LMFDB - Embedded newform 464.2.y.e.353.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(33,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("464.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.y (of order $14$, degree $6$, not 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 232)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			353.6
Character	$\chi$	$=$	464.353
Dual form			464.2.y.e.209.6

$q$-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 $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{14}\right)$

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	0.134032	−	0.990977i	$-0.457208\pi$
$3$	1.18604	−	0.270705i	0.684759	−	0.156292i	0.550727	+	0.834685i	$0.314350\pi$
$4$		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	0.996216	−	0.0869115i	$-0.0276997\pi$
$7$	0.161250	+	0.706484i	0.0609469	+	0.267026i	−0.935269	+	0.353937i	$0.884843\pi$
$8$		0			0
$9$	−1.36950	+	0.659517i	−0.456501	+	0.219839i
$10$		0			0
$11$	1.22355	−	2.54073i	0.368914	−	0.766058i	−0.631039	−	0.775751i	$-0.717371\pi$
$11$	1.22355	−	2.54073i	0.368914	−	0.766058i	0.999953	+	0.00969294i	$0.00308541\pi$
$12$		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	−0.238111	−	0.971238i	$-0.576528\pi$
$19$	−3.80988	−	0.869580i	−0.874046	−	0.199495i	−0.635935	+	0.771743i	$0.719385\pi$
$20$		0			0
$21$	0.382498	+	0.794266i	0.0834679	+	0.173323i
$22$		0			0
$23$	1.27957	−	1.60454i	0.266810	−	0.334569i	−0.630320	−	0.776335i	$-0.717077\pi$
$23$	1.27957	−	1.60454i	0.266810	−	0.334569i	0.897130	+	0.441766i	$0.145648\pi$
$24$		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	−0.516522	−	0.856274i	$-0.672774\pi$
$31$	1.13218	−	0.902887i	0.203346	−	0.162163i	0.719868	+	0.694111i	$0.244202\pi$
$32$		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	$0.0976125\pi$
$43$	9.57251	+	7.63382i	1.45979	+	1.16415i	0.506446	+	0.862272i	$0.330959\pi$
$44$		0			0
$45$	−4.05802	−	1.95424i	−0.604934	−	0.291321i
$46$		0			0
$47$	1.65877	−	3.44448i	0.241957	−	0.502429i	−0.744259	−	0.667891i	$-0.767197\pi$
$47$	1.65877	−	3.44448i	0.241957	−	0.502429i	0.986216	+	0.165462i	$0.0529116\pi$
$48$		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	$-0.756218\pi$
$59$	−11.0729			−1.44157			−0.720784	+	0.693160i	$0.756218\pi$
$60$		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	−0.923921	−	0.382584i	$-0.875034\pi$
$67$	−9.82946	+	4.73362i	−1.20086	+	0.578304i	−0.276939	+	0.960888i	$0.589320\pi$
$68$		0			0
$69$	1.08327	−	2.24943i	0.130410	−	0.270799i
$70$		0			0
$71$	−5.16682	−	2.48821i	−0.613189	−	0.295296i	0.101395	−	0.994846i	$-0.467670\pi$
$71$	−5.16682	−	2.48821i	−0.613189	−	0.295296i	−0.714584	+	0.699550i	$0.753384\pi$
$72$		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	0.678915	−	0.734217i	$-0.262450\pi$
$79$	−2.83014	−	5.87684i	−0.318415	−	0.661196i	−0.997330	+	0.0730206i	$0.976736\pi$
$80$		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	$-0.740644\pi$
$83$	2.25710	−	9.88900i	0.247749	−	1.08546i	0.933769	−	0.357876i	$-0.116499\pi$
$84$		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	0.960353	−	0.278786i	$-0.0899320\pi$
$103$	13.6113	+	6.55485i	1.34116	+	0.645869i	0.380807	+	0.924655i	$0.375646\pi$
$104$		0			0
$105$	−1.13340	+	2.35352i	−0.110608	+	0.229680i
$106$		0			0
$107$	−13.5245	+	6.51305i	−1.30746	+	0.629641i	−0.952300	−	0.305164i	$-0.901289\pi$
$107$	−13.5245	+	6.51305i	−1.30746	+	0.629641i	−0.355163	+	0.934805i	$0.615574\pi$
$108$		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	$-0.655595\pi$
$127$	5.78650	−	12.0158i	0.513469	−	1.06623i	0.983050	−	0.183339i	$-0.0586907\pi$
$128$		0			0
$129$	13.4199	+	6.46267i	1.18155	+	0.569006i
$130$		0			0
$131$	−13.7547	−	10.9690i	−1.20175	−	0.958366i	−0.201974	−	0.979391i	$-0.564736\pi$
$131$	−13.7547	−	10.9690i	−1.20175	−	0.958366i	−0.999779	+	0.0210245i	$0.993307\pi$
$132$		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	−0.962944	−	0.269700i	$-0.913075\pi$
$139$	−5.72668	+	7.18103i	−0.485731	+	0.609087i	0.477214	+	0.878787i	$0.341647\pi$
$140$		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	−0.532208	−	0.846614i	$-0.678638\pi$
$151$	5.05791	−	6.34241i	0.411607	−	0.516138i	0.943815	+	0.330475i	$0.107209\pi$
$152$		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	−0.920438	−	0.390889i	$-0.872168\pi$
$163$	−0.522746	+	1.08549i	−0.0409446	+	0.0850224i	0.879493	+	0.475912i	$0.157882\pi$
$164$		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	$0.165493\pi$
$167$	3.89624	+	17.0706i	0.301500	+	1.32096i	−0.566363	+	0.824156i	$0.691650\pi$
$168$		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	$-0.877907\pi$
$179$	−14.5274	−	18.2168i	−1.08583	−	1.36159i	−0.158495	−	0.987360i	$-0.550664\pi$
$180$		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	$0.185419\pi$
$191$			15.2057i			1.10025i	−0.835084	+	0.550123i	$0.814581\pi$
$192$		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	−0.992198	−	0.124669i	$-0.960213\pi$
$199$	−0.623047	+	2.72975i	−0.0441666	+	0.193507i	0.948032	+	0.318176i	$0.103070\pi$
$200$		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	$0.199048\pi$
$211$	11.0820	+	23.0121i	0.762919	+	1.58422i	−0.0478528	+	0.998854i	$0.515238\pi$
$212$		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	−0.188380	−	0.982096i	$-0.560324\pi$
$223$	6.89915	−	3.32246i	0.462002	−	0.222488i	0.650381	+	0.759608i	$0.274609\pi$
$224$		0			0
$225$	−1.27861	−	5.60195i	−0.0852405	−	0.373463i
$226$		0			0
$227$	−2.08040	−	2.60874i	−0.138081	−	0.173148i	0.707983	−	0.706230i	$-0.249605\pi$
$227$	−2.08040	−	2.60874i	−0.138081	−	0.173148i	−0.846064	+	0.533081i	$0.821034\pi$
$228$		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	$0.200534\pi$
$239$	5.18885	+	22.7339i	0.335639	+	1.47053i	−0.472391	+	0.881389i	$0.656609\pi$
$240$		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	0.506857	−	0.862030i	$-0.330807\pi$
$251$	9.33943	+	2.13166i	0.589500	+	0.134549i	0.0826421	+	0.996579i	$0.473664\pi$
$252$		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	−0.287557	−	0.957763i	$-0.592843\pi$
$263$	9.44179	−	7.52958i	0.582206	−	0.464294i	0.869763	+	0.493470i	$0.164272\pi$
$264$		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	0.998817	−	0.0486215i	$-0.0154828\pi$
$271$	30.9096	+	7.05491i	1.87762	+	0.428556i	0.878807	+	0.477177i	$0.158340\pi$
$272$		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	0.993187	−	0.116529i	$-0.0371766\pi$
$283$	0.804064	+	3.52283i	0.0477966	+	0.209411i	−0.945391	+	0.325939i	$0.894320\pi$
$284$		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	$0.220697\pi$
$307$			22.3962i			1.27822i	−0.769116	+	0.639109i	$0.779303\pi$
$308$		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	$-0.914975\pi$
$311$	−10.0436	−	20.8558i	−0.569521	−	1.18262i	0.395016	−	0.918674i	$-0.370739\pi$
$312$		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	$-0.910369\pi$
$331$		−	10.1111i		−	0.555755i	0.960617	−	0.277877i	$-0.0896309\pi$
$332$		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	$-0.341011\pi$
$347$	17.8444			0.957938			0.478969	+	0.877832i	$0.341011\pi$
$348$		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	−0.935644	−	0.352945i	$-0.885180\pi$
$359$	−1.44636	+	3.00339i	−0.0763358	+	0.158513i	0.859308	+	0.511458i	$0.170894\pi$
$360$		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	−0.755840	−	0.654756i	$-0.772771\pi$
$367$	−32.9680	−	7.52474i	−1.72092	−	0.392788i	−0.965077	+	0.261968i	$0.915629\pi$
$368$		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	−0.840951	−	0.541111i	$-0.818004\pi$
$379$	−9.74439	+	7.77089i	−0.500535	+	0.399164i	0.340415	+	0.940275i	$0.389432\pi$
$380$		0			0
$381$	3.61027	−	15.8176i	0.184960	−	0.810361i
$382$		0			0
$383$	5.70818	−	7.15783i	0.291674	−	0.365748i	−0.614306	−	0.789068i	$-0.710564\pi$
$383$	5.70818	−	7.15783i	0.291674	−	0.365748i	0.905980	+	0.423320i	$0.139135\pi$
$384$		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	0.701021	−	0.713140i	$-0.252728\pi$
$419$	11.8835	+	5.72278i	0.580546	+	0.279576i	−0.120476	+	0.992716i	$0.538442\pi$
$420$		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	$0.427494\pi$
$431$	−8.31072	+	36.4116i	−0.400313	+	1.75389i	−0.626131	+	0.779718i	$0.715363\pi$
$432$		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	$0.254854\pi$
$439$	−5.08084	+	22.2606i	−0.242495	+	1.06244i	−0.938737	+	0.344634i	$0.888003\pi$
$440$		0			0
$441$	−6.13640	+	7.69481i	−0.292210	+	0.366419i
$442$		0			0
$443$	−0.245308	−	0.509388i	−0.0116550	−	0.0242018i	0.895060	−	0.445945i	$-0.147132\pi$
$443$	−0.245308	−	0.509388i	−0.0116550	−	0.0242018i	−0.906715	+	0.421744i	$0.861418\pi$
$444$		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	$-0.525116\pi$
$463$	−3.39217			−0.157648			−0.0788239	+	0.996889i	$0.525116\pi$
$464$		0			0
$465$	5.22014			0.242078
$466$		0			0
$467$	30.1904	−	6.89076i	1.39704	−	0.318866i	0.543291	−	0.839544i	$-0.317178\pi$
$467$	30.1904	−	6.89076i	1.39704	−	0.318866i	0.853753	+	0.520678i	$0.174321\pi$
$468$		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	0.436749	−	0.899583i	$-0.356130\pi$
$479$	−7.50897	−	5.98820i	−0.343094	−	0.273608i	−0.779843	+	0.625975i	$0.784701\pi$
$480$		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	−0.258698	−	0.965958i	$-0.583294\pi$
$487$	16.3438	−	20.4944i	0.740607	−	0.928692i	0.999305	+	0.0372663i	$0.0118650\pi$
$488$		0			0
$489$	−0.326148	+	1.42895i	−0.0147489	+	0.0646192i
$490$		0			0
$491$	−11.7516	+	9.37162i	−0.530344	+	0.422935i	−0.851705	−	0.524022i	$-0.824431\pi$
$491$	−11.7516	+	9.37162i	−0.530344	+	0.422935i	0.321361	+	0.946957i	$0.395860\pi$
$492$		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	−0.647558	−	0.762016i	$-0.724210\pi$
$499$	5.34886	−	6.70725i	0.239448	−	0.300258i	0.887006	+	0.461758i	$0.152781\pi$
$500$		0			0
$501$	9.24218	+	19.1916i	0.412910	+	0.857417i
$502$		0			0
$503$	20.3227	+	4.63853i	0.906145	+	0.206822i	0.650105	−	0.759844i	$-0.274725\pi$
$503$	20.3227	+	4.63853i	0.906145	+	0.206822i	0.256040	+	0.966666i	$0.417582\pi$
$504$		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	$-0.454795\pi$
$523$	6.47374			0.283077			0.141538	+	0.989933i	$0.454795\pi$
$524$		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	$0.310006\pi$
$547$	−7.09123	+	31.0687i	−0.303199	+	1.32840i	−0.865267	+	0.501311i	$0.832851\pi$
$548$		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	$-0.966825\pi$
$563$		−	4.93691i		−	0.208066i	0.994574	−	0.104033i	$-0.0331748\pi$
$564$		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	$0.746658\pi$
$571$	−40.4906	+	19.4992i	−1.69448	+	0.816017i	−0.994833	+	0.101526i	$0.967627\pi$
$572$		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	0.937002	−	0.349325i	$-0.113589\pi$
$587$	−1.42398	−	6.23888i	−0.0587741	−	0.257506i	−0.995776	+	0.0918188i	$0.970732\pi$
$588$		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	0.354369	−	0.935106i	$-0.384696\pi$
$599$	6.55712	+	1.49662i	0.267917	+	0.0611502i	−0.0864521	+	0.996256i	$0.527553\pi$
$600$		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	$0.730615\pi$
$607$	−37.9488	+	30.2632i	−1.54029	+	1.22834i	−0.877535	+	0.479512i	$0.840814\pi$
$608$		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	−0.122060	−	0.992523i	$-0.538950\pi$
$619$	−16.4871	−	3.76306i	−0.662671	−	0.151250i	−0.540611	+	0.841272i	$0.681807\pi$
$620$		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	0.999471	−	0.0325143i	$-0.0103515\pi$
$631$	2.13194	+	9.34066i	0.0848713	+	0.371846i	−0.914600	+	0.404360i	$0.867494\pi$
$632$		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	$-0.823361\pi$
$643$	−29.7819	−	37.3453i	−1.17448	−	1.47275i	−0.324544	−	0.945871i	$-0.605211\pi$
$644$		0			0
$645$	9.82113	+	43.0292i	0.386707	+	1.69427i
$646$		0			0
$647$	14.0796	−	6.78036i	0.553525	−	0.266563i	−0.136143	−	0.990689i	$-0.543471\pi$
$647$	14.0796	−	6.78036i	0.553525	−	0.266563i	0.689668	+	0.724126i	$0.257757\pi$
$648$		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	0.991464	−	0.130382i	$-0.0416204\pi$
$659$	6.96607	+	14.4652i	0.271360	+	0.563484i	−0.720104	+	0.693866i	$0.755906\pi$
$660$		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	0.638901	−	0.769289i	$-0.279389\pi$
$683$	11.3892	+	5.48473i	0.435794	+	0.209867i	−0.203107	+	0.979157i	$0.565104\pi$
$684$		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	0.751460	−	0.659779i	$-0.229350\pi$
$691$	−1.55072	−	1.94455i	−0.0589923	−	0.0739740i	−0.810452	+	0.585805i	$0.800779\pi$
$692$		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	−0.483825	−	0.875165i	$-0.660753\pi$
$719$	12.7919	−	16.0406i	0.477059	−	0.598213i	0.960884	+	0.276952i	$0.0893243\pi$
$720$		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	$-0.407070\pi$
$727$	34.6619	−	27.6419i	1.28554	−	1.02518i	0.997719	−	0.0674968i	$-0.0215012\pi$
$728$		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	0.768165	−	0.640252i	$-0.221170\pi$
$739$	8.56036	+	6.82666i	0.314898	+	0.251123i	−0.453267	+	0.891375i	$0.649742\pi$
$740$		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	$-0.714257\pi$
$743$	10.2649	−	21.3152i	0.376581	−	0.781979i	1.00000		9.08456e-5i	$-2.89170e-5\pi$
$744$		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	−0.284182	−	0.958770i	$-0.591722\pi$
$751$	−3.40435	+	0.777021i	−0.124227	+	0.0283539i	0.159956	+	0.987124i	$0.448865\pi$
$752$		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	$0.208542\pi$
$787$	−5.21319	+	22.8405i	−0.185830	+	0.814176i	−0.978784	+	0.204894i	$0.934315\pi$
$788$		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	$-0.650144\pi$
$811$	−25.8805			−0.908789			−0.454394	+	0.890801i	$0.650144\pi$
$812$		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	$-0.692380\pi$
$823$	12.3181	−	25.5788i	0.429382	−	0.891622i	0.997633	−	0.0687661i	$-0.0219062\pi$
$824$		0			0
$825$	11.6842	+	5.62680i	0.406791	+	0.195900i
$826$		0			0
$827$	9.96266	+	7.94496i	0.346436	+	0.276273i	0.781213	−	0.624265i	$-0.214601\pi$
$827$	9.96266	+	7.94496i	0.346436	+	0.276273i	−0.434777	+	0.900538i	$0.643173\pi$
$828$		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	−0.664558	−	0.747236i	$-0.731380\pi$
$839$	−2.43121	+	1.93883i	−0.0839348	+	0.0669358i	0.580623	+	0.814172i	$0.302809\pi$
$840$		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	−0.993495	−	0.113871i	$-0.963675\pi$
$859$	−8.35394	+	17.3471i	−0.285033	+	0.591877i	0.708463	+	0.705748i	$0.249389\pi$
$860$		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	$-0.946466\pi$
$863$	−5.00175	−	21.9141i	−0.170262	−	0.745964i	0.815629	−	0.578575i	$-0.196391\pi$
$864$		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	0.866162	−	0.499763i	$-0.166580\pi$
$883$	30.1751	+	14.5316i	1.01547	+	0.489027i	0.149312	+	0.988790i	$0.452294\pi$
$884$		0			0
$885$	−31.2070	−	24.8868i	−1.04901	−	0.836560i
$886$		0			0
$887$		−	12.7174i		−	0.427007i	−0.976942	−	0.213504i	$-0.931512\pi$
$887$		−	12.7174i		−	0.427007i	0.976942	−	0.213504i	$-0.0684875\pi$
$888$		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	$0.0488784\pi$
$907$	14.8072	+	30.7474i	0.491664	+	1.02095i	−0.496570	+	0.867997i	$0.665407\pi$
$908$		0			0
$909$	6.55070	+	1.49515i	0.217273	+	0.0495911i
$910$		0			0
$911$		−	22.9200i		−	0.759372i	−0.925115	−	0.379686i	$-0.876032\pi$
$911$		−	22.9200i		−	0.759372i	0.925115	−	0.379686i	$-0.123968\pi$
$912$		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	0.340015	−	0.940420i	$-0.389568\pi$
$919$	39.0233	−	18.7926i	1.28726	−	0.619912i	0.947246	+	0.320508i	$0.103854\pi$
$920$		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	−0.180709	−	0.983537i	$-0.557839\pi$
$947$	−23.7036	−	5.41018i	−0.770262	−	0.175807i	−0.589554	+	0.807729i	$0.700696\pi$
$948$		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	0.600133	−	0.799900i	$-0.295114\pi$
$967$	24.6836	+	5.63387i	0.793770	+	0.181173i	0.193637	+	0.981073i	$0.437971\pi$
$968$		0			0
$969$		−	23.2874i		−	0.748098i
$970$		0			0
$971$	−19.1810	−	15.2963i	−0.615547	−	0.490882i	0.265374	−	0.964145i	$-0.414504\pi$
$971$	−19.1810	−	15.2963i	−0.615547	−	0.490882i	−0.880921	+	0.473263i	$0.843076\pi$
$972$		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	0.198499	−	0.980101i	$-0.436393\pi$
$983$	25.1635	−	5.74340i	0.802590	−	0.183186i	0.604091	+	0.796915i	$0.293536\pi$
$984$		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	0.967619	−	0.252415i	$-0.0812248\pi$
$991$	15.9358	+	19.9829i	0.506217	+	0.634776i	−0.461402	+	0.887191i	$0.652653\pi$
$992$		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	464.2.y.e.353.6		48
4.3	odd	2		232.2.q.a.121.3	✓	48
29.6	even	14	inner	464.2.y.e.209.6		48
116.35	odd	14		232.2.q.a.209.3	yes	48
116.79	even	28		6728.2.a.be.1.9		24
116.95	even	28		6728.2.a.bf.1.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.q.a.121.3	✓	48	4.3	odd	2
232.2.q.a.209.3	yes	48	116.35	odd	14
464.2.y.e.209.6		48	29.6	even	14	inner
464.2.y.e.353.6		48	1.1	even	1	trivial
6728.2.a.be.1.9		24	116.79	even	28
6728.2.a.bf.1.16		24	116.95	even	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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.y (of order \(14\), degree \(6\), not 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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