LMFDB - Embedded newform 1470.2.n.j.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(79,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1470.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.n (of order $6$, degree $2$, not 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.7652750400000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} - 14 x^{9} + 21 x^{8} - 108 x^{7} + 368 x^{6} - 216 x^{5} + 84 x^{4} + \cdots + 64 $ x^12 - 6x^11 + 18x^10 - 14x^9 + 21x^8 - 108x^7 + 368x^6 - 216x^5 + 84x^4 - 112x^3 + 288x^2 - 192*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.4
Root			$1.68566 + 1.68566i$ of defining polynomial
Character	$\chi$	$=$	1470.79
Dual form			1470.2.n.j.949.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.20942 + 0.344208i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.20942 + 0.344208i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.08551 - 0.806615i) q^{10} +(-0.838505 - 1.45233i) q^{11} +(-0.866025 - 0.500000i) q^{12} -4.48261i q^{13} +(1.74131 - 1.40280i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.59150 - 3.80560i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.24131 + 3.88206i) q^{19} +(-1.40280 - 1.74131i) q^{20} -1.67701i q^{22} +(0.417955 + 0.241306i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.76304 - 1.52100i) q^{25} +(2.24131 - 3.88206i) q^{26} +1.00000i q^{27} -1.19440 q^{29} +(2.20942 - 0.344208i) q^{30} +(-1.74131 - 3.01603i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.45233 + 0.838505i) q^{33} +7.61121 q^{34} +1.00000 q^{36} +(-0.417955 - 0.241306i) q^{37} +(-3.88206 + 2.24131i) q^{38} +(2.24131 + 3.88206i) q^{39} +(-0.344208 - 2.20942i) q^{40} +12.0938 q^{41} -2.00000i q^{43} +(0.838505 - 1.45233i) q^{44} +(-0.806615 + 2.08551i) q^{45} +(0.241306 + 0.417955i) q^{46} +(9.91412 + 5.72392i) q^{47} -1.00000i q^{48} +(4.88541 + 1.06430i) q^{50} +(-3.80560 + 6.59150i) q^{51} +(3.88206 - 2.24131i) q^{52} +(8.29343 - 4.78822i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.35251 + 2.92019i) q^{55} -4.48261i q^{57} +(-1.03438 - 0.597199i) q^{58} +(-2.88541 - 4.99768i) q^{59} +(2.08551 + 0.806615i) q^{60} +(-5.28822 + 9.15946i) q^{61} -3.48261i q^{62} -1.00000 q^{64} +(1.54295 + 9.90396i) q^{65} +(0.838505 + 1.45233i) q^{66} +(2.90467 - 1.67701i) q^{67} +(6.59150 + 3.80560i) q^{68} -0.482613 q^{69} +6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(-0.241306 - 0.417955i) q^{74} +(-3.36441 + 3.69874i) q^{75} -4.48261 q^{76} +4.48261i q^{78} +(2.25869 - 3.91217i) q^{79} +(0.806615 - 2.08551i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(10.4736 + 6.04691i) q^{82} -1.87141i q^{83} +(-13.2534 + 10.6770i) q^{85} +(1.00000 - 1.73205i) q^{86} +(1.03438 - 0.597199i) q^{87} +(1.45233 - 0.838505i) q^{88} +(1.67701 - 2.90467i) q^{89} +(-1.74131 + 1.40280i) q^{90} +0.482613i q^{92} +(3.01603 + 1.74131i) q^{93} +(5.72392 + 9.91412i) q^{94} +(3.61574 - 9.34856i) q^{95} +(0.500000 - 0.866025i) q^{96} -17.7708i q^{97} -1.67701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 12 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 - 12 * q^6 + 6 * q^9	$ 12 q + 6 q^{4} - 12 q^{6} + 6 q^{9} - 6 q^{11} - 6 q^{16} - 6 q^{19} - 6 q^{24} + 6 q^{26} - 48 q^{29} + 24 q^{34} + 12 q^{36} + 6 q^{39} + 36 q^{41} + 6 q^{44} - 18 q^{46} - 12 q^{51} - 6 q^{54} - 60 q^{55} + 24 q^{59} + 12 q^{61} - 12 q^{64} - 30 q^{65} + 6 q^{66} + 36 q^{69} + 72 q^{71} + 18 q^{74} - 12 q^{76} + 48 q^{79} - 6 q^{81} + 12 q^{86} + 12 q^{89} + 6 q^{94} + 6 q^{96} - 12 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 - 12 * q^6 + 6 * q^9 - 6 * q^11 - 6 * q^16 - 6 * q^19 - 6 * q^24 + 6 * q^26 - 48 * q^29 + 24 * q^34 + 12 * q^36 + 6 * q^39 + 36 * q^41 + 6 * q^44 - 18 * q^46 - 12 * q^51 - 6 * q^54 - 60 * q^55 + 24 * q^59 + 12 * q^61 - 12 * q^64 - 30 * q^65 + 6 * q^66 + 36 * q^69 + 72 * q^71 + 18 * q^74 - 12 * q^76 + 48 * q^79 - 6 * q^81 + 12 * q^86 + 12 * q^89 + 6 * q^94 + 6 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.20942	+	0.344208i	−0.988081	+	0.153935i
$5$	−2.20942	+	0.344208i	−0.988081	+	0.153935i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.08551	−	0.806615i	−0.659498	−	0.255074i
$11$	−0.838505	−	1.45233i	−0.252819	−	0.437895i	0.711482	−	0.702704i	$-0.248024\pi$
$11$	−0.838505	−	1.45233i	−0.252819	−	0.437895i	−0.964301	+	0.264809i	$0.914691\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$		−	4.48261i		−	1.24325i	−0.783314	−	0.621627i	$-0.786472\pi$
$13$		−	4.48261i		−	1.24325i	0.783314	−	0.621627i	$-0.213528\pi$
$14$		0			0
$15$	1.74131	−	1.40280i	0.449603	−	0.362202i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.59150	−	3.80560i	1.59867	−	0.922994i	0.606930	−	0.794756i	$-0.292401\pi$
$17$	6.59150	−	3.80560i	1.59867	−	0.922994i	0.991743	−	0.128239i	$-0.0409324\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−2.24131	+	3.88206i	−0.514191	+	0.890605i	0.485673	+	0.874140i	$0.338574\pi$
$19$	−2.24131	+	3.88206i	−0.514191	+	0.890605i	−0.999864	+	0.0164646i	$0.994759\pi$
$20$	−1.40280	−	1.74131i	−0.313676	−	0.389368i
$21$		0			0
$22$		−	1.67701i		−	0.357540i
$23$	0.417955	+	0.241306i	0.0871497	+	0.0503159i	0.542942	−	0.839771i	$-0.317311\pi$
$23$	0.417955	+	0.241306i	0.0871497	+	0.0503159i	−0.455792	+	0.890086i	$0.650644\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.76304	−	1.52100i	0.952608	−	0.304200i
$26$	2.24131	−	3.88206i	0.439556	−	0.761334i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−1.19440			−0.221794			−0.110897	−	0.993832i	$-0.535372\pi$
$29$	−1.19440			−0.221794			−0.110897	+	0.993832i	$0.535372\pi$
$30$	2.20942	−	0.344208i	0.403382	−	0.0628436i
$31$	−1.74131	−	3.01603i	−0.312748	−	0.541695i	0.666208	−	0.745766i	$-0.267916\pi$
$31$	−1.74131	−	3.01603i	−0.312748	−	0.541695i	−0.978956	+	0.204070i	$0.934583\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.45233	+	0.838505i	0.252819	+	0.145965i
$34$	7.61121			1.30531
$35$		0			0
$36$	1.00000			0.166667
$37$	−0.417955	−	0.241306i	−0.0687114	−	0.0396705i	0.465251	−	0.885179i	$-0.345964\pi$
$37$	−0.417955	−	0.241306i	−0.0687114	−	0.0396705i	−0.533962	+	0.845508i	$0.679298\pi$
$38$	−3.88206	+	2.24131i	−0.629753	+	0.363588i
$39$	2.24131	+	3.88206i	0.358896	+	0.621627i
$40$	−0.344208	−	2.20942i	−0.0544241	−	0.349339i
$41$	12.0938			1.88874			0.944369	−	0.328889i	$-0.106674\pi$
$41$	12.0938			1.88874			0.944369	+	0.328889i	$0.106674\pi$
$42$		0			0
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	0.838505	−	1.45233i	0.126409	−	0.218947i
$45$	−0.806615	+	2.08551i	−0.120243	+	0.310890i
$46$	0.241306	+	0.417955i	0.0355787	+	0.0616241i
$47$	9.91412	+	5.72392i	1.44612	+	0.834919i	0.998248	−	0.0591765i	$-0.0188475\pi$
$47$	9.91412	+	5.72392i	1.44612	+	0.834919i	0.447875	+	0.894096i	$0.352181\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	4.88541	+	1.06430i	0.690902	+	0.150514i
$51$	−3.80560	+	6.59150i	−0.532891	+	0.922994i
$52$	3.88206	−	2.24131i	0.538344	−	0.310813i
$53$	8.29343	−	4.78822i	1.13919	−	0.657712i	0.192961	−	0.981207i	$-0.438191\pi$
$53$	8.29343	−	4.78822i	1.13919	−	0.657712i	0.946230	+	0.323494i	$0.104858\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	2.35251	+	2.92019i	0.317213	+	0.393758i
$56$		0			0
$57$		−	4.48261i		−	0.593737i
$58$	−1.03438	−	0.597199i	−0.135821	−	0.0784160i
$59$	−2.88541	−	4.99768i	−0.375649	−	0.650643i	0.614775	−	0.788703i	$-0.289247\pi$
$59$	−2.88541	−	4.99768i	−0.375649	−	0.650643i	−0.990424	+	0.138059i	$0.955913\pi$
$60$	2.08551	+	0.806615i	0.269239	+	0.104134i
$61$	−5.28822	+	9.15946i	−0.677087	+	1.17275i	0.298768	+	0.954326i	$0.403424\pi$
$61$	−5.28822	+	9.15946i	−0.677087	+	1.17275i	−0.975854	+	0.218423i	$0.929909\pi$
$62$		−	3.48261i		−	0.442292i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.54295	+	9.90396i	0.191380	+	1.22843i
$66$	0.838505	+	1.45233i	0.103213	+	0.178770i
$67$	2.90467	−	1.67701i	0.354862	−	0.204879i	−0.311963	−	0.950094i	$-0.600986\pi$
$67$	2.90467	−	1.67701i	0.354862	−	0.204879i	0.666824	+	0.745215i	$0.267653\pi$
$68$	6.59150	+	3.80560i	0.799336	+	0.461497i
$69$	−0.482613			−0.0580998
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−3.46410	+	2.00000i	−0.405442	+	0.234082i	−0.688830	−	0.724923i	$-0.741875\pi$
$73$	−3.46410	+	2.00000i	−0.405442	+	0.234082i	0.283387	+	0.959006i	$0.408542\pi$
$74$	−0.241306	−	0.417955i	−0.0280513	−	0.0485863i
$75$	−3.36441	+	3.69874i	−0.388489	+	0.427094i
$76$	−4.48261			−0.514191
$77$		0			0
$78$			4.48261i			0.507556i
$79$	2.25869	−	3.91217i	0.254123	−	0.440154i	−0.710534	−	0.703663i	$-0.751547\pi$
$79$	2.25869	−	3.91217i	0.254123	−	0.440154i	0.964657	+	0.263509i	$0.0848799\pi$
$80$	0.806615	−	2.08551i	0.0901823	−	0.233168i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	10.4736	+	6.04691i	1.15661	+	0.667769i
$83$		−	1.87141i		−	0.205414i	−0.994712	−	0.102707i	$-0.967250\pi$
$83$		−	1.87141i		−	0.205414i	0.994712	−	0.102707i	$-0.0327503\pi$
$84$		0			0
$85$	−13.2534	+	10.6770i	−1.43754	+	1.15808i
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	1.03438	−	0.597199i	0.110897	−	0.0640264i
$88$	1.45233	−	0.838505i	0.154819	−	0.0893849i
$89$	1.67701	−	2.90467i	0.177763	−	0.307894i	−0.763351	−	0.645984i	$-0.776447\pi$
$89$	1.67701	−	2.90467i	0.177763	−	0.307894i	0.941114	+	0.338090i	$0.109781\pi$
$90$	−1.74131	+	1.40280i	−0.183550	+	0.147868i
$91$		0			0
$92$			0.482613i			0.0503159i
$93$	3.01603	+	1.74131i	0.312748	+	0.180565i
$94$	5.72392	+	9.91412i	0.590377	+	1.02256i
$95$	3.61574	−	9.34856i	0.370967	−	0.959142i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	17.7708i		−	1.80435i	−0.431366	−	0.902177i	$-0.641968\pi$
$97$		−	17.7708i		−	1.80435i	0.431366	−	0.902177i	$-0.358032\pi$
$98$		0			0
$99$	−1.67701			−0.168546
$100$	3.69874	+	3.36441i	0.369874	+	0.336441i
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	0.595466	−	0.803380i	$-0.296967\pi$
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	−0.993481	+	0.113998i	$0.963634\pi$
$102$	−6.59150	+	3.80560i	−0.652656	+	0.376811i
$103$	−11.7876	−	6.80560i	−1.16147	−	0.670576i	−0.209815	−	0.977741i	$-0.567286\pi$
$103$	−11.7876	−	6.80560i	−1.16147	−	0.670576i	−0.951656	+	0.307165i	$0.900620\pi$
$104$	4.48261			0.439556
$105$		0			0
$106$	9.57643			0.930145
$107$	3.35274	+	1.93570i	0.324121	+	0.187132i	0.653228	−	0.757161i	$-0.273414\pi$
$107$	3.35274	+	1.93570i	0.324121	+	0.187132i	−0.329107	+	0.944293i	$0.606748\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	8.61121	+	14.9150i	0.824804	+	1.42860i	0.902069	+	0.431592i	$0.142048\pi$
$109$	8.61121	+	14.9150i	0.824804	+	1.42860i	−0.0772652	+	0.997011i	$0.524619\pi$
$110$	0.577241	+	3.70521i	0.0550378	+	0.353278i
$111$	0.482613			0.0458076
$112$		0			0
$113$		−	8.96523i		−	0.843378i	−0.906741	−	0.421689i	$-0.861437\pi$
$113$		−	8.96523i		−	0.843378i	0.906741	−	0.421689i	$-0.138563\pi$
$114$	2.24131	−	3.88206i	0.209918	−	0.363588i
$115$	−1.00650	−	0.389283i	−0.0938563	−	0.0363008i
$116$	−0.597199	−	1.03438i	−0.0554485	−	0.0960396i
$117$	−3.88206	−	2.24131i	−0.358896	−	0.207209i
$118$		−	5.77083i		−	0.531248i
$119$		0			0
$120$	1.40280	+	1.74131i	0.128058	+	0.158959i
$121$	4.09382	−	7.09070i	0.372165	−	0.644609i
$122$	−9.15946	+	5.28822i	−0.829258	+	0.478773i
$123$	−10.4736	+	6.04691i	−0.944369	+	0.545231i
$124$	1.74131	−	3.01603i	0.156374	−	0.270848i
$125$	−10.0000	+	5.00000i	−0.894427	+	0.447214i
$126$		0			0
$127$		−	13.9342i		−	1.23646i	−0.785997	−	0.618230i	$-0.787850\pi$
$127$		−	13.9342i		−	1.23646i	0.785997	−	0.618230i	$-0.212150\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$	−3.61574	+	9.34856i	−0.317122	+	0.819923i
$131$	1.64411	−	2.84768i	0.143646	−	0.248803i	−0.785221	−	0.619216i	$-0.787451\pi$
$131$	1.64411	−	2.84768i	0.143646	−	0.248803i	0.928867	+	0.370413i	$0.120784\pi$
$132$			1.67701i			0.145965i
$133$		0			0
$134$	3.35402			0.289743
$135$	−0.344208	−	2.20942i	−0.0296247	−	0.190156i
$136$	3.80560	+	6.59150i	0.326328	+	0.565216i
$137$	3.68683	−	2.12859i	0.314987	−	0.181858i	−0.334169	−	0.942513i	$-0.608456\pi$
$137$	3.68683	−	2.12859i	0.314987	−	0.181858i	0.649156	+	0.760655i	$0.275122\pi$
$138$	−0.417955	−	0.241306i	−0.0355787	−	0.0205414i
$139$	18.9652			1.60861			0.804305	−	0.594217i	$-0.202538\pi$
$139$	18.9652			1.60861			0.804305	+	0.594217i	$0.202538\pi$
$140$		0			0
$141$	−11.4478			−0.964082
$142$	5.19615	+	3.00000i	0.436051	+	0.251754i
$143$	−6.51025	+	3.75869i	−0.544414	+	0.314318i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	2.63892	−	0.411122i	0.219150	−	0.0341418i
$146$	−4.00000			−0.331042
$147$		0			0
$148$		−	0.482613i		−	0.0396705i
$149$	3.51739	−	6.09229i	0.288156	−	0.499100i	−0.685214	−	0.728342i	$-0.740291\pi$
$149$	3.51739	−	6.09229i	0.288156	−	0.499100i	0.973370	+	0.229242i	$0.0736246\pi$
$150$	−4.76304	+	1.52100i	−0.388901	+	0.124189i
$151$	3.22392	+	5.58399i	0.262359	+	0.454419i	0.966868	−	0.255276i	$-0.0821663\pi$
$151$	3.22392	+	5.58399i	0.262359	+	0.454419i	−0.704509	+	0.709695i	$0.748833\pi$
$152$	−3.88206	−	2.24131i	−0.314876	−	0.181794i
$153$		−	7.61121i		−	0.615330i
$154$		0			0
$155$	4.88541	+	6.06430i	0.392406	+	0.487096i
$156$	−2.24131	+	3.88206i	−0.179448	+	0.310813i
$157$	−0.0812493	+	0.0469093i	−0.00648440	+	0.00374377i	−0.503239	−	0.864147i	$-0.667858\pi$
$157$	−0.0812493	+	0.0469093i	−0.00648440	+	0.00374377i	0.496754	+	0.867891i	$0.334525\pi$
$158$	3.91217	−	2.25869i	0.311236	−	0.179692i
$159$	−4.78822	+	8.29343i	−0.379730	+	0.657712i
$160$	1.74131	−	1.40280i	0.137662	−	0.110901i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−17.8197	−	10.2882i	−1.39575	−	0.805835i	−0.401804	−	0.915726i	$-0.631617\pi$
$163$	−17.8197	−	10.2882i	−1.39575	−	0.805835i	−0.993944	+	0.109890i	$0.964950\pi$
$164$	6.04691	+	10.4736i	0.472184	+	0.817847i
$165$	−3.49743	−	1.35270i	−0.272275	−	0.105308i
$166$	0.935704	−	1.62069i	0.0726247	−	0.125790i
$167$			14.0938i			1.09061i	0.838237	+	0.545306i	$0.183587\pi$
$167$			14.0938i			1.09061i	−0.838237	+	0.545306i	$0.816413\pi$
$168$		0			0
$169$	−7.09382			−0.545678
$170$	−16.8163	+	2.61984i	−1.28975	+	0.200933i
$171$	2.24131	+	3.88206i	0.171397	+	0.296868i
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	0.977390	+	0.564296i	0.0743096	+	0.0429027i	0.536694	−	0.843777i	$-0.319673\pi$
$173$	0.977390	+	0.564296i	0.0743096	+	0.0429027i	−0.462385	+	0.886679i	$0.653006\pi$
$174$	1.19440			0.0905470
$175$		0			0
$176$	1.67701			0.126409
$177$	4.99768	+	2.88541i	0.375649	+	0.216881i
$178$	2.90467	−	1.67701i	0.217714	−	0.125697i
$179$	−1.72392	−	2.98592i	−0.128852	−	0.223178i	0.794380	−	0.607421i	$-0.207796\pi$
$179$	−1.72392	−	2.98592i	−0.128852	−	0.223178i	−0.923232	+	0.384243i	$0.874462\pi$
$180$	−2.20942	+	0.344208i	−0.164680	+	0.0256558i
$181$	−22.8957			−1.70182			−0.850911	−	0.525310i	$-0.823950\pi$
$181$	−22.8957			−1.70182			−0.850911	+	0.525310i	$0.823950\pi$
$182$		0			0
$183$		−	10.5764i		−	0.781832i
$184$	−0.241306	+	0.417955i	−0.0177893	+	0.0308121i
$185$	1.00650	+	0.389283i	0.0739991	+	0.0286206i
$186$	1.74131	+	3.01603i	0.127679	+	0.221146i
$187$	−11.0540	−	6.38203i	−0.808349	−	0.466701i
$188$			11.4478i			0.834919i
$189$		0			0
$190$	7.80560	−	6.28822i	0.566278	−	0.456195i
$191$	−12.5764	+	21.7830i	−0.909999	+	1.57616i	−0.0959355	+	0.995388i	$0.530584\pi$
$191$	−12.5764	+	21.7830i	−0.909999	+	1.57616i	−0.814063	+	0.580776i	$0.802749\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−11.0900	+	6.40280i	−0.798274	+	0.460884i	−0.842867	−	0.538121i	$-0.819134\pi$
$193$	−11.0900	+	6.40280i	−0.798274	+	0.460884i	0.0445932	+	0.999005i	$0.485801\pi$
$194$	8.88541	−	15.3900i	0.637936	−	1.10494i
$195$	−6.28822	−	7.80560i	−0.450308	−	0.558971i
$196$		0			0
$197$		−	2.87141i		−	0.204579i	−0.994755	−	0.102290i	$-0.967383\pi$
$197$		−	2.87141i		−	0.204579i	0.994755	−	0.102290i	$-0.0326169\pi$
$198$	−1.45233	−	0.838505i	−0.103213	−	0.0595900i
$199$	1.51739	+	2.62819i	0.107565	+	0.186308i	0.914783	−	0.403945i	$-0.132361\pi$
$199$	1.51739	+	2.62819i	0.107565	+	0.186308i	−0.807218	+	0.590253i	$0.799028\pi$
$200$	1.52100	+	4.76304i	0.107551	+	0.336798i
$201$	−1.67701	+	2.90467i	−0.118287	+	0.204879i
$202$		−	8.00000i		−	0.562878i
$203$		0			0
$204$	−7.61121			−0.532891
$205$	−26.7203	+	4.16279i	−1.86623	+	0.290742i
$206$	−6.80560	−	11.7876i	−0.474169	−	0.821284i
$207$	0.417955	−	0.241306i	0.0290499	−	0.0167720i
$208$	3.88206	+	2.24131i	0.269172	+	0.155407i
$209$	7.51739			0.519989
$210$		0			0
$211$	−10.4826			−0.721653			−0.360826	−	0.932633i	$-0.617505\pi$
$211$	−10.4826			−0.721653			−0.360826	+	0.932633i	$0.617505\pi$
$212$	8.29343	+	4.78822i	0.569595	+	0.328856i
$213$	−5.19615	+	3.00000i	−0.356034	+	0.205557i
$214$	1.93570	+	3.35274i	0.132322	+	0.229188i
$215$	0.688417	+	4.41883i	0.0469496	+	0.301362i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$			17.2224i			1.16645i
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	−1.35270	+	3.49743i	−0.0911991	+	0.235797i
$221$	−17.0590	−	29.5471i	−1.14752	−	1.98756i
$222$	0.417955	+	0.241306i	0.0280513	+	0.0161954i
$223$			15.1248i			1.01283i	0.862288	+	0.506417i	$0.169030\pi$
$223$			15.1248i			1.01283i	−0.862288	+	0.506417i	$0.830970\pi$
$224$		0			0
$225$	1.06430	−	4.88541i	0.0709531	−	0.325694i
$226$	4.48261	−	7.76411i	0.298179	−	0.516461i
$227$	18.2678	−	10.5469i	1.21248	−	0.700023i	0.249177	−	0.968458i	$-0.419840\pi$
$227$	18.2678	−	10.5469i	1.21248	−	0.700023i	0.963298	+	0.268435i	$0.0865064\pi$
$228$	3.88206	−	2.24131i	0.257095	−	0.148434i
$229$	11.6112	−	20.1112i	0.767290	−	1.32899i	−0.171737	−	0.985143i	$-0.554938\pi$
$229$	11.6112	−	20.1112i	0.767290	−	1.32899i	0.939027	−	0.343843i	$-0.111729\pi$
$230$	−0.677010	−	0.840377i	−0.0446407	−	0.0554128i
$231$		0			0
$232$		−	1.19440i		−	0.0784160i
$233$	−7.42741	−	4.28822i	−0.486586	−	0.280930i	0.236571	−	0.971614i	$-0.423976\pi$
$233$	−7.42741	−	4.28822i	−0.486586	−	0.280930i	−0.723157	+	0.690684i	$0.757310\pi$
$234$	−2.24131	−	3.88206i	−0.146519	−	0.253778i
$235$	−23.8746	−	9.23400i	−1.55741	−	0.602360i
$236$	2.88541	−	4.99768i	0.187824	−	0.325322i
$237$			4.51739i			0.293436i
$238$		0			0
$239$	4.57643			0.296025			0.148012	−	0.988986i	$-0.452712\pi$
$239$	4.57643			0.296025			0.148012	+	0.988986i	$0.452712\pi$
$240$	0.344208	+	2.20942i	0.0222186	+	0.142617i
$241$	4.98261	+	8.63014i	0.320958	+	0.555916i	0.980686	−	0.195589i	$-0.0626617\pi$
$241$	4.98261	+	8.63014i	0.320958	+	0.555916i	−0.659728	+	0.751505i	$0.729328\pi$
$242$	7.09070	−	4.09382i	0.455808	−	0.263161i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−10.5764			−0.677087
$245$		0			0
$246$	−12.0938			−0.771074
$247$	17.4018	+	10.0469i	1.10725	+	0.639270i
$248$	3.01603	−	1.74131i	0.191518	−	0.110573i
$249$	0.935704	+	1.62069i	0.0592978	+	0.102707i
$250$	−11.1603	−	0.669873i	−0.705836	−	0.0423665i
$251$	4.38505			0.276782			0.138391	−	0.990378i	$-0.455807\pi$
$251$	4.38505			0.276782			0.138391	+	0.990378i	$0.455807\pi$
$252$		0			0
$253$		−	0.809347i		−	0.0508832i
$254$	6.96710	−	12.0674i	0.437155	−	0.757174i
$255$	6.13931	−	15.8733i	0.384459	−	0.994024i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.07728	−	2.35402i	−0.254334	−	0.146840i	0.367413	−	0.930058i	$-0.380243\pi$
$257$	−4.07728	−	2.35402i	−0.254334	−	0.146840i	−0.621747	+	0.783218i	$0.713577\pi$
$258$			2.00000i			0.124515i
$259$		0			0
$260$	−7.80560	+	6.28822i	−0.484083	+	0.389979i
$261$	−0.597199	+	1.03438i	−0.0369657	+	0.0640264i
$262$	2.84768	−	1.64411i	0.175930	−	0.101573i
$263$	−14.1329	+	8.15962i	−0.871471	+	0.503144i	−0.867837	−	0.496849i	$-0.834490\pi$
$263$	−14.1329	+	8.15962i	−0.871471	+	0.503144i	−0.00363409	+	0.999993i	$0.501157\pi$
$264$	−0.838505	+	1.45233i	−0.0516064	+	0.0893849i
$265$	−16.6755	+	13.4338i	−1.02437	+	0.825234i
$266$		0			0
$267$			3.35402i			0.205263i
$268$	2.90467	+	1.67701i	0.177431	+	0.102440i
$269$	9.88541	+	17.1220i	0.602724	+	1.04395i	0.992407	+	0.123000i	$0.0392515\pi$
$269$	9.88541	+	17.1220i	0.602724	+	1.04395i	−0.389682	+	0.920949i	$0.627415\pi$
$270$	0.806615	−	2.08551i	0.0490890	−	0.126920i
$271$	−1.13010	+	1.95739i	−0.0686487	+	0.118903i	−0.898307	−	0.439369i	$-0.855202\pi$
$271$	−1.13010	+	1.95739i	−0.0686487	+	0.118903i	0.829658	+	0.558272i	$0.188535\pi$
$272$			7.61121i			0.461497i
$273$		0			0
$274$	4.25719			0.257186
$275$	−6.20283	−	5.64216i	−0.374045	−	0.340235i
$276$	−0.241306	−	0.417955i	−0.0145249	−	0.0251579i
$277$	15.8112	−	9.12859i	0.950002	−	0.548484i	0.0569205	−	0.998379i	$-0.481872\pi$
$277$	15.8112	−	9.12859i	0.950002	−	0.548484i	0.893082	+	0.449895i	$0.148539\pi$
$278$	16.4244	+	9.48261i	0.985068	+	0.568729i
$279$	−3.48261			−0.208499
$280$		0			0
$281$	10.4826			0.625340			0.312670	−	0.949862i	$-0.398777\pi$
$281$	10.4826			0.625340			0.312670	+	0.949862i	$0.398777\pi$
$282$	−9.91412	−	5.72392i	−0.590377	−	0.340854i
$283$	−0.613181	+	0.354020i	−0.0364498	+	0.0210443i	−0.518114	−	0.855311i	$-0.673366\pi$
$283$	−0.613181	+	0.354020i	−0.0364498	+	0.0210443i	0.481664	+	0.876356i	$0.340032\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	1.54295	+	9.90396i	0.0913967	+	0.586660i
$286$	−7.51739			−0.444512
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	20.4652	−	35.4468i	1.20384	−	2.08511i
$290$	2.49093	+	0.963419i	0.146273	+	0.0565739i
$291$	8.88541	+	15.3900i	0.520872	+	0.902177i
$292$	−3.46410	−	2.00000i	−0.202721	−	0.117041i
$293$		−	12.6112i		−	0.736755i	−0.929676	−	0.368377i	$-0.879913\pi$
$293$		−	12.6112i		−	0.736755i	0.929676	−	0.368377i	$-0.120087\pi$
$294$		0			0
$295$	8.09533	+	10.0488i	0.471328	+	0.585063i
$296$	0.241306	−	0.417955i	0.0140257	−	0.0242931i
$297$	1.45233	−	0.838505i	0.0842729	−	0.0486550i
$298$	6.09229	−	3.51739i	0.352917	−	0.203757i
$299$	1.08168	−	1.87353i	0.0625554	−	0.108349i
$300$	−4.88541	−	1.06430i	−0.282060	−	0.0614472i
$301$		0			0
$302$			6.44784i			0.371031i
$303$	6.92820	+	4.00000i	0.398015	+	0.229794i
$304$	−2.24131	−	3.88206i	−0.128548	−	0.222651i
$305$	8.53111	−	22.0573i	0.488490	−	1.26300i
$306$	3.80560	−	6.59150i	0.217552	−	0.376811i
$307$			9.54166i			0.544571i	0.962216	+	0.272286i	$0.0877795\pi$
$307$			9.54166i			0.544571i	−0.962216	+	0.272286i	$0.912220\pi$
$308$		0			0
$309$	13.6112			0.774314
$310$	1.19874	+	7.69454i	0.0680841	+	0.437021i
$311$	−10.4826	−	18.1564i	−0.594414	−	1.02956i	−0.993629	−	0.112699i	$-0.964051\pi$
$311$	−10.4826	−	18.1564i	−0.594414	−	1.02956i	0.399215	−	0.916857i	$-0.369283\pi$
$312$	−3.88206	+	2.24131i	−0.219778	+	0.126889i
$313$	−13.1587	−	7.59720i	−0.743776	−	0.429419i	0.0796649	−	0.996822i	$-0.474615\pi$
$313$	−13.1587	−	7.59720i	−0.743776	−	0.429419i	−0.823440	+	0.567403i	$0.807948\pi$
$314$	−0.0938186			−0.00529449
$315$		0			0
$316$	4.51739			0.254123
$317$	−15.9763	−	9.22392i	−0.897318	−	0.518067i	−0.0209891	−	0.999780i	$-0.506682\pi$
$317$	−15.9763	−	9.22392i	−0.897318	−	0.518067i	−0.876329	+	0.481713i	$0.840015\pi$
$318$	−8.29343	+	4.78822i	−0.465073	+	0.268510i
$319$	1.00151	+	1.73466i	0.0560737	+	0.0971225i
$320$	2.20942	−	0.344208i	0.123510	−	0.0192418i
$321$	−3.87141			−0.216081
$322$		0			0
$323$			34.1181i			1.89838i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−6.81805	−	21.3509i	−0.378197	−	1.18433i
$326$	−10.2882	−	17.8197i	−0.569812	−	0.986943i
$327$	−14.9150	−	8.61121i	−0.824804	−	0.476201i
$328$			12.0938i			0.667769i
$329$		0			0
$330$	−2.35251	−	2.92019i	−0.129502	−	0.160751i
$331$	−11.4009	+	19.7470i	−0.626652	+	1.08539i	0.361567	+	0.932346i	$0.382242\pi$
$331$	−11.4009	+	19.7470i	−0.626652	+	1.08539i	−0.988219	+	0.153047i	$0.951092\pi$
$332$	1.62069	−	0.935704i	0.0889467	−	0.0513534i
$333$	−0.417955	+	0.241306i	−0.0229038	+	0.0132235i
$334$	−7.04691	+	12.2056i	−0.385590	+	0.667861i
$335$	−5.84038	+	4.70502i	−0.319094	+	0.257063i
$336$		0			0
$337$			9.12485i			0.497062i	0.968624	+	0.248531i	$0.0799478\pi$
$337$			9.12485i			0.497062i	−0.968624	+	0.248531i	$0.920052\pi$
$338$	−6.14343	−	3.54691i	−0.334158	−	0.192926i
$339$	4.48261	+	7.76411i	0.243462	+	0.421689i
$340$	−15.8733	−	6.13931i	−0.860850	−	0.332951i
$341$	−2.92019	+	5.05791i	−0.158137	+	0.273901i
$342$			4.48261i			0.242392i
$343$		0			0
$344$	2.00000			0.107833
$345$	1.06629	−	0.166119i	0.0574073	−	0.00894357i
$346$	0.564296	+	0.977390i	0.0303368	+	0.0525448i
$347$	−16.6471	+	9.61121i	−0.893663	+	0.515957i	−0.875139	−	0.483872i	$-0.839230\pi$
$347$	−16.6471	+	9.61121i	−0.893663	+	0.515957i	−0.0185241	+	0.999828i	$0.505897\pi$
$348$	1.03438	+	0.597199i	0.0554485	+	0.0320132i
$349$	−6.18764			−0.331217			−0.165608	−	0.986192i	$-0.552959\pi$
$349$	−6.18764			−0.331217			−0.165608	+	0.986192i	$0.552959\pi$
$350$		0			0
$351$	4.48261			0.239264
$352$	1.45233	+	0.838505i	0.0774096	+	0.0446925i
$353$	9.71889	−	5.61121i	0.517284	−	0.298654i	−0.218538	−	0.975828i	$-0.570129\pi$
$353$	9.71889	−	5.61121i	0.517284	−	0.298654i	0.735823	+	0.677174i	$0.236796\pi$
$354$	2.88541	+	4.99768i	0.153358	+	0.265624i
$355$	−13.2565	+	2.06525i	−0.703582	+	0.109612i
$356$	3.35402			0.177763
$357$		0			0
$358$		−	3.44784i		−	0.182224i
$359$	4.80560	−	8.32355i	0.253630	−	0.439300i	−0.710892	−	0.703301i	$-0.751709\pi$
$359$	4.80560	−	8.32355i	0.253630	−	0.439300i	0.964523	+	0.264001i	$0.0850421\pi$
$360$	−2.08551	−	0.806615i	−0.109916	−	0.0425123i
$361$	−0.546909	−	0.947275i	−0.0287847	−	0.0498566i
$362$	−19.8282	−	11.4478i	−1.04215	−	0.601685i
$363$			8.18764i			0.429740i
$364$		0			0
$365$	6.96523	−	5.61121i	0.364577	−	0.293704i
$366$	5.28822	−	9.15946i	0.276419	−	0.478773i
$367$	−22.7361	+	13.1267i	−1.18682	+	0.685209i	−0.957582	−	0.288162i	$-0.906956\pi$
$367$	−22.7361	+	13.1267i	−1.18682	+	0.685209i	−0.229235	+	0.973371i	$0.573623\pi$
$368$	−0.417955	+	0.241306i	−0.0217874	+	0.0125790i
$369$	6.04691	−	10.4736i	0.314790	−	0.545231i
$370$	0.677010	+	0.840377i	0.0351961	+	0.0436891i
$371$		0			0
$372$			3.48261i			0.180565i
$373$	15.1378	+	8.73980i	0.783804	+	0.452530i	0.837777	−	0.546013i	$-0.183855\pi$
$373$	15.1378	+	8.73980i	0.783804	+	0.452530i	−0.0539726	+	0.998542i	$0.517188\pi$
$374$	−6.38203	−	11.0540i	−0.330007	−	0.571589i
$375$	6.16025	−	9.33013i	0.318114	−	0.481806i
$376$	−5.72392	+	9.91412i	−0.295189	+	0.511282i
$377$			5.35402i			0.275746i
$378$		0			0
$379$	−32.2815			−1.65819			−0.829094	−	0.559110i	$-0.811143\pi$
$379$	−32.2815			−1.65819			−0.829094	+	0.559110i	$0.811143\pi$
$380$	9.90396	−	1.54295i	0.508062	−	0.0791518i
$381$	6.96710	+	12.0674i	0.356935	+	0.618230i
$382$	−21.7830	+	12.5764i	−1.11452	+	0.643466i
$383$	−15.6697	−	9.04691i	−0.800685	−	0.462275i	0.0430259	−	0.999074i	$-0.486300\pi$
$383$	−15.6697	−	9.04691i	−0.800685	−	0.462275i	−0.843710	+	0.536798i	$0.819634\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−12.8056			−0.651788
$387$	−1.73205	−	1.00000i	−0.0880451	−	0.0508329i
$388$	15.3900	−	8.88541i	0.781308	−	0.451089i
$389$	−4.09382	−	7.09070i	−0.207565	−	0.359513i	0.743382	−	0.668867i	$-0.233220\pi$
$389$	−4.09382	−	7.09070i	−0.207565	−	0.359513i	−0.950947	+	0.309354i	$0.899887\pi$
$390$	−1.54295	−	9.90396i	−0.0781305	−	0.501506i
$391$	3.67327			0.185765
$392$		0			0
$393$			3.28822i			0.165869i
$394$	1.43570	−	2.48671i	0.0723297	−	0.125279i
$395$	−3.64379	+	9.42108i	−0.183339	+	0.474026i
$396$	−0.838505	−	1.45233i	−0.0421365	−	0.0729825i
$397$	31.3394	+	18.0938i	1.57288	+	0.908103i	0.995814	+	0.0914054i	$0.0291359\pi$
$397$	31.3394	+	18.0938i	1.57288	+	0.908103i	0.577066	+	0.816697i	$0.304197\pi$
$398$			3.03477i			0.152119i
$399$		0			0
$400$	−1.06430	+	4.88541i	−0.0532148	+	0.244271i
$401$	15.4947	−	26.8377i	0.773771	−	1.34021i	−0.161712	−	0.986838i	$-0.551702\pi$
$401$	15.4947	−	26.8377i	0.773771	−	1.34021i	0.935483	−	0.353372i	$-0.114965\pi$
$402$	−2.90467	+	1.67701i	−0.144872	+	0.0836417i
$403$	−13.5197	+	7.80560i	−0.673464	+	0.388825i
$404$	4.00000	−	6.92820i	0.199007	−	0.344691i
$405$	1.40280	+	1.74131i	0.0697058	+	0.0865262i
$406$		0			0
$407$			0.809347i			0.0401178i
$408$	−6.59150	−	3.80560i	−0.326328	−	0.188405i
$409$	−6.54691	−	11.3396i	−0.323724	−	0.560706i	0.657529	−	0.753429i	$-0.271602\pi$
$409$	−6.54691	−	11.3396i	−0.323724	−	0.560706i	−0.981253	+	0.192723i	$0.938268\pi$
$410$	−25.2218	−	9.75505i	−1.24562	−	0.481768i
$411$	−2.12859	+	3.68683i	−0.104996	+	0.181858i
$412$		−	13.6112i		−	0.670576i
$413$		0			0
$414$	0.482613			0.0237191
$415$	0.644154	+	4.13472i	0.0316203	+	0.202965i
$416$	2.24131	+	3.88206i	0.109889	+	0.190333i
$417$	−16.4244	+	9.48261i	−0.804305	+	0.464366i
$418$	6.51025	+	3.75869i	0.318427	+	0.183844i
$419$	33.3783			1.63064			0.815318	−	0.579013i	$-0.196562\pi$
$419$	33.3783			1.63064			0.815318	+	0.579013i	$0.196562\pi$
$420$		0			0
$421$	−6.90317			−0.336440			−0.168220	−	0.985750i	$-0.553802\pi$
$421$	−6.90317			−0.336440			−0.168220	+	0.985750i	$0.553802\pi$
$422$	−9.07821	−	5.24131i	−0.441920	−	0.255143i
$423$	9.91412	−	5.72392i	0.482041	−	0.278306i
$424$	4.78822	+	8.29343i	0.232536	+	0.402765i
$425$	25.6073	−	28.1519i	1.24213	−	1.36557i
$426$	−6.00000			−0.290701
$427$		0			0
$428$			3.87141i			0.187132i
$429$	3.75869	−	6.51025i	0.181471	−	0.314318i
$430$	−1.61323	+	4.17103i	−0.0777969	+	0.201145i
$431$	13.0590	+	22.6189i	0.629032	+	1.08952i	0.987746	+	0.156068i	$0.0498819\pi$
$431$	13.0590	+	22.6189i	0.629032	+	1.08952i	−0.358714	+	0.933447i	$0.616785\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			25.9305i			1.24614i	0.782167	+	0.623069i	$0.214114\pi$
$433$			25.9305i			1.24614i	−0.782167	+	0.623069i	$0.785886\pi$
$434$		0			0
$435$	−2.07981	+	1.67550i	−0.0997193	+	0.0803342i
$436$	−8.61121	+	14.9150i	−0.412402	+	0.714301i
$437$	−1.87353	+	1.08168i	−0.0896231	+	0.0517439i
$438$	3.46410	−	2.00000i	0.165521	−	0.0955637i
$439$	3.77608	−	6.54036i	0.180222	−	0.312155i	−0.761734	−	0.647890i	$-0.775652\pi$
$439$	3.77608	−	6.54036i	0.180222	−	0.312155i	0.941956	+	0.335736i	$0.108985\pi$
$440$	−2.92019	+	2.35251i	−0.139215	+	0.112152i
$441$		0			0
$442$		−	34.1181i		−	1.62283i
$443$	21.0585	+	12.1581i	1.00052	+	0.577649i	0.908402	−	0.418099i	$-0.137303\pi$
$443$	21.0585	+	12.1581i	1.00052	+	0.577649i	0.0921167	+	0.995748i	$0.470637\pi$
$444$	0.241306	+	0.417955i	0.0114519	+	0.0198353i
$445$	−2.70540	+	6.99486i	−0.128248	+	0.331588i
$446$	−7.56242	+	13.0985i	−0.358091	+	0.620232i
$447$			7.03477i			0.332733i
$448$		0			0
$449$	−14.7398			−0.695614			−0.347807	−	0.937566i	$-0.613074\pi$
$449$	−14.7398			−0.695614			−0.347807	+	0.937566i	$0.613074\pi$
$450$	3.36441	−	3.69874i	0.158600	−	0.174360i
$451$	−10.1407	−	17.5643i	−0.477508	−	0.827069i
$452$	7.76411	−	4.48261i	0.365193	−	0.210844i
$453$	−5.58399	−	3.22392i	−0.262359	−	0.151473i
$454$	21.0938			0.989982
$455$		0			0
$456$	4.48261			0.209918
$457$	−0.697673	−	0.402801i	−0.0326357	−	0.0188423i	0.483593	−	0.875293i	$-0.339331\pi$
$457$	−0.697673	−	0.402801i	−0.0326357	−	0.0188423i	−0.516229	+	0.856451i	$0.672665\pi$
$458$	20.1112	−	11.6112i	0.939735	−	0.542556i
$459$	3.80560	+	6.59150i	0.177630	+	0.307665i
$460$	−0.166119	−	1.06629i	−0.00774536	−	0.0497162i
$461$	−23.8609			−1.11131			−0.555657	−	0.831412i	$-0.687533\pi$
$461$	−23.8609			−1.11131			−0.555657	+	0.831412i	$0.687533\pi$
$462$		0			0
$463$		−	9.19065i		−	0.427126i	−0.976929	−	0.213563i	$-0.931493\pi$
$463$		−	9.19065i		−	0.427126i	0.976929	−	0.213563i	$-0.0685068\pi$
$464$	0.597199	−	1.03438i	0.0277242	−	0.0480198i
$465$	−7.26304	−	2.80913i	−0.336815	−	0.130270i
$466$	−4.28822	−	7.42741i	−0.198648	−	0.344068i
$467$	19.1548	+	11.0590i	0.886380	+	0.511752i	0.872757	−	0.488156i	$-0.162330\pi$
$467$	19.1548	+	11.0590i	0.886380	+	0.511752i	0.0136231	+	0.999907i	$0.495664\pi$
$468$		−	4.48261i		−	0.207209i
$469$		0			0
$470$	−16.0590	−	19.9342i	−0.740748	−	0.919496i
$471$	0.0469093	−	0.0812493i	0.00216147	−	0.00374377i
$472$	4.99768	−	2.88541i	0.230037	−	0.132812i
$473$	−2.90467	+	1.67701i	−0.133557	+	0.0771090i
$474$	−2.25869	+	3.91217i	−0.103745	+	0.179692i
$475$	−4.77083	+	21.8994i	−0.218901	+	1.00481i
$476$		0			0
$477$		−	9.57643i		−	0.438475i
$478$	3.96331	+	2.28822i	0.181277	+	0.104661i
$479$	16.7050	+	28.9340i	0.763272	+	1.32203i	0.941155	+	0.337974i	$0.109742\pi$
$479$	16.7050	+	28.9340i	0.763272	+	1.32203i	−0.177883	+	0.984052i	$0.556925\pi$
$480$	−0.806615	+	2.08551i	−0.0368168	+	0.0951903i
$481$	−1.08168	+	1.87353i	−0.0493205	+	0.0854256i
$482$			9.96523i			0.453904i
$483$		0			0
$484$	8.18764			0.372165
$485$	6.11687	+	39.2632i	0.277753	+	1.78285i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−2.03279	+	1.17363i	−0.0921144	+	0.0531823i	−0.545350	−	0.838209i	$-0.683603\pi$
$487$	−2.03279	+	1.17363i	−0.0921144	+	0.0531823i	0.453235	+	0.891391i	$0.350270\pi$
$488$	−9.15946	−	5.28822i	−0.414629	−	0.239386i
$489$	20.5764			0.930498
$490$		0			0
$491$	23.3820			1.05522			0.527608	−	0.849488i	$-0.323089\pi$
$491$	23.3820			1.05522			0.527608	+	0.849488i	$0.323089\pi$
$492$	−10.4736	−	6.04691i	−0.472184	−	0.272616i
$493$	−7.87287	+	4.54540i	−0.354576	+	0.204715i
$494$	10.0469	+	17.4018i	0.452032	+	0.782942i
$495$	3.70521	−	0.577241i	0.166537	−	0.0259451i
$496$	3.48261			0.156374
$497$		0			0
$498$			1.87141i			0.0838598i
$499$	7.48261	−	12.9603i	0.334968	−	0.580181i	−0.648511	−	0.761205i	$-0.724608\pi$
$499$	7.48261	−	12.9603i	0.334968	−	0.580181i	0.983479	+	0.181024i	$0.0579412\pi$
$500$	−9.33013	−	6.16025i	−0.417256	−	0.275495i
$501$	−7.04691	−	12.2056i	−0.314833	−	0.545306i
$502$	3.79757	+	2.19253i	0.169494	+	0.0978572i
$503$		−	5.35402i		−	0.238724i	−0.992851	−	0.119362i	$-0.961915\pi$
$503$		−	5.35402i		−	0.238724i	0.992851	−	0.119362i	$-0.0380849\pi$
$504$		0			0
$505$	11.2224	+	13.9305i	0.499391	+	0.619897i
$506$	0.404673	−	0.700915i	0.0179899	−	0.0311595i
$507$	6.14343	−	3.54691i	0.272839	−	0.157524i
$508$	12.0674	−	6.96710i	0.535403	−	0.309115i
$509$	10.4618	−	18.1204i	0.463713	−	0.803175i	−0.535429	−	0.844580i	$-0.679850\pi$
$509$	10.4618	−	18.1204i	0.463713	−	0.803175i	0.999142	+	0.0414053i	$0.0131835\pi$
$510$	13.2534	−	10.6770i	0.586872	−	0.472786i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−3.88206	−	2.24131i	−0.171397	−	0.0989561i
$514$	−2.35402	−	4.07728i	−0.103831	−	0.179841i
$515$	28.3864	+	10.9790i	1.25085	+	0.483793i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$		−	19.1981i		−	0.844333i
$518$		0			0
$519$	−1.12859			−0.0495397
$520$	−9.90396	+	1.54295i	−0.434317	+	0.0676630i
$521$	2.17550	+	3.76808i	0.0953105	+	0.165083i	0.909738	−	0.415183i	$-0.136282\pi$
$521$	2.17550	+	3.76808i	0.0953105	+	0.165083i	−0.814428	+	0.580265i	$0.802949\pi$
$522$	−1.03438	+	0.597199i	−0.0452735	+	0.0261387i
$523$	−34.0214	−	19.6422i	−1.48765	−	0.858895i	−0.487749	−	0.872984i	$-0.662182\pi$
$523$	−34.0214	−	19.6422i	−1.48765	−	0.858895i	−0.999901	+	0.0140889i	$0.995515\pi$
$524$	3.28822			0.143646
$525$		0			0
$526$	−16.3192			−0.711553
$527$	−22.9556	−	13.2534i	−0.999963	−	0.577329i
$528$	−1.45233	+	0.838505i	−0.0632047	+	0.0364912i
$529$	−11.3835	−	19.7169i	−0.494937	−	0.857255i
$530$	−21.1583	+	3.29629i	−0.919059	+	0.143182i
$531$	−5.77083			−0.250433
$532$		0			0
$533$		−	54.2119i		−	2.34818i
$534$	−1.67701	+	2.90467i	−0.0725713	+	0.125697i
$535$	−8.07388	−	3.12273i	−0.349064	−	0.135008i
$536$	1.67701	+	2.90467i	0.0724358	+	0.125462i
$537$	2.98592	+	1.72392i	0.128852	+	0.0743926i
$538$			19.7708i			0.852381i
$539$		0			0
$540$	1.74131	−	1.40280i	0.0749339	−	0.0603670i
$541$	−7.45158	+	12.9065i	−0.320369	+	0.554895i	−0.980564	−	0.196199i	$-0.937140\pi$
$541$	−7.45158	+	12.9065i	−0.320369	+	0.554895i	0.660196	+	0.751094i	$0.270473\pi$
$542$	−1.95739	+	1.13010i	−0.0840772	+	0.0485420i
$543$	19.8282	−	11.4478i	0.850911	−	0.491274i
$544$	−3.80560	+	6.59150i	−0.163164	+	0.282608i
$545$	−24.1596	−	29.9895i	−1.03488	−	1.28461i
$546$		0			0
$547$			43.9865i			1.88073i	0.340173	+	0.940363i	$0.389515\pi$
$547$			43.9865i			1.88073i	−0.340173	+	0.940363i	$0.610485\pi$
$548$	3.68683	+	2.12859i	0.157494	+	0.0909290i
$549$	5.28822	+	9.15946i	0.225696	+	0.390916i
$550$	−2.55073	−	7.98767i	−0.108764	−	0.340595i
$551$	2.67701	−	4.63672i	0.114044	−	0.197531i
$552$		−	0.482613i		−	0.0205414i
$553$		0			0
$554$	18.2572			0.775673
$555$	−1.06629	+	0.166119i	−0.0452616	+	0.00705138i
$556$	9.48261	+	16.4244i	0.402152	+	0.696548i
$557$	−4.21615	+	2.43420i	−0.178644	+	0.103140i	−0.586655	−	0.809837i	$-0.699556\pi$
$557$	−4.21615	+	2.43420i	−0.178644	+	0.103140i	0.408011	+	0.912977i	$0.366222\pi$
$558$	−3.01603	−	1.74131i	−0.127679	−	0.0737154i
$559$	−8.96523			−0.379189
$560$		0			0
$561$	12.7641			0.538899
$562$	9.07821	+	5.24131i	0.382941	+	0.221091i
$563$	−4.63411	+	2.67550i	−0.195304	+	0.112759i	−0.594463	−	0.804123i	$-0.702635\pi$
$563$	−4.63411	+	2.67550i	−0.195304	+	0.112759i	0.399159	+	0.916882i	$0.369302\pi$
$564$	−5.72392	−	9.91412i	−0.241020	−	0.417460i
$565$	3.08591	+	19.8079i	0.129825	+	0.833325i
$566$	−0.708040			−0.0297612
$567$		0			0
$568$			6.00000i			0.251754i
$569$	4.07794	−	7.06320i	0.170956	−	0.296105i	−0.767798	−	0.640692i	$-0.778648\pi$
$569$	4.07794	−	7.06320i	0.170956	−	0.296105i	0.938754	+	0.344587i	$0.111981\pi$
$570$	−3.61574	+	9.34856i	−0.151447	+	0.391568i
$571$	2.80560	+	4.85945i	0.117411	+	0.203362i	0.918741	−	0.394861i	$-0.129207\pi$
$571$	2.80560	+	4.85945i	0.117411	+	0.203362i	−0.801330	+	0.598222i	$0.795874\pi$
$572$	−6.51025	−	3.75869i	−0.272207	−	0.157159i
$573$		−	25.1529i		−	1.05078i
$574$		0			0
$575$	2.35776	+	0.513643i	0.0983256	+	0.0214204i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	4.04780	−	2.33700i	0.168512	−	0.0972905i	−0.413372	−	0.910562i	$-0.635649\pi$
$577$	4.04780	−	2.33700i	0.168512	−	0.0972905i	0.581884	+	0.813272i	$0.302316\pi$
$578$	35.4468	−	20.4652i	1.47439	−	0.851241i
$579$	6.40280	−	11.0900i	0.266091	−	0.460884i
$580$	1.67550	+	2.07981i	0.0695714	+	0.0863595i
$581$		0			0
$582$			17.7708i			0.736625i
$583$	−13.9082	−	8.02989i	−0.576018	−	0.332564i
$584$	−2.00000	−	3.46410i	−0.0827606	−	0.143346i
$585$	9.34856	+	3.61574i	0.386515	+	0.149493i
$586$	6.30560	−	10.9216i	0.260482	−	0.451168i
$587$			18.9062i			0.780342i	0.920742	+	0.390171i	$0.127584\pi$
$587$			18.9062i			0.780342i	−0.920742	+	0.390171i	$0.872416\pi$
$588$		0			0
$589$	15.6112			0.643249
$590$	1.98637	+	12.7502i	0.0817775	+	0.524916i
$591$	1.43570	+	2.48671i	0.0590570	+	0.102290i
$592$	0.417955	−	0.241306i	0.0171778	−	0.00991763i
$593$	18.6556	+	10.7708i	0.766095	+	0.442305i	0.831480	−	0.555555i	$-0.187494\pi$
$593$	18.6556	+	10.7708i	0.766095	+	0.442305i	−0.0653851	+	0.997860i	$0.520828\pi$
$594$	1.67701			0.0688086
$595$		0			0
$596$	7.03477			0.288156
$597$	−2.62819	−	1.51739i	−0.107565	−	0.0621025i
$598$	1.87353	−	1.08168i	0.0766144	−	0.0442333i
$599$	17.3820	+	30.1066i	0.710211	+	1.23012i	0.964778	+	0.263066i	$0.0847337\pi$
$599$	17.3820	+	30.1066i	0.710211	+	1.23012i	−0.254567	+	0.967055i	$0.581933\pi$
$600$	−3.69874	−	3.36441i	−0.151001	−	0.137352i
$601$	−4.19814			−0.171246			−0.0856229	−	0.996328i	$-0.527288\pi$
$601$	−4.19814			−0.171246			−0.0856229	+	0.996328i	$0.527288\pi$
$602$		0			0
$603$		−	3.35402i		−	0.136586i
$604$	−3.22392	+	5.58399i	−0.131179	+	0.227209i
$605$	−6.60427	+	17.0754i	−0.268502	+	0.694215i
$606$	4.00000	+	6.92820i	0.162489	+	0.281439i
$607$	36.4786	+	21.0609i	1.48062	+	0.854836i	0.999759	−	0.0219606i	$-0.00699085\pi$
$607$	36.4786	+	21.0609i	1.48062	+	0.854836i	0.480861	+	0.876797i	$0.340324\pi$
$608$		−	4.48261i		−	0.181794i
$609$		0			0
$610$	18.4168	−	14.8366i	0.745675	−	0.600718i
$611$	25.6581	−	44.4412i	1.03802	−	1.79790i
$612$	6.59150	−	3.80560i	0.266445	−	0.153832i
$613$	−16.0666	+	9.27608i	−0.648926	+	0.374657i	−0.788044	−	0.615618i	$-0.788906\pi$
$613$	−16.0666	+	9.27608i	−0.648926	+	0.374657i	0.139119	+	0.990276i	$0.455573\pi$
$614$	−4.77083	+	8.26332i	−0.192535	+	0.333480i
$615$	21.0590	−	16.9652i	0.849183	−	0.684104i
$616$		0			0
$617$			13.4236i			0.540413i	0.962802	+	0.270206i	$0.0870919\pi$
$617$			13.4236i			0.540413i	−0.962802	+	0.270206i	$0.912908\pi$
$618$	11.7876	+	6.80560i	0.474169	+	0.273761i
$619$	15.5606	+	26.9517i	0.625431	+	1.08328i	0.988457	+	0.151500i	$0.0484103\pi$
$619$	15.5606	+	26.9517i	0.625431	+	1.08328i	−0.363026	+	0.931779i	$0.618256\pi$
$620$	−2.80913	+	7.26304i	−0.112817	+	0.291691i
$621$	−0.241306	+	0.417955i	−0.00968329	+	0.0167720i
$622$		−	20.9652i		−	0.840629i
$623$		0			0
$624$	−4.48261			−0.179448
$625$	20.3731	−	14.4892i	0.814925	−	0.579567i
$626$	−7.59720	−	13.1587i	−0.303645	−	0.525929i
$627$	−6.51025	+	3.75869i	−0.259994	+	0.150108i
$628$	−0.0812493	−	0.0469093i	−0.00324220	−	0.00187188i
$629$	−3.67327			−0.146463
$630$		0			0
$631$	−1.15588			−0.0460148			−0.0230074	−	0.999735i	$-0.507324\pi$
$631$	−1.15588			−0.0460148			−0.0230074	+	0.999735i	$0.507324\pi$
$632$	3.91217	+	2.25869i	0.155618	+	0.0898460i
$633$	9.07821	−	5.24131i	0.360826	−	0.208323i
$634$	−9.22392	−	15.9763i	−0.366329	−	0.634500i
$635$	4.79627	+	30.7864i	0.190334	+	1.22172i
$636$	−9.57643			−0.379730
$637$		0			0
$638$			2.00302i			0.0793002i
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	2.08551	+	0.806615i	0.0824372	+	0.0318843i
$641$	7.52952	+	13.0415i	0.297398	+	0.515109i	0.975540	−	0.219822i	$-0.0705478\pi$
$641$	7.52952	+	13.0415i	0.297398	+	0.515109i	−0.678142	+	0.734931i	$0.737214\pi$
$642$	−3.35274	−	1.93570i	−0.132322	−	0.0763961i
$643$		−	35.2149i		−	1.38874i	−0.719618	−	0.694371i	$-0.755683\pi$
$643$		−	35.2149i		−	1.38874i	0.719618	−	0.694371i	$-0.244317\pi$
$644$		0			0
$645$	−2.80560	−	3.48261i	−0.110471	−	0.137128i
$646$	−17.0590	+	29.5471i	−0.671179	+	1.16252i
$647$	3.82183	−	2.20653i	0.150251	−	0.0867477i	−0.422989	−	0.906135i	$-0.639019\pi$
$647$	3.82183	−	2.20653i	0.150251	−	0.0867477i	0.573241	+	0.819387i	$0.305686\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−4.83887	+	8.38117i	−0.189942	+	0.328990i
$650$	4.77083	−	21.8994i	0.187127	−	0.858966i
$651$		0			0
$652$		−	20.5764i		−	0.805835i
$653$	15.6723	+	9.04842i	0.613305	+	0.354092i	0.774258	−	0.632870i	$-0.218123\pi$
$653$	15.6723	+	9.04842i	0.613305	+	0.354092i	−0.160953	+	0.986962i	$0.551457\pi$
$654$	−8.61121	−	14.9150i	−0.336725	−	0.583224i
$655$	−2.65232	+	6.85762i	−0.103635	+	0.267950i
$656$	−6.04691	+	10.4736i	−0.236092	+	0.408924i
$657$			4.00000i			0.156055i
$658$		0			0
$659$	−25.6112			−0.997671			−0.498835	−	0.866697i	$-0.666239\pi$
$659$	−25.6112			−0.997671			−0.498835	+	0.866697i	$0.666239\pi$
$660$	−0.577241	−	3.70521i	−0.0224691	−	0.144225i
$661$	11.1248	+	19.2688i	0.432706	+	0.749470i	0.997105	−	0.0760326i	$-0.0242253\pi$
$661$	11.1248	+	19.2688i	0.432706	+	0.749470i	−0.564399	+	0.825502i	$0.690892\pi$
$662$	−19.7470	+	11.4009i	−0.767489	+	0.443110i
$663$	29.5471	+	17.0590i	1.14752	+	0.662518i
$664$	1.87141			0.0726247
$665$		0			0
$666$	−0.482613			−0.0187009
$667$	−0.499204	−	0.288216i	−0.0193293	−	0.0111598i
$668$	−12.2056	+	7.04691i	−0.472249	+	0.272653i
$669$	−7.56242	−	13.0985i	−0.292380	−	0.506417i
$670$	−7.41043	+	1.15448i	−0.286290	+	0.0446015i
$671$	17.7368			0.684721
$672$		0			0
$673$			36.5349i			1.40832i	0.710043	+	0.704158i	$0.248676\pi$
$673$			36.5349i			1.40832i	−0.710043	+	0.704158i	$0.751324\pi$
$674$	−4.56242	+	7.90235i	−0.175738	+	0.304387i
$675$	1.52100	+	4.76304i	0.0585433	+	0.183330i
$676$	−3.54691	−	6.14343i	−0.136420	−	0.236286i
$677$	−24.7780	−	14.3056i	−0.952297	−	0.549809i	−0.0585033	−	0.998287i	$-0.518633\pi$
$677$	−24.7780	−	14.3056i	−0.952297	−	0.549809i	−0.893794	+	0.448478i	$0.851966\pi$
$678$			8.96523i			0.344307i
$679$		0			0
$680$	−10.6770	−	13.2534i	−0.409445	−	0.508246i
$681$	−10.5469	+	18.2678i	−0.404158	+	0.700023i
$682$	−5.05791	+	2.92019i	−0.193678	+	0.111820i
$683$	10.8339	−	6.25495i	0.414547	−	0.239339i	−0.278194	−	0.960525i	$-0.589736\pi$
$683$	10.8339	−	6.25495i	0.414547	−	0.239339i	0.692742	+	0.721186i	$0.256403\pi$
$684$	−2.24131	+	3.88206i	−0.0856985	+	0.148434i
$685$	−7.41306	+	5.97199i	−0.283239	+	0.228178i
$686$		0			0
$687$			23.2224i			0.885990i
$688$	1.73205	+	1.00000i	0.0660338	+	0.0381246i
$689$	−21.4637	−	37.1762i	−0.817703	−	1.41630i
$690$	1.00650	+	0.389283i	0.0383167	+	0.0148197i
$691$	9.22241	−	15.9737i	0.350837	−	0.607668i	−0.635559	−	0.772052i	$-0.719230\pi$
$691$	9.22241	−	15.9737i	0.350837	−	0.607668i	0.986396	+	0.164384i	$0.0525638\pi$
$692$			1.12859i			0.0429027i
$693$		0			0
$694$	−19.2224			−0.729673
$695$	−41.9021	+	6.52799i	−1.58944	+	0.247621i
$696$	0.597199	+	1.03438i	0.0226368	+	0.0392080i
$697$	79.7164	−	46.0243i	3.01947	−	1.74329i
$698$	−5.35865	−	3.09382i	−0.202828	−	0.117103i
$699$	8.57643			0.324390
$700$		0			0
$701$	−2.15962			−0.0815678			−0.0407839	−	0.999168i	$-0.512986\pi$
$701$	−2.15962			−0.0815678			−0.0407839	+	0.999168i	$0.512986\pi$
$702$	3.88206	+	2.24131i	0.146519	+	0.0845927i
$703$	1.87353	−	1.08168i	0.0706615	−	0.0407965i
$704$	0.838505	+	1.45233i	0.0316023	+	0.0547369i
$705$	25.2930	−	3.94044i	0.952591	−	0.148406i
$706$	11.2224			0.422361
$707$		0			0
$708$			5.77083i			0.216881i
$709$	−9.80186	+	16.9773i	−0.368117	+	0.637597i	−0.989271	−	0.146092i	$-0.953331\pi$
$709$	−9.80186	+	16.9773i	−0.368117	+	0.637597i	0.621155	+	0.783688i	$0.286664\pi$
$710$	−12.5131	−	4.83969i	−0.469608	−	0.181630i
$711$	−2.25869	−	3.91217i	−0.0847076	−	0.146718i
$712$	2.90467	+	1.67701i	0.108857	+	0.0628486i
$713$		−	1.68075i		−	0.0629447i
$714$		0			0
$715$	13.0901	−	10.5454i	0.489541	−	0.394376i
$716$	1.72392	−	2.98592i	0.0644259	−	0.111589i
$717$	−3.96331	+	2.28822i	−0.148012	+	0.0854550i
$718$	8.32355	−	4.80560i	0.310632	−	0.179344i
$719$	−26.5106	+	45.9178i	−0.988680	+	1.71244i	−0.364399	+	0.931243i	$0.618726\pi$
$719$	−26.5106	+	45.9178i	−0.988680	+	1.71244i	−0.624280	+	0.781200i	$0.714608\pi$
$720$	−1.40280	−	1.74131i	−0.0522793	−	0.0648947i
$721$		0			0
$722$		−	1.09382i		−	0.0407077i
$723$	−8.63014	−	4.98261i	−0.320958	−	0.185305i
$724$	−11.4478	−	19.8282i	−0.425456	−	0.736911i
$725$	−5.68896	+	1.81668i	−0.211283	+	0.0674697i
$726$	−4.09382	+	7.09070i	−0.151936	+	0.263161i
$727$		−	28.3155i		−	1.05016i	−0.851052	−	0.525082i	$-0.824035\pi$
$727$		−	28.3155i		−	1.05016i	0.851052	−	0.525082i	$-0.175965\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	8.83767	−	1.37683i	0.327097	−	0.0509589i
$731$	−7.61121	−	13.1830i	−0.281511	−	0.487591i
$732$	9.15946	−	5.28822i	0.338543	−	0.195458i
$733$	21.6415	+	12.4947i	0.799348	+	0.461504i	0.843243	−	0.537532i	$-0.180643\pi$
$733$	21.6415	+	12.4947i	0.799348	+	0.461504i	−0.0438948	+	0.999036i	$0.513977\pi$
$734$	−26.2534			−0.969032
$735$		0			0
$736$	−0.482613			−0.0177893
$737$	−4.87116	−	2.81236i	−0.179431	−	0.103595i
$738$	10.4736	−	6.04691i	0.385537	−	0.222590i
$739$	21.6233	+	37.4527i	0.795427	+	1.37772i	0.922567	+	0.385836i	$0.126087\pi$
$739$	21.6233	+	37.4527i	0.795427	+	1.37772i	−0.127140	+	0.991885i	$0.540580\pi$
$740$	0.166119	+	1.06629i	0.00610667	+	0.0391977i
$741$	−20.0938			−0.738165
$742$		0			0
$743$		−	21.9062i		−	0.803660i	−0.915714	−	0.401830i	$-0.868374\pi$
$743$		−	21.9062i		−	0.803660i	0.915714	−	0.401830i	$-0.131626\pi$
$744$	−1.74131	+	3.01603i	−0.0638394	+	0.110573i
$745$	−5.67435	+	14.6711i	−0.207892	+	0.537508i
$746$	8.73980	+	15.1378i	0.319987	+	0.554233i
$747$	−1.62069	−	0.935704i	−0.0592978	−	0.0342356i
$748$		−	12.7641i		−	0.466701i
$749$		0			0
$750$	10.0000	−	5.00000i	0.365148	−	0.182574i
$751$	−13.4463	+	23.2897i	−0.490664	+	0.849854i	−0.999942	−	0.0107474i	$-0.996579\pi$
$751$	−13.4463	+	23.2897i	−0.490664	+	0.849854i	0.509279	+	0.860602i	$0.329912\pi$
$752$	−9.91412	+	5.72392i	−0.361531	+	0.208730i
$753$	−3.79757	+	2.19253i	−0.138391	+	0.0799001i
$754$	−2.67701	+	4.63672i	−0.0974910	+	0.168859i
$755$	−9.04504	−	11.2277i	−0.329183	−	0.408617i
$756$		0			0
$757$		−	11.1529i		−	0.405358i	−0.979245	−	0.202679i	$-0.935035\pi$
$757$		−	11.1529i		−	0.405358i	0.979245	−	0.202679i	$-0.0649647\pi$
$758$	−27.9566	−	16.1407i	−1.01543	−	0.586258i
$759$	0.404673	+	0.700915i	0.0146887	+	0.0254416i
$760$	9.34856	+	3.61574i	0.339108	+	0.131157i
$761$	0.793468	−	1.37433i	0.0287632	−	0.0498193i	−0.851285	−	0.524703i	$-0.824176\pi$
$761$	0.793468	−	1.37433i	0.0287632	−	0.0498193i	0.880049	+	0.474883i	$0.157510\pi$
$762$			13.9342i			0.504783i
$763$		0			0
$764$	−25.1529			−0.909999
$765$	2.61984	+	16.8163i	0.0947206	+	0.607995i
$766$	−9.04691	−	15.6697i	−0.326878	−	0.566170i
$767$	−22.4027	+	12.9342i	−0.808914	+	0.467027i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	19.2572			0.694432			0.347216	−	0.937785i	$-0.387127\pi$
$769$	19.2572			0.694432			0.347216	+	0.937785i	$0.387127\pi$
$770$		0			0
$771$	4.70804			0.169556
$772$	−11.0900	−	6.40280i	−0.399137	−	0.230442i
$773$	−26.2245	+	15.1407i	−0.943230	+	0.544574i	−0.890971	−	0.454059i	$-0.849975\pi$
$773$	−26.2245	+	15.1407i	−0.943230	+	0.544574i	−0.0522587	+	0.998634i	$0.516642\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$	−12.8813	−	11.7170i	−0.462710	−	0.420885i
$776$	17.7708			0.637936
$777$		0			0
$778$		−	8.18764i		−	0.293541i
$779$	−27.1060	+	46.9489i	−0.971172	+	1.68212i
$780$	3.61574	−	9.34856i	0.129464	−	0.334732i
$781$	−5.03103	−	8.71400i	−0.180024	−	0.311811i
$782$	3.18114	+	1.83663i	0.113757	+	0.0656779i
$783$		−	1.19440i		−	0.0426843i
$784$		0			0
$785$	0.163367	−	0.131609i	0.00583081	−	0.00469732i
$786$	−1.64411	+	2.84768i	−0.0586434	+	0.101573i
$787$	−28.7715	+	16.6112i	−1.02559	+	0.592126i	−0.915719	−	0.401820i	$-0.868378\pi$
$787$	−28.7715	+	16.6112i	−1.02559	+	0.592126i	−0.109873	+	0.993946i	$0.535044\pi$
$788$	2.48671	−	1.43570i	0.0885854	−	0.0511448i
$789$	8.15962	−	14.1329i	0.290490	−	0.503144i
$790$	−7.86616	+	6.33700i	−0.279865	+	0.225460i
$791$		0			0
$792$		−	1.67701i		−	0.0595900i
$793$	41.0583	+	23.7050i	1.45802	+	0.841790i
$794$	18.0938	+	31.3394i	0.642126	+	1.11219i
$795$	7.72449	−	19.9718i	0.273960	−	0.708326i
$796$	−1.51739	+	2.62819i	−0.0537824	+	0.0931538i
$797$		−	41.7883i		−	1.48022i	−0.672486	−	0.740109i	$-0.734774\pi$
$797$		−	41.7883i		−	1.48022i	0.672486	−	0.740109i	$-0.265226\pi$
$798$		0			0
$799$	87.1319			3.08250
$800$	−3.36441	+	3.69874i	−0.118950	+	0.130770i
$801$	−1.67701	−	2.90467i	−0.0592542	−	0.102631i
$802$	26.8377	−	15.4947i	0.947672	−	0.547139i
$803$	5.80933	+	3.35402i	0.205007	+	0.118361i
$804$	−3.35402			−0.118287
$805$		0			0
$806$	−15.6112			−0.549881
$807$	−17.1220	−	9.88541i	−0.602724	−	0.347983i
$808$	6.92820	−	4.00000i	0.243733	−	0.140720i
$809$	2.52952	+	4.38126i	0.0889333	+	0.154037i	0.907060	−	0.421000i	$-0.138321\pi$
$809$	2.52952	+	4.38126i	0.0889333	+	0.154037i	−0.818127	+	0.575037i	$0.804988\pi$
$810$	0.344208	+	2.20942i	0.0120943	+	0.0776310i
$811$	33.5039			1.17648			0.588240	−	0.808686i	$-0.299821\pi$
$811$	33.5039			1.17648			0.588240	+	0.808686i	$0.299821\pi$
$812$		0			0
$813$		−	2.26020i		−	0.0792687i
$814$	−0.404673	+	0.700915i	−0.0141838	+	0.0245671i
$815$	42.9125	+	16.5973i	1.50316	+	0.581377i
$816$	−3.80560	−	6.59150i	−0.133223	−	0.230749i
$817$	7.76411	+	4.48261i	0.271632	+	0.156827i
$818$		−	13.0938i		−	0.457815i
$819$		0			0
$820$	−16.9652	−	21.0590i	−0.592451	−	0.735414i
$821$	−14.8506	+	25.7221i	−0.518291	+	0.897706i	0.481483	+	0.876455i	$0.340098\pi$
$821$	−14.8506	+	25.7221i	−0.518291	+	0.897706i	−0.999774	+	0.0212509i	$0.993235\pi$
$822$	−3.68683	+	2.12859i	−0.128593	+	0.0742432i
$823$	−33.1252	+	19.1248i	−1.15467	+	0.666650i	−0.950021	−	0.312185i	$-0.898939\pi$
$823$	−33.1252	+	19.1248i	−1.15467	+	0.666650i	−0.204651	+	0.978835i	$0.565606\pi$
$824$	6.80560	−	11.7876i	0.237084	−	0.410642i
$825$	8.19289	+	1.78484i	0.285240	+	0.0621400i
$826$		0			0
$827$		−	13.3510i		−	0.464260i	−0.972685	−	0.232130i	$-0.925431\pi$
$827$		−	13.3510i		−	0.464260i	0.972685	−	0.232130i	$-0.0745695\pi$
$828$	0.417955	+	0.241306i	0.0145249	+	0.00838598i
$829$	1.80560	+	3.12740i	0.0627112	+	0.108619i	0.895676	−	0.444706i	$-0.146692\pi$
$829$	1.80560	+	3.12740i	0.0627112	+	0.108619i	−0.832965	+	0.553325i	$0.813359\pi$
$830$	−1.50951	+	3.90285i	−0.0523957	+	0.135470i
$831$	−9.12859	+	15.8112i	−0.316667	+	0.548484i
$832$			4.48261i			0.155407i
$833$		0			0
$834$	−18.9652			−0.656712
$835$	−4.85121	−	31.1391i	−0.167883	−	1.07761i
$836$	3.75869	+	6.51025i	0.129997	+	0.225162i
$837$	3.01603	−	1.74131i	0.104249	−	0.0601884i
$838$	28.9064	+	16.6891i	0.998557	+	0.576517i
$839$	1.68075			0.0580261			0.0290130	−	0.999579i	$-0.490764\pi$
$839$	1.68075			0.0580261			0.0290130	+	0.999579i	$0.490764\pi$
$840$		0			0
$841$	−27.5734			−0.950807
$842$	−5.97832	−	3.45158i	−0.206026	−	0.118949i
$843$	−9.07821	+	5.24131i	−0.312670	+	0.180520i
$844$	−5.24131	−	9.07821i	−0.180413	−	0.312485i
$845$	15.6732	−	2.44175i	0.539174	−	0.0839988i
$846$	11.4478			0.393585
$847$		0			0
$848$			9.57643i			0.328856i
$849$	0.354020	−	0.613181i	0.0121499	−	0.0210443i
$850$	36.2525	−	11.5766i	1.24345	−	0.397075i
$851$	−0.116458	−	0.201711i	−0.00399212	−	0.00691455i
$852$	−5.19615	−	3.00000i	−0.178017	−	0.102778i
$853$		−	1.70502i		−	0.0583789i	−0.999574	−	0.0291895i	$-0.990707\pi$
$853$		−	1.70502i		−	0.0583789i	0.999574	−	0.0291895i	$-0.00929261\pi$
$854$		0			0
$855$	−6.28822	−	7.80560i	−0.215052	−	0.266946i
$856$	−1.93570	+	3.35274i	−0.0661610	+	0.114594i
$857$	−24.8502	+	14.3473i	−0.848866	+	0.490093i	−0.860268	−	0.509842i	$-0.829704\pi$
$857$	−24.8502	+	14.3473i	−0.848866	+	0.490093i	0.0114020	+	0.999935i	$0.496371\pi$
$858$	6.51025	−	3.75869i	0.222256	−	0.128320i
$859$	13.3820	−	23.1784i	0.456589	−	0.790836i	−0.542189	−	0.840257i	$-0.682404\pi$
$859$	13.3820	−	23.1784i	0.456589	−	0.790836i	0.998778	+	0.0494211i	$0.0157376\pi$
$860$	−3.48261	+	2.80560i	−0.118756	+	0.0956703i
$861$		0			0
$862$			26.1181i			0.889586i
$863$	27.7338	+	16.0121i	0.944071	+	0.545059i	0.891234	−	0.453544i	$-0.149840\pi$
$863$	27.7338	+	16.0121i	0.944071	+	0.545059i	0.0528366	+	0.998603i	$0.483174\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−2.35370	−	0.910340i	−0.0800281	−	0.0309525i
$866$	−12.9652	+	22.4564i	−0.440576	+	0.763101i
$867$			40.9305i			1.39007i
$868$		0			0
$869$	−7.57570			−0.256988
$870$	−2.63892	+	0.411122i	−0.0894678	+	0.0139383i
$871$	−7.51739	−	13.0205i	−0.254717	−	0.441183i
$872$	−14.9150	+	8.61121i	−0.505087	+	0.291612i
$873$	−15.3900	−	8.88541i	−0.520872	−	0.300726i
$874$	−2.16337			−0.0731770
$875$		0			0
$876$	4.00000			0.135147
$877$	−15.7299	−	9.08168i	−0.531162	−	0.306667i	0.210327	−	0.977631i	$-0.432547\pi$
$877$	−15.7299	−	9.08168i	−0.531162	−	0.306667i	−0.741490	+	0.670964i	$0.765880\pi$
$878$	6.54036	−	3.77608i	0.220727	−	0.127437i
$879$	6.30560	+	10.9216i	0.212683	+	0.368377i
$880$	−3.70521	+	0.577241i	−0.124903	+	0.0194588i
$881$	24.2254			0.816175			0.408088	−	0.912943i	$-0.366196\pi$
$881$	24.2254			0.816175			0.408088	+	0.912943i	$0.366196\pi$
$882$		0			0
$883$		−	32.3753i		−	1.08951i	−0.838594	−	0.544757i	$-0.816622\pi$
$883$		−	32.3753i		−	1.08951i	0.838594	−	0.544757i	$-0.183378\pi$
$884$	17.0590	−	29.5471i	0.573758	−	0.993778i
$885$	−12.0351	−	4.65484i	−0.404557	−	0.156471i
$886$	12.1581	+	21.0585i	0.408460	+	0.707473i
$887$	−28.5370	−	16.4759i	−0.958179	−	0.553205i	−0.0625670	−	0.998041i	$-0.519929\pi$
$887$	−28.5370	−	16.4759i	−0.958179	−	0.553205i	−0.895612	+	0.444836i	$0.853262\pi$
$888$			0.482613i			0.0161954i
$889$		0			0
$890$	−5.84038	+	4.70502i	−0.195770	+	0.157713i
$891$	−0.838505	+	1.45233i	−0.0280910	+	0.0486550i
$892$	−13.0985	+	7.56242i	−0.438570	+	0.253209i
$893$	−44.4412	+	25.6581i	−1.48717	+	0.858616i
$894$	−3.51739	+	6.09229i	−0.117639	+	0.203757i
$895$	4.83663	+	6.00374i	0.161671	+	0.200683i
$896$		0			0
$897$			2.16337i			0.0722327i
$898$	−12.7650	−	7.36990i	−0.425975	−	0.245937i
$899$	2.07981	+	3.60234i	0.0693656	+	0.120145i
$900$	4.76304	−	1.52100i	0.158768	−	0.0507000i
$901$	36.4441	−	63.1230i	1.21413	−	2.10293i
$902$		−	20.2815i		−	0.675299i
$903$		0			0
$904$	8.96523			0.298179
$905$	50.5861	−	7.88089i	1.68154	−	0.261969i
$906$	−3.22392	−	5.58399i	−0.107108	−	0.185516i
$907$	6.87446	−	3.96897i	0.228263	−	0.131787i	−0.381508	−	0.924366i	$-0.624595\pi$
$907$	6.87446	−	3.96897i	0.228263	−	0.131787i	0.609770	+	0.792578i	$0.291262\pi$
$908$	18.2678	+	10.5469i	0.606238	+	0.350011i
$909$	−8.00000			−0.265343
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	3.88206	+	2.24131i	0.128548	+	0.0742171i
$913$	−2.71791	+	1.56918i	−0.0899496	+	0.0519324i
$914$	−0.402801	−	0.697673i	−0.0133235	−	0.0230770i
$915$	3.64050	+	23.3677i	0.120351	+	0.772514i
$916$	23.2224			0.767290
$917$		0			0
$918$			7.61121i			0.251207i
$919$	0.576432	−	0.998409i	0.0190147	−	0.0329345i	−0.856361	−	0.516377i	$-0.827280\pi$
$919$	0.576432	−	0.998409i	0.0190147	−	0.0329345i	0.875376	+	0.483442i	$0.160614\pi$
$920$	0.389283	−	1.00650i	0.0128343	−	0.0331832i
$921$	−4.77083	−	8.26332i	−0.157204	−	0.272286i
$922$	−20.6641	−	11.9305i	−0.680537	−	0.392909i
$923$		−	26.8957i		−	0.885282i
$924$		0			0
$925$	−2.35776	−	0.513643i	−0.0775228	−	0.0168885i
$926$	4.59533	−	7.95934i	0.151012	−	0.261560i
$927$	−11.7876	+	6.80560i	−0.387157	+	0.223525i
$928$	1.03438	−	0.597199i	0.0339551	−	0.0196040i
$929$	−29.4600	+	51.0262i	−0.966550	+	1.67411i	−0.261160	+	0.965296i	$0.584105\pi$
$929$	−29.4600	+	51.0262i	−0.966550	+	1.67411i	−0.705391	+	0.708819i	$0.749228\pi$
$930$	−4.88541	−	6.06430i	−0.160199	−	0.198856i
$931$		0			0
$932$		−	8.57643i		−	0.280930i
$933$	18.1564	+	10.4826i	0.594414	+	0.343185i
$934$	11.0590	+	19.1548i	0.361863	+	0.626765i
$935$	26.6197	+	10.2957i	0.870556	+	0.336705i
$936$	2.24131	−	3.88206i	0.0732594	−	0.126889i
$937$		−	42.4168i		−	1.38570i	−0.721083	−	0.692848i	$-0.756356\pi$
$937$		−	42.4168i		−	1.38570i	0.721083	−	0.692848i	$-0.243644\pi$
$938$		0			0
$939$	15.1944			0.495850
$940$	−3.94044	−	25.2930i	−0.128523	−	0.824968i
$941$	21.3333	+	36.9503i	0.695444	+	1.20454i	0.970031	+	0.242982i	$0.0781257\pi$
$941$	21.3333	+	36.9503i	0.695444	+	1.20454i	−0.274587	+	0.961562i	$0.588541\pi$
$942$	0.0812493	−	0.0469093i	0.00264724	−	0.00152839i
$943$	5.05467	+	2.91832i	0.164603	+	0.0950335i
$944$	5.77083			0.187824
$945$		0			0
$946$	−3.35402			−0.109049
$947$	46.5847	+	26.8957i	1.51380	+	0.873992i	0.999869	+	0.0161595i	$0.00514396\pi$
$947$	46.5847	+	26.8957i	1.51380	+	0.873992i	0.513929	+	0.857833i	$0.328189\pi$
$948$	−3.91217	+	2.25869i	−0.127061	+	0.0733590i
$949$	8.96523	+	15.5282i	0.291024	+	0.504068i
$950$	−15.0814	+	16.5800i	−0.489304	+	0.537928i
$951$	18.4478			0.598212
$952$		0			0
$953$		−	6.24970i		−	0.202448i	−0.994864	−	0.101224i	$-0.967724\pi$
$953$		−	6.24970i		−	0.202448i	0.994864	−	0.101224i	$-0.0322758\pi$
$954$	4.78822	−	8.29343i	0.155024	−	0.268510i
$955$	20.2887	−	52.4567i	0.656526	−	1.69746i
$956$	2.28822	+	3.96331i	0.0740062	+	0.128182i
$957$	−1.73466	−	1.00151i	−0.0560737	−	0.0323742i
$958$			33.4100i			1.07943i
$959$		0			0
$960$	−1.74131	+	1.40280i	−0.0562004	+	0.0452752i
$961$	9.43570	−	16.3431i	0.304378	−	0.527197i
$962$	−1.87353	+	1.08168i	−0.0604051	+	0.0348749i
$963$	3.35274	−	1.93570i	0.108040	−	0.0623772i
$964$	−4.98261	+	8.63014i	−0.160479	+	0.277958i
$965$	22.2985	−	17.9637i	0.717813	−	0.578273i
$966$		0			0
$967$		−	31.9585i		−	1.02771i	−0.857876	−	0.513857i	$-0.828216\pi$
$967$		−	31.9585i		−	1.02771i	0.857876	−	0.513857i	$-0.171784\pi$
$968$	7.09070	+	4.09382i	0.227904	+	0.131580i
$969$	−17.0590	−	29.5471i	−0.548015	−	0.949191i
$970$	−14.3342	+	37.0613i	−0.460244	+	1.18997i
$971$	−11.5088	+	19.9337i	−0.369334	+	0.639704i	−0.989461	−	0.144796i	$-0.953747\pi$
$971$	−11.5088	+	19.9337i	−0.369334	+	0.639704i	0.620128	+	0.784501i	$0.287081\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	−2.34726			−0.0752111
$975$	16.5800	+	15.0814i	0.530986	+	0.482990i
$976$	−5.28822	−	9.15946i	−0.169272	−	0.293187i
$977$	6.81423	−	3.93420i	0.218006	−	0.125866i	−0.387020	−	0.922071i	$-0.626496\pi$
$977$	6.81423	−	3.93420i	0.218006	−	0.125866i	0.605027	+	0.796205i	$0.293162\pi$
$978$	17.8197	+	10.2882i	0.569812	+	0.328981i
$979$	−5.62473			−0.179767
$980$		0			0
$981$	17.2224			0.549869
$982$	20.2494	+	11.6910i	0.646185	+	0.373075i
$983$	10.4736	−	6.04691i	0.334054	−	0.192866i	−0.323585	−	0.946199i	$-0.604888\pi$
$983$	10.4736	−	6.04691i	0.334054	−	0.192866i	0.657640	+	0.753333i	$0.271555\pi$
$984$	−6.04691	−	10.4736i	−0.192768	−	0.333885i
$985$	0.988363	+	6.34413i	0.0314919	+	0.202141i
$986$	−9.09080			−0.289510
$987$		0			0
$988$			20.0938i			0.639270i
$989$	0.482613	−	0.835910i	0.0153462	−	0.0265804i
$990$	3.49743	+	1.35270i	0.111156	+	0.0429917i
$991$	−13.1891	−	22.8443i	−0.418967	−	0.725672i	0.576869	−	0.816837i	$-0.304274\pi$
$991$	−13.1891	−	22.8443i	−0.418967	−	0.725672i	−0.995836	+	0.0911647i	$0.970941\pi$
$992$	3.01603	+	1.74131i	0.0957591	+	0.0552865i
$993$		−	22.8019i		−	0.723595i
$994$		0			0
$995$	−4.25719	−	5.28447i	−0.134962	−	0.167529i
$996$	−0.935704	+	1.62069i	−0.0296489	+	0.0513534i
$997$	−13.0690	+	7.54540i	−0.413900	+	0.238965i	−0.692464	−	0.721452i	$-0.743475\pi$
$997$	−13.0690	+	7.54540i	−0.413900	+	0.238965i	0.278564	+	0.960418i	$0.410142\pi$
$998$	12.9603	−	7.48261i	0.410250	−	0.236858i
$999$	0.241306	−	0.417955i	0.00763460	−	0.0132235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.j.79.4		12
5.4	even	2	inner	1470.2.n.j.79.2		12
7.2	even	3		1470.2.g.h.589.3		6
7.3	odd	6		210.2.n.b.109.2	yes	12
7.4	even	3	inner	1470.2.n.j.949.2		12
7.5	odd	6		1470.2.g.i.589.1		6
7.6	odd	2		210.2.n.b.79.6	yes	12
21.17	even	6		630.2.u.f.109.5		12
21.20	even	2		630.2.u.f.289.1		12
28.3	even	6		1680.2.di.c.529.5		12
28.27	even	2		1680.2.di.c.289.3		12
35.2	odd	12		7350.2.a.dp.1.2		3
35.3	even	12		1050.2.i.v.151.1		6
35.4	even	6	inner	1470.2.n.j.949.4		12
35.9	even	6		1470.2.g.h.589.6		6
35.12	even	12		7350.2.a.dq.1.2		3
35.13	even	4		1050.2.i.v.751.1		6
35.17	even	12		1050.2.i.u.151.3		6
35.19	odd	6		1470.2.g.i.589.4		6
35.23	odd	12		7350.2.a.do.1.2		3
35.24	odd	6		210.2.n.b.109.6	yes	12
35.27	even	4		1050.2.i.u.751.3		6
35.33	even	12		7350.2.a.dn.1.2		3
35.34	odd	2		210.2.n.b.79.2	✓	12
105.59	even	6		630.2.u.f.109.1		12
105.104	even	2		630.2.u.f.289.5		12
140.59	even	6		1680.2.di.c.529.3		12
140.139	even	2		1680.2.di.c.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.b.79.2	✓	12	35.34	odd	2
210.2.n.b.79.6	yes	12	7.6	odd	2
210.2.n.b.109.2	yes	12	7.3	odd	6
210.2.n.b.109.6	yes	12	35.24	odd	6
630.2.u.f.109.1		12	105.59	even	6
630.2.u.f.109.5		12	21.17	even	6
630.2.u.f.289.1		12	21.20	even	2
630.2.u.f.289.5		12	105.104	even	2
1050.2.i.u.151.3		6	35.17	even	12
1050.2.i.u.751.3		6	35.27	even	4
1050.2.i.v.151.1		6	35.3	even	12
1050.2.i.v.751.1		6	35.13	even	4
1470.2.g.h.589.3		6	7.2	even	3
1470.2.g.h.589.6		6	35.9	even	6
1470.2.g.i.589.1		6	7.5	odd	6
1470.2.g.i.589.4		6	35.19	odd	6
1470.2.n.j.79.2		12	5.4	even	2	inner
1470.2.n.j.79.4		12	1.1	even	1	trivial
1470.2.n.j.949.2		12	7.4	even	3	inner
1470.2.n.j.949.4		12	35.4	even	6	inner
1680.2.di.c.289.3		12	28.27	even	2
1680.2.di.c.289.5		12	140.139	even	2
1680.2.di.c.529.3		12	140.59	even	6
1680.2.di.c.529.5		12	28.3	even	6
7350.2.a.dn.1.2		3	35.33	even	12
7350.2.a.do.1.2		3	35.23	odd	12
7350.2.a.dp.1.2		3	35.2	odd	12
7350.2.a.dq.1.2		3	35.12	even	12

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.20942 + 0.344208i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.20942 + 0.344208i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.08551 - 0.806615i) q^{10} +(-0.838505 - 1.45233i) q^{11} +(-0.866025 - 0.500000i) q^{12} -4.48261i q^{13} +(1.74131 - 1.40280i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.59150 - 3.80560i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.24131 + 3.88206i) q^{19} +(-1.40280 - 1.74131i) q^{20} -1.67701i q^{22} +(0.417955 + 0.241306i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.76304 - 1.52100i) q^{25} +(2.24131 - 3.88206i) q^{26} +1.00000i q^{27} -1.19440 q^{29} +(2.20942 - 0.344208i) q^{30} +(-1.74131 - 3.01603i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.45233 + 0.838505i) q^{33} +7.61121 q^{34} +1.00000 q^{36} +(-0.417955 - 0.241306i) q^{37} +(-3.88206 + 2.24131i) q^{38} +(2.24131 + 3.88206i) q^{39} +(-0.344208 - 2.20942i) q^{40} +12.0938 q^{41} -2.00000i q^{43} +(0.838505 - 1.45233i) q^{44} +(-0.806615 + 2.08551i) q^{45} +(0.241306 + 0.417955i) q^{46} +(9.91412 + 5.72392i) q^{47} -1.00000i q^{48} +(4.88541 + 1.06430i) q^{50} +(-3.80560 + 6.59150i) q^{51} +(3.88206 - 2.24131i) q^{52} +(8.29343 - 4.78822i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.35251 + 2.92019i) q^{55} -4.48261i q^{57} +(-1.03438 - 0.597199i) q^{58} +(-2.88541 - 4.99768i) q^{59} +(2.08551 + 0.806615i) q^{60} +(-5.28822 + 9.15946i) q^{61} -3.48261i q^{62} -1.00000 q^{64} +(1.54295 + 9.90396i) q^{65} +(0.838505 + 1.45233i) q^{66} +(2.90467 - 1.67701i) q^{67} +(6.59150 + 3.80560i) q^{68} -0.482613 q^{69} +6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(-0.241306 - 0.417955i) q^{74} +(-3.36441 + 3.69874i) q^{75} -4.48261 q^{76} +4.48261i q^{78} +(2.25869 - 3.91217i) q^{79} +(0.806615 - 2.08551i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(10.4736 + 6.04691i) q^{82} -1.87141i q^{83} +(-13.2534 + 10.6770i) q^{85} +(1.00000 - 1.73205i) q^{86} +(1.03438 - 0.597199i) q^{87} +(1.45233 - 0.838505i) q^{88} +(1.67701 - 2.90467i) q^{89} +(-1.74131 + 1.40280i) q^{90} +0.482613i q^{92} +(3.01603 + 1.74131i) q^{93} +(5.72392 + 9.91412i) q^{94} +(3.61574 - 9.34856i) q^{95} +(0.500000 - 0.866025i) q^{96} -17.7708i q^{97} -1.67701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 12 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 - 12 * q^6 + 6 * q^9	\( 12 q + 6 q^{4} - 12 q^{6} + 6 q^{9} - 6 q^{11} - 6 q^{16} - 6 q^{19} - 6 q^{24} + 6 q^{26} - 48 q^{29} + 24 q^{34} + 12 q^{36} + 6 q^{39} + 36 q^{41} + 6 q^{44} - 18 q^{46} - 12 q^{51} - 6 q^{54} - 60 q^{55} + 24 q^{59} + 12 q^{61} - 12 q^{64} - 30 q^{65} + 6 q^{66} + 36 q^{69} + 72 q^{71} + 18 q^{74} - 12 q^{76} + 48 q^{79} - 6 q^{81} + 12 q^{86} + 12 q^{89} + 6 q^{94} + 6 q^{96} - 12 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 - 12 * q^6 + 6 * q^9 - 6 * q^11 - 6 * q^16 - 6 * q^19 - 6 * q^24 + 6 * q^26 - 48 * q^29 + 24 * q^34 + 12 * q^36 + 6 * q^39 + 36 * q^41 + 6 * q^44 - 18 * q^46 - 12 * q^51 - 6 * q^54 - 60 * q^55 + 24 * q^59 + 12 * q^61 - 12 * q^64 - 30 * q^65 + 6 * q^66 + 36 * q^69 + 72 * q^71 + 18 * q^74 - 12 * q^76 + 48 * q^79 - 6 * q^81 + 12 * q^86 + 12 * q^89 + 6 * q^94 + 6 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more