LMFDB - Embedded newform 1216.2.t.d.1185.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(353,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1216.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.t (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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1185.2
Character	$\chi$	$=$	1216.1185
Dual form			1216.2.t.d.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.17731 + 1.25707i) q^{3} +(-2.95556 + 1.70639i) q^{5} +2.54486 q^{7} +(1.66044 - 2.87597i) q^{9} +O(q^{10})$	\(q+(-2.17731 + 1.25707i) q^{3} +(-2.95556 + 1.70639i) q^{5} +2.54486 q^{7} +(1.66044 - 2.87597i) q^{9} +1.25431i q^{11} +(4.22968 + 2.44201i) q^{13} +(4.29011 - 7.43068i) q^{15} +(3.99152 + 6.91351i) q^{17} +(3.96224 - 1.81677i) q^{19} +(-5.54095 + 3.19907i) q^{21} +(0.355422 - 0.615609i) q^{23} +(3.32356 - 5.75657i) q^{25} +0.806748i q^{27} +(2.45168 + 1.41548i) q^{29} -5.32450 q^{31} +(-1.57676 - 2.73103i) q^{33} +(-7.52150 + 4.34254i) q^{35} +3.20708i q^{37} -12.2791 q^{39} +(5.26481 + 9.11893i) q^{41} +(5.69906 - 3.29035i) q^{43} +11.3335i q^{45} +(-4.00670 + 6.93981i) q^{47} -0.523666 q^{49} +(-17.3815 - 10.0352i) q^{51} +(-0.905488 - 0.522784i) q^{53} +(-2.14035 - 3.70720i) q^{55} +(-6.34320 + 8.93648i) q^{57} +(6.46940 - 3.73511i) q^{59} +(-11.9058 - 6.87382i) q^{61} +(4.22560 - 7.31895i) q^{63} -16.6681 q^{65} +(-2.72163 - 1.57133i) q^{67} +1.78716i q^{69} +(-6.34526 - 10.9903i) q^{71} +(3.03579 + 5.25815i) q^{73} +16.7118i q^{75} +3.19206i q^{77} +(-1.17783 - 2.04006i) q^{79} +(3.96719 + 6.87137i) q^{81} +12.2452i q^{83} +(-23.5943 - 13.6222i) q^{85} -7.11741 q^{87} +(1.39043 - 2.40830i) q^{89} +(10.7640 + 6.21458i) q^{91} +(11.5931 - 6.69327i) q^{93} +(-8.61051 + 12.1307i) q^{95} +(-5.77233 - 9.99797i) q^{97} +(3.60737 + 2.08272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) $ 24 * q - 6 * q^5 + 8 * q^9	$ 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) $ 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	−2.17731	+	1.25707i	−1.25707	+	0.725769i	−0.972504	−	0.232888i	$-0.925182\pi$
$3$	−2.17731	+	1.25707i	−1.25707	+	0.725769i	−0.284565	+	0.958657i	$0.591849\pi$
$4$		0			0
$5$	−2.95556	+	1.70639i	−1.32177	+	0.763122i	−0.984010	−	0.178111i	$-0.943001\pi$
$5$	−2.95556	+	1.70639i	−1.32177	+	0.763122i	−0.337756	+	0.941234i	$0.609668\pi$
$6$		0			0
$7$	2.54486			0.961868			0.480934	−	0.876757i	$-0.340298\pi$
$7$	2.54486			0.961868			0.480934	+	0.876757i	$0.340298\pi$
$8$		0			0
$9$	1.66044	−	2.87597i	0.553481	−	0.958657i
$10$		0			0
$11$			1.25431i			0.378190i	0.981959	+	0.189095i	$0.0605554\pi$
$11$			1.25431i			0.378190i	−0.981959	+	0.189095i	$0.939445\pi$
$12$		0			0
$13$	4.22968	+	2.44201i	1.17310	+	0.677291i	0.954409	−	0.298502i	$-0.0964869\pi$
$13$	4.22968	+	2.44201i	1.17310	+	0.677291i	0.218694	+	0.975793i	$0.429820\pi$
$14$		0			0
$15$	4.29011	−	7.43068i	1.10770	−	1.91859i
$16$		0			0
$17$	3.99152	+	6.91351i	0.968085	+	1.67677i	0.701088	+	0.713075i	$0.252698\pi$
$17$	3.99152	+	6.91351i	0.968085	+	1.67677i	0.266997	+	0.963697i	$0.413968\pi$
$18$		0			0
$19$	3.96224	−	1.81677i	0.909000	−	0.416796i
$19$	3.96224	−	1.81677i	0.909000	−	0.416796i
$20$		0			0
$21$	−5.54095	+	3.19907i	−1.20913	+	0.698094i
$22$		0			0
$23$	0.355422	−	0.615609i	0.0741106	−	0.128363i	−0.826589	−	0.562807i	$-0.809722\pi$
$23$	0.355422	−	0.615609i	0.0741106	−	0.128363i	0.900699	+	0.434443i	$0.143055\pi$
$24$		0			0
$25$	3.32356	−	5.75657i	0.664711	−	1.15131i
$26$		0			0
$27$			0.806748i			0.155259i
$28$		0			0
$29$	2.45168	+	1.41548i	0.455265	+	0.262848i	0.710051	−	0.704150i	$-0.248672\pi$
$29$	2.45168	+	1.41548i	0.455265	+	0.262848i	−0.254786	+	0.966997i	$0.582005\pi$
$30$		0			0
$31$	−5.32450			−0.956309			−0.478155	−	0.878276i	$-0.658694\pi$
$31$	−5.32450			−0.956309			−0.478155	+	0.878276i	$0.658694\pi$
$32$		0			0
$33$	−1.57676	−	2.73103i	−0.274479	−	0.475411i
$34$		0			0
$35$	−7.52150	+	4.34254i	−1.27137	+	0.734023i
$36$		0			0
$37$			3.20708i			0.527240i	0.964627	+	0.263620i	$0.0849165\pi$
$37$			3.20708i			0.527240i	−0.964627	+	0.263620i	$0.915083\pi$
$38$		0			0
$39$	−12.2791			−1.96623
$40$		0			0
$41$	5.26481	+	9.11893i	0.822226	+	1.42414i	0.904021	+	0.427488i	$0.140601\pi$
$41$	5.26481	+	9.11893i	0.822226	+	1.42414i	−0.0817952	+	0.996649i	$0.526065\pi$
$42$		0			0
$43$	5.69906	−	3.29035i	0.869098	−	0.501774i	0.00204985	−	0.999998i	$-0.499348\pi$
$43$	5.69906	−	3.29035i	0.869098	−	0.501774i	0.867049	+	0.498224i	$0.166014\pi$
$44$		0			0
$45$			11.3335i			1.68949i
$46$		0			0
$47$	−4.00670	+	6.93981i	−0.584437	+	1.01227i	0.410508	+	0.911857i	$0.365351\pi$
$47$	−4.00670	+	6.93981i	−0.584437	+	1.01227i	−0.994945	+	0.100418i	$0.967982\pi$
$48$		0			0
$49$	−0.523666			−0.0748094
$50$		0			0
$51$	−17.3815	−	10.0352i	−2.43390	−	1.40521i
$52$		0			0
$53$	−0.905488	−	0.522784i	−0.124378	−	0.0718099i	0.436520	−	0.899695i	$-0.356211\pi$
$53$	−0.905488	−	0.522784i	−0.124378	−	0.0718099i	−0.560898	+	0.827885i	$0.689544\pi$
$54$		0			0
$55$	−2.14035	−	3.70720i	−0.288605	−	0.499879i
$56$		0			0
$57$	−6.34320	+	8.93648i	−0.840177	+	1.18367i
$58$		0			0
$59$	6.46940	−	3.73511i	0.842244	−	0.486270i	−0.0157823	−	0.999875i	$-0.505024\pi$
$59$	6.46940	−	3.73511i	0.842244	−	0.486270i	0.858026	+	0.513606i	$0.171691\pi$
$60$		0			0
$61$	−11.9058	−	6.87382i	−1.52438	−	0.880102i	−0.999583	−	0.0288763i	$-0.990807\pi$
$61$	−11.9058	−	6.87382i	−1.52438	−	0.880102i	−0.524799	−	0.851226i	$-0.675860\pi$
$62$		0			0
$63$	4.22560	−	7.31895i	0.532376	−	0.922102i
$64$		0			0
$65$	−16.6681			−2.06742
$66$		0			0
$67$	−2.72163	−	1.57133i	−0.332500	−	0.191969i	0.324450	−	0.945903i	$-0.394821\pi$
$67$	−2.72163	−	1.57133i	−0.332500	−	0.191969i	−0.656951	+	0.753934i	$0.728154\pi$
$68$		0			0
$69$			1.78716i			0.215149i
$70$		0			0
$71$	−6.34526	−	10.9903i	−0.753043	−	1.30431i	−0.946341	−	0.323169i	$-0.895252\pi$
$71$	−6.34526	−	10.9903i	−0.753043	−	1.30431i	0.193298	−	0.981140i	$-0.438082\pi$
$72$		0			0
$73$	3.03579	+	5.25815i	0.355313	+	0.615419i	0.987171	−	0.159664i	$-0.0510411\pi$
$73$	3.03579	+	5.25815i	0.355313	+	0.615419i	−0.631859	+	0.775083i	$0.717708\pi$
$74$		0			0
$75$			16.7118i			1.92971i
$76$		0			0
$77$			3.19206i			0.363769i
$78$		0			0
$79$	−1.17783	−	2.04006i	−0.132516	−	0.229525i	0.792130	−	0.610353i	$-0.208972\pi$
$79$	−1.17783	−	2.04006i	−0.132516	−	0.229525i	−0.924646	+	0.380828i	$0.875639\pi$
$80$		0			0
$81$	3.96719	+	6.87137i	0.440799	+	0.763486i
$82$		0			0
$83$			12.2452i			1.34409i	0.740510	+	0.672045i	$0.234584\pi$
$83$			12.2452i			1.34409i	−0.740510	+	0.672045i	$0.765416\pi$
$84$		0			0
$85$	−23.5943	−	13.6222i	−2.55916	−	1.47753i
$86$		0			0
$87$	−7.11741			−0.763066
$88$		0			0
$89$	1.39043	−	2.40830i	0.147385	−	0.255279i	−0.782875	−	0.622179i	$-0.786248\pi$
$89$	1.39043	−	2.40830i	0.147385	−	0.255279i	0.930260	+	0.366900i	$0.119581\pi$
$90$		0			0
$91$	10.7640	+	6.21458i	1.12837	+	0.651465i
$92$		0			0
$93$	11.5931	−	6.69327i	1.20215	−	0.694059i
$94$		0			0
$95$	−8.61051	+	12.1307i	−0.883419	+	1.24459i
$96$		0			0
$97$	−5.77233	−	9.99797i	−0.586092	−	1.01514i	−0.994738	−	0.102448i	$-0.967333\pi$
$97$	−5.77233	−	9.99797i	−0.586092	−	1.01514i	0.408647	−	0.912693i	$-0.366001\pi$
$98$		0			0
$99$	3.60737	+	2.08272i	0.362555	+	0.209321i
$100$		0			0
$101$	5.36280	+	3.09621i	0.533618	+	0.308085i	0.742489	−	0.669859i	$-0.233645\pi$
$101$	5.36280	+	3.09621i	0.533618	+	0.308085i	−0.208870	+	0.977943i	$0.566979\pi$
$102$		0			0
$103$	−4.42028			−0.435543			−0.217772	−	0.976000i	$-0.569879\pi$
$103$	−4.42028			−0.435543			−0.217772	+	0.976000i	$0.569879\pi$
$104$		0			0
$105$	10.9177	−	18.9101i	1.06546	−	1.84543i
$106$		0			0
$107$			11.8222i			1.14290i	0.820637	+	0.571450i	$0.193619\pi$
$107$			11.8222i			1.14290i	−0.820637	+	0.571450i	$0.806381\pi$
$108$		0			0
$109$	−14.6832	+	8.47736i	−1.40640	+	0.811984i	−0.995039	−	0.0994901i	$-0.968279\pi$
$109$	−14.6832	+	8.47736i	−1.40640	+	0.811984i	−0.411358	+	0.911474i	$0.634946\pi$
$110$		0			0
$111$	−4.03151	−	6.98279i	−0.382654	−	0.662777i
$112$		0			0
$113$	0.817599			0.0769132			0.0384566	−	0.999260i	$-0.487756\pi$
$113$	0.817599			0.0769132			0.0384566	+	0.999260i	$0.487756\pi$
$114$		0			0
$115$			2.42596i			0.226222i
$116$		0			0
$117$	14.0463	−	8.10963i	1.29858	−	0.749736i
$118$		0			0
$119$	10.1579	+	17.5939i	0.931170	+	1.61283i
$120$		0			0
$121$	9.42669			0.856972
$122$		0			0
$123$	−22.9262	−	13.2365i	−2.06719	−	1.19349i
$124$		0			0
$125$			5.62125i			0.502779i
$126$		0			0
$127$	−0.759932	+	1.31624i	−0.0674330	+	0.116797i	−0.897771	−	0.440463i	$-0.854814\pi$
$127$	−0.759932	+	1.31624i	−0.0674330	+	0.116797i	0.830338	+	0.557261i	$0.188148\pi$
$128$		0			0
$129$	−8.27240	+	14.3282i	−0.728344	+	1.26153i
$130$		0			0
$131$	−4.05996	+	2.34402i	−0.354720	+	0.204798i	−0.666762	−	0.745270i	$-0.732320\pi$
$131$	−4.05996	+	2.34402i	−0.354720	+	0.204798i	0.312042	+	0.950068i	$0.398987\pi$
$132$		0			0
$133$	10.0834	−	4.62344i	0.874338	−	0.400903i
$134$		0			0
$135$	−1.37663	−	2.38439i	−0.118481	−	0.205216i
$136$		0			0
$137$	2.65292	−	4.59500i	0.226655	−	0.392577i	−0.730160	−	0.683276i	$-0.760554\pi$
$137$	2.65292	−	4.59500i	0.226655	−	0.392577i	0.956815	+	0.290699i	$0.0938878\pi$
$138$		0			0
$139$	13.0038	+	7.50775i	1.10297	+	0.636799i	0.936999	−	0.349332i	$-0.113592\pi$
$139$	13.0038	+	7.50775i	1.10297	+	0.636799i	0.165969	+	0.986131i	$0.446925\pi$
$140$		0			0
$141$		−	20.1468i		−	1.69666i
$142$		0			0
$143$	−3.06305	+	5.30536i	−0.256145	+	0.443656i
$144$		0			0
$145$	−9.66145			−0.802339
$146$		0			0
$147$	1.14018	−	0.658284i	0.0940405	−	0.0542943i
$148$		0			0
$149$	−17.0410	+	9.83861i	−1.39605	+	0.806011i	−0.993976	−	0.109596i	$-0.965044\pi$
$149$	−17.0410	+	9.83861i	−1.39605	+	0.806011i	−0.402075	+	0.915607i	$0.631711\pi$
$150$		0			0
$151$	22.4999			1.83102			0.915510	−	0.402296i	$-0.131788\pi$
$151$	22.4999			1.83102			0.915510	+	0.402296i	$0.131788\pi$
$152$		0			0
$153$	26.5107			2.14327
$154$		0			0
$155$	15.7369	−	9.08570i	1.26402	−	0.729781i
$156$		0			0
$157$	5.35902	−	3.09403i	0.427696	−	0.246931i	−0.270668	−	0.962673i	$-0.587245\pi$
$157$	5.35902	−	3.09403i	0.427696	−	0.246931i	0.698365	+	0.715742i	$0.253911\pi$
$158$		0			0
$159$	2.62870			0.208469
$160$		0			0
$161$	0.904501	−	1.56664i	0.0712847	−	0.123469i
$162$		0			0
$163$		−	7.52027i		−	0.589033i	−0.955646	−	0.294516i	$-0.904841\pi$
$163$		−	7.52027i		−	0.589033i	0.955646	−	0.294516i	$-0.0951586\pi$
$164$		0			0
$165$	9.32042	+	5.38114i	0.725593	+	0.418922i
$166$		0			0
$167$	7.11147	−	12.3174i	0.550302	−	0.953151i	−0.447951	−	0.894058i	$-0.647846\pi$
$167$	7.11147	−	12.3174i	0.550302	−	0.953151i	0.998253	−	0.0590926i	$-0.0188207\pi$
$168$		0			0
$169$	5.42682	+	9.39952i	0.417447	+	0.723040i
$170$		0			0
$171$	1.35408	−	14.4119i	0.103549	−	1.10211i
$172$		0			0
$173$	11.2682	−	6.50571i	0.856706	−	0.494620i	−0.00620155	−	0.999981i	$-0.501974\pi$
$173$	11.2682	−	6.50571i	0.856706	−	0.494620i	0.862908	+	0.505361i	$0.168641\pi$
$174$		0			0
$175$	8.45800	−	14.6497i	0.639365	−	1.10741i
$176$		0			0
$177$	−9.39058	+	16.2650i	−0.705839	+	1.22255i
$178$		0			0
$179$		−	0.503659i		−	0.0376452i	−0.999823	−	0.0188226i	$-0.994008\pi$
$179$		−	0.503659i		−	0.0376452i	0.999823	−	0.0188226i	$-0.00599178\pi$
$180$		0			0
$181$	16.2259	+	9.36803i	1.20606	+	0.696320i	0.961897	−	0.273413i	$-0.0881527\pi$
$181$	16.2259	+	9.36803i	1.20606	+	0.696320i	0.244165	+	0.969734i	$0.421486\pi$
$182$		0			0
$183$	34.5634			2.55500
$184$		0			0
$185$	−5.47253	−	9.47871i	−0.402349	−	0.696888i
$186$		0			0
$187$	−8.67172	+	5.00662i	−0.634139	+	0.366120i
$188$		0			0
$189$			2.05306i			0.149338i
$190$		0			0
$191$	−15.3309			−1.10930			−0.554651	−	0.832083i	$-0.687148\pi$
$191$	−15.3309			−1.10930			−0.554651	+	0.832083i	$0.687148\pi$
$192$		0			0
$193$	−8.31994	−	14.4106i	−0.598882	−	1.03729i	−0.992986	−	0.118229i	$-0.962278\pi$
$193$	−8.31994	−	14.4106i	−0.598882	−	1.03729i	0.394104	−	0.919066i	$-0.371055\pi$
$194$		0			0
$195$	36.2916	−	20.9530i	2.59889	−	1.50047i
$196$		0			0
$197$			0.155717i			0.0110943i	0.999985	+	0.00554717i	$0.00176573\pi$
$197$			0.155717i			0.0110943i	−0.999985	+	0.00554717i	$0.998234\pi$
$198$		0			0
$199$	−4.88153	+	8.45506i	−0.346043	+	0.599363i	−0.985543	−	0.169428i	$-0.945808\pi$
$199$	−4.88153	+	8.45506i	−0.346043	+	0.599363i	0.639500	+	0.768791i	$0.279141\pi$
$200$		0			0
$201$	7.90110			0.557300
$202$		0			0
$203$	6.23919	+	3.60220i	0.437905	+	0.252825i
$204$		0			0
$205$	−31.1210	−	17.9677i	−2.17358	−	1.25492i
$206$		0			0
$207$	−1.18032	−	2.04437i	−0.0820376	−	0.142093i
$208$		0			0
$209$	2.27881	+	4.96990i	0.157628	+	0.343775i
$210$		0			0
$211$	−19.8853	+	11.4808i	−1.36896	+	0.790368i	−0.990795	−	0.135372i	$-0.956777\pi$
$211$	−19.8853	+	11.4808i	−1.36896	+	0.790368i	−0.378162	+	0.925739i	$0.623444\pi$
$212$		0			0
$213$	27.6311	+	15.9528i	1.89325	+	1.09307i
$214$		0			0
$215$	−11.2293	+	19.4497i	−0.765830	+	1.32646i
$216$		0			0
$217$	−13.5501			−0.919844
$218$		0			0
$219$	−13.2197	−	7.63240i	−0.893304	−	0.515750i
$220$		0			0
$221$			38.9893i			2.62270i
$222$		0			0
$223$	5.46950	+	9.47346i	0.366265	+	0.634390i	0.988978	−	0.148061i	$-0.0473030\pi$
$223$	5.46950	+	9.47346i	0.366265	+	0.634390i	−0.622713	+	0.782450i	$0.713970\pi$
$224$		0			0
$225$	−11.0371	−	19.1169i	−0.735810	−	1.27446i
$226$		0			0
$227$		−	16.6384i		−	1.10433i	−0.833736	−	0.552164i	$-0.813802\pi$
$227$		−	16.6384i		−	1.10433i	0.833736	−	0.552164i	$-0.186198\pi$
$228$		0			0
$229$		−	7.56617i		−	0.499986i	−0.968248	−	0.249993i	$-0.919572\pi$
$229$		−	7.56617i		−	0.499986i	0.968248	−	0.249993i	$-0.0804284\pi$
$230$		0			0
$231$	−4.01264	−	6.95010i	−0.264012	−	0.457283i
$232$		0			0
$233$	2.50589	+	4.34033i	0.164166	+	0.284345i	0.936359	−	0.351044i	$-0.114173\pi$
$233$	2.50589	+	4.34033i	0.164166	+	0.284345i	−0.772193	+	0.635389i	$0.780840\pi$
$234$		0			0
$235$		−	27.3480i		−	1.78399i
$236$		0			0
$237$	5.12899	+	2.96122i	0.333164	+	0.192352i
$238$		0			0
$239$	−15.8860			−1.02758			−0.513791	−	0.857915i	$-0.671759\pi$
$239$	−15.8860			−1.02758			−0.513791	+	0.857915i	$0.671759\pi$
$240$		0			0
$241$	−1.00532	+	1.74127i	−0.0647585	+	0.112165i	−0.896587	−	0.442868i	$-0.853961\pi$
$241$	−1.00532	+	1.74127i	−0.0647585	+	0.112165i	0.831828	+	0.555033i	$0.187294\pi$
$242$		0			0
$243$	−19.3716	−	11.1842i	−1.24269	−	0.717465i
$244$		0			0
$245$	1.54773	−	0.893580i	0.0988806	−	0.0570887i
$246$		0			0
$247$	21.1956	+	1.99145i	1.34864	+	0.126713i
$248$		0			0
$249$	−15.3931	−	26.6616i	−0.975499	−	1.68961i
$250$		0			0
$251$	−22.2501	−	12.8461i	−1.40441	−	0.810839i	−0.409572	−	0.912278i	$-0.634322\pi$
$251$	−22.2501	−	12.8461i	−1.40441	−	0.810839i	−0.994842	+	0.101439i	$0.967655\pi$
$252$		0			0
$253$	0.772168	+	0.445811i	0.0485458	+	0.0280279i
$254$		0			0
$255$	68.4961			4.28939
$256$		0			0
$257$	7.11189	−	12.3182i	0.443628	−	0.768385i	−0.554328	−	0.832298i	$-0.687025\pi$
$257$	7.11189	−	12.3182i	0.443628	−	0.768385i	0.997955	+	0.0639129i	$0.0203580\pi$
$258$		0			0
$259$			8.16157i			0.507136i
$260$		0			0
$261$	8.14174	−	4.70064i	0.503961	−	0.290962i
$262$		0			0
$263$	−7.24739	−	12.5529i	−0.446893	−	0.774042i	0.551289	−	0.834315i	$-0.314136\pi$
$263$	−7.24739	−	12.5529i	−0.446893	−	0.774042i	−0.998182	+	0.0602727i	$0.980803\pi$
$264$		0			0
$265$	3.56830			0.219199
$266$		0			0
$267$			6.99146i			0.427871i
$268$		0			0
$269$	11.1770	−	6.45302i	0.681471	−	0.393448i	−0.118938	−	0.992902i	$-0.537949\pi$
$269$	11.1770	−	6.45302i	0.681471	−	0.393448i	0.800409	+	0.599454i	$0.204616\pi$
$270$		0			0
$271$	9.89868	+	17.1450i	0.601302	+	1.04149i	0.992624	+	0.121232i	$0.0386845\pi$
$271$	9.89868	+	17.1450i	0.601302	+	1.04149i	−0.391322	+	0.920254i	$0.627982\pi$
$272$		0			0
$273$	−31.2486			−1.89125
$274$		0			0
$275$	7.22055	+	4.16879i	0.435416	+	0.251387i
$276$		0			0
$277$		−	2.10309i		−	0.126362i	−0.998002	−	0.0631812i	$-0.979875\pi$
$277$		−	2.10309i		−	0.126362i	0.998002	−	0.0631812i	$-0.0201246\pi$
$278$		0			0
$279$	−8.84103	+	15.3131i	−0.529299	+	0.916772i
$280$		0			0
$281$	2.20156	−	3.81321i	0.131334	−	0.227477i	−0.792857	−	0.609408i	$-0.791407\pi$
$281$	2.20156	−	3.81321i	0.131334	−	0.227477i	0.924191	+	0.381931i	$0.124741\pi$
$282$		0			0
$283$	0.911785	−	0.526419i	0.0542000	−	0.0312924i	−0.472655	−	0.881247i	$-0.656704\pi$
$283$	0.911785	−	0.526419i	0.0542000	−	0.0312924i	0.526855	+	0.849955i	$0.323371\pi$
$284$		0			0
$285$	3.49857	−	37.2363i	0.207237	−	2.20569i
$286$		0			0
$287$	13.3982	+	23.2064i	0.790873	+	1.36983i
$288$		0			0
$289$	−23.3644	+	40.4683i	−1.37438	+	2.38049i
$290$		0			0
$291$	25.1363	+	14.5124i	1.47351	+	0.850734i
$292$		0			0
$293$			8.56042i			0.500105i	0.968232	+	0.250052i	$0.0804479\pi$
$293$			8.56042i			0.500105i	−0.968232	+	0.250052i	$0.919552\pi$
$294$		0			0
$295$	−12.7471	+	22.0787i	−0.742167	+	1.28547i
$296$		0			0
$297$	−1.01192			−0.0587173
$298$		0			0
$299$	3.00665	−	1.73589i	0.173879	−	0.100389i
$300$		0			0
$301$	14.5033	−	8.37350i	0.835958	−	0.482641i
$302$		0			0
$303$	−15.5686			−0.894393
$304$		0			0
$305$	46.9178			2.68650
$306$		0			0
$307$	16.9636	−	9.79391i	0.968161	−	0.558968i	0.0694860	−	0.997583i	$-0.477864\pi$
$307$	16.9636	−	9.79391i	0.968161	−	0.558968i	0.898675	+	0.438615i	$0.144531\pi$
$308$		0			0
$309$	9.62431	−	5.55660i	0.547508	−	0.316104i
$310$		0			0
$311$	−25.7890			−1.46236			−0.731179	−	0.682186i	$-0.761029\pi$
$311$	−25.7890			−1.46236			−0.731179	+	0.682186i	$0.761029\pi$
$312$		0			0
$313$	5.50828	−	9.54062i	0.311346	−	0.539268i	−0.667308	−	0.744782i	$-0.732553\pi$
$313$	5.50828	−	9.54062i	0.311346	−	0.539268i	0.978654	+	0.205514i	$0.0658868\pi$
$314$		0			0
$315$			28.8421i			1.62507i
$316$		0			0
$317$	−15.6002	−	9.00676i	−0.876193	−	0.505870i	−0.00679167	−	0.999977i	$-0.502162\pi$
$317$	−15.6002	−	9.00676i	−0.876193	−	0.505870i	−0.869401	+	0.494107i	$0.835495\pi$
$318$		0			0
$319$	−1.77545	+	3.07518i	−0.0994064	+	0.172177i
$320$		0			0
$321$	−14.8614	−	25.7406i	−0.829481	−	1.43670i
$322$		0			0
$323$	28.3756	+	20.1413i	1.57886	+	1.12069i
$324$		0			0
$325$	28.1152	−	16.2323i	1.55955	−	0.900407i
$326$		0			0
$327$	21.3132	−	36.9156i	1.17862	−	2.04144i
$328$		0			0
$329$	−10.1965	+	17.6609i	−0.562151	+	0.973675i
$330$		0			0
$331$		−	31.3668i		−	1.72407i	−0.506846	−	0.862037i	$-0.669189\pi$
$331$		−	31.3668i		−	1.72407i	0.506846	−	0.862037i	$-0.330811\pi$
$332$		0			0
$333$	9.22346	+	5.32517i	0.505442	+	0.291817i
$334$		0			0
$335$	10.7253			0.585983
$336$		0			0
$337$	9.22394	+	15.9763i	0.502460	+	0.870286i	0.999996	+	0.00284285i	$0.000904908\pi$
$337$	9.22394	+	15.9763i	0.502460	+	0.870286i	−0.497536	+	0.867443i	$0.665762\pi$
$338$		0			0
$339$	−1.78016	+	1.02778i	−0.0966852	+	0.0558212i
$340$		0			0
$341$		−	6.67861i		−	0.361667i
$342$		0			0
$343$	−19.1467			−1.03383
$344$		0			0
$345$	−3.04960	−	5.28206i	−0.164185	−	0.284376i
$346$		0			0
$347$	−4.77429	+	2.75644i	−0.256297	+	0.147973i	−0.622644	−	0.782505i	$-0.713942\pi$
$347$	−4.77429	+	2.75644i	−0.256297	+	0.147973i	0.366347	+	0.930478i	$0.380608\pi$
$348$		0			0
$349$			30.1208i			1.61233i	0.591690	+	0.806166i	$0.298461\pi$
$349$			30.1208i			1.61233i	−0.591690	+	0.806166i	$0.701539\pi$
$350$		0			0
$351$	−1.97008	+	3.41229i	−0.105155	+	0.182134i
$352$		0			0
$353$	−19.5925			−1.04280			−0.521402	−	0.853311i	$-0.674591\pi$
$353$	−19.5925			−1.04280			−0.521402	+	0.853311i	$0.674591\pi$
$354$		0			0
$355$	37.5076	+	21.6550i	1.99069	+	1.14933i
$356$		0			0
$357$	−44.2336	−	25.5383i	−2.34109	−	1.35163i
$358$		0			0
$359$	9.14429	+	15.8384i	0.482617	+	0.835917i	0.999801	−	0.0199571i	$-0.00635297\pi$
$359$	9.14429	+	15.8384i	0.482617	+	0.835917i	−0.517184	+	0.855874i	$0.673020\pi$
$360$		0			0
$361$	12.3987	−	14.3970i	0.652562	−	0.757736i
$362$		0			0
$363$	−20.5248	+	11.8500i	−1.07727	+	0.621964i
$364$		0			0
$365$	−17.9449	−	10.3605i	−0.939281	−	0.542294i
$366$		0			0
$367$	−1.03238	+	1.78813i	−0.0538896	+	0.0933395i	−0.891712	−	0.452604i	$-0.850495\pi$
$367$	−1.03238	+	1.78813i	−0.0538896	+	0.0933395i	0.837822	+	0.545943i	$0.183829\pi$
$368$		0			0
$369$	34.9677			1.82034
$370$		0			0
$371$	−2.30434	−	1.33041i	−0.119636	−	0.0690716i
$372$		0			0
$373$		−	22.5069i		−	1.16536i	−0.812701	−	0.582680i	$-0.802004\pi$
$373$		−	22.5069i		−	1.16536i	0.812701	−	0.582680i	$-0.197996\pi$
$374$		0			0
$375$	−7.06629	−	12.2392i	−0.364902	−	0.632028i
$376$		0			0
$377$	6.91322	+	11.9740i	0.356049	+	0.616695i
$378$		0			0
$379$			27.4490i			1.40996i	0.709228	+	0.704980i	$0.249044\pi$
$379$			27.4490i			1.40996i	−0.709228	+	0.704980i	$0.750956\pi$
$380$		0			0
$381$		−	3.82115i		−	0.195763i
$382$		0			0
$383$	−10.0380	−	17.3863i	−0.512918	−	0.888399i	−0.999888	−	0.0149807i	$-0.995231\pi$
$383$	−10.0380	−	17.3863i	−0.512918	−	0.888399i	0.486970	−	0.873419i	$-0.338102\pi$
$384$		0			0
$385$	−5.44691	−	9.43433i	−0.277600	−	0.480818i
$386$		0			0
$387$		−	21.8538i		−	1.11089i
$388$		0			0
$389$	−14.7087	−	8.49210i	−0.745763	−	0.430567i	0.0783979	−	0.996922i	$-0.475020\pi$
$389$	−14.7087	−	8.49210i	−0.745763	−	0.430567i	−0.824161	+	0.566356i	$0.808353\pi$
$390$		0			0
$391$	5.67469			0.286982
$392$		0			0
$393$	5.89318	−	10.2073i	0.297272	−	0.514890i
$394$		0			0
$395$	6.96229	+	4.01968i	0.350311	+	0.202252i
$396$		0			0
$397$	−2.01293	+	1.16217i	−0.101026	+	0.0583274i	−0.549662	−	0.835387i	$-0.685243\pi$
$397$	−2.01293	+	1.16217i	−0.101026	+	0.0583274i	0.448636	+	0.893715i	$0.351910\pi$
$398$		0			0
$399$	−16.1426	+	22.7421i	−0.808140	+	1.13853i
$400$		0			0
$401$	−6.79543	−	11.7700i	−0.339348	−	0.587767i	0.644963	−	0.764214i	$-0.276873\pi$
$401$	−6.79543	−	11.7700i	−0.339348	−	0.587767i	−0.984310	+	0.176447i	$0.943540\pi$
$402$		0			0
$403$	−22.5210	−	13.0025i	−1.12185	−	0.647700i
$404$		0			0
$405$	−23.4505	−	13.5392i	−1.16527	−	0.672767i
$406$		0			0
$407$	−4.02268			−0.199397
$408$		0			0
$409$	1.93142	−	3.34532i	0.0955025	−	0.165415i	−0.814316	−	0.580422i	$-0.802888\pi$
$409$	1.93142	−	3.34532i	0.0955025	−	0.165415i	0.909818	+	0.415007i	$0.136221\pi$
$410$		0			0
$411$			13.3396i			0.657995i
$412$		0			0
$413$	16.4637	−	9.50535i	0.810128	−	0.467728i
$414$		0			0
$415$	−20.8952	−	36.1915i	−1.02571	−	1.77657i
$416$		0			0
$417$	−37.7510			−1.84867
$418$		0			0
$419$			14.0401i			0.685904i	0.939353	+	0.342952i	$0.111427\pi$
$419$			14.0401i			0.685904i	−0.939353	+	0.342952i	$0.888573\pi$
$420$		0			0
$421$	26.7712	−	15.4564i	1.30475	−	0.753298i	0.323535	−	0.946216i	$-0.395129\pi$
$421$	26.7712	−	15.4564i	1.30475	−	0.753298i	0.981215	+	0.192919i	$0.0617953\pi$
$422$		0			0
$423$	13.3058	+	23.0463i	0.646949	+	1.12055i
$424$		0			0
$425$	53.0641			2.57399
$426$		0			0
$427$	−30.2987	−	17.4929i	−1.46625	−	0.846543i
$428$		0			0
$429$		−	15.4018i		−	0.743608i
$430$		0			0
$431$	−2.67813	+	4.63865i	−0.129001	+	0.223436i	−0.923290	−	0.384104i	$-0.874510\pi$
$431$	−2.67813	+	4.63865i	−0.129001	+	0.223436i	0.794289	+	0.607540i	$0.207844\pi$
$432$		0			0
$433$	−12.1157	+	20.9850i	−0.582242	+	1.00847i	0.412971	+	0.910744i	$0.364491\pi$
$433$	−12.1157	+	20.9850i	−0.582242	+	1.00847i	−0.995213	+	0.0977288i	$0.968842\pi$
$434$		0			0
$435$	21.0359	−	12.1451i	1.00860	−	0.582313i
$436$		0			0
$437$	0.289845	−	3.08491i	0.0138652	−	0.147571i
$438$		0			0
$439$	5.93350	+	10.2771i	0.283190	+	0.490500i	0.972169	−	0.234282i	$-0.0752738\pi$
$439$	5.93350	+	10.2771i	0.283190	+	0.490500i	−0.688978	+	0.724782i	$0.741941\pi$
$440$		0			0
$441$	−0.869517	+	1.50605i	−0.0414056	+	0.0717165i
$442$		0			0
$443$	6.68234	+	3.85805i	0.317488	+	0.183302i	0.650272	−	0.759701i	$-0.274655\pi$
$443$	6.68234	+	3.85805i	0.317488	+	0.183302i	−0.332784	+	0.943003i	$0.607988\pi$
$444$		0			0
$445$			9.49048i			0.449892i
$446$		0			0
$447$	24.7356	−	42.8433i	1.16995	−	2.02642i
$448$		0			0
$449$	9.64706			0.455273			0.227636	−	0.973746i	$-0.426900\pi$
$449$	9.64706			0.455273			0.227636	+	0.973746i	$0.426900\pi$
$450$		0			0
$451$	−11.4380	+	6.60374i	−0.538595	+	0.310958i
$452$		0			0
$453$	−48.9893	+	28.2840i	−2.30172	+	1.32890i
$454$		0			0
$455$	−42.4181			−1.98859
$456$		0			0
$457$	−33.8154			−1.58182			−0.790908	−	0.611935i	$-0.790391\pi$
$457$	−33.8154			−1.58182			−0.790908	+	0.611935i	$0.790391\pi$
$458$		0			0
$459$	−5.57746	+	3.22015i	−0.260333	+	0.150304i
$460$		0			0
$461$	22.0916	−	12.7546i	1.02891	−	0.594042i	0.112238	−	0.993681i	$-0.464198\pi$
$461$	22.0916	−	12.7546i	1.02891	−	0.594042i	0.916672	+	0.399640i	$0.130865\pi$
$462$		0			0
$463$	18.6279			0.865713			0.432856	−	0.901463i	$-0.357506\pi$
$463$	18.6279			0.865713			0.432856	+	0.901463i	$0.357506\pi$
$464$		0			0
$465$	−22.8427	+	39.5647i	−1.05930	+	1.83477i
$466$		0			0
$467$			30.6406i			1.41788i	0.705270	+	0.708939i	$0.250826\pi$
$467$			30.6406i			1.41788i	−0.705270	+	0.708939i	$0.749174\pi$
$468$		0			0
$469$	−6.92618	−	3.99883i	−0.319821	−	0.184649i
$470$		0			0
$471$	−7.77882	+	13.4733i	−0.358429	+	0.620817i
$472$		0			0
$473$	4.12714	+	7.14841i	0.189766	+	0.328684i
$474$		0			0
$475$	2.71035	−	28.8470i	0.124359	−	1.32359i
$476$		0			0
$477$	−3.00702	+	1.73610i	−0.137682	+	0.0794907i
$478$		0			0
$479$	−19.2670	+	33.3715i	−0.880333	+	1.52478i	−0.0293614	+	0.999569i	$0.509347\pi$
$479$	−19.2670	+	33.3715i	−0.880333	+	1.52478i	−0.850971	+	0.525212i	$0.823986\pi$
$480$		0			0
$481$	−7.83171	+	13.5649i	−0.357095	+	0.618507i
$482$		0			0
$483$			4.54808i			0.206945i
$484$		0			0
$485$	34.1210	+	19.6997i	1.54935	+	0.894519i
$486$		0			0
$487$	12.2713			0.556064			0.278032	−	0.960572i	$-0.410318\pi$
$487$	12.2713			0.556064			0.278032	+	0.960572i	$0.410318\pi$
$488$		0			0
$489$	9.45349	+	16.3739i	0.427502	+	0.740455i
$490$		0			0
$491$	1.79067	−	1.03384i	0.0808117	−	0.0466567i	−0.459050	−	0.888411i	$-0.651810\pi$
$491$	1.79067	−	1.03384i	0.0808117	−	0.0466567i	0.539861	+	0.841754i	$0.318477\pi$
$492$		0			0
$493$			22.5996i			1.01784i
$494$		0			0
$495$	−14.2157			−0.638950
$496$		0			0
$497$	−16.1478	−	27.9688i	−0.724328	−	1.25457i
$498$		0			0
$499$	−22.5746	+	13.0335i	−1.01058	+	0.583458i	−0.911361	−	0.411607i	$-0.864968\pi$
$499$	−22.5746	+	13.0335i	−1.01058	+	0.583458i	−0.0992183	+	0.995066i	$0.531634\pi$
$500$		0			0
$501$			35.7584i			1.59757i
$502$		0			0
$503$	18.4953	−	32.0348i	0.824664	−	1.42836i	−0.0775123	−	0.996991i	$-0.524698\pi$
$503$	18.4953	−	32.0348i	0.824664	−	1.42836i	0.902176	−	0.431368i	$-0.141969\pi$
$504$		0			0
$505$	−21.1334			−0.940425
$506$		0			0
$507$	−23.6317	−	13.6438i	−1.04952	−	0.605941i
$508$		0			0
$509$	3.49285	+	2.01660i	0.154818	+	0.0893840i	0.575407	−	0.817867i	$-0.304843\pi$
$509$	3.49285	+	2.01660i	0.154818	+	0.0893840i	−0.420590	+	0.907251i	$0.638177\pi$
$510$		0			0
$511$	7.72568	+	13.3813i	0.341764	+	0.591952i
$512$		0			0
$513$	1.46568	+	3.19653i	0.0647112	+	0.141130i
$514$		0			0
$515$	13.0644	−	7.54274i	0.575687	−	0.332373i
$516$		0			0
$517$	−8.70470	−	5.02566i	−0.382832	−	0.221028i
$518$		0			0
$519$	−16.3562	+	28.3298i	−0.717959	+	1.24354i
$520$		0			0
$521$	−15.8053			−0.692443			−0.346222	−	0.938153i	$-0.612536\pi$
$521$	−15.8053			−0.692443			−0.346222	+	0.938153i	$0.612536\pi$
$522$		0			0
$523$	6.25047	+	3.60871i	0.273314	+	0.157798i	0.630393	−	0.776276i	$-0.282894\pi$
$523$	6.25047	+	3.60871i	0.273314	+	0.157798i	−0.357079	+	0.934074i	$0.616227\pi$
$524$		0			0
$525$			42.5291i			1.85612i
$526$		0			0
$527$	−21.2528	−	36.8110i	−0.925789	−	1.60351i
$528$		0			0
$529$	11.2474	+	19.4810i	0.489015	+	0.846999i
$530$		0			0
$531$		−	24.8077i		−	1.07656i
$532$		0			0
$533$			51.4269i			2.22755i
$534$		0			0
$535$	−20.1734	−	34.9413i	−0.872172	−	1.51065i
$536$		0			0
$537$	0.633134	+	1.09662i	0.0273217	+	0.0473226i
$538$		0			0
$539$		−	0.656842i		−	0.0282922i
$540$		0			0
$541$	3.82654	+	2.20926i	0.164516	+	0.0949833i	0.579997	−	0.814618i	$-0.303054\pi$
$541$	3.82654	+	2.20926i	0.164516	+	0.0949833i	−0.415481	+	0.909602i	$0.636387\pi$
$542$		0			0
$543$	−47.1050			−2.02147
$544$		0			0
$545$	28.9314	−	50.1107i	1.23929	−	2.14651i
$546$		0			0
$547$	−4.90706	−	2.83309i	−0.209811	−	0.121134i	0.391413	−	0.920215i	$-0.371987\pi$
$547$	−4.90706	−	2.83309i	−0.209811	−	0.121134i	−0.601223	+	0.799081i	$0.705320\pi$
$548$		0			0
$549$	−39.5378	+	22.8272i	−1.68743	+	0.974240i
$550$		0			0
$551$	12.2857	+	1.15432i	0.523390	+	0.0491755i
$552$		0			0
$553$	−2.99742	−	5.19168i	−0.127463	−	0.220773i
$554$		0			0
$555$	23.8308	+	13.7587i	1.01156	+	0.584024i
$556$		0			0
$557$	22.0524	+	12.7319i	0.934389	+	0.539470i	0.888197	−	0.459463i	$-0.151958\pi$
$557$	22.0524	+	12.7319i	0.934389	+	0.539470i	0.0461920	+	0.998933i	$0.485291\pi$
$558$		0			0
$559$	32.1403			1.35939
$560$		0			0
$561$	12.5873	−	21.8019i	0.531437	−	0.920476i
$562$		0			0
$563$		−	29.5332i		−	1.24468i	−0.782748	−	0.622339i	$-0.786183\pi$
$563$		−	29.5332i		−	1.24468i	0.782748	−	0.622339i	$-0.213817\pi$
$564$		0			0
$565$	−2.41646	+	1.39515i	−0.101661	+	0.0586942i
$566$		0			0
$567$	10.0960	+	17.4867i	0.423990	+	0.734373i
$568$		0			0
$569$	29.8114			1.24976			0.624879	−	0.780722i	$-0.285148\pi$
$569$	29.8114			1.24976			0.624879	+	0.780722i	$0.285148\pi$
$570$		0			0
$571$		−	2.87084i		−	0.120141i	−0.998194	−	0.0600705i	$-0.980867\pi$
$571$		−	2.87084i		−	0.120141i	0.998194	−	0.0600705i	$-0.0191326\pi$
$572$		0			0
$573$	33.3800	−	19.2719i	1.39447	−	0.805097i
$574$		0			0
$575$	−2.36253	−	4.09202i	−0.0985244	−	0.170649i
$576$		0			0
$577$	38.3067			1.59473			0.797364	−	0.603499i	$-0.206227\pi$
$577$	38.3067			1.59473			0.797364	+	0.603499i	$0.206227\pi$
$578$		0			0
$579$	36.2301	+	20.9175i	1.50567	+	0.869300i
$580$		0			0
$581$			31.1625i			1.29284i
$582$		0			0
$583$	0.655735	−	1.13577i	0.0271578	−	0.0470387i
$584$		0			0
$585$	−27.6764	+	47.9370i	−1.14428	+	1.98195i
$586$		0			0
$587$	−18.9662	+	10.9501i	−0.782819	+	0.451961i	−0.837428	−	0.546547i	$-0.815942\pi$
$587$	−18.9662	+	10.9501i	−0.782819	+	0.451961i	0.0546095	+	0.998508i	$0.482609\pi$
$588$		0			0
$589$	−21.0970	+	9.67341i	−0.869285	+	0.398586i
$590$		0			0
$591$	−0.195746	−	0.339043i	−0.00805193	−	0.0139464i
$592$		0			0
$593$	10.0441	−	17.3968i	0.412461	−	0.714403i	−0.582697	−	0.812689i	$-0.698003\pi$
$593$	10.0441	−	17.3968i	0.412461	−	0.714403i	0.995158	+	0.0982863i	$0.0313361\pi$
$594$		0			0
$595$	−60.0444	−	34.6666i	−2.46158	−	1.42119i
$596$		0			0
$597$		−	24.5457i		−	1.00459i
$598$		0			0
$599$	−1.88758	+	3.26938i	−0.0771244	+	0.133583i	−0.902008	−	0.431719i	$-0.857907\pi$
$599$	−1.88758	+	3.26938i	−0.0771244	+	0.133583i	0.824884	+	0.565302i	$0.191241\pi$
$600$		0			0
$601$	9.29129			0.379000			0.189500	−	0.981881i	$-0.439313\pi$
$601$	9.29129			0.379000			0.189500	+	0.981881i	$0.439313\pi$
$602$		0			0
$603$	−9.03822	+	5.21822i	−0.368065	+	0.212502i
$604$		0			0
$605$	−27.8612	+	16.0856i	−1.13272	+	0.653975i
$606$		0			0
$607$	1.55590			0.0631519			0.0315759	−	0.999501i	$-0.489947\pi$
$607$	1.55590			0.0631519			0.0315759	+	0.999501i	$0.489947\pi$
$608$		0			0
$609$	−18.1128			−0.733969
$610$		0			0
$611$	−33.8941	+	19.5688i	−1.37121	+	0.791668i
$612$		0			0
$613$	−19.9323	+	11.5079i	−0.805059	+	0.464801i	−0.845237	−	0.534391i	$-0.820541\pi$
$613$	−19.9323	+	11.5079i	−0.805059	+	0.464801i	0.0401778	+	0.999193i	$0.487208\pi$
$614$		0			0
$615$	90.3465			3.64312
$616$		0			0
$617$	5.63489	−	9.75992i	0.226852	−	0.392920i	−0.730021	−	0.683424i	$-0.760490\pi$
$617$	5.63489	−	9.75992i	0.226852	−	0.392920i	0.956874	+	0.290505i	$0.0938232\pi$
$618$		0			0
$619$			4.18227i			0.168100i	0.996462	+	0.0840498i	$0.0267855\pi$
$619$			4.18227i			0.168100i	−0.996462	+	0.0840498i	$0.973215\pi$
$620$		0			0
$621$	0.496641	+	0.286736i	0.0199295	+	0.0115063i
$622$		0			0
$623$	3.53846	−	6.12879i	0.141765	−	0.245545i
$624$		0			0
$625$	7.02573	+	12.1689i	0.281029	+	0.486757i
$626$		0			0
$627$	−11.2092	−	7.95637i	−0.447651	−	0.317747i
$628$		0			0
$629$	−22.1722	+	12.8011i	−0.884062	+	0.510413i
$630$		0			0
$631$	19.6870	−	34.0989i	0.783728	−	1.35746i	−0.146029	−	0.989280i	$-0.546649\pi$
$631$	19.6870	−	34.0989i	0.783728	−	1.35746i	0.929756	−	0.368176i	$-0.120018\pi$
$632$		0			0
$633$	28.8642	−	49.9942i	1.14725	−	1.98709i
$634$		0			0
$635$		−	5.18697i		−	0.205839i
$636$		0			0
$637$	−2.21494	−	1.27880i	−0.0877592	−	0.0506678i
$638$		0			0
$639$	−42.1437			−1.66718
$640$		0			0
$641$	−1.89633	−	3.28455i	−0.0749007	−	0.129732i	0.826142	−	0.563461i	$-0.190531\pi$
$641$	−1.89633	−	3.28455i	−0.0749007	−	0.129732i	−0.901043	+	0.433730i	$0.857197\pi$
$642$		0			0
$643$	−12.4215	+	7.17154i	−0.489855	+	0.282818i	−0.724514	−	0.689260i	$-0.757936\pi$
$643$	−12.4215	+	7.17154i	−0.489855	+	0.282818i	0.234659	+	0.972078i	$0.424603\pi$
$644$		0			0
$645$		−	56.4639i		−	2.22326i
$646$		0			0
$647$	4.09464			0.160977			0.0804884	−	0.996756i	$-0.474352\pi$
$647$	4.09464			0.160977			0.0804884	+	0.996756i	$0.474352\pi$
$648$		0			0
$649$	4.68500	+	8.11466i	0.183902	+	0.318528i
$650$		0			0
$651$	29.5028	−	17.0335i	1.15631	−	0.667594i
$652$		0			0
$653$			41.4592i			1.62242i	0.584753	+	0.811211i	$0.301191\pi$
$653$			41.4592i			1.62242i	−0.584753	+	0.811211i	$0.698809\pi$
$654$		0			0
$655$	7.99963	−	13.8558i	0.312572	−	0.541390i
$656$		0			0
$657$	20.1630			0.786635
$658$		0			0
$659$	1.94461	+	1.12272i	0.0757514	+	0.0437351i	0.537397	−	0.843329i	$-0.319408\pi$
$659$	1.94461	+	1.12272i	0.0757514	+	0.0437351i	−0.461646	+	0.887064i	$0.652741\pi$
$660$		0			0
$661$	−12.6664	−	7.31294i	−0.492665	−	0.284440i	0.233014	−	0.972473i	$-0.425141\pi$
$661$	−12.6664	−	7.31294i	−0.492665	−	0.284440i	−0.725679	+	0.688033i	$0.758474\pi$
$662$		0			0
$663$	−49.0122	−	84.8916i	−1.90348	−	3.29692i
$664$		0			0
$665$	−21.9126	+	30.8710i	−0.849733	+	1.19713i
$666$		0			0
$667$	1.74276	−	1.00618i	0.0674800	−	0.0389596i
$668$		0			0
$669$	−23.8176	−	13.7511i	−0.920840	−	0.531647i
$670$		0			0
$671$	8.62193	−	14.9336i	0.332846	−	0.576506i
$672$		0			0
$673$	21.2119			0.817659			0.408829	−	0.912611i	$-0.365937\pi$
$673$	21.2119			0.817659			0.408829	+	0.912611i	$0.365937\pi$
$674$		0			0
$675$	4.64410	+	2.68127i	0.178751	+	0.103202i
$676$		0			0
$677$			10.0144i			0.384885i	0.981308	+	0.192443i	$0.0616409\pi$
$677$			10.0144i			0.384885i	−0.981308	+	0.192443i	$0.938359\pi$
$678$		0			0
$679$	−14.6898	−	25.4435i	−0.563743	−	0.976431i
$680$		0			0
$681$	20.9156	+	36.2268i	0.801486	+	1.38822i
$682$		0			0
$683$			3.77839i			0.144576i	0.997384	+	0.0722881i	$0.0230301\pi$
$683$			3.77839i			0.144576i	−0.997384	+	0.0722881i	$0.976970\pi$
$684$		0			0
$685$			18.1077i			0.691861i
$686$		0			0
$687$	9.51119	+	16.4739i	0.362874	+	0.628517i
$688$		0			0
$689$	−2.55328	−	4.42242i	−0.0972724	−	0.168481i
$690$		0			0
$691$			27.7719i			1.05649i	0.849091	+	0.528246i	$0.177150\pi$
$691$			27.7719i			1.05649i	−0.849091	+	0.528246i	$0.822850\pi$
$692$		0			0
$693$	9.18027	+	5.30023i	0.348730	+	0.201339i
$694$		0			0
$695$	−51.2447			−1.94382
$696$		0			0
$697$	−42.0292	+	72.7967i	−1.59197	+	2.75737i
$698$		0			0
$699$	−10.9122	−	6.30015i	−0.412737	−	0.238294i
$700$		0			0
$701$	25.2750	−	14.5925i	0.954622	−	0.551151i	0.0601085	−	0.998192i	$-0.480855\pi$
$701$	25.2750	−	14.5925i	0.954622	−	0.551151i	0.894514	+	0.447040i	$0.147522\pi$
$702$		0			0
$703$	5.82653	+	12.7072i	0.219752	+	0.479261i
$704$		0			0
$705$	34.3783	+	59.5450i	1.29476	+	2.24259i
$706$		0			0
$707$	13.6476	+	7.87944i	0.513271	+	0.296337i
$708$		0			0
$709$	3.35449	+	1.93671i	0.125980	+	0.0727348i	0.561666	−	0.827364i	$-0.310161\pi$
$709$	3.35449	+	1.93671i	0.125980	+	0.0727348i	−0.435685	+	0.900099i	$0.643494\pi$
$710$		0			0
$711$	−7.82287			−0.293381
$712$		0			0
$713$	−1.89245	+	3.27781i	−0.0708727	+	0.122755i
$714$		0			0
$715$		−	20.9071i		−	0.781880i
$716$		0			0
$717$	34.5887	−	19.9698i	1.29174	−	0.745787i
$718$		0			0
$719$	9.24280	+	16.0090i	0.344698	+	0.597035i	0.985299	−	0.170839i	$-0.0546479\pi$
$719$	9.24280	+	16.0090i	0.344698	+	0.597035i	−0.640601	+	0.767874i	$0.721315\pi$
$720$		0			0
$721$	−11.2490			−0.418935
$722$		0			0
$723$		−	5.05504i		−	0.187999i
$724$		0			0
$725$	16.2966	−	9.40884i	0.605240	−	0.349436i
$726$		0			0
$727$	24.8764	+	43.0871i	0.922613	+	1.59801i	0.795355	+	0.606144i	$0.207284\pi$
$727$	24.8764	+	43.0871i	0.922613	+	1.59801i	0.127258	+	0.991870i	$0.459382\pi$
$728$		0			0
$729$	32.4340			1.20126
$730$		0			0
$731$	45.4958	+	26.2670i	1.68272	+	0.971520i
$732$		0			0
$733$		−	15.3497i		−	0.566954i	−0.958979	−	0.283477i	$-0.908512\pi$
$733$		−	15.3497i		−	0.566954i	0.958979	−	0.283477i	$-0.0914879\pi$
$734$		0			0
$735$	−2.24658	+	3.89119i	−0.0828664	+	0.143529i
$736$		0			0
$737$	1.97095	−	3.41378i	0.0726008	−	0.125748i
$738$		0			0
$739$	12.0680	−	6.96744i	0.443927	−	0.256302i	−0.261335	−	0.965248i	$-0.584163\pi$
$739$	12.0680	−	6.96744i	0.443927	−	0.256302i	0.705262	+	0.708947i	$0.250829\pi$
$740$		0			0
$741$	−48.6527	+	22.3083i	−1.78730	+	0.819516i
$742$		0			0
$743$	−24.7117	−	42.8020i	−0.906585	−	1.57025i	−0.818775	−	0.574114i	$-0.805347\pi$
$743$	−24.7117	−	42.8020i	−0.906585	−	1.57025i	−0.0878096	−	0.996137i	$-0.527987\pi$
$744$		0			0
$745$	33.5771	−	58.1572i	1.23017	−	2.13072i
$746$		0			0
$747$	35.2170	+	20.3325i	1.28852	+	0.743928i
$748$		0			0
$749$			30.0860i			1.09932i
$750$		0			0
$751$	14.9614	−	25.9140i	0.545951	−	0.945615i	−0.452596	−	0.891716i	$-0.649502\pi$
$751$	14.9614	−	25.9140i	0.545951	−	0.945615i	0.998546	−	0.0538987i	$-0.0171648\pi$
$752$		0			0
$753$	64.5937			2.35393
$754$		0			0
$755$	−66.4999	+	38.3938i	−2.42018	+	1.39729i
$756$		0			0
$757$	41.5430	−	23.9849i	1.50991	−	0.871744i	0.509972	−	0.860191i	$-0.329656\pi$
$757$	41.5430	−	23.9849i	1.50991	−	0.871744i	0.999933	−	0.0115535i	$-0.00367768\pi$
$758$		0			0
$759$	−2.24166			−0.0813671
$760$		0			0
$761$	−42.6841			−1.54730			−0.773648	−	0.633616i	$-0.781570\pi$
$761$	−42.6841			−1.54730			−0.773648	+	0.633616i	$0.781570\pi$
$762$		0			0
$763$	−37.3668	+	21.5737i	−1.35277	+	0.781021i
$764$		0			0
$765$	−78.3541	+	45.2377i	−2.83290	+	1.63557i
$766$		0			0
$767$	36.4847			1.31739
$768$		0			0
$769$	15.0008	−	25.9821i	0.540942	−	0.936940i	−0.457908	−	0.889000i	$-0.651401\pi$
$769$	15.0008	−	25.9821i	0.540942	−	0.936940i	0.998850	−	0.0479400i	$-0.0152656\pi$
$770$		0			0
$771$			35.7605i			1.28788i
$772$		0			0
$773$	16.0137	+	9.24549i	0.575971	+	0.332537i	0.759531	−	0.650471i	$-0.225429\pi$
$773$	16.0137	+	9.24549i	0.575971	+	0.332537i	−0.183559	+	0.983009i	$0.558762\pi$
$774$		0			0
$775$	−17.6963	+	30.6509i	−0.635670	+	1.10101i
$776$		0			0
$777$	−10.2597	−	17.7702i	−0.368063	−	0.637504i
$778$		0			0
$779$	37.4275	+	26.5664i	1.34098	+	0.951840i
$780$		0			0
$781$	13.7853	−	7.95895i	0.493277	−	0.284794i
$782$		0			0
$783$	−1.14193	+	1.97789i	−0.0408094	+	0.0706839i
$784$		0			0
$785$	−10.5593	+	18.2892i	−0.376876	+	0.652769i
$786$		0			0
$787$		−	38.4519i		−	1.37066i	−0.728232	−	0.685331i	$-0.759658\pi$
$787$		−	38.4519i		−	1.37066i	0.728232	−	0.685331i	$-0.240342\pi$
$788$		0			0
$789$	31.5596	+	18.2209i	1.12355	+	0.648682i
$790$		0			0
$791$	2.08068			0.0739804
$792$		0			0
$793$	−33.5719	−	58.1482i	−1.19217	−	2.06490i
$794$		0			0
$795$	−7.76928	+	4.48559i	−0.275548	+	0.159088i
$796$		0			0
$797$		−	17.9520i		−	0.635894i	−0.948108	−	0.317947i	$-0.897007\pi$
$797$		−	17.9520i		−	0.635894i	0.948108	−	0.317947i	$-0.102993\pi$
$798$		0			0
$799$	−63.9712			−2.26314
$800$		0			0
$801$	−4.61746	−	7.99767i	−0.163150	−	0.282584i
$802$		0			0
$803$	−6.59537	+	3.80784i	−0.232746	+	0.134376i
$804$		0			0
$805$			6.17374i			0.217596i
$806$		0			0
$807$	−16.2238	+	28.1004i	−0.571104	+	0.989181i
$808$		0			0
$809$	9.79345			0.344319			0.172160	−	0.985069i	$-0.444926\pi$
$809$	9.79345			0.344319			0.172160	+	0.985069i	$0.444926\pi$
$810$		0			0
$811$	2.14857	+	1.24048i	0.0754466	+	0.0435591i	0.537249	−	0.843424i	$-0.319464\pi$
$811$	2.14857	+	1.24048i	0.0754466	+	0.0435591i	−0.461802	+	0.886983i	$0.652797\pi$
$812$		0			0
$813$	−43.1049	−	24.8866i	−1.51176	−	0.872812i
$814$		0			0
$815$	12.8325	+	22.2266i	0.449504	+	0.778564i
$816$		0			0
$817$	16.6032	−	23.3911i	0.580873	−	0.818350i
$818$		0			0
$819$	35.7459	−	20.6379i	1.24906	−	0.721147i
$820$		0			0
$821$	−3.52896	−	2.03744i	−0.123161	−	0.0711073i	0.437154	−	0.899387i	$-0.355987\pi$
$821$	−3.52896	−	2.03744i	−0.123161	−	0.0711073i	−0.560315	+	0.828280i	$0.689320\pi$
$822$		0			0
$823$	10.1999	−	17.6667i	0.355546	−	0.615824i	−0.631665	−	0.775241i	$-0.717628\pi$
$823$	10.1999	−	17.6667i	0.355546	−	0.615824i	0.987211	+	0.159417i	$0.0509616\pi$
$824$		0			0
$825$	−20.9618			−0.729796
$826$		0			0
$827$	−0.834378	−	0.481728i	−0.0290142	−	0.0167513i	0.485423	−	0.874280i	$-0.338666\pi$
$827$	−0.834378	−	0.481728i	−0.0290142	−	0.0167513i	−0.514437	+	0.857528i	$0.671999\pi$
$828$		0			0
$829$		−	42.2284i		−	1.46665i	−0.679877	−	0.733326i	$-0.737967\pi$
$829$		−	42.2284i		−	1.46665i	0.679877	−	0.733326i	$-0.262033\pi$
$830$		0			0
$831$	2.64373	+	4.57907i	0.0917098	+	0.158846i
$832$		0			0
$833$	−2.09022	−	3.62037i	−0.0724219	−	0.125438i
$834$		0			0
$835$			48.5398i			1.67979i
$836$		0			0
$837$		−	4.29553i		−	0.148475i
$838$		0			0
$839$	9.78057	+	16.9404i	0.337663	+	0.584849i	0.983993	−	0.178209i	$-0.0570304\pi$
$839$	9.78057	+	16.9404i	0.337663	+	0.584849i	−0.646330	+	0.763058i	$0.723697\pi$
$840$		0			0
$841$	−10.4928	−	18.1741i	−0.361822	−	0.626695i
$842$		0			0
$843$			11.0700i			0.381272i
$844$		0			0
$845$	−32.0786	−	18.5206i	−1.10354	−	0.637127i
$846$		0			0
$847$	23.9897			0.824294
$848$		0			0
$849$	−1.32349	+	2.29235i	−0.0454221	+	0.0786733i
$850$		0			0
$851$	1.97431	+	1.13987i	0.0676783	+	0.0390741i
$852$		0			0
$853$	36.8552	−	21.2783i	1.26190	−	0.728557i	0.288456	−	0.957493i	$-0.406858\pi$
$853$	36.8552	−	21.2783i	1.26190	−	0.728557i	0.973441	+	0.228936i	$0.0735248\pi$
$854$		0			0
$855$	20.5903	+	44.9059i	0.704175	+	1.53575i
$856$		0			0
$857$	−2.35963	−	4.08700i	−0.0806034	−	0.139609i	0.822906	−	0.568178i	$-0.192351\pi$
$857$	−2.35963	−	4.08700i	−0.0806034	−	0.139609i	−0.903509	+	0.428569i	$0.859018\pi$
$858$		0			0
$859$	10.8933	+	6.28925i	0.371675	+	0.214586i	0.674190	−	0.738558i	$-0.264493\pi$
$859$	10.8933	+	6.28925i	0.371675	+	0.214586i	−0.302515	+	0.953145i	$0.597826\pi$
$860$		0			0
$861$	−58.3441	−	33.6850i	−1.98836	−	1.14798i
$862$		0			0
$863$	−34.0264			−1.15827			−0.579136	−	0.815231i	$-0.696610\pi$
$863$	−34.0264			−1.15827			−0.579136	+	0.815231i	$0.696610\pi$
$864$		0			0
$865$	−22.2026	+	38.4560i	−0.754911	+	1.30754i
$866$		0			0
$867$		−	117.483i		−	3.98992i
$868$		0			0
$869$	2.55888	−	1.47737i	0.0868040	−	0.0501163i
$870$		0			0
$871$	−7.67442	−	13.2925i	−0.260038	−	0.450399i
$872$		0			0
$873$	−38.3385			−1.29756
$874$		0			0
$875$			14.3053i			0.483608i
$876$		0			0
$877$	−23.7837	+	13.7315i	−0.803118	+	0.463680i	−0.844560	−	0.535461i	$-0.820138\pi$
$877$	−23.7837	+	13.7315i	−0.803118	+	0.463680i	0.0414425	+	0.999141i	$0.486805\pi$
$878$		0			0
$879$	−10.7610	−	18.6387i	−0.362961	−	0.628666i
$880$		0			0
$881$	−5.72336			−0.192825			−0.0964125	−	0.995341i	$-0.530737\pi$
$881$	−5.72336			−0.192825			−0.0964125	+	0.995341i	$0.530737\pi$
$882$		0			0
$883$	3.35118	+	1.93480i	0.112776	+	0.0651113i	0.555327	−	0.831632i	$-0.312593\pi$
$883$	3.35118	+	1.93480i	0.112776	+	0.0651113i	−0.442551	+	0.896743i	$0.645926\pi$
$884$		0			0
$885$		−	64.0961i		−	2.15457i
$886$		0			0
$887$	−3.84382	+	6.65769i	−0.129063	+	0.223543i	−0.923314	−	0.384046i	$-0.874530\pi$
$887$	−3.84382	+	6.65769i	−0.129063	+	0.223543i	0.794251	+	0.607590i	$0.207864\pi$
$888$		0			0
$889$	−1.93392	+	3.34965i	−0.0648617	+	0.112344i
$890$		0			0
$891$	−8.61887	+	4.97611i	−0.288743	+	0.166706i
$892$		0			0
$893$	−3.26745	+	34.7764i	−0.109341	+	1.16375i
$894$		0			0
$895$	0.859440	+	1.48859i	0.0287279	+	0.0497582i
$896$		0			0
$897$	−4.36426	+	7.55912i	−0.145718	+	0.252392i
$898$		0			0
$899$	−13.0540	−	7.53672i	−0.435374	−	0.251364i
$900$		0			0
$901$		−	8.34680i		−	0.278072i
$902$		0			0
$903$	−21.0521	+	36.4634i	−0.700571	+	1.21342i
$904$		0			0
$905$	−63.9422			−2.12551
$906$		0			0
$907$	−10.3905	+	5.99895i	−0.345011	+	0.199192i	−0.662486	−	0.749075i	$-0.730498\pi$
$907$	−10.3905	+	5.99895i	−0.345011	+	0.199192i	0.317475	+	0.948267i	$0.397165\pi$
$908$		0			0
$909$	17.8092	−	10.2822i	0.590695	−	0.341038i
$910$		0			0
$911$	−55.3423			−1.83357			−0.916786	−	0.399379i	$-0.869226\pi$
$911$	−55.3423			−1.83357			−0.916786	+	0.399379i	$0.869226\pi$
$912$		0			0
$913$	−15.3594			−0.508322
$914$		0			0
$915$	−102.154	+	58.9788i	−3.37712	+	1.94978i
$916$		0			0
$917$	−10.3320	+	5.96521i	−0.341194	+	0.196989i
$918$		0			0
$919$	−31.6427			−1.04380			−0.521898	−	0.853008i	$-0.674776\pi$
$919$	−31.6427			−1.04380			−0.521898	+	0.853008i	$0.674776\pi$
$920$		0			0
$921$	−24.6232	+	42.6487i	−0.811363	+	1.40532i
$922$		0			0
$923$		−	61.9807i		−	2.04012i
$924$		0			0
$925$	18.4618	+	10.6589i	0.607019	+	0.350462i
$926$		0			0
$927$	−7.33962	+	12.7126i	−0.241065	+	0.417537i
$928$		0			0
$929$	−17.6814	−	30.6251i	−0.580108	−	1.00478i	−0.995466	−	0.0951179i	$-0.969677\pi$
$929$	−17.6814	−	30.6251i	−0.580108	−	1.00478i	0.415358	−	0.909658i	$-0.363656\pi$
$930$		0			0
$931$	−2.07489	+	0.951382i	−0.0680017	+	0.0311803i
$932$		0			0
$933$	56.1504	−	32.4185i	1.83828	−	1.06133i
$934$		0			0
$935$	17.0865	−	29.5947i	0.558789	−	0.967851i
$936$		0			0
$937$	9.25555	−	16.0311i	0.302366	−	0.523713i	−0.674306	−	0.738452i	$-0.735557\pi$
$937$	9.25555	−	16.0311i	0.302366	−	0.523713i	0.976671	+	0.214740i	$0.0688903\pi$
$938$		0			0
$939$			27.6971i			0.903862i
$940$		0			0
$941$	7.54814	+	4.35792i	0.246062	+	0.142064i	0.617960	−	0.786210i	$-0.287959\pi$
$941$	7.54814	+	4.35792i	0.246062	+	0.142064i	−0.371898	+	0.928274i	$0.621293\pi$
$942$		0			0
$943$	7.48493			0.243743
$944$		0			0
$945$	−3.50333	−	6.06795i	−0.113963	−	0.197390i
$946$		0			0
$947$	6.67019	−	3.85104i	0.216752	−	0.125142i	−0.387693	−	0.921788i	$-0.626728\pi$
$947$	6.67019	−	3.85104i	0.216752	−	0.125142i	0.604445	+	0.796647i	$0.293395\pi$
$948$		0			0
$949$			29.6537i			0.962601i
$950$		0			0
$951$	45.2885			1.46858
$952$		0			0
$953$	23.8018	+	41.2260i	0.771017	+	1.33544i	0.937006	+	0.349313i	$0.113585\pi$
$953$	23.8018	+	41.2260i	0.771017	+	1.33544i	−0.165989	+	0.986128i	$0.553082\pi$
$954$		0			0
$955$	45.3113	−	26.1605i	1.46624	−	0.846533i
$956$		0			0
$957$		−	8.92747i		−	0.288584i
$958$		0			0
$959$	6.75133	−	11.6937i	0.218012	−	0.377608i
$960$		0			0
$961$	−2.64965			−0.0854726
$962$		0			0
$963$	34.0004	+	19.6301i	1.09565	+	0.632573i
$964$		0			0
$965$	49.1802	+	28.3942i	1.58317	+	0.914041i
$966$		0			0
$967$	14.4711	+	25.0646i	0.465359	+	0.806025i	0.999218	−	0.0395489i	$-0.0125921\pi$
$967$	14.4711	+	25.0646i	0.465359	+	0.806025i	−0.533859	+	0.845573i	$0.679259\pi$
$968$		0			0
$969$	−87.1014	−	8.18368i	−2.79810	−	0.262898i
$970$		0			0
$971$	30.8807	−	17.8290i	0.991008	−	0.572159i	0.0854328	−	0.996344i	$-0.472773\pi$
$971$	30.8807	−	17.8290i	0.991008	−	0.572159i	0.905576	+	0.424185i	$0.139439\pi$
$972$		0			0
$973$	33.0929	+	19.1062i	1.06091	+	0.612516i
$974$		0			0
$975$	−40.8103	+	70.6854i	−1.30697	+	2.26375i
$976$		0			0
$977$	−23.0289			−0.736760			−0.368380	−	0.929675i	$-0.620087\pi$
$977$	−23.0289			−0.736760			−0.368380	+	0.929675i	$0.620087\pi$
$978$		0			0
$979$	3.02076	+	1.74404i	0.0965439	+	0.0557397i
$980$		0			0
$981$			56.3047i			1.79767i
$982$		0			0
$983$	2.26068	+	3.91561i	0.0721045	+	0.124889i	0.899823	−	0.436254i	$-0.143695\pi$
$983$	2.26068	+	3.91561i	0.0721045	+	0.124889i	−0.827719	+	0.561143i	$0.810362\pi$
$984$		0			0
$985$	−0.265714	−	0.460230i	−0.00846634	−	0.0146641i
$986$		0			0
$987$		−	51.2708i		−	1.63197i
$988$		0			0
$989$		−	4.67786i		−	0.148747i
$990$		0			0
$991$	−19.8577	−	34.3945i	−0.630800	−	1.09258i	−0.987389	−	0.158316i	$-0.949394\pi$
$991$	−19.8577	−	34.3945i	−0.630800	−	1.09258i	0.356589	−	0.934261i	$-0.383940\pi$
$992$		0			0
$993$	39.4302	+	68.2950i	1.25128	+	2.16728i
$994$		0			0
$995$		−	33.3193i		−	1.05629i
$996$		0			0
$997$	−18.7366	−	10.8176i	−0.593394	−	0.342596i	0.173044	−	0.984914i	$-0.444640\pi$
$997$	−18.7366	−	10.8176i	−0.593394	−	0.342596i	−0.766438	+	0.642318i	$0.777973\pi$
$998$		0			0
$999$	−2.58730			−0.0818586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.t.d.1185.2	yes	24
4.3	odd	2	inner	1216.2.t.d.1185.12	yes	24
8.3	odd	2		1216.2.t.e.1185.2	yes	24
8.5	even	2		1216.2.t.e.1185.12	yes	24
19.11	even	3		1216.2.t.e.353.12	yes	24
76.11	odd	6		1216.2.t.e.353.2	yes	24
152.11	odd	6	inner	1216.2.t.d.353.12	yes	24
152.125	even	6	inner	1216.2.t.d.353.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.t.d.353.2	✓	24	152.125	even	6	inner
1216.2.t.d.353.12	yes	24	152.11	odd	6	inner
1216.2.t.d.1185.2	yes	24	1.1	even	1	trivial
1216.2.t.d.1185.12	yes	24	4.3	odd	2	inner
1216.2.t.e.353.2	yes	24	76.11	odd	6
1216.2.t.e.353.12	yes	24	19.11	even	3
1216.2.t.e.1185.2	yes	24	8.3	odd	2
1216.2.t.e.1185.12	yes	24	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.17731 + 1.25707i) q^{3} +(-2.95556 + 1.70639i) q^{5} +2.54486 q^{7} +(1.66044 - 2.87597i) q^{9} +O(q^{10})\)	\(q+(-2.17731 + 1.25707i) q^{3} +(-2.95556 + 1.70639i) q^{5} +2.54486 q^{7} +(1.66044 - 2.87597i) q^{9} +1.25431i q^{11} +(4.22968 + 2.44201i) q^{13} +(4.29011 - 7.43068i) q^{15} +(3.99152 + 6.91351i) q^{17} +(3.96224 - 1.81677i) q^{19} +(-5.54095 + 3.19907i) q^{21} +(0.355422 - 0.615609i) q^{23} +(3.32356 - 5.75657i) q^{25} +0.806748i q^{27} +(2.45168 + 1.41548i) q^{29} -5.32450 q^{31} +(-1.57676 - 2.73103i) q^{33} +(-7.52150 + 4.34254i) q^{35} +3.20708i q^{37} -12.2791 q^{39} +(5.26481 + 9.11893i) q^{41} +(5.69906 - 3.29035i) q^{43} +11.3335i q^{45} +(-4.00670 + 6.93981i) q^{47} -0.523666 q^{49} +(-17.3815 - 10.0352i) q^{51} +(-0.905488 - 0.522784i) q^{53} +(-2.14035 - 3.70720i) q^{55} +(-6.34320 + 8.93648i) q^{57} +(6.46940 - 3.73511i) q^{59} +(-11.9058 - 6.87382i) q^{61} +(4.22560 - 7.31895i) q^{63} -16.6681 q^{65} +(-2.72163 - 1.57133i) q^{67} +1.78716i q^{69} +(-6.34526 - 10.9903i) q^{71} +(3.03579 + 5.25815i) q^{73} +16.7118i q^{75} +3.19206i q^{77} +(-1.17783 - 2.04006i) q^{79} +(3.96719 + 6.87137i) q^{81} +12.2452i q^{83} +(-23.5943 - 13.6222i) q^{85} -7.11741 q^{87} +(1.39043 - 2.40830i) q^{89} +(10.7640 + 6.21458i) q^{91} +(11.5931 - 6.69327i) q^{93} +(-8.61051 + 12.1307i) q^{95} +(-5.77233 - 9.99797i) q^{97} +(3.60737 + 2.08272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 24 * q - 6 * q^5 + 8 * q^9	\( 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97}+O(q^{100}) \) 24 * q - 6 * q^5 + 8 * q^9 + 30 * q^13 + 6 * q^17 + 24 * q^21 + 6 * q^25 + 42 * q^29 - 14 * q^33 - 24 * q^41 + 24 * q^49 - 18 * q^53 - 42 * q^57 + 18 * q^61 - 20 * q^65 - 16 * q^73 + 52 * q^81 - 78 * q^85 + 14 * q^89 + 60 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more