LMFDB - Embedded newform 855.2.k.k.676.6

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			676.6
Root			$-0.832197 + 1.44141i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.k.406.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33220 - 2.30743i) q^{2} +(-2.54950 - 4.41586i) q^{4} +(0.500000 - 0.866025i) q^{5} +4.51669 q^{7} -8.25696 q^{8} +(-1.33220 - 2.30743i) q^{10} +1.88045 q^{11} +(-2.21597 - 3.83818i) q^{13} +(6.01713 - 10.4220i) q^{14} +(-5.90090 + 10.2207i) q^{16} +(-0.818122 + 1.41703i) q^{17} +(-1.60125 - 4.05413i) q^{19} -5.09900 q^{20} +(2.50513 - 4.33901i) q^{22} +(3.47432 + 6.01770i) q^{23} +(-0.500000 - 0.866025i) q^{25} -11.8085 q^{26} +(-11.5153 - 19.9451i) q^{28} +(3.37483 + 5.84538i) q^{29} -2.32879 q^{31} +(7.46537 + 12.9304i) q^{32} +(2.17980 + 3.77552i) q^{34} +(2.25835 - 3.91157i) q^{35} -7.21276 q^{37} +(-11.4878 - 1.70612i) q^{38} +(-4.12848 + 7.15074i) q^{40} +(-3.12715 + 5.41639i) q^{41} +(1.41761 - 2.45538i) q^{43} +(-4.79420 - 8.30381i) q^{44} +18.5139 q^{46} +(-4.67129 - 8.09090i) q^{47} +13.4005 q^{49} -2.66439 q^{50} +(-11.2993 + 19.5709i) q^{52} +(5.90556 + 10.2287i) q^{53} +(0.940224 - 1.62852i) q^{55} -37.2941 q^{56} +17.9838 q^{58} +(1.24502 - 2.15644i) q^{59} +(7.28601 + 12.6197i) q^{61} +(-3.10241 + 5.37353i) q^{62} +16.1778 q^{64} -4.43195 q^{65} +(-0.479229 - 0.830050i) q^{67} +8.34321 q^{68} +(-6.01713 - 10.4220i) q^{70} +(-2.80004 + 4.84982i) q^{71} +(-0.664474 + 1.15090i) q^{73} +(-9.60882 + 16.6430i) q^{74} +(-13.8201 + 17.4069i) q^{76} +8.49341 q^{77} +(1.46452 - 2.53662i) q^{79} +(5.90090 + 10.2207i) q^{80} +(8.33197 + 14.4314i) q^{82} +12.9855 q^{83} +(0.818122 + 1.41703i) q^{85} +(-3.77708 - 6.54209i) q^{86} -15.5268 q^{88} +(-2.43379 - 4.21545i) q^{89} +(-10.0089 - 17.3359i) q^{91} +(17.7156 - 30.6843i) q^{92} -24.8923 q^{94} +(-4.31161 - 0.640341i) q^{95} +(9.04997 - 15.6750i) q^{97} +(17.8521 - 30.9208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 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}+ \cdots + 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

Character values

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

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.33220	−	2.30743i	0.942006	−	1.63160i	0.180368	−	0.983599i	$-0.442271\pi$
$2$	1.33220	−	2.30743i	0.942006	−	1.63160i	0.761638	−	0.648003i	$-0.224396\pi$
$3$		0			0
$3$		0			0
$4$	−2.54950	−	4.41586i	−1.27475	−	2.20793i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	4.51669			1.70715			0.853575	−	0.520971i	$-0.174430\pi$
$7$	4.51669			1.70715			0.853575	+	0.520971i	$0.174430\pi$
$8$	−8.25696			−2.91928
$9$		0			0
$10$	−1.33220	−	2.30743i	−0.421278	−	0.729675i
$11$	1.88045			0.566977			0.283488	−	0.958976i	$-0.408508\pi$
$11$	1.88045			0.566977			0.283488	+	0.958976i	$0.408508\pi$
$12$		0			0
$13$	−2.21597	−	3.83818i	−0.614601	−	1.06452i	−0.990454	−	0.137841i	$-0.955984\pi$
$13$	−2.21597	−	3.83818i	−0.614601	−	1.06452i	0.375854	−	0.926679i	$-0.377349\pi$
$14$	6.01713	−	10.4220i	1.60814	−	2.78539i
$15$		0			0
$16$	−5.90090	+	10.2207i	−1.47523	+	2.55517i
$17$	−0.818122	+	1.41703i	−0.198424	+	0.343680i	−0.948017	−	0.318218i	$-0.896916\pi$
$17$	−0.818122	+	1.41703i	−0.198424	+	0.343680i	0.749594	+	0.661898i	$0.230249\pi$
$18$		0			0
$19$	−1.60125	−	4.05413i	−0.367353	−	0.930082i
$19$	−1.60125	−	4.05413i	−0.367353	−	0.930082i
$20$	−5.09900			−1.14017
$21$		0			0
$22$	2.50513	−	4.33901i	0.534095	−	0.925080i
$23$	3.47432	+	6.01770i	0.724446	+	1.25478i	0.959202	+	0.282723i	$0.0912376\pi$
$23$	3.47432	+	6.01770i	0.724446	+	1.25478i	−0.234756	+	0.972054i	$0.575429\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−11.8085			−2.31583
$27$		0			0
$28$	−11.5153	−	19.9451i	−2.17619	−	3.76927i
$29$	3.37483	+	5.84538i	0.626690	+	1.08546i	0.988211	+	0.153095i	$0.0489242\pi$
$29$	3.37483	+	5.84538i	0.626690	+	1.08546i	−0.361521	+	0.932364i	$0.617743\pi$
$30$		0			0
$31$	−2.32879			−0.418263			−0.209132	−	0.977888i	$-0.567064\pi$
$31$	−2.32879			−0.418263			−0.209132	+	0.977888i	$0.567064\pi$
$32$	7.46537	+	12.9304i	1.31970	+	2.28579i
$33$		0			0
$34$	2.17980	+	3.77552i	0.373832	+	0.647497i
$35$	2.25835	−	3.91157i	0.381730	−	0.661176i
$36$		0			0
$37$	−7.21276			−1.18577			−0.592885	−	0.805287i	$-0.702011\pi$
$37$	−7.21276			−1.18577			−0.592885	+	0.805287i	$0.702011\pi$
$38$	−11.4878	−	1.70612i	−1.86357	−	0.276769i
$39$		0			0
$40$	−4.12848	+	7.15074i	−0.652770	+	1.13063i
$41$	−3.12715	+	5.41639i	−0.488379	+	0.845897i	−0.999911	−	0.0133671i	$-0.995745\pi$
$41$	−3.12715	+	5.41639i	−0.488379	+	0.845897i	0.511532	+	0.859264i	$0.329078\pi$
$42$		0			0
$43$	1.41761	−	2.45538i	0.216184	−	0.374441i	−0.737454	−	0.675397i	$-0.763972\pi$
$43$	1.41761	−	2.45538i	0.216184	−	0.374441i	0.953638	+	0.300956i	$0.0973056\pi$
$44$	−4.79420	−	8.30381i	−0.722753	−	1.25185i
$45$		0			0
$46$	18.5139			2.72973
$47$	−4.67129	−	8.09090i	−0.681377	−	1.18018i	−0.974561	−	0.224124i	$-0.928048\pi$
$47$	−4.67129	−	8.09090i	−0.681377	−	1.18018i	0.293184	−	0.956056i	$-0.405285\pi$
$48$		0			0
$49$	13.4005			1.91436
$50$	−2.66439			−0.376802
$51$		0			0
$52$	−11.2993	+	19.5709i	−1.56692	+	2.71399i
$53$	5.90556	+	10.2287i	0.811191	+	1.40502i	0.912031	+	0.410121i	$0.134514\pi$
$53$	5.90556	+	10.2287i	0.811191	+	1.40502i	−0.100840	+	0.994903i	$0.532153\pi$
$54$		0			0
$55$	0.940224	−	1.62852i	0.126780	−	0.219589i
$56$	−37.2941			−4.98364
$57$		0			0
$58$	17.9838			2.36138
$59$	1.24502	−	2.15644i	0.162088	−	0.280744i	−0.773529	−	0.633760i	$-0.781511\pi$
$59$	1.24502	−	2.15644i	0.162088	−	0.280744i	0.935617	+	0.353016i	$0.114844\pi$
$60$		0			0
$61$	7.28601	+	12.6197i	0.932878	+	1.61579i	0.778375	+	0.627799i	$0.216044\pi$
$61$	7.28601	+	12.6197i	0.932878	+	1.61579i	0.154502	+	0.987992i	$0.450623\pi$
$62$	−3.10241	+	5.37353i	−0.394006	+	0.682439i
$63$		0			0
$64$	16.1778			2.02222
$65$	−4.43195			−0.549716
$66$		0			0
$67$	−0.479229	−	0.830050i	−0.0585472	−	0.101407i	0.835266	−	0.549846i	$-0.185313\pi$
$67$	−0.479229	−	0.830050i	−0.0585472	−	0.101407i	−0.893813	+	0.448439i	$0.851980\pi$
$68$	8.34321			1.01176
$69$		0			0
$70$	−6.01713	−	10.4220i	−0.719184	−	1.24566i
$71$	−2.80004	+	4.84982i	−0.332304	+	0.575568i	−0.982963	−	0.183802i	$-0.941159\pi$
$71$	−2.80004	+	4.84982i	−0.332304	+	0.575568i	0.650659	+	0.759370i	$0.274493\pi$
$72$		0			0
$73$	−0.664474	+	1.15090i	−0.0777708	+	0.134703i	−0.902288	−	0.431134i	$-0.858114\pi$
$73$	−0.664474	+	1.15090i	−0.0777708	+	0.134703i	0.824517	+	0.565837i	$0.191447\pi$
$74$	−9.60882	+	16.6430i	−1.11700	+	1.93471i
$75$		0			0
$76$	−13.8201	+	17.4069i	−1.58527	+	1.99671i
$77$	8.49341			0.967914
$78$		0			0
$79$	1.46452	−	2.53662i	0.164771	−	0.285392i	−0.771803	−	0.635862i	$-0.780645\pi$
$79$	1.46452	−	2.53662i	0.164771	−	0.285392i	0.936574	+	0.350470i	$0.113978\pi$
$80$	5.90090	+	10.2207i	0.659741	+	1.14270i
$81$		0			0
$82$	8.33197	+	14.4314i	0.920112	+	1.59368i
$83$	12.9855			1.42535			0.712675	−	0.701495i	$-0.247484\pi$
$83$	12.9855			1.42535			0.712675	+	0.701495i	$0.247484\pi$
$84$		0			0
$85$	0.818122	+	1.41703i	0.0887378	+	0.153698i
$86$	−3.77708	−	6.54209i	−0.407293	−	0.705452i
$87$		0			0
$88$	−15.5268			−1.65516
$89$	−2.43379	−	4.21545i	−0.257981	−	0.446837i	0.707720	−	0.706493i	$-0.249724\pi$
$89$	−2.43379	−	4.21545i	−0.257981	−	0.446837i	−0.965701	+	0.259657i	$0.916391\pi$
$90$		0			0
$91$	−10.0089	−	17.3359i	−1.04921	−	1.81729i
$92$	17.7156	−	30.6843i	1.84697	−	3.19905i
$93$		0			0
$94$	−24.8923			−2.56744
$95$	−4.31161	−	0.640341i	−0.442362	−	0.0656976i
$96$		0			0
$97$	9.04997	−	15.6750i	0.918885	−	1.59156i	0.117775	−	0.993040i	$-0.462424\pi$
$97$	9.04997	−	15.6750i	0.918885	−	1.59156i	0.801111	−	0.598516i	$-0.204243\pi$
$98$	17.8521	−	30.9208i	1.80334	−	3.12347i
$99$		0			0
$100$	−2.54950	+	4.41586i	−0.254950	+	0.441586i
$101$	−5.31587	−	9.20736i	−0.528949	−	0.916166i	−0.999430	−	0.0337562i	$-0.989253\pi$
$101$	−5.31587	−	9.20736i	−0.528949	−	0.916166i	0.470481	−	0.882410i	$-0.344080\pi$
$102$		0			0
$103$	3.36712			0.331772			0.165886	−	0.986145i	$-0.446952\pi$
$103$	3.36712			0.331772			0.165886	+	0.986145i	$0.446952\pi$
$104$	18.2972	+	31.6917i	1.79419	+	3.10763i
$105$		0			0
$106$	31.4695			3.05659
$107$	−1.11074			−0.107380			−0.0536898	−	0.998558i	$-0.517098\pi$
$107$	−1.11074			−0.107380			−0.0536898	+	0.998558i	$0.517098\pi$
$108$		0			0
$109$	2.92296	−	5.06272i	0.279969	−	0.484921i	−0.691408	−	0.722465i	$-0.743009\pi$
$109$	2.92296	−	5.06272i	0.279969	−	0.484921i	0.971377	+	0.237544i	$0.0763424\pi$
$110$	−2.50513	−	4.33901i	−0.238855	−	0.413708i
$111$		0			0
$112$	−26.6526	+	46.1636i	−2.51843	+	4.36205i
$113$	−12.7544			−1.19983			−0.599915	−	0.800064i	$-0.704799\pi$
$113$	−12.7544			−1.19983			−0.599915	+	0.800064i	$0.704799\pi$
$114$		0			0
$115$	6.94864			0.647964
$116$	17.2083	−	29.8056i	1.59775	−	2.76738i
$117$		0			0
$118$	−3.31723	−	5.74561i	−0.305375	−	0.528926i
$119$	−3.69520	+	6.40028i	−0.338739	+	0.586713i
$120$		0			0
$121$	−7.46391			−0.678538
$122$	38.8256			3.51510
$123$		0			0
$124$	5.93725	+	10.2836i	0.533181	+	0.923496i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	3.70994	+	6.42581i	0.329204	+	0.570199i	0.982354	−	0.187030i	$-0.0598862\pi$
$127$	3.70994	+	6.42581i	0.329204	+	0.570199i	−0.653150	+	0.757229i	$0.726553\pi$
$128$	6.62127	−	11.4684i	0.585243	−	1.01367i
$129$		0			0
$130$	−5.90423	+	10.2264i	−0.517835	+	0.896917i
$131$	1.67881	−	2.90779i	0.146678	−	0.254054i	−0.783319	−	0.621619i	$-0.786475\pi$
$131$	1.67881	−	2.90779i	0.146678	−	0.254054i	0.929998	+	0.367565i	$0.119808\pi$
$132$		0			0
$133$	−7.23236	−	18.3113i	−0.627126	−	1.58779i
$134$	−2.55371			−0.220607
$135$		0			0
$136$	6.75520	−	11.7003i	0.579254	−	1.00330i
$137$	3.55570	+	6.15865i	0.303784	+	0.526169i	0.976990	−	0.213286i	$-0.0684166\pi$
$137$	3.55570	+	6.15865i	0.303784	+	0.526169i	−0.673206	+	0.739455i	$0.735083\pi$
$138$		0			0
$139$	7.13412	+	12.3567i	0.605108	+	1.04808i	0.992034	+	0.125968i	$0.0402036\pi$
$139$	7.13412	+	12.3567i	0.605108	+	1.04808i	−0.386926	+	0.922111i	$0.626463\pi$
$140$	−23.0306			−1.94644
$141$		0			0
$142$	7.46043	+	12.9218i	0.626065	+	1.08438i
$143$	−4.16703	−	7.21750i	−0.348464	−	0.603558i
$144$		0			0
$145$	6.74966			0.560529
$146$	1.77042	+	3.06646i	0.146521	+	0.253782i
$147$		0			0
$148$	18.3889	+	31.8506i	1.51156	+	2.61810i
$149$	9.50361	−	16.4607i	0.778566	−	1.34852i	−0.154202	−	0.988039i	$-0.549281\pi$
$149$	9.50361	−	16.4607i	0.778566	−	1.34852i	0.932768	−	0.360477i	$-0.117386\pi$
$150$		0			0
$151$	−10.2727			−0.835982			−0.417991	−	0.908451i	$-0.637266\pi$
$151$	−10.2727			−0.835982			−0.417991	+	0.908451i	$0.637266\pi$
$152$	13.2215	+	33.4748i	1.07240	+	2.71517i
$153$		0			0
$154$	11.3149	−	19.5980i	0.911780	−	1.57925i
$155$	−1.16439	+	2.01679i	−0.0935265	+	0.161993i
$156$		0			0
$157$	10.6692	−	18.4796i	0.851497	−	1.47484i	−0.0283608	−	0.999598i	$-0.509029\pi$
$157$	10.6692	−	18.4796i	0.851497	−	1.47484i	0.879857	−	0.475238i	$-0.157638\pi$
$158$	−3.90206	−	6.75856i	−0.310431	−	0.537682i
$159$		0			0
$160$	14.9307			1.18038
$161$	15.6924	+	27.1801i	1.23674	+	2.14209i
$162$		0			0
$163$	17.4134			1.36392			0.681960	−	0.731389i	$-0.261128\pi$
$163$	17.4134			1.36392			0.681960	+	0.731389i	$0.261128\pi$
$164$	31.8907			2.49025
$165$		0			0
$166$	17.2993	−	29.9633i	1.34269	−	2.32560i
$167$	8.48787	+	14.7014i	0.656811	+	1.13763i	0.981437	+	0.191787i	$0.0614284\pi$
$167$	8.48787	+	14.7014i	0.656811	+	1.13763i	−0.324626	+	0.945843i	$0.605238\pi$
$168$		0			0
$169$	−3.32108	+	5.75229i	−0.255468	+	0.442483i
$170$	4.35960			0.334366
$171$		0			0
$172$	−14.4568			−1.10232
$173$	−0.244205	+	0.422976i	−0.0185666	+	0.0321583i	−0.875159	−	0.483835i	$-0.839244\pi$
$173$	−0.244205	+	0.422976i	−0.0185666	+	0.0321583i	0.856593	+	0.515993i	$0.172577\pi$
$174$		0			0
$175$	−2.25835	−	3.91157i	−0.170715	−	0.295687i
$176$	−11.0963	+	19.2194i	−0.836418	+	1.44872i
$177$		0			0
$178$	−12.9692			−0.972079
$179$	−17.0592			−1.27507			−0.637533	−	0.770423i	$-0.720045\pi$
$179$	−17.0592			−1.27507			−0.637533	+	0.770423i	$0.720045\pi$
$180$		0			0
$181$	2.25090	+	3.89867i	0.167308	+	0.289786i	0.937473	−	0.348059i	$-0.113159\pi$
$181$	2.25090	+	3.89867i	0.167308	+	0.289786i	−0.770164	+	0.637845i	$0.779826\pi$
$182$	−53.3352			−3.95347
$183$		0			0
$184$	−28.6873	−	49.6879i	−2.11486	−	3.66304i
$185$	−3.60638	+	6.24644i	−0.265146	+	0.459247i
$186$		0			0
$187$	−1.53844	+	2.66465i	−0.112502	+	0.194858i
$188$	−23.8189	+	41.2555i	−1.73717	+	3.00887i
$189$		0			0
$190$	−7.22146	+	9.09569i	−0.523900	+	0.659871i
$191$	−1.64135			−0.118764			−0.0593818	−	0.998235i	$-0.518913\pi$
$191$	−1.64135			−0.118764			−0.0593818	+	0.998235i	$0.518913\pi$
$192$		0			0
$193$	−12.9749	+	22.4732i	−0.933953	+	1.61765i	−0.157462	+	0.987525i	$0.550331\pi$
$193$	−12.9749	+	22.4732i	−0.933953	+	1.61765i	−0.776491	+	0.630129i	$0.783002\pi$
$194$	−24.1127	−	41.7644i	−1.73119	−	2.99851i
$195$		0			0
$196$	−34.1646	−	59.1748i	−2.44033	−	4.22677i
$197$	−5.66403			−0.403546			−0.201773	−	0.979432i	$-0.564670\pi$
$197$	−5.66403			−0.403546			−0.201773	+	0.979432i	$0.564670\pi$
$198$		0			0
$199$	−0.546183	−	0.946016i	−0.0387179	−	0.0670613i	0.846017	−	0.533156i	$-0.178994\pi$
$199$	−0.546183	−	0.946016i	−0.0387179	−	0.0670613i	−0.884735	+	0.466094i	$0.845661\pi$
$200$	4.12848	+	7.15074i	0.291928	+	0.505634i
$201$		0			0
$202$	−28.3272			−1.99309
$203$	15.2431	+	26.4018i	1.06985	+	1.85304i
$204$		0			0
$205$	3.12715	+	5.41639i	0.218410	+	0.378297i
$206$	4.48567	−	7.76941i	0.312532	−	0.541321i
$207$		0			0
$208$	52.3050			3.62670
$209$	−3.01107	−	7.62359i	−0.208280	−	0.527335i
$210$		0			0
$211$	1.42499	−	2.46816i	0.0981006	−	0.169915i	−0.812798	−	0.582546i	$-0.802057\pi$
$211$	1.42499	−	2.46816i	0.0981006	−	0.169915i	0.910898	+	0.412631i	$0.135390\pi$
$212$	30.1124	−	52.1563i	2.06813	−	3.58211i
$213$		0			0
$214$	−1.47973	+	2.56297i	−0.101152	+	0.175201i
$215$	−1.41761	−	2.45538i	−0.0966803	−	0.167455i
$216$		0			0
$217$	−10.5184			−0.714037
$218$	−7.78793	−	13.4891i	−0.527465	−	0.913596i
$219$		0			0
$220$	−9.58841			−0.646450
$221$	7.25175			0.487805
$222$		0			0
$223$	−7.97774	+	13.8178i	−0.534229	+	0.925312i	0.464971	+	0.885326i	$0.346065\pi$
$223$	−7.97774	+	13.8178i	−0.534229	+	0.925312i	−0.999200	+	0.0399859i	$0.987269\pi$
$224$	33.7188	+	58.4027i	2.25293	+	3.90219i
$225$		0			0
$226$	−16.9913	+	29.4299i	−1.13025	+	1.95765i
$227$	16.7113			1.10917			0.554583	−	0.832128i	$-0.312878\pi$
$227$	16.7113			1.10917			0.554583	+	0.832128i	$0.312878\pi$
$228$		0			0
$229$	1.43075			0.0945464			0.0472732	−	0.998882i	$-0.484947\pi$
$229$	1.43075			0.0945464			0.0472732	+	0.998882i	$0.484947\pi$
$230$	9.25696	−	16.0335i	0.610386	−	1.05722i
$231$		0			0
$232$	−27.8658	−	48.2650i	−1.82948	−	3.16876i
$233$	0.889166	−	1.54008i	0.0582512	−	0.100894i	−0.835429	−	0.549598i	$-0.814781\pi$
$233$	0.889166	−	1.54008i	0.0582512	−	0.100894i	0.893680	+	0.448704i	$0.148114\pi$
$234$		0			0
$235$	−9.34257			−0.609442
$236$	−12.6967			−0.826486
$237$		0			0
$238$	9.84548	+	17.0529i	0.638188	+	1.10537i
$239$	−14.6228			−0.945873			−0.472937	−	0.881096i	$-0.656806\pi$
$239$	−14.6228			−0.945873			−0.472937	+	0.881096i	$0.656806\pi$
$240$		0			0
$241$	−3.96473	−	6.86712i	−0.255391	−	0.442350i	0.709611	−	0.704594i	$-0.248871\pi$
$241$	−3.96473	−	6.86712i	−0.255391	−	0.442350i	−0.965002	+	0.262244i	$0.915538\pi$
$242$	−9.94341	+	17.2225i	−0.639186	+	1.10710i
$243$		0			0
$244$	37.1514	−	64.3480i	2.37837	−	4.11946i
$245$	6.70025	−	11.6052i	0.428063	−	0.741428i
$246$		0			0
$247$	−12.0122	+	15.1297i	−0.764315	+	0.962683i
$248$	19.2287			1.22103
$249$		0			0
$250$	−1.33220	+	2.30743i	−0.0842556	+	0.145935i
$251$	11.0212	+	19.0892i	0.695650	+	1.20490i	0.969961	+	0.243260i	$0.0782170\pi$
$251$	11.0212	+	19.0892i	0.695650	+	1.20490i	−0.274311	+	0.961641i	$0.588450\pi$
$252$		0			0
$253$	6.53328	+	11.3160i	0.410744	+	0.711429i
$254$	19.7695			1.24045
$255$		0			0
$256$	−1.46389	−	2.53553i	−0.0914931	−	0.158471i
$257$	6.38142	+	11.0529i	0.398062	+	0.689464i	0.993487	−	0.113947i	$-0.0363496\pi$
$257$	6.38142	+	11.0529i	0.398062	+	0.689464i	−0.595425	+	0.803411i	$0.703016\pi$
$258$		0			0
$259$	−32.5778			−2.02429
$260$	11.2993	+	19.5709i	0.700750	+	1.21373i
$261$		0			0
$262$	−4.47301	−	7.74749i	−0.276344	−	0.478641i
$263$	−14.6760	+	25.4196i	−0.904963	+	1.56744i	−0.0839962	+	0.996466i	$0.526768\pi$
$263$	−14.6760	+	25.4196i	−0.904963	+	1.56744i	−0.820967	+	0.570976i	$0.806565\pi$
$264$		0			0
$265$	11.8111			0.725551
$266$	−51.8870	−	7.70602i	−3.18139	−	0.472487i
$267$		0			0
$268$	−2.44359	+	4.23242i	−0.149266	+	0.258536i
$269$	8.09111	−	14.0142i	0.493323	−	0.854461i	−0.506647	−	0.862154i	$-0.669115\pi$
$269$	8.09111	−	14.0142i	0.493323	−	0.854461i	0.999970	+	0.00769238i	$0.00244859\pi$
$270$		0			0
$271$	5.82336	−	10.0864i	0.353744	−	0.612702i	−0.633158	−	0.774022i	$-0.718242\pi$
$271$	5.82336	−	10.0864i	0.353744	−	0.612702i	0.986902	+	0.161320i	$0.0515751\pi$
$272$	−9.65531	−	16.7235i	−0.585439	−	1.01401i
$273$		0			0
$274$	18.9476			1.14466
$275$	−0.940224	−	1.62852i	−0.0566977	−	0.0982032i
$276$		0			0
$277$	−24.3273			−1.46168			−0.730842	−	0.682547i	$-0.760872\pi$
$277$	−24.3273			−1.46168			−0.730842	+	0.682547i	$0.760872\pi$
$278$	38.0162			2.28006
$279$		0			0
$280$	−18.6471	+	32.2977i	−1.11438	+	1.93016i
$281$	−7.50719	−	13.0028i	−0.447841	−	0.775684i	0.550404	−	0.834899i	$-0.314474\pi$
$281$	−7.50719	−	13.0028i	−0.447841	−	0.775684i	−0.998245	+	0.0592145i	$0.981140\pi$
$282$		0			0
$283$	5.11877	−	8.86596i	0.304279	−	0.527027i	−0.672821	−	0.739805i	$-0.734918\pi$
$283$	5.11877	−	8.86596i	0.304279	−	0.527027i	0.977101	+	0.212778i	$0.0682511\pi$
$284$	28.5549			1.69442
$285$		0			0
$286$	−22.2052			−1.31302
$287$	−14.1244	+	24.4641i	−0.833736	+	1.44407i
$288$		0			0
$289$	7.16135	+	12.4038i	0.421256	+	0.729637i
$290$	8.99188	−	15.5744i	0.528021	−	0.914560i
$291$		0			0
$292$	6.77631			0.396554
$293$	8.33200			0.486760			0.243380	−	0.969931i	$-0.421744\pi$
$293$	8.33200			0.486760			0.243380	+	0.969931i	$0.421744\pi$
$294$		0			0
$295$	−1.24502	−	2.15644i	−0.0724879	−	0.125553i
$296$	59.5555			3.46159
$297$		0			0
$298$	−25.3214	−	43.8579i	−1.46683	−	2.54062i
$299$	15.3980	−	26.6701i	0.890490	−	1.54237i
$300$		0			0
$301$	6.40292	−	11.0902i	0.369058	−	0.639227i
$302$	−13.6853	+	23.7036i	−0.787500	+	1.36399i
$303$		0			0
$304$	50.8848	+	7.55718i	2.91844	+	0.433434i
$305$	14.5720			0.834391
$306$		0			0
$307$	−2.99821	+	5.19305i	−0.171117	+	0.296383i	−0.938811	−	0.344434i	$-0.888071\pi$
$307$	−2.99821	+	5.19305i	−0.171117	+	0.296383i	0.767694	+	0.640817i	$0.221404\pi$
$308$	−21.6539	−	37.5057i	−1.23385	−	2.13709i
$309$		0			0
$310$	3.10241	+	5.37353i	0.176205	+	0.305196i
$311$	−23.0404			−1.30650			−0.653252	−	0.757141i	$-0.726596\pi$
$311$	−23.0404			−1.30650			−0.653252	+	0.757141i	$0.726596\pi$
$312$		0			0
$313$	7.90040	+	13.6839i	0.446557	+	0.773460i	0.998159	−	0.0606477i	$-0.0193166\pi$
$313$	7.90040	+	13.6839i	0.446557	+	0.773460i	−0.551602	+	0.834107i	$0.685983\pi$
$314$	−28.4270	−	49.2370i	−1.60423	−	2.77861i
$315$		0			0
$316$	−14.9352			−0.840169
$317$	1.65437	+	2.86546i	0.0929188	+	0.160940i	0.908738	−	0.417367i	$-0.137047\pi$
$317$	1.65437	+	2.86546i	0.0929188	+	0.160940i	−0.815819	+	0.578307i	$0.803714\pi$
$318$		0			0
$319$	6.34619	+	10.9919i	0.355319	+	0.615430i
$320$	8.08890	−	14.0104i	0.452183	−	0.783204i
$321$		0			0
$322$	83.6217			4.66005
$323$	7.05484	+	1.04775i	0.392542	+	0.0582986i
$324$		0			0
$325$	−2.21597	+	3.83818i	−0.122920	+	0.212904i
$326$	23.1981	−	40.1802i	1.28482	−	2.22538i
$327$		0			0
$328$	25.8208	−	44.7229i	1.42571	−	2.46941i
$329$	−21.0988	−	36.5441i	−1.16321	−	2.01474i
$330$		0			0
$331$	−17.6455			−0.969886			−0.484943	−	0.874546i	$-0.661160\pi$
$331$	−17.6455			−0.969886			−0.484943	+	0.874546i	$0.661160\pi$
$332$	−33.1067	−	57.3424i	−1.81696	−	3.14707i
$333$		0			0
$334$	45.2301			2.47488
$335$	−0.958459			−0.0523662
$336$		0			0
$337$	1.49807	−	2.59473i	0.0816049	−	0.141344i	−0.822335	−	0.569004i	$-0.807329\pi$
$337$	1.49807	−	2.59473i	0.0816049	−	0.141344i	0.903939	+	0.427660i	$0.140662\pi$
$338$	8.84868	+	15.3264i	0.481305	+	0.833644i
$339$		0			0
$340$	4.17160	−	7.22543i	0.226237	−	0.391854i
$341$	−4.37917			−0.237145
$342$		0			0
$343$	28.9091			1.56095
$344$	−11.7052	+	20.2739i	−0.631100	+	1.09310i
$345$		0			0
$346$	0.650659	+	1.12697i	0.0349797	+	0.0605865i
$347$	−9.23585	+	15.9970i	−0.495806	+	0.858762i	−0.999988	−	0.00483560i	$-0.998461\pi$
$347$	−9.23585	+	15.9970i	−0.495806	+	0.858762i	0.504182	+	0.863597i	$0.331794\pi$
$348$		0			0
$349$	−8.28156			−0.443302			−0.221651	−	0.975126i	$-0.571145\pi$
$349$	−8.28156			−0.443302			−0.221651	+	0.975126i	$0.571145\pi$
$350$	−12.0343			−0.643258
$351$		0			0
$352$	14.0383	+	24.3150i	0.748241	+	1.29599i
$353$	11.2013			0.596182			0.298091	−	0.954537i	$-0.403650\pi$
$353$	11.2013			0.596182			0.298091	+	0.954537i	$0.403650\pi$
$354$		0			0
$355$	2.80004	+	4.84982i	0.148611	+	0.257402i
$356$	−12.4099	+	21.4946i	−0.657723	+	1.13921i
$357$		0			0
$358$	−22.7263	+	39.3630i	−1.20112	+	2.08040i
$359$	−2.97676	+	5.15590i	−0.157107	+	0.272118i	−0.933824	−	0.357732i	$-0.883550\pi$
$359$	−2.97676	+	5.15590i	−0.157107	+	0.272118i	0.776717	+	0.629850i	$0.216884\pi$
$360$		0			0
$361$	−13.8720	+	12.9834i	−0.730104	+	0.683336i
$362$	11.9946			0.630421
$363$		0			0
$364$	−51.0352	+	88.3956i	−2.67497	+	4.63319i
$365$	0.664474	+	1.15090i	0.0347802	+	0.0602410i
$366$		0			0
$367$	−7.01251	−	12.1460i	−0.366050	−	0.634017i	0.622894	−	0.782306i	$-0.285957\pi$
$367$	−7.01251	−	12.1460i	−0.366050	−	0.634017i	−0.988944	+	0.148289i	$0.952623\pi$
$368$	−82.0065			−4.27488
$369$		0			0
$370$	9.60882	+	16.6430i	0.499539	+	0.865227i
$371$	26.6736	+	46.2000i	1.38482	+	2.39859i
$372$		0			0
$373$	21.7329			1.12529			0.562643	−	0.826700i	$-0.309785\pi$
$373$	21.7329			1.12529			0.562643	+	0.826700i	$0.309785\pi$
$374$	4.09900	+	7.09968i	0.211954	+	0.367116i
$375$		0			0
$376$	38.5706	+	66.8063i	1.98913	+	3.44527i
$377$	14.9571	−	25.9064i	0.770328	−	1.33425i
$378$		0			0
$379$	−21.2847			−1.09332			−0.546662	−	0.837353i	$-0.684102\pi$
$379$	−21.2847			−1.09332			−0.546662	+	0.837353i	$0.684102\pi$
$380$	8.16479	+	20.6720i	0.418845	+	1.06045i
$381$		0			0
$382$	−2.18660	+	3.78730i	−0.111876	+	0.193775i
$383$	−9.33435	+	16.1676i	−0.476963	+	0.826125i	−0.999651	−	0.0263993i	$-0.991596\pi$
$383$	−9.33435	+	16.1676i	−0.476963	+	0.826125i	0.522688	+	0.852524i	$0.324929\pi$
$384$		0			0
$385$	4.24670	−	7.35551i	0.216432	−	0.374871i
$386$	34.5702	+	59.8774i	1.75958	+	3.04768i
$387$		0			0
$388$	−92.2916			−4.68540
$389$	−4.17221	−	7.22648i	−0.211540	−	0.366397i	0.740657	−	0.671883i	$-0.234514\pi$
$389$	−4.17221	−	7.22648i	−0.211540	−	0.366397i	−0.952197	+	0.305486i	$0.901181\pi$
$390$		0			0
$391$	−11.3697			−0.574989
$392$	−110.647			−5.58854
$393$		0			0
$394$	−7.54561	+	13.0694i	−0.380142	+	0.658426i
$395$	−1.46452	−	2.53662i	−0.0736880	−	0.127631i
$396$		0			0
$397$	−7.00796	+	12.1381i	−0.351719	+	0.609196i	−0.986551	−	0.163455i	$-0.947736\pi$
$397$	−7.00796	+	12.1381i	−0.351719	+	0.609196i	0.634831	+	0.772651i	$0.281070\pi$
$398$	−2.91049			−0.145890
$399$		0			0
$400$	11.8018			0.590090
$401$	18.5113	−	32.0625i	0.924411	−	1.60113i	0.131905	−	0.991262i	$-0.457890\pi$
$401$	18.5113	−	32.0625i	0.924411	−	1.60113i	0.792506	−	0.609865i	$-0.208776\pi$
$402$		0			0
$403$	5.16054	+	8.93831i	0.257065	+	0.445249i
$404$	−27.1056	+	46.9483i	−1.34856	+	2.33577i
$405$		0			0
$406$	81.2271			4.03123
$407$	−13.5632			−0.672304
$408$		0			0
$409$	−8.58224	−	14.8649i	−0.424365	−	0.735021i	0.571996	−	0.820256i	$-0.306169\pi$
$409$	−8.58224	−	14.8649i	−0.424365	−	0.735021i	−0.996361	+	0.0852352i	$0.972836\pi$
$410$	16.6639			0.822973
$411$		0			0
$412$	−8.58448	−	14.8688i	−0.422927	−	0.732531i
$413$	5.62337	−	9.73997i	0.276708	−	0.479273i
$414$		0			0
$415$	6.49277	−	11.2458i	0.318718	−	0.552035i
$416$	33.0861	−	57.3069i	1.62218	−	2.80970i
$417$		0			0
$418$	−21.6023	−	3.20827i	−1.05660	−	0.156922i
$419$	−36.1617			−1.76661			−0.883307	−	0.468795i	$-0.844688\pi$
$419$	−36.1617			−1.76661			−0.883307	+	0.468795i	$0.844688\pi$
$420$		0			0
$421$	−11.5673	+	20.0352i	−0.563757	+	0.976455i	0.433407	+	0.901198i	$0.357311\pi$
$421$	−11.5673	+	20.0352i	−0.563757	+	0.976455i	−0.997164	+	0.0752572i	$0.976022\pi$
$422$	−3.79674	−	6.57615i	−0.184823	−	0.320122i
$423$		0			0
$424$	−48.7620	−	84.4582i	−2.36809	−	4.10165i
$425$	1.63624			0.0793695
$426$		0			0
$427$	32.9087	+	56.9995i	1.59256	+	2.75840i
$428$	2.83184	+	4.90489i	0.136882	+	0.237087i
$429$		0			0
$430$	−7.55416			−0.364294
$431$	−13.5896	−	23.5380i	−0.654590	−	1.13378i	−0.981996	−	0.188900i	$-0.939508\pi$
$431$	−13.5896	−	23.5380i	−0.654590	−	1.13378i	0.327406	−	0.944884i	$-0.393825\pi$
$432$		0			0
$433$	2.42502	+	4.20025i	0.116539	+	0.201851i	0.918394	−	0.395667i	$-0.129487\pi$
$433$	2.42502	+	4.20025i	0.116539	+	0.201851i	−0.801855	+	0.597519i	$0.796153\pi$
$434$	−14.0126	+	24.2706i	−0.672627	+	1.16502i
$435$		0			0
$436$	−29.8084			−1.42756
$437$	18.8333	−	23.7212i	0.900918	−	1.13474i
$438$		0			0
$439$	−1.49026	+	2.58121i	−0.0711264	+	0.123195i	−0.899395	−	0.437136i	$-0.855993\pi$
$439$	−1.49026	+	2.58121i	−0.0711264	+	0.123195i	0.828269	+	0.560331i	$0.189326\pi$
$440$	−7.76340	+	13.4466i	−0.370105	+	0.641041i
$441$		0			0
$442$	9.66076	−	16.7329i	0.459515	−	0.795904i
$443$	6.95331	+	12.0435i	0.330362	+	0.572203i	0.982583	−	0.185825i	$-0.0594959\pi$
$443$	6.95331	+	12.0435i	0.330362	+	0.572203i	−0.652221	+	0.758029i	$0.726163\pi$
$444$		0			0
$445$	−4.86758			−0.230745
$446$	21.2558	+	36.8162i	1.00649	+	1.74330i
$447$		0			0
$448$	73.0701			3.45224
$449$	−0.142915			−0.00674457			−0.00337228	−	0.999994i	$-0.501073\pi$
$449$	−0.142915			−0.00674457			−0.00337228	+	0.999994i	$0.501073\pi$
$450$		0			0
$451$	−5.88045	+	10.1852i	−0.276900	+	0.479604i
$452$	32.5173	+	56.3216i	1.52948	+	2.64914i
$453$		0			0
$454$	22.2627	−	38.5602i	1.04484	−	1.80972i
$455$	−20.0177			−0.938446
$456$		0			0
$457$	−20.9389			−0.979481			−0.489741	−	0.871868i	$-0.662909\pi$
$457$	−20.9389			−0.979481			−0.489741	+	0.871868i	$0.662909\pi$
$458$	1.90604	−	3.30135i	0.0890633	−	0.154262i
$459$		0			0
$460$	−17.7156	−	30.6843i	−0.825992	−	1.43066i
$461$	2.59825	−	4.50030i	0.121012	−	0.209600i	−0.799155	−	0.601125i	$-0.794719\pi$
$461$	2.59825	−	4.50030i	0.121012	−	0.209600i	0.920167	+	0.391526i	$0.128053\pi$
$462$		0			0
$463$	−5.87258			−0.272922			−0.136461	−	0.990645i	$-0.543573\pi$
$463$	−5.87258			−0.272922			−0.136461	+	0.990645i	$0.543573\pi$
$464$	−79.6582			−3.69804
$465$		0			0
$466$	−2.36909	−	4.10338i	−0.109746	−	0.190086i
$467$	−20.4523			−0.946420			−0.473210	−	0.880950i	$-0.656905\pi$
$467$	−20.4523			−0.946420			−0.473210	+	0.880950i	$0.656905\pi$
$468$		0			0
$469$	−2.16453	−	3.74908i	−0.0999488	−	0.173116i
$470$	−12.4462	+	21.5574i	−0.574098	+	0.994367i
$471$		0			0
$472$	−10.2801	+	17.8056i	−0.473179	+	0.819571i
$473$	2.66575	−	4.61721i	0.122571	−	0.212299i
$474$		0			0
$475$	−2.71036	+	3.41379i	−0.124360	+	0.156636i
$476$	37.6837			1.72723
$477$		0			0
$478$	−19.4805	+	33.7412i	−0.891018	+	1.54329i
$479$	6.62827	+	11.4805i	0.302853	+	0.524557i	0.976781	−	0.214240i	$-0.0687275\pi$
$479$	6.62827	+	11.4805i	0.302853	+	0.524557i	−0.673928	+	0.738797i	$0.735394\pi$
$480$		0			0
$481$	15.9833	+	27.6839i	0.728776	+	1.26228i
$482$	−21.1272			−0.962319
$483$		0			0
$484$	19.0292	+	32.9596i	0.864966	+	1.49816i
$485$	−9.04997	−	15.6750i	−0.410938	−	0.711766i
$486$		0			0
$487$	17.6333			0.799039			0.399520	−	0.916725i	$-0.369177\pi$
$487$	17.6333			0.799039			0.399520	+	0.916725i	$0.369177\pi$
$488$	−60.1603	−	104.201i	−2.72333	−	4.71694i
$489$		0			0
$490$	−17.8521	−	30.9208i	−0.806477	−	1.39686i
$491$	−0.490857	+	0.850189i	−0.0221521	+	0.0383685i	−0.876889	−	0.480693i	$-0.840385\pi$
$491$	−0.490857	+	0.850189i	−0.0221521	+	0.0383685i	0.854737	+	0.519062i	$0.173718\pi$
$492$		0			0
$493$	−11.0441			−0.497401
$494$	18.9083	+	47.8731i	0.850726	+	2.15391i
$495$		0			0
$496$	13.7420	−	23.8018i	0.617032	−	1.06873i
$497$	−12.6469	+	21.9051i	−0.567293	+	0.982580i
$498$		0			0
$499$	2.12821	−	3.68617i	0.0952718	−	0.165016i	−0.814450	−	0.580233i	$-0.802961\pi$
$499$	2.12821	−	3.68617i	0.0952718	−	0.165016i	0.909722	+	0.415218i	$0.136295\pi$
$500$	2.54950	+	4.41586i	0.114017	+	0.197483i
$501$		0			0
$502$	58.7295			2.62123
$503$	−3.62562	−	6.27975i	−0.161658	−	0.280000i	0.773805	−	0.633424i	$-0.218351\pi$
$503$	−3.62562	−	6.27975i	−0.161658	−	0.280000i	−0.935464	+	0.353423i	$0.885018\pi$
$504$		0			0
$505$	−10.6317			−0.473106
$506$	34.8145			1.54769
$507$		0			0
$508$	18.9170	−	32.7652i	0.839307	−	1.45372i
$509$	8.38731	+	14.5272i	0.371761	+	0.643909i	0.989837	−	0.142210i	$-0.0454208\pi$
$509$	8.38731	+	14.5272i	0.371761	+	0.643909i	−0.618076	+	0.786119i	$0.712087\pi$
$510$		0			0
$511$	−3.00123	+	5.19828i	−0.132766	+	0.229958i
$512$	18.6843			0.825739
$513$		0			0
$514$	34.0052			1.49991
$515$	1.68356	−	2.91601i	0.0741866	−	0.128495i
$516$		0			0
$517$	−8.78411	−	15.2145i	−0.386325	−	0.669134i
$518$	−43.4001	+	75.1712i	−1.90689	+	3.30283i
$519$		0			0
$520$	36.5944			1.60477
$521$	−6.04583			−0.264873			−0.132436	−	0.991192i	$-0.542280\pi$
$521$	−6.04583			−0.264873			−0.132436	+	0.991192i	$0.542280\pi$
$522$		0			0
$523$	−11.5640	−	20.0295i	−0.505659	−	0.875827i	−0.999979	−	0.00654663i	$-0.997916\pi$
$523$	−11.5640	−	20.0295i	−0.505659	−	0.875827i	0.494320	−	0.869280i	$-0.335417\pi$
$524$	−17.1205			−0.747913
$525$		0			0
$526$	39.1028	+	67.7280i	1.70496	+	2.95308i
$527$	1.90523	−	3.29996i	0.0829933	−	0.143749i
$528$		0			0
$529$	−12.6418	+	21.8962i	−0.549644	+	0.952011i
$530$	15.7347	−	27.2534i	0.683474	−	1.18381i
$531$		0			0
$532$	−62.4212	+	78.6217i	−2.70630	+	3.40868i
$533$	27.7188			1.20063
$534$		0			0
$535$	−0.555372	+	0.961932i	−0.0240108	+	0.0415879i
$536$	3.95698	+	6.85369i	0.170915	+	0.296034i
$537$		0			0
$538$	−21.5579	−	37.3394i	−0.929427	−	1.60981i
$539$	25.1990			1.08540
$540$		0			0
$541$	−3.59500	−	6.22672i	−0.154561	−	0.267708i	0.778338	−	0.627846i	$-0.216063\pi$
$541$	−3.59500	−	6.22672i	−0.154561	−	0.267708i	−0.932899	+	0.360138i	$0.882730\pi$
$542$	−15.5157	−	26.8740i	−0.666458	−	1.15434i
$543$		0			0
$544$	−24.4303			−1.04744
$545$	−2.92296	−	5.06272i	−0.125206	−	0.216863i
$546$		0			0
$547$	−7.45323	−	12.9094i	−0.318677	−	0.551965i	0.661535	−	0.749914i	$-0.269905\pi$
$547$	−7.45323	−	12.9094i	−0.318677	−	0.551965i	−0.980212	+	0.197949i	$0.936572\pi$
$548$	18.1305	−	31.4029i	0.774497	−	1.34147i
$549$		0			0
$550$	−5.01026			−0.213638
$551$	18.2940	−	23.0419i	0.779350	−	0.981619i
$552$		0			0
$553$	6.61478	−	11.4571i	0.281289	−	0.487207i
$554$	−32.4087	+	56.1336i	−1.37692	+	2.38489i
$555$		0			0
$556$	36.3769	−	63.0066i	1.54272	−	2.67208i
$557$	−8.51591	−	14.7500i	−0.360831	−	0.624977i	0.627267	−	0.778804i	$-0.284173\pi$
$557$	−8.51591	−	14.7500i	−0.360831	−	0.624977i	−0.988098	+	0.153827i	$0.950840\pi$
$558$		0			0
$559$	−12.5656			−0.531467
$560$	26.6526	+	46.1636i	1.12628	+	1.95077i
$561$		0			0
$562$	−40.0042			−1.68748
$563$	−29.5414			−1.24502			−0.622512	−	0.782610i	$-0.713888\pi$
$563$	−29.5414			−1.24502			−0.622512	+	0.782610i	$0.713888\pi$
$564$		0			0
$565$	−6.37719	+	11.0456i	−0.268290	+	0.464692i
$566$	−13.6384	−	23.6224i	−0.573265	−	0.992925i
$567$		0			0
$568$	23.1199	−	40.0448i	0.970088	−	1.68024i
$569$	−40.3731			−1.69253			−0.846264	−	0.532764i	$-0.821153\pi$
$569$	−40.3731			−1.69253			−0.846264	+	0.532764i	$0.821153\pi$
$570$		0			0
$571$	29.1918			1.22164			0.610819	−	0.791770i	$-0.290840\pi$
$571$	29.1918			1.22164			0.610819	+	0.791770i	$0.290840\pi$
$572$	−21.2477	+	36.8020i	−0.888410	+	1.53877i
$573$		0			0
$574$	37.6329	+	65.1822i	1.57077	+	2.72065i
$575$	3.47432	−	6.01770i	0.144889	−	0.250955i
$576$		0			0
$577$	10.8930			0.453483			0.226741	−	0.973955i	$-0.427193\pi$
$577$	10.8930			0.453483			0.226741	+	0.973955i	$0.427193\pi$
$578$	38.1613			1.58730
$579$		0			0
$580$	−17.2083	−	29.8056i	−0.714534	−	1.23761i
$581$	58.6517			2.43328
$582$		0			0
$583$	11.1051	+	19.2346i	0.459926	+	0.796616i
$584$	5.48654	−	9.50296i	0.227035	−	0.393235i
$585$		0			0
$586$	11.0999	−	19.2255i	0.458531	−	0.794199i
$587$	10.7066	−	18.5444i	0.441909	−	0.765409i	−0.555922	−	0.831234i	$-0.687635\pi$
$587$	10.7066	−	18.5444i	0.441909	−	0.765409i	0.997831	+	0.0658255i	$0.0209681\pi$
$588$		0			0
$589$	3.72898	+	9.44122i	0.153650	+	0.389019i
$590$	−6.63445			−0.273136
$591$		0			0
$592$	42.5618	−	73.7192i	1.74928	−	3.02984i
$593$	14.6972	+	25.4563i	0.603541	+	1.04536i	0.992280	+	0.124016i	$0.0395774\pi$
$593$	14.6972	+	25.4563i	0.603541	+	1.04536i	−0.388739	+	0.921348i	$0.627089\pi$
$594$		0			0
$595$	3.69520	+	6.40028i	0.151489	+	0.262386i
$596$	−96.9179			−3.96991
$597$		0			0
$598$	−41.0264	−	71.0598i	−1.67769	−	2.90585i
$599$	−15.5165	−	26.8754i	−0.633988	−	1.09810i	−0.986729	−	0.162379i	$-0.948083\pi$
$599$	−15.5165	−	26.8754i	−0.633988	−	1.09810i	0.352740	−	0.935721i	$-0.385250\pi$
$600$		0			0
$601$	−31.8939			−1.30098			−0.650490	−	0.759515i	$-0.725436\pi$
$601$	−31.8939			−1.30098			−0.650490	+	0.759515i	$0.725436\pi$
$602$	−17.0599	−	29.5486i	−0.695310	−	1.20431i
$603$		0			0
$604$	26.1903	+	45.3629i	1.06567	+	1.84579i
$605$	−3.73196	+	6.46394i	−0.151726	+	0.262796i
$606$		0			0
$607$	15.2357			0.618398			0.309199	−	0.950997i	$-0.399939\pi$
$607$	15.2357			0.618398			0.309199	+	0.950997i	$0.399939\pi$
$608$	40.4676	−	50.9705i	1.64118	−	2.06713i
$609$		0			0
$610$	19.4128	−	33.6240i	0.786001	−	1.36139i
$611$	−20.7029	+	35.8585i	−0.837550	+	1.45068i
$612$		0			0
$613$	13.1709	−	22.8127i	0.531968	−	0.921395i	−0.467336	−	0.884080i	$-0.654786\pi$
$613$	13.1709	−	22.8127i	0.531968	−	0.921395i	0.999304	−	0.0373154i	$-0.0118806\pi$
$614$	7.98842	+	13.8363i	0.322386	+	0.558389i
$615$		0			0
$616$	−70.1297			−2.82561
$617$	−16.7665	−	29.0404i	−0.674993	−	1.16912i	−0.976471	−	0.215650i	$-0.930813\pi$
$617$	−16.7665	−	29.0404i	−0.674993	−	1.16912i	0.301477	−	0.953473i	$-0.402520\pi$
$618$		0			0
$619$	−13.6427			−0.548347			−0.274173	−	0.961680i	$-0.588404\pi$
$619$	−13.6427			−0.548347			−0.274173	+	0.961680i	$0.588404\pi$
$620$	11.8745			0.476891
$621$		0			0
$622$	−30.6944	+	53.1643i	−1.23073	+	2.13169i
$623$	−10.9927	−	19.0399i	−0.440412	−	0.762817i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	42.0996			1.68264
$627$		0			0
$628$	−108.805			−4.34178
$629$	5.90092	−	10.2207i	0.235285	−	0.407526i
$630$		0			0
$631$	−15.6058	−	27.0300i	−0.621256	−	1.07605i	−0.989252	−	0.146220i	$-0.953289\pi$
$631$	−15.6058	−	27.0300i	−0.621256	−	1.07605i	0.367996	−	0.929827i	$-0.380044\pi$
$632$	−12.0925	+	20.9448i	−0.481013	+	0.833139i
$633$		0			0
$634$	8.81580			0.350120
$635$	7.41989			0.294449
$636$		0			0
$637$	−29.6952	−	51.4336i	−1.17657	−	2.03787i
$638$	33.8175			1.33885
$639$		0			0
$640$	−6.62127	−	11.4684i	−0.261729	−	0.453328i
$641$	2.43993	−	4.22607i	0.0963713	−	0.166920i	−0.813809	−	0.581133i	$-0.802610\pi$
$641$	2.43993	−	4.22607i	0.0963713	−	0.166920i	0.910180	+	0.414213i	$0.135943\pi$
$642$		0			0
$643$	20.2215	−	35.0246i	0.797456	−	1.38123i	−0.123811	−	0.992306i	$-0.539512\pi$
$643$	20.2215	−	35.0246i	0.797456	−	1.38123i	0.921268	−	0.388929i	$-0.127155\pi$
$644$	80.0157	−	138.591i	3.15306	−	5.46126i
$645$		0			0
$646$	11.8161	−	14.8828i	0.464897	−	0.585554i
$647$	−3.10173			−0.121942			−0.0609709	−	0.998140i	$-0.519420\pi$
$647$	−3.10173			−0.121942			−0.0609709	+	0.998140i	$0.519420\pi$
$648$		0			0
$649$	2.34120	−	4.05507i	0.0919000	−	0.159176i
$650$	5.90423	+	10.2264i	0.231583	+	0.401113i
$651$		0			0
$652$	−44.3954	−	76.8951i	−1.73866	−	3.01144i
$653$	50.1213			1.96140			0.980700	−	0.195520i	$-0.0626395\pi$
$653$	50.1213			1.96140			0.980700	+	0.195520i	$0.0626395\pi$
$654$		0			0
$655$	−1.67881	−	2.90779i	−0.0655966	−	0.113617i
$656$	−36.9060	−	63.9231i	−1.44094	−	2.49578i
$657$		0			0
$658$	−112.431			−4.38301
$659$	9.81970	+	17.0082i	0.382521	+	0.662546i	0.991422	−	0.130700i	$-0.0417226\pi$
$659$	9.81970	+	17.0082i	0.382521	+	0.662546i	−0.608901	+	0.793246i	$0.708389\pi$
$660$		0			0
$661$	16.2367	+	28.1228i	0.631535	+	1.09385i	0.987238	+	0.159251i	$0.0509080\pi$
$661$	16.2367	+	28.1228i	0.631535	+	1.09385i	−0.355703	+	0.934599i	$0.615759\pi$
$662$	−23.5073	+	40.7159i	−0.913638	+	1.58247i
$663$		0			0
$664$	−107.221			−4.16099
$665$	−19.4742	−	2.89222i	−0.755177	−	0.112156i
$666$		0			0
$667$	−23.4505	+	40.6174i	−0.908006	+	1.57271i
$668$	43.2796	−	74.9625i	1.67454	−	2.90039i
$669$		0			0
$670$	−1.27686	+	2.21158i	−0.0493293	+	0.0854408i
$671$	13.7010	+	23.7308i	0.528920	+	0.916116i
$672$		0			0
$673$	42.1609			1.62518			0.812591	−	0.582835i	$-0.198056\pi$
$673$	42.1609			1.62518			0.812591	+	0.582835i	$0.198056\pi$
$674$	−3.99144	−	6.91338i	−0.153745	−	0.266294i
$675$		0			0
$676$	33.8684			1.30263
$677$	−5.35812			−0.205929			−0.102965	−	0.994685i	$-0.532833\pi$
$677$	−5.35812			−0.205929			−0.102965	+	0.994685i	$0.532833\pi$
$678$		0			0
$679$	40.8759	−	70.7992i	1.56867	−	2.71702i
$680$	−6.75520	−	11.7003i	−0.259050	−	0.448688i
$681$		0			0
$682$	−5.83392	+	10.1046i	−0.223392	+	0.386927i
$683$	−33.7370			−1.29091			−0.645454	−	0.763799i	$-0.723332\pi$
$683$	−33.7370			−1.29091			−0.645454	+	0.763799i	$0.723332\pi$
$684$		0			0
$685$	7.11139			0.271712
$686$	38.5126	−	66.7059i	1.47042	−	2.54684i
$687$		0			0
$688$	16.7304	+	28.9779i	0.637840	+	1.10477i
$689$	26.1731	−	45.3332i	0.997117	−	1.72706i
$690$		0			0
$691$	6.49582			0.247113			0.123556	−	0.992338i	$-0.460570\pi$
$691$	6.49582			0.247113			0.123556	+	0.992338i	$0.460570\pi$
$692$	2.49040			0.0946710
$693$		0			0
$694$	24.6080	+	42.6222i	0.934105	+	1.61792i
$695$	14.2682			0.541225
$696$		0			0
$697$	−5.11678	−	8.86253i	−0.193812	−	0.335692i
$698$	−11.0327	+	19.1091i	−0.417593	+	0.723292i
$699$		0			0
$700$	−11.5153	+	19.9451i	−0.435238	+	0.753854i
$701$	−22.8294	+	39.5416i	−0.862253	+	1.49347i	0.00749659	+	0.999972i	$0.497614\pi$
$701$	−22.8294	+	39.5416i	−0.862253	+	1.49347i	−0.869749	+	0.493494i	$0.835720\pi$
$702$		0			0
$703$	11.5495	+	29.2415i	0.435596	+	1.10286i
$704$	30.4215			1.14655
$705$		0			0
$706$	14.9223	−	25.8461i	0.561607	−	0.972732i
$707$	−24.0101	−	41.5868i	−0.902994	−	1.56403i
$708$		0			0
$709$	−7.34917	−	12.7291i	−0.276004	−	0.478052i	0.694384	−	0.719604i	$-0.255677\pi$
$709$	−7.34917	−	12.7291i	−0.276004	−	0.478052i	−0.970388	+	0.241552i	$0.922344\pi$
$710$	14.9209			0.559970
$711$		0			0
$712$	20.0957	+	34.8068i	0.753119	+	1.30444i
$713$	−8.09096	−	14.0140i	−0.303009	−	0.524827i
$714$		0			0
$715$	−8.33405			−0.311676
$716$	43.4925	+	75.3312i	1.62539	+	2.81526i
$717$		0			0
$718$	7.93127	+	13.7374i	0.295992	+	0.512674i
$719$	−8.47967	+	14.6872i	−0.316238	+	0.547741i	−0.979700	−	0.200470i	$-0.935753\pi$
$719$	−8.47967	+	14.6872i	−0.316238	+	0.547741i	0.663462	+	0.748210i	$0.269087\pi$
$720$		0			0
$721$	15.2083			0.566385
$722$	11.4781	+	49.3051i	0.427170	+	1.83495i
$723$		0			0
$724$	11.4773	−	19.8793i	0.426552	−	0.738810i
$725$	3.37483	−	5.84538i	0.125338	−	0.217092i
$726$		0			0
$727$	8.11714	−	14.0593i	0.301048	−	0.521431i	−0.675326	−	0.737520i	$-0.735997\pi$
$727$	8.11714	−	14.0593i	0.301048	−	0.521431i	0.976374	+	0.216089i	$0.0693302\pi$
$728$	82.6429	+	143.142i	3.06295	+	5.30518i
$729$		0			0
$730$	3.54084			0.131053
$731$	2.31956	+	4.01759i	0.0857920	+	0.148596i
$732$		0			0
$733$	3.72156			0.137459			0.0687295	−	0.997635i	$-0.478105\pi$
$733$	3.72156			0.137459			0.0687295	+	0.997635i	$0.478105\pi$
$734$	−37.3682			−1.37929
$735$		0			0
$736$	−51.8742	+	89.8487i	−1.91211	+	3.31187i
$737$	−0.901166	−	1.56087i	−0.0331949	−	0.0574952i
$738$		0			0
$739$	−16.0421	+	27.7857i	−0.590117	+	1.02211i	0.404099	+	0.914715i	$0.367585\pi$
$739$	−16.0421	+	27.7857i	−0.590117	+	1.02211i	−0.994216	+	0.107398i	$0.965748\pi$
$740$	36.7779			1.35198
$741$		0			0
$742$	142.138			5.21805
$743$	−25.4107	+	44.0127i	−0.932229	+	1.61467i	−0.152728	+	0.988268i	$0.548806\pi$
$743$	−25.4107	+	44.0127i	−0.932229	+	1.61467i	−0.779501	+	0.626401i	$0.784527\pi$
$744$		0			0
$745$	−9.50361	−	16.4607i	−0.348185	−	0.603075i
$746$	28.9525	−	50.1472i	1.06003	−	1.83602i
$747$		0			0
$748$	15.6890			0.573646
$749$	−5.01688			−0.183313
$750$		0			0
$751$	−13.5576	−	23.4824i	−0.494723	−	0.856885i	0.505259	−	0.862968i	$-0.331397\pi$
$751$	−13.5576	−	23.4824i	−0.494723	−	0.856885i	−0.999981	+	0.00608317i	$0.998064\pi$
$752$	110.259			4.02074
$753$		0			0
$754$	−39.8515	−	69.0249i	−1.45131	−	2.51374i
$755$	−5.13636	+	8.89644i	−0.186931	+	0.323774i
$756$		0			0
$757$	2.05907	−	3.56641i	0.0748381	−	0.129623i	−0.826178	−	0.563410i	$-0.809489\pi$
$757$	2.05907	−	3.56641i	0.0748381	−	0.129623i	0.901016	+	0.433786i	$0.142823\pi$
$758$	−28.3555	+	49.1131i	−1.02992	+	1.78387i
$759$		0			0
$760$	35.6008	+	5.28727i	1.29138	+	0.191789i
$761$	1.95450			0.0708506			0.0354253	−	0.999372i	$-0.488721\pi$
$761$	1.95450			0.0708506			0.0354253	+	0.999372i	$0.488721\pi$
$762$		0			0
$763$	13.2021	−	22.8667i	0.477949	−	0.827832i
$764$	4.18461	+	7.24796i	0.151394	+	0.262222i
$765$		0			0
$766$	24.8704	+	43.0768i	0.898604	+	1.55643i
$767$	−11.0357			−0.398477
$768$		0			0
$769$	−18.1734	−	31.4772i	−0.655349	−	1.13510i	−0.981806	−	0.189886i	$-0.939188\pi$
$769$	−18.1734	−	31.4772i	−0.655349	−	1.13510i	0.326457	−	0.945212i	$-0.394145\pi$
$770$	−11.3149	−	19.5980i	−0.407761	−	0.706262i
$771$		0			0
$772$	132.318			4.76223
$773$	−2.98175	−	5.16454i	−0.107246	−	0.185756i	0.807408	−	0.589994i	$-0.200870\pi$
$773$	−2.98175	−	5.16454i	−0.107246	−	0.185756i	−0.914654	+	0.404238i	$0.867537\pi$
$774$		0			0
$775$	1.16439	+	2.01679i	0.0418263	+	0.0724453i
$776$	−74.7253	+	129.428i	−2.68248	+	4.64619i
$777$		0			0
$778$	−22.2328			−0.797086
$779$	26.9661	+	4.00489i	0.966161	+	0.143490i
$780$		0			0
$781$	−5.26534	+	9.11984i	−0.188409	+	0.326333i
$782$	−15.1466	+	26.2348i	−0.541643	+	0.938153i
$783$		0			0
$784$	−79.0751	+	136.962i	−2.82411	+	4.89150i
$785$	−10.6692	−	18.4796i	−0.380801	−	0.659566i
$786$		0			0
$787$	50.2017			1.78950			0.894749	−	0.446569i	$-0.147354\pi$
$787$	50.2017			1.78950			0.894749	+	0.446569i	$0.147354\pi$
$788$	14.4405	+	25.0116i	0.514420	+	0.891001i
$789$		0			0
$790$	−7.80412			−0.277658
$791$	−57.6076			−2.04829
$792$		0			0
$793$	32.2912	−	55.9300i	1.14669	−	1.98613i
$794$	18.6720	+	32.3408i	0.662643	+	1.14773i
$795$		0			0
$796$	−2.78498	+	4.82374i	−0.0987112	+	0.170973i
$797$	34.8676			1.23508			0.617538	−	0.786541i	$-0.288130\pi$
$797$	34.8676			1.23508			0.617538	+	0.786541i	$0.288130\pi$
$798$		0			0
$799$	15.2867			0.540805
$800$	7.46537	−	12.9304i	0.263941	−	0.457159i
$801$		0			0
$802$	−49.3215	−	85.4273i	−1.74160	−	3.01654i
$803$	−1.24951	+	2.16421i	−0.0440942	+	0.0763735i
$804$		0			0
$805$	31.3849			1.10617
$806$	27.4994			0.968626
$807$		0			0
$808$	43.8929	+	76.0248i	1.54415	+	2.67454i
$809$	−29.0835			−1.02252			−0.511261	−	0.859425i	$-0.670822\pi$
$809$	−29.0835			−1.02252			−0.511261	+	0.859425i	$0.670822\pi$
$810$		0			0
$811$	−23.7180	−	41.0808i	−0.832853	−	1.44254i	−0.895767	−	0.444524i	$-0.853373\pi$
$811$	−23.7180	−	41.0808i	−0.832853	−	1.44254i	0.0629142	−	0.998019i	$-0.479961\pi$
$812$	77.7244	−	134.623i	2.72759	−	4.72433i
$813$		0			0
$814$	−18.0689	+	31.2963i	−0.633315	+	1.09693i
$815$	8.70669	−	15.0804i	0.304982	−	0.528244i
$816$		0			0
$817$	−12.2244	−	1.81551i	−0.427677	−	0.0635166i
$818$	−45.7330			−1.59902
$819$		0			0
$820$	15.9453	−	27.6182i	0.556836	−	0.964468i
$821$	−20.7041	−	35.8605i	−0.722577	−	1.25154i	−0.959964	−	0.280124i	$-0.909624\pi$
$821$	−20.7041	−	35.8605i	−0.722577	−	1.25154i	0.237387	−	0.971415i	$-0.423709\pi$
$822$		0			0
$823$	5.59572	+	9.69207i	0.195054	+	0.337844i	0.946918	−	0.321474i	$-0.104178\pi$
$823$	5.59572	+	9.69207i	0.195054	+	0.337844i	−0.751864	+	0.659318i	$0.770845\pi$
$824$	−27.8022			−0.968535
$825$		0			0
$826$	−14.9829	−	25.9511i	−0.521321	−	0.902955i
$827$	11.6195	+	20.1256i	0.404050	+	0.699835i	0.994210	−	0.107451i	$-0.0342689\pi$
$827$	11.6195	+	20.1256i	0.404050	+	0.699835i	−0.590161	+	0.807286i	$0.700936\pi$
$828$		0			0
$829$	8.29502			0.288098			0.144049	−	0.989571i	$-0.453988\pi$
$829$	8.29502			0.288098			0.144049	+	0.989571i	$0.453988\pi$
$830$	−17.2993	−	29.9633i	−0.600468	−	1.04004i
$831$		0			0
$832$	−35.8496	−	62.0933i	−1.24286	−	2.15270i
$833$	−10.9632	+	18.9889i	−0.379854	+	0.657926i
$834$		0			0
$835$	16.9757			0.587470
$836$	−25.9880	+	32.7328i	−0.898814	+	1.13209i
$837$		0			0
$838$	−48.1745	+	83.4407i	−1.66416	+	2.88241i
$839$	3.83072	−	6.63500i	0.132251	−	0.229066i	−0.792293	−	0.610141i	$-0.791113\pi$
$839$	3.83072	−	6.63500i	0.132251	−	0.229066i	0.924544	+	0.381075i	$0.124446\pi$
$840$		0			0
$841$	−8.27895	+	14.3396i	−0.285481	+	0.494468i
$842$	30.8199	+	53.3817i	1.06212	+	1.83965i
$843$		0			0
$844$	−14.5321			−0.500215
$845$	3.32108	+	5.75229i	0.114249	+	0.197885i
$846$		0			0
$847$	−33.7122			−1.15836
$848$	−139.393			−4.78676
$849$		0			0
$850$	2.17980	−	3.77552i	0.0747665	−	0.129499i
$851$	−25.0594	−	43.4042i	−0.859027	−	1.48788i
$852$		0			0
$853$	−15.6915	+	27.1784i	−0.537266	+	0.930572i	0.461784	+	0.886992i	$0.347209\pi$
$853$	−15.6915	+	27.1784i	−0.537266	+	0.930572i	−0.999050	+	0.0435793i	$0.986124\pi$
$854$	175.363			6.00081
$855$		0			0
$856$	9.17136			0.313471
$857$	−7.62506	+	13.2070i	−0.260467	+	0.451142i	−0.966366	−	0.257170i	$-0.917210\pi$
$857$	−7.62506	+	13.2070i	−0.260467	+	0.451142i	0.705899	+	0.708313i	$0.250543\pi$
$858$		0			0
$859$	9.17194	+	15.8863i	0.312942	+	0.542032i	0.978998	−	0.203870i	$-0.0653520\pi$
$859$	9.17194	+	15.8863i	0.312942	+	0.542032i	−0.666056	+	0.745902i	$0.732019\pi$
$860$	−7.22840	+	12.5200i	−0.246487	+	0.426927i
$861$		0			0
$862$	−72.4164			−2.46651
$863$	15.7389			0.535757			0.267878	−	0.963453i	$-0.413677\pi$
$863$	15.7389			0.535757			0.267878	+	0.963453i	$0.413677\pi$
$864$		0			0
$865$	0.244205	+	0.422976i	0.00830323	+	0.0143816i
$866$	12.9224			0.439121
$867$		0			0
$868$	26.8167	+	46.4479i	0.910219	+	1.57655i
$869$	2.75395	−	4.76999i	0.0934215	−	0.161811i
$870$		0			0
$871$	−2.12392	+	3.67874i	−0.0719663	+	0.124649i
$872$	−24.1348	+	41.8027i	−0.817307	+	1.41562i
$873$		0			0
$874$	−29.6455	−	75.0579i	−1.00277	−	2.53887i
$875$	−4.51669			−0.152692
$876$		0			0
$877$	20.9449	−	36.2776i	0.707259	−	1.22501i	−0.258611	−	0.965981i	$-0.583265\pi$
$877$	20.9449	−	36.2776i	0.707259	−	1.22501i	0.965870	−	0.259027i	$-0.0834018\pi$
$878$	3.97065	+	6.87737i	0.134003	+	0.232100i
$879$		0			0
$880$	11.0963	+	19.2194i	0.374058	+	0.647887i
$881$	−36.6761			−1.23565			−0.617825	−	0.786315i	$-0.711986\pi$
$881$	−36.6761			−1.23565			−0.617825	+	0.786315i	$0.711986\pi$
$882$		0			0
$883$	4.74307	+	8.21524i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$883$	4.74307	+	8.21524i	0.159617	+	0.276465i	−0.775114	+	0.631822i	$0.782307\pi$
$884$	−18.4883	−	32.0227i	−0.621830	−	1.07704i
$885$		0			0
$886$	37.0527			1.24481
$887$	−5.06704	−	8.77638i	−0.170135	−	0.294682i	0.768332	−	0.640051i	$-0.221087\pi$
$887$	−5.06704	−	8.77638i	−0.170135	−	0.294682i	−0.938467	+	0.345369i	$0.887754\pi$
$888$		0			0
$889$	16.7567	+	29.0234i	0.562001	+	0.973414i
$890$	−6.48458	+	11.2316i	−0.217364	+	0.376485i
$891$		0			0
$892$	81.3570			2.72403
$893$	−25.3217	+	31.8936i	−0.847358	+	1.06728i
$894$		0			0
$895$	−8.52961	+	14.7737i	−0.285113	+	0.493831i
$896$	29.9062	−	51.7991i	0.999098	−	1.73049i
$897$		0			0
$898$	−0.190391	+	0.329767i	−0.00635342	+	0.0110045i
$899$	−7.85927	−	13.6127i	−0.262121	−	0.454007i
$900$		0			0
$901$	−19.3259			−0.643838
$902$	15.6678	+	27.1375i	0.521682	+	0.903580i
$903$		0			0
$904$	105.312			3.50264
$905$	4.50180			0.149645
$906$		0			0
$907$	8.21216	−	14.2239i	0.272680	−	0.472296i	−0.696867	−	0.717200i	$-0.745423\pi$
$907$	8.21216	−	14.2239i	0.272680	−	0.472296i	0.969547	+	0.244904i	$0.0787565\pi$
$908$	−42.6054	−	73.7947i	−1.41391	−	2.44896i
$909$		0			0
$910$	−26.6676	+	46.1896i	−0.884022	+	1.53117i
$911$	40.7261			1.34931			0.674657	−	0.738131i	$-0.264291\pi$
$911$	40.7261			1.34931			0.674657	+	0.738131i	$0.264291\pi$
$912$		0			0
$913$	24.4187			0.808140
$914$	−27.8948	+	48.3152i	−0.922677	+	1.59812i
$915$		0			0
$916$	−3.64769	−	6.31799i	−0.120523	−	0.208752i
$917$	7.58267	−	13.1336i	0.250402	−	0.433709i
$918$		0			0
$919$	21.4531			0.707673			0.353837	−	0.935307i	$-0.384877\pi$
$919$	21.4531			0.707673			0.353837	+	0.935307i	$0.384877\pi$
$920$	−57.3747			−1.89159
$921$		0			0
$922$	−6.92276	−	11.9906i	−0.227989	−	0.394888i
$923$	24.8193			0.816938
$924$		0			0
$925$	3.60638	+	6.24644i	0.118577	+	0.205382i
$926$	−7.82343	+	13.5506i	−0.257094	+	0.445300i
$927$		0			0
$928$	−50.3887	+	87.2758i	−1.65409	+	2.86497i
$929$	−0.375163	+	0.649802i	−0.0123087	+	0.0213193i	−0.872114	−	0.489302i	$-0.837251\pi$
$929$	−0.375163	+	0.649802i	−0.0123087	+	0.0213193i	0.859805	+	0.510622i	$0.170585\pi$
$930$		0			0
$931$	−21.4576	−	54.3274i	−0.703244	−	1.78051i
$932$	−9.06772			−0.297023
$933$		0			0
$934$	−27.2465	+	47.1923i	−0.891533	+	1.54418i
$935$	1.53844	+	2.66465i	0.0503122	+	0.0871433i
$936$		0			0
$937$	30.3240	+	52.5228i	0.990643	+	1.71584i	0.613516	+	0.789682i	$0.289755\pi$
$937$	30.3240	+	52.5228i	0.990643	+	1.71584i	0.377127	+	0.926161i	$0.376912\pi$
$938$	−11.5343			−0.376609
$939$		0			0
$940$	23.8189	+	41.2555i	0.776887	+	1.34561i
$941$	8.00297	+	13.8616i	0.260889	+	0.451874i	0.966479	−	0.256747i	$-0.0826509\pi$
$941$	8.00297	+	13.8616i	0.260889	+	0.451874i	−0.705589	+	0.708621i	$0.749318\pi$
$942$		0			0
$943$	−43.4589			−1.41522
$944$	14.6935	+	25.4499i	0.478232	+	0.828323i
$945$		0			0
$946$	−7.10260	−	12.3021i	−0.230926	−	0.399975i
$947$	−21.1841	+	36.6919i	−0.688390	+	1.19233i	0.283969	+	0.958834i	$0.408349\pi$
$947$	−21.1841	+	36.6919i	−0.688390	+	1.19233i	−0.972359	+	0.233493i	$0.924985\pi$
$948$		0			0
$949$	5.88983			0.191192
$950$	4.26637	+	10.8018i	0.138419	+	0.350457i
$951$		0			0
$952$	30.5112	−	52.8469i	0.988872	−	1.71278i
$953$	23.7881	−	41.2022i	0.770573	−	1.33467i	−0.166677	−	0.986012i	$-0.553304\pi$
$953$	23.7881	−	41.2022i	0.770573	−	1.33467i	0.937249	−	0.348660i	$-0.113363\pi$
$954$		0			0
$955$	−0.820673	+	1.42145i	−0.0265564	+	0.0459969i
$956$	37.2809	+	64.5725i	1.20575	+	2.08842i
$957$		0			0
$958$	35.3206			1.14116
$959$	16.0600	+	27.8167i	0.518604	+	0.898249i
$960$		0			0
$961$	−25.5767			−0.825056
$962$	85.1716			2.74604
$963$		0			0
$964$	−20.2162	+	35.0155i	−0.651119	+	1.12777i
$965$	12.9749	+	22.4732i	0.417676	+	0.723437i
$966$		0			0
$967$	−20.0961	+	34.8074i	−0.646246	+	1.11933i	0.337766	+	0.941230i	$0.390329\pi$
$967$	−20.0961	+	34.8074i	−0.646246	+	1.11933i	−0.984012	+	0.178101i	$0.943005\pi$
$968$	61.6292			1.98084
$969$		0			0
$970$	−48.2254			−1.54842
$971$	−12.3086	+	21.3191i	−0.395002	+	0.684163i	−0.993101	−	0.117259i	$-0.962589\pi$
$971$	−12.3086	+	21.3191i	−0.395002	+	0.684163i	0.598100	+	0.801422i	$0.295923\pi$
$972$		0			0
$973$	32.2226	+	55.8112i	1.03301	+	1.78923i
$974$	23.4910	−	40.6876i	0.752700	−	1.30371i
$975$		0			0
$976$	−171.976			−5.50482
$977$	−2.08364			−0.0666616			−0.0333308	−	0.999444i	$-0.510611\pi$
$977$	−2.08364			−0.0666616			−0.0333308	+	0.999444i	$0.510611\pi$
$978$		0			0
$979$	−4.57662	−	7.92693i	−0.146269	−	0.253346i
$980$	−68.3292			−2.18270
$981$		0			0
$982$	1.30784	+	2.26524i	0.0417347	+	0.0722867i
$983$	−7.74204	+	13.4096i	−0.246933	+	0.427700i	−0.962673	−	0.270666i	$-0.912756\pi$
$983$	−7.74204	+	13.4096i	−0.246933	+	0.427700i	0.715740	+	0.698366i	$0.246089\pi$
$984$		0			0
$985$	−2.83202	+	4.90520i	−0.0902355	+	0.156293i
$986$	−14.7129	+	25.4835i	−0.468554	+	0.811560i
$987$		0			0
$988$	97.4359	+	14.4707i	3.09985	+	0.460376i
$989$	19.7010			0.626454
$990$		0			0
$991$	−12.9988	+	22.5146i	−0.412921	+	0.715201i	−0.995208	−	0.0977829i	$-0.968825\pi$
$991$	−12.9988	+	22.5146i	−0.412921	+	0.715201i	0.582286	+	0.812984i	$0.302158\pi$
$992$	−17.3853	−	30.1122i	−0.551983	−	0.956063i
$993$		0			0
$994$	33.6964	+	58.3640i	1.06879	+	1.85119i
$995$	−1.09237			−0.0346303
$996$		0			0
$997$	−22.2632	−	38.5610i	−0.705083	−	1.22124i	−0.966662	−	0.256057i	$-0.917576\pi$
$997$	−22.2632	−	38.5610i	−0.705083	−	1.22124i	0.261579	−	0.965182i	$-0.415757\pi$
$998$	−5.67039	−	9.82141i	−0.179493	−	0.310891i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.k.676.6	yes	12
3.2	odd	2		855.2.k.j.676.1	yes	12
19.7	even	3	inner	855.2.k.k.406.6	yes	12
57.26	odd	6		855.2.k.j.406.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.k.j.406.1	✓	12	57.26	odd	6
855.2.k.j.676.1	yes	12	3.2	odd	2
855.2.k.k.406.6	yes	12	19.7	even	3	inner
855.2.k.k.676.6	yes	12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.33220 - 2.30743i) q^{2} +(-2.54950 - 4.41586i) q^{4} +(0.500000 - 0.866025i) q^{5} +4.51669 q^{7} -8.25696 q^{8} +(-1.33220 - 2.30743i) q^{10} +1.88045 q^{11} +(-2.21597 - 3.83818i) q^{13} +(6.01713 - 10.4220i) q^{14} +(-5.90090 + 10.2207i) q^{16} +(-0.818122 + 1.41703i) q^{17} +(-1.60125 - 4.05413i) q^{19} -5.09900 q^{20} +(2.50513 - 4.33901i) q^{22} +(3.47432 + 6.01770i) q^{23} +(-0.500000 - 0.866025i) q^{25} -11.8085 q^{26} +(-11.5153 - 19.9451i) q^{28} +(3.37483 + 5.84538i) q^{29} -2.32879 q^{31} +(7.46537 + 12.9304i) q^{32} +(2.17980 + 3.77552i) q^{34} +(2.25835 - 3.91157i) q^{35} -7.21276 q^{37} +(-11.4878 - 1.70612i) q^{38} +(-4.12848 + 7.15074i) q^{40} +(-3.12715 + 5.41639i) q^{41} +(1.41761 - 2.45538i) q^{43} +(-4.79420 - 8.30381i) q^{44} +18.5139 q^{46} +(-4.67129 - 8.09090i) q^{47} +13.4005 q^{49} -2.66439 q^{50} +(-11.2993 + 19.5709i) q^{52} +(5.90556 + 10.2287i) q^{53} +(0.940224 - 1.62852i) q^{55} -37.2941 q^{56} +17.9838 q^{58} +(1.24502 - 2.15644i) q^{59} +(7.28601 + 12.6197i) q^{61} +(-3.10241 + 5.37353i) q^{62} +16.1778 q^{64} -4.43195 q^{65} +(-0.479229 - 0.830050i) q^{67} +8.34321 q^{68} +(-6.01713 - 10.4220i) q^{70} +(-2.80004 + 4.84982i) q^{71} +(-0.664474 + 1.15090i) q^{73} +(-9.60882 + 16.6430i) q^{74} +(-13.8201 + 17.4069i) q^{76} +8.49341 q^{77} +(1.46452 - 2.53662i) q^{79} +(5.90090 + 10.2207i) q^{80} +(8.33197 + 14.4314i) q^{82} +12.9855 q^{83} +(0.818122 + 1.41703i) q^{85} +(-3.77708 - 6.54209i) q^{86} -15.5268 q^{88} +(-2.43379 - 4.21545i) q^{89} +(-10.0089 - 17.3359i) q^{91} +(17.7156 - 30.6843i) q^{92} -24.8923 q^{94} +(-4.31161 - 0.640341i) q^{95} +(9.04997 - 15.6750i) q^{97} +(17.8521 - 30.9208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 3 q^{10} - 8 q^{13} + 10 q^{14} - 3 q^{16} + 4 q^{17} - 6 q^{19} - 10 q^{20} - 2 q^{23} - 6 q^{25} - 40 q^{26} - 26 q^{28} + 4 q^{29} + 24 q^{31}+ \cdots + 49 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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