LMFDB - Embedded newform 1216.2.t.d.353.2

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			353.2
Character	$\chi$	$=$	1216.353
Dual form			1216.2.t.d.1185.2

$q$-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 $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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	−0.284565	−	0.958657i	$-0.591849\pi$
$3$	−2.17731	−	1.25707i	−1.25707	−	0.725769i	−0.972504	+	0.232888i	$0.925182\pi$
$4$		0			0
$5$	−2.95556	−	1.70639i	−1.32177	−	0.763122i	−0.337756	−	0.941234i	$-0.609668\pi$
$5$	−2.95556	−	1.70639i	−1.32177	−	0.763122i	−0.984010	+	0.178111i	$0.943001\pi$
$6$		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	$-0.939445\pi$
$11$		−	1.25431i		−	0.378190i	0.981959	−	0.189095i	$-0.0605554\pi$
$12$		0			0
$13$	4.22968	−	2.44201i	1.17310	−	0.677291i	0.218694	−	0.975793i	$-0.429820\pi$
$13$	4.22968	−	2.44201i	1.17310	−	0.677291i	0.954409	+	0.298502i	$0.0964869\pi$
$14$		0			0
$15$	4.29011	+	7.43068i	1.10770	+	1.91859i
$16$		0			0
$17$	3.99152	−	6.91351i	0.968085	−	1.67677i	0.266997	−	0.963697i	$-0.413968\pi$
$17$	3.99152	−	6.91351i	0.968085	−	1.67677i	0.701088	−	0.713075i	$-0.252698\pi$
$18$		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	0.900699	−	0.434443i	$-0.143055\pi$
$23$	0.355422	+	0.615609i	0.0741106	+	0.128363i	−0.826589	+	0.562807i	$0.809722\pi$
$24$		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	−0.254786	−	0.966997i	$-0.582005\pi$
$29$	2.45168	−	1.41548i	0.455265	−	0.262848i	0.710051	+	0.704150i	$0.248672\pi$
$30$		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	$-0.915083\pi$
$37$		−	3.20708i		−	0.527240i	0.964627	−	0.263620i	$-0.0849165\pi$
$38$		0			0
$39$	−12.2791			−1.96623
$40$		0			0
$41$	5.26481	−	9.11893i	0.822226	−	1.42414i	−0.0817952	−	0.996649i	$-0.526065\pi$
$41$	5.26481	−	9.11893i	0.822226	−	1.42414i	0.904021	−	0.427488i	$-0.140601\pi$
$42$		0			0
$43$	5.69906	+	3.29035i	0.869098	+	0.501774i	0.867049	−	0.498224i	$-0.166014\pi$
$43$	5.69906	+	3.29035i	0.869098	+	0.501774i	0.00204985	+	0.999998i	$0.499348\pi$
$44$		0			0
$45$		−	11.3335i		−	1.68949i
$46$		0			0
$47$	−4.00670	−	6.93981i	−0.584437	−	1.01227i	−0.994945	−	0.100418i	$-0.967982\pi$
$47$	−4.00670	−	6.93981i	−0.584437	−	1.01227i	0.410508	−	0.911857i	$-0.365351\pi$
$48$		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	−0.560898	−	0.827885i	$-0.689544\pi$
$53$	−0.905488	+	0.522784i	−0.124378	+	0.0718099i	0.436520	+	0.899695i	$0.356211\pi$
$54$		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	0.858026	−	0.513606i	$-0.171691\pi$
$59$	6.46940	+	3.73511i	0.842244	+	0.486270i	−0.0157823	+	0.999875i	$0.505024\pi$
$60$		0			0
$61$	−11.9058	+	6.87382i	−1.52438	+	0.880102i	−0.524799	+	0.851226i	$0.675860\pi$
$61$	−11.9058	+	6.87382i	−1.52438	+	0.880102i	−0.999583	+	0.0288763i	$0.990807\pi$
$62$		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	−0.656951	−	0.753934i	$-0.728154\pi$
$67$	−2.72163	+	1.57133i	−0.332500	+	0.191969i	0.324450	+	0.945903i	$0.394821\pi$
$68$		0			0
$69$		−	1.78716i		−	0.215149i
$70$		0			0
$71$	−6.34526	+	10.9903i	−0.753043	+	1.30431i	0.193298	+	0.981140i	$0.438082\pi$
$71$	−6.34526	+	10.9903i	−0.753043	+	1.30431i	−0.946341	+	0.323169i	$0.895252\pi$
$72$		0			0
$73$	3.03579	−	5.25815i	0.355313	−	0.615419i	−0.631859	−	0.775083i	$-0.717708\pi$
$73$	3.03579	−	5.25815i	0.355313	−	0.615419i	0.987171	+	0.159664i	$0.0510411\pi$
$74$		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	−0.924646	−	0.380828i	$-0.875639\pi$
$79$	−1.17783	+	2.04006i	−0.132516	+	0.229525i	0.792130	+	0.610353i	$0.208972\pi$
$80$		0			0
$81$	3.96719	−	6.87137i	0.440799	−	0.763486i
$82$		0			0
$83$		−	12.2452i		−	1.34409i	−0.740510	−	0.672045i	$-0.765416\pi$
$83$		−	12.2452i		−	1.34409i	0.740510	−	0.672045i	$-0.234584\pi$
$84$		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	0.930260	−	0.366900i	$-0.119581\pi$
$89$	1.39043	+	2.40830i	0.147385	+	0.255279i	−0.782875	+	0.622179i	$0.786248\pi$
$90$		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	0.408647	+	0.912693i	$0.366001\pi$
$97$	−5.77233	+	9.99797i	−0.586092	+	1.01514i	−0.994738	+	0.102448i	$0.967333\pi$
$98$		0			0
$99$	3.60737	−	2.08272i	0.362555	−	0.209321i
$100$		0			0
$101$	5.36280	−	3.09621i	0.533618	−	0.308085i	−0.208870	−	0.977943i	$-0.566979\pi$
$101$	5.36280	−	3.09621i	0.533618	−	0.308085i	0.742489	+	0.669859i	$0.233645\pi$
$102$		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	$-0.806381\pi$
$107$		−	11.8222i		−	1.14290i	0.820637	−	0.571450i	$-0.193619\pi$
$108$		0			0
$109$	−14.6832	−	8.47736i	−1.40640	−	0.811984i	−0.411358	−	0.911474i	$-0.634946\pi$
$109$	−14.6832	−	8.47736i	−1.40640	−	0.811984i	−0.995039	+	0.0994901i	$0.968279\pi$
$110$		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	0.830338	−	0.557261i	$-0.188148\pi$
$127$	−0.759932	−	1.31624i	−0.0674330	−	0.116797i	−0.897771	+	0.440463i	$0.854814\pi$
$128$		0			0
$129$	−8.27240	−	14.3282i	−0.728344	−	1.26153i
$130$		0			0
$131$	−4.05996	−	2.34402i	−0.354720	−	0.204798i	0.312042	−	0.950068i	$-0.398987\pi$
$131$	−4.05996	−	2.34402i	−0.354720	−	0.204798i	−0.666762	+	0.745270i	$0.732320\pi$
$132$		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	0.956815	−	0.290699i	$-0.0938878\pi$
$137$	2.65292	+	4.59500i	0.226655	+	0.392577i	−0.730160	+	0.683276i	$0.760554\pi$
$138$		0			0
$139$	13.0038	−	7.50775i	1.10297	−	0.636799i	0.165969	−	0.986131i	$-0.446925\pi$
$139$	13.0038	−	7.50775i	1.10297	−	0.636799i	0.936999	+	0.349332i	$0.113592\pi$
$140$		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	−0.402075	−	0.915607i	$-0.631711\pi$
$149$	−17.0410	−	9.83861i	−1.39605	−	0.806011i	−0.993976	+	0.109596i	$0.965044\pi$
$150$		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	0.698365	−	0.715742i	$-0.253911\pi$
$157$	5.35902	+	3.09403i	0.427696	+	0.246931i	−0.270668	+	0.962673i	$0.587245\pi$
$158$		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	$0.0951586\pi$
$163$			7.52027i			0.589033i	−0.955646	+	0.294516i	$0.904841\pi$
$164$		0			0
$165$	9.32042	−	5.38114i	0.725593	−	0.418922i
$166$		0			0
$167$	7.11147	+	12.3174i	0.550302	+	0.953151i	0.998253	+	0.0590926i	$0.0188207\pi$
$167$	7.11147	+	12.3174i	0.550302	+	0.953151i	−0.447951	+	0.894058i	$0.647846\pi$
$168$		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	0.862908	−	0.505361i	$-0.168641\pi$
$173$	11.2682	+	6.50571i	0.856706	+	0.494620i	−0.00620155	+	0.999981i	$0.501974\pi$
$174$		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	$0.00599178\pi$
$179$			0.503659i			0.0376452i	−0.999823	+	0.0188226i	$0.994008\pi$
$180$		0			0
$181$	16.2259	−	9.36803i	1.20606	−	0.696320i	0.244165	−	0.969734i	$-0.421486\pi$
$181$	16.2259	−	9.36803i	1.20606	−	0.696320i	0.961897	+	0.273413i	$0.0881527\pi$
$182$		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	0.394104	+	0.919066i	$0.371055\pi$
$193$	−8.31994	+	14.4106i	−0.598882	+	1.03729i	−0.992986	+	0.118229i	$0.962278\pi$
$194$		0			0
$195$	36.2916	+	20.9530i	2.59889	+	1.50047i
$196$		0			0
$197$		−	0.155717i		−	0.0110943i	−0.999985	−	0.00554717i	$-0.998234\pi$
$197$		−	0.155717i		−	0.0110943i	0.999985	−	0.00554717i	$-0.00176573\pi$
$198$		0			0
$199$	−4.88153	−	8.45506i	−0.346043	−	0.599363i	0.639500	−	0.768791i	$-0.279141\pi$
$199$	−4.88153	−	8.45506i	−0.346043	−	0.599363i	−0.985543	+	0.169428i	$0.945808\pi$
$200$		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	−0.378162	−	0.925739i	$-0.623444\pi$
$211$	−19.8853	−	11.4808i	−1.36896	−	0.790368i	−0.990795	+	0.135372i	$0.956777\pi$
$212$		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	−0.622713	−	0.782450i	$-0.713970\pi$
$223$	5.46950	−	9.47346i	0.366265	−	0.634390i	0.988978	+	0.148061i	$0.0473030\pi$
$224$		0			0
$225$	−11.0371	+	19.1169i	−0.735810	+	1.27446i
$226$		0			0
$227$			16.6384i			1.10433i	0.833736	+	0.552164i	$0.186198\pi$
$227$			16.6384i			1.10433i	−0.833736	+	0.552164i	$0.813802\pi$
$228$		0			0
$229$			7.56617i			0.499986i	0.968248	+	0.249993i	$0.0804284\pi$
$229$			7.56617i			0.499986i	−0.968248	+	0.249993i	$0.919572\pi$
$230$		0			0
$231$	−4.01264	+	6.95010i	−0.264012	+	0.457283i
$232$		0			0
$233$	2.50589	−	4.34033i	0.164166	−	0.284345i	−0.772193	−	0.635389i	$-0.780840\pi$
$233$	2.50589	−	4.34033i	0.164166	−	0.284345i	0.936359	+	0.351044i	$0.114173\pi$
$234$		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	0.831828	−	0.555033i	$-0.187294\pi$
$241$	−1.00532	−	1.74127i	−0.0647585	−	0.112165i	−0.896587	+	0.442868i	$0.853961\pi$
$242$		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	−0.994842	−	0.101439i	$-0.967655\pi$
$251$	−22.2501	+	12.8461i	−1.40441	+	0.810839i	−0.409572	+	0.912278i	$0.634322\pi$
$252$		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	0.997955	−	0.0639129i	$-0.0203580\pi$
$257$	7.11189	+	12.3182i	0.443628	+	0.768385i	−0.554328	+	0.832298i	$0.687025\pi$
$258$		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	−0.998182	−	0.0602727i	$-0.980803\pi$
$263$	−7.24739	+	12.5529i	−0.446893	+	0.774042i	0.551289	+	0.834315i	$0.314136\pi$
$264$		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	0.800409	−	0.599454i	$-0.204616\pi$
$269$	11.1770	+	6.45302i	0.681471	+	0.393448i	−0.118938	+	0.992902i	$0.537949\pi$
$270$		0			0
$271$	9.89868	−	17.1450i	0.601302	−	1.04149i	−0.391322	−	0.920254i	$-0.627982\pi$
$271$	9.89868	−	17.1450i	0.601302	−	1.04149i	0.992624	−	0.121232i	$-0.0386845\pi$
$272$		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	$0.0201246\pi$
$277$			2.10309i			0.126362i	−0.998002	+	0.0631812i	$0.979875\pi$
$278$		0			0
$279$	−8.84103	−	15.3131i	−0.529299	−	0.916772i
$280$		0			0
$281$	2.20156	+	3.81321i	0.131334	+	0.227477i	0.924191	−	0.381931i	$-0.124741\pi$
$281$	2.20156	+	3.81321i	0.131334	+	0.227477i	−0.792857	+	0.609408i	$0.791407\pi$
$282$		0			0
$283$	0.911785	+	0.526419i	0.0542000	+	0.0312924i	0.526855	−	0.849955i	$-0.323371\pi$
$283$	0.911785	+	0.526419i	0.0542000	+	0.0312924i	−0.472655	+	0.881247i	$0.656704\pi$
$284$		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	$-0.919552\pi$
$293$		−	8.56042i		−	0.500105i	0.968232	−	0.250052i	$-0.0804479\pi$
$294$		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	0.898675	−	0.438615i	$-0.144531\pi$
$307$	16.9636	+	9.79391i	0.968161	+	0.558968i	0.0694860	+	0.997583i	$0.477864\pi$
$308$		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	0.978654	−	0.205514i	$-0.0658868\pi$
$313$	5.50828	+	9.54062i	0.311346	+	0.539268i	−0.667308	+	0.744782i	$0.732553\pi$
$314$		0			0
$315$		−	28.8421i		−	1.62507i
$316$		0			0
$317$	−15.6002	+	9.00676i	−0.876193	+	0.505870i	−0.869401	−	0.494107i	$-0.835495\pi$
$317$	−15.6002	+	9.00676i	−0.876193	+	0.505870i	−0.00679167	+	0.999977i	$0.502162\pi$
$318$		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	$0.330811\pi$
$331$			31.3668i			1.72407i	−0.506846	+	0.862037i	$0.669189\pi$
$332$		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	−0.497536	−	0.867443i	$-0.665762\pi$
$337$	9.22394	−	15.9763i	0.502460	−	0.870286i	0.999996	−	0.00284285i	$-0.000904908\pi$
$338$		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	0.366347	−	0.930478i	$-0.380608\pi$
$347$	−4.77429	−	2.75644i	−0.256297	−	0.147973i	−0.622644	+	0.782505i	$0.713942\pi$
$348$		0			0
$349$		−	30.1208i		−	1.61233i	−0.591690	−	0.806166i	$-0.701539\pi$
$349$		−	30.1208i		−	1.61233i	0.591690	−	0.806166i	$-0.298461\pi$
$350$		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	−0.517184	−	0.855874i	$-0.673020\pi$
$359$	9.14429	−	15.8384i	0.482617	−	0.835917i	0.999801	+	0.0199571i	$0.00635297\pi$
$360$		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	0.837822	−	0.545943i	$-0.183829\pi$
$367$	−1.03238	−	1.78813i	−0.0538896	−	0.0933395i	−0.891712	+	0.452604i	$0.850495\pi$
$368$		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	$0.197996\pi$
$373$			22.5069i			1.16536i	−0.812701	+	0.582680i	$0.802004\pi$
$374$		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	$-0.750956\pi$
$379$		−	27.4490i		−	1.40996i	0.709228	−	0.704980i	$-0.249044\pi$
$380$		0			0
$381$			3.82115i			0.195763i
$382$		0			0
$383$	−10.0380	+	17.3863i	−0.512918	+	0.888399i	0.486970	+	0.873419i	$0.338102\pi$
$383$	−10.0380	+	17.3863i	−0.512918	+	0.888399i	−0.999888	+	0.0149807i	$0.995231\pi$
$384$		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	−0.824161	−	0.566356i	$-0.808353\pi$
$389$	−14.7087	+	8.49210i	−0.745763	+	0.430567i	0.0783979	+	0.996922i	$0.475020\pi$
$390$		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	0.448636	−	0.893715i	$-0.351910\pi$
$397$	−2.01293	−	1.16217i	−0.101026	−	0.0583274i	−0.549662	+	0.835387i	$0.685243\pi$
$398$		0			0
$399$	−16.1426	−	22.7421i	−0.808140	−	1.13853i
$400$		0			0
$401$	−6.79543	+	11.7700i	−0.339348	+	0.587767i	−0.984310	−	0.176447i	$-0.943540\pi$
$401$	−6.79543	+	11.7700i	−0.339348	+	0.587767i	0.644963	+	0.764214i	$0.276873\pi$
$402$		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	0.909818	−	0.415007i	$-0.136221\pi$
$409$	1.93142	+	3.34532i	0.0955025	+	0.165415i	−0.814316	+	0.580422i	$0.802888\pi$
$410$		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	$-0.888573\pi$
$419$		−	14.0401i		−	0.685904i	0.939353	−	0.342952i	$-0.111427\pi$
$420$		0			0
$421$	26.7712	+	15.4564i	1.30475	+	0.753298i	0.981215	−	0.192919i	$-0.0617953\pi$
$421$	26.7712	+	15.4564i	1.30475	+	0.753298i	0.323535	+	0.946216i	$0.395129\pi$
$422$		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	0.794289	−	0.607540i	$-0.207844\pi$
$431$	−2.67813	−	4.63865i	−0.129001	−	0.223436i	−0.923290	+	0.384104i	$0.874510\pi$
$432$		0			0
$433$	−12.1157	−	20.9850i	−0.582242	−	1.00847i	−0.995213	−	0.0977288i	$-0.968842\pi$
$433$	−12.1157	−	20.9850i	−0.582242	−	1.00847i	0.412971	−	0.910744i	$-0.364491\pi$
$434$		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	−0.688978	−	0.724782i	$-0.741941\pi$
$439$	5.93350	−	10.2771i	0.283190	−	0.490500i	0.972169	+	0.234282i	$0.0752738\pi$
$440$		0			0
$441$	−0.869517	−	1.50605i	−0.0414056	−	0.0717165i
$442$		0			0
$443$	6.68234	−	3.85805i	0.317488	−	0.183302i	−0.332784	−	0.943003i	$-0.607988\pi$
$443$	6.68234	−	3.85805i	0.317488	−	0.183302i	0.650272	+	0.759701i	$0.274655\pi$
$444$		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	0.916672	−	0.399640i	$-0.130865\pi$
$461$	22.0916	+	12.7546i	1.02891	+	0.594042i	0.112238	+	0.993681i	$0.464198\pi$
$462$		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	$-0.749174\pi$
$467$		−	30.6406i		−	1.41788i	0.705270	−	0.708939i	$-0.250826\pi$
$468$		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	−0.850971	−	0.525212i	$-0.823986\pi$
$479$	−19.2670	−	33.3715i	−0.880333	−	1.52478i	−0.0293614	−	0.999569i	$-0.509347\pi$
$480$		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	0.539861	−	0.841754i	$-0.318477\pi$
$491$	1.79067	+	1.03384i	0.0808117	+	0.0466567i	−0.459050	+	0.888411i	$0.651810\pi$
$492$		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	−0.0992183	−	0.995066i	$-0.531634\pi$
$499$	−22.5746	−	13.0335i	−1.01058	−	0.583458i	−0.911361	+	0.411607i	$0.864968\pi$
$500$		0			0
$501$		−	35.7584i		−	1.59757i
$502$		0			0
$503$	18.4953	+	32.0348i	0.824664	+	1.42836i	0.902176	+	0.431368i	$0.141969\pi$
$503$	18.4953	+	32.0348i	0.824664	+	1.42836i	−0.0775123	+	0.996991i	$0.524698\pi$
$504$		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	−0.420590	−	0.907251i	$-0.638177\pi$
$509$	3.49285	−	2.01660i	0.154818	−	0.0893840i	0.575407	+	0.817867i	$0.304843\pi$
$510$		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	−0.357079	−	0.934074i	$-0.616227\pi$
$523$	6.25047	−	3.60871i	0.273314	−	0.157798i	0.630393	+	0.776276i	$0.282894\pi$
$524$		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	−0.415481	−	0.909602i	$-0.636387\pi$
$541$	3.82654	−	2.20926i	0.164516	−	0.0949833i	0.579997	+	0.814618i	$0.303054\pi$
$542$		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	−0.601223	−	0.799081i	$-0.705320\pi$
$547$	−4.90706	+	2.83309i	−0.209811	+	0.121134i	0.391413	+	0.920215i	$0.371987\pi$
$548$		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	0.0461920	−	0.998933i	$-0.485291\pi$
$557$	22.0524	−	12.7319i	0.934389	−	0.539470i	0.888197	+	0.459463i	$0.151958\pi$
$558$		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	$0.213817\pi$
$563$			29.5332i			1.24468i	−0.782748	+	0.622339i	$0.786183\pi$
$564$		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	$0.0191326\pi$
$571$			2.87084i			0.120141i	−0.998194	+	0.0600705i	$0.980867\pi$
$572$		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	0.0546095	−	0.998508i	$-0.482609\pi$
$587$	−18.9662	−	10.9501i	−0.782819	−	0.451961i	−0.837428	+	0.546547i	$0.815942\pi$
$588$		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	0.995158	−	0.0982863i	$-0.0313361\pi$
$593$	10.0441	+	17.3968i	0.412461	+	0.714403i	−0.582697	+	0.812689i	$0.698003\pi$
$594$		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	0.824884	−	0.565302i	$-0.191241\pi$
$599$	−1.88758	−	3.26938i	−0.0771244	−	0.133583i	−0.902008	+	0.431719i	$0.857907\pi$
$600$		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	0.0401778	−	0.999193i	$-0.487208\pi$
$613$	−19.9323	−	11.5079i	−0.805059	−	0.464801i	−0.845237	+	0.534391i	$0.820541\pi$
$614$		0			0
$615$	90.3465			3.64312
$616$		0			0
$617$	5.63489	+	9.75992i	0.226852	+	0.392920i	0.956874	−	0.290505i	$-0.0938232\pi$
$617$	5.63489	+	9.75992i	0.226852	+	0.392920i	−0.730021	+	0.683424i	$0.760490\pi$
$618$		0			0
$619$		−	4.18227i		−	0.168100i	−0.996462	−	0.0840498i	$-0.973215\pi$
$619$		−	4.18227i		−	0.168100i	0.996462	−	0.0840498i	$-0.0267855\pi$
$620$		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	0.929756	+	0.368176i	$0.120018\pi$
$631$	19.6870	+	34.0989i	0.783728	+	1.35746i	−0.146029	+	0.989280i	$0.546649\pi$
$632$		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	−0.901043	−	0.433730i	$-0.857197\pi$
$641$	−1.89633	+	3.28455i	−0.0749007	+	0.129732i	0.826142	+	0.563461i	$0.190531\pi$
$642$		0			0
$643$	−12.4215	−	7.17154i	−0.489855	−	0.282818i	0.234659	−	0.972078i	$-0.424603\pi$
$643$	−12.4215	−	7.17154i	−0.489855	−	0.282818i	−0.724514	+	0.689260i	$0.757936\pi$
$644$		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	$-0.698809\pi$
$653$		−	41.4592i		−	1.62242i	0.584753	−	0.811211i	$-0.301191\pi$
$654$		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	−0.461646	−	0.887064i	$-0.652741\pi$
$659$	1.94461	−	1.12272i	0.0757514	−	0.0437351i	0.537397	+	0.843329i	$0.319408\pi$
$660$		0			0
$661$	−12.6664	+	7.31294i	−0.492665	+	0.284440i	−0.725679	−	0.688033i	$-0.758474\pi$
$661$	−12.6664	+	7.31294i	−0.492665	+	0.284440i	0.233014	+	0.972473i	$0.425141\pi$
$662$		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	$-0.938359\pi$
$677$		−	10.0144i		−	0.384885i	0.981308	−	0.192443i	$-0.0616409\pi$
$678$		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	$-0.976970\pi$
$683$		−	3.77839i		−	0.144576i	0.997384	−	0.0722881i	$-0.0230301\pi$
$684$		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	$-0.822850\pi$
$691$		−	27.7719i		−	1.05649i	0.849091	−	0.528246i	$-0.177150\pi$
$692$		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	0.894514	−	0.447040i	$-0.147522\pi$
$701$	25.2750	+	14.5925i	0.954622	+	0.551151i	0.0601085	+	0.998192i	$0.480855\pi$
$702$		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	−0.435685	−	0.900099i	$-0.643494\pi$
$709$	3.35449	−	1.93671i	0.125980	−	0.0727348i	0.561666	+	0.827364i	$0.310161\pi$
$710$		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	−0.640601	−	0.767874i	$-0.721315\pi$
$719$	9.24280	−	16.0090i	0.344698	−	0.597035i	0.985299	+	0.170839i	$0.0546479\pi$
$720$		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	0.127258	−	0.991870i	$-0.459382\pi$
$727$	24.8764	−	43.0871i	0.922613	−	1.59801i	0.795355	−	0.606144i	$-0.207284\pi$
$728$		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	$0.0914879\pi$
$733$			15.3497i			0.566954i	−0.958979	+	0.283477i	$0.908512\pi$
$734$		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	0.705262	−	0.708947i	$-0.250829\pi$
$739$	12.0680	+	6.96744i	0.443927	+	0.256302i	−0.261335	+	0.965248i	$0.584163\pi$
$740$		0			0
$741$	−48.6527	−	22.3083i	−1.78730	−	0.819516i
$742$		0			0
$743$	−24.7117	+	42.8020i	−0.906585	+	1.57025i	−0.0878096	+	0.996137i	$0.527987\pi$
$743$	−24.7117	+	42.8020i	−0.906585	+	1.57025i	−0.818775	+	0.574114i	$0.805347\pi$
$744$		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	0.998546	+	0.0538987i	$0.0171648\pi$
$751$	14.9614	+	25.9140i	0.545951	+	0.945615i	−0.452596	+	0.891716i	$0.649502\pi$
$752$		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	0.999933	+	0.0115535i	$0.00367768\pi$
$757$	41.5430	+	23.9849i	1.50991	+	0.871744i	0.509972	+	0.860191i	$0.329656\pi$
$758$		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	0.998850	+	0.0479400i	$0.0152656\pi$
$769$	15.0008	+	25.9821i	0.540942	+	0.936940i	−0.457908	+	0.889000i	$0.651401\pi$
$770$		0			0
$771$		−	35.7605i		−	1.28788i
$772$		0			0
$773$	16.0137	−	9.24549i	0.575971	−	0.332537i	−0.183559	−	0.983009i	$-0.558762\pi$
$773$	16.0137	−	9.24549i	0.575971	−	0.332537i	0.759531	+	0.650471i	$0.225429\pi$
$774$		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	$0.240342\pi$
$787$			38.4519i			1.37066i	−0.728232	+	0.685331i	$0.759658\pi$
$788$		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	$0.102993\pi$
$797$			17.9520i			0.635894i	−0.948108	+	0.317947i	$0.897007\pi$
$798$		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	−0.461802	−	0.886983i	$-0.652797\pi$
$811$	2.14857	−	1.24048i	0.0754466	−	0.0435591i	0.537249	+	0.843424i	$0.319464\pi$
$812$		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	−0.560315	−	0.828280i	$-0.689320\pi$
$821$	−3.52896	+	2.03744i	−0.123161	+	0.0711073i	0.437154	+	0.899387i	$0.355987\pi$
$822$		0			0
$823$	10.1999	+	17.6667i	0.355546	+	0.615824i	0.987211	−	0.159417i	$-0.0509616\pi$
$823$	10.1999	+	17.6667i	0.355546	+	0.615824i	−0.631665	+	0.775241i	$0.717628\pi$
$824$		0			0
$825$	−20.9618			−0.729796
$826$		0			0
$827$	−0.834378	+	0.481728i	−0.0290142	+	0.0167513i	−0.514437	−	0.857528i	$-0.671999\pi$
$827$	−0.834378	+	0.481728i	−0.0290142	+	0.0167513i	0.485423	+	0.874280i	$0.338666\pi$
$828$		0			0
$829$			42.2284i			1.46665i	0.679877	+	0.733326i	$0.262033\pi$
$829$			42.2284i			1.46665i	−0.679877	+	0.733326i	$0.737967\pi$
$830$		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	−0.646330	−	0.763058i	$-0.723697\pi$
$839$	9.78057	−	16.9404i	0.337663	−	0.584849i	0.983993	+	0.178209i	$0.0570304\pi$
$840$		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	0.973441	−	0.228936i	$-0.0735248\pi$
$853$	36.8552	+	21.2783i	1.26190	+	0.728557i	0.288456	+	0.957493i	$0.406858\pi$
$854$		0			0
$855$	20.5903	−	44.9059i	0.704175	−	1.53575i
$856$		0			0
$857$	−2.35963	+	4.08700i	−0.0806034	+	0.139609i	−0.903509	−	0.428569i	$-0.859018\pi$
$857$	−2.35963	+	4.08700i	−0.0806034	+	0.139609i	0.822906	+	0.568178i	$0.192351\pi$
$858$		0			0
$859$	10.8933	−	6.28925i	0.371675	−	0.214586i	−0.302515	−	0.953145i	$-0.597826\pi$
$859$	10.8933	−	6.28925i	0.371675	−	0.214586i	0.674190	+	0.738558i	$0.264493\pi$
$860$		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	0.0414425	−	0.999141i	$-0.486805\pi$
$877$	−23.7837	−	13.7315i	−0.803118	−	0.463680i	−0.844560	+	0.535461i	$0.820138\pi$
$878$		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	−0.442551	−	0.896743i	$-0.645926\pi$
$883$	3.35118	−	1.93480i	0.112776	−	0.0651113i	0.555327	+	0.831632i	$0.312593\pi$
$884$		0			0
$885$			64.0961i			2.15457i
$886$		0			0
$887$	−3.84382	−	6.65769i	−0.129063	−	0.223543i	0.794251	−	0.607590i	$-0.207864\pi$
$887$	−3.84382	−	6.65769i	−0.129063	−	0.223543i	−0.923314	+	0.384046i	$0.874530\pi$
$888$		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	0.317475	−	0.948267i	$-0.397165\pi$
$907$	−10.3905	−	5.99895i	−0.345011	−	0.199192i	−0.662486	+	0.749075i	$0.730498\pi$
$908$		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	0.415358	+	0.909658i	$0.363656\pi$
$929$	−17.6814	+	30.6251i	−0.580108	+	1.00478i	−0.995466	+	0.0951179i	$0.969677\pi$
$930$		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	0.976671	−	0.214740i	$-0.0688903\pi$
$937$	9.25555	+	16.0311i	0.302366	+	0.523713i	−0.674306	+	0.738452i	$0.735557\pi$
$938$		0			0
$939$		−	27.6971i		−	0.903862i
$940$		0			0
$941$	7.54814	−	4.35792i	0.246062	−	0.142064i	−0.371898	−	0.928274i	$-0.621293\pi$
$941$	7.54814	−	4.35792i	0.246062	−	0.142064i	0.617960	+	0.786210i	$0.287959\pi$
$942$		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	0.604445	−	0.796647i	$-0.293395\pi$
$947$	6.67019	+	3.85104i	0.216752	+	0.125142i	−0.387693	+	0.921788i	$0.626728\pi$
$948$		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	−0.165989	−	0.986128i	$-0.553082\pi$
$953$	23.8018	−	41.2260i	0.771017	−	1.33544i	0.937006	−	0.349313i	$-0.113585\pi$
$954$		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	−0.533859	−	0.845573i	$-0.679259\pi$
$967$	14.4711	−	25.0646i	0.465359	−	0.806025i	0.999218	+	0.0395489i	$0.0125921\pi$
$968$		0			0
$969$	−87.1014	+	8.18368i	−2.79810	+	0.262898i
$970$		0			0
$971$	30.8807	+	17.8290i	0.991008	+	0.572159i	0.905576	−	0.424185i	$-0.139439\pi$
$971$	30.8807	+	17.8290i	0.991008	+	0.572159i	0.0854328	+	0.996344i	$0.472773\pi$
$972$		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	−0.827719	−	0.561143i	$-0.810362\pi$
$983$	2.26068	−	3.91561i	0.0721045	−	0.124889i	0.899823	+	0.436254i	$0.143695\pi$
$984$		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	0.356589	+	0.934261i	$0.383940\pi$
$991$	−19.8577	+	34.3945i	−0.630800	+	1.09258i	−0.987389	+	0.158316i	$0.949394\pi$
$992$		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	−0.766438	−	0.642318i	$-0.777973\pi$
$997$	−18.7366	+	10.8176i	−0.593394	+	0.342596i	0.173044	+	0.984914i	$0.444640\pi$
$998$		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.353.2	✓	24
4.3	odd	2	inner	1216.2.t.d.353.12	yes	24
8.3	odd	2		1216.2.t.e.353.2	yes	24
8.5	even	2		1216.2.t.e.353.12	yes	24
19.7	even	3		1216.2.t.e.1185.12	yes	24
76.7	odd	6		1216.2.t.e.1185.2	yes	24
152.45	even	6	inner	1216.2.t.d.1185.2	yes	24
152.83	odd	6	inner	1216.2.t.d.1185.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.t.d.353.2	✓	24	1.1	even	1	trivial
1216.2.t.d.353.12	yes	24	4.3	odd	2	inner
1216.2.t.d.1185.2	yes	24	152.45	even	6	inner
1216.2.t.d.1185.12	yes	24	152.83	odd	6	inner
1216.2.t.e.353.2	yes	24	8.3	odd	2
1216.2.t.e.353.12	yes	24	8.5	even	2
1216.2.t.e.1185.2	yes	24	76.7	odd	6
1216.2.t.e.1185.12	yes	24	19.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
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

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