LMFDB - Embedded newform 855.2.k.i.676.5

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.5
Root			$-1.12375 - 1.94639i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.i.406.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.12375 - 1.94639i) q^{2} +(-1.52562 - 2.64245i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.16638 q^{7} -2.36264 q^{8} +(-1.12375 - 1.94639i) q^{10} -4.81770 q^{11} +(-0.583191 - 1.01012i) q^{13} +(3.55821 - 6.16301i) q^{14} +(0.396220 - 0.686273i) q^{16} +(2.92184 - 5.06077i) q^{17} +(3.21554 + 2.94284i) q^{19} -3.05123 q^{20} +(-5.41388 + 9.37711i) q^{22} +(-4.29873 - 7.44562i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.62144 q^{26} +(-4.83069 - 8.36699i) q^{28} +(3.65634 + 6.33297i) q^{29} -5.10247 q^{31} +(-3.25314 - 5.63461i) q^{32} +(-6.56681 - 11.3741i) q^{34} +(1.58319 - 2.74217i) q^{35} +7.26885 q^{37} +(9.34136 - 2.95167i) q^{38} +(-1.18132 + 2.04611i) q^{40} +(-1.24750 + 2.16072i) q^{41} +(-0.583191 + 1.01012i) q^{43} +(7.34996 + 12.7305i) q^{44} -19.3227 q^{46} +(4.68830 + 8.12038i) q^{47} +3.02597 q^{49} -2.24750 q^{50} +(-1.77945 + 3.08210i) q^{52} +(-1.37689 - 2.38485i) q^{53} +(-2.40885 + 4.17225i) q^{55} -7.48103 q^{56} +16.4352 q^{58} +(-5.05626 + 8.75770i) q^{59} +(2.55418 + 4.42398i) q^{61} +(-5.73389 + 9.93138i) q^{62} -13.0380 q^{64} -1.16638 q^{65} +(-0.519277 - 0.899414i) q^{67} -17.8304 q^{68} +(-3.55821 - 6.16301i) q^{70} +(-2.16135 + 3.74358i) q^{71} +(-1.81673 + 3.14666i) q^{73} +(8.16835 - 14.1480i) q^{74} +(2.87062 - 12.9865i) q^{76} -15.2547 q^{77} +(7.53826 - 13.0567i) q^{79} +(-0.396220 - 0.686273i) q^{80} +(2.80374 + 4.85622i) q^{82} +8.98408 q^{83} +(-2.92184 - 5.06077i) q^{85} +(1.31072 + 2.27023i) q^{86} +11.3825 q^{88} +(2.08614 + 3.61330i) q^{89} +(-1.84661 - 3.19841i) q^{91} +(-13.1164 + 22.7183i) q^{92} +21.0739 q^{94} +(4.15634 - 1.31332i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(3.40043 - 5.88972i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) $ 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * 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 $

$2$	1.12375	−	1.94639i	0.794609	−	1.37630i	−0.128477	−	0.991712i	$-0.541009\pi$
$2$	1.12375	−	1.94639i	0.794609	−	1.37630i	0.923087	−	0.384592i	$-0.125658\pi$
$3$		0			0
$3$		0			0
$4$	−1.52562	−	2.64245i	−0.762808	−	1.32122i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	3.16638			1.19678			0.598390	−	0.801205i	$-0.295807\pi$
$7$	3.16638			1.19678			0.598390	+	0.801205i	$0.295807\pi$
$8$	−2.36264			−0.835320
$9$		0			0
$10$	−1.12375	−	1.94639i	−0.355360	−	0.615502i
$11$	−4.81770			−1.45259			−0.726295	−	0.687383i	$-0.758760\pi$
$11$	−4.81770			−1.45259			−0.726295	+	0.687383i	$0.758760\pi$
$12$		0			0
$13$	−0.583191	−	1.01012i	−0.161748	−	0.280156i	0.773748	−	0.633494i	$-0.218380\pi$
$13$	−0.583191	−	1.01012i	−0.161748	−	0.280156i	−0.935496	+	0.353338i	$0.885047\pi$
$14$	3.55821	−	6.16301i	0.950973	−	1.64713i
$15$		0			0
$16$	0.396220	−	0.686273i	0.0990549	−	0.171568i
$17$	2.92184	−	5.06077i	0.708649	−	1.22742i	−0.256709	−	0.966489i	$-0.582638\pi$
$17$	2.92184	−	5.06077i	0.708649	−	1.22742i	0.965358	−	0.260928i	$-0.0840286\pi$
$18$		0			0
$19$	3.21554	+	2.94284i	0.737695	+	0.675134i
$19$	3.21554	+	2.94284i	0.737695	+	0.675134i
$20$	−3.05123			−0.682277
$21$		0			0
$22$	−5.41388	+	9.37711i	−1.15424	+	1.99921i
$23$	−4.29873	−	7.44562i	−0.896347	−	1.55252i	−0.832129	−	0.554583i	$-0.812878\pi$
$23$	−4.29873	−	7.44562i	−0.896347	−	1.55252i	−0.0642183	−	0.997936i	$-0.520455\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.62144			−0.514106
$27$		0			0
$28$	−4.83069	−	8.36699i	−0.912914	−	1.58121i
$29$	3.65634	+	6.33297i	0.678966	+	1.17600i	0.975293	+	0.220917i	$0.0709050\pi$
$29$	3.65634	+	6.33297i	0.678966	+	1.17600i	−0.296326	+	0.955087i	$0.595762\pi$
$30$		0			0
$31$	−5.10247			−0.916430			−0.458215	−	0.888841i	$-0.651511\pi$
$31$	−5.10247			−0.916430			−0.458215	+	0.888841i	$0.651511\pi$
$32$	−3.25314	−	5.63461i	−0.575080	−	0.996068i
$33$		0			0
$34$	−6.56681	−	11.3741i	−1.12620	−	1.95063i
$35$	1.58319	−	2.74217i	0.267608	−	0.463511i
$36$		0			0
$37$	7.26885			1.19499			0.597496	−	0.801872i	$-0.296162\pi$
$37$	7.26885			1.19499			0.597496	+	0.801872i	$0.296162\pi$
$38$	9.34136	−	2.95167i	1.51537	−	0.478825i
$39$		0			0
$40$	−1.18132	+	2.04611i	−0.186783	+	0.323518i
$41$	−1.24750	+	2.16072i	−0.194826	+	0.337449i	−0.946843	−	0.321695i	$-0.895748\pi$
$41$	−1.24750	+	2.16072i	−0.194826	+	0.337449i	0.752017	+	0.659143i	$0.229081\pi$
$42$		0			0
$43$	−0.583191	+	1.01012i	−0.0889358	+	0.154041i	−0.907062	−	0.420998i	$-0.861680\pi$
$43$	−0.583191	+	1.01012i	−0.0889358	+	0.154041i	0.818126	+	0.575039i	$0.195013\pi$
$44$	7.34996	+	12.7305i	1.10805	+	1.91920i
$45$		0			0
$46$	−19.3227			−2.84898
$47$	4.68830	+	8.12038i	0.683859	+	1.18448i	0.973794	+	0.227432i	$0.0730330\pi$
$47$	4.68830	+	8.12038i	0.683859	+	1.18448i	−0.289935	+	0.957046i	$0.593634\pi$
$48$		0			0
$49$	3.02597			0.432282
$50$	−2.24750			−0.317844
$51$		0			0
$52$	−1.77945	+	3.08210i	−0.246766	+	0.427411i
$53$	−1.37689	−	2.38485i	−0.189131	−	0.327584i	0.755830	−	0.654768i	$-0.227234\pi$
$53$	−1.37689	−	2.38485i	−0.189131	−	0.327584i	−0.944961	+	0.327184i	$0.893900\pi$
$54$		0			0
$55$	−2.40885	+	4.17225i	−0.324809	+	0.562586i
$56$	−7.48103			−0.999695
$57$		0			0
$58$	16.4352			2.15805
$59$	−5.05626	+	8.75770i	−0.658269	+	1.14016i	0.322794	+	0.946469i	$0.395378\pi$
$59$	−5.05626	+	8.75770i	−0.658269	+	1.14016i	−0.981063	+	0.193687i	$0.937956\pi$
$60$		0			0
$61$	2.55418	+	4.42398i	0.327030	+	0.566432i	0.981921	−	0.189291i	$-0.0606189\pi$
$61$	2.55418	+	4.42398i	0.327030	+	0.566432i	−0.654891	+	0.755723i	$0.727286\pi$
$62$	−5.73389	+	9.93138i	−0.728204	+	1.26129i
$63$		0			0
$64$	−13.0380			−1.62975
$65$	−1.16638			−0.144672
$66$		0			0
$67$	−0.519277	−	0.899414i	−0.0634398	−	0.109881i	0.832561	−	0.553933i	$-0.186874\pi$
$67$	−0.519277	−	0.899414i	−0.0634398	−	0.109881i	−0.896001	+	0.444052i	$0.853540\pi$
$68$	−17.8304			−2.16226
$69$		0			0
$70$	−3.55821	−	6.16301i	−0.425288	−	0.736620i
$71$	−2.16135	+	3.74358i	−0.256506	+	0.444281i	−0.965303	−	0.261131i	$-0.915905\pi$
$71$	−2.16135	+	3.74358i	−0.256506	+	0.444281i	0.708798	+	0.705412i	$0.249238\pi$
$72$		0			0
$73$	−1.81673	+	3.14666i	−0.212632	+	0.368289i	−0.952537	−	0.304422i	$-0.901537\pi$
$73$	−1.81673	+	3.14666i	−0.212632	+	0.368289i	0.739906	+	0.672711i	$0.234870\pi$
$74$	8.16835	−	14.1480i	0.949552	−	1.64467i
$75$		0			0
$76$	2.87062	−	12.9865i	0.329283	−	1.48966i
$77$	−15.2547			−1.73843
$78$		0			0
$79$	7.53826	−	13.0567i	0.848121	−	1.46899i	−0.0347620	−	0.999396i	$-0.511067\pi$
$79$	7.53826	−	13.0567i	0.848121	−	1.46899i	0.882883	−	0.469593i	$-0.155599\pi$
$80$	−0.396220	−	0.686273i	−0.0442987	−	0.0767276i
$81$		0			0
$82$	2.80374	+	4.85622i	0.309621	+	0.536280i
$83$	8.98408			0.986131			0.493065	−	0.869992i	$-0.335876\pi$
$83$	8.98408			0.986131			0.493065	+	0.869992i	$0.335876\pi$
$84$		0			0
$85$	−2.92184	−	5.06077i	−0.316918	−	0.548918i
$86$	1.31072	+	2.27023i	0.141338	+	0.244805i
$87$		0			0
$88$	11.3825			1.21338
$89$	2.08614	+	3.61330i	0.221130	+	0.383009i	0.955152	−	0.296118i	$-0.0956920\pi$
$89$	2.08614	+	3.61330i	0.221130	+	0.383009i	−0.734021	+	0.679127i	$0.762359\pi$
$90$		0			0
$91$	−1.84661	−	3.19841i	−0.193577	−	0.335285i
$92$	−13.1164	+	22.7183i	−1.36748	+	2.36855i
$93$		0			0
$94$	21.0739			2.17360
$95$	4.15634	−	1.31332i	0.426432	−	0.134743i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	3.40043	−	5.88972i	0.343495	−	0.594952i
$99$		0			0
$100$	−1.52562	+	2.64245i	−0.152562	+	0.264245i
$101$	5.46008	+	9.45714i	0.543299	+	0.941021i	0.998712	+	0.0507406i	$0.0161582\pi$
$101$	5.46008	+	9.45714i	0.543299	+	0.941021i	−0.455413	+	0.890280i	$0.650508\pi$
$102$		0			0
$103$	−5.72113			−0.563720			−0.281860	−	0.959456i	$-0.590951\pi$
$103$	−5.72113			−0.563720			−0.281860	+	0.959456i	$0.590951\pi$
$104$	1.37787	+	2.38654i	0.135111	+	0.234020i
$105$		0			0
$106$	−6.18912			−0.601140
$107$	2.98408			0.288482			0.144241	−	0.989543i	$-0.453926\pi$
$107$	2.98408			0.288482			0.144241	+	0.989543i	$0.453926\pi$
$108$		0			0
$109$	−6.43315	+	11.1425i	−0.616184	+	1.06726i	0.373991	+	0.927432i	$0.377989\pi$
$109$	−6.43315	+	11.1425i	−0.616184	+	1.06726i	−0.990175	+	0.139830i	$0.955344\pi$
$110$	5.41388	+	9.37711i	0.516193	+	0.894072i
$111$		0			0
$112$	1.25458	−	2.17300i	0.118547	−	0.205329i
$113$	16.7739			1.57796			0.788978	−	0.614422i	$-0.210611\pi$
$113$	16.7739			1.57796			0.788978	+	0.614422i	$0.210611\pi$
$114$		0			0
$115$	−8.59746			−0.801717
$116$	11.1564	−	19.3234i	1.03584	−	1.79413i
$117$		0			0
$118$	11.3639	+	19.6829i	1.04613	+	1.81196i
$119$	9.25165	−	16.0243i	0.848097	−	1.46895i
$120$		0			0
$121$	12.2102			1.11002
$122$	11.4810			1.03944
$123$		0			0
$124$	7.78441	+	13.4830i	0.699061	+	1.21081i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.0512339	−	0.0887398i	−0.00454628	−	0.00787438i	0.863743	−	0.503932i	$-0.168114\pi$
$127$	−0.0512339	−	0.0887398i	−0.00454628	−	0.00787438i	−0.868290	+	0.496058i	$0.834780\pi$
$128$	−8.14510	+	14.1077i	−0.719932	+	1.24696i
$129$		0			0
$130$	−1.31072	+	2.27023i	−0.114958	+	0.199112i
$131$	6.78366	−	11.7497i	0.592691	−	1.02657i	−0.401177	−	0.916001i	$-0.631399\pi$
$131$	6.78366	−	11.7497i	0.592691	−	1.02657i	0.993868	−	0.110571i	$-0.0352680\pi$
$132$		0			0
$133$	10.1816	+	9.31816i	0.882859	+	0.807987i
$134$	−2.33414			−0.201639
$135$		0			0
$136$	−6.90326	+	11.9568i	−0.591949	+	1.02529i
$137$	7.92184	+	13.7210i	0.676808	+	1.17227i	0.975937	+	0.218053i	$0.0699707\pi$
$137$	7.92184	+	13.7210i	0.676808	+	1.17227i	−0.299129	+	0.954213i	$0.596696\pi$
$138$		0			0
$139$	2.15634	+	3.73490i	0.182899	+	0.316790i	0.942866	−	0.333171i	$-0.108119\pi$
$139$	2.15634	+	3.73490i	0.182899	+	0.316790i	−0.759968	+	0.649961i	$0.774785\pi$
$140$	−9.66137			−0.816535
$141$		0			0
$142$	4.85763	+	8.41367i	0.407644	+	0.706059i
$143$	2.80964	+	4.86644i	0.234954	+	0.406952i
$144$		0			0
$145$	7.31269			0.607286
$146$	4.08308	+	7.07211i	0.337918	+	0.585292i
$147$		0			0
$148$	−11.0895	−	19.2075i	−0.911550	−	1.57885i
$149$	4.78869	−	8.29426i	0.392305	−	0.679492i	−0.600448	−	0.799664i	$-0.705011\pi$
$149$	4.78869	−	8.29426i	0.392305	−	0.679492i	0.992753	+	0.120172i	$0.0383445\pi$
$150$		0			0
$151$	1.90169			0.154757			0.0773786	−	0.997002i	$-0.475345\pi$
$151$	1.90169			0.154757			0.0773786	+	0.997002i	$0.475345\pi$
$152$	−7.59717	−	6.95288i	−0.616212	−	0.563953i
$153$		0			0
$154$	−17.1424	+	29.6915i	−1.38137	+	2.39261i
$155$	−2.55123	+	4.41887i	−0.204920	+	0.354932i
$156$		0			0
$157$	9.19333	−	15.9233i	0.733708	−	1.27082i	−0.221581	−	0.975142i	$-0.571122\pi$
$157$	9.19333	−	15.9233i	0.733708	−	1.27082i	0.955288	−	0.295677i	$-0.0955451\pi$
$158$	−16.9422	−	29.3448i	−1.34785	−	2.33454i
$159$		0			0
$160$	−6.50629			−0.514367
$161$	−13.6114	−	23.5757i	−1.07273	−	1.85802i
$162$		0			0
$163$	−10.6234			−0.832091			−0.416046	−	0.909344i	$-0.636584\pi$
$163$	−10.6234			−0.832091			−0.416046	+	0.909344i	$0.636584\pi$
$164$	7.61280			0.594460
$165$		0			0
$166$	10.0958	−	17.4865i	0.783589	−	1.35722i
$167$	7.30974	+	12.6608i	0.565645	+	0.979725i	0.996989	+	0.0775380i	$0.0247059\pi$
$167$	7.30974	+	12.6608i	0.565645	+	0.979725i	−0.431345	+	0.902187i	$0.641961\pi$
$168$		0			0
$169$	5.81978	−	10.0801i	0.447675	−	0.775396i
$170$	−13.1336			−1.00730
$171$		0			0
$172$	3.55890			0.271364
$173$	−0.328608	+	0.569166i	−0.0249836	+	0.0432729i	−0.878247	−	0.478207i	$-0.841287\pi$
$173$	−0.328608	+	0.569166i	−0.0249836	+	0.0432729i	0.853263	+	0.521480i	$0.174620\pi$
$174$		0			0
$175$	−1.58319	−	2.74217i	−0.119678	−	0.207288i
$176$	−1.90887	+	3.30625i	−0.143886	+	0.249218i
$177$		0			0
$178$	9.37718			0.702849
$179$	23.2647			1.73889			0.869444	−	0.494032i	$-0.164477\pi$
$179$	23.2647			1.73889			0.869444	+	0.494032i	$0.164477\pi$
$180$		0			0
$181$	−0.725576	−	1.25673i	−0.0539316	−	0.0934123i	0.837799	−	0.545978i	$-0.183842\pi$
$181$	−0.725576	−	1.25673i	−0.0539316	−	0.0934123i	−0.891731	+	0.452566i	$0.850509\pi$
$182$	−8.30047			−0.615272
$183$		0			0
$184$	10.1564	+	17.5913i	0.748737	+	1.29685i
$185$	3.63442	−	6.29501i	0.267208	−	0.462818i
$186$		0			0
$187$	−14.0765	+	24.3813i	−1.02938	+	1.78293i
$188$	14.3051	−	24.7772i	1.04331	−	1.80706i
$189$		0			0
$190$	2.11446	−	9.56569i	0.153399	−	0.693968i
$191$	−19.0598			−1.37912			−0.689559	−	0.724229i	$-0.742196\pi$
$191$	−19.0598			−1.37912			−0.689559	+	0.724229i	$0.742196\pi$
$192$		0			0
$193$	−7.84789	+	13.5929i	−0.564903	+	0.978441i	0.432156	+	0.901799i	$0.357753\pi$
$193$	−7.84789	+	13.5929i	−0.564903	+	0.978441i	−0.997059	+	0.0766418i	$0.975580\pi$
$194$	2.24750	+	3.89278i	0.161361	+	0.279485i
$195$		0			0
$196$	−4.61648	−	7.99597i	−0.329748	−	0.571141i
$197$	−8.23620			−0.586805			−0.293402	−	0.955989i	$-0.594788\pi$
$197$	−8.23620			−0.586805			−0.293402	+	0.955989i	$0.594788\pi$
$198$		0			0
$199$	−8.69459	−	15.0595i	−0.616343	−	1.06754i	−0.990147	−	0.140030i	$-0.955280\pi$
$199$	−8.69459	−	15.0595i	−0.616343	−	1.06754i	0.373804	−	0.927508i	$-0.378053\pi$
$200$	1.18132	+	2.04611i	0.0835320	+	0.144682i
$201$		0			0
$202$	24.5430			1.72684
$203$	11.5774	+	20.0526i	0.812573	+	1.40742i
$204$		0			0
$205$	1.24750	+	2.16072i	0.0871288	+	0.150912i
$206$	−6.42911	+	11.1355i	−0.447937	+	0.775850i
$207$		0			0
$208$	−0.924287			−0.0640878
$209$	−15.4915	−	14.1777i	−1.07157	−	0.980694i
$210$		0			0
$211$	−10.5412	+	18.2579i	−0.725687	+	1.25693i	0.233003	+	0.972476i	$0.425145\pi$
$211$	−10.5412	+	18.2579i	−0.725687	+	1.25693i	−0.958691	+	0.284451i	$0.908189\pi$
$212$	−4.20122	+	7.27673i	−0.288541	+	0.499768i
$213$		0			0
$214$	3.35335	−	5.80818i	0.229231	−	0.397039i
$215$	0.583191	+	1.01012i	0.0397733	+	0.0688894i
$216$		0			0
$217$	−16.1564			−1.09677
$218$	14.4585	+	25.0428i	0.979252	+	1.69611i
$219$		0			0
$220$	14.6999			0.991069
$221$	−6.81595			−0.458491
$222$		0			0
$223$	−0.464804	+	0.805064i	−0.0311256	+	0.0539111i	−0.881169	−	0.472802i	$-0.843243\pi$
$223$	−0.464804	+	0.805064i	−0.0311256	+	0.0539111i	0.850043	+	0.526713i	$0.176576\pi$
$224$	−10.3007	−	17.8413i	−0.688244	−	1.19207i
$225$		0			0
$226$	18.8496	−	32.6485i	1.25386	−	2.17175i
$227$	−2.53770			−0.168433			−0.0842165	−	0.996447i	$-0.526839\pi$
$227$	−2.53770			−0.168433			−0.0842165	+	0.996447i	$0.526839\pi$
$228$		0			0
$229$	−0.912322			−0.0602879			−0.0301440	−	0.999546i	$-0.509597\pi$
$229$	−0.912322			−0.0602879			−0.0301440	+	0.999546i	$0.509597\pi$
$230$	−9.66137	+	16.7340i	−0.637052	+	1.10341i
$231$		0			0
$232$	−8.63864	−	14.9626i	−0.567154	−	0.982340i
$233$	−11.4894	+	19.9003i	−0.752697	+	1.30371i	0.193815	+	0.981038i	$0.437914\pi$
$233$	−11.4894	+	19.9003i	−0.752697	+	1.30371i	−0.946511	+	0.322671i	$0.895419\pi$
$234$		0			0
$235$	9.37660			0.611662
$236$	30.8557			2.00853
$237$		0			0
$238$	−20.7930	−	36.0146i	−1.34781	−	2.33448i
$239$	−21.1849			−1.37033			−0.685167	−	0.728386i	$-0.740271\pi$
$239$	−21.1849			−1.37033			−0.685167	+	0.728386i	$0.740271\pi$
$240$		0			0
$241$	2.15132	+	3.72619i	0.138578	+	0.240025i	0.926959	−	0.375163i	$-0.122413\pi$
$241$	2.15132	+	3.72619i	0.138578	+	0.240025i	−0.788380	+	0.615188i	$0.789080\pi$
$242$	13.7212	−	23.7658i	0.882032	−	1.52773i
$243$		0			0
$244$	7.79341	−	13.4986i	0.498922	−	0.864158i
$245$	1.51299	−	2.62057i	0.0966612	−	0.167422i
$246$		0			0
$247$	1.09734	−	4.96431i	0.0698220	−	0.315871i
$248$	12.0553			0.765513
$249$		0			0
$250$	−1.12375	+	1.94639i	−0.0710720	+	0.123100i
$251$	−6.77149	−	11.7286i	−0.427413	−	0.740301i	0.569230	−	0.822179i	$-0.307242\pi$
$251$	−6.77149	−	11.7286i	−0.427413	−	0.740301i	−0.996642	+	0.0818779i	$0.973908\pi$
$252$		0			0
$253$	20.7100	+	35.8707i	1.30203	+	2.25517i
$254$	−0.230296			−0.0144501
$255$		0			0
$256$	5.26810	+	9.12462i	0.329256	+	0.570289i
$257$	−10.9601	−	18.9835i	−0.683672	−	1.18416i	−0.973852	−	0.227183i	$-0.927048\pi$
$257$	−10.9601	−	18.9835i	−0.683672	−	1.18416i	0.290180	−	0.956972i	$-0.406285\pi$
$258$		0			0
$259$	23.0160			1.43014
$260$	1.77945	+	3.08210i	0.110357	+	0.191144i
$261$		0			0
$262$	−15.2463	−	26.4073i	−0.941917	−	1.63145i
$263$	−9.58645	+	16.6042i	−0.591126	+	1.02386i	0.402955	+	0.915220i	$0.367983\pi$
$263$	−9.58645	+	16.6042i	−0.591126	+	1.02386i	−0.994081	+	0.108640i	$0.965350\pi$
$264$		0			0
$265$	−2.75378			−0.169164
$266$	29.5783	−	9.34612i	1.81356	−	0.573048i
$267$		0			0
$268$	−1.58444	+	2.74432i	−0.0967848	+	0.167636i
$269$	10.2026	−	17.6714i	0.622062	−	1.07744i	−0.367040	−	0.930205i	$-0.619629\pi$
$269$	10.2026	−	17.6714i	0.622062	−	1.07744i	0.989101	−	0.147237i	$-0.0470380\pi$
$270$		0			0
$271$	−8.16106	+	14.1354i	−0.495749	+	0.858663i	−0.999988	−	0.00490125i	$-0.998440\pi$
$271$	−8.16106	+	14.1354i	−0.495749	+	0.858663i	0.504239	+	0.863564i	$0.331773\pi$
$272$	−2.31538	−	4.01035i	−0.140390	−	0.243163i
$273$		0			0
$274$	35.6086			2.15119
$275$	2.40885	+	4.17225i	0.145259	+	0.251596i
$276$		0			0
$277$	7.08065			0.425435			0.212717	−	0.977114i	$-0.431769\pi$
$277$	7.08065			0.425435			0.212717	+	0.977114i	$0.431769\pi$
$278$	9.69275			0.581332
$279$		0			0
$280$	−3.74052	+	6.47876i	−0.223539	+	0.387180i
$281$	−5.06129	−	8.76641i	−0.301931	−	0.522960i	0.674642	−	0.738145i	$-0.264298\pi$
$281$	−5.06129	−	8.76641i	−0.301931	−	0.522960i	−0.976573	+	0.215185i	$0.930965\pi$
$282$		0			0
$283$	−7.25556	+	12.5670i	−0.431298	+	0.747030i	−0.996985	−	0.0775897i	$-0.975278\pi$
$283$	−7.25556	+	12.5670i	−0.431298	+	0.747030i	0.565687	+	0.824620i	$0.308611\pi$
$284$	13.1896			0.782658
$285$		0			0
$286$	12.6293			0.746786
$287$	−3.95005	+	6.84168i	−0.233164	+	0.403852i
$288$		0			0
$289$	−8.57426	−	14.8511i	−0.504368	−	0.873591i
$290$	8.21762	−	14.2333i	0.482555	−	0.835810i
$291$		0			0
$292$	11.0865			0.648789
$293$	−6.10837			−0.356855			−0.178427	−	0.983953i	$-0.557101\pi$
$293$	−6.10837			−0.356855			−0.178427	+	0.983953i	$0.557101\pi$
$294$		0			0
$295$	5.05626	+	8.75770i	0.294387	+	0.509893i
$296$	−17.1737			−0.998201
$297$		0			0
$298$	−10.7626	−	18.6413i	−0.623458	−	1.07986i
$299$	−5.01396	+	8.68443i	−0.289965	+	0.502234i
$300$		0			0
$301$	−1.84661	+	3.19841i	−0.106437	+	0.184354i
$302$	2.13702	−	3.70142i	0.122972	−	0.212993i
$303$		0			0
$304$	3.29365	−	1.04072i	0.188904	−	0.0596896i
$305$	5.10837			0.292504
$306$		0			0
$307$	−6.27147	+	10.8625i	−0.357932	+	0.619956i	−0.987615	−	0.156896i	$-0.949851\pi$
$307$	−6.27147	+	10.8625i	−0.357932	+	0.619956i	0.629683	+	0.776852i	$0.283185\pi$
$308$	23.2728	+	40.3097i	1.32609	+	2.29686i
$309$		0			0
$310$	5.73389	+	9.93138i	0.325663	+	0.564065i
$311$	17.9682			1.01888			0.509440	−	0.860506i	$-0.329852\pi$
$311$	17.9682			1.01888			0.509440	+	0.860506i	$0.329852\pi$
$312$		0			0
$313$	−3.77236	−	6.53393i	−0.213227	−	0.369319i	0.739496	−	0.673161i	$-0.235064\pi$
$313$	−3.77236	−	6.53393i	−0.213227	−	0.369319i	−0.952723	+	0.303842i	$0.901731\pi$
$314$	−20.6620	−	35.7876i	−1.16602	−	2.01961i
$315$		0			0
$316$	−46.0020			−2.58782
$317$	2.25851	+	3.91185i	0.126850	+	0.219711i	0.922455	−	0.386105i	$-0.126180\pi$
$317$	2.25851	+	3.91185i	0.126850	+	0.219711i	−0.795604	+	0.605817i	$0.792847\pi$
$318$		0			0
$319$	−17.6152	−	30.5104i	−0.986260	−	1.70825i
$320$	−6.51899	+	11.2912i	−0.364422	+	0.631198i
$321$		0			0
$322$	−61.1832			−3.40961
$323$	24.2883	−	7.67459i	1.35144	−	0.427026i
$324$		0			0
$325$	−0.583191	+	1.01012i	−0.0323496	+	0.0560312i
$326$	−11.9381	+	20.6773i	−0.661188	+	1.14521i
$327$		0			0
$328$	2.94739	−	5.10502i	0.162742	−	0.281878i
$329$	14.8450	+	25.7122i	0.818429	+	1.41756i
$330$		0			0
$331$	16.7674			0.921619			0.460809	−	0.887499i	$-0.347559\pi$
$331$	16.7674			0.921619			0.460809	+	0.887499i	$0.347559\pi$
$332$	−13.7063	−	23.7399i	−0.752229	−	1.30290i
$333$		0			0
$334$	32.8572			1.79787
$335$	−1.03855			−0.0567423
$336$		0			0
$337$	8.71682	−	15.0980i	0.474835	−	0.822439i	−0.524749	−	0.851257i	$-0.675841\pi$
$337$	8.71682	−	15.0980i	0.474835	−	0.822439i	0.999585	+	0.0288179i	$0.00917429\pi$
$338$	−13.0799	−	22.6551i	−0.711454	−	1.23227i
$339$		0			0
$340$	−8.91521	+	15.4416i	−0.483495	+	0.837438i
$341$	24.5822			1.33120
$342$		0			0
$343$	−12.5833			−0.679433
$344$	1.37787	−	2.38654i	0.0742899	−	0.128674i
$345$		0			0
$346$	0.738545	+	1.27920i	0.0397044	+	0.0687701i
$347$	−15.5446	+	26.9240i	−0.834475	+	1.44535i	0.0599815	+	0.998199i	$0.480896\pi$
$347$	−15.5446	+	26.9240i	−0.834475	+	1.44535i	−0.894457	+	0.447154i	$0.852437\pi$
$348$		0			0
$349$	0.887477			0.0475055			0.0237528	−	0.999718i	$-0.492439\pi$
$349$	0.887477			0.0475055			0.0237528	+	0.999718i	$0.492439\pi$
$350$	−7.11643			−0.380389
$351$		0			0
$352$	15.6727	+	27.1459i	0.835356	+	1.44688i
$353$	5.27079			0.280536			0.140268	−	0.990114i	$-0.455204\pi$
$353$	5.27079			0.280536			0.140268	+	0.990114i	$0.455204\pi$
$354$		0			0
$355$	2.16135	+	3.74358i	0.114713	+	0.198688i
$356$	6.36530	−	11.0250i	0.337360	−	0.584325i
$357$		0			0
$358$	26.1437	−	45.2822i	1.38174	−	2.39324i
$359$	−13.6315	+	23.6104i	−0.719443	+	1.24611i	0.241778	+	0.970332i	$0.422269\pi$
$359$	−13.6315	+	23.6104i	−0.719443	+	1.24611i	−0.961221	+	0.275780i	$0.911064\pi$
$360$		0			0
$361$	1.67937	+	18.9256i	0.0883879	+	0.996086i
$362$	−3.26145			−0.171418
$363$		0			0
$364$	−5.63442	+	9.75911i	−0.295324	+	0.511516i
$365$	1.81673	+	3.14666i	0.0950918	+	0.164704i
$366$		0			0
$367$	−0.685659	−	1.18760i	−0.0357911	−	0.0619920i	0.847575	−	0.530676i	$-0.178062\pi$
$367$	−0.685659	−	1.18760i	−0.0357911	−	0.0619920i	−0.883366	+	0.468684i	$0.844728\pi$
$368$	−6.81296			−0.355150
$369$		0			0
$370$	−8.16835	−	14.1480i	−0.424652	−	0.735520i
$371$	−4.35977	−	7.55134i	−0.226348	−	0.392046i
$372$		0			0
$373$	33.1801			1.71800			0.859001	−	0.511974i	$-0.171086\pi$
$373$	33.1801			1.71800			0.859001	+	0.511974i	$0.171086\pi$
$374$	31.6369	+	54.7968i	1.63591	+	2.83347i
$375$		0			0
$376$	−11.0768	−	19.1856i	−0.571241	−	0.989419i
$377$	4.26469	−	7.38667i	0.219643	−	0.380433i
$378$		0			0
$379$	−31.1642			−1.60080			−0.800399	−	0.599468i	$-0.795379\pi$
$379$	−31.1642			−1.60080			−0.800399	+	0.599468i	$0.795379\pi$
$380$	−9.81136	−	8.97930i	−0.503312	−	0.460628i
$381$		0			0
$382$	−21.4184	+	37.0977i	−1.09586	+	1.89809i
$383$	14.8307	−	25.6875i	0.757814	−	1.31257i	−0.186150	−	0.982521i	$-0.559601\pi$
$383$	14.8307	−	25.6875i	0.757814	−	1.31257i	0.943963	−	0.330050i	$-0.107066\pi$
$384$		0			0
$385$	−7.62734	+	13.2109i	−0.388725	+	0.673292i
$386$	17.6381	+	30.5501i	0.897755	+	1.55496i
$387$		0			0
$388$	6.10247			0.309806
$389$	−10.0190	−	17.3534i	−0.507983	−	0.879852i	−0.999957	−	0.00924244i	$-0.997058\pi$
$389$	−10.0190	−	17.3534i	−0.507983	−	0.879852i	0.491974	−	0.870610i	$-0.336275\pi$
$390$		0			0
$391$	−50.2407			−2.54078
$392$	−7.14930			−0.361094
$393$		0			0
$394$	−9.25540	+	16.0308i	−0.466281	+	0.807622i
$395$	−7.53826	−	13.0567i	−0.379291	−	0.656952i
$396$		0			0
$397$	9.73540	−	16.8622i	0.488606	−	0.846290i	−0.511309	−	0.859397i	$-0.670839\pi$
$397$	9.73540	−	16.8622i	0.488606	−	0.846290i	0.999914	+	0.0131075i	$0.00417238\pi$
$398$	−39.0821			−1.95901
$399$		0			0
$400$	−0.792439			−0.0396220
$401$	−18.3816	+	31.8379i	−0.917935	+	1.58991i	−0.115388	+	0.993320i	$0.536811\pi$
$401$	−18.3816	+	31.8379i	−0.917935	+	1.58991i	−0.802547	+	0.596589i	$0.796522\pi$
$402$		0			0
$403$	2.97571	+	5.15409i	0.148231	+	0.256743i
$404$	16.6600	−	28.8560i	0.828866	−	1.43564i
$405$		0			0
$406$	52.0402			2.58271
$407$	−35.0191			−1.73583
$408$		0			0
$409$	6.28240	+	10.8814i	0.310645	+	0.538053i	0.978502	−	0.206237i	$-0.0661217\pi$
$409$	6.28240	+	10.8814i	0.310645	+	0.538053i	−0.667857	+	0.744289i	$0.732788\pi$
$410$	5.60748			0.276934
$411$		0			0
$412$	8.72825	+	15.1178i	0.430010	+	0.744799i
$413$	−16.0101	+	27.7302i	−0.787803	+	1.36452i
$414$		0			0
$415$	4.49204	−	7.78044i	0.220506	−	0.381927i
$416$	−3.79441	+	6.57211i	−0.186036	+	0.322224i
$417$		0			0
$418$	−45.0039	+	14.2203i	−2.20121	+	0.695536i
$419$	−23.8674			−1.16600			−0.583000	−	0.812472i	$-0.698121\pi$
$419$	−23.8674			−1.16600			−0.583000	+	0.812472i	$0.698121\pi$
$420$		0			0
$421$	3.30504	−	5.72449i	0.161078	−	0.278995i	−0.774178	−	0.632968i	$-0.781836\pi$
$421$	3.30504	−	5.72449i	0.161078	−	0.278995i	0.935255	+	0.353974i	$0.115170\pi$
$422$	23.6913	+	41.0346i	1.15328	+	1.99753i
$423$		0			0
$424$	3.25311	+	5.63454i	0.157985	+	0.273638i
$425$	−5.84367			−0.283460
$426$		0			0
$427$	8.08752	+	14.0080i	0.391383	+	0.677895i
$428$	−4.55256	−	7.88527i	−0.220056	−	0.381149i
$429$		0			0
$430$	2.62144			0.126417
$431$	−3.73156	−	6.46325i	−0.179743	−	0.311324i	0.762050	−	0.647519i	$-0.224193\pi$
$431$	−3.73156	−	6.46325i	−0.179743	−	0.311324i	−0.941792	+	0.336195i	$0.890860\pi$
$432$		0			0
$433$	−10.7976	−	18.7019i	−0.518898	−	0.898758i	−0.999759	−	0.0219608i	$-0.993009\pi$
$433$	−10.7976	−	18.7019i	−0.518898	−	0.898758i	0.480861	−	0.876797i	$-0.340324\pi$
$434$	−18.1557	+	31.4465i	−0.871500	+	1.50948i
$435$		0			0
$436$	39.2581			1.88012
$437$	8.08854	−	36.5921i	0.386928	−	1.75044i
$438$		0			0
$439$	16.8740	−	29.2266i	0.805351	−	1.39491i	−0.110703	−	0.993854i	$-0.535310\pi$
$439$	16.8740	−	29.2266i	0.805351	−	1.39491i	0.916054	−	0.401055i	$-0.131356\pi$
$440$	5.69125	−	9.85754i	0.271320	−	0.469940i
$441$		0			0
$442$	−7.65941	+	13.2665i	−0.364321	+	0.631023i
$443$	−3.85053	−	6.66931i	−0.182944	−	0.316868i	0.759938	−	0.649996i	$-0.225229\pi$
$443$	−3.85053	−	6.66931i	−0.182944	−	0.316868i	−0.942882	+	0.333127i	$0.891896\pi$
$444$		0			0
$445$	4.17228			0.197785
$446$	1.04464	+	1.80938i	0.0494653	+	0.0856765i
$447$		0			0
$448$	−41.2832			−1.95045
$449$	−4.84306			−0.228558			−0.114279	−	0.993449i	$-0.536456\pi$
$449$	−4.84306			−0.228558			−0.114279	+	0.993449i	$0.536456\pi$
$450$		0			0
$451$	6.01006	−	10.4097i	0.283002	−	0.490175i
$452$	−25.5905	−	44.3241i	−1.20368	−	2.08483i
$453$		0			0
$454$	−2.85173	+	4.93935i	−0.133838	+	0.231815i
$455$	−3.69321			−0.173140
$456$		0			0
$457$	−18.2322			−0.852868			−0.426434	−	0.904519i	$-0.640230\pi$
$457$	−18.2322			−0.852868			−0.426434	+	0.904519i	$0.640230\pi$
$458$	−1.02522	+	1.77573i	−0.0479054	+	0.0829745i
$459$		0			0
$460$	13.1164	+	22.7183i	0.611557	+	1.05925i
$461$	−16.2778	+	28.1940i	−0.758134	+	1.31313i	0.185668	+	0.982613i	$0.440555\pi$
$461$	−16.2778	+	28.1940i	−0.758134	+	1.31313i	−0.943801	+	0.330513i	$0.892778\pi$
$462$		0			0
$463$	−30.9666			−1.43914			−0.719569	−	0.694421i	$-0.755661\pi$
$463$	−30.9666			−1.43914			−0.719569	+	0.694421i	$0.755661\pi$
$464$	5.79486			0.269020
$465$		0			0
$466$	25.8224	+	44.7257i	1.19620	+	2.07188i
$467$	26.4956			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$467$	26.4956			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$468$		0			0
$469$	−1.64423	−	2.84789i	−0.0759234	−	0.131503i
$470$	10.5369	−	18.2505i	0.486033	−	0.841833i
$471$		0			0
$472$	11.9461	−	20.6913i	0.549866	−	0.952395i
$473$	2.80964	−	4.86644i	0.129187	−	0.223759i
$474$		0			0
$475$	0.940806	−	4.25616i	0.0431672	−	0.195286i
$476$	−56.4579			−2.58774
$477$		0			0
$478$	−23.8064	+	41.2340i	−1.08888	+	1.88600i
$479$	−11.5726	−	20.0443i	−0.528766	−	0.915849i	−0.999437	−	0.0335408i	$-0.989322\pi$
$479$	−11.5726	−	20.0443i	−0.528766	−	0.915849i	0.470671	−	0.882309i	$-0.344012\pi$
$480$		0			0
$481$	−4.23913	−	7.34238i	−0.193288	−	0.334784i
$482$	9.67015			0.440463
$483$		0			0
$484$	−18.6281	−	32.2649i	−0.846733	−	1.46658i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	−38.3075			−1.73588			−0.867939	−	0.496671i	$-0.834555\pi$
$487$	−38.3075			−1.73588			−0.867939	+	0.496671i	$0.834555\pi$
$488$	−6.03462	−	10.4523i	−0.273175	−	0.473152i
$489$		0			0
$490$	−3.40043	−	5.88972i	−0.153616	−	0.266070i
$491$	11.8873	−	20.5893i	0.536464	−	0.929183i	−0.462627	−	0.886553i	$-0.653093\pi$
$491$	11.8873	−	20.5893i	0.536464	−	0.929183i	0.999091	−	0.0426302i	$-0.0135737\pi$
$492$		0			0
$493$	42.7330			1.92460
$494$	−8.42933	−	7.71448i	−0.379254	−	0.347091i
$495$		0			0
$496$	−2.02170	+	3.50168i	−0.0907769	+	0.157230i
$497$	−6.84367	+	11.8536i	−0.306981	+	0.531706i
$498$		0			0
$499$	−0.210818	+	0.365147i	−0.00943749	+	0.0163462i	−0.870706	−	0.491805i	$-0.836337\pi$
$499$	−0.210818	+	0.365147i	−0.00943749	+	0.0163462i	0.861268	+	0.508151i	$0.169671\pi$
$500$	1.52562	+	2.64245i	0.0682277	+	0.118174i
$501$		0			0
$502$	−30.4378			−1.35851
$503$	13.7328	+	23.7858i	0.612313	+	1.06056i	0.990850	+	0.134971i	$0.0430942\pi$
$503$	13.7328	+	23.7858i	0.612313	+	1.06056i	−0.378536	+	0.925586i	$0.623572\pi$
$504$		0			0
$505$	10.9202			0.485941
$506$	93.0912			4.13841
$507$		0			0
$508$	−0.156327	+	0.270766i	−0.00693588	+	0.0120133i
$509$	3.91889	+	6.78771i	0.173702	+	0.300860i	0.939711	−	0.341969i	$-0.111094\pi$
$509$	3.91889	+	6.78771i	0.173702	+	0.300860i	−0.766010	+	0.642829i	$0.777761\pi$
$510$		0			0
$511$	−5.75245	+	9.96353i	−0.254473	+	0.440761i
$512$	−8.90034			−0.393343
$513$		0			0
$514$	−49.2655			−2.17301
$515$	−2.86057	+	4.95464i	−0.126052	+	0.218328i
$516$		0			0
$517$	−22.5868	−	39.1215i	−0.993367	−	1.72056i
$518$	25.8641	−	44.7980i	1.13640	−	1.96831i
$519$		0			0
$520$	2.75574			0.120847
$521$	4.93772			0.216325			0.108163	−	0.994133i	$-0.465503\pi$
$521$	4.93772			0.216325			0.108163	+	0.994133i	$0.465503\pi$
$522$		0			0
$523$	8.55988	+	14.8261i	0.374297	+	0.648302i	0.990222	−	0.139503i	$-0.0445506\pi$
$523$	8.55988	+	14.8261i	0.374297	+	0.648302i	−0.615924	+	0.787805i	$0.711217\pi$
$524$	−41.3971			−1.80844
$525$		0			0
$526$	21.5455	+	37.3179i	0.939428	+	1.62714i
$527$	−14.9086	+	25.8224i	−0.649428	+	1.12484i
$528$		0			0
$529$	−25.4581	+	44.0948i	−1.10688	+	1.91716i
$530$	−3.09456	+	5.35993i	−0.134419	+	0.232821i
$531$		0			0
$532$	9.08948	−	41.1203i	0.394079	−	1.78279i
$533$	2.91011			0.126051
$534$		0			0
$535$	1.49204	−	2.58429i	0.0645065	−	0.111729i
$536$	1.22687	+	2.12499i	0.0529925	+	0.0917858i
$537$		0			0
$538$	−22.9302	−	39.7163i	−0.988592	−	1.71229i
$539$	−14.5782			−0.627929
$540$		0			0
$541$	3.04946	+	5.28183i	0.131107	+	0.227083i	0.924103	−	0.382142i	$-0.124814\pi$
$541$	3.04946	+	5.28183i	0.131107	+	0.227083i	−0.792997	+	0.609226i	$0.791480\pi$
$542$	18.3420	+	31.7692i	0.787854	+	1.36460i
$543$		0			0
$544$	−38.0206			−1.63012
$545$	6.43315	+	11.1425i	0.275566	+	0.477294i
$546$		0			0
$547$	11.4882	+	19.8981i	0.491198	+	0.850780i	0.999949	−	0.0101341i	$-0.00322583\pi$
$547$	11.4882	+	19.8981i	0.491198	+	0.850780i	−0.508751	+	0.860914i	$0.669892\pi$
$548$	24.1714	−	41.8661i	1.03255	−	1.78843i
$549$		0			0
$550$	10.8278			0.461697
$551$	−6.87982	+	31.1240i	−0.293090	+	1.32593i
$552$		0			0
$553$	23.8690	−	41.3424i	1.01501	−	1.75806i
$554$	7.95686	−	13.7817i	0.338055	−	0.585528i
$555$		0			0
$556$	6.57951	−	11.3960i	0.279033	−	0.483300i
$557$	−3.49499	−	6.05350i	−0.148087	−	0.256495i	0.782433	−	0.622735i	$-0.213978\pi$
$557$	−3.49499	−	6.05350i	−0.148087	−	0.256495i	−0.930521	+	0.366240i	$0.880645\pi$
$558$		0			0
$559$	1.36045			0.0575408
$560$	−1.25458	−	2.17300i	−0.0530158	−	0.0918261i
$561$		0			0
$562$	−22.7504			−0.959670
$563$	12.7111			0.535708			0.267854	−	0.963460i	$-0.413686\pi$
$563$	12.7111			0.535708			0.267854	+	0.963460i	$0.413686\pi$
$564$		0			0
$565$	8.38695	−	14.5266i	0.352842	−	0.611139i
$566$	16.3068	+	28.2442i	0.685427	+	1.18719i
$567$		0			0
$568$	5.10651	−	8.84473i	0.214264	−	0.371117i
$569$	28.0036			1.17397			0.586986	−	0.809597i	$-0.300315\pi$
$569$	28.0036			1.17397			0.586986	+	0.809597i	$0.300315\pi$
$570$		0			0
$571$	39.0506			1.63422			0.817108	−	0.576484i	$-0.195576\pi$
$571$	39.0506			1.63422			0.817108	+	0.576484i	$0.195576\pi$
$572$	8.57286	−	14.8486i	0.358449	−	0.620853i
$573$		0			0
$574$	8.87771	+	15.3766i	0.370548	+	0.641809i
$575$	−4.29873	+	7.44562i	−0.179269	+	0.310504i
$576$		0			0
$577$	18.5294			0.771389			0.385694	−	0.922627i	$-0.373962\pi$
$577$	18.5294			0.771389			0.385694	+	0.922627i	$0.373962\pi$
$578$	−38.5412			−1.60310
$579$		0			0
$580$	−11.1564	−	19.3234i	−0.463243	−	0.802360i
$581$	28.4470			1.18018
$582$		0			0
$583$	6.63345	+	11.4895i	0.274730	+	0.475845i
$584$	4.29228	−	7.43444i	0.177616	−	0.307639i
$585$		0			0
$586$	−6.86426	+	11.8893i	−0.283560	+	0.491140i
$587$	9.61458	−	16.6529i	0.396836	−	0.687341i	−0.596497	−	0.802615i	$-0.703441\pi$
$587$	9.61458	−	16.6529i	0.396836	−	0.687341i	0.993334	+	0.115274i	$0.0367747\pi$
$588$		0			0
$589$	−16.4072	−	15.0158i	−0.676046	−	0.618713i
$590$	22.7278			0.935691
$591$		0			0
$592$	2.88006	−	4.98841i	0.118370	−	0.205022i
$593$	−15.5293	−	26.8976i	−0.637714	−	1.10455i	−0.985933	−	0.167140i	$-0.946547\pi$
$593$	−15.5293	−	26.8976i	−0.637714	−	1.10455i	0.348219	−	0.937413i	$-0.386786\pi$
$594$		0			0
$595$	−9.25165	−	16.0243i	−0.379281	−	0.656933i
$596$	−29.2228			−1.19701
$597$		0			0
$598$	11.2688	+	19.5182i	0.460818	+	0.798159i
$599$	−4.84691	−	8.39510i	−0.198039	−	0.343014i	0.749853	−	0.661604i	$-0.230124\pi$
$599$	−4.84691	−	8.39510i	−0.198039	−	0.343014i	−0.947893	+	0.318590i	$0.896791\pi$
$600$		0			0
$601$	9.02069			0.367962			0.183981	−	0.982930i	$-0.441102\pi$
$601$	9.02069			0.367962			0.183981	+	0.982930i	$0.441102\pi$
$602$	4.15024	+	7.18842i	0.169151	+	0.292978i
$603$		0			0
$604$	−2.90125	−	5.02511i	−0.118050	−	0.204469i
$605$	6.10511	−	10.5744i	0.248208	−	0.429909i
$606$		0			0
$607$	−38.5916			−1.56638			−0.783192	−	0.621780i	$-0.786410\pi$
$607$	−38.5916			−1.56638			−0.783192	+	0.621780i	$0.786410\pi$
$608$	6.12116	−	27.6918i	0.248246	−	1.12305i
$609$		0			0
$610$	5.74052	−	9.94286i	0.232427	−	0.402575i
$611$	5.46835	−	9.47146i	0.221226	−	0.383174i
$612$		0			0
$613$	10.3707	−	17.9626i	0.418869	−	0.725502i	−0.576957	−	0.816774i	$-0.695760\pi$
$613$	10.3707	−	17.9626i	0.418869	−	0.725502i	0.995826	+	0.0912724i	$0.0290934\pi$
$614$	14.0951	+	24.4134i	0.568832	+	0.985246i
$615$		0			0
$616$	36.0413			1.45215
$617$	−15.2005	−	26.3280i	−0.611949	−	1.05993i	−0.990912	−	0.134514i	$-0.957053\pi$
$617$	−15.2005	−	26.3280i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$618$		0			0
$619$	−9.69562			−0.389700			−0.194850	−	0.980833i	$-0.562422\pi$
$619$	−9.69562			−0.389700			−0.194850	+	0.980833i	$0.562422\pi$
$620$	15.5688			0.625259
$621$		0			0
$622$	20.1917	−	34.9730i	0.809612	−	1.40229i
$623$	6.60552	+	11.4411i	0.264645	+	0.458378i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−16.9567			−0.677728
$627$		0			0
$628$	−56.1020			−2.23871
$629$	21.2384	−	36.7860i	0.846830	−	1.46675i
$630$		0			0
$631$	1.85131	+	3.20656i	0.0736994	+	0.127651i	0.900520	−	0.434815i	$-0.143186\pi$
$631$	1.85131	+	3.20656i	0.0736994	+	0.127651i	−0.826821	+	0.562466i	$0.809853\pi$
$632$	−17.8102	+	30.8482i	−0.708453	+	1.22708i
$633$		0			0
$634$	10.1520			0.403186
$635$	−0.102468			−0.00406631
$636$		0			0
$637$	−1.76472	−	3.05659i	−0.0699208	−	0.121106i
$638$	−79.1800			−3.13477
$639$		0			0
$640$	8.14510	+	14.1077i	0.321963	+	0.557657i
$641$	9.89794	−	17.1437i	0.390945	−	0.677137i	−0.601629	−	0.798775i	$-0.705482\pi$
$641$	9.89794	−	17.1437i	0.390945	−	0.677137i	0.992574	+	0.121639i	$0.0388149\pi$
$642$		0			0
$643$	2.63442	−	4.56296i	0.103892	−	0.179945i	−0.809393	−	0.587267i	$-0.800204\pi$
$643$	2.63442	−	4.56296i	0.103892	−	0.179945i	0.913285	+	0.407322i	$0.133537\pi$
$644$	−41.5316	+	71.9349i	−1.63658	+	2.83463i
$645$		0			0
$646$	12.3562	−	55.8988i	0.486148	−	2.19931i
$647$	−25.3370			−0.996098			−0.498049	−	0.867149i	$-0.665950\pi$
$647$	−25.3370			−0.996098			−0.498049	+	0.867149i	$0.665950\pi$
$648$		0			0
$649$	24.3595	−	42.1920i	0.956196	−	1.65618i
$650$	1.31072	+	2.27023i	0.0514106	+	0.0890458i
$651$		0			0
$652$	16.2073	+	28.0718i	0.634726	+	1.09938i
$653$	−12.3697			−0.484065			−0.242032	−	0.970268i	$-0.577814\pi$
$653$	−12.3697			−0.484065			−0.242032	+	0.970268i	$0.577814\pi$
$654$		0			0
$655$	−6.78366	−	11.7497i	−0.265060	−	0.459097i
$656$	0.988564	+	1.71224i	0.0385969	+	0.0668519i
$657$		0			0
$658$	66.7279			2.60133
$659$	−11.4551	−	19.8407i	−0.446226	−	0.772885i	0.551911	−	0.833903i	$-0.313899\pi$
$659$	−11.4551	−	19.8407i	−0.446226	−	0.772885i	−0.998137	+	0.0610175i	$0.980565\pi$
$660$		0			0
$661$	−1.64082	−	2.84198i	−0.0638203	−	0.110540i	0.832350	−	0.554251i	$-0.186995\pi$
$661$	−1.64082	−	2.84198i	−0.0638203	−	0.110540i	−0.896170	+	0.443711i	$0.853662\pi$
$662$	18.8423	−	32.6358i	0.732327	−	1.26843i
$663$		0			0
$664$	−21.2262			−0.823735
$665$	13.1606	−	4.15846i	0.510345	−	0.161258i
$666$		0			0
$667$	31.4353	−	54.4475i	1.21718	−	2.10821i
$668$	22.3037	−	38.6312i	0.862957	−	1.49469i
$669$		0			0
$670$	−1.16707	+	2.02143i	−0.0450879	+	0.0780946i
$671$	−12.3053	−	21.3134i	−0.475040	−	0.822794i
$672$		0			0
$673$	29.2183			1.12628			0.563142	−	0.826360i	$-0.309592\pi$
$673$	29.2183			1.12628			0.563142	+	0.826360i	$0.309592\pi$
$674$	−19.5910	−	33.9326i	−0.754617	−	1.30704i
$675$		0			0
$676$	−35.5150			−1.36596
$677$	36.0085			1.38392			0.691960	−	0.721936i	$-0.256747\pi$
$677$	36.0085			1.38392			0.691960	+	0.721936i	$0.256747\pi$
$678$		0			0
$679$	−3.16638	+	5.48433i	−0.121515	+	0.210469i
$680$	6.90326	+	11.9568i	0.264728	+	0.458522i
$681$		0			0
$682$	27.6241	−	47.8464i	1.05778	−	1.83213i
$683$	−32.7395			−1.25274			−0.626371	−	0.779525i	$-0.715460\pi$
$683$	−32.7395			−1.25274			−0.626371	+	0.779525i	$0.715460\pi$
$684$		0			0
$685$	15.8437			0.605356
$686$	−14.1404	+	24.4919i	−0.539884	+	0.935107i
$687$		0			0
$688$	0.462143	+	0.800456i	0.0176191	+	0.0305171i
$689$	−1.60598	+	2.78164i	−0.0611831	+	0.105972i
$690$		0			0
$691$	−17.3452			−0.659842			−0.329921	−	0.944009i	$-0.607022\pi$
$691$	−17.3452			−0.659842			−0.329921	+	0.944009i	$0.607022\pi$
$692$	2.00532			0.0762308
$693$		0			0
$694$	34.9363	+	60.5115i	1.32616	+	2.29698i
$695$	4.31269			0.163590
$696$		0			0
$697$	7.28995	+	12.6266i	0.276127	+	0.478265i
$698$	0.997300	−	1.72737i	0.0377484	−	0.0653821i
$699$		0			0
$700$	−4.83069	+	8.36699i	−0.182583	+	0.316243i
$701$	1.21218	−	2.09956i	0.0457834	−	0.0792992i	−0.842226	−	0.539125i	$-0.818755\pi$
$701$	1.21218	−	2.09956i	0.0457834	−	0.0792992i	0.888009	+	0.459826i	$0.152088\pi$
$702$		0			0
$703$	23.3733	+	21.3911i	0.881539	+	0.806780i
$704$	62.8130			2.36736
$705$		0			0
$706$	5.92304	−	10.2590i	0.222917	−	0.386103i
$707$	17.2887	+	29.9449i	0.650209	+	1.12619i
$708$		0			0
$709$	−5.25378	−	9.09982i	−0.197310	−	0.341751i	0.750345	−	0.661046i	$-0.229887\pi$
$709$	−5.25378	−	9.09982i	−0.197310	−	0.341751i	−0.947655	+	0.319295i	$0.896554\pi$
$710$	9.71527			0.364607
$711$		0			0
$712$	−4.92881	−	8.53694i	−0.184715	−	0.319935i
$713$	21.9341	+	37.9910i	0.821439	+	1.42277i
$714$		0			0
$715$	5.61928			0.210149
$716$	−35.4931	−	61.4758i	−1.32644	−	2.29746i
$717$		0			0
$718$	30.6367	+	53.0643i	1.14335	+	1.98034i
$719$	−7.74161	+	13.4089i	−0.288713	+	0.500066i	−0.973503	−	0.228675i	$-0.926561\pi$
$719$	−7.74161	+	13.4089i	−0.288713	+	0.500066i	0.684789	+	0.728741i	$0.259894\pi$
$720$		0			0
$721$	−18.1153			−0.674648
$722$	38.7238	+	17.9989i	1.44115	+	0.669851i
$723$		0			0
$724$	−2.21390	+	3.83459i	−0.0822790	+	0.142511i
$725$	3.65634	−	6.33297i	0.135793	−	0.235201i
$726$		0			0
$727$	−9.03690	+	15.6524i	−0.335160	+	0.580514i	−0.983516	−	0.180823i	$-0.942124\pi$
$727$	−9.03690	+	15.6524i	−0.335160	+	0.580514i	0.648355	+	0.761338i	$0.275457\pi$
$728$	4.36287	+	7.55671i	0.161699	+	0.280070i
$729$		0			0
$730$	8.16617			0.302243
$731$	3.40798	+	5.90279i	0.126049	+	0.218323i
$732$		0			0
$733$	−32.5312			−1.20157			−0.600784	−	0.799411i	$-0.705145\pi$
$733$	−32.5312			−1.20157			−0.600784	+	0.799411i	$0.705145\pi$
$734$	−3.08203			−0.113760
$735$		0			0
$736$	−27.9688	+	48.4433i	−1.03094	+	1.78565i
$737$	2.50172	+	4.33311i	0.0921520	+	0.159612i
$738$		0			0
$739$	−23.9823	+	41.5386i	−0.882205	+	1.52802i	−0.0333206	+	0.999445i	$0.510608\pi$
$739$	−23.9823	+	41.5386i	−0.882205	+	1.52802i	−0.848884	+	0.528579i	$0.822725\pi$
$740$	−22.1790			−0.815315
$741$		0			0
$742$	−19.5971			−0.719433
$743$	−12.8553	+	22.2660i	−0.471615	+	0.816861i	−0.999473	−	0.0324716i	$-0.989662\pi$
$743$	−12.8553	+	22.2660i	−0.471615	+	0.816861i	0.527858	+	0.849333i	$0.322995\pi$
$744$		0			0
$745$	−4.78869	−	8.29426i	−0.175444	−	0.303878i
$746$	37.2861	−	64.5814i	1.36514	−	2.36449i
$747$		0			0
$748$	85.9016			3.14087
$749$	9.44874			0.345249
$750$		0			0
$751$	4.55713	+	7.89319i	0.166292	+	0.288026i	0.937113	−	0.349025i	$-0.113487\pi$
$751$	4.55713	+	7.89319i	0.166292	+	0.288026i	−0.770821	+	0.637051i	$0.780154\pi$
$752$	7.43039			0.270958
$753$		0			0
$754$	−9.58488	−	16.6015i	−0.349061	−	0.604591i
$755$	0.950844	−	1.64691i	0.0346048	−	0.0599372i
$756$		0			0
$757$	19.5958	−	33.9409i	0.712222	−	1.23360i	−0.251800	−	0.967779i	$-0.581022\pi$
$757$	19.5958	−	33.9409i	0.712222	−	1.23360i	0.964021	−	0.265825i	$-0.0856442\pi$
$758$	−35.0207	+	60.6576i	−1.27201	+	2.20318i
$759$		0			0
$760$	−9.81996	+	3.10290i	−0.356207	+	0.112554i
$761$	−52.4574			−1.90158			−0.950790	−	0.309837i	$-0.899725\pi$
$761$	−52.4574			−1.90158			−0.950790	+	0.309837i	$0.899725\pi$
$762$		0			0
$763$	−20.3698	+	35.2816i	−0.737437	+	1.27728i
$764$	29.0779	+	50.3645i	1.05200	+	1.82212i
$765$		0			0
$766$	−33.3319	−	57.7326i	−1.20433	−	2.08596i
$767$	11.7951			0.425895
$768$		0			0
$769$	−11.8286	−	20.4878i	−0.426551	−	0.738807i	0.570013	−	0.821635i	$-0.306938\pi$
$769$	−11.8286	−	20.4878i	−0.426551	−	0.738807i	−0.996564	+	0.0828283i	$0.973605\pi$
$770$	17.1424	+	29.6915i	0.617769	+	1.07001i
$771$		0			0
$772$	47.8915			1.72365
$773$	−2.67555	−	4.63418i	−0.0962328	−	0.166680i	0.813890	−	0.581019i	$-0.197346\pi$
$773$	−2.67555	−	4.63418i	−0.0962328	−	0.166680i	−0.910122	+	0.414339i	$0.864013\pi$
$774$		0			0
$775$	2.55123	+	4.41887i	0.0916430	+	0.158730i
$776$	2.36264	−	4.09222i	0.0848139	−	0.146902i
$777$		0			0
$778$	−45.0352			−1.61459
$779$	−10.3700	+	3.27671i	−0.371545	+	0.117400i
$780$		0			0
$781$	10.4128	−	18.0354i	0.372598	−	0.645358i
$782$	−56.4579	+	97.7880i	−2.01893	+	3.49689i
$783$		0			0
$784$	1.19895	−	2.07664i	0.0428197	−	0.0741658i
$785$	−9.19333	−	15.9233i	−0.328124	−	0.568327i
$786$		0			0
$787$	26.2322			0.935078			0.467539	−	0.883972i	$-0.345141\pi$
$787$	26.2322			0.935078			0.467539	+	0.883972i	$0.345141\pi$
$788$	12.5653	+	21.7637i	0.447620	+	0.775300i
$789$		0			0
$790$	−33.8844			−1.20555
$791$	53.1126			1.88847
$792$		0			0
$793$	2.97915	−	5.16005i	0.105793	−	0.183239i
$794$	−21.8803	−	37.8977i	−0.776501	−	1.34494i
$795$		0			0
$796$	−26.5292	+	45.9500i	−0.940304	+	1.62865i
$797$	−4.25354			−0.150668			−0.0753341	−	0.997158i	$-0.524002\pi$
$797$	−4.25354			−0.150668			−0.0753341	+	0.997158i	$0.524002\pi$
$798$		0			0
$799$	54.7938			1.93847
$800$	−3.25314	+	5.63461i	−0.115016	+	0.199214i
$801$		0			0
$802$	41.3126	+	71.5556i	1.45880	+	2.52671i
$803$	8.75244	−	15.1597i	0.308867	−	0.534973i
$804$		0			0
$805$	−27.2228			−0.959479
$806$	13.3758			0.471143
$807$		0			0
$808$	−12.9002	−	22.3438i	−0.453828	−	0.786054i
$809$	12.2708			0.431419			0.215710	−	0.976458i	$-0.430794\pi$
$809$	12.2708			0.431419			0.215710	+	0.976458i	$0.430794\pi$
$810$		0			0
$811$	5.22559	+	9.05099i	0.183495	+	0.317823i	0.943068	−	0.332599i	$-0.107925\pi$
$811$	5.22559	+	9.05099i	0.183495	+	0.317823i	−0.759573	+	0.650422i	$0.774592\pi$
$812$	35.3253	−	61.1852i	1.23968	−	2.14718i
$813$		0			0
$814$	−39.3527	+	68.1608i	−1.37931	+	2.38903i
$815$	−5.31172	+	9.20016i	−0.186061	+	0.322268i
$816$		0			0
$817$	−4.84789	+	1.53183i	−0.169606	+	0.0535919i
$818$	28.2393			0.987365
$819$		0			0
$820$	3.80640	−	6.59288i	0.132925	−	0.230233i
$821$	5.03353	+	8.71832i	0.175671	+	0.304272i	0.940393	−	0.340089i	$-0.110457\pi$
$821$	5.03353	+	8.71832i	0.175671	+	0.304272i	−0.764722	+	0.644360i	$0.777124\pi$
$822$		0			0
$823$	−21.6974	−	37.5810i	−0.756324	−	1.30999i	−0.944713	−	0.327897i	$-0.893660\pi$
$823$	−21.6974	−	37.5810i	−0.756324	−	1.30999i	0.188390	−	0.982094i	$-0.439673\pi$
$824$	13.5170			0.470887
$825$		0			0
$826$	35.9825	+	62.3236i	1.25199	+	2.16851i
$827$	−7.36950	−	12.7643i	−0.256263	−	0.443860i	0.708975	−	0.705233i	$-0.249158\pi$
$827$	−7.36950	−	12.7643i	−0.256263	−	0.443860i	−0.965238	+	0.261374i	$0.915824\pi$
$828$		0			0
$829$	54.5313			1.89395			0.946974	−	0.321309i	$-0.104123\pi$
$829$	54.5313			1.89395			0.946974	+	0.321309i	$0.104123\pi$
$830$	−10.0958	−	17.4865i	−0.350432	−	0.606965i
$831$		0			0
$832$	7.60363	+	13.1699i	0.263608	+	0.456583i
$833$	8.84140	−	15.3138i	0.306336	−	0.530590i
$834$		0			0
$835$	14.6195			0.505928
$836$	−13.8298	+	62.5652i	−0.478313	+	2.16386i
$837$		0			0
$838$	−26.8210	+	46.4553i	−0.926515	+	1.60477i
$839$	18.7632	−	32.4988i	0.647777	−	1.12198i	−0.335876	−	0.941906i	$-0.609032\pi$
$839$	18.7632	−	32.4988i	0.647777	−	1.12198i	0.983653	−	0.180076i	$-0.0576344\pi$
$840$		0			0
$841$	−12.2377	+	21.1963i	−0.421990	+	0.730908i
$842$	−7.42805	−	12.8658i	−0.255988	−	0.443384i
$843$		0			0
$844$	64.3274			2.21424
$845$	−5.81978	−	10.0801i	−0.200206	−	0.346768i
$846$		0			0
$847$	38.6622			1.32845
$848$	−2.18221			−0.0749373
$849$		0			0
$850$	−6.56681	+	11.3741i	−0.225240	+	0.390127i
$851$	−31.2468	−	54.1211i	−1.07113	−	1.85525i
$852$		0			0
$853$	−0.876485	+	1.51812i	−0.0300103	+	0.0519793i	−0.880640	−	0.473785i	$-0.842887\pi$
$853$	−0.876485	+	1.51812i	−0.0300103	+	0.0519793i	0.850630	+	0.525764i	$0.176221\pi$
$854$	36.3533			1.24399
$855$		0			0
$856$	−7.05032			−0.240975
$857$	15.2630	−	26.4363i	0.521375	−	0.903048i	−0.478316	−	0.878188i	$-0.658753\pi$
$857$	15.2630	−	26.4363i	0.521375	−	0.903048i	0.999691	−	0.0248601i	$-0.00791404\pi$
$858$		0			0
$859$	−3.63363	−	6.29363i	−0.123978	−	0.214736i	0.797355	−	0.603510i	$-0.206232\pi$
$859$	−3.63363	−	6.29363i	−0.123978	−	0.214736i	−0.921333	+	0.388775i	$0.872898\pi$
$860$	1.77945	−	3.08210i	0.0606788	−	0.105099i
$861$		0			0
$862$	−16.7733			−0.571301
$863$	30.4383			1.03613			0.518066	−	0.855341i	$-0.326652\pi$
$863$	30.4383			1.03613			0.518066	+	0.855341i	$0.326652\pi$
$864$		0			0
$865$	0.328608	+	0.569166i	0.0111730	+	0.0193522i
$866$	−48.5350			−1.64929
$867$		0			0
$868$	24.6484	+	42.6923i	0.836622	+	1.44907i
$869$	−36.3171	+	62.9030i	−1.23197	+	2.13384i
$870$		0			0
$871$	−0.605675	+	1.04906i	−0.0205225	+	0.0355460i
$872$	15.1992	−	26.3259i	0.514711	−	0.891506i
$873$		0			0
$874$	−62.1330	−	56.8638i	−2.10168	−	1.92345i
$875$	−3.16638			−0.107043
$876$		0			0
$877$	−23.3318	+	40.4119i	−0.787860	+	1.36461i	0.139416	+	0.990234i	$0.455478\pi$
$877$	−23.3318	+	40.4119i	−0.787860	+	1.36461i	−0.927276	+	0.374379i	$0.877856\pi$
$878$	−37.9242	−	65.6866i	−1.27988	−	2.21682i
$879$		0			0
$880$	1.90887	+	3.30625i	0.0643479	+	0.111454i
$881$	31.2809			1.05388			0.526939	−	0.849903i	$-0.323340\pi$
$881$	31.2809			1.05388			0.526939	+	0.849903i	$0.323340\pi$
$882$		0			0
$883$	−3.87059	−	6.70405i	−0.130256	−	0.225609i	0.793519	−	0.608545i	$-0.208246\pi$
$883$	−3.87059	−	6.70405i	−0.130256	−	0.225609i	−0.923775	+	0.382936i	$0.874913\pi$
$884$	10.3985	+	18.0108i	0.349741	+	0.605769i
$885$		0			0
$886$	−17.3081			−0.581476
$887$	−2.49594	−	4.32310i	−0.0838056	−	0.145156i	0.821076	−	0.570819i	$-0.193374\pi$
$887$	−2.49594	−	4.32310i	−0.0838056	−	0.145156i	−0.904882	+	0.425663i	$0.860041\pi$
$888$		0			0
$889$	−0.162226	−	0.280984i	−0.00544089	−	0.00942390i
$890$	4.68859	−	8.12088i	0.157162	−	0.272212i
$891$		0			0
$892$	2.83645			0.0949714
$893$	−8.82157	+	39.9083i	−0.295203	+	1.33548i
$894$		0			0
$895$	11.6324	−	20.1478i	0.388827	−	0.673468i
$896$	−25.7905	+	44.6705i	−0.861600	+	1.49234i
$897$		0			0
$898$	−5.44238	+	9.42647i	−0.181614	+	0.314565i
$899$	−18.6564	−	32.3138i	−0.622225	−	1.07773i
$900$		0			0
$901$	−16.0922			−0.536110
$902$	−13.5076	−	23.3958i	−0.449753	−	0.778995i
$903$		0			0
$904$	−39.6307			−1.31810
$905$	−1.45115			−0.0482379
$906$		0			0
$907$	−26.6993	+	46.2446i	−0.886537	+	1.53553i	−0.0425957	+	0.999092i	$0.513563\pi$
$907$	−26.6993	+	46.2446i	−0.886537	+	1.53553i	−0.843942	+	0.536435i	$0.819771\pi$
$908$	3.87156	+	6.70573i	0.128482	+	0.222538i
$909$		0			0
$910$	−4.15024	+	7.18842i	−0.137579	+	0.238294i
$911$	−22.8765			−0.757933			−0.378967	−	0.925410i	$-0.623720\pi$
$911$	−22.8765			−0.757933			−0.378967	+	0.925410i	$0.623720\pi$
$912$		0			0
$913$	−43.2826			−1.43244
$914$	−20.4884	+	35.4870i	−0.677697	+	1.17381i
$915$		0			0
$916$	1.39185	+	2.41076i	0.0459881	+	0.0796538i
$917$	21.4797	−	37.2039i	0.709321	−	1.22858i
$918$		0			0
$919$	−3.88045			−0.128004			−0.0640021	−	0.997950i	$-0.520386\pi$
$919$	−3.88045			−0.128004			−0.0640021	+	0.997950i	$0.520386\pi$
$920$	20.3127			0.669691
$921$		0			0
$922$	36.5843	+	63.3659i	1.20484	+	2.08684i
$923$	5.04193			0.165957
$924$		0			0
$925$	−3.63442	−	6.29501i	−0.119499	−	0.206979i
$926$	−34.7986	+	60.2729i	−1.14355	+	1.98069i
$927$		0			0
$928$	23.7892	−	41.2042i	0.780920	−	1.35259i
$929$	25.8821	−	44.8290i	0.849163	−	1.47079i	−0.0327938	−	0.999462i	$-0.510440\pi$
$929$	25.8821	−	44.8290i	0.849163	−	1.47079i	0.881956	−	0.471331i	$-0.156226\pi$
$930$		0			0
$931$	9.73014	+	8.90496i	0.318892	+	0.291848i
$932$	70.1138			2.29665
$933$		0			0
$934$	29.7744	−	51.5708i	0.974248	−	1.68745i
$935$	14.0765	+	24.3813i	0.460352	+	0.797353i
$936$		0			0
$937$	2.11094	+	3.65625i	0.0689613	+	0.119444i	0.898444	−	0.439087i	$-0.144698\pi$
$937$	2.11094	+	3.65625i	0.0689613	+	0.119444i	−0.829483	+	0.558532i	$0.811365\pi$
$938$	−7.39079			−0.241318
$939$		0			0
$940$	−14.3051	−	24.7772i	−0.466581	−	0.808142i
$941$	−8.88263	−	15.3852i	−0.289566	−	0.501542i	0.684140	−	0.729350i	$-0.260178\pi$
$941$	−8.88263	−	15.3852i	−0.289566	−	0.501542i	−0.973706	+	0.227808i	$0.926844\pi$
$942$		0			0
$943$	21.4506			0.698527
$944$	4.00678	+	6.93995i	0.130410	+	0.225876i
$945$		0			0
$946$	−6.31465	−	10.9373i	−0.205307	−	0.355602i
$947$	6.73396	−	11.6636i	0.218824	−	0.379015i	−0.735624	−	0.677390i	$-0.763111\pi$
$947$	6.73396	−	11.6636i	0.218824	−	0.379015i	0.954449	+	0.298375i	$0.0964445\pi$
$948$		0			0
$949$	4.23799			0.137571
$950$	−7.22691	−	6.61402i	−0.234472	−	0.214587i
$951$		0			0
$952$	−21.8583	+	37.8598i	−0.708433	+	1.22704i
$953$	−13.3390	+	23.1037i	−0.432091	+	0.748404i	−0.997053	−	0.0767132i	$-0.975557\pi$
$953$	−13.3390	+	23.1037i	−0.432091	+	0.748404i	0.564962	+	0.825117i	$0.308891\pi$
$954$		0			0
$955$	−9.52990	+	16.5063i	−0.308380	+	0.534130i
$956$	32.3200	+	55.9799i	1.04530	+	1.81052i
$957$		0			0
$958$	−52.0188			−1.68065
$959$	25.0836	+	43.4460i	0.809990	+	1.40294i
$960$		0			0
$961$	−4.96482			−0.160156
$962$	−19.0548			−0.614353
$963$		0			0
$964$	6.56417	−	11.3695i	0.211418	−	0.366186i
$965$	7.84789	+	13.5929i	0.252632	+	0.437572i
$966$		0			0
$967$	7.10344	−	12.3035i	0.228431	−	0.395655i	−0.728912	−	0.684607i	$-0.759974\pi$
$967$	7.10344	−	12.3035i	0.228431	−	0.395655i	0.957343	+	0.288953i	$0.0933071\pi$
$968$	−28.8484			−0.927222
$969$		0			0
$970$	4.49499			0.144325
$971$	9.20622	−	15.9456i	0.295442	−	0.511720i	−0.679646	−	0.733540i	$-0.737867\pi$
$971$	9.20622	−	15.9456i	0.295442	−	0.511720i	0.975088	+	0.221821i	$0.0711999\pi$
$972$		0			0
$973$	6.82781	+	11.8261i	0.218890	+	0.379128i
$974$	−43.0479	+	74.5612i	−1.37934	+	2.38909i
$975$		0			0
$976$	4.04807			0.129576
$977$	3.75672			0.120188			0.0600941	−	0.998193i	$-0.480860\pi$
$977$	3.75672			0.120188			0.0600941	+	0.998193i	$0.480860\pi$
$978$		0			0
$979$	−10.0504	−	17.4078i	−0.321212	−	0.556356i
$980$	−9.23296			−0.294936
$981$		0			0
$982$	−26.7165	−	46.2744i	−0.852559	−	1.47668i
$983$	−5.73076	+	9.92597i	−0.182783	+	0.316589i	−0.942827	−	0.333282i	$-0.891844\pi$
$983$	−5.73076	+	9.92597i	−0.182783	+	0.316589i	0.760044	+	0.649871i	$0.225177\pi$
$984$		0			0
$985$	−4.11810	+	7.13275i	−0.131214	+	0.227268i
$986$	48.0211	−	83.1749i	1.52930	−	2.64883i
$987$		0			0
$988$	−14.7920	+	4.67397i	−0.470597	+	0.148699i
$989$	10.0279			0.318869
$990$		0			0
$991$	4.54948	−	7.87993i	0.144519	−	0.250314i	−0.784674	−	0.619908i	$-0.787170\pi$
$991$	4.54948	−	7.87993i	0.144519	−	0.250314i	0.929193	+	0.369594i	$0.120503\pi$
$992$	16.5991	+	28.7504i	0.527021	+	0.912827i
$993$		0			0
$994$	15.3811	+	26.6409i	0.487860	+	0.844998i
$995$	−17.3892			−0.551274
$996$		0			0
$997$	−12.3463	−	21.3844i	−0.391012	−	0.677252i	0.601572	−	0.798819i	$-0.294541\pi$
$997$	−12.3463	−	21.3844i	−0.391012	−	0.677252i	−0.992583	+	0.121567i	$0.961208\pi$
$998$	0.473811	+	0.820665i	0.0149982	+	0.0259777i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.i.676.5		10
3.2	odd	2		285.2.i.f.106.1	✓	10
19.7	even	3	inner	855.2.k.i.406.5		10
57.8	even	6		5415.2.a.z.1.1		5
57.11	odd	6		5415.2.a.y.1.5		5
57.26	odd	6		285.2.i.f.121.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.1	✓	10	3.2	odd	2
285.2.i.f.121.1	yes	10	57.26	odd	6
855.2.k.i.406.5		10	19.7	even	3	inner
855.2.k.i.676.5		10	1.1	even	1	trivial
5415.2.a.y.1.5		5	57.11	odd	6
5415.2.a.z.1.1		5	57.8	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.12375 - 1.94639i) q^{2} +(-1.52562 - 2.64245i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.16638 q^{7} -2.36264 q^{8} +(-1.12375 - 1.94639i) q^{10} -4.81770 q^{11} +(-0.583191 - 1.01012i) q^{13} +(3.55821 - 6.16301i) q^{14} +(0.396220 - 0.686273i) q^{16} +(2.92184 - 5.06077i) q^{17} +(3.21554 + 2.94284i) q^{19} -3.05123 q^{20} +(-5.41388 + 9.37711i) q^{22} +(-4.29873 - 7.44562i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.62144 q^{26} +(-4.83069 - 8.36699i) q^{28} +(3.65634 + 6.33297i) q^{29} -5.10247 q^{31} +(-3.25314 - 5.63461i) q^{32} +(-6.56681 - 11.3741i) q^{34} +(1.58319 - 2.74217i) q^{35} +7.26885 q^{37} +(9.34136 - 2.95167i) q^{38} +(-1.18132 + 2.04611i) q^{40} +(-1.24750 + 2.16072i) q^{41} +(-0.583191 + 1.01012i) q^{43} +(7.34996 + 12.7305i) q^{44} -19.3227 q^{46} +(4.68830 + 8.12038i) q^{47} +3.02597 q^{49} -2.24750 q^{50} +(-1.77945 + 3.08210i) q^{52} +(-1.37689 - 2.38485i) q^{53} +(-2.40885 + 4.17225i) q^{55} -7.48103 q^{56} +16.4352 q^{58} +(-5.05626 + 8.75770i) q^{59} +(2.55418 + 4.42398i) q^{61} +(-5.73389 + 9.93138i) q^{62} -13.0380 q^{64} -1.16638 q^{65} +(-0.519277 - 0.899414i) q^{67} -17.8304 q^{68} +(-3.55821 - 6.16301i) q^{70} +(-2.16135 + 3.74358i) q^{71} +(-1.81673 + 3.14666i) q^{73} +(8.16835 - 14.1480i) q^{74} +(2.87062 - 12.9865i) q^{76} -15.2547 q^{77} +(7.53826 - 13.0567i) q^{79} +(-0.396220 - 0.686273i) q^{80} +(2.80374 + 4.85622i) q^{82} +8.98408 q^{83} +(-2.92184 - 5.06077i) q^{85} +(1.31072 + 2.27023i) q^{86} +11.3825 q^{88} +(2.08614 + 3.61330i) q^{89} +(-1.84661 - 3.19841i) q^{91} +(-13.1164 + 22.7183i) q^{92} +21.0739 q^{94} +(4.15634 - 1.31332i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(3.40043 - 5.88972i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) \) 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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