LMFDB - Embedded newform 315.2.j.e.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	315.226
Dual form			315.2.j.e.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207107 + 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.58579 q^{8} +O(q^{10})$	\(q+(-0.207107 + 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.58579 q^{8} +(0.207107 + 0.358719i) q^{10} +(2.41421 + 4.18154i) q^{11} +0.828427 q^{13} +(-0.414214 - 1.01461i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.414214 - 0.717439i) q^{17} +(1.41421 - 2.44949i) q^{19} +1.82843 q^{20} -2.00000 q^{22} +(-1.20711 + 2.09077i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.171573 + 0.297173i) q^{26} +(-4.79289 - 0.655892i) q^{28} +1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-2.20711 - 3.82282i) q^{32} +0.343146 q^{34} +(1.00000 + 2.44949i) q^{35} +(0.585786 + 1.01461i) q^{38} +(-0.792893 + 1.37333i) q^{40} +2.17157 q^{41} +6.41421 q^{43} +(-4.41421 + 7.64564i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} +(-1.74264 - 6.77962i) q^{49} +0.414214 q^{50} +(0.757359 + 1.31178i) q^{52} +(-3.41421 - 5.91359i) q^{53} +4.82843 q^{55} +(2.57107 - 3.31552i) q^{56} +(-0.207107 + 0.358719i) q^{58} +(-6.24264 - 10.8126i) q^{59} +(5.74264 - 9.94655i) q^{61} -2.48528 q^{62} -4.17157 q^{64} +(0.414214 - 0.717439i) q^{65} +(-6.20711 - 10.7510i) q^{67} +(0.757359 - 1.31178i) q^{68} +(-1.08579 - 0.148586i) q^{70} +12.4853 q^{71} +(-2.41421 - 4.18154i) q^{73} +5.17157 q^{76} +(-12.6569 - 1.73205i) q^{77} +(-4.58579 + 7.94282i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.449747 + 0.778985i) q^{82} +11.7279 q^{83} -0.828427 q^{85} +(-1.32843 + 2.30090i) q^{86} +(-3.82843 - 6.63103i) q^{88} +(1.32843 - 2.30090i) q^{89} +(-1.34315 + 1.73205i) q^{91} -4.41421 q^{92} +(0.414214 + 0.717439i) q^{94} +(-1.41421 - 2.44949i) q^{95} +0.343146 q^{97} +(2.79289 + 0.778985i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 2 q^{10} + 4 q^{11} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 4 q^{17} - 4 q^{20} - 8 q^{22} - 2 q^{23} - 2 q^{25} - 12 q^{26} - 22 q^{28} + 4 q^{29} + 12 q^{31} - 6 q^{32} + 24 q^{34} + 4 q^{35} + 8 q^{38} - 6 q^{40} + 20 q^{41} + 20 q^{43} - 12 q^{44} - 2 q^{46} + 4 q^{47} + 10 q^{49} - 4 q^{50} + 20 q^{52} - 8 q^{53} + 8 q^{55} - 18 q^{56} + 2 q^{58} - 8 q^{59} + 6 q^{61} + 24 q^{62} - 28 q^{64} - 4 q^{65} - 22 q^{67} + 20 q^{68} - 10 q^{70} + 16 q^{71} - 4 q^{73} + 32 q^{76} - 28 q^{77} - 24 q^{79} + 6 q^{80} + 18 q^{82} - 4 q^{83} + 8 q^{85} + 6 q^{86} - 4 q^{88} - 6 q^{89} - 28 q^{91} - 12 q^{92} - 4 q^{94} + 24 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 2 * q^10 + 4 * q^11 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 4 * q^17 - 4 * q^20 - 8 * q^22 - 2 * q^23 - 2 * q^25 - 12 * q^26 - 22 * q^28 + 4 * q^29 + 12 * q^31 - 6 * q^32 + 24 * q^34 + 4 * q^35 + 8 * q^38 - 6 * q^40 + 20 * q^41 + 20 * q^43 - 12 * q^44 - 2 * q^46 + 4 * q^47 + 10 * q^49 - 4 * q^50 + 20 * q^52 - 8 * q^53 + 8 * q^55 - 18 * q^56 + 2 * q^58 - 8 * q^59 + 6 * q^61 + 24 * q^62 - 28 * q^64 - 4 * q^65 - 22 * q^67 + 20 * q^68 - 10 * q^70 + 16 * q^71 - 4 * q^73 + 32 * q^76 - 28 * q^77 - 24 * q^79 + 6 * q^80 + 18 * q^82 - 4 * q^83 + 8 * q^85 + 6 * q^86 - 4 * q^88 - 6 * q^89 - 28 * q^91 - 12 * q^92 - 4 * q^94 + 24 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	−0.929912	−	0.367783i	$-0.880117\pi$
$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	0.783465	+	0.621436i	$0.213450\pi$
$3$		0			0
$3$		0			0
$4$	0.914214	+	1.58346i	0.457107	+	0.791732i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$8$	−1.58579			−0.560660
$9$		0			0
$10$	0.207107	+	0.358719i	0.0654929	+	0.113437i
$11$	2.41421	+	4.18154i	0.727913	+	1.26078i	0.957764	+	0.287556i	$0.0928428\pi$
$11$	2.41421	+	4.18154i	0.727913	+	1.26078i	−0.229851	+	0.973226i	$0.573824\pi$
$12$		0			0
$13$	0.828427			0.229764			0.114882	−	0.993379i	$-0.463351\pi$
$13$	0.828427			0.229764			0.114882	+	0.993379i	$0.463351\pi$
$14$	−0.414214	−	1.01461i	−0.110703	−	0.271166i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−0.414214	−	0.717439i	−0.100462	−	0.174005i	0.811413	−	0.584473i	$-0.198699\pi$
$17$	−0.414214	−	0.717439i	−0.100462	−	0.174005i	−0.911875	+	0.410468i	$0.865365\pi$
$18$		0			0
$19$	1.41421	−	2.44949i	0.324443	−	0.561951i	−0.656957	−	0.753928i	$-0.728157\pi$
$19$	1.41421	−	2.44949i	0.324443	−	0.561951i	0.981399	+	0.191977i	$0.0614899\pi$
$20$	1.82843			0.408849
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−1.20711	+	2.09077i	−0.251699	+	0.435956i	−0.963994	−	0.265925i	$-0.914323\pi$
$23$	−1.20711	+	2.09077i	−0.251699	+	0.435956i	0.712295	+	0.701881i	$0.247656\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.171573	+	0.297173i	−0.0336482	+	0.0582804i
$27$		0			0
$28$	−4.79289	−	0.655892i	−0.905772	−	0.123952i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−2.20711	−	3.82282i	−0.390165	−	0.675786i
$33$		0			0
$34$	0.343146			0.0588490
$35$	1.00000	+	2.44949i	0.169031	+	0.414039i
$36$		0			0
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	0.585786	+	1.01461i	0.0950271	+	0.164592i
$39$		0			0
$40$	−0.792893	+	1.37333i	−0.125367	+	0.217143i
$41$	2.17157			0.339143			0.169571	−	0.985518i	$-0.445762\pi$
$41$	2.17157			0.339143			0.169571	+	0.985518i	$0.445762\pi$
$42$		0			0
$43$	6.41421			0.978158			0.489079	−	0.872239i	$-0.337333\pi$
$43$	6.41421			0.978158			0.489079	+	0.872239i	$0.337333\pi$
$44$	−4.41421	+	7.64564i	−0.665468	+	1.15262i
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	0.414214			0.0585786
$51$		0			0
$52$	0.757359	+	1.31178i	0.105027	+	0.181912i
$53$	−3.41421	−	5.91359i	−0.468978	−	0.812294i	0.530393	−	0.847752i	$-0.322044\pi$
$53$	−3.41421	−	5.91359i	−0.468978	−	0.812294i	−0.999371	+	0.0354577i	$0.988711\pi$
$54$		0			0
$55$	4.82843			0.651065
$56$	2.57107	−	3.31552i	0.343573	−	0.443054i
$57$		0			0
$58$	−0.207107	+	0.358719i	−0.0271945	+	0.0471022i
$59$	−6.24264	−	10.8126i	−0.812723	−	1.40768i	−0.910952	−	0.412513i	$-0.864651\pi$
$59$	−6.24264	−	10.8126i	−0.812723	−	1.40768i	0.0982291	−	0.995164i	$-0.468682\pi$
$60$		0			0
$61$	5.74264	−	9.94655i	0.735270	−	1.27352i	−0.219335	−	0.975650i	$-0.570389\pi$
$61$	5.74264	−	9.94655i	0.735270	−	1.27352i	0.954605	−	0.297875i	$-0.0962779\pi$
$62$	−2.48528			−0.315631
$63$		0			0
$64$	−4.17157			−0.521447
$65$	0.414214	−	0.717439i	0.0513769	−	0.0889873i
$66$		0			0
$67$	−6.20711	−	10.7510i	−0.758319	−	1.31345i	−0.943707	−	0.330781i	$-0.892688\pi$
$67$	−6.20711	−	10.7510i	−0.758319	−	1.31345i	0.185389	−	0.982665i	$-0.440646\pi$
$68$	0.757359	−	1.31178i	0.0918433	−	0.159077i
$69$		0			0
$70$	−1.08579	−	0.148586i	−0.129776	−	0.0177595i
$71$	12.4853			1.48173			0.740865	−	0.671654i	$-0.234416\pi$
$71$	12.4853			1.48173			0.740865	+	0.671654i	$0.234416\pi$
$72$		0			0
$73$	−2.41421	−	4.18154i	−0.282562	−	0.489412i	0.689453	−	0.724331i	$-0.257851\pi$
$73$	−2.41421	−	4.18154i	−0.282562	−	0.489412i	−0.972015	+	0.234918i	$0.924518\pi$
$74$		0			0
$75$		0			0
$76$	5.17157			0.593220
$77$	−12.6569	−	1.73205i	−1.44238	−	0.197386i
$78$		0			0
$79$	−4.58579	+	7.94282i	−0.515941	+	0.893637i	0.483887	+	0.875130i	$0.339224\pi$
$79$	−4.58579	+	7.94282i	−0.515941	+	0.893637i	−0.999829	+	0.0185063i	$0.994109\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$	−0.449747	+	0.778985i	−0.0496663	+	0.0860246i
$83$	11.7279			1.28731			0.643653	−	0.765317i	$-0.277418\pi$
$83$	11.7279			1.28731			0.643653	+	0.765317i	$0.277418\pi$
$84$		0			0
$85$	−0.828427			−0.0898555
$86$	−1.32843	+	2.30090i	−0.143248	+	0.248113i
$87$		0			0
$88$	−3.82843	−	6.63103i	−0.408112	−	0.706870i
$89$	1.32843	−	2.30090i	0.140813	−	0.243895i	−0.786990	−	0.616966i	$-0.788362\pi$
$89$	1.32843	−	2.30090i	0.140813	−	0.243895i	0.927803	+	0.373070i	$0.121695\pi$
$90$		0			0
$91$	−1.34315	+	1.73205i	−0.140800	+	0.181568i
$92$	−4.41421			−0.460214
$93$		0			0
$94$	0.414214	+	0.717439i	0.0427229	+	0.0739982i
$95$	−1.41421	−	2.44949i	−0.145095	−	0.251312i
$96$		0			0
$97$	0.343146			0.0348412			0.0174206	−	0.999848i	$-0.494455\pi$
$97$	0.343146			0.0348412			0.0174206	+	0.999848i	$0.494455\pi$
$98$	2.79289	+	0.778985i	0.282125	+	0.0786894i
$99$		0			0
$100$	0.914214	−	1.58346i	0.0914214	−	0.158346i
$101$	6.15685	+	10.6640i	0.612630	+	1.06111i	0.990795	+	0.135368i	$0.0432217\pi$
$101$	6.15685	+	10.6640i	0.612630	+	1.06111i	−0.378165	+	0.925738i	$0.623445\pi$
$102$		0			0
$103$	−0.207107	+	0.358719i	−0.0204068	+	0.0353457i	−0.876048	−	0.482223i	$-0.839829\pi$
$103$	−0.207107	+	0.358719i	−0.0204068	+	0.0353457i	0.855642	+	0.517569i	$0.173163\pi$
$104$	−1.31371			−0.128820
$105$		0			0
$106$	2.82843			0.274721
$107$	1.37868	−	2.38794i	0.133282	−	0.230851i	−0.791658	−	0.610965i	$-0.790782\pi$
$107$	1.37868	−	2.38794i	0.133282	−	0.230851i	0.924940	+	0.380113i	$0.124115\pi$
$108$		0			0
$109$	−1.74264	−	3.01834i	−0.166915	−	0.289105i	0.770419	−	0.637538i	$-0.220047\pi$
$109$	−1.74264	−	3.01834i	−0.166915	−	0.289105i	−0.937334	+	0.348433i	$0.886714\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	−3.00000	−	7.34847i	−0.283473	−	0.694365i
$113$	−12.4853			−1.17452			−0.587258	−	0.809400i	$-0.699793\pi$
$113$	−12.4853			−1.17452			−0.587258	+	0.809400i	$0.699793\pi$
$114$		0			0
$115$	1.20711	+	2.09077i	0.112563	+	0.194965i
$116$	0.914214	+	1.58346i	0.0848826	+	0.147021i
$117$		0			0
$118$	5.17157			0.476082
$119$	2.17157	+	0.297173i	0.199068	+	0.0272418i
$120$		0			0
$121$	−6.15685	+	10.6640i	−0.559714	+	0.969453i
$122$	2.37868	+	4.11999i	0.215356	+	0.373007i
$123$		0			0
$124$	−5.48528	+	9.50079i	−0.492593	+	0.853196i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	13.3137			1.18140			0.590700	−	0.806891i	$-0.298852\pi$
$127$	13.3137			1.18140			0.590700	+	0.806891i	$0.298852\pi$
$128$	5.27817	−	9.14207i	0.466529	−	0.808052i
$129$		0			0
$130$	0.171573	+	0.297173i	0.0150479	+	0.0260638i
$131$	1.65685	−	2.86976i	0.144760	−	0.250732i	−0.784523	−	0.620099i	$-0.787092\pi$
$131$	1.65685	−	2.86976i	0.144760	−	0.250732i	0.929283	+	0.369368i	$0.120426\pi$
$132$		0			0
$133$	2.82843	+	6.92820i	0.245256	+	0.600751i
$134$	5.14214			0.444213
$135$		0			0
$136$	0.656854	+	1.13770i	0.0563248	+	0.0975574i
$137$	0.828427	+	1.43488i	0.0707773	+	0.122590i	0.899242	−	0.437451i	$-0.144119\pi$
$137$	0.828427	+	1.43488i	0.0707773	+	0.122590i	−0.828465	+	0.560041i	$0.810785\pi$
$138$		0			0
$139$	12.1421			1.02988			0.514941	−	0.857225i	$-0.327814\pi$
$139$	12.1421			1.02988			0.514941	+	0.857225i	$0.327814\pi$
$140$	−2.96447	+	3.82282i	−0.250543	+	0.323087i
$141$		0			0
$142$	−2.58579	+	4.47871i	−0.216994	+	0.375845i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$		0			0
$145$	0.500000	−	0.866025i	0.0415227	−	0.0719195i
$146$	2.00000			0.165521
$147$		0			0
$148$		0			0
$149$	−3.91421	+	6.77962i	−0.320665	+	0.555408i	−0.980625	−	0.195892i	$-0.937240\pi$
$149$	−3.91421	+	6.77962i	−0.320665	+	0.555408i	0.659961	+	0.751300i	$0.270573\pi$
$150$		0			0
$151$	−0.171573	−	0.297173i	−0.0139624	−	0.0241836i	0.858960	−	0.512043i	$-0.171111\pi$
$151$	−0.171573	−	0.297173i	−0.0139624	−	0.0241836i	−0.872922	+	0.487859i	$0.837778\pi$
$152$	−2.24264	+	3.88437i	−0.181902	+	0.315064i
$153$		0			0
$154$	3.24264	−	4.18154i	0.261299	−	0.336958i
$155$	6.00000			0.481932
$156$		0			0
$157$	2.65685	+	4.60181i	0.212040	+	0.367264i	0.952353	−	0.304998i	$-0.0986559\pi$
$157$	2.65685	+	4.60181i	0.212040	+	0.367264i	−0.740313	+	0.672263i	$0.765323\pi$
$158$	−1.89949	−	3.29002i	−0.151116	−	0.261740i
$159$		0			0
$160$	−4.41421			−0.348974
$161$	−2.41421	−	5.91359i	−0.190267	−	0.466056i
$162$		0			0
$163$	−11.8284	+	20.4874i	−0.926474	+	1.60470i	−0.137301	+	0.990529i	$0.543843\pi$
$163$	−11.8284	+	20.4874i	−0.926474	+	1.60470i	−0.789173	+	0.614170i	$0.789491\pi$
$164$	1.98528	+	3.43861i	0.155024	+	0.268510i
$165$		0			0
$166$	−2.42893	+	4.20703i	−0.188522	+	0.326529i
$167$	−19.5858			−1.51559			−0.757797	−	0.652491i	$-0.773724\pi$
$167$	−19.5858			−1.51559			−0.757797	+	0.652491i	$0.773724\pi$
$168$		0			0
$169$	−12.3137			−0.947208
$170$	0.171573	−	0.297173i	0.0131590	−	0.0227921i
$171$		0			0
$172$	5.86396	+	10.1567i	0.447123	+	0.774439i
$173$	−9.65685	+	16.7262i	−0.734197	+	1.27167i	0.220878	+	0.975302i	$0.429108\pi$
$173$	−9.65685	+	16.7262i	−0.734197	+	1.27167i	−0.955075	+	0.296365i	$0.904226\pi$
$174$		0			0
$175$	2.62132	+	0.358719i	0.198153	+	0.0271166i
$176$	−14.4853			−1.09187
$177$		0			0
$178$	0.550253	+	0.953065i	0.0412432	+	0.0714353i
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$		0			0
$181$	−8.65685			−0.643459			−0.321729	−	0.946832i	$-0.604264\pi$
$181$	−8.65685			−0.643459			−0.321729	+	0.946832i	$0.604264\pi$
$182$	−0.343146	−	0.840532i	−0.0254357	−	0.0623044i
$183$		0			0
$184$	1.91421	−	3.31552i	0.141118	−	0.244423i
$185$		0			0
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	3.65685			0.266704
$189$		0			0
$190$	1.17157			0.0849948
$191$	−3.58579	+	6.21076i	−0.259458	+	0.449395i	−0.966097	−	0.258180i	$-0.916877\pi$
$191$	−3.58579	+	6.21076i	−0.259458	+	0.449395i	0.706639	+	0.707575i	$0.250211\pi$
$192$		0			0
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−0.0710678	+	0.123093i	−0.00510237	+	0.00883757i
$195$		0			0
$196$	9.14214	−	8.95743i	0.653010	−	0.639816i
$197$	23.6569			1.68548			0.842741	−	0.538320i	$-0.180941\pi$
$197$	23.6569			1.68548			0.842741	+	0.538320i	$0.180941\pi$
$198$		0			0
$199$	−0.828427	−	1.43488i	−0.0587256	−	0.101716i	0.835168	−	0.549995i	$-0.185370\pi$
$199$	−0.828427	−	1.43488i	−0.0587256	−	0.101716i	−0.893894	+	0.448279i	$0.852037\pi$
$200$	0.792893	+	1.37333i	0.0560660	+	0.0971092i
$201$		0			0
$202$	−5.10051			−0.358870
$203$	−1.62132	+	2.09077i	−0.113794	+	0.146743i
$204$		0			0
$205$	1.08579	−	1.88064i	0.0758346	−	0.131349i
$206$	−0.0857864	−	0.148586i	−0.00597702	−	0.0103525i
$207$		0			0
$208$	−1.24264	+	2.15232i	−0.0861616	+	0.149236i
$209$	13.6569			0.944664
$210$		0			0
$211$	3.51472			0.241963			0.120982	−	0.992655i	$-0.461396\pi$
$211$	3.51472			0.241963			0.120982	+	0.992655i	$0.461396\pi$
$212$	6.24264	−	10.8126i	0.428746	−	0.742610i
$213$		0			0
$214$	0.571068	+	0.989118i	0.0390374	+	0.0676147i
$215$	3.20711	−	5.55487i	0.218723	−	0.378839i
$216$		0			0
$217$	−15.7279	−	2.15232i	−1.06768	−	0.146109i
$218$	1.44365			0.0977764
$219$		0			0
$220$	4.41421	+	7.64564i	0.297606	+	0.515469i
$221$	−0.343146	−	0.594346i	−0.0230825	−	0.0399800i
$222$		0			0
$223$	11.6569			0.780601			0.390300	−	0.920688i	$-0.372371\pi$
$223$	11.6569			0.780601			0.390300	+	0.920688i	$0.372371\pi$
$224$	11.5711	+	1.58346i	0.773124	+	0.105800i
$225$		0			0
$226$	2.58579	−	4.47871i	0.172004	−	0.297920i
$227$	13.4853	+	23.3572i	0.895050	+	1.55027i	0.833743	+	0.552152i	$0.186193\pi$
$227$	13.4853	+	23.3572i	0.895050	+	1.55027i	0.0613063	+	0.998119i	$0.480473\pi$
$228$		0			0
$229$	0.171573	−	0.297173i	0.0113379	−	0.0196377i	−0.860301	−	0.509787i	$-0.829724\pi$
$229$	0.171573	−	0.297173i	0.0113379	−	0.0196377i	0.871639	+	0.490149i	$0.163058\pi$
$230$	−1.00000			−0.0659380
$231$		0			0
$232$	−1.58579			−0.104112
$233$	−5.58579	+	9.67487i	−0.365937	+	0.633822i	−0.988926	−	0.148409i	$-0.952585\pi$
$233$	−5.58579	+	9.67487i	−0.365937	+	0.633822i	0.622989	+	0.782231i	$0.285918\pi$
$234$		0			0
$235$	−1.00000	−	1.73205i	−0.0652328	−	0.112987i
$236$	11.4142	−	19.7700i	0.743002	−	1.28692i
$237$		0			0
$238$	−0.556349	+	0.717439i	−0.0360628	+	0.0465047i
$239$	−1.31371			−0.0849767			−0.0424884	−	0.999097i	$-0.513529\pi$
$239$	−1.31371			−0.0849767			−0.0424884	+	0.999097i	$0.513529\pi$
$240$		0			0
$241$	−8.17157	−	14.1536i	−0.526377	−	0.911712i	−0.999528	−	0.0307305i	$-0.990217\pi$
$241$	−8.17157	−	14.1536i	−0.526377	−	0.911712i	0.473150	−	0.880982i	$-0.343117\pi$
$242$	−2.55025	−	4.41717i	−0.163936	−	0.283946i
$243$		0			0
$244$	21.0000			1.34439
$245$	−6.74264	−	1.88064i	−0.430772	−	0.120150i
$246$		0			0
$247$	1.17157	−	2.02922i	0.0745454	−	0.129116i
$248$	−4.75736	−	8.23999i	−0.302093	−	0.523240i
$249$		0			0
$250$	0.207107	−	0.358719i	0.0130986	−	0.0226874i
$251$	−13.3137			−0.840354			−0.420177	−	0.907442i	$-0.638032\pi$
$251$	−13.3137			−0.840354			−0.420177	+	0.907442i	$0.638032\pi$
$252$		0			0
$253$	−11.6569			−0.732860
$254$	−2.75736	+	4.77589i	−0.173012	+	0.299666i
$255$		0			0
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	8.82843	−	15.2913i	0.550702	−	0.953844i	−0.447522	−	0.894273i	$-0.647693\pi$
$257$	8.82843	−	15.2913i	0.550702	−	0.953844i	0.998224	−	0.0595711i	$-0.0189733\pi$
$258$		0			0
$259$		0			0
$260$	1.51472			0.0939389
$261$		0			0
$262$	0.686292	+	1.18869i	0.0423992	+	0.0734376i
$263$	9.52082	+	16.4905i	0.587079	+	1.01685i	0.994613	+	0.103660i	$0.0330554\pi$
$263$	9.52082	+	16.4905i	0.587079	+	1.01685i	−0.407534	+	0.913190i	$0.633611\pi$
$264$		0			0
$265$	−6.82843			−0.419467
$266$	−3.07107	−	0.420266i	−0.188299	−	0.0257682i
$267$		0			0
$268$	11.3492	−	19.6575i	0.693265	−	1.20077i
$269$	−15.2279	−	26.3755i	−0.928463	−	1.60814i	−0.785895	−	0.618360i	$-0.787798\pi$
$269$	−15.2279	−	26.3755i	−0.928463	−	1.60814i	−0.142568	−	0.989785i	$-0.545536\pi$
$270$		0			0
$271$	0.242641	−	0.420266i	0.0147394	−	0.0255293i	−0.858562	−	0.512710i	$-0.828641\pi$
$271$	0.242641	−	0.420266i	0.0147394	−	0.0255293i	0.873301	+	0.487181i	$0.161975\pi$
$272$	2.48528			0.150692
$273$		0			0
$274$	−0.686292			−0.0414604
$275$	2.41421	−	4.18154i	0.145583	−	0.252156i
$276$		0			0
$277$	6.07107	+	10.5154i	0.364775	+	0.631809i	0.988740	−	0.149643i	$-0.0478125\pi$
$277$	6.07107	+	10.5154i	0.364775	+	0.631809i	−0.623965	+	0.781452i	$0.714479\pi$
$278$	−2.51472	+	4.35562i	−0.150823	+	0.261233i
$279$		0			0
$280$	−1.58579	−	3.88437i	−0.0947689	−	0.232135i
$281$	−26.2843			−1.56799			−0.783994	−	0.620768i	$-0.786821\pi$
$281$	−26.2843			−1.56799			−0.783994	+	0.620768i	$0.786821\pi$
$282$		0			0
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$	11.4142	+	19.7700i	0.677309	+	1.17313i
$285$		0			0
$286$	−1.65685			−0.0979718
$287$	−3.52082	+	4.54026i	−0.207827	+	0.268003i
$288$		0			0
$289$	8.15685	−	14.1281i	0.479815	−	0.831064i
$290$	0.207107	+	0.358719i	0.0121617	+	0.0210647i
$291$		0			0
$292$	4.41421	−	7.64564i	0.258322	−	0.447427i
$293$	16.0000			0.934730			0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000			0.934730			0.467365	+	0.884064i	$0.345203\pi$
$294$		0			0
$295$	−12.4853			−0.726921
$296$		0			0
$297$		0			0
$298$	−1.62132	−	2.80821i	−0.0939206	−	0.162675i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	−10.3995	+	13.4106i	−0.599417	+	0.772977i
$302$	0.142136			0.00817899
$303$		0			0
$304$	4.24264	+	7.34847i	0.243332	+	0.421464i
$305$	−5.74264	−	9.94655i	−0.328823	−	0.569538i
$306$		0			0
$307$	−13.2426			−0.755797			−0.377899	−	0.925847i	$-0.623353\pi$
$307$	−13.2426			−0.755797			−0.377899	+	0.925847i	$0.623353\pi$
$308$	−8.82843	−	21.6251i	−0.503046	−	1.23221i
$309$		0			0
$310$	−1.24264	+	2.15232i	−0.0705772	+	0.122243i
$311$	−9.41421	−	16.3059i	−0.533831	−	0.924623i	−0.999219	−	0.0395157i	$-0.987418\pi$
$311$	−9.41421	−	16.3059i	−0.533831	−	0.924623i	0.465388	−	0.885107i	$-0.345915\pi$
$312$		0			0
$313$	8.82843	−	15.2913i	0.499012	−	0.864314i	−0.500987	−	0.865455i	$-0.667030\pi$
$313$	8.82843	−	15.2913i	0.499012	−	0.864314i	0.999999	+	0.00114023i	$0.000362947\pi$
$314$	−2.20101			−0.124210
$315$		0			0
$316$	−16.7696			−0.943361
$317$	12.8995	−	22.3426i	0.724508	−	1.25488i	−0.234668	−	0.972075i	$-0.575400\pi$
$317$	12.8995	−	22.3426i	0.724508	−	1.25488i	0.959176	−	0.282809i	$-0.0912662\pi$
$318$		0			0
$319$	2.41421	+	4.18154i	0.135170	+	0.234121i
$320$	−2.08579	+	3.61269i	−0.116599	+	0.201955i
$321$		0			0
$322$	2.62132	+	0.358719i	0.146080	+	0.0199907i
$323$	−2.34315			−0.130376
$324$		0			0
$325$	−0.414214	−	0.717439i	−0.0229764	−	0.0397964i
$326$	−4.89949	−	8.48617i	−0.271358	−	0.470006i
$327$		0			0
$328$	−3.44365			−0.190144
$329$	2.00000	+	4.89898i	0.110264	+	0.270089i
$330$		0			0
$331$	5.48528	−	9.50079i	0.301498	−	0.522210i	−0.674977	−	0.737839i	$-0.735847\pi$
$331$	5.48528	−	9.50079i	0.301498	−	0.522210i	0.976476	+	0.215628i	$0.0691799\pi$
$332$	10.7218	+	18.5707i	0.588437	+	1.01920i
$333$		0			0
$334$	4.05635	−	7.02580i	0.221954	−	0.384435i
$335$	−12.4142			−0.678261
$336$		0			0
$337$	14.8284			0.807756			0.403878	−	0.914813i	$-0.367662\pi$
$337$	14.8284			0.807756			0.403878	+	0.914813i	$0.367662\pi$
$338$	2.55025	−	4.41717i	0.138715	−	0.240262i
$339$		0			0
$340$	−0.757359	−	1.31178i	−0.0410736	−	0.0711415i
$341$	−14.4853	+	25.0892i	−0.784422	+	1.35866i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	−10.1716			−0.548414
$345$		0			0
$346$	−4.00000	−	6.92820i	−0.215041	−	0.372463i
$347$	11.0355	+	19.1141i	0.592418	+	1.02610i	0.993906	+	0.110234i	$0.0351601\pi$
$347$	11.0355	+	19.1141i	0.592418	+	1.02610i	−0.401487	+	0.915865i	$0.631507\pi$
$348$		0			0
$349$	−26.6569			−1.42691			−0.713454	−	0.700702i	$-0.752870\pi$
$349$	−26.6569			−1.42691			−0.713454	+	0.700702i	$0.752870\pi$
$350$	−0.671573	+	0.866025i	−0.0358971	+	0.0462910i
$351$		0			0
$352$	10.6569	−	18.4582i	0.568012	−	0.983826i
$353$	−10.5858	−	18.3351i	−0.563425	−	0.975880i	−0.997194	−	0.0748562i	$-0.976150\pi$
$353$	−10.5858	−	18.3351i	−0.563425	−	0.975880i	0.433770	−	0.901024i	$-0.357183\pi$
$354$		0			0
$355$	6.24264	−	10.8126i	0.331325	−	0.573872i
$356$	4.85786			0.257466
$357$		0			0
$358$	4.14214			0.218919
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$		0			0
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	1.79289	−	3.10538i	0.0942324	−	0.163215i
$363$		0			0
$364$	−3.97056	−	0.543359i	−0.208114	−	0.0284798i
$365$	−4.82843			−0.252731
$366$		0			0
$367$	5.62132	+	9.73641i	0.293431	+	0.508237i	0.974619	−	0.223872i	$-0.0718697\pi$
$367$	5.62132	+	9.73641i	0.293431	+	0.508237i	−0.681188	+	0.732108i	$0.738536\pi$
$368$	−3.62132	−	6.27231i	−0.188774	−	0.326967i
$369$		0			0
$370$		0			0
$371$	17.8995	+	2.44949i	0.929295	+	0.127171i
$372$		0			0
$373$	−6.48528	+	11.2328i	−0.335795	+	0.581614i	−0.983637	−	0.180160i	$-0.942338\pi$
$373$	−6.48528	+	11.2328i	−0.335795	+	0.581614i	0.647842	+	0.761775i	$0.275672\pi$
$374$	0.828427	+	1.43488i	0.0428369	+	0.0741958i
$375$		0			0
$376$	−1.58579	+	2.74666i	−0.0817807	+	0.141648i
$377$	0.828427			0.0426662
$378$		0			0
$379$	21.1716			1.08751			0.543755	−	0.839244i	$-0.317002\pi$
$379$	21.1716			1.08751			0.543755	+	0.839244i	$0.317002\pi$
$380$	2.58579	−	4.47871i	0.132648	−	0.229753i
$381$		0			0
$382$	−1.48528	−	2.57258i	−0.0759936	−	0.131625i
$383$	8.44975	−	14.6354i	0.431762	−	0.747834i	−0.565263	−	0.824911i	$-0.691225\pi$
$383$	8.44975	−	14.6354i	0.431762	−	0.747834i	0.997025	+	0.0770770i	$0.0245587\pi$
$384$		0			0
$385$	−7.82843	+	10.0951i	−0.398974	+	0.514496i
$386$	−0.828427			−0.0421658
$387$		0			0
$388$	0.313708	+	0.543359i	0.0159261	+	0.0275849i
$389$	6.17157	+	10.6895i	0.312911	+	0.541978i	0.978991	−	0.203902i	$-0.0653625\pi$
$389$	6.17157	+	10.6895i	0.312911	+	0.541978i	−0.666080	+	0.745880i	$0.732029\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	2.76346	+	10.7510i	0.139576	+	0.543009i
$393$		0			0
$394$	−4.89949	+	8.48617i	−0.246833	+	0.427527i
$395$	4.58579	+	7.94282i	0.230736	+	0.399646i
$396$		0			0
$397$	−14.3137	+	24.7921i	−0.718384	+	1.24428i	0.243255	+	0.969962i	$0.421785\pi$
$397$	−14.3137	+	24.7921i	−0.718384	+	1.24428i	−0.961640	+	0.274316i	$0.911549\pi$
$398$	0.686292			0.0344007
$399$		0			0
$400$	3.00000			0.150000
$401$	3.84315	−	6.65652i	0.191918	−	0.332411i	−0.753968	−	0.656911i	$-0.771863\pi$
$401$	3.84315	−	6.65652i	0.191918	−	0.332411i	0.945886	+	0.324500i	$0.105196\pi$
$402$		0			0
$403$	2.48528	+	4.30463i	0.123801	+	0.214429i
$404$	−11.2574	+	19.4983i	−0.560075	+	0.970078i
$405$		0			0
$406$	−0.414214	−	1.01461i	−0.0205571	−	0.0503543i
$407$		0			0
$408$		0			0
$409$	−12.3995	−	21.4766i	−0.613116	−	1.06195i	−0.990712	−	0.135977i	$-0.956583\pi$
$409$	−12.3995	−	21.4766i	−0.613116	−	1.06195i	0.377596	−	0.925970i	$-0.376751\pi$
$410$	0.449747	+	0.778985i	0.0222114	+	0.0384713i
$411$		0			0
$412$	−0.757359			−0.0373124
$413$	32.7279	+	4.47871i	1.61044	+	0.220383i
$414$		0			0
$415$	5.86396	−	10.1567i	0.287851	−	0.498572i
$416$	−1.82843	−	3.16693i	−0.0896460	−	0.155271i
$417$		0			0
$418$	−2.82843	+	4.89898i	−0.138343	+	0.239617i
$419$	23.3137			1.13895			0.569475	−	0.822009i	$-0.307147\pi$
$419$	23.3137			1.13895			0.569475	+	0.822009i	$0.307147\pi$
$420$		0			0
$421$	−3.48528			−0.169862			−0.0849311	−	0.996387i	$-0.527067\pi$
$421$	−3.48528			−0.169862			−0.0849311	+	0.996387i	$0.527067\pi$
$422$	−0.727922	+	1.26080i	−0.0354347	+	0.0613747i
$423$		0			0
$424$	5.41421	+	9.37769i	0.262937	+	0.455421i
$425$	−0.414214	+	0.717439i	−0.0200923	+	0.0348009i
$426$		0			0
$427$	11.4853	+	28.1331i	0.555812	+	1.36146i
$428$	5.04163			0.243696
$429$		0			0
$430$	1.32843	+	2.30090i	0.0640624	+	0.110959i
$431$	−10.8995	−	18.8785i	−0.525010	−	0.909344i	−0.999576	−	0.0291242i	$-0.990728\pi$
$431$	−10.8995	−	18.8785i	−0.525010	−	0.909344i	0.474566	−	0.880220i	$-0.342605\pi$
$432$		0			0
$433$	−31.7990			−1.52816			−0.764081	−	0.645120i	$-0.776807\pi$
$433$	−31.7990			−1.52816			−0.764081	+	0.645120i	$0.776807\pi$
$434$	4.02944	−	5.19615i	0.193419	−	0.249423i
$435$		0			0
$436$	3.18629	−	5.51882i	0.152596	−	0.264303i
$437$	3.41421	+	5.91359i	0.163324	+	0.282885i
$438$		0			0
$439$	−16.9706	+	29.3939i	−0.809961	+	1.40289i	0.102930	+	0.994689i	$0.467178\pi$
$439$	−16.9706	+	29.3939i	−0.809961	+	1.40289i	−0.912890	+	0.408205i	$0.866155\pi$
$440$	−7.65685			−0.365026
$441$		0			0
$442$	0.284271			0.0135214
$443$	−6.10660	+	10.5769i	−0.290133	+	0.502526i	−0.973841	−	0.227230i	$-0.927033\pi$
$443$	−6.10660	+	10.5769i	−0.290133	+	0.502526i	0.683708	+	0.729756i	$0.260366\pi$
$444$		0			0
$445$	−1.32843	−	2.30090i	−0.0629735	−	0.109073i
$446$	−2.41421	+	4.18154i	−0.114316	+	0.198002i
$447$		0			0
$448$	6.76346	−	8.72180i	0.319543	−	0.412066i
$449$	1.82843			0.0862888			0.0431444	−	0.999069i	$-0.486262\pi$
$449$	1.82843			0.0862888			0.0431444	+	0.999069i	$0.486262\pi$
$450$		0			0
$451$	5.24264	+	9.08052i	0.246866	+	0.427585i
$452$	−11.4142	−	19.7700i	−0.536879	−	0.929902i
$453$		0			0
$454$	−11.1716			−0.524308
$455$	0.828427	+	2.02922i	0.0388373	+	0.0951315i
$456$		0			0
$457$	16.1421	−	27.9590i	0.755097	−	1.30787i	−0.190229	−	0.981740i	$-0.560923\pi$
$457$	16.1421	−	27.9590i	0.755097	−	1.30787i	0.945326	−	0.326127i	$-0.105744\pi$
$458$	0.0710678	+	0.123093i	0.00332078	+	0.00575176i
$459$		0			0
$460$	−2.20711	+	3.82282i	−0.102907	+	0.178240i
$461$	−18.6863			−0.870307			−0.435154	−	0.900356i	$-0.643306\pi$
$461$	−18.6863			−0.870307			−0.435154	+	0.900356i	$0.643306\pi$
$462$		0			0
$463$	11.0416			0.513148			0.256574	−	0.966525i	$-0.417406\pi$
$463$	11.0416			0.513148			0.256574	+	0.966525i	$0.417406\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	−2.31371	−	4.00746i	−0.107180	−	0.185642i
$467$	−11.4497	+	19.8315i	−0.529831	+	0.917694i	0.469563	+	0.882899i	$0.344411\pi$
$467$	−11.4497	+	19.8315i	−0.529831	+	0.917694i	−0.999394	+	0.0347956i	$0.988922\pi$
$468$		0			0
$469$	32.5416	+	4.45322i	1.50263	+	0.205631i
$470$	0.828427			0.0382125
$471$		0			0
$472$	9.89949	+	17.1464i	0.455661	+	0.789228i
$473$	15.4853	+	26.8213i	0.712014	+	1.23324i
$474$		0			0
$475$	−2.82843			−0.129777
$476$	1.51472	+	3.71029i	0.0694270	+	0.170061i
$477$		0			0
$478$	0.272078	−	0.471253i	0.0124446	−	0.0215546i
$479$	−12.1716	−	21.0818i	−0.556133	−	0.963251i	−0.997814	−	0.0660791i	$-0.978951\pi$
$479$	−12.1716	−	21.0818i	−0.556133	−	0.963251i	0.441681	−	0.897172i	$-0.354382\pi$
$480$		0			0
$481$		0			0
$482$	6.76955			0.308345
$483$		0			0
$484$	−22.5147			−1.02340
$485$	0.171573	−	0.297173i	0.00779072	−	0.0134939i
$486$		0			0
$487$	−7.82843	−	13.5592i	−0.354740	−	0.614428i	0.632334	−	0.774696i	$-0.282097\pi$
$487$	−7.82843	−	13.5592i	−0.354740	−	0.614428i	−0.987073	+	0.160269i	$0.948764\pi$
$488$	−9.10660	+	15.7731i	−0.412236	+	0.714015i
$489$		0			0
$490$	2.07107	−	2.02922i	0.0935613	−	0.0916710i
$491$	13.3137			0.600839			0.300420	−	0.953807i	$-0.402873\pi$
$491$	13.3137			0.600839			0.300420	+	0.953807i	$0.402873\pi$
$492$		0			0
$493$	−0.414214	−	0.717439i	−0.0186552	−	0.0323118i
$494$	0.485281	+	0.840532i	0.0218338	+	0.0378173i
$495$		0			0
$496$	−18.0000			−0.808224
$497$	−20.2426	+	26.1039i	−0.908007	+	1.17092i
$498$		0			0
$499$	−2.41421	+	4.18154i	−0.108075	+	0.187191i	−0.914990	−	0.403476i	$-0.867802\pi$
$499$	−2.41421	+	4.18154i	−0.108075	+	0.187191i	0.806915	+	0.590667i	$0.201135\pi$
$500$	−0.914214	−	1.58346i	−0.0408849	−	0.0708147i
$501$		0			0
$502$	2.75736	−	4.77589i	0.123067	−	0.213158i
$503$	−37.8701			−1.68854			−0.844271	−	0.535916i	$-0.819966\pi$
$503$	−37.8701			−1.68854			−0.844271	+	0.535916i	$0.819966\pi$
$504$		0			0
$505$	12.3137			0.547953
$506$	2.41421	−	4.18154i	0.107325	−	0.185892i
$507$		0			0
$508$	12.1716	+	21.0818i	0.540026	+	0.935353i
$509$	12.3284	−	21.3535i	0.546448	−	0.946476i	−0.452066	−	0.891984i	$-0.649313\pi$
$509$	12.3284	−	21.3535i	0.546448	−	0.946476i	0.998514	−	0.0544912i	$-0.0173537\pi$
$510$		0			0
$511$	12.6569	+	1.73205i	0.559906	+	0.0766214i
$512$	22.7574			1.00574
$513$		0			0
$514$	3.65685	+	6.33386i	0.161297	+	0.279374i
$515$	0.207107	+	0.358719i	0.00912622	+	0.0158071i
$516$		0			0
$517$	9.65685			0.424708
$518$		0			0
$519$		0			0
$520$	−0.656854	+	1.13770i	−0.0288050	+	0.0498917i
$521$	−9.48528	−	16.4290i	−0.415558	−	0.719767i	0.579929	−	0.814667i	$-0.303080\pi$
$521$	−9.48528	−	16.4290i	−0.415558	−	0.719767i	−0.995487	+	0.0948999i	$0.969747\pi$
$522$		0			0
$523$	−12.1716	+	21.0818i	−0.532226	+	0.921842i	0.467066	+	0.884222i	$0.345311\pi$
$523$	−12.1716	+	21.0818i	−0.532226	+	0.921842i	−0.999292	+	0.0376197i	$0.988022\pi$
$524$	6.05887			0.264683
$525$		0			0
$526$	−7.88730			−0.343903
$527$	2.48528	−	4.30463i	0.108261	−	0.187513i
$528$		0			0
$529$	8.58579	+	14.8710i	0.373295	+	0.646566i
$530$	1.41421	−	2.44949i	0.0614295	−	0.106399i
$531$		0			0
$532$	−8.38478	+	10.8126i	−0.363526	+	0.468784i
$533$	1.79899			0.0779229
$534$		0			0
$535$	−1.37868	−	2.38794i	−0.0596055	−	0.103240i
$536$	9.84315	+	17.0488i	0.425159	+	0.736397i
$537$		0			0
$538$	12.6152			0.543881
$539$	24.1421	−	23.6544i	1.03988	−	1.01887i
$540$		0			0
$541$	−9.32843	+	16.1573i	−0.401060	+	0.694657i	−0.993854	−	0.110697i	$-0.964692\pi$
$541$	−9.32843	+	16.1573i	−0.401060	+	0.694657i	0.592794	+	0.805354i	$0.298025\pi$
$542$	0.100505	+	0.174080i	0.00431706	+	0.00747737i
$543$		0			0
$544$	−1.82843	+	3.16693i	−0.0783932	+	0.135781i
$545$	−3.48528			−0.149293
$546$		0			0
$547$	5.10051			0.218082			0.109041	−	0.994037i	$-0.465222\pi$
$547$	5.10051			0.218082			0.109041	+	0.994037i	$0.465222\pi$
$548$	−1.51472	+	2.62357i	−0.0647056	+	0.112073i
$549$		0			0
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	1.41421	−	2.44949i	0.0602475	−	0.104352i
$552$		0			0
$553$	−9.17157	−	22.4657i	−0.390015	−	0.955338i
$554$	−5.02944			−0.213680
$555$		0			0
$556$	11.1005	+	19.2266i	0.470766	+	0.815391i
$557$	−17.1421	−	29.6910i	−0.726336	−	1.25805i	−0.958422	−	0.285355i	$-0.907889\pi$
$557$	−17.1421	−	29.6910i	−0.726336	−	1.25805i	0.232086	−	0.972695i	$-0.425445\pi$
$558$		0			0
$559$	5.31371			0.224746
$560$	−7.86396	−	1.07616i	−0.332313	−	0.0454760i
$561$		0			0
$562$	5.44365	−	9.42868i	0.229627	−	0.397725i
$563$	8.13604	+	14.0920i	0.342893	+	0.593908i	0.984969	−	0.172733i	$-0.0552598\pi$
$563$	8.13604	+	14.0920i	0.342893	+	0.593908i	−0.642076	+	0.766641i	$0.721926\pi$
$564$		0			0
$565$	−6.24264	+	10.8126i	−0.262630	+	0.454888i
$566$	5.79899			0.243750
$567$		0			0
$568$	−19.7990			−0.830747
$569$	−1.82843	+	3.16693i	−0.0766517	+	0.132765i	−0.901803	−	0.432147i	$-0.857756\pi$
$569$	−1.82843	+	3.16693i	−0.0766517	+	0.132765i	0.825152	+	0.564911i	$0.191090\pi$
$570$		0			0
$571$	−7.41421	−	12.8418i	−0.310275	−	0.537412i	0.668147	−	0.744030i	$-0.267088\pi$
$571$	−7.41421	−	12.8418i	−0.310275	−	0.537412i	−0.978422	+	0.206617i	$0.933755\pi$
$572$	−3.65685	+	6.33386i	−0.152901	+	0.264832i
$573$		0			0
$574$	−0.899495	−	2.20330i	−0.0375442	−	0.0919641i
$575$	2.41421			0.100680
$576$		0			0
$577$	−11.9706	−	20.7336i	−0.498341	−	0.863152i	0.501657	−	0.865067i	$-0.332724\pi$
$577$	−11.9706	−	20.7336i	−0.498341	−	0.863152i	−0.999998	+	0.00191453i	$0.999391\pi$
$578$	3.37868	+	5.85204i	0.140535	+	0.243413i
$579$		0			0
$580$	1.82843			0.0759213
$581$	−19.0147	+	24.5204i	−0.788863	+	1.01728i
$582$		0			0
$583$	16.4853	−	28.5533i	0.682751	−	1.18256i
$584$	3.82843	+	6.63103i	0.158421	+	0.274394i
$585$		0			0
$586$	−3.31371	+	5.73951i	−0.136888	+	0.237097i
$587$	−22.2843			−0.919770			−0.459885	−	0.887978i	$-0.652109\pi$
$587$	−22.2843			−0.919770			−0.459885	+	0.887978i	$0.652109\pi$
$588$		0			0
$589$	16.9706			0.699260
$590$	2.58579	−	4.47871i	0.106455	−	0.184386i
$591$		0			0
$592$		0			0
$593$	21.8995	−	37.9310i	0.899304	−	1.55764i	0.0709193	−	0.997482i	$-0.477407\pi$
$593$	21.8995	−	37.9310i	0.899304	−	1.55764i	0.828385	−	0.560159i	$-0.189260\pi$
$594$		0			0
$595$	1.34315	−	1.73205i	0.0550636	−	0.0710072i
$596$	−14.3137			−0.586312
$597$		0			0
$598$	−0.414214	−	0.717439i	−0.0169385	−	0.0293383i
$599$	8.82843	+	15.2913i	0.360720	+	0.624785i	0.988079	−	0.153945i	$-0.0491977\pi$
$599$	8.82843	+	15.2913i	0.360720	+	0.624785i	−0.627360	+	0.778730i	$0.715864\pi$
$600$		0			0
$601$	8.34315			0.340324			0.170162	−	0.985416i	$-0.445571\pi$
$601$	8.34315			0.340324			0.170162	+	0.985416i	$0.445571\pi$
$602$	−2.65685	−	6.50794i	−0.108285	−	0.265244i
$603$		0			0
$604$	0.313708	−	0.543359i	0.0127646	−	0.0221090i
$605$	6.15685	+	10.6640i	0.250312	+	0.433553i
$606$		0			0
$607$	2.10660	−	3.64874i	0.0855043	−	0.148098i	−0.820102	−	0.572218i	$-0.806083\pi$
$607$	2.10660	−	3.64874i	0.0855043	−	0.148098i	0.905606	+	0.424120i	$0.139417\pi$
$608$	−12.4853			−0.506345
$609$		0			0
$610$	4.75736			0.192620
$611$	0.828427	−	1.43488i	0.0335146	−	0.0580489i
$612$		0			0
$613$	7.72792	+	13.3852i	0.312128	+	0.540621i	0.978823	−	0.204709i	$-0.0656249\pi$
$613$	7.72792	+	13.3852i	0.312128	+	0.540621i	−0.666695	+	0.745331i	$0.732292\pi$
$614$	2.74264	−	4.75039i	0.110684	−	0.191710i
$615$		0			0
$616$	20.0711	+	2.74666i	0.808686	+	0.110666i
$617$	11.3137			0.455473			0.227736	−	0.973723i	$-0.426868\pi$
$617$	11.3137			0.455473			0.227736	+	0.973723i	$0.426868\pi$
$618$		0			0
$619$	−21.2426	−	36.7933i	−0.853814	−	1.47885i	−0.877741	−	0.479135i	$-0.840950\pi$
$619$	−21.2426	−	36.7933i	−0.853814	−	1.47885i	0.0239273	−	0.999714i	$-0.492383\pi$
$620$	5.48528	+	9.50079i	0.220294	+	0.381561i
$621$		0			0
$622$	7.79899			0.312711
$623$	2.65685	+	6.50794i	0.106445	+	0.260735i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.65685	+	6.33386i	0.146157	+	0.253152i
$627$		0			0
$628$	−4.85786	+	8.41407i	−0.193850	+	0.335758i
$629$		0			0
$630$		0			0
$631$	8.14214			0.324133			0.162067	−	0.986780i	$-0.448184\pi$
$631$	8.14214			0.324133			0.162067	+	0.986780i	$0.448184\pi$
$632$	7.27208	−	12.5956i	0.289268	−	0.501026i
$633$		0			0
$634$	5.34315	+	9.25460i	0.212203	+	0.367547i
$635$	6.65685	−	11.5300i	0.264169	−	0.457554i
$636$		0			0
$637$	−1.44365	−	5.61642i	−0.0571995	−	0.222531i
$638$	−2.00000			−0.0791808
$639$		0			0
$640$	−5.27817	−	9.14207i	−0.208638	−	0.361372i
$641$	7.25736	+	12.5701i	0.286648	+	0.496490i	0.973008	−	0.230773i	$-0.0741255\pi$
$641$	7.25736	+	12.5701i	0.286648	+	0.496490i	−0.686359	+	0.727263i	$0.740792\pi$
$642$		0			0
$643$	−30.2843			−1.19430			−0.597148	−	0.802131i	$-0.703699\pi$
$643$	−30.2843			−1.19430			−0.597148	+	0.802131i	$0.703699\pi$
$644$	7.15685	−	9.22911i	0.282020	−	0.363678i
$645$		0			0
$646$	0.485281	−	0.840532i	0.0190931	−	0.0330703i
$647$	8.52082	+	14.7585i	0.334988	+	0.580216i	0.983482	−	0.181003i	$-0.0579345\pi$
$647$	8.52082	+	14.7585i	0.334988	+	0.580216i	−0.648495	+	0.761219i	$0.724601\pi$
$648$		0			0
$649$	30.1421	−	52.2077i	1.18318	−	2.04933i
$650$	0.343146			0.0134593
$651$		0			0
$652$	−43.2548			−1.69399
$653$	−12.4142	+	21.5020i	−0.485806	+	0.841440i	−0.999867	−	0.0163133i	$-0.994807\pi$
$653$	−12.4142	+	21.5020i	−0.485806	+	0.841440i	0.514061	+	0.857754i	$0.328140\pi$
$654$		0			0
$655$	−1.65685	−	2.86976i	−0.0647387	−	0.112131i
$656$	−3.25736	+	5.64191i	−0.127179	+	0.220280i
$657$		0			0
$658$	−2.17157	−	0.297173i	−0.0846567	−	0.0115850i
$659$	−26.8284			−1.04509			−0.522544	−	0.852613i	$-0.675017\pi$
$659$	−26.8284			−1.04509			−0.522544	+	0.852613i	$0.675017\pi$
$660$		0			0
$661$	−13.0858	−	22.6652i	−0.508978	−	0.881576i	−0.999946	−	0.0103982i	$-0.996690\pi$
$661$	−13.0858	−	22.6652i	−0.508978	−	0.881576i	0.490968	−	0.871178i	$-0.336643\pi$
$662$	2.27208	+	3.93535i	0.0883068	+	0.152952i
$663$		0			0
$664$	−18.5980			−0.721742
$665$	7.41421	+	1.01461i	0.287511	+	0.0393450i
$666$		0			0
$667$	−1.20711	+	2.09077i	−0.0467394	+	0.0809549i
$668$	−17.9056	−	31.0134i	−0.692788	−	1.19994i
$669$		0			0
$670$	2.57107	−	4.45322i	0.0993290	−	0.172043i
$671$	55.4558			2.14085
$672$		0			0
$673$	18.3431			0.707076			0.353538	−	0.935420i	$-0.384978\pi$
$673$	18.3431			0.707076			0.353538	+	0.935420i	$0.384978\pi$
$674$	−3.07107	+	5.31925i	−0.118293	+	0.204890i
$675$		0			0
$676$	−11.2574	−	19.4983i	−0.432975	−	0.749935i
$677$	0.0710678	−	0.123093i	0.00273136	−	0.00473085i	−0.864656	−	0.502364i	$-0.832464\pi$
$677$	0.0710678	−	0.123093i	0.00273136	−	0.00473085i	0.867388	+	0.497633i	$0.165797\pi$
$678$		0			0
$679$	−0.556349	+	0.717439i	−0.0213507	+	0.0275328i
$680$	1.31371			0.0503784
$681$		0			0
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−21.6213	−	37.4492i	−0.827317	−	1.43295i	−0.900136	−	0.435610i	$-0.856533\pi$
$683$	−21.6213	−	37.4492i	−0.827317	−	1.43295i	0.0728189	−	0.997345i	$-0.476801\pi$
$684$		0			0
$685$	1.65685			0.0633051
$686$	−6.15685	+	4.57631i	−0.235070	+	0.174724i
$687$		0			0
$688$	−9.62132	+	16.6646i	−0.366809	+	0.635333i
$689$	−2.82843	−	4.89898i	−0.107754	−	0.186636i
$690$		0			0
$691$	2.41421	−	4.18154i	0.0918410	−	0.159073i	−0.816445	−	0.577423i	$-0.804058\pi$
$691$	2.41421	−	4.18154i	0.0918410	−	0.159073i	0.908286	+	0.418350i	$0.137392\pi$
$692$	−35.3137			−1.34243
$693$		0			0
$694$	−9.14214			−0.347031
$695$	6.07107	−	10.5154i	0.230289	−	0.398872i
$696$		0			0
$697$	−0.899495	−	1.55797i	−0.0340708	−	0.0590124i
$698$	5.52082	−	9.56233i	0.208966	−	0.361940i
$699$		0			0
$700$	1.82843	+	4.47871i	0.0691080	+	0.169279i
$701$	42.7990			1.61650			0.808248	−	0.588843i	$-0.200416\pi$
$701$	42.7990			1.61650			0.808248	+	0.588843i	$0.200416\pi$
$702$		0			0
$703$		0			0
$704$	−10.0711	−	17.4436i	−0.379568	−	0.657430i
$705$		0			0
$706$	8.76955			0.330046
$707$	−32.2782	−	4.41717i	−1.21395	−	0.166125i
$708$		0			0
$709$	−19.1569	+	33.1806i	−0.719451	+	1.24613i	0.241767	+	0.970334i	$0.422273\pi$
$709$	−19.1569	+	33.1806i	−0.719451	+	1.24613i	−0.961218	+	0.275791i	$0.911060\pi$
$710$	2.58579	+	4.47871i	0.0970428	+	0.168083i
$711$		0			0
$712$	−2.10660	+	3.64874i	−0.0789482	+	0.136742i
$713$	−14.4853			−0.542478
$714$		0			0
$715$	4.00000			0.149592
$716$	9.14214	−	15.8346i	0.341658	−	0.591768i
$717$		0			0
$718$	−2.07107	−	3.58719i	−0.0772916	−	0.133873i
$719$	−20.5563	+	35.6046i	−0.766622	+	1.32783i	0.172762	+	0.984964i	$0.444731\pi$
$719$	−20.5563	+	35.6046i	−0.766622	+	1.32783i	−0.939385	+	0.342865i	$0.888602\pi$
$720$		0			0
$721$	−0.414214	−	1.01461i	−0.0154261	−	0.0377861i
$722$	−4.55635			−0.169570
$723$		0			0
$724$	−7.91421	−	13.7078i	−0.294129	−	0.509447i
$725$	−0.500000	−	0.866025i	−0.0185695	−	0.0321634i
$726$		0			0
$727$	−40.4142			−1.49888			−0.749440	−	0.662072i	$-0.769677\pi$
$727$	−40.4142			−1.49888			−0.749440	+	0.662072i	$0.769677\pi$
$728$	2.12994	−	2.74666i	0.0789409	−	0.101798i
$729$		0			0
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$	−2.65685	−	4.60181i	−0.0982673	−	0.170204i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	−4.65685			−0.171888
$735$		0			0
$736$	10.6569			0.392817
$737$	29.9706	−	51.9105i	1.10398	−	1.91215i
$738$		0			0
$739$	−20.5563	−	35.6046i	−0.756178	−	1.30974i	−0.944787	−	0.327686i	$-0.893731\pi$
$739$	−20.5563	−	35.6046i	−0.756178	−	1.30974i	0.188609	−	0.982052i	$-0.439602\pi$
$740$		0			0
$741$		0			0
$742$	−4.58579	+	5.91359i	−0.168350	+	0.217095i
$743$	1.92893			0.0707657			0.0353828	−	0.999374i	$-0.488735\pi$
$743$	1.92893			0.0707657			0.0353828	+	0.999374i	$0.488735\pi$
$744$		0			0
$745$	3.91421	+	6.77962i	0.143406	+	0.248386i
$746$	−2.68629	−	4.65279i	−0.0983521	−	0.170351i
$747$		0			0
$748$	7.31371			0.267416
$749$	2.75736	+	6.75412i	0.100752	+	0.246790i
$750$		0			0
$751$	20.8284	−	36.0759i	0.760040	−	1.31643i	−0.182789	−	0.983152i	$-0.558513\pi$
$751$	20.8284	−	36.0759i	0.760040	−	1.31643i	0.942829	−	0.333276i	$-0.108154\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$	−0.171573	+	0.297173i	−0.00624832	+	0.0108224i
$755$	−0.343146			−0.0124884
$756$		0			0
$757$	19.4558			0.707135			0.353567	−	0.935409i	$-0.384969\pi$
$757$	19.4558			0.707135			0.353567	+	0.935409i	$0.384969\pi$
$758$	−4.38478	+	7.59466i	−0.159262	+	0.275850i
$759$		0			0
$760$	2.24264	+	3.88437i	0.0813491	+	0.140901i
$761$	−6.65685	+	11.5300i	−0.241311	+	0.417963i	−0.961088	−	0.276243i	$-0.910911\pi$
$761$	−6.65685	+	11.5300i	−0.241311	+	0.417963i	0.719777	+	0.694205i	$0.244244\pi$
$762$		0			0
$763$	9.13604	+	1.25024i	0.330747	+	0.0452617i
$764$	−13.1127			−0.474401
$765$		0			0
$766$	3.50000	+	6.06218i	0.126460	+	0.219035i
$767$	−5.17157	−	8.95743i	−0.186735	−	0.323434i
$768$		0			0
$769$	44.6274			1.60931			0.804653	−	0.593745i	$-0.202351\pi$
$769$	44.6274			1.60931			0.804653	+	0.593745i	$0.202351\pi$
$770$	−2.00000	−	4.89898i	−0.0720750	−	0.176547i
$771$		0			0
$772$	−1.82843	+	3.16693i	−0.0658065	+	0.113980i
$773$	12.5563	+	21.7482i	0.451620	+	0.782230i	0.998487	−	0.0549903i	$-0.0175128\pi$
$773$	12.5563	+	21.7482i	0.451620	+	0.782230i	−0.546866	+	0.837220i	$0.684179\pi$
$774$		0			0
$775$	3.00000	−	5.19615i	0.107763	−	0.186651i
$776$	−0.544156			−0.0195341
$777$		0			0
$778$	−5.11270			−0.183299
$779$	3.07107	−	5.31925i	0.110032	−	0.190582i
$780$		0			0
$781$	30.1421	+	52.2077i	1.07857	+	1.86814i
$782$	−0.414214	+	0.717439i	−0.0148122	+	0.0256556i
$783$		0			0
$784$	20.2279	+	5.64191i	0.722426	+	0.201497i
$785$	5.31371			0.189654
$786$		0			0
$787$	14.2782	+	24.7305i	0.508962	+	0.881548i	0.999946	+	0.0103795i	$0.00330395\pi$
$787$	14.2782	+	24.7305i	0.508962	+	0.881548i	−0.490984	+	0.871168i	$0.663363\pi$
$788$	21.6274	+	37.4598i	0.770445	+	1.33445i
$789$		0			0
$790$	−3.79899			−0.135162
$791$	20.2426	−	26.1039i	0.719745	−	0.928146i
$792$		0			0
$793$	4.75736	−	8.23999i	0.168939	−	0.292611i
$794$	−5.92893	−	10.2692i	−0.210410	−	0.364441i
$795$		0			0
$796$	1.51472	−	2.62357i	0.0536878	−	0.0929900i
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$	−1.65685			−0.0586153
$800$	−2.20711	+	3.82282i	−0.0780330	+	0.135157i
$801$		0			0
$802$	1.59188	+	2.75722i	0.0562113	+	0.0973609i
$803$	11.6569	−	20.1903i	0.411361	−	0.712499i
$804$		0			0
$805$	−6.32843	−	0.866025i	−0.223048	−	0.0305234i
$806$	−2.05887			−0.0725208
$807$		0			0
$808$	−9.76346	−	16.9108i	−0.343477	−	0.594920i
$809$	−4.81371	−	8.33759i	−0.169241	−	0.293134i	0.768912	−	0.639354i	$-0.220798\pi$
$809$	−4.81371	−	8.33759i	−0.169241	−	0.293134i	−0.938153	+	0.346220i	$0.887465\pi$
$810$		0			0
$811$	24.6274			0.864786			0.432393	−	0.901685i	$-0.357669\pi$
$811$	24.6274			0.864786			0.432393	+	0.901685i	$0.357669\pi$
$812$	−4.79289	−	0.655892i	−0.168198	−	0.0230173i
$813$		0			0
$814$		0			0
$815$	11.8284	+	20.4874i	0.414332	+	0.717644i
$816$		0			0
$817$	9.07107	−	15.7116i	0.317356	−	0.549678i
$818$	10.2721			0.359155
$819$		0			0
$820$	3.97056			0.138658
$821$	−9.97056	+	17.2695i	−0.347975	+	0.602710i	−0.985890	−	0.167397i	$-0.946464\pi$
$821$	−9.97056	+	17.2695i	−0.347975	+	0.602710i	0.637915	+	0.770107i	$0.279797\pi$
$822$		0			0
$823$	6.03553	+	10.4539i	0.210385	+	0.364398i	0.951835	−	0.306610i	$-0.0991948\pi$
$823$	6.03553	+	10.4539i	0.210385	+	0.364398i	−0.741450	+	0.671008i	$0.765861\pi$
$824$	0.328427	−	0.568852i	0.0114413	−	0.0198169i
$825$		0			0
$826$	−8.38478	+	10.8126i	−0.291744	+	0.376217i
$827$	−16.2132			−0.563788			−0.281894	−	0.959446i	$-0.590963\pi$
$827$	−16.2132			−0.563788			−0.281894	+	0.959446i	$0.590963\pi$
$828$		0			0
$829$	−3.34315	−	5.79050i	−0.116112	−	0.201112i	0.802112	−	0.597174i	$-0.203710\pi$
$829$	−3.34315	−	5.79050i	−0.116112	−	0.201112i	−0.918224	+	0.396062i	$0.870377\pi$
$830$	2.42893	+	4.20703i	0.0843095	+	0.146028i
$831$		0			0
$832$	−3.45584			−0.119810
$833$	−4.14214	+	4.05845i	−0.143516	+	0.140617i
$834$		0			0
$835$	−9.79289	+	16.9618i	−0.338897	+	0.586987i
$836$	12.4853	+	21.6251i	0.431812	+	0.747921i
$837$		0			0
$838$	−4.82843	+	8.36308i	−0.166795	+	0.288898i
$839$	−20.8284			−0.719077			−0.359539	−	0.933130i	$-0.617066\pi$
$839$	−20.8284			−0.719077			−0.359539	+	0.933130i	$0.617066\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	0.721825	−	1.25024i	0.0248757	−	0.0430861i
$843$		0			0
$844$	3.21320	+	5.56543i	0.110603	+	0.191570i
$845$	−6.15685	+	10.6640i	−0.211802	+	0.366852i
$846$		0			0
$847$	−12.3137	−	30.1623i	−0.423104	−	1.03639i
$848$	20.4853			0.703467
$849$		0			0
$850$	−0.171573	−	0.297173i	−0.00588490	−	0.0101929i
$851$		0			0
$852$		0			0
$853$	53.4558			1.83029			0.915147	−	0.403121i	$-0.132075\pi$
$853$	53.4558			1.83029			0.915147	+	0.403121i	$0.132075\pi$
$854$	−12.4706	−	1.70656i	−0.426734	−	0.0583972i
$855$		0			0
$856$	−2.18629	+	3.78677i	−0.0747259	+	0.129429i
$857$	−11.1421	−	19.2987i	−0.380608	−	0.659233i	0.610541	−	0.791985i	$-0.290952\pi$
$857$	−11.1421	−	19.2987i	−0.380608	−	0.659233i	−0.991149	+	0.132752i	$0.957619\pi$
$858$		0			0
$859$	−23.3137	+	40.3805i	−0.795453	+	1.37777i	0.127097	+	0.991890i	$0.459434\pi$
$859$	−23.3137	+	40.3805i	−0.795453	+	1.37777i	−0.922551	+	0.385876i	$0.873899\pi$
$860$	11.7279			0.399919
$861$		0			0
$862$	9.02944			0.307544
$863$	−8.27817	+	14.3382i	−0.281792	+	0.488079i	−0.971826	−	0.235698i	$-0.924262\pi$
$863$	−8.27817	+	14.3382i	−0.281792	+	0.488079i	0.690034	+	0.723777i	$0.257596\pi$
$864$		0			0
$865$	9.65685	+	16.7262i	0.328343	+	0.568707i
$866$	6.58579	−	11.4069i	0.223794	−	0.387623i
$867$		0			0
$868$	−10.9706	−	26.8723i	−0.372365	−	0.912105i
$869$	−44.2843			−1.50224
$870$		0			0
$871$	−5.14214	−	8.90644i	−0.174235	−	0.301783i
$872$	2.76346	+	4.78645i	0.0935824	+	0.162090i
$873$		0			0
$874$	−2.82843			−0.0956730
$875$	1.62132	−	2.09077i	0.0548106	−	0.0706809i
$876$		0			0
$877$	−15.4142	+	26.6982i	−0.520501	+	0.901534i	0.479215	+	0.877698i	$0.340921\pi$
$877$	−15.4142	+	26.6982i	−0.520501	+	0.901534i	−0.999716	+	0.0238366i	$0.992412\pi$
$878$	−7.02944	−	12.1753i	−0.237232	−	0.410898i
$879$		0			0
$880$	−7.24264	+	12.5446i	−0.244149	+	0.422879i
$881$	3.82843			0.128983			0.0644915	−	0.997918i	$-0.479457\pi$
$881$	3.82843			0.128983			0.0644915	+	0.997918i	$0.479457\pi$
$882$		0			0
$883$	−38.2843			−1.28837			−0.644184	−	0.764870i	$-0.722803\pi$
$883$	−38.2843			−1.28837			−0.644184	+	0.764870i	$0.722803\pi$
$884$	0.627417	−	1.08672i	0.0211023	−	0.0365503i
$885$		0			0
$886$	−2.52944	−	4.38111i	−0.0849781	−	0.147186i
$887$	22.0355	−	38.1667i	0.739881	−	1.28151i	−0.212668	−	0.977125i	$-0.568215\pi$
$887$	22.0355	−	38.1667i	0.739881	−	1.28151i	0.952549	−	0.304387i	$-0.0984515\pi$
$888$		0			0
$889$	−21.5858	+	27.8359i	−0.723964	+	0.933586i
$890$	1.10051			0.0368890
$891$		0			0
$892$	10.6569	+	18.4582i	0.356818	+	0.618027i
$893$	−2.82843	−	4.89898i	−0.0946497	−	0.163938i
$894$		0			0
$895$	−10.0000			−0.334263
$896$	10.5563	+	25.8577i	0.352663	+	0.863844i
$897$		0			0
$898$	−0.378680	+	0.655892i	−0.0126367	+	0.0218874i
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$		0			0
$901$	−2.82843	+	4.89898i	−0.0942286	+	0.163209i
$902$	−4.34315			−0.144611
$903$		0			0
$904$	19.7990			0.658505
$905$	−4.32843	+	7.49706i	−0.143882	+	0.249211i
$906$		0			0
$907$	−14.1066	−	24.4334i	−0.468402	−	0.811296i	0.530946	−	0.847406i	$-0.321837\pi$
$907$	−14.1066	−	24.4334i	−0.468402	−	0.811296i	−0.999348	+	0.0361097i	$0.988503\pi$
$908$	−24.6569	+	42.7069i	−0.818266	+	1.41728i
$909$		0			0
$910$	−0.899495	−	0.123093i	−0.0298180	−	0.00408050i
$911$	49.7990			1.64991			0.824957	−	0.565195i	$-0.191199\pi$
$911$	49.7990			1.64991			0.824957	+	0.565195i	$0.191199\pi$
$912$		0			0
$913$	28.3137	+	49.0408i	0.937047	+	1.62301i
$914$	6.68629	+	11.5810i	0.221163	+	0.383065i
$915$		0			0
$916$	0.627417			0.0207304
$917$	3.31371	+	8.11689i	0.109428	+	0.268043i
$918$		0			0
$919$	−9.55635	+	16.5521i	−0.315235	+	0.546003i	−0.979487	−	0.201505i	$-0.935417\pi$
$919$	−9.55635	+	16.5521i	−0.315235	+	0.546003i	0.664253	+	0.747508i	$0.268750\pi$
$920$	−1.91421	−	3.31552i	−0.0631098	−	0.109309i
$921$		0			0
$922$	3.87006	−	6.70314i	0.127454	−	0.220756i
$923$	10.3431			0.340449
$924$		0			0
$925$		0			0
$926$	−2.28680	+	3.96085i	−0.0751488	+	0.130162i
$927$		0			0
$928$	−2.20711	−	3.82282i	−0.0724518	−	0.125490i
$929$	−5.74264	+	9.94655i	−0.188410	+	0.326336i	−0.944720	−	0.327877i	$-0.893667\pi$
$929$	−5.74264	+	9.94655i	−0.188410	+	0.326336i	0.756310	+	0.654213i	$0.227000\pi$
$930$		0			0
$931$	−19.0711	−	5.31925i	−0.625029	−	0.174331i
$932$	−20.4264			−0.669089
$933$		0			0
$934$	−4.74264	−	8.21449i	−0.155184	−	0.268786i
$935$	−2.00000	−	3.46410i	−0.0654070	−	0.113288i
$936$		0			0
$937$	−10.6274			−0.347183			−0.173591	−	0.984818i	$-0.555537\pi$
$937$	−10.6274			−0.347183			−0.173591	+	0.984818i	$0.555537\pi$
$938$	−8.33705	+	10.7510i	−0.272214	+	0.351033i
$939$		0			0
$940$	1.82843	−	3.16693i	0.0596367	−	0.103294i
$941$	5.14214	+	8.90644i	0.167629	+	0.290342i	0.937586	−	0.347754i	$-0.113056\pi$
$941$	5.14214	+	8.90644i	0.167629	+	0.290342i	−0.769957	+	0.638096i	$0.779722\pi$
$942$		0			0
$943$	−2.62132	+	4.54026i	−0.0853619	+	0.147851i
$944$	37.4558			1.21908
$945$		0			0
$946$	−12.8284			−0.417088
$947$	−21.5919	+	37.3982i	−0.701642	+	1.21528i	0.266248	+	0.963905i	$0.414216\pi$
$947$	−21.5919	+	37.3982i	−0.701642	+	1.21528i	−0.967890	+	0.251375i	$0.919117\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	0.585786	−	1.01461i	0.0190054	−	0.0329184i
$951$		0			0
$952$	−3.44365	−	0.471253i	−0.111609	−	0.0152734i
$953$	2.34315			0.0759019			0.0379510	−	0.999280i	$-0.487917\pi$
$953$	2.34315			0.0759019			0.0379510	+	0.999280i	$0.487917\pi$
$954$		0			0
$955$	3.58579	+	6.21076i	0.116033	+	0.200976i
$956$	−1.20101	−	2.08021i	−0.0388434	−	0.0672788i
$957$		0			0
$958$	10.0833			0.325775
$959$	−4.34315	−	0.594346i	−0.140247	−	0.0191924i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$		0			0
$964$	14.9411	−	25.8788i	0.481221	−	0.833500i
$965$	2.00000			0.0643823
$966$		0			0
$967$	−27.5269			−0.885206			−0.442603	−	0.896718i	$-0.645945\pi$
$967$	−27.5269			−0.885206			−0.442603	+	0.896718i	$0.645945\pi$
$968$	9.76346	−	16.9108i	0.313809	−	0.543534i
$969$		0			0
$970$	0.0710678	+	0.123093i	0.00228185	+	0.00395228i
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	−0.991783	−	0.127933i	$-0.959166\pi$
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	0.606685	+	0.794943i	$0.292499\pi$
$972$		0			0
$973$	−19.6863	+	25.3864i	−0.631114	+	0.813851i
$974$	6.48528			0.207802
$975$		0			0
$976$	17.2279	+	29.8396i	0.551452	+	0.955143i
$977$	10.6569	+	18.4582i	0.340943	+	0.590531i	0.984608	−	0.174777i	$-0.0559204\pi$
$977$	10.6569	+	18.4582i	0.340943	+	0.590531i	−0.643665	+	0.765307i	$0.722587\pi$
$978$		0			0
$979$	12.8284			0.409998
$980$	−3.18629	−	12.3960i	−0.101782	−	0.395977i
$981$		0			0
$982$	−2.75736	+	4.77589i	−0.0879909	+	0.152405i
$983$	−7.10660	−	12.3090i	−0.226665	−	0.392596i	0.730152	−	0.683284i	$-0.239449\pi$
$983$	−7.10660	−	12.3090i	−0.226665	−	0.392596i	−0.956818	+	0.290688i	$0.906116\pi$
$984$		0			0
$985$	11.8284	−	20.4874i	0.376885	−	0.652784i
$986$	0.343146			0.0109280
$987$		0			0
$988$	4.28427			0.136301
$989$	−7.74264	+	13.4106i	−0.246202	+	0.426434i
$990$		0			0
$991$	7.82843	+	13.5592i	0.248678	+	0.430723i	0.963159	−	0.268931i	$-0.0866705\pi$
$991$	7.82843	+	13.5592i	0.248678	+	0.430723i	−0.714481	+	0.699655i	$0.753337\pi$
$992$	13.2426	−	22.9369i	0.420454	−	0.728248i
$993$		0			0
$994$	−5.17157	−	12.6677i	−0.164032	−	0.401796i
$995$	−1.65685			−0.0525258
$996$		0			0
$997$	8.72792	+	15.1172i	0.276416	+	0.478767i	0.970491	−	0.241136i	$-0.0775199\pi$
$997$	8.72792	+	15.1172i	0.276416	+	0.478767i	−0.694075	+	0.719902i	$0.744187\pi$
$998$	−1.00000	−	1.73205i	−0.0316544	−	0.0548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.e.226.1		4
3.2	odd	2		35.2.e.a.16.2	yes	4
7.2	even	3		2205.2.a.n.1.2		2
7.4	even	3	inner	315.2.j.e.46.1		4
7.5	odd	6		2205.2.a.q.1.2		2
12.11	even	2		560.2.q.k.401.2		4
15.2	even	4		175.2.k.a.149.3		8
15.8	even	4		175.2.k.a.149.2		8
15.14	odd	2		175.2.e.c.51.1		4
21.2	odd	6		245.2.a.h.1.1		2
21.5	even	6		245.2.a.g.1.1		2
21.11	odd	6		35.2.e.a.11.2	✓	4
21.17	even	6		245.2.e.e.116.2		4
21.20	even	2		245.2.e.e.226.2		4
84.11	even	6		560.2.q.k.81.2		4
84.23	even	6		3920.2.a.bq.1.1		2
84.47	odd	6		3920.2.a.bv.1.2		2
105.2	even	12		1225.2.b.g.99.2		4
105.23	even	12		1225.2.b.g.99.3		4
105.32	even	12		175.2.k.a.74.2		8
105.44	odd	6		1225.2.a.k.1.2		2
105.47	odd	12		1225.2.b.h.99.2		4
105.53	even	12		175.2.k.a.74.3		8
105.68	odd	12		1225.2.b.h.99.3		4
105.74	odd	6		175.2.e.c.151.1		4
105.89	even	6		1225.2.a.m.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.2	✓	4	21.11	odd	6
35.2.e.a.16.2	yes	4	3.2	odd	2
175.2.e.c.51.1		4	15.14	odd	2
175.2.e.c.151.1		4	105.74	odd	6
175.2.k.a.74.2		8	105.32	even	12
175.2.k.a.74.3		8	105.53	even	12
175.2.k.a.149.2		8	15.8	even	4
175.2.k.a.149.3		8	15.2	even	4
245.2.a.g.1.1		2	21.5	even	6
245.2.a.h.1.1		2	21.2	odd	6
245.2.e.e.116.2		4	21.17	even	6
245.2.e.e.226.2		4	21.20	even	2
315.2.j.e.46.1		4	7.4	even	3	inner
315.2.j.e.226.1		4	1.1	even	1	trivial
560.2.q.k.81.2		4	84.11	even	6
560.2.q.k.401.2		4	12.11	even	2
1225.2.a.k.1.2		2	105.44	odd	6
1225.2.a.m.1.2		2	105.89	even	6
1225.2.b.g.99.2		4	105.2	even	12
1225.2.b.g.99.3		4	105.23	even	12
1225.2.b.h.99.2		4	105.47	odd	12
1225.2.b.h.99.3		4	105.68	odd	12
2205.2.a.n.1.2		2	7.2	even	3
2205.2.a.q.1.2		2	7.5	odd	6
3920.2.a.bq.1.1		2	84.23	even	6
3920.2.a.bv.1.2		2	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.58579 q^{8} +O(q^{10})\)	\(q+(-0.207107 + 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.58579 q^{8} +(0.207107 + 0.358719i) q^{10} +(2.41421 + 4.18154i) q^{11} +0.828427 q^{13} +(-0.414214 - 1.01461i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.414214 - 0.717439i) q^{17} +(1.41421 - 2.44949i) q^{19} +1.82843 q^{20} -2.00000 q^{22} +(-1.20711 + 2.09077i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.171573 + 0.297173i) q^{26} +(-4.79289 - 0.655892i) q^{28} +1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-2.20711 - 3.82282i) q^{32} +0.343146 q^{34} +(1.00000 + 2.44949i) q^{35} +(0.585786 + 1.01461i) q^{38} +(-0.792893 + 1.37333i) q^{40} +2.17157 q^{41} +6.41421 q^{43} +(-4.41421 + 7.64564i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} +(-1.74264 - 6.77962i) q^{49} +0.414214 q^{50} +(0.757359 + 1.31178i) q^{52} +(-3.41421 - 5.91359i) q^{53} +4.82843 q^{55} +(2.57107 - 3.31552i) q^{56} +(-0.207107 + 0.358719i) q^{58} +(-6.24264 - 10.8126i) q^{59} +(5.74264 - 9.94655i) q^{61} -2.48528 q^{62} -4.17157 q^{64} +(0.414214 - 0.717439i) q^{65} +(-6.20711 - 10.7510i) q^{67} +(0.757359 - 1.31178i) q^{68} +(-1.08579 - 0.148586i) q^{70} +12.4853 q^{71} +(-2.41421 - 4.18154i) q^{73} +5.17157 q^{76} +(-12.6569 - 1.73205i) q^{77} +(-4.58579 + 7.94282i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.449747 + 0.778985i) q^{82} +11.7279 q^{83} -0.828427 q^{85} +(-1.32843 + 2.30090i) q^{86} +(-3.82843 - 6.63103i) q^{88} +(1.32843 - 2.30090i) q^{89} +(-1.34315 + 1.73205i) q^{91} -4.41421 q^{92} +(0.414214 + 0.717439i) q^{94} +(-1.41421 - 2.44949i) q^{95} +0.343146 q^{97} +(2.79289 + 0.778985i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} - 2 q^{10} + 4 q^{11} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 4 q^{17} - 4 q^{20} - 8 q^{22} - 2 q^{23} - 2 q^{25} - 12 q^{26} - 22 q^{28} + 4 q^{29} + 12 q^{31} - 6 q^{32} + 24 q^{34} + 4 q^{35} + 8 q^{38} - 6 q^{40} + 20 q^{41} + 20 q^{43} - 12 q^{44} - 2 q^{46} + 4 q^{47} + 10 q^{49} - 4 q^{50} + 20 q^{52} - 8 q^{53} + 8 q^{55} - 18 q^{56} + 2 q^{58} - 8 q^{59} + 6 q^{61} + 24 q^{62} - 28 q^{64} - 4 q^{65} - 22 q^{67} + 20 q^{68} - 10 q^{70} + 16 q^{71} - 4 q^{73} + 32 q^{76} - 28 q^{77} - 24 q^{79} + 6 q^{80} + 18 q^{82} - 4 q^{83} + 8 q^{85} + 6 q^{86} - 4 q^{88} - 6 q^{89} - 28 q^{91} - 12 q^{92} - 4 q^{94} + 24 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 - 2 * q^10 + 4 * q^11 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 4 * q^17 - 4 * q^20 - 8 * q^22 - 2 * q^23 - 2 * q^25 - 12 * q^26 - 22 * q^28 + 4 * q^29 + 12 * q^31 - 6 * q^32 + 24 * q^34 + 4 * q^35 + 8 * q^38 - 6 * q^40 + 20 * q^41 + 20 * q^43 - 12 * q^44 - 2 * q^46 + 4 * q^47 + 10 * q^49 - 4 * q^50 + 20 * q^52 - 8 * q^53 + 8 * q^55 - 18 * q^56 + 2 * q^58 - 8 * q^59 + 6 * q^61 + 24 * q^62 - 28 * q^64 - 4 * q^65 - 22 * q^67 + 20 * q^68 - 10 * q^70 + 16 * q^71 - 4 * q^73 + 32 * q^76 - 28 * q^77 - 24 * q^79 + 6 * q^80 + 18 * q^82 - 4 * q^83 + 8 * q^85 + 6 * q^86 - 4 * q^88 - 6 * q^89 - 28 * q^91 - 12 * q^92 - 4 * q^94 + 24 * q^97 + 14 * q^98

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