LMFDB - Embedded newform 1470.2.n.j.949.6

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			949.6
Root			$0.406761 - 0.406761i$ of defining polynomial
Character	$\chi$	$=$	1470.949
Dual form			1470.2.n.j.79.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.40280 - 1.74131i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.40280 - 1.74131i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.344208 - 2.20942i) q^{10} +(2.39213 - 4.14329i) q^{11} +(-0.866025 + 0.500000i) q^{12} -3.17103i q^{13} +(-2.08551 + 0.806615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.52625 + 2.61323i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.58551 + 2.74619i) q^{19} +(-0.806615 - 2.08551i) q^{20} -4.78426i q^{22} +(-6.21029 + 3.58551i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.06430 - 4.88541i) q^{25} +(-1.58551 - 2.74619i) q^{26} -1.00000i q^{27} -2.38677 q^{29} +(-1.40280 + 1.74131i) q^{30} +(2.08551 - 3.61222i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.14329 + 2.39213i) q^{33} +5.22646 q^{34} +1.00000 q^{36} +(6.21029 - 3.58551i) q^{37} +(2.74619 + 1.58551i) q^{38} +(-1.58551 + 2.74619i) q^{39} +(-1.74131 - 1.40280i) q^{40} +2.05543 q^{41} +2.00000i q^{43} +(-2.39213 - 4.14329i) q^{44} +(2.20942 + 0.344208i) q^{45} +(-3.58551 + 6.21029i) q^{46} +(-9.97063 + 5.75654i) q^{47} +1.00000i q^{48} +(-3.36441 - 3.69874i) q^{50} +(-2.61323 - 4.52625i) q^{51} +(-2.74619 - 1.58551i) q^{52} +(-7.02832 - 4.05780i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-3.85906 - 9.97764i) q^{55} -3.17103i q^{57} +(-2.06700 + 1.19339i) q^{58} +(5.36441 - 9.29144i) q^{59} +(-0.344208 + 2.20942i) q^{60} +(3.55780 + 6.16229i) q^{61} -4.17103i q^{62} -1.00000 q^{64} +(-5.52173 - 4.44833i) q^{65} +(-2.39213 + 4.14329i) q^{66} +(-8.28658 - 4.78426i) q^{67} +(4.52625 - 2.61323i) q^{68} +7.17103 q^{69} +6.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(3.58551 - 6.21029i) q^{74} +(-1.52100 + 4.76304i) q^{75} +3.17103 q^{76} +3.17103i q^{78} +(6.08551 + 10.5404i) q^{79} +(-2.20942 - 0.344208i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.78005 - 1.02771i) q^{82} -3.39749i q^{83} +(10.8999 - 4.21574i) q^{85} +(1.00000 + 1.73205i) q^{86} +(2.06700 + 1.19339i) q^{87} +(-4.14329 - 2.39213i) q^{88} +(-4.78426 - 8.28658i) q^{89} +(2.08551 - 0.806615i) q^{90} +7.17103i q^{92} +(-3.61222 + 2.08551i) q^{93} +(-5.75654 + 9.97063i) q^{94} +(7.00613 + 1.09150i) q^{95} +(0.500000 + 0.866025i) q^{96} +1.27117i q^{97} +4.78426 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 $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$5$	1.40280	−	1.74131i	0.627352	−	0.778736i
$5$	1.40280	−	1.74131i	0.627352	−	0.778736i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.344208	−	2.20942i	0.108848	−	0.698679i
$11$	2.39213	−	4.14329i	0.721254	−	1.24925i	−0.239243	−	0.970960i	$-0.576899\pi$
$11$	2.39213	−	4.14329i	0.721254	−	1.24925i	0.960497	−	0.278289i	$-0.0897674\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$		−	3.17103i		−	0.879485i	−0.898124	−	0.439743i	$-0.855070\pi$
$13$		−	3.17103i		−	0.879485i	0.898124	−	0.439743i	$-0.144930\pi$
$14$		0			0
$15$	−2.08551	+	0.806615i	−0.538478	+	0.208267i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.52625	+	2.61323i	1.09778	+	0.633801i	0.935636	−	0.352966i	$-0.114827\pi$
$17$	4.52625	+	2.61323i	1.09778	+	0.633801i	0.162140	+	0.986768i	$0.448160\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	1.58551	+	2.74619i	0.363742	+	0.630020i	0.988573	−	0.150740i	$-0.0481656\pi$
$19$	1.58551	+	2.74619i	0.363742	+	0.630020i	−0.624831	+	0.780760i	$0.714832\pi$
$20$	−0.806615	−	2.08551i	−0.180365	−	0.466335i
$21$		0			0
$22$		−	4.78426i		−	1.02001i
$23$	−6.21029	+	3.58551i	−1.29494	+	0.747632i	−0.979525	−	0.201324i	$-0.935476\pi$
$23$	−6.21029	+	3.58551i	−1.29494	+	0.747632i	−0.315411	+	0.948955i	$0.602142\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−1.06430	−	4.88541i	−0.212859	−	0.977083i
$26$	−1.58551	−	2.74619i	−0.310945	−	0.538573i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−2.38677			−0.443212			−0.221606	−	0.975136i	$-0.571130\pi$
$29$	−2.38677			−0.443212			−0.221606	+	0.975136i	$0.571130\pi$
$30$	−1.40280	+	1.74131i	−0.256115	+	0.317918i
$31$	2.08551	−	3.61222i	0.374570	−	0.648773i	−0.615693	−	0.787986i	$-0.711124\pi$
$31$	2.08551	−	3.61222i	0.374570	−	0.648773i	0.990263	+	0.139213i	$0.0444572\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.14329	+	2.39213i	−0.721254	+	0.416416i
$34$	5.22646			0.896330
$35$		0			0
$36$	1.00000			0.166667
$37$	6.21029	−	3.58551i	1.02097	−	0.589455i	0.106582	−	0.994304i	$-0.466009\pi$
$37$	6.21029	−	3.58551i	1.02097	−	0.589455i	0.914384	+	0.404849i	$0.132676\pi$
$38$	2.74619	+	1.58551i	0.445491	+	0.257204i
$39$	−1.58551	+	2.74619i	−0.253886	+	0.439743i
$40$	−1.74131	−	1.40280i	−0.275325	−	0.221802i
$41$	2.05543			0.321004			0.160502	−	0.987035i	$-0.448689\pi$
$41$	2.05543			0.321004			0.160502	+	0.987035i	$0.448689\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−2.39213	−	4.14329i	−0.360627	−	0.624625i
$45$	2.20942	+	0.344208i	0.329360	+	0.0513116i
$46$	−3.58551	+	6.21029i	−0.528655	+	0.915658i
$47$	−9.97063	+	5.75654i	−1.45437	+	0.839678i	−0.998725	−	0.0504854i	$-0.983923\pi$
$47$	−9.97063	+	5.75654i	−1.45437	+	0.839678i	−0.455641	+	0.890164i	$0.650590\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$	−3.36441	−	3.69874i	−0.475800	−	0.523081i
$51$	−2.61323	−	4.52625i	−0.365925	−	0.633801i
$52$	−2.74619	−	1.58551i	−0.380828	−	0.219871i
$53$	−7.02832	−	4.05780i	−0.965413	−	0.557382i	−0.0675785	−	0.997714i	$-0.521527\pi$
$53$	−7.02832	−	4.05780i	−0.965413	−	0.557382i	−0.897835	+	0.440332i	$0.854861\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−3.85906	−	9.97764i	−0.520355	−	1.34539i
$56$		0			0
$57$		−	3.17103i		−	0.420013i
$58$	−2.06700	+	1.19339i	−0.271411	+	0.156699i
$59$	5.36441	−	9.29144i	0.698387	−	1.20964i	−0.270638	−	0.962681i	$-0.587235\pi$
$59$	5.36441	−	9.29144i	0.698387	−	1.20964i	0.969025	−	0.246961i	$-0.0794320\pi$
$60$	−0.344208	+	2.20942i	−0.0444371	+	0.285234i
$61$	3.55780	+	6.16229i	0.455530	+	0.789000i	0.998718	−	0.0506101i	$-0.0161166\pi$
$61$	3.55780	+	6.16229i	0.455530	+	0.789000i	−0.543189	+	0.839611i	$0.682783\pi$
$62$		−	4.17103i		−	0.529721i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.52173	−	4.44833i	−0.684887	−	0.551747i
$66$	−2.39213	+	4.14329i	−0.294451	+	0.510004i
$67$	−8.28658	−	4.78426i	−1.01237	−	0.584490i	−0.100483	−	0.994939i	$-0.532039\pi$
$67$	−8.28658	−	4.78426i	−1.01237	−	0.584490i	−0.911884	+	0.410448i	$0.865372\pi$
$68$	4.52625	−	2.61323i	0.548888	−	0.316901i
$69$	7.17103			0.863291
$70$		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	0.283387	−	0.959006i	$-0.408542\pi$
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	−0.688830	+	0.724923i	$0.741875\pi$
$74$	3.58551	−	6.21029i	0.416808	−	0.721932i
$75$	−1.52100	+	4.76304i	−0.175630	+	0.549989i
$76$	3.17103			0.363742
$77$		0			0
$78$			3.17103i			0.359048i
$79$	6.08551	+	10.5404i	0.684674	+	1.18589i	0.973539	+	0.228520i	$0.0733887\pi$
$79$	6.08551	+	10.5404i	0.684674	+	1.18589i	−0.288865	+	0.957370i	$0.593278\pi$
$80$	−2.20942	−	0.344208i	−0.247020	−	0.0384837i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.78005	−	1.02771i	0.196574	−	0.113492i
$83$		−	3.39749i		−	0.372923i	−0.982462	−	0.186461i	$-0.940298\pi$
$83$		−	3.39749i		−	0.372923i	0.982462	−	0.186461i	$-0.0597019\pi$
$84$		0			0
$85$	10.8999	−	4.21574i	1.18226	−	0.457261i
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	2.06700	+	1.19339i	0.221606	+	0.127944i
$88$	−4.14329	−	2.39213i	−0.441676	−	0.255002i
$89$	−4.78426	−	8.28658i	−0.507131	−	0.878376i	−0.999966	−	0.00825326i	$-0.997373\pi$
$89$	−4.78426	−	8.28658i	−0.507131	−	0.878376i	0.492835	−	0.870123i	$-0.335960\pi$
$90$	2.08551	−	0.806615i	0.219833	−	0.0850247i
$91$		0			0
$92$			7.17103i			0.747632i
$93$	−3.61222	+	2.08551i	−0.374570	+	0.216258i
$94$	−5.75654	+	9.97063i	−0.593742	+	1.02839i
$95$	7.00613	+	1.09150i	0.718813	+	0.111985i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$			1.27117i			0.129068i	0.997916	+	0.0645339i	$0.0205561\pi$
$97$			1.27117i			0.129068i	−0.997916	+	0.0645339i	$0.979444\pi$
$98$		0			0
$99$	4.78426			0.480836
$100$	−4.76304	−	1.52100i	−0.476304	−	0.152100i
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	−0.993481	−	0.113998i	$-0.963634\pi$
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	0.595466	+	0.803380i	$0.296967\pi$
$102$	−4.52625	−	2.61323i	−0.448165	−	0.258748i
$103$	−9.72240	+	5.61323i	−0.957976	+	0.553088i	−0.895550	−	0.444962i	$-0.853217\pi$
$103$	−9.72240	+	5.61323i	−0.957976	+	0.553088i	−0.0624268	+	0.998050i	$0.519884\pi$
$104$	−3.17103			−0.310945
$105$		0			0
$106$	−8.11560			−0.788257
$107$	−1.21026	+	0.698745i	−0.117000	+	0.0675502i	−0.557358	−	0.830272i	$-0.688185\pi$
$107$	−1.21026	+	0.698745i	−0.117000	+	0.0675502i	0.440358	+	0.897822i	$0.354852\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	6.22646	−	10.7845i	0.596387	−	1.03297i	−0.396963	−	0.917835i	$-0.629936\pi$
$109$	6.22646	−	10.7845i	0.596387	−	1.03297i	0.993350	−	0.115137i	$-0.0367308\pi$
$110$	−8.33086	−	6.71137i	−0.794317	−	0.639904i
$111$	−7.17103			−0.680644
$112$		0			0
$113$		−	6.34206i		−	0.596611i	−0.954470	−	0.298305i	$-0.903579\pi$
$113$		−	6.34206i		−	0.596611i	0.954470	−	0.298305i	$-0.0964214\pi$
$114$	−1.58551	−	2.74619i	−0.148497	−	0.257204i
$115$	−2.46833	+	15.8438i	−0.230173	+	1.47744i
$116$	−1.19339	+	2.06700i	−0.110803	+	0.191916i
$117$	2.74619	−	1.58551i	0.253886	−	0.146581i
$118$		−	10.7288i		−	0.987669i
$119$		0			0
$120$	0.806615	+	2.08551i	0.0736335	+	0.190381i
$121$	−5.94457	−	10.2963i	−0.540415	−	0.936027i
$122$	6.16229	+	3.55780i	0.557908	+	0.322108i
$123$	−1.78005	−	1.02771i	−0.160502	−	0.0926659i
$124$	−2.08551	−	3.61222i	−0.187285	−	0.324387i
$125$	−10.0000	−	5.00000i	−0.894427	−	0.447214i
$126$		0			0
$127$			18.0107i			1.59819i	0.601203	+	0.799096i	$0.294688\pi$
$127$			18.0107i			1.59819i	−0.601203	+	0.799096i	$0.705312\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	−7.00613	−	1.09150i	−0.614478	−	0.0957305i
$131$	−2.77890	−	4.81320i	−0.242794	−	0.420531i	0.718715	−	0.695304i	$-0.244730\pi$
$131$	−2.77890	−	4.81320i	−0.242794	−	0.420531i	−0.961509	+	0.274774i	$0.911397\pi$
$132$			4.78426i			0.416416i
$133$		0			0
$134$	−9.56852			−0.826594
$135$	−1.74131	−	1.40280i	−0.149868	−	0.120734i
$136$	2.61323	−	4.52625i	0.224083	−	0.388122i
$137$	12.8128	+	7.39749i	1.09467	+	0.632010i	0.934817	−	0.355130i	$-0.115563\pi$
$137$	12.8128	+	7.39749i	1.09467	+	0.632010i	0.159857	+	0.987140i	$0.448897\pi$
$138$	6.21029	−	3.58551i	0.528655	−	0.305219i
$139$	3.65794			0.310262			0.155131	−	0.987894i	$-0.450420\pi$
$139$	3.65794			0.310262			0.155131	+	0.987894i	$0.450420\pi$
$140$		0			0
$141$	11.5131			0.969577
$142$	5.19615	−	3.00000i	0.436051	−	0.251754i
$143$	−13.1385	−	7.58551i	−1.09870	−	0.634333i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−3.34816	+	4.15610i	−0.278050	+	0.345145i
$146$	−4.00000			−0.331042
$147$		0			0
$148$		−	7.17103i		−	0.589455i
$149$	11.1710	+	19.3488i	0.915166	+	1.58511i	0.806657	+	0.591019i	$0.201274\pi$
$149$	11.1710	+	19.3488i	0.915166	+	1.58511i	0.108509	+	0.994095i	$0.465392\pi$
$150$	1.06430	+	4.88541i	0.0868994	+	0.398892i
$151$	−8.25654	+	14.3008i	−0.671908	+	1.16378i	0.305454	+	0.952207i	$0.401192\pi$
$151$	−8.25654	+	14.3008i	−0.671908	+	1.16378i	−0.977362	+	0.211572i	$0.932142\pi$
$152$	2.74619	−	1.58551i	0.222746	−	0.128602i
$153$			5.22646i			0.422534i
$154$		0			0
$155$	−3.36441	−	8.69874i	−0.270236	−	0.698700i
$156$	1.58551	+	2.74619i	0.126943	+	0.219871i
$157$	8.61225	+	4.97229i	0.687332	+	0.396832i	0.802612	−	0.596502i	$-0.203443\pi$
$157$	8.61225	+	4.97229i	0.687332	+	0.396832i	−0.115280	+	0.993333i	$0.536776\pi$
$158$	10.5404	+	6.08551i	0.838551	+	0.484138i
$159$	4.05780	+	7.02832i	0.321804	+	0.557382i
$160$	−2.08551	+	0.806615i	−0.164874	+	0.0637685i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	−2.49796	+	1.44220i	−0.195656	+	0.112962i	−0.594627	−	0.804001i	$-0.702700\pi$
$163$	−2.49796	+	1.44220i	−0.195656	+	0.112962i	0.398972	+	0.916963i	$0.369367\pi$
$164$	1.02771	−	1.78005i	0.0802511	−	0.138999i
$165$	−1.64678	+	10.5704i	−0.128202	+	0.822906i
$166$	−1.69874	−	2.94231i	−0.131848	−	0.228368i
$167$		−	4.05543i		−	0.313819i	−0.987613	−	0.156909i	$-0.949847\pi$
$167$		−	4.05543i		−	0.313819i	0.987613	−	0.156909i	$-0.0501530\pi$
$168$		0			0
$169$	2.94457			0.226505
$170$	7.33169	−	9.10087i	0.562315	−	0.698005i
$171$	−1.58551	+	2.74619i	−0.121247	+	0.210007i
$172$	1.73205	+	1.00000i	0.132068	+	0.0762493i
$173$	5.54039	−	3.19874i	0.421228	−	0.243196i	−0.274375	−	0.961623i	$-0.588471\pi$
$173$	5.54039	−	3.19874i	0.421228	−	0.243196i	0.695603	+	0.718427i	$0.255137\pi$
$174$	2.38677			0.180941
$175$		0			0
$176$	−4.78426			−0.360627
$177$	−9.29144	+	5.36441i	−0.698387	+	0.403214i
$178$	−8.28658	−	4.78426i	−0.621105	−	0.358595i
$179$	9.75654	−	16.8988i	0.729238	−	1.26308i	−0.227967	−	0.973669i	$-0.573208\pi$
$179$	9.75654	−	16.8988i	0.729238	−	1.26308i	0.957206	−	0.289409i	$-0.0934588\pi$
$180$	1.40280	−	1.74131i	0.104559	−	0.129789i
$181$	23.0262			1.71152			0.855761	−	0.517371i	$-0.173089\pi$
$181$	23.0262			1.71152			0.855761	+	0.517371i	$0.173089\pi$
$182$		0			0
$183$		−	7.11560i		−	0.526000i
$184$	3.58551	+	6.21029i	0.264328	+	0.457829i
$185$	2.46833	−	15.8438i	0.181475	−	1.16486i
$186$	−2.08551	+	3.61222i	−0.152917	+	0.264861i
$187$	21.6547	−	12.5024i	1.58355	−	0.914264i
$188$			11.5131i			0.839678i
$189$		0			0
$190$	6.61323	−	2.55780i	0.479774	−	0.185562i
$191$	5.11560	+	8.86048i	0.370152	+	0.641122i	0.989589	−	0.143925i	$-0.0459723\pi$
$191$	5.11560	+	8.86048i	0.370152	+	0.641122i	−0.619437	+	0.785047i	$0.712639\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−10.0574	−	5.80661i	−0.723944	−	0.417969i	0.0922586	−	0.995735i	$-0.470591\pi$
$193$	−10.0574	−	5.80661i	−0.723944	−	0.417969i	−0.816203	+	0.577766i	$0.803925\pi$
$194$	0.635585	+	1.10087i	0.0456324	+	0.0790376i
$195$	2.55780	+	6.61323i	0.183168	+	0.473583i
$196$		0			0
$197$		−	2.39749i		−	0.170814i	−0.996346	−	0.0854070i	$-0.972781\pi$
$197$		−	2.39749i		−	0.170814i	0.996346	−	0.0854070i	$-0.0272191\pi$
$198$	4.14329	−	2.39213i	0.294451	−	0.170001i
$199$	9.17103	−	15.8847i	0.650117	−	1.12604i	−0.332977	−	0.942935i	$-0.608053\pi$
$199$	9.17103	−	15.8847i	0.650117	−	1.12604i	0.983094	−	0.183101i	$-0.0586135\pi$
$200$	−4.88541	+	1.06430i	−0.345451	+	0.0752571i
$201$	4.78426	+	8.28658i	0.337456	+	0.584490i
$202$			8.00000i			0.562878i
$203$		0			0
$204$	−5.22646			−0.365925
$205$	2.88336	−	3.57913i	0.201383	−	0.249978i
$206$	−5.61323	+	9.72240i	−0.391092	+	0.677392i
$207$	−6.21029	−	3.58551i	−0.431645	−	0.249211i
$208$	−2.74619	+	1.58551i	−0.190414	+	0.109936i
$209$	15.1710			1.04940
$210$		0			0
$211$	−2.82897			−0.194754			−0.0973772	−	0.995248i	$-0.531045\pi$
$211$	−2.82897			−0.194754			−0.0973772	+	0.995248i	$0.531045\pi$
$212$	−7.02832	+	4.05780i	−0.482707	+	0.278691i
$213$	−5.19615	−	3.00000i	−0.356034	−	0.205557i
$214$	−0.698745	+	1.21026i	−0.0477652	+	0.0827318i
$215$	3.48261	+	2.80560i	0.237512	+	0.191341i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$		−	12.4529i		−	0.843418i
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$	−10.5704	−	1.64678i	−0.712658	−	0.111026i
$221$	8.28663	−	14.3529i	0.557419	−	0.965478i
$222$	−6.21029	+	3.58551i	−0.416808	+	0.240644i
$223$			14.2973i			0.957421i	0.877973	+	0.478711i	$0.158896\pi$
$223$			14.2973i			0.957421i	−0.877973	+	0.478711i	$0.841104\pi$
$224$		0			0
$225$	3.69874	−	3.36441i	0.246583	−	0.224294i
$226$	−3.17103	−	5.49238i	−0.210934	−	0.365348i
$227$	9.57428	+	5.52771i	0.635467	+	0.366887i	0.782866	−	0.622190i	$-0.213757\pi$
$227$	9.57428	+	5.52771i	0.635467	+	0.366887i	−0.147399	+	0.989077i	$0.547090\pi$
$228$	−2.74619	−	1.58551i	−0.181871	−	0.105003i
$229$	9.22646	+	15.9807i	0.609702	+	1.05603i	0.991289	+	0.131702i	$0.0420441\pi$
$229$	9.22646	+	15.9807i	0.609702	+	1.05603i	−0.381588	+	0.924333i	$0.624623\pi$
$230$	5.78426	+	14.9553i	0.381403	+	0.986123i
$231$		0			0
$232$			2.38677i			0.156699i
$233$	7.89434	−	4.55780i	0.517175	−	0.298591i	−0.218603	−	0.975814i	$-0.570150\pi$
$233$	7.89434	−	4.55780i	0.517175	−	0.298591i	0.735778	+	0.677223i	$0.236817\pi$
$234$	1.58551	−	2.74619i	0.103648	−	0.179524i
$235$	−3.96290	+	25.4372i	−0.258511	+	1.65934i
$236$	−5.36441	−	9.29144i	−0.349194	−	0.604821i
$237$		−	12.1710i		−	0.790593i
$238$		0			0
$239$	−13.1156			−0.848378			−0.424189	−	0.905574i	$-0.639441\pi$
$239$	−13.1156			−0.848378			−0.424189	+	0.905574i	$0.639441\pi$
$240$	1.74131	+	1.40280i	0.112401	+	0.0905504i
$241$	−2.67103	+	4.62636i	−0.172056	+	0.298010i	−0.939139	−	0.343539i	$-0.888374\pi$
$241$	−2.67103	+	4.62636i	−0.172056	+	0.298010i	0.767082	+	0.641549i	$0.221708\pi$
$242$	−10.2963	−	5.94457i	−0.661871	−	0.382131i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	7.11560			0.455530
$245$		0			0
$246$	−2.05543			−0.131049
$247$	8.70826	−	5.02771i	0.554093	−	0.319906i
$248$	−3.61222	−	2.08551i	−0.229376	−	0.132430i
$249$	−1.69874	+	2.94231i	−0.107654	+	0.186461i
$250$	−11.1603	+	0.669873i	−0.705836	+	0.0423665i
$251$	−27.9213			−1.76238			−0.881188	−	0.472765i	$-0.843256\pi$
$251$	−27.9213			−1.76238			−0.881188	+	0.472765i	$0.843256\pi$
$252$		0			0
$253$			34.3081i			2.15693i
$254$	9.00536	+	15.5977i	0.565047	+	0.978689i
$255$	−11.5474	−	1.79899i	−0.723128	−	0.112657i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	18.3052	−	10.5685i	1.14185	−	0.659246i	0.194960	−	0.980811i	$-0.437542\pi$
$257$	18.3052	−	10.5685i	1.14185	−	0.659246i	0.946887	+	0.321565i	$0.104209\pi$
$258$		−	2.00000i		−	0.124515i
$259$		0			0
$260$	−6.61323	+	2.55780i	−0.410135	+	0.158628i
$261$	−1.19339	−	2.06700i	−0.0738687	−	0.127944i
$262$	−4.81320	−	2.77890i	−0.297360	−	0.171681i
$263$	10.3149	+	5.95529i	0.636042	+	0.367219i	0.783088	−	0.621911i	$-0.213643\pi$
$263$	10.3149	+	5.95529i	0.636042	+	0.367219i	−0.147046	+	0.989130i	$0.546977\pi$
$264$	2.39213	+	4.14329i	0.147225	+	0.255002i
$265$	−16.9252	+	6.54616i	−1.03971	+	0.402128i
$266$		0			0
$267$			9.56852i			0.585584i
$268$	−8.28658	+	4.78426i	−0.506183	+	0.292245i
$269$	1.63559	−	2.83292i	0.0997234	−	0.172726i	−0.811847	−	0.583871i	$-0.801538\pi$
$269$	1.63559	−	2.83292i	0.0997234	−	0.172726i	0.911570	+	0.411145i	$0.134871\pi$
$270$	−2.20942	−	0.344208i	−0.134461	−	0.0209479i
$271$	0.311975	+	0.540356i	0.0189511	+	0.0328243i	0.875345	−	0.483498i	$-0.160634\pi$
$271$	0.311975	+	0.540356i	0.0189511	+	0.0328243i	−0.856394	+	0.516322i	$0.827301\pi$
$272$		−	5.22646i		−	0.316901i
$273$		0			0
$274$	14.7950			0.893797
$275$	−22.7876	−	7.27686i	−1.37415	−	0.438811i
$276$	3.58551	−	6.21029i	0.215823	−	0.373816i
$277$	24.9372	+	14.3975i	1.49833	+	0.865061i	0.999998	−	0.00192499i	$-0.000612744\pi$
$277$	24.9372	+	14.3975i	1.49833	+	0.865061i	0.498332	+	0.866986i	$0.333946\pi$
$278$	3.16787	−	1.82897i	0.189996	−	0.109694i
$279$	4.17103			0.249713
$280$		0			0
$281$	2.82897			0.168762			0.0843811	−	0.996434i	$-0.473109\pi$
$281$	2.82897			0.168762			0.0843811	+	0.996434i	$0.473109\pi$
$282$	9.97063	−	5.75654i	0.593742	−	0.342797i
$283$	21.7693	+	12.5685i	1.29405	+	0.747121i	0.979370	−	0.202076i	$-0.0647689\pi$
$283$	21.7693	+	12.5685i	1.29405	+	0.747121i	0.314682	+	0.949197i	$0.398102\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	−5.52173	−	4.44833i	−0.327079	−	0.263496i
$286$	−15.1710			−0.897082
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	5.15794	+	8.93381i	0.303408	+	0.525519i
$290$	−0.821546	+	5.27337i	−0.0482429	+	0.309663i
$291$	0.635585	−	1.10087i	0.0372587	−	0.0645339i
$292$	−3.46410	+	2.00000i	−0.202721	+	0.117041i
$293$			10.2265i			0.597436i	0.954341	+	0.298718i	$0.0965590\pi$
$293$			10.2265i			0.597436i	−0.954341	+	0.298718i	$0.903441\pi$
$294$		0			0
$295$	−8.65403	−	22.3751i	−0.503857	−	1.30273i
$296$	−3.58551	−	6.21029i	−0.208404	−	0.360966i
$297$	−4.14329	−	2.39213i	−0.240418	−	0.138805i
$298$	19.3488	+	11.1710i	1.12085	+	0.647120i
$299$	11.3698	+	19.6930i	0.657531	+	1.13888i
$300$	3.36441	+	3.69874i	0.194245	+	0.213547i
$301$		0			0
$302$			16.5131i			0.950222i
$303$	6.92820	−	4.00000i	0.398015	−	0.229794i
$304$	1.58551	−	2.74619i	0.0909355	−	0.157505i
$305$	15.7213	+	2.44925i	0.900200	+	0.140244i
$306$	2.61323	+	4.52625i	0.149388	+	0.258748i
$307$			23.4577i			1.33880i	0.742902	+	0.669400i	$0.233449\pi$
$307$			23.4577i			1.33880i	−0.742902	+	0.669400i	$0.766551\pi$
$308$		0			0
$309$	11.2265			0.638651
$310$	−7.26304	−	5.85113i	−0.412513	−	0.332322i
$311$	−2.82897	+	4.89992i	−0.160416	+	0.277849i	−0.935018	−	0.354600i	$-0.884617\pi$
$311$	−2.82897	+	4.89992i	−0.160416	+	0.277849i	0.774602	+	0.632449i	$0.217950\pi$
$312$	2.74619	+	1.58551i	0.155473	+	0.0897621i
$313$	−14.1914	+	8.19339i	−0.802143	+	0.463118i	−0.844220	−	0.535997i	$-0.819936\pi$
$313$	−14.1914	+	8.19339i	−0.802143	+	0.463118i	0.0420769	+	0.999114i	$0.486603\pi$
$314$	9.94457			0.561205
$315$		0			0
$316$	12.1710			0.684674
$317$	3.90845	−	2.25654i	0.219520	−	0.126740i	−0.386208	−	0.922412i	$-0.626215\pi$
$317$	3.90845	−	2.25654i	0.219520	−	0.126740i	0.605728	+	0.795672i	$0.292882\pi$
$318$	7.02832	+	4.05780i	0.394128	+	0.227550i
$319$	−5.70946	+	9.88908i	−0.319669	+	0.553682i
$320$	−1.40280	+	1.74131i	−0.0784190	+	0.0973420i
$321$	1.39749			0.0780003
$322$		0			0
$323$			16.5733i			0.922161i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−15.4918	+	3.37492i	−0.859330	+	0.187207i
$326$	−1.44220	+	2.49796i	−0.0798761	+	0.138349i
$327$	−10.7845	+	6.22646i	−0.596387	+	0.344324i
$328$		−	2.05543i		−	0.113492i
$329$		0			0
$330$	3.85906	+	9.97764i	0.212434	+	0.549251i
$331$	6.54080	+	11.3290i	0.359515	+	0.622698i	0.987880	−	0.155220i	$-0.0496088\pi$
$331$	6.54080	+	11.3290i	0.359515	+	0.622698i	−0.628365	+	0.777919i	$0.716275\pi$
$332$	−2.94231	−	1.69874i	−0.161480	−	0.0932307i
$333$	6.21029	+	3.58551i	0.340322	+	0.196485i
$334$	−2.02771	−	3.51211i	−0.110952	−	0.192174i
$335$	−19.9553	+	7.71811i	−1.09027	+	0.421685i
$336$		0			0
$337$			20.2973i			1.10567i	0.833292	+	0.552834i	$0.186453\pi$
$337$			20.2973i			1.10567i	−0.833292	+	0.552834i	$0.813547\pi$
$338$	2.55007	−	1.47229i	0.138706	−	0.0800817i
$339$	−3.17103	+	5.49238i	−0.172227	+	0.298305i
$340$	1.79899	−	11.5474i	0.0975640	−	0.626247i
$341$	−9.97764	−	17.2818i	−0.540320	−	0.935861i
$342$			3.17103i			0.171470i
$343$		0			0
$344$	2.00000			0.107833
$345$	10.0595	−	12.4870i	0.541587	−	0.672275i
$346$	3.19874	−	5.54039i	0.171966	−	0.297853i
$347$	−12.5166	−	7.22646i	−0.671926	−	0.387937i	0.124880	−	0.992172i	$-0.460145\pi$
$347$	−12.5166	−	7.22646i	−0.671926	−	0.387937i	−0.796806	+	0.604235i	$0.793479\pi$
$348$	2.06700	−	1.19339i	0.110803	−	0.0639722i
$349$	13.8891			0.743469			0.371734	−	0.928339i	$-0.378763\pi$
$349$	13.8891			0.743469			0.371734	+	0.928339i	$0.378763\pi$
$350$		0			0
$351$	−3.17103			−0.169257
$352$	−4.14329	+	2.39213i	−0.220838	+	0.127501i
$353$	5.58839	+	3.22646i	0.297440	+	0.171727i	0.641292	−	0.767297i	$-0.278399\pi$
$353$	5.58839	+	3.22646i	0.297440	+	0.171727i	−0.343852	+	0.939024i	$0.611732\pi$
$354$	−5.36441	+	9.29144i	−0.285115	+	0.493834i
$355$	8.41681	−	10.4478i	0.446718	−	0.554514i
$356$	−9.56852			−0.507131
$357$		0			0
$358$		−	19.5131i		−	1.03130i
$359$	3.61323	+	6.25830i	0.190699	+	0.330300i	0.945482	−	0.325674i	$-0.105591\pi$
$359$	3.61323	+	6.25830i	0.190699	+	0.330300i	−0.754783	+	0.655974i	$0.772258\pi$
$360$	0.344208	−	2.20942i	0.0181414	−	0.116446i
$361$	4.47229	−	7.74622i	0.235383	−	0.407696i
$362$	19.9413	−	11.5131i	1.04809	−	0.605115i
$363$			11.8891i			0.624018i
$364$		0			0
$365$	−8.34206	+	3.22646i	−0.436643	+	0.168881i
$366$	−3.55780	−	6.16229i	−0.185969	−	0.322108i
$367$	−1.81878	−	1.05007i	−0.0949393	−	0.0548132i	0.451779	−	0.892130i	$-0.350790\pi$
$367$	−1.81878	−	1.05007i	−0.0949393	−	0.0548132i	−0.546718	+	0.837317i	$0.684123\pi$
$368$	6.21029	+	3.58551i	0.323734	+	0.186908i
$369$	1.02771	+	1.78005i	0.0535007	+	0.0926659i
$370$	−5.78426	−	14.9553i	−0.300709	−	0.777488i
$371$		0			0
$372$			4.17103i			0.216258i
$373$	20.1333	−	11.6239i	1.04246	−	0.601865i	0.121932	−	0.992538i	$-0.461091\pi$
$373$	20.1333	−	11.6239i	1.04246	−	0.601865i	0.920529	+	0.390673i	$0.127758\pi$
$374$	12.5024	−	21.6547i	0.646482	−	1.11974i
$375$	6.16025	+	9.33013i	0.318114	+	0.481806i
$376$	5.75654	+	9.97063i	0.296871	+	0.514196i
$377$			7.56852i			0.389799i
$378$		0			0
$379$	−2.16629			−0.111275			−0.0556374	−	0.998451i	$-0.517719\pi$
$379$	−2.16629			−0.111275			−0.0556374	+	0.998451i	$0.517719\pi$
$380$	4.44833	−	5.52173i	0.228194	−	0.283259i
$381$	9.00536	−	15.5977i	0.461359	−	0.799096i
$382$	8.86048	+	5.11560i	0.453342	+	0.261737i
$383$	−6.97621	+	4.02771i	−0.356468	+	0.205807i	−0.667530	−	0.744583i	$-0.732648\pi$
$383$	−6.97621	+	4.02771i	−0.356468	+	0.205807i	0.311063	+	0.950389i	$0.399315\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−11.6132			−0.591098
$387$	−1.73205	+	1.00000i	−0.0880451	+	0.0508329i
$388$	1.10087	+	0.635585i	0.0558880	+	0.0322669i
$389$	5.94457	−	10.2963i	0.301402	−	0.522043i	−0.675052	−	0.737770i	$-0.735879\pi$
$389$	5.94457	−	10.2963i	0.301402	−	0.522043i	0.976454	+	0.215727i	$0.0692122\pi$
$390$	5.52173	+	4.44833i	0.279604	+	0.225250i
$391$	−37.4791			−1.89540
$392$		0			0
$393$			5.55780i			0.280354i
$394$	−1.19874	−	2.07629i	−0.0603919	−	0.104602i
$395$	26.8909	+	4.18937i	1.35303	+	0.210790i
$396$	2.39213	−	4.14329i	0.120209	−	0.208208i
$397$	13.9524	−	8.05543i	0.700252	−	0.404290i	−0.107190	−	0.994239i	$-0.534185\pi$
$397$	13.9524	−	8.05543i	0.700252	−	0.404290i	0.807441	+	0.589948i	$0.200852\pi$
$398$		−	18.3421i		−	0.919404i
$399$		0			0
$400$	−3.69874	+	3.36441i	−0.184937	+	0.168221i
$401$	−12.4854	−	21.6253i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$401$	−12.4854	−	21.6253i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$402$	8.28658	+	4.78426i	0.413297	+	0.238617i
$403$	−11.4545	−	6.61323i	−0.570587	−	0.329428i
$404$	4.00000	+	6.92820i	0.199007	+	0.344691i
$405$	0.806615	+	2.08551i	0.0400810	+	0.103630i
$406$		0			0
$407$		−	34.3081i		−	1.70059i
$408$	−4.52625	+	2.61323i	−0.224083	+	0.129374i
$409$	−1.52771	+	2.64608i	−0.0755406	+	0.130840i	−0.901321	−	0.433151i	$-0.857402\pi$
$409$	−1.52771	+	2.64608i	−0.0755406	+	0.130840i	0.825781	+	0.563991i	$0.190735\pi$
$410$	0.707496	−	4.54130i	0.0349408	−	0.224279i
$411$	−7.39749	−	12.8128i	−0.364891	−	0.632010i
$412$			11.2265i			0.553088i
$413$		0			0
$414$	−7.17103			−0.352437
$415$	−5.91607	−	4.76600i	−0.290408	−	0.233954i
$416$	−1.58551	+	2.74619i	−0.0777363	+	0.134643i
$417$	−3.16787	−	1.82897i	−0.155131	−	0.0895651i
$418$	13.1385	−	7.58551i	0.642625	−	0.371020i
$419$	−20.1972			−0.986698			−0.493349	−	0.869831i	$-0.664227\pi$
$419$	−20.1972			−0.986698			−0.493349	+	0.869831i	$0.664227\pi$
$420$		0			0
$421$	−30.3635			−1.47983			−0.739913	−	0.672702i	$-0.765133\pi$
$421$	−30.3635			−1.47983			−0.739913	+	0.672702i	$0.765133\pi$
$422$	−2.44996	+	1.41449i	−0.119262	+	0.0688561i
$423$	−9.97063	−	5.75654i	−0.484789	−	0.279893i
$424$	−4.05780	+	7.02832i	−0.197064	+	0.341325i
$425$	7.94944	−	24.8938i	0.385605	−	1.20753i
$426$	−6.00000			−0.290701
$427$		0			0
$428$			1.39749i			0.0675502i
$429$	7.58551	+	13.1385i	0.366232	+	0.634333i
$430$	4.41883	+	0.688417i	0.213095	+	0.0331984i
$431$	−12.2866	+	21.2811i	−0.591826	+	1.02507i	0.402160	+	0.915569i	$0.368259\pi$
$431$	−12.2866	+	21.2811i	−0.591826	+	1.02507i	−0.993986	+	0.109504i	$0.965074\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$			4.68412i			0.225104i	0.993646	+	0.112552i	$0.0359026\pi$
$433$			4.68412i			0.225104i	−0.993646	+	0.112552i	$0.964097\pi$
$434$		0			0
$435$	4.97764	−	1.92520i	0.238660	−	0.0923065i
$436$	−6.22646	−	10.7845i	−0.298193	−	0.516486i
$437$	−19.6930	−	11.3698i	−0.942045	−	0.543890i
$438$	3.46410	+	2.00000i	0.165521	+	0.0955637i
$439$	15.2565	+	26.4251i	0.728155	+	1.26120i	0.957662	+	0.287895i	$0.0929553\pi$
$439$	15.2565	+	26.4251i	0.728155	+	1.26120i	−0.229507	+	0.973307i	$0.573711\pi$
$440$	−9.97764	+	3.85906i	−0.475666	+	0.183973i
$441$		0			0
$442$		−	16.5733i		−	0.788310i
$443$	8.23447	−	4.75417i	0.391232	−	0.225878i	−0.291462	−	0.956582i	$-0.594142\pi$
$443$	8.23447	−	4.75417i	0.391232	−	0.225878i	0.682694	+	0.730705i	$0.260808\pi$
$444$	−3.58551	+	6.21029i	−0.170161	+	0.294728i
$445$	−21.1408	−	3.29357i	−1.00217	−	0.156130i
$446$	7.14867	+	12.3819i	0.338500	+	0.586298i
$447$		−	22.3421i		−	1.05674i
$448$		0			0
$449$	−17.6239			−0.831726			−0.415863	−	0.909427i	$-0.636520\pi$
$449$	−17.6239			−0.831726			−0.415863	+	0.909427i	$0.636520\pi$
$450$	1.52100	−	4.76304i	0.0717006	−	0.224532i
$451$	4.91686	−	8.51624i	0.231526	−	0.401014i
$452$	−5.49238	−	3.17103i	−0.258340	−	0.149153i
$453$	14.3008	−	8.25654i	0.671908	−	0.387926i
$454$	11.0554			0.518857
$455$		0			0
$456$	−3.17103			−0.148497
$457$	0.334953	−	0.193385i	0.0156684	−	0.00904617i	−0.492145	−	0.870513i	$-0.663787\pi$
$457$	0.334953	−	0.193385i	0.0156684	−	0.00904617i	0.507814	+	0.861467i	$0.330454\pi$
$458$	15.9807	+	9.22646i	0.746729	+	0.431124i
$459$	2.61323	−	4.52625i	0.121975	−	0.211267i
$460$	12.4870	+	10.0595i	0.582208	+	0.469028i
$461$	37.3682			1.74041			0.870206	−	0.492688i	$-0.163986\pi$
$461$	37.3682			1.74041			0.870206	+	0.492688i	$0.163986\pi$
$462$		0			0
$463$		−	24.3081i		−	1.12969i	−0.825196	−	0.564846i	$-0.808936\pi$
$463$		−	24.3081i		−	1.12969i	0.825196	−	0.564846i	$-0.191064\pi$
$464$	1.19339	+	2.06700i	0.0554015	+	0.0959582i
$465$	−1.43570	+	9.21554i	−0.0665792	+	0.427360i
$466$	4.55780	−	7.89434i	0.211136	−	0.365698i
$467$	−24.7452	+	14.2866i	−1.14507	+	0.661106i	−0.947681	−	0.319219i	$-0.896579\pi$
$467$	−24.7452	+	14.2866i	−1.14507	+	0.661106i	−0.197389	+	0.980325i	$0.563246\pi$
$468$		−	3.17103i		−	0.146581i
$469$		0			0
$470$	9.28663	+	24.0107i	0.428360	+	1.10753i
$471$	−4.97229	−	8.61225i	−0.229111	−	0.396832i
$472$	−9.29144	−	5.36441i	−0.427673	−	0.246917i
$473$	8.28658	+	4.78426i	0.381017	+	0.219980i
$474$	−6.08551	−	10.5404i	−0.279517	−	0.484138i
$475$	11.7288	−	10.6687i	0.538156	−	0.489512i
$476$		0			0
$477$		−	8.11560i		−	0.371588i
$478$	−11.3584	+	6.55780i	−0.519523	+	0.299947i
$479$	4.28189	−	7.41645i	0.195645	−	0.338866i	−0.751467	−	0.659771i	$-0.770653\pi$
$479$	4.28189	−	7.41645i	0.195645	−	0.338866i	0.947112	+	0.320904i	$0.103987\pi$
$480$	2.20942	+	0.344208i	0.100846	+	0.0157109i
$481$	−11.3698	−	19.6930i	−0.518417	−	0.897925i
$482$			5.34206i			0.243324i
$483$		0			0
$484$	−11.8891			−0.540415
$485$	2.21350	+	1.78320i	0.100510	+	0.0809709i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	27.5781	+	15.9222i	1.24968	+	0.721504i	0.971046	−	0.238892i	$-0.0767843\pi$
$487$	27.5781	+	15.9222i	1.24968	+	0.721504i	0.278636	+	0.960397i	$0.410118\pi$
$488$	6.16229	−	3.55780i	0.278954	−	0.161054i
$489$	2.88440			0.130437
$490$		0			0
$491$	4.49763			0.202975			0.101488	−	0.994837i	$-0.467640\pi$
$491$	4.49763			0.202975			0.101488	+	0.994837i	$0.467640\pi$
$492$	−1.78005	+	1.02771i	−0.0802511	+	0.0463330i
$493$	−10.8031	−	6.23718i	−0.486548	−	0.280908i
$494$	5.02771	−	8.70826i	0.226208	−	0.391803i
$495$	6.71137	−	8.33086i	0.301653	−	0.374444i
$496$	−4.17103			−0.187285
$497$		0			0
$498$			3.39749i			0.152245i
$499$	−0.171030	−	0.296232i	−0.00765634	−	0.0132612i	0.862172	−	0.506616i	$-0.169104\pi$
$499$	−0.171030	−	0.296232i	−0.00765634	−	0.0132612i	−0.869828	+	0.493355i	$0.835770\pi$
$500$	−9.33013	+	6.16025i	−0.417256	+	0.275495i
$501$	−2.02771	+	3.51211i	−0.0905916	+	0.156909i
$502$	−24.1806	+	13.9606i	−1.07923	+	0.623094i
$503$		−	7.56852i		−	0.337464i	−0.985662	−	0.168732i	$-0.946033\pi$
$503$		−	7.56852i		−	0.337464i	0.985662	−	0.168732i	$-0.0539672\pi$
$504$		0			0
$505$	6.45292	+	16.6841i	0.287151	+	0.742434i
$506$	17.1540	+	29.7117i	0.762590	+	1.32084i
$507$	−2.55007	−	1.47229i	−0.113253	−	0.0653865i
$508$	15.5977	+	9.00536i	0.692038	+	0.399548i
$509$	−15.4800	−	26.8122i	−0.686140	−	1.18843i	−0.973077	−	0.230479i	$-0.925971\pi$
$509$	−15.4800	−	26.8122i	−0.686140	−	1.18843i	0.286938	−	0.957949i	$-0.407363\pi$
$510$	−10.8999	+	4.21574i	−0.482654	+	0.186676i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	2.74619	−	1.58551i	0.121247	−	0.0700022i
$514$	10.5685	−	18.3052i	0.466157	−	0.807408i
$515$	−3.86424	+	24.8039i	−0.170279	+	1.09299i
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$			55.0816i			2.42249i
$518$		0			0
$519$	−6.39749			−0.280819
$520$	−4.44833	+	5.52173i	−0.195072	+	0.242144i
$521$	2.42520	−	4.20058i	0.106250	−	0.184031i	−0.807998	−	0.589185i	$-0.799449\pi$
$521$	2.42520	−	4.20058i	0.106250	−	0.184031i	0.914248	+	0.405154i	$0.132782\pi$
$522$	−2.06700	−	1.19339i	−0.0904703	−	0.0522330i
$523$	3.68289	−	2.12632i	0.161042	−	0.0929774i	−0.417313	−	0.908763i	$-0.637028\pi$
$523$	3.68289	−	2.12632i	0.161042	−	0.0929774i	0.578355	+	0.815785i	$0.303695\pi$
$524$	−5.55780			−0.242794
$525$		0			0
$526$	11.9106			0.519326
$527$	18.8791	−	10.8999i	0.822387	−	0.474805i
$528$	4.14329	+	2.39213i	0.180314	+	0.104104i
$529$	14.2118	−	24.6156i	0.617906	−	1.07024i
$530$	−11.3846	+	14.1317i	−0.494514	+	0.613844i
$531$	10.7288			0.465592
$532$		0			0
$533$		−	6.51783i		−	0.282319i
$534$	4.78426	+	8.28658i	0.207035	+	0.358595i
$535$	−0.481028	+	3.08764i	−0.0207966	+	0.133490i
$536$	−4.78426	+	8.28658i	−0.206649	+	0.357926i
$537$	−16.8988	+	9.75654i	−0.729238	+	0.421026i
$538$		−	3.27117i		−	0.141030i
$539$		0			0
$540$	−2.08551	+	0.806615i	−0.0897463	+	0.0347112i
$541$	−19.1817	−	33.2238i	−0.824688	−	1.42840i	−0.902158	−	0.431406i	$-0.858017\pi$
$541$	−19.1817	−	33.2238i	−0.824688	−	1.42840i	0.0774699	−	0.996995i	$-0.475316\pi$
$542$	0.540356	+	0.311975i	0.0232103	+	0.0134005i
$543$	−19.9413	−	11.5131i	−0.855761	−	0.494074i
$544$	−2.61323	−	4.52625i	−0.112041	−	0.194061i
$545$	−10.0447	−	25.9707i	−0.430268	−	1.11246i
$546$		0			0
$547$		−	1.44818i		−	0.0619197i	−0.999521	−	0.0309598i	$-0.990144\pi$
$547$		−	1.44818i		−	0.0619197i	0.999521	−	0.0309598i	$-0.00985640\pi$
$548$	12.8128	−	7.39749i	0.547337	−	0.316005i
$549$	−3.55780	+	6.16229i	−0.151843	+	0.263000i
$550$	−23.3731	+	5.09187i	−0.996632	+	0.217118i
$551$	−3.78426	−	6.55453i	−0.161215	−	0.279232i
$552$		−	7.17103i		−	0.305219i
$553$		0			0
$554$	28.7950			1.22338
$555$	−10.0595	+	12.4870i	−0.427003	+	0.530042i
$556$	1.82897	−	3.16787i	0.0775656	−	0.134348i
$557$	−11.2769	−	6.51072i	−0.477817	−	0.275868i	0.241689	−	0.970354i	$-0.422299\pi$
$557$	−11.2769	−	6.51072i	−0.477817	−	0.275868i	−0.719506	+	0.694486i	$0.755632\pi$
$558$	3.61222	−	2.08551i	0.152917	−	0.0882869i
$559$	6.34206			0.268241
$560$		0			0
$561$	−25.0047			−1.05570
$562$	2.44996	−	1.41449i	0.103345	−	0.0596665i
$563$	−5.06660	−	2.92520i	−0.213532	−	0.123283i	0.389420	−	0.921060i	$-0.372676\pi$
$563$	−5.06660	−	2.92520i	−0.213532	−	0.123283i	−0.602952	+	0.797778i	$0.706009\pi$
$564$	5.75654	−	9.97063i	0.242394	−	0.419839i
$565$	−11.0435	−	8.89665i	−0.464602	−	0.374285i
$566$	25.1370			1.05659
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	−20.3251	−	35.2040i	−0.852071	−	1.47583i	−0.879336	−	0.476202i	$-0.842013\pi$
$569$	−20.3251	−	35.2040i	−0.852071	−	1.47583i	0.0272649	−	0.999628i	$-0.491320\pi$
$570$	−7.00613	−	1.09150i	−0.293454	−	0.0457177i
$571$	1.61323	−	2.79420i	0.0675116	−	0.116933i	−0.830294	−	0.557326i	$-0.811827\pi$
$571$	1.61323	−	2.79420i	0.0675116	−	0.116933i	0.897805	+	0.440393i	$0.145161\pi$
$572$	−13.1385	+	7.58551i	−0.549348	+	0.317166i
$573$		−	10.2312i		−	0.427415i
$574$		0			0
$575$	24.1263	+	26.5238i	1.00614	+	1.10612i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	10.0759	+	5.81733i	0.419466	+	0.242179i	0.694849	−	0.719156i	$-0.255471\pi$
$577$	10.0759	+	5.81733i	0.419466	+	0.242179i	−0.275383	+	0.961335i	$0.588805\pi$
$578$	8.93381	+	5.15794i	0.371598	+	0.214542i
$579$	5.80661	+	10.0574i	0.241315	+	0.417969i
$580$	1.92520	+	4.97764i	0.0799398	+	0.206685i
$581$		0			0
$582$		−	1.27117i		−	0.0526917i
$583$	−33.6253	+	19.4136i	−1.39262	+	0.804028i
$584$	−2.00000	+	3.46410i	−0.0827606	+	0.143346i
$585$	1.09150	−	7.00613i	0.0451278	−	0.289668i
$586$	5.11323	+	8.85637i	0.211226	+	0.365853i
$587$		−	28.9446i		−	1.19467i	−0.801992	−	0.597335i	$-0.796226\pi$
$587$		−	28.9446i		−	1.19467i	0.801992	−	0.597335i	$-0.203774\pi$
$588$		0			0
$589$	13.2265			0.544987
$590$	−18.6822	−	15.0504i	−0.769133	−	0.619616i
$591$	−1.19874	+	2.07629i	−0.0493098	+	0.0854070i
$592$	−6.21029	−	3.58551i	−0.255242	−	0.147364i
$593$	−9.92262	+	5.72883i	−0.407473	+	0.235255i	−0.689704	−	0.724092i	$-0.742259\pi$
$593$	−9.92262	+	5.72883i	−0.407473	+	0.235255i	0.282230	+	0.959347i	$0.408926\pi$
$594$	−4.78426			−0.196301
$595$		0			0
$596$	22.3421			0.915166
$597$	−15.8847	+	9.17103i	−0.650117	+	0.375345i
$598$	19.6930	+	11.3698i	0.805308	+	0.464945i
$599$	−1.50237	+	2.60218i	−0.0613852	+	0.106322i	−0.895085	−	0.445896i	$-0.852885\pi$
$599$	−1.50237	+	2.60218i	−0.0613852	+	0.106322i	0.833700	+	0.552218i	$0.186218\pi$
$600$	4.76304	+	1.52100i	0.194450	+	0.0620945i
$601$	−40.0816			−1.63496			−0.817481	−	0.575955i	$-0.804630\pi$
$601$	−40.0816			−1.63496			−0.817481	+	0.575955i	$0.804630\pi$
$602$		0			0
$603$		−	9.56852i		−	0.389660i
$604$	8.25654	+	14.3008i	0.335954	+	0.581889i
$605$	−26.2681	−	4.09234i	−1.06795	−	0.166377i
$606$	4.00000	−	6.92820i	0.162489	−	0.281439i
$607$	22.6220	−	13.0608i	0.918197	−	0.530121i	0.0351374	−	0.999382i	$-0.488813\pi$
$607$	22.6220	−	13.0608i	0.918197	−	0.530121i	0.883059	+	0.469261i	$0.155480\pi$
$608$		−	3.17103i		−	0.128602i
$609$		0			0
$610$	14.8397	−	5.73955i	0.600841	−	0.232388i
$611$	18.2542	+	31.6172i	0.738485	+	1.27909i
$612$	4.52625	+	2.61323i	0.182963	+	0.105634i
$613$	−35.9514	−	20.7565i	−1.45206	−	0.838349i	−0.453464	−	0.891274i	$-0.649812\pi$
$613$	−35.9514	−	20.7565i	−1.45206	−	0.838349i	−0.998598	+	0.0529254i	$0.983145\pi$
$614$	11.7288	+	20.3149i	0.473337	+	0.819844i
$615$	−4.28663	+	1.65794i	−0.172854	+	0.0668546i
$616$		0			0
$617$		−	31.1156i		−	1.25267i	−0.779555	−	0.626333i	$-0.784555\pi$
$617$		−	31.1156i		−	1.25267i	0.779555	−	0.626333i	$-0.215445\pi$
$618$	9.72240	−	5.61323i	0.391092	−	0.225797i
$619$	−16.4961	+	28.5721i	−0.663034	+	1.14841i	0.316780	+	0.948499i	$0.397398\pi$
$619$	−16.4961	+	28.5721i	−0.663034	+	1.14841i	−0.979814	+	0.199910i	$0.935935\pi$
$620$	−9.21554	−	1.43570i	−0.370105	−	0.0576592i
$621$	3.58551	+	6.21029i	0.143882	+	0.249211i
$622$			5.65794i			0.226863i
$623$		0			0
$624$	3.17103			0.126943
$625$	−22.7345	+	10.3991i	−0.909382	+	0.415962i
$626$	−8.19339	+	14.1914i	−0.327474	+	0.567201i
$627$	−13.1385	−	7.58551i	−0.524701	−	0.302936i
$628$	8.61225	−	4.97229i	0.343666	−	0.198416i
$629$	37.4791			1.49439
$630$		0			0
$631$	47.6501			1.89692			0.948461	−	0.316894i	$-0.102640\pi$
$631$	47.6501			1.89692			0.948461	+	0.316894i	$0.102640\pi$
$632$	10.5404	−	6.08551i	0.419275	−	0.242069i
$633$	2.44996	+	1.41449i	0.0973772	+	0.0562207i
$634$	2.25654	−	3.90845i	0.0896188	−	0.155224i
$635$	31.3622	+	25.2655i	1.24457	+	1.00263i
$636$	8.11560			0.321804
$637$		0			0
$638$			11.4189i			0.452080i
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$	−0.344208	+	2.20942i	−0.0136060	+	0.0873348i
$641$	−5.14331	+	8.90848i	−0.203149	+	0.351864i	−0.949541	−	0.313642i	$-0.898451\pi$
$641$	−5.14331	+	8.90848i	−0.203149	+	0.351864i	0.746393	+	0.665506i	$0.231784\pi$
$642$	1.21026	−	0.698745i	0.0477652	−	0.0275773i
$643$		−	38.9368i		−	1.53552i	−0.640740	−	0.767758i	$-0.721372\pi$
$643$		−	38.9368i		−	1.53552i	0.640740	−	0.767758i	$-0.278628\pi$
$644$		0			0
$645$	−1.61323	−	4.17103i	−0.0635209	−	0.164234i
$646$	8.28663	+	14.3529i	0.326033	+	0.564706i
$647$	−29.3194	−	16.9276i	−1.15267	−	0.665492i	−0.203130	−	0.979152i	$-0.565111\pi$
$647$	−29.3194	−	16.9276i	−1.15267	−	0.665492i	−0.949535	+	0.313660i	$0.898445\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−25.6648	−	44.4527i	−1.00743	−	1.74492i
$650$	−11.7288	+	10.6687i	−0.460043	+	0.418459i
$651$		0			0
$652$			2.88440i			0.112962i
$653$	−4.64493	+	2.68175i	−0.181770	+	0.104945i	−0.588124	−	0.808771i	$-0.700133\pi$
$653$	−4.64493	+	2.68175i	−0.181770	+	0.104945i	0.406354	+	0.913716i	$0.366800\pi$
$654$	−6.22646	+	10.7845i	−0.243474	+	0.421709i
$655$	−12.2795	−	1.91304i	−0.479800	−	0.0747487i
$656$	−1.02771	−	1.78005i	−0.0401255	−	0.0694995i
$657$		−	4.00000i		−	0.156055i
$658$		0			0
$659$	−23.2265			−0.904774			−0.452387	−	0.891822i	$-0.649427\pi$
$659$	−23.2265			−0.904774			−0.452387	+	0.891822i	$0.649427\pi$
$660$	8.33086	+	6.71137i	0.324278	+	0.261240i
$661$	−18.2973	+	31.6919i	−0.711684	+	1.23267i	0.252540	+	0.967586i	$0.418734\pi$
$661$	−18.2973	+	31.6919i	−0.711684	+	1.23267i	−0.964224	+	0.265087i	$0.914599\pi$
$662$	11.3290	+	6.54080i	0.440314	+	0.254216i
$663$	−14.3529	+	8.28663i	−0.557419	+	0.321826i
$664$	−3.39749			−0.131848
$665$		0			0
$666$	7.17103			0.277872
$667$	14.8225	−	8.55780i	0.573931	−	0.331359i
$668$	−3.51211	−	2.02771i	−0.135887	−	0.0784546i
$669$	7.14867	−	12.3819i	0.276384	−	0.478711i
$670$	−13.4227	+	16.6617i	−0.518565	+	0.643699i
$671$	34.0429			1.31421
$672$		0			0
$673$			17.7336i			0.683579i	0.939777	+	0.341789i	$0.111033\pi$
$673$			17.7336i			0.683579i	−0.939777	+	0.341789i	$0.888967\pi$
$674$	10.1487	+	17.5780i	0.390912	+	0.677080i
$675$	−4.88541	+	1.06430i	−0.188040	+	0.0409648i
$676$	1.47229	−	2.55007i	0.0566263	−	0.0980797i
$677$	−22.7128	+	13.1132i	−0.872923	+	0.503982i	−0.868319	−	0.496007i	$-0.834799\pi$
$677$	−22.7128	+	13.1132i	−0.872923	+	0.503982i	−0.00460456	+	0.999989i	$0.501466\pi$
$678$			6.34206i			0.243565i
$679$		0			0
$680$	−4.21574	−	10.8999i	−0.161666	−	0.417991i
$681$	−5.52771	−	9.57428i	−0.211822	−	0.366887i
$682$	−17.2818	−	9.97764i	−0.661754	−	0.382064i
$683$	−42.6246	−	24.6093i	−1.63098	−	0.941650i	−0.983790	−	0.179325i	$-0.942609\pi$
$683$	−42.6246	−	24.6093i	−1.63098	−	0.941650i	−0.647195	−	0.762324i	$-0.724058\pi$
$684$	1.58551	+	2.74619i	0.0606237	+	0.105003i
$685$	30.8551	−	11.9339i	1.17891	−	0.455969i
$686$		0			0
$687$		−	18.4529i		−	0.704023i
$688$	1.73205	−	1.00000i	0.0660338	−	0.0381246i
$689$	−12.8674	+	22.2870i	−0.490209	+	0.849067i
$690$	2.46833	−	15.8438i	0.0939677	−	0.603163i
$691$	4.45292	+	7.71268i	0.169397	+	0.293404i	0.938208	−	0.346072i	$-0.112485\pi$
$691$	4.45292	+	7.71268i	0.169397	+	0.293404i	−0.768811	+	0.639476i	$0.779151\pi$
$692$		−	6.39749i		−	0.243196i
$693$		0			0
$694$	−14.4529			−0.548625
$695$	5.13136	−	6.36960i	0.194644	−	0.241613i
$696$	1.19339	−	2.06700i	0.0452351	−	0.0783496i
$697$	9.30338	+	5.37131i	0.352391	+	0.203453i
$698$	12.0283	−	6.94457i	0.455280	−	0.262856i
$699$	−9.11560			−0.344784
$700$		0			0
$701$	11.9553			0.451545			0.225773	−	0.974180i	$-0.427509\pi$
$701$	11.9553			0.451545			0.225773	+	0.974180i	$0.427509\pi$
$702$	−2.74619	+	1.58551i	−0.103648	+	0.0598414i
$703$	19.6930	+	11.3698i	0.742737	+	0.428819i
$704$	−2.39213	+	4.14329i	−0.0901568	+	0.156156i
$705$	16.1506	−	20.0478i	0.608266	−	0.755044i
$706$	6.45292			0.242859
$707$		0			0
$708$			10.7288i			0.403214i
$709$	26.0816	+	45.1747i	0.979515	+	1.69657i	0.664149	+	0.747600i	$0.268794\pi$
$709$	26.0816	+	45.1747i	0.979515	+	1.69657i	0.315367	+	0.948970i	$0.397872\pi$
$710$	2.06525	−	13.2565i	0.0775075	−	0.497508i
$711$	−6.08551	+	10.5404i	−0.228225	+	0.395297i
$712$	−8.28658	+	4.78426i	−0.310553	+	0.179298i
$713$			29.9106i			1.12016i
$714$		0			0
$715$	−31.6394	+	12.2372i	−1.18325	+	0.457645i
$716$	−9.75654	−	16.8988i	−0.364619	−	0.631539i
$717$	11.3584	+	6.55780i	0.424189	+	0.244906i
$718$	6.25830	+	3.61323i	0.233558	+	0.134845i
$719$	−12.8951	−	22.3350i	−0.480907	−	0.832955i	0.518853	−	0.854863i	$-0.326359\pi$
$719$	−12.8951	−	22.3350i	−0.480907	−	0.832955i	−0.999760	+	0.0219083i	$0.993026\pi$
$720$	−0.806615	−	2.08551i	−0.0300608	−	0.0777226i
$721$		0			0
$722$		−	8.94457i		−	0.332882i
$723$	4.62636	−	2.67103i	0.172056	−	0.0993367i
$724$	11.5131	−	19.9413i	0.427881	−	0.741111i
$725$	2.54023	+	11.6604i	0.0943418	+	0.433055i
$726$	5.94457	+	10.2963i	0.220624	+	0.382131i
$727$		−	34.6054i		−	1.28344i	−0.766937	−	0.641722i	$-0.778220\pi$
$727$		−	34.6054i		−	1.28344i	0.766937	−	0.641722i	$-0.221780\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−5.61121	+	6.96523i	−0.207680	+	0.257795i
$731$	−5.22646	+	9.05249i	−0.193308	+	0.334819i
$732$	−6.16229	−	3.55780i	−0.227765	−	0.131500i
$733$	−26.8215	+	15.4854i	−0.990673	+	0.571965i	−0.905475	−	0.424399i	$-0.860485\pi$
$733$	−26.8215	+	15.4854i	−0.990673	+	0.571965i	−0.0851976	+	0.996364i	$0.527152\pi$
$734$	−2.10014			−0.0775176
$735$		0			0
$736$	7.17103			0.264328
$737$	−39.6452	+	22.8891i	−1.46035	+	0.843132i
$738$	1.78005	+	1.02771i	0.0655247	+	0.0378307i
$739$	−1.08788	+	1.88427i	−0.0400185	+	0.0693141i	−0.885341	−	0.464942i	$-0.846075\pi$
$739$	−1.08788	+	1.88427i	−0.0400185	+	0.0693141i	0.845322	+	0.534257i	$0.179408\pi$
$740$	−12.4870	−	10.0595i	−0.459030	−	0.369796i
$741$	−10.0554			−0.369395
$742$		0			0
$743$			31.9446i			1.17193i	0.810335	+	0.585966i	$0.199285\pi$
$743$			31.9446i			1.17193i	−0.810335	+	0.585966i	$0.800715\pi$
$744$	2.08551	+	3.61222i	0.0764587	+	0.132430i
$745$	49.3629	+	7.69033i	1.80852	+	0.281752i
$746$	11.6239	−	20.1333i	0.425583	−	0.737131i
$747$	2.94231	−	1.69874i	0.107654	−	0.0621538i
$748$		−	25.0047i		−	0.914264i
$749$		0			0
$750$	10.0000	+	5.00000i	0.365148	+	0.182574i
$751$	2.80363	+	4.85602i	0.102306	+	0.177199i	0.912634	−	0.408777i	$-0.134045\pi$
$751$	2.80363	+	4.85602i	0.102306	+	0.177199i	−0.810329	+	0.585976i	$0.800711\pi$
$752$	9.97063	+	5.75654i	0.363591	+	0.209920i
$753$	24.1806	+	13.9606i	0.881188	+	0.508754i
$754$	3.78426	+	6.55453i	0.137815	+	0.238702i
$755$	13.3197	+	34.4383i	0.484754	+	1.25334i
$756$		0			0
$757$		−	24.2312i		−	0.880698i	−0.897827	−	0.440349i	$-0.854855\pi$
$757$		−	24.2312i		−	0.880698i	0.897827	−	0.440349i	$-0.145145\pi$
$758$	−1.87606	+	1.08314i	−0.0681416	+	0.0393416i
$759$	17.1540	−	29.7117i	0.622652	−	1.07846i
$760$	1.09150	−	7.00613i	0.0395927	−	0.254139i
$761$	19.9276	+	34.5156i	0.722374	+	1.25119i	0.960046	+	0.279843i	$0.0902824\pi$
$761$	19.9276	+	34.5156i	0.722374	+	1.25119i	−0.237672	+	0.971346i	$0.576384\pi$
$762$		−	18.0107i		−	0.652460i
$763$		0			0
$764$	10.2312			0.370152
$765$	9.10087	+	7.33169i	0.329043	+	0.265078i
$766$	−4.02771	+	6.97621i	−0.145527	+	0.252061i
$767$	−29.4634	−	17.0107i	−1.06386	−	0.614221i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	29.7950			1.07443			0.537217	−	0.843444i	$-0.319476\pi$
$769$	29.7950			1.07443			0.537217	+	0.843444i	$0.319476\pi$
$770$		0			0
$771$	−21.1370			−0.761232
$772$	−10.0574	+	5.80661i	−0.361972	+	0.208985i
$773$	−0.144011	−	0.0831449i	−0.00517972	−	0.00299051i	0.497408	−	0.867517i	$-0.334285\pi$
$773$	−0.144011	−	0.0831449i	−0.00517972	−	0.00299051i	−0.502588	+	0.864526i	$0.667619\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	−19.8668	−	6.34413i	−0.713636	−	0.227888i
$776$	1.27117			0.0456324
$777$		0			0
$778$		−	11.8891i		−	0.426246i
$779$	3.25891	+	5.64461i	0.116763	+	0.202239i
$780$	7.00613	+	1.09150i	0.250860	+	0.0390818i
$781$	14.3528	−	24.8597i	0.513583	−	0.889552i
$782$	−32.4579	+	18.7395i	−1.16069	+	0.670125i
$783$			2.38677i			0.0852962i
$784$		0			0
$785$	20.7395	−	8.02144i	0.740226	−	0.286297i
$786$	2.77890	+	4.81320i	0.0991201	+	0.171681i
$787$	−24.6410	−	14.2265i	−0.878355	−	0.507119i	−0.00823936	−	0.999966i	$-0.502623\pi$
$787$	−24.6410	−	14.2265i	−0.878355	−	0.507119i	−0.870116	+	0.492848i	$0.835956\pi$
$788$	−2.07629	−	1.19874i	−0.0739647	−	0.0427035i
$789$	−5.95529	−	10.3149i	−0.212014	−	0.367219i
$790$	25.3829	−	9.81733i	0.903082	−	0.349285i
$791$		0			0
$792$		−	4.78426i		−	0.170001i
$793$	19.5408	−	11.2819i	0.693914	−	0.400632i
$794$	8.05543	−	13.9524i	0.285877	−	0.495153i
$795$	17.9307	+	2.79346i	0.635938	+	0.0990737i
$796$	−9.17103	−	15.8847i	−0.325059	−	0.563018i
$797$		−	36.6334i		−	1.29762i	−0.760949	−	0.648811i	$-0.775266\pi$
$797$		−	36.6334i		−	1.29762i	0.760949	−	0.648811i	$-0.224734\pi$
$798$		0			0
$799$	−60.1727			−2.12876
$800$	−1.52100	+	4.76304i	−0.0537755	+	0.168399i
$801$	4.78426	−	8.28658i	0.169044	−	0.292792i
$802$	−21.6253	−	12.4854i	−0.763616	−	0.440874i
$803$	−16.5732	+	9.56852i	−0.584854	+	0.337666i
$804$	9.56852			0.337456
$805$		0			0
$806$	−13.2265			−0.465882
$807$	−2.83292	+	1.63559i	−0.0997234	+	0.0575753i
$808$	6.92820	+	4.00000i	0.243733	+	0.140720i
$809$	−10.1433	+	17.5687i	−0.356620	+	0.617684i	−0.987394	−	0.158283i	$-0.949404\pi$
$809$	−10.1433	+	17.5687i	−0.356620	+	0.617684i	0.630774	+	0.775967i	$0.282738\pi$
$810$	1.74131	+	1.40280i	0.0611833	+	0.0492894i
$811$	−1.38079			−0.0484861			−0.0242431	−	0.999706i	$-0.507718\pi$
$811$	−1.38079			−0.0484861			−0.0242431	+	0.999706i	$0.507718\pi$
$812$		0			0
$813$		−	0.623949i		−	0.0218829i
$814$	−17.1540	−	29.7117i	−0.601249	−	1.04139i
$815$	−0.992835	+	6.37284i	−0.0347775	+	0.223231i
$816$	−2.61323	+	4.52625i	−0.0914813	+	0.158450i
$817$	−5.49238	+	3.17103i	−0.192154	+	0.110940i
$818$			3.05543i			0.106831i
$819$		0			0
$820$	−1.65794	−	4.28663i	−0.0578978	−	0.149696i
$821$	8.70647	+	15.0801i	0.303858	+	0.526298i	0.977006	−	0.213210i	$-0.0683918\pi$
$821$	8.70647	+	15.0801i	0.303858	+	0.526298i	−0.673148	+	0.739507i	$0.735058\pi$
$822$	−12.8128	−	7.39749i	−0.446899	−	0.258017i
$823$	17.8355	+	10.2973i	0.621708	+	0.358943i	0.777534	−	0.628842i	$-0.216471\pi$
$823$	17.8355	+	10.2973i	0.621708	+	0.358943i	−0.155826	+	0.987785i	$0.549804\pi$
$824$	5.61323	+	9.72240i	0.195546	+	0.338696i
$825$	16.0962	+	17.6958i	0.560399	+	0.616087i
$826$		0			0
$827$			13.8504i			0.481626i	0.970572	+	0.240813i	$0.0774140\pi$
$827$			13.8504i			0.481626i	−0.970572	+	0.240813i	$0.922586\pi$
$828$	−6.21029	+	3.58551i	−0.215823	+	0.124605i
$829$	0.613230	−	1.06215i	0.0212984	−	0.0368898i	−0.855180	−	0.518331i	$-0.826553\pi$
$829$	0.613230	−	1.06215i	0.0212984	−	0.0368898i	0.876478	+	0.481442i	$0.159887\pi$
$830$	−7.50647	−	1.16944i	−0.260553	−	0.0405920i
$831$	−14.3975	−	24.9372i	−0.499443	−	0.865061i
$832$			3.17103i			0.109936i
$833$		0			0
$834$	−3.65794			−0.126664
$835$	−7.06175	−	5.68896i	−0.244382	−	0.196875i
$836$	7.58551	−	13.1385i	0.262351	−	0.454404i
$837$	−3.61222	−	2.08551i	−0.124857	−	0.0720859i
$838$	−17.4913	+	10.0986i	−0.604227	+	0.348850i
$839$	29.9106			1.03263			0.516314	−	0.856399i	$-0.327304\pi$
$839$	29.9106			1.03263			0.516314	+	0.856399i	$0.327304\pi$
$840$		0			0
$841$	−23.3033			−0.803563
$842$	−26.2956	+	15.1817i	−0.906205	+	0.523198i
$843$	−2.44996	−	1.41449i	−0.0843811	−	0.0487175i
$844$	−1.41449	+	2.44996i	−0.0486886	+	0.0843311i
$845$	4.13065	−	5.12740i	0.142099	−	0.176388i
$846$	−11.5131			−0.395828
$847$		0			0
$848$			8.11560i			0.278691i
$849$	−12.5685	−	21.7693i	−0.431350	−	0.747121i
$850$	−5.56250	−	25.5334i	−0.190792	−	0.875789i
$851$	−25.7118	+	44.5342i	−0.881390	+	1.52661i
$852$	−5.19615	+	3.00000i	−0.178017	+	0.102778i
$853$		−	10.7181i		−	0.366981i	−0.983021	−	0.183491i	$-0.941260\pi$
$853$		−	10.7181i		−	0.366981i	0.983021	−	0.183491i	$-0.0587397\pi$
$854$		0			0
$855$	2.55780	+	6.61323i	0.0874749	+	0.226168i
$856$	0.698745	+	1.21026i	0.0238826	+	0.0413659i
$857$	34.3716	+	19.8444i	1.17411	+	0.677873i	0.954645	−	0.297747i	$-0.0962353\pi$
$857$	34.3716	+	19.8444i	1.17411	+	0.677873i	0.219465	+	0.975620i	$0.429569\pi$
$858$	13.1385	+	7.58551i	0.448541	+	0.258965i
$859$	−5.50237	−	9.53038i	−0.187738	−	0.325173i	0.756757	−	0.653696i	$-0.226782\pi$
$859$	−5.50237	−	9.53038i	−0.187738	−	0.325173i	−0.944496	+	0.328523i	$0.893449\pi$
$860$	4.17103	−	1.61323i	0.142231	−	0.0550107i
$861$		0			0
$862$			24.5733i			0.836969i
$863$	−7.47266	+	4.31434i	−0.254372	+	0.146862i	−0.621765	−	0.783204i	$-0.713584\pi$
$863$	−7.47266	+	4.31434i	−0.254372	+	0.146862i	0.367392	+	0.930066i	$0.380251\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	2.20207	−	14.1347i	0.0748726	−	0.480595i
$866$	2.34206	+	4.05657i	0.0795864	+	0.137848i
$867$		−	10.3159i		−	0.350346i
$868$		0			0
$869$	58.2294			1.97530
$870$	3.34816	−	4.15610i	0.113513	−	0.140905i
$871$	−15.1710	+	26.2770i	−0.514051	+	0.890362i
$872$	−10.7845	−	6.22646i	−0.365211	−	0.210855i
$873$	−1.10087	+	0.635585i	−0.0372587	+	0.0215113i
$874$	−22.7395			−0.769177
$875$		0			0
$876$	4.00000			0.135147
$877$	−33.5494	+	19.3698i	−1.13288	+	0.654071i	−0.944659	−	0.328055i	$-0.893607\pi$
$877$	−33.5494	+	19.3698i	−1.13288	+	0.654071i	−0.188225	+	0.982126i	$0.560274\pi$
$878$	26.4251	+	15.2565i	0.891804	+	0.514883i
$879$	5.11323	−	8.85637i	0.172465	−	0.298718i
$880$	−6.71137	+	8.33086i	−0.226240	+	0.280833i
$881$	6.03399			0.203290			0.101645	−	0.994821i	$-0.467589\pi$
$881$	6.03399			0.203290			0.101645	+	0.994821i	$0.467589\pi$
$882$		0			0
$883$		−	7.77828i		−	0.261760i	−0.991398	−	0.130880i	$-0.958220\pi$
$883$		−	7.77828i		−	0.261760i	0.991398	−	0.130880i	$-0.0417803\pi$
$884$	−8.28663	−	14.3529i	−0.278710	−	0.482739i
$885$	−3.69295	+	23.7045i	−0.124137	+	0.796816i
$886$	4.75417	−	8.23447i	0.159720	−	0.276642i
$887$	21.5587	−	12.4469i	0.723871	−	0.417927i	−0.0923045	−	0.995731i	$-0.529423\pi$
$887$	21.5587	−	12.4469i	0.723871	−	0.417927i	0.816176	+	0.577803i	$0.196090\pi$
$888$			7.17103i			0.240644i
$889$		0			0
$890$	−19.9553	+	7.71811i	−0.668903	+	0.258712i
$891$	2.39213	+	4.14329i	0.0801394	+	0.138805i
$892$	12.3819	+	7.14867i	0.414576	+	0.239355i
$893$	−31.6172	−	18.2542i	−1.05803	−	0.610853i
$894$	−11.1710	−	19.3488i	−0.373615	−	0.647120i
$895$	−15.7395	−	40.6948i	−0.526115	−	1.36028i
$896$		0			0
$897$		−	22.7395i		−	0.759251i
$898$	−15.2628	+	8.81197i	−0.509326	+	0.294059i
$899$	−4.97764	+	8.62153i	−0.166014	+	0.287544i
$900$	−1.06430	−	4.88541i	−0.0354765	−	0.162847i
$901$	−21.2079	−	36.7332i	−0.706539	−	1.22376i
$902$		−	9.83371i		−	0.327427i
$903$		0			0
$904$	−6.34206			−0.210934
$905$	32.3012	−	40.0956i	1.07373	−	1.33282i
$906$	8.25654	−	14.3008i	0.274305	−	0.475111i
$907$	40.4482	+	23.3528i	1.34306	+	0.775416i	0.987255	−	0.159144i	$-0.0508734\pi$
$907$	40.4482	+	23.3528i	1.34306	+	0.775416i	0.355805	+	0.934560i	$0.384207\pi$
$908$	9.57428	−	5.52771i	0.317734	−	0.183444i
$909$	−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	$0.531691\pi$
$912$	−2.74619	+	1.58551i	−0.0909355	+	0.0525016i
$913$	−14.0768	−	8.12724i	−0.465874	−	0.268972i
$914$	0.193385	−	0.334953i	0.00639661	−	0.0110793i
$915$	−12.3904	−	9.98177i	−0.409615	−	0.329987i
$916$	18.4529			0.609702
$917$		0			0
$918$		−	5.22646i		−	0.172499i
$919$	−17.1156	−	29.6451i	−0.564592	−	0.977901i	−0.997088	−	0.0762654i	$-0.975700\pi$
$919$	−17.1156	−	29.6451i	−0.564592	−	0.977901i	0.432496	−	0.901636i	$-0.357633\pi$
$920$	15.8438	+	2.46833i	0.522354	+	0.0813784i
$921$	11.7288	−	20.3149i	0.386478	−	0.669400i
$922$	32.3618	−	18.6841i	1.06578	−	0.615329i
$923$		−	19.0262i		−	0.626254i
$924$		0			0
$925$	−24.1263	−	26.5238i	−0.793268	−	0.872097i
$926$	−12.1540	−	21.0514i	−0.399406	−	0.691792i
$927$	−9.72240	−	5.61323i	−0.319325	−	0.184363i
$928$	2.06700	+	1.19339i	0.0678527	+	0.0391748i
$929$	13.8274	+	23.9498i	0.453663	+	0.785768i	0.998610	−	0.0527025i	$-0.0167835\pi$
$929$	13.8274	+	23.9498i	0.453663	+	0.785768i	−0.544947	+	0.838471i	$0.683450\pi$
$930$	3.36441	+	8.69874i	0.110324	+	0.285243i
$931$		0			0
$932$		−	9.11560i		−	0.298591i
$933$	4.89992	−	2.82897i	0.160416	−	0.0926163i
$934$	−14.2866	+	24.7452i	−0.467473	+	0.809687i
$935$	8.60684	−	55.2459i	0.281474	−	1.80673i
$936$	−1.58551	−	2.74619i	−0.0518242	−	0.0897621i
$937$			38.8397i			1.26884i	0.772990	+	0.634419i	$0.218760\pi$
$937$			38.8397i			1.26884i	−0.772990	+	0.634419i	$0.781240\pi$
$938$		0			0
$939$	16.3868			0.534762
$940$	20.0478	+	16.1506i	0.653888	+	0.526774i
$941$	−9.87750	+	17.1083i	−0.321997	+	0.557716i	−0.980900	−	0.194512i	$-0.937688\pi$
$941$	−9.87750	+	17.1083i	−0.321997	+	0.557716i	0.658903	+	0.752228i	$0.271021\pi$
$942$	−8.61225	−	4.97229i	−0.280602	−	0.162006i
$943$	−12.7648	+	7.36977i	−0.415680	+	0.239993i
$944$	−10.7288			−0.349194
$945$		0			0
$946$	9.56852			0.311099
$947$	−32.9543	+	19.0262i	−1.07087	+	0.618268i	−0.928419	−	0.371534i	$-0.878832\pi$
$947$	−32.9543	+	19.0262i	−1.07087	+	0.618268i	−0.142452	+	0.989802i	$0.545499\pi$
$948$	−10.5404	−	6.08551i	−0.342337	−	0.197648i
$949$	−6.34206	+	10.9848i	−0.205872	+	0.356581i
$950$	4.82313	−	15.1037i	0.156483	−	0.490030i
$951$	−4.51309			−0.146347
$952$		0			0
$953$		−	52.5947i		−	1.70371i	−0.523778	−	0.851855i	$-0.675478\pi$
$953$		−	52.5947i		−	1.70371i	0.523778	−	0.851855i	$-0.324522\pi$
$954$	−4.05780	−	7.02832i	−0.131376	−	0.227550i
$955$	22.6050	+	3.52167i	0.731480	+	0.113958i
$956$	−6.55780	+	11.3584i	−0.212094	+	0.367358i
$957$	9.88908	−	5.70946i	0.319669	−	0.184561i
$958$		−	8.56378i		−	0.276683i
$959$		0			0
$960$	2.08551	−	0.806615i	0.0673097	−	0.0260334i
$961$	6.80126	+	11.7801i	0.219395	+	0.380004i
$962$	−19.6930	−	11.3698i	−0.634929	−	0.366576i
$963$	−1.21026	−	0.698745i	−0.0390001	−	0.0225167i
$964$	2.67103	+	4.62636i	0.0860281	+	0.149005i
$965$	−24.2196	+	9.36740i	−0.779655	+	0.301547i
$966$		0			0
$967$		−	4.61797i		−	0.148504i	−0.997240	−	0.0742520i	$-0.976343\pi$
$967$		−	4.61797i		−	0.148504i	0.997240	−	0.0742520i	$-0.0236569\pi$
$968$	−10.2963	+	5.94457i	−0.330936	+	0.191066i
$969$	8.28663	−	14.3529i	0.266205	−	0.461080i
$970$	2.80854	+	0.437548i	0.0901769	+	0.0140488i
$971$	19.4523	+	33.6924i	0.624254	+	1.08124i	0.988685	+	0.150009i	$0.0479303\pi$
$971$	19.4523	+	33.6924i	0.624254	+	1.08124i	−0.364431	+	0.931231i	$0.618736\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	31.8444			1.02036
$975$	15.1037	+	4.82313i	0.483707	+	0.154464i
$976$	3.55780	−	6.16229i	0.113882	−	0.197250i
$977$	13.8750	+	8.01072i	0.443900	+	0.256286i	0.705250	−	0.708958i	$-0.250835\pi$
$977$	13.8750	+	8.01072i	0.443900	+	0.256286i	−0.261351	+	0.965244i	$0.584168\pi$
$978$	2.49796	−	1.44220i	0.0798761	−	0.0461165i
$979$	−45.7783			−1.46308
$980$		0			0
$981$	12.4529			0.397591
$982$	3.89506	−	2.24881i	0.124296	−	0.0717626i
$983$	1.78005	+	1.02771i	0.0567749	+	0.0327790i	0.528119	−	0.849171i	$-0.322898\pi$
$983$	1.78005	+	1.02771i	0.0567749	+	0.0327790i	−0.471344	+	0.881950i	$0.656231\pi$
$984$	−1.02771	+	1.78005i	−0.0327624	+	0.0567461i
$985$	−4.17476	−	3.36320i	−0.133019	−	0.107161i
$986$	−12.4744			−0.397264
$987$		0			0
$988$		−	10.0554i		−	0.319906i
$989$	−7.17103	−	12.4206i	−0.228025	−	0.394952i
$990$	1.64678	−	10.5704i	0.0523382	−	0.335950i
$991$	13.5986	−	23.5535i	0.431974	−	0.748201i	−0.565069	−	0.825043i	$-0.691151\pi$
$991$	13.5986	−	23.5535i	0.431974	−	0.748201i	0.997043	+	0.0768427i	$0.0244839\pi$
$992$	−3.61222	+	2.08551i	−0.114688	+	0.0662152i
$993$		−	13.0816i		−	0.415132i
$994$		0			0
$995$	−14.7950	−	38.2526i	−0.469032	−	1.21269i
$996$	1.69874	+	2.94231i	0.0538268	+	0.0932307i
$997$	−15.9993	−	9.23718i	−0.506702	−	0.292544i	0.224775	−	0.974411i	$-0.427835\pi$
$997$	−15.9993	−	9.23718i	−0.506702	−	0.292544i	−0.731477	+	0.681866i	$0.761169\pi$
$998$	−0.296232	−	0.171030i	−0.00937707	−	0.00541385i
$999$	−3.58551	−	6.21029i	−0.113441	−	0.196485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.j.949.6		12
5.4	even	2	inner	1470.2.n.j.949.1		12
7.2	even	3	inner	1470.2.n.j.79.1		12
7.3	odd	6		1470.2.g.i.589.5		6
7.4	even	3		1470.2.g.h.589.5		6
7.5	odd	6		210.2.n.b.79.3	✓	12
7.6	odd	2		210.2.n.b.109.4	yes	12
21.5	even	6		630.2.u.f.289.4		12
21.20	even	2		630.2.u.f.109.3		12
28.19	even	6		1680.2.di.c.289.6		12
28.27	even	2		1680.2.di.c.529.1		12
35.3	even	12		7350.2.a.dq.1.1		3
35.4	even	6		1470.2.g.h.589.2		6
35.9	even	6	inner	1470.2.n.j.79.6		12
35.12	even	12		1050.2.i.v.751.2		6
35.13	even	4		1050.2.i.u.151.2		6
35.17	even	12		7350.2.a.dn.1.1		3
35.18	odd	12		7350.2.a.dp.1.1		3
35.19	odd	6		210.2.n.b.79.4	yes	12
35.24	odd	6		1470.2.g.i.589.2		6
35.27	even	4		1050.2.i.v.151.2		6
35.32	odd	12		7350.2.a.do.1.1		3
35.33	even	12		1050.2.i.u.751.2		6
35.34	odd	2		210.2.n.b.109.3	yes	12
105.89	even	6		630.2.u.f.289.3		12
105.104	even	2		630.2.u.f.109.4		12
140.19	even	6		1680.2.di.c.289.1		12
140.139	even	2		1680.2.di.c.529.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.b.79.3	✓	12	7.5	odd	6
210.2.n.b.79.4	yes	12	35.19	odd	6
210.2.n.b.109.3	yes	12	35.34	odd	2
210.2.n.b.109.4	yes	12	7.6	odd	2
630.2.u.f.109.3		12	21.20	even	2
630.2.u.f.109.4		12	105.104	even	2
630.2.u.f.289.3		12	105.89	even	6
630.2.u.f.289.4		12	21.5	even	6
1050.2.i.u.151.2		6	35.13	even	4
1050.2.i.u.751.2		6	35.33	even	12
1050.2.i.v.151.2		6	35.27	even	4
1050.2.i.v.751.2		6	35.12	even	12
1470.2.g.h.589.2		6	35.4	even	6
1470.2.g.h.589.5		6	7.4	even	3
1470.2.g.i.589.2		6	35.24	odd	6
1470.2.g.i.589.5		6	7.3	odd	6
1470.2.n.j.79.1		12	7.2	even	3	inner
1470.2.n.j.79.6		12	35.9	even	6	inner
1470.2.n.j.949.1		12	5.4	even	2	inner
1470.2.n.j.949.6		12	1.1	even	1	trivial
1680.2.di.c.289.1		12	140.19	even	6
1680.2.di.c.289.6		12	28.19	even	6
1680.2.di.c.529.1		12	28.27	even	2
1680.2.di.c.529.6		12	140.139	even	2
7350.2.a.dn.1.1		3	35.17	even	12
7350.2.a.do.1.1		3	35.32	odd	12
7350.2.a.dp.1.1		3	35.18	odd	12
7350.2.a.dq.1.1		3	35.3	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.40280 - 1.74131i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.40280 - 1.74131i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.344208 - 2.20942i) q^{10} +(2.39213 - 4.14329i) q^{11} +(-0.866025 + 0.500000i) q^{12} -3.17103i q^{13} +(-2.08551 + 0.806615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.52625 + 2.61323i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.58551 + 2.74619i) q^{19} +(-0.806615 - 2.08551i) q^{20} -4.78426i q^{22} +(-6.21029 + 3.58551i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.06430 - 4.88541i) q^{25} +(-1.58551 - 2.74619i) q^{26} -1.00000i q^{27} -2.38677 q^{29} +(-1.40280 + 1.74131i) q^{30} +(2.08551 - 3.61222i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.14329 + 2.39213i) q^{33} +5.22646 q^{34} +1.00000 q^{36} +(6.21029 - 3.58551i) q^{37} +(2.74619 + 1.58551i) q^{38} +(-1.58551 + 2.74619i) q^{39} +(-1.74131 - 1.40280i) q^{40} +2.05543 q^{41} +2.00000i q^{43} +(-2.39213 - 4.14329i) q^{44} +(2.20942 + 0.344208i) q^{45} +(-3.58551 + 6.21029i) q^{46} +(-9.97063 + 5.75654i) q^{47} +1.00000i q^{48} +(-3.36441 - 3.69874i) q^{50} +(-2.61323 - 4.52625i) q^{51} +(-2.74619 - 1.58551i) q^{52} +(-7.02832 - 4.05780i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-3.85906 - 9.97764i) q^{55} -3.17103i q^{57} +(-2.06700 + 1.19339i) q^{58} +(5.36441 - 9.29144i) q^{59} +(-0.344208 + 2.20942i) q^{60} +(3.55780 + 6.16229i) q^{61} -4.17103i q^{62} -1.00000 q^{64} +(-5.52173 - 4.44833i) q^{65} +(-2.39213 + 4.14329i) q^{66} +(-8.28658 - 4.78426i) q^{67} +(4.52625 - 2.61323i) q^{68} +7.17103 q^{69} +6.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(3.58551 - 6.21029i) q^{74} +(-1.52100 + 4.76304i) q^{75} +3.17103 q^{76} +3.17103i q^{78} +(6.08551 + 10.5404i) q^{79} +(-2.20942 - 0.344208i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.78005 - 1.02771i) q^{82} -3.39749i q^{83} +(10.8999 - 4.21574i) q^{85} +(1.00000 + 1.73205i) q^{86} +(2.06700 + 1.19339i) q^{87} +(-4.14329 - 2.39213i) q^{88} +(-4.78426 - 8.28658i) q^{89} +(2.08551 - 0.806615i) q^{90} +7.17103i q^{92} +(-3.61222 + 2.08551i) q^{93} +(-5.75654 + 9.97063i) q^{94} +(7.00613 + 1.09150i) q^{95} +(0.500000 + 0.866025i) q^{96} +1.27117i q^{97} +4.78426 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