LMFDB - Embedded newform 232.2.q.a.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,2,Mod(9,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("232.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	232.q (of order $14$, degree $6$, 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:	$1.85252932689$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	232.121
Dual form			232.2.q.a.209.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18604 + 0.270705i) q^{3} +(1.84749 + 2.31668i) q^{5} +(-0.161250 - 0.706484i) q^{7} +(-1.36950 + 0.659517i) q^{9} +O(q^{10})$	\(q+(-1.18604 + 0.270705i) q^{3} +(1.84749 + 2.31668i) q^{5} +(-0.161250 - 0.706484i) q^{7} +(-1.36950 + 0.659517i) q^{9} +(-1.22355 + 2.54073i) q^{11} +(3.17169 + 1.52740i) q^{13} +(-2.81833 - 2.24754i) q^{15} +4.89842i q^{17} +(3.80988 + 0.869580i) q^{19} +(0.382498 + 0.794266i) q^{21} +(-1.27957 + 1.60454i) q^{23} +(-0.841172 + 3.68541i) q^{25} +(4.29913 - 3.42844i) q^{27} +(1.02298 - 5.28711i) q^{29} +(-1.13218 + 0.902887i) q^{31} +(0.763388 - 3.34462i) q^{33} +(1.33879 - 1.67878i) q^{35} +(-1.92038 - 3.98772i) q^{37} +(-4.17522 - 0.952967i) q^{39} -6.63260i q^{41} +(-9.57251 - 7.63382i) q^{43} +(-4.05802 - 1.95424i) q^{45} +(-1.65877 + 3.44448i) q^{47} +(5.83366 - 2.80934i) q^{49} +(-1.32603 - 5.80971i) q^{51} +(2.21277 + 2.77473i) q^{53} +(-8.14653 + 1.85939i) q^{55} -4.75406 q^{57} +11.0729 q^{59} +(2.36693 - 0.540237i) q^{61} +(0.686771 + 0.861184i) q^{63} +(2.32115 + 10.1696i) q^{65} +(9.82946 - 4.73362i) q^{67} +(1.08327 - 2.24943i) q^{69} +(5.16682 + 2.48821i) q^{71} +(-12.5229 - 9.98665i) q^{73} -4.59875i q^{75} +(1.99228 + 0.454725i) q^{77} +(2.83014 + 5.87684i) q^{79} +(-1.32766 + 1.66484i) q^{81} +(-2.25710 + 9.88900i) q^{83} +(-11.3480 + 9.04976i) q^{85} +(0.217955 + 6.54764i) q^{87} +(5.08526 - 4.05536i) q^{89} +(0.567651 - 2.48704i) q^{91} +(1.09840 - 1.37735i) q^{93} +(5.02417 + 10.4328i) q^{95} +(2.88891 + 0.659375i) q^{97} -4.28648i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9	$ 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9} + 10 q^{13} + 14 q^{15} + 14 q^{21} + 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} + 8 q^{35} - 38 q^{45} - 14 q^{47} - 18 q^{49} - 56 q^{51} - 48 q^{53} - 28 q^{55} - 12 q^{57} - 128 q^{59} - 28 q^{61} + 42 q^{63} - 28 q^{65} - 4 q^{67} + 28 q^{69} - 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} + 80 q^{83} - 112 q^{87} + 42 q^{89} - 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) $ 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9 + 10 * q^13 + 14 * q^15 + 14 * q^21 + 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 + 8 * q^35 - 38 * q^45 - 14 * q^47 - 18 * q^49 - 56 * q^51 - 48 * q^53 - 28 * q^55 - 12 * q^57 - 128 * q^59 - 28 * q^61 + 42 * q^63 - 28 * q^65 - 4 * q^67 + 28 * q^69 - 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 + 80 * q^83 - 112 * q^87 + 42 * q^89 - 28 * q^91 + 6 * q^93 + 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{11}{14}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.18604	+	0.270705i	−0.684759	+	0.156292i	−0.550727	−	0.834685i	$-0.685650\pi$
$3$	−1.18604	+	0.270705i	−0.684759	+	0.156292i	−0.134032	+	0.990977i	$0.542792\pi$
$4$		0			0
$5$	1.84749	+	2.31668i	0.826221	+	1.03605i	0.998697	+	0.0510348i	$0.0162519\pi$
$5$	1.84749	+	2.31668i	0.826221	+	1.03605i	−0.172476	+	0.985014i	$0.555177\pi$
$6$		0			0
$7$	−0.161250	−	0.706484i	−0.0609469	−	0.267026i	0.935269	−	0.353937i	$-0.115157\pi$
$7$	−0.161250	−	0.706484i	−0.0609469	−	0.267026i	−0.996216	+	0.0869115i	$0.972300\pi$
$8$		0			0
$9$	−1.36950	+	0.659517i	−0.456501	+	0.219839i
$10$		0			0
$11$	−1.22355	+	2.54073i	−0.368914	+	0.766058i	−0.999953	−	0.00969294i	$-0.996915\pi$
$11$	−1.22355	+	2.54073i	−0.368914	+	0.766058i	0.631039	+	0.775751i	$0.282629\pi$
$12$		0			0
$13$	3.17169	+	1.52740i	0.879668	+	0.423626i	0.818503	−	0.574502i	$-0.194804\pi$
$13$	3.17169	+	1.52740i	0.879668	+	0.423626i	0.0611648	+	0.998128i	$0.480518\pi$
$14$		0			0
$15$	−2.81833	−	2.24754i	−0.727689	−	0.580312i
$16$		0			0
$17$			4.89842i			1.18804i	0.804450	+	0.594020i	$0.202460\pi$
$17$			4.89842i			1.18804i	−0.804450	+	0.594020i	$0.797540\pi$
$18$		0			0
$19$	3.80988	+	0.869580i	0.874046	+	0.199495i	0.635935	−	0.771743i	$-0.280615\pi$
$19$	3.80988	+	0.869580i	0.874046	+	0.199495i	0.238111	+	0.971238i	$0.423472\pi$
$20$		0			0
$21$	0.382498	+	0.794266i	0.0834679	+	0.173323i
$22$		0			0
$23$	−1.27957	+	1.60454i	−0.266810	+	0.334569i	−0.897130	−	0.441766i	$-0.854352\pi$
$23$	−1.27957	+	1.60454i	−0.266810	+	0.334569i	0.630320	+	0.776335i	$0.282923\pi$
$24$		0			0
$25$	−0.841172	+	3.68541i	−0.168234	+	0.737083i
$26$		0			0
$27$	4.29913	−	3.42844i	0.827368	−	0.659804i
$28$		0			0
$29$	1.02298	−	5.28711i	0.189963	−	0.981791i
$29$	1.02298	−	5.28711i	0.189963	−	0.981791i
$30$		0			0
$31$	−1.13218	+	0.902887i	−0.203346	+	0.162163i	−0.719868	−	0.694111i	$-0.755798\pi$
$31$	−1.13218	+	0.902887i	−0.203346	+	0.162163i	0.516522	+	0.856274i	$0.327226\pi$
$32$		0			0
$33$	0.763388	−	3.34462i	0.132889	−	0.582224i
$34$		0			0
$35$	1.33879	−	1.67878i	0.226296	−	0.283766i
$36$		0			0
$37$	−1.92038	−	3.98772i	−0.315709	−	0.655577i	0.681371	−	0.731938i	$-0.261384\pi$
$37$	−1.92038	−	3.98772i	−0.315709	−	0.655577i	−0.997080	+	0.0763612i	$0.975670\pi$
$38$		0			0
$39$	−4.17522	−	0.952967i	−0.668570	−	0.152597i
$40$		0			0
$41$		−	6.63260i		−	1.03584i	−0.855429	−	0.517919i	$-0.826707\pi$
$41$		−	6.63260i		−	1.03584i	0.855429	−	0.517919i	$-0.173293\pi$
$42$		0			0
$43$	−9.57251	−	7.63382i	−1.45979	−	1.16415i	−0.953348	−	0.301875i	$-0.902387\pi$
$43$	−9.57251	−	7.63382i	−1.45979	−	1.16415i	−0.506446	−	0.862272i	$-0.669041\pi$
$44$		0			0
$45$	−4.05802	−	1.95424i	−0.604934	−	0.291321i
$46$		0			0
$47$	−1.65877	+	3.44448i	−0.241957	+	0.502429i	−0.986216	−	0.165462i	$-0.947088\pi$
$47$	−1.65877	+	3.44448i	−0.241957	+	0.502429i	0.744259	+	0.667891i	$0.232803\pi$
$48$		0			0
$49$	5.83366	−	2.80934i	0.833381	−	0.401335i
$50$		0			0
$51$	−1.32603	−	5.80971i	−0.185681	−	0.813522i
$52$		0			0
$53$	2.21277	+	2.77473i	0.303948	+	0.381138i	0.910224	−	0.414116i	$-0.135909\pi$
$53$	2.21277	+	2.77473i	0.303948	+	0.381138i	−0.606277	+	0.795254i	$0.707338\pi$
$54$		0			0
$55$	−8.14653	+	1.85939i	−1.09848	+	0.250721i
$56$		0			0
$57$	−4.75406			−0.629691
$58$		0			0
$59$	11.0729			1.44157			0.720784	−	0.693160i	$-0.243782\pi$
$59$	11.0729			1.44157			0.720784	+	0.693160i	$0.243782\pi$
$60$		0			0
$61$	2.36693	−	0.540237i	0.303055	−	0.0691702i	−0.0682895	−	0.997666i	$-0.521754\pi$
$61$	2.36693	−	0.540237i	0.303055	−	0.0691702i	0.371344	+	0.928495i	$0.378897\pi$
$62$		0			0
$63$	0.686771	+	0.861184i	0.0865250	+	0.108499i
$64$		0			0
$65$	2.32115	+	10.1696i	0.287903	+	1.26139i
$66$		0			0
$67$	9.82946	−	4.73362i	1.20086	−	0.578304i	0.276939	−	0.960888i	$-0.410680\pi$
$67$	9.82946	−	4.73362i	1.20086	−	0.578304i	0.923921	+	0.382584i	$0.124966\pi$
$68$		0			0
$69$	1.08327	−	2.24943i	0.130410	−	0.270799i
$70$		0			0
$71$	5.16682	+	2.48821i	0.613189	+	0.295296i	0.714584	−	0.699550i	$-0.246616\pi$
$71$	5.16682	+	2.48821i	0.613189	+	0.295296i	−0.101395	+	0.994846i	$0.532330\pi$
$72$		0			0
$73$	−12.5229	−	9.98665i	−1.46569	−	1.16885i	−0.950072	−	0.312029i	$-0.898991\pi$
$73$	−12.5229	−	9.98665i	−1.46569	−	1.16885i	−0.515617	−	0.856819i	$-0.672437\pi$
$74$		0			0
$75$		−	4.59875i		−	0.531018i
$76$		0			0
$77$	1.99228	+	0.454725i	0.227042	+	0.0518208i
$78$		0			0
$79$	2.83014	+	5.87684i	0.318415	+	0.661196i	0.997330	−	0.0730206i	$-0.0232639\pi$
$79$	2.83014	+	5.87684i	0.318415	+	0.661196i	−0.678915	+	0.734217i	$0.737550\pi$
$80$		0			0
$81$	−1.32766	+	1.66484i	−0.147518	+	0.184982i
$82$		0			0
$83$	−2.25710	+	9.88900i	−0.247749	+	1.08546i	0.686020	+	0.727582i	$0.259356\pi$
$83$	−2.25710	+	9.88900i	−0.247749	+	1.08546i	−0.933769	+	0.357876i	$0.883501\pi$
$84$		0			0
$85$	−11.3480	+	9.04976i	−1.23087	+	0.981584i
$86$		0			0
$87$	0.217955	+	6.54764i	0.0233672	+	0.701980i
$88$		0			0
$89$	5.08526	−	4.05536i	0.539036	−	0.429867i	−0.315754	−	0.948841i	$-0.602257\pi$
$89$	5.08526	−	4.05536i	0.539036	−	0.429867i	0.854790	+	0.518974i	$0.173686\pi$
$90$		0			0
$91$	0.567651	−	2.48704i	0.0595060	−	0.260713i
$92$		0			0
$93$	1.09840	−	1.37735i	0.113899	−	0.142824i
$94$		0			0
$95$	5.02417	+	10.4328i	0.515468	+	1.07038i
$96$		0			0
$97$	2.88891	+	0.659375i	0.293324	+	0.0669494i	0.366651	−	0.930359i	$-0.380504\pi$
$97$	2.88891	+	0.659375i	0.293324	+	0.0669494i	−0.0733265	+	0.997308i	$0.523362\pi$
$98$		0			0
$99$		−	4.28648i		−	0.430808i
$100$		0			0
$101$	−3.45601	−	2.75608i	−0.343886	−	0.274240i	0.436282	−	0.899810i	$-0.356295\pi$
$101$	−3.45601	−	2.75608i	−0.343886	−	0.274240i	−0.780168	+	0.625570i	$0.784866\pi$
$102$		0			0
$103$	−13.6113	−	6.55485i	−1.34116	−	0.645869i	−0.380807	−	0.924655i	$-0.624354\pi$
$103$	−13.6113	−	6.55485i	−1.34116	−	0.645869i	−0.960353	+	0.278786i	$0.910068\pi$
$104$		0			0
$105$	−1.13340	+	2.35352i	−0.110608	+	0.229680i
$106$		0			0
$107$	13.5245	−	6.51305i	1.30746	−	0.629641i	0.355163	−	0.934805i	$-0.384426\pi$
$107$	13.5245	−	6.51305i	1.30746	−	0.629641i	0.952300	+	0.305164i	$0.0987112\pi$
$108$		0			0
$109$	−0.0382839	−	0.167733i	−0.00366693	−	0.0160659i	0.973061	−	0.230546i	$-0.0740513\pi$
$109$	−0.0382839	−	0.167733i	−0.00366693	−	0.0160659i	−0.976728	+	0.214480i	$0.931194\pi$
$110$		0			0
$111$	3.35715	+	4.20973i	0.318646	+	0.399570i
$112$		0			0
$113$	−10.7922	+	2.46324i	−1.01524	+	0.231722i	−0.697599	−	0.716488i	$-0.745748\pi$
$113$	−10.7922	+	2.46324i	−1.01524	+	0.231722i	−0.317643	+	0.948211i	$0.602891\pi$
$114$		0			0
$115$	−6.08118			−0.567073
$116$		0			0
$117$	−5.35098			−0.494699
$118$		0			0
$119$	3.46065	−	0.789872i	0.317238	−	0.0724074i
$120$		0			0
$121$	1.90016	+	2.38273i	0.172742	+	0.216612i
$122$		0			0
$123$	1.79548	+	7.86652i	0.161893	+	0.709300i
$124$		0			0
$125$	3.25652	−	1.56826i	0.291272	−	0.140269i
$126$		0			0
$127$	−5.78650	+	12.0158i	−0.513469	+	1.06623i	0.469581	+	0.882889i	$0.344405\pi$
$127$	−5.78650	+	12.0158i	−0.513469	+	1.06623i	−0.983050	+	0.183339i	$0.941309\pi$
$128$		0			0
$129$	13.4199	+	6.46267i	1.18155	+	0.569006i
$130$		0			0
$131$	13.7547	+	10.9690i	1.20175	+	0.958366i	0.999779	−	0.0210245i	$-0.00669279\pi$
$131$	13.7547	+	10.9690i	1.20175	+	0.958366i	0.201974	+	0.979391i	$0.435264\pi$
$132$		0			0
$133$		−	2.83184i		−	0.245552i
$134$		0			0
$135$	15.8852	+	3.62569i	1.36718	+	0.312050i
$136$		0			0
$137$	−2.72107	−	5.65036i	−0.232477	−	0.482743i	0.751797	−	0.659395i	$-0.229187\pi$
$137$	−2.72107	−	5.65036i	−0.232477	−	0.482743i	−0.984273	+	0.176652i	$0.943473\pi$
$138$		0			0
$139$	5.72668	−	7.18103i	0.485731	−	0.609087i	−0.477214	−	0.878787i	$-0.658353\pi$
$139$	5.72668	−	7.18103i	0.485731	−	0.609087i	0.962944	+	0.269700i	$0.0869246\pi$
$140$		0			0
$141$	1.03493	−	4.53432i	0.0871567	−	0.381859i
$142$		0			0
$143$	−7.76144	+	6.18954i	−0.649044	+	0.517596i
$144$		0			0
$145$	14.1385	−	7.39795i	1.17413	−	0.614366i
$146$		0			0
$147$	−6.15844	+	4.91119i	−0.507940	+	0.405068i
$148$		0			0
$149$	−5.27767	+	23.1230i	−0.432363	+	1.89431i	0.0148685	+	0.999889i	$0.495267\pi$
$149$	−5.27767	+	23.1230i	−0.432363	+	1.89431i	−0.447232	+	0.894418i	$0.647590\pi$
$150$		0			0
$151$	−5.05791	+	6.34241i	−0.411607	+	0.516138i	−0.943815	−	0.330475i	$-0.892791\pi$
$151$	−5.05791	+	6.34241i	−0.411607	+	0.516138i	0.532208	+	0.846614i	$0.321362\pi$
$152$		0			0
$153$	−3.23059	−	6.70839i	−0.261178	−	0.542341i
$154$		0			0
$155$	−4.18339	−	0.954832i	−0.336018	−	0.0766939i
$156$		0			0
$157$			1.65786i			0.132312i	0.997809	+	0.0661559i	$0.0210735\pi$
$157$			1.65786i			0.132312i	−0.997809	+	0.0661559i	$0.978927\pi$
$158$		0			0
$159$	−3.37557	−	2.69192i	−0.267700	−	0.213483i
$160$		0			0
$161$	1.33991	+	0.645267i	0.105600	+	0.0508542i
$162$		0			0
$163$	0.522746	−	1.08549i	0.0409446	−	0.0850224i	−0.879493	−	0.475912i	$-0.842118\pi$
$163$	0.522746	−	1.08549i	0.0409446	−	0.0850224i	0.920438	+	0.390889i	$0.127832\pi$
$164$		0			0
$165$	9.15875	−	4.41062i	0.713008	−	0.343366i
$166$		0			0
$167$	−3.89624	−	17.0706i	−0.301500	−	1.32096i	−0.867863	−	0.496803i	$-0.834507\pi$
$167$	−3.89624	−	17.0706i	−0.301500	−	1.32096i	0.566363	−	0.824156i	$-0.308350\pi$
$168$		0			0
$169$	−0.378725	−	0.474906i	−0.0291327	−	0.0365312i
$170$		0			0
$171$	−5.79114	+	1.32179i	−0.442859	+	0.101080i
$172$		0			0
$173$	−23.7453			−1.80532			−0.902661	−	0.430351i	$-0.858390\pi$
$173$	−23.7453			−1.80532			−0.902661	+	0.430351i	$0.858390\pi$
$174$		0			0
$175$	2.73933			0.207074
$176$		0			0
$177$	−13.1329	+	2.99749i	−0.987127	+	0.225305i
$178$		0			0
$179$	14.5274	+	18.2168i	1.08583	+	1.36159i	0.927336	+	0.374229i	$0.122093\pi$
$179$	14.5274	+	18.2168i	1.08583	+	1.36159i	0.158495	+	0.987360i	$0.449336\pi$
$180$		0			0
$181$	0.923443	+	4.04587i	0.0686390	+	0.300727i	0.997582	−	0.0694949i	$-0.0221388\pi$
$181$	0.923443	+	4.04587i	0.0686390	+	0.300727i	−0.928943	+	0.370222i	$0.879282\pi$
$182$		0			0
$183$	−2.66103	+	1.28148i	−0.196709	+	0.0947299i
$184$		0			0
$185$	5.69037	−	11.8162i	0.418364	−	0.868742i
$186$		0			0
$187$	−12.4455	−	5.99346i	−0.910109	−	0.438285i
$188$		0			0
$189$	−3.11538	−	2.48443i	−0.226610	−	0.180716i
$190$		0			0
$191$		−	15.2057i		−	1.10025i	−0.835084	−	0.550123i	$-0.814581\pi$
$191$		−	15.2057i		−	1.10025i	0.835084	−	0.550123i	$-0.185419\pi$
$192$		0			0
$193$	18.1816	+	4.14983i	1.30874	+	0.298711i	0.819319	−	0.573337i	$-0.194352\pi$
$193$	18.1816	+	4.14983i	1.30874	+	0.298711i	0.489419	+	0.872049i	$0.337209\pi$
$194$		0			0
$195$	−5.50595	−	11.4332i	−0.394289	−	0.818750i
$196$		0			0
$197$	4.33808	−	5.43978i	0.309075	−	0.387568i	−0.602898	−	0.797819i	$-0.705987\pi$
$197$	4.33808	−	5.43978i	0.309075	−	0.387568i	0.911973	+	0.410250i	$0.134559\pi$
$198$		0			0
$199$	0.623047	−	2.72975i	0.0441666	−	0.193507i	−0.948032	−	0.318176i	$-0.896930\pi$
$199$	0.623047	−	2.72975i	0.0441666	−	0.193507i	0.992198	+	0.124669i	$0.0397869\pi$
$200$		0			0
$201$	−10.3767	+	8.27514i	−0.731916	+	0.583683i
$202$		0			0
$203$	−3.90021	+	0.129829i	−0.273741	+	0.00911218i
$204$		0			0
$205$	15.3656	−	12.2536i	1.07318	−	0.855832i
$206$		0			0
$207$	0.694161	−	3.04132i	0.0482475	−	0.211386i
$208$		0			0
$209$	−6.87094	+	8.61589i	−0.475273	+	0.595974i
$210$		0			0
$211$	−11.0820	−	23.0121i	−0.762919	−	1.58422i	−0.810772	−	0.585363i	$-0.800952\pi$
$211$	−11.0820	−	23.0121i	−0.762919	−	1.58422i	0.0478528	−	0.998854i	$-0.484762\pi$
$212$		0			0
$213$	−6.80162	−	1.55243i	−0.466039	−	0.106370i
$214$		0			0
$215$		−	36.2798i		−	2.47426i
$216$		0			0
$217$	0.820441	+	0.654280i	0.0556951	+	0.0444154i
$218$		0			0
$219$	17.5560	+	8.45454i	1.18633	+	0.571305i
$220$		0			0
$221$	−7.48187	+	15.5363i	−0.503285	+	1.04508i
$222$		0			0
$223$	−6.89915	+	3.32246i	−0.462002	+	0.222488i	−0.650381	−	0.759608i	$-0.725391\pi$
$223$	−6.89915	+	3.32246i	−0.462002	+	0.222488i	0.188380	+	0.982096i	$0.439676\pi$
$224$		0			0
$225$	−1.27861	−	5.60195i	−0.0852405	−	0.373463i
$226$		0			0
$227$	2.08040	+	2.60874i	0.138081	+	0.173148i	0.846064	−	0.533081i	$-0.178966\pi$
$227$	2.08040	+	2.60874i	0.138081	+	0.173148i	−0.707983	+	0.706230i	$0.750395\pi$
$228$		0			0
$229$	25.7547	−	5.87834i	1.70192	−	0.388451i	0.742368	−	0.669993i	$-0.233703\pi$
$229$	25.7547	−	5.87834i	1.70192	−	0.388451i	0.959549	+	0.281541i	$0.0908457\pi$
$230$		0			0
$231$	−2.48602			−0.163568
$232$		0			0
$233$	11.1059			0.727574			0.363787	−	0.931482i	$-0.381484\pi$
$233$	11.1059			0.727574			0.363787	+	0.931482i	$0.381484\pi$
$234$		0			0
$235$	−11.0443	+	2.52079i	−0.720450	+	0.164438i
$236$		0			0
$237$	−4.94754	−	6.20402i	−0.321377	−	0.402995i
$238$		0			0
$239$	−5.18885	−	22.7339i	−0.335639	−	1.47053i	−0.808030	−	0.589142i	$-0.799466\pi$
$239$	−5.18885	−	22.7339i	−0.335639	−	1.47053i	0.472391	−	0.881389i	$-0.343391\pi$
$240$		0			0
$241$	1.65248	−	0.795790i	0.106445	−	0.0512614i	−0.379903	−	0.925026i	$-0.624043\pi$
$241$	1.65248	−	0.795790i	0.106445	−	0.0512614i	0.486349	+	0.873765i	$0.338328\pi$
$242$		0			0
$243$	−6.03354	+	12.5288i	−0.387052	+	0.803721i
$244$		0			0
$245$	17.2860	+	8.32448i	1.10436	+	0.531831i
$246$		0			0
$247$	10.7555	+	8.57726i	0.684359	+	0.545758i
$248$		0			0
$249$		−	12.3397i		−	0.781999i
$250$		0			0
$251$	−9.33943	−	2.13166i	−0.589500	−	0.134549i	−0.0826421	−	0.996579i	$-0.526336\pi$
$251$	−9.33943	−	2.13166i	−0.589500	−	0.134549i	−0.506857	+	0.862030i	$0.669193\pi$
$252$		0			0
$253$	−2.51107	−	5.21428i	−0.157869	−	0.327819i
$254$		0			0
$255$	11.0094	−	13.8053i	0.689435	−	0.864524i
$256$		0			0
$257$	−0.806692	+	3.53435i	−0.0503200	+	0.220467i	−0.993836	−	0.110861i	$-0.964639\pi$
$257$	−0.806692	+	3.53435i	−0.0503200	+	0.220467i	0.943516	+	0.331327i	$0.107496\pi$
$258$		0			0
$259$	−2.50760	+	1.99974i	−0.155815	+	0.124258i
$260$		0			0
$261$	2.08597	+	7.91538i	0.129118	+	0.489950i
$262$		0			0
$263$	−9.44179	+	7.52958i	−0.582206	+	0.464294i	−0.869763	−	0.493470i	$-0.835728\pi$
$263$	−9.44179	+	7.52958i	−0.582206	+	0.464294i	0.287557	+	0.957763i	$0.407157\pi$
$264$		0			0
$265$	−2.34008	+	10.2525i	−0.143750	+	0.629809i
$266$		0			0
$267$	−4.93350	+	6.18641i	−0.301925	+	0.378602i
$268$		0			0
$269$	−8.54750	−	17.7491i	−0.521151	−	1.08218i	−0.980968	−	0.194167i	$-0.937800\pi$
$269$	−8.54750	−	17.7491i	−0.521151	−	1.08218i	0.459818	−	0.888013i	$-0.347915\pi$
$270$		0			0
$271$	−30.9096	−	7.05491i	−1.87762	−	0.428556i	−0.878807	−	0.477177i	$-0.841660\pi$
$271$	−30.9096	−	7.05491i	−1.87762	−	0.428556i	−0.998817	+	0.0486215i	$0.984517\pi$
$272$		0			0
$273$			3.10339i			0.187826i
$274$		0			0
$275$	−8.33442	−	6.64648i	−0.502584	−	0.400798i
$276$		0			0
$277$	17.7140	+	8.53060i	1.06433	+	0.512554i	0.882275	−	0.470734i	$-0.156011\pi$
$277$	17.7140	+	8.53060i	1.06433	+	0.512554i	0.182055	+	0.983288i	$0.441725\pi$
$278$		0			0
$279$	0.955059	−	1.98320i	0.0571779	−	0.118731i
$280$		0			0
$281$	−6.38898	+	3.07677i	−0.381135	+	0.183545i	−0.614635	−	0.788812i	$-0.710697\pi$
$281$	−6.38898	+	3.07677i	−0.381135	+	0.183545i	0.233500	+	0.972357i	$0.424982\pi$
$282$		0			0
$283$	−0.804064	−	3.52283i	−0.0477966	−	0.209411i	0.945391	−	0.325939i	$-0.105680\pi$
$283$	−0.804064	−	3.52283i	−0.0477966	−	0.209411i	−0.993187	+	0.116529i	$0.962823\pi$
$284$		0			0
$285$	−8.78306	−	11.0136i	−0.520264	−	0.652390i
$286$		0			0
$287$	−4.68583	+	1.06951i	−0.276596	+	0.0631312i
$288$		0			0
$289$	−6.99449			−0.411441
$290$		0			0
$291$	−3.60485			−0.211320
$292$		0			0
$293$	21.0660	−	4.80817i	1.23069	−	0.280897i	0.442747	−	0.896647i	$-0.354004\pi$
$293$	21.0660	−	4.80817i	1.23069	−	0.280897i	0.787941	+	0.615750i	$0.211147\pi$
$294$		0			0
$295$	20.4570	+	25.6523i	1.19105	+	1.49353i
$296$		0			0
$297$	3.45054	+	15.1178i	0.200221	+	0.877224i
$298$		0			0
$299$	−6.50919	+	3.13466i	−0.376436	+	0.181282i
$300$		0			0
$301$	−3.84960	+	7.99378i	−0.221887	+	0.460754i
$302$		0			0
$303$	4.84505	+	2.33325i	0.278341	+	0.134042i
$304$		0			0
$305$	5.62443	+	4.48533i	0.322054	+	0.256829i
$306$		0			0
$307$		−	22.3962i		−	1.27822i	−0.769116	−	0.639109i	$-0.779303\pi$
$307$		−	22.3962i		−	1.27822i	0.769116	−	0.639109i	$-0.220697\pi$
$308$		0			0
$309$	17.9179	+	4.08965i	1.01932	+	0.232652i
$310$		0			0
$311$	10.0436	+	20.8558i	0.569521	+	1.18262i	0.964537	+	0.263948i	$0.0850246\pi$
$311$	10.0436	+	20.8558i	0.569521	+	1.18262i	−0.395016	+	0.918674i	$0.629261\pi$
$312$		0			0
$313$	10.1241	−	12.6952i	0.572246	−	0.717574i	−0.408523	−	0.912748i	$-0.633956\pi$
$313$	10.1241	−	12.6952i	0.572246	−	0.717574i	0.980769	+	0.195175i	$0.0625273\pi$
$314$		0			0
$315$	−0.726282	+	3.18205i	−0.0409214	+	0.179288i
$316$		0			0
$317$	−19.9730	+	15.9279i	−1.12180	+	0.894602i	−0.995249	−	0.0973583i	$-0.968961\pi$
$317$	−19.9730	+	15.9279i	−1.12180	+	0.894602i	−0.126546	+	0.991961i	$0.540389\pi$
$318$		0			0
$319$	12.1814	+	9.06816i	0.682029	+	0.507719i
$320$		0			0
$321$	−14.2774	+	11.3859i	−0.796889	+	0.635498i
$322$		0			0
$323$	−4.25956	+	18.6624i	−0.237009	+	1.03840i
$324$		0			0
$325$	−8.29705	+	10.4042i	−0.460238	+	0.577120i
$326$		0			0
$327$	0.0908124	+	0.188574i	0.00502193	+	0.0104282i
$328$		0			0
$329$	2.70095	+	0.616473i	0.148908	+	0.0339873i
$330$		0			0
$331$			10.1111i			0.555755i	0.960617	+	0.277877i	$0.0896309\pi$
$331$			10.1111i			0.555755i	−0.960617	+	0.277877i	$0.910369\pi$
$332$		0			0
$333$	5.25994	+	4.19466i	0.288243	+	0.229866i
$334$		0			0
$335$	29.1261	+	14.0264i	1.59133	+	0.766342i
$336$		0			0
$337$	−8.74139	+	18.1517i	−0.476174	+	0.988785i	0.515120	+	0.857118i	$0.327747\pi$
$337$	−8.74139	+	18.1517i	−0.476174	+	0.988785i	−0.991294	+	0.131667i	$0.957967\pi$
$338$		0			0
$339$	12.1331	−	5.84300i	0.658980	−	0.317348i
$340$		0			0
$341$	−0.908706	−	3.98130i	−0.0492092	−	0.215600i
$342$		0			0
$343$	−6.08813	−	7.63428i	−0.328728	−	0.412212i
$344$		0			0
$345$	7.21252	−	1.64621i	0.388309	−	0.0886290i
$346$		0			0
$347$	−17.8444			−0.957938			−0.478969	−	0.877832i	$-0.658989\pi$
$347$	−17.8444			−0.957938			−0.478969	+	0.877832i	$0.658989\pi$
$348$		0			0
$349$	−7.19398			−0.385085			−0.192543	−	0.981289i	$-0.561673\pi$
$349$	−7.19398			−0.385085			−0.192543	+	0.981289i	$0.561673\pi$
$350$		0			0
$351$	18.8721	−	4.30744i	1.00732	−	0.229914i
$352$		0			0
$353$	−12.0858	−	15.1551i	−0.643260	−	0.806623i	0.348146	−	0.937440i	$-0.386811\pi$
$353$	−12.0858	−	15.1551i	−0.643260	−	0.806623i	−0.991407	+	0.130817i	$0.958240\pi$
$354$		0			0
$355$	3.78126	+	16.5668i	0.200688	+	0.879274i
$356$		0			0
$357$	−3.89064	+	1.87364i	−0.205915	+	0.0991633i
$358$		0			0
$359$	1.44636	−	3.00339i	0.0763358	−	0.158513i	−0.859308	−	0.511458i	$-0.829106\pi$
$359$	1.44636	−	3.00339i	0.0763358	−	0.158513i	0.935644	+	0.352945i	$0.114820\pi$
$360$		0			0
$361$	−3.35941	−	1.61780i	−0.176811	−	0.0851476i
$362$		0			0
$363$	−2.89868	−	2.31162i	−0.152141	−	0.121329i
$364$		0			0
$365$		−	47.4616i		−	2.48425i
$366$		0			0
$367$	32.9680	+	7.52474i	1.72092	+	0.392788i	0.965077	−	0.261968i	$-0.0843714\pi$
$367$	32.9680	+	7.52474i	1.72092	+	0.392788i	0.755840	+	0.654756i	$0.227229\pi$
$368$		0			0
$369$	4.37432	+	9.08336i	0.227718	+	0.472861i
$370$		0			0
$371$	1.60349	−	2.01071i	0.0832491	−	0.104391i
$372$		0			0
$373$	−8.33564	+	36.5208i	−0.431603	+	1.89098i	0.0219744	+	0.999759i	$0.493005\pi$
$373$	−8.33564	+	36.5208i	−0.431603	+	1.89098i	−0.453577	+	0.891217i	$0.649852\pi$
$374$		0			0
$375$	−3.43782	+	2.74157i	−0.177528	+	0.141574i
$376$		0			0
$377$	11.3201	−	15.2066i	0.583016	−	0.783177i
$378$		0			0
$379$	9.74439	−	7.77089i	0.500535	−	0.399164i	−0.340415	−	0.940275i	$-0.610568\pi$
$379$	9.74439	−	7.77089i	0.500535	−	0.399164i	0.840951	+	0.541111i	$0.181996\pi$
$380$		0			0
$381$	3.61027	−	15.8176i	0.184960	−	0.810361i
$382$		0			0
$383$	−5.70818	+	7.15783i	−0.291674	+	0.365748i	−0.905980	−	0.423320i	$-0.860865\pi$
$383$	−5.70818	+	7.15783i	−0.291674	+	0.365748i	0.614306	+	0.789068i	$0.289436\pi$
$384$		0			0
$385$	2.62726	+	5.45557i	0.133898	+	0.278042i
$386$		0			0
$387$	18.1442	+	4.14130i	0.922322	+	0.210514i
$388$		0			0
$389$			14.6428i			0.742417i	0.928549	+	0.371209i	$0.121057\pi$
$389$			14.6428i			0.742417i	−0.928549	+	0.371209i	$0.878943\pi$
$390$		0			0
$391$	−7.85968	−	6.26789i	−0.397481	−	0.316981i
$392$		0			0
$393$	−19.2830	−	9.28618i	−0.972697	−	0.468426i
$394$		0			0
$395$	−8.38609	+	17.4139i	−0.421950	+	0.876188i
$396$		0			0
$397$	−1.83610	+	0.884217i	−0.0921510	+	0.0443776i	−0.479392	−	0.877601i	$-0.659143\pi$
$397$	−1.83610	+	0.884217i	−0.0921510	+	0.0443776i	0.387240	+	0.921979i	$0.373428\pi$
$398$		0			0
$399$	0.766594	+	3.35867i	0.0383777	+	0.168144i
$400$		0			0
$401$	−11.6940	−	14.6638i	−0.583972	−	0.732277i	0.398813	−	0.917032i	$-0.369422\pi$
$401$	−11.6940	−	14.6638i	−0.583972	−	0.732277i	−0.982785	+	0.184755i	$0.940851\pi$
$402$		0			0
$403$	−4.97001	+	1.13437i	−0.247574	+	0.0565071i
$404$		0			0
$405$	−6.30972			−0.313533
$406$		0			0
$407$	12.4814			0.618680
$408$		0			0
$409$	11.6171	−	2.65153i	0.574430	−	0.131110i	0.0745695	−	0.997216i	$-0.476242\pi$
$409$	11.6171	−	2.65153i	0.574430	−	0.131110i	0.499861	+	0.866106i	$0.333385\pi$
$410$		0			0
$411$	4.75687	+	5.96493i	0.234639	+	0.294228i
$412$		0			0
$413$	−1.78551	−	7.82282i	−0.0878591	−	0.384936i
$414$		0			0
$415$	−27.0796	+	13.0408i	−1.32928	+	0.640149i
$416$		0			0
$417$	−4.84812	+	10.0672i	−0.237413	+	0.492994i
$418$		0			0
$419$	−11.8835	−	5.72278i	−0.580546	−	0.279576i	0.120476	−	0.992716i	$-0.461558\pi$
$419$	−11.8835	−	5.72278i	−0.580546	−	0.279576i	−0.701021	+	0.713140i	$0.747272\pi$
$420$		0			0
$421$	−12.1448	−	9.68512i	−0.591899	−	0.472024i	0.281145	−	0.959665i	$-0.409286\pi$
$421$	−12.1448	−	9.68512i	−0.591899	−	0.472024i	−0.873044	+	0.487642i	$0.837857\pi$
$422$		0			0
$423$		−	5.81121i		−	0.282551i
$424$		0			0
$425$	−18.0527	−	4.12041i	−0.875684	−	0.199869i
$426$		0			0
$427$	−0.763337	−	1.58509i	−0.0369405	−	0.0767077i
$428$		0			0
$429$	7.52982	−	9.44210i	0.363543	−	0.455869i
$430$		0			0
$431$	8.31072	−	36.4116i	0.400313	−	1.75389i	−0.225818	−	0.974169i	$-0.572506\pi$
$431$	8.31072	−	36.4116i	0.400313	−	1.75389i	0.626131	−	0.779718i	$-0.284637\pi$
$432$		0			0
$433$	−18.1813	+	14.4991i	−0.873739	+	0.696784i	−0.953941	−	0.299995i	$-0.903015\pi$
$433$	−18.1813	+	14.4991i	−0.873739	+	0.696784i	0.0802018	+	0.996779i	$0.474444\pi$
$434$		0			0
$435$	−14.7661	+	12.6016i	−0.707979	+	0.604201i
$436$		0			0
$437$	−6.27029	+	5.00039i	−0.299949	+	0.239201i
$438$		0			0
$439$	5.08084	−	22.2606i	0.242495	−	1.06244i	−0.696242	−	0.717807i	$-0.745146\pi$
$439$	5.08084	−	22.2606i	0.242495	−	1.06244i	0.938737	−	0.344634i	$-0.111997\pi$
$440$		0			0
$441$	−6.13640	+	7.69481i	−0.292210	+	0.366419i
$442$		0			0
$443$	0.245308	+	0.509388i	0.0116550	+	0.0242018i	0.906715	−	0.421744i	$-0.138582\pi$
$443$	0.245308	+	0.509388i	0.0116550	+	0.0242018i	−0.895060	+	0.445945i	$0.852868\pi$
$444$		0			0
$445$	18.7899	+	4.28867i	0.890726	+	0.203302i
$446$		0			0
$447$		−	28.8534i		−	1.36472i
$448$		0			0
$449$	23.4023	+	18.6627i	1.10442	+	0.880746i	0.993584	−	0.113093i	$-0.0360757\pi$
$449$	23.4023	+	18.6627i	1.10442	+	0.880746i	0.110836	+	0.993839i	$0.464647\pi$
$450$		0			0
$451$	16.8516	+	8.11532i	0.793513	+	0.382136i
$452$		0			0
$453$	4.28194	−	8.89155i	0.201183	−	0.417761i
$454$		0			0
$455$	6.81040	−	3.27971i	0.319276	−	0.153755i
$456$		0			0
$457$	−5.85881	−	25.6691i	−0.274063	−	1.20075i	−0.905168	−	0.425053i	$-0.860255\pi$
$457$	−5.85881	−	25.6691i	−0.274063	−	1.20075i	0.631105	−	0.775697i	$-0.282602\pi$
$458$		0			0
$459$	16.7939	+	21.0589i	0.783874	+	0.982947i
$460$		0			0
$461$	−4.06162	+	0.927038i	−0.189168	+	0.0431765i	−0.316055	−	0.948741i	$-0.602359\pi$
$461$	−4.06162	+	0.927038i	−0.189168	+	0.0431765i	0.126887	+	0.991917i	$0.459501\pi$
$462$		0			0
$463$	3.39217			0.157648			0.0788239	−	0.996889i	$-0.474884\pi$
$463$	3.39217			0.157648			0.0788239	+	0.996889i	$0.474884\pi$
$464$		0			0
$465$	5.22014			0.242078
$466$		0			0
$467$	−30.1904	+	6.89076i	−1.39704	+	0.318866i	−0.853753	−	0.520678i	$-0.825679\pi$
$467$	−30.1904	+	6.89076i	−1.39704	+	0.318866i	−0.543291	+	0.839544i	$0.682822\pi$
$468$		0			0
$469$	−4.92923	−	6.18106i	−0.227611	−	0.285415i
$470$		0			0
$471$	−0.448792	−	1.96629i	−0.0206793	−	0.0906017i
$472$		0			0
$473$	31.1079	−	14.9808i	1.43034	−	0.688817i
$474$		0			0
$475$	−6.40952	+	13.3095i	−0.294089	+	0.610682i
$476$		0			0
$477$	−4.86038	−	2.34063i	−0.222541	−	0.107170i
$478$		0			0
$479$	7.50897	+	5.98820i	0.343094	+	0.273608i	0.779843	−	0.625975i	$-0.215299\pi$
$479$	7.50897	+	5.98820i	0.343094	+	0.273608i	−0.436749	+	0.899583i	$0.643870\pi$
$480$		0			0
$481$		−	15.5810i		−	0.710433i
$482$		0			0
$483$	−1.76386	−	0.402590i	−0.0802585	−	0.0183185i
$484$		0			0
$485$	3.80966	+	7.91085i	0.172988	+	0.359213i
$486$		0			0
$487$	−16.3438	+	20.4944i	−0.740607	+	0.928692i	−0.999305	−	0.0372663i	$-0.988135\pi$
$487$	−16.3438	+	20.4944i	−0.740607	+	0.928692i	0.258698	+	0.965958i	$0.416706\pi$
$488$		0			0
$489$	−0.326148	+	1.42895i	−0.0147489	+	0.0646192i
$490$		0			0
$491$	11.7516	−	9.37162i	0.530344	−	0.422935i	−0.321361	−	0.946957i	$-0.604140\pi$
$491$	11.7516	−	9.37162i	0.530344	−	0.422935i	0.851705	+	0.524022i	$0.175569\pi$
$492$		0			0
$493$	25.8985	+	5.01099i	1.16641	+	0.225683i
$494$		0			0
$495$	9.93039	−	7.91922i	0.446338	−	0.355943i
$496$		0			0
$497$	0.924729	−	4.05150i	0.0414798	−	0.181735i
$498$		0			0
$499$	−5.34886	+	6.70725i	−0.239448	+	0.300258i	−0.887006	−	0.461758i	$-0.847219\pi$
$499$	−5.34886	+	6.70725i	−0.239448	+	0.300258i	0.647558	+	0.762016i	$0.275790\pi$
$500$		0			0
$501$	9.24218	+	19.1916i	0.412910	+	0.857417i
$502$		0			0
$503$	−20.3227	−	4.63853i	−0.906145	−	0.206822i	−0.256040	−	0.966666i	$-0.582418\pi$
$503$	−20.3227	−	4.63853i	−0.906145	−	0.206822i	−0.650105	+	0.759844i	$0.725275\pi$
$504$		0			0
$505$		−	13.0983i		−	0.582866i
$506$		0			0
$507$	0.577741	+	0.460733i	0.0256584	+	0.0204619i
$508$		0			0
$509$	−33.7769	−	16.2661i	−1.49713	−	0.720982i	−0.507110	−	0.861881i	$-0.669286\pi$
$509$	−33.7769	−	16.2661i	−1.49713	−	0.720982i	−0.990024	+	0.140900i	$0.955001\pi$
$510$		0			0
$511$	−5.03609	+	10.4575i	−0.222784	+	0.462615i
$512$		0			0
$513$	19.3605	−	9.32351i	0.854786	−	0.411643i
$514$		0			0
$515$	−9.96122	−	43.6429i	−0.438944	−	1.92314i
$516$		0			0
$517$	−6.72189	−	8.42898i	−0.295628	−	0.370706i
$518$		0			0
$519$	28.1628	−	6.42799i	1.23621	−	0.282157i
$520$		0			0
$521$	−38.5983			−1.69102			−0.845512	−	0.533957i	$-0.820704\pi$
$521$	−38.5983			−1.69102			−0.845512	+	0.533957i	$0.820704\pi$
$522$		0			0
$523$	−6.47374			−0.283077			−0.141538	−	0.989933i	$-0.545205\pi$
$523$	−6.47374			−0.283077			−0.141538	+	0.989933i	$0.545205\pi$
$524$		0			0
$525$	−3.24894	+	0.741550i	−0.141796	+	0.0323639i
$526$		0			0
$527$	−4.42272	−	5.54591i	−0.192657	−	0.241584i
$528$		0			0
$529$	4.18076	+	18.3171i	0.181772	+	0.796395i
$530$		0			0
$531$	−15.1643	+	7.30277i	−0.658077	+	0.316913i
$532$		0			0
$533$	10.1307	−	21.0366i	0.438808	−	0.911194i
$534$		0			0
$535$	40.0750	+	19.2991i	1.73259	+	0.834372i
$536$		0			0
$537$	−22.1615	−	17.6732i	−0.956338	−	0.762654i
$538$		0			0
$539$			18.2591i			0.786476i
$540$		0			0
$541$	−28.7696	−	6.56646i	−1.23690	−	0.282314i	−0.446432	−	0.894818i	$-0.647305\pi$
$541$	−28.7696	−	6.56646i	−1.23690	−	0.282314i	−0.790468	+	0.612503i	$0.790163\pi$
$542$		0			0
$543$	−2.19048	−	4.54857i	−0.0940024	−	0.195198i
$544$		0			0
$545$	0.317853	−	0.398575i	0.0136153	−	0.0170731i
$546$		0			0
$547$	7.09123	−	31.0687i	0.303199	−	1.32840i	−0.562068	−	0.827091i	$-0.689994\pi$
$547$	7.09123	−	31.0687i	0.303199	−	1.32840i	0.865267	−	0.501311i	$-0.167149\pi$
$548$		0			0
$549$	−2.88522	+	2.30089i	−0.123138	+	0.0981995i
$550$		0			0
$551$	8.49499	−	19.2537i	0.361899	−	0.820234i
$552$		0			0
$553$	3.69553	−	2.94709i	0.157150	−	0.125323i
$554$		0			0
$555$	−3.55029	+	15.5548i	−0.150701	+	0.660266i
$556$		0			0
$557$	−9.31590	+	11.6818i	−0.394728	+	0.494973i	−0.938991	−	0.343942i	$-0.888238\pi$
$557$	−9.31590	+	11.6818i	−0.394728	+	0.494973i	0.544263	+	0.838914i	$0.316809\pi$
$558$		0			0
$559$	−18.7011	−	38.8332i	−0.790971	−	1.64247i
$560$		0			0
$561$	16.3834	+	3.73939i	0.691706	+	0.157877i
$562$		0			0
$563$			4.93691i			0.208066i	0.994574	+	0.104033i	$0.0331748\pi$
$563$			4.93691i			0.208066i	−0.994574	+	0.104033i	$0.966825\pi$
$564$		0			0
$565$	−25.6449	−	20.4511i	−1.07889	−	0.860386i
$566$		0			0
$567$	1.39027	+	0.669517i	0.0583857	+	0.0281171i
$568$		0			0
$569$	0.879472	−	1.82624i	0.0368694	−	0.0765600i	−0.881721	−	0.471772i	$-0.843615\pi$
$569$	0.879472	−	1.82624i	0.0368694	−	0.0765600i	0.918590	+	0.395212i	$0.129329\pi$
$570$		0			0
$571$	40.4906	−	19.4992i	1.69448	−	0.816017i	0.699645	−	0.714491i	$-0.253342\pi$
$571$	40.4906	−	19.4992i	1.69448	−	0.816017i	0.994833	−	0.101526i	$-0.0323726\pi$
$572$		0			0
$573$	4.11627	+	18.0345i	0.171959	+	0.753404i
$574$		0			0
$575$	−4.83704	−	6.06545i	−0.201718	−	0.252947i
$576$		0			0
$577$	1.98664	−	0.453438i	0.0827050	−	0.0188769i	−0.180968	−	0.983489i	$-0.557923\pi$
$577$	1.98664	−	0.453438i	0.0827050	−	0.0188769i	0.263673	+	0.964612i	$0.415066\pi$
$578$		0			0
$579$	−22.6874			−0.942857
$580$		0			0
$581$	7.35038			0.304945
$582$		0			0
$583$	−9.75727	+	2.22703i	−0.404105	+	0.0922343i
$584$		0			0
$585$	−9.88587	−	12.3965i	−0.408730	−	0.512532i
$586$		0			0
$587$	1.42398	+	6.23888i	0.0587741	+	0.257506i	0.995776	−	0.0918188i	$-0.0292681\pi$
$587$	1.42398	+	6.23888i	0.0587741	+	0.257506i	−0.937002	+	0.349325i	$0.886411\pi$
$588$		0			0
$589$	−5.09862	+	2.45536i	−0.210085	+	0.101172i
$590$		0			0
$591$	−3.67255	+	7.62613i	−0.151069	+	0.313697i
$592$		0			0
$593$	−19.5222	−	9.40139i	−0.801680	−	0.386069i	−0.0122621	−	0.999925i	$-0.503903\pi$
$593$	−19.5222	−	9.40139i	−0.801680	−	0.386069i	−0.789418	+	0.613856i	$0.789618\pi$
$594$		0			0
$595$	8.22339	+	6.55793i	0.337126	+	0.268849i
$596$		0			0
$597$			3.40625i			0.139408i
$598$		0			0
$599$	−6.55712	−	1.49662i	−0.267917	−	0.0611502i	0.0864521	−	0.996256i	$-0.472447\pi$
$599$	−6.55712	−	1.49662i	−0.267917	−	0.0611502i	−0.354369	+	0.935106i	$0.615304\pi$
$600$		0			0
$601$	6.84283	+	14.2093i	0.279125	+	0.579609i	0.992650	−	0.121021i	$-0.0386168\pi$
$601$	6.84283	+	14.2093i	0.279125	+	0.579609i	−0.713525	+	0.700630i	$0.752903\pi$
$602$		0			0
$603$	−10.3396	+	12.9654i	−0.421059	+	0.527992i
$604$		0			0
$605$	−2.00948	+	8.80412i	−0.0816971	+	0.357938i
$606$		0			0
$607$	37.9488	−	30.2632i	1.54029	−	1.22834i	0.662759	−	0.748832i	$-0.269385\pi$
$607$	37.9488	−	30.2632i	1.54029	−	1.22834i	0.877535	−	0.479512i	$-0.159186\pi$
$608$		0			0
$609$	4.59066	−	1.20979i	0.186023	−	0.0490232i
$610$		0			0
$611$	−10.5222	+	8.39119i	−0.425683	+	0.339471i
$612$		0			0
$613$	4.77215	−	20.9082i	0.192745	−	0.844473i	−0.782377	−	0.622805i	$-0.785993\pi$
$613$	4.77215	−	20.9082i	0.192745	−	0.844473i	0.975122	−	0.221668i	$-0.0711500\pi$
$614$		0			0
$615$	−14.9070	+	18.6928i	−0.601110	+	0.753768i
$616$		0			0
$617$	4.23374	+	8.79145i	0.170444	+	0.353930i	0.968640	−	0.248467i	$-0.0799267\pi$
$617$	4.23374	+	8.79145i	0.170444	+	0.353930i	−0.798197	+	0.602397i	$0.794212\pi$
$618$		0			0
$619$	16.4871	+	3.76306i	0.662671	+	0.151250i	0.540611	−	0.841272i	$-0.318193\pi$
$619$	16.4871	+	3.76306i	0.662671	+	0.151250i	0.122060	+	0.992523i	$0.461050\pi$
$620$		0			0
$621$			11.2851i			0.452854i
$622$		0			0
$623$	−3.68504	−	2.93872i	−0.147638	−	0.117737i
$624$		0			0
$625$	26.6787	+	12.8478i	1.06715	+	0.513911i
$626$		0			0
$627$	5.81683	−	12.0788i	0.232302	−	0.482380i
$628$		0			0
$629$	19.5335	−	9.40685i	0.778852	−	0.375076i
$630$		0			0
$631$	−2.13194	−	9.34066i	−0.0848713	−	0.371846i	0.914600	−	0.404360i	$-0.132506\pi$
$631$	−2.13194	−	9.34066i	−0.0848713	−	0.371846i	−0.999471	+	0.0325143i	$0.989649\pi$
$632$		0			0
$633$	19.3732	+	24.2932i	0.770016	+	0.965570i
$634$		0			0
$635$	−38.5272	+	8.79357i	−1.52890	+	0.348962i
$636$		0			0
$637$	22.7936			0.903114
$638$		0			0
$639$	−8.71699			−0.344839
$640$		0			0
$641$	9.79740	−	2.23619i	0.386974	−	0.0883243i	−0.0246077	−	0.999697i	$-0.507834\pi$
$641$	9.79740	−	2.23619i	0.386974	−	0.0883243i	0.411582	+	0.911373i	$0.364977\pi$
$642$		0			0
$643$	29.7819	+	37.3453i	1.17448	+	1.47275i	0.849938	+	0.526883i	$0.176639\pi$
$643$	29.7819	+	37.3453i	1.17448	+	1.47275i	0.324544	+	0.945871i	$0.394789\pi$
$644$		0			0
$645$	9.82113	+	43.0292i	0.386707	+	1.69427i
$646$		0			0
$647$	−14.0796	+	6.78036i	−0.553525	+	0.266563i	−0.689668	−	0.724126i	$-0.742243\pi$
$647$	−14.0796	+	6.78036i	−0.553525	+	0.266563i	0.136143	+	0.990689i	$0.456529\pi$
$648$		0			0
$649$	−13.5482	+	28.1332i	−0.531815	+	1.10433i
$650$		0			0
$651$	−1.15019	−	0.553903i	−0.0450795	−	0.0217092i
$652$		0			0
$653$	3.04580	+	2.42894i	0.119191	+	0.0950520i	0.681272	−	0.732031i	$-0.261427\pi$
$653$	3.04580	+	2.42894i	0.119191	+	0.0950520i	−0.562080	+	0.827083i	$0.689999\pi$
$654$		0			0
$655$			52.1303i			2.03690i
$656$		0			0
$657$	23.7364	+	5.41769i	0.926047	+	0.211364i
$658$		0			0
$659$	−6.96607	−	14.4652i	−0.271360	−	0.563484i	0.720104	−	0.693866i	$-0.244094\pi$
$659$	−6.96607	−	14.4652i	−0.271360	−	0.563484i	−0.991464	+	0.130382i	$0.958380\pi$
$660$		0			0
$661$	−28.5993	+	35.8624i	−1.11239	+	1.39489i	−0.202876	+	0.979204i	$0.565029\pi$
$661$	−28.5993	+	35.8624i	−1.11239	+	1.39489i	−0.909510	+	0.415683i	$0.863543\pi$
$662$		0			0
$663$	4.66803	−	20.4520i	0.181291	−	0.794289i
$664$		0			0
$665$	6.56045	−	5.23178i	0.254403	−	0.202880i
$666$		0			0
$667$	7.17437	+	8.40666i	0.277793	+	0.325507i
$668$		0			0
$669$	7.28325	−	5.80820i	0.281587	−	0.224558i
$670$		0			0
$671$	−1.52347	+	6.67474i	−0.0588127	+	0.257675i
$672$		0			0
$673$	19.8371	−	24.8750i	0.764665	−	0.958860i	−0.235249	−	0.971935i	$-0.575591\pi$
$673$	19.8371	−	24.8750i	0.764665	−	0.958860i	0.999915	+	0.0130749i	$0.00416200\pi$
$674$		0			0
$675$	9.01892	+	18.7280i	0.347139	+	0.720841i
$676$		0			0
$677$	−15.6226	−	3.56575i	−0.600424	−	0.137043i	−0.0885039	−	0.996076i	$-0.528209\pi$
$677$	−15.6226	−	3.56575i	−0.600424	−	0.137043i	−0.511920	+	0.859033i	$0.671066\pi$
$678$		0			0
$679$		−	2.14729i		−	0.0824055i
$680$		0			0
$681$	−3.17363	−	2.53089i	−0.121614	−	0.0969838i
$682$		0			0
$683$	−11.3892	−	5.48473i	−0.435794	−	0.209867i	0.203107	−	0.979157i	$-0.434896\pi$
$683$	−11.3892	−	5.48473i	−0.435794	−	0.209867i	−0.638901	+	0.769289i	$0.720611\pi$
$684$		0			0
$685$	8.06290	−	16.7428i	0.308068	−	0.639709i
$686$		0			0
$687$	−28.9547	+	13.9439i	−1.10469	+	0.531991i
$688$		0			0
$689$	2.78009	+	12.1804i	0.105913	+	0.464035i
$690$		0			0
$691$	1.55072	+	1.94455i	0.0589923	+	0.0739740i	0.810452	−	0.585805i	$-0.199221\pi$
$691$	1.55072	+	1.94455i	0.0589923	+	0.0739740i	−0.751460	+	0.659779i	$0.770650\pi$
$692$		0			0
$693$	−3.02833	+	0.691197i	−0.115037	+	0.0262564i
$694$		0			0
$695$	27.2161			1.03236
$696$		0			0
$697$	32.4893			1.23062
$698$		0			0
$699$	−13.1721	+	3.00644i	−0.498213	+	0.113714i
$700$		0			0
$701$	23.1761	+	29.0619i	0.875350	+	1.09765i	0.994496	+	0.104777i	$0.0334130\pi$
$701$	23.1761	+	29.0619i	0.875350	+	1.09765i	−0.119146	+	0.992877i	$0.538016\pi$
$702$		0			0
$703$	−3.84879	−	16.8627i	−0.145160	−	0.635987i
$704$		0			0
$705$	12.4166	−	5.97950i	0.467635	−	0.225201i
$706$		0			0
$707$	−1.38984	+	2.88604i	−0.0522704	+	0.108541i
$708$		0			0
$709$	−1.97970	−	0.953374i	−0.0743493	−	0.0358047i	0.396340	−	0.918104i	$-0.370280\pi$
$709$	−1.97970	−	0.953374i	−0.0743493	−	0.0358047i	−0.470689	+	0.882299i	$0.655995\pi$
$710$		0			0
$711$	−7.75176	−	6.18182i	−0.290714	−	0.231836i
$712$		0			0
$713$		−	2.97194i		−	0.111300i
$714$		0			0
$715$	−28.6783	−	6.54564i	−1.07251	−	0.244793i
$716$		0			0
$717$	12.3084	+	25.5586i	0.459664	+	0.954502i
$718$		0			0
$719$	−12.7919	+	16.0406i	−0.477059	+	0.598213i	−0.960884	−	0.276952i	$-0.910676\pi$
$719$	−12.7919	+	16.0406i	−0.477059	+	0.598213i	0.483825	+	0.875165i	$0.339247\pi$
$720$		0			0
$721$	−2.43607	+	10.6731i	−0.0907241	+	0.397488i
$722$		0			0
$723$	−1.74447	+	1.39117i	−0.0648777	+	0.0517382i
$724$		0			0
$725$	18.6247	+	8.21747i	0.691703	+	0.305189i
$726$		0			0
$727$	−34.6619	+	27.6419i	−1.28554	+	1.02518i	−0.287818	+	0.957685i	$0.592930\pi$
$727$	−34.6619	+	27.6419i	−1.28554	+	1.02518i	−0.997719	+	0.0674968i	$0.978499\pi$
$728$		0			0
$729$	5.18591	−	22.7210i	0.192071	−	0.841517i
$730$		0			0
$731$	37.3936	−	46.8901i	1.38305	−	1.73429i
$732$		0			0
$733$	−0.753825	−	1.56533i	−0.0278431	−	0.0578169i	0.886583	−	0.462569i	$-0.153072\pi$
$733$	−0.753825	−	1.56533i	−0.0278431	−	0.0578169i	−0.914427	+	0.404752i	$0.867358\pi$
$734$		0			0
$735$	−22.7553	−	5.19374i	−0.839341	−	0.191574i
$736$		0			0
$737$			30.7658i			1.13327i
$738$		0			0
$739$	−8.56036	−	6.82666i	−0.314898	−	0.251123i	0.453267	−	0.891375i	$-0.350258\pi$
$739$	−8.56036	−	6.82666i	−0.314898	−	0.251123i	−0.768165	+	0.640252i	$0.778830\pi$
$740$		0			0
$741$	−15.0784	−	7.26137i	−0.553919	−	0.266753i
$742$		0			0
$743$	−10.2649	+	21.3152i	−0.376581	+	0.781979i	0.623419	+	0.781888i	$0.285743\pi$
$743$	−10.2649	+	21.3152i	−0.376581	+	0.781979i	−1.00000		9.08456e-5i	$0.999971\pi$
$744$		0			0
$745$	−63.3188	+	30.4927i	−2.31982	+	1.11717i
$746$		0			0
$747$	−3.43086	−	15.0316i	−0.125529	−	0.549977i
$748$		0			0
$749$	−6.78220	−	8.50461i	−0.247816	−	0.310752i
$750$		0			0
$751$	3.40435	−	0.777021i	0.124227	−	0.0283539i	−0.159956	−	0.987124i	$-0.551135\pi$
$751$	3.40435	−	0.777021i	0.124227	−	0.0283539i	0.284182	+	0.958770i	$0.408278\pi$
$752$		0			0
$753$	11.6540			0.424694
$754$		0			0
$755$	−24.0377			−0.874822
$756$		0			0
$757$	−4.29672	+	0.980698i	−0.156167	+	0.0356441i	−0.299890	−	0.953974i	$-0.596950\pi$
$757$	−4.29672	+	0.980698i	−0.156167	+	0.0356441i	0.143723	+	0.989618i	$0.454093\pi$
$758$		0			0
$759$	4.38975	+	5.50458i	0.159338	+	0.199803i
$760$		0			0
$761$	1.40630	+	6.16139i	0.0509782	+	0.223350i	0.994000	−	0.109381i	$-0.0348869\pi$
$761$	1.40630	+	6.16139i	0.0509782	+	0.223350i	−0.943022	+	0.332731i	$0.892030\pi$
$762$		0			0
$763$	−0.112327	+	0.0540940i	−0.00406652	+	0.00195833i
$764$		0			0
$765$	9.57269	−	19.8779i	0.346101	−	0.718687i
$766$		0			0
$767$	35.1198	+	16.9128i	1.26810	+	0.610685i
$768$		0			0
$769$	7.60924	+	6.06816i	0.274396	+	0.218824i	0.751013	−	0.660288i	$-0.229566\pi$
$769$	7.60924	+	6.06816i	0.274396	+	0.218824i	−0.476617	+	0.879111i	$0.658137\pi$
$770$		0			0
$771$		−	4.41025i		−	0.158831i
$772$		0			0
$773$	−10.0031	−	2.28313i	−0.359785	−	0.0821186i	0.0388074	−	0.999247i	$-0.487644\pi$
$773$	−10.0031	−	2.28313i	−0.359785	−	0.0821186i	−0.398593	+	0.917128i	$0.630501\pi$
$774$		0			0
$775$	−2.37515	−	4.93205i	−0.0853179	−	0.177165i
$776$		0			0
$777$	2.43277	−	3.05059i	0.0872750	−	0.109439i
$778$		0			0
$779$	5.76758	−	25.2694i	0.206645	−	0.905371i
$780$		0			0
$781$	−12.6437	+	10.0830i	−0.452428	+	0.360800i
$782$		0			0
$783$	−13.7286	−	26.2372i	−0.490621	−	0.937641i
$784$		0			0
$785$	−3.84073	+	3.06288i	−0.137081	+	0.109319i
$786$		0			0
$787$	5.21319	−	22.8405i	0.185830	−	0.814176i	−0.792954	−	0.609282i	$-0.791458\pi$
$787$	5.21319	−	22.8405i	0.185830	−	0.814176i	0.978784	−	0.204894i	$-0.0656850\pi$
$788$		0			0
$789$	9.16002	−	11.4863i	0.326105	−	0.408923i
$790$		0			0
$791$	3.48048	+	7.22730i	0.123752	+	0.256973i
$792$		0			0
$793$	8.33233	+	1.90180i	0.295890	+	0.0675349i
$794$		0			0
$795$		−	12.7934i		−	0.453734i
$796$		0			0
$797$	8.38598	+	6.68760i	0.297047	+	0.236887i	0.760660	−	0.649151i	$-0.224876\pi$
$797$	8.38598	+	6.68760i	0.297047	+	0.236887i	−0.463613	+	0.886038i	$0.653447\pi$
$798$		0			0
$799$	−16.8725	−	8.12536i	−0.596906	−	0.287455i
$800$		0			0
$801$	−4.28969	+	8.90763i	−0.151569	+	0.314736i
$802$		0			0
$803$	40.6957	−	19.5980i	1.43612	−	0.691599i
$804$		0			0
$805$	0.980593	+	4.29626i	0.0345614	+	0.151423i
$806$		0			0
$807$	14.9424	+	18.7372i	0.525999	+	0.659581i
$808$		0			0
$809$	−17.9505	+	4.09708i	−0.631106	+	0.144046i	−0.526096	−	0.850425i	$-0.676345\pi$
$809$	−17.9505	+	4.09708i	−0.631106	+	0.144046i	−0.105010	+	0.994471i	$0.533487\pi$
$810$		0			0
$811$	25.8805			0.908789			0.454394	−	0.890801i	$-0.349856\pi$
$811$	25.8805			0.908789			0.454394	+	0.890801i	$0.349856\pi$
$812$		0			0
$813$	38.5698			1.35270
$814$		0			0
$815$	3.48050	−	0.794402i	0.121917	−	0.0278267i
$816$		0			0
$817$	−29.8319	−	37.4080i	−1.04369	−	1.30874i
$818$		0			0
$819$	0.862848	+	3.78038i	0.0301504	+	0.132097i
$820$		0			0
$821$	40.4099	−	19.4604i	1.41032	−	0.679173i	0.435091	−	0.900386i	$-0.356716\pi$
$821$	40.4099	−	19.4604i	1.41032	−	0.679173i	0.975225	+	0.221214i	$0.0710018\pi$
$822$		0			0
$823$	−12.3181	+	25.5788i	−0.429382	+	0.891622i	0.568250	+	0.822856i	$0.307620\pi$
$823$	−12.3181	+	25.5788i	−0.429382	+	0.891622i	−0.997633	+	0.0687661i	$0.978094\pi$
$824$		0			0
$825$	11.6842	+	5.62680i	0.406791	+	0.195900i
$826$		0			0
$827$	−9.96266	−	7.94496i	−0.346436	−	0.276273i	0.434777	−	0.900538i	$-0.356827\pi$
$827$	−9.96266	−	7.94496i	−0.346436	−	0.276273i	−0.781213	+	0.624265i	$0.785399\pi$
$828$		0			0
$829$		−	3.79481i		−	0.131799i	−0.997826	−	0.0658996i	$-0.979008\pi$
$829$		−	3.79481i		−	0.131799i	0.997826	−	0.0658996i	$-0.0209917\pi$
$830$		0			0
$831$	−23.3187	−	5.32235i	−0.808918	−	0.184630i
$832$		0			0
$833$	13.7613	+	28.5757i	0.476802	+	0.990090i
$834$		0			0
$835$	32.3487	−	40.5640i	1.11947	−	1.40377i
$836$		0			0
$837$	−1.77191	+	7.76326i	−0.0612463	+	0.268338i
$838$		0			0
$839$	2.43121	−	1.93883i	0.0839348	−	0.0669358i	−0.580623	−	0.814172i	$-0.697191\pi$
$839$	2.43121	−	1.93883i	0.0839348	−	0.0669358i	0.664558	+	0.747236i	$0.268620\pi$
$840$		0			0
$841$	−26.9070	−	10.8172i	−0.927828	−	0.373008i
$842$		0			0
$843$	6.74468	−	5.37870i	0.232299	−	0.185252i
$844$		0			0
$845$	0.400513	−	1.75476i	0.0137781	−	0.0603657i
$846$		0			0
$847$	1.37696	−	1.72665i	0.0473128	−	0.0593284i
$848$		0			0
$849$	1.90730	+	3.96055i	0.0654584	+	0.135926i
$850$		0			0
$851$	8.85571	+	2.02126i	0.303570	+	0.0692879i
$852$		0			0
$853$		−	0.125350i		−	0.00429189i	−0.999998	−	0.00214594i	$-0.999317\pi$
$853$		−	0.125350i		−	0.00429189i	0.999998	−	0.00214594i	$-0.000683076\pi$
$854$		0			0
$855$	−13.7612	−	10.9742i	−0.470623	−	0.375310i
$856$		0			0
$857$	−15.1606	−	7.30095i	−0.517875	−	0.249396i	0.156641	−	0.987656i	$-0.449933\pi$
$857$	−15.1606	−	7.30095i	−0.517875	−	0.249396i	−0.674516	+	0.738260i	$0.735648\pi$
$858$		0			0
$859$	8.35394	−	17.3471i	0.285033	−	0.591877i	−0.708463	−	0.705748i	$-0.750611\pi$
$859$	8.35394	−	17.3471i	0.285033	−	0.591877i	0.993495	+	0.113871i	$0.0363252\pi$
$860$		0			0
$861$	5.26805	−	2.53696i	0.179535	−	0.0864593i
$862$		0			0
$863$	5.00175	+	21.9141i	0.170262	+	0.745964i	0.985891	+	0.167390i	$0.0535338\pi$
$863$	5.00175	+	21.9141i	0.170262	+	0.745964i	−0.815629	+	0.578575i	$0.803609\pi$
$864$		0			0
$865$	−43.8692	−	55.0102i	−1.49160	−	1.87040i
$866$		0			0
$867$	8.29573	−	1.89345i	0.281738	−	0.0643048i
$868$		0			0
$869$	−18.3943			−0.623983
$870$		0			0
$871$	38.4061			1.30134
$872$		0			0
$873$	−4.39124	+	1.00227i	−0.148621	+	0.0339217i
$874$		0			0
$875$	−1.63306	−	2.04780i	−0.0552076	−	0.0692282i
$876$		0			0
$877$	−3.91217	−	17.1403i	−0.132105	−	0.578788i	−0.997039	−	0.0769025i	$-0.975497\pi$
$877$	−3.91217	−	17.1403i	−0.132105	−	0.578788i	0.864934	−	0.501886i	$-0.167360\pi$
$878$		0			0
$879$	−23.6835	+	11.4054i	−0.798823	+	0.384693i
$880$		0			0
$881$	20.0183	−	41.5684i	0.674434	−	1.40048i	−0.229715	−	0.973258i	$-0.573779\pi$
$881$	20.0183	−	41.5684i	0.674434	−	1.40048i	0.904148	−	0.427218i	$-0.140506\pi$
$882$		0			0
$883$	−30.1751	−	14.5316i	−1.01547	−	0.489027i	−0.149312	−	0.988790i	$-0.547706\pi$
$883$	−30.1751	−	14.5316i	−1.01547	−	0.489027i	−0.866162	+	0.499763i	$0.833420\pi$
$884$		0			0
$885$	−31.2070	−	24.8868i	−1.04901	−	0.836560i
$886$		0			0
$887$			12.7174i			0.427007i	0.976942	+	0.213504i	$0.0684875\pi$
$887$			12.7174i			0.427007i	−0.976942	+	0.213504i	$0.931512\pi$
$888$		0			0
$889$	9.42204	+	2.15052i	0.316005	+	0.0721261i
$890$		0			0
$891$	−2.60543	−	5.41024i	−0.0872853	−	0.181250i
$892$		0			0
$893$	−9.31497	+	11.6806i	−0.311714	+	0.390876i
$894$		0			0
$895$	−15.3632	+	67.3107i	−0.513536	+	2.24995i
$896$		0			0
$897$	6.87157	−	5.47990i	0.229435	−	0.182968i
$898$		0			0
$899$	3.61546	+	6.90962i	0.120582	+	0.230449i
$900$		0			0
$901$	−13.5918	+	10.8391i	−0.452808	+	0.361102i
$902$		0			0
$903$	2.40181	−	10.5230i	0.0799274	−	0.350185i
$904$		0			0
$905$	−7.66692	+	9.61401i	−0.254857	+	0.319580i
$906$		0			0
$907$	−14.8072	−	30.7474i	−0.491664	−	1.02095i	−0.988233	−	0.152953i	$-0.951122\pi$
$907$	−14.8072	−	30.7474i	−0.491664	−	1.02095i	0.496570	−	0.867997i	$-0.334593\pi$
$908$		0			0
$909$	6.55070	+	1.49515i	0.217273	+	0.0495911i
$910$		0			0
$911$			22.9200i			0.759372i	0.925115	+	0.379686i	$0.123968\pi$
$911$			22.9200i			0.759372i	−0.925115	+	0.379686i	$0.876032\pi$
$912$		0			0
$913$	−22.3636	−	17.8344i	−0.740126	−	0.590231i
$914$		0			0
$915$	−7.88499	−	3.79721i	−0.260670	−	0.125532i
$916$		0			0
$917$	5.53148	−	11.4862i	0.182665	−	0.379309i
$918$		0			0
$919$	−39.0233	+	18.7926i	−1.28726	+	0.619912i	−0.947246	−	0.320508i	$-0.896146\pi$
$919$	−39.0233	+	18.7926i	−1.28726	+	0.619912i	−0.340015	+	0.940420i	$0.610432\pi$
$920$		0			0
$921$	6.06277	+	26.5627i	0.199775	+	0.875272i
$922$		0			0
$923$	12.5870	+	15.7837i	0.414308	+	0.519525i
$924$		0			0
$925$	16.3118	−	3.72305i	0.536328	−	0.122413i
$926$		0			0
$927$	22.9637			0.754228
$928$		0			0
$929$	−42.9957			−1.41064			−0.705321	−	0.708888i	$-0.749197\pi$
$929$	−42.9957			−1.41064			−0.705321	+	0.708888i	$0.749197\pi$
$930$		0			0
$931$	24.6685	−	5.63042i	0.808477	−	0.184530i
$932$		0			0
$933$	−17.5579	−	22.0169i	−0.574819	−	0.720800i
$934$		0			0
$935$	−9.10808	−	39.9051i	−0.297866	−	1.30504i
$936$		0			0
$937$	16.4992	−	7.94560i	0.539006	−	0.259571i	−0.144515	−	0.989503i	$-0.546162\pi$
$937$	16.4992	−	7.94560i	0.539006	−	0.259571i	0.683521	+	0.729931i	$0.260448\pi$
$938$		0			0
$939$	−8.57087	+	17.7976i	−0.279700	+	0.580803i
$940$		0			0
$941$	−4.16806	−	2.00723i	−0.135875	−	0.0654339i	0.364711	−	0.931121i	$-0.381168\pi$
$941$	−4.16806	−	2.00723i	−0.135875	−	0.0654339i	−0.500586	+	0.865687i	$0.666882\pi$
$942$		0			0
$943$	10.6423	+	8.48691i	0.346559	+	0.276372i
$944$		0			0
$945$		−	11.8073i		−	0.384091i
$946$		0			0
$947$	23.7036	+	5.41018i	0.770262	+	0.175807i	0.589554	−	0.807729i	$-0.299304\pi$
$947$	23.7036	+	5.41018i	0.770262	+	0.175807i	0.180709	+	0.983537i	$0.442161\pi$
$948$		0			0
$949$	−24.4650	−	50.8020i	−0.794166	−	1.64910i
$950$		0			0
$951$	19.3770	−	24.2979i	0.628341	−	0.787915i
$952$		0			0
$953$	0.259391	−	1.13647i	0.00840250	−	0.0368138i	−0.970553	−	0.240888i	$-0.922561\pi$
$953$	0.259391	−	1.13647i	0.00840250	−	0.0368138i	0.978955	+	0.204074i	$0.0654184\pi$
$954$		0			0
$955$	35.2267	−	28.0923i	1.13991	−	0.909046i
$956$		0			0
$957$	−16.9024	−	7.45760i	−0.546378	−	0.241070i
$958$		0			0
$959$	−3.55311	+	2.83351i	−0.114736	+	0.0914989i
$960$		0			0
$961$	−6.43151	+	28.1783i	−0.207468	+	0.908977i
$962$		0			0
$963$	−14.2264	+	17.8393i	−0.458438	+	0.574863i
$964$		0			0
$965$	23.9764	+	49.7876i	0.771829	+	1.60272i
$966$		0			0
$967$	−24.6836	−	5.63387i	−0.793770	−	0.181173i	−0.193637	−	0.981073i	$-0.562029\pi$
$967$	−24.6836	−	5.63387i	−0.793770	−	0.181173i	−0.600133	+	0.799900i	$0.704886\pi$
$968$		0			0
$969$		−	23.2874i		−	0.748098i
$970$		0			0
$971$	19.1810	+	15.2963i	0.615547	+	0.490882i	0.880921	−	0.473263i	$-0.156924\pi$
$971$	19.1810	+	15.2963i	0.615547	+	0.490882i	−0.265374	+	0.964145i	$0.585496\pi$
$972$		0			0
$973$	−5.99671	−	2.88786i	−0.192246	−	0.0925807i
$974$		0			0
$975$	7.02415	−	14.5858i	0.224953	−	0.467120i
$976$		0			0
$977$	−13.2888	+	6.39953i	−0.425145	+	0.204739i	−0.634207	−	0.773163i	$-0.718673\pi$
$977$	−13.2888	+	6.39953i	−0.425145	+	0.204739i	0.209062	+	0.977902i	$0.432959\pi$
$978$		0			0
$979$	4.08149	+	17.8822i	0.130445	+	0.571517i
$980$		0			0
$981$	0.163053	+	0.204461i	0.00520587	+	0.00652795i
$982$		0			0
$983$	−25.1635	+	5.74340i	−0.802590	+	0.183186i	−0.604091	−	0.796915i	$-0.706464\pi$
$983$	−25.1635	+	5.74340i	−0.802590	+	0.183186i	−0.198499	+	0.980101i	$0.563607\pi$
$984$		0			0
$985$	20.6168			0.656904
$986$		0			0
$987$	−3.37031			−0.107278
$988$		0			0
$989$	24.4975	−	5.59139i	0.778974	−	0.177796i
$990$		0			0
$991$	−15.9358	−	19.9829i	−0.506217	−	0.634776i	0.461402	−	0.887191i	$-0.347347\pi$
$991$	−15.9358	−	19.9829i	−0.506217	−	0.634776i	−0.967619	+	0.252415i	$0.918775\pi$
$992$		0			0
$993$	−2.73712	−	11.9921i	−0.0868599	−	0.380558i
$994$		0			0
$995$	7.47501	−	3.59978i	0.236974	−	0.114121i
$996$		0			0
$997$	17.3639	−	36.0564i	0.549919	−	1.14192i	−0.421999	−	0.906596i	$-0.638671\pi$
$997$	17.3639	−	36.0564i	0.549919	−	1.14192i	0.971918	−	0.235322i	$-0.0756144\pi$
$998$		0			0
$999$	−21.9277	−	10.5598i	−0.693760	−	0.334097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.2.q.a.121.3	✓	48
4.3	odd	2		464.2.y.e.353.6		48
29.6	even	14	inner	232.2.q.a.209.3	yes	48
29.8	odd	28		6728.2.a.bf.1.16		24
29.21	odd	28		6728.2.a.be.1.9		24
116.35	odd	14		464.2.y.e.209.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.q.a.121.3	✓	48	1.1	even	1	trivial
232.2.q.a.209.3	yes	48	29.6	even	14	inner
464.2.y.e.209.6		48	116.35	odd	14
464.2.y.e.353.6		48	4.3	odd	2
6728.2.a.be.1.9		24	29.21	odd	28
6728.2.a.bf.1.16		24	29.8	odd	28

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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.q (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18604 + 0.270705i) q^{3} +(1.84749 + 2.31668i) q^{5} +(-0.161250 - 0.706484i) q^{7} +(-1.36950 + 0.659517i) q^{9} +O(q^{10})\)	\(q+(-1.18604 + 0.270705i) q^{3} +(1.84749 + 2.31668i) q^{5} +(-0.161250 - 0.706484i) q^{7} +(-1.36950 + 0.659517i) q^{9} +(-1.22355 + 2.54073i) q^{11} +(3.17169 + 1.52740i) q^{13} +(-2.81833 - 2.24754i) q^{15} +4.89842i q^{17} +(3.80988 + 0.869580i) q^{19} +(0.382498 + 0.794266i) q^{21} +(-1.27957 + 1.60454i) q^{23} +(-0.841172 + 3.68541i) q^{25} +(4.29913 - 3.42844i) q^{27} +(1.02298 - 5.28711i) q^{29} +(-1.13218 + 0.902887i) q^{31} +(0.763388 - 3.34462i) q^{33} +(1.33879 - 1.67878i) q^{35} +(-1.92038 - 3.98772i) q^{37} +(-4.17522 - 0.952967i) q^{39} -6.63260i q^{41} +(-9.57251 - 7.63382i) q^{43} +(-4.05802 - 1.95424i) q^{45} +(-1.65877 + 3.44448i) q^{47} +(5.83366 - 2.80934i) q^{49} +(-1.32603 - 5.80971i) q^{51} +(2.21277 + 2.77473i) q^{53} +(-8.14653 + 1.85939i) q^{55} -4.75406 q^{57} +11.0729 q^{59} +(2.36693 - 0.540237i) q^{61} +(0.686771 + 0.861184i) q^{63} +(2.32115 + 10.1696i) q^{65} +(9.82946 - 4.73362i) q^{67} +(1.08327 - 2.24943i) q^{69} +(5.16682 + 2.48821i) q^{71} +(-12.5229 - 9.98665i) q^{73} -4.59875i q^{75} +(1.99228 + 0.454725i) q^{77} +(2.83014 + 5.87684i) q^{79} +(-1.32766 + 1.66484i) q^{81} +(-2.25710 + 9.88900i) q^{83} +(-11.3480 + 9.04976i) q^{85} +(0.217955 + 6.54764i) q^{87} +(5.08526 - 4.05536i) q^{89} +(0.567651 - 2.48704i) q^{91} +(1.09840 - 1.37735i) q^{93} +(5.02417 + 10.4328i) q^{95} +(2.88891 + 0.659375i) q^{97} -4.28648i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9	\( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9} + 10 q^{13} + 14 q^{15} + 14 q^{21} + 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} + 8 q^{35} - 38 q^{45} - 14 q^{47} - 18 q^{49} - 56 q^{51} - 48 q^{53} - 28 q^{55} - 12 q^{57} - 128 q^{59} - 28 q^{61} + 42 q^{63} - 28 q^{65} - 4 q^{67} + 28 q^{69} - 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} + 80 q^{83} - 112 q^{87} + 42 q^{89} - 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) \) 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9 + 10 * q^13 + 14 * q^15 + 14 * q^21 + 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 + 8 * q^35 - 38 * q^45 - 14 * q^47 - 18 * q^49 - 56 * q^51 - 48 * q^53 - 28 * q^55 - 12 * q^57 - 128 * q^59 - 28 * q^61 + 42 * q^63 - 28 * q^65 - 4 * q^67 + 28 * q^69 - 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 + 80 * q^83 - 112 * q^87 + 42 * q^89 - 28 * q^91 + 6 * q^93 + 70 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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