LMFDB - Embedded newform 855.2.k.j.676.1

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			676.1
Root			$-0.832197 + 1.44141i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.j.406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33220 + 2.30743i) q^{2} +(-2.54950 - 4.41586i) q^{4} +(-0.500000 + 0.866025i) q^{5} +4.51669 q^{7} +8.25696 q^{8} +(-1.33220 - 2.30743i) q^{10} -1.88045 q^{11} +(-2.21597 - 3.83818i) q^{13} +(-6.01713 + 10.4220i) q^{14} +(-5.90090 + 10.2207i) q^{16} +(0.818122 - 1.41703i) q^{17} +(-1.60125 - 4.05413i) q^{19} +5.09900 q^{20} +(2.50513 - 4.33901i) q^{22} +(-3.47432 - 6.01770i) q^{23} +(-0.500000 - 0.866025i) q^{25} +11.8085 q^{26} +(-11.5153 - 19.9451i) q^{28} +(-3.37483 - 5.84538i) q^{29} -2.32879 q^{31} +(-7.46537 - 12.9304i) q^{32} +(2.17980 + 3.77552i) q^{34} +(-2.25835 + 3.91157i) q^{35} -7.21276 q^{37} +(11.4878 + 1.70612i) q^{38} +(-4.12848 + 7.15074i) q^{40} +(3.12715 - 5.41639i) q^{41} +(1.41761 - 2.45538i) q^{43} +(4.79420 + 8.30381i) q^{44} +18.5139 q^{46} +(4.67129 + 8.09090i) q^{47} +13.4005 q^{49} +2.66439 q^{50} +(-11.2993 + 19.5709i) q^{52} +(-5.90556 - 10.2287i) q^{53} +(0.940224 - 1.62852i) q^{55} +37.2941 q^{56} +17.9838 q^{58} +(-1.24502 + 2.15644i) q^{59} +(7.28601 + 12.6197i) q^{61} +(3.10241 - 5.37353i) q^{62} +16.1778 q^{64} +4.43195 q^{65} +(-0.479229 - 0.830050i) q^{67} -8.34321 q^{68} +(-6.01713 - 10.4220i) q^{70} +(2.80004 - 4.84982i) q^{71} +(-0.664474 + 1.15090i) q^{73} +(9.60882 - 16.6430i) q^{74} +(-13.8201 + 17.4069i) q^{76} -8.49341 q^{77} +(1.46452 - 2.53662i) q^{79} +(-5.90090 - 10.2207i) q^{80} +(8.33197 + 14.4314i) q^{82} -12.9855 q^{83} +(0.818122 + 1.41703i) q^{85} +(3.77708 + 6.54209i) q^{86} -15.5268 q^{88} +(2.43379 + 4.21545i) q^{89} +(-10.0089 - 17.3359i) q^{91} +(-17.7156 + 30.6843i) q^{92} -24.8923 q^{94} +(4.31161 + 0.640341i) q^{95} +(9.04997 - 15.6750i) q^{97} +(-17.8521 + 30.9208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.557729\pi$
$2$	−1.33220	+	2.30743i	−0.942006	+	1.63160i	−0.761638	+	0.648003i	$0.775604\pi$
$3$		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	$-0.591492\pi$
$11$	−1.88045			−0.566977			−0.283488	+	0.958976i	$0.591492\pi$
$12$		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	−0.749594	−	0.661898i	$-0.769751\pi$
$17$	0.818122	−	1.41703i	0.198424	−	0.343680i	0.948017	+	0.318218i	$0.103084\pi$
$18$		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	$-0.908762\pi$
$23$	−3.47432	−	6.01770i	−0.724446	−	1.25478i	0.234756	−	0.972054i	$-0.424571\pi$
$24$		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	$-0.951076\pi$
$29$	−3.37483	−	5.84538i	−0.626690	−	1.08546i	0.361521	−	0.932364i	$-0.382257\pi$
$30$		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	−0.511532	−	0.859264i	$-0.670922\pi$
$41$	3.12715	−	5.41639i	0.488379	−	0.845897i	0.999911	+	0.0133671i	$0.00425500\pi$
$42$		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	$0.0719519\pi$
$47$	4.67129	+	8.09090i	0.681377	+	1.18018i	−0.293184	+	0.956056i	$0.594715\pi$
$48$		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	$-0.865486\pi$
$53$	−5.90556	−	10.2287i	−0.811191	−	1.40502i	0.100840	−	0.994903i	$-0.467847\pi$
$54$		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	−0.935617	−	0.353016i	$-0.885156\pi$
$59$	−1.24502	+	2.15644i	−0.162088	+	0.280744i	0.773529	+	0.633760i	$0.218489\pi$
$60$		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	−0.650659	−	0.759370i	$-0.725507\pi$
$71$	2.80004	−	4.84982i	0.332304	−	0.575568i	0.982963	+	0.183802i	$0.0588406\pi$
$72$		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	$-0.752516\pi$
$83$	−12.9855			−1.42535			−0.712675	+	0.701495i	$0.752516\pi$
$84$		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	0.965701	−	0.259657i	$-0.0836094\pi$
$89$	2.43379	+	4.21545i	0.257981	+	0.446837i	−0.707720	+	0.706493i	$0.750276\pi$
$90$		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	$0.0107470\pi$
$101$	5.31587	+	9.20736i	0.528949	+	0.916166i	−0.470481	+	0.882410i	$0.655920\pi$
$102$		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	$-0.482902\pi$
$107$	1.11074			0.107380			0.0536898	+	0.998558i	$0.482902\pi$
$108$		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	$-0.295201\pi$
$113$	12.7544			1.19983			0.599915	+	0.800064i	$0.295201\pi$
$114$		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	−0.929998	−	0.367565i	$-0.880192\pi$
$131$	−1.67881	+	2.90779i	−0.146678	+	0.254054i	0.783319	+	0.621619i	$0.213525\pi$
$132$		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	0.673206	−	0.739455i	$-0.264917\pi$
$137$	−3.55570	−	6.15865i	−0.303784	−	0.526169i	−0.976990	+	0.213286i	$0.931583\pi$
$138$		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	$0.450719\pi$
$149$	−9.50361	+	16.4607i	−0.778566	+	1.34852i	−0.932768	+	0.360477i	$0.882614\pi$
$150$		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	$-0.938572\pi$
$167$	−8.48787	−	14.7014i	−0.656811	−	1.13763i	0.324626	−	0.945843i	$-0.394762\pi$
$168$		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	−0.856593	−	0.515993i	$-0.827423\pi$
$173$	0.244205	−	0.422976i	0.0185666	−	0.0321583i	0.875159	+	0.483835i	$0.160756\pi$
$174$		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	$-0.279955\pi$
$179$	17.0592			1.27507			0.637533	+	0.770423i	$0.279955\pi$
$180$		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	$-0.481087\pi$
$191$	1.64135			0.118764			0.0593818	+	0.998235i	$0.481087\pi$
$192$		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	$-0.435330\pi$
$197$	5.66403			0.403546			0.201773	+	0.979432i	$0.435330\pi$
$198$		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	$-0.687122\pi$
$227$	−16.7113			−1.10917			−0.554583	+	0.832128i	$0.687122\pi$
$228$		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	−0.893680	−	0.448704i	$-0.851886\pi$
$233$	−0.889166	+	1.54008i	−0.0582512	+	0.100894i	0.835429	+	0.549598i	$0.185219\pi$
$234$		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	$-0.343194\pi$
$239$	14.6228			0.945873			0.472937	+	0.881096i	$0.343194\pi$
$240$		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	$-0.921783\pi$
$251$	−11.0212	−	19.0892i	−0.695650	−	1.20490i	0.274311	−	0.961641i	$-0.411550\pi$
$252$		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	0.595425	−	0.803411i	$-0.296984\pi$
$257$	−6.38142	−	11.0529i	−0.398062	−	0.689464i	−0.993487	+	0.113947i	$0.963650\pi$
$258$		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	$-0.473232\pi$
$263$	14.6760	−	25.4196i	0.904963	−	1.56744i	0.820967	−	0.570976i	$-0.193435\pi$
$264$		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	−0.999970	−	0.00769238i	$-0.997551\pi$
$269$	−8.09111	+	14.0142i	−0.493323	+	0.854461i	0.506647	+	0.862154i	$0.330885\pi$
$270$		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	0.998245	−	0.0592145i	$-0.0188596\pi$
$281$	7.50719	+	13.0028i	0.447841	+	0.775684i	−0.550404	+	0.834899i	$0.685526\pi$
$282$		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	$-0.578256\pi$
$293$	−8.33200			−0.486760			−0.243380	+	0.969931i	$0.578256\pi$
$294$		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	$-0.273404\pi$
$311$	23.0404			1.30650			0.653252	+	0.757141i	$0.273404\pi$
$312$		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	0.815819	−	0.578307i	$-0.196286\pi$
$317$	−1.65437	−	2.86546i	−0.0929188	−	0.160940i	−0.908738	+	0.417367i	$0.862953\pi$
$318$		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	−0.504182	−	0.863597i	$-0.668206\pi$
$347$	9.23585	−	15.9970i	0.495806	−	0.858762i	0.999988	+	0.00483560i	$0.00153923\pi$
$348$		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	$-0.596350\pi$
$353$	−11.2013			−0.596182			−0.298091	+	0.954537i	$0.596350\pi$
$354$		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	−0.776717	−	0.629850i	$-0.783116\pi$
$359$	2.97676	−	5.15590i	0.157107	−	0.272118i	0.933824	+	0.357732i	$0.116450\pi$
$360$		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	−0.522688	−	0.852524i	$-0.675071\pi$
$383$	9.33435	−	16.1676i	0.476963	−	0.826125i	0.999651	+	0.0263993i	$0.00840414\pi$
$384$		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	0.952197	−	0.305486i	$-0.0988190\pi$
$389$	4.17221	+	7.22648i	0.211540	+	0.366397i	−0.740657	+	0.671883i	$0.765486\pi$
$390$		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	$0.542110\pi$
$401$	−18.5113	+	32.0625i	−0.924411	+	1.60113i	−0.792506	+	0.609865i	$0.791224\pi$
$402$		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	$-0.155312\pi$
$419$	36.1617			1.76661			0.883307	+	0.468795i	$0.155312\pi$
$420$		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	$0.0604922\pi$
$431$	13.5896	+	23.5380i	0.654590	+	1.13378i	−0.327406	+	0.944884i	$0.606175\pi$
$432$		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	0.652221	−	0.758029i	$-0.273837\pi$
$443$	−6.95331	−	12.0435i	−0.330362	−	0.572203i	−0.982583	+	0.185825i	$0.940504\pi$
$444$		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	$-0.498927\pi$
$449$	0.142915			0.00674457			0.00337228	+	0.999994i	$0.498927\pi$
$450$		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	−0.920167	−	0.391526i	$-0.871947\pi$
$461$	−2.59825	+	4.50030i	−0.121012	+	0.209600i	0.799155	+	0.601125i	$0.205281\pi$
$462$		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	$-0.343095\pi$
$467$	20.4523			0.946420			0.473210	+	0.880950i	$0.343095\pi$
$468$		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	0.673928	−	0.738797i	$-0.264606\pi$
$479$	−6.62827	−	11.4805i	−0.302853	−	0.524557i	−0.976781	+	0.214240i	$0.931273\pi$
$480$		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	−0.854737	−	0.519062i	$-0.826282\pi$
$491$	0.490857	−	0.850189i	0.0221521	−	0.0383685i	0.876889	+	0.480693i	$0.159615\pi$
$492$		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	0.935464	−	0.353423i	$-0.114982\pi$
$503$	3.62562	+	6.27975i	0.161658	+	0.280000i	−0.773805	+	0.633424i	$0.781649\pi$
$504$		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	0.618076	−	0.786119i	$-0.287913\pi$
$509$	−8.38731	−	14.5272i	−0.371761	−	0.643909i	−0.989837	+	0.142210i	$0.954579\pi$
$510$		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	$-0.457720\pi$
$521$	6.04583			0.264873			0.132436	+	0.991192i	$0.457720\pi$
$522$		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	0.988098	−	0.153827i	$-0.0491599\pi$
$557$	8.51591	+	14.7500i	0.360831	+	0.624977i	−0.627267	+	0.778804i	$0.715827\pi$
$558$		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	$-0.286112\pi$
$563$	29.5414			1.24502			0.622512	+	0.782610i	$0.286112\pi$
$564$		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	$-0.178847\pi$
$569$	40.3731			1.69253			0.846264	+	0.532764i	$0.178847\pi$
$570$		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	−0.997831	−	0.0658255i	$-0.979032\pi$
$587$	−10.7066	+	18.5444i	−0.441909	+	0.765409i	0.555922	+	0.831234i	$0.312365\pi$
$588$		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	$-0.960423\pi$
$593$	−14.6972	−	25.4563i	−0.603541	−	1.04536i	0.388739	−	0.921348i	$-0.372911\pi$
$594$		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	$0.0519166\pi$
$599$	15.5165	+	26.8754i	0.633988	+	1.09810i	−0.352740	+	0.935721i	$0.614750\pi$
$600$		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	$0.0691869\pi$
$617$	16.7665	+	29.0404i	0.674993	+	1.16912i	−0.301477	+	0.953473i	$0.597480\pi$
$618$		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	−0.910180	−	0.414213i	$-0.864057\pi$
$641$	−2.43993	+	4.22607i	−0.0963713	+	0.166920i	0.813809	+	0.581133i	$0.197390\pi$
$642$		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	$-0.480580\pi$
$647$	3.10173			0.121942			0.0609709	+	0.998140i	$0.480580\pi$
$648$		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	$-0.937361\pi$
$653$	−50.1213			−1.96140			−0.980700	+	0.195520i	$0.937361\pi$
$654$		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	0.608901	−	0.793246i	$-0.291611\pi$
$659$	−9.81970	−	17.0082i	−0.382521	−	0.662546i	−0.991422	+	0.130700i	$0.958277\pi$
$660$		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	$-0.467167\pi$
$677$	5.35812			0.205929			0.102965	+	0.994685i	$0.467167\pi$
$678$		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	$-0.276668\pi$
$683$	33.7370			1.29091			0.645454	+	0.763799i	$0.276668\pi$
$684$		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	$-0.502386\pi$
$701$	22.8294	−	39.5416i	0.862253	−	1.49347i	0.869749	−	0.493494i	$-0.164280\pi$
$702$		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	−0.663462	−	0.748210i	$-0.730913\pi$
$719$	8.47967	−	14.6872i	0.316238	−	0.547741i	0.979700	+	0.200470i	$0.0642468\pi$
$720$		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	$-0.451194\pi$
$743$	25.4107	−	44.0127i	0.932229	−	1.61467i	0.779501	−	0.626401i	$-0.215473\pi$
$744$		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	$-0.511279\pi$
$761$	−1.95450			−0.0708506			−0.0354253	+	0.999372i	$0.511279\pi$
$762$		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	0.914654	−	0.404238i	$-0.132463\pi$
$773$	2.98175	+	5.16454i	0.107246	+	0.185756i	−0.807408	+	0.589994i	$0.799130\pi$
$774$		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	$-0.711870\pi$
$797$	−34.8676			−1.23508			−0.617538	+	0.786541i	$0.711870\pi$
$798$		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	$-0.329178\pi$
$809$	29.0835			1.02252			0.511261	+	0.859425i	$0.329178\pi$
$810$		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	$0.0903757\pi$
$821$	20.7041	+	35.8605i	0.722577	+	1.25154i	−0.237387	+	0.971415i	$0.576291\pi$
$822$		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	0.590161	−	0.807286i	$-0.299064\pi$
$827$	−11.6195	−	20.1256i	−0.404050	−	0.699835i	−0.994210	+	0.107451i	$0.965731\pi$
$828$		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	−0.924544	−	0.381075i	$-0.875554\pi$
$839$	−3.83072	+	6.63500i	−0.132251	+	0.229066i	0.792293	+	0.610141i	$0.208887\pi$
$840$		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	−0.705899	−	0.708313i	$-0.749457\pi$
$857$	7.62506	−	13.2070i	0.260467	−	0.451142i	0.966366	+	0.257170i	$0.0827901\pi$
$858$		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	$-0.586323\pi$
$863$	−15.7389			−0.535757			−0.267878	+	0.963453i	$0.586323\pi$
$864$		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	$-0.288014\pi$
$881$	36.6761			1.23565			0.617825	+	0.786315i	$0.288014\pi$
$882$		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	0.938467	−	0.345369i	$-0.112246\pi$
$887$	5.06704	+	8.77638i	0.170135	+	0.294682i	−0.768332	+	0.640051i	$0.778913\pi$
$888$		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	$-0.735709\pi$
$911$	−40.7261			−1.34931			−0.674657	+	0.738131i	$0.735709\pi$
$912$		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	−0.859805	−	0.510622i	$-0.829415\pi$
$929$	0.375163	−	0.649802i	0.0123087	−	0.0213193i	0.872114	+	0.489302i	$0.162749\pi$
$930$		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	0.705589	−	0.708621i	$-0.250682\pi$
$941$	−8.00297	−	13.8616i	−0.260889	−	0.451874i	−0.966479	+	0.256747i	$0.917349\pi$
$942$		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	$-0.591651\pi$
$947$	21.1841	−	36.6919i	0.688390	−	1.19233i	0.972359	−	0.233493i	$-0.0750154\pi$
$948$		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	$0.446696\pi$
$953$	−23.7881	+	41.2022i	−0.770573	+	1.33467i	−0.937249	+	0.348660i	$0.886637\pi$
$954$		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	−0.598100	−	0.801422i	$-0.704077\pi$
$971$	12.3086	−	21.3191i	0.395002	−	0.684163i	0.993101	+	0.117259i	$0.0374106\pi$
$972$		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	$-0.489389\pi$
$977$	2.08364			0.0666616			0.0333308	+	0.999444i	$0.489389\pi$
$978$		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	−0.715740	−	0.698366i	$-0.753911\pi$
$983$	7.74204	−	13.4096i	0.246933	−	0.427700i	0.962673	+	0.270666i	$0.0872440\pi$
$984$		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.j.676.1	yes	12
3.2	odd	2		855.2.k.k.676.6	yes	12
19.7	even	3	inner	855.2.k.j.406.1	✓	12
57.26	odd	6		855.2.k.k.406.6	yes	12

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

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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