LMFDB - Embedded newform 1260.2.cj.c.209.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1260,2,Mod(209,1260)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1260.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1260, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.cj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0,0,0,0,0,0,4,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.3
Character	$\chi$	$=$	1260.209
Dual form			1260.2.cj.c.1049.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69802 - 0.341647i) q^{3} +(-2.12845 - 0.685343i) q^{5} +(-2.64558 - 0.0305430i) q^{7} +(2.76656 + 1.16025i) q^{9} +(3.70953 + 2.14170i) q^{11} +(1.37914 + 2.38874i) q^{13} +(3.38001 + 1.89091i) q^{15} -2.13278i q^{17} +0.346129i q^{19} +(4.48181 + 0.955714i) q^{21} +(1.20329 + 2.08415i) q^{23} +(4.06061 + 2.91744i) q^{25} +(-4.30128 - 2.91531i) q^{27} +(-3.56111 - 2.05601i) q^{29} +(-2.72485 + 1.57319i) q^{31} +(-5.56716 - 4.90400i) q^{33} +(5.61005 + 1.87814i) q^{35} -8.64188i q^{37} +(-1.52571 - 4.52731i) q^{39} +(-4.48722 - 7.77210i) q^{41} +(-8.92726 - 5.15416i) q^{43} +(-5.09331 - 4.36557i) q^{45} +(1.39333 + 0.804437i) q^{47} +(6.99813 + 0.161608i) q^{49} +(-0.728657 + 3.62151i) q^{51} +8.53014 q^{53} +(-6.42776 - 7.10081i) q^{55} +(0.118254 - 0.587735i) q^{57} +(0.598881 + 1.03729i) q^{59} +(-7.25327 - 4.18768i) q^{61} +(-7.28369 - 3.15402i) q^{63} +(-1.29833 - 6.02951i) q^{65} +(-6.26283 + 3.61585i) q^{67} +(-1.33116 - 3.95004i) q^{69} -15.5677i q^{71} -7.73314 q^{73} +(-5.89827 - 6.34117i) q^{75} +(-9.74843 - 5.77933i) q^{77} +(-5.00745 + 8.67315i) q^{79} +(6.30765 + 6.41977i) q^{81} +(4.29606 + 2.48033i) q^{83} +(-1.46169 + 4.53952i) q^{85} +(5.34441 + 4.70779i) q^{87} +17.3907 q^{89} +(-3.57566 - 6.36172i) q^{91} +(5.16433 - 1.74038i) q^{93} +(0.237217 - 0.736719i) q^{95} +(7.76586 - 13.4509i) q^{97} +(7.77773 + 10.2291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{9} + 24 q^{11} + 12 q^{15} + 2 q^{21} - 40 q^{25} + 12 q^{29} + 32 q^{39} + 62 q^{49} - 32 q^{51} - 36 q^{65} + 16 q^{79} - 28 q^{81} + 10 q^{85} + 28 q^{91} + 60 q^{95} + 124 q^{99}+O(q^{100}) $ 80 * q + 4 * q^9 + 24 * q^11 + 12 * q^15 + 2 * q^21 - 40 * q^25 + 12 * q^29 + 32 * q^39 + 62 * q^49 - 32 * q^51 - 36 * q^65 + 16 * q^79 - 28 * q^81 + 10 * q^85 + 28 * q^91 + 60 * q^95 + 124 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$-1$

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
$3$	−1.69802	−	0.341647i	−0.980353	−	0.197250i
$3$	−1.69802	−	0.341647i	−0.980353	−	0.197250i
$4$		0			0
$5$	−2.12845	−	0.685343i	−0.951872	−	0.306495i
$5$	−2.12845	−	0.685343i	−0.951872	−	0.306495i
$6$		0			0
$7$	−2.64558	−	0.0305430i	−0.999933	−	0.0115442i
$7$	−2.64558	−	0.0305430i	−0.999933	−	0.0115442i
$8$		0			0
$9$	2.76656	+	1.16025i	0.922185	+	0.386749i
$10$		0			0
$11$	3.70953	+	2.14170i	1.11847	+	0.645747i	0.941009	−	0.338382i	$-0.109879\pi$
$11$	3.70953	+	2.14170i	1.11847	+	0.645747i	0.177457	+	0.984128i	$0.443213\pi$
$12$		0			0
$13$	1.37914	+	2.38874i	0.382505	+	0.662518i	0.991420	−	0.130718i	$-0.0417282\pi$
$13$	1.37914	+	2.38874i	0.382505	+	0.662518i	−0.608915	+	0.793236i	$0.708395\pi$
$14$		0			0
$15$	3.38001	+	1.89091i	0.872715	+	0.488230i
$16$		0			0
$17$		−	2.13278i		−	0.517275i	−0.965974	−	0.258637i	$-0.916726\pi$
$17$		−	2.13278i		−	0.517275i	0.965974	−	0.258637i	$-0.0832735\pi$
$18$		0			0
$19$			0.346129i			0.0794075i	0.999211	+	0.0397038i	$0.0126414\pi$
$19$			0.346129i			0.0794075i	−0.999211	+	0.0397038i	$0.987359\pi$
$20$		0			0
$21$	4.48181	+	0.955714i	0.978011	+	0.208554i
$22$		0			0
$23$	1.20329	+	2.08415i	0.250903	+	0.434576i	0.963775	−	0.266718i	$-0.0859393\pi$
$23$	1.20329	+	2.08415i	0.250903	+	0.434576i	−0.712872	+	0.701294i	$0.752606\pi$
$24$		0			0
$25$	4.06061	+	2.91744i	0.812122	+	0.583488i
$26$		0			0
$27$	−4.30128	−	2.91531i	−0.827781	−	0.561051i
$28$		0			0
$29$	−3.56111	−	2.05601i	−0.661281	−	0.381791i	0.131484	−	0.991318i	$-0.458026\pi$
$29$	−3.56111	−	2.05601i	−0.661281	−	0.381791i	−0.792765	+	0.609527i	$0.791359\pi$
$30$		0			0
$31$	−2.72485	+	1.57319i	−0.489397	+	0.282554i	−0.724324	−	0.689459i	$-0.757848\pi$
$31$	−2.72485	+	1.57319i	−0.489397	+	0.282554i	0.234927	+	0.972013i	$0.424515\pi$
$32$		0			0
$33$	−5.56716	−	4.90400i	−0.969119	−	0.853677i
$34$		0			0
$35$	5.61005	+	1.87814i	0.948271	+	0.317463i
$36$		0			0
$37$		−	8.64188i		−	1.42072i	−0.703840	−	0.710358i	$-0.748533\pi$
$37$		−	8.64188i		−	1.42072i	0.703840	−	0.710358i	$-0.251467\pi$
$38$		0			0
$39$	−1.52571	−	4.52731i	−0.244308	−	0.724950i
$40$		0			0
$41$	−4.48722	−	7.77210i	−0.700786	−	1.21380i	−0.968191	−	0.250213i	$-0.919499\pi$
$41$	−4.48722	−	7.77210i	−0.700786	−	1.21380i	0.267404	−	0.963584i	$-0.413834\pi$
$42$		0			0
$43$	−8.92726	−	5.15416i	−1.36139	−	0.786001i	−0.371585	−	0.928399i	$-0.621186\pi$
$43$	−8.92726	−	5.15416i	−1.36139	−	0.786001i	−0.989810	+	0.142398i	$0.954519\pi$
$44$		0			0
$45$	−5.09331	−	4.36557i	−0.759266	−	0.650780i
$46$		0			0
$47$	1.39333	+	0.804437i	0.203237	+	0.117339i	0.598165	−	0.801373i	$-0.295897\pi$
$47$	1.39333	+	0.804437i	0.203237	+	0.117339i	−0.394927	+	0.918712i	$0.629230\pi$
$48$		0			0
$49$	6.99813	+	0.161608i	0.999733	+	0.0230868i
$50$		0			0
$51$	−0.728657	+	3.62151i	−0.102032	+	0.507112i
$52$		0			0
$53$	8.53014			1.17170			0.585852	−	0.810418i	$-0.300760\pi$
$53$	8.53014			1.17170			0.585852	+	0.810418i	$0.300760\pi$
$54$		0			0
$55$	−6.42776	−	7.10081i	−0.866719	−	0.957473i
$56$		0			0
$57$	0.118254	−	0.587735i	0.0156631	−	0.0778474i
$58$		0			0
$59$	0.598881	+	1.03729i	0.0779676	+	0.135044i	0.902373	−	0.430956i	$-0.141824\pi$
$59$	0.598881	+	1.03729i	0.0779676	+	0.135044i	−0.824405	+	0.566000i	$0.808490\pi$
$60$		0			0
$61$	−7.25327	−	4.18768i	−0.928686	−	0.536177i	−0.0422904	−	0.999105i	$-0.513465\pi$
$61$	−7.25327	−	4.18768i	−0.928686	−	0.536177i	−0.886396	+	0.462928i	$0.846799\pi$
$62$		0			0
$63$	−7.28369	−	3.15402i	−0.917659	−	0.397369i
$64$		0			0
$65$	−1.29833	−	6.02951i	−0.161038	−	0.747868i
$66$		0			0
$67$	−6.26283	+	3.61585i	−0.765126	+	0.441746i	−0.831133	−	0.556073i	$-0.812307\pi$
$67$	−6.26283	+	3.61585i	−0.765126	+	0.441746i	0.0660070	+	0.997819i	$0.478974\pi$
$68$		0			0
$69$	−1.33116	−	3.95004i	−0.160253	−	0.475528i
$70$		0			0
$71$		−	15.5677i		−	1.84755i	−0.382935	−	0.923775i	$-0.625087\pi$
$71$		−	15.5677i		−	1.84755i	0.382935	−	0.923775i	$-0.374913\pi$
$72$		0			0
$73$	−7.73314			−0.905096			−0.452548	−	0.891740i	$-0.649485\pi$
$73$	−7.73314			−0.905096			−0.452548	+	0.891740i	$0.649485\pi$
$74$		0			0
$75$	−5.89827	−	6.34117i	−0.681074	−	0.732215i
$76$		0			0
$77$	−9.74843	−	5.77933i	−1.11094	−	0.658616i
$78$		0			0
$79$	−5.00745	+	8.67315i	−0.563382	+	0.975806i	0.433816	+	0.901001i	$0.357167\pi$
$79$	−5.00745	+	8.67315i	−0.563382	+	0.975806i	−0.997198	+	0.0748046i	$0.976167\pi$
$80$		0			0
$81$	6.30765	+	6.41977i	0.700851	+	0.713308i
$82$		0			0
$83$	4.29606	+	2.48033i	0.471554	+	0.272252i	0.716890	−	0.697186i	$-0.245565\pi$
$83$	4.29606	+	2.48033i	0.471554	+	0.272252i	−0.245336	+	0.969438i	$0.578898\pi$
$84$		0			0
$85$	−1.46169	+	4.53952i	−0.158542	+	0.492380i
$86$		0			0
$87$	5.34441	+	4.70779i	0.572981	+	0.504728i
$88$		0			0
$89$	17.3907			1.84341			0.921706	−	0.387888i	$-0.126795\pi$
$89$	17.3907			1.84341			0.921706	+	0.387888i	$0.126795\pi$
$90$		0			0
$91$	−3.57566	−	6.36172i	−0.374831	−	0.666889i
$92$		0			0
$93$	5.16433	−	1.74038i	0.535516	−	0.180469i
$94$		0			0
$95$	0.237217	−	0.736719i	0.0243380	−	0.0755858i
$96$		0			0
$97$	7.76586	−	13.4509i	0.788503	−	1.36573i	−0.138380	−	0.990379i	$-0.544190\pi$
$97$	7.76586	−	13.4509i	0.788503	−	1.36573i	0.926884	−	0.375349i	$-0.122477\pi$
$98$		0			0
$99$	7.77773	+	10.2291i	0.781691	+	1.02806i
$100$		0			0
$101$	5.42303	−	9.39296i	0.539611	−	0.934634i	−0.459313	−	0.888274i	$-0.651904\pi$
$101$	5.42303	−	9.39296i	0.539611	−	0.934634i	0.998925	−	0.0463601i	$-0.0147622\pi$
$102$		0			0
$103$	0.0964875	+	0.167121i	0.00950720	+	0.0164669i	0.870740	−	0.491744i	$-0.163640\pi$
$103$	0.0964875	+	0.167121i	0.00950720	+	0.0164669i	−0.861233	+	0.508211i	$0.830307\pi$
$104$		0			0
$105$	−8.88432	−	5.10577i	−0.867021	−	0.498272i
$106$		0			0
$107$	1.49878			0.144892			0.0724461	−	0.997372i	$-0.476919\pi$
$107$	1.49878			0.144892			0.0724461	+	0.997372i	$0.476919\pi$
$108$		0			0
$109$	−11.6461			−1.11550			−0.557748	−	0.830011i	$-0.688334\pi$
$109$	−11.6461			−1.11550			−0.557748	+	0.830011i	$0.688334\pi$
$110$		0			0
$111$	−2.95247	+	14.6741i	−0.280236	+	1.39280i
$112$		0			0
$113$	1.94798	+	3.37400i	0.183251	+	0.317399i	0.942986	−	0.332834i	$-0.108005\pi$
$113$	1.94798	+	3.37400i	0.183251	+	0.317399i	−0.759735	+	0.650233i	$0.774671\pi$
$114$		0			0
$115$	−1.13278	−	5.26068i	−0.105632	−	0.490561i
$116$		0			0
$117$	1.04394	+	8.20873i	0.0965122	+	0.758897i
$118$		0			0
$119$	−0.0651415	+	5.64243i	−0.00597151	+	0.517241i
$120$		0			0
$121$	3.67376	+	6.36314i	0.333978	+	0.578467i
$122$		0			0
$123$	4.96409	+	14.7302i	0.447597	+	1.32818i
$124$		0			0
$125$	−6.64336	−	8.99254i	−0.594201	−	0.804317i
$126$		0			0
$127$		−	15.7059i		−	1.39367i	−0.717232	−	0.696835i	$-0.754591\pi$
$127$		−	15.7059i		−	1.39367i	0.717232	−	0.696835i	$-0.245409\pi$
$128$		0			0
$129$	13.3978	+	11.8018i	1.17961	+	1.03909i
$130$		0			0
$131$	1.10830	+	1.91963i	0.0968325	+	0.167719i	0.910372	−	0.413791i	$-0.135796\pi$
$131$	1.10830	+	1.91963i	0.0968325	+	0.167719i	−0.813539	+	0.581510i	$0.802462\pi$
$132$		0			0
$133$	0.0105718	−	0.915711i	0.000916693	−	0.0794022i
$134$		0			0
$135$	7.15707	+	9.15294i	0.615983	+	0.787760i
$136$		0			0
$137$	9.89083	−	17.1314i	0.845030	−	1.46364i	−0.0405642	−	0.999177i	$-0.512916\pi$
$137$	9.89083	−	17.1314i	0.845030	−	1.46364i	0.885595	−	0.464459i	$-0.153751\pi$
$138$		0			0
$139$	−5.87212	+	3.39027i	−0.498066	+	0.287559i	−0.727915	−	0.685668i	$-0.759510\pi$
$139$	−5.87212	+	3.39027i	−0.498066	+	0.287559i	0.229848	+	0.973226i	$0.426177\pi$
$140$		0			0
$141$	−2.09106	−	1.84198i	−0.176099	−	0.155122i
$142$		0			0
$143$			11.8148i			0.988005i
$144$		0			0
$145$	6.17058	+	6.81669i	0.512439	+	0.566096i
$146$		0			0
$147$	−11.8278	−	2.66530i	−0.975538	−	0.219830i
$148$		0			0
$149$	−7.13187	+	4.11759i	−0.584265	+	0.337326i	−0.762827	−	0.646603i	$-0.776189\pi$
$149$	−7.13187	+	4.11759i	−0.584265	+	0.337326i	0.178561	+	0.983929i	$0.442856\pi$
$150$		0			0
$151$	−4.52849	+	7.84358i	−0.368524	+	0.638302i	−0.989335	−	0.145658i	$-0.953470\pi$
$151$	−4.52849	+	7.84358i	−0.368524	+	0.638302i	0.620811	+	0.783960i	$0.286803\pi$
$152$		0			0
$153$	2.47455	−	5.90045i	0.200056	−	0.477023i
$154$		0			0
$155$	6.87788	−	1.48101i	0.552445	−	0.118957i
$156$		0			0
$157$	−0.367182	−	0.635978i	−0.0293043	−	0.0507566i	0.851001	−	0.525164i	$-0.175996\pi$
$157$	−0.367182	−	0.635978i	−0.0293043	−	0.0507566i	−0.880306	+	0.474407i	$0.842663\pi$
$158$		0			0
$159$	−14.4844	−	2.91429i	−1.14868	−	0.231118i
$160$		0			0
$161$	−3.11973	−	5.55053i	−0.245869	−	0.437443i
$162$		0			0
$163$		−	1.08999i		−	0.0853745i	−0.999088	−	0.0426873i	$-0.986408\pi$
$163$		−	1.08999i		−	0.0853745i	0.999088	−	0.0426873i	$-0.0135919\pi$
$164$		0			0
$165$	8.48851	+	14.2533i	0.660830	+	1.10962i
$166$		0			0
$167$	1.67239	−	0.965552i	0.129413	−	0.0747167i	−0.433896	−	0.900963i	$-0.642861\pi$
$167$	1.67239	−	0.965552i	0.129413	−	0.0747167i	0.563309	+	0.826246i	$0.309528\pi$
$168$		0			0
$169$	2.69594	−	4.66951i	0.207380	−	0.359193i
$170$		0			0
$171$	−0.401595	+	0.957586i	−0.0307108	+	0.0732284i
$172$		0			0
$173$	−7.68318	−	4.43589i	−0.584141	−	0.337254i	0.178636	−	0.983915i	$-0.442832\pi$
$173$	−7.68318	−	4.43589i	−0.584141	−	0.337254i	−0.762777	+	0.646661i	$0.776165\pi$
$174$		0			0
$175$	−10.6535	−	7.84233i	−0.805332	−	0.592824i
$176$		0			0
$177$	−0.662525	−	1.96595i	−0.0497984	−	0.147770i
$178$		0			0
$179$		−	16.3073i		−	1.21886i	−0.792839	−	0.609431i	$-0.791398\pi$
$179$		−	16.3073i		−	1.21886i	0.792839	−	0.609431i	$-0.208602\pi$
$180$		0			0
$181$		−	23.6833i		−	1.76037i	−0.474633	−	0.880184i	$-0.657419\pi$
$181$		−	23.6833i		−	1.76037i	0.474633	−	0.880184i	$-0.342581\pi$
$182$		0			0
$183$	10.8855	+	9.58882i	0.804680	+	0.708826i
$184$		0			0
$185$	−5.92265	+	18.3938i	−0.435442	+	1.35234i
$186$		0			0
$187$	4.56777	−	7.91162i	0.334029	−	0.578555i
$188$		0			0
$189$	11.2903	+	7.84404i	0.821249	+	0.570570i
$190$		0			0
$191$	−9.28174	−	5.35881i	−0.671603	−	0.387750i	0.125081	−	0.992147i	$-0.460081\pi$
$191$	−9.28174	−	5.35881i	−0.671603	−	0.387750i	−0.796684	+	0.604396i	$0.793414\pi$
$192$		0			0
$193$	−9.09405	+	5.25045i	−0.654604	+	0.377936i	−0.790218	−	0.612826i	$-0.790033\pi$
$193$	−9.09405	+	5.25045i	−0.654604	+	0.377936i	0.135614	+	0.990762i	$0.456699\pi$
$194$		0			0
$195$	0.144626	+	10.6818i	0.0103569	+	0.764940i
$196$		0			0
$197$	−13.3390			−0.950366			−0.475183	−	0.879887i	$-0.657618\pi$
$197$	−13.3390			−0.950366			−0.475183	+	0.879887i	$0.657618\pi$
$198$		0			0
$199$			0.909948i			0.0645045i	0.999480	+	0.0322523i	$0.0102680\pi$
$199$			0.909948i			0.0645045i	−0.999480	+	0.0322523i	$0.989732\pi$
$200$		0			0
$201$	11.8698	−	4.00011i	0.837228	−	0.282146i
$202$		0			0
$203$	9.35839	+	5.54809i	0.656830	+	0.389399i
$204$		0			0
$205$	4.22428	+	19.6178i	0.295037	+	1.37017i
$206$		0			0
$207$	0.910826	+	7.16203i	0.0633068	+	0.497796i
$208$		0			0
$209$	−0.741305	+	1.28398i	−0.0512772	+	0.0888146i
$210$		0			0
$211$	−4.59148	−	7.95268i	−0.316091	−	0.547485i	0.663578	−	0.748107i	$-0.269037\pi$
$211$	−4.59148	−	7.95268i	−0.316091	−	0.547485i	−0.979669	+	0.200622i	$0.935704\pi$
$212$		0			0
$213$	−5.31867	+	26.4344i	−0.364429	+	1.81125i
$214$		0			0
$215$	15.4689	+	17.0886i	1.05497	+	1.16543i
$216$		0			0
$217$	7.25684	−	4.07877i	0.492627	−	0.276885i
$218$		0			0
$219$	13.1310	+	2.64200i	0.887313	+	0.178530i
$220$		0			0
$221$	5.09466	−	2.94140i	0.342704	−	0.197860i
$222$		0			0
$223$	5.22090	−	9.04286i	0.349617	−	0.605555i	−0.636564	−	0.771224i	$-0.719645\pi$
$223$	5.22090	−	9.04286i	0.349617	−	0.605555i	0.986181	+	0.165669i	$0.0529783\pi$
$224$		0			0
$225$	7.84895	+	12.7826i	0.523264	+	0.852171i
$226$		0			0
$227$	10.8980	+	6.29195i	0.723324	+	0.417611i	0.815975	−	0.578087i	$-0.196201\pi$
$227$	10.8980	+	6.29195i	0.723324	+	0.417611i	−0.0926508	+	0.995699i	$0.529534\pi$
$228$		0			0
$229$	−19.5072	+	11.2625i	−1.28907	+	0.744247i	−0.978489	−	0.206298i	$-0.933858\pi$
$229$	−19.5072	+	11.2625i	−1.28907	+	0.744247i	−0.310585	+	0.950546i	$0.600525\pi$
$230$		0			0
$231$	14.5786	+	13.1439i	0.959199	+	0.864808i
$232$		0			0
$233$	16.8342			1.10285			0.551424	−	0.834225i	$-0.314085\pi$
$233$	16.8342			1.10285			0.551424	+	0.834225i	$0.314085\pi$
$234$		0			0
$235$	−2.41431	−	2.66711i	−0.157492	−	0.173983i
$236$		0			0
$237$	11.4659	−	13.0164i	0.744791	−	0.845508i
$238$		0			0
$239$	−6.36365	+	3.67406i	−0.411631	+	0.237655i	−0.691490	−	0.722386i	$-0.743045\pi$
$239$	−6.36365	+	3.67406i	−0.411631	+	0.237655i	0.279860	+	0.960041i	$0.409712\pi$
$240$		0			0
$241$	24.2344	+	13.9917i	1.56107	+	0.901287i	0.997149	+	0.0754616i	$0.0240430\pi$
$241$	24.2344	+	13.9917i	1.56107	+	0.901287i	0.563926	+	0.825825i	$0.309290\pi$
$242$		0			0
$243$	−8.51724	−	13.0559i	−0.546381	−	0.837537i
$244$		0			0
$245$	−14.7844	−	5.14010i	−0.944543	−	0.328389i
$246$		0			0
$247$	−0.826814	+	0.477361i	−0.0526089	+	0.0303738i
$248$		0			0
$249$	−6.44741	−	5.67940i	−0.408588	−	0.359917i
$250$		0			0
$251$	−25.9957			−1.64083			−0.820417	−	0.571765i	$-0.806259\pi$
$251$	−25.9957			−1.64083			−0.820417	+	0.571765i	$0.806259\pi$
$252$		0			0
$253$			10.3083i			0.648078i
$254$		0			0
$255$	4.03288	−	7.20882i	0.252549	−	0.451434i
$256$		0			0
$257$	22.1950	−	12.8143i	1.38449	−	0.799335i	0.391802	−	0.920050i	$-0.371852\pi$
$257$	22.1950	−	12.8143i	1.38449	−	0.799335i	0.992687	+	0.120715i	$0.0385186\pi$
$258$		0			0
$259$	−0.263949	+	22.8627i	−0.0164010	+	1.42062i
$260$		0			0
$261$	−7.46653	−	9.81982i	−0.462167	−	0.607832i
$262$		0			0
$263$	−2.08441	+	3.61030i	−0.128530	+	0.222621i	−0.923107	−	0.384542i	$-0.874359\pi$
$263$	−2.08441	+	3.61030i	−0.128530	+	0.222621i	0.794577	+	0.607163i	$0.207693\pi$
$264$		0			0
$265$	−18.1560	−	5.84607i	−1.11531	−	0.359121i
$266$		0			0
$267$	−29.5298	−	5.94148i	−1.80720	−	0.363613i
$268$		0			0
$269$	15.6718			0.955525			0.477762	−	0.878489i	$-0.341448\pi$
$269$	15.6718			0.955525			0.477762	+	0.878489i	$0.341448\pi$
$270$		0			0
$271$			0.149723i			0.00909502i	0.999990	+	0.00454751i	$0.00144752\pi$
$271$			0.149723i			0.00909502i	−0.999990	+	0.00454751i	$0.998552\pi$
$272$		0			0
$273$	3.89809	+	12.0239i	0.235923	+	0.727723i
$274$		0			0
$275$	8.81469	+	19.5189i	0.531546	+	1.17704i
$276$		0			0
$277$	−20.5905	−	11.8879i	−1.23717	−	0.714278i	−0.268651	−	0.963238i	$-0.586578\pi$
$277$	−20.5905	−	11.8879i	−1.23717	−	0.714278i	−0.968514	+	0.248960i	$0.919911\pi$
$278$		0			0
$279$	−9.36374	+	1.19083i	−0.560592	+	0.0712929i
$280$		0			0
$281$	−9.40064	−	5.42746i	−0.560795	−	0.323775i	0.192669	−	0.981264i	$-0.438286\pi$
$281$	−9.40064	−	5.42746i	−0.560795	−	0.323775i	−0.753465	+	0.657488i	$0.771619\pi$
$282$		0			0
$283$	16.6100	+	28.7694i	0.987363	+	1.71016i	0.630923	+	0.775846i	$0.282677\pi$
$283$	16.6100	+	28.7694i	0.987363	+	1.71016i	0.356441	+	0.934318i	$0.383990\pi$
$284$		0			0
$285$	−0.654498	+	1.16992i	−0.0387691	+	0.0693001i
$286$		0			0
$287$	11.6339	+	20.6987i	0.686727	+	1.22181i
$288$		0			0
$289$	12.4513			0.732427
$290$		0			0
$291$	−17.7820	+	20.1867i	−1.04240	+	1.18336i
$292$		0			0
$293$	5.51318	−	3.18304i	0.322084	−	0.185955i	−0.330237	−	0.943898i	$-0.607129\pi$
$293$	5.51318	−	3.18304i	0.322084	−	0.185955i	0.652321	+	0.757943i	$0.273795\pi$
$294$		0			0
$295$	−0.563788	−	2.61826i	−0.0328250	−	0.152441i
$296$		0			0
$297$	−9.71201	−	20.0265i	−0.563548	−	1.16205i
$298$		0			0
$299$	−3.31900	+	5.74868i	−0.191943	+	0.332455i
$300$		0			0
$301$	23.4603	+	13.9084i	1.35223	+	0.801665i
$302$		0			0
$303$	−12.4175	+	14.0967i	−0.713366	+	0.809834i
$304$		0			0
$305$	12.5682	+	13.8842i	0.719655	+	0.795010i
$306$		0			0
$307$	26.6866			1.52309			0.761543	−	0.648115i	$-0.224442\pi$
$307$	26.6866			1.52309			0.761543	+	0.648115i	$0.224442\pi$
$308$		0			0
$309$	−0.106741	−	0.316740i	−0.00607231	−	0.0180187i
$310$		0			0
$311$	10.1102	+	17.5114i	0.573297	+	0.992979i	0.996224	+	0.0868156i	$0.0276691\pi$
$311$	10.1102	+	17.5114i	0.573297	+	0.992979i	−0.422928	+	0.906163i	$0.638998\pi$
$312$		0			0
$313$	12.2020	−	21.1345i	0.689698	−	1.19459i	−0.282238	−	0.959345i	$-0.591077\pi$
$313$	12.2020	−	21.1345i	0.689698	−	1.19459i	0.971936	−	0.235247i	$-0.0755900\pi$
$314$		0			0
$315$	13.3414	+	11.7050i	0.751703	+	0.659502i
$316$		0			0
$317$	−2.23508	+	3.87127i	−0.125534	+	0.217432i	−0.921942	−	0.387329i	$-0.873398\pi$
$317$	−2.23508	+	3.87127i	−0.125534	+	0.217432i	0.796407	+	0.604761i	$0.206731\pi$
$318$		0			0
$319$	−8.80670	−	15.2537i	−0.493081	−	0.854041i
$320$		0			0
$321$	−2.54496	−	0.512052i	−0.142046	−	0.0285800i
$322$		0			0
$323$	0.738217			0.0410755
$324$		0			0
$325$	−1.36885	+	13.7233i	−0.0759304	+	0.761232i
$326$		0			0
$327$	19.7754	+	3.97886i	1.09358	+	0.220031i
$328$		0			0
$329$	−3.66158	−	2.17075i	−0.201869	−	0.119678i
$330$		0			0
$331$	−5.97922	+	10.3563i	−0.328648	+	0.569235i	−0.982244	−	0.187609i	$-0.939926\pi$
$331$	−5.97922	+	10.3563i	−0.328648	+	0.569235i	0.653596	+	0.756844i	$0.273260\pi$
$332$		0			0
$333$	10.0267	−	23.9082i	0.549461	−	1.31016i
$334$		0			0
$335$	15.8082	−	3.40397i	0.863695	−	0.185978i
$336$		0			0
$337$	−13.7406	+	7.93316i	−0.748500	+	0.432147i	−0.825152	−	0.564911i	$-0.808910\pi$
$337$	−13.7406	+	7.93316i	−0.748500	+	0.432147i	0.0766518	+	0.997058i	$0.475577\pi$
$338$		0			0
$339$	−2.15500	−	6.39465i	−0.117043	−	0.347309i
$340$		0			0
$341$	−13.4772			−0.729833
$342$		0			0
$343$	−18.5092	−	0.641289i	−0.999400	−	0.0346263i
$344$		0			0
$345$	0.126185	+	9.31976i	0.00679356	+	0.501759i
$346$		0			0
$347$	−9.11589	−	15.7892i	−0.489367	−	0.847608i	0.510559	−	0.859843i	$-0.329439\pi$
$347$	−9.11589	−	15.7892i	−0.489367	−	0.847608i	−0.999925	+	0.0122352i	$0.996105\pi$
$348$		0			0
$349$	−15.6374	−	9.02828i	−0.837053	−	0.483273i	0.0192087	−	0.999815i	$-0.493885\pi$
$349$	−15.6374	−	9.02828i	−0.837053	−	0.483273i	−0.856261	+	0.516543i	$0.827219\pi$
$350$		0			0
$351$	1.03185	−	14.2953i	0.0550763	−	0.763024i
$352$		0			0
$353$	9.63520	+	5.56289i	0.512830	+	0.296083i	0.733996	−	0.679154i	$-0.237653\pi$
$353$	9.63520	+	5.56289i	0.512830	+	0.296083i	−0.221166	+	0.975236i	$0.570986\pi$
$354$		0			0
$355$	−10.6692	+	33.1352i	−0.566265	+	1.75863i
$356$		0			0
$357$	2.03833	−	9.55871i	0.107880	−	0.505901i
$358$		0			0
$359$		−	23.2660i		−	1.22793i	−0.789332	−	0.613966i	$-0.789573\pi$
$359$		−	23.2660i		−	1.22793i	0.789332	−	0.613966i	$-0.210427\pi$
$360$		0			0
$361$	18.8802			0.993694
$362$		0			0
$363$	−4.06418	−	12.0599i	−0.213314	−	0.632979i
$364$		0			0
$365$	16.4596	+	5.29985i	0.861535	+	0.277407i
$366$		0			0
$367$	2.75639	−	4.77421i	0.143883	−	0.249212i	−0.785073	−	0.619403i	$-0.787375\pi$
$367$	2.75639	−	4.77421i	0.143883	−	0.249212i	0.928955	+	0.370191i	$0.120708\pi$
$368$		0			0
$369$	−3.39660	−	26.7082i	−0.176820	−	1.39037i
$370$		0			0
$371$	−22.5671	−	0.260536i	−1.17163	−	0.0135263i
$372$		0			0
$373$	8.15009	−	4.70546i	0.421996	−	0.243639i	−0.273935	−	0.961748i	$-0.588325\pi$
$373$	8.15009	−	4.70546i	0.421996	−	0.243639i	0.695931	+	0.718109i	$0.254992\pi$
$374$		0			0
$375$	8.20831	+	17.5392i	0.423875	+	0.905721i
$376$		0			0
$377$		−	11.3421i		−	0.584148i
$378$		0			0
$379$	−10.1546			−0.521607			−0.260804	−	0.965392i	$-0.583988\pi$
$379$	−10.1546			−0.521607			−0.260804	+	0.965392i	$0.583988\pi$
$380$		0			0
$381$	−5.36585	+	26.6689i	−0.274901	+	1.36629i
$382$		0			0
$383$	0.167578	−	0.0967510i	0.00856282	−	0.00494374i	−0.495712	−	0.868487i	$-0.665093\pi$
$383$	0.167578	−	0.0967510i	0.00856282	−	0.00494374i	0.504275	+	0.863543i	$0.331760\pi$
$384$		0			0
$385$	16.7882	+	18.9820i	0.855608	+	0.967414i
$386$		0			0
$387$	−18.7177	−	24.6171i	−0.951472	−	1.25136i
$388$		0			0
$389$	15.6085	+	9.01156i	0.791381	+	0.456904i	0.840448	−	0.541891i	$-0.182292\pi$
$389$	15.6085	+	9.01156i	0.791381	+	0.456904i	−0.0490675	+	0.998795i	$0.515625\pi$
$390$		0			0
$391$	4.44504	−	2.56634i	0.224795	−	0.129786i
$392$		0			0
$393$	−1.22608	−	3.63822i	−0.0618476	−	0.183524i
$394$		0			0
$395$	16.6022	−	15.0286i	0.835347	−	0.756169i
$396$		0			0
$397$	−31.1532			−1.56353			−0.781766	−	0.623572i	$-0.785681\pi$
$397$	−31.1532			−1.56353			−0.781766	+	0.623572i	$0.785681\pi$
$398$		0			0
$399$	−0.330801	+	1.55129i	−0.0165608	+	0.0776614i
$400$		0			0
$401$	1.35629	−	0.783054i	0.0677298	−	0.0391038i	−0.465753	−	0.884915i	$-0.654216\pi$
$401$	1.35629	−	0.783054i	0.0677298	−	0.0391038i	0.533482	+	0.845811i	$0.320883\pi$
$402$		0			0
$403$	−7.51590	−	4.33931i	−0.374394	−	0.216156i
$404$		0			0
$405$	−9.02579	−	17.9871i	−0.448495	−	0.893785i
$406$		0			0
$407$	18.5083	−	32.0573i	0.917423	−	1.58902i
$408$		0			0
$409$	−12.9573	+	7.48092i	−0.640699	+	0.369908i	−0.784884	−	0.619643i	$-0.787277\pi$
$409$	−12.9573	+	7.48092i	−0.640699	+	0.369908i	0.144185	+	0.989551i	$0.453944\pi$
$410$		0			0
$411$	−22.6477	+	25.7103i	−1.11713	+	1.26820i
$412$		0			0
$413$	−1.55270	−	2.76252i	−0.0764035	−	0.135935i
$414$		0			0
$415$	−7.44408	−	8.22355i	−0.365416	−	0.403678i
$416$		0			0
$417$	11.1293	−	3.75056i	0.545002	−	0.183666i
$418$		0			0
$419$	−11.9778	−	20.7462i	−0.585155	−	1.01352i	−0.994856	−	0.101299i	$-0.967700\pi$
$419$	−11.9778	−	20.7462i	−0.585155	−	1.01352i	0.409701	−	0.912220i	$-0.365633\pi$
$420$		0			0
$421$	−14.6525	+	25.3789i	−0.714121	+	1.23689i	0.249176	+	0.968458i	$0.419840\pi$
$421$	−14.6525	+	25.3789i	−0.714121	+	1.23689i	−0.963298	+	0.268436i	$0.913493\pi$
$422$		0			0
$423$	2.92137	+	3.84212i	0.142042	+	0.186810i
$424$		0			0
$425$	6.22225	−	8.66039i	0.301824	−	0.420090i
$426$		0			0
$427$	19.0612	+	11.3004i	0.922435	+	0.546862i
$428$		0			0
$429$	4.03649	−	20.0618i	0.194884	−	0.968594i
$430$		0			0
$431$		−	3.61546i		−	0.174151i	−0.996202	−	0.0870754i	$-0.972248\pi$
$431$		−	3.61546i		−	0.174151i	0.996202	−	0.0870754i	$-0.0277521\pi$
$432$		0			0
$433$	−0.611625			−0.0293928			−0.0146964	−	0.999892i	$-0.504678\pi$
$433$	−0.611625			−0.0293928			−0.0146964	+	0.999892i	$0.504678\pi$
$434$		0			0
$435$	−8.14887	−	13.6830i	−0.390709	−	0.656052i
$436$		0			0
$437$	−0.721386	+	0.416493i	−0.0345086	+	0.0199235i
$438$		0			0
$439$	5.69916	+	3.29041i	0.272006	+	0.157043i	0.629799	−	0.776758i	$-0.283137\pi$
$439$	5.69916	+	3.29041i	0.272006	+	0.157043i	−0.357793	+	0.933801i	$0.616471\pi$
$440$		0			0
$441$	19.1732	+	8.56666i	0.913010	+	0.407936i
$442$		0			0
$443$	−17.5041	+	30.3181i	−0.831647	+	1.44045i	0.0650847	+	0.997880i	$0.479268\pi$
$443$	−17.5041	+	30.3181i	−0.831647	+	1.44045i	−0.896732	+	0.442575i	$0.854065\pi$
$444$		0			0
$445$	−37.0153	−	11.9186i	−1.75469	−	0.564996i
$446$		0			0
$447$	13.5168	−	4.55517i	0.639324	−	0.215452i
$448$		0			0
$449$			34.6774i			1.63653i	0.574841	+	0.818265i	$0.305064\pi$
$449$			34.6774i			1.63653i	−0.574841	+	0.818265i	$0.694936\pi$
$450$		0			0
$451$		−	38.4411i		−	1.81012i
$452$		0			0
$453$	10.3692	−	11.7714i	0.487188	−	0.553070i
$454$		0			0
$455$	3.25066	+	15.9912i	0.152393	+	0.749677i
$456$		0			0
$457$	−0.773990	−	0.446863i	−0.0362057	−	0.0209034i	0.481788	−	0.876288i	$-0.339988\pi$
$457$	−0.773990	−	0.446863i	−0.0362057	−	0.0209034i	−0.517994	+	0.855384i	$0.673321\pi$
$458$		0			0
$459$	−6.21771	+	9.17367i	−0.290218	+	0.428190i
$460$		0			0
$461$	−9.10914	+	15.7775i	−0.424255	+	0.734831i	−0.996351	−	0.0853557i	$-0.972797\pi$
$461$	−9.10914	+	15.7775i	−0.424255	+	0.734831i	0.572095	+	0.820187i	$0.306131\pi$
$462$		0			0
$463$	2.63661	−	1.52225i	0.122534	−	0.0707448i	−0.437480	−	0.899228i	$-0.644129\pi$
$463$	2.63661	−	1.52225i	0.122534	−	0.0707448i	0.560014	+	0.828483i	$0.310796\pi$
$464$		0			0
$465$	−12.1848	+	0.164976i	−0.565056	+	0.00765056i
$466$		0			0
$467$		−	33.2644i		−	1.53929i	−0.638471	−	0.769646i	$-0.720433\pi$
$467$		−	33.2644i		−	1.53929i	0.638471	−	0.769646i	$-0.279567\pi$
$468$		0			0
$469$	16.6792	−	9.37470i	0.770175	−	0.432884i
$470$		0			0
$471$	0.406204	+	1.20535i	0.0187169	+	0.0555397i
$472$		0			0
$473$	−22.0773	−	38.2390i	−1.01512	−	1.75823i
$474$		0			0
$475$	−1.00981	+	1.40550i	−0.0463333	+	0.0644886i
$476$		0			0
$477$	23.5991	+	9.89706i	1.08053	+	0.453155i
$478$		0			0
$479$	6.15474	−	10.6603i	0.281217	−	0.487083i	−0.690467	−	0.723363i	$-0.742595\pi$
$479$	6.15474	−	10.6603i	0.281217	−	0.487083i	0.971685	+	0.236281i	$0.0759284\pi$
$480$		0			0
$481$	20.6432	−	11.9184i	0.941250	−	0.543431i
$482$		0			0
$483$	3.40104	+	10.4908i	0.154753	+	0.477347i
$484$		0			0
$485$	−25.7477	+	23.3072i	−1.16914	+	1.05833i
$486$		0			0
$487$		−	9.64903i		−	0.437239i	−0.975810	−	0.218620i	$-0.929845\pi$
$487$		−	9.64903i		−	0.437239i	0.975810	−	0.218620i	$-0.0701554\pi$
$488$		0			0
$489$	−0.372391	+	1.85082i	−0.0168401	+	0.0836972i
$490$		0			0
$491$	26.2176	−	15.1367i	1.18318	−	0.683111i	0.226434	−	0.974026i	$-0.427293\pi$
$491$	26.2176	−	15.1367i	1.18318	−	0.683111i	0.956749	+	0.290916i	$0.0939599\pi$
$492$		0			0
$493$	−4.38501	+	7.59506i	−0.197491	+	0.342064i
$494$		0			0
$495$	−9.54407	−	27.1026i	−0.428974	−	1.21817i
$496$		0			0
$497$	−0.475485	+	41.1856i	−0.0213284	+	1.84743i
$498$		0			0
$499$	−14.4570	−	25.0403i	−0.647185	−	1.12096i	−0.983792	−	0.179312i	$-0.942613\pi$
$499$	−14.4570	−	25.0403i	−0.647185	−	1.12096i	0.336607	−	0.941645i	$-0.390721\pi$
$500$		0			0
$501$	−3.16963	+	1.06816i	−0.141608	+	0.0477220i
$502$		0			0
$503$		−	0.957888i		−	0.0427101i	−0.999772	−	0.0213550i	$-0.993202\pi$
$503$		−	0.957888i		−	0.0427101i	0.999772	−	0.0213550i	$-0.00679804\pi$
$504$		0			0
$505$	−17.9801	+	16.2758i	−0.800102	+	0.724265i
$506$		0			0
$507$	−6.17309	+	7.00787i	−0.274156	+	0.311230i
$508$		0			0
$509$	−3.51350	−	6.08557i	−0.155733	−	0.269738i	0.777593	−	0.628769i	$-0.216441\pi$
$509$	−3.51350	−	6.08557i	−0.155733	−	0.269738i	−0.933326	+	0.359031i	$0.883107\pi$
$510$		0			0
$511$	20.4586	+	0.236193i	0.905035	+	0.0104486i
$512$		0			0
$513$	1.00907	−	1.48880i	0.0445517	−	0.0657320i
$514$		0			0
$515$	−0.0908336	−	0.421837i	−0.00400261	−	0.0185883i
$516$		0			0
$517$	3.44573	+	5.96817i	0.151543	+	0.262480i
$518$		0			0
$519$	11.5307	+	10.1572i	0.506142	+	0.445850i
$520$		0			0
$521$	−40.1160			−1.75751			−0.878757	−	0.477270i	$-0.841626\pi$
$521$	−40.1160			−1.75751			−0.878757	+	0.477270i	$0.841626\pi$
$522$		0			0
$523$	−14.5004			−0.634057			−0.317029	−	0.948416i	$-0.602685\pi$
$523$	−14.5004			−0.634057			−0.317029	+	0.948416i	$0.602685\pi$
$524$		0			0
$525$	15.4106	+	16.9562i	0.672575	+	0.740029i
$526$		0			0
$527$	3.35527	+	5.81150i	0.146158	+	0.253153i
$528$		0			0
$529$	8.60420	−	14.9029i	0.374096	−	0.647953i
$530$		0			0
$531$	0.453322	+	3.56457i	0.0196725	+	0.154689i
$532$		0			0
$533$	12.3770	−	21.4376i	0.536108	−	0.928567i
$534$		0			0
$535$	−3.19007	−	1.02718i	−0.137919	−	0.0444087i
$536$		0			0
$537$	−5.57132	+	27.6901i	−0.240420	+	1.19492i
$538$		0			0
$539$	25.6137	+	15.5874i	1.10326	+	0.671397i
$540$		0			0
$541$	32.2880			1.38817			0.694084	−	0.719894i	$-0.255810\pi$
$541$	32.2880			1.38817			0.694084	+	0.719894i	$0.255810\pi$
$542$		0			0
$543$	−8.09133	+	40.2148i	−0.347232	+	1.72578i
$544$		0			0
$545$	24.7882	+	7.98158i	1.06181	+	0.341893i
$546$		0			0
$547$	5.42139	+	3.13004i	0.231802	+	0.133831i	0.611403	−	0.791319i	$-0.290605\pi$
$547$	5.42139	+	3.13004i	0.231802	+	0.133831i	−0.379601	+	0.925150i	$0.623939\pi$
$548$		0			0
$549$	−15.2078	−	20.0010i	−0.649055	−	0.853623i
$550$		0			0
$551$	0.711644	−	1.23260i	0.0303171	−	0.0525107i
$552$		0			0
$553$	13.5125	−	22.7925i	0.574609	−	0.969237i
$554$		0			0
$555$	16.3410	−	29.2097i	0.693636	−	1.23988i
$556$		0			0
$557$	−22.5574			−0.955787			−0.477893	−	0.878418i	$-0.658599\pi$
$557$	−22.5574			−0.955787			−0.477893	+	0.878418i	$0.658599\pi$
$558$		0			0
$559$		−	28.4332i		−	1.20260i
$560$		0			0
$561$	−10.4592	+	11.8735i	−0.441586	+	0.501301i
$562$		0			0
$563$	−31.9908	+	18.4699i	−1.34825	+	0.778414i	−0.988002	−	0.154442i	$-0.950642\pi$
$563$	−31.9908	+	18.4699i	−1.34825	+	0.778414i	−0.360250	+	0.932856i	$0.617309\pi$
$564$		0			0
$565$	−1.83383	−	8.51643i	−0.0771499	−	0.358289i
$566$		0			0
$567$	−16.4913	−	17.1766i	−0.692569	−	0.721351i
$568$		0			0
$569$	−24.6918	−	14.2558i	−1.03513	−	0.597635i	−0.116683	−	0.993169i	$-0.537226\pi$
$569$	−24.6918	−	14.2558i	−1.03513	−	0.597635i	−0.918451	+	0.395534i	$0.870559\pi$
$570$		0			0
$571$	−8.81393	−	15.2662i	−0.368852	−	0.638870i	0.620535	−	0.784179i	$-0.286916\pi$
$571$	−8.81393	−	15.2662i	−0.368852	−	0.638870i	−0.989386	+	0.145309i	$0.953582\pi$
$572$		0			0
$573$	13.9298	+	12.2705i	0.581924	+	0.512606i
$574$		0			0
$575$	−1.19431	+	11.9734i	−0.0498062	+	0.499327i
$576$		0			0
$577$	−39.6838			−1.65206			−0.826028	−	0.563629i	$-0.809405\pi$
$577$	−39.6838			−1.65206			−0.826028	+	0.563629i	$0.809405\pi$
$578$		0			0
$579$	17.2357	−	5.80843i	0.716291	−	0.241390i
$580$		0			0
$581$	−11.2898	−	6.69312i	−0.468380	−	0.277678i
$582$		0			0
$583$	31.6428	+	18.2690i	1.31051	+	0.756624i
$584$		0			0
$585$	3.40382	−	18.1873i	0.140731	−	0.751954i
$586$		0			0
$587$	−28.2479	−	16.3090i	−1.16592	−	0.673143i	−0.213202	−	0.977008i	$-0.568389\pi$
$587$	−28.2479	−	16.3090i	−1.16592	−	0.673143i	−0.952715	+	0.303865i	$0.901723\pi$
$588$		0			0
$589$	−0.544528	−	0.943150i	−0.0224369	−	0.0388618i
$590$		0			0
$591$	22.6499	+	4.55723i	0.931694	+	0.187459i
$592$		0			0
$593$			4.73830i			0.194579i	0.995256	+	0.0972893i	$0.0310172\pi$
$593$			4.73830i			0.194579i	−0.995256	+	0.0972893i	$0.968983\pi$
$594$		0			0
$595$	4.00565	−	11.9650i	0.164216	−	0.490517i
$596$		0			0
$597$	0.310881	−	1.54511i	0.0127235	−	0.0632372i
$598$		0			0
$599$	31.7120	−	18.3090i	1.29572	−	0.748084i	0.316057	−	0.948740i	$-0.397641\pi$
$599$	31.7120	−	18.3090i	1.29572	−	0.748084i	0.979662	+	0.200657i	$0.0643076\pi$
$600$		0			0
$601$	6.81561	+	3.93499i	0.278014	+	0.160512i	0.632524	−	0.774541i	$-0.282019\pi$
$601$	6.81561	+	3.93499i	0.278014	+	0.160512i	−0.354510	+	0.935052i	$0.615352\pi$
$602$		0			0
$603$	−21.5217	+	2.73701i	−0.876433	+	0.111460i
$604$		0			0
$605$	−3.45848	−	16.0614i	−0.140607	−	0.652989i
$606$		0			0
$607$	4.73509	+	8.20141i	0.192191	+	0.332885i	0.945976	−	0.324236i	$-0.105107\pi$
$607$	4.73509	+	8.20141i	0.192191	+	0.332885i	−0.753785	+	0.657121i	$0.771774\pi$
$608$		0			0
$609$	−13.9953	−	12.6180i	−0.567116	−	0.511309i
$610$		0			0
$611$			4.43773i			0.179531i
$612$		0			0
$613$			7.15407i			0.288950i	0.989508	+	0.144475i	$0.0461493\pi$
$613$			7.15407i			0.288950i	−0.989508	+	0.144475i	$0.953851\pi$
$614$		0			0
$615$	−0.470561	−	34.7547i	−0.0189748	−	1.40144i
$616$		0			0
$617$	2.96136	+	5.12923i	0.119220	+	0.206495i	0.919459	−	0.393186i	$-0.128627\pi$
$617$	2.96136	+	5.12923i	0.119220	+	0.206495i	−0.800239	+	0.599681i	$0.795294\pi$
$618$		0			0
$619$	12.1693	+	7.02595i	0.489125	+	0.282397i	0.724211	−	0.689578i	$-0.242204\pi$
$619$	12.1693	+	7.02595i	0.489125	+	0.282397i	−0.235086	+	0.971975i	$0.575537\pi$
$620$		0			0
$621$	0.900282	−	12.4725i	0.0361271	−	0.500503i
$622$		0			0
$623$	−46.0085	−	0.531165i	−1.84329	−	0.0212807i
$624$		0			0
$625$	7.97711	+	23.6932i	0.319084	+	0.947726i
$626$		0			0
$627$	1.69742	−	1.92696i	0.0677884	−	0.0769553i
$628$		0			0
$629$	−18.4312			−0.734901
$630$		0			0
$631$	35.2765			1.40434			0.702169	−	0.712011i	$-0.252215\pi$
$631$	35.2765			1.40434			0.702169	+	0.712011i	$0.252215\pi$
$632$		0			0
$633$	5.07943	+	15.0725i	0.201889	+	0.599078i
$634$		0			0
$635$	−10.7639	+	33.4291i	−0.427152	+	1.32660i
$636$		0			0
$637$	9.26537	+	16.9396i	0.367107	+	0.671172i
$638$		0			0
$639$	18.0624	−	43.0690i	0.714538	−	1.70378i
$640$		0			0
$641$	20.5063	+	11.8393i	0.809951	+	0.467626i	0.846939	−	0.531690i	$-0.178443\pi$
$641$	20.5063	+	11.8393i	0.809951	+	0.467626i	−0.0369876	+	0.999316i	$0.511776\pi$
$642$		0			0
$643$	−12.3801	−	21.4429i	−0.488223	−	0.845627i	0.511685	−	0.859173i	$-0.329021\pi$
$643$	−12.3801	−	21.4429i	−0.488223	−	0.845627i	−0.999908	+	0.0135458i	$0.995688\pi$
$644$		0			0
$645$	−20.4282	−	34.3017i	−0.804360	−	1.35063i
$646$		0			0
$647$			1.54003i			0.0605449i	0.999542	+	0.0302725i	$0.00963750\pi$
$647$			1.54003i			0.0605449i	−0.999542	+	0.0302725i	$0.990363\pi$
$648$		0			0
$649$			5.13049i			0.201389i
$650$		0			0
$651$	−13.7158	+	4.44657i	−0.537564	+	0.174275i
$652$		0			0
$653$	−12.7197	−	22.0312i	−0.497760	−	0.862146i	0.502236	−	0.864730i	$-0.332511\pi$
$653$	−12.7197	−	22.0312i	−0.497760	−	0.862146i	−0.999997	+	0.00258435i	$0.999177\pi$
$654$		0			0
$655$	−1.04336	−	4.84540i	−0.0407673	−	0.189326i
$656$		0			0
$657$	−21.3942	−	8.97235i	−0.834666	−	0.350045i
$658$		0			0
$659$	31.5730	+	18.2287i	1.22991	+	0.710088i	0.967011	−	0.254736i	$-0.0819885\pi$
$659$	31.5730	+	18.2287i	1.22991	+	0.710088i	0.262898	+	0.964824i	$0.415322\pi$
$660$		0			0
$661$	27.8076	−	16.0547i	1.08159	−	0.624457i	0.150265	−	0.988646i	$-0.451987\pi$
$661$	27.8076	−	16.0547i	1.08159	−	0.624457i	0.931325	+	0.364189i	$0.118654\pi$
$662$		0			0
$663$	−9.65576	+	3.25399i	−0.374999	+	0.126375i
$664$		0			0
$665$	−0.650078	+	1.94180i	−0.0252089	+	0.0752998i
$666$		0			0
$667$		−	9.89586i		−	0.383169i
$668$		0			0
$669$	−11.9547	+	13.5713i	−0.462194	+	0.524696i
$670$		0			0
$671$	−17.9375	−	31.0687i	−0.692469	−	1.19939i
$672$		0			0
$673$	33.5398	+	19.3642i	1.29287	+	0.746436i	0.979161	−	0.203084i	$-0.0650966\pi$
$673$	33.5398	+	19.3642i	1.29287	+	0.746436i	0.313704	+	0.949521i	$0.398430\pi$
$674$		0			0
$675$	−8.96057	−	24.3866i	−0.344893	−	0.938642i
$676$		0			0
$677$	12.7782	+	7.37752i	0.491107	+	0.283541i	0.725034	−	0.688713i	$-0.241824\pi$
$677$	12.7782	+	7.37752i	0.491107	+	0.283541i	−0.233926	+	0.972254i	$0.575157\pi$
$678$		0			0
$679$	−20.9560	+	35.3481i	−0.804217	+	1.35653i
$680$		0			0
$681$	−16.3554	−	14.4071i	−0.626739	−	0.552082i
$682$		0			0
$683$	28.9474			1.10764			0.553820	−	0.832636i	$-0.313170\pi$
$683$	28.9474			1.10764			0.553820	+	0.832636i	$0.313170\pi$
$684$		0			0
$685$	−32.7930	+	29.6848i	−1.25296	+	1.13420i
$686$		0			0
$687$	36.9715	−	12.4594i	1.41055	−	0.475356i
$688$		0			0
$689$	11.7643	+	20.3763i	0.448183	+	0.776275i
$690$		0			0
$691$	5.99348	+	3.46034i	0.228003	+	0.131638i	0.609650	−	0.792670i	$-0.291310\pi$
$691$	5.99348	+	3.46034i	0.228003	+	0.131638i	−0.381648	+	0.924308i	$0.624643\pi$
$692$		0			0
$693$	−20.2641	−	27.2994i	−0.769771	−	1.03702i
$694$		0			0
$695$	14.8220	−	3.19161i	0.562231	−	0.121065i
$696$		0			0
$697$	−16.5762	+	9.57025i	−0.627867	+	0.362499i
$698$		0			0
$699$	−28.5849	−	5.75136i	−1.08118	−	0.217537i
$700$		0			0
$701$			3.20191i			0.120935i	0.998170	+	0.0604673i	$0.0192591\pi$
$701$			3.20191i			0.120935i	−0.998170	+	0.0604673i	$0.980741\pi$
$702$		0			0
$703$	2.99121			0.112816
$704$		0			0
$705$	3.18834	+	5.35365i	0.120080	+	0.201630i
$706$		0			0
$707$	−14.6339	+	24.6841i	−0.550365	+	0.928343i
$708$		0			0
$709$	20.4978	−	35.5032i	0.769810	−	1.33335i	−0.167856	−	0.985812i	$-0.553684\pi$
$709$	20.4978	−	35.5032i	0.769810	−	1.33335i	0.937666	−	0.347539i	$-0.112982\pi$
$710$		0			0
$711$	−23.9164	+	18.1849i	−0.896934	+	0.681986i
$712$		0			0
$713$	−6.55755	−	3.78600i	−0.245582	−	0.141787i
$714$		0			0
$715$	8.09721	−	25.1473i	0.302818	−	0.940455i
$716$		0			0
$717$	12.0609	−	4.06451i	0.450421	−	0.151792i
$718$		0			0
$719$	−19.5783			−0.730146			−0.365073	−	0.930979i	$-0.618956\pi$
$719$	−19.5783			−0.730146			−0.365073	+	0.930979i	$0.618956\pi$
$720$		0			0
$721$	−0.250161	−	0.445079i	−0.00931647	−	0.0165756i
$722$		0			0
$723$	−36.3703	−	32.0379i	−1.35263	−	1.19150i
$724$		0			0
$725$	−8.46200	−	18.7380i	−0.314271	−	0.695910i
$726$		0			0
$727$	18.3379	−	31.7621i	0.680114	−	1.17799i	−0.294832	−	0.955549i	$-0.595264\pi$
$727$	18.3379	−	31.7621i	0.680114	−	1.17799i	0.974946	−	0.222443i	$-0.0714031\pi$
$728$		0			0
$729$	10.0020	+	25.0791i	0.370443	+	0.928855i
$730$		0			0
$731$	−10.9927	+	19.0399i	−0.406579	+	0.704215i
$732$		0			0
$733$	6.51978	+	11.2926i	0.240813	+	0.417101i	0.960946	−	0.276735i	$-0.0892525\pi$
$733$	6.51978	+	11.2926i	0.240813	+	0.417101i	−0.720133	+	0.693836i	$0.755919\pi$
$734$		0			0
$735$	23.3482	+	13.7790i	0.861211	+	0.508248i
$736$		0			0
$737$	−30.9762			−1.14102
$738$		0			0
$739$	12.8263			0.471823			0.235912	−	0.971775i	$-0.424192\pi$
$739$	12.8263			0.471823			0.235912	+	0.971775i	$0.424192\pi$
$740$		0			0
$741$	1.56704	−	0.528091i	0.0575665	−	0.0193999i
$742$		0			0
$743$	2.69367	+	4.66557i	0.0988211	+	0.171163i	0.911197	−	0.411971i	$-0.135160\pi$
$743$	2.69367	+	4.66557i	0.0988211	+	0.171163i	−0.812376	+	0.583134i	$0.801826\pi$
$744$		0			0
$745$	18.0018	−	3.87631i	0.659535	−	0.142017i
$746$		0			0
$747$	9.00750	+	11.8465i	0.329567	+	0.433440i
$748$		0			0
$749$	−3.96513	−	0.0457771i	−0.144883	−	0.00167266i
$750$		0			0
$751$	17.6704	+	30.6060i	0.644802	+	1.11683i	0.984347	+	0.176240i	$0.0563935\pi$
$751$	17.6704	+	30.6060i	0.644802	+	1.11683i	−0.339545	+	0.940590i	$0.610273\pi$
$752$		0			0
$753$	44.1413	+	8.88135i	1.60860	+	0.323654i
$754$		0			0
$755$	15.0142	−	13.5911i	0.546423	−	0.494631i
$756$		0			0
$757$			17.4393i			0.633841i	0.948452	+	0.316921i	$0.102649\pi$
$757$			17.4393i			0.633841i	−0.948452	+	0.316921i	$0.897351\pi$
$758$		0			0
$759$	3.52180	−	17.5037i	0.127833	−	0.635345i
$760$		0			0
$761$	−22.4481	−	38.8813i	−0.813744	−	1.40945i	−0.910227	−	0.414110i	$-0.864093\pi$
$761$	−22.4481	−	38.8813i	−0.813744	−	1.40945i	0.0964831	−	0.995335i	$-0.469241\pi$
$762$		0			0
$763$	30.8107	+	0.355707i	1.11542	+	0.0128775i
$764$		0			0
$765$	−9.31079	+	10.8629i	−0.336632	+	0.392749i
$766$		0			0
$767$	−1.65188	+	2.86114i	−0.0596460	+	0.103310i
$768$		0			0
$769$	−26.3792	+	15.2301i	−0.951260	+	0.549210i	−0.893472	−	0.449119i	$-0.851738\pi$
$769$	−26.3792	+	15.2301i	−0.951260	+	0.549210i	−0.0577877	+	0.998329i	$0.518405\pi$
$770$		0			0
$771$	−42.0656	+	14.1761i	−1.51496	+	0.510541i
$772$		0			0
$773$			26.9502i			0.969333i	0.874699	+	0.484666i	$0.161059\pi$
$773$			26.9502i			0.969333i	−0.874699	+	0.484666i	$0.838941\pi$
$774$		0			0
$775$	−15.6542	−	1.56146i	−0.562317	−	0.0560893i
$776$		0			0
$777$	8.25917	−	38.7313i	0.296296	−	1.38948i
$778$		0			0
$779$	2.69015	−	1.55316i	0.0963846	−	0.0556477i
$780$		0			0
$781$	33.3414	−	57.7490i	1.19305	−	2.06642i
$782$		0			0
$783$	9.32342	+	19.2252i	0.333192	+	0.687052i
$784$		0			0
$785$	0.345666	+	1.60529i	0.0123374	+	0.0572954i
$786$		0			0
$787$	1.10635	+	1.91626i	0.0394372	+	0.0683072i	0.885070	−	0.465457i	$-0.154110\pi$
$787$	1.10635	+	1.91626i	0.0394372	+	0.0683072i	−0.845633	+	0.533765i	$0.820777\pi$
$788$		0			0
$789$	4.77282	−	5.41824i	0.169917	−	0.192894i
$790$		0			0
$791$	−5.05047	−	8.98567i	−0.179574	−	0.319494i
$792$		0			0
$793$		−	23.1016i		−	0.820361i
$794$		0			0
$795$	28.8320	+	16.1297i	1.02256	+	0.572061i
$796$		0			0
$797$	−16.7807	+	9.68833i	−0.594402	+	0.343178i	−0.766836	−	0.641843i	$-0.778170\pi$
$797$	−16.7807	+	9.68833i	−0.594402	+	0.343178i	0.172434	+	0.985021i	$0.444837\pi$
$798$		0			0
$799$	1.71569	−	2.97166i	0.0606966	−	0.105130i
$800$		0			0
$801$	48.1124	+	20.1775i	1.69997	+	0.712938i
$802$		0			0
$803$	−28.6863	−	16.5621i	−1.01232	−	0.584463i
$804$		0			0
$805$	2.83617	+	13.9521i	0.0999618	+	0.491748i
$806$		0			0
$807$	−26.6110	−	5.35421i	−0.936752	−	0.188477i
$808$		0			0
$809$			47.2683i			1.66187i	0.556372	+	0.830933i	$0.312193\pi$
$809$			47.2683i			1.66187i	−0.556372	+	0.830933i	$0.687807\pi$
$810$		0			0
$811$		−	35.6802i		−	1.25290i	−0.779461	−	0.626451i	$-0.784507\pi$
$811$		−	35.6802i		−	1.25290i	0.779461	−	0.626451i	$-0.215493\pi$
$812$		0			0
$813$	0.0511523	−	0.254233i	0.00179399	−	0.00891633i
$814$		0			0
$815$	−0.747016	+	2.31999i	−0.0261668	+	0.0812656i
$816$		0			0
$817$	1.78400	−	3.08999i	0.0624144	−	0.108105i
$818$		0			0
$819$	−2.51110	−	21.7487i	−0.0877449	−	0.759961i
$820$		0			0
$821$	4.03145	+	2.32756i	0.140699	+	0.0812324i	0.568697	−	0.822547i	$-0.307448\pi$
$821$	4.03145	+	2.32756i	0.140699	+	0.0812324i	−0.427998	+	0.903780i	$0.640781\pi$
$822$		0			0
$823$	−33.6094	+	19.4044i	−1.17155	+	0.676396i	−0.954045	−	0.299663i	$-0.903126\pi$
$823$	−33.6094	+	19.4044i	−1.17155	+	0.676396i	−0.217506	+	0.976059i	$0.569792\pi$
$824$		0			0
$825$	−8.29895	−	36.1551i	−0.288932	−	1.25876i
$826$		0			0
$827$	−10.9775			−0.381724			−0.190862	−	0.981617i	$-0.561128\pi$
$827$	−10.9775			−0.381724			−0.190862	+	0.981617i	$0.561128\pi$
$828$		0			0
$829$			39.5241i			1.37273i	0.727258	+	0.686364i	$0.240794\pi$
$829$			39.5241i			1.37273i	−0.727258	+	0.686364i	$0.759206\pi$
$830$		0			0
$831$	30.9017	+	27.2207i	1.07197	+	0.944275i
$832$		0			0
$833$	0.344673	−	14.9255i	0.0119422	−	0.517137i
$834$		0			0
$835$	−4.22133	+	0.908973i	−0.146085	+	0.0314563i
$836$		0			0
$837$	16.3067	+	1.17704i	0.563641	+	0.0406845i
$838$		0			0
$839$	4.28259	−	7.41766i	0.147851	−	0.256086i	−0.782582	−	0.622548i	$-0.786098\pi$
$839$	4.28259	−	7.41766i	0.147851	−	0.256086i	0.930433	+	0.366462i	$0.119431\pi$
$840$		0			0
$841$	−6.04567	−	10.4714i	−0.208471	−	0.361083i
$842$		0			0
$843$	14.1082	+	12.4276i	0.485913	+	0.428031i
$844$		0			0
$845$	−8.93839	+	8.09117i	−0.307490	+	0.278345i
$846$		0			0
$847$	−9.52485	−	16.9464i	−0.327278	−	0.582284i
$848$		0			0
$849$	−18.3752	−	54.5258i	−0.630636	−	1.87132i
$850$		0			0
$851$	18.0110	−	10.3987i	0.617409	−	0.356461i
$852$		0			0
$853$	−24.3432	+	42.1636i	−0.833495	+	1.44366i	0.0617555	+	0.998091i	$0.480330\pi$
$853$	−24.3432	+	42.1636i	−0.833495	+	1.44366i	−0.895250	+	0.445564i	$0.853003\pi$
$854$		0			0
$855$	1.51105	−	1.76294i	0.0516769	−	0.0602914i
$856$		0			0
$857$	−24.3603	−	14.0644i	−0.832132	−	0.480432i	0.0224500	−	0.999748i	$-0.492853\pi$
$857$	−24.3603	−	14.0644i	−0.832132	−	0.480432i	−0.854582	+	0.519316i	$0.826187\pi$
$858$		0			0
$859$	37.0828	−	21.4097i	1.26525	−	0.730491i	0.291163	−	0.956674i	$-0.405958\pi$
$859$	37.0828	−	21.4097i	1.26525	−	0.730491i	0.974085	+	0.226183i	$0.0726246\pi$
$860$		0			0
$861$	−12.6830	−	39.1216i	−0.432234	−	1.33326i
$862$		0			0
$863$	−21.0474			−0.716462			−0.358231	−	0.933633i	$-0.616620\pi$
$863$	−21.0474			−0.716462			−0.358231	+	0.933633i	$0.616620\pi$
$864$		0			0
$865$	13.3132	+	14.7072i	0.452661	+	0.500059i
$866$		0			0
$867$	−21.1425	−	4.25393i	−0.718037	−	0.144471i
$868$		0			0
$869$	−37.1506	+	21.4489i	−1.26025	+	0.727604i
$870$		0			0
$871$	−17.2746	−	9.97352i	−0.585329	−	0.337940i
$872$		0			0
$873$	37.0910	−	28.2022i	1.25534	−	0.954501i
$874$		0			0
$875$	17.3009	+	23.9933i	0.584876	+	0.811123i
$876$		0			0
$877$	28.6471	−	16.5394i	0.967343	−	0.558496i	0.0689181	−	0.997622i	$-0.478045\pi$
$877$	28.6471	−	16.5394i	0.967343	−	0.558496i	0.898425	+	0.439126i	$0.144712\pi$
$878$		0			0
$879$	−10.4490	+	3.52131i	−0.352435	+	0.118771i
$880$		0			0
$881$	−11.5605			−0.389482			−0.194741	−	0.980855i	$-0.562387\pi$
$881$	−11.5605			−0.389482			−0.194741	+	0.980855i	$0.562387\pi$
$882$		0			0
$883$		−	13.1817i		−	0.443601i	−0.975092	−	0.221800i	$-0.928807\pi$
$883$		−	13.1817i		−	0.443601i	0.975092	−	0.221800i	$-0.0711934\pi$
$884$		0			0
$885$	0.0628027	+	4.63848i	0.00211109	+	0.155921i
$886$		0			0
$887$	−17.7116	+	10.2258i	−0.594698	+	0.343349i	−0.766953	−	0.641703i	$-0.778228\pi$
$887$	−17.7116	+	10.2258i	−0.594698	+	0.343349i	0.172255	+	0.985052i	$0.444895\pi$
$888$		0			0
$889$	−0.479704	+	41.5510i	−0.0160887	+	1.39358i
$890$		0			0
$891$	9.64923	+	37.3235i	0.323261	+	1.25038i
$892$		0			0
$893$	−0.278439	+	0.482271i	−0.00931761	+	0.0161386i
$894$		0			0
$895$	−11.1761	+	34.7092i	−0.373575	+	1.16020i
$896$		0			0
$897$	7.59975	−	8.62746i	0.253748	−	0.288062i
$898$		0			0
$899$	12.9380			0.431506
$900$		0			0
$901$		−	18.1929i		−	0.606093i
$902$		0			0
$903$	−35.0844	−	31.6319i	−1.16753	−	1.05264i
$904$		0			0
$905$	−16.2312	+	50.4088i	−0.539543	+	1.67565i
$906$		0			0
$907$	23.9204	+	13.8105i	0.794265	+	0.458569i	0.841462	−	0.540317i	$-0.181695\pi$
$907$	23.9204	+	13.8105i	0.794265	+	0.458569i	−0.0471969	+	0.998886i	$0.515029\pi$
$908$		0			0
$909$	25.9013	−	19.6941i	0.859090	−	0.653212i
$910$		0			0
$911$	20.7831	+	11.9991i	0.688575	+	0.397549i	0.803078	−	0.595874i	$-0.203194\pi$
$911$	20.7831	+	11.9991i	0.688575	+	0.397549i	−0.114503	+	0.993423i	$0.536528\pi$
$912$		0			0
$913$	10.6243	+	18.4018i	0.351612	+	0.609009i
$914$		0			0
$915$	−16.5976	−	27.8696i	−0.548701	−	0.921342i
$916$		0			0
$917$	−2.87346	−	5.11238i	−0.0948899	−	0.168826i
$918$		0			0
$919$	−12.9276			−0.426441			−0.213220	−	0.977004i	$-0.568395\pi$
$919$	−12.9276			−0.426441			−0.213220	+	0.977004i	$0.568395\pi$
$920$		0			0
$921$	−45.3145	−	9.11739i	−1.49316	−	0.300428i
$922$		0			0
$923$	37.1873	−	21.4701i	1.22404	−	0.706697i
$924$		0			0
$925$	25.2122	−	35.0913i	0.828971	−	1.15380i
$926$		0			0
$927$	0.0730361	+	0.574300i	0.00239882	+	0.0188625i
$928$		0			0
$929$	−3.86173	+	6.68872i	−0.126699	+	0.219450i	−0.922396	−	0.386246i	$-0.873772\pi$
$929$	−3.86173	+	6.68872i	−0.126699	+	0.219450i	0.795697	+	0.605695i	$0.207105\pi$
$930$		0			0
$931$	−0.0559371	+	2.42226i	−0.00183326	+	0.0793863i
$932$		0			0
$933$	−11.1846	−	33.1888i	−0.366168	−	1.08655i
$934$		0			0
$935$	−15.1445	+	13.7090i	−0.495277	+	0.448332i
$936$		0			0
$937$	36.5949			1.19550			0.597751	−	0.801682i	$-0.296061\pi$
$937$	36.5949			1.19550			0.597751	+	0.801682i	$0.296061\pi$
$938$		0			0
$939$	−27.9398	+	31.7180i	−0.911781	+	1.03508i
$940$		0			0
$941$	−26.1593	−	45.3092i	−0.852768	−	1.47704i	−0.878700	−	0.477374i	$-0.841589\pi$
$941$	−26.1593	−	45.3092i	−0.852768	−	1.47704i	0.0259323	−	0.999664i	$-0.491745\pi$
$942$		0			0
$943$	10.7988	−	18.7041i	0.351658	−	0.609090i
$944$		0			0
$945$	−18.6550	−	24.4334i	−0.606847	−	0.794818i
$946$		0			0
$947$	−6.99813	+	12.1211i	−0.227409	+	0.393883i	−0.957039	−	0.289958i	$-0.906359\pi$
$947$	−6.99813	+	12.1211i	−0.227409	+	0.393883i	0.729631	+	0.683841i	$0.239692\pi$
$948$		0			0
$949$	−10.6651	−	18.4725i	−0.346203	−	0.599642i
$950$		0			0
$951$	5.11782	−	5.80989i	0.165957	−	0.188399i
$952$		0			0
$953$	−31.4101			−1.01747			−0.508736	−	0.860922i	$-0.669887\pi$
$953$	−31.4101			−1.01747			−0.508736	+	0.860922i	$0.669887\pi$
$954$		0			0
$955$	16.0831	+	17.7671i	0.520437	+	0.574931i
$956$		0			0
$957$	9.74261	+	28.9098i	0.314934	+	0.934522i
$958$		0			0
$959$	−26.6902	+	45.0204i	−0.861871	+	1.45378i
$960$		0			0
$961$	−10.5501	+	18.2734i	−0.340327	+	0.589463i
$962$		0			0
$963$	4.14645	+	1.73895i	0.133618	+	0.0560369i
$964$		0			0
$965$	22.9546	−	4.94279i	0.738935	−	0.159114i
$966$		0			0
$967$	−21.7492	+	12.5569i	−0.699407	+	0.403803i	−0.807126	−	0.590379i	$-0.798978\pi$
$967$	−21.7492	+	12.5569i	−0.699407	+	0.403803i	0.107720	+	0.994181i	$0.465645\pi$
$968$		0			0
$969$	−1.25351	−	0.252210i	−0.0402685	−	0.00810214i
$970$		0			0
$971$	−38.9983			−1.25151			−0.625757	−	0.780018i	$-0.715210\pi$
$971$	−38.9983			−1.25151			−0.625757	+	0.780018i	$0.715210\pi$
$972$		0			0
$973$	15.6387	−	8.78986i	0.501353	−	0.281790i
$974$		0			0
$975$	7.01287	−	22.8348i	0.224591	−	0.731299i
$976$		0			0
$977$	4.06344	+	7.03809i	0.130001	+	0.225168i	0.923677	−	0.383173i	$-0.125169\pi$
$977$	4.06344	+	7.03809i	0.130001	+	0.225168i	−0.793676	+	0.608341i	$0.791835\pi$
$978$		0			0
$979$	64.5115	+	37.2457i	2.06180	+	1.19038i
$980$		0			0
$981$	−32.2196	−	13.5124i	−1.02869	−	0.431417i
$982$		0			0
$983$	9.16936	+	5.29393i	0.292457	+	0.168850i	0.639049	−	0.769166i	$-0.279328\pi$
$983$	9.16936	+	5.29393i	0.292457	+	0.168850i	−0.346592	+	0.938016i	$0.612661\pi$
$984$		0			0
$985$	28.3915	+	9.14181i	0.904627	+	0.291282i
$986$		0			0
$987$	5.47581	+	4.93695i	0.174297	+	0.157145i
$988$		0			0
$989$		−	24.8077i		−	0.788839i
$990$		0			0
$991$	−53.8090			−1.70930			−0.854650	−	0.519204i	$-0.826228\pi$
$991$	−53.8090			−1.70930			−0.854650	+	0.519204i	$0.826228\pi$
$992$		0			0
$993$	13.6910	−	15.5425i	0.434472	−	0.493225i
$994$		0			0
$995$	0.623627	−	1.93678i	0.0197703	−	0.0614001i
$996$		0			0
$997$	−21.7889	+	37.7394i	−0.690060	+	1.19522i	0.281758	+	0.959486i	$0.409083\pi$
$997$	−21.7889	+	37.7394i	−0.690060	+	1.19522i	−0.971818	+	0.235734i	$0.924251\pi$
$998$		0			0
$999$	−25.1938	+	37.1711i	−0.797095	+	1.17604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.cj.c.209.3	✓	80
3.2	odd	2		3780.2.cj.c.629.37		80
5.4	even	2	inner	1260.2.cj.c.209.38	yes	80
7.6	odd	2	inner	1260.2.cj.c.209.37	yes	80
9.4	even	3		3780.2.cj.c.3149.24		80
9.5	odd	6	inner	1260.2.cj.c.1049.4	yes	80
15.14	odd	2		3780.2.cj.c.629.17		80
21.20	even	2		3780.2.cj.c.629.4		80
35.34	odd	2	inner	1260.2.cj.c.209.4	yes	80
45.4	even	6		3780.2.cj.c.3149.4		80
45.14	odd	6	inner	1260.2.cj.c.1049.37	yes	80
63.13	odd	6		3780.2.cj.c.3149.17		80
63.41	even	6	inner	1260.2.cj.c.1049.38	yes	80
105.104	even	2		3780.2.cj.c.629.24		80
315.104	even	6	inner	1260.2.cj.c.1049.3	yes	80
315.139	odd	6		3780.2.cj.c.3149.37		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.cj.c.209.3	✓	80	1.1	even	1	trivial
1260.2.cj.c.209.4	yes	80	35.34	odd	2	inner
1260.2.cj.c.209.37	yes	80	7.6	odd	2	inner
1260.2.cj.c.209.38	yes	80	5.4	even	2	inner
1260.2.cj.c.1049.3	yes	80	315.104	even	6	inner
1260.2.cj.c.1049.4	yes	80	9.5	odd	6	inner
1260.2.cj.c.1049.37	yes	80	45.14	odd	6	inner
1260.2.cj.c.1049.38	yes	80	63.41	even	6	inner
3780.2.cj.c.629.4		80	21.20	even	2
3780.2.cj.c.629.17		80	15.14	odd	2
3780.2.cj.c.629.24		80	105.104	even	2
3780.2.cj.c.629.37		80	3.2	odd	2
3780.2.cj.c.3149.4		80	45.4	even	6
3780.2.cj.c.3149.17		80	63.13	odd	6
3780.2.cj.c.3149.24		80	9.4	even	3
3780.2.cj.c.3149.37		80	315.139	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69802 - 0.341647i) q^{3} +(-2.12845 - 0.685343i) q^{5} +(-2.64558 - 0.0305430i) q^{7} +(2.76656 + 1.16025i) q^{9} +(3.70953 + 2.14170i) q^{11} +(1.37914 + 2.38874i) q^{13} +(3.38001 + 1.89091i) q^{15} -2.13278i q^{17} +0.346129i q^{19} +(4.48181 + 0.955714i) q^{21} +(1.20329 + 2.08415i) q^{23} +(4.06061 + 2.91744i) q^{25} +(-4.30128 - 2.91531i) q^{27} +(-3.56111 - 2.05601i) q^{29} +(-2.72485 + 1.57319i) q^{31} +(-5.56716 - 4.90400i) q^{33} +(5.61005 + 1.87814i) q^{35} -8.64188i q^{37} +(-1.52571 - 4.52731i) q^{39} +(-4.48722 - 7.77210i) q^{41} +(-8.92726 - 5.15416i) q^{43} +(-5.09331 - 4.36557i) q^{45} +(1.39333 + 0.804437i) q^{47} +(6.99813 + 0.161608i) q^{49} +(-0.728657 + 3.62151i) q^{51} +8.53014 q^{53} +(-6.42776 - 7.10081i) q^{55} +(0.118254 - 0.587735i) q^{57} +(0.598881 + 1.03729i) q^{59} +(-7.25327 - 4.18768i) q^{61} +(-7.28369 - 3.15402i) q^{63} +(-1.29833 - 6.02951i) q^{65} +(-6.26283 + 3.61585i) q^{67} +(-1.33116 - 3.95004i) q^{69} -15.5677i q^{71} -7.73314 q^{73} +(-5.89827 - 6.34117i) q^{75} +(-9.74843 - 5.77933i) q^{77} +(-5.00745 + 8.67315i) q^{79} +(6.30765 + 6.41977i) q^{81} +(4.29606 + 2.48033i) q^{83} +(-1.46169 + 4.53952i) q^{85} +(5.34441 + 4.70779i) q^{87} +17.3907 q^{89} +(-3.57566 - 6.36172i) q^{91} +(5.16433 - 1.74038i) q^{93} +(0.237217 - 0.736719i) q^{95} +(7.76586 - 13.4509i) q^{97} +(7.77773 + 10.2291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{9} + 24 q^{11} + 12 q^{15} + 2 q^{21} - 40 q^{25} + 12 q^{29} + 32 q^{39} + 62 q^{49} - 32 q^{51} - 36 q^{65} + 16 q^{79} - 28 q^{81} + 10 q^{85} + 28 q^{91} + 60 q^{95} + 124 q^{99}+O(q^{100}) \) 80 * q + 4 * q^9 + 24 * q^11 + 12 * q^15 + 2 * q^21 - 40 * q^25 + 12 * q^29 + 32 * q^39 + 62 * q^49 - 32 * q^51 - 36 * q^65 + 16 * q^79 - 28 * q^81 + 10 * q^85 + 28 * q^91 + 60 * q^95 + 124 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more