LMFDB - Embedded newform 855.2.k.k.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + \cdots + 4 $ x^12 - 3x^11 + 13x^10 - 10x^9 + 44x^8 - 20x^7 + 119x^6 + 13x^5 + 83x^4 + 14x^3 + 46x^2 + 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.2
Root			$0.964458 + 1.67049i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.k.676.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.464458 - 0.804466i) q^{2} +(0.568557 - 0.984769i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.66299 q^{7} -2.91412 q^{8} +O(q^{10})$	\(q+(-0.464458 - 0.804466i) q^{2} +(0.568557 - 0.984769i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.66299 q^{7} -2.91412 q^{8} +(0.464458 - 0.804466i) q^{10} -1.41795 q^{11} +(1.38214 - 2.39394i) q^{13} +(1.70131 + 2.94675i) q^{14} +(0.216373 + 0.374768i) q^{16} +(1.62252 + 2.81029i) q^{17} +(-4.34588 + 0.336682i) q^{19} +1.13711 q^{20} +(0.658577 + 1.14069i) q^{22} +(-4.21364 + 7.29823i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.56778 q^{26} +(-2.08262 + 3.60720i) q^{28} +(-0.917170 + 1.58858i) q^{29} +4.85783 q^{31} +(-2.71313 + 4.69927i) q^{32} +(1.50719 - 2.61053i) q^{34} +(-1.83150 - 3.17225i) q^{35} -9.00891 q^{37} +(2.28933 + 3.33973i) q^{38} +(-1.45706 - 2.52370i) q^{40} +(1.82098 + 3.15403i) q^{41} +(-4.41899 - 7.65392i) q^{43} +(-0.806183 + 1.39635i) q^{44} +7.82823 q^{46} +(-5.37200 + 9.30458i) q^{47} +6.41753 q^{49} +0.928917 q^{50} +(-1.57165 - 2.72218i) q^{52} +(3.56193 - 6.16945i) q^{53} +(-0.708973 - 1.22798i) q^{55} +10.6744 q^{56} +1.70395 q^{58} +(-2.65227 - 4.59387i) q^{59} +(1.64399 - 2.84747i) q^{61} +(-2.25626 - 3.90796i) q^{62} +5.90603 q^{64} +2.76428 q^{65} +(-6.32544 + 10.9560i) q^{67} +3.68999 q^{68} +(-1.70131 + 2.94675i) q^{70} +(-7.28608 - 12.6199i) q^{71} +(-0.964193 - 1.67003i) q^{73} +(4.18426 + 7.24736i) q^{74} +(-2.13932 + 4.47111i) q^{76} +5.19393 q^{77} +(6.25028 + 10.8258i) q^{79} +(-0.216373 + 0.374768i) q^{80} +(1.69154 - 2.92983i) q^{82} -6.46857 q^{83} +(-1.62252 + 2.81029i) q^{85} +(-4.10487 + 7.10985i) q^{86} +4.13206 q^{88} +(-5.27117 + 9.12994i) q^{89} +(-5.06277 + 8.76897i) q^{91} +(4.79138 + 8.29892i) q^{92} +9.98029 q^{94} +(-2.46451 - 3.59530i) q^{95} +(0.311714 + 0.539905i) q^{97} +(-2.98067 - 5.16268i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 5 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8	$ 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 3 q^{10} - 8 q^{13} + 10 q^{14} - 3 q^{16} + 4 q^{17} - 6 q^{19} - 10 q^{20} - 2 q^{23} - 6 q^{25} - 40 q^{26} - 26 q^{28} + 4 q^{29} + 24 q^{31} + 15 q^{32} + 7 q^{34} + 2 q^{35} - 29 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} + 6 q^{44} + 48 q^{46} + 6 q^{47} + 32 q^{49} - 6 q^{50} - 20 q^{52} + 26 q^{53} - 44 q^{56} - 20 q^{58} + 16 q^{59} + 20 q^{61} - 25 q^{62} + 28 q^{64} - 16 q^{65} - 12 q^{67} + 54 q^{68} - 10 q^{70} - 8 q^{71} - 4 q^{73} - 16 q^{74} - 66 q^{76} + 48 q^{77} - 12 q^{79} + 3 q^{80} + 26 q^{82} - 44 q^{83} - 4 q^{85} - 44 q^{86} - 32 q^{88} - 8 q^{89} + 2 q^{91} + 36 q^{92} - 14 q^{94} - 6 q^{95} + 30 q^{97} + 49 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 5 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8 - 3 * q^10 - 8 * q^13 + 10 * q^14 - 3 * q^16 + 4 * q^17 - 6 * q^19 - 10 * q^20 - 2 * q^23 - 6 * q^25 - 40 * q^26 - 26 * q^28 + 4 * q^29 + 24 * q^31 + 15 * q^32 + 7 * q^34 + 2 * q^35 - 29 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 + 6 * q^44 + 48 * q^46 + 6 * q^47 + 32 * q^49 - 6 * q^50 - 20 * q^52 + 26 * q^53 - 44 * q^56 - 20 * q^58 + 16 * q^59 + 20 * q^61 - 25 * q^62 + 28 * q^64 - 16 * q^65 - 12 * q^67 + 54 * q^68 - 10 * q^70 - 8 * q^71 - 4 * q^73 - 16 * q^74 - 66 * q^76 + 48 * q^77 - 12 * q^79 + 3 * q^80 + 26 * q^82 - 44 * q^83 - 4 * q^85 - 44 * q^86 - 32 * q^88 - 8 * q^89 + 2 * q^91 + 36 * q^92 - 14 * q^94 - 6 * q^95 + 30 * q^97 + 49 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.464458	−	0.804466i	−0.328422	−	0.568843i	0.653777	−	0.756687i	$-0.273183\pi$
$2$	−0.464458	−	0.804466i	−0.328422	−	0.568843i	−0.982199	+	0.187844i	$0.939850\pi$
$3$		0			0
$3$		0			0
$4$	0.568557	−	0.984769i	0.284278	−	0.492385i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−3.66299			−1.38448			−0.692241	−	0.721667i	$-0.743376\pi$
$7$	−3.66299			−1.38448			−0.692241	+	0.721667i	$0.743376\pi$
$8$	−2.91412			−1.03030
$9$		0			0
$10$	0.464458	−	0.804466i	0.146875	−	0.254394i
$11$	−1.41795			−0.427527			−0.213763	−	0.976885i	$-0.568572\pi$
$11$	−1.41795			−0.427527			−0.213763	+	0.976885i	$0.568572\pi$
$12$		0			0
$13$	1.38214	−	2.39394i	0.383336	−	0.663958i	−0.608200	−	0.793784i	$-0.708108\pi$
$13$	1.38214	−	2.39394i	0.383336	−	0.663958i	0.991537	+	0.129825i	$0.0414416\pi$
$14$	1.70131	+	2.94675i	0.454694	+	0.787553i
$15$		0			0
$16$	0.216373	+	0.374768i	0.0540931	+	0.0936921i
$17$	1.62252	+	2.81029i	0.393520	+	0.681596i	0.992911	−	0.118860i	$-0.0379239\pi$
$17$	1.62252	+	2.81029i	0.393520	+	0.681596i	−0.599391	+	0.800456i	$0.704591\pi$
$18$		0			0
$19$	−4.34588	+	0.336682i	−0.997013	+	0.0772401i
$19$	−4.34588	+	0.336682i	−0.997013	+	0.0772401i
$20$	1.13711			0.254266
$21$		0			0
$22$	0.658577	+	1.14069i	0.140409	+	0.243196i
$23$	−4.21364	+	7.29823i	−0.878604	+	1.52179i	−0.0257305	+	0.999669i	$0.508191\pi$
$23$	−4.21364	+	7.29823i	−0.878604	+	1.52179i	−0.852873	+	0.522118i	$0.825142\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.56778			−0.503584
$27$		0			0
$28$	−2.08262	+	3.60720i	−0.393578	+	0.681698i
$29$	−0.917170	+	1.58858i	−0.170314	+	0.294993i	−0.938530	−	0.345199i	$-0.887812\pi$
$29$	−0.917170	+	1.58858i	−0.170314	+	0.294993i	0.768216	+	0.640191i	$0.221145\pi$
$30$		0			0
$31$	4.85783			0.872493			0.436246	−	0.899827i	$-0.356308\pi$
$31$	4.85783			0.872493			0.436246	+	0.899827i	$0.356308\pi$
$32$	−2.71313	+	4.69927i	−0.479617	+	0.830722i
$33$		0			0
$34$	1.50719	−	2.61053i	0.258481	−	0.447702i
$35$	−1.83150	−	3.17225i	−0.309580	−	0.536207i
$36$		0			0
$37$	−9.00891			−1.48106			−0.740528	−	0.672026i	$-0.765424\pi$
$37$	−9.00891			−1.48106			−0.740528	+	0.672026i	$0.765424\pi$
$38$	2.28933	+	3.33973i	0.371378	+	0.541776i
$39$		0			0
$40$	−1.45706	−	2.52370i	−0.230381	−	0.399032i
$41$	1.82098	+	3.15403i	0.284390	+	0.492577i	0.972461	−	0.233066i	$-0.0748757\pi$
$41$	1.82098	+	3.15403i	0.284390	+	0.492577i	−0.688071	+	0.725643i	$0.741542\pi$
$42$		0			0
$43$	−4.41899	−	7.65392i	−0.673890	−	1.16721i	−0.976792	−	0.214190i	$-0.931289\pi$
$43$	−4.41899	−	7.65392i	−0.673890	−	1.16721i	0.302902	−	0.953022i	$-0.402044\pi$
$44$	−0.806183	+	1.39635i	−0.121537	+	0.210508i
$45$		0			0
$46$	7.82823			1.15421
$47$	−5.37200	+	9.30458i	−0.783587	+	1.35721i	0.146252	+	0.989247i	$0.453279\pi$
$47$	−5.37200	+	9.30458i	−0.783587	+	1.35721i	−0.929839	+	0.367966i	$0.880054\pi$
$48$		0			0
$49$	6.41753			0.916789
$50$	0.928917			0.131369
$51$		0			0
$52$	−1.57165	−	2.72218i	−0.217949	−	0.377498i
$53$	3.56193	−	6.16945i	0.489269	−	0.847439i	−0.510655	−	0.859786i	$-0.670597\pi$
$53$	3.56193	−	6.16945i	0.489269	−	0.847439i	0.999924	+	0.0123469i	$0.00393024\pi$
$54$		0			0
$55$	−0.708973	−	1.22798i	−0.0955979	−	0.165580i
$56$	10.6744			1.42643
$57$		0			0
$58$	1.70395			0.223739
$59$	−2.65227	−	4.59387i	−0.345296	−	0.598070i	0.640111	−	0.768282i	$-0.278888\pi$
$59$	−2.65227	−	4.59387i	−0.345296	−	0.598070i	−0.985408	+	0.170212i	$0.945555\pi$
$60$		0			0
$61$	1.64399	−	2.84747i	0.210491	−	0.364581i	−0.741377	−	0.671088i	$-0.765827\pi$
$61$	1.64399	−	2.84747i	0.210491	−	0.364581i	0.951868	+	0.306507i	$0.0991604\pi$
$62$	−2.25626	−	3.90796i	−0.286545	−	0.496311i
$63$		0			0
$64$	5.90603			0.738253
$65$	2.76428			0.342867
$66$		0			0
$67$	−6.32544	+	10.9560i	−0.772775	+	1.33849i	0.163262	+	0.986583i	$0.447799\pi$
$67$	−6.32544	+	10.9560i	−0.772775	+	1.33849i	−0.936037	+	0.351903i	$0.885535\pi$
$68$	3.68999			0.447477
$69$		0			0
$70$	−1.70131	+	2.94675i	−0.203345	+	0.352204i
$71$	−7.28608	−	12.6199i	−0.864699	−	1.49770i	−0.867346	−	0.497706i	$-0.834176\pi$
$71$	−7.28608	−	12.6199i	−0.864699	−	1.49770i	0.00264644	−	0.999996i	$-0.499158\pi$
$72$		0			0
$73$	−0.964193	−	1.67003i	−0.112850	−	0.195462i	0.804068	−	0.594537i	$-0.202665\pi$
$73$	−0.964193	−	1.67003i	−0.112850	−	0.195462i	−0.916918	+	0.399075i	$0.869331\pi$
$74$	4.18426	+	7.24736i	0.486411	+	0.842488i
$75$		0			0
$76$	−2.13932	+	4.47111i	−0.245397	+	0.512871i
$77$	5.19393			0.591903
$78$		0			0
$79$	6.25028	+	10.8258i	0.703211	+	1.21800i	0.967333	+	0.253508i	$0.0815845\pi$
$79$	6.25028	+	10.8258i	0.703211	+	1.21800i	−0.264122	+	0.964489i	$0.585082\pi$
$80$	−0.216373	+	0.374768i	−0.0241912	+	0.0419004i
$81$		0			0
$82$	1.69154	−	2.92983i	0.186799	−	0.323546i
$83$	−6.46857			−0.710018			−0.355009	−	0.934863i	$-0.615522\pi$
$83$	−6.46857			−0.710018			−0.355009	+	0.934863i	$0.615522\pi$
$84$		0			0
$85$	−1.62252	+	2.81029i	−0.175987	+	0.304819i
$86$	−4.10487	+	7.10985i	−0.442640	+	0.766675i
$87$		0			0
$88$	4.13206			0.440479
$89$	−5.27117	+	9.12994i	−0.558743	+	0.967772i	0.438858	+	0.898556i	$0.355383\pi$
$89$	−5.27117	+	9.12994i	−0.558743	+	0.967772i	−0.997602	+	0.0692157i	$0.977950\pi$
$90$		0			0
$91$	−5.06277	+	8.76897i	−0.530722	+	0.919238i
$92$	4.79138	+	8.29892i	0.499536	+	0.865222i
$93$		0			0
$94$	9.98029			1.02939
$95$	−2.46451	−	3.59530i	−0.252854	−	0.368870i
$96$		0			0
$97$	0.311714	+	0.539905i	0.0316498	+	0.0548190i	0.881416	−	0.472340i	$-0.156591\pi$
$97$	0.311714	+	0.539905i	0.0316498	+	0.0548190i	−0.849767	+	0.527159i	$0.823257\pi$
$98$	−2.98067	−	5.16268i	−0.301094	−	0.521509i
$99$		0			0
$100$	0.568557	+	0.984769i	0.0568557	+	0.0984769i
$101$	6.10551	−	10.5751i	0.607521	−	1.05226i	−0.384126	−	0.923281i	$-0.625497\pi$
$101$	6.10551	−	10.5751i	0.607521	−	1.05226i	0.991648	−	0.128977i	$-0.0411694\pi$
$102$		0			0
$103$	12.7435			1.25566			0.627828	−	0.778352i	$-0.283944\pi$
$103$	12.7435			1.25566			0.627828	+	0.778352i	$0.283944\pi$
$104$	−4.02772	+	6.97621i	−0.394950	+	0.684074i
$105$		0			0
$106$	−6.61748			−0.642746
$107$	−16.3829			−1.58379			−0.791896	−	0.610656i	$-0.790906\pi$
$107$	−16.3829			−1.58379			−0.791896	+	0.610656i	$0.790906\pi$
$108$		0			0
$109$	2.72026	+	4.71164i	0.260554	+	0.451293i	0.966389	−	0.257083i	$-0.0827615\pi$
$109$	2.72026	+	4.71164i	0.260554	+	0.451293i	−0.705835	+	0.708376i	$0.749428\pi$
$110$	−0.658577	+	1.14069i	−0.0627928	+	0.108760i
$111$		0			0
$112$	−0.792572	−	1.37277i	−0.0748910	−	0.129715i
$113$	9.46975			0.890839			0.445420	−	0.895322i	$-0.353054\pi$
$113$	9.46975			0.890839			0.445420	+	0.895322i	$0.353054\pi$
$114$		0			0
$115$	−8.42727			−0.785847
$116$	1.04293	+	1.80640i	0.0968333	+	0.167720i
$117$		0			0
$118$	−2.46374	+	4.26732i	−0.226805	+	0.392839i
$119$	−5.94330	−	10.2941i	−0.544821	−	0.943658i
$120$		0			0
$121$	−8.98943			−0.817221
$122$	−3.05425			−0.276519
$123$		0			0
$124$	2.76195	−	4.78385i	0.248031	−	0.429602i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	0.171100	−	0.296354i	0.0151827	−	0.0262971i	−0.858334	−	0.513091i	$-0.828500\pi$
$127$	0.171100	−	0.296354i	0.0151827	−	0.0262971i	0.873517	+	0.486794i	$0.161834\pi$
$128$	2.68315	+	4.64735i	0.237159	+	0.410771i
$129$		0			0
$130$	−1.28389	−	2.22377i	−0.112605	−	0.195037i
$131$	0.618905	+	1.07198i	0.0540740	+	0.0936590i	0.891795	−	0.452439i	$-0.149446\pi$
$131$	0.618905	+	1.07198i	0.0540740	+	0.0936590i	−0.837721	+	0.546098i	$0.816113\pi$
$132$		0			0
$133$	15.9189	−	1.23326i	1.38035	−	0.106938i
$134$	11.7516			1.01518
$135$		0			0
$136$	−4.72823	−	8.18953i	−0.405442	−	0.702246i
$137$	2.87141	−	4.97344i	0.245322	−	0.424909i	−0.716900	−	0.697176i	$-0.754440\pi$
$137$	2.87141	−	4.97344i	0.245322	−	0.424909i	0.962222	+	0.272266i	$0.0877731\pi$
$138$		0			0
$139$	10.3730	−	17.9666i	0.879830	−	1.52391i	0.0283041	−	0.999599i	$-0.490989\pi$
$139$	10.3730	−	17.9666i	0.879830	−	1.52391i	0.851526	−	0.524312i	$-0.175677\pi$
$140$	−4.16524			−0.352027
$141$		0			0
$142$	−6.76817	+	11.7228i	−0.567972	+	0.983756i
$143$	−1.95980	+	3.39447i	−0.163887	+	0.283860i
$144$		0			0
$145$	−1.83434			−0.152334
$146$	−0.895655	+	1.55132i	−0.0741250	+	0.128388i
$147$		0			0
$148$	−5.12208	+	8.87170i	−0.421032	+	0.729249i
$149$	−10.6969	−	18.5276i	−0.876324	−	1.51784i	−0.855346	−	0.518057i	$-0.826655\pi$
$149$	−10.6969	−	18.5276i	−0.876324	−	1.51784i	−0.0209780	−	0.999780i	$-0.506678\pi$
$150$		0			0
$151$	−1.35031			−0.109886			−0.0549432	−	0.998489i	$-0.517498\pi$
$151$	−1.35031			−0.109886			−0.0549432	+	0.998489i	$0.517498\pi$
$152$	12.6644	−	0.981131i	1.02722	−	0.0795802i
$153$		0			0
$154$	−2.41236	−	4.17834i	−0.194394	−	0.336700i
$155$	2.42892	+	4.20701i	0.195095	+	0.337915i
$156$		0			0
$157$	−6.14413	−	10.6419i	−0.490355	−	0.849319i	0.509584	−	0.860421i	$-0.329799\pi$
$157$	−6.14413	−	10.6419i	−0.490355	−	0.849319i	−0.999938	+	0.0111018i	$0.996466\pi$
$158$	5.80599	−	10.0563i	0.461900	−	0.800034i
$159$		0			0
$160$	−5.42625			−0.428983
$161$	15.4345	−	26.7334i	1.21641	−	2.10689i
$162$		0			0
$163$	1.45723			0.114139			0.0570696	−	0.998370i	$-0.481824\pi$
$163$	1.45723			0.114139			0.0570696	+	0.998370i	$0.481824\pi$
$164$	4.14133			0.323383
$165$		0			0
$166$	3.00438	+	5.20375i	0.233185	+	0.403889i
$167$	8.08781	−	14.0085i	0.625854	−	1.08401i	−0.362521	−	0.931975i	$-0.618084\pi$
$167$	8.08781	−	14.0085i	0.625854	−	1.08401i	0.988375	−	0.152035i	$-0.0485827\pi$
$168$		0			0
$169$	2.67938	+	4.64083i	0.206106	+	0.356987i
$170$	3.01438			0.231192
$171$		0			0
$172$	−10.0498			−0.766289
$173$	−1.82710	−	3.16463i	−0.138912	−	0.240603i	0.788173	−	0.615454i	$-0.211027\pi$
$173$	−1.82710	−	3.16463i	−0.138912	−	0.240603i	−0.927085	+	0.374851i	$0.877694\pi$
$174$		0			0
$175$	1.83150	−	3.17225i	0.138448	−	0.239799i
$176$	−0.306805	−	0.531401i	−0.0231263	−	0.0400559i
$177$		0			0
$178$	9.79297			0.734014
$179$	−9.16937			−0.685351			−0.342676	−	0.939454i	$-0.611333\pi$
$179$	−9.16937			−0.685351			−0.342676	+	0.939454i	$0.611333\pi$
$180$		0			0
$181$	3.81471	−	6.60727i	0.283545	−	0.491115i	−0.688710	−	0.725037i	$-0.741823\pi$
$181$	3.81471	−	6.60727i	0.283545	−	0.491115i	0.972255	+	0.233922i	$0.0751561\pi$
$182$	9.40578			0.697203
$183$		0			0
$184$	12.2790	−	21.2679i	0.905222	−	1.56789i
$185$	−4.50445	−	7.80194i	−0.331174	−	0.573610i
$186$		0			0
$187$	−2.30065	−	3.98485i	−0.168240	−	0.291401i
$188$	6.10858	+	10.5804i	0.445514	+	0.771653i
$189$		0			0
$190$	−1.74763	+	3.65248i	−0.126786	+	0.264979i
$191$	8.25384			0.597227			0.298613	−	0.954374i	$-0.403476\pi$
$191$	8.25384			0.597227			0.298613	+	0.954374i	$0.403476\pi$
$192$		0			0
$193$	−1.64118	−	2.84261i	−0.118135	−	0.204615i	0.800894	−	0.598806i	$-0.204358\pi$
$193$	−1.64118	−	2.84261i	−0.118135	−	0.204615i	−0.919029	+	0.394191i	$0.871025\pi$
$194$	0.289557	−	0.501527i	0.0207889	−	0.0360075i
$195$		0			0
$196$	3.64873	−	6.31978i	0.260623	−	0.451413i
$197$	−13.8640			−0.987770			−0.493885	−	0.869527i	$-0.664424\pi$
$197$	−13.8640			−0.987770			−0.493885	+	0.869527i	$0.664424\pi$
$198$		0			0
$199$	−7.02823	+	12.1733i	−0.498218	+	0.862939i	−0.999998	−	0.00205634i	$-0.999345\pi$
$199$	−7.02823	+	12.1733i	−0.498218	+	0.862939i	0.501780	+	0.864995i	$0.332679\pi$
$200$	1.45706	−	2.52370i	0.103030	−	0.178453i
$201$		0			0
$202$	−11.3430			−0.798093
$203$	3.35959	−	5.81898i	0.235797	−	0.408412i
$204$		0			0
$205$	−1.82098	+	3.15403i	−0.127183	+	0.220287i
$206$	−5.91883	−	10.2517i	−0.412385	−	0.714271i
$207$		0			0
$208$	1.19623			0.0829435
$209$	6.16222	−	0.477397i	0.426250	−	0.0330222i
$210$		0			0
$211$	2.72258	+	4.71564i	0.187430	+	0.324638i	0.944393	−	0.328820i	$-0.106651\pi$
$211$	2.72258	+	4.71564i	0.187430	+	0.324638i	−0.756963	+	0.653458i	$0.773318\pi$
$212$	−4.05032	−	7.01537i	−0.278177	−	0.481817i
$213$		0			0
$214$	7.60916	+	13.1795i	0.520151	+	0.900929i
$215$	4.41899	−	7.65392i	0.301373	−	0.521993i
$216$		0			0
$217$	−17.7942			−1.20795
$218$	2.52690	−	4.37672i	0.171143	−	0.296429i
$219$		0			0
$220$	−1.61237			−0.108706
$221$	8.97022			0.603402
$222$		0			0
$223$	−5.51057	−	9.54459i	−0.369015	−	0.639153i	0.620397	−	0.784288i	$-0.286972\pi$
$223$	−5.51057	−	9.54459i	−0.369015	−	0.639153i	−0.989412	+	0.145135i	$0.953638\pi$
$224$	9.93816	−	17.2134i	0.664021	−	1.15012i
$225$		0			0
$226$	−4.39831	−	7.61809i	−0.292571	−	0.506748i
$227$	10.1940			0.676603			0.338301	−	0.941038i	$-0.390148\pi$
$227$	10.1940			0.676603			0.338301	+	0.941038i	$0.390148\pi$
$228$		0			0
$229$	−5.53708			−0.365901			−0.182950	−	0.983122i	$-0.558565\pi$
$229$	−5.53708			−0.365901			−0.182950	+	0.983122i	$0.558565\pi$
$230$	3.91412	+	6.77945i	0.258089	+	0.447024i
$231$		0			0
$232$	2.67274	−	4.62932i	0.175474	−	0.303930i
$233$	−4.76246	−	8.24882i	−0.311999	−	0.540398i	0.666796	−	0.745240i	$-0.267665\pi$
$233$	−4.76246	−	8.24882i	−0.311999	−	0.540398i	−0.978795	+	0.204842i	$0.934332\pi$
$234$		0			0
$235$	−10.7440			−0.700862
$236$	−6.03186			−0.392641
$237$		0			0
$238$	−5.52083	+	9.56235i	−0.357862	+	0.619835i
$239$	10.9781			0.710117			0.355059	−	0.934844i	$-0.384461\pi$
$239$	10.9781			0.710117			0.355059	+	0.934844i	$0.384461\pi$
$240$		0			0
$241$	−3.38450	+	5.86213i	−0.218015	+	0.377613i	−0.954201	−	0.299166i	$-0.903292\pi$
$241$	−3.38450	+	5.86213i	−0.218015	+	0.377613i	0.736186	+	0.676779i	$0.236625\pi$
$242$	4.17522	+	7.23169i	0.268393	+	0.464870i
$243$		0			0
$244$	−1.86940	−	3.23790i	−0.119676	−	0.207285i
$245$	3.20876	+	5.55774i	0.205000	+	0.355071i
$246$		0			0
$247$	−5.20061	+	10.8691i	−0.330907	+	0.691584i
$248$	−14.1563			−0.898926
$249$		0			0
$250$	0.464458	+	0.804466i	0.0293749	+	0.0508789i
$251$	−9.63128	+	16.6819i	−0.607921	+	1.05295i	0.383661	+	0.923474i	$0.374663\pi$
$251$	−9.63128	+	16.6819i	−0.607921	+	1.05295i	−0.991582	+	0.129477i	$0.958670\pi$
$252$		0			0
$253$	5.97471	−	10.3485i	0.375627	−	0.650605i
$254$	−0.317875			−0.0199452
$255$		0			0
$256$	8.39845	−	14.5465i	0.524903	−	0.909158i
$257$	−4.99004	+	8.64300i	−0.311270	+	0.539135i	−0.978638	−	0.205593i	$-0.934088\pi$
$257$	−4.99004	+	8.64300i	−0.311270	+	0.539135i	0.667368	+	0.744728i	$0.267421\pi$
$258$		0			0
$259$	32.9996			2.05049
$260$	1.57165	−	2.72218i	0.0974696	−	0.168822i
$261$		0			0
$262$	0.574912	−	0.995776i	0.0355182	−	0.0615193i
$263$	1.73632	+	3.00739i	0.107066	+	0.185444i	0.914580	−	0.404404i	$-0.132521\pi$
$263$	1.73632	+	3.00739i	0.107066	+	0.185444i	−0.807514	+	0.589848i	$0.799188\pi$
$264$		0			0
$265$	7.12387			0.437616
$266$	−8.38579	−	12.2334i	−0.514166	−	0.750079i
$267$		0			0
$268$	7.19274	+	12.4582i	0.439366	+	0.761005i
$269$	11.5745	+	20.0476i	0.705708	+	1.22232i	0.966435	+	0.256910i	$0.0827045\pi$
$269$	11.5745	+	20.0476i	0.705708	+	1.22232i	−0.260727	+	0.965413i	$0.583962\pi$
$270$		0			0
$271$	−10.8902	−	18.8624i	−0.661532	−	1.14581i	−0.980213	−	0.197946i	$-0.936573\pi$
$271$	−10.8902	−	18.8624i	−0.661532	−	1.14581i	0.318681	−	0.947862i	$-0.396760\pi$
$272$	−0.702140	+	1.21614i	−0.0425735	+	0.0737394i
$273$		0			0
$274$	−5.33461			−0.322276
$275$	0.708973	−	1.22798i	0.0427527	−	0.0740498i
$276$		0			0
$277$	−20.7409			−1.24620			−0.623101	−	0.782141i	$-0.714127\pi$
$277$	−20.7409			−1.24620			−0.623101	+	0.782141i	$0.714127\pi$
$278$	−19.2714			−1.15582
$279$		0			0
$280$	5.33720	+	9.24430i	0.318959	+	0.552452i
$281$	−12.7958	+	22.1629i	−0.763332	+	1.32213i	0.177793	+	0.984068i	$0.443104\pi$
$281$	−12.7958	+	22.1629i	−0.763332	+	1.32213i	−0.941124	+	0.338061i	$0.890229\pi$
$282$		0			0
$283$	7.04996	+	12.2109i	0.419077	+	0.725862i	0.995847	−	0.0910442i	$-0.0290205\pi$
$283$	7.04996	+	12.2109i	0.419077	+	0.725862i	−0.576770	+	0.816907i	$0.695687\pi$
$284$	−16.5702			−0.983261
$285$		0			0
$286$	3.64098			0.215296
$287$	−6.67025	−	11.5532i	−0.393732	−	0.681964i
$288$		0			0
$289$	3.23483	−	5.60289i	0.190284	−	0.329582i
$290$	0.851974	+	1.47566i	0.0500297	+	0.0866539i
$291$		0			0
$292$	−2.19280			−0.128324
$293$	−2.14559			−0.125347			−0.0626733	−	0.998034i	$-0.519963\pi$
$293$	−2.14559			−0.125347			−0.0626733	+	0.998034i	$0.519963\pi$
$294$		0			0
$295$	2.65227	−	4.59387i	0.154421	−	0.267465i
$296$	26.2530			1.52593
$297$		0			0
$298$	−9.93653	+	17.2106i	−0.575607	+	0.996981i
$299$	11.6477	+	20.1743i	0.673602	+	1.16671i
$300$		0			0
$301$	16.1867	+	28.0363i	0.932988	+	1.61598i
$302$	0.627161	+	1.08627i	0.0360891	+	0.0625081i
$303$		0			0
$304$	−1.06651	−	1.55585i	−0.0611683	−	0.0892340i
$305$	3.28797			0.188269
$306$		0			0
$307$	−6.17252	−	10.6911i	−0.352285	−	0.610175i	0.634365	−	0.773034i	$-0.281262\pi$
$307$	−6.17252	−	10.6911i	−0.352285	−	0.610175i	−0.986649	+	0.162859i	$0.947928\pi$
$308$	2.95304	−	5.11482i	0.168265	−	0.291444i
$309$		0			0
$310$	2.25626	−	3.90796i	0.128147	−	0.221957i
$311$	−31.2434			−1.77165			−0.885825	−	0.464020i	$-0.846407\pi$
$311$	−31.2434			−1.77165			−0.885825	+	0.464020i	$0.846407\pi$
$312$		0			0
$313$	16.7182	−	28.9568i	0.944970	−	1.63674i	0.189158	−	0.981947i	$-0.439424\pi$
$313$	16.7182	−	28.9568i	0.944970	−	1.63674i	0.755812	−	0.654789i	$-0.227243\pi$
$314$	−5.70738	+	9.88548i	−0.322086	+	0.557870i
$315$		0			0
$316$	14.2146			0.799631
$317$	3.05432	−	5.29024i	0.171548	−	0.297129i	−0.767413	−	0.641153i	$-0.778457\pi$
$317$	3.05432	−	5.29024i	0.171548	−	0.297129i	0.938961	+	0.344023i	$0.111790\pi$
$318$		0			0
$319$	1.30050	−	2.25253i	0.0728139	−	0.126117i
$320$	2.95301	+	5.11477i	0.165078	+	0.285924i
$321$		0			0
$322$	−28.6748			−1.59798
$323$	−7.99747	−	11.6669i	−0.444991	−	0.649165i
$324$		0			0
$325$	1.38214	+	2.39394i	0.0766673	+	0.132792i
$326$	−0.676823	−	1.17229i	−0.0374858	−	0.0649272i
$327$		0			0
$328$	−5.30656	−	9.19122i	−0.293006	−	0.507500i
$329$	19.6776	−	34.0826i	1.08486	−	1.87904i
$330$		0			0
$331$	−3.39081			−0.186376			−0.0931879	−	0.995649i	$-0.529706\pi$
$331$	−3.39081			−0.186376			−0.0931879	+	0.995649i	$0.529706\pi$
$332$	−3.67775	+	6.37005i	−0.201843	+	0.349602i
$333$		0			0
$334$	−15.0258			−0.822176
$335$	−12.6509			−0.691191
$336$		0			0
$337$	1.08496	+	1.87920i	0.0591013	+	0.102366i	0.894062	−	0.447943i	$-0.147843\pi$
$337$	1.08496	+	1.87920i	0.0591013	+	0.102366i	−0.834961	+	0.550309i	$0.814510\pi$
$338$	2.48892	−	4.31094i	0.135380	−	0.234484i
$339$		0			0
$340$	1.84499	+	3.19562i	0.100059	+	0.173307i
$341$	−6.88815			−0.373014
$342$		0			0
$343$	2.13360			0.115203
$344$	12.8775	+	22.3044i	0.694306	+	1.20257i
$345$		0			0
$346$	−1.69723	+	2.93968i	−0.0912434	+	0.158038i
$347$	−1.37869	−	2.38796i	−0.0740118	−	0.128192i	0.826644	−	0.562725i	$-0.190247\pi$
$347$	−1.37869	−	2.38796i	−0.0740118	−	0.128192i	−0.900656	+	0.434533i	$0.856914\pi$
$348$		0			0
$349$	−20.7472			−1.11057			−0.555285	−	0.831660i	$-0.687391\pi$
$349$	−20.7472			−1.11057			−0.555285	+	0.831660i	$0.687391\pi$
$350$	−3.40262			−0.181878
$351$		0			0
$352$	3.84706	−	6.66331i	0.205049	−	0.355156i
$353$	10.5842			0.563341			0.281670	−	0.959511i	$-0.409112\pi$
$353$	10.5842			0.563341			0.281670	+	0.959511i	$0.409112\pi$
$354$		0			0
$355$	7.28608	−	12.6199i	0.386705	−	0.669793i
$356$	5.99393	+	10.3818i	0.317677	+	0.550233i
$357$		0			0
$358$	4.25879	+	7.37645i	0.225084	+	0.389857i
$359$	−17.6905	−	30.6408i	−0.933666	−	1.61716i	−0.776995	−	0.629507i	$-0.783257\pi$
$359$	−17.6905	−	30.6408i	−0.933666	−	1.61716i	−0.156671	−	0.987651i	$-0.550076\pi$
$360$		0			0
$361$	18.7733	−	2.92636i	0.988068	−	0.154019i
$362$	−7.08710			−0.372490
$363$		0			0
$364$	5.75694	+	9.97132i	0.301746	+	0.522639i
$365$	0.964193	−	1.67003i	0.0504682	−	0.0874135i
$366$		0			0
$367$	−12.3001	+	21.3045i	−0.642062	+	1.11208i	0.342909	+	0.939368i	$0.388588\pi$
$367$	−12.3001	+	21.3045i	−0.642062	+	1.11208i	−0.984972	+	0.172716i	$0.944746\pi$
$368$	−3.64686			−0.190106
$369$		0			0
$370$	−4.18426	+	7.24736i	−0.217529	+	0.376772i
$371$	−13.0473	+	22.5987i	−0.677384	+	1.17326i
$372$		0			0
$373$	6.14967			0.318418			0.159209	−	0.987245i	$-0.449106\pi$
$373$	6.14967			0.318418			0.159209	+	0.987245i	$0.449106\pi$
$374$	−2.13711	+	3.70159i	−0.110508	+	0.191405i
$375$		0			0
$376$	15.6546	−	27.1146i	0.807327	−	1.39833i
$377$	2.53531	+	4.39129i	0.130575	+	0.226163i
$378$		0			0
$379$	26.9469			1.38417			0.692084	−	0.721817i	$-0.256693\pi$
$379$	26.9469			1.38417			0.692084	+	0.721817i	$0.256693\pi$
$380$	−4.94176	+	0.382846i	−0.253507	+	0.0196396i
$381$		0			0
$382$	−3.83356	−	6.63993i	−0.196142	−	0.339728i
$383$	10.9735	+	19.0067i	0.560721	+	0.971197i	0.997434	+	0.0715958i	$0.0228092\pi$
$383$	10.9735	+	19.0067i	0.560721	+	0.971197i	−0.436713	+	0.899601i	$0.643857\pi$
$384$		0			0
$385$	2.59696	+	4.49807i	0.132354	+	0.229243i
$386$	−1.52452	+	2.64055i	−0.0775960	+	0.134400i
$387$		0			0
$388$	0.708909			0.0359894
$389$	3.56161	−	6.16889i	0.180581	−	0.312775i	−0.761498	−	0.648168i	$-0.775536\pi$
$389$	3.56161	−	6.16889i	0.180581	−	0.312775i	0.942079	+	0.335392i	$0.108869\pi$
$390$		0			0
$391$	−27.3469			−1.38299
$392$	−18.7014			−0.944565
$393$		0			0
$394$	6.43926	+	11.1531i	0.324405	+	0.561886i
$395$	−6.25028	+	10.8258i	−0.314486	+	0.544705i
$396$		0			0
$397$	15.4994	+	26.8457i	0.777891	+	1.34735i	0.933155	+	0.359474i	$0.117044\pi$
$397$	15.4994	+	26.8457i	0.777891	+	1.34735i	−0.155264	+	0.987873i	$0.549623\pi$
$398$	13.0573			0.654502
$399$		0			0
$400$	−0.432745			−0.0216373
$401$	16.4801	+	28.5444i	0.822978	+	1.42544i	0.903455	+	0.428684i	$0.141023\pi$
$401$	16.4801	+	28.5444i	0.822978	+	1.42544i	−0.0804761	+	0.996757i	$0.525644\pi$
$402$		0			0
$403$	6.71420	−	11.6293i	0.334458	−	0.579299i
$404$	−6.94266	−	12.0250i	−0.345410	−	0.598268i
$405$		0			0
$406$	−6.24155			−0.309763
$407$	12.7741			0.633191
$408$		0			0
$409$	−0.452483	+	0.783723i	−0.0223738	+	0.0387526i	−0.876996	−	0.480499i	$-0.840456\pi$
$409$	−0.452483	+	0.783723i	−0.0223738	+	0.0387526i	0.854622	+	0.519251i	$0.173789\pi$
$410$	3.38308			0.167078
$411$		0			0
$412$	7.24541	−	12.5494i	0.356956	−	0.618266i
$413$	9.71525	+	16.8273i	0.478056	+	0.828017i
$414$		0			0
$415$	−3.23429	−	5.60195i	−0.158765	−	0.274989i
$416$	7.49983	+	12.9901i	0.367710	+	0.636892i
$417$		0			0
$418$	−3.24614	−	4.73556i	−0.158774	−	0.231624i
$419$	−8.99889			−0.439625			−0.219812	−	0.975542i	$-0.570544\pi$
$419$	−8.99889			−0.439625			−0.219812	+	0.975542i	$0.570544\pi$
$420$		0			0
$421$	18.6169	+	32.2454i	0.907331	+	1.57154i	0.817758	+	0.575563i	$0.195217\pi$
$421$	18.6169	+	32.2454i	0.907331	+	1.57154i	0.0895733	+	0.995980i	$0.471450\pi$
$422$	2.52905	−	4.38044i	0.123112	−	0.213236i
$423$		0			0
$424$	−10.3799	+	17.9785i	−0.504092	+	0.873113i
$425$	−3.24505			−0.157408
$426$		0			0
$427$	−6.02192	+	10.4303i	−0.291421	+	0.504756i
$428$	−9.31459	+	16.1333i	−0.450238	+	0.779835i
$429$		0			0
$430$	−8.20975			−0.395909
$431$	7.09976	−	12.2971i	0.341983	−	0.592332i	−0.642818	−	0.766019i	$-0.722235\pi$
$431$	7.09976	−	12.2971i	0.341983	−	0.592332i	0.984801	+	0.173687i	$0.0555681\pi$
$432$		0			0
$433$	−15.9712	+	27.6630i	−0.767528	+	1.32940i	0.171371	+	0.985207i	$0.445180\pi$
$433$	−15.9712	+	27.6630i	−0.767528	+	1.32940i	−0.938899	+	0.344192i	$0.888153\pi$
$434$	8.26467	+	14.3148i	0.396717	+	0.687134i
$435$		0			0
$436$	6.18650			0.296280
$437$	15.8548	−	33.1359i	0.758436	−	1.58510i
$438$		0			0
$439$	−1.17614	−	2.03713i	−0.0561340	−	0.0972270i	0.836593	−	0.547825i	$-0.184544\pi$
$439$	−1.17614	−	2.03713i	−0.0561340	−	0.0972270i	−0.892727	+	0.450598i	$0.851211\pi$
$440$	2.06603	+	3.57847i	0.0984941	+	0.170597i
$441$		0			0
$442$	−4.16629	−	7.21623i	−0.198170	−	0.343241i
$443$	−19.0498	+	32.9952i	−0.905082	+	1.56765i	−0.0842740	+	0.996443i	$0.526857\pi$
$443$	−19.0498	+	32.9952i	−0.905082	+	1.56765i	−0.820808	+	0.571205i	$0.806476\pi$
$444$		0			0
$445$	−10.5423			−0.499755
$446$	−5.11886	+	8.86613i	−0.242385	+	0.419824i
$447$		0			0
$448$	−21.6337			−1.02210
$449$	−37.3376			−1.76207			−0.881034	−	0.473053i	$-0.843152\pi$
$449$	−37.3376			−1.76207			−0.881034	+	0.473053i	$0.843152\pi$
$450$		0			0
$451$	−2.58205	−	4.47225i	−0.121584	−	0.210590i
$452$	5.38409	−	9.32552i	0.253246	−	0.438636i
$453$		0			0
$454$	−4.73471	−	8.20076i	−0.222211	−	0.384881i
$455$	−10.1255			−0.474692
$456$		0			0
$457$	1.83835			0.0859946			0.0429973	−	0.999075i	$-0.486309\pi$
$457$	1.83835			0.0859946			0.0429973	+	0.999075i	$0.486309\pi$
$458$	2.57175	+	4.45439i	0.120170	+	0.208140i
$459$		0			0
$460$	−4.79138	+	8.29892i	−0.223399	+	0.386939i
$461$	1.53672	+	2.66167i	0.0715720	+	0.123966i	0.899590	−	0.436735i	$-0.143865\pi$
$461$	1.53672	+	2.66167i	0.0715720	+	0.123966i	−0.828018	+	0.560701i	$0.810532\pi$
$462$		0			0
$463$	19.8824			0.924013			0.462007	−	0.886876i	$-0.347130\pi$
$463$	19.8824			0.924013			0.462007	+	0.886876i	$0.347130\pi$
$464$	−0.793802			−0.0368513
$465$		0			0
$466$	−4.42393	+	7.66247i	−0.204934	+	0.354957i
$467$	−23.0483			−1.06655			−0.533273	−	0.845943i	$-0.679038\pi$
$467$	−23.0483			−1.06655			−0.533273	+	0.845943i	$0.679038\pi$
$468$		0			0
$469$	23.1700	−	40.1317i	1.06989	−	1.85311i
$470$	4.99014	+	8.64318i	0.230178	+	0.398680i
$471$		0			0
$472$	7.72902	+	13.3871i	0.355757	+	0.616190i
$473$	6.26589	+	10.8528i	0.288106	+	0.499014i
$474$		0			0
$475$	1.88136	−	3.93198i	0.0863229	−	0.180412i
$476$	−13.5164			−0.619524
$477$		0			0
$478$	−5.09889	−	8.83154i	−0.233218	−	0.403945i
$479$	−15.2877	+	26.4791i	−0.698515	+	1.20986i	0.270467	+	0.962729i	$0.412822\pi$
$479$	−15.2877	+	26.4791i	−0.698515	+	1.20986i	−0.968981	+	0.247134i	$0.920511\pi$
$480$		0			0
$481$	−12.4516	+	21.5667i	−0.567742	+	0.983359i
$482$	6.28784			0.286403
$483$		0			0
$484$	−5.11100	+	8.85251i	−0.232318	+	0.402387i
$485$	−0.311714	+	0.539905i	−0.0141542	+	0.0245158i
$486$		0			0
$487$	35.0987			1.59047			0.795237	−	0.606299i	$-0.207347\pi$
$487$	35.0987			1.59047			0.795237	+	0.606299i	$0.207347\pi$
$488$	−4.79077	+	8.29786i	−0.216868	+	0.375627i
$489$		0			0
$490$	2.98067	−	5.16268i	0.134653	−	0.233226i
$491$	12.7839	+	22.1424i	0.576930	+	0.999272i	0.995829	+	0.0912390i	$0.0290827\pi$
$491$	12.7839	+	22.1424i	0.576930	+	0.999272i	−0.418899	+	0.908033i	$0.637584\pi$
$492$		0			0
$493$	−5.95252			−0.268088
$494$	11.1593	−	0.864527i	0.502080	−	0.0388969i
$495$		0			0
$496$	1.05110	+	1.82056i	0.0471959	+	0.0817457i
$497$	26.6889	+	46.2265i	1.19716	+	2.07354i
$498$		0			0
$499$	19.2357	+	33.3171i	0.861106	+	1.49148i	0.870862	+	0.491527i	$0.163561\pi$
$499$	19.2357	+	33.3171i	0.861106	+	1.49148i	−0.00975600	+	0.999952i	$0.503105\pi$
$500$	−0.568557	+	0.984769i	−0.0254266	+	0.0440402i
$501$		0			0
$502$	17.8933			0.798618
$503$	19.0094	−	32.9252i	0.847587	−	1.46806i	−0.0357690	−	0.999360i	$-0.511388\pi$
$503$	19.0094	−	32.9252i	0.847587	−	1.46806i	0.883356	−	0.468703i	$-0.155279\pi$
$504$		0			0
$505$	12.2110			0.543384
$506$	−11.1000			−0.493456
$507$		0			0
$508$	−0.194560	−	0.336988i	−0.00863220	−	0.0149514i
$509$	−6.63084	+	11.4850i	−0.293907	+	0.509062i	−0.974730	−	0.223386i	$-0.928289\pi$
$509$	−6.63084	+	11.4850i	−0.293907	+	0.509062i	0.680823	+	0.732448i	$0.261622\pi$
$510$		0			0
$511$	3.53183	+	6.11732i	0.156239	+	0.270614i
$512$	−4.87032			−0.215240
$513$		0			0
$514$	9.27066			0.408911
$515$	6.37176	+	11.0362i	0.280773	+	0.486313i
$516$		0			0
$517$	7.61721	−	13.1934i	0.335005	−	0.580245i
$518$	−15.3269	−	26.5470i	−0.673427	−	1.16641i
$519$		0			0
$520$	−8.05543			−0.353254
$521$	−37.1676			−1.62834			−0.814171	−	0.580625i	$-0.802808\pi$
$521$	−37.1676			−1.62834			−0.814171	+	0.580625i	$0.802808\pi$
$522$		0			0
$523$	−12.9538	+	22.4367i	−0.566431	+	0.981087i	0.430484	+	0.902598i	$0.358343\pi$
$523$	−12.9538	+	22.4367i	−0.566431	+	0.981087i	−0.996915	+	0.0784886i	$0.974991\pi$
$524$	1.40753			0.0614883
$525$		0			0
$526$	1.61289	−	2.79362i	0.0703256	−	0.121807i
$527$	7.88195	+	13.6519i	0.343343	+	0.594688i
$528$		0			0
$529$	−24.0095	−	41.5856i	−1.04389	−	1.80807i
$530$	−3.30874	−	5.73090i	−0.143722	−	0.248935i
$531$		0			0
$532$	7.83633	−	16.3776i	0.339748	−	0.710061i
$533$	10.0674			0.436068
$534$		0			0
$535$	−8.19143	−	14.1880i	−0.354147	−	0.613400i
$536$	18.4331	−	31.9270i	0.796187	−	1.37904i
$537$		0			0
$538$	10.7517	−	18.6225i	0.463540	−	0.802875i
$539$	−9.09970			−0.391952
$540$		0			0
$541$	1.08156	−	1.87332i	0.0465000	−	0.0805403i	−0.841839	−	0.539729i	$-0.818527\pi$
$541$	1.08156	−	1.87332i	0.0465000	−	0.0805403i	0.888339	+	0.459189i	$0.151860\pi$
$542$	−10.1161	+	17.5216i	−0.434523	+	0.752616i
$543$		0			0
$544$	−17.6084			−0.754956
$545$	−2.72026	+	4.71164i	−0.116523	+	0.201824i
$546$		0			0
$547$	2.95615	−	5.12020i	0.126396	−	0.218924i	−0.795882	−	0.605452i	$-0.792992\pi$
$547$	2.95615	−	5.12020i	0.126396	−	0.218924i	0.922278	+	0.386528i	$0.126326\pi$
$548$	−3.26512	−	5.65536i	−0.139479	−	0.241585i
$549$		0			0
$550$	−1.31715			−0.0561636
$551$	3.45106	−	7.21259i	0.147020	−	0.307267i
$552$		0			0
$553$	−22.8947	−	39.6548i	−0.973583	−	1.68630i
$554$	9.63330	+	16.6854i	0.409280	+	0.708893i
$555$		0			0
$556$	−11.7953	−	20.4301i	−0.500234	−	0.866430i
$557$	1.03098	−	1.78570i	0.0436839	−	0.0756627i	−0.843357	−	0.537354i	$-0.819424\pi$
$557$	1.03098	−	1.78570i	0.0436839	−	0.0756627i	0.887041	+	0.461691i	$0.152757\pi$
$558$		0			0
$559$	−24.4306			−1.03331
$560$	0.792572	−	1.37277i	0.0334923	−	0.0580103i
$561$		0			0
$562$	23.7724			1.00278
$563$	2.26488			0.0954533			0.0477267	−	0.998860i	$-0.484802\pi$
$563$	2.26488			0.0954533			0.0477267	+	0.998860i	$0.484802\pi$
$564$		0			0
$565$	4.73488	+	8.20105i	0.199198	+	0.345021i
$566$	6.54883	−	11.3429i	0.275268	−	0.476778i
$567$		0			0
$568$	21.2325	+	36.7758i	0.890896	+	1.54308i
$569$	23.5361			0.986687			0.493343	−	0.869835i	$-0.335775\pi$
$569$	23.5361			0.986687			0.493343	+	0.869835i	$0.335775\pi$
$570$		0			0
$571$	−22.3091			−0.933607			−0.466803	−	0.884361i	$-0.654594\pi$
$571$	−22.3091			−0.933607			−0.466803	+	0.884361i	$0.654594\pi$
$572$	2.22851	+	3.85990i	0.0931788	+	0.161390i
$573$		0			0
$574$	−6.19610	+	10.7320i	−0.258620	+	0.447944i
$575$	−4.21364	−	7.29823i	−0.175721	−	0.304357i
$576$		0			0
$577$	16.4111			0.683203			0.341601	−	0.939845i	$-0.389031\pi$
$577$	16.4111			0.683203			0.341601	+	0.939845i	$0.389031\pi$
$578$	−6.00978			−0.249974
$579$		0			0
$580$	−1.04293	+	1.80640i	−0.0433052	+	0.0750067i
$581$	23.6944			0.983007
$582$		0			0
$583$	−5.05063	+	8.74795i	−0.209176	+	0.362303i
$584$	2.80977	+	4.86667i	0.116269	+	0.201384i
$585$		0			0
$586$	0.996536	+	1.72605i	0.0411665	+	0.0713025i
$587$	−13.6467	−	23.6368i	−0.563261	−	0.975596i	−0.997209	−	0.0746585i	$-0.976213\pi$
$587$	−13.6467	−	23.6368i	−0.563261	−	0.975596i	0.433948	−	0.900938i	$-0.357120\pi$
$588$		0			0
$589$	−21.1115	+	1.63554i	−0.869886	+	0.0673915i
$590$	−4.92748			−0.202861
$591$		0			0
$592$	−1.94928	−	3.37625i	−0.0801149	−	0.138763i
$593$	−15.1560	+	26.2510i	−0.622383	+	1.07800i	0.366657	+	0.930356i	$0.380502\pi$
$593$	−15.1560	+	26.2510i	−0.622383	+	1.07800i	−0.989041	+	0.147644i	$0.952831\pi$
$594$		0			0
$595$	5.94330	−	10.2941i	0.243651	−	0.422017i
$596$	−24.3272			−0.996480
$597$		0			0
$598$	10.8197	−	18.7403i	0.442451	−	0.766347i
$599$	0.449215	−	0.778062i	0.0183544	−	0.0317908i	−0.856702	−	0.515811i	$-0.827491\pi$
$599$	0.449215	−	0.778062i	0.0183544	−	0.0317908i	0.875057	+	0.484020i	$0.160824\pi$
$600$		0			0
$601$	−0.853573			−0.0348180			−0.0174090	−	0.999848i	$-0.505542\pi$
$601$	−0.853573			−0.0348180			−0.0174090	+	0.999848i	$0.505542\pi$
$602$	15.0361	−	26.0433i	0.612827	−	1.06145i
$603$		0			0
$604$	−0.767726	+	1.32974i	−0.0312383	+	0.0541064i
$605$	−4.49471	−	7.78507i	−0.182736	−	0.316508i
$606$		0			0
$607$	2.19123			0.0889392			0.0444696	−	0.999011i	$-0.485840\pi$
$607$	2.19123			0.0889392			0.0444696	+	0.999011i	$0.485840\pi$
$608$	10.2087	−	21.3359i	0.414019	−	0.865286i
$609$		0			0
$610$	−1.52713	−	2.64506i	−0.0618316	−	0.107095i
$611$	14.8497	+	25.7205i	0.600755	+	1.04054i
$612$		0			0
$613$	−13.8771	−	24.0359i	−0.560492	−	0.970800i	−0.997453	−	0.0713203i	$-0.977279\pi$
$613$	−13.8771	−	24.0359i	−0.560492	−	0.970800i	0.436962	−	0.899480i	$-0.356055\pi$
$614$	−5.73376	+	9.93116i	−0.231396	+	0.400789i
$615$		0			0
$616$	−15.1357			−0.609835
$617$	6.78871	−	11.7584i	0.273303	−	0.473375i	−0.696403	−	0.717651i	$-0.745217\pi$
$617$	6.78871	−	11.7584i	0.273303	−	0.473375i	0.969706	+	0.244277i	$0.0785505\pi$
$618$		0			0
$619$	2.70380			0.108675			0.0543375	−	0.998523i	$-0.482695\pi$
$619$	2.70380			0.108675			0.0543375	+	0.998523i	$0.482695\pi$
$620$	5.52391			0.221846
$621$		0			0
$622$	14.5113	+	25.1342i	0.581848	+	1.00779i
$623$	19.3083	−	33.4429i	0.773570	−	1.33986i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−31.0597			−1.24139
$627$		0			0
$628$	−13.9731			−0.557589
$629$	−14.6172	−	25.3177i	−0.582825	−	1.00948i
$630$		0			0
$631$	−3.22888	+	5.59259i	−0.128540	+	0.222638i	−0.923111	−	0.384533i	$-0.874362\pi$
$631$	−3.22888	+	5.59259i	−0.128540	+	0.222638i	0.794571	+	0.607171i	$0.207696\pi$
$632$	−18.2140	−	31.5476i	−0.724516	−	1.25490i
$633$		0			0
$634$	−5.67442			−0.225360
$635$	0.342200			0.0135798
$636$		0			0
$637$	8.86992	−	15.3631i	0.351439	−	0.608710i
$638$	−2.41611			−0.0956546
$639$		0			0
$640$	−2.68315	+	4.64735i	−0.106061	+	0.183703i
$641$	12.2784	+	21.2668i	0.484968	+	0.839989i	0.999851	−	0.0172712i	$-0.00549787\pi$
$641$	12.2784	+	21.2668i	0.484968	+	0.839989i	−0.514883	+	0.857261i	$0.672165\pi$
$642$		0			0
$643$	−10.7699	−	18.6540i	−0.424722	−	0.735641i	0.571672	−	0.820482i	$-0.306295\pi$
$643$	−10.7699	−	18.6540i	−0.424722	−	0.735641i	−0.996394	+	0.0848414i	$0.972962\pi$
$644$	−17.5508	−	30.3989i	−0.691599	−	1.19788i
$645$		0			0
$646$	−5.67114	+	11.8525i	−0.223128	+	0.466330i
$647$	17.5491			0.689926			0.344963	−	0.938616i	$-0.387891\pi$
$647$	17.5491			0.689926			0.344963	+	0.938616i	$0.387891\pi$
$648$		0			0
$649$	3.76077	+	6.51385i	0.147623	+	0.255691i
$650$	1.28389	−	2.22377i	0.0503584	−	0.0872233i
$651$		0			0
$652$	0.828518	−	1.43504i	0.0324473	−	0.0562003i
$653$	13.6647			0.534740			0.267370	−	0.963594i	$-0.413845\pi$
$653$	13.6647			0.534740			0.267370	+	0.963594i	$0.413845\pi$
$654$		0			0
$655$	−0.618905	+	1.07198i	−0.0241826	+	0.0418856i
$656$	−0.788021	+	1.36489i	−0.0307671	+	0.0532901i
$657$		0			0
$658$	−36.5577			−1.42517
$659$	2.56623	−	4.44485i	0.0999662	−	0.173147i	−0.811704	−	0.584069i	$-0.801460\pi$
$659$	2.56623	−	4.44485i	0.0999662	−	0.173147i	0.911670	+	0.410922i	$0.134793\pi$
$660$		0			0
$661$	−12.5958	+	21.8166i	−0.489921	+	0.848569i	−0.999933	−	0.0115990i	$-0.996308\pi$
$661$	−12.5958	+	21.8166i	−0.489921	+	0.848569i	0.510011	+	0.860168i	$0.329641\pi$
$662$	1.57489	+	2.72779i	0.0612099	+	0.106019i
$663$		0			0
$664$	18.8502			0.731529
$665$	9.02750	+	13.1696i	0.350071	+	0.510694i
$666$		0			0
$667$	−7.72924	−	13.3874i	−0.299277	−	0.518364i
$668$	−9.19676	−	15.9293i	−0.355833	−	0.616322i
$669$		0			0
$670$	5.87580	+	10.1772i	0.227002	+	0.393179i
$671$	−2.33109	+	4.03756i	−0.0899905	+	0.155868i
$672$		0			0
$673$	17.1038			0.659304			0.329652	−	0.944103i	$-0.393069\pi$
$673$	17.1038			0.659304			0.329652	+	0.944103i	$0.393069\pi$
$674$	1.00783	−	1.74562i	0.0388203	−	0.0672387i
$675$		0			0
$676$	6.09352			0.234366
$677$	0.430567			0.0165480			0.00827401	−	0.999966i	$-0.497366\pi$
$677$	0.430567			0.0165480			0.00827401	+	0.999966i	$0.497366\pi$
$678$		0			0
$679$	−1.14181	−	1.97767i	−0.0438185	−	0.0758959i
$680$	4.72823	−	8.18953i	0.181319	−	0.314054i
$681$		0			0
$682$	3.19926	+	5.54128i	0.122506	+	0.212186i
$683$	−27.9032			−1.06769			−0.533843	−	0.845584i	$-0.679253\pi$
$683$	−27.9032			−1.06769			−0.533843	+	0.845584i	$0.679253\pi$
$684$		0			0
$685$	5.74283			0.219422
$686$	−0.990967	−	1.71641i	−0.0378353	−	0.0655327i
$687$		0			0
$688$	1.91230	−	3.31220i	0.0729056	−	0.126276i
$689$	−9.84618	−	17.0541i	−0.375109	−	0.649709i
$690$		0			0
$691$	10.4084			0.395954			0.197977	−	0.980207i	$-0.436563\pi$
$691$	10.4084			0.395954			0.197977	+	0.980207i	$0.436563\pi$
$692$	−4.15525			−0.157959
$693$		0			0
$694$	−1.28069	+	2.21821i	−0.0486141	+	0.0842022i
$695$	20.7461			0.786944
$696$		0			0
$697$	−5.90917	+	10.2350i	−0.223826	+	0.387678i
$698$	9.63619	+	16.6904i	0.364735	+	0.631740i
$699$		0			0
$700$	−2.08262	−	3.60720i	−0.0787157	−	0.136340i
$701$	10.8642	+	18.8173i	0.410335	+	0.710721i	0.994926	−	0.100607i	$-0.0320785\pi$
$701$	10.8642	+	18.8173i	0.410335	+	0.710721i	−0.584591	+	0.811328i	$0.698745\pi$
$702$		0			0
$703$	39.1516	−	3.03314i	1.47663	−	0.114397i
$704$	−8.37442			−0.315623
$705$		0			0
$706$	−4.91593	−	8.51464i	−0.185013	−	0.320453i
$707$	−22.3645	+	38.7364i	−0.841102	+	1.45683i
$708$		0			0
$709$	−12.0501	+	20.8713i	−0.452550	+	0.783840i	−0.998544	−	0.0539495i	$-0.982819\pi$
$709$	−12.0501	+	20.8713i	−0.452550	+	0.783840i	0.545993	+	0.837789i	$0.316152\pi$
$710$	−13.5363			−0.508009
$711$		0			0
$712$	15.3608	−	26.6057i	0.575671	−	0.997092i
$713$	−20.4691	+	35.4536i	−0.766575	+	1.32775i
$714$		0			0
$715$	−3.91960			−0.146585
$716$	−5.21331	+	9.02972i	−0.194831	+	0.337456i
$717$		0			0
$718$	−16.4330	+	28.4627i	−0.613273	+	1.06222i
$719$	−3.05117	−	5.28479i	−0.113790	−	0.197089i	0.803506	−	0.595297i	$-0.202966\pi$
$719$	−3.05117	−	5.28479i	−0.113790	−	0.197089i	−0.917295	+	0.398208i	$0.869632\pi$
$720$		0			0
$721$	−46.6794			−1.73843
$722$	−11.0736	−	13.7433i	−0.412115	−	0.511472i
$723$		0			0
$724$	−4.33776	−	7.51322i	−0.161212	−	0.279227i
$725$	−0.917170	−	1.58858i	−0.0340628	−	0.0589986i
$726$		0			0
$727$	−5.35126	−	9.26866i	−0.198467	−	0.343756i	0.749564	−	0.661932i	$-0.230263\pi$
$727$	−5.35126	−	9.26866i	−0.198467	−	0.343756i	−0.948032	+	0.318176i	$0.896930\pi$
$728$	14.7535	−	25.5538i	0.546801	−	0.947087i
$729$		0			0
$730$	−1.79131			−0.0662994
$731$	14.3398	−	24.8373i	0.530378	−	0.918642i
$732$		0			0
$733$	−12.7580			−0.471226			−0.235613	−	0.971847i	$-0.575710\pi$
$733$	−12.7580			−0.471226			−0.235613	+	0.971847i	$0.575710\pi$
$734$	22.8516			0.843469
$735$		0			0
$736$	−22.8642	−	39.6020i	−0.842787	−	1.45975i
$737$	8.96913	−	15.5350i	0.330382	−	0.572238i
$738$		0			0
$739$	−6.64437	−	11.5084i	−0.244417	−	0.423343i	0.717551	−	0.696506i	$-0.245263\pi$
$739$	−6.64437	−	11.5084i	−0.244417	−	0.423343i	−0.961968	+	0.273164i	$0.911930\pi$
$740$	−10.2442			−0.376583
$741$		0			0
$742$	24.2398			0.889871
$743$	18.1671	+	31.4663i	0.666486	+	1.15439i	0.978880	+	0.204436i	$0.0655359\pi$
$743$	18.1671	+	31.4663i	0.666486	+	1.15439i	−0.312394	+	0.949953i	$0.601131\pi$
$744$		0			0
$745$	10.6969	−	18.5276i	0.391904	−	0.678798i
$746$	−2.85627	−	4.94720i	−0.104575	−	0.181130i
$747$		0			0
$748$	−5.23220			−0.191308
$749$	60.0103			2.19273
$750$		0			0
$751$	3.79143	−	6.56696i	0.138351	−	0.239632i	−0.788521	−	0.615007i	$-0.789153\pi$
$751$	3.79143	−	6.56696i	0.138351	−	0.239632i	0.926873	+	0.375376i	$0.122486\pi$
$752$	−4.64942			−0.169547
$753$		0			0
$754$	2.35509	−	4.07914i	0.0857675	−	0.148554i
$755$	−0.675153	−	1.16940i	−0.0245713	−	0.0425588i
$756$		0			0
$757$	9.24433	+	16.0116i	0.335991	+	0.581953i	0.983675	−	0.179956i	$-0.0575956\pi$
$757$	9.24433	+	16.0116i	0.335991	+	0.581953i	−0.647684	+	0.761909i	$0.724262\pi$
$758$	−12.5157	−	21.6778i	−0.454591	−	0.787374i
$759$		0			0
$760$	7.18188	+	10.4771i	0.260514	+	0.380045i
$761$	−6.84628			−0.248177			−0.124089	−	0.992271i	$-0.539601\pi$
$761$	−6.84628			−0.248177			−0.124089	+	0.992271i	$0.539601\pi$
$762$		0			0
$763$	−9.96431	−	17.2587i	−0.360732	−	0.624807i
$764$	4.69278	−	8.12813i	0.169779	−	0.294065i
$765$		0			0
$766$	10.1935	−	17.6556i	0.368306	−	0.637924i
$767$	−14.6632			−0.529458
$768$		0			0
$769$	−10.0541	+	17.4141i	−0.362558	+	0.627970i	−0.988381	−	0.151996i	$-0.951430\pi$
$769$	−10.0541	+	17.4141i	−0.362558	+	0.627970i	0.625823	+	0.779965i	$0.284763\pi$
$770$	2.41236	−	4.17834i	0.0869355	−	0.150577i
$771$		0			0
$772$	−3.73242			−0.134333
$773$	27.0407	−	46.8359i	0.972587	−	1.68457i	0.284910	−	0.958554i	$-0.408036\pi$
$773$	27.0407	−	46.8359i	0.972587	−	1.68457i	0.687677	−	0.726017i	$-0.258631\pi$
$774$		0			0
$775$	−2.42892	+	4.20701i	−0.0872493	+	0.151120i
$776$	−0.908372	−	1.57335i	−0.0326086	−	0.0564798i
$777$		0			0
$778$	−6.61688			−0.237227
$779$	−8.97567	−	13.0939i	−0.321587	−	0.469139i
$780$		0			0
$781$	10.3313	+	17.8943i	0.369682	+	0.640308i
$782$	12.7015	+	21.9996i	0.454205	+	0.786706i
$783$		0			0
$784$	1.38858	+	2.40509i	0.0495920	+	0.0858959i
$785$	6.14413	−	10.6419i	0.219293	−	0.379827i
$786$		0			0
$787$	−2.34881			−0.0837262			−0.0418631	−	0.999123i	$-0.513329\pi$
$787$	−2.34881			−0.0837262			−0.0418631	+	0.999123i	$0.513329\pi$
$788$	−7.88248	+	13.6529i	−0.280802	+	0.486363i
$789$		0			0
$790$	11.6120			0.413136
$791$	−34.6876			−1.23335
$792$		0			0
$793$	−4.54444	−	7.87120i	−0.161378	−	0.279514i
$794$	14.3976	−	24.9374i	0.510953	−	0.884996i
$795$		0			0
$796$	7.99190	+	13.8424i	0.283265	+	0.490630i
$797$	51.8121			1.83528			0.917639	−	0.397414i	$-0.130092\pi$
$797$	51.8121			1.83528			0.917639	+	0.397414i	$0.130092\pi$
$798$		0			0
$799$	−34.8648			−1.23343
$800$	−2.71313	−	4.69927i	−0.0959235	−	0.166144i
$801$		0			0
$802$	15.3087	−	26.5154i	0.540568	−	0.936291i
$803$	1.36717	+	2.36801i	0.0482465	+	0.0835654i
$804$		0			0
$805$	30.8691			1.08799
$806$	−12.4739			−0.439373
$807$		0			0
$808$	−17.7922	+	30.8170i	−0.625927	+	1.08414i
$809$	38.1517			1.34134			0.670672	−	0.741754i	$-0.266006\pi$
$809$	38.1517			1.34134			0.670672	+	0.741754i	$0.266006\pi$
$810$		0			0
$811$	18.4673	−	31.9863i	0.648474	−	1.12319i	−0.335013	−	0.942214i	$-0.608741\pi$
$811$	18.4673	−	31.9863i	0.648474	−	1.12319i	0.983487	−	0.180977i	$-0.0579260\pi$
$812$	−3.82023	−	6.61684i	−0.134064	−	0.232205i
$813$		0			0
$814$	−5.93306	−	10.2764i	−0.207954	−	0.360186i
$815$	0.728615	+	1.26200i	0.0255223	+	0.0442059i
$816$		0			0
$817$	21.7813	+	31.7752i	0.762032	+	1.11167i
$818$	0.840638			0.0293922
$819$		0			0
$820$	2.07066	+	3.58649i	0.0723107	+	0.125246i
$821$	21.5360	−	37.3014i	0.751611	−	1.30183i	−0.195430	−	0.980718i	$-0.562610\pi$
$821$	21.5360	−	37.3014i	0.751611	−	1.30183i	0.947041	−	0.321111i	$-0.104056\pi$
$822$		0			0
$823$	14.6142	−	25.3126i	0.509419	−	0.882340i	−0.490521	−	0.871429i	$-0.663194\pi$
$823$	14.6142	−	25.3126i	0.509419	−	0.882340i	0.999940	−	0.0109108i	$-0.00347309\pi$
$824$	−37.1361			−1.29370
$825$		0			0
$826$	9.02466	−	15.6312i	0.314008	−	0.543878i
$827$	4.17748	−	7.23561i	0.145265	−	0.251607i	−0.784207	−	0.620500i	$-0.786930\pi$
$827$	4.17748	−	7.23561i	0.145265	−	0.251607i	0.929472	+	0.368893i	$0.120263\pi$
$828$		0			0
$829$	−11.1879			−0.388572			−0.194286	−	0.980945i	$-0.562239\pi$
$829$	−11.1879			−0.388572			−0.194286	+	0.980945i	$0.562239\pi$
$830$	−3.00438	+	5.20375i	−0.104284	+	0.180625i
$831$		0			0
$832$	8.16295	−	14.1386i	0.282999	−	0.490169i
$833$	10.4126	+	18.0351i	0.360775	+	0.624880i
$834$		0			0
$835$	16.1756			0.559781
$836$	3.03345	−	6.33979i	0.104914	−	0.219266i
$837$		0			0
$838$	4.17961	+	7.23930i	0.144382	+	0.250077i
$839$	23.4172	+	40.5598i	0.808451	+	1.40028i	0.913936	+	0.405857i	$0.133027\pi$
$839$	23.4172	+	40.5598i	0.808451	+	1.40028i	−0.105486	+	0.994421i	$0.533640\pi$
$840$		0			0
$841$	12.8176	+	22.2007i	0.441986	+	0.765543i
$842$	17.2935	−	29.9533i	0.595974	−	1.03226i
$843$		0			0
$844$	6.19176			0.213129
$845$	−2.67938	+	4.64083i	−0.0921735	+	0.159649i
$846$		0			0
$847$	32.9282			1.13143
$848$	3.08282			0.105864
$849$		0			0
$850$	1.50719	+	2.61053i	0.0516962	+	0.0895404i
$851$	37.9603	−	65.7491i	1.30126	−	2.25385i
$852$		0			0
$853$	−6.94739	−	12.0332i	−0.237874	−	0.412010i	0.722230	−	0.691653i	$-0.243117\pi$
$853$	−6.94739	−	12.0332i	−0.237874	−	0.412010i	−0.960104	+	0.279643i	$0.909784\pi$
$854$	11.1877			0.382836
$855$		0			0
$856$	47.7416			1.63177
$857$	−4.85669	−	8.41204i	−0.165901	−	0.287350i	0.771074	−	0.636746i	$-0.219720\pi$
$857$	−4.85669	−	8.41204i	−0.165901	−	0.287350i	−0.936975	+	0.349396i	$0.886387\pi$
$858$		0			0
$859$	−19.2503	+	33.3424i	−0.656811	+	1.13763i	0.324626	+	0.945842i	$0.394762\pi$
$859$	−19.2503	+	33.3424i	−0.656811	+	1.13763i	−0.981437	+	0.191787i	$0.938572\pi$
$860$	−5.02489	−	8.70337i	−0.171347	−	0.296783i
$861$		0			0
$862$	−13.1902			−0.449259
$863$	−44.5378			−1.51608			−0.758042	−	0.652206i	$-0.773844\pi$
$863$	−44.5378			−1.51608			−0.758042	+	0.652206i	$0.773844\pi$
$864$		0			0
$865$	1.82710	−	3.16463i	0.0621233	−	0.107601i
$866$	29.6719			1.00829
$867$		0			0
$868$	−10.1170	+	17.5232i	−0.343394	+	0.594776i
$869$	−8.86256	−	15.3504i	−0.300642	−	0.520727i
$870$		0			0
$871$	17.4853	+	30.2854i	0.592466	+	1.02618i
$872$	−7.92717	−	13.7303i	−0.268448	−	0.464965i
$873$		0			0
$874$	−34.0205	+	2.63563i	−1.15076	+	0.0891514i
$875$	3.66299			0.123832
$876$		0			0
$877$	20.2438	+	35.0634i	0.683586	+	1.18401i	0.973879	+	0.227068i	$0.0729138\pi$
$877$	20.2438	+	35.0634i	0.683586	+	1.18401i	−0.290293	+	0.956938i	$0.593753\pi$
$878$	−1.09254	+	1.89233i	−0.0368713	+	0.0638629i
$879$		0			0
$880$	0.306805	−	0.531401i	0.0103424	−	0.0179135i
$881$	−10.3049			−0.347182			−0.173591	−	0.984818i	$-0.555537\pi$
$881$	−10.3049			−0.347182			−0.173591	+	0.984818i	$0.555537\pi$
$882$		0			0
$883$	−16.2482	+	28.1427i	−0.546795	+	0.947077i	0.451696	+	0.892172i	$0.350819\pi$
$883$	−16.2482	+	28.1427i	−0.546795	+	0.947077i	−0.998492	+	0.0549056i	$0.982514\pi$
$884$	5.10008	−	8.83360i	0.171534	−	0.297106i
$885$		0			0
$886$	35.3913			1.18899
$887$	−15.8979	+	27.5359i	−0.533798	+	0.924565i	0.465423	+	0.885088i	$0.345902\pi$
$887$	−15.8979	+	27.5359i	−0.533798	+	0.924565i	−0.999221	+	0.0394761i	$0.987431\pi$
$888$		0			0
$889$	−0.626738	+	1.08554i	−0.0210201	+	0.0364079i
$890$	4.89648	+	8.48096i	0.164130	+	0.284282i
$891$		0			0
$892$	−12.5323			−0.419612
$893$	20.2134	−	42.2452i	0.676415	−	1.41368i
$894$		0			0
$895$	−4.58469	−	7.94091i	−0.153249	−	0.265435i
$896$	−9.82835	−	17.0232i	−0.328342	−	0.568705i
$897$		0			0
$898$	17.3417	+	30.0368i	0.578701	+	1.00234i
$899$	−4.45546	+	7.71708i	−0.148598	+	0.257379i
$900$		0			0
$901$	23.1173			0.770149
$902$	−2.39851	+	4.15435i	−0.0798618	+	0.138325i
$903$		0			0
$904$	−27.5960			−0.917828
$905$	7.62942			0.253611
$906$		0			0
$907$	−12.7387	−	22.0640i	−0.422981	−	0.732624i	0.573249	−	0.819381i	$-0.305683\pi$
$907$	−12.7387	−	22.0640i	−0.422981	−	0.732624i	−0.996229	+	0.0867575i	$0.972349\pi$
$908$	5.79589	−	10.0388i	0.192344	−	0.333149i
$909$		0			0
$910$	4.70289	+	8.14564i	0.155899	+	0.270025i
$911$	2.34067			0.0775500			0.0387750	−	0.999248i	$-0.487654\pi$
$911$	2.34067			0.0775500			0.0387750	+	0.999248i	$0.487654\pi$
$912$		0			0
$913$	9.17209			0.303552
$914$	−0.853839	−	1.47889i	−0.0282425	−	0.0489174i
$915$		0			0
$916$	−3.14815	+	5.45275i	−0.104018	+	0.180164i
$917$	−2.26705	−	3.92664i	−0.0748645	−	0.129669i
$918$		0			0
$919$	−48.7435			−1.60790			−0.803949	−	0.594698i	$-0.797272\pi$
$919$	−48.7435			−1.60790			−0.803949	+	0.594698i	$0.797272\pi$
$920$	24.5581			0.809655
$921$		0			0
$922$	1.42748	−	2.47247i	0.0470116	−	0.0814264i
$923$	−40.2815			−1.32588
$924$		0			0
$925$	4.50445	−	7.80194i	0.148106	−	0.256526i
$926$	−9.23454	−	15.9947i	−0.303466	−	0.525618i
$927$		0			0
$928$	−4.97679	−	8.62006i	−0.163371	−	0.282967i
$929$	11.8730	+	20.5646i	0.389539	+	0.674702i	0.992388	−	0.123154i	$-0.0393008\pi$
$929$	11.8730	+	20.5646i	0.389539	+	0.674702i	−0.602848	+	0.797856i	$0.705968\pi$
$930$		0			0
$931$	−27.8898	+	2.16067i	−0.914051	+	0.0708129i
$932$	−10.8309			−0.354778
$933$		0			0
$934$	10.7050	+	18.5415i	0.350277	+	0.606698i
$935$	2.30065	−	3.98485i	0.0752393	−	0.130318i
$936$		0			0
$937$	−3.36857	+	5.83453i	−0.110046	+	0.190606i	−0.915789	−	0.401660i	$-0.868433\pi$
$937$	−3.36857	+	5.83453i	−0.110046	+	0.190606i	0.805742	+	0.592266i	$0.201767\pi$
$938$	−43.0461			−1.40550
$939$		0			0
$940$	−6.10858	+	10.5804i	−0.199240	+	0.345094i
$941$	10.7451	−	18.6110i	0.350280	−	0.606702i	−0.636019	−	0.771674i	$-0.719420\pi$
$941$	10.7451	−	18.6110i	0.350280	−	0.606702i	0.986298	+	0.164971i	$0.0527532\pi$
$942$		0			0
$943$	−30.6918			−0.999463
$944$	1.14776	−	1.98797i	0.0373563	−	0.0647030i
$945$		0			0
$946$	5.82049	−	10.0814i	0.189240	−	0.327774i
$947$	−5.64415	−	9.77596i	−0.183410	−	0.317676i	0.759629	−	0.650356i	$-0.225380\pi$
$947$	−5.64415	−	9.77596i	−0.183410	−	0.317676i	−0.943040	+	0.332680i	$0.892047\pi$
$948$		0			0
$949$	−5.33060			−0.173039
$950$	−4.03696	+	0.312750i	−0.130976	+	0.0101469i
$951$		0			0
$952$	17.3195	+	29.9982i	0.561327	+	0.972247i
$953$	16.5349	+	28.6393i	0.535618	+	0.927718i	0.999133	+	0.0416291i	$0.0132548\pi$
$953$	16.5349	+	28.6393i	0.535618	+	0.927718i	−0.463515	+	0.886089i	$0.653412\pi$
$954$		0			0
$955$	4.12692	+	7.14803i	0.133544	+	0.231305i
$956$	6.24170	−	10.8109i	0.201871	−	0.349651i
$957$		0			0
$958$	28.4021			0.917629
$959$	−10.5180	+	18.2177i	−0.339643	+	0.588279i
$960$		0			0
$961$	−7.40145			−0.238757
$962$	23.1329			0.745836
$963$		0			0
$964$	3.84857	+	6.66591i	0.123954	+	0.214695i
$965$	1.64118	−	2.84261i	0.0528315	−	0.0915068i
$966$		0			0
$967$	−14.4068	−	24.9533i	−0.463292	−	0.802446i	0.535830	−	0.844326i	$-0.319999\pi$
$967$	−14.4068	−	24.9533i	−0.463292	−	0.802446i	−0.999123	+	0.0418800i	$0.986665\pi$
$968$	26.1963			0.841979
$969$		0			0
$970$	0.579113			0.0185942
$971$	16.2058	+	28.0693i	0.520070	+	0.900787i	0.999728	+	0.0233315i	$0.00742731\pi$
$971$	16.2058	+	28.0693i	0.520070	+	0.900787i	−0.479658	+	0.877455i	$0.659239\pi$
$972$		0			0
$973$	−37.9964	+	65.8117i	−1.21811	+	2.10983i
$974$	−16.3019	−	28.2357i	−0.522346	−	0.904730i
$975$		0			0
$976$	1.42286			0.0455445
$977$	−41.7534			−1.33581			−0.667905	−	0.744246i	$-0.732809\pi$
$977$	−41.7534			−1.33581			−0.667905	+	0.744246i	$0.732809\pi$
$978$		0			0
$979$	7.47424	−	12.9458i	0.238878	−	0.413748i
$980$	7.29746			0.233109
$981$		0			0
$982$	11.8752	−	20.5684i	0.378953	−	0.656365i
$983$	−23.0214	−	39.8742i	−0.734269	−	1.27179i	−0.955043	−	0.296466i	$-0.904192\pi$
$983$	−23.0214	−	39.8742i	−0.734269	−	1.27179i	0.220775	−	0.975325i	$-0.429141\pi$
$984$		0			0
$985$	−6.93201	−	12.0066i	−0.220872	−	0.382562i
$986$	2.76470	+	4.78860i	0.0880459	+	0.152500i
$987$		0			0
$988$	7.74670	+	11.3011i	0.246455	+	0.359536i
$989$	74.4801			2.36833
$990$		0			0
$991$	7.00933	+	12.1405i	0.222659	+	0.385656i	0.955614	−	0.294620i	$-0.0951931\pi$
$991$	7.00933	+	12.1405i	0.222659	+	0.385656i	−0.732956	+	0.680276i	$0.761860\pi$
$992$	−13.1799	+	22.8283i	−0.418463	+	0.724798i
$993$		0			0
$994$	24.7918	−	42.9406i	0.786347	−	1.36199i
$995$	−14.0565			−0.445620
$996$		0			0
$997$	−3.94790	+	6.83796i	−0.125031	+	0.216560i	−0.921745	−	0.387796i	$-0.873236\pi$
$997$	−3.94790	+	6.83796i	−0.125031	+	0.216560i	0.796714	+	0.604357i	$0.206570\pi$
$998$	17.8683	−	30.9488i	0.565612	−	0.979668i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.k.406.2	yes	12
3.2	odd	2		855.2.k.j.406.5	✓	12
19.11	even	3	inner	855.2.k.k.676.2	yes	12
57.11	odd	6		855.2.k.j.676.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.k.j.406.5	✓	12	3.2	odd	2
855.2.k.j.676.5	yes	12	57.11	odd	6
855.2.k.k.406.2	yes	12	1.1	even	1	trivial
855.2.k.k.676.2	yes	12	19.11	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.464458 - 0.804466i) q^{2} +(0.568557 - 0.984769i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.66299 q^{7} -2.91412 q^{8} +O(q^{10})\)	\(q+(-0.464458 - 0.804466i) q^{2} +(0.568557 - 0.984769i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.66299 q^{7} -2.91412 q^{8} +(0.464458 - 0.804466i) q^{10} -1.41795 q^{11} +(1.38214 - 2.39394i) q^{13} +(1.70131 + 2.94675i) q^{14} +(0.216373 + 0.374768i) q^{16} +(1.62252 + 2.81029i) q^{17} +(-4.34588 + 0.336682i) q^{19} +1.13711 q^{20} +(0.658577 + 1.14069i) q^{22} +(-4.21364 + 7.29823i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.56778 q^{26} +(-2.08262 + 3.60720i) q^{28} +(-0.917170 + 1.58858i) q^{29} +4.85783 q^{31} +(-2.71313 + 4.69927i) q^{32} +(1.50719 - 2.61053i) q^{34} +(-1.83150 - 3.17225i) q^{35} -9.00891 q^{37} +(2.28933 + 3.33973i) q^{38} +(-1.45706 - 2.52370i) q^{40} +(1.82098 + 3.15403i) q^{41} +(-4.41899 - 7.65392i) q^{43} +(-0.806183 + 1.39635i) q^{44} +7.82823 q^{46} +(-5.37200 + 9.30458i) q^{47} +6.41753 q^{49} +0.928917 q^{50} +(-1.57165 - 2.72218i) q^{52} +(3.56193 - 6.16945i) q^{53} +(-0.708973 - 1.22798i) q^{55} +10.6744 q^{56} +1.70395 q^{58} +(-2.65227 - 4.59387i) q^{59} +(1.64399 - 2.84747i) q^{61} +(-2.25626 - 3.90796i) q^{62} +5.90603 q^{64} +2.76428 q^{65} +(-6.32544 + 10.9560i) q^{67} +3.68999 q^{68} +(-1.70131 + 2.94675i) q^{70} +(-7.28608 - 12.6199i) q^{71} +(-0.964193 - 1.67003i) q^{73} +(4.18426 + 7.24736i) q^{74} +(-2.13932 + 4.47111i) q^{76} +5.19393 q^{77} +(6.25028 + 10.8258i) q^{79} +(-0.216373 + 0.374768i) q^{80} +(1.69154 - 2.92983i) q^{82} -6.46857 q^{83} +(-1.62252 + 2.81029i) q^{85} +(-4.10487 + 7.10985i) q^{86} +4.13206 q^{88} +(-5.27117 + 9.12994i) q^{89} +(-5.06277 + 8.76897i) q^{91} +(4.79138 + 8.29892i) q^{92} +9.98029 q^{94} +(-2.46451 - 3.59530i) q^{95} +(0.311714 + 0.539905i) q^{97} +(-2.98067 - 5.16268i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 5 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8	\( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 3 q^{10} - 8 q^{13} + 10 q^{14} - 3 q^{16} + 4 q^{17} - 6 q^{19} - 10 q^{20} - 2 q^{23} - 6 q^{25} - 40 q^{26} - 26 q^{28} + 4 q^{29} + 24 q^{31} + 15 q^{32} + 7 q^{34} + 2 q^{35} - 29 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} + 6 q^{44} + 48 q^{46} + 6 q^{47} + 32 q^{49} - 6 q^{50} - 20 q^{52} + 26 q^{53} - 44 q^{56} - 20 q^{58} + 16 q^{59} + 20 q^{61} - 25 q^{62} + 28 q^{64} - 16 q^{65} - 12 q^{67} + 54 q^{68} - 10 q^{70} - 8 q^{71} - 4 q^{73} - 16 q^{74} - 66 q^{76} + 48 q^{77} - 12 q^{79} + 3 q^{80} + 26 q^{82} - 44 q^{83} - 4 q^{85} - 44 q^{86} - 32 q^{88} - 8 q^{89} + 2 q^{91} + 36 q^{92} - 14 q^{94} - 6 q^{95} + 30 q^{97} + 49 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 5 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8 - 3 * q^10 - 8 * q^13 + 10 * q^14 - 3 * q^16 + 4 * q^17 - 6 * q^19 - 10 * q^20 - 2 * q^23 - 6 * q^25 - 40 * q^26 - 26 * q^28 + 4 * q^29 + 24 * q^31 + 15 * q^32 + 7 * q^34 + 2 * q^35 - 29 * q^38 - 6 * q^40 + 12 * q^41 - 4 * q^43 + 6 * q^44 + 48 * q^46 + 6 * q^47 + 32 * q^49 - 6 * q^50 - 20 * q^52 + 26 * q^53 - 44 * q^56 - 20 * q^58 + 16 * q^59 + 20 * q^61 - 25 * q^62 + 28 * q^64 - 16 * q^65 - 12 * q^67 + 54 * q^68 - 10 * q^70 - 8 * q^71 - 4 * q^73 - 16 * q^74 - 66 * q^76 + 48 * q^77 - 12 * q^79 + 3 * q^80 + 26 * q^82 - 44 * q^83 - 4 * q^85 - 44 * q^86 - 32 * q^88 - 8 * q^89 + 2 * q^91 + 36 * q^92 - 14 * q^94 - 6 * q^95 + 30 * q^97 + 49 * q^98

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