LMFDB - Embedded newform 552.2.q.d.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	552.193
Dual form			552.2.q.d.409.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(0.609195 + 4.23705i) q^{5} +(-0.135120 + 0.295872i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(0.609195 + 4.23705i) q^{5} +(-0.135120 + 0.295872i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-0.0387628 - 0.0113818i) q^{11} +(-1.32704 - 2.90580i) q^{13} +(-2.80321 + 3.23507i) q^{15} +(5.67498 + 3.64709i) q^{17} +(-4.11919 + 2.64724i) q^{19} +(-0.312090 + 0.0916379i) q^{21} +(-2.42869 - 4.13539i) q^{23} +(-12.7840 + 3.75372i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-2.37829 - 1.52843i) q^{29} +(6.92359 - 7.99024i) q^{31} +(-0.0167825 - 0.0367485i) q^{33} +(-1.33594 - 0.392267i) q^{35} +(-1.11893 + 7.78231i) q^{37} +(1.32704 - 2.90580i) q^{39} +(0.380737 + 2.64808i) q^{41} +(2.72169 + 3.14099i) q^{43} -4.28062 q^{45} +8.84010 q^{47} +(4.51474 + 5.21029i) q^{49} +(0.960036 + 6.67720i) q^{51} +(-0.372178 + 0.814955i) q^{53} +(0.0246111 - 0.171174i) q^{55} +(-4.69815 - 1.37950i) q^{57} +(-0.850152 - 1.86157i) q^{59} +(1.16211 - 1.34114i) q^{61} +(-0.273631 - 0.175852i) q^{63} +(11.5036 - 7.39291i) q^{65} +(-3.80626 + 1.11762i) q^{67} +(1.53486 - 4.54359i) q^{69} +(10.7814 - 3.16569i) q^{71} +(1.18943 - 0.764399i) q^{73} +(-11.2086 - 7.20333i) q^{75} +(0.00860520 - 0.00993093i) q^{77} +(-1.86979 - 4.09426i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.234419 - 1.63042i) q^{83} +(-11.9957 + 26.2669i) q^{85} +(-0.402335 - 2.79830i) q^{87} +(10.7484 + 12.4043i) q^{89} +1.03906 q^{91} +10.5726 q^{93} +(-13.7259 - 15.8405i) q^{95} +(-1.43038 - 9.94849i) q^{97} +(0.0167825 - 0.0367485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$1$	$1$

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
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	0.609195	+	4.23705i	0.272440	+	1.89486i	0.422783	+	0.906231i	$0.361053\pi$
$5$	0.609195	+	4.23705i	0.272440	+	1.89486i	−0.150343	+	0.988634i	$0.548038\pi$
$6$		0			0
$7$	−0.135120	+	0.295872i	−0.0510707	+	0.111829i	−0.933447	−	0.358715i	$-0.883215\pi$
$7$	−0.135120	+	0.295872i	−0.0510707	+	0.111829i	0.882377	+	0.470544i	$0.155942\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−0.0387628	−	0.0113818i	−0.0116874	−	0.00343174i	0.275884	−	0.961191i	$-0.411030\pi$
$11$	−0.0387628	−	0.0113818i	−0.0116874	−	0.00343174i	−0.287571	+	0.957759i	$0.592848\pi$
$12$		0			0
$13$	−1.32704	−	2.90580i	−0.368053	−	0.805925i	−0.999534	−	0.0305328i	$-0.990280\pi$
$13$	−1.32704	−	2.90580i	−0.368053	−	0.805925i	0.631480	−	0.775392i	$-0.282448\pi$
$14$		0			0
$15$	−2.80321	+	3.23507i	−0.723785	+	0.835293i
$16$		0			0
$17$	5.67498	+	3.64709i	1.37638	+	0.884549i	0.999136	−	0.0415635i	$-0.0132339\pi$
$17$	5.67498	+	3.64709i	1.37638	+	0.884549i	0.377249	+	0.926112i	$0.376870\pi$
$18$		0			0
$19$	−4.11919	+	2.64724i	−0.945007	+	0.607319i	−0.919810	−	0.392364i	$-0.871657\pi$
$19$	−4.11919	+	2.64724i	−0.945007	+	0.607319i	−0.0251964	+	0.999683i	$0.508021\pi$
$20$		0			0
$21$	−0.312090	+	0.0916379i	−0.0681036	+	0.0199970i
$22$		0			0
$23$	−2.42869	−	4.13539i	−0.506418	−	0.862288i
$23$	−2.42869	−	4.13539i	−0.506418	−	0.862288i
$24$		0			0
$25$	−12.7840	+	3.75372i	−2.55680	+	0.750743i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	−2.37829	−	1.52843i	−0.441637	−	0.283823i	0.300865	−	0.953667i	$-0.402725\pi$
$29$	−2.37829	−	1.52843i	−0.441637	−	0.283823i	−0.742502	+	0.669844i	$0.766361\pi$
$30$		0			0
$31$	6.92359	−	7.99024i	1.24351	−	1.43509i	0.384508	−	0.923121i	$-0.374371\pi$
$31$	6.92359	−	7.99024i	1.24351	−	1.43509i	0.859004	−	0.511969i	$-0.171084\pi$
$32$		0			0
$33$	−0.0167825	−	0.0367485i	−0.00292145	−	0.00639709i
$34$		0			0
$35$	−1.33594	−	0.392267i	−0.225815	−	0.0663052i
$36$		0			0
$37$	−1.11893	+	7.78231i	−0.183951	+	1.27940i	0.663358	+	0.748302i	$0.269131\pi$
$37$	−1.11893	+	7.78231i	−0.183951	+	1.27940i	−0.847308	+	0.531101i	$0.821778\pi$
$38$		0			0
$39$	1.32704	−	2.90580i	0.212496	−	0.465301i
$40$		0			0
$41$	0.380737	+	2.64808i	0.0594611	+	0.413561i	0.997712	+	0.0676058i	$0.0215360\pi$
$41$	0.380737	+	2.64808i	0.0594611	+	0.413561i	−0.938251	+	0.345955i	$0.887555\pi$
$42$		0			0
$43$	2.72169	+	3.14099i	0.415053	+	0.478997i	0.924324	−	0.381609i	$-0.124630\pi$
$43$	2.72169	+	3.14099i	0.415053	+	0.478997i	−0.509270	+	0.860607i	$0.670085\pi$
$44$		0			0
$45$	−4.28062			−0.638117
$46$		0			0
$47$	8.84010			1.28946			0.644731	−	0.764410i	$-0.276969\pi$
$47$	8.84010			1.28946			0.644731	+	0.764410i	$0.276969\pi$
$48$		0			0
$49$	4.51474	+	5.21029i	0.644963	+	0.744327i
$50$		0			0
$51$	0.960036	+	6.67720i	0.134432	+	0.934995i
$52$		0			0
$53$	−0.372178	+	0.814955i	−0.0511225	+	0.111943i	−0.933470	−	0.358656i	$-0.883235\pi$
$53$	−0.372178	+	0.814955i	−0.0511225	+	0.111943i	0.882347	+	0.470599i	$0.155962\pi$
$54$		0			0
$55$	0.0246111	−	0.171174i	0.00331856	−	0.0230811i
$56$		0			0
$57$	−4.69815	−	1.37950i	−0.622285	−	0.182719i
$58$		0			0
$59$	−0.850152	−	1.86157i	−0.110680	−	0.242356i	0.846184	−	0.532891i	$-0.178894\pi$
$59$	−0.850152	−	1.86157i	−0.110680	−	0.242356i	−0.956865	+	0.290534i	$0.906167\pi$
$60$		0			0
$61$	1.16211	−	1.34114i	0.148793	−	0.171716i	−0.676460	−	0.736479i	$-0.736487\pi$
$61$	1.16211	−	1.34114i	0.148793	−	0.171716i	0.825253	+	0.564763i	$0.191032\pi$
$62$		0			0
$63$	−0.273631	−	0.175852i	−0.0344743	−	0.0221553i
$64$		0			0
$65$	11.5036	−	7.39291i	1.42685	−	0.916978i
$66$		0			0
$67$	−3.80626	+	1.11762i	−0.465008	+	0.136539i	−0.505840	−	0.862627i	$-0.668817\pi$
$67$	−3.80626	+	1.11762i	−0.465008	+	0.136539i	0.0408318	+	0.999166i	$0.486999\pi$
$68$		0			0
$69$	1.53486	−	4.54359i	0.184776	−	0.546984i
$70$		0			0
$71$	10.7814	−	3.16569i	1.27951	−	0.375699i	0.429790	−	0.902929i	$-0.358588\pi$
$71$	10.7814	−	3.16569i	1.27951	−	0.375699i	0.849722	+	0.527230i	$0.176770\pi$
$72$		0			0
$73$	1.18943	−	0.764399i	0.139212	−	0.0894661i	−0.469181	−	0.883102i	$-0.655451\pi$
$73$	1.18943	−	0.764399i	0.139212	−	0.0894661i	0.608393	+	0.793636i	$0.291814\pi$
$74$		0			0
$75$	−11.2086	−	7.20333i	−1.29426	−	0.831769i
$76$		0			0
$77$	0.00860520	−	0.00993093i	0.000980654	−	0.00113173i
$78$		0			0
$79$	−1.86979	−	4.09426i	−0.210367	−	0.460640i	0.774807	−	0.632198i	$-0.217847\pi$
$79$	−1.86979	−	4.09426i	−0.210367	−	0.460640i	−0.985174	+	0.171558i	$0.945120\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	0.234419	−	1.63042i	0.0257309	−	0.178962i	−0.972903	−	0.231213i	$-0.925731\pi$
$83$	0.234419	−	1.63042i	0.0257309	−	0.178962i	0.998634	+	0.0522511i	$0.0166396\pi$
$84$		0			0
$85$	−11.9957	+	26.2669i	−1.30112	+	2.84905i
$86$		0			0
$87$	−0.402335	−	2.79830i	−0.0431348	−	0.300009i
$88$		0			0
$89$	10.7484	+	12.4043i	1.13932	+	1.31485i	0.942421	+	0.334428i	$0.108543\pi$
$89$	10.7484	+	12.4043i	1.13932	+	1.31485i	0.196903	+	0.980423i	$0.436911\pi$
$90$		0			0
$91$	1.03906			0.108923
$92$		0			0
$93$	10.5726			1.09633
$94$		0			0
$95$	−13.7259	−	15.8405i	−1.40825	−	1.62520i
$96$		0			0
$97$	−1.43038	−	9.94849i	−0.145233	−	1.01012i	−0.923888	−	0.382664i	$-0.875007\pi$
$97$	−1.43038	−	9.94849i	−0.145233	−	1.01012i	0.778655	−	0.627452i	$-0.215902\pi$
$98$		0			0
$99$	0.0167825	−	0.0367485i	0.00168670	−	0.00369336i
$100$		0			0
$101$	1.86067	−	12.9412i	0.185143	−	1.28770i	−0.659229	−	0.751942i	$-0.729117\pi$
$101$	1.86067	−	12.9412i	0.185143	−	1.28770i	0.844372	−	0.535757i	$-0.179974\pi$
$102$		0			0
$103$	2.84934	+	0.836643i	0.280754	+	0.0824369i	0.419078	−	0.907950i	$-0.362353\pi$
$103$	2.84934	+	0.836643i	0.280754	+	0.0824369i	−0.138324	+	0.990387i	$0.544172\pi$
$104$		0			0
$105$	−0.578398	−	1.26652i	−0.0564459	−	0.123599i
$106$		0			0
$107$	5.26328	−	6.07415i	0.508820	−	0.587210i	−0.441976	−	0.897027i	$-0.645722\pi$
$107$	5.26328	−	6.07415i	0.508820	−	0.587210i	0.950796	+	0.309817i	$0.100268\pi$
$108$		0			0
$109$	5.33567	+	3.42903i	0.511065	+	0.328441i	0.770629	−	0.637285i	$-0.219942\pi$
$109$	5.33567	+	3.42903i	0.511065	+	0.328441i	−0.259564	+	0.965726i	$0.583579\pi$
$110$		0			0
$111$	−6.61422	+	4.25070i	−0.627794	+	0.403459i
$112$		0			0
$113$	1.39705	−	0.410211i	0.131424	−	0.0385894i	−0.215359	−	0.976535i	$-0.569092\pi$
$113$	1.39705	−	0.410211i	0.131424	−	0.0385894i	0.346783	+	0.937945i	$0.387274\pi$
$114$		0			0
$115$	16.0423	−	12.8098i	1.49595	−	1.19452i
$116$		0			0
$117$	3.06508	−	0.899990i	0.283367	−	0.0832041i
$118$		0			0
$119$	−1.84588	+	1.18627i	−0.169211	+	0.108745i
$120$		0			0
$121$	−9.25242	−	5.94617i	−0.841129	−	0.540561i
$122$		0			0
$123$	−1.75196	+	2.02187i	−0.157969	+	0.182306i
$124$		0			0
$125$	−14.8014	−	32.4107i	−1.32388	−	2.89890i
$126$		0			0
$127$	−18.2539	−	5.35983i	−1.61977	−	0.475608i	−0.658815	−	0.752305i	$-0.728942\pi$
$127$	−18.2539	−	5.35983i	−1.61977	−	0.475608i	−0.960957	+	0.276697i	$0.910760\pi$
$128$		0			0
$129$	−0.591479	+	4.11383i	−0.0520768	+	0.362202i
$130$		0			0
$131$	−8.13250	+	17.8077i	−0.710540	+	1.55587i	0.116165	+	0.993230i	$0.462940\pi$
$131$	−8.13250	+	17.8077i	−0.710540	+	1.55587i	−0.826705	+	0.562635i	$0.809788\pi$
$132$		0			0
$133$	−0.226659	−	1.57645i	−0.0196538	−	0.136695i
$134$		0			0
$135$	−2.80321	−	3.23507i	−0.241262	−	0.278431i
$136$		0			0
$137$	17.1306			1.46357			0.731783	−	0.681538i	$-0.238688\pi$
$137$	17.1306			1.46357			0.731783	+	0.681538i	$0.238688\pi$
$138$		0			0
$139$	6.41404			0.544032			0.272016	−	0.962293i	$-0.412310\pi$
$139$	6.41404			0.544032			0.272016	+	0.962293i	$0.412310\pi$
$140$		0			0
$141$	5.78904	+	6.68090i	0.487525	+	0.562634i
$142$		0			0
$143$	0.0183664	+	0.127741i	0.00153588	+	0.0106823i
$144$		0			0
$145$	5.02720	−	11.0080i	0.417486	−	0.914167i
$146$		0			0
$147$	−0.981147	+	6.82403i	−0.0809237	+	0.562836i
$148$		0			0
$149$	2.50213	+	0.734690i	0.204982	+	0.0601882i	0.382612	−	0.923909i	$-0.375025\pi$
$149$	2.50213	+	0.734690i	0.204982	+	0.0601882i	−0.177630	+	0.984097i	$0.556843\pi$
$150$		0			0
$151$	−6.68071	−	14.6287i	−0.543669	−	1.19047i	−0.959676	−	0.281107i	$-0.909298\pi$
$151$	−6.68071	−	14.6287i	−0.543669	−	1.19047i	0.416007	−	0.909361i	$-0.363429\pi$
$152$		0			0
$153$	−4.41760	+	5.09818i	−0.357142	+	0.412163i
$154$		0			0
$155$	38.0729	+	24.4679i	3.05808	+	1.96531i
$156$		0			0
$157$	5.20376	−	3.34425i	0.415305	−	0.266900i	−0.316259	−	0.948673i	$-0.602427\pi$
$157$	5.20376	−	3.34425i	0.415305	−	0.266900i	0.731564	+	0.681772i	$0.238791\pi$
$158$		0			0
$159$	−0.859627	+	0.252409i	−0.0681728	+	0.0200174i
$160$		0			0
$161$	1.55171	−	0.159808i	0.122292	−	0.0125946i
$162$		0			0
$163$	11.4466	−	3.36101i	0.896563	−	0.263255i	0.199188	−	0.979961i	$-0.436169\pi$
$163$	11.4466	−	3.36101i	0.896563	−	0.263255i	0.697375	+	0.716706i	$0.254351\pi$
$164$		0			0
$165$	0.145481	−	0.0934951i	0.0113257	−	0.00727859i
$166$		0			0
$167$	−7.75692	−	4.98507i	−0.600249	−	0.385756i	0.204940	−	0.978774i	$-0.434300\pi$
$167$	−7.75692	−	4.98507i	−0.600249	−	0.385756i	−0.805189	+	0.593018i	$0.797936\pi$
$168$		0			0
$169$	1.83052	−	2.11254i	0.140809	−	0.162503i
$170$		0			0
$171$	−2.03407	−	4.45400i	−0.155550	−	0.340606i
$172$		0			0
$173$	16.7944	+	4.93129i	1.27686	+	0.374919i	0.848743	−	0.528806i	$-0.177360\pi$
$173$	16.7944	+	4.93129i	1.27686	+	0.374919i	0.428113	+	0.903725i	$0.359178\pi$
$174$		0			0
$175$	0.616755	−	4.28963i	0.0466223	−	0.324265i
$176$		0			0
$177$	0.850152	−	1.86157i	0.0639014	−	0.139924i
$178$		0			0
$179$	2.02440	+	14.0800i	0.151311	+	1.05239i	0.914027	+	0.405654i	$0.132956\pi$
$179$	2.02440	+	14.0800i	0.151311	+	1.05239i	−0.762716	+	0.646733i	$0.776135\pi$
$180$		0			0
$181$	−2.81650	−	3.25042i	−0.209349	−	0.241602i	0.641358	−	0.767242i	$-0.278371\pi$
$181$	−2.81650	−	3.25042i	−0.209349	−	0.241602i	−0.850707	+	0.525640i	$0.823826\pi$
$182$		0			0
$183$	1.77459			0.131181
$184$		0			0
$185$	−33.6557			−2.47441
$186$		0			0
$187$	−0.178468	−	0.205963i	−0.0130509	−	0.0150615i
$188$		0			0
$189$	−0.0462901	−	0.321955i	−0.00336711	−	0.0234188i
$190$		0			0
$191$	−4.51780	+	9.89261i	−0.326897	+	0.715804i	−0.999712	−	0.0240066i	$-0.992358\pi$
$191$	−4.51780	+	9.89261i	−0.326897	+	0.715804i	0.672815	+	0.739811i	$0.265085\pi$
$192$		0			0
$193$	0.835310	−	5.80971i	0.0601269	−	0.418192i	−0.937421	−	0.348199i	$-0.886793\pi$
$193$	0.835310	−	5.80971i	0.0601269	−	0.418192i	0.997547	−	0.0699928i	$-0.0222976\pi$
$194$		0			0
$195$	13.1204	+	3.85251i	0.939575	+	0.275884i
$196$		0			0
$197$	−6.88223	−	15.0700i	−0.490339	−	1.07369i	−0.979490	−	0.201493i	$-0.935421\pi$
$197$	−6.88223	−	15.0700i	−0.490339	−	1.07369i	0.489151	−	0.872199i	$-0.337307\pi$
$198$		0			0
$199$	−3.72228	+	4.29575i	−0.263866	+	0.304517i	−0.872186	−	0.489174i	$-0.837298\pi$
$199$	−3.72228	+	4.29575i	−0.263866	+	0.304517i	0.608320	+	0.793692i	$0.291844\pi$
$200$		0			0
$201$	−3.33721	−	2.14469i	−0.235388	−	0.151275i
$202$		0			0
$203$	0.773575	−	0.497147i	0.0542943	−	0.0348929i
$204$		0			0
$205$	−10.9881	+	3.22640i	−0.767443	+	0.225341i
$206$		0			0
$207$	4.43894	−	1.81545i	0.308527	−	0.126182i
$208$		0			0
$209$	0.189802	−	0.0557308i	0.0131289	−	0.00385498i
$210$		0			0
$211$	6.53730	−	4.20127i	0.450047	−	0.289227i	−0.295918	−	0.955213i	$-0.595625\pi$
$211$	6.53730	−	4.20127i	0.450047	−	0.289227i	0.745964	+	0.665986i	$0.231989\pi$
$212$		0			0
$213$	9.45276	+	6.07492i	0.647692	+	0.416247i
$214$		0			0
$215$	−11.6505	+	13.4454i	−0.794558	+	0.916968i
$216$		0			0
$217$	1.42857	+	3.12814i	0.0969779	+	0.212352i
$218$		0			0
$219$	1.35660	+	0.398335i	0.0916708	+	0.0269170i
$220$		0			0
$221$	3.06682	−	21.3302i	0.206296	−	1.43482i
$222$		0			0
$223$	2.61496	−	5.72597i	0.175111	−	0.383439i	−0.801643	−	0.597803i	$-0.796040\pi$
$223$	2.61496	−	5.72597i	0.175111	−	0.383439i	0.976754	+	0.214364i	$0.0687678\pi$
$224$		0			0
$225$	−1.89616	−	13.1881i	−0.126411	−	0.879205i
$226$		0			0
$227$	−15.4880	−	17.8741i	−1.02797	−	1.18635i	−0.982286	−	0.187389i	$-0.939997\pi$
$227$	−15.4880	−	17.8741i	−1.02797	−	1.18635i	−0.0456881	−	0.998956i	$-0.514548\pi$
$228$		0			0
$229$	−27.4480			−1.81382			−0.906908	−	0.421328i	$-0.861564\pi$
$229$	−27.4480			−1.81382			−0.906908	+	0.421328i	$0.861564\pi$
$230$		0			0
$231$	0.0131405			0.000864582
$232$		0			0
$233$	3.62642	+	4.18511i	0.237575	+	0.274176i	0.862000	−	0.506909i	$-0.169212\pi$
$233$	3.62642	+	4.18511i	0.237575	+	0.274176i	−0.624425	+	0.781085i	$0.714667\pi$
$234$		0			0
$235$	5.38535	+	37.4559i	0.351302	+	2.44336i
$236$		0			0
$237$	1.86979	−	4.09426i	0.121456	−	0.265951i
$238$		0			0
$239$	−3.84550	+	26.7461i	−0.248745	+	1.73006i	0.356742	+	0.934203i	$0.383888\pi$
$239$	−3.84550	+	26.7461i	−0.248745	+	1.73006i	−0.605487	+	0.795855i	$0.707022\pi$
$240$		0			0
$241$	−17.6292	−	5.17641i	−1.13560	−	0.333442i	−0.340693	−	0.940175i	$-0.610662\pi$
$241$	−17.6292	−	5.17641i	−1.13560	−	0.333442i	−0.794906	+	0.606733i	$0.792480\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−19.3259	+	22.3033i	−1.23469	+	1.42490i
$246$		0			0
$247$	13.1587	+	8.45657i	0.837266	+	0.538078i
$248$		0			0
$249$	1.38570	−	0.890537i	0.0878153	−	0.0564355i
$250$		0			0
$251$	7.58096	−	2.22597i	0.478506	−	0.140502i	−0.0335805	−	0.999436i	$-0.510691\pi$
$251$	7.58096	−	2.22597i	0.478506	−	0.140502i	0.512086	+	0.858934i	$0.328873\pi$
$252$		0			0
$253$	0.0470749	+	0.187942i	0.00295957	+	0.0118158i
$254$		0			0
$255$	−27.7067	+	8.13543i	−1.73506	+	0.509461i
$256$		0			0
$257$	−0.311386	+	0.200115i	−0.0194237	+	0.0124829i	−0.550317	−	0.834956i	$-0.685493\pi$
$257$	−0.311386	+	0.200115i	−0.0194237	+	0.0124829i	0.530893	+	0.847439i	$0.321857\pi$
$258$		0			0
$259$	−2.15138	−	1.38261i	−0.133680	−	0.0859110i
$260$		0			0
$261$	1.85134	−	2.13656i	0.114595	−	0.132250i
$262$		0			0
$263$	−5.02181	−	10.9962i	−0.309658	−	0.678056i	0.689263	−	0.724512i	$-0.257935\pi$
$263$	−5.02181	−	10.9962i	−0.309658	−	0.678056i	−0.998920	+	0.0464556i	$0.985207\pi$
$264$		0			0
$265$	−3.67973	−	1.08047i	−0.226044	−	0.0663726i
$266$		0			0
$267$	−2.33584	+	16.2461i	−0.142951	+	0.994248i
$268$		0			0
$269$	−7.38069	+	16.1615i	−0.450009	+	0.985382i	0.539643	+	0.841894i	$0.318559\pi$
$269$	−7.38069	+	16.1615i	−0.450009	+	0.985382i	−0.989652	+	0.143488i	$0.954168\pi$
$270$		0			0
$271$	3.14965	+	21.9063i	0.191328	+	1.33071i	0.828499	+	0.559991i	$0.189195\pi$
$271$	3.14965	+	21.9063i	0.191328	+	1.33071i	−0.637171	+	0.770722i	$0.719896\pi$
$272$		0			0
$273$	0.680437	+	0.785266i	0.0411819	+	0.0475264i
$274$		0			0
$275$	0.538268			0.0324588
$276$		0			0
$277$	25.6109			1.53881			0.769403	−	0.638763i	$-0.220554\pi$
$277$	25.6109			1.53881			0.769403	+	0.638763i	$0.220554\pi$
$278$		0			0
$279$	6.92359	+	7.99024i	0.414504	+	0.478363i
$280$		0			0
$281$	−1.52323	−	10.5943i	−0.0908681	−	0.632002i	−0.983459	−	0.181133i	$-0.942023\pi$
$281$	−1.52323	−	10.5943i	−0.0908681	−	0.632002i	0.892590	−	0.450868i	$-0.148886\pi$
$282$		0			0
$283$	6.11186	−	13.3831i	0.363312	−	0.795543i	−0.636395	−	0.771363i	$-0.719575\pi$
$283$	6.11186	−	13.3831i	0.363312	−	0.795543i	0.999708	−	0.0241797i	$-0.00769738\pi$
$284$		0			0
$285$	2.98292	−	20.7467i	0.176693	−	1.22893i
$286$		0			0
$287$	−0.834939	−	0.245160i	−0.0492849	−	0.0144713i
$288$		0			0
$289$	11.8421	+	25.9305i	0.696593	+	1.52533i
$290$		0			0
$291$	6.58187	−	7.59588i	0.385836	−	0.445278i
$292$		0			0
$293$	15.4091	+	9.90285i	0.900211	+	0.578531i	0.906853	−	0.421447i	$-0.138478\pi$
$293$	15.4091	+	9.90285i	0.900211	+	0.578531i	−0.00664166	+	0.999978i	$0.502114\pi$
$294$		0			0
$295$	7.36967	−	4.73620i	0.429079	−	0.275752i
$296$		0			0
$297$	0.0387628	−	0.0113818i	0.00224925	−	0.000660439i
$298$		0			0
$299$	−8.79366	+	12.5451i	−0.508551	+	0.725503i
$300$		0			0
$301$	−1.29709	+	0.380859i	−0.0747629	+	0.0219524i
$302$		0			0
$303$	10.9988	−	7.06850i	0.631864	−	0.406075i
$304$		0			0
$305$	6.39044	+	4.10689i	0.365916	+	0.235160i
$306$		0			0
$307$	−9.63246	+	11.1165i	−0.549753	+	0.634449i	−0.960826	−	0.277153i	$-0.910609\pi$
$307$	−9.63246	+	11.1165i	−0.549753	+	0.634449i	0.411072	+	0.911603i	$0.365154\pi$
$308$		0			0
$309$	1.23363	+	2.70127i	0.0701788	+	0.153670i
$310$		0			0
$311$	−22.5104	−	6.60964i	−1.27645	−	0.374798i	−0.427855	−	0.903847i	$-0.640731\pi$
$311$	−22.5104	−	6.60964i	−1.27645	−	0.374798i	−0.848591	+	0.529049i	$0.822549\pi$
$312$		0			0
$313$	0.0372833	−	0.259311i	0.00210737	−	0.0146571i	−0.988741	−	0.149639i	$-0.952189\pi$
$313$	0.0372833	−	0.259311i	0.00210737	−	0.0146571i	0.990848	+	0.134982i	$0.0430978\pi$
$314$		0			0
$315$	0.578398	−	1.26652i	0.0325890	−	0.0713600i
$316$		0			0
$317$	1.99293	+	13.8611i	0.111934	+	0.778520i	0.966035	+	0.258412i	$0.0831991\pi$
$317$	1.99293	+	13.8611i	0.111934	+	0.778520i	−0.854101	+	0.520108i	$0.825892\pi$
$318$		0			0
$319$	0.0747929	+	0.0863156i	0.00418760	+	0.00483274i
$320$		0			0
$321$	8.03725			0.448595
$322$		0			0
$323$	−33.0310			−1.83790
$324$		0			0
$325$	27.8724	+	32.1664i	1.54608	+	1.78427i
$326$		0			0
$327$	0.902636	+	6.27797i	0.0499159	+	0.347172i
$328$		0			0
$329$	−1.19448	+	2.61554i	−0.0658537	+	0.144199i
$330$		0			0
$331$	−2.23344	+	15.5339i	−0.122761	+	0.853821i	0.831645	+	0.555308i	$0.187400\pi$
$331$	−2.23344	+	15.5339i	−0.122761	+	0.853821i	−0.954406	+	0.298513i	$0.903509\pi$
$332$		0			0
$333$	−7.54386	−	2.21508i	−0.413401	−	0.121385i
$334$		0			0
$335$	−7.05415	−	15.4464i	−0.385410	−	0.843929i
$336$		0			0
$337$	5.10499	−	5.89147i	0.278086	−	0.320929i	−0.599475	−	0.800394i	$-0.704624\pi$
$337$	5.10499	−	5.89147i	0.278086	−	0.320929i	0.877561	+	0.479465i	$0.159169\pi$
$338$		0			0
$339$	1.22489	+	0.787190i	0.0665269	+	0.0427543i
$340$		0			0
$341$	−0.359321	+	0.230922i	−0.0194583	+	0.0125051i
$342$		0			0
$343$	−4.33624	+	1.27324i	−0.234135	+	0.0687483i
$344$		0			0
$345$	20.1864	+	3.73535i	1.08680	+	0.201105i
$346$		0			0
$347$	−19.7372	+	5.79535i	−1.05955	+	0.311111i	−0.764668	−	0.644424i	$-0.777097\pi$
$347$	−19.7372	+	5.79535i	−1.05955	+	0.311111i	−0.294878	+	0.955535i	$0.595279\pi$
$348$		0			0
$349$	14.6332	−	9.40419i	0.783298	−	0.503395i	−0.0868288	−	0.996223i	$-0.527673\pi$
$349$	14.6332	−	9.40419i	0.783298	−	0.503395i	0.870127	+	0.492828i	$0.164037\pi$
$350$		0			0
$351$	2.68737	+	1.72707i	0.143441	+	0.0921840i
$352$		0			0
$353$	−5.01775	+	5.79079i	−0.267068	+	0.308213i	−0.873405	−	0.486995i	$-0.838093\pi$
$353$	−5.01775	+	5.79079i	−0.267068	+	0.308213i	0.606337	+	0.795208i	$0.292638\pi$
$354$		0			0
$355$	19.9811	+	43.7526i	1.06049	+	2.32215i
$356$		0			0
$357$	−2.10532	−	0.618177i	−0.111425	−	0.0327174i
$358$		0			0
$359$	−1.18256	+	8.22490i	−0.0624133	+	0.434094i	0.934525	+	0.355898i	$0.115825\pi$
$359$	−1.18256	+	8.22490i	−0.0624133	+	0.434094i	−0.996938	+	0.0781956i	$0.975084\pi$
$360$		0			0
$361$	2.06694	−	4.52597i	0.108786	−	0.238209i
$362$		0			0
$363$	−1.56523	−	10.8864i	−0.0821533	−	0.571389i
$364$		0			0
$365$	3.96339	+	4.57399i	0.207453	+	0.239414i
$366$		0			0
$367$	−13.4693			−0.703093			−0.351546	−	0.936170i	$-0.614344\pi$
$367$	−13.4693			−0.703093			−0.351546	+	0.936170i	$0.614344\pi$
$368$		0			0
$369$	−2.67531			−0.139271
$370$		0			0
$371$	−0.190834	−	0.220234i	−0.00990760	−	0.0114340i
$372$		0			0
$373$	1.29418	+	9.00122i	0.0670101	+	0.466066i	0.995504	+	0.0947182i	$0.0301950\pi$
$373$	1.29418	+	9.00122i	0.0670101	+	0.466066i	−0.928494	+	0.371347i	$0.878896\pi$
$374$		0			0
$375$	14.8014	−	32.4107i	0.764343	−	1.67368i
$376$		0			0
$377$	−1.28525	+	8.93912i	−0.0661938	+	0.460388i
$378$		0			0
$379$	−13.8142	−	4.05621i	−0.709587	−	0.208354i	−0.0930293	−	0.995663i	$-0.529655\pi$
$379$	−13.8142	−	4.05621i	−0.709587	−	0.208354i	−0.616558	+	0.787310i	$0.711473\pi$
$380$		0			0
$381$	−7.90307	−	17.3053i	−0.404887	−	0.886578i
$382$		0			0
$383$	24.5826	−	28.3699i	1.25611	−	1.44963i	0.414052	−	0.910253i	$-0.364113\pi$
$383$	24.5826	−	28.3699i	1.25611	−	1.44963i	0.842063	−	0.539380i	$-0.181341\pi$
$384$		0			0
$385$	0.0473201	+	0.0304108i	0.00241165	+	0.00154988i
$386$		0			0
$387$	−3.49636	+	2.24697i	−0.177730	+	0.114220i
$388$		0			0
$389$	11.8688	−	3.48499i	0.601771	−	0.176696i	0.0333637	−	0.999443i	$-0.489378\pi$
$389$	11.8688	−	3.48499i	0.601771	−	0.176696i	0.568407	+	0.822747i	$0.307560\pi$
$390$		0			0
$391$	1.29934	−	32.3259i	0.0657104	−	1.63479i
$392$		0			0
$393$	−18.7838	+	5.51542i	−0.947518	+	0.278216i
$394$		0			0
$395$	16.2085	−	10.4166i	0.815538	−	0.524115i
$396$		0			0
$397$	−24.0855	−	15.4788i	−1.20882	−	0.776860i	−0.228357	−	0.973577i	$-0.573335\pi$
$397$	−24.0855	−	15.4788i	−1.20882	−	0.776860i	−0.980460	+	0.196718i	$0.936972\pi$
$398$		0			0
$399$	1.04297	−	1.20365i	0.0522138	−	0.0602580i
$400$		0			0
$401$	11.8683	+	25.9880i	0.592675	+	1.29778i	0.933812	+	0.357763i	$0.116461\pi$
$401$	11.8683	+	25.9880i	0.592675	+	1.29778i	−0.341137	+	0.940013i	$0.610812\pi$
$402$		0			0
$403$	−32.4059	−	9.51524i	−1.61425	−	0.473988i
$404$		0			0
$405$	0.609195	−	4.23705i	0.0302712	−	0.210541i
$406$		0			0
$407$	0.131949	−	0.288929i	0.00654049	−	0.0143217i
$408$		0			0
$409$	−5.57105	−	38.7475i	−0.275471	−	1.91594i	−0.386812	−	0.922159i	$-0.626424\pi$
$409$	−5.57105	−	38.7475i	−0.275471	−	1.91594i	0.111341	−	0.993782i	$-0.464485\pi$
$410$		0			0
$411$	11.2182	+	12.9464i	0.553351	+	0.638601i
$412$		0			0
$413$	0.665660			0.0327550
$414$		0			0
$415$	7.05098			0.346119
$416$		0			0
$417$	4.20030	+	4.84741i	0.205690	+	0.237379i
$418$		0			0
$419$	0.0602825	+	0.419274i	0.00294499	+	0.0204829i	0.991241	−	0.132066i	$-0.0421610\pi$
$419$	0.0602825	+	0.419274i	0.00294499	+	0.0204829i	−0.988296	+	0.152549i	$0.951252\pi$
$420$		0			0
$421$	12.9152	−	28.2803i	0.629448	−	1.37830i	−0.278996	−	0.960292i	$-0.590001\pi$
$421$	12.9152	−	28.2803i	0.629448	−	1.37830i	0.908444	−	0.418007i	$-0.137271\pi$
$422$		0			0
$423$	−1.25808	+	8.75012i	−0.0611698	+	0.425446i
$424$		0			0
$425$	−86.2389	−	25.3220i	−4.18320	−	1.22830i
$426$		0			0
$427$	0.239783	+	0.525051i	0.0116039	+	0.0254090i
$428$		0			0
$429$	−0.0845129	+	0.0975331i	−0.00408032	+	0.00470894i
$430$		0			0
$431$	−13.2128	−	8.49137i	−0.636439	−	0.409015i	0.182249	−	0.983252i	$-0.441662\pi$
$431$	−13.2128	−	8.49137i	−0.636439	−	0.409015i	−0.818689	+	0.574238i	$0.805299\pi$
$432$		0			0
$433$	28.4996	−	18.3156i	1.36960	−	0.880191i	0.370782	−	0.928720i	$-0.379090\pi$
$433$	28.4996	−	18.3156i	1.36960	−	0.880191i	0.998822	+	0.0485293i	$0.0154534\pi$
$434$		0			0
$435$	11.6114	−	3.40942i	0.556725	−	0.163469i
$436$		0			0
$437$	20.9516	+	10.6051i	1.00225	+	0.507311i
$438$		0			0
$439$	18.2755	−	5.36618i	0.872244	−	0.256114i	0.185174	−	0.982706i	$-0.440715\pi$
$439$	18.2755	−	5.36618i	0.872244	−	0.256114i	0.687069	+	0.726592i	$0.258897\pi$
$440$		0			0
$441$	−5.79977	+	3.72729i	−0.276180	+	0.177490i
$442$		0			0
$443$	−11.9398	−	7.67324i	−0.567276	−	0.364566i	0.225346	−	0.974279i	$-0.427649\pi$
$443$	−11.9398	−	7.67324i	−0.567276	−	0.364566i	−0.792623	+	0.609712i	$0.791285\pi$
$444$		0			0
$445$	−46.0096	+	53.0980i	−2.18107	+	2.51708i
$446$		0			0
$447$	1.08330	+	2.37210i	0.0512384	+	0.112197i
$448$		0			0
$449$	−15.8586	−	4.65649i	−0.748412	−	0.219754i	−0.114783	−	0.993391i	$-0.536617\pi$
$449$	−15.8586	−	4.65649i	−0.748412	−	0.219754i	−0.633629	+	0.773637i	$0.718435\pi$
$450$		0			0
$451$	0.0153815	−	0.106981i	0.000724287	−	0.00503752i
$452$		0			0
$453$	6.68071	−	14.6287i	0.313887	−	0.687317i
$454$		0			0
$455$	0.632988	+	4.40253i	0.0296749	+	0.206394i
$456$		0			0
$457$	−20.0670	−	23.1586i	−0.938696	−	1.08331i	−0.996383	−	0.0849780i	$-0.972918\pi$
$457$	−20.0670	−	23.1586i	−0.938696	−	1.08331i	0.0576870	−	0.998335i	$-0.481627\pi$
$458$		0			0
$459$	−6.74586			−0.314870
$460$		0			0
$461$	−29.6655			−1.38166			−0.690830	−	0.723017i	$-0.742755\pi$
$461$	−29.6655			−1.38166			−0.690830	+	0.723017i	$0.742755\pi$
$462$		0			0
$463$	−6.04892	−	6.98082i	−0.281117	−	0.324426i	0.597577	−	0.801811i	$-0.296130\pi$
$463$	−6.04892	−	6.98082i	−0.281117	−	0.324426i	−0.878694	+	0.477385i	$0.841585\pi$
$464$		0			0
$465$	6.44078	+	44.7966i	0.298684	+	2.07739i
$466$		0			0
$467$	−9.53942	+	20.8884i	−0.441432	+	0.966600i	0.549902	+	0.835229i	$0.314665\pi$
$467$	−9.53942	+	20.8884i	−0.441432	+	0.966600i	−0.991333	+	0.131371i	$0.958062\pi$
$468$		0			0
$469$	0.183630	−	1.27718i	0.00847927	−	0.0589746i
$470$		0			0
$471$	5.93515	+	1.74272i	0.273477	+	0.0803002i
$472$		0			0
$473$	−0.0697502	−	0.152732i	−0.00320712	−	0.00702261i
$474$		0			0
$475$	42.7226	−	49.3046i	1.96025	−	2.26225i
$476$		0			0
$477$	−0.753694	−	0.484370i	−0.0345093	−	0.0221778i
$478$		0			0
$479$	−4.27546	+	2.74767i	−0.195351	+	0.125544i	−0.634660	−	0.772792i	$-0.718860\pi$
$479$	−4.27546	+	2.74767i	−0.195351	+	0.125544i	0.439309	+	0.898336i	$0.355223\pi$
$480$		0			0
$481$	24.0987	−	7.07602i	1.09881	−	0.322639i
$482$		0			0
$483$	1.13693	+	1.06805i	0.0517321	+	0.0485981i
$484$		0			0
$485$	41.2808	−	12.1211i	1.87447	−	0.550393i
$486$		0			0
$487$	10.3791	−	6.67021i	0.470320	−	0.302256i	−0.283929	−	0.958845i	$-0.591638\pi$
$487$	10.3791	−	6.67021i	0.470320	−	0.302256i	0.754248	+	0.656589i	$0.228002\pi$
$488$		0			0
$489$	10.0360	+	6.44973i	0.453843	+	0.291667i
$490$		0			0
$491$	9.67476	−	11.1653i	0.436616	−	0.503882i	−0.494211	−	0.869342i	$-0.664543\pi$
$491$	9.67476	−	11.1653i	0.436616	−	0.503882i	0.930827	+	0.365460i	$0.119088\pi$
$492$		0			0
$493$	−7.92240	−	17.3476i	−0.356807	−	0.781299i
$494$		0			0
$495$	0.165929	+	0.0487211i	0.00745795	+	0.00218985i
$496$		0			0
$497$	−0.520140	+	3.61765i	−0.0233315	+	0.162274i
$498$		0			0
$499$	7.38245	−	16.1653i	0.330484	−	0.723659i	−0.669330	−	0.742966i	$-0.733419\pi$
$499$	7.38245	−	16.1653i	0.330484	−	0.723659i	0.999814	+	0.0193066i	$0.00614586\pi$
$500$		0			0
$501$	−1.31224	−	9.12682i	−0.0586265	−	0.407756i
$502$		0			0
$503$	−6.28434	−	7.25252i	−0.280205	−	0.323374i	0.598149	−	0.801385i	$-0.295903\pi$
$503$	−6.28434	−	7.25252i	−0.280205	−	0.323374i	−0.878354	+	0.478011i	$0.841358\pi$
$504$		0			0
$505$	55.9661			2.49046
$506$		0			0
$507$	2.79529			0.124143
$508$		0			0
$509$	−2.46838	−	2.84866i	−0.109409	−	0.126265i	0.698404	−	0.715704i	$-0.253894\pi$
$509$	−2.46838	−	2.84866i	−0.109409	−	0.126265i	−0.807813	+	0.589440i	$0.799349\pi$
$510$		0			0
$511$	0.0654485	+	0.455204i	0.00289527	+	0.0201370i
$512$		0			0
$513$	2.03407	−	4.45400i	0.0898066	−	0.196649i
$514$		0			0
$515$	−1.80909	+	12.5825i	−0.0797179	+	0.554450i
$516$		0			0
$517$	−0.342668	−	0.100616i	−0.0150705	−	0.00442510i
$518$		0			0
$519$	7.27119	+	15.9217i	0.319170	+	0.698884i
$520$		0			0
$521$	−5.49491	+	6.34147i	−0.240736	+	0.277825i	−0.863242	−	0.504791i	$-0.831570\pi$
$521$	−5.49491	+	6.34147i	−0.240736	+	0.277825i	0.622505	+	0.782616i	$0.286115\pi$
$522$		0			0
$523$	−30.8370	−	19.8178i	−1.34841	−	0.866570i	−0.350853	−	0.936430i	$-0.614108\pi$
$523$	−30.8370	−	19.8178i	−1.34841	−	0.866570i	−0.997557	+	0.0698600i	$0.977745\pi$
$524$		0			0
$525$	3.64577	−	2.34300i	0.159115	−	0.102257i
$526$		0			0
$527$	68.4323	−	20.0935i	2.98096	−	0.875288i
$528$		0			0
$529$	−11.2029	+	20.0872i	−0.487082	+	0.873356i
$530$		0			0
$531$	1.96361	−	0.576569i	0.0852136	−	0.0250210i
$532$		0			0
$533$	7.18955	−	4.62045i	0.311414	−	0.200134i
$534$		0			0
$535$	28.9428	+	18.6004i	1.25131	+	0.804166i
$536$		0			0
$537$	−9.31525	+	10.7504i	−0.401983	+	0.463913i
$538$		0			0
$539$	−0.115702	−	0.253352i	−0.00498363	−	0.0109126i
$540$		0			0
$541$	−13.7957	−	4.05078i	−0.593123	−	0.174157i	−0.0286237	−	0.999590i	$-0.509112\pi$
$541$	−13.7957	−	4.05078i	−0.593123	−	0.174157i	−0.564499	+	0.825434i	$0.690931\pi$
$542$		0			0
$543$	0.612084	−	4.25714i	0.0262671	−	0.182691i
$544$		0			0
$545$	−11.2785	+	24.6964i	−0.483117	+	1.05788i
$546$		0			0
$547$	−2.97948	−	20.7227i	−0.127393	−	0.886039i	−0.948841	−	0.315755i	$-0.897742\pi$
$547$	−2.97948	−	20.7227i	−0.127393	−	0.886039i	0.821448	−	0.570284i	$-0.193167\pi$
$548$		0			0
$549$	1.16211	+	1.34114i	0.0495976	+	0.0572386i
$550$		0			0
$551$	13.8427			0.589721
$552$		0			0
$553$	1.46402			0.0622566
$554$		0			0
$555$	−22.0398	−	25.4352i	−0.935536	−	1.07967i
$556$		0			0
$557$	−0.410603	−	2.85580i	−0.0173978	−	0.121004i	0.979272	−	0.202551i	$-0.0649231\pi$
$557$	−0.410603	−	2.85580i	−0.0173978	−	0.121004i	−0.996670	+	0.0815466i	$0.974014\pi$
$558$		0			0
$559$	5.51533	−	12.0769i	0.233274	−	0.510798i
$560$		0			0
$561$	0.0387848	−	0.269754i	0.00163749	−	0.0113890i
$562$		0			0
$563$	18.4414	+	5.41489i	0.777213	+	0.228210i	0.646198	−	0.763170i	$-0.276358\pi$
$563$	18.4414	+	5.41489i	0.777213	+	0.228210i	0.131015	+	0.991380i	$0.458176\pi$
$564$		0			0
$565$	2.58916	+	5.66947i	0.108927	+	0.238517i
$566$		0			0
$567$	0.213004	−	0.245819i	0.00894532	−	0.0103234i
$568$		0			0
$569$	17.3802	+	11.1696i	0.728615	+	0.468252i	0.851624	−	0.524153i	$-0.175618\pi$
$569$	17.3802	+	11.1696i	0.728615	+	0.468252i	−0.123009	+	0.992406i	$0.539254\pi$
$570$		0			0
$571$	−34.3096	+	22.0494i	−1.43581	+	0.922740i	−0.436073	+	0.899912i	$0.643631\pi$
$571$	−34.3096	+	22.0494i	−1.43581	+	0.922740i	−0.999739	+	0.0228288i	$0.992733\pi$
$572$		0			0
$573$	−10.4349	+	3.06395i	−0.435923	+	0.127999i
$574$		0			0
$575$	46.5715	+	43.7501i	1.94216	+	1.82451i
$576$		0			0
$577$	−20.2602	+	5.94893i	−0.843442	+	0.247657i	−0.674782	−	0.738017i	$-0.735762\pi$
$577$	−20.2602	+	5.94893i	−0.843442	+	0.247657i	−0.168660	+	0.985674i	$0.553944\pi$
$578$		0			0
$579$	4.93770	−	3.17327i	0.205204	−	0.131876i
$580$		0			0
$581$	0.450722	+	0.289661i	0.0186991	+	0.0120172i
$582$		0			0
$583$	0.0237023	−	0.0273539i	0.000981650	−	0.00113288i
$584$		0			0
$585$	5.68053	+	12.4386i	0.234861	+	0.514274i
$586$		0			0
$587$	26.9396	+	7.91018i	1.11192	+	0.326488i	0.785577	−	0.618764i	$-0.212366\pi$
$587$	26.9396	+	7.91018i	1.11192	+	0.326488i	0.326340	+	0.945252i	$0.394185\pi$
$588$		0			0
$589$	−7.36745	+	51.2417i	−0.303570	+	2.11138i
$590$		0			0
$591$	6.88223	−	15.0700i	0.283097	−	0.619896i
$592$		0			0
$593$	−3.10737	−	21.6122i	−0.127604	−	0.887508i	−0.948578	−	0.316542i	$-0.897478\pi$
$593$	−3.10737	−	21.6122i	−0.127604	−	0.887508i	0.820974	−	0.570966i	$-0.193431\pi$
$594$		0			0
$595$	−6.15079	−	7.09839i	−0.252158	−	0.291006i
$596$		0			0
$597$	−5.68409			−0.232634
$598$		0			0
$599$	−41.0274			−1.67634			−0.838168	−	0.545413i	$-0.816373\pi$
$599$	−41.0274			−1.67634			−0.838168	+	0.545413i	$0.816373\pi$
$600$		0			0
$601$	−7.56592	−	8.73153i	−0.308620	−	0.356167i	0.580158	−	0.814504i	$-0.302991\pi$
$601$	−7.56592	−	8.73153i	−0.308620	−	0.356167i	−0.888778	+	0.458337i	$0.848445\pi$
$602$		0			0
$603$	−0.564555	−	3.92657i	−0.0229905	−	0.159902i
$604$		0			0
$605$	19.5577	−	42.8253i	0.795132	−	1.74110i
$606$		0			0
$607$	−2.07338	+	14.4207i	−0.0841561	+	0.585318i	0.903489	+	0.428611i	$0.140997\pi$
$607$	−2.07338	+	14.4207i	−0.0841561	+	0.585318i	−0.987645	+	0.156707i	$0.949912\pi$
$608$		0			0
$609$	0.882302	+	0.259067i	0.0357527	+	0.0104979i
$610$		0			0
$611$	−11.7311	−	25.6876i	−0.474591	−	1.03921i
$612$		0			0
$613$	14.0252	−	16.1859i	0.566473	−	0.653744i	−0.398168	−	0.917312i	$-0.630354\pi$
$613$	14.0252	−	16.1859i	0.566473	−	0.653744i	0.964641	+	0.263568i	$0.0848994\pi$
$614$		0			0
$615$	−9.63403	−	6.19141i	−0.388482	−	0.249662i
$616$		0			0
$617$	12.6032	−	8.09961i	0.507387	−	0.326078i	−0.261778	−	0.965128i	$-0.584309\pi$
$617$	12.6032	−	8.09961i	0.507387	−	0.326078i	0.769165	+	0.639050i	$0.220672\pi$
$618$		0			0
$619$	−29.8603	+	8.76778i	−1.20019	+	0.352407i	−0.819924	−	0.572472i	$-0.805985\pi$
$619$	−29.8603	+	8.76778i	−1.20019	+	0.352407i	−0.380263	+	0.924878i	$0.624166\pi$
$620$		0			0
$621$	4.27891	+	2.16586i	0.171707	+	0.0869130i
$622$		0			0
$623$	−5.12240	+	1.50407i	−0.205225	+	0.0602594i
$624$		0			0
$625$	72.2655	−	46.4422i	2.89062	−	1.85769i
$626$		0			0
$627$	0.166412	+	0.106947i	0.00664587	+	0.00427104i
$628$		0			0
$629$	−34.7326	+	40.0836i	−1.38488	+	1.59824i
$630$		0			0
$631$	12.7179	+	27.8483i	0.506291	+	1.10862i	0.974373	+	0.224938i	$0.0722178\pi$
$631$	12.7179	+	27.8483i	0.506291	+	1.10862i	−0.468082	+	0.883685i	$0.655055\pi$
$632$		0			0
$633$	7.45613	+	2.18932i	0.296355	+	0.0870176i
$634$		0			0
$635$	11.5897	−	80.6078i	0.459921	−	3.19882i
$636$		0			0
$637$	9.14885	−	20.0332i	0.362491	−	0.793744i
$638$		0			0
$639$	1.59912	+	11.1221i	0.0632603	+	0.439985i
$640$		0			0
$641$	−12.1764	−	14.0523i	−0.480939	−	0.555033i	0.462483	−	0.886628i	$-0.346959\pi$
$641$	−12.1764	−	14.0523i	−0.480939	−	0.555033i	−0.943422	+	0.331595i	$0.892413\pi$
$642$		0			0
$643$	8.05468			0.317646			0.158823	−	0.987307i	$-0.449230\pi$
$643$	8.05468			0.317646			0.158823	+	0.987307i	$0.449230\pi$
$644$		0			0
$645$	−17.7908			−0.700512
$646$		0			0
$647$	−23.9353	−	27.6228i	−0.940992	−	1.08596i	−0.996166	−	0.0874859i	$-0.972117\pi$
$647$	−23.9353	−	27.6228i	−0.940992	−	1.08596i	0.0551738	−	0.998477i	$-0.482429\pi$
$648$		0			0
$649$	0.0117663	+	0.0818362i	0.000461866	+	0.00321235i
$650$		0			0
$651$	−1.42857	+	3.12814i	−0.0559902	+	0.122601i
$652$		0			0
$653$	−4.92775	+	34.2733i	−0.192838	+	1.34122i	0.631613	+	0.775284i	$0.282393\pi$
$653$	−4.92775	+	34.2733i	−0.192838	+	1.34122i	−0.824451	+	0.565933i	$0.808516\pi$
$654$		0			0
$655$	−80.4063	−	23.6094i	−3.14173	−	0.922496i
$656$		0			0
$657$	0.587345	+	1.28611i	0.0229145	+	0.0501758i
$658$		0			0
$659$	−29.9051	+	34.5123i	−1.16494	+	1.34441i	−0.237072	+	0.971492i	$0.576188\pi$
$659$	−29.9051	+	34.5123i	−1.16494	+	1.34441i	−0.927865	+	0.372916i	$0.878358\pi$
$660$		0			0
$661$	20.7186	+	13.3150i	0.805860	+	0.517895i	0.877523	−	0.479534i	$-0.159194\pi$
$661$	20.7186	+	13.3150i	0.805860	+	0.517895i	−0.0716629	+	0.997429i	$0.522831\pi$
$662$		0			0
$663$	18.1286	−	11.6506i	0.704057	−	0.452470i
$664$		0			0
$665$	6.54141	−	1.92073i	0.253665	−	0.0744827i
$666$		0			0
$667$	−0.544531	+	13.5472i	−0.0210843	+	0.524551i
$668$		0			0
$669$	6.03984	−	1.77346i	0.233514	−	0.0685658i
$670$		0			0
$671$	−0.0603113	+	0.0387597i	−0.00232829	+	0.00149630i
$672$		0			0
$673$	13.3246	+	8.56320i	0.513626	+	0.330087i	0.771646	−	0.636052i	$-0.219434\pi$
$673$	13.3246	+	8.56320i	0.513626	+	0.330087i	−0.258020	+	0.966140i	$0.583070\pi$
$674$		0			0
$675$	8.72516	−	10.0694i	0.335831	−	0.387570i
$676$		0			0
$677$	−13.8370	−	30.2989i	−0.531800	−	1.16448i	−0.964776	−	0.263074i	$-0.915264\pi$
$677$	−13.8370	−	30.2989i	−0.531800	−	1.16448i	0.432975	−	0.901406i	$-0.357464\pi$
$678$		0			0
$679$	3.13675	+	0.921034i	0.120378	+	0.0353460i
$680$		0			0
$681$	3.36586	−	23.4101i	0.128980	−	0.897076i
$682$		0			0
$683$	3.79809	−	8.31666i	0.145330	−	0.318228i	−0.822943	−	0.568124i	$-0.807669\pi$
$683$	3.79809	−	8.31666i	0.145330	−	0.318228i	0.968273	+	0.249896i	$0.0803965\pi$
$684$		0			0
$685$	10.4359	+	72.5832i	0.398735	+	2.77326i
$686$		0			0
$687$	−17.9746	−	20.7438i	−0.685775	−	0.791427i
$688$		0			0
$689$	2.86199			0.109033
$690$		0			0
$691$	−26.9601			−1.02561			−0.512805	−	0.858505i	$-0.671393\pi$
$691$	−26.9601			−1.02561			−0.512805	+	0.858505i	$0.671393\pi$
$692$		0			0
$693$	0.00860520	+	0.00993093i	0.000326885	+	0.000377245i
$694$		0			0
$695$	3.90740	+	27.1766i	0.148216	+	1.03087i
$696$		0			0
$697$	−7.49711	+	16.4164i	−0.283973	+	0.621815i
$698$		0			0
$699$	−0.788097	+	5.48133i	−0.0298086	+	0.207323i
$700$		0			0
$701$	−6.05732	−	1.77859i	−0.228782	−	0.0671765i	0.165332	−	0.986238i	$-0.447130\pi$
$701$	−6.05732	−	1.77859i	−0.228782	−	0.0671765i	−0.394114	+	0.919061i	$0.628949\pi$
$702$		0			0
$703$	−15.9926	−	35.0189i	−0.603172	−	1.32076i
$704$		0			0
$705$	−24.7807	+	28.5984i	−0.933293	+	1.07708i
$706$		0			0
$707$	3.57753	+	2.29914i	0.134547	+	0.0864681i
$708$		0			0
$709$	−1.88857	+	1.21371i	−0.0709266	+	0.0455818i	−0.575624	−	0.817715i	$-0.695241\pi$
$709$	−1.88857	+	1.21371i	−0.0709266	+	0.0455818i	0.504697	+	0.863297i	$0.331604\pi$
$710$		0			0
$711$	4.31868	−	1.26808i	0.161963	−	0.0475567i
$712$		0			0
$713$	−49.8580	−	9.22586i	−1.86720	−	0.345511i
$714$		0			0
$715$	−0.530057	+	0.155639i	−0.0198230	+	0.00582056i
$716$		0			0
$717$	−22.7316	+	14.6087i	−0.848927	+	0.545572i
$718$		0			0
$719$	−7.73499	−	4.97098i	−0.288467	−	0.185386i	0.388402	−	0.921490i	$-0.373027\pi$
$719$	−7.73499	−	4.97098i	−0.288467	−	0.185386i	−0.676869	+	0.736104i	$0.736664\pi$
$720$		0			0
$721$	−0.632543	+	0.729994i	−0.0235571	+	0.0271864i
$722$		0			0
$723$	−7.63263	−	16.7131i	−0.283860	−	0.621568i
$724$		0			0
$725$	36.1413	+	10.6120i	1.34225	+	0.394121i
$726$		0			0
$727$	2.97979	−	20.7249i	0.110514	−	0.768644i	−0.856907	−	0.515472i	$-0.827617\pi$
$727$	2.97979	−	20.7249i	0.110514	−	0.768644i	0.967421	−	0.253173i	$-0.0814741\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	3.99004	+	27.7513i	0.147577	+	1.02642i
$732$		0			0
$733$	−23.1517	−	26.7185i	−0.855128	−	0.986871i	0.144868	−	0.989451i	$-0.453724\pi$
$733$	−23.1517	−	26.7185i	−0.855128	−	0.986871i	−0.999997	+	0.00258035i	$0.999179\pi$
$734$		0			0
$735$	−29.5114			−1.08855
$736$		0			0
$737$	0.160262			0.00590332
$738$		0			0
$739$	30.4282	+	35.1161i	1.11932	+	1.29177i	0.952080	+	0.305849i	$0.0989403\pi$
$739$	30.4282	+	35.1161i	1.11932	+	1.29177i	0.167241	+	0.985916i	$0.446514\pi$
$740$		0			0
$741$	2.22605	+	15.4825i	0.0817761	+	0.568765i
$742$		0			0
$743$	12.3039	−	26.9418i	0.451386	−	0.988398i	−0.537980	−	0.842957i	$-0.680813\pi$
$743$	12.3039	−	26.9418i	0.451386	−	0.988398i	0.989367	−	0.145441i	$-0.0464601\pi$
$744$		0			0
$745$	−1.58863	+	11.0492i	−0.0582031	+	0.404811i
$746$		0			0
$747$	1.58047	+	0.464066i	0.0578262	+	0.0169793i
$748$		0			0
$749$	1.08599	+	2.37800i	0.0396814	+	0.0868901i
$750$		0			0
$751$	−12.8755	+	14.8592i	−0.469835	+	0.542219i	−0.940366	−	0.340165i	$-0.889517\pi$
$751$	−12.8755	+	14.8592i	−0.469835	+	0.542219i	0.470531	+	0.882384i	$0.344063\pi$
$752$		0			0
$753$	6.64675	+	4.27160i	0.242221	+	0.155666i
$754$		0			0
$755$	57.9127	−	37.2183i	2.10766	−	1.35451i
$756$		0			0
$757$	−19.0747	+	5.60084i	−0.693283	+	0.203566i	−0.609345	−	0.792905i	$-0.708568\pi$
$757$	−19.0747	+	5.60084i	−0.693283	+	0.203566i	−0.0839372	+	0.996471i	$0.526750\pi$
$758$		0			0
$759$	−0.111210	+	0.158653i	−0.00403666	+	0.00575874i
$760$		0			0
$761$	30.5509	−	8.97056i	1.10747	−	0.325183i	0.323654	−	0.946175i	$-0.395089\pi$
$761$	30.5509	−	8.97056i	1.10747	−	0.325183i	0.783816	+	0.620993i	$0.213270\pi$
$762$		0			0
$763$	−1.73551	+	1.11535i	−0.0628297	+	0.0403782i
$764$		0			0
$765$	−24.2924	−	15.6118i	−0.878294	−	0.564445i
$766$		0			0
$767$	−4.28118	+	4.94075i	−0.154585	+	0.178400i
$768$		0			0
$769$	1.63138	+	3.57223i	0.0588292	+	0.128818i	0.936763	−	0.349963i	$-0.113806\pi$
$769$	1.63138	+	3.57223i	0.0588292	+	0.128818i	−0.877934	+	0.478781i	$0.841079\pi$
$770$		0			0
$771$	−0.355151	−	0.104282i	−0.0127905	−	0.00375562i
$772$		0			0
$773$	−1.09084	+	7.58693i	−0.0392346	+	0.272883i	−0.999990	−	0.00451481i	$-0.998563\pi$
$773$	−1.09084	+	7.58693i	−0.0392346	+	0.272883i	0.960755	+	0.277398i	$0.0894720\pi$
$774$		0			0
$775$	−58.5179	+	128.136i	−2.10202	+	4.60279i
$776$		0			0
$777$	−0.363949	−	2.53132i	−0.0130566	−	0.0908105i
$778$		0			0
$779$	−8.57844	−	9.90005i	−0.307355	−	0.354706i
$780$		0			0
$781$	−0.453947			−0.0162435
$782$		0			0
$783$	2.82708			0.101031
$784$		0			0
$785$	17.3399	+	20.0113i	0.618886	+	0.714233i
$786$		0			0
$787$	−5.24410	−	36.4735i	−0.186932	−	1.30014i	−0.839894	−	0.542751i	$-0.817383\pi$
$787$	−5.24410	−	36.4735i	−0.186932	−	1.30014i	0.652962	−	0.757391i	$-0.273526\pi$
$788$		0			0
$789$	5.02181	−	10.9962i	0.178781	−	0.391476i
$790$		0			0
$791$	−0.0673999	+	0.468776i	−0.00239646	+	0.0166678i
$792$		0			0
$793$	−5.43926	−	1.59711i	−0.193154	−	0.0567151i
$794$		0			0
$795$	−1.59315	−	3.48851i	−0.0565032	−	0.123725i
$796$		0			0
$797$	19.1625	−	22.1147i	0.678771	−	0.783343i	−0.306951	−	0.951725i	$-0.599309\pi$
$797$	19.1625	−	22.1147i	0.678771	−	0.783343i	0.985722	+	0.168382i	$0.0538543\pi$
$798$		0			0
$799$	50.1674	+	32.2406i	1.77479	+	1.14059i
$800$		0			0
$801$	−13.8077	+	8.87365i	−0.487870	+	0.313535i
$802$		0			0
$803$	−0.0548058	+	0.0160924i	−0.00193406	+	0.000567890i
$804$		0			0
$805$	1.62241	+	6.47732i	0.0571824	+	0.228296i
$806$		0			0
$807$	−17.0473	+	5.00555i	−0.600095	+	0.176204i
$808$		0			0
$809$	7.95460	−	5.11211i	0.279669	−	0.179732i	−0.393285	−	0.919417i	$-0.628661\pi$
$809$	7.95460	−	5.11211i	0.279669	−	0.179732i	0.672954	+	0.739684i	$0.265025\pi$
$810$		0			0
$811$	34.3190	+	22.0555i	1.20510	+	0.774473i	0.979832	−	0.199823i	$-0.0640366\pi$
$811$	34.3190	+	22.0555i	1.20510	+	0.774473i	0.225272	+	0.974296i	$0.427673\pi$
$812$		0			0
$813$	−14.4931	+	16.7259i	−0.508295	+	0.586604i
$814$		0			0
$815$	21.2140	+	46.4521i	0.743092	+	1.62715i
$816$		0			0
$817$	−19.5261	−	5.73338i	−0.683132	−	0.200586i
$818$		0			0
$819$	−0.147873	+	1.02848i	−0.00516710	+	0.0359380i
$820$		0			0
$821$	22.4034	−	49.0565i	0.781882	−	1.71208i	0.0833333	−	0.996522i	$-0.473443\pi$
$821$	22.4034	−	49.0565i	0.781882	−	1.71208i	0.698549	−	0.715562i	$-0.253829\pi$
$822$		0			0
$823$	2.07432	+	14.4272i	0.0723062	+	0.502900i	0.993503	+	0.113804i	$0.0363036\pi$
$823$	2.07432	+	14.4272i	0.0723062	+	0.502900i	−0.921197	+	0.389096i	$0.872787\pi$
$824$		0			0
$825$	0.352490	+	0.406795i	0.0122721	+	0.0141628i
$826$		0			0
$827$	−14.9278			−0.519092			−0.259546	−	0.965731i	$-0.583573\pi$
$827$	−14.9278			−0.519092			−0.259546	+	0.965731i	$0.583573\pi$
$828$		0			0
$829$	−14.0688			−0.488631			−0.244315	−	0.969696i	$-0.578563\pi$
$829$	−14.0688			−0.488631			−0.244315	+	0.969696i	$0.578563\pi$
$830$		0			0
$831$	16.7715	+	19.3554i	0.581798	+	0.671431i
$832$		0			0
$833$	6.61868	+	46.0339i	0.229324	+	1.59498i
$834$		0			0
$835$	16.3965	−	35.9033i	0.567424	−	1.24249i
$836$		0			0
$837$	−1.50464	+	10.4650i	−0.0520079	+	0.361723i
$838$		0			0
$839$	19.7962	+	5.81269i	0.683440	+	0.200676i	0.604980	−	0.796241i	$-0.293181\pi$
$839$	19.7962	+	5.81269i	0.683440	+	0.200676i	0.0784608	+	0.996917i	$0.474999\pi$
$840$		0			0
$841$	−8.72689	−	19.1092i	−0.300927	−	0.658939i
$842$		0			0
$843$	7.00912	−	8.08895i	0.241407	−	0.278598i
$844$		0			0
$845$	10.0661	+	6.46906i	0.346283	+	0.222543i
$846$		0			0
$847$	3.00949	−	1.93408i	0.103407	−	0.0664559i
$848$		0			0
$849$	14.1167	−	4.14503i	0.484483	−	0.142257i
$850$		0			0
$851$	34.9004	−	14.2736i	1.19637	−	0.489294i
$852$		0			0
$853$	7.12338	−	2.09161i	0.243900	−	0.0716155i	−0.157498	−	0.987519i	$-0.550343\pi$
$853$	7.12338	−	2.09161i	0.243900	−	0.0716155i	0.401398	+	0.915904i	$0.368525\pi$
$854$		0			0
$855$	17.6327	−	11.3318i	0.603025	−	0.387540i
$856$		0			0
$857$	9.90827	+	6.36766i	0.338460	+	0.217515i	0.698819	−	0.715299i	$-0.253709\pi$
$857$	9.90827	+	6.36766i	0.338460	+	0.217515i	−0.360359	+	0.932814i	$0.617346\pi$
$858$		0			0
$859$	−6.93897	+	8.00800i	−0.236755	+	0.273229i	−0.861677	−	0.507458i	$-0.830585\pi$
$859$	−6.93897	+	8.00800i	−0.236755	+	0.273229i	0.624922	+	0.780687i	$0.285131\pi$
$860$		0			0
$861$	−0.361489	−	0.791550i	−0.0123195	−	0.0269760i
$862$		0			0
$863$	9.08402	+	2.66731i	0.309224	+	0.0907963i	0.432663	−	0.901556i	$-0.357574\pi$
$863$	9.08402	+	2.66731i	0.309224	+	0.0907963i	−0.123439	+	0.992352i	$0.539392\pi$
$864$		0			0
$865$	−10.6630	+	74.1629i	−0.362553	+	2.52161i
$866$		0			0
$867$	−11.8421	+	25.9305i	−0.402178	+	0.880647i
$868$		0			0
$869$	0.0258782	+	0.179987i	0.000877857	+	0.00610563i
$870$		0			0
$871$	8.29862	+	9.57711i	0.281188	+	0.324508i
$872$		0			0
$873$	10.0508			0.340168
$874$		0			0
$875$	11.5894			0.391793
$876$		0			0
$877$	11.3465	+	13.0946i	0.383145	+	0.442172i	0.914261	−	0.405127i	$-0.132773\pi$
$877$	11.3465	+	13.0946i	0.383145	+	0.442172i	−0.531116	+	0.847299i	$0.678227\pi$
$878$		0			0
$879$	2.60676	+	18.1304i	0.0879239	+	0.611524i
$880$		0			0
$881$	−16.6133	+	36.3781i	−0.559717	+	1.22561i	0.392377	+	0.919804i	$0.371653\pi$
$881$	−16.6133	+	36.3781i	−0.559717	+	1.22561i	−0.952094	+	0.305805i	$0.901075\pi$
$882$		0			0
$883$	4.61756	−	32.1158i	0.155393	−	1.08078i	−0.751594	−	0.659626i	$-0.770715\pi$
$883$	4.61756	−	32.1158i	0.155393	−	1.08078i	0.906987	−	0.421158i	$-0.138376\pi$
$884$		0			0
$885$	8.40548	+	2.46807i	0.282547	+	0.0829634i
$886$		0			0
$887$	4.75728	+	10.4170i	0.159734	+	0.349768i	0.972529	−	0.232781i	$-0.0747825\pi$
$887$	4.75728	+	10.4170i	0.159734	+	0.349768i	−0.812795	+	0.582549i	$0.802055\pi$
$888$		0			0
$889$	4.05230	−	4.67660i	0.135910	−	0.156848i
$890$		0			0
$891$	0.0339861	+	0.0218415i	0.00113858	+	0.000731718i
$892$		0			0
$893$	−36.4141	+	23.4019i	−1.21855	+	0.783114i
$894$		0			0
$895$	−58.4243	+	17.1549i	−1.95291	+	0.573426i
$896$		0			0
$897$	−15.2396	+	1.56950i	−0.508835	+	0.0524040i
$898$		0			0
$899$	−28.6788	+	8.42086i	−0.956492	+	0.280851i
$900$		0			0
$901$	−5.08431	+	3.26749i	−0.169383	+	0.108856i
$902$		0			0
$903$	−1.13725	−	0.730864i	−0.0378452	−	0.0243216i
$904$		0			0
$905$	12.0564	−	13.9138i	0.400767	−	0.462510i
$906$		0			0
$907$	22.8609	+	50.0584i	0.759084	+	1.66216i	0.749319	+	0.662209i	$0.230381\pi$
$907$	22.8609	+	50.0584i	0.759084	+	1.66216i	0.00976427	+	0.999952i	$0.496892\pi$
$908$		0			0
$909$	12.5447	+	3.68346i	0.416081	+	0.122172i
$910$		0			0
$911$	−6.23383	+	43.3572i	−0.206536	+	1.43649i	0.577813	+	0.816169i	$0.303906\pi$
$911$	−6.23383	+	43.3572i	−0.206536	+	1.43649i	−0.784349	+	0.620320i	$0.787003\pi$
$912$		0			0
$913$	−0.0276439	+	0.0605317i	−0.000914879	+	0.00200331i
$914$		0			0
$915$	1.08107	+	7.51901i	0.0357391	+	0.248571i
$916$		0			0
$917$	−4.16993	−	4.81236i	−0.137703	−	0.158918i
$918$		0			0
$919$	−1.37016			−0.0451973			−0.0225987	−	0.999745i	$-0.507194\pi$
$919$	−1.37016			−0.0451973			−0.0225987	+	0.999745i	$0.507194\pi$
$920$		0			0
$921$	−14.7092			−0.484684
$922$		0			0
$923$	−23.5061	−	27.1275i	−0.773714	−	0.892913i
$924$		0			0
$925$	−14.9082	−	103.689i	−0.490180	−	3.40927i
$926$		0			0
$927$	−1.23363	+	2.70127i	−0.0405178	+	0.0887215i
$928$		0			0
$929$	−5.14732	+	35.8004i	−0.168878	+	1.17457i	0.712330	+	0.701845i	$0.247640\pi$
$929$	−5.14732	+	35.8004i	−0.168878	+	1.17457i	−0.881208	+	0.472729i	$0.843269\pi$
$930$		0			0
$931$	−32.3900	−	9.51055i	−1.06154	−	0.311696i
$932$		0			0
$933$	−9.74593	−	21.3406i	−0.319067	−	0.698660i
$934$		0			0
$935$	0.763953	−	0.881648i	0.0249839	−	0.0288330i
$936$		0			0
$937$	−11.0572	−	7.10606i	−0.361224	−	0.232145i	0.347422	−	0.937709i	$-0.387057\pi$
$937$	−11.0572	−	7.10606i	−0.361224	−	0.232145i	−0.708646	+	0.705564i	$0.750694\pi$
$938$		0			0
$939$	0.220389	−	0.141636i	0.00719213	−	0.00462210i
$940$		0			0
$941$	−43.5492	+	12.7872i	−1.41966	+	0.416850i	−0.899389	−	0.437150i	$-0.855988\pi$
$941$	−43.5492	+	12.7872i	−1.41966	+	0.416850i	−0.520273	+	0.854000i	$0.674170\pi$
$942$		0			0
$943$	10.0262	−	8.00588i	0.326497	−	0.260707i
$944$		0			0
$945$	1.33594	−	0.392267i	0.0434581	−	0.0127604i
$946$		0			0
$947$	14.3617	−	9.22973i	0.466694	−	0.299926i	−0.286079	−	0.958206i	$-0.592352\pi$
$947$	14.3617	−	9.22973i	0.466694	−	0.299926i	0.752773	+	0.658280i	$0.228716\pi$
$948$		0			0
$949$	−3.79961	−	2.44186i	−0.123340	−	0.0792661i
$950$		0			0
$951$	−9.17046	+	10.5833i	−0.297373	+	0.343186i
$952$		0			0
$953$	−11.9562	−	26.1805i	−0.387300	−	0.848070i	−0.998402	−	0.0565171i	$-0.982000\pi$
$953$	−11.9562	−	26.1805i	−0.387300	−	0.848070i	0.611101	−	0.791552i	$-0.290727\pi$
$954$		0			0
$955$	−44.6677	−	13.1156i	−1.44541	−	0.424411i
$956$		0			0
$957$	−0.0162540	+	0.113049i	−0.000525419	+	0.00365437i
$958$		0			0
$959$	−2.31469	+	5.06847i	−0.0747453	+	0.163669i
$960$		0			0
$961$	−11.4962	−	79.9578i	−0.370845	−	2.57928i
$962$		0			0
$963$	5.26328	+	6.07415i	0.169607	+	0.195737i
$964$		0			0
$965$	25.1249			0.808798
$966$		0			0
$967$	−36.3962			−1.17042			−0.585211	−	0.810881i	$-0.698988\pi$
$967$	−36.3962			−1.17042			−0.585211	+	0.810881i	$0.698988\pi$
$968$		0			0
$969$	−21.6307	−	24.9632i	−0.694879	−	0.801933i
$970$		0			0
$971$	4.17707	+	29.0522i	0.134049	+	0.932328i	0.940201	+	0.340620i	$0.110637\pi$
$971$	4.17707	+	29.0522i	0.134049	+	0.932328i	−0.806152	+	0.591708i	$0.798454\pi$
$972$		0			0
$973$	−0.866667	+	1.89774i	−0.0277841	+	0.0608386i
$974$		0			0
$975$	−6.05724	+	42.1290i	−0.193987	+	1.34921i
$976$		0			0
$977$	50.9342	+	14.9556i	1.62953	+	0.478473i	0.963557	−	0.267502i	$-0.0861982\pi$
$977$	50.9342	+	14.9556i	1.62953	+	0.478473i	0.665974	+	0.745975i	$0.268016\pi$
$978$		0			0
$979$	−0.275454	−	0.603161i	−0.00880356	−	0.0192771i
$980$		0			0
$981$	−4.15347	+	4.79336i	−0.132610	+	0.153040i
$982$		0			0
$983$	−16.3852	−	10.5302i	−0.522608	−	0.335860i	0.252595	−	0.967572i	$-0.418716\pi$
$983$	−16.3852	−	10.5302i	−0.522608	−	0.335860i	−0.775203	+	0.631712i	$0.782352\pi$
$984$		0			0
$985$	59.6596	−	38.3409i	1.90091	−	1.22164i
$986$		0			0
$987$	−2.75891	+	0.810089i	−0.0878170	+	0.0257854i
$988$		0			0
$989$	6.37909	−	18.8838i	0.202843	−	0.600468i
$990$		0			0
$991$	48.8616	−	14.3471i	1.55214	−	0.455750i	0.610402	−	0.792092i	$-0.291008\pi$
$991$	48.8616	−	14.3471i	1.55214	−	0.455750i	0.941740	+	0.336342i	$0.109190\pi$
$992$		0			0
$993$	−13.2023	+	8.48462i	−0.418963	+	0.269251i
$994$		0			0
$995$	−20.4689	−	13.1545i	−0.648907	−	0.417027i
$996$		0			0
$997$	−7.66609	+	8.84714i	−0.242788	+	0.280192i	−0.864045	−	0.503415i	$-0.832077\pi$
$997$	−7.66609	+	8.84714i	−0.242788	+	0.280192i	0.621257	+	0.783607i	$0.286622\pi$
$998$		0			0
$999$	−3.26613	−	7.15183i	−0.103336	−	0.226274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.d.193.3	✓	30
23.18	even	11	inner	552.2.q.d.409.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.d.193.3	✓	30	1.1	even	1	trivial
552.2.q.d.409.3	yes	30	23.18	even	11	inner

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(0.609195 + 4.23705i) q^{5} +(-0.135120 + 0.295872i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(0.609195 + 4.23705i) q^{5} +(-0.135120 + 0.295872i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-0.0387628 - 0.0113818i) q^{11} +(-1.32704 - 2.90580i) q^{13} +(-2.80321 + 3.23507i) q^{15} +(5.67498 + 3.64709i) q^{17} +(-4.11919 + 2.64724i) q^{19} +(-0.312090 + 0.0916379i) q^{21} +(-2.42869 - 4.13539i) q^{23} +(-12.7840 + 3.75372i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(-2.37829 - 1.52843i) q^{29} +(6.92359 - 7.99024i) q^{31} +(-0.0167825 - 0.0367485i) q^{33} +(-1.33594 - 0.392267i) q^{35} +(-1.11893 + 7.78231i) q^{37} +(1.32704 - 2.90580i) q^{39} +(0.380737 + 2.64808i) q^{41} +(2.72169 + 3.14099i) q^{43} -4.28062 q^{45} +8.84010 q^{47} +(4.51474 + 5.21029i) q^{49} +(0.960036 + 6.67720i) q^{51} +(-0.372178 + 0.814955i) q^{53} +(0.0246111 - 0.171174i) q^{55} +(-4.69815 - 1.37950i) q^{57} +(-0.850152 - 1.86157i) q^{59} +(1.16211 - 1.34114i) q^{61} +(-0.273631 - 0.175852i) q^{63} +(11.5036 - 7.39291i) q^{65} +(-3.80626 + 1.11762i) q^{67} +(1.53486 - 4.54359i) q^{69} +(10.7814 - 3.16569i) q^{71} +(1.18943 - 0.764399i) q^{73} +(-11.2086 - 7.20333i) q^{75} +(0.00860520 - 0.00993093i) q^{77} +(-1.86979 - 4.09426i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(0.234419 - 1.63042i) q^{83} +(-11.9957 + 26.2669i) q^{85} +(-0.402335 - 2.79830i) q^{87} +(10.7484 + 12.4043i) q^{89} +1.03906 q^{91} +10.5726 q^{93} +(-13.7259 - 15.8405i) q^{95} +(-1.43038 - 9.94849i) q^{97} +(0.0167825 - 0.0367485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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