LMFDB - Embedded newform 396.2.i.e.133.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(133,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("396.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.5206055409.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + 9x^{5} - 23x^{4} + 27x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + 9x^5 - 23x^4 + 27x^3 + 9x^2 - 81x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.4
Root			$-1.72895 - 0.103515i$ of defining polynomial
Character	$\chi$	$=$	396.133
Dual form			396.2.i.e.265.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72895 + 0.103515i) q^{3} +(-1.27483 - 2.20807i) q^{5} +(0.679294 - 1.17657i) q^{7} +(2.97857 + 0.357947i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.345151 - 0.597819i) q^{13} +(-1.97556 - 3.94962i) q^{15} -0.859359 q^{17} +4.90825 q^{19} +(1.29626 - 1.96392i) q^{21} +(-3.52823 - 6.11107i) q^{23} +(-0.750386 + 1.29971i) q^{25} +(5.11276 + 0.927201i) q^{27} +(-1.88380 + 3.26284i) q^{29} +(3.13720 + 5.43380i) q^{31} +(0.954124 - 1.44556i) q^{33} -3.46394 q^{35} -1.95111 q^{37} +(-0.534867 - 1.06933i) q^{39} +(4.15786 + 7.20163i) q^{41} +(-5.93648 + 10.2823i) q^{43} +(-3.00680 - 7.03321i) q^{45} +(-0.619982 + 1.07384i) q^{47} +(2.57712 + 4.46370i) q^{49} +(-1.48579 - 0.0889568i) q^{51} +3.26684 q^{53} -2.54966 q^{55} +(8.48614 + 0.508079i) q^{57} +(-5.88759 - 10.1976i) q^{59} +(0.228955 - 0.396561i) q^{61} +(2.44447 - 3.26135i) q^{63} +(-0.880018 + 1.52424i) q^{65} +(-3.74961 - 6.49452i) q^{67} +(-5.46756 - 10.9310i) q^{69} -4.48478 q^{71} +9.26838 q^{73} +(-1.43192 + 2.16946i) q^{75} +(-0.679294 - 1.17657i) q^{77} +(-8.00379 + 13.8630i) q^{79} +(8.74375 + 2.13234i) q^{81} +(-4.38303 + 7.59163i) q^{83} +(1.09554 + 1.89753i) q^{85} +(-3.59477 + 5.44631i) q^{87} -3.59252 q^{89} -0.937836 q^{91} +(4.86160 + 9.71954i) q^{93} +(-6.25718 - 10.8378i) q^{95} +(-3.25340 + 5.63505i) q^{97} +(1.79928 - 2.40054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{3} - 4 q^{5} + q^{7} + 7 q^{9} + 4 q^{11} - q^{13} - 22 q^{15} + 2 q^{17} + 18 q^{19} + 21 q^{21} + q^{23} - 6 q^{25} + 9 q^{27} - 13 q^{31} - 3 q^{33} + 52 q^{35} - 28 q^{37} - 14 q^{39}+ \cdots + 2 q^{99}+O(q^{100}) $ 8 * q - 3 * q^3 - 4 * q^5 + q^7 + 7 * q^9 + 4 * q^11 - q^13 - 22 * q^15 + 2 * q^17 + 18 * q^19 + 21 * q^21 + q^23 - 6 * q^25 + 9 * q^27 - 13 * q^31 - 3 * q^33 + 52 * q^35 - 28 * q^37 - 14 * q^39 + 12 * q^41 + 3 * q^43 + 22 * q^45 + 3 * q^47 - 21 * q^49 - 19 * q^51 - 4 * q^53 - 8 * q^55 + 5 * q^57 - 9 * q^59 - 15 * q^61 - 7 * q^63 - 15 * q^65 - 30 * q^67 - 26 * q^69 + 12 * q^71 + 44 * q^73 + 16 * q^75 - q^77 - 41 * q^79 + 31 * q^81 - 20 * q^83 + 7 * q^85 - 27 * q^87 - 50 * q^89 + 58 * q^91 + 7 * q^93 - 4 * q^95 - 3 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.72895	+	0.103515i	0.998212	+	0.0597646i
$3$	1.72895	+	0.103515i	0.998212	+	0.0597646i
$4$		0			0
$5$	−1.27483	−	2.20807i	−0.570122	−	0.987479i	−0.996553	−	0.0829595i	$-0.973563\pi$
$5$	−1.27483	−	2.20807i	−0.570122	−	0.987479i	0.426431	−	0.904520i	$-0.359771\pi$
$6$		0			0
$7$	0.679294	−	1.17657i	0.256749	−	0.444702i	−0.708620	−	0.705590i	$-0.750682\pi$
$7$	0.679294	−	1.17657i	0.256749	−	0.444702i	0.965369	+	0.260888i	$0.0840153\pi$
$8$		0			0
$9$	2.97857	+	0.357947i	0.992856	+	0.119316i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−0.345151	−	0.597819i	−0.0957277	−	0.165805i	0.814184	−	0.580606i	$-0.197184\pi$
$13$	−0.345151	−	0.597819i	−0.0957277	−	0.165805i	−0.909912	+	0.414801i	$0.863851\pi$
$14$		0			0
$15$	−1.97556	−	3.94962i	−0.510086	−	1.01979i
$16$		0			0
$17$	−0.859359			−0.208425			−0.104213	−	0.994555i	$-0.533232\pi$
$17$	−0.859359			−0.208425			−0.104213	+	0.994555i	$0.533232\pi$
$18$		0			0
$19$	4.90825			1.12603			0.563015	−	0.826447i	$-0.309641\pi$
$19$	4.90825			1.12603			0.563015	+	0.826447i	$0.309641\pi$
$20$		0			0
$21$	1.29626	−	1.96392i	0.282867	−	0.428563i
$22$		0			0
$23$	−3.52823	−	6.11107i	−0.735687	−	1.27425i	−0.954421	−	0.298463i	$-0.903526\pi$
$23$	−3.52823	−	6.11107i	−0.735687	−	1.27425i	0.218734	−	0.975784i	$-0.429807\pi$
$24$		0			0
$25$	−0.750386	+	1.29971i	−0.150077	+	0.259941i
$26$		0			0
$27$	5.11276	+	0.927201i	0.983951	+	0.178440i
$28$		0			0
$29$	−1.88380	+	3.26284i	−0.349814	+	0.605895i	−0.986216	−	0.165462i	$-0.947088\pi$
$29$	−1.88380	+	3.26284i	−0.349814	+	0.605895i	0.636403	+	0.771357i	$0.280422\pi$
$30$		0			0
$31$	3.13720	+	5.43380i	0.563458	+	0.975938i	0.997191	+	0.0748970i	$0.0238628\pi$
$31$	3.13720	+	5.43380i	0.563458	+	0.975938i	−0.433733	+	0.901041i	$0.642804\pi$
$32$		0			0
$33$	0.954124	−	1.44556i	0.166092	−	0.251640i
$34$		0			0
$35$	−3.46394			−0.585512
$36$		0			0
$37$	−1.95111			−0.320761			−0.160380	−	0.987055i	$-0.551272\pi$
$37$	−1.95111			−0.320761			−0.160380	+	0.987055i	$0.551272\pi$
$38$		0			0
$39$	−0.534867	−	1.06933i	−0.0856473	−	0.171230i
$40$		0			0
$41$	4.15786	+	7.20163i	0.649349	+	1.12471i	0.983279	+	0.182108i	$0.0582919\pi$
$41$	4.15786	+	7.20163i	0.649349	+	1.12471i	−0.333930	+	0.942598i	$0.608375\pi$
$42$		0			0
$43$	−5.93648	+	10.2823i	−0.905305	+	1.56803i	−0.0847966	+	0.996398i	$0.527024\pi$
$43$	−5.93648	+	10.2823i	−0.905305	+	1.56803i	−0.820508	+	0.571635i	$0.806309\pi$
$44$		0			0
$45$	−3.00680	−	7.03321i	−0.448227	−	1.04845i
$46$		0			0
$47$	−0.619982	+	1.07384i	−0.0904336	+	0.156636i	−0.907694	−	0.419633i	$-0.862159\pi$
$47$	−0.619982	+	1.07384i	−0.0904336	+	0.156636i	0.817260	+	0.576269i	$0.195492\pi$
$48$		0			0
$49$	2.57712	+	4.46370i	0.368160	+	0.637672i
$50$		0			0
$51$	−1.48579	−	0.0889568i	−0.208053	−	0.0124564i
$52$		0			0
$53$	3.26684			0.448734			0.224367	−	0.974505i	$-0.427968\pi$
$53$	3.26684			0.448734			0.224367	+	0.974505i	$0.427968\pi$
$54$		0			0
$55$	−2.54966			−0.343796
$56$		0			0
$57$	8.48614	+	0.508079i	1.12402	+	0.0672967i
$58$		0			0
$59$	−5.88759	−	10.1976i	−0.766499	−	1.32761i	−0.939451	−	0.342685i	$-0.888664\pi$
$59$	−5.88759	−	10.1976i	−0.766499	−	1.32761i	0.172952	−	0.984930i	$-0.444670\pi$
$60$		0			0
$61$	0.228955	−	0.396561i	0.0293147	−	0.0507745i	−0.850996	−	0.525172i	$-0.824001\pi$
$61$	0.228955	−	0.396561i	0.0293147	−	0.0507745i	0.880311	+	0.474398i	$0.157334\pi$
$62$		0			0
$63$	2.44447	−	3.26135i	0.307975	−	0.410891i
$64$		0			0
$65$	−0.880018	+	1.52424i	−0.109153	+	0.189058i
$66$		0			0
$67$	−3.74961	−	6.49452i	−0.458088	−	0.793432i	0.540772	−	0.841169i	$-0.318132\pi$
$67$	−3.74961	−	6.49452i	−0.458088	−	0.793432i	−0.998860	+	0.0477372i	$0.984799\pi$
$68$		0			0
$69$	−5.46756	−	10.9310i	−0.658217	−	1.31594i
$70$		0			0
$71$	−4.48478			−0.532246			−0.266123	−	0.963939i	$-0.585743\pi$
$71$	−4.48478			−0.532246			−0.266123	+	0.963939i	$0.585743\pi$
$72$		0			0
$73$	9.26838			1.08478			0.542391	−	0.840126i	$-0.317519\pi$
$73$	9.26838			1.08478			0.542391	+	0.840126i	$0.317519\pi$
$74$		0			0
$75$	−1.43192	+	2.16946i	−0.165344	+	0.250507i
$76$		0			0
$77$	−0.679294	−	1.17657i	−0.0774127	−	0.134083i
$78$		0			0
$79$	−8.00379	+	13.8630i	−0.900496	+	1.55971i	−0.0736449	+	0.997285i	$0.523463\pi$
$79$	−8.00379	+	13.8630i	−0.900496	+	1.55971i	−0.826851	+	0.562421i	$0.809870\pi$
$80$		0			0
$81$	8.74375	+	2.13234i	0.971528	+	0.236926i
$82$		0			0
$83$	−4.38303	+	7.59163i	−0.481100	+	0.833290i	−0.999765	−	0.0216877i	$-0.993096\pi$
$83$	−4.38303	+	7.59163i	−0.481100	+	0.833290i	0.518664	+	0.854978i	$0.326429\pi$
$84$		0			0
$85$	1.09554	+	1.89753i	0.118828	+	0.205816i
$86$		0			0
$87$	−3.59477	+	5.44631i	−0.385399	+	0.583905i
$88$		0			0
$89$	−3.59252			−0.380807			−0.190403	−	0.981706i	$-0.560980\pi$
$89$	−3.59252			−0.380807			−0.190403	+	0.981706i	$0.560980\pi$
$90$		0			0
$91$	−0.937836			−0.0983119
$92$		0			0
$93$	4.86160	+	9.71954i	0.504125	+	1.00787i
$94$		0			0
$95$	−6.25718	−	10.8378i	−0.641974	−	1.11193i
$96$		0			0
$97$	−3.25340	+	5.63505i	−0.330333	+	0.572153i	−0.982577	−	0.185856i	$-0.940494\pi$
$97$	−3.25340	+	5.63505i	−0.330333	+	0.572153i	0.652244	+	0.758009i	$0.273828\pi$
$98$		0			0
$99$	1.79928	−	2.40054i	0.180834	−	0.241264i
$100$		0			0
$101$	−0.0526751	+	0.0912359i	−0.00524136	+	0.00907831i	−0.868634	−	0.495454i	$-0.835002\pi$
$101$	−0.0526751	+	0.0912359i	−0.00524136	+	0.00907831i	0.863393	+	0.504532i	$0.168335\pi$
$102$		0			0
$103$	−1.40446	−	2.43260i	−0.138386	−	0.239691i	0.788500	−	0.615035i	$-0.210858\pi$
$103$	−1.40446	−	2.43260i	−0.138386	−	0.239691i	−0.926886	+	0.375344i	$0.877525\pi$
$104$		0			0
$105$	−5.98899	−	0.358571i	−0.584466	−	0.0349929i
$106$		0			0
$107$	−12.6759			−1.22542			−0.612711	−	0.790307i	$-0.709921\pi$
$107$	−12.6759			−1.22542			−0.612711	+	0.790307i	$0.709921\pi$
$108$		0			0
$109$	12.0565			1.15480			0.577400	−	0.816462i	$-0.304067\pi$
$109$	12.0565			1.15480			0.577400	+	0.816462i	$0.304067\pi$
$110$		0			0
$111$	−3.37338	−	0.201970i	−0.320187	−	0.0191701i
$112$		0			0
$113$	6.31727	+	10.9418i	0.594279	+	1.02932i	0.993648	+	0.112531i	$0.0358957\pi$
$113$	6.31727	+	10.9418i	0.594279	+	1.02932i	−0.399370	+	0.916790i	$0.630771\pi$
$114$		0			0
$115$	−8.99579	+	15.5812i	−0.838862	+	1.45295i
$116$		0			0
$117$	−0.814069	−	1.90419i	−0.0752607	−	0.176043i
$118$		0			0
$119$	−0.583757	+	1.01110i	−0.0535129	+	0.0926871i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	6.44328	+	12.8817i	0.580971	+	1.16150i
$124$		0			0
$125$	−8.92185			−0.797994
$126$		0			0
$127$	3.63987			0.322986			0.161493	−	0.986874i	$-0.448369\pi$
$127$	3.63987			0.322986			0.161493	+	0.986874i	$0.448369\pi$
$128$		0			0
$129$	−11.3283	+	17.1631i	−0.997399	+	1.51113i
$130$		0			0
$131$	7.05646	+	12.2221i	0.616526	+	1.06785i	0.990115	+	0.140260i	$0.0447937\pi$
$131$	7.05646	+	12.2221i	0.616526	+	1.06785i	−0.373589	+	0.927594i	$0.621873\pi$
$132$		0			0
$133$	3.33414	−	5.77490i	0.289107	−	0.500748i
$134$		0			0
$135$	−4.47057	−	12.4714i	−0.384766	−	1.07336i
$136$		0			0
$137$	5.31348	−	9.20322i	0.453961	−	0.786284i	−0.544666	−	0.838653i	$-0.683344\pi$
$137$	5.31348	−	9.20322i	0.453961	−	0.786284i	0.998628	+	0.0523685i	$0.0166770\pi$
$138$		0			0
$139$	−10.3195	−	17.8739i	−0.875290	−	1.51605i	−0.856454	−	0.516223i	$-0.827337\pi$
$139$	−10.3195	−	17.8739i	−0.875290	−	1.51605i	−0.0188355	−	0.999823i	$-0.505996\pi$
$140$		0			0
$141$	−1.18308	+	1.79244i	−0.0996332	+	0.150951i
$142$		0			0
$143$	−0.690302			−0.0577260
$144$		0			0
$145$	9.60612			0.797745
$146$		0			0
$147$	3.99366	+	7.98431i	0.329392	+	0.658535i
$148$		0			0
$149$	6.62678	+	11.4779i	0.542887	+	0.940308i	0.998737	+	0.0502511i	$0.0160022\pi$
$149$	6.62678	+	11.4779i	0.542887	+	0.940308i	−0.455850	+	0.890057i	$0.650665\pi$
$150$		0			0
$151$	6.39439	−	11.0754i	0.520368	−	0.901304i	−0.479352	−	0.877623i	$-0.659128\pi$
$151$	6.39439	−	11.0754i	0.520368	−	0.901304i	0.999720	−	0.0236808i	$-0.00753853\pi$
$152$		0			0
$153$	−2.55966	−	0.307605i	−0.206936	−	0.0248684i
$154$		0			0
$155$	7.99880	−	13.8543i	0.642479	−	1.11281i
$156$		0			0
$157$	−7.01781	−	12.1552i	−0.560082	−	0.970091i	−0.997489	−	0.0708267i	$-0.977436\pi$
$157$	−7.01781	−	12.1552i	−0.560082	−	0.970091i	0.437407	−	0.899264i	$-0.355897\pi$
$158$		0			0
$159$	5.64821	+	0.338168i	0.447932	+	0.0268184i
$160$		0			0
$161$	−9.58682			−0.755547
$162$		0			0
$163$	1.41590			0.110902			0.0554508	−	0.998461i	$-0.482340\pi$
$163$	1.41590			0.110902			0.0554508	+	0.998461i	$0.482340\pi$
$164$		0			0
$165$	−4.40825	−	0.263929i	−0.343182	−	0.0205468i
$166$		0			0
$167$	−6.84094	−	11.8489i	−0.529368	−	0.916892i	−0.999413	−	0.0342500i	$-0.989096\pi$
$167$	−6.84094	−	11.8489i	−0.529368	−	0.916892i	0.470045	−	0.882642i	$-0.344238\pi$
$168$		0			0
$169$	6.26174	−	10.8457i	0.481672	−	0.834281i
$170$		0			0
$171$	14.6196	+	1.75689i	1.11799	+	0.134353i
$172$		0			0
$173$	−2.53865	+	4.39708i	−0.193010	+	0.334303i	−0.946246	−	0.323447i	$-0.895158\pi$
$173$	−2.53865	+	4.39708i	−0.193010	+	0.334303i	0.753236	+	0.657750i	$0.228492\pi$
$174$		0			0
$175$	1.01946	+	1.76576i	0.0770643	+	0.133479i
$176$		0			0
$177$	−9.12377	−	18.2407i	−0.685784	−	1.37105i
$178$		0			0
$179$	19.5295			1.45970			0.729852	−	0.683605i	$-0.239589\pi$
$179$	19.5295			1.45970			0.729852	+	0.683605i	$0.239589\pi$
$180$		0			0
$181$	−3.21038			−0.238625			−0.119313	−	0.992857i	$-0.538069\pi$
$181$	−3.21038			−0.238625			−0.119313	+	0.992857i	$0.538069\pi$
$182$		0			0
$183$	0.436903	−	0.661936i	0.0322968	−	0.0489317i
$184$		0			0
$185$	2.48733	+	4.30819i	0.182872	+	0.316744i
$186$		0			0
$187$	−0.429679	+	0.744226i	−0.0314213	+	0.0544232i
$188$		0			0
$189$	4.56398	−	5.38568i	0.331981	−	0.391751i
$190$		0			0
$191$	4.21475	−	7.30016i	0.304968	−	0.528221i	−0.672286	−	0.740292i	$-0.734687\pi$
$191$	4.21475	−	7.30016i	0.304968	−	0.528221i	0.977254	+	0.212071i	$0.0680208\pi$
$192$		0			0
$193$	9.14821	+	15.8452i	0.658503	+	1.14056i	0.981003	+	0.193991i	$0.0621432\pi$
$193$	9.14821	+	15.8452i	0.658503	+	1.14056i	−0.322501	+	0.946569i	$0.604523\pi$
$194$		0			0
$195$	−1.67929	+	2.54424i	−0.120257	+	0.182197i
$196$		0			0
$197$	21.9150			1.56138			0.780689	−	0.624920i	$-0.214869\pi$
$197$	21.9150			1.56138			0.780689	+	0.624920i	$0.214869\pi$
$198$		0			0
$199$	−3.88895			−0.275680			−0.137840	−	0.990455i	$-0.544016\pi$
$199$	−3.88895			−0.275680			−0.137840	+	0.990455i	$0.544016\pi$
$200$		0			0
$201$	−5.81063	−	11.6169i	−0.409850	−	0.819391i
$202$		0			0
$203$	2.55931	+	4.43286i	0.179628	+	0.311126i
$204$		0			0
$205$	10.6011	−	18.3617i	0.740416	−	1.28244i
$206$		0			0
$207$	−8.32164	−	19.4652i	−0.578394	−	1.35292i
$208$		0			0
$209$	2.45412	−	4.25067i	0.169755	−	0.294025i
$210$		0			0
$211$	−11.4128	−	19.7676i	−0.785690	−	1.36085i	−0.928586	−	0.371117i	$-0.878975\pi$
$211$	−11.4128	−	19.7676i	−0.785690	−	1.36085i	0.142896	−	0.989738i	$-0.454359\pi$
$212$		0			0
$213$	−7.75399	−	0.464244i	−0.531294	−	0.0318094i
$214$		0			0
$215$	30.2720			2.06453
$216$		0			0
$217$	8.52433			0.578669
$218$		0			0
$219$	16.0246	+	0.959419i	1.08284	+	0.0648315i
$220$		0			0
$221$	0.296609	+	0.513741i	0.0199521	+	0.0345580i
$222$		0			0
$223$	−8.21509	+	14.2290i	−0.550123	+	0.952842i	0.448142	+	0.893963i	$0.352086\pi$
$223$	−8.21509	+	14.2290i	−0.550123	+	0.952842i	−0.998265	+	0.0588792i	$0.981247\pi$
$224$		0			0
$225$	−2.70030	+	3.60267i	−0.180020	+	0.240178i
$226$		0			0
$227$	4.20830	−	7.28898i	0.279314	−	0.483787i	−0.691900	−	0.721993i	$-0.743226\pi$
$227$	4.20830	−	7.28898i	0.279314	−	0.483787i	0.971215	+	0.238207i	$0.0765595\pi$
$228$		0			0
$229$	−13.3952	−	23.2011i	−0.885177	−	1.53317i	−0.845511	−	0.533959i	$-0.820704\pi$
$229$	−13.3952	−	23.2011i	−0.885177	−	1.53317i	−0.0396665	−	0.999213i	$-0.512630\pi$
$230$		0			0
$231$	−1.05268	−	2.10456i	−0.0692609	−	0.138470i
$232$		0			0
$233$	4.83697			0.316881			0.158440	−	0.987369i	$-0.449353\pi$
$233$	4.83697			0.316881			0.158440	+	0.987369i	$0.449353\pi$
$234$		0			0
$235$	3.16149			0.206233
$236$		0			0
$237$	−15.2732	+	23.1399i	−0.992102	+	1.50310i
$238$		0			0
$239$	7.17852	+	12.4336i	0.464340	+	0.804261i	0.999171	−	0.0406982i	$-0.0129582\pi$
$239$	7.17852	+	12.4336i	0.464340	+	0.804261i	−0.534831	+	0.844959i	$0.679625\pi$
$240$		0			0
$241$	−8.86314	+	15.3514i	−0.570925	+	0.988872i	0.425546	+	0.904937i	$0.360082\pi$
$241$	−8.86314	+	15.3514i	−0.570925	+	0.988872i	−0.996471	+	0.0839348i	$0.973251\pi$
$242$		0			0
$243$	14.8968	+	4.59183i	0.955631	+	0.294566i
$244$		0			0
$245$	6.57078	−	11.3809i	0.419792	−	0.727101i
$246$		0			0
$247$	−1.69409	−	2.93425i	−0.107792	−	0.186702i
$248$		0			0
$249$	−8.36392	+	12.6719i	−0.530042	+	0.803048i
$250$		0			0
$251$	−5.12704			−0.323616			−0.161808	−	0.986822i	$-0.551733\pi$
$251$	−5.12704			−0.323616			−0.161808	+	0.986822i	$0.551733\pi$
$252$		0			0
$253$	−7.05646			−0.443636
$254$		0			0
$255$	1.69771	+	3.39414i	0.106315	+	0.212549i
$256$		0			0
$257$	4.79205	+	8.30008i	0.298920	+	0.517745i	0.975889	−	0.218267i	$-0.0700403\pi$
$257$	4.79205	+	8.30008i	0.298920	+	0.517745i	−0.676969	+	0.736011i	$0.736707\pi$
$258$		0			0
$259$	−1.32538	+	2.29562i	−0.0823549	+	0.142643i
$260$		0			0
$261$	−6.77896	+	9.04430i	−0.419607	+	0.559828i
$262$		0			0
$263$	−0.399021	+	0.691125i	−0.0246047	+	0.0426166i	−0.878066	−	0.478540i	$-0.841166\pi$
$263$	−0.399021	+	0.691125i	−0.0246047	+	0.0426166i	0.853461	+	0.521157i	$0.174499\pi$
$264$		0			0
$265$	−4.16466	−	7.21341i	−0.255833	−	0.443116i
$266$		0			0
$267$	−6.21131	−	0.371881i	−0.380126	−	0.0227588i
$268$		0			0
$269$	−0.399907			−0.0243827			−0.0121914	−	0.999926i	$-0.503881\pi$
$269$	−0.399907			−0.0243827			−0.0121914	+	0.999926i	$0.503881\pi$
$270$		0			0
$271$	24.6717			1.49870			0.749349	−	0.662175i	$-0.230366\pi$
$271$	24.6717			1.49870			0.749349	+	0.662175i	$0.230366\pi$
$272$		0			0
$273$	−1.62148	−	0.0970804i	−0.0981362	−	0.00587557i
$274$		0			0
$275$	0.750386	+	1.29971i	0.0452500	+	0.0783752i
$276$		0			0
$277$	13.6123	−	23.5773i	0.817886	−	1.41662i	−0.0893511	−	0.996000i	$-0.528479\pi$
$277$	13.6123	−	23.5773i	0.817886	−	1.41662i	0.907237	−	0.420620i	$-0.138187\pi$
$278$		0			0
$279$	7.39937	+	17.3079i	0.442989	+	1.03620i
$280$		0			0
$281$	−14.6537	+	25.3809i	−0.874164	+	1.51410i	−0.0165127	+	0.999864i	$0.505256\pi$
$281$	−14.6537	+	25.3809i	−0.874164	+	1.51410i	−0.857651	+	0.514232i	$0.828077\pi$
$282$		0			0
$283$	−3.66242	−	6.34350i	−0.217708	−	0.377082i	0.736399	−	0.676548i	$-0.236525\pi$
$283$	−3.66242	−	6.34350i	−0.217708	−	0.377082i	−0.954107	+	0.299466i	$0.903191\pi$
$284$		0			0
$285$	−9.69652	−	19.3857i	−0.574372	−	1.14831i
$286$		0			0
$287$	11.2976			0.666879
$288$		0			0
$289$	−16.2615			−0.956559
$290$		0			0
$291$	−6.20830	+	9.40598i	−0.363937	+	0.551388i
$292$		0			0
$293$	−6.18609	−	10.7146i	−0.361395	−	0.625955i	0.626795	−	0.779184i	$-0.284366\pi$
$293$	−6.18609	−	10.7146i	−0.361395	−	0.625955i	−0.988191	+	0.153229i	$0.951033\pi$
$294$		0			0
$295$	−15.0114	+	26.0004i	−0.873995	+	1.51380i
$296$		0			0
$297$	3.35936	−	3.96418i	0.194930	−	0.230025i
$298$		0			0
$299$	−2.43555	+	4.21849i	−0.140851	+	0.243961i
$300$		0			0
$301$	8.06523	+	13.9694i	0.464872	+	0.805182i
$302$		0			0
$303$	−0.100517	+	0.152290i	−0.00577456	+	0.00874883i
$304$		0			0
$305$	−1.16751			−0.0668517
$306$		0			0
$307$	−34.8873			−1.99112			−0.995560	−	0.0941261i	$-0.969994\pi$
$307$	−34.8873			−1.99112			−0.995560	+	0.0941261i	$0.969994\pi$
$308$		0			0
$309$	−2.17644	−	4.35124i	−0.123813	−	0.247533i
$310$		0			0
$311$	1.23575	+	2.14039i	0.0700732	+	0.121370i	0.898933	−	0.438086i	$-0.144343\pi$
$311$	1.23575	+	2.14039i	0.0700732	+	0.121370i	−0.828860	+	0.559456i	$0.811010\pi$
$312$		0			0
$313$	8.91659	−	15.4440i	0.503995	−	0.872946i	−0.495994	−	0.868326i	$-0.665196\pi$
$313$	8.91659	−	15.4440i	0.503995	−	0.872946i	0.999989	−	0.00461974i	$-0.00147052\pi$
$314$		0			0
$315$	−10.3176	−	1.23990i	−0.581330	−	0.0698607i
$316$		0			0
$317$	10.3372	−	17.9045i	0.580593	−	1.00562i	−0.414817	−	0.909905i	$-0.636154\pi$
$317$	10.3372	−	17.9045i	0.580593	−	1.00562i	0.995409	−	0.0957108i	$-0.0305124\pi$
$318$		0			0
$319$	1.88380	+	3.26284i	0.105473	+	0.182684i
$320$		0			0
$321$	−21.9160	−	1.31215i	−1.22323	−	0.0732368i
$322$		0			0
$323$	−4.21795			−0.234693
$324$		0			0
$325$	1.03599			0.0574661
$326$		0			0
$327$	20.8451	+	1.24803i	1.15274	+	0.0690161i
$328$		0			0
$329$	0.842299	+	1.45891i	0.0464375	+	0.0804320i
$330$		0			0
$331$	8.05947	−	13.9594i	0.442989	−	0.767279i	−0.554921	−	0.831903i	$-0.687251\pi$
$331$	8.05947	−	13.9594i	0.442989	−	0.767279i	0.997910	+	0.0646240i	$0.0205848\pi$
$332$		0			0
$333$	−5.81152	−	0.698393i	−0.318469	−	0.0382717i
$334$		0			0
$335$	−9.56025	+	16.5588i	−0.522332	+	0.904706i
$336$		0			0
$337$	−15.3982	−	26.6704i	−0.838792	−	1.45283i	−0.890905	−	0.454189i	$-0.849929\pi$
$337$	−15.3982	−	26.6704i	−0.838792	−	1.45283i	0.0521133	−	0.998641i	$-0.483404\pi$
$338$		0			0
$339$	9.78962	+	19.5719i	0.531699	+	1.06300i
$340$		0			0
$341$	6.27441			0.339778
$342$		0			0
$343$	16.5126			0.891597
$344$		0			0
$345$	−17.1662	+	26.0079i	−0.924197	+	1.40022i
$346$		0			0
$347$	−4.88605	−	8.46288i	−0.262297	−	0.454311i	0.704555	−	0.709649i	$-0.251147\pi$
$347$	−4.88605	−	8.46288i	−0.262297	−	0.454311i	−0.966852	+	0.255338i	$0.917813\pi$
$348$		0			0
$349$	−2.09778	+	3.63346i	−0.112292	+	0.194495i	−0.916694	−	0.399590i	$-0.869152\pi$
$349$	−2.09778	+	3.63346i	−0.112292	+	0.194495i	0.804402	+	0.594085i	$0.202486\pi$
$350$		0			0
$351$	−1.21038	−	3.37653i	−0.0646051	−	0.180226i
$352$		0			0
$353$	−10.3802	+	17.9790i	−0.552481	+	0.956926i	0.445613	+	0.895225i	$0.352986\pi$
$353$	−10.3802	+	17.9790i	−0.552481	+	0.956926i	−0.998095	+	0.0617002i	$0.980348\pi$
$354$		0			0
$355$	5.71734	+	9.90272i	0.303445	+	0.525582i
$356$		0			0
$357$	−1.11395	+	1.68771i	−0.0589567	+	0.0893232i
$358$		0			0
$359$	−30.3509			−1.60186			−0.800929	−	0.598760i	$-0.795660\pi$
$359$	−30.3509			−1.60186			−0.800929	+	0.598760i	$0.795660\pi$
$360$		0			0
$361$	5.09090			0.267942
$362$		0			0
$363$	−0.774830	−	1.54908i	−0.0406681	−	0.0813054i
$364$		0			0
$365$	−11.8156	−	20.4652i	−0.618457	−	1.07120i
$366$		0			0
$367$	12.1440	−	21.0340i	0.633912	−	1.09797i	−0.352833	−	0.935686i	$-0.614782\pi$
$367$	12.1440	−	21.0340i	0.633912	−	1.09797i	0.986745	−	0.162281i	$-0.0518851\pi$
$368$		0			0
$369$	9.80668	+	22.9388i	0.510516	+	1.19415i
$370$		0			0
$371$	2.21914	−	3.84367i	0.115212	−	0.199553i
$372$		0			0
$373$	1.78448	+	3.09081i	0.0923970	+	0.160036i	0.908519	−	0.417843i	$-0.137214\pi$
$373$	1.78448	+	3.09081i	0.0923970	+	0.160036i	−0.816122	+	0.577879i	$0.803880\pi$
$374$		0			0
$375$	−15.4255	−	0.923548i	−0.796568	−	0.0476918i
$376$		0			0
$377$	2.60079			0.133947
$378$		0			0
$379$	17.1467			0.880765			0.440383	−	0.897810i	$-0.354843\pi$
$379$	17.1467			0.880765			0.440383	+	0.897810i	$0.354843\pi$
$380$		0			0
$381$	6.29317	+	0.376782i	0.322409	+	0.0193031i
$382$		0			0
$383$	14.5284	+	25.1639i	0.742366	+	1.28582i	0.951415	+	0.307911i	$0.0996298\pi$
$383$	14.5284	+	25.1639i	0.742366	+	1.28582i	−0.209049	+	0.977905i	$0.567037\pi$
$384$		0			0
$385$	−1.73197	+	2.99986i	−0.0882693	+	0.152887i
$386$		0			0
$387$	−21.3627	+	28.5015i	−1.08593	+	1.44882i
$388$		0			0
$389$	−14.5949	+	25.2792i	−0.739992	+	1.28170i	0.212506	+	0.977160i	$0.431838\pi$
$389$	−14.5949	+	25.2792i	−0.739992	+	1.28170i	−0.952498	+	0.304544i	$0.901496\pi$
$390$		0			0
$391$	3.03202	+	5.25160i	0.153336	+	0.265585i
$392$		0			0
$393$	10.9351	+	21.8620i	0.551604	+	1.10279i
$394$		0			0
$395$	40.8139			2.05357
$396$		0			0
$397$	−25.4582			−1.27771			−0.638856	−	0.769326i	$-0.720592\pi$
$397$	−25.4582			−1.27771			−0.638856	+	0.769326i	$0.720592\pi$
$398$		0			0
$399$	6.36237	−	9.63941i	0.318517	−	0.482574i
$400$		0			0
$401$	11.1474	+	19.3079i	0.556677	+	0.964192i	0.997771	+	0.0667315i	$0.0212571\pi$
$401$	11.1474	+	19.3079i	0.556677	+	0.964192i	−0.441094	+	0.897461i	$0.645410\pi$
$402$		0			0
$403$	2.16562	−	3.75096i	0.107877	−	0.186849i
$404$		0			0
$405$	−6.43845	−	22.0252i	−0.319929	−	1.09444i
$406$		0			0
$407$	−0.975555	+	1.68971i	−0.0483565	+	0.0837559i
$408$		0			0
$409$	1.22274	+	2.11785i	0.0604607	+	0.104721i	0.894671	−	0.446725i	$-0.147410\pi$
$409$	1.22274	+	2.11785i	0.0604607	+	0.104721i	−0.834211	+	0.551446i	$0.814076\pi$
$410$		0			0
$411$	10.1394	−	15.3619i	0.500142	−	0.757748i
$412$		0			0
$413$	−15.9976			−0.787191
$414$		0			0
$415$	22.3505			1.09714
$416$		0			0
$417$	−15.9917	−	31.9714i	−0.783119	−	1.56565i
$418$		0			0
$419$	−12.3864	−	21.4539i	−0.605115	−	1.04809i	−0.992033	−	0.125976i	$-0.959794\pi$
$419$	−12.3864	−	21.4539i	−0.605115	−	1.04809i	0.386918	−	0.922114i	$-0.373540\pi$
$420$		0			0
$421$	−13.1932	+	22.8514i	−0.642999	+	1.11371i	0.341761	+	0.939787i	$0.388977\pi$
$421$	−13.1932	+	22.8514i	−0.642999	+	1.11371i	−0.984760	+	0.173920i	$0.944357\pi$
$422$		0			0
$423$	−2.23104	+	2.97659i	−0.108477	+	0.144727i
$424$		0			0
$425$	0.644850	−	1.11691i	0.0312798	−	0.0541783i
$426$		0			0
$427$	−0.311055	−	0.538763i	−0.0150530	−	0.0260726i
$428$		0			0
$429$	−1.19350	−	0.0714568i	−0.0576228	−	0.00344997i
$430$		0			0
$431$	−22.6717			−1.09206			−0.546029	−	0.837767i	$-0.683861\pi$
$431$	−22.6717			−1.09206			−0.546029	+	0.837767i	$0.683861\pi$
$432$		0			0
$433$	−15.9496			−0.766487			−0.383244	−	0.923647i	$-0.625193\pi$
$433$	−15.9496			−0.766487			−0.383244	+	0.923647i	$0.625193\pi$
$434$		0			0
$435$	16.6085	+	0.994381i	0.796319	+	0.0476769i
$436$		0			0
$437$	−17.3174	−	29.9947i	−0.828405	−	1.43484i
$438$		0			0
$439$	−12.1827	+	21.1010i	−0.581446	+	1.00709i	0.413862	+	0.910340i	$0.364180\pi$
$439$	−12.1827	+	21.1010i	−0.581446	+	1.00709i	−0.995308	+	0.0967550i	$0.969154\pi$
$440$		0			0
$441$	6.07836	+	14.2179i	0.289446	+	0.677044i
$442$		0			0
$443$	13.7850	−	23.8763i	0.654945	−	1.13440i	−0.326963	−	0.945037i	$-0.606025\pi$
$443$	13.7850	−	23.8763i	0.654945	−	1.13440i	0.981908	−	0.189360i	$-0.0606414\pi$
$444$		0			0
$445$	4.57986	+	7.93255i	0.217106	+	0.376039i
$446$		0			0
$447$	10.2693	+	20.5308i	0.485720	+	0.971073i
$448$		0			0
$449$	26.7668			1.26320			0.631601	−	0.775294i	$-0.282398\pi$
$449$	26.7668			1.26320			0.631601	+	0.775294i	$0.282398\pi$
$450$		0			0
$451$	8.31573			0.391572
$452$		0			0
$453$	12.2021	−	18.4870i	0.573304	−	0.868593i
$454$		0			0
$455$	1.19558	+	2.07081i	0.0560497	+	0.0970810i
$456$		0			0
$457$	−1.13342	+	1.96314i	−0.0530191	+	0.0918317i	−0.891317	−	0.453381i	$-0.850218\pi$
$457$	−1.13342	+	1.96314i	−0.0530191	+	0.0918317i	0.838298	+	0.545213i	$0.183551\pi$
$458$		0			0
$459$	−4.39369	−	0.796798i	−0.205080	−	0.0371914i
$460$		0			0
$461$	−13.7824	+	23.8718i	−0.641910	+	1.11182i	0.343095	+	0.939301i	$0.388525\pi$
$461$	−13.7824	+	23.8718i	−0.641910	+	1.11182i	−0.985006	+	0.172521i	$0.944809\pi$
$462$		0			0
$463$	4.40103	+	7.62280i	0.204533	+	0.354262i	0.949984	−	0.312299i	$-0.101099\pi$
$463$	4.40103	+	7.62280i	0.204533	+	0.354262i	−0.745451	+	0.666561i	$0.767766\pi$
$464$		0			0
$465$	15.2637	−	23.1255i	0.707837	−	1.07242i
$466$		0			0
$467$	−5.49474			−0.254266			−0.127133	−	0.991886i	$-0.540578\pi$
$467$	−5.49474			−0.254266			−0.127133	+	0.991886i	$0.540578\pi$
$468$		0			0
$469$	−10.1884			−0.470455
$470$		0			0
$471$	−10.8752	−	21.7422i	−0.501104	−	1.00183i
$472$		0			0
$473$	5.93648	+	10.2823i	0.272960	+	0.472780i
$474$		0			0
$475$	−3.68308	+	6.37928i	−0.168991	+	0.292701i
$476$		0			0
$477$	9.73050	+	1.16935i	0.445529	+	0.0535410i
$478$		0			0
$479$	12.1971	−	21.1260i	0.557300	−	0.965272i	−0.440421	−	0.897791i	$-0.645171\pi$
$479$	12.1971	−	21.1260i	0.557300	−	0.965272i	0.997721	−	0.0674801i	$-0.0214959\pi$
$480$		0			0
$481$	0.673428	+	1.16641i	0.0307057	+	0.0531838i
$482$		0			0
$483$	−16.5752	−	0.992382i	−0.754197	−	0.0451550i
$484$		0			0
$485$	16.5901			0.753319
$486$		0			0
$487$	−18.0936			−0.819900			−0.409950	−	0.912108i	$-0.634454\pi$
$487$	−18.0936			−0.819900			−0.409950	+	0.912108i	$0.634454\pi$
$488$		0			0
$489$	2.44802	+	0.146567i	0.110703	+	0.00662798i
$490$		0			0
$491$	−16.1990	−	28.0575i	−0.731050	−	1.26622i	−0.956435	−	0.291946i	$-0.905697\pi$
$491$	−16.1990	−	28.0575i	−0.731050	−	1.26622i	0.225384	−	0.974270i	$-0.427636\pi$
$492$		0			0
$493$	1.61886	−	2.80395i	0.0729099	−	0.126284i
$494$		0			0
$495$	−7.59434	−	0.912642i	−0.341340	−	0.0410202i
$496$		0			0
$497$	−3.04648	+	5.27667i	−0.136654	+	0.236691i
$498$		0			0
$499$	6.42667	+	11.1313i	0.287697	+	0.498306i	0.973260	−	0.229708i	$-0.0737770\pi$
$499$	6.42667	+	11.1313i	0.287697	+	0.498306i	−0.685563	+	0.728014i	$0.740444\pi$
$500$		0			0
$501$	−10.6011	−	21.1943i	−0.473624	−	0.946891i
$502$		0			0
$503$	−33.4453			−1.49125			−0.745627	−	0.666364i	$-0.767850\pi$
$503$	−33.4453			−1.49125			−0.745627	+	0.666364i	$0.767850\pi$
$504$		0			0
$505$	0.268607			0.0119529
$506$		0			0
$507$	11.9490	−	18.1035i	0.530672	−	0.804003i
$508$		0			0
$509$	18.9789	+	32.8724i	0.841226	+	1.45705i	0.888859	+	0.458181i	$0.151499\pi$
$509$	18.9789	+	32.8724i	0.841226	+	1.45705i	−0.0476334	+	0.998865i	$0.515168\pi$
$510$		0			0
$511$	6.29595	−	10.9049i	0.278517	−	0.482405i
$512$		0			0
$513$	25.0947	+	4.55093i	1.10796	+	0.200929i
$514$		0			0
$515$	−3.58091	+	6.20231i	−0.157794	+	0.273306i
$516$		0			0
$517$	0.619982	+	1.07384i	0.0272668	+	0.0472274i
$518$		0			0
$519$	−4.84438	+	7.33955i	−0.212645	+	0.322171i
$520$		0			0
$521$	−23.6337			−1.03541			−0.517705	−	0.855559i	$-0.673214\pi$
$521$	−23.6337			−1.03541			−0.517705	+	0.855559i	$0.673214\pi$
$522$		0			0
$523$	−43.8130			−1.91581			−0.957905	−	0.287085i	$-0.907314\pi$
$523$	−43.8130			−1.91581			−0.957905	+	0.287085i	$0.907314\pi$
$524$		0			0
$525$	1.57982	+	3.15846i	0.0689492	+	0.137846i
$526$		0			0
$527$	−2.69598	−	4.66958i	−0.117439	−	0.203410i
$528$		0			0
$529$	−13.3968	+	23.2040i	−0.582470	+	1.00887i
$530$		0			0
$531$	−13.8864	−	32.4817i	−0.602618	−	1.40959i
$532$		0			0
$533$	2.87018	−	4.97130i	0.124321	−	0.215331i
$534$		0			0
$535$	16.1596	+	27.9892i	0.698639	+	1.21008i
$536$		0			0
$537$	33.7656	+	2.02160i	1.45709	+	0.0872386i
$538$		0			0
$539$	5.15424			0.222009
$540$		0			0
$541$	32.9434			1.41635			0.708173	−	0.706039i	$-0.249519\pi$
$541$	32.9434			1.41635			0.708173	+	0.706039i	$0.249519\pi$
$542$		0			0
$543$	−5.55059	−	0.332323i	−0.238199	−	0.0142613i
$544$		0			0
$545$	−15.3699	−	26.6215i	−0.658376	−	1.14034i
$546$		0			0
$547$	−5.44312	+	9.42775i	−0.232731	+	0.403102i	−0.958611	−	0.284720i	$-0.908099\pi$
$547$	−5.44312	+	9.42775i	−0.232731	+	0.403102i	0.725880	+	0.687821i	$0.241433\pi$
$548$		0			0
$549$	0.823905	−	1.09923i	0.0351634	−	0.0469141i
$550$		0			0
$551$	−9.24618	+	16.0148i	−0.393900	+	0.682255i
$552$		0			0
$553$	10.8738	+	18.8340i	0.462403	+	0.800905i
$554$		0			0
$555$	3.85453	+	7.70614i	0.163616	+	0.327108i
$556$		0			0
$557$	−13.3964			−0.567625			−0.283813	−	0.958880i	$-0.591599\pi$
$557$	−13.3964			−0.567625			−0.283813	+	0.958880i	$0.591599\pi$
$558$		0			0
$559$	8.19593			0.346651
$560$		0			0
$561$	−0.819935	+	1.24226i	−0.0346177	+	0.0524481i
$562$		0			0
$563$	4.48579	+	7.76962i	0.189054	+	0.327450i	0.944935	−	0.327258i	$-0.106125\pi$
$563$	4.48579	+	7.76962i	0.189054	+	0.327450i	−0.755881	+	0.654709i	$0.772791\pi$
$564$		0			0
$565$	16.1069	−	27.8980i	0.677622	−	1.17368i
$566$		0			0
$567$	8.44842	−	8.83916i	0.354800	−	0.371210i
$568$		0			0
$569$	17.8669	−	30.9464i	0.749021	−	1.29734i	−0.199272	−	0.979944i	$-0.563858\pi$
$569$	17.8669	−	30.9464i	0.749021	−	1.29734i	0.948293	−	0.317398i	$-0.102809\pi$
$570$		0			0
$571$	−7.33052	−	12.6968i	−0.306773	−	0.531346i	0.670882	−	0.741564i	$-0.265916\pi$
$571$	−7.33052	−	12.6968i	−0.306773	−	0.531346i	−0.977654	+	0.210218i	$0.932582\pi$
$572$		0			0
$573$	8.04279	−	12.1853i	0.335992	−	0.509050i
$574$		0			0
$575$	10.5901			0.441639
$576$		0			0
$577$	2.04772			0.0852476			0.0426238	−	0.999091i	$-0.486428\pi$
$577$	2.04772			0.0852476			0.0426238	+	0.999091i	$0.486428\pi$
$578$		0			0
$579$	14.1766	+	28.3426i	0.589161	+	1.17788i
$580$		0			0
$581$	5.95473	+	10.3139i	0.247044	+	0.427893i
$582$		0			0
$583$	1.63342	−	2.82916i	0.0676493	−	0.117172i
$584$		0			0
$585$	−3.16679	+	4.22504i	−0.130931	+	0.174684i
$586$		0			0
$587$	17.0254	−	29.4888i	0.702713	−	1.21713i	−0.264798	−	0.964304i	$-0.585305\pi$
$587$	17.0254	−	29.4888i	0.702713	−	1.21713i	0.967511	−	0.252830i	$-0.0813613\pi$
$588$		0			0
$589$	15.3982	+	26.6704i	0.634471	+	1.09894i
$590$		0			0
$591$	37.8900	+	2.26853i	1.55859	+	0.0933151i
$592$		0			0
$593$	0.780511			0.0320518			0.0160259	−	0.999872i	$-0.494899\pi$
$593$	0.780511			0.0320518			0.0160259	+	0.999872i	$0.494899\pi$
$594$		0			0
$595$	2.97677			0.122035
$596$		0			0
$597$	−6.72381	−	0.402565i	−0.275187	−	0.0164759i
$598$		0			0
$599$	7.08712	+	12.2752i	0.289572	+	0.501553i	0.973708	−	0.227802i	$-0.0731538\pi$
$599$	7.08712	+	12.2752i	0.289572	+	0.501553i	−0.684136	+	0.729355i	$0.739820\pi$
$600$		0			0
$601$	6.43346	−	11.1431i	0.262426	−	0.454536i	−0.704460	−	0.709744i	$-0.748811\pi$
$601$	6.43346	−	11.1431i	0.262426	−	0.454536i	0.966886	+	0.255208i	$0.0821439\pi$
$602$		0			0
$603$	−8.84379	−	20.6865i	−0.360147	−	0.842421i
$604$		0			0
$605$	−1.27483	+	2.20807i	−0.0518292	+	0.0897709i
$606$		0			0
$607$	−5.32295	−	9.21962i	−0.216052	−	0.374213i	0.737546	−	0.675297i	$-0.235985\pi$
$607$	−5.32295	−	9.21962i	−0.216052	−	0.374213i	−0.953597	+	0.301085i	$0.902651\pi$
$608$		0			0
$609$	3.96607	+	7.92914i	0.160713	+	0.321305i
$610$		0			0
$611$	0.855949			0.0346280
$612$		0			0
$613$	−15.9360			−0.643648			−0.321824	−	0.946800i	$-0.604296\pi$
$613$	−15.9360			−0.643648			−0.321824	+	0.946800i	$0.604296\pi$
$614$		0			0
$615$	20.2296	−	30.6492i	0.815737	−	1.23589i
$616$		0			0
$617$	5.43629	+	9.41594i	0.218857	+	0.379071i	0.954459	−	0.298343i	$-0.0964339\pi$
$617$	5.43629	+	9.41594i	0.218857	+	0.379071i	−0.735602	+	0.677414i	$0.763101\pi$
$618$		0			0
$619$	−11.7006	+	20.2661i	−0.470289	+	0.814564i	−0.999423	−	0.0339743i	$-0.989184\pi$
$619$	−11.7006	+	20.2661i	−0.470289	+	0.814564i	0.529134	+	0.848538i	$0.322517\pi$
$620$		0			0
$621$	−12.3728	−	34.5158i	−0.496503	−	1.38507i
$622$		0			0
$623$	−2.44038	+	4.22686i	−0.0977717	+	0.169346i
$624$		0			0
$625$	15.1258	+	26.1986i	0.605031	+	1.04794i
$626$		0			0
$627$	4.68308	−	7.09517i	0.187024	−	0.283354i
$628$		0			0
$629$	1.67670			0.0668546
$630$		0			0
$631$	41.6204			1.65688			0.828441	−	0.560076i	$-0.189228\pi$
$631$	41.6204			1.65688			0.828441	+	0.560076i	$0.189228\pi$
$632$		0			0
$633$	−17.6860	−	35.3586i	−0.702955	−	1.40538i
$634$		0			0
$635$	−4.64022	−	8.03709i	−0.184141	−	0.318942i
$636$		0			0
$637$	1.77899	−	3.08130i	0.0704862	−	0.122086i
$638$		0			0
$639$	−13.3582	−	1.60531i	−0.528444	−	0.0635052i
$640$		0			0
$641$	4.85600	−	8.41083i	0.191800	−	0.332208i	−0.754047	−	0.656821i	$-0.771901\pi$
$641$	4.85600	−	8.41083i	0.191800	−	0.332208i	0.945847	+	0.324613i	$0.105234\pi$
$642$		0			0
$643$	−9.03279	−	15.6452i	−0.356218	−	0.616988i	0.631107	−	0.775695i	$-0.282601\pi$
$643$	−9.03279	−	15.6452i	−0.356218	−	0.616988i	−0.987326	+	0.158707i	$0.949267\pi$
$644$		0			0
$645$	52.3389	+	3.13362i	2.06084	+	0.123386i
$646$		0			0
$647$	−43.2031			−1.69849			−0.849245	−	0.527999i	$-0.822943\pi$
$647$	−43.2031			−1.69849			−0.849245	+	0.527999i	$0.822943\pi$
$648$		0			0
$649$	−11.7752			−0.462216
$650$		0			0
$651$	14.7382	+	0.882399i	0.577635	+	0.0345839i
$652$		0			0
$653$	−24.5125	−	42.4569i	−0.959247	−	1.66146i	−0.724335	−	0.689448i	$-0.757853\pi$
$653$	−24.5125	−	42.4569i	−0.959247	−	1.66146i	−0.234912	−	0.972017i	$-0.575480\pi$
$654$		0			0
$655$	17.9916	−	31.1623i	0.702989	−	1.21761i
$656$		0			0
$657$	27.6065	+	3.31758i	1.07703	+	0.129431i
$658$		0			0
$659$	2.25239	−	3.90125i	0.0877406	−	0.151971i	−0.818815	−	0.574057i	$-0.805369\pi$
$659$	2.25239	−	3.90125i	0.0877406	−	0.151971i	0.906556	+	0.422086i	$0.138702\pi$
$660$		0			0
$661$	16.5238	+	28.6201i	0.642703	+	1.11319i	0.984827	+	0.173539i	$0.0555203\pi$
$661$	16.5238	+	28.6201i	0.642703	+	1.11319i	−0.342124	+	0.939655i	$0.611146\pi$
$662$		0			0
$663$	0.459643	+	0.918939i	0.0178510	+	0.0356886i
$664$		0			0
$665$	−17.0019			−0.659304
$666$		0			0
$667$	26.5860			1.02941
$668$		0			0
$669$	−15.6764	+	23.7508i	−0.606086	+	0.918261i
$670$		0			0
$671$	−0.228955	−	0.396561i	−0.00883870	−	0.0153091i
$672$		0			0
$673$	15.7869	−	27.3437i	0.608540	−	1.05402i	−0.382942	−	0.923773i	$-0.625089\pi$
$673$	15.7869	−	27.3437i	0.608540	−	1.05402i	0.991481	−	0.130249i	$-0.0415777\pi$
$674$		0			0
$675$	−5.04163	+	5.94932i	−0.194052	+	0.228990i
$676$		0			0
$677$	10.2710	−	17.7898i	0.394745	−	0.683719i	−0.598323	−	0.801255i	$-0.704166\pi$
$677$	10.2710	−	17.7898i	0.394745	−	0.683719i	0.993069	+	0.117536i	$0.0374995\pi$
$678$		0			0
$679$	4.42003	+	7.65571i	0.169625	+	0.293799i
$680$		0			0
$681$	8.03047	−	12.1667i	0.307728	−	0.466229i
$682$		0			0
$683$	13.0151			0.498011			0.249005	−	0.968502i	$-0.419896\pi$
$683$	13.0151			0.498011			0.249005	+	0.968502i	$0.419896\pi$
$684$		0			0
$685$	−27.0952			−1.03525
$686$		0			0
$687$	−20.7580	−	41.5003i	−0.791965	−	1.58333i
$688$		0			0
$689$	−1.12755	−	1.95298i	−0.0429563	−	0.0744025i
$690$		0			0
$691$	−4.96892	+	8.60642i	−0.189027	+	0.327404i	−0.944926	−	0.327284i	$-0.893867\pi$
$691$	−4.96892	+	8.60642i	−0.189027	+	0.327404i	0.755899	+	0.654688i	$0.227200\pi$
$692$		0			0
$693$	−1.60217	−	3.74765i	−0.0608616	−	0.142361i
$694$		0			0
$695$	−26.3113	+	45.5724i	−0.998043	+	1.72866i
$696$		0			0
$697$	−3.57310	−	6.18878i	−0.135341	−	0.234417i
$698$		0			0
$699$	8.36291	+	0.500701i	0.316314	+	0.0189382i
$700$		0			0
$701$	−44.4418			−1.67854			−0.839271	−	0.543713i	$-0.817018\pi$
$701$	−44.4418			−1.67854			−0.839271	+	0.543713i	$0.817018\pi$
$702$		0			0
$703$	−9.57653			−0.361186
$704$		0			0
$705$	5.46607	+	0.327262i	0.205864	+	0.0123254i
$706$		0			0
$707$	0.0715637	+	0.123952i	0.00269143	+	0.00466169i
$708$		0			0
$709$	14.9579	−	25.9079i	0.561756	−	0.972990i	−0.435587	−	0.900146i	$-0.643459\pi$
$709$	14.9579	−	25.9079i	0.561756	−	0.972990i	0.997343	−	0.0728436i	$-0.0232074\pi$
$710$		0			0
$711$	−28.8020	+	38.4269i	−1.08016	+	1.44112i
$712$		0			0
$713$	22.1376	−	38.3434i	0.829058	−	1.43597i
$714$		0			0
$715$	0.880018	+	1.52424i	0.0329108	+	0.0570032i
$716$		0			0
$717$	11.1243	+	22.2402i	0.415444	+	0.830574i
$718$		0			0
$719$	−20.4897			−0.764138			−0.382069	−	0.924134i	$-0.624788\pi$
$719$	−20.4897			−0.764138			−0.382069	+	0.924134i	$0.624788\pi$
$720$		0			0
$721$	−3.81617			−0.142122
$722$		0			0
$723$	−16.9131	+	25.6244i	−0.629004	+	0.952983i
$724$		0			0
$725$	−2.82716	−	4.89678i	−0.104998	−	0.181862i
$726$		0			0
$727$	−3.18367	+	5.51427i	−0.118076	+	0.204513i	−0.919005	−	0.394246i	$-0.871006\pi$
$727$	−3.18367	+	5.51427i	−0.118076	+	0.204513i	0.800929	+	0.598759i	$0.204339\pi$
$728$		0			0
$729$	25.2806	+	9.48111i	0.936318	+	0.351152i
$730$		0			0
$731$	5.10156	−	8.83617i	0.188688	−	0.326818i
$732$		0			0
$733$	11.1541	+	19.3194i	0.411985	+	0.713579i	0.995107	−	0.0988056i	$-0.0315022\pi$
$733$	11.1541	+	19.3194i	0.411985	+	0.713579i	−0.583122	+	0.812385i	$0.698169\pi$
$734$		0			0
$735$	12.5387	−	18.9969i	0.462496	−	0.700712i
$736$		0			0
$737$	−7.49923			−0.276238
$738$		0			0
$739$	6.27749			0.230921			0.115461	−	0.993312i	$-0.463166\pi$
$739$	6.27749			0.230921			0.115461	+	0.993312i	$0.463166\pi$
$740$		0			0
$741$	−2.62526	−	5.24854i	−0.0964414	−	0.192810i
$742$		0			0
$743$	−3.34499	−	5.79369i	−0.122716	−	0.212550i	0.798122	−	0.602496i	$-0.205827\pi$
$743$	−3.34499	−	5.79369i	−0.122716	−	0.212550i	−0.920838	+	0.389946i	$0.872494\pi$
$744$		0			0
$745$	16.8960	−	29.2648i	0.619023	−	1.07218i
$746$		0			0
$747$	−15.7726	+	21.0433i	−0.577088	+	0.769935i
$748$		0			0
$749$	−8.61063	+	14.9140i	−0.314626	+	0.544947i
$750$		0			0
$751$	11.6552	+	20.1874i	0.425304	+	0.736648i	0.996449	−	0.0842010i	$-0.0268338\pi$
$751$	11.6552	+	20.1874i	0.425304	+	0.736648i	−0.571145	+	0.820849i	$0.693500\pi$
$752$		0			0
$753$	−8.86442	−	0.530727i	−0.323038	−	0.0193408i
$754$		0			0
$755$	−32.6070			−1.18669
$756$		0			0
$757$	−47.9217			−1.74174			−0.870872	−	0.491510i	$-0.836445\pi$
$757$	−47.9217			−1.74174			−0.870872	+	0.491510i	$0.836445\pi$
$758$		0			0
$759$	−12.2003	−	0.730452i	−0.442843	−	0.0265137i
$760$		0			0
$761$	−3.19587	−	5.53541i	−0.115850	−	0.200658i	0.802269	−	0.596963i	$-0.203626\pi$
$761$	−3.19587	−	5.53541i	−0.115850	−	0.200658i	−0.918119	+	0.396304i	$0.870293\pi$
$762$		0			0
$763$	8.18988	−	14.1853i	0.296494	−	0.513542i
$764$		0			0
$765$	2.58392	+	6.04405i	0.0934218	+	0.218523i
$766$		0			0
$767$	−4.06422	+	7.03943i	−0.146750	+	0.254179i
$768$		0			0
$769$	21.8854	+	37.9066i	0.789207	+	1.36695i	0.926453	+	0.376410i	$0.122842\pi$
$769$	21.8854	+	37.9066i	0.789207	+	1.36695i	−0.137246	+	0.990537i	$0.543825\pi$
$770$		0			0
$771$	7.42606	+	14.8465i	0.267443	+	0.534684i
$772$		0			0
$773$	47.3107			1.70165			0.850824	−	0.525451i	$-0.176103\pi$
$773$	47.3107			1.70165			0.850824	+	0.525451i	$0.176103\pi$
$774$		0			0
$775$	−9.41645			−0.338249
$776$		0			0
$777$	−2.52915	+	3.83183i	−0.0907327	+	0.137466i
$778$		0			0
$779$	20.4078	+	35.3474i	0.731186	+	1.26645i
$780$		0			0
$781$	−2.24239	+	3.88394i	−0.0802391	+	0.138978i
$782$		0			0
$783$	−12.6567	+	14.9355i	−0.452315	+	0.533750i
$784$		0			0
$785$	−17.8930	+	30.9916i	−0.638630	+	1.10614i
$786$		0			0
$787$	−18.9833	−	32.8800i	−0.676681	−	1.17205i	−0.975974	−	0.217885i	$-0.930084\pi$
$787$	−18.9833	−	32.8800i	−0.676681	−	1.17205i	0.299293	−	0.954161i	$-0.403249\pi$
$788$		0			0
$789$	−0.761432	+	1.15362i	−0.0271077	+	0.0410699i
$790$		0			0
$791$	17.1651			0.610322
$792$		0			0
$793$	−0.316096			−0.0112249
$794$		0			0
$795$	−6.45381	−	12.9028i	−0.228893	−	0.457614i
$796$		0			0
$797$	−12.0126	−	20.8064i	−0.425508	−	0.737001i	0.570960	−	0.820978i	$-0.306571\pi$
$797$	−12.0126	−	20.8064i	−0.425508	−	0.737001i	−0.996468	+	0.0839769i	$0.973238\pi$
$798$		0			0
$799$	0.532787	−	0.922814i	0.0188486	−	0.0326468i
$800$		0			0
$801$	−10.7006	−	1.28593i	−0.378086	−	0.0454361i
$802$		0			0
$803$	4.63419	−	8.02665i	0.163537	−	0.283254i
$804$		0			0
$805$	12.2216	+	21.1684i	0.430754	+	0.746087i
$806$		0			0
$807$	−0.691421	−	0.0413965i	−0.0243392	−	0.00145722i
$808$		0			0
$809$	−10.0802			−0.354403			−0.177201	−	0.984175i	$-0.556704\pi$
$809$	−10.0802			−0.354403			−0.177201	+	0.984175i	$0.556704\pi$
$810$		0			0
$811$	−33.8289			−1.18789			−0.593946	−	0.804505i	$-0.702431\pi$
$811$	−33.8289			−1.18789			−0.593946	+	0.804505i	$0.702431\pi$
$812$		0			0
$813$	42.6562	+	2.55390i	1.49602	+	0.0895691i
$814$		0			0
$815$	−1.80503	−	3.12640i	−0.0632273	−	0.109513i
$816$		0			0
$817$	−29.1377	+	50.4680i	−1.01940	+	1.76565i
$818$		0			0
$819$	−2.79341	−	0.335695i	−0.0976096	−	0.0117301i
$820$		0			0
$821$	−22.5989	+	39.1424i	−0.788707	+	1.36608i	0.138052	+	0.990425i	$0.455916\pi$
$821$	−22.5989	+	39.1424i	−0.788707	+	1.36608i	−0.926759	+	0.375656i	$0.877418\pi$
$822$		0			0
$823$	1.54422	+	2.67467i	0.0538281	+	0.0932330i	0.891684	−	0.452659i	$-0.149524\pi$
$823$	1.54422	+	2.67467i	0.0538281	+	0.0932330i	−0.837856	+	0.545892i	$0.816191\pi$
$824$		0			0
$825$	1.16284	+	2.32481i	0.0404850	+	0.0809395i
$826$		0			0
$827$	40.9992			1.42568			0.712840	−	0.701327i	$-0.247409\pi$
$827$	40.9992			1.42568			0.712840	+	0.701327i	$0.247409\pi$
$828$		0			0
$829$	−21.7836			−0.756576			−0.378288	−	0.925688i	$-0.623487\pi$
$829$	−21.7836			−0.756576			−0.378288	+	0.925688i	$0.623487\pi$
$830$		0			0
$831$	25.9757	−	39.3549i	0.901088	−	1.36521i
$832$		0			0
$833$	−2.21467	−	3.83592i	−0.0767338	−	0.132907i
$834$		0			0
$835$	−17.4421	+	30.2106i	−0.603608	+	1.04548i
$836$		0			0
$837$	11.0015	+	30.6905i	0.380269	+	1.06082i
$838$		0			0
$839$	−19.5026	+	33.7795i	−0.673304	+	1.16620i	0.303657	+	0.952781i	$0.401792\pi$
$839$	−19.5026	+	33.7795i	−0.673304	+	1.16620i	−0.976961	+	0.213416i	$0.931541\pi$
$840$		0			0
$841$	7.40257	+	12.8216i	0.255261	+	0.442125i
$842$		0			0
$843$	−27.9628	+	42.3655i	−0.963090	+	1.45915i
$844$		0			0
$845$	−31.9306			−1.09845
$846$		0			0
$847$	−1.35859			−0.0466816
$848$		0			0
$849$	−5.67551	−	11.3467i	−0.194783	−	0.389419i
$850$		0			0
$851$	6.88397	+	11.9234i	0.235979	+	0.408728i
$852$		0			0
$853$	−9.20243	+	15.9391i	−0.315085	+	0.545744i	−0.979456	−	0.201660i	$-0.935366\pi$
$853$	−9.20243	+	15.9391i	−0.315085	+	0.545744i	0.664370	+	0.747403i	$0.268700\pi$
$854$		0			0
$855$	−14.7581	−	34.5208i	−0.504717	−	1.18059i
$856$		0			0
$857$	15.1658	−	26.2679i	0.518053	−	0.897294i	−0.481727	−	0.876321i	$-0.659990\pi$
$857$	15.1658	−	26.2679i	0.518053	−	0.897294i	0.999780	−	0.0209730i	$-0.00667641\pi$
$858$		0			0
$859$	13.9186	+	24.1078i	0.474898	+	0.822548i	0.999587	−	0.0287465i	$-0.00915156\pi$
$859$	13.9186	+	24.1078i	0.474898	+	0.822548i	−0.524689	+	0.851294i	$0.675818\pi$
$860$		0			0
$861$	19.5331	+	1.16948i	0.665687	+	0.0398557i
$862$		0			0
$863$	−22.4455			−0.764053			−0.382027	−	0.924151i	$-0.624774\pi$
$863$	−22.4455			−0.764053			−0.382027	+	0.924151i	$0.624774\pi$
$864$		0			0
$865$	12.9454			0.440157
$866$		0			0
$867$	−28.1154	−	1.68331i	−0.954849	−	0.0571684i
$868$		0			0
$869$	8.00379	+	13.8630i	0.271510	+	0.470269i
$870$		0			0
$871$	−2.58837	+	4.48318i	−0.0877035	+	0.151907i
$872$		0			0
$873$	−11.7075	+	15.6199i	−0.396240	+	0.528652i
$874$		0			0
$875$	−6.06056	+	10.4972i	−0.204884	+	0.354870i
$876$		0			0
$877$	−1.88172	−	3.25924i	−0.0635413	−	0.110057i	0.832505	−	0.554018i	$-0.186906\pi$
$877$	−1.88172	−	3.25924i	−0.0635413	−	0.110057i	−0.896046	+	0.443961i	$0.853573\pi$
$878$		0			0
$879$	−9.58635	−	19.1655i	−0.323339	−	0.646435i
$880$		0			0
$881$	7.42795			0.250254			0.125127	−	0.992141i	$-0.460066\pi$
$881$	7.42795			0.250254			0.125127	+	0.992141i	$0.460066\pi$
$882$		0			0
$883$	−28.6823			−0.965235			−0.482617	−	0.875831i	$-0.660314\pi$
$883$	−28.6823			−0.965235			−0.482617	+	0.875831i	$0.660314\pi$
$884$		0			0
$885$	−28.6454	+	43.3997i	−0.962905	+	1.45886i
$886$		0			0
$887$	20.4698	+	35.4547i	0.687309	+	1.19045i	0.972705	+	0.232044i	$0.0745414\pi$
$887$	20.4698	+	35.4547i	0.687309	+	1.19045i	−0.285397	+	0.958410i	$0.592125\pi$
$888$		0			0
$889$	2.47254	−	4.28257i	0.0829264	−	0.143633i
$890$		0			0
$891$	6.21853	−	6.50614i	0.208329	−	0.217964i
$892$		0			0
$893$	−3.04302	+	5.27067i	−0.101831	+	0.176376i
$894$		0			0
$895$	−24.8968	−	43.1226i	−0.832209	−	1.44143i
$896$		0			0
$897$	−4.64763	+	7.04146i	−0.155180	+	0.235107i
$898$		0			0
$899$	−23.6395			−0.788421
$900$		0			0
$901$	−2.80738			−0.0935275
$902$		0			0
$903$	12.4984	+	24.9873i	0.415920	+	0.831525i
$904$		0			0
$905$	4.09268	+	7.08874i	0.136045	+	0.235638i
$906$		0			0
$907$	6.67100	−	11.5545i	0.221507	−	0.383661i	−0.733759	−	0.679410i	$-0.762236\pi$
$907$	6.67100	−	11.5545i	0.221507	−	0.383661i	0.955266	+	0.295749i	$0.0955691\pi$
$908$		0			0
$909$	−0.189554	+	0.252898i	−0.00628711	+	0.00838808i
$910$		0			0
$911$	7.31839	−	12.6758i	0.242469	−	0.419969i	−0.718948	−	0.695064i	$-0.755376\pi$
$911$	7.31839	−	12.6758i	0.242469	−	0.419969i	0.961417	+	0.275095i	$0.0887093\pi$
$912$		0			0
$913$	4.38303	+	7.59163i	0.145057	+	0.251246i
$914$		0			0
$915$	−2.01858	−	0.120856i	−0.0667322	−	0.00399536i
$916$		0			0
$917$	19.1736			0.633169
$918$		0			0
$919$	−0.644127			−0.0212478			−0.0106239	−	0.999944i	$-0.503382\pi$
$919$	−0.644127			−0.0212478			−0.0106239	+	0.999944i	$0.503382\pi$
$920$		0			0
$921$	−60.3185	−	3.61136i	−1.98756	−	0.118999i
$922$		0			0
$923$	1.54793	+	2.68109i	0.0509507	+	0.0882491i
$924$		0			0
$925$	1.46409	−	2.53587i	0.0481388	−	0.0833789i
$926$		0			0
$927$	−3.31255	−	7.74840i	−0.108798	−	0.254491i
$928$		0			0
$929$	11.3106	−	19.5906i	0.371090	−	0.642746i	−0.618644	−	0.785672i	$-0.712318\pi$
$929$	11.3106	−	19.5906i	0.371090	−	0.642746i	0.989733	+	0.142925i	$0.0456509\pi$
$930$		0			0
$931$	12.6491	+	21.9090i	0.414559	+	0.718037i
$932$		0			0
$933$	1.91500	+	3.82855i	0.0626943	+	0.125341i
$934$		0			0
$935$	2.19107			0.0716558
$936$		0			0
$937$	−15.5459			−0.507861			−0.253931	−	0.967222i	$-0.581724\pi$
$937$	−15.5459			−0.507861			−0.253931	+	0.967222i	$0.581724\pi$
$938$		0			0
$939$	17.0151	−	25.7790i	0.555266	−	0.841264i
$940$		0			0
$941$	−19.7753	−	34.2519i	−0.644658	−	1.11658i	−0.984380	−	0.176054i	$-0.943667\pi$
$941$	−19.7753	−	34.2519i	−0.644658	−	1.11658i	0.339723	−	0.940526i	$-0.389667\pi$
$942$		0			0
$943$	29.3398	−	50.8180i	0.955435	−	1.65486i
$944$		0			0
$945$	−17.7103	−	3.21177i	−0.576115	−	0.104479i
$946$		0			0
$947$	16.5253	−	28.6227i	0.537000	−	0.930112i	−0.462063	−	0.886847i	$-0.652891\pi$
$947$	16.5253	−	28.6227i	0.537000	−	0.930112i	0.999064	−	0.0432647i	$-0.0137759\pi$
$948$		0			0
$949$	−3.19899	−	5.54082i	−0.103844	−	0.179862i
$950$		0			0
$951$	19.7259	−	29.8860i	0.639655	−	0.969119i
$952$		0			0
$953$	43.0708			1.39520			0.697599	−	0.716488i	$-0.254252\pi$
$953$	43.0708			1.39520			0.697599	+	0.716488i	$0.254252\pi$
$954$		0			0
$955$	−21.4924			−0.695476
$956$		0			0
$957$	2.91926	+	5.83631i	0.0943662	+	0.188661i
$958$		0			0
$959$	−7.21883	−	12.5034i	−0.233108	−	0.403755i
$960$		0			0
$961$	−4.18409	+	7.24705i	−0.134971	+	0.233776i
$962$		0			0
$963$	−37.7559	−	4.53728i	−1.21667	−	0.146212i
$964$		0			0
$965$	23.3248	−	40.3998i	0.750853	−	1.30052i
$966$		0			0
$967$	−18.7115	−	32.4093i	−0.601721	−	1.04221i	−0.992560	−	0.121753i	$-0.961149\pi$
$967$	−18.7115	−	32.4093i	−0.601721	−	1.04221i	0.390839	−	0.920459i	$-0.372185\pi$
$968$		0			0
$969$	−7.29264	−	0.436622i	−0.234273	−	0.0140263i
$970$		0			0
$971$	19.0324			0.610780			0.305390	−	0.952227i	$-0.401213\pi$
$971$	19.0324			0.610780			0.305390	+	0.952227i	$0.401213\pi$
$972$		0			0
$973$	−28.0399			−0.898919
$974$		0			0
$975$	1.79117	+	0.107240i	0.0573634	+	0.00343444i
$976$		0			0
$977$	6.45490	+	11.1802i	0.206510	+	0.357687i	0.950613	−	0.310379i	$-0.100456\pi$
$977$	6.45490	+	11.1802i	0.206510	+	0.357687i	−0.744103	+	0.668065i	$0.767123\pi$
$978$		0			0
$979$	−1.79626	+	3.11122i	−0.0574088	+	0.0994349i
$980$		0			0
$981$	35.9110	+	4.31557i	1.14655	+	0.137785i
$982$		0			0
$983$	−13.3637	+	23.1467i	−0.426237	+	0.738264i	−0.996535	−	0.0831739i	$-0.973494\pi$
$983$	−13.3637	+	23.1467i	−0.426237	+	0.738264i	0.570298	+	0.821438i	$0.306828\pi$
$984$		0			0
$985$	−27.9379	−	48.3898i	−0.890175	−	1.54183i
$986$		0			0
$987$	1.30528	+	2.60957i	0.0415475	+	0.0830636i
$988$		0			0
$989$	83.7811			2.66408
$990$		0			0
$991$	42.3863			1.34644			0.673222	−	0.739441i	$-0.264910\pi$
$991$	42.3863			1.34644			0.673222	+	0.739441i	$0.264910\pi$
$992$		0			0
$993$	15.3795	−	23.3009i	0.488053	−	0.739433i
$994$		0			0
$995$	4.95775	+	8.58707i	0.157171	+	0.272228i
$996$		0			0
$997$	0.629333	−	1.09004i	0.0199312	−	0.0345218i	−0.855888	−	0.517162i	$-0.826989\pi$
$997$	0.629333	−	1.09004i	0.0199312	−	0.0345218i	0.875819	+	0.482640i	$0.160322\pi$
$998$		0			0
$999$	−9.97556	−	1.80907i	−0.315613	−	0.0572365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.i.e.133.4	✓	8
3.2	odd	2		1188.2.i.e.397.3		8
9.2	odd	6		3564.2.a.m.1.2		4
9.4	even	3	inner	396.2.i.e.265.4	yes	8
9.5	odd	6		1188.2.i.e.793.3		8
9.7	even	3		3564.2.a.n.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.2.i.e.133.4	✓	8	1.1	even	1	trivial
396.2.i.e.265.4	yes	8	9.4	even	3	inner
1188.2.i.e.397.3		8	3.2	odd	2
1188.2.i.e.793.3		8	9.5	odd	6
3564.2.a.m.1.2		4	9.2	odd	6
3564.2.a.n.1.3		4	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72895 + 0.103515i) q^{3} +(-1.27483 - 2.20807i) q^{5} +(0.679294 - 1.17657i) q^{7} +(2.97857 + 0.357947i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.345151 - 0.597819i) q^{13} +(-1.97556 - 3.94962i) q^{15} -0.859359 q^{17} +4.90825 q^{19} +(1.29626 - 1.96392i) q^{21} +(-3.52823 - 6.11107i) q^{23} +(-0.750386 + 1.29971i) q^{25} +(5.11276 + 0.927201i) q^{27} +(-1.88380 + 3.26284i) q^{29} +(3.13720 + 5.43380i) q^{31} +(0.954124 - 1.44556i) q^{33} -3.46394 q^{35} -1.95111 q^{37} +(-0.534867 - 1.06933i) q^{39} +(4.15786 + 7.20163i) q^{41} +(-5.93648 + 10.2823i) q^{43} +(-3.00680 - 7.03321i) q^{45} +(-0.619982 + 1.07384i) q^{47} +(2.57712 + 4.46370i) q^{49} +(-1.48579 - 0.0889568i) q^{51} +3.26684 q^{53} -2.54966 q^{55} +(8.48614 + 0.508079i) q^{57} +(-5.88759 - 10.1976i) q^{59} +(0.228955 - 0.396561i) q^{61} +(2.44447 - 3.26135i) q^{63} +(-0.880018 + 1.52424i) q^{65} +(-3.74961 - 6.49452i) q^{67} +(-5.46756 - 10.9310i) q^{69} -4.48478 q^{71} +9.26838 q^{73} +(-1.43192 + 2.16946i) q^{75} +(-0.679294 - 1.17657i) q^{77} +(-8.00379 + 13.8630i) q^{79} +(8.74375 + 2.13234i) q^{81} +(-4.38303 + 7.59163i) q^{83} +(1.09554 + 1.89753i) q^{85} +(-3.59477 + 5.44631i) q^{87} -3.59252 q^{89} -0.937836 q^{91} +(4.86160 + 9.71954i) q^{93} +(-6.25718 - 10.8378i) q^{95} +(-3.25340 + 5.63505i) q^{97} +(1.79928 - 2.40054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} - 4 q^{5} + q^{7} + 7 q^{9} + 4 q^{11} - q^{13} - 22 q^{15} + 2 q^{17} + 18 q^{19} + 21 q^{21} + q^{23} - 6 q^{25} + 9 q^{27} - 13 q^{31} - 3 q^{33} + 52 q^{35} - 28 q^{37} - 14 q^{39}+ \cdots + 2 q^{99}+O(q^{100}) \) 8 * q - 3 * q^3 - 4 * q^5 + q^7 + 7 * q^9 + 4 * q^11 - q^13 - 22 * q^15 + 2 * q^17 + 18 * q^19 + 21 * q^21 + q^23 - 6 * q^25 + 9 * q^27 - 13 * q^31 - 3 * q^33 + 52 * q^35 - 28 * q^37 - 14 * q^39 + 12 * q^41 + 3 * q^43 + 22 * q^45 + 3 * q^47 - 21 * q^49 - 19 * q^51 - 4 * q^53 - 8 * q^55 + 5 * q^57 - 9 * q^59 - 15 * q^61 - 7 * q^63 - 15 * q^65 - 30 * q^67 - 26 * q^69 + 12 * q^71 + 44 * q^73 + 16 * q^75 - q^77 - 41 * q^79 + 31 * q^81 - 20 * q^83 + 7 * q^85 - 27 * q^87 - 50 * q^89 + 58 * q^91 + 7 * q^93 - 4 * q^95 - 3 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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