LMFDB - Embedded newform 336.2.bj.e.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(95,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))

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

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

chi := DirichletCharacter("336.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.8275904784.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 4x^{4} - 18x^{3} + 45x^{2} - 81x + 81 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 4x^4 - 18x^3 + 45x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.3
Root			$-1.37009 + 1.05965i$ of defining polynomial
Character	$\chi$	$=$	336.191
Dual form			336.2.bj.e.95.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.232633 - 1.71636i) q^{3} +(-0.581054 - 0.335472i) q^{5} +(-2.63746 + 0.209313i) q^{7} +(-2.89176 + 0.798564i) q^{9} +O(q^{10})$	\(q+(-0.232633 - 1.71636i) q^{3} +(-0.581054 - 0.335472i) q^{5} +(-2.63746 + 0.209313i) q^{7} +(-2.89176 + 0.798564i) q^{9} +(-2.62440 - 4.54559i) q^{11} +2.00000 q^{13} +(-0.440617 + 1.07534i) q^{15} +(-3.64607 + 2.10506i) q^{17} +(-1.13746 - 0.656712i) q^{19} +(0.972818 + 4.47813i) q^{21} +(1.60273 - 2.77600i) q^{23} +(-2.27492 - 3.94027i) q^{25} +(2.04334 + 4.77753i) q^{27} +6.22295i q^{29} +(-1.50000 + 0.866025i) q^{31} +(-7.19133 + 5.56186i) q^{33} +(1.60273 + 0.763171i) q^{35} +(3.13746 - 5.43424i) q^{37} +(-0.465267 - 3.43271i) q^{39} -9.76212i q^{41} -9.55505i q^{43} +(1.94817 + 0.506096i) q^{45} +(-4.80818 + 8.32801i) q^{47} +(6.91238 - 1.10411i) q^{49} +(4.46123 + 5.76825i) q^{51} +(10.1974 - 5.88748i) q^{53} +3.52165i q^{55} +(-0.862541 + 2.10506i) q^{57} +(3.78651 + 6.55842i) q^{59} +(1.86254 - 3.22602i) q^{61} +(7.45976 - 2.71146i) q^{63} +(-1.16211 - 0.670944i) q^{65} +(2.58762 - 1.49397i) q^{67} +(-5.13746 - 2.10506i) q^{69} +4.08668 q^{71} +(-0.137459 - 0.238085i) q^{73} +(-6.23369 + 4.82121i) q^{75} +(7.87319 + 11.4395i) q^{77} +(-4.50000 - 2.59808i) q^{79} +(7.72459 - 4.61852i) q^{81} +2.04334 q^{83} +2.82475 q^{85} +(10.6808 - 1.44767i) q^{87} +(-12.1003 - 6.98612i) q^{89} +(-5.27492 + 0.418627i) q^{91} +(1.83536 + 2.37307i) q^{93} +(0.440617 + 0.763171i) q^{95} -3.27492 q^{97} +(11.2191 + 11.0490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{3} - 6 q^{7} - q^{9}+O(q^{10}) $ 8 * q - 3 * q^3 - 6 * q^7 - q^9	$ 8 q - 3 q^{3} - 6 q^{7} - q^{9} + 16 q^{13} + 6 q^{19} - 19 q^{21} + 12 q^{25} - 12 q^{31} - 11 q^{33} + 10 q^{37} - 6 q^{39} - 17 q^{45} + 10 q^{49} + 9 q^{51} - 22 q^{57} + 30 q^{61} + 27 q^{63} + 66 q^{67} - 26 q^{69} + 14 q^{73} - 66 q^{75} - 36 q^{79} + 7 q^{81} - 68 q^{85} + 54 q^{87} - 12 q^{91} + 3 q^{93} + 4 q^{97}+O(q^{100}) $ 8 * q - 3 * q^3 - 6 * q^7 - q^9 + 16 * q^13 + 6 * q^19 - 19 * q^21 + 12 * q^25 - 12 * q^31 - 11 * q^33 + 10 * q^37 - 6 * q^39 - 17 * q^45 + 10 * q^49 + 9 * q^51 - 22 * q^57 + 30 * q^61 + 27 * q^63 + 66 * q^67 - 26 * q^69 + 14 * q^73 - 66 * q^75 - 36 * q^79 + 7 * q^81 - 68 * q^85 + 54 * q^87 - 12 * q^91 + 3 * q^93 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.232633	−	1.71636i	−0.134311	−	0.990939i
$3$	−0.232633	−	1.71636i	−0.134311	−	0.990939i
$4$		0			0
$5$	−0.581054	−	0.335472i	−0.259855	−	0.150028i	0.364413	−	0.931237i	$-0.381270\pi$
$5$	−0.581054	−	0.335472i	−0.259855	−	0.150028i	−0.624269	+	0.781210i	$0.714603\pi$
$6$		0			0
$7$	−2.63746	+	0.209313i	−0.996866	+	0.0791130i
$7$	−2.63746	+	0.209313i	−0.996866	+	0.0791130i
$8$		0			0
$9$	−2.89176	+	0.798564i	−0.963921	+	0.266188i
$10$		0			0
$11$	−2.62440	−	4.54559i	−0.791285	−	1.37055i	−0.925171	−	0.379550i	$-0.876079\pi$
$11$	−2.62440	−	4.54559i	−0.791285	−	1.37055i	0.133886	−	0.990997i	$-0.457254\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	−0.440617	+	1.07534i	−0.113767	+	0.277651i
$16$		0			0
$17$	−3.64607	+	2.10506i	−0.884301	+	0.510552i	−0.872074	−	0.489374i	$-0.837225\pi$
$17$	−3.64607	+	2.10506i	−0.884301	+	0.510552i	−0.0122271	+	0.999925i	$0.503892\pi$
$18$		0			0
$19$	−1.13746	−	0.656712i	−0.260951	−	0.150660i	0.363817	−	0.931470i	$-0.381473\pi$
$19$	−1.13746	−	0.656712i	−0.260951	−	0.150660i	−0.624768	+	0.780810i	$0.714807\pi$
$20$		0			0
$21$	0.972818	+	4.47813i	0.212286	+	0.977208i
$22$		0			0
$23$	1.60273	−	2.77600i	0.334191	−	0.578836i	−0.649138	−	0.760671i	$-0.724870\pi$
$23$	1.60273	−	2.77600i	0.334191	−	0.578836i	0.983329	+	0.181834i	$0.0582035\pi$
$24$		0			0
$25$	−2.27492	−	3.94027i	−0.454983	−	0.788054i
$26$		0			0
$27$	2.04334	+	4.77753i	0.393241	+	0.919435i
$28$		0			0
$29$			6.22295i			1.15557i	0.816188	+	0.577786i	$0.196083\pi$
$29$			6.22295i			1.15557i	−0.816188	+	0.577786i	$0.803917\pi$
$30$		0			0
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−7.19133	+	5.56186i	−1.25185	+	0.968195i
$34$		0			0
$35$	1.60273	+	0.763171i	0.270910	+	0.128999i
$36$		0			0
$37$	3.13746	−	5.43424i	0.515795	−	0.893383i	−0.484037	−	0.875048i	$-0.660830\pi$
$37$	3.13746	−	5.43424i	0.515795	−	0.893383i	0.999832	−	0.0183356i	$-0.00583672\pi$
$38$		0			0
$39$	−0.465267	−	3.43271i	−0.0745023	−	0.549674i
$40$		0			0
$41$		−	9.76212i		−	1.52459i	−0.647231	−	0.762294i	$-0.724073\pi$
$41$		−	9.76212i		−	1.52459i	0.647231	−	0.762294i	$-0.275927\pi$
$42$		0			0
$43$		−	9.55505i		−	1.45713i	−0.684976	−	0.728566i	$-0.740187\pi$
$43$		−	9.55505i		−	1.45713i	0.684976	−	0.728566i	$-0.259813\pi$
$44$		0			0
$45$	1.94817	+	0.506096i	0.290416	+	0.0754443i
$46$		0			0
$47$	−4.80818	+	8.32801i	−0.701345	+	1.21476i	0.266650	+	0.963793i	$0.414083\pi$
$47$	−4.80818	+	8.32801i	−0.701345	+	1.21476i	−0.967995	+	0.250971i	$0.919250\pi$
$48$		0			0
$49$	6.91238	−	1.10411i	0.987482	−	0.157730i
$50$		0			0
$51$	4.46123	+	5.76825i	0.624697	+	0.807716i
$52$		0			0
$53$	10.1974	−	5.88748i	1.40072	−	0.808707i	0.406255	−	0.913760i	$-0.366834\pi$
$53$	10.1974	−	5.88748i	1.40072	−	0.808707i	0.994467	+	0.105053i	$0.0335011\pi$
$54$		0			0
$55$			3.52165i			0.474859i
$56$		0			0
$57$	−0.862541	+	2.10506i	−0.114246	+	0.278822i
$58$		0			0
$59$	3.78651	+	6.55842i	0.492961	+	0.853834i	0.999967	−	0.00810892i	$-0.00258118\pi$
$59$	3.78651	+	6.55842i	0.492961	+	0.853834i	−0.507006	+	0.861942i	$0.669248\pi$
$60$		0			0
$61$	1.86254	−	3.22602i	0.238474	−	0.413049i	−0.721803	−	0.692099i	$-0.756686\pi$
$61$	1.86254	−	3.22602i	0.238474	−	0.413049i	0.960277	+	0.279050i	$0.0900195\pi$
$62$		0			0
$63$	7.45976	−	2.71146i	0.939841	−	0.341612i
$64$		0			0
$65$	−1.16211	−	0.670944i	−0.144142	−	0.0832203i
$66$		0			0
$67$	2.58762	−	1.49397i	0.316129	−	0.182517i	−0.333537	−	0.942737i	$-0.608242\pi$
$67$	2.58762	−	1.49397i	0.316129	−	0.182517i	0.649666	+	0.760220i	$0.274909\pi$
$68$		0			0
$69$	−5.13746	−	2.10506i	−0.618477	−	0.253419i
$70$		0			0
$71$	4.08668			0.485000			0.242500	−	0.970151i	$-0.422033\pi$
$71$	4.08668			0.485000			0.242500	+	0.970151i	$0.422033\pi$
$72$		0			0
$73$	−0.137459	−	0.238085i	−0.0160883	−	0.0278658i	0.857869	−	0.513868i	$-0.171788\pi$
$73$	−0.137459	−	0.238085i	−0.0160883	−	0.0278658i	−0.873957	+	0.486002i	$0.838455\pi$
$74$		0			0
$75$	−6.23369	+	4.82121i	−0.719805	+	0.556705i
$76$		0			0
$77$	7.87319	+	11.4395i	0.897233	+	1.30365i
$78$		0			0
$79$	−4.50000	−	2.59808i	−0.506290	−	0.292306i	0.225018	−	0.974355i	$-0.427756\pi$
$79$	−4.50000	−	2.59808i	−0.506290	−	0.292306i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	7.72459	−	4.61852i	0.858288	−	0.513169i
$82$		0			0
$83$	2.04334			0.224286			0.112143	−	0.993692i	$-0.464229\pi$
$83$	2.04334			0.224286			0.112143	+	0.993692i	$0.464229\pi$
$84$		0			0
$85$	2.82475			0.306387
$86$		0			0
$87$	10.6808	−	1.44767i	1.14510	−	0.155206i
$88$		0			0
$89$	−12.1003	−	6.98612i	−1.28263	−	0.740527i	−0.305302	−	0.952256i	$-0.598757\pi$
$89$	−12.1003	−	6.98612i	−1.28263	−	0.740527i	−0.977329	+	0.211728i	$0.932091\pi$
$90$		0			0
$91$	−5.27492	+	0.418627i	−0.552962	+	0.0438840i
$92$		0			0
$93$	1.83536	+	2.37307i	0.190318	+	0.246076i
$94$		0			0
$95$	0.440617	+	0.763171i	0.0452063	+	0.0782997i
$96$		0			0
$97$	−3.27492			−0.332517			−0.166259	−	0.986082i	$-0.553169\pi$
$97$	−3.27492			−0.332517			−0.166259	+	0.986082i	$0.553169\pi$
$98$		0			0
$99$	11.2191	+	11.0490i	1.12756	+	1.11047i
$100$		0			0
$101$	2.48396	−	1.43411i	0.247163	−	0.142700i	−0.371301	−	0.928512i	$-0.621088\pi$
$101$	2.48396	−	1.43411i	0.247163	−	0.142700i	0.618465	+	0.785813i	$0.287755\pi$
$102$		0			0
$103$	14.6873	+	8.47971i	1.44718	+	0.835531i	0.998313	−	0.0580665i	$-0.0184936\pi$
$103$	14.6873	+	8.47971i	1.44718	+	0.835531i	0.448869	+	0.893597i	$0.351827\pi$
$104$		0			0
$105$	0.937026	−	2.92839i	0.0914444	−	0.285781i
$106$		0			0
$107$	−5.82985	+	10.0976i	−0.563593	+	0.976171i	0.433586	+	0.901112i	$0.357248\pi$
$107$	−5.82985	+	10.0976i	−0.563593	+	0.976171i	−0.997179	+	0.0750592i	$0.976085\pi$
$108$		0			0
$109$	−7.41238	−	12.8386i	−0.709977	−	1.22972i	−0.964865	−	0.262745i	$-0.915372\pi$
$109$	−7.41238	−	12.8386i	−0.709977	−	1.22972i	0.254888	−	0.966970i	$-0.417961\pi$
$110$		0			0
$111$	−10.0570	−	4.12081i	−0.954565	−	0.391130i
$112$		0			0
$113$			9.76212i			0.918343i	0.888348	+	0.459172i	$0.151854\pi$
$113$			9.76212i			0.918343i	−0.888348	+	0.459172i	$0.848146\pi$
$114$		0			0
$115$	−1.86254	+	1.07534i	−0.173683	+	0.100276i
$116$		0			0
$117$	−5.78353	+	1.59713i	−0.534687	+	0.147655i
$118$		0			0
$119$	9.17574	−	6.31518i	0.841138	−	0.578911i
$120$		0			0
$121$	−8.27492	+	14.3326i	−0.752265	+	1.30296i
$122$		0			0
$123$	−16.7553	+	2.27100i	−1.51077	+	0.204769i
$124$		0			0
$125$			6.40740i			0.573095i
$126$		0			0
$127$		−	0.418627i		−	0.0371471i	−0.999827	−	0.0185736i	$-0.994088\pi$
$127$		−	0.418627i		−	0.0371471i	0.999827	−	0.0185736i	$-0.00591249\pi$
$128$		0			0
$129$	−16.3999	+	2.22282i	−1.44393	+	0.195709i
$130$		0			0
$131$	2.62440	−	4.54559i	0.229295	−	0.397150i	−0.728305	−	0.685253i	$-0.759691\pi$
$131$	2.62440	−	4.54559i	0.229295	−	0.397150i	0.957599	+	0.288104i	$0.0930247\pi$
$132$		0			0
$133$	3.13746	+	1.49397i	0.272052	+	0.129543i
$134$		0			0
$135$	0.415433	−	3.46149i	0.0357547	−	0.297917i
$136$		0			0
$137$	13.2624	−	7.65706i	1.13309	−	0.654187i	0.188376	−	0.982097i	$-0.439678\pi$
$137$	13.2624	−	7.65706i	1.13309	−	0.654187i	0.944709	+	0.327910i	$0.106344\pi$
$138$		0			0
$139$		−	13.9715i		−	1.18505i	−0.805553	−	0.592523i	$-0.798132\pi$
$139$		−	13.9715i		−	1.18505i	0.805553	−	0.592523i	$-0.201868\pi$
$140$		0			0
$141$	15.4124	+	6.31518i	1.29796	+	0.531834i
$142$		0			0
$143$	−5.24879	−	9.09118i	−0.438926	−	0.760242i
$144$		0			0
$145$	2.08762	−	3.61587i	0.173368	−	0.300282i
$146$		0			0
$147$	−3.50310	−	11.6073i	−0.288931	−	0.957350i
$148$		0			0
$149$	−12.1003	−	6.98612i	−0.991296	−	0.572325i	−0.0856347	−	0.996327i	$-0.527292\pi$
$149$	−12.1003	−	6.98612i	−0.991296	−	0.572325i	−0.905662	+	0.424001i	$0.860625\pi$
$150$		0			0
$151$	−6.77492	+	3.91150i	−0.551335	+	0.318313i	−0.749660	−	0.661823i	$-0.769783\pi$
$151$	−6.77492	+	3.91150i	−0.551335	+	0.318313i	0.198325	+	0.980136i	$0.436450\pi$
$152$		0			0
$153$	8.86254	−	8.99895i	0.716494	−	0.727522i
$154$		0			0
$155$	1.16211			0.0933428
$156$		0			0
$157$	11.6873	+	20.2430i	0.932748	+	1.61557i	0.778602	+	0.627518i	$0.215929\pi$
$157$	11.6873	+	20.2430i	0.932748	+	1.61557i	0.154145	+	0.988048i	$0.450738\pi$
$158$		0			0
$159$	−12.4773	−	16.1328i	−0.989512	−	1.27941i
$160$		0			0
$161$	−3.64607	+	7.65706i	−0.287350	+	0.603461i
$162$		0			0
$163$	−1.86254	−	1.07534i	−0.145886	−	0.0842270i	0.425281	−	0.905062i	$-0.360175\pi$
$163$	−1.86254	−	1.07534i	−0.145886	−	0.0842270i	−0.571166	+	0.820835i	$0.693509\pi$
$164$		0			0
$165$	6.04440	−	0.819253i	0.470556	−	0.0637787i
$166$		0			0
$167$	−20.9952			−1.62466			−0.812328	−	0.583201i	$-0.801800\pi$
$167$	−20.9952			−1.62466			−0.812328	+	0.583201i	$0.801800\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	3.81369	+	0.990722i	0.291640	+	0.0757624i
$172$		0			0
$173$	−14.4245	−	8.32801i	−1.09668	−	0.633167i	−0.161331	−	0.986900i	$-0.551579\pi$
$173$	−14.4245	−	8.32801i	−1.09668	−	0.633167i	−0.935346	+	0.353734i	$0.884912\pi$
$174$		0			0
$175$	6.82475	+	9.91613i	0.515903	+	0.749589i
$176$		0			0
$177$	10.3757	−	8.02470i	0.779887	−	0.603174i
$178$		0			0
$179$	−8.01363	−	13.8800i	−0.598967	−	1.03744i	−0.992974	−	0.118333i	$-0.962245\pi$
$179$	−8.01363	−	13.8800i	−0.598967	−	1.03744i	0.394007	−	0.919107i	$-0.371088\pi$
$180$		0			0
$181$	−15.0997			−1.12235			−0.561175	−	0.827697i	$-0.689650\pi$
$181$	−15.0997			−1.12235			−0.561175	+	0.827697i	$0.689650\pi$
$182$		0			0
$183$	−5.97029	−	2.44631i	−0.441336	−	0.180836i
$184$		0			0
$185$	−3.64607	+	2.10506i	−0.268064	+	0.154767i
$186$		0			0
$187$	19.1375	+	11.0490i	1.39947	+	0.807984i
$188$		0			0
$189$	−6.38923	−	12.1728i	−0.464748	−	0.885443i
$190$		0			0
$191$	5.97029	−	10.3408i	0.431995	−	0.748237i	−0.565050	−	0.825056i	$-0.691143\pi$
$191$	5.97029	−	10.3408i	0.431995	−	0.748237i	0.997045	+	0.0768197i	$0.0244766\pi$
$192$		0			0
$193$	9.04983	+	15.6748i	0.651421	+	1.12829i	0.982778	+	0.184789i	$0.0591603\pi$
$193$	9.04983	+	15.6748i	0.651421	+	1.12829i	−0.331357	+	0.943506i	$0.607506\pi$
$194$		0			0
$195$	−0.881234	+	2.15068i	−0.0631065	+	0.154013i
$196$		0			0
$197$		−	7.07835i		−	0.504311i	−0.967687	−	0.252156i	$-0.918861\pi$
$197$		−	7.07835i		−	0.504311i	0.967687	−	0.252156i	$-0.0811395\pi$
$198$		0			0
$199$	−22.1375	+	12.7811i	−1.56928	+	0.906026i	−0.573030	+	0.819534i	$0.694232\pi$
$199$	−22.1375	+	12.7811i	−1.56928	+	0.906026i	−0.996253	+	0.0864917i	$0.972434\pi$
$200$		0			0
$201$	−3.16615	−	4.09374i	−0.223323	−	0.288750i
$202$		0			0
$203$	−1.30255	−	16.4128i	−0.0914208	−	1.15195i
$204$		0			0
$205$	−3.27492	+	5.67232i	−0.228730	+	0.396172i
$206$		0			0
$207$	−2.41789	+	9.30742i	−0.168055	+	0.646910i
$208$		0			0
$209$			6.89389i			0.476860i
$210$		0			0
$211$		−	15.6460i		−	1.07712i	−0.842589	−	0.538558i	$-0.818969\pi$
$211$		−	15.6460i		−	1.07712i	0.842589	−	0.538558i	$-0.181031\pi$
$212$		0			0
$213$	−0.950700	−	7.01421i	−0.0651409	−	0.480606i
$214$		0			0
$215$	−3.20545	+	5.55200i	−0.218610	+	0.378644i
$216$		0			0
$217$	3.77492	−	2.59808i	0.256258	−	0.176369i
$218$		0			0
$219$	−0.376662	+	0.291315i	−0.0254525	+	0.0196852i
$220$		0			0
$221$	−7.29214	+	4.21012i	−0.490522	+	0.283203i
$222$		0			0
$223$			11.7633i			0.787727i	0.919169	+	0.393864i	$0.128862\pi$
$223$			11.7633i			0.787727i	−0.919169	+	0.393864i	$0.871138\pi$
$224$		0			0
$225$	9.72508	+	9.57767i	0.648339	+	0.638511i
$226$		0			0
$227$	3.50563	+	6.07193i	0.232677	+	0.403008i	0.958595	−	0.284773i	$-0.0919182\pi$
$227$	3.50563	+	6.07193i	0.232677	+	0.403008i	−0.725918	+	0.687781i	$0.758585\pi$
$228$		0			0
$229$	−8.13746	+	14.0945i	−0.537738	+	0.931390i	0.461287	+	0.887251i	$0.347388\pi$
$229$	−8.13746	+	14.0945i	−0.537738	+	0.931390i	−0.999025	+	0.0441392i	$0.985945\pi$
$230$		0			0
$231$	17.8027	−	16.1744i	1.17133	−	1.06420i
$232$		0			0
$233$	13.2624	+	7.65706i	0.868850	+	0.501631i	0.866966	−	0.498367i	$-0.166067\pi$
$233$	13.2624	+	7.65706i	0.868850	+	0.501631i	0.00188417	+	0.999998i	$0.499400\pi$
$234$		0			0
$235$	5.58762	−	3.22602i	0.364496	−	0.210442i
$236$		0			0
$237$	−3.41238	+	8.32801i	−0.221658	+	0.540962i
$238$		0			0
$239$	8.73512			0.565028			0.282514	−	0.959263i	$-0.408832\pi$
$239$	8.73512			0.565028			0.282514	+	0.959263i	$0.408832\pi$
$240$		0			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$		0			0
$243$	−9.72402	−	12.1837i	−0.623796	−	0.781587i
$244$		0			0
$245$	−4.38686	−	1.67736i	−0.280266	−	0.107163i
$246$		0			0
$247$	−2.27492	−	1.31342i	−0.144750	−	0.0835712i
$248$		0			0
$249$	−0.475350	−	3.50711i	−0.0301241	−	0.222254i
$250$		0			0
$251$	10.7785			0.680331			0.340165	−	0.940366i	$-0.389517\pi$
$251$	10.7785			0.680331			0.340165	+	0.940366i	$0.389517\pi$
$252$		0			0
$253$	−16.8248			−1.05776
$254$		0			0
$255$	−0.657132	−	4.84828i	−0.0411512	−	0.303611i
$256$		0			0
$257$	19.3924	+	11.1962i	1.20967	+	0.698402i	0.962687	−	0.270618i	$-0.0872281\pi$
$257$	19.3924	+	11.1962i	1.20967	+	0.698402i	0.246981	+	0.969020i	$0.420561\pi$
$258$		0			0
$259$	−7.13746	+	14.9893i	−0.443500	+	0.931389i
$260$		0			0
$261$	−4.96942	−	17.9953i	−0.307600	−	1.11388i
$262$		0			0
$263$	9.17574	+	15.8928i	0.565800	+	0.979995i	0.996975	+	0.0777261i	$0.0247660\pi$
$263$	9.17574	+	15.8928i	0.565800	+	0.979995i	−0.431175	+	0.902269i	$0.641901\pi$
$264$		0			0
$265$	−7.90033			−0.485313
$266$		0			0
$267$	−9.17574	+	22.3937i	−0.561546	+	1.37047i
$268$		0			0
$269$	−0.581054	+	0.335472i	−0.0354275	+	0.0204541i	−0.517609	−	0.855617i	$-0.673178\pi$
$269$	−0.581054	+	0.335472i	−0.0354275	+	0.0204541i	0.482182	+	0.876071i	$0.339845\pi$
$270$		0			0
$271$	18.0498	+	10.4211i	1.09645	+	0.633035i	0.935286	−	0.353892i	$-0.115142\pi$
$271$	18.0498	+	10.4211i	1.09645	+	0.633035i	0.161163	+	0.986928i	$0.448475\pi$
$272$		0			0
$273$	1.94564	+	8.95625i	0.117755	+	0.542057i
$274$		0			0
$275$	−11.9406	+	20.6817i	−0.720044	+	1.24715i
$276$		0			0
$277$	−2.86254	−	4.95807i	−0.171993	−	0.297901i	0.767123	−	0.641500i	$-0.221687\pi$
$277$	−2.86254	−	4.95807i	−0.171993	−	0.297901i	−0.939117	+	0.343598i	$0.888354\pi$
$278$		0			0
$279$	3.64607	−	3.70219i	0.218284	−	0.221644i
$280$		0			0
$281$		−	2.68378i		−	0.160101i	−0.996791	−	0.0800503i	$-0.974492\pi$
$281$		−	2.68378i		−	0.160101i	0.996791	−	0.0800503i	$-0.0255081\pi$
$282$		0			0
$283$	16.2371	−	9.37451i	0.965197	−	0.557257i	0.0674284	−	0.997724i	$-0.478521\pi$
$283$	16.2371	−	9.37451i	0.965197	−	0.557257i	0.897769	+	0.440467i	$0.145187\pi$
$284$		0			0
$285$	1.20737	−	0.933795i	0.0715185	−	0.0553132i
$286$		0			0
$287$	2.04334	+	25.7472i	0.120615	+	1.51981i
$288$		0			0
$289$	0.362541	−	0.627940i	0.0213260	−	0.0369377i
$290$		0			0
$291$	0.761855	+	5.62093i	0.0446608	+	0.329505i
$292$		0			0
$293$		−	23.0634i		−	1.34738i	−0.739014	−	0.673690i	$-0.764709\pi$
$293$		−	23.0634i		−	1.34738i	0.739014	−	0.673690i	$-0.235291\pi$
$294$		0			0
$295$		−	5.08106i		−	0.295831i
$296$		0			0
$297$	16.3541	−	21.8263i	0.948963	−	1.26649i
$298$		0			0
$299$	3.20545	−	5.55200i	0.185376	−	0.321081i
$300$		0			0
$301$	2.00000	+	25.2011i	0.115278	+	1.45256i
$302$		0			0
$303$	−3.03930	−	3.92974i	−0.174604	−	0.225758i
$304$		0			0
$305$	−2.16448	+	1.24966i	−0.123938	+	0.0715554i
$306$		0			0
$307$		−	17.3205i		−	0.988534i	−0.869310	−	0.494267i	$-0.835437\pi$
$307$		−	17.3205i		−	0.988534i	0.869310	−	0.494267i	$-0.164563\pi$
$308$		0			0
$309$	11.1375	−	27.1813i	0.633588	−	1.54629i
$310$		0			0
$311$	2.48396	+	4.30234i	0.140852	+	0.243964i	0.927818	−	0.373034i	$-0.121682\pi$
$311$	2.48396	+	4.30234i	0.140852	+	0.243964i	−0.786965	+	0.616997i	$0.788349\pi$
$312$		0			0
$313$	9.77492	−	16.9307i	0.552511	−	0.956977i	−0.445582	−	0.895241i	$-0.647003\pi$
$313$	9.77492	−	16.9307i	0.552511	−	0.956977i	0.998093	−	0.0617357i	$-0.0196636\pi$
$314$		0			0
$315$	−5.24414	−	0.927030i	−0.295474	−	0.0522322i
$316$		0			0
$317$	7.87319	+	4.54559i	0.442202	+	0.255306i	0.704531	−	0.709673i	$-0.251157\pi$
$317$	7.87319	+	4.54559i	0.442202	+	0.255306i	−0.262329	+	0.964979i	$0.584491\pi$
$318$		0			0
$319$	28.2870	−	16.3315i	1.58377	−	0.914388i
$320$		0			0
$321$	18.6873	+	7.65706i	1.04302	+	0.427376i
$322$		0			0
$323$	5.52967			0.307679
$324$		0			0
$325$	−4.54983	−	7.88054i	−0.252379	−	0.437134i
$326$		0			0
$327$	−20.3113	+	15.7090i	−1.12322	+	0.868708i
$328$		0			0
$329$	10.9382	−	22.9712i	0.603043	−	1.26644i
$330$		0			0
$331$	1.96221	+	1.13288i	0.107853	+	0.0622689i	0.552956	−	0.833210i	$-0.313500\pi$
$331$	1.96221	+	1.13288i	0.107853	+	0.0622689i	−0.445103	+	0.895479i	$0.646833\pi$
$332$		0			0
$333$	−4.73320	+	18.2200i	−0.259378	+	0.998449i
$334$		0			0
$335$	−2.00473			−0.109530
$336$		0			0
$337$	1.82475			0.0994006			0.0497003	−	0.998764i	$-0.484173\pi$
$337$	1.82475			0.0994006			0.0497003	+	0.998764i	$0.484173\pi$
$338$		0			0
$339$	16.7553	−	2.27100i	0.910022	−	0.123344i
$340$		0			0
$341$	7.87319	+	4.54559i	0.426357	+	0.246157i
$342$		0			0
$343$	−18.0000	+	4.35890i	−0.971909	+	0.235358i
$344$		0			0
$345$	2.27895	+	2.94663i	0.122695	+	0.158641i
$346$		0			0
$347$	2.48396	+	4.30234i	0.133346	+	0.230962i	0.924964	−	0.380054i	$-0.124095\pi$
$347$	2.48396	+	4.30234i	0.133346	+	0.230962i	−0.791618	+	0.611016i	$0.790761\pi$
$348$		0			0
$349$	20.5498			1.10001			0.550004	−	0.835162i	$-0.314626\pi$
$349$	20.5498			1.10001			0.550004	+	0.835162i	$0.314626\pi$
$350$		0			0
$351$	4.08668	+	9.55505i	0.218131	+	0.510011i
$352$		0			0
$353$	−3.64607	+	2.10506i	−0.194061	+	0.112041i	−0.593882	−	0.804552i	$-0.702405\pi$
$353$	−3.64607	+	2.10506i	−0.194061	+	0.112041i	0.399821	+	0.916593i	$0.369072\pi$
$354$		0			0
$355$	−2.37459	−	1.37097i	−0.126030	−	0.0727634i
$356$		0			0
$357$	−12.9737	−	14.2797i	−0.686640	−	0.755763i
$358$		0			0
$359$	14.1437	−	24.4975i	0.746474	−	1.29293i	−0.203030	−	0.979173i	$-0.565079\pi$
$359$	14.1437	−	24.4975i	0.746474	−	1.29293i	0.949503	−	0.313758i	$-0.101588\pi$
$360$		0			0
$361$	−8.63746	−	14.9605i	−0.454603	−	0.787396i
$362$		0			0
$363$	26.5248	+	10.8685i	1.39219	+	0.570447i
$364$		0			0
$365$			0.184454i			0.00965476i
$366$		0			0
$367$	−4.59967	+	2.65562i	−0.240101	+	0.138622i	−0.615223	−	0.788353i	$-0.710934\pi$
$367$	−4.59967	+	2.65562i	−0.240101	+	0.138622i	0.375122	+	0.926975i	$0.377601\pi$
$368$		0			0
$369$	7.79568	+	28.2297i	0.405827	+	1.46958i
$370$		0			0
$371$	−25.6629	+	17.6624i	−1.33235	+	0.916988i
$372$		0			0
$373$	−3.58762	+	6.21395i	−0.185760	+	0.321746i	−0.943832	−	0.330425i	$-0.892808\pi$
$373$	−3.58762	+	6.21395i	−0.185760	+	0.321746i	0.758072	+	0.652171i	$0.226141\pi$
$374$		0			0
$375$	10.9974	−	1.49058i	0.567903	−	0.0769730i
$376$		0			0
$377$			12.4459i			0.640996i
$378$		0			0
$379$		−	10.3923i		−	0.533817i	−0.963722	−	0.266908i	$-0.913998\pi$
$379$		−	10.3923i		−	0.533817i	0.963722	−	0.266908i	$-0.0860021\pi$
$380$		0			0
$381$	−0.718513	+	0.0973866i	−0.0368105	+	0.00498927i
$382$		0			0
$383$	3.92694	−	6.80166i	0.200657	−	0.347549i	−0.748083	−	0.663605i	$-0.769026\pi$
$383$	3.92694	−	6.80166i	0.200657	−	0.347549i	0.948740	+	0.316056i	$0.102359\pi$
$384$		0			0
$385$	−0.737127	−	9.28819i	−0.0375675	−	0.473370i
$386$		0			0
$387$	7.63032	+	27.6309i	0.387871	+	1.40456i
$388$		0			0
$389$	−9.77610	+	5.64423i	−0.495668	+	0.286174i	−0.726923	−	0.686719i	$-0.759050\pi$
$389$	−9.77610	+	5.64423i	−0.495668	+	0.286174i	0.231255	+	0.972893i	$0.425717\pi$
$390$		0			0
$391$			13.4953i			0.682488i
$392$		0			0
$393$	−8.41238	−	3.44695i	−0.424348	−	0.173875i
$394$		0			0
$395$	1.74316	+	3.01925i	0.0877081	+	0.151915i
$396$		0			0
$397$	15.6873	−	27.1712i	0.787323	−	1.36368i	−0.140279	−	0.990112i	$-0.544800\pi$
$397$	15.6873	−	27.1712i	0.787323	−	1.36368i	0.927602	−	0.373571i	$-0.121867\pi$
$398$		0			0
$399$	1.83430	−	5.73255i	0.0918299	−	0.286986i
$400$		0			0
$401$	1.00237	+	0.578717i	0.0500558	+	0.0288997i	0.524819	−	0.851214i	$-0.324133\pi$
$401$	1.00237	+	0.578717i	0.0500558	+	0.0288997i	−0.474763	+	0.880114i	$0.657466\pi$
$402$		0			0
$403$	−3.00000	+	1.73205i	−0.149441	+	0.0862796i
$404$		0			0
$405$	−6.03779	+	0.0922270i	−0.300020	+	0.00458280i
$406$		0			0
$407$	−32.9357			−1.63256
$408$		0			0
$409$	15.7749	+	27.3230i	0.780019	+	1.35103i	0.931930	+	0.362639i	$0.118124\pi$
$409$	15.7749	+	27.3230i	0.780019	+	1.35103i	−0.151910	+	0.988394i	$0.548542\pi$
$410$		0			0
$411$	−16.2275	−	20.9818i	−0.800445	−	1.03495i
$412$		0			0
$413$	−11.3595	−	16.5050i	−0.558965	−	0.812158i
$414$		0			0
$415$	−1.18729	−	0.685484i	−0.0582819	−	0.0336491i
$416$		0			0
$417$	−23.9801	+	3.25024i	−1.17431	+	0.159165i
$418$		0			0
$419$	34.3787			1.67951			0.839755	−	0.542965i	$-0.182698\pi$
$419$	34.3787			1.67951			0.839755	+	0.542965i	$0.182698\pi$
$420$		0			0
$421$	−19.0997			−0.930861			−0.465430	−	0.885084i	$-0.654100\pi$
$421$	−19.0997			−0.930861			−0.465430	+	0.885084i	$0.654100\pi$
$422$		0			0
$423$	7.25366	−	27.9223i	0.352685	−	1.35763i
$424$		0			0
$425$	16.5890	+	9.57767i	0.804685	+	0.464585i
$426$		0			0
$427$	−4.23713	+	8.89834i	−0.205049	+	0.430621i
$428$		0			0
$429$	−14.3827	+	11.1237i	−0.694401	+	0.537058i
$430$		0			0
$431$	0.721492	+	1.24966i	0.0347530	+	0.0601940i	0.882879	−	0.469601i	$-0.155602\pi$
$431$	0.721492	+	1.24966i	0.0347530	+	0.0601940i	−0.848126	+	0.529795i	$0.822269\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	−6.69178	−	2.74194i	−0.320846	−	0.131466i
$436$		0			0
$437$	−3.64607	+	2.10506i	−0.174415	+	0.100699i
$438$		0			0
$439$	−14.3248	−	8.27040i	−0.683683	−	0.394725i	0.117558	−	0.993066i	$-0.462493\pi$
$439$	−14.3248	−	8.27040i	−0.683683	−	0.394725i	−0.801241	+	0.598341i	$0.795827\pi$
$440$		0			0
$441$	−19.1073	+	8.71280i	−0.909869	+	0.414895i
$442$		0			0
$443$	2.90527	−	5.03208i	0.138034	−	0.239081i	−0.788719	−	0.614754i	$-0.789255\pi$
$443$	2.90527	−	5.03208i	0.138034	−	0.239081i	0.926752	+	0.375673i	$0.122588\pi$
$444$		0			0
$445$	4.68729	+	8.11863i	0.222199	+	0.384860i
$446$		0			0
$447$	−9.17574	+	22.3937i	−0.433997	+	1.05918i
$448$		0			0
$449$		−	15.1297i		−	0.714013i	−0.934102	−	0.357007i	$-0.883797\pi$
$449$		−	15.1297i		−	0.714013i	0.934102	−	0.357007i	$-0.116203\pi$
$450$		0			0
$451$	−44.3746	+	25.6197i	−2.08952	+	1.20638i
$452$		0			0
$453$	8.28960	+	10.7182i	0.389480	+	0.503586i
$454$		0			0
$455$	3.20545	+	1.52634i	0.150274	+	0.0715560i
$456$		0			0
$457$	8.32475	−	14.4189i	0.389415	−	0.674487i	−0.602956	−	0.797775i	$-0.706010\pi$
$457$	8.32475	−	14.4189i	0.389415	−	0.674487i	0.992371	+	0.123287i	$0.0393437\pi$
$458$		0			0
$459$	−17.5071	−	13.1178i	−0.817163	−	0.612288i
$460$		0			0
$461$			12.4459i			0.579663i	0.957078	+	0.289832i	$0.0935993\pi$
$461$			12.4459i			0.579663i	−0.957078	+	0.289832i	$0.906401\pi$
$462$		0			0
$463$		−	20.8997i		−	0.971291i	−0.874156	−	0.485646i	$-0.838585\pi$
$463$		−	20.8997i		−	0.971291i	0.874156	−	0.485646i	$-0.161415\pi$
$464$		0			0
$465$	−0.270345	−	1.99459i	−0.0125370	−	0.0924971i
$466$		0			0
$467$	3.92694	−	6.80166i	0.181717	−	0.314744i	−0.760748	−	0.649047i	$-0.775168\pi$
$467$	3.92694	−	6.80166i	0.181717	−	0.314744i	0.942465	+	0.334304i	$0.108501\pi$
$468$		0			0
$469$	−6.51204	+	4.48190i	−0.300698	+	0.206955i
$470$		0			0
$471$	32.0253	−	24.7688i	1.47565	−	1.14128i
$472$		0			0
$473$	−43.4333	+	25.0762i	−1.99707	+	1.15301i
$474$		0			0
$475$			5.97586i			0.274191i
$476$		0			0
$477$	−24.7870	+	25.1685i	−1.13492	+	1.15239i
$478$		0			0
$479$	−16.4679	−	28.5232i	−0.752436	−	1.30326i	−0.946639	−	0.322296i	$-0.895545\pi$
$479$	−16.4679	−	28.5232i	−0.752436	−	1.30326i	0.194202	−	0.980961i	$-0.437788\pi$
$480$		0			0
$481$	6.27492	−	10.8685i	0.286112	−	0.495560i
$482$		0			0
$483$	13.9905	+	4.47667i	0.636588	+	0.203695i
$484$		0			0
$485$	1.90290	+	1.09864i	0.0864065	+	0.0498868i
$486$		0			0
$487$	9.77492	−	5.64355i	0.442944	−	0.255734i	−0.261902	−	0.965095i	$-0.584350\pi$
$487$	9.77492	−	5.64355i	0.442944	−	0.255734i	0.704846	+	0.709361i	$0.251016\pi$
$488$		0			0
$489$	−1.41238	+	3.44695i	−0.0638698	+	0.155876i
$490$		0			0
$491$	−6.69178			−0.301996			−0.150998	−	0.988534i	$-0.548249\pi$
$491$	−6.69178			−0.301996			−0.150998	+	0.988534i	$0.548249\pi$
$492$		0			0
$493$	−13.0997	−	22.6893i	−0.589979	−	1.02187i
$494$		0			0
$495$	−2.81226	−	10.1838i	−0.126402	−	0.457726i
$496$		0			0
$497$	−10.7785	+	0.855398i	−0.483480	+	0.0383698i
$498$		0			0
$499$	−3.31271	−	1.91259i	−0.148297	−	0.0856194i	0.424015	−	0.905655i	$-0.360620\pi$
$499$	−3.31271	−	1.91259i	−0.148297	−	0.0856194i	−0.572313	+	0.820036i	$0.693954\pi$
$500$		0			0
$501$	4.88418	+	36.0352i	0.218209	+	1.60993i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	−1.92442			−0.0856356
$506$		0			0
$507$	2.09370	+	15.4472i	0.0929845	+	0.686035i
$508$		0			0
$509$	10.1974	+	5.88748i	0.451992	+	0.260958i	0.708671	−	0.705539i	$-0.249295\pi$
$509$	10.1974	+	5.88748i	0.451992	+	0.260958i	−0.256679	+	0.966497i	$0.582628\pi$
$510$		0			0
$511$	0.412376	+	0.599168i	0.0182424	+	0.0265056i
$512$		0			0
$513$	0.813241	−	6.77613i	0.0359055	−	0.299173i
$514$		0			0
$515$	−5.68941	−	9.85435i	−0.250705	−	0.434234i
$516$		0			0
$517$	50.4743			2.21986
$518$		0			0
$519$	−10.9382	+	26.6950i	−0.480134	+	1.17178i
$520$		0			0
$521$	27.8467	−	16.0773i	1.21999	−	0.704359i	0.255071	−	0.966922i	$-0.417901\pi$
$521$	27.8467	−	16.0773i	1.21999	−	0.704359i	0.964915	+	0.262563i	$0.0845678\pi$
$522$		0			0
$523$	−4.96221	−	2.86493i	−0.216982	−	0.125275i	0.387570	−	0.921840i	$-0.373315\pi$
$523$	−4.96221	−	2.86493i	−0.216982	−	0.125275i	−0.604552	+	0.796566i	$0.706648\pi$
$524$		0			0
$525$	15.4320	−	14.0205i	0.673506	−	0.611906i
$526$		0			0
$527$	3.64607	−	6.31518i	0.158825	−	0.275093i
$528$		0			0
$529$	6.36254	+	11.0202i	0.276632	+	0.479141i
$530$		0			0
$531$	−16.1870	−	15.9416i	−0.702456	−	0.691808i
$532$		0			0
$533$		−	19.5242i		−	0.845689i
$534$		0			0
$535$	6.77492	−	3.91150i	0.292905	−	0.169109i
$536$		0			0
$537$	−21.9588	+	16.9832i	−0.947593	+	0.732879i
$538$		0			0
$539$	−23.1597	−	28.5232i	−0.997557	−	1.22858i
$540$		0			0
$541$	17.1375	−	29.6829i	0.736797	−	1.27617i	−0.217134	−	0.976142i	$-0.569671\pi$
$541$	17.1375	−	29.6829i	0.736797	−	1.27617i	0.953930	−	0.300028i	$-0.0969959\pi$
$542$		0			0
$543$	3.51269	+	25.9164i	0.150744	+	1.11218i
$544$		0			0
$545$			9.94658i			0.426064i
$546$		0			0
$547$		−	4.30136i		−	0.183913i	−0.995763	−	0.0919563i	$-0.970688\pi$
$547$		−	4.30136i		−	0.183913i	0.995763	−	0.0919563i	$-0.0293120\pi$
$548$		0			0
$549$	−2.80985	+	10.8162i	−0.119921	+	0.461626i
$550$		0			0
$551$	4.08668	−	7.07835i	0.174099	−	0.301548i
$552$		0			0
$553$	12.4124	+	5.91041i	0.527828	+	0.251336i
$554$		0			0
$555$	4.46123	+	5.76825i	0.189369	+	0.244848i
$556$		0			0
$557$	−19.8138	+	11.4395i	−0.839536	+	0.484706i	−0.857106	−	0.515139i	$-0.827740\pi$
$557$	−19.8138	+	11.4395i	−0.839536	+	0.484706i	0.0175705	+	0.999846i	$0.494407\pi$
$558$		0			0
$559$		−	19.1101i		−	0.808271i
$560$		0			0
$561$	14.5120	−	35.4171i	0.612699	−	1.49531i
$562$		0			0
$563$	−15.1653	−	26.2671i	−0.639142	−	1.10703i	−0.985621	−	0.168969i	$-0.945956\pi$
$563$	−15.1653	−	26.2671i	−0.639142	−	1.10703i	0.346479	−	0.938058i	$-0.387377\pi$
$564$		0			0
$565$	3.27492	−	5.67232i	0.137777	−	0.238636i
$566$		0			0
$567$	−19.4066	+	13.7980i	−0.814999	+	0.579462i
$568$		0			0
$569$	−27.5272	−	15.8928i	−1.15400	−	0.666263i	−0.204142	−	0.978941i	$-0.565440\pi$
$569$	−27.5272	−	15.8928i	−1.15400	−	0.666263i	−0.949859	+	0.312679i	$0.898774\pi$
$570$		0			0
$571$	10.9622	−	6.32904i	0.458754	−	0.264862i	−0.252766	−	0.967527i	$-0.581340\pi$
$571$	10.9622	−	6.32904i	0.458754	−	0.264862i	0.711520	+	0.702666i	$0.248007\pi$
$572$		0			0
$573$	−19.1375	−	7.84152i	−0.799479	−	0.327584i
$574$		0			0
$575$	−14.5843			−0.608206
$576$		0			0
$577$	1.95017	+	3.37779i	0.0811865	+	0.140619i	0.903760	−	0.428040i	$-0.140796\pi$
$577$	1.95017	+	3.37779i	0.0811865	+	0.140619i	−0.822573	+	0.568659i	$0.807462\pi$
$578$		0			0
$579$	24.7982	−	19.1792i	1.03058	−	0.797061i
$580$		0			0
$581$	−5.38923	+	0.427699i	−0.223583	+	0.0177439i
$582$		0			0
$583$	−53.5241	−	30.9021i	−2.21674	−	1.27984i
$584$		0			0
$585$	3.89634	+	1.01219i	0.161094	+	0.0418490i
$586$		0			0
$587$	−2.04334			−0.0843378			−0.0421689	−	0.999110i	$-0.513427\pi$
$587$	−2.04334			−0.0843378			−0.0421689	+	0.999110i	$0.513427\pi$
$588$		0			0
$589$	2.27492			0.0937363
$590$		0			0
$591$	−12.1490	+	1.64666i	−0.499742	+	0.0677346i
$592$		0			0
$593$	2.48396	+	1.43411i	0.102004	+	0.0588920i	0.550134	−	0.835076i	$-0.314577\pi$
$593$	2.48396	+	1.43411i	0.102004	+	0.0588920i	−0.448130	+	0.893968i	$0.647910\pi$
$594$		0			0
$595$	−7.45017	+	0.591258i	−0.305427	+	0.0242392i
$596$		0			0
$597$	27.0868	+	35.0225i	1.10859	+	1.43337i
$598$		0			0
$599$	13.2624	+	22.9712i	0.541888	+	0.938577i	0.998796	+	0.0490632i	$0.0156236\pi$
$599$	13.2624	+	22.9712i	0.541888	+	0.938577i	−0.456908	+	0.889514i	$0.651043\pi$
$600$		0			0
$601$	−34.9244			−1.42460			−0.712298	−	0.701877i	$-0.752346\pi$
$601$	−34.9244			−1.42460			−0.712298	+	0.701877i	$0.752346\pi$
$602$		0			0
$603$	−6.28977	+	6.38658i	−0.256139	+	0.260082i
$604$		0			0
$605$	9.61635	−	5.55200i	0.390960	−	0.225721i
$606$		0			0
$607$	14.9502	+	8.63148i	0.606809	+	0.350341i	0.771715	−	0.635968i	$-0.219399\pi$
$607$	14.9502	+	8.63148i	0.606809	+	0.350341i	−0.164907	+	0.986309i	$0.552732\pi$
$608$		0			0
$609$	−27.8672	+	6.05379i	−1.12923	+	0.245312i
$610$		0			0
$611$	−9.61635	+	16.6560i	−0.389036	+	0.673830i
$612$		0			0
$613$	−7.58762	−	13.1422i	−0.306461	−	0.530806i	0.671124	−	0.741345i	$-0.265812\pi$
$613$	−7.58762	−	13.1422i	−0.306461	−	0.530806i	−0.977586	+	0.210538i	$0.932478\pi$
$614$		0			0
$615$	10.4976	+	4.30136i	0.423304	+	0.173447i
$616$		0			0
$617$		−	23.9188i		−	0.962935i	−0.876464	−	0.481468i	$-0.840104\pi$
$617$		−	23.9188i		−	0.962935i	0.876464	−	0.481468i	$-0.159896\pi$
$618$		0			0
$619$	16.9622	−	9.79314i	0.681769	−	0.393619i	−0.118752	−	0.992924i	$-0.537889\pi$
$619$	16.9622	−	9.79314i	0.681769	−	0.393619i	0.800521	+	0.599305i	$0.204556\pi$
$620$		0			0
$621$	16.5373	+	1.98474i	0.663621	+	0.0796449i
$622$		0			0
$623$	33.3764	+	15.8928i	1.33720	+	0.636733i
$624$		0			0
$625$	−9.22508	+	15.9783i	−0.369003	+	0.639132i
$626$		0			0
$627$	11.8324	−	1.60375i	0.472540	−	0.0640476i
$628$		0			0
$629$			26.4181i			1.05336i
$630$		0			0
$631$			28.3616i			1.12906i	0.825413	+	0.564529i	$0.190942\pi$
$631$			28.3616i			1.12906i	−0.825413	+	0.564529i	$0.809058\pi$
$632$		0			0
$633$	−26.8541	+	3.63978i	−1.06736	+	0.144668i
$634$		0			0
$635$	−0.140438	+	0.243245i	−0.00557309	+	0.00965288i
$636$		0			0
$637$	13.8248	−	2.20822i	0.547757	−	0.0874929i
$638$		0			0
$639$	−11.8177	+	3.26348i	−0.467502	+	0.129101i
$640$		0			0
$641$	−12.1003	+	6.98612i	−0.477934	+	0.275935i	−0.719555	−	0.694436i	$-0.755654\pi$
$641$	−12.1003	+	6.98612i	−0.477934	+	0.275935i	0.241621	+	0.970371i	$0.422321\pi$
$642$		0			0
$643$			2.62685i			0.103593i	0.998658	+	0.0517964i	$0.0164947\pi$
$643$			2.62685i			0.103593i	−0.998658	+	0.0517964i	$0.983505\pi$
$644$		0			0
$645$	10.2749	+	4.21012i	0.404574	+	0.165773i
$646$		0			0
$647$	15.3058	+	26.5104i	0.601732	+	1.04223i	0.992559	+	0.121766i	$0.0388557\pi$
$647$	15.3058	+	26.5104i	0.601732	+	1.04223i	−0.390827	+	0.920464i	$0.627811\pi$
$648$		0			0
$649$	19.8746	−	34.4238i	0.780146	−	1.35125i
$650$		0			0
$651$	−5.33740	−	5.87471i	−0.209189	−	0.230248i
$652$		0			0
$653$	29.4301	+	16.9915i	1.15169	+	0.664928i	0.949298	−	0.314377i	$-0.101795\pi$
$653$	29.4301	+	16.9915i	1.15169	+	0.664928i	0.202391	+	0.979305i	$0.435129\pi$
$654$		0			0
$655$	−3.04983	+	1.76082i	−0.119167	+	0.0688010i
$656$		0			0
$657$	0.587624	+	0.578717i	0.0229254	+	0.0225779i
$658$		0			0
$659$	33.2552			1.29544			0.647720	−	0.761879i	$-0.275723\pi$
$659$	33.2552			1.29544			0.647720	+	0.761879i	$0.275723\pi$
$660$		0			0
$661$	−10.8625	−	18.8145i	−0.422504	−	0.731798i	0.573680	−	0.819080i	$-0.305515\pi$
$661$	−10.8625	−	18.8145i	−0.422504	−	0.731798i	−0.996184	+	0.0872815i	$0.972182\pi$
$662$		0			0
$663$	8.92246	+	11.5365i	0.346520	+	0.448040i
$664$		0			0
$665$	−1.32185	−	1.92060i	−0.0512592	−	0.0744778i
$666$		0			0
$667$	17.2749	+	9.97368i	0.668887	+	0.386182i
$668$		0			0
$669$	20.1900	−	2.73653i	0.780590	−	0.105800i
$670$		0			0
$671$	−19.5522			−0.754804
$672$		0			0
$673$	4.72508			0.182139			0.0910693	−	0.995845i	$-0.470972\pi$
$673$	4.72508			0.182139			0.0910693	+	0.995845i	$0.470972\pi$
$674$		0			0
$675$	14.1763	−	18.9198i	0.545647	−	0.728223i
$676$		0			0
$677$	33.2359	+	19.1888i	1.27736	+	0.737484i	0.976362	−	0.216140i	$-0.0693469\pi$
$677$	33.2359	+	19.1888i	1.27736	+	0.737484i	0.300998	+	0.953625i	$0.402680\pi$
$678$		0			0
$679$	8.63746	−	0.685484i	0.331475	−	0.0263065i
$680$		0			0
$681$	9.60607	−	7.42945i	0.368106	−	0.284697i
$682$		0			0
$683$	18.3708	+	31.8191i	0.702938	+	1.21752i	0.967430	+	0.253137i	$0.0814623\pi$
$683$	18.3708	+	31.8191i	0.702938	+	1.21752i	−0.264492	+	0.964388i	$0.585204\pi$
$684$		0			0
$685$	−10.2749			−0.392584
$686$		0			0
$687$	26.0842	+	10.6879i	0.995175	+	0.407770i
$688$		0			0
$689$	20.3948	−	11.7750i	0.776981	−	0.448590i
$690$		0			0
$691$	7.23713	+	4.17836i	0.275313	+	0.158952i	0.631300	−	0.775539i	$-0.282522\pi$
$691$	7.23713	+	4.17836i	0.275313	+	0.158952i	−0.355986	+	0.934491i	$0.615855\pi$
$692$		0			0
$693$	−31.9026	−	26.7930i	−1.21188	−	1.01778i
$694$		0			0
$695$	−4.68704	+	8.11820i	−0.177790	+	0.307941i
$696$		0			0
$697$	20.5498	+	35.5934i	0.778380	+	1.34819i
$698$		0			0
$699$	10.0570	−	24.5443i	0.380390	−	0.928352i
$700$		0			0
$701$			8.90672i			0.336402i	0.985753	+	0.168201i	$0.0537958\pi$
$701$			8.90672i			0.336402i	−0.985753	+	0.168201i	$0.946204\pi$
$702$		0			0
$703$	−7.13746	+	4.12081i	−0.269194	+	0.155419i
$704$		0			0
$705$	−6.83686	−	8.83988i	−0.257491	−	0.332929i
$706$		0			0
$707$	−6.25116	+	4.30234i	−0.235099	+	0.161806i
$708$		0			0
$709$	−8.68729	+	15.0468i	−0.326258	+	0.565096i	−0.981766	−	0.190093i	$-0.939121\pi$
$709$	−8.68729	+	15.0468i	−0.326258	+	0.565096i	0.655508	+	0.755188i	$0.272455\pi$
$710$		0			0
$711$	15.0877	+	3.91948i	0.565832	+	0.146992i
$712$		0			0
$713$			5.55200i			0.207924i
$714$		0			0
$715$			7.04329i			0.263404i
$716$		0			0
$717$	−2.03208	−	14.9926i	−0.0758895	−	0.559908i
$718$		0			0
$719$	5.68941	−	9.85435i	0.212179	−	0.367505i	−0.740217	−	0.672368i	$-0.765277\pi$
$719$	5.68941	−	9.85435i	0.212179	−	0.367505i	0.952396	+	0.304863i	$0.0986106\pi$
$720$		0			0
$721$	−40.5120	−	19.2906i	−1.50875	−	0.718421i
$722$		0			0
$723$	−9.59064	+	7.41752i	−0.356680	+	0.275860i
$724$		0			0
$725$	24.5201	−	14.1567i	0.910654	−	0.525766i
$726$		0			0
$727$		−	32.5479i		−	1.20713i	−0.797312	−	0.603567i	$-0.793746\pi$
$727$		−	32.5479i		−	1.20713i	0.797312	−	0.603567i	$-0.206254\pi$
$728$		0			0
$729$	−18.6495	+	19.5242i	−0.690722	+	0.723120i
$730$		0			0
$731$	20.1139	+	34.8384i	0.743941	+	1.28854i
$732$		0			0
$733$	−12.8625	+	22.2786i	−0.475089	+	0.822878i	−0.999593	−	0.0285300i	$-0.990917\pi$
$733$	−12.8625	+	22.2786i	−0.475089	+	0.822878i	0.524504	+	0.851408i	$0.324251\pi$
$734$		0			0
$735$	−1.85842	+	7.91964i	−0.0685487	+	0.292120i
$736$		0			0
$737$	−13.5819	−	7.84152i	−0.500296	−	0.288846i
$738$		0			0
$739$	−28.3368	+	16.3603i	−1.04239	+	0.601822i	−0.920508	−	0.390723i	$-0.872225\pi$
$739$	−28.3368	+	16.3603i	−1.04239	+	0.601822i	−0.121878	+	0.992545i	$0.538892\pi$
$740$		0			0
$741$	−1.72508	+	4.21012i	−0.0633725	+	0.154663i
$742$		0			0
$743$	−17.4702			−0.640921			−0.320460	−	0.947262i	$-0.603838\pi$
$743$	−17.4702			−0.640921			−0.320460	+	0.947262i	$0.603838\pi$
$744$		0			0
$745$	4.68729	+	8.11863i	0.171729	+	0.297444i
$746$		0			0
$747$	−5.90886	+	1.63174i	−0.216194	+	0.0597023i
$748$		0			0
$749$	13.2624	−	27.8522i	0.484598	−	1.01770i
$750$		0			0
$751$	22.5997	+	13.0479i	0.824674	+	0.476126i	0.852025	−	0.523500i	$-0.175374\pi$
$751$	22.5997	+	13.0479i	0.824674	+	0.476126i	−0.0273518	+	0.999626i	$0.508707\pi$
$752$		0			0
$753$	−2.50743	−	18.4997i	−0.0913759	−	0.674166i
$754$		0			0
$755$	5.24879			0.191023
$756$		0			0
$757$	15.0997			0.548807			0.274403	−	0.961615i	$-0.411520\pi$
$757$	15.0997			0.548807			0.274403	+	0.961615i	$0.411520\pi$
$758$		0			0
$759$	3.91400	+	28.8773i	0.142069	+	1.04818i
$760$		0			0
$761$	−31.3330	−	18.0901i	−1.13582	−	0.655767i	−0.190429	−	0.981701i	$-0.560988\pi$
$761$	−31.3330	−	18.0901i	−1.13582	−	0.655767i	−0.945392	+	0.325934i	$0.894321\pi$
$762$		0			0
$763$	22.2371	+	32.3098i	0.805038	+	1.16969i
$764$		0			0
$765$	−8.16851	+	2.25575i	−0.295333	+	0.0815567i
$766$		0			0
$767$	7.57301	+	13.1168i	0.273446	+	0.473622i
$768$		0			0
$769$	−6.17525			−0.222685			−0.111343	−	0.993782i	$-0.535515\pi$
$769$	−6.17525			−0.222685			−0.111343	+	0.993782i	$0.535515\pi$
$770$		0			0
$771$	14.7054	−	35.8890i	0.529602	−	1.29251i
$772$		0			0
$773$	−5.12766	+	2.96046i	−0.184429	+	0.106480i	−0.589372	−	0.807862i	$-0.700625\pi$
$773$	−5.12766	+	2.96046i	−0.184429	+	0.106480i	0.404943	+	0.914342i	$0.367291\pi$
$774$		0			0
$775$	6.82475	+	3.94027i	0.245152	+	0.141539i
$776$		0			0
$777$	27.3874	+	8.76342i	0.982517	+	0.314386i
$778$		0			0
$779$	−6.41090	+	11.1040i	−0.229694	+	0.397842i
$780$		0			0
$781$	−10.7251	−	18.5764i	−0.383774	−	0.664715i
$782$		0			0
$783$	−29.7303	+	12.7156i	−1.06247	+	0.454419i
$784$		0			0
$785$		−	15.6830i		−	0.559751i
$786$		0			0
$787$	−1.23713	+	0.714256i	−0.0440988	+	0.0254605i	−0.521887	−	0.853014i	$-0.674772\pi$
$787$	−1.23713	+	0.714256i	−0.0440988	+	0.0254605i	0.477788	+	0.878475i	$0.341439\pi$
$788$		0			0
$789$	25.1432	−	19.4460i	0.895122	−	0.692298i
$790$		0			0
$791$	−2.04334	−	25.7472i	−0.0726529	−	0.915465i
$792$		0			0
$793$	3.72508	−	6.45203i	0.132282	−	0.229118i
$794$		0			0
$795$	1.83788	+	13.5598i	0.0651829	+	0.480916i
$796$		0			0
$797$			0.855398i			0.0302997i	0.999885	+	0.0151499i	$0.00482254\pi$
$797$			0.855398i			0.0302997i	−0.999885	+	0.0151499i	$0.995177\pi$
$798$		0			0
$799$		−	40.4860i		−	1.43229i
$800$		0			0
$801$	40.5701	+	10.5393i	1.43347	+	0.372389i
$802$		0			0
$803$	−0.721492	+	1.24966i	−0.0254609	+	0.0440996i
$804$		0			0
$805$	4.68729	−	3.22602i	0.165205	−	0.113702i
$806$		0			0
$807$	0.710962	+	0.919255i	0.0250271	+	0.0323593i
$808$		0			0
$809$	20.2351	−	11.6827i	0.711427	−	0.410743i	−0.100162	−	0.994971i	$-0.531936\pi$
$809$	20.2351	−	11.6827i	0.711427	−	0.410743i	0.811589	+	0.584228i	$0.198603\pi$
$810$		0			0
$811$		−	21.7370i		−	0.763288i	−0.924309	−	0.381644i	$-0.875358\pi$
$811$		−	21.7370i		−	0.763288i	0.924309	−	0.381644i	$-0.124642\pi$
$812$		0			0
$813$	13.6873	−	33.4043i	0.480034	−	1.17154i
$814$		0			0
$815$	0.721492	+	1.24966i	0.0252728	+	0.0437737i
$816$		0			0
$817$	−6.27492	+	10.8685i	−0.219532	+	0.380240i
$818$		0			0
$819$	14.9195	−	5.42293i	0.521330	−	0.189493i
$820$		0			0
$821$	11.6790	+	6.74287i	0.407600	+	0.235328i	0.689758	−	0.724040i	$-0.257717\pi$
$821$	11.6790	+	6.74287i	0.407600	+	0.235328i	−0.282158	+	0.959368i	$0.591050\pi$
$822$		0			0
$823$	−5.58762	+	3.22602i	−0.194772	+	0.112452i	−0.594215	−	0.804306i	$-0.702537\pi$
$823$	−5.58762	+	3.22602i	−0.194772	+	0.112452i	0.399442	+	0.916758i	$0.369204\pi$
$824$		0			0
$825$	38.2749	+	15.6830i	1.33256	+	0.546013i
$826$		0			0
$827$	−27.6870			−0.962770			−0.481385	−	0.876509i	$-0.659866\pi$
$827$	−27.6870			−0.962770			−0.481385	+	0.876509i	$0.659866\pi$
$828$		0			0
$829$	13.6873	+	23.7071i	0.475379	+	0.823381i	0.999602	−	0.0281999i	$-0.00897749\pi$
$829$	13.6873	+	23.7071i	0.475379	+	0.823381i	−0.524223	+	0.851581i	$0.675644\pi$
$830$		0			0
$831$	−7.84389	+	6.06656i	−0.272102	+	0.210446i
$832$		0			0
$833$	−22.8788	+	18.5766i	−0.792703	+	0.643642i
$834$		0			0
$835$	12.1993	+	7.04329i	0.422175	+	0.243743i
$836$		0			0
$837$	−7.20247	−	5.39670i	−0.248954	−	0.186537i
$838$		0			0
$839$	−8.17337			−0.282176			−0.141088	−	0.989997i	$-0.545060\pi$
$839$	−8.17337			−0.282176			−0.141088	+	0.989997i	$0.545060\pi$
$840$		0			0
$841$	−9.72508			−0.335348
$842$		0			0
$843$	−4.60632	+	0.624336i	−0.158650	+	0.0215033i
$844$		0			0
$845$	5.22949	+	3.01925i	0.179900	+	0.103865i
$846$		0			0
$847$	18.8248	−	39.5336i	0.646826	−	1.35839i
$848$		0			0
$849$	−19.8673	−	25.6879i	−0.681844	−	0.881606i
$850$		0			0
$851$	−10.0570	−	17.4192i	−0.344749	−	0.597122i
$852$		0			0
$853$	23.4502			0.802918			0.401459	−	0.915877i	$-0.368503\pi$
$853$	23.4502			0.802918			0.401459	+	0.915877i	$0.368503\pi$
$854$		0			0
$855$	−1.88360	−	1.85505i	−0.0644178	−	0.0634413i
$856$		0			0
$857$	−16.7487	+	9.66989i	−0.572126	+	0.330317i	−0.757998	−	0.652257i	$-0.773822\pi$
$857$	−16.7487	+	9.66989i	−0.572126	+	0.330317i	0.185872	+	0.982574i	$0.440489\pi$
$858$		0			0
$859$	6.51204	+	3.75973i	0.222188	+	0.128280i	0.606963	−	0.794730i	$-0.292388\pi$
$859$	6.51204	+	3.75973i	0.222188	+	0.128280i	−0.384775	+	0.923010i	$0.625721\pi$
$860$		0			0
$861$	43.7160	−	9.49676i	1.48984	−	0.323649i
$862$		0			0
$863$	1.60273	−	2.77600i	0.0545574	−	0.0944962i	−0.837457	−	0.546503i	$-0.815959\pi$
$863$	1.60273	−	2.77600i	0.0545574	−	0.0944962i	0.892014	+	0.452007i	$0.149292\pi$
$864$		0			0
$865$	5.58762	+	9.67805i	0.189985	+	0.329064i
$866$		0			0
$867$	−1.16211	−	0.476171i	−0.0394673	−	0.0161716i
$868$		0			0
$869$			27.2735i			0.925191i
$870$		0			0
$871$	5.17525	−	2.98793i	0.175357	−	0.101242i
$872$		0			0
$873$	9.47029	−	2.61523i	0.320521	−	0.0885122i
$874$		0			0
$875$	−1.34115	−	16.8993i	−0.0453393	−	0.571299i
$876$		0			0
$877$	−5.41238	+	9.37451i	−0.182763	+	0.316555i	−0.942820	−	0.333301i	$-0.891837\pi$
$877$	−5.41238	+	9.37451i	−0.182763	+	0.316555i	0.760057	+	0.649856i	$0.225171\pi$
$878$		0			0
$879$	−39.5851	+	5.36532i	−1.33517	+	0.180968i
$880$		0			0
$881$		−	44.4160i		−	1.49641i	−0.663465	−	0.748207i	$-0.730915\pi$
$881$		−	44.4160i		−	1.49641i	0.663465	−	0.748207i	$-0.269085\pi$
$882$		0			0
$883$			38.1051i			1.28234i	0.767399	+	0.641170i	$0.221551\pi$
$883$			38.1051i			1.28234i	−0.767399	+	0.641170i	$0.778449\pi$
$884$		0			0
$885$	−8.72092	+	1.18203i	−0.293151	+	0.0397334i
$886$		0			0
$887$	−0.721492	+	1.24966i	−0.0242253	+	0.0419595i	−0.877884	−	0.478874i	$-0.841045\pi$
$887$	−0.721492	+	1.24966i	−0.0242253	+	0.0419595i	0.853659	+	0.520833i	$0.174379\pi$
$888$		0			0
$889$	0.0876242	+	1.10411i	0.00293882	+	0.0370307i
$890$		0			0
$891$	−41.2663	−	22.9920i	−1.38247	−	0.770261i
$892$		0			0
$893$	10.9382	−	6.31518i	0.366033	−	0.211329i
$894$		0			0
$895$			10.7534i			0.359446i
$896$		0			0
$897$	−10.2749	−	4.21012i	−0.343070	−	0.140572i
$898$		0			0
$899$	−5.38923	−	9.33442i	−0.179741	−	0.311320i
$900$		0			0
$901$	−24.7870	+	42.9323i	−0.825773	+	1.43028i
$902$		0			0
$903$	42.7887	−	9.29532i	1.42392	−	0.309329i
$904$		0			0
$905$	8.77373	+	5.06551i	0.291649	+	0.168383i
$906$		0			0
$907$	3.51204	−	2.02768i	0.116616	−	0.0673280i	−0.440558	−	0.897724i	$-0.645219\pi$
$907$	3.51204	−	2.02768i	0.116616	−	0.0673280i	0.557173	+	0.830396i	$0.311886\pi$
$908$		0			0
$909$	−6.03779	+	6.13072i	−0.200261	+	0.203343i
$910$		0			0
$911$	37.9037			1.25580			0.627902	−	0.778292i	$-0.283914\pi$
$911$	37.9037			1.25580			0.627902	+	0.778292i	$0.283914\pi$
$912$		0			0
$913$	−5.36254	−	9.28819i	−0.177474	−	0.307394i
$914$		0			0
$915$	2.64839	+	3.42430i	0.0875532	+	0.113204i
$916$		0			0
$917$	−5.97029	+	12.5381i	−0.197156	+	0.414045i
$918$		0			0
$919$	34.1375	+	19.7093i	1.12609	+	0.650149i	0.942949	−	0.332938i	$-0.108040\pi$
$919$	34.1375	+	19.7093i	1.12609	+	0.650149i	0.183142	+	0.983086i	$0.441373\pi$
$920$		0			0
$921$	−29.7282	+	4.02933i	−0.979577	+	0.132771i
$922$		0			0
$923$	8.17337			0.269030
$924$		0			0
$925$	−28.5498			−0.938713
$926$		0			0
$927$	−49.2438	−	12.7926i	−1.61738	−	0.420163i
$928$		0			0
$929$	−22.8788	−	13.2091i	−0.750628	−	0.433375i	0.0752926	−	0.997161i	$-0.476011\pi$
$929$	−22.8788	−	13.2091i	−0.750628	−	0.433375i	−0.825921	+	0.563786i	$0.809344\pi$
$930$		0			0
$931$	−8.58762	−	3.28356i	−0.281448	−	0.107614i
$932$		0			0
$933$	6.80651	−	5.26423i	0.222835	−	0.172343i
$934$		0			0
$935$	−7.41327	−	12.8402i	−0.242440	−	0.419918i
$936$		0			0
$937$	−49.8248			−1.62770			−0.813852	−	0.581072i	$-0.802633\pi$
$937$	−49.8248			−1.62770			−0.813852	+	0.581072i	$0.802633\pi$
$938$		0			0
$939$	−31.3330	−	12.8386i	−1.02251	−	0.418972i
$940$		0			0
$941$	−17.4895	+	10.0976i	−0.570143	+	0.329172i	−0.757206	−	0.653176i	$-0.773436\pi$
$941$	−17.4895	+	10.0976i	−0.570143	+	0.329172i	0.187064	+	0.982348i	$0.440103\pi$
$942$		0			0
$943$	−27.0997	−	15.6460i	−0.882487	−	0.509504i
$944$		0			0
$945$	−0.371151	+	9.21648i	−0.0120735	+	0.299812i
$946$		0			0
$947$	12.1003	−	20.9584i	0.393207	−	0.681055i	−0.599663	−	0.800252i	$-0.704699\pi$
$947$	12.1003	−	20.9584i	0.393207	−	0.681055i	0.992871	+	0.119197i	$0.0380321\pi$
$948$		0			0
$949$	−0.274917	−	0.476171i	−0.00892419	−	0.0154572i
$950$		0			0
$951$	5.97029	−	14.5707i	0.193600	−	0.472486i
$952$		0			0
$953$			50.5214i			1.63655i	0.574828	+	0.818274i	$0.305069\pi$
$953$			50.5214i			1.63655i	−0.574828	+	0.818274i	$0.694931\pi$
$954$		0			0
$955$	−6.93812	+	4.00573i	−0.224512	+	0.129622i
$956$		0			0
$957$	−34.6112	−	44.7513i	−1.11882	−	1.44660i
$958$		0			0
$959$	−33.3764	+	22.9712i	−1.07778	+	0.741778i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$	8.79496	−	33.8554i	0.283414	−	1.09097i
$964$		0			0
$965$		−	12.1439i		−	0.390925i
$966$		0			0
$967$			9.02134i			0.290107i	0.989424	+	0.145053i	$0.0463354\pi$
$967$			9.02134i			0.290107i	−0.989424	+	0.145053i	$0.953665\pi$
$968$		0			0
$969$	−1.28639	−	9.49089i	−0.0413247	−	0.304891i
$970$		0			0
$971$	−3.50563	+	6.07193i	−0.112501	+	0.194858i	−0.916778	−	0.399397i	$-0.869219\pi$
$971$	−3.50563	+	6.07193i	−0.112501	+	0.194858i	0.804277	+	0.594255i	$0.202553\pi$
$972$		0			0
$973$	2.92442	+	36.8492i	0.0937526	+	1.18133i
$974$		0			0
$975$	−12.4674	+	9.64242i	−0.399276	+	0.308805i
$976$		0			0
$977$	34.8193	−	20.1030i	1.11397	−	0.643151i	0.174115	−	0.984725i	$-0.444294\pi$
$977$	34.8193	−	20.1030i	1.11397	−	0.643151i	0.939855	+	0.341575i	$0.110960\pi$
$978$		0			0
$979$			73.3374i			2.34387i
$980$		0			0
$981$	31.6873	+	31.2070i	1.01170	+	0.996362i
$982$		0			0
$983$	−16.1870	−	28.0367i	−0.516285	−	0.894232i	−0.999821	−	0.0189076i	$-0.993981\pi$
$983$	−16.1870	−	28.0367i	−0.516285	−	0.894232i	0.483536	−	0.875324i	$-0.339352\pi$
$984$		0			0
$985$	−2.37459	+	4.11290i	−0.0756606	+	0.131048i
$986$		0			0
$987$	−41.9714	−	13.4300i	−1.33596	−	0.427482i
$988$		0			0
$989$	−26.5248	−	15.3141i	−0.843441	−	0.486961i
$990$		0			0
$991$	13.5997	−	7.85177i	0.432008	−	0.249420i	−0.268194	−	0.963365i	$-0.586427\pi$
$991$	13.5997	−	7.85177i	0.432008	−	0.249420i	0.700202	+	0.713945i	$0.253093\pi$
$992$		0			0
$993$	1.48796	−	3.63140i	0.0472188	−	0.115239i
$994$		0			0
$995$	17.1508			0.543716
$996$		0			0
$997$	−6.86254	−	11.8863i	−0.217339	−	0.376442i	0.736655	−	0.676269i	$-0.236404\pi$
$997$	−6.86254	−	11.8863i	−0.217339	−	0.376442i	−0.953994	+	0.299827i	$0.903071\pi$
$998$		0			0
$999$	32.3731	+	3.88528i	1.02424	+	0.122925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bj.e.191.3	yes	8
3.2	odd	2	inner	336.2.bj.e.191.4	yes	8
4.3	odd	2		336.2.bj.g.191.2	yes	8
7.2	even	3		2352.2.h.n.2255.8		8
7.4	even	3		336.2.bj.g.95.1	yes	8
7.5	odd	6		2352.2.h.m.2255.1		8
12.11	even	2		336.2.bj.g.191.1	yes	8
21.2	odd	6		2352.2.h.n.2255.2		8
21.5	even	6		2352.2.h.m.2255.7		8
21.11	odd	6		336.2.bj.g.95.2	yes	8
28.11	odd	6	inner	336.2.bj.e.95.4	yes	8
28.19	even	6		2352.2.h.m.2255.8		8
28.23	odd	6		2352.2.h.n.2255.1		8
84.11	even	6	inner	336.2.bj.e.95.3	✓	8
84.23	even	6		2352.2.h.n.2255.7		8
84.47	odd	6		2352.2.h.m.2255.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bj.e.95.3	✓	8	84.11	even	6	inner
336.2.bj.e.95.4	yes	8	28.11	odd	6	inner
336.2.bj.e.191.3	yes	8	1.1	even	1	trivial
336.2.bj.e.191.4	yes	8	3.2	odd	2	inner
336.2.bj.g.95.1	yes	8	7.4	even	3
336.2.bj.g.95.2	yes	8	21.11	odd	6
336.2.bj.g.191.1	yes	8	12.11	even	2
336.2.bj.g.191.2	yes	8	4.3	odd	2
2352.2.h.m.2255.1		8	7.5	odd	6
2352.2.h.m.2255.2		8	84.47	odd	6
2352.2.h.m.2255.7		8	21.5	even	6
2352.2.h.m.2255.8		8	28.19	even	6
2352.2.h.n.2255.1		8	28.23	odd	6
2352.2.h.n.2255.2		8	21.2	odd	6
2352.2.h.n.2255.7		8	84.23	even	6
2352.2.h.n.2255.8		8	7.2	even	3

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.232633 - 1.71636i) q^{3} +(-0.581054 - 0.335472i) q^{5} +(-2.63746 + 0.209313i) q^{7} +(-2.89176 + 0.798564i) q^{9} +O(q^{10})\)	\(q+(-0.232633 - 1.71636i) q^{3} +(-0.581054 - 0.335472i) q^{5} +(-2.63746 + 0.209313i) q^{7} +(-2.89176 + 0.798564i) q^{9} +(-2.62440 - 4.54559i) q^{11} +2.00000 q^{13} +(-0.440617 + 1.07534i) q^{15} +(-3.64607 + 2.10506i) q^{17} +(-1.13746 - 0.656712i) q^{19} +(0.972818 + 4.47813i) q^{21} +(1.60273 - 2.77600i) q^{23} +(-2.27492 - 3.94027i) q^{25} +(2.04334 + 4.77753i) q^{27} +6.22295i q^{29} +(-1.50000 + 0.866025i) q^{31} +(-7.19133 + 5.56186i) q^{33} +(1.60273 + 0.763171i) q^{35} +(3.13746 - 5.43424i) q^{37} +(-0.465267 - 3.43271i) q^{39} -9.76212i q^{41} -9.55505i q^{43} +(1.94817 + 0.506096i) q^{45} +(-4.80818 + 8.32801i) q^{47} +(6.91238 - 1.10411i) q^{49} +(4.46123 + 5.76825i) q^{51} +(10.1974 - 5.88748i) q^{53} +3.52165i q^{55} +(-0.862541 + 2.10506i) q^{57} +(3.78651 + 6.55842i) q^{59} +(1.86254 - 3.22602i) q^{61} +(7.45976 - 2.71146i) q^{63} +(-1.16211 - 0.670944i) q^{65} +(2.58762 - 1.49397i) q^{67} +(-5.13746 - 2.10506i) q^{69} +4.08668 q^{71} +(-0.137459 - 0.238085i) q^{73} +(-6.23369 + 4.82121i) q^{75} +(7.87319 + 11.4395i) q^{77} +(-4.50000 - 2.59808i) q^{79} +(7.72459 - 4.61852i) q^{81} +2.04334 q^{83} +2.82475 q^{85} +(10.6808 - 1.44767i) q^{87} +(-12.1003 - 6.98612i) q^{89} +(-5.27492 + 0.418627i) q^{91} +(1.83536 + 2.37307i) q^{93} +(0.440617 + 0.763171i) q^{95} -3.27492 q^{97} +(11.2191 + 11.0490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} - 6 q^{7} - q^{9}+O(q^{10}) \) 8 * q - 3 * q^3 - 6 * q^7 - q^9	\( 8 q - 3 q^{3} - 6 q^{7} - q^{9} + 16 q^{13} + 6 q^{19} - 19 q^{21} + 12 q^{25} - 12 q^{31} - 11 q^{33} + 10 q^{37} - 6 q^{39} - 17 q^{45} + 10 q^{49} + 9 q^{51} - 22 q^{57} + 30 q^{61} + 27 q^{63} + 66 q^{67} - 26 q^{69} + 14 q^{73} - 66 q^{75} - 36 q^{79} + 7 q^{81} - 68 q^{85} + 54 q^{87} - 12 q^{91} + 3 q^{93} + 4 q^{97}+O(q^{100}) \) 8 * q - 3 * q^3 - 6 * q^7 - q^9 + 16 * q^13 + 6 * q^19 - 19 * q^21 + 12 * q^25 - 12 * q^31 - 11 * q^33 + 10 * q^37 - 6 * q^39 - 17 * q^45 + 10 * q^49 + 9 * q^51 - 22 * q^57 + 30 * q^61 + 27 * q^63 + 66 * q^67 - 26 * q^69 + 14 * q^73 - 66 * q^75 - 36 * q^79 + 7 * q^81 - 68 * q^85 + 54 * q^87 - 12 * q^91 + 3 * q^93 + 4 * q^97

Introduction

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