348i
$639$	2.64880	+	8.06126i	0.104785	+	0.318898i
$640$	21.9089	+	12.6491i	0.866025	+	0.500000i
$641$	−13.5554	+	7.82624i	−0.535408	+	0.309118i	−0.743216	−	0.669052i	$-0.766700\pi$
$641$	−13.5554	+	7.82624i	−0.535408	+	0.309118i	0.207808	+	0.978170i	$0.433367\pi$
$642$	−2.82843	−	6.32456i	−0.111629	−	0.249610i
$643$	−10.9545	+	6.32456i	−0.432001	+	0.249416i	−0.700199	−	0.713948i	$-0.746905\pi$
$643$	−10.9545	+	6.32456i	−0.432001	+	0.249416i	0.268198	+	0.963364i	$0.413572\pi$
$644$	15.4919	−	8.94427i	0.610468	−	0.352454i
$645$	5.00000	+	11.1803i	0.196875	+	0.440225i
$646$	−10.0000	−	17.3205i	−0.393445	−	0.681466i
$647$	0.707107	−	1.22474i	0.0277992	−	0.0481497i	−0.851791	−	0.523882i	$-0.824483\pi$
$647$	0.707107	−	1.22474i	0.0277992	−	0.0481497i	0.879590	+	0.475732i	$0.157817\pi$
$648$	23.3231	+	10.1996i	0.916219	+	0.400679i
$649$		0			0
$650$		0			0
$651$	−7.07107	−	15.8114i	−0.277137	−	0.619697i
$652$	−21.9089	−	12.6491i	−0.858019	−	0.495377i
$653$	−27.1109	−	15.6525i	−1.06093	−	0.612529i	−0.135241	−	0.990813i	$-0.543181\pi$
$653$	−27.1109	−	15.6525i	−1.06093	−	0.612529i	−0.925690	+	0.378284i	$0.876514\pi$
$654$	−17.2379	+	23.8087i	−0.674055	+	0.930994i
$655$		−	15.8114i		−	0.617802i
$656$	38.7298	−	22.3607i	1.51215	−	0.873038i
$657$	−8.80948	−	1.84205i	−0.343690	−	0.0718652i
$658$		−	12.6491i		−	0.493114i
$659$	11.3137	+	19.5959i	0.440720	+	0.763349i	0.997743	−	0.0671481i	$-0.0213900\pi$
$659$	11.3137	+	19.5959i	0.440720	+	0.763349i	−0.557024	+	0.830497i	$0.688057\pi$
$660$	3.38105	−	32.6890i	0.131607	−	1.27242i
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	−0.982632	−	0.185565i	$-0.940588\pi$
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	0.652020	+	0.758202i	$0.273922\pi$
$662$			17.8885i			0.695258i
$663$	−13.7437	+	2.47212i	−0.533760	+	0.0960093i
$664$	−28.0000			−1.08661
$665$	38.7298	+	22.3607i	1.50188	+	0.867110i
$666$	−1.32440	−	4.03063i	−0.0513194	−	0.156184i
$667$	−16.4317	+	9.48683i	−0.636237	+	0.367332i
$668$	11.3137			0.437741
$669$	−13.3095	−	9.63628i	−0.514574	−	0.372560i
$670$	10.0000	+	17.3205i	0.386334	+	0.669150i
$671$	4.24264			0.163785
$672$	−25.0966	−	18.1703i	−0.968122	−	0.700936i
$673$	−13.5000	+	23.3827i	−0.520387	+	0.901336i	0.479332	+	0.877633i	$0.340879\pi$
$673$	−13.5000	+	23.3827i	−0.520387	+	0.901336i	−0.999719	+	0.0237028i	$0.992454\pi$
$674$	3.53553	−	6.12372i	0.136184	−	0.235877i
$675$		0			0
$676$	−1.00000	−	25.9808i	−0.0384615	−	0.999260i
$677$			44.7214i			1.71878i	0.511319	+	0.859391i	$0.329157\pi$
$677$			44.7214i			1.71878i	−0.511319	+	0.859391i	$0.670843\pi$
$678$	−1.69052	+	16.3445i	−0.0649242	+	0.627706i
$679$	43.8178	+	25.2982i	1.68157	+	0.970857i
$680$	−7.07107	−	12.2474i	−0.271163	−	0.469668i
$681$	14.0000	+	31.3050i	0.536481	+	1.19961i
$682$	−16.4317	+	9.48683i	−0.629201	+	0.363270i
$683$	9.19239	+	15.9217i	0.351737	+	0.609226i	0.986554	−	0.163436i	$-0.0522578\pi$
$683$	9.19239	+	15.9217i	0.351737	+	0.609226i	−0.634817	+	0.772663i	$0.718924\pi$
$684$	28.2843	+	25.2982i	1.08148	+	0.967302i
$685$	−17.5000	−	30.3109i	−0.668641	−	1.15812i
$686$	−15.4919	−	8.94427i	−0.591485	−	0.341494i
$687$	−13.7829	−	1.42558i	−0.525850	−	0.0543891i
$688$		−	12.6491i		−	0.482243i
$689$	1.93649	−	7.82624i	0.0737745	−	0.298156i
$690$	−14.1421	+	6.32456i	−0.538382	+	0.240772i
$691$	8.21584	+	4.74342i	0.312545	+	0.180448i	0.648065	−	0.761585i	$-0.275579\pi$
$691$	8.21584	+	4.74342i	0.312545	+	0.180448i	−0.335520	+	0.942033i	$0.608912\pi$
$692$	30.9839	+	17.8885i	1.17783	+	0.680020i
$693$	−8.23790	+	39.3972i	−0.312932	+	1.49657i
$694$	−12.0000			−0.455514
$695$	14.1421	+	24.4949i	0.536442	+	0.929144i
$696$	26.6190	+	19.2726i	1.00899	+	0.730524i
$697$	−25.0000			−0.946943
$698$	8.48528	+	14.6969i	0.321173	+	0.556287i
$699$	−4.78153	+	46.2292i	−0.180854	+	1.74855i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	23.3095	−	12.5964i	0.879759	−	0.475419i
$703$		−	6.32456i		−	0.238535i
$704$	−16.9706	+	29.3939i	−0.639602	+	1.10782i
$705$	−1.12702	+	10.8963i	−0.0424459	+	0.410379i
$706$	8.21584	−	4.74342i	0.309207	−	0.178521i
$707$	−21.2132			−0.797805
$708$		0			0
$709$	−8.50000	−	14.7224i	−0.319224	−	0.552913i	0.661102	−	0.750296i	$-0.270089\pi$
$709$	−8.50000	−	14.7224i	−0.319224	−	0.552913i	−0.980326	+	0.197383i	$0.936756\pi$
$710$			8.94427i			0.335673i
$711$	7.76677	−	37.1440i	0.291277	−	1.39301i
$712$	−10.9545	−	6.32456i	−0.410535	−	0.237023i
$713$	7.74597	+	4.47214i	0.290089	+	0.167483i
$714$	7.07107	+	15.8114i	0.264628	+	0.591726i
$715$	−24.6475	−	23.7171i	−0.921765	−	0.886969i
$716$	−31.1127			−1.16274
$717$	26.8014	+	2.77209i	1.00092	+	0.103526i
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	−11.3137	−	19.5959i	−0.421930	−	0.730804i	0.574198	−	0.818716i	$-0.305314\pi$
$719$	−11.3137	−	19.5959i	−0.421930	−	0.730804i	−0.996128	+	0.0879120i	$0.971981\pi$
$720$	20.0000	+	17.8885i	0.745356	+	0.666667i
$721$	−10.0000	−	17.3205i	−0.372419	−	0.645049i
$722$	14.8492	+	25.7196i	0.552632	+	0.957186i
$723$	−4.94975	−	11.0680i	−0.184083	−	0.411622i
$724$	21.0000	+	36.3731i	0.780459	+	1.35179i
$725$		0			0
$726$	17.0554	+	1.76406i	0.632987	+	0.0654704i
$727$			3.16228i			0.117282i	0.998279	+	0.0586412i	$0.0186768\pi$
$727$			3.16228i			0.117282i	−0.998279	+	0.0586412i	$0.981323\pi$
$728$	−30.9839	+	8.94427i	−1.14834	+	0.331497i
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	−8.21584	−	4.74342i	−0.304082	−	0.175562i
$731$	−3.53553	+	6.12372i	−0.130766	+	0.226494i
$732$	−2.03151	+	2.80588i	−0.0750866	+	0.103708i
$733$	13.0000			0.480166			0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000			0.480166			0.240083	+	0.970752i	$0.422825\pi$
$734$	23.2379	−	13.4164i	0.857727	−	0.495209i
$735$	−9.41122	−	6.81388i	−0.347138	−	0.251334i
$736$	16.0000			0.589768
$737$	−23.2379	+	13.4164i	−0.855979	+	0.494200i
$738$	45.0638	−	14.8072i	1.65882	−	0.545062i
$739$	43.8178	+	25.2982i	1.61186	+	0.930610i	0.988938	+	0.148329i	$0.0473896\pi$
$739$	43.8178	+	25.2982i	1.61186	+	0.930610i	0.622926	+	0.782281i	$0.285944\pi$
$740$		−	4.47214i		−	0.164399i
$741$	38.8730	−	6.99222i	1.42803	−	0.256866i
$742$	−10.0000			−0.367112
$743$	11.3137	−	19.5959i	0.415060	−	0.718905i	−0.580375	−	0.814349i	$-0.697094\pi$
$743$	11.3137	−	19.5959i	0.415060	−	0.718905i	0.995435	+	0.0954448i	$0.0304274\pi$
$744$	1.59384	−	15.4097i	0.0584331	−	0.564948i
$745$	−22.5000	−	38.9711i	−0.824336	−	1.42779i
$746$	4.24264			0.155334
$747$	−29.0698	−	6.07846i	−1.06361	−	0.222399i
$748$	16.4317	−	9.48683i	0.600802	−	0.346873i
$749$			8.94427i			0.326817i
$750$	22.1825	+	16.0605i	0.809989	+	0.586445i
$751$	19.1703	+	11.0680i	0.699534	+	0.403876i	0.807174	−	0.590314i	$-0.200996\pi$
$751$	19.1703	+	11.0680i	0.699534	+	0.403876i	−0.107640	+	0.994190i	$0.534329\pi$
$752$	5.65685	−	9.79796i	0.206284	−	0.357295i
$753$	−17.0000	−	38.0132i	−0.619514	−	1.38528i
$754$	32.8634	−	9.48683i	1.19681	−	0.345490i
$755$	14.1421			0.514685
$756$	−22.1109	−	24.3127i	−0.804165	−	0.884245i
$757$	−10.0000	+	17.3205i	−0.363456	+	0.629525i	−0.988527	−	0.151043i	$-0.951737\pi$
$757$	−10.0000	+	17.3205i	−0.363456	+	0.629525i	0.625071	+	0.780568i	$0.285070\pi$
$758$	3.87298	−	2.23607i	0.140673	−	0.0812176i
$759$	−8.48528	−	18.9737i	−0.307996	−	0.688700i
$760$	20.0000	+	34.6410i	0.725476	+	1.25656i
$761$	38.7298	−	22.3607i	1.40396	−	0.810574i	0.409160	−	0.912463i	$-0.365822\pi$
$761$	38.7298	−	22.3607i	1.40396	−	0.810574i	0.994796	+	0.101889i	$0.0324886\pi$
$762$	7.07107	−	3.16228i	0.256158	−	0.114557i
$763$	32.8634	−	18.9737i	1.18973	−	0.686893i
$764$	−18.3848	+	31.8434i	−0.665138	+	1.15205i
$765$	−4.68246	−	14.2504i	−0.169295	−	0.515225i
$766$	−24.0000			−0.867155
$767$		0			0
$768$	−11.3137	−	25.2982i	−0.408248	−	0.912871i
$769$	−8.00000	+	13.8564i	−0.288487	+	0.499675i	−0.973449	−	0.228904i	$-0.926486\pi$
$769$	−8.00000	+	13.8564i	−0.288487	+	0.499675i	0.684962	+	0.728579i	$0.259819\pi$
$770$	−21.2132	+	36.7423i	−0.764471	+	1.32410i
$771$	15.6854	+	11.3565i	0.564895	+	0.408993i
$772$	−46.0000			−1.65558
$773$	−38.7298	+	22.3607i	−1.39302	+	0.804258i	−0.993648	−	0.112533i	$-0.964104\pi$
$773$	−38.7298	+	22.3607i	−1.39302	+	0.804258i	−0.399367	+	0.916791i	$0.630770\pi$
$774$	2.74597	−	13.1324i	0.0987017	−	0.472034i
$775$		0			0
$776$	22.6274	+	39.1918i	0.812277	+	1.40690i
$777$	−0.563508	+	5.44816i	−0.0202157	+	0.195452i
$778$	35.6020	+	20.5548i	1.27639	+	0.736925i
$779$	70.7107			2.53347
$780$	27.4874	−	4.94425i	0.984205	−	0.177032i
$781$	−12.0000			−0.429394
$782$	−7.74597	−	4.47214i	−0.276995	−	0.159923i
$783$	23.4521	+	25.7875i	0.838111	+	0.921572i
$784$	6.00000	+	10.3923i	0.214286	+	0.371154i
$785$		−	24.5967i		−	0.877896i
$786$	−10.1575	+	14.0294i	−0.362307	+	0.500413i
$787$	24.6475	−	14.2302i	0.878589	−	0.507254i	0.00839610	−	0.999965i	$-0.497327\pi$
$787$	24.6475	−	14.2302i	0.878589	−	0.507254i	0.870193	+	0.492711i	$0.163994\pi$
$788$			17.8885i			0.637253i
$789$	−4.30948	+	5.95218i	−0.153421	+	0.211903i
$790$	20.0000	−	34.6410i	0.711568	−	1.23247i
$791$	10.6066	−	18.3712i	0.377127	−	0.653204i
$792$	−24.0000	+	26.8328i	−0.852803	+	0.953463i
$793$	1.00000	+	3.46410i	0.0355110	+	0.123014i
$794$	−28.2843			−1.00377
$795$	8.61430	+	0.890985i	0.305518	+	0.0316000i
$796$	−10.9545	−	6.32456i	−0.388270	−	0.224168i
$797$	23.2379	−	13.4164i	0.823129	−	0.475234i	−0.0283655	−	0.999598i	$-0.509030\pi$
$797$	23.2379	−	13.4164i	0.823129	−	0.475234i	0.851494	+	0.524364i	$0.175697\pi$
$798$	−20.0000	−	44.7214i	−0.707992	−	1.58312i
$799$	−5.47723	+	3.16228i	−0.193770	+	0.111873i
$800$		0			0
$801$	−10.0000	−	8.94427i	−0.353333	−	0.316030i
$802$	−19.1703	+	11.0680i	−0.676926	+	0.390824i
$803$	6.36396	−	11.0227i	0.224579	−	0.388983i
$804$	2.25403	−	21.7926i	0.0794936	−	0.768567i
$805$	20.0000			0.704907
$806$	−11.6190	−	11.1803i	−0.409260	−	0.393811i
$807$	28.2843	−	12.6491i	0.995654	−	0.445270i
$808$	−16.4317	−	9.48683i	−0.578064	−	0.333746i
$809$	−25.1744	−	14.5344i	−0.885084	−	0.511004i	−0.0127530	−	0.999919i	$-0.504060\pi$
$809$	−25.1744	−	14.5344i	−0.885084	−	0.511004i	−0.872331	+	0.488915i	$0.837393\pi$
$810$	16.8807	+	22.9138i	0.593129	+	0.805107i
$811$			47.4342i			1.66564i	0.553545	+	0.832819i	$0.313275\pi$
$811$			47.4342i			1.66564i	−0.553545	+	0.832819i	$0.686725\pi$
$812$	−21.2132	−	36.7423i	−0.744438	−	1.28940i
$813$	−17.7460	−	12.8484i	−0.622378	−	0.450612i
$814$	6.00000			0.210300
$815$	−14.1421	−	24.4949i	−0.495377	−	0.858019i
$816$	−1.59384	+	15.4097i	−0.0557956	+	0.539448i
$817$	10.0000	−	17.3205i	0.349856	−	0.605968i
$818$	−29.6985			−1.03838
$819$	−34.1093	+	2.55978i	−1.19188	+	0.0894461i
$820$	50.0000			1.74608
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	−3.94456	+	38.1371i	−0.137582	+	1.33019i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		−	17.8885i		−	0.623177i
$825$		0			0
$826$		0			0
$827$	−33.9411			−1.18025			−0.590124	−	0.807312i	$-0.700921\pi$
$827$	−33.9411			−1.18025			−0.590124	+	0.807312i	$0.700921\pi$
$828$	16.6113	+	3.47340i	0.577283	+	0.120709i
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	−0.754567	−	0.656223i	$-0.772153\pi$
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	0.945589	+	0.325362i	$0.105486\pi$
$830$	−27.1109	−	15.6525i	−0.941033	−	0.543305i
$831$	−7.77817	−	17.3925i	−0.269822	−	0.603340i
$832$	−28.0000	−	6.92820i	−0.970725	−	0.240192i
$833$		−	6.70820i		−	0.232425i
$834$	3.18768	−	30.8195i	0.110380	−	1.06719i
$835$	10.9545	+	6.32456i	0.379094	+	0.218870i
$836$	−46.4758	+	26.8328i	−1.60740	+	0.928032i
$837$	5.00000	−	15.6525i	0.172825	−	0.541029i
$838$	−11.0000	−	19.0526i	−0.379989	−	0.658160i
$839$	7.77817	+	13.4722i	0.268532	+	0.465112i	0.968483	−	0.249079i	$-0.0801280\pi$
$839$	7.77817	+	13.4722i	0.268532	+	0.465112i	−0.699951	+	0.714191i	$0.746795\pi$
$840$	−14.1421	−	31.6228i	−0.487950	−	1.09109i
$841$	8.00000	+	13.8564i	0.275862	+	0.477807i
$842$	13.4350	−	23.2702i	0.463002	−	0.801942i
$843$	−2.78922	+	26.9670i	−0.0960660	+	0.928794i
$844$			6.32456i			0.217700i
$845$	13.5554	−	25.7148i	0.466321	−	0.884615i
$846$	8.00000	−	8.94427i	0.275046	−	0.307510i
$847$	−19.1703	−	11.0680i	−0.658699	−	0.380300i
$848$	−7.74597	−	4.47214i	−0.265998	−	0.153574i
$849$	4.43649	+	3.21209i	0.152260	+	0.110239i
$850$		0			0
$851$	−1.41421	−	2.44949i	−0.0484786	−	0.0839674i
$852$	5.74597	−	7.93624i	0.196854	−	0.271891i
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$	3.87298	−	2.23607i	0.132531	−	0.0765167i
$855$	13.2440	+	40.3063i	0.452935	+	1.37845i
$856$	−4.00000	+	6.92820i	−0.136717	+	0.236801i
$857$		−	24.5967i		−	0.840209i	−0.907476	−	0.420104i	$-0.861993\pi$
$857$		−	24.5967i		−	0.840209i	0.907476	−	0.420104i	$-0.138007\pi$
$858$	6.63340	+	36.8782i	0.226461	+	1.25900i
$859$		−	6.32456i		−	0.215791i	−0.994162	−	0.107896i	$-0.965589\pi$
$859$		−	6.32456i		−	0.215791i	0.994162	−	0.107896i	$-0.0344112\pi$
$860$	7.07107	−	12.2474i	0.241121	−	0.417635i
$861$	−60.9123	−	6.30021i	−2.07589	−	0.214711i
$862$	−17.0000	−	29.4449i	−0.579022	−	1.00290i
$863$	18.3848			0.625825			0.312913	−	0.949782i	$-0.398695\pi$
$863$	18.3848			0.625825			0.312913	+	0.949782i	$0.398695\pi$
$864$	−6.25403	−	28.7208i	−0.212767	−	0.977103i
$865$	20.0000	+	34.6410i	0.680020	+	1.17783i
$866$	−32.5269			−1.10531
$867$	−12.1890	+	16.8353i	−0.413961	+	0.571757i
$868$	−10.0000	+	17.3205i	−0.339422	+	0.587896i
$869$	46.4758	+	26.8328i	1.57658	+	0.910241i
$870$	15.0000	+	33.5410i	0.508548	+	1.13715i
$871$	−16.4317	−	15.8114i	−0.556766	−	0.535748i
$872$	33.9411			1.14939
$873$	14.9839	+	45.6014i	0.507127	+	1.54337i
$874$	21.9089	+	12.6491i	0.741080	+	0.427863i
$875$	−17.6777	−	30.6186i	−0.597614	−	1.03510i
$876$	4.24264	+	9.48683i	0.143346	+	0.320530i
$877$	19.5000	+	33.7750i	0.658468	+	1.14050i	0.981012	+	0.193946i	$0.0621286\pi$
$877$	19.5000	+	33.7750i	0.658468	+	1.14050i	−0.322544	+	0.946554i	$0.604538\pi$
$878$	−11.6190	+	6.70820i	−0.392121	+	0.226391i
$879$	−31.8198	+	14.2302i	−1.07326	+	0.479974i
$880$	−32.8634	+	18.9737i	−1.10782	+	0.639602i
$881$	−9.68246	−	5.59017i	−0.326210	−	0.188338i	0.327947	−	0.944696i	$-0.393643\pi$
$881$	−9.68246	−	5.59017i	−0.326210	−	0.188338i	−0.654157	+	0.756359i	$0.726977\pi$
$882$	3.97320	+	12.0919i	0.133785	+	0.407155i
$883$		−	22.1359i		−	0.744934i	−0.928045	−	0.372467i	$-0.878512\pi$
$883$		−	22.1359i		−	0.744934i	0.928045	−	0.372467i	$-0.121488\pi$
$884$	11.6190	+	11.1803i	0.390788	+	0.376036i
$885$		0			0
$886$	8.00000	−	13.8564i	0.268765	−	0.465515i
$887$	−19.7990	+	34.2929i	−0.664785	+	1.15144i	0.314559	+	0.949238i	$0.398144\pi$
$887$	−19.7990	+	34.2929i	−0.664785	+	1.15144i	−0.979344	+	0.202203i	$0.935190\pi$
$888$	−2.87298	+	3.96812i	−0.0964110	+	0.133161i
$889$	−10.0000			−0.335389
$890$	−7.07107	−	12.2474i	−0.237023	−	0.410535i
$891$	−30.7420	+	22.6479i	−1.02990	+	0.758733i
$892$			18.9737i			0.635285i
$893$	15.4919	−	8.94427i	0.518418	−	0.299309i
$894$	−5.07157	+	49.0334i	−0.169619	+	1.63992i
$895$	−30.1247	−	17.3925i	−1.00696	−	0.581368i
$896$			35.7771i			1.19523i
$897$	13.4919	−	11.4003i	0.450483	−	0.380646i
$898$		−	12.6491i		−	0.422106i
$899$	10.6066	−	18.3712i	0.353750	−	0.612713i
$900$		0			0
$901$	2.50000	+	4.33013i	0.0832871	+	0.144257i
$902$			67.0820i			2.23359i
$903$	−10.1575	+	14.0294i	−0.338021	+	0.466870i
$904$	16.4317	−	9.48683i	0.546509	−	0.315527i
$905$			46.9574i			1.56092i
$906$	−12.5483	−	9.08517i	−0.416889	−	0.301835i
$907$	−32.8634	−	18.9737i	−1.09121	−	0.630010i	−0.157311	−	0.987549i	$-0.550283\pi$
$907$	−32.8634	−	18.9737i	−1.09121	−	0.630010i	−0.933898	+	0.357539i	$0.883616\pi$
$908$	19.7990	−	34.2929i	0.657053	−	1.13805i
$909$	−15.0000	−	13.4164i	−0.497519	−	0.444994i
$910$	−35.0000	−	8.66025i	−1.16024	−	0.287085i
$911$	45.2548			1.49936			0.749680	−	0.661801i	$-0.230208\pi$
$911$	45.2548			1.49936			0.749680	+	0.661801i	$0.230208\pi$
$912$	4.50807	−	43.5853i	0.149277	−	1.44325i
$913$	21.0000	−	36.3731i	0.694999	−	1.20377i
$914$	−0.707107	−	1.22474i	−0.0233890	−	0.0405110i
$915$	−3.53553	+	1.58114i	−0.116881	+	0.0522708i
$916$	8.00000	+	13.8564i	0.264327	+	0.457829i
$917$	19.3649	−	11.1803i	0.639486	−	0.369207i
$918$	−5.00000	+	15.6525i	−0.165025	+	0.516609i
$919$	−46.5564	+	26.8794i	−1.53575	+	0.886668i	−0.536674	+	0.843790i	$0.680320\pi$
$919$	−46.5564	+	26.8794i	−1.53575	+	0.886668i	−0.999080	+	0.0428787i	$0.986347\pi$
$920$	15.4919	+	8.94427i	0.510754	+	0.294884i
$921$	3.38105	−	32.6890i	0.111409	−	1.07714i
$922$			15.8114i			0.520720i
$923$	−2.82843	−	9.79796i	−0.0930988	−	0.322504i
$924$	42.4264	−	18.9737i	1.39573	−	0.624188i
$925$		0			0
$926$	−27.1109	−	15.6525i	−0.890919	−	0.514372i
$927$	3.88338	−	18.5720i	0.127547	−	0.609985i
$928$		−	37.9473i		−	1.24568i
$929$	−1.93649	+	1.11803i	−0.0635342	+	0.0366815i	−0.531431	−	0.847102i	$-0.678345\pi$
$929$	−1.93649	+	1.11803i	−0.0635342	+	0.0366815i	0.467896	+	0.883783i	$0.345012\pi$
$930$	10.1575	−	14.0294i	0.333079	−	0.460043i
$931$			18.9737i			0.621837i
$932$	46.4758	−	26.8328i	1.52237	−	0.878938i
$933$	53.6028	+	5.54419i	1.75488	+	0.181509i
$934$	9.00000	−	15.5885i	0.294489	−	0.510070i
$935$	21.2132			0.693746
$936$	−27.5658	−	13.2714i	−0.901015	−	0.433788i
$937$	21.0000			0.686040			0.343020	−	0.939328i	$-0.388550\pi$
$937$	21.0000			0.686040			0.343020	+	0.939328i	$0.388550\pi$
$938$	−14.1421	+	24.4949i	−0.461757	+	0.799787i
$939$	−13.7829	−	1.42558i	−0.449787	−	0.0465219i
$940$	10.9545	−	6.32456i	0.357295	−	0.206284i
$941$		−	8.94427i		−	0.291575i	−0.989316	−	0.145787i	$-0.953428\pi$
$941$		−	8.94427i		−	0.291575i	0.989316	−	0.145787i	$-0.0465716\pi$
$942$	−15.8014	+	21.8247i	−0.514838	+	0.711086i
$943$	27.3861	−	15.8114i	0.891815	−	0.514890i
$944$		0			0
$945$	−7.81754	−	35.9011i	−0.254305	−	1.16786i
$946$	16.4317	+	9.48683i	0.534240	+	0.308444i
$947$	−6.36396	+	11.0227i	−0.206801	+	0.358190i	−0.950705	−	0.310097i	$-0.899639\pi$
$947$	−6.36396	+	11.0227i	−0.206801	+	0.358190i	0.743904	+	0.668286i	$0.232972\pi$
$948$	−40.0000	+	17.8885i	−1.29914	+	0.580993i
$949$	10.5000	+	2.59808i	0.340844	+	0.0843371i
$950$		0			0
$951$	−1.99230	+	19.2622i	−0.0646048	+	0.624618i
$952$	10.0000	−	17.3205i	0.324102	−	0.561361i
$953$	19.3649	−	11.1803i	0.627291	−	0.362167i	−0.152411	−	0.988317i	$-0.548704\pi$
$953$	19.3649	−	11.1803i	0.627291	−	0.362167i	0.779702	+	0.626150i	$0.215370\pi$
$954$	−7.07107	−	6.32456i	−0.228934	−	0.204765i
$955$	−35.6020	+	20.5548i	−1.15205	+	0.665138i
$956$	−15.5563	−	26.9444i	−0.503128	−	0.871444i
$957$	−45.0000	+	20.1246i	−1.45464	+	0.650536i
$958$	15.0000	+	25.9808i	0.484628	+	0.839400i
$959$	24.7487	−	42.8661i	0.799178	−	1.38422i
$960$	3.18768	−	30.8195i	0.102882	−	0.994694i
$961$	21.0000			0.677419
$962$	1.41421	+	4.89898i	0.0455961	+	0.157949i
$963$	−5.65685	+	6.32456i	−0.182290	+	0.203806i
$964$	−7.00000	+	12.1244i	−0.225455	+	0.390499i
$965$	−44.5393	−	25.7148i	−1.43377	−	0.827788i
$966$	−17.7460	−	12.8484i	−0.570967	−	0.413390i
$967$		−	44.2719i		−	1.42369i	−0.702338	−	0.711844i	$-0.747860\pi$
$967$		−	44.2719i		−	1.42369i	0.702338	−	0.711844i	$-0.252140\pi$
$968$	−9.89949	−	17.1464i	−0.318182	−	0.551107i
$969$	−14.3649	+	19.8406i	−0.461468	+	0.637372i
$970$			50.5964i			1.62455i
$971$	3.53553	+	6.12372i	0.113461	+	0.196520i	0.917163	−	0.398511i	$-0.130473\pi$
$971$	3.53553	+	6.12372i	0.113461	+	0.196520i	−0.803703	+	0.595031i	$0.797140\pi$
$972$	−0.258035	−	31.1758i	−0.00827648	−	0.999966i
$973$	−20.0000	+	34.6410i	−0.641171	+	1.11054i
$974$			31.3050i			1.00308i
$975$		0			0
$976$	4.00000			0.128037
$977$	1.93649	+	1.11803i	0.0619539	+	0.0357691i	0.530657	−	0.847587i	$-0.321945\pi$
$977$	1.93649	+	1.11803i	0.0619539	+	0.0357691i	−0.468703	+	0.883356i	$0.655279\pi$
$978$	−3.18768	+	30.8195i	−0.101931	+	0.985497i
$979$	16.4317	−	9.48683i	0.525159	−	0.303200i
$980$			13.4164i			0.428571i
$981$	35.2379	+	7.36820i	1.12506	+	0.235249i
$982$	23.0000	+	39.8372i	0.733959	+	1.27126i
$983$	1.41421			0.0451064			0.0225532	−	0.999746i	$-0.492820\pi$
$983$	1.41421			0.0451064			0.0225532	+	0.999746i	$0.492820\pi$
$984$	−44.3649	−	32.1209i	−1.41430	−	1.02398i
$985$	−10.0000	+	17.3205i	−0.318626	+	0.551877i
$986$	−10.6066	+	18.3712i	−0.337783	+	0.585057i
$987$	−14.1421	+	6.32456i	−0.450149	+	0.201313i
$988$	−32.8634	−	31.6228i	−1.04552	−	1.00605i
$989$		−	8.94427i		−	0.284411i
$990$	−38.2379	+	12.5644i	−1.21528	+	0.399321i
$991$	5.47723	+	3.16228i	0.173990	+	0.100453i	0.584466	−	0.811418i	$-0.301304\pi$
$991$	5.47723	+	3.16228i	0.173990	+	0.100453i	−0.410476	+	0.911871i	$0.634637\pi$
$992$	−15.4919	+	8.94427i	−0.491869	+	0.283981i
$993$	20.0000	−	8.94427i	0.634681	−	0.283838i
$994$	−10.9545	+	6.32456i	−0.347454	+	0.200603i
$995$	−7.07107	−	12.2474i	−0.224168	−	0.388270i
$996$	14.0000	+	31.3050i	0.443607	+	0.991935i
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	−0.997963	−	0.0637961i	$-0.979679\pi$
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	0.443732	−	0.896159i	$-0.353654\pi$
$998$	42.6028	+	24.5967i	1.34857	+	0.778596i
$999$	−3.84418	+	3.49604i	−0.121624	+	0.110610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.p.a.35.2	yes	8
3.2	odd	2	inner	156.2.p.a.35.4	yes	8
4.3	odd	2	inner	156.2.p.a.35.3	yes	8
12.11	even	2	inner	156.2.p.a.35.1	✓	8
13.3	even	3	inner	156.2.p.a.107.1	yes	8
39.29	odd	6	inner	156.2.p.a.107.3	yes	8
52.3	odd	6	inner	156.2.p.a.107.4	yes	8
156.107	even	6	inner	156.2.p.a.107.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.p.a.35.1	✓	8	12.11	even	2	inner
156.2.p.a.35.2	yes	8	1.1	even	1	trivial
156.2.p.a.35.3	yes	8	4.3	odd	2	inner
156.2.p.a.35.4	yes	8	3.2	odd	2	inner
156.2.p.a.107.1	yes	8	13.3	even	3	inner
156.2.p.a.107.2	yes	8	156.107	even	6	inner
156.2.p.a.107.3	yes	8	39.29	odd	6	inner
156.2.p.a.107.4	yes	8	52.3	odd	6	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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.72286 + 0.178197i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.23607i q^{5} +(-1.43649 + 1.98406i) q^{6} +(2.73861 - 1.58114i) q^{7} +2.82843 q^{8} +(2.93649 + 0.614017i) q^{9} +(2.73861 + 1.58114i) q^{10} +(-2.12132 + 3.67423i) q^{11} +(-1.41421 - 3.16228i) q^{12} +(-3.50000 - 0.866025i) q^{13} +4.47214i q^{14} +(0.398461 - 3.85243i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.93649 - 1.11803i) q^{17} +(-2.82843 + 3.16228i) q^{18} +(-5.47723 + 3.16228i) q^{19} +(-3.87298 + 2.23607i) q^{20} +(5.00000 - 2.23607i) q^{21} +(-3.00000 - 5.19615i) q^{22} +(-1.41421 + 2.44949i) q^{23} +(4.87298 + 0.504017i) q^{24} +(3.53553 - 3.67423i) q^{26} +(4.94975 + 1.58114i) q^{27} +(-5.47723 - 3.16228i) q^{28} +(5.80948 + 3.35410i) q^{29} +(4.43649 + 3.21209i) q^{30} -3.16228i q^{31} +(-2.82843 - 4.89898i) q^{32} +(-4.30948 + 5.95218i) q^{33} +3.16228i q^{34} +(-3.53553 - 6.12372i) q^{35} +(-1.87298 - 5.70017i) q^{36} +(-0.500000 + 0.866025i) q^{37} -8.94427i q^{38} +(-5.87569 - 2.11573i) q^{39} -6.32456i q^{40} +(-9.68246 - 5.59017i) q^{41} +(-0.796921 + 7.70486i) q^{42} +(-2.73861 + 1.58114i) q^{43} +8.48528 q^{44} +(1.37298 - 6.56619i) q^{45} +(-2.00000 - 3.46410i) q^{46} -2.82843 q^{47} +(-4.06301 + 5.61177i) q^{48} +(1.50000 - 2.59808i) q^{49} +(3.53553 - 1.58114i) q^{51} +(2.00000 + 6.92820i) q^{52} +2.23607i q^{53} +(-5.43649 + 4.94414i) q^{54} +(8.21584 + 4.74342i) q^{55} +(7.74597 - 4.47214i) q^{56} +(-10.0000 + 4.47214i) q^{57} +(-8.21584 + 4.74342i) q^{58} +(-7.07107 + 3.16228i) q^{60} +(-0.500000 - 0.866025i) q^{61} +(3.87298 + 2.23607i) q^{62} +(9.01276 - 2.96145i) q^{63} +8.00000 q^{64} +(-1.93649 + 7.82624i) q^{65} +(-4.24264 - 9.48683i) q^{66} +(5.47723 + 3.16228i) q^{67} +(-3.87298 - 2.23607i) q^{68} +(-2.87298 + 3.96812i) q^{69} +10.0000 q^{70} +(1.41421 + 2.44949i) q^{71} +(8.30565 + 1.73670i) q^{72} -3.00000 q^{73} +(-0.707107 - 1.22474i) q^{74} +(10.9545 + 6.32456i) q^{76} +13.4164i q^{77} +(6.74597 - 5.70017i) q^{78} -12.6491i q^{79} +(7.74597 + 4.47214i) q^{80} +(8.24597 + 3.60611i) q^{81} +(13.6931 - 7.90569i) q^{82} -9.89949 q^{83} +(-8.87298 - 6.42419i) q^{84} +(-2.50000 - 4.33013i) q^{85} -4.47214i q^{86} +(9.41122 + 6.81388i) q^{87} +(-6.00000 + 10.3923i) q^{88} +(-3.87298 - 2.23607i) q^{89} +(7.07107 + 6.32456i) q^{90} +(-10.9545 + 3.16228i) q^{91} +5.65685 q^{92} +(0.563508 - 5.44816i) q^{93} +(2.00000 - 3.46410i) q^{94} +(7.07107 + 12.2474i) q^{95} +(-4.00000 - 8.94427i) q^{96} +(8.00000 + 13.8564i) q^{97} +(2.12132 + 3.67423i) q^{98} +(-8.48528 + 9.48683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{6} + 8 q^{9} - 28 q^{13} - 16 q^{16} + 40 q^{21} - 24 q^{22} + 8 q^{24} + 20 q^{30} + 12 q^{33} + 16 q^{36} - 4 q^{37} - 20 q^{45} - 16 q^{46} + 12 q^{49} + 16 q^{52} - 28 q^{54} - 80 q^{57}+ \cdots + 64 q^{97}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^6 + 8 * q^9 - 28 * q^13 - 16 * q^16 + 40 * q^21 - 24 * q^22 + 8 * q^24 + 20 * q^30 + 12 * q^33 + 16 * q^36 - 4 * q^37 - 20 * q^45 - 16 * q^46 + 12 * q^49 + 16 * q^52 - 28 * q^54 - 80 * q^57 - 4 * q^61 + 64 * q^64 + 8 * q^69 + 80 * q^70 - 24 * q^73 - 8 * q^78 + 4 * q^81 - 40 * q^84 - 20 * q^85 - 48 * q^88 + 20 * q^93 + 16 * q^94 - 32 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

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Database

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