LMFDB - Embedded newform 336.2.bj.e.95.4

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			95.4
Root			$0.232633 + 1.71636i$ of defining polynomial
Character	$\chi$	$=$	336.95
Dual form			336.2.bj.e.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37009 - 1.05965i) q^{3} +(0.581054 - 0.335472i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(0.754305 - 2.90362i) q^{9} +O(q^{10})$	\(q+(1.37009 - 1.05965i) q^{3} +(0.581054 - 0.335472i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(0.754305 - 2.90362i) q^{9} +(2.62440 - 4.54559i) q^{11} +2.00000 q^{13} +(0.440617 - 1.07534i) q^{15} +(3.64607 + 2.10506i) q^{17} +(-1.13746 + 0.656712i) q^{19} +(-3.83536 + 2.50799i) q^{21} +(-1.60273 - 2.77600i) q^{23} +(-2.27492 + 3.94027i) q^{25} +(-2.04334 - 4.77753i) q^{27} +6.22295i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-1.22105 - 9.00880i) q^{33} +(-1.60273 + 0.763171i) q^{35} +(3.13746 + 5.43424i) q^{37} +(2.74018 - 2.11929i) q^{39} -9.76212i q^{41} +9.55505i q^{43} +(-0.535792 - 1.94021i) q^{45} +(4.80818 + 8.32801i) q^{47} +(6.91238 + 1.10411i) q^{49} +(7.22606 - 0.979414i) q^{51} +(-10.1974 - 5.88748i) q^{53} -3.52165i q^{55} +(-0.862541 + 2.10506i) q^{57} +(-3.78651 + 6.55842i) q^{59} +(1.86254 + 3.22602i) q^{61} +(-2.59721 + 7.50030i) q^{63} +(1.16211 - 0.670944i) q^{65} +(2.58762 + 1.49397i) q^{67} +(-5.13746 - 2.10506i) q^{69} -4.08668 q^{71} +(-0.137459 + 0.238085i) q^{73} +(1.05844 + 7.80914i) q^{75} +(-7.87319 + 11.4395i) q^{77} +(-4.50000 + 2.59808i) q^{79} +(-7.86205 - 4.38043i) q^{81} -2.04334 q^{83} +2.82475 q^{85} +(6.59412 + 8.52601i) q^{87} +(12.1003 - 6.98612i) q^{89} +(-5.27492 - 0.418627i) q^{91} +(-2.97282 + 0.402933i) q^{93} +(-0.440617 + 0.763171i) q^{95} -3.27492 q^{97} +(-11.2191 - 11.0490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.37009	−	1.05965i	0.791023	−	0.611786i
$3$	1.37009	−	1.05965i	0.791023	−	0.611786i
$4$		0			0
$5$	0.581054	−	0.335472i	0.259855	−	0.150028i	−0.364413	−	0.931237i	$-0.618730\pi$
$5$	0.581054	−	0.335472i	0.259855	−	0.150028i	0.624269	+	0.781210i	$0.285397\pi$
$6$		0			0
$7$	−2.63746	−	0.209313i	−0.996866	−	0.0791130i
$7$	−2.63746	−	0.209313i	−0.996866	−	0.0791130i
$8$		0			0
$9$	0.754305	−	2.90362i	0.251435	−	0.967874i
$10$		0			0
$11$	2.62440	−	4.54559i	0.791285	−	1.37055i	−0.133886	−	0.990997i	$-0.542746\pi$
$11$	2.62440	−	4.54559i	0.791285	−	1.37055i	0.925171	−	0.379550i	$-0.123921\pi$
$12$		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	$-0.162775\pi$
$17$	3.64607	+	2.10506i	0.884301	+	0.510552i	0.0122271	+	0.999925i	$0.496108\pi$
$18$		0			0
$19$	−1.13746	+	0.656712i	−0.260951	+	0.150660i	−0.624768	−	0.780810i	$-0.714807\pi$
$19$	−1.13746	+	0.656712i	−0.260951	+	0.150660i	0.363817	+	0.931470i	$0.381473\pi$
$20$		0			0
$21$	−3.83536	+	2.50799i	−0.836944	+	0.547289i
$22$		0			0
$23$	−1.60273	−	2.77600i	−0.334191	−	0.578836i	0.649138	−	0.760671i	$-0.275130\pi$
$23$	−1.60273	−	2.77600i	−0.334191	−	0.578836i	−0.983329	+	0.181834i	$0.941797\pi$
$24$		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	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	−1.22105	−	9.00880i	−0.212557	−	1.56823i
$34$		0			0
$35$	−1.60273	+	0.763171i	−0.270910	+	0.128999i
$36$		0			0
$37$	3.13746	+	5.43424i	0.515795	+	0.893383i	0.999832	+	0.0183356i	$0.00583672\pi$
$37$	3.13746	+	5.43424i	0.515795	+	0.893383i	−0.484037	+	0.875048i	$0.660830\pi$
$38$		0			0
$39$	2.74018	−	2.11929i	0.438781	−	0.339358i
$40$		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	$0.259813\pi$
$43$			9.55505i			1.45713i	−0.684976	+	0.728566i	$0.740187\pi$
$44$		0			0
$45$	−0.535792	−	1.94021i	−0.0798711	−	0.289230i
$46$		0			0
$47$	4.80818	+	8.32801i	0.701345	+	1.21476i	0.967995	+	0.250971i	$0.0807499\pi$
$47$	4.80818	+	8.32801i	0.701345	+	1.21476i	−0.266650	+	0.963793i	$0.585917\pi$
$48$		0			0
$49$	6.91238	+	1.10411i	0.987482	+	0.157730i
$50$		0			0
$51$	7.22606	−	0.979414i	1.01185	−	0.137145i
$52$		0			0
$53$	−10.1974	−	5.88748i	−1.40072	−	0.808707i	−0.406255	−	0.913760i	$-0.633166\pi$
$53$	−10.1974	−	5.88748i	−1.40072	−	0.808707i	−0.994467	+	0.105053i	$0.966499\pi$
$54$		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	$-0.997419\pi$
$59$	−3.78651	+	6.55842i	−0.492961	+	0.853834i	0.507006	+	0.861942i	$0.330752\pi$
$60$		0			0
$61$	1.86254	+	3.22602i	0.238474	+	0.413049i	0.960277	−	0.279050i	$-0.0900195\pi$
$61$	1.86254	+	3.22602i	0.238474	+	0.413049i	−0.721803	+	0.692099i	$0.756686\pi$
$62$		0			0
$63$	−2.59721	+	7.50030i	−0.327218	+	0.944949i
$64$		0			0
$65$	1.16211	−	0.670944i	0.144142	−	0.0832203i
$66$		0			0
$67$	2.58762	+	1.49397i	0.316129	+	0.182517i	0.649666	−	0.760220i	$-0.274909\pi$
$67$	2.58762	+	1.49397i	0.316129	+	0.182517i	−0.333537	+	0.942737i	$0.608242\pi$
$68$		0			0
$69$	−5.13746	−	2.10506i	−0.618477	−	0.253419i
$70$		0			0
$71$	−4.08668			−0.485000			−0.242500	−	0.970151i	$-0.577967\pi$
$71$	−4.08668			−0.485000			−0.242500	+	0.970151i	$0.577967\pi$
$72$		0			0
$73$	−0.137459	+	0.238085i	−0.0160883	+	0.0278658i	−0.873957	−	0.486002i	$-0.838455\pi$
$73$	−0.137459	+	0.238085i	−0.0160883	+	0.0278658i	0.857869	+	0.513868i	$0.171788\pi$
$74$		0			0
$75$	1.05844	+	7.80914i	0.122219	+	0.901722i
$76$		0			0
$77$	−7.87319	+	11.4395i	−0.897233	+	1.30365i
$78$		0			0
$79$	−4.50000	+	2.59808i	−0.506290	+	0.292306i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−4.50000	+	2.59808i	−0.506290	+	0.292306i	0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	−7.86205	−	4.38043i	−0.873561	−	0.486715i
$82$		0			0
$83$	−2.04334			−0.224286			−0.112143	−	0.993692i	$-0.535771\pi$
$83$	−2.04334			−0.224286			−0.112143	+	0.993692i	$0.535771\pi$
$84$		0			0
$85$	2.82475			0.306387
$86$		0			0
$87$	6.59412	+	8.52601i	0.706963	+	0.914084i
$88$		0			0
$89$	12.1003	−	6.98612i	1.28263	−	0.740527i	0.305302	−	0.952256i	$-0.401243\pi$
$89$	12.1003	−	6.98612i	1.28263	−	0.740527i	0.977329	+	0.211728i	$0.0679092\pi$
$90$		0			0
$91$	−5.27492	−	0.418627i	−0.552962	−	0.0438840i
$92$		0			0
$93$	−2.97282	+	0.402933i	−0.308267	+	0.0417822i
$94$		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	$-0.378912\pi$
$101$	−2.48396	−	1.43411i	−0.247163	−	0.142700i	−0.618465	+	0.785813i	$0.712245\pi$
$102$		0			0
$103$	14.6873	−	8.47971i	1.44718	−	0.835531i	0.448869	−	0.893597i	$-0.351827\pi$
$103$	14.6873	−	8.47971i	1.44718	−	0.835531i	0.998313	+	0.0580665i	$0.0184936\pi$
$104$		0			0
$105$	−1.38719	+	2.74393i	−0.135376	+	0.267781i
$106$		0			0
$107$	5.82985	+	10.0976i	0.563593	+	0.976171i	0.997179	+	0.0750592i	$0.0239146\pi$
$107$	5.82985	+	10.0976i	0.563593	+	0.976171i	−0.433586	+	0.901112i	$0.642752\pi$
$108$		0			0
$109$	−7.41238	+	12.8386i	−0.709977	+	1.22972i	0.254888	+	0.966970i	$0.417961\pi$
$109$	−7.41238	+	12.8386i	−0.709977	+	1.22972i	−0.964865	+	0.262745i	$0.915372\pi$
$110$		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
$117$	1.50861	−	5.80725i	0.139471	−	0.536880i
$118$		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
$123$	−10.3444	−	13.3750i	−0.932722	−	1.20598i
$124$		0			0
$125$			6.40740i			0.573095i
$126$		0			0
$127$			0.418627i			0.0371471i	0.999827	+	0.0185736i	$0.00591249\pi$
$127$			0.418627i			0.0371471i	−0.999827	+	0.0185736i	$0.994088\pi$
$128$		0			0
$129$	10.1250	+	13.0913i	0.891453	+	1.15262i
$130$		0			0
$131$	−2.62440	−	4.54559i	−0.229295	−	0.397150i	0.728305	−	0.685253i	$-0.240309\pi$
$131$	−2.62440	−	4.54559i	−0.229295	−	0.397150i	−0.957599	+	0.288104i	$0.906975\pi$
$132$		0			0
$133$	3.13746	−	1.49397i	0.272052	−	0.129543i
$134$		0			0
$135$	−2.79002	−	2.09052i	−0.240127	−	0.179923i
$136$		0			0
$137$	−13.2624	−	7.65706i	−1.13309	−	0.654187i	−0.188376	−	0.982097i	$-0.560322\pi$
$137$	−13.2624	−	7.65706i	−1.13309	−	0.654187i	−0.944709	+	0.327910i	$0.893656\pi$
$138$		0			0
$139$			13.9715i			1.18505i	0.805553	+	0.592523i	$0.201868\pi$
$139$			13.9715i			1.18505i	−0.805553	+	0.592523i	$0.798132\pi$
$140$		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
$147$	10.6406	−	5.81193i	0.877618	−	0.479360i
$148$		0			0
$149$	12.1003	−	6.98612i	0.991296	−	0.572325i	0.0856347	−	0.996327i	$-0.472708\pi$
$149$	12.1003	−	6.98612i	0.991296	−	0.572325i	0.905662	+	0.424001i	$0.139375\pi$
$150$		0			0
$151$	−6.77492	−	3.91150i	−0.551335	−	0.318313i	0.198325	−	0.980136i	$-0.436450\pi$
$151$	−6.77492	−	3.91150i	−0.551335	−	0.318313i	−0.749660	+	0.661823i	$0.769783\pi$
$152$		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	0.154145	−	0.988048i	$-0.450738\pi$
$157$	11.6873	−	20.2430i	0.932748	−	1.61557i	0.778602	−	0.627518i	$-0.215929\pi$
$158$		0			0
$159$	−20.2100	+	2.73925i	−1.60276	+	0.217237i
$160$		0			0
$161$	3.64607	+	7.65706i	0.287350	+	0.603461i
$162$		0			0
$163$	−1.86254	+	1.07534i	−0.145886	+	0.0842270i	−0.571166	−	0.820835i	$-0.693509\pi$
$163$	−1.86254	+	1.07534i	−0.145886	+	0.0842270i	0.425281	+	0.905062i	$0.360175\pi$
$164$		0			0
$165$	−3.73169	−	4.82498i	−0.290512	−	0.375624i
$166$		0			0
$167$	20.9952			1.62466			0.812328	−	0.583201i	$-0.198200\pi$
$167$	20.9952			1.62466			0.812328	+	0.583201i	$0.198200\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	1.04885	+	3.79811i	0.0802078	+	0.290449i
$172$		0			0
$173$	14.4245	−	8.32801i	1.09668	−	0.633167i	0.161331	−	0.986900i	$-0.448421\pi$
$173$	14.4245	−	8.32801i	1.09668	−	0.633167i	0.935346	+	0.353734i	$0.115088\pi$
$174$		0			0
$175$	6.82475	−	9.91613i	0.515903	−	0.749589i
$176$		0			0
$177$	1.76174	+	12.9980i	0.132420	+	0.976989i
$178$		0			0
$179$	8.01363	−	13.8800i	0.598967	−	1.03744i	−0.394007	−	0.919107i	$-0.628912\pi$
$179$	8.01363	−	13.8800i	0.598967	−	1.03744i	0.992974	−	0.118333i	$-0.0377551\pi$
$180$		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
$189$	4.38923	+	13.0282i	0.319270	+	0.947664i
$190$		0			0
$191$	−5.97029	−	10.3408i	−0.431995	−	0.748237i	0.565050	−	0.825056i	$-0.308857\pi$
$191$	−5.97029	−	10.3408i	−0.431995	−	0.748237i	−0.997045	+	0.0768197i	$0.975523\pi$
$192$		0			0
$193$	9.04983	−	15.6748i	0.651421	−	1.12829i	−0.331357	−	0.943506i	$-0.607506\pi$
$193$	9.04983	−	15.6748i	0.651421	−	1.12829i	0.982778	−	0.184789i	$-0.0591603\pi$
$194$		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	−0.996253	−	0.0864917i	$-0.972434\pi$
$199$	−22.1375	−	12.7811i	−1.56928	−	0.906026i	−0.573030	−	0.819534i	$-0.694232\pi$
$200$		0			0
$201$	5.12836	−	0.695093i	0.361726	−	0.0490281i
$202$		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
$207$	−9.26941	+	2.55976i	−0.644268	+	0.177916i
$208$		0			0
$209$			6.89389i			0.476860i
$210$		0			0
$211$			15.6460i			1.07712i	0.842589	+	0.538558i	$0.181031\pi$
$211$			15.6460i			1.07712i	−0.842589	+	0.538558i	$0.818969\pi$
$212$		0			0
$213$	−5.59913	+	4.33044i	−0.383646	+	0.296717i
$214$		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
$219$	0.0639550	+	0.471856i	0.00432168	+	0.0318851i
$220$		0			0
$221$	7.29214	+	4.21012i	0.490522	+	0.283203i
$222$		0			0
$223$		−	11.7633i		−	0.787727i	−0.919169	−	0.393864i	$-0.871138\pi$
$223$		−	11.7633i		−	0.787727i	0.919169	−	0.393864i	$-0.128862\pi$
$224$		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	$-0.908082\pi$
$227$	−3.50563	+	6.07193i	−0.232677	+	0.403008i	0.725918	+	0.687781i	$0.241415\pi$
$228$		0			0
$229$	−8.13746	−	14.0945i	−0.537738	−	0.931390i	−0.999025	−	0.0441392i	$-0.985945\pi$
$229$	−8.13746	−	14.0945i	−0.537738	−	0.931390i	0.461287	−	0.887251i	$-0.347388\pi$
$230$		0			0
$231$	1.33479	+	24.0159i	0.0878229	+	1.58013i
$232$		0			0
$233$	−13.2624	+	7.65706i	−0.868850	+	0.501631i	−0.866966	−	0.498367i	$-0.833933\pi$
$233$	−13.2624	+	7.65706i	−0.868850	+	0.501631i	−0.00188417	+	0.999998i	$0.500600\pi$
$234$		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	$-0.591168\pi$
$239$	−8.73512			−0.565028			−0.282514	+	0.959263i	$0.591168\pi$
$240$		0			0
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	−0.956456	−	0.291877i	$-0.905720\pi$
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	0.731001	+	0.682376i	$0.239053\pi$
$242$		0			0
$243$	−15.4134	+	2.32939i	−0.988772	+	0.149430i
$244$		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
$249$	−2.79957	+	2.16522i	−0.177415	+	0.137215i
$250$		0			0
$251$	−10.7785			−0.680331			−0.340165	−	0.940366i	$-0.610483\pi$
$251$	−10.7785			−0.680331			−0.340165	+	0.940366i	$0.610483\pi$
$252$		0			0
$253$	−16.8248			−1.05776
$254$		0			0
$255$	3.87017	−	2.99323i	0.242359	−	0.187444i
$256$		0			0
$257$	−19.3924	+	11.1962i	−1.20967	+	0.698402i	−0.962687	−	0.270618i	$-0.912772\pi$
$257$	−19.3924	+	11.1962i	−1.20967	+	0.698402i	−0.246981	+	0.969020i	$0.579439\pi$
$258$		0			0
$259$	−7.13746	−	14.9893i	−0.443500	−	0.931389i
$260$		0			0
$261$	18.0691	+	4.69400i	1.11845	+	0.290551i
$262$		0			0
$263$	−9.17574	+	15.8928i	−0.565800	+	0.979995i	0.431175	+	0.902269i	$0.358099\pi$
$263$	−9.17574	+	15.8928i	−0.565800	+	0.979995i	−0.996975	+	0.0777261i	$0.975234\pi$
$264$		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	$-0.326822\pi$
$269$	0.581054	+	0.335472i	0.0354275	+	0.0204541i	−0.482182	+	0.876071i	$0.660155\pi$
$270$		0			0
$271$	18.0498	−	10.4211i	1.09645	−	0.633035i	0.161163	−	0.986928i	$-0.448475\pi$
$271$	18.0498	−	10.4211i	1.09645	−	0.633035i	0.935286	+	0.353892i	$0.115142\pi$
$272$		0			0
$273$	−7.67072	+	5.01598i	−0.464253	+	0.303581i
$274$		0			0
$275$	11.9406	+	20.6817i	0.720044	+	1.24715i
$276$		0			0
$277$	−2.86254	+	4.95807i	−0.171993	+	0.297901i	−0.939117	−	0.343598i	$-0.888354\pi$
$277$	−2.86254	+	4.95807i	−0.171993	+	0.297901i	0.767123	+	0.641500i	$0.221687\pi$
$278$		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	0.897769	−	0.440467i	$-0.145187\pi$
$283$	16.2371	+	9.37451i	0.965197	+	0.557257i	0.0674284	+	0.997724i	$0.478521\pi$
$284$		0			0
$285$	0.205004	+	1.51251i	0.0121434	+	0.0895935i
$286$		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
$291$	−4.48694	+	3.47025i	−0.263029	+	0.203430i
$292$		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
$297$	−27.0792	−	3.24993i	−1.57130	−	0.188580i
$298$		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
$303$	−4.92291	+	0.667246i	−0.282814	+	0.0383323i
$304$		0			0
$305$	2.16448	+	1.24966i	0.123938	+	0.0715554i
$306$		0			0
$307$			17.3205i			0.988534i	0.869310	+	0.494267i	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$		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	$-0.878318\pi$
$311$	−2.48396	+	4.30234i	−0.140852	+	0.243964i	0.786965	+	0.616997i	$0.211651\pi$
$312$		0			0
$313$	9.77492	+	16.9307i	0.552511	+	0.956977i	0.998093	+	0.0617357i	$0.0196636\pi$
$313$	9.77492	+	16.9307i	0.552511	+	0.956977i	−0.445582	+	0.895241i	$0.647003\pi$
$314$		0			0
$315$	1.00702	+	5.22937i	0.0567390	+	0.294642i
$316$		0			0
$317$	−7.87319	+	4.54559i	−0.442202	+	0.255306i	−0.704531	−	0.709673i	$-0.748843\pi$
$317$	−7.87319	+	4.54559i	−0.442202	+	0.255306i	0.262329	+	0.964979i	$0.415509\pi$
$318$		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
$327$	3.44873	+	25.4446i	0.190715	+	1.40709i
$328$		0			0
$329$	−10.9382	−	22.9712i	−0.603043	−	1.26644i
$330$		0			0
$331$	1.96221	−	1.13288i	0.107853	−	0.0622689i	−0.445103	−	0.895479i	$-0.646833\pi$
$331$	1.96221	−	1.13288i	0.107853	−	0.0622689i	0.552956	+	0.833210i	$0.313500\pi$
$332$		0			0
$333$	18.1456	−	5.01092i	0.994371	−	0.274597i
$334$		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
$339$	10.3444	+	13.3750i	0.561830	+	0.726431i
$340$		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
$345$	−3.69133	+	0.500320i	−0.198735	+	0.0269363i
$346$		0			0
$347$	−2.48396	+	4.30234i	−0.133346	+	0.230962i	−0.924964	−	0.380054i	$-0.875905\pi$
$347$	−2.48396	+	4.30234i	−0.133346	+	0.230962i	0.791618	+	0.611016i	$0.209239\pi$
$348$		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	$-0.297595\pi$
$353$	3.64607	+	2.10506i	0.194061	+	0.112041i	−0.399821	+	0.916593i	$0.630928\pi$
$354$		0			0
$355$	−2.37459	+	1.37097i	−0.126030	+	0.0727634i
$356$		0			0
$357$	−19.2634	+	1.07065i	−1.01953	+	0.0566649i
$358$		0			0
$359$	−14.1437	−	24.4975i	−0.746474	−	1.29293i	−0.949503	−	0.313758i	$-0.898412\pi$
$359$	−14.1437	−	24.4975i	−0.746474	−	1.29293i	0.203030	−	0.979173i	$-0.434921\pi$
$360$		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	0.375122	−	0.926975i	$-0.377601\pi$
$367$	−4.59967	−	2.65562i	−0.240101	−	0.138622i	−0.615223	+	0.788353i	$0.710934\pi$
$368$		0			0
$369$	−28.3455	−	7.36361i	−1.47561	−	0.383334i
$370$		0			0
$371$	25.6629	+	17.6624i	1.33235	+	0.916988i
$372$		0			0
$373$	−3.58762	−	6.21395i	−0.185760	−	0.321746i	0.758072	−	0.652171i	$-0.226141\pi$
$373$	−3.58762	−	6.21395i	−0.185760	−	0.321746i	−0.943832	+	0.330425i	$0.892808\pi$
$374$		0			0
$375$	6.78957	+	8.77873i	0.350612	+	0.453332i
$376$		0			0
$377$			12.4459i			0.640996i
$378$		0			0
$379$			10.3923i			0.533817i	0.963722	+	0.266908i	$0.0860021\pi$
$379$			10.3923i			0.533817i	−0.963722	+	0.266908i	$0.913998\pi$
$380$		0			0
$381$	0.443596	+	0.573557i	0.0227261	+	0.0293842i
$382$		0			0
$383$	−3.92694	−	6.80166i	−0.200657	−	0.347549i	0.748083	−	0.663605i	$-0.230974\pi$
$383$	−3.92694	−	6.80166i	−0.200657	−	0.347549i	−0.948740	+	0.316056i	$0.897641\pi$
$384$		0			0
$385$	−0.737127	+	9.28819i	−0.0375675	+	0.473370i
$386$		0			0
$387$	27.7443	+	7.20742i	1.41032	+	0.366374i
$388$		0			0
$389$	9.77610	+	5.64423i	0.495668	+	0.286174i	0.726923	−	0.686719i	$-0.240950\pi$
$389$	9.77610	+	5.64423i	0.495668	+	0.286174i	−0.231255	+	0.972893i	$0.574283\pi$
$390$		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	0.927602	+	0.373571i	$0.121867\pi$
$397$	15.6873	+	27.1712i	0.787323	+	1.36368i	−0.140279	+	0.990112i	$0.544800\pi$
$398$		0			0
$399$	2.71553	−	5.37146i	0.135947	−	0.268909i
$400$		0			0
$401$	−1.00237	+	0.578717i	−0.0500558	+	0.0288997i	−0.524819	−	0.851214i	$-0.675867\pi$
$401$	−1.00237	+	0.578717i	−0.0500558	+	0.0288997i	0.474763	+	0.880114i	$0.342534\pi$
$402$		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	−0.151910	−	0.988394i	$-0.548542\pi$
$409$	15.7749	−	27.3230i	0.780019	−	1.35103i	0.931930	−	0.362639i	$-0.118124\pi$
$410$		0			0
$411$	−26.2845	+	3.56258i	−1.29652	+	0.175729i
$412$		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
$417$	14.8048	+	19.1422i	0.724995	+	0.937399i
$418$		0			0
$419$	−34.3787			−1.67951			−0.839755	−	0.542965i	$-0.817302\pi$
$419$	−34.3787			−1.67951			−0.839755	+	0.542965i	$0.817302\pi$
$420$		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
$423$	27.8082	−	7.67928i	1.35208	−	0.373379i
$424$		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
$429$	−2.44209	−	18.0176i	−0.117905	−	0.869898i
$430$		0			0
$431$	−0.721492	+	1.24966i	−0.0347530	+	0.0601940i	−0.882879	−	0.469601i	$-0.844398\pi$
$431$	−0.721492	+	1.24966i	−0.0347530	+	0.0601940i	0.848126	+	0.529795i	$0.177731\pi$
$432$		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	−0.801241	−	0.598341i	$-0.795827\pi$
$439$	−14.3248	+	8.27040i	−0.683683	+	0.394725i	0.117558	+	0.993066i	$0.462493\pi$
$440$		0			0
$441$	8.41996	−	19.2381i	0.400950	−	0.916100i
$442$		0			0
$443$	−2.90527	−	5.03208i	−0.138034	−	0.239081i	0.788719	−	0.614754i	$-0.210745\pi$
$443$	−2.90527	−	5.03208i	−0.138034	−	0.239081i	−0.926752	+	0.375673i	$0.877412\pi$
$444$		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
$453$	−13.4271	+	1.81989i	−0.630858	+	0.0855060i
$454$		0			0
$455$	−3.20545	+	1.52634i	−0.150274	+	0.0715560i
$456$		0			0
$457$	8.32475	+	14.4189i	0.389415	+	0.674487i	0.992371	−	0.123287i	$-0.0393437\pi$
$457$	8.32475	+	14.4189i	0.389415	+	0.674487i	−0.602956	+	0.797775i	$0.706010\pi$
$458$		0			0
$459$	2.60680	−	21.7205i	0.121675	−	1.01383i
$460$		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	$0.161415\pi$
$463$			20.8997i			0.971291i	−0.874156	+	0.485646i	$0.838585\pi$
$464$		0			0
$465$	−1.59220	+	1.23142i	−0.0738363	+	0.0571059i
$466$		0			0
$467$	−3.92694	−	6.80166i	−0.181717	−	0.314744i	0.760748	−	0.649047i	$-0.224832\pi$
$467$	−3.92694	−	6.80166i	−0.181717	−	0.314744i	−0.942465	+	0.334304i	$0.891499\pi$
$468$		0			0
$469$	−6.51204	−	4.48190i	−0.300698	−	0.206955i
$470$		0			0
$471$	−5.43771	−	40.1191i	−0.250557	−	1.84859i
$472$		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	−0.194202	−	0.980961i	$-0.562212\pi$
$479$	16.4679	−	28.5232i	0.752436	−	1.30326i	0.946639	−	0.322296i	$-0.104455\pi$
$480$		0			0
$481$	6.27492	+	10.8685i	0.286112	+	0.495560i
$482$		0			0
$483$	13.1092	+	6.62734i	0.596490	+	0.301555i
$484$		0			0
$485$	−1.90290	+	1.09864i	−0.0864065	+	0.0498868i
$486$		0			0
$487$	9.77492	+	5.64355i	0.442944	+	0.255734i	0.704846	−	0.709361i	$-0.251016\pi$
$487$	9.77492	+	5.64355i	0.442944	+	0.255734i	−0.261902	+	0.965095i	$0.584350\pi$
$488$		0			0
$489$	−1.41238	+	3.44695i	−0.0638698	+	0.155876i
$490$		0			0
$491$	6.69178			0.301996			0.150998	−	0.988534i	$-0.451751\pi$
$491$	6.69178			0.301996			0.150998	+	0.988534i	$0.451751\pi$
$492$		0			0
$493$	−13.0997	+	22.6893i	−0.589979	+	1.02187i
$494$		0			0
$495$	−10.2255	−	2.65639i	−0.459603	−	0.119396i
$496$		0			0
$497$	10.7785	+	0.855398i	0.483480	+	0.0383698i
$498$		0			0
$499$	−3.31271	+	1.91259i	−0.148297	+	0.0856194i	−0.572313	−	0.820036i	$-0.693954\pi$
$499$	−3.31271	+	1.91259i	−0.148297	+	0.0856194i	0.424015	+	0.905655i	$0.360620\pi$
$500$		0			0
$501$	28.7653	−	22.2474i	1.28514	−	0.993942i
$502$		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
$507$	−12.3308	+	9.53681i	−0.547631	+	0.423544i
$508$		0			0
$509$	−10.1974	+	5.88748i	−0.451992	+	0.260958i	−0.708671	−	0.705539i	$-0.750705\pi$
$509$	−10.1974	+	5.88748i	−0.451992	+	0.260958i	0.256679	+	0.966497i	$0.417372\pi$
$510$		0			0
$511$	0.412376	−	0.599168i	0.0182424	−	0.0265056i
$512$		0			0
$513$	5.46168	+	4.09235i	0.241139	+	0.180682i
$514$		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	$-0.582099\pi$
$521$	−27.8467	−	16.0773i	−1.21999	−	0.704359i	−0.964915	+	0.262563i	$0.915432\pi$
$522$		0			0
$523$	−4.96221	+	2.86493i	−0.216982	+	0.125275i	−0.604552	−	0.796566i	$-0.706648\pi$
$523$	−4.96221	+	2.86493i	−0.216982	+	0.125275i	0.387570	+	0.921840i	$0.373315\pi$
$524$		0			0
$525$	−1.15704	−	20.8178i	−0.0504976	−	0.908565i
$526$		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
$537$	−3.72848	−	27.5085i	−0.160896	−	1.18708i
$538$		0			0
$539$	23.1597	−	28.5232i	0.997557	−	1.22858i
$540$		0			0
$541$	17.1375	+	29.6829i	0.736797	+	1.27617i	0.953930	+	0.300028i	$0.0969959\pi$
$541$	17.1375	+	29.6829i	0.736797	+	1.27617i	−0.217134	+	0.976142i	$0.569671\pi$
$542$		0			0
$543$	−20.6879	+	16.0003i	−0.887804	+	0.686638i
$544$		0			0
$545$			9.94658i			0.426064i
$546$		0			0
$547$			4.30136i			0.183913i	0.995763	+	0.0919563i	$0.0293120\pi$
$547$			4.30136i			0.183913i	−0.995763	+	0.0919563i	$0.970688\pi$
$548$		0			0
$549$	10.7721	−	2.97472i	0.459740	−	0.126958i
$550$		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
$555$	7.22606	−	0.979414i	0.306729	−	0.0415738i
$556$		0			0
$557$	19.8138	+	11.4395i	0.839536	+	0.484706i	0.857106	−	0.515139i	$-0.172260\pi$
$557$	19.8138	+	11.4395i	0.839536	+	0.484706i	−0.0175705	+	0.999846i	$0.505593\pi$
$558$		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	−0.346479	−	0.938058i	$-0.612623\pi$
$563$	15.1653	−	26.2671i	0.639142	−	1.10703i	0.985621	−	0.168969i	$-0.0540439\pi$
$564$		0			0
$565$	3.27492	+	5.67232i	0.137777	+	0.238636i
$566$		0			0
$567$	19.8189	+	13.1988i	0.832317	+	0.554299i
$568$		0			0
$569$	27.5272	−	15.8928i	1.15400	−	0.666263i	0.204142	−	0.978941i	$-0.434560\pi$
$569$	27.5272	−	15.8928i	1.15400	−	0.666263i	0.949859	+	0.312679i	$0.101226\pi$
$570$		0			0
$571$	10.9622	+	6.32904i	0.458754	+	0.264862i	0.711520	−	0.702666i	$-0.248007\pi$
$571$	10.9622	+	6.32904i	0.458754	+	0.264862i	−0.252766	+	0.967527i	$0.581340\pi$
$572$		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	−0.822573	−	0.568659i	$-0.807462\pi$
$577$	1.95017	−	3.37779i	0.0811865	−	0.140619i	0.903760	+	0.428040i	$0.140796\pi$
$578$		0			0
$579$	−4.21059	−	31.0655i	−0.174986	−	1.29104i
$580$		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
$585$	−1.07158	−	3.88042i	−0.0443045	−	0.160436i
$586$		0			0
$587$	2.04334			0.0843378			0.0421689	−	0.999110i	$-0.486573\pi$
$587$	2.04334			0.0843378			0.0421689	+	0.999110i	$0.486573\pi$
$588$		0			0
$589$	2.27492			0.0937363
$590$		0			0
$591$	−7.50053	−	9.69799i	−0.308531	−	0.398922i
$592$		0			0
$593$	−2.48396	+	1.43411i	−0.102004	+	0.0588920i	−0.550134	−	0.835076i	$-0.685423\pi$
$593$	−2.48396	+	1.43411i	−0.102004	+	0.0588920i	0.448130	+	0.893968i	$0.352090\pi$
$594$		0			0
$595$	−7.45017	−	0.591258i	−0.305427	−	0.0242392i
$596$		0			0
$597$	−43.8738	+	5.94661i	−1.79563	+	0.243378i
$598$		0			0
$599$	−13.2624	+	22.9712i	−0.541888	+	0.938577i	0.456908	+	0.889514i	$0.348957\pi$
$599$	−13.2624	+	22.9712i	−0.541888	+	0.938577i	−0.998796	+	0.0490632i	$0.984376\pi$
$600$		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	−0.164907	−	0.986309i	$-0.552732\pi$
$607$	14.9502	−	8.63148i	0.606809	−	0.350341i	0.771715	+	0.635968i	$0.219399\pi$
$608$		0			0
$609$	−15.6071	−	23.8672i	−0.632432	−	0.967149i
$610$		0			0
$611$	9.61635	+	16.6560i	0.389036	+	0.673830i
$612$		0			0
$613$	−7.58762	+	13.1422i	−0.306461	+	0.530806i	−0.977586	−	0.210538i	$-0.932478\pi$
$613$	−7.58762	+	13.1422i	−0.306461	+	0.530806i	0.671124	+	0.741345i	$0.265812\pi$
$614$		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	0.800521	−	0.599305i	$-0.204556\pi$
$619$	16.9622	+	9.79314i	0.681769	+	0.393619i	−0.118752	+	0.992924i	$0.537889\pi$
$620$		0			0
$621$	−9.98750	+	13.3294i	−0.400785	+	0.534890i
$622$		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
$627$	7.30508	+	9.44527i	0.291737	+	0.377208i
$628$		0			0
$629$			26.4181i			1.05336i
$630$		0			0
$631$		−	28.3616i		−	1.12906i	−0.825413	−	0.564529i	$-0.809058\pi$
$631$		−	28.3616i		−	1.12906i	0.825413	−	0.564529i	$-0.190942\pi$
$632$		0			0
$633$	16.5792	+	21.4365i	0.658964	+	0.852023i
$634$		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
$639$	−3.08261	+	11.8662i	−0.121946	+	0.469419i
$640$		0			0
$641$	12.1003	+	6.98612i	0.477934	+	0.275935i	0.719555	−	0.694436i	$-0.244346\pi$
$641$	12.1003	+	6.98612i	0.477934	+	0.275935i	−0.241621	+	0.970371i	$0.577679\pi$
$642$		0			0
$643$		−	2.62685i		−	0.103593i	−0.998658	−	0.0517964i	$-0.983505\pi$
$643$		−	2.62685i		−	0.103593i	0.998658	−	0.0517964i	$-0.0164947\pi$
$644$		0			0
$645$	10.2749	+	4.21012i	0.404574	+	0.165773i
$646$		0			0
$647$	−15.3058	+	26.5104i	−0.601732	+	1.04223i	0.390827	+	0.920464i	$0.372189\pi$
$647$	−15.3058	+	26.5104i	−0.601732	+	1.04223i	−0.992559	+	0.121766i	$0.961144\pi$
$648$		0			0
$649$	19.8746	+	34.4238i	0.780146	+	1.35125i
$650$		0			0
$651$	7.92502	−	0.440469i	0.310606	−	0.0172633i
$652$		0			0
$653$	−29.4301	+	16.9915i	−1.15169	+	0.664928i	−0.949298	−	0.314377i	$-0.898205\pi$
$653$	−29.4301	+	16.9915i	−1.15169	+	0.664928i	−0.202391	+	0.979305i	$0.564871\pi$
$654$		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	$-0.724277\pi$
$659$	−33.2552			−1.29544			−0.647720	+	0.761879i	$0.724277\pi$
$660$		0			0
$661$	−10.8625	+	18.8145i	−0.422504	+	0.731798i	−0.996184	−	0.0872815i	$-0.972182\pi$
$661$	−10.8625	+	18.8145i	−0.422504	+	0.731798i	0.573680	+	0.819080i	$0.305515\pi$
$662$		0			0
$663$	14.4521	−	1.95883i	0.561274	−	0.0760746i
$664$		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
$669$	−12.4649	−	16.1168i	−0.481921	−	0.623110i
$670$		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
$675$	23.4732	+	2.81715i	0.903483	+	0.108432i
$676$		0			0
$677$	−33.2359	+	19.1888i	−1.27736	+	0.737484i	−0.976362	−	0.216140i	$-0.930653\pi$
$677$	−33.2359	+	19.1888i	−1.27736	+	0.737484i	−0.300998	+	0.953625i	$0.597320\pi$
$678$		0			0
$679$	8.63746	+	0.685484i	0.331475	+	0.0263065i
$680$		0			0
$681$	1.63105	+	12.0338i	0.0625021	+	0.461137i
$682$		0			0
$683$	−18.3708	+	31.8191i	−0.702938	+	1.21752i	0.264492	+	0.964388i	$0.414796\pi$
$683$	−18.3708	+	31.8191i	−0.702938	+	1.21752i	−0.967430	+	0.253137i	$0.918538\pi$
$684$		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	−0.355986	−	0.934491i	$-0.615855\pi$
$691$	7.23713	−	4.17836i	0.275313	−	0.158952i	0.631300	+	0.775539i	$0.282522\pi$
$692$		0			0
$693$	27.2771	+	31.4896i	1.03617	+	1.19619i
$694$		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
$705$	11.0740	−	1.50096i	0.417071	−	0.0565294i
$706$		0			0
$707$	6.25116	+	4.30234i	0.235099	+	0.161806i
$708$		0			0
$709$	−8.68729	−	15.0468i	−0.326258	−	0.565096i	0.655508	−	0.755188i	$-0.272455\pi$
$709$	−8.68729	−	15.0468i	−0.326258	−	0.565096i	−0.981766	+	0.190093i	$0.939121\pi$
$710$		0			0
$711$	4.14946	+	15.0260i	0.155617	+	0.563521i
$712$		0			0
$713$			5.55200i			0.207924i
$714$		0			0
$715$		−	7.04329i		−	0.263404i
$716$		0			0
$717$	−11.9679	+	9.25613i	−0.446950	+	0.345676i
$718$		0			0
$719$	−5.68941	−	9.85435i	−0.212179	−	0.367505i	0.740217	−	0.672368i	$-0.234723\pi$
$719$	−5.68941	−	9.85435i	−0.212179	−	0.367505i	−0.952396	+	0.304863i	$0.901389\pi$
$720$		0			0
$721$	−40.5120	+	19.2906i	−1.50875	+	0.718421i
$722$		0			0
$723$	1.62843	+	12.0145i	0.0605621	+	0.446824i
$724$		0			0
$725$	−24.5201	−	14.1567i	−0.910654	−	0.525766i
$726$		0			0
$727$			32.5479i			1.20713i	0.797312	+	0.603567i	$0.206254\pi$
$727$			32.5479i			1.20713i	−0.797312	+	0.603567i	$0.793746\pi$
$728$		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	0.524504	−	0.851408i	$-0.324251\pi$
$733$	−12.8625	−	22.2786i	−0.475089	−	0.822878i	−0.999593	+	0.0285300i	$0.990917\pi$
$734$		0			0
$735$	4.23300	−	6.94666i	0.156137	−	0.256231i
$736$		0			0
$737$	13.5819	−	7.84152i	0.500296	−	0.288846i
$738$		0			0
$739$	−28.3368	−	16.3603i	−1.04239	−	0.601822i	−0.121878	−	0.992545i	$-0.538892\pi$
$739$	−28.3368	−	16.3603i	−1.04239	−	0.601822i	−0.920508	+	0.390723i	$0.872225\pi$
$740$		0			0
$741$	−1.72508	+	4.21012i	−0.0633725	+	0.154663i
$742$		0			0
$743$	17.4702			0.640921			0.320460	−	0.947262i	$-0.396162\pi$
$743$	17.4702			0.640921			0.320460	+	0.947262i	$0.396162\pi$
$744$		0			0
$745$	4.68729	−	8.11863i	0.171729	−	0.297444i
$746$		0			0
$747$	−1.54130	+	5.93310i	−0.0563933	+	0.217081i
$748$		0			0
$749$	−13.2624	−	27.8522i	−0.484598	−	1.01770i
$750$		0			0
$751$	22.5997	−	13.0479i	0.824674	−	0.476126i	−0.0273518	−	0.999626i	$-0.508707\pi$
$751$	22.5997	−	13.0479i	0.824674	−	0.476126i	0.852025	+	0.523500i	$0.175374\pi$
$752$		0			0
$753$	−14.7675	+	11.4213i	−0.538157	+	0.416217i
$754$		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
$759$	−23.0515	+	17.8283i	−0.836715	+	0.647125i
$760$		0			0
$761$	31.3330	−	18.0901i	1.13582	−	0.655767i	0.190429	−	0.981701i	$-0.439012\pi$
$761$	31.3330	−	18.0901i	1.13582	−	0.655767i	0.945392	+	0.325934i	$0.105679\pi$
$762$		0			0
$763$	22.2371	−	32.3098i	0.805038	−	1.16969i
$764$		0			0
$765$	2.13072	−	8.20201i	0.0770365	−	0.296544i
$766$		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	$-0.299375\pi$
$773$	5.12766	+	2.96046i	0.184429	+	0.106480i	−0.404943	+	0.914342i	$0.632709\pi$
$774$		0			0
$775$	6.82475	−	3.94027i	0.245152	−	0.141539i
$776$		0			0
$777$	−25.6623	−	12.9735i	−0.920630	−	0.465423i
$778$		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	0.477788	−	0.878475i	$-0.341439\pi$
$787$	−1.23713	−	0.714256i	−0.0440988	−	0.0254605i	−0.521887	+	0.853014i	$0.674772\pi$
$788$		0			0
$789$	4.26917	+	31.4977i	0.151986	+	1.12135i
$790$		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
$795$	−10.8242	+	8.37155i	−0.383894	+	0.296908i
$796$		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
$801$	−11.1577	−	40.4044i	−0.394239	−	1.42762i
$802$		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
$807$	1.15158	−	0.156084i	0.0405375	−	0.00549442i
$808$		0			0
$809$	−20.2351	−	11.6827i	−0.711427	−	0.410743i	0.100162	−	0.994971i	$-0.468064\pi$
$809$	−20.2351	−	11.6827i	−0.711427	−	0.410743i	−0.811589	+	0.584228i	$0.801397\pi$
$810$		0			0
$811$			21.7370i			0.763288i	0.924309	+	0.381644i	$0.124642\pi$
$811$			21.7370i			0.763288i	−0.924309	+	0.381644i	$0.875358\pi$
$812$		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
$819$	−5.19443	+	15.0006i	−0.181508	+	0.524163i
$820$		0			0
$821$	−11.6790	+	6.74287i	−0.407600	+	0.235328i	−0.689758	−	0.724040i	$-0.742283\pi$
$821$	−11.6790	+	6.74287i	−0.407600	+	0.235328i	0.282158	+	0.959368i	$0.408950\pi$
$822$		0			0
$823$	−5.58762	−	3.22602i	−0.194772	−	0.112452i	0.399442	−	0.916758i	$-0.369204\pi$
$823$	−5.58762	−	3.22602i	−0.194772	−	0.112452i	−0.594215	+	0.804306i	$0.702537\pi$
$824$		0			0
$825$	38.2749	+	15.6830i	1.33256	+	0.546013i
$826$		0			0
$827$	27.6870			0.962770			0.481385	−	0.876509i	$-0.340134\pi$
$827$	27.6870			0.962770			0.481385	+	0.876509i	$0.340134\pi$
$828$		0			0
$829$	13.6873	−	23.7071i	0.475379	−	0.823381i	−0.524223	−	0.851581i	$-0.675644\pi$
$829$	13.6873	−	23.7071i	0.475379	−	0.823381i	0.999602	+	0.0281999i	$0.00897749\pi$
$830$		0			0
$831$	1.33185	+	9.82629i	0.0462012	+	0.340870i
$832$		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
$837$	−1.07244	+	8.93587i	−0.0370691	+	0.308869i
$838$		0			0
$839$	8.17337			0.282176			0.141088	−	0.989997i	$-0.454940\pi$
$839$	8.17337			0.282176			0.141088	+	0.989997i	$0.454940\pi$
$840$		0			0
$841$	−9.72508			−0.335348
$842$		0			0
$843$	−2.84385	−	3.67702i	−0.0979474	−	0.126643i
$844$		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
$849$	32.1800	−	4.36165i	1.10442	−	0.149691i
$850$		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	$-0.226178\pi$
$857$	16.7487	+	9.66989i	0.572126	+	0.330317i	−0.185872	+	0.982574i	$0.559511\pi$
$858$		0			0
$859$	6.51204	−	3.75973i	0.222188	−	0.128280i	−0.384775	−	0.923010i	$-0.625721\pi$
$859$	6.51204	−	3.75973i	0.222188	−	0.128280i	0.606963	+	0.794730i	$0.292388\pi$
$860$		0			0
$861$	24.4833	+	37.4412i	0.834389	+	1.27599i
$862$		0			0
$863$	−1.60273	−	2.77600i	−0.0545574	−	0.0944962i	0.837457	−	0.546503i	$-0.184041\pi$
$863$	−1.60273	−	2.77600i	−0.0545574	−	0.0944962i	−0.892014	+	0.452007i	$0.850708\pi$
$864$		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
$873$	−2.47029	+	9.50912i	−0.0836065	+	0.321835i
$874$		0			0
$875$	1.34115	−	16.8993i	0.0453393	−	0.571299i
$876$		0			0
$877$	−5.41238	−	9.37451i	−0.182763	−	0.316555i	0.760057	−	0.649856i	$-0.225171\pi$
$877$	−5.41238	−	9.37451i	−0.182763	−	0.316555i	−0.942820	+	0.333301i	$0.891837\pi$
$878$		0			0
$879$	−24.4390	−	31.5990i	−0.824308	−	1.06581i
$880$		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	$-0.778449\pi$
$883$		−	38.1051i		−	1.28234i	0.767399	−	0.641170i	$-0.221551\pi$
$884$		0			0
$885$	5.38413	+	6.96153i	0.180985	+	0.234009i
$886$		0			0
$887$	0.721492	+	1.24966i	0.0242253	+	0.0419595i	0.877884	−	0.478874i	$-0.158955\pi$
$887$	0.721492	+	1.24966i	0.0242253	+	0.0419595i	−0.853659	+	0.520833i	$0.825621\pi$
$888$		0			0
$889$	0.0876242	−	1.10411i	0.00293882	−	0.0370307i
$890$		0			0
$891$	−40.5448	+	24.2416i	−1.35830	+	0.812126i
$892$		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
$903$	−23.9640	−	36.6471i	−0.797472	−	1.21954i
$904$		0			0
$905$	−8.77373	+	5.06551i	−0.291649	+	0.168383i
$906$		0			0
$907$	3.51204	+	2.02768i	0.116616	+	0.0673280i	0.557173	−	0.830396i	$-0.311886\pi$
$907$	3.51204	+	2.02768i	0.116616	+	0.0673280i	−0.440558	+	0.897724i	$0.645219\pi$
$908$		0			0
$909$	−6.03779	+	6.13072i	−0.200261	+	0.203343i
$910$		0			0
$911$	−37.9037			−1.25580			−0.627902	−	0.778292i	$-0.716086\pi$
$911$	−37.9037			−1.25580			−0.627902	+	0.778292i	$0.716086\pi$
$912$		0			0
$913$	−5.36254	+	9.28819i	−0.177474	+	0.307394i
$914$		0			0
$915$	4.28973	−	0.581426i	0.141814	−	0.0192213i
$916$		0			0
$917$	5.97029	+	12.5381i	0.197156	+	0.414045i
$918$		0			0
$919$	34.1375	−	19.7093i	1.12609	−	0.650149i	0.183142	−	0.983086i	$-0.441373\pi$
$919$	34.1375	−	19.7093i	1.12609	−	0.650149i	0.942949	+	0.332938i	$0.108040\pi$
$920$		0			0
$921$	18.3536	+	23.7307i	0.604771	+	0.781953i
$922$		0			0
$923$	−8.17337			−0.269030
$924$		0			0
$925$	−28.5498			−0.938713
$926$		0			0
$927$	−13.5432	−	49.0426i	−0.444817	−	1.61077i
$928$		0			0
$929$	22.8788	−	13.2091i	0.750628	−	0.433375i	−0.0752926	−	0.997161i	$-0.523989\pi$
$929$	22.8788	−	13.2091i	0.750628	−	0.433375i	0.825921	+	0.563786i	$0.190656\pi$
$930$		0			0
$931$	−8.58762	+	3.28356i	−0.281448	+	0.107614i
$932$		0			0
$933$	1.15570	+	8.52672i	0.0378361	+	0.279152i
$934$		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	$-0.226564\pi$
$941$	17.4895	+	10.0976i	0.570143	+	0.329172i	−0.187064	+	0.982348i	$0.559897\pi$
$942$		0			0
$943$	−27.0997	+	15.6460i	−0.882487	+	0.509504i
$944$		0			0
$945$	6.92099	+	6.09764i	0.225140	+	0.198356i
$946$		0			0
$947$	−12.1003	−	20.9584i	−0.393207	−	0.681055i	0.599663	−	0.800252i	$-0.295301\pi$
$947$	−12.1003	−	20.9584i	−0.393207	−	0.681055i	−0.992871	+	0.119197i	$0.961968\pi$
$948$		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
$957$	56.0613	−	7.59850i	1.81221	−	0.245625i
$958$		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
$963$	33.7171	−	9.31102i	1.08652	−	0.300043i
$964$		0			0
$965$		−	12.1439i		−	0.390925i
$966$		0			0
$967$		−	9.02134i		−	0.290107i	−0.989424	−	0.145053i	$-0.953665\pi$
$967$		−	9.02134i		−	0.290107i	0.989424	−	0.145053i	$-0.0463354\pi$
$968$		0			0
$969$	−7.57616	+	5.85949i	−0.243381	+	0.188234i
$970$		0			0
$971$	3.50563	+	6.07193i	0.112501	+	0.194858i	0.916778	−	0.399397i	$-0.130781\pi$
$971$	3.50563	+	6.07193i	0.112501	+	0.194858i	−0.804277	+	0.594255i	$0.797447\pi$
$972$		0			0
$973$	2.92442	−	36.8492i	0.0937526	−	1.18133i
$974$		0			0
$975$	2.11689	+	15.6183i	0.0677947	+	0.500185i
$976$		0			0
$977$	−34.8193	−	20.1030i	−1.11397	−	0.643151i	−0.174115	−	0.984725i	$-0.555706\pi$
$977$	−34.8193	−	20.1030i	−1.11397	−	0.643151i	−0.939855	+	0.341575i	$0.889040\pi$
$978$		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	−0.483536	−	0.875324i	$-0.660648\pi$
$983$	16.1870	−	28.0367i	0.516285	−	0.894232i	0.999821	−	0.0189076i	$-0.00601882\pi$
$984$		0			0
$985$	−2.37459	−	4.11290i	−0.0756606	−	0.131048i
$986$		0			0
$987$	−39.3277	−	19.8820i	−1.25181	−	0.632852i
$988$		0			0
$989$	26.5248	−	15.3141i	0.843441	−	0.486961i
$990$		0			0
$991$	13.5997	+	7.85177i	0.432008	+	0.249420i	0.700202	−	0.713945i	$-0.253093\pi$
$991$	13.5997	+	7.85177i	0.432008	+	0.249420i	−0.268194	+	0.963365i	$0.586427\pi$
$992$		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	−0.953994	−	0.299827i	$-0.903071\pi$
$997$	−6.86254	+	11.8863i	−0.217339	+	0.376442i	0.736655	+	0.676269i	$0.236404\pi$
$998$		0			0
$999$	19.5513	−	26.0933i	0.618576	−	0.825555i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bj.e.95.3	✓	8	3.2	odd	2	inner
336.2.bj.e.95.4	yes	8	1.1	even	1	trivial
336.2.bj.e.191.3	yes	8	28.23	odd	6	inner
336.2.bj.e.191.4	yes	8	84.23	even	6	inner
336.2.bj.g.95.1	yes	8	4.3	odd	2
336.2.bj.g.95.2	yes	8	12.11	even	2
336.2.bj.g.191.1	yes	8	21.2	odd	6
336.2.bj.g.191.2	yes	8	7.2	even	3
2352.2.h.m.2255.1		8	28.3	even	6
2352.2.h.m.2255.2		8	21.17	even	6
2352.2.h.m.2255.7		8	84.59	odd	6
2352.2.h.m.2255.8		8	7.3	odd	6
2352.2.h.n.2255.1		8	7.4	even	3
2352.2.h.n.2255.2		8	84.11	even	6
2352.2.h.n.2255.7		8	21.11	odd	6
2352.2.h.n.2255.8		8	28.11	odd	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37009 - 1.05965i) q^{3} +(0.581054 - 0.335472i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(0.754305 - 2.90362i) q^{9} +O(q^{10})\)	\(q+(1.37009 - 1.05965i) q^{3} +(0.581054 - 0.335472i) q^{5} +(-2.63746 - 0.209313i) q^{7} +(0.754305 - 2.90362i) q^{9} +(2.62440 - 4.54559i) q^{11} +2.00000 q^{13} +(0.440617 - 1.07534i) q^{15} +(3.64607 + 2.10506i) q^{17} +(-1.13746 + 0.656712i) q^{19} +(-3.83536 + 2.50799i) q^{21} +(-1.60273 - 2.77600i) q^{23} +(-2.27492 + 3.94027i) q^{25} +(-2.04334 - 4.77753i) q^{27} +6.22295i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-1.22105 - 9.00880i) q^{33} +(-1.60273 + 0.763171i) q^{35} +(3.13746 + 5.43424i) q^{37} +(2.74018 - 2.11929i) q^{39} -9.76212i q^{41} +9.55505i q^{43} +(-0.535792 - 1.94021i) q^{45} +(4.80818 + 8.32801i) q^{47} +(6.91238 + 1.10411i) q^{49} +(7.22606 - 0.979414i) q^{51} +(-10.1974 - 5.88748i) q^{53} -3.52165i q^{55} +(-0.862541 + 2.10506i) q^{57} +(-3.78651 + 6.55842i) q^{59} +(1.86254 + 3.22602i) q^{61} +(-2.59721 + 7.50030i) q^{63} +(1.16211 - 0.670944i) q^{65} +(2.58762 + 1.49397i) q^{67} +(-5.13746 - 2.10506i) q^{69} -4.08668 q^{71} +(-0.137459 + 0.238085i) q^{73} +(1.05844 + 7.80914i) q^{75} +(-7.87319 + 11.4395i) q^{77} +(-4.50000 + 2.59808i) q^{79} +(-7.86205 - 4.38043i) q^{81} -2.04334 q^{83} +2.82475 q^{85} +(6.59412 + 8.52601i) q^{87} +(12.1003 - 6.98612i) q^{89} +(-5.27492 - 0.418627i) q^{91} +(-2.97282 + 0.402933i) q^{93} +(-0.440617 + 0.763171i) q^{95} -3.27492 q^{97} +(-11.2191 - 11.0490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} - 6 q^{7} - q^{9}+O(q^{10}) \) 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

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