LMFDB - Embedded newform 1216.2.t.d.353.1

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			353.1
Character	$\chi$	$=$	1216.353
Dual form			1216.2.t.d.1185.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.17731 - 1.25707i) q^{3} +(0.891744 + 0.514849i) q^{5} -4.18166 q^{7} +(1.66044 + 2.87597i) q^{9} +O(q^{10})$	\(q+(-2.17731 - 1.25707i) q^{3} +(0.891744 + 0.514849i) q^{5} -4.18166 q^{7} +(1.66044 + 2.87597i) q^{9} +2.06106i q^{11} +(2.25164 - 1.29999i) q^{13} +(-1.29440 - 2.24197i) q^{15} +(-3.49152 + 6.04748i) q^{17} +(1.09104 - 4.22015i) q^{19} +(9.10477 + 5.25664i) q^{21} +(2.14740 + 3.71941i) q^{23} +(-1.96986 - 3.41190i) q^{25} -0.806748i q^{27} +(5.17322 - 2.98676i) q^{29} +2.70194 q^{31} +(2.59090 - 4.48756i) q^{33} +(-3.72897 - 2.15292i) q^{35} -9.93361i q^{37} -6.53669 q^{39} +(-2.42979 + 4.20853i) q^{41} +(8.57026 + 4.94804i) q^{43} +3.41951i q^{45} +(-2.86468 - 4.96176i) q^{47} +10.4863 q^{49} +(15.2042 - 8.77815i) q^{51} +(-4.00929 + 2.31477i) q^{53} +(-1.06114 + 1.83794i) q^{55} +(-7.68054 + 7.81704i) q^{57} +(-0.382736 - 0.220973i) q^{59} +(3.59219 - 2.07395i) q^{61} +(-6.94341 - 12.0263i) q^{63} +2.67719 q^{65} +(1.07089 - 0.618281i) q^{67} -10.7977i q^{69} +(7.69496 - 13.3281i) q^{71} +(0.846177 - 1.46562i) q^{73} +9.90500i q^{75} -8.61867i q^{77} +(6.13586 - 10.6276i) q^{79} +(3.96719 - 6.87137i) q^{81} -8.92986i q^{83} +(-6.22708 + 3.59521i) q^{85} -15.0182 q^{87} +(5.55809 + 9.62689i) q^{89} +(-9.41562 + 5.43611i) q^{91} +(-5.88296 - 3.39653i) q^{93} +(3.14566 - 3.20157i) q^{95} +(4.11189 - 7.12200i) q^{97} +(-5.92755 + 3.42228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.891744	+	0.514849i	0.398800	+	0.230247i	0.685966	−	0.727634i	$-0.259380\pi$
$5$	0.891744	+	0.514849i	0.398800	+	0.230247i	−0.287166	+	0.957881i	$0.592713\pi$
$6$		0			0
$7$	−4.18166			−1.58052			−0.790260	−	0.612771i	$-0.790055\pi$
$7$	−4.18166			−1.58052			−0.790260	+	0.612771i	$0.790055\pi$
$8$		0			0
$9$	1.66044	+	2.87597i	0.553481	+	0.958657i
$10$		0			0
$11$			2.06106i			0.621434i	0.950503	+	0.310717i	$0.100569\pi$
$11$			2.06106i			0.621434i	−0.950503	+	0.310717i	$0.899431\pi$
$12$		0			0
$13$	2.25164	−	1.29999i	0.624493	−	0.360551i	−0.154123	−	0.988052i	$-0.549255\pi$
$13$	2.25164	−	1.29999i	0.624493	−	0.360551i	0.778616	+	0.627500i	$0.215922\pi$
$14$		0			0
$15$	−1.29440	−	2.24197i	−0.334213	−	0.578873i
$16$		0			0
$17$	−3.49152	+	6.04748i	−0.846817	+	1.46673i	0.0372165	+	0.999307i	$0.488151\pi$
$17$	−3.49152	+	6.04748i	−0.846817	+	1.46673i	−0.884034	+	0.467423i	$0.845182\pi$
$18$		0			0
$19$	1.09104	−	4.22015i	0.250301	−	0.968168i
$19$	1.09104	−	4.22015i	0.250301	−	0.968168i
$20$		0			0
$21$	9.10477	+	5.25664i	1.98682	+	1.14709i
$22$		0			0
$23$	2.14740	+	3.71941i	0.447765	+	0.775551i	0.998240	−	0.0593002i	$-0.0188869\pi$
$23$	2.14740	+	3.71941i	0.447765	+	0.775551i	−0.550476	+	0.834851i	$0.685554\pi$
$24$		0			0
$25$	−1.96986	−	3.41190i	−0.393972	−	0.682380i
$26$		0			0
$27$		−	0.806748i		−	0.155259i
$28$		0			0
$29$	5.17322	−	2.98676i	0.960643	−	0.554628i	0.0642721	−	0.997932i	$-0.479527\pi$
$29$	5.17322	−	2.98676i	0.960643	−	0.554628i	0.896371	+	0.443305i	$0.146194\pi$
$30$		0			0
$31$	2.70194			0.485283			0.242642	−	0.970116i	$-0.421986\pi$
$31$	2.70194			0.485283			0.242642	+	0.970116i	$0.421986\pi$
$32$		0			0
$33$	2.59090	−	4.48756i	0.451017	−	0.781185i
$34$		0			0
$35$	−3.72897	−	2.15292i	−0.630312	−	0.363911i
$36$		0			0
$37$		−	9.93361i		−	1.63307i	−0.577293	−	0.816537i	$-0.695891\pi$
$37$		−	9.93361i		−	1.63307i	0.577293	−	0.816537i	$-0.304109\pi$
$38$		0			0
$39$	−6.53669			−1.04671
$40$		0			0
$41$	−2.42979	+	4.20853i	−0.379470	+	0.657261i	−0.990985	−	0.133971i	$-0.957227\pi$
$41$	−2.42979	+	4.20853i	−0.379470	+	0.657261i	0.611515	+	0.791233i	$0.290560\pi$
$42$		0			0
$43$	8.57026	+	4.94804i	1.30695	+	0.754569i	0.981586	−	0.191019i	$-0.0611792\pi$
$43$	8.57026	+	4.94804i	1.30695	+	0.754569i	0.325366	+	0.945588i	$0.394512\pi$
$44$		0			0
$45$			3.41951i			0.509750i
$46$		0			0
$47$	−2.86468	−	4.96176i	−0.417856	−	0.723748i	0.577868	−	0.816131i	$-0.303885\pi$
$47$	−2.86468	−	4.96176i	−0.417856	−	0.723748i	−0.995724	+	0.0923828i	$0.970552\pi$
$48$		0			0
$49$	10.4863			1.49805
$50$		0			0
$51$	15.2042	−	8.77815i	2.12901	−	1.22919i
$52$		0			0
$53$	−4.00929	+	2.31477i	−0.550718	+	0.317957i	−0.749412	−	0.662104i	$-0.769664\pi$
$53$	−4.00929	+	2.31477i	−0.550718	+	0.317957i	0.198693	+	0.980062i	$0.436330\pi$
$54$		0			0
$55$	−1.06114	+	1.83794i	−0.143083	+	0.247828i
$56$		0			0
$57$	−7.68054	+	7.81704i	−1.01731	+	1.03539i
$58$		0			0
$59$	−0.382736	−	0.220973i	−0.0498279	−	0.0287682i	0.474879	−	0.880051i	$-0.342492\pi$
$59$	−0.382736	−	0.220973i	−0.0498279	−	0.0287682i	−0.524707	+	0.851283i	$0.675825\pi$
$60$		0			0
$61$	3.59219	−	2.07395i	0.459933	−	0.265542i	−0.252083	−	0.967706i	$-0.581116\pi$
$61$	3.59219	−	2.07395i	0.459933	−	0.265542i	0.712016	+	0.702163i	$0.247782\pi$
$62$		0			0
$63$	−6.94341	−	12.0263i	−0.874788	−	1.51518i
$64$		0			0
$65$	2.67719			0.332064
$66$		0			0
$67$	1.07089	−	0.618281i	0.130831	−	0.0755351i	−0.433156	−	0.901319i	$-0.642600\pi$
$67$	1.07089	−	0.618281i	0.130831	−	0.0755351i	0.563987	+	0.825784i	$0.309267\pi$
$68$		0			0
$69$		−	10.7977i		−	1.29989i
$70$		0			0
$71$	7.69496	−	13.3281i	0.913224	−	1.58175i	0.103742	−	0.994604i	$-0.466918\pi$
$71$	7.69496	−	13.3281i	0.913224	−	1.58175i	0.809482	−	0.587145i	$-0.199748\pi$
$72$		0			0
$73$	0.846177	−	1.46562i	0.0990375	−	0.171538i	−0.812249	−	0.583311i	$-0.801757\pi$
$73$	0.846177	−	1.46562i	0.0990375	−	0.171538i	0.911287	+	0.411773i	$0.135090\pi$
$74$		0			0
$75$			9.90500i			1.14373i
$76$		0			0
$77$		−	8.61867i		−	0.982189i
$78$		0			0
$79$	6.13586	−	10.6276i	0.690338	−	1.19570i	−0.281390	−	0.959594i	$-0.590795\pi$
$79$	6.13586	−	10.6276i	0.690338	−	1.19570i	0.971727	−	0.236106i	$-0.0758714\pi$
$80$		0			0
$81$	3.96719	−	6.87137i	0.440799	−	0.763486i
$82$		0			0
$83$		−	8.92986i		−	0.980180i	−0.871672	−	0.490090i	$-0.836964\pi$
$83$		−	8.92986i		−	0.980180i	0.871672	−	0.490090i	$-0.163036\pi$
$84$		0			0
$85$	−6.22708	+	3.59521i	−0.675421	+	0.389955i
$86$		0			0
$87$	−15.0182			−1.61013
$88$		0			0
$89$	5.55809	+	9.62689i	0.589156	+	1.02045i	0.994343	+	0.106214i	$0.0338730\pi$
$89$	5.55809	+	9.62689i	0.589156	+	1.02045i	−0.405187	+	0.914234i	$0.632794\pi$
$90$		0			0
$91$	−9.41562	+	5.43611i	−0.987025	+	0.569859i
$92$		0			0
$93$	−5.88296	−	3.39653i	−0.610034	−	0.352203i
$94$		0			0
$95$	3.14566	−	3.20157i	0.322738	−	0.328474i
$96$		0			0
$97$	4.11189	−	7.12200i	0.417499	−	0.723130i	−0.578188	−	0.815904i	$-0.696240\pi$
$97$	4.11189	−	7.12200i	0.417499	−	0.723130i	0.995687	+	0.0927737i	$0.0295733\pi$
$98$		0			0
$99$	−5.92755	+	3.42228i	−0.595742	+	0.343952i
$100$		0			0
$101$	0.389733	−	0.225012i	0.0387799	−	0.0223896i	−0.480485	−	0.877003i	$-0.659539\pi$
$101$	0.389733	−	0.225012i	0.0387799	−	0.0223896i	0.519265	+	0.854614i	$0.326206\pi$
$102$		0			0
$103$	9.03278			0.890026			0.445013	−	0.895524i	$-0.353199\pi$
$103$	9.03278			0.890026			0.445013	+	0.895524i	$0.353199\pi$
$104$		0			0
$105$	5.41275	+	9.37515i	0.528230	+	0.914921i
$106$		0			0
$107$			3.56698i			0.344833i	0.985024	+	0.172416i	$0.0551574\pi$
$107$			3.56698i			0.344833i	−0.985024	+	0.172416i	$0.944843\pi$
$108$		0			0
$109$	−5.01057	−	2.89285i	−0.479925	−	0.277085i	0.240460	−	0.970659i	$-0.422702\pi$
$109$	−5.01057	−	2.89285i	−0.479925	−	0.277085i	−0.720385	+	0.693574i	$0.756035\pi$
$110$		0			0
$111$	−12.4872	+	21.6285i	−1.18523	+	2.05289i
$112$		0			0
$113$	−3.13848			−0.295244			−0.147622	−	0.989044i	$-0.547162\pi$
$113$	−3.13848			−0.295244			−0.147622	+	0.989044i	$0.547162\pi$
$114$		0			0
$115$			4.42235i			0.412386i
$116$		0			0
$117$	7.47745	+	4.31711i	0.691290	+	0.399117i
$118$		0			0
$119$	14.6004	−	25.2886i	1.33841	−	2.31820i
$120$		0			0
$121$	6.75202			0.613820
$122$		0			0
$123$	10.5808	−	6.10883i	0.954039	−	0.550815i
$124$		0			0
$125$		−	9.20521i		−	0.823339i
$126$		0			0
$127$	3.09540	+	5.36138i	0.274672	+	0.475746i	0.970052	−	0.242896i	$-0.0780974\pi$
$127$	3.09540	+	5.36138i	0.274672	+	0.475746i	−0.695380	+	0.718642i	$0.744764\pi$
$128$		0			0
$129$	−12.4401	−	21.5468i	−1.09529	−	1.89709i
$130$		0			0
$131$	16.1196	+	9.30667i	1.40838	+	0.813128i	0.995232	−	0.0975369i	$-0.0310964\pi$
$131$	16.1196	+	9.30667i	1.40838	+	0.813128i	0.413147	+	0.910665i	$0.364430\pi$
$132$		0			0
$133$	−4.56235	+	17.6472i	−0.395606	+	1.53021i
$134$		0			0
$135$	0.415353	−	0.719412i	0.0357479	−	0.0619171i
$136$		0			0
$137$	4.84254	+	8.38752i	0.413726	+	0.716595i	0.995294	−	0.0969034i	$-0.0308938\pi$
$137$	4.84254	+	8.38752i	0.413726	+	0.716595i	−0.581568	+	0.813498i	$0.697560\pi$
$138$		0			0
$139$	−0.323654	+	0.186862i	−0.0274520	+	0.0158494i	−0.513663	−	0.857992i	$-0.671712\pi$
$139$	−0.323654	+	0.186862i	−0.0274520	+	0.0158494i	0.486211	+	0.873841i	$0.338379\pi$
$140$		0			0
$141$			14.4044i			1.21307i
$142$		0			0
$143$	2.67935	+	4.64078i	0.224059	+	0.388081i
$144$		0			0
$145$	6.15092			0.510806
$146$		0			0
$147$	−22.8319	−	13.1820i	−1.88315	−	1.08723i
$148$		0			0
$149$	−2.66874	−	1.54080i	−0.218632	−	0.126227i	0.386685	−	0.922212i	$-0.373620\pi$
$149$	−2.66874	−	1.54080i	−0.218632	−	0.126227i	−0.605317	+	0.795985i	$0.706954\pi$
$150$		0			0
$151$	−6.56461			−0.534220			−0.267110	−	0.963666i	$-0.586069\pi$
$151$	−6.56461			−0.534220			−0.267110	+	0.963666i	$0.586069\pi$
$152$		0			0
$153$	−23.1898			−1.87479
$154$		0			0
$155$	2.40944	+	1.39109i	0.193531	+	0.111735i
$156$		0			0
$157$	0.768214	+	0.443528i	0.0613101	+	0.0353974i	0.530342	−	0.847784i	$-0.322064\pi$
$157$	0.768214	+	0.443528i	0.0613101	+	0.0353974i	−0.469032	+	0.883181i	$0.655397\pi$
$158$		0			0
$159$	11.6393			0.923054
$160$		0			0
$161$	−8.97972	−	15.5533i	−0.707701	−	1.22577i
$162$		0			0
$163$		−	16.9688i		−	1.32910i	−0.747245	−	0.664549i	$-0.768624\pi$
$163$		−	16.9688i		−	1.32910i	0.747245	−	0.664549i	$-0.231376\pi$
$164$		0			0
$165$	4.62083	−	2.66784i	0.359731	−	0.207691i
$166$		0			0
$167$	7.04866	+	12.2086i	0.545442	+	0.944733i	0.998579	+	0.0532924i	$0.0169715\pi$
$167$	7.04866	+	12.2086i	0.545442	+	0.944733i	−0.453137	+	0.891441i	$0.649695\pi$
$168$		0			0
$169$	−3.12007	+	5.40412i	−0.240005	+	0.415701i
$170$		0			0
$171$	13.9486	−	3.86952i	1.06668	−	0.295909i
$172$		0			0
$173$	15.8590	+	9.15621i	1.20574	+	0.696134i	0.961826	−	0.273663i	$-0.0882354\pi$
$173$	15.8590	+	9.15621i	1.20574	+	0.696134i	0.243913	+	0.969797i	$0.421569\pi$
$174$		0			0
$175$	8.23730	+	14.2674i	0.622681	+	1.07852i
$176$		0			0
$177$	0.555555	+	0.962250i	0.0417581	+	0.0723271i
$178$		0			0
$179$			8.19827i			0.612767i	0.951908	+	0.306384i	$0.0991190\pi$
$179$			8.19827i			0.612767i	−0.951908	+	0.306384i	$0.900881\pi$
$180$		0			0
$181$	14.6301	−	8.44671i	1.08745	−	0.627839i	0.154553	−	0.987985i	$-0.450606\pi$
$181$	14.6301	−	8.44671i	1.08745	−	0.627839i	0.932896	+	0.360146i	$0.117273\pi$
$182$		0			0
$183$	−10.4284			−0.770889
$184$		0			0
$185$	5.11430	−	8.85823i	0.376011	−	0.651270i
$186$		0			0
$187$	−12.4642	−	7.19623i	−0.911476	−	0.526241i
$188$		0			0
$189$			3.37355i			0.245389i
$190$		0			0
$191$	−27.0669			−1.95849			−0.979245	−	0.202679i	$-0.935035\pi$
$191$	−27.0669			−1.95849			−0.979245	+	0.202679i	$0.935035\pi$
$192$		0			0
$193$	−1.96267	+	3.39944i	−0.141276	+	0.244697i	−0.927977	−	0.372636i	$-0.878454\pi$
$193$	−1.96267	+	3.39944i	−0.141276	+	0.244697i	0.786701	+	0.617334i	$0.211787\pi$
$194$		0			0
$195$	−5.82905	−	3.36541i	−0.417427	−	0.241002i
$196$		0			0
$197$		−	22.9351i		−	1.63406i	−0.576594	−	0.817031i	$-0.695619\pi$
$197$		−	22.9351i		−	1.63406i	0.576594	−	0.817031i	$-0.304381\pi$
$198$		0			0
$199$	10.6672	+	18.4761i	0.756175	+	1.30973i	0.944788	+	0.327682i	$0.106268\pi$
$199$	10.6672	+	18.4761i	0.756175	+	1.30973i	−0.188613	+	0.982051i	$0.560399\pi$
$200$		0			0
$201$	−3.10889			−0.219284
$202$		0			0
$203$	−21.6327	+	12.4896i	−1.51832	+	0.876600i
$204$		0			0
$205$	−4.33351	+	2.50195i	−0.302665	+	0.174744i
$206$		0			0
$207$	−7.13128	+	12.3517i	−0.495658	+	0.858505i
$208$		0			0
$209$	8.69799	+	2.24870i	0.601652	+	0.155546i
$210$		0			0
$211$	8.90794	+	5.14300i	0.613248	+	0.354059i	0.774236	−	0.632898i	$-0.218135\pi$
$211$	8.90794	+	5.14300i	0.613248	+	0.354059i	−0.160988	+	0.986956i	$0.551468\pi$
$212$		0			0
$213$	−33.5086	+	19.3462i	−2.29597	+	1.32558i
$214$		0			0
$215$	5.09498	+	8.82477i	0.347475	+	0.601845i
$216$		0			0
$217$	−11.2986			−0.767000
$218$		0			0
$219$	−3.68477	+	2.12740i	−0.248994	+	0.143757i
$220$		0			0
$221$			18.1557i			1.22128i
$222$		0			0
$223$	−14.7424	+	25.5345i	−0.987222	+	1.70992i	−0.355611	+	0.934634i	$0.615727\pi$
$223$	−14.7424	+	25.5345i	−0.987222	+	1.70992i	−0.631611	+	0.775285i	$0.717606\pi$
$224$		0			0
$225$	6.54168	−	11.3305i	0.436112	−	0.755369i
$226$		0			0
$227$			3.15930i			0.209690i	0.994489	+	0.104845i	$0.0334347\pi$
$227$			3.15930i			0.209690i	−0.994489	+	0.104845i	$0.966565\pi$
$228$		0			0
$229$		−	24.9567i		−	1.64919i	−0.565725	−	0.824594i	$-0.691404\pi$
$229$		−	24.9567i		−	1.64919i	0.565725	−	0.824594i	$-0.308596\pi$
$230$		0			0
$231$	−10.8343	+	18.7655i	−0.712842	+	1.23468i
$232$		0			0
$233$	−12.8833	+	22.3146i	−0.844015	+	1.46188i	0.0424596	+	0.999098i	$0.486481\pi$
$233$	−12.8833	+	22.3146i	−0.844015	+	1.46188i	−0.886474	+	0.462778i	$0.846853\pi$
$234$		0			0
$235$		−	5.89950i		−	0.384841i
$236$		0			0
$237$	−26.7193	+	15.4264i	−1.73560	+	1.00205i
$238$		0			0
$239$	12.0688			0.780665			0.390333	−	0.920674i	$-0.372360\pi$
$239$	12.0688			0.780665			0.390333	+	0.920674i	$0.372360\pi$
$240$		0			0
$241$	12.8969	+	22.3381i	0.830762	+	1.43892i	0.897435	+	0.441147i	$0.145428\pi$
$241$	12.8969	+	22.3381i	0.830762	+	1.43892i	−0.0666731	+	0.997775i	$0.521238\pi$
$242$		0			0
$243$	−19.3716	+	11.1842i	−1.24269	+	0.717465i
$244$		0			0
$245$	9.35111	+	5.39887i	0.597421	+	0.344921i
$246$		0			0
$247$	−3.02951	−	10.9206i	−0.192763	−	0.694861i
$248$		0			0
$249$	−11.2255	+	19.4431i	−0.711384	+	1.23215i
$250$		0			0
$251$	−5.86304	+	3.38503i	−0.370072	+	0.213661i	−0.673490	−	0.739197i	$-0.735205\pi$
$251$	−5.86304	+	3.38503i	−0.370072	+	0.213661i	0.303418	+	0.952858i	$0.401872\pi$
$252$		0			0
$253$	−7.66594	+	4.42593i	−0.481954	+	0.278256i
$254$		0			0
$255$	18.0777			1.13207
$256$		0			0
$257$	−2.77233	−	4.80182i	−0.172933	−	0.299529i	0.766511	−	0.642231i	$-0.221991\pi$
$257$	−2.77233	−	4.80182i	−0.172933	−	0.299529i	−0.939444	+	0.342702i	$0.888658\pi$
$258$		0			0
$259$			41.5390i			2.58111i
$260$		0			0
$261$	17.1797	+	9.91869i	1.06339	+	0.613951i
$262$		0			0
$263$	−1.66289	+	2.88020i	−0.102538	+	0.177601i	−0.912730	−	0.408564i	$-0.866030\pi$
$263$	−1.66289	+	2.88020i	−0.102538	+	0.177601i	0.810192	+	0.586165i	$0.199363\pi$
$264$		0			0
$265$	−4.76701			−0.292835
$266$		0			0
$267$		−	27.9476i		−	1.71036i
$268$		0			0
$269$	22.5542	+	13.0217i	1.37515	+	0.793944i	0.991571	−	0.129563i	$-0.0413575\pi$
$269$	22.5542	+	13.0217i	1.37515	+	0.793944i	0.383581	+	0.923507i	$0.374691\pi$
$270$		0			0
$271$	11.0407	−	19.1231i	0.670675	−	1.16164i	−0.307038	−	0.951697i	$-0.599338\pi$
$271$	11.0407	−	19.1231i	0.670675	−	1.16164i	0.977713	−	0.209946i	$-0.0673288\pi$
$272$		0			0
$273$	27.3342			1.65434
$274$		0			0
$275$	7.03214	−	4.06001i	0.424054	−	0.244828i
$276$		0			0
$277$			17.9658i			1.07946i	0.841838	+	0.539730i	$0.181474\pi$
$277$			17.9658i			1.07946i	−0.841838	+	0.539730i	$0.818526\pi$
$278$		0			0
$279$	4.48642	+	7.77071i	0.268595	+	0.465220i
$280$		0			0
$281$	−13.8903	−	24.0587i	−0.828624	−	1.43522i	−0.899118	−	0.437707i	$-0.855791\pi$
$281$	−13.8903	−	24.0587i	−0.828624	−	1.43522i	0.0704935	−	0.997512i	$-0.477543\pi$
$282$		0			0
$283$	−12.4157	−	7.16819i	−0.738035	−	0.426105i	0.0833196	−	0.996523i	$-0.473448\pi$
$283$	−12.4157	−	7.16819i	−0.738035	−	0.426105i	−0.821354	+	0.570418i	$0.806781\pi$
$284$		0			0
$285$	−10.8737	+	3.01649i	−0.644100	+	0.178681i
$286$		0			0
$287$	10.1606	−	17.5986i	0.599760	−	1.03881i
$288$		0			0
$289$	−15.8814	−	27.5074i	−0.934199	−	1.61808i
$290$		0			0
$291$	−17.9057	+	10.3379i	−1.04965	+	0.606016i
$292$		0			0
$293$			24.8210i			1.45006i	0.688718	+	0.725030i	$0.258174\pi$
$293$			24.8210i			1.45006i	−0.688718	+	0.725030i	$0.741826\pi$
$294$		0			0
$295$	−0.227535	−	0.394102i	−0.0132476	−	0.0229455i
$296$		0			0
$297$	1.66276			0.0964830
$298$		0			0
$299$	9.67037	+	5.58319i	0.559252	+	0.322884i
$300$		0			0
$301$	−35.8380	−	20.6911i	−2.06567	−	1.19261i
$302$		0			0
$303$	−1.13142			−0.0649986
$304$		0			0
$305$	4.27108			0.244562
$306$		0			0
$307$	−24.1285	−	13.9306i	−1.37709	−	0.795062i	−0.385280	−	0.922800i	$-0.625895\pi$
$307$	−24.1285	−	13.9306i	−1.37709	−	0.795062i	−0.991808	+	0.127737i	$0.959229\pi$
$308$		0			0
$309$	−19.6671	−	11.3548i	−1.11882	−	0.645953i
$310$		0			0
$311$	26.9135			1.52613			0.763064	−	0.646323i	$-0.223694\pi$
$311$	26.9135			1.52613			0.763064	+	0.646323i	$0.223694\pi$
$312$		0			0
$313$	−1.54562	−	2.67710i	−0.0873639	−	0.151319i	0.819032	−	0.573748i	$-0.194511\pi$
$313$	−1.54562	−	2.67710i	−0.0873639	−	0.151319i	−0.906396	+	0.422429i	$0.861178\pi$
$314$		0			0
$315$		−	14.2992i		−	0.805670i
$316$		0			0
$317$	−1.97144	+	1.13821i	−0.110727	+	0.0639283i	−0.554341	−	0.832290i	$-0.687030\pi$
$317$	−1.97144	+	1.13821i	−0.110727	+	0.0639283i	0.443614	+	0.896218i	$0.353696\pi$
$318$		0			0
$319$	6.15590	+	10.6623i	0.344664	+	0.596976i
$320$		0			0
$321$	4.48393	−	7.76640i	0.250269	−	0.433478i
$322$		0			0
$323$	21.7119	+	21.3327i	1.20808	+	1.18699i
$324$		0			0
$325$	−8.87085	−	5.12159i	−0.492066	−	0.284095i
$326$		0			0
$327$	7.27302	+	12.5972i	0.402199	+	0.696629i
$328$		0			0
$329$	11.9791	+	20.7484i	0.660430	+	1.14390i
$330$		0			0
$331$			9.12923i			0.501788i	0.968015	+	0.250894i	$0.0807246\pi$
$331$			9.12923i			0.501788i	−0.968015	+	0.250894i	$0.919275\pi$
$332$		0			0
$333$	28.5688	−	16.4942i	1.56556	−	0.903875i
$334$		0			0
$335$	1.27328			0.0695670
$336$		0			0
$337$	8.52133	−	14.7594i	0.464186	−	0.803994i	−0.534978	−	0.844866i	$-0.679680\pi$
$337$	8.52133	−	14.7594i	0.464186	−	0.803994i	0.999164	+	0.0408718i	$0.0130135\pi$
$338$		0			0
$339$	6.83344	+	3.94529i	0.371142	+	0.214279i
$340$		0			0
$341$			5.56887i			0.301571i
$342$		0			0
$343$	−14.5786			−0.787171
$344$		0			0
$345$	5.55920	−	9.62881i	0.299297	−	0.518398i
$346$		0			0
$347$	22.2574	+	12.8503i	1.19484	+	0.689842i	0.959401	−	0.282047i	$-0.0910133\pi$
$347$	22.2574	+	12.8503i	1.19484	+	0.689842i	0.235441	+	0.971889i	$0.424347\pi$
$348$		0			0
$349$		−	17.9677i		−	0.961789i	−0.876778	−	0.480895i	$-0.840312\pi$
$349$		−	17.9677i		−	0.961789i	0.876778	−	0.480895i	$-0.159688\pi$
$350$		0			0
$351$	−1.04876	−	1.81651i	−0.0559787	−	0.0969580i
$352$		0			0
$353$	−22.2672			−1.18516			−0.592581	−	0.805511i	$-0.701891\pi$
$353$	−22.2672			−1.18516			−0.592581	+	0.805511i	$0.701891\pi$
$354$		0			0
$355$	13.7239	−	7.92348i	0.728387	−	0.420534i
$356$		0			0
$357$	−63.5789	+	36.7073i	−3.36495	+	1.94276i
$358$		0			0
$359$	4.29270	−	7.43517i	0.226560	−	0.392413i	−0.730226	−	0.683205i	$-0.760585\pi$
$359$	4.29270	−	7.43517i	0.226560	−	0.392413i	0.956786	+	0.290792i	$0.0939188\pi$
$360$		0			0
$361$	−16.6193	−	9.20868i	−0.874699	−	0.484667i
$362$		0			0
$363$	−14.7012	−	8.48775i	−0.771614	−	0.445492i
$364$		0			0
$365$	1.50915	−	0.871306i	0.0789923	−	0.0456062i
$366$		0			0
$367$	−3.47432	−	6.01769i	−0.181358	−	0.314121i	0.760985	−	0.648769i	$-0.224716\pi$
$367$	−3.47432	−	6.01769i	−0.181358	−	0.314121i	−0.942343	+	0.334648i	$0.891383\pi$
$368$		0			0
$369$	−16.1381			−0.840117
$370$		0			0
$371$	16.7655	−	9.67957i	0.870422	−	0.502538i
$372$		0			0
$373$		−	29.3371i		−	1.51902i	−0.650497	−	0.759509i	$-0.725439\pi$
$373$		−	29.3371i		−	1.51902i	0.650497	−	0.759509i	$-0.274561\pi$
$374$		0			0
$375$	−11.5716	+	20.0426i	−0.597554	+	1.03499i
$376$		0			0
$377$	7.76550	−	13.4502i	0.399943	−	0.692722i
$378$		0			0
$379$		−	16.4390i		−	0.844414i	−0.906499	−	0.422207i	$-0.861256\pi$
$379$		−	16.4390i		−	0.844414i	0.906499	−	0.422207i	$-0.138744\pi$
$380$		0			0
$381$		−	15.5645i		−	0.797393i
$382$		0			0
$383$	1.49748	−	2.59370i	0.0765175	−	0.132532i	−0.825228	−	0.564800i	$-0.808953\pi$
$383$	1.49748	−	2.59370i	0.0765175	−	0.132532i	0.901745	+	0.432268i	$0.142287\pi$
$384$		0			0
$385$	4.43731	−	7.68565i	0.226146	−	0.391697i
$386$		0			0
$387$			32.8638i			1.67056i
$388$		0			0
$389$	17.1395	−	9.89551i	0.869008	−	0.501722i	0.00198960	−	0.999998i	$-0.499367\pi$
$389$	17.1395	−	9.89551i	0.869008	−	0.501722i	0.867018	+	0.498276i	$0.166033\pi$
$390$		0			0
$391$	−29.9908			−1.51670
$392$		0			0
$393$	−23.3982	−	40.5270i	−1.18029	−	2.04431i
$394$		0			0
$395$	10.9432	−	6.31807i	0.550613	−	0.317897i
$396$		0			0
$397$	−9.59876	−	5.54185i	−0.481748	−	0.278137i	0.239397	−	0.970922i	$-0.423050\pi$
$397$	−9.59876	−	5.54185i	−0.481748	−	0.278137i	−0.721145	+	0.692785i	$0.756384\pi$
$398$		0			0
$399$	32.1174	−	32.6883i	1.60788	−	1.63646i
$400$		0			0
$401$	12.6118	−	21.8442i	0.629802	−	1.09085i	−0.357789	−	0.933802i	$-0.616469\pi$
$401$	12.6118	−	21.8442i	0.629802	−	1.09085i	0.987591	−	0.157047i	$-0.0501974\pi$
$402$		0			0
$403$	6.08381	−	3.51249i	0.303056	−	0.174970i
$404$		0			0
$405$	7.07543	−	4.08500i	0.351581	−	0.202985i
$406$		0			0
$407$	20.4738			1.01485
$408$		0			0
$409$	7.43641	+	12.8802i	0.367707	+	0.636887i	0.989207	−	0.146527i	$-0.0468096\pi$
$409$	7.43641	+	12.8802i	0.367707	+	0.636887i	−0.621500	+	0.783414i	$0.713476\pi$
$410$		0			0
$411$		−	24.3496i		−	1.20108i
$412$		0			0
$413$	1.60047	+	0.924033i	0.0787541	+	0.0454687i
$414$		0			0
$415$	4.59753	−	7.96315i	0.225684	−	0.390896i
$416$		0			0
$417$	0.939592			0.0460120
$418$		0			0
$419$			10.1076i			0.493787i	0.969043	+	0.246894i	$0.0794099\pi$
$419$			10.1076i			0.493787i	−0.969043	+	0.246894i	$0.920590\pi$
$420$		0			0
$421$	−0.377455	−	0.217924i	−0.0183960	−	0.0106210i	0.490774	−	0.871287i	$-0.336714\pi$
$421$	−0.377455	−	0.217924i	−0.0183960	−	0.0106210i	−0.509170	+	0.860666i	$0.670047\pi$
$422$		0			0
$423$	9.51326	−	16.4774i	0.462550	−	0.801161i
$424$		0			0
$425$	27.5112			1.33449
$426$		0			0
$427$	−15.0213	+	8.67257i	−0.726933	+	0.419695i
$428$		0			0
$429$		−	13.4725i		−	0.650460i
$430$		0			0
$431$	−14.1185	−	24.4540i	−0.680064	−	1.17791i	−0.974961	−	0.222377i	$-0.928618\pi$
$431$	−14.1185	−	24.4540i	−0.680064	−	1.17791i	0.294896	−	0.955529i	$-0.404715\pi$
$432$		0			0
$433$	7.50311	+	12.9958i	0.360576	+	0.624536i	0.988056	−	0.154097i	$-0.0492467\pi$
$433$	7.50311	+	12.9958i	0.360576	+	0.624536i	−0.627479	+	0.778633i	$0.715913\pi$
$434$		0			0
$435$	−13.3924	−	7.73212i	−0.642118	−	0.370727i
$436$		0			0
$437$	18.0394	−	5.00434i	0.862940	−	0.239390i
$438$		0			0
$439$	−1.72649	+	2.99037i	−0.0824010	+	0.142723i	−0.904281	−	0.426938i	$-0.859592\pi$
$439$	−1.72649	+	2.99037i	−0.0824010	+	0.142723i	0.821880	+	0.569661i	$0.192925\pi$
$440$		0			0
$441$	17.4119	+	30.1583i	0.829139	+	1.43611i
$442$		0			0
$443$	29.5447	−	17.0577i	1.40371	−	0.810434i	0.408941	−	0.912561i	$-0.365898\pi$
$443$	29.5447	−	17.0577i	1.40371	−	0.810434i	0.994771	+	0.102127i	$0.0325649\pi$
$444$		0			0
$445$			11.4463i			0.542606i
$446$		0			0
$447$	3.87378	+	6.70959i	0.183224	+	0.317353i
$448$		0			0
$449$	17.1361			0.808701			0.404351	−	0.914604i	$-0.367498\pi$
$449$	17.1361			0.808701			0.404351	+	0.914604i	$0.367498\pi$
$450$		0			0
$451$	−8.67403	−	5.00796i	−0.408444	−	0.235815i
$452$		0			0
$453$	14.2932	+	8.25216i	0.671551	+	0.387720i
$454$		0			0
$455$	−11.1951			−0.524834
$456$		0			0
$457$	30.0050			1.40357			0.701787	−	0.712387i	$-0.252386\pi$
$457$	30.0050			1.40357			0.701787	+	0.712387i	$0.252386\pi$
$458$		0			0
$459$	4.87879	+	2.81677i	0.227723	+	0.131476i
$460$		0			0
$461$	17.8621	+	10.3127i	0.831920	+	0.480309i	0.854509	−	0.519436i	$-0.173858\pi$
$461$	17.8621	+	10.3127i	0.831920	+	0.480309i	−0.0225899	+	0.999745i	$0.507191\pi$
$462$		0			0
$463$	−13.8950			−0.645755			−0.322878	−	0.946441i	$-0.604650\pi$
$463$	−13.8950			−0.645755			−0.322878	+	0.946441i	$0.604650\pi$
$464$		0			0
$465$	−3.49739	−	6.05766i	−0.162188	−	0.280917i
$466$		0			0
$467$		−	8.27925i		−	0.383118i	−0.981481	−	0.191559i	$-0.938646\pi$
$467$		−	8.27925i		−	0.383118i	0.981481	−	0.191559i	$-0.0613543\pi$
$468$		0			0
$469$	−4.47812	+	2.58544i	−0.206780	+	0.119385i
$470$		0			0
$471$	−1.11509	−	1.93139i	−0.0513807	−	0.0889940i
$472$		0			0
$473$	−10.1982	+	17.6638i	−0.468915	+	0.812184i
$474$		0			0
$475$	−16.5479	+	4.59059i	−0.759270	+	0.210631i
$476$		0			0
$477$	−13.3144	−	7.68707i	−0.609624	−	0.351967i
$478$		0			0
$479$	7.89208	+	13.6695i	0.360598	+	0.624575i	0.988059	−	0.154073i	$-0.0492392\pi$
$479$	7.89208	+	13.6695i	0.360598	+	0.624575i	−0.627461	+	0.778648i	$0.715906\pi$
$480$		0			0
$481$	−12.9136	−	22.3669i	−0.588807	−	1.01984i
$482$		0			0
$483$			45.1525i			2.05451i
$484$		0			0
$485$	7.33351	−	4.23400i	0.332997	−	0.192256i
$486$		0			0
$487$	24.4487			1.10788			0.553938	−	0.832558i	$-0.313125\pi$
$487$	24.4487			1.10788			0.553938	+	0.832558i	$0.313125\pi$
$488$		0			0
$489$	−21.3309	+	36.9462i	−0.964618	+	1.67077i
$490$		0			0
$491$	−9.88254	−	5.70569i	−0.445993	−	0.257494i	0.260143	−	0.965570i	$-0.416230\pi$
$491$	−9.88254	−	5.70569i	−0.445993	−	0.257494i	−0.706136	+	0.708076i	$0.749563\pi$
$492$		0			0
$493$			41.7133i			1.87867i
$494$		0			0
$495$	−7.04781			−0.316776
$496$		0			0
$497$	−32.1777	+	55.7335i	−1.44337	+	2.49999i
$498$		0			0
$499$	11.7725	+	6.79688i	0.527011	+	0.304270i	0.739799	−	0.672828i	$-0.234921\pi$
$499$	11.7725	+	6.79688i	0.527011	+	0.304270i	−0.212787	+	0.977099i	$0.568254\pi$
$500$		0			0
$501$		−	35.4426i		−	1.58346i
$502$		0			0
$503$	1.40759	+	2.43802i	0.0627614	+	0.108706i	0.895699	−	0.444661i	$-0.146676\pi$
$503$	1.40759	+	2.43802i	0.0627614	+	0.108706i	−0.832937	+	0.553367i	$0.813343\pi$
$504$		0			0
$505$	0.463389			0.0206206
$506$		0			0
$507$	13.5867	−	7.84428i	0.603406	−	0.348377i
$508$		0			0
$509$	−20.8465	+	12.0358i	−0.924007	+	0.533475i	−0.884911	−	0.465760i	$-0.845781\pi$
$509$	−20.8465	+	12.0358i	−0.924007	+	0.533475i	−0.0390956	+	0.999235i	$0.512448\pi$
$510$		0			0
$511$	−3.53843	+	6.12874i	−0.156531	+	0.271119i
$512$		0			0
$513$	−3.40459	−	0.880192i	−0.150316	−	0.0388614i
$514$		0			0
$515$	8.05492	+	4.65051i	0.354942	+	0.204926i
$516$		0			0
$517$	10.2265	−	5.90428i	0.449761	−	0.259670i
$518$		0			0
$519$	−23.0200	−	39.8717i	−1.01046	−	1.75018i
$520$		0			0
$521$	7.91921			0.346947			0.173473	−	0.984839i	$-0.444501\pi$
$521$	7.91921			0.346947			0.173473	+	0.984839i	$0.444501\pi$
$522$		0			0
$523$	−6.15565	+	3.55397i	−0.269168	+	0.155404i	−0.628509	−	0.777802i	$-0.716335\pi$
$523$	−6.15565	+	3.55397i	−0.269168	+	0.155404i	0.359341	+	0.933206i	$0.383001\pi$
$524$		0			0
$525$		−	41.4194i		−	1.80769i
$526$		0			0
$527$	−9.43388	+	16.3400i	−0.410946	+	0.711780i
$528$		0			0
$529$	2.27731	−	3.94443i	0.0990137	−	0.171497i
$530$		0			0
$531$		−	1.46765i		−	0.0636905i
$532$		0			0
$533$			12.6348i			0.547274i
$534$		0			0
$535$	−1.83645	+	3.18083i	−0.0793968	+	0.137519i
$536$		0			0
$537$	10.3058	−	17.8501i	0.444727	−	0.770290i
$538$		0			0
$539$			21.6130i			0.930936i
$540$		0			0
$541$	−16.0098	+	9.24326i	−0.688315	+	0.397399i	−0.802980	−	0.596005i	$-0.796754\pi$
$541$	−16.0098	+	9.24326i	−0.688315	+	0.397399i	0.114666	+	0.993404i	$0.463420\pi$
$542$		0			0
$543$	−42.4723			−1.82266
$544$		0			0
$545$	−2.97876	−	5.15937i	−0.127596	−	0.221003i
$546$		0			0
$547$	−2.76878	+	1.59855i	−0.118384	+	0.0683492i	−0.558023	−	0.829826i	$-0.688440\pi$
$547$	−2.76878	+	1.59855i	−0.118384	+	0.0683492i	0.439639	+	0.898175i	$0.355107\pi$
$548$		0			0
$549$	11.9292	+	6.88735i	0.509128	+	0.293945i
$550$		0			0
$551$	−6.96039	−	25.0904i	−0.296522	−	1.06889i
$552$		0			0
$553$	−25.6581	+	44.4411i	−1.09109	+	1.88983i
$554$		0			0
$555$	−22.2708	+	12.8581i	−0.945343	+	0.545794i
$556$		0			0
$557$	7.08032	−	4.08783i	0.300003	−	0.173207i	−0.342441	−	0.939539i	$-0.611254\pi$
$557$	7.08032	−	4.08783i	0.300003	−	0.173207i	0.642444	+	0.766332i	$0.277920\pi$
$558$		0			0
$559$	25.7296			1.08824
$560$		0			0
$561$	18.0923	+	31.3368i	0.763858	+	1.32304i
$562$		0			0
$563$		−	46.7841i		−	1.97171i	−0.167587	−	0.985857i	$-0.553597\pi$
$563$		−	46.7841i		−	1.97171i	0.167587	−	0.985857i	$-0.446403\pi$
$564$		0			0
$565$	−2.79872	−	1.61584i	−0.117743	−	0.0679791i
$566$		0			0
$567$	−16.5895	+	28.7338i	−0.696692	+	1.20671i
$568$		0			0
$569$	23.1806			0.971782			0.485891	−	0.874019i	$-0.338495\pi$
$569$	23.1806			0.971782			0.485891	+	0.874019i	$0.338495\pi$
$570$		0			0
$571$		−	23.6221i		−	0.988554i	−0.869304	−	0.494277i	$-0.835433\pi$
$571$		−	23.6221i		−	0.988554i	0.869304	−	0.494277i	$-0.164567\pi$
$572$		0			0
$573$	58.9329	+	34.0249i	2.46196	+	1.42141i
$574$		0			0
$575$	8.46018	−	14.6535i	0.352814	−	0.611091i
$576$		0			0
$577$	−25.5137			−1.06215			−0.531074	−	0.847325i	$-0.678211\pi$
$577$	−25.5137			−1.06215			−0.531074	+	0.847325i	$0.678211\pi$
$578$		0			0
$579$	8.54667	−	4.93442i	0.355187	−	0.205067i
$580$		0			0
$581$			37.3417i			1.54919i
$582$		0			0
$583$	−4.77088	−	8.26340i	−0.197589	−	0.342235i
$584$		0			0
$585$	4.44531	+	7.69951i	0.183791	+	0.318335i
$586$		0			0
$587$	−10.4598	−	6.03898i	−0.431723	−	0.249256i	0.268357	−	0.963319i	$-0.413519\pi$
$587$	−10.4598	−	6.03898i	−0.431723	−	0.249256i	−0.700080	+	0.714064i	$0.746853\pi$
$588$		0			0
$589$	2.94792	−	11.4026i	0.121467	−	0.469836i
$590$		0			0
$591$	−28.8310	+	49.9368i	−1.18595	+	2.05413i
$592$		0			0
$593$	−11.5527	−	20.0099i	−0.474414	−	0.821710i	0.525156	−	0.851006i	$-0.324007\pi$
$593$	−11.5527	−	20.0099i	−0.474414	−	0.821710i	−0.999571	+	0.0292958i	$0.990674\pi$
$594$		0			0
$595$	26.0396	−	15.0339i	1.06752	−	0.616332i
$596$		0			0
$597$		−	53.6374i		−	2.19523i
$598$		0			0
$599$	−14.5328	−	25.1715i	−0.593793	−	1.02848i	−0.993716	−	0.111931i	$-0.964296\pi$
$599$	−14.5328	−	25.1715i	−0.593793	−	1.02848i	0.399923	−	0.916549i	$-0.369037\pi$
$600$		0			0
$601$	2.23739			0.0912648			0.0456324	−	0.998958i	$-0.485470\pi$
$601$	2.23739			0.0912648			0.0456324	+	0.998958i	$0.485470\pi$
$602$		0			0
$603$	3.55632	+	2.05324i	0.144824	+	0.0836144i
$604$		0			0
$605$	6.02107	+	3.47627i	0.244791	+	0.141330i
$606$		0			0
$607$	−31.1940			−1.26612			−0.633062	−	0.774101i	$-0.718202\pi$
$607$	−31.1940			−1.26612			−0.633062	+	0.774101i	$0.718202\pi$
$608$		0			0
$609$	62.8013			2.54484
$610$		0			0
$611$	−12.9005	−	7.44808i	−0.521897	−	0.301317i
$612$		0			0
$613$	32.7164	+	18.8888i	1.32140	+	0.762912i	0.983952	−	0.178431i	$-0.0571021\pi$
$613$	32.7164	+	18.8888i	1.32140	+	0.762912i	0.337451	+	0.941343i	$0.390435\pi$
$614$		0			0
$615$	12.5805			0.507295
$616$		0			0
$617$	−8.42297	−	14.5890i	−0.339096	−	0.587331i	0.645167	−	0.764042i	$-0.276788\pi$
$617$	−8.42297	−	14.5890i	−0.339096	−	0.587331i	−0.984263	+	0.176710i	$0.943454\pi$
$618$		0			0
$619$			19.9654i			0.802477i	0.915974	+	0.401239i	$0.131420\pi$
$619$			19.9654i			0.802477i	−0.915974	+	0.401239i	$0.868580\pi$
$620$		0			0
$621$	3.00063	−	1.73241i	0.120411	−	0.0695193i
$622$		0			0
$623$	−23.2421	−	40.2564i	−0.931173	−	1.61284i
$624$		0			0
$625$	−5.11002	+	8.85081i	−0.204401	+	0.354033i
$626$		0			0
$627$	−16.1114	−	15.8301i	−0.643428	−	0.632192i
$628$		0			0
$629$	60.0733	+	34.6833i	2.39528	+	1.38292i
$630$		0			0
$631$	1.75918	+	3.04700i	0.0700320	+	0.121299i	0.898915	−	0.438123i	$-0.144357\pi$
$631$	1.75918	+	3.04700i	0.0700320	+	0.121299i	−0.828883	+	0.559422i	$0.811023\pi$
$632$		0			0
$633$	−12.9302	−	22.3958i	−0.513930	−	0.890152i
$634$		0			0
$635$			6.37464i			0.252970i
$636$		0			0
$637$	23.6114	−	13.6321i	0.935520	−	0.540122i
$638$		0			0
$639$	51.1081			2.02181
$640$		0			0
$641$	−23.8544	+	41.3170i	−0.942192	+	1.63192i	−0.180914	+	0.983499i	$0.557905\pi$
$641$	−23.8544	+	41.3170i	−0.942192	+	1.63192i	−0.761278	+	0.648425i	$0.775428\pi$
$642$		0			0
$643$	−1.77682	−	1.02585i	−0.0700708	−	0.0404554i	0.464555	−	0.885544i	$-0.346214\pi$
$643$	−1.77682	−	1.02585i	−0.0700708	−	0.0404554i	−0.534626	+	0.845089i	$0.679548\pi$
$644$		0			0
$645$		−	25.6190i		−	1.00875i
$646$		0			0
$647$	−20.5920			−0.809556			−0.404778	−	0.914415i	$-0.632651\pi$
$647$	−20.5920			−0.809556			−0.404778	+	0.914415i	$0.632651\pi$
$648$		0			0
$649$	0.455438	−	0.788842i	0.0178775	−	0.0309648i
$650$		0			0
$651$	24.6006	+	14.2031i	0.964172	+	0.556665i
$652$		0			0
$653$		−	40.4105i		−	1.58138i	−0.612215	−	0.790692i	$-0.709721\pi$
$653$		−	40.4105i		−	1.58138i	0.612215	−	0.790692i	$-0.290279\pi$
$654$		0			0
$655$	9.58305	+	16.5983i	0.374441	+	0.648551i
$656$		0			0
$657$	5.62011			0.219261
$658$		0			0
$659$	3.59885	−	2.07780i	0.140191	−	0.0809395i	−0.428264	−	0.903654i	$-0.640875\pi$
$659$	3.59885	−	2.07780i	0.140191	−	0.0809395i	0.568455	+	0.822714i	$0.307541\pi$
$660$		0			0
$661$	−1.70326	+	0.983378i	−0.0662491	+	0.0382490i	−0.532759	−	0.846267i	$-0.678845\pi$
$661$	−1.70326	+	0.983378i	−0.0662491	+	0.0382490i	0.466510	+	0.884516i	$0.345511\pi$
$662$		0			0
$663$	22.8230	−	39.5305i	0.886370	−	1.53524i
$664$		0			0
$665$	−13.1541	+	13.3879i	−0.510094	+	0.519160i
$666$		0			0
$667$	22.2180	+	12.8276i	0.860284	+	0.496685i
$668$		0			0
$669$	64.1973	−	37.0643i	2.48201	−	1.43299i
$670$		0			0
$671$	4.27454	+	7.40373i	0.165017	+	0.285818i
$672$		0			0
$673$	43.6670			1.68324			0.841619	−	0.540071i	$-0.181603\pi$
$673$	43.6670			1.68324			0.841619	+	0.540071i	$0.181603\pi$
$674$		0			0
$675$	−2.75254	+	1.58918i	−0.105945	+	0.0611676i
$676$		0			0
$677$			3.02152i			0.116127i	0.998313	+	0.0580633i	$0.0184925\pi$
$677$			3.02152i			0.116127i	−0.998313	+	0.0580633i	$0.981507\pi$
$678$		0			0
$679$	−17.1945	+	29.7818i	−0.659866	+	1.14292i
$680$		0			0
$681$	3.97146	−	6.87877i	0.152187	−	0.263595i
$682$		0			0
$683$		−	32.7404i		−	1.25278i	−0.779511	−	0.626388i	$-0.784532\pi$
$683$		−	32.7404i		−	1.25278i	0.779511	−	0.626388i	$-0.215468\pi$
$684$		0			0
$685$			9.97270i			0.381037i
$686$		0			0
$687$	−31.3723	+	54.3385i	−1.19693	+	2.07314i
$688$		0			0
$689$	−6.01833	+	10.4240i	−0.229280	+	0.397125i
$690$		0			0
$691$		−	18.5783i		−	0.706753i	−0.935481	−	0.353376i	$-0.885034\pi$
$691$		−	18.5783i		−	0.706753i	0.935481	−	0.353376i	$-0.114966\pi$
$692$		0			0
$693$	24.7870	−	14.3108i	0.941582	−	0.543623i
$694$		0			0
$695$	−0.384822			−0.0145971
$696$		0			0
$697$	−16.9673	−	29.3883i	−0.642683	−	1.11316i
$698$		0			0
$699$	56.1019	−	32.3904i	2.12197	−	1.22512i
$700$		0			0
$701$	4.47757	+	2.58513i	0.169115	+	0.0976388i	0.582169	−	0.813068i	$-0.302204\pi$
$701$	4.47757	+	2.58513i	0.169115	+	0.0976388i	−0.413053	+	0.910707i	$0.635538\pi$
$702$		0			0
$703$	−41.9213	−	10.8379i	−1.58109	−	0.408761i
$704$		0			0
$705$	−7.41607	+	12.8450i	−0.279305	+	0.483771i
$706$		0			0
$707$	−1.62973	+	0.940927i	−0.0612924	+	0.0353872i
$708$		0			0
$709$	−32.2533	+	18.6215i	−1.21130	+	0.699344i	−0.963042	−	0.269350i	$-0.913191\pi$
$709$	−32.2533	+	18.6215i	−1.21130	+	0.699344i	−0.248257	+	0.968694i	$0.579858\pi$
$710$		0			0
$711$	40.7529			1.52835
$712$		0			0
$713$	5.80216	+	10.0496i	0.217293	+	0.376362i
$714$		0			0
$715$			5.51785i			0.206356i
$716$		0			0
$717$	−26.2775	−	15.1713i	−0.981350	−	0.566583i
$718$		0			0
$719$	5.47043	−	9.47506i	0.204013	−	0.353360i	−0.745805	−	0.666164i	$-0.767935\pi$
$719$	5.47043	−	9.47506i	0.204013	−	0.353360i	0.949818	+	0.312804i	$0.101268\pi$
$720$		0			0
$721$	−37.7720			−1.40670
$722$		0			0
$723$		−	64.8491i		−	2.41176i
$724$		0			0
$725$	−20.3811	−	11.7670i	−0.756934	−	0.437016i
$726$		0			0
$727$	−15.1688	+	26.2731i	−0.562579	+	0.974416i	0.434691	+	0.900580i	$0.356858\pi$
$727$	−15.1688	+	26.2731i	−0.562579	+	0.974416i	−0.997270	+	0.0738363i	$0.976476\pi$
$728$		0			0
$729$	32.4340			1.20126
$730$		0			0
$731$	−59.8464	+	34.5523i	−2.21350	+	1.27796i
$732$		0			0
$733$		−	0.261803i		−	0.00966991i	−0.999988	−	0.00483495i	$-0.998461\pi$
$733$		−	0.261803i		−	0.00966991i	0.999988	−	0.00483495i	$-0.00153902\pi$
$734$		0			0
$735$	−13.5735	−	23.5100i	−0.500666	−	0.867179i
$736$		0			0
$737$	1.27432	+	2.20718i	0.0469400	+	0.0813025i
$738$		0			0
$739$	−13.1211	−	7.57547i	−0.482668	−	0.278668i	0.238860	−	0.971054i	$-0.423226\pi$
$739$	−13.1211	−	7.57547i	−0.482668	−	0.278668i	−0.721528	+	0.692386i	$0.756560\pi$
$740$		0			0
$741$	−7.13178	+	27.5858i	−0.261992	+	1.01339i
$742$		0			0
$743$	16.5383	−	28.6451i	0.606730	−	1.05089i	−0.385045	−	0.922898i	$-0.625814\pi$
$743$	16.5383	−	28.6451i	0.606730	−	1.05089i	0.991775	−	0.127990i	$-0.0408525\pi$
$744$		0			0
$745$	−1.58656	−	2.74800i	−0.0581270	−	0.100679i
$746$		0			0
$747$	25.6820	−	14.8275i	0.939656	−	0.542511i
$748$		0			0
$749$		−	14.9159i		−	0.545015i
$750$		0			0
$751$	−4.25417	−	7.36844i	−0.155237	−	0.268878i	0.777908	−	0.628378i	$-0.216281\pi$
$751$	−4.25417	−	7.36844i	−0.155237	−	0.268878i	−0.933145	+	0.359500i	$0.882947\pi$
$752$		0			0
$753$	17.0208			0.620274
$754$		0			0
$755$	−5.85395	−	3.37978i	−0.213047	−	0.123003i
$756$		0			0
$757$	−23.1177	−	13.3470i	−0.840226	−	0.485105i	0.0171148	−	0.999854i	$-0.494552\pi$
$757$	−23.1177	−	13.3470i	−0.840226	−	0.485105i	−0.857341	+	0.514749i	$0.827885\pi$
$758$		0			0
$759$	22.2548			0.807798
$760$		0			0
$761$	−21.6462			−0.784673			−0.392336	−	0.919822i	$-0.628333\pi$
$761$	−21.6462			−0.784673			−0.392336	+	0.919822i	$0.628333\pi$
$762$		0			0
$763$	20.9525	+	12.0969i	0.758532	+	0.437938i
$764$		0			0
$765$	−20.6794	−	11.9393i	−0.747666	−	0.431665i
$766$		0			0
$767$	−1.14905			−0.0414896
$768$		0			0
$769$	−1.94332	−	3.36592i	−0.0700778	−	0.121378i	0.828857	−	0.559460i	$-0.188991\pi$
$769$	−1.94332	−	3.36592i	−0.0700778	−	0.121378i	−0.898935	+	0.438082i	$0.855658\pi$
$770$		0			0
$771$			13.9400i			0.502039i
$772$		0			0
$773$	27.7731	−	16.0348i	0.998930	−	0.576733i	0.0909986	−	0.995851i	$-0.470994\pi$
$773$	27.7731	−	16.0348i	0.998930	−	0.576733i	0.907932	+	0.419118i	$0.137661\pi$
$774$		0			0
$775$	−5.32245	−	9.21876i	−0.191188	−	0.331148i
$776$		0			0
$777$	52.2174	−	90.4431i	1.87329	−	3.24463i
$778$		0			0
$779$	15.1096	+	14.8457i	0.541357	+	0.531904i
$780$		0			0
$781$	27.4700	+	15.8598i	0.982952	+	0.567508i
$782$		0			0
$783$	−2.40956	−	4.17348i	−0.0861107	−	0.149148i
$784$		0			0
$785$	0.456700	+	0.791028i	0.0163003	+	0.0282330i
$786$		0			0
$787$		−	9.62592i		−	0.343127i	−0.985173	−	0.171564i	$-0.945118\pi$
$787$		−	9.62592i		−	0.343127i	0.985173	−	0.171564i	$-0.0548819\pi$
$788$		0			0
$789$	7.24122	−	4.18072i	0.257794	−	0.148838i
$790$		0			0
$791$	13.1241			0.466639
$792$		0			0
$793$	5.39222	−	9.33959i	0.191483	−	0.331659i
$794$		0			0
$795$	10.3793	+	5.99246i	0.368114	+	0.212531i
$796$		0			0
$797$			22.3299i			0.790967i	0.918473	+	0.395484i	$0.129423\pi$
$797$			22.3299i			0.790967i	−0.918473	+	0.395484i	$0.870577\pi$
$798$		0			0
$799$	40.0083			1.41539
$800$		0			0
$801$	−18.4578	+	31.9698i	−0.652173	+	1.12960i
$802$		0			0
$803$	3.02074	+	1.74402i	0.106599	+	0.0615452i
$804$		0			0
$805$		−	18.4928i		−	0.651785i
$806$		0			0
$807$	−32.7382	−	56.7043i	−1.15244	−	1.99608i
$808$		0			0
$809$	3.58584			0.126071			0.0630357	−	0.998011i	$-0.479922\pi$
$809$	3.58584			0.126071			0.0630357	+	0.998011i	$0.479922\pi$
$810$		0			0
$811$	−24.3179	+	14.0400i	−0.853918	+	0.493010i	−0.861971	−	0.506958i	$-0.830770\pi$
$811$	−24.3179	+	14.0400i	−0.853918	+	0.493010i	0.00805307	+	0.999968i	$0.497437\pi$
$812$		0			0
$813$	−48.0780	+	27.7578i	−1.68617	+	0.973510i
$814$		0			0
$815$	8.73635	−	15.1318i	0.306021	−	0.530044i
$816$		0			0
$817$	30.2319	−	30.7693i	1.05768	−	1.07648i
$818$		0			0
$819$	−31.2682	−	18.0527i	−1.09260	−	0.630812i
$820$		0			0
$821$	−35.3454	+	20.4067i	−1.23356	+	0.712198i	−0.967771	−	0.251833i	$-0.918967\pi$
$821$	−35.3454	+	20.4067i	−1.23356	+	0.712198i	−0.265792	+	0.964030i	$0.585633\pi$
$822$		0			0
$823$	−22.3858	−	38.7734i	−0.780320	−	1.35155i	−0.931755	−	0.363087i	$-0.881723\pi$
$823$	−22.3858	−	38.7734i	−0.780320	−	1.35155i	0.151435	−	0.988467i	$-0.451611\pi$
$824$		0			0
$825$	−20.4148			−0.710753
$826$		0			0
$827$	−37.4010	+	21.5935i	−1.30056	+	0.750879i	−0.980500	−	0.196518i	$-0.937037\pi$
$827$	−37.4010	+	21.5935i	−1.30056	+	0.750879i	−0.320061	+	0.947397i	$0.603703\pi$
$828$		0			0
$829$		−	2.69891i		−	0.0937369i	−0.998901	−	0.0468684i	$-0.985076\pi$
$829$		−	2.69891i		−	0.0937369i	0.998901	−	0.0468684i	$-0.0149242\pi$
$830$		0			0
$831$	22.5842	−	39.1170i	0.783438	−	1.35696i
$832$		0			0
$833$	−36.6132	+	63.4159i	−1.26857	+	2.19723i
$834$		0			0
$835$			14.5160i			0.502346i
$836$		0			0
$837$		−	2.17979i		−	0.0753444i
$838$		0			0
$839$	−12.8410	+	22.2412i	−0.443319	+	0.767851i	−0.997933	−	0.0642562i	$-0.979532\pi$
$839$	−12.8410	+	22.2412i	−0.443319	+	0.767851i	0.554614	+	0.832108i	$0.312866\pi$
$840$		0			0
$841$	3.34148	−	5.78761i	0.115223	−	0.199573i
$842$		0			0
$843$			69.8441i			2.40556i
$844$		0			0
$845$	−5.56461	+	3.21273i	−0.191428	+	0.110521i
$846$		0			0
$847$	−28.2347			−0.970155
$848$		0			0
$849$	18.0218	+	31.2147i	0.618507	+	1.07129i
$850$		0			0
$851$	36.9472	−	21.3315i	1.26653	−	0.731233i
$852$		0			0
$853$	12.1546	+	7.01743i	0.416164	+	0.240272i	0.693435	−	0.720519i	$-0.256097\pi$
$853$	12.1546	+	7.01743i	0.416164	+	0.240272i	−0.277271	+	0.960792i	$0.589430\pi$
$854$		0			0
$855$	14.4308	+	3.73081i	0.493523	+	0.127591i
$856$		0			0
$857$	6.39883	−	11.0831i	0.218580	−	0.378592i	−0.735794	−	0.677205i	$-0.763191\pi$
$857$	6.39883	−	11.0831i	0.218580	−	0.378592i	0.954374	+	0.298614i	$0.0965242\pi$
$858$		0			0
$859$	−16.1384	+	9.31752i	−0.550636	+	0.317910i	−0.749378	−	0.662142i	$-0.769648\pi$
$859$	−16.1384	+	9.31752i	−0.550636	+	0.317910i	0.198743	+	0.980052i	$0.436314\pi$
$860$		0			0
$861$	−44.2454	+	25.5451i	−1.50788	+	0.870574i
$862$		0			0
$863$	10.0423			0.341845			0.170923	−	0.985284i	$-0.445325\pi$
$863$	10.0423			0.341845			0.170923	+	0.985284i	$0.445325\pi$
$864$		0			0
$865$	9.42812	+	16.3300i	0.320566	+	0.555236i
$866$		0			0
$867$			79.8559i			2.71205i
$868$		0			0
$869$	21.9042	+	12.6464i	0.743048	+	0.428999i
$870$		0			0
$871$	1.60751	−	2.78430i	0.0544686	−	0.0943423i
$872$		0			0
$873$	27.3102			0.924311
$874$		0			0
$875$			38.4931i			1.30130i
$876$		0			0
$877$	18.3930	+	10.6192i	0.621087	+	0.358585i	0.777292	−	0.629140i	$-0.216593\pi$
$877$	18.3930	+	10.6192i	0.621087	+	0.358585i	−0.156205	+	0.987725i	$0.549926\pi$
$878$		0			0
$879$	31.2017	−	54.0430i	1.05241	−	1.82282i
$880$		0			0
$881$	−45.6834			−1.53911			−0.769556	−	0.638579i	$-0.779523\pi$
$881$	−45.6834			−1.53911			−0.769556	+	0.638579i	$0.779523\pi$
$882$		0			0
$883$	45.6602	−	26.3619i	1.53659	−	0.887150i	0.537554	−	0.843229i	$-0.319348\pi$
$883$	45.6602	−	26.3619i	1.53659	−	0.887150i	0.999035	−	0.0439207i	$-0.0139849\pi$
$884$		0			0
$885$			1.14411i			0.0384587i
$886$		0			0
$887$	−10.9489	−	18.9641i	−0.367630	−	0.636753i	0.621565	−	0.783363i	$-0.286497\pi$
$887$	−10.9489	−	18.9641i	−0.367630	−	0.636753i	−0.989194	+	0.146610i	$0.953164\pi$
$888$		0			0
$889$	−12.9439	−	22.4195i	−0.434125	−	0.751926i
$890$		0			0
$891$	14.1623	+	8.17663i	0.474456	+	0.273927i
$892$		0			0
$893$	−24.0648	+	6.67588i	−0.805299	+	0.223400i
$894$		0			0
$895$	−4.22087	+	7.31075i	−0.141088	+	0.244372i
$896$		0			0
$897$	−14.0369	−	24.3126i	−0.468679	−	0.811775i
$898$		0			0
$899$	13.9777	−	8.07006i	0.466184	−	0.269151i
$900$		0			0
$901$		−	32.3282i		−	1.07701i
$902$		0			0
$903$	52.0201	+	90.1015i	1.73112	+	2.99839i
$904$		0			0
$905$	17.3951			0.578233
$906$		0			0
$907$	21.2739	+	12.2825i	0.706388	+	0.407833i	0.809722	−	0.586813i	$-0.199618\pi$
$907$	21.2739	+	12.2825i	0.706388	+	0.407833i	−0.103334	+	0.994647i	$0.532951\pi$
$908$		0			0
$909$	1.29426	+	0.747241i	0.0429278	+	0.0247844i
$910$		0			0
$911$	20.3666			0.674774			0.337387	−	0.941366i	$-0.390457\pi$
$911$	20.3666			0.674774			0.337387	+	0.941366i	$0.390457\pi$
$912$		0			0
$913$	18.4050			0.609117
$914$		0			0
$915$	−9.29946	−	5.36904i	−0.307431	−	0.177495i
$916$		0			0
$917$	−67.4069	−	38.9174i	−2.22597	−	1.28517i
$918$		0			0
$919$	24.2670			0.800493			0.400247	−	0.916407i	$-0.368924\pi$
$919$	24.2670			0.800493			0.400247	+	0.916407i	$0.368924\pi$
$920$		0			0
$921$	35.0235	+	60.6624i	1.15406	+	1.99890i
$922$		0			0
$923$		−	40.0134i		−	1.31706i
$924$		0			0
$925$	−33.8925	+	19.5678i	−1.11438	+	0.643386i
$926$		0			0
$927$	14.9984	+	25.9780i	0.492612	+	0.853229i
$928$		0			0
$929$	−16.4937	+	28.5680i	−0.541141	+	0.937284i	0.457698	+	0.889108i	$0.348674\pi$
$929$	−16.4937	+	28.5680i	−0.541141	+	0.937284i	−0.998839	+	0.0481763i	$0.984659\pi$
$930$		0			0
$931$	11.4410	−	44.2538i	0.374963	−	1.45036i
$932$		0			0
$933$	−58.5990	−	33.8322i	−1.91845	−	1.10762i
$934$		0			0
$935$	−7.40994	−	12.8344i	−0.242331	−	0.419730i
$936$		0			0
$937$	4.93823	+	8.55326i	0.161325	+	0.279423i	0.935344	−	0.353739i	$-0.115090\pi$
$937$	4.93823	+	8.55326i	0.161325	+	0.279423i	−0.774019	+	0.633162i	$0.781757\pi$
$938$		0			0
$939$			7.77182i			0.253624i
$940$		0			0
$941$	38.1270	−	22.0126i	1.24290	−	0.717591i	0.273219	−	0.961952i	$-0.411912\pi$
$941$	38.1270	−	22.0126i	1.24290	−	0.717591i	0.969684	+	0.244361i	$0.0785782\pi$
$942$		0			0
$943$	−20.8710			−0.679653
$944$		0			0
$945$	−1.73687	+	3.00834i	−0.0565003	+	0.0978613i
$946$		0			0
$947$	−4.51898	−	2.60903i	−0.146847	−	0.0847821i	0.424776	−	0.905298i	$-0.360353\pi$
$947$	−4.51898	−	2.60903i	−0.146847	−	0.0847821i	−0.571623	+	0.820516i	$0.693686\pi$
$948$		0			0
$949$		−	4.40007i		−	0.142832i
$950$		0			0
$951$	5.72324			0.185589
$952$		0			0
$953$	14.7639	−	25.5718i	0.478250	−	0.828353i	−0.521439	−	0.853289i	$-0.674605\pi$
$953$	14.7639	−	25.5718i	0.478250	−	0.828353i	0.999689	+	0.0249352i	$0.00793795\pi$
$954$		0			0
$955$	−24.1367	−	13.9353i	−0.781046	−	0.450937i
$956$		0			0
$957$		−	30.9536i		−	1.00059i
$958$		0			0
$959$	−20.2499	−	35.0738i	−0.653903	−	1.13259i
$960$		0			0
$961$	−23.6995			−0.764500
$962$		0			0
$963$	−10.2585	+	5.92276i	−0.330576	+	0.190858i
$964$		0			0
$965$	−3.50040	+	2.02096i	−0.112682	+	0.0650568i
$966$		0			0
$967$	−16.0392	+	27.7806i	−0.515784	+	0.893365i	0.484048	+	0.875042i	$0.339166\pi$
$967$	−16.0392	+	27.7806i	−0.515784	+	0.893365i	−0.999832	+	0.0183232i	$0.994167\pi$
$968$		0			0
$969$	−20.4567	−	73.7413i	−0.657165	−	2.36891i
$970$		0			0
$971$	2.00632	+	1.15835i	0.0643857	+	0.0371731i	0.531847	−	0.846840i	$-0.321498\pi$
$971$	2.00632	+	1.15835i	0.0643857	+	0.0371731i	−0.467462	+	0.884013i	$0.654831\pi$
$972$		0			0
$973$	1.35341	−	0.781393i	0.0433884	−	0.0250503i
$974$		0			0
$975$	12.8764	+	22.3025i	0.412374	+	0.714253i
$976$		0			0
$977$	−4.52990			−0.144924			−0.0724622	−	0.997371i	$-0.523086\pi$
$977$	−4.52990			−0.144924			−0.0724622	+	0.997371i	$0.523086\pi$
$978$		0			0
$979$	−19.8416	+	11.4556i	−0.634141	+	0.366121i
$980$		0			0
$981$		−	19.2137i		−	0.613445i
$982$		0			0
$983$	−11.7795	+	20.4028i	−0.375709	+	0.650747i	−0.990433	−	0.137996i	$-0.955934\pi$
$983$	−11.7795	+	20.4028i	−0.375709	+	0.650747i	0.614724	+	0.788742i	$0.289267\pi$
$984$		0			0
$985$	11.8081	−	20.4523i	0.376238	−	0.651664i
$986$		0			0
$987$		−	60.2343i		−	1.91728i
$988$		0			0
$989$			42.5018i			1.35148i
$990$		0			0
$991$	−11.4343	+	19.8047i	−0.363221	+	0.629117i	−0.988489	−	0.151293i	$-0.951656\pi$
$991$	−11.4343	+	19.8047i	−0.363221	+	0.629117i	0.625268	+	0.780410i	$0.284990\pi$
$992$		0			0
$993$	11.4761	−	19.8771i	0.364182	−	0.630782i
$994$		0			0
$995$			21.9679i			0.696429i
$996$		0			0
$997$	−33.2525	+	19.1984i	−1.05312	+	0.608018i	−0.923521	−	0.383549i	$-0.874702\pi$
$997$	−33.2525	+	19.1984i	−1.05312	+	0.608018i	−0.129597	+	0.991567i	$0.541368\pi$
$998$		0			0
$999$	−8.01391			−0.253549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.t.d.353.1	✓	24
4.3	odd	2	inner	1216.2.t.d.353.11	yes	24
8.3	odd	2		1216.2.t.e.353.1	yes	24
8.5	even	2		1216.2.t.e.353.11	yes	24
19.7	even	3		1216.2.t.e.1185.11	yes	24
76.7	odd	6		1216.2.t.e.1185.1	yes	24
152.45	even	6	inner	1216.2.t.d.1185.1	yes	24
152.83	odd	6	inner	1216.2.t.d.1185.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.t.d.353.1	✓	24	1.1	even	1	trivial
1216.2.t.d.353.11	yes	24	4.3	odd	2	inner
1216.2.t.d.1185.1	yes	24	152.45	even	6	inner
1216.2.t.d.1185.11	yes	24	152.83	odd	6	inner
1216.2.t.e.353.1	yes	24	8.3	odd	2
1216.2.t.e.353.11	yes	24	8.5	even	2
1216.2.t.e.1185.1	yes	24	76.7	odd	6
1216.2.t.e.1185.11	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)

\(f(q)\)	\(=\)	\(q+(-2.17731 - 1.25707i) q^{3} +(0.891744 + 0.514849i) q^{5} -4.18166 q^{7} +(1.66044 + 2.87597i) q^{9} +O(q^{10})\)	\(q+(-2.17731 - 1.25707i) q^{3} +(0.891744 + 0.514849i) q^{5} -4.18166 q^{7} +(1.66044 + 2.87597i) q^{9} +2.06106i q^{11} +(2.25164 - 1.29999i) q^{13} +(-1.29440 - 2.24197i) q^{15} +(-3.49152 + 6.04748i) q^{17} +(1.09104 - 4.22015i) q^{19} +(9.10477 + 5.25664i) q^{21} +(2.14740 + 3.71941i) q^{23} +(-1.96986 - 3.41190i) q^{25} -0.806748i q^{27} +(5.17322 - 2.98676i) q^{29} +2.70194 q^{31} +(2.59090 - 4.48756i) q^{33} +(-3.72897 - 2.15292i) q^{35} -9.93361i q^{37} -6.53669 q^{39} +(-2.42979 + 4.20853i) q^{41} +(8.57026 + 4.94804i) q^{43} +3.41951i q^{45} +(-2.86468 - 4.96176i) q^{47} +10.4863 q^{49} +(15.2042 - 8.77815i) q^{51} +(-4.00929 + 2.31477i) q^{53} +(-1.06114 + 1.83794i) q^{55} +(-7.68054 + 7.81704i) q^{57} +(-0.382736 - 0.220973i) q^{59} +(3.59219 - 2.07395i) q^{61} +(-6.94341 - 12.0263i) q^{63} +2.67719 q^{65} +(1.07089 - 0.618281i) q^{67} -10.7977i q^{69} +(7.69496 - 13.3281i) q^{71} +(0.846177 - 1.46562i) q^{73} +9.90500i q^{75} -8.61867i q^{77} +(6.13586 - 10.6276i) q^{79} +(3.96719 - 6.87137i) q^{81} -8.92986i q^{83} +(-6.22708 + 3.59521i) q^{85} -15.0182 q^{87} +(5.55809 + 9.62689i) q^{89} +(-9.41562 + 5.43611i) q^{91} +(-5.88296 - 3.39653i) q^{93} +(3.14566 - 3.20157i) q^{95} +(4.11189 - 7.12200i) q^{97} +(-5.92755 + 3.42228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{5} + 8 q^{9}+O(q^{10}) \) 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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