LMFDB - Embedded newform 1040.2.da.e.641.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.6
Root			$1.34408 + 0.439820i$ of defining polynomial
Character	$\chi$	$=$	1040.641
Dual form			1040.2.da.e.881.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05294 - 1.82374i) q^{3} -1.00000i q^{5} +(2.22378 - 1.28390i) q^{7} +(-0.717351 - 1.24249i) q^{9} +O(q^{10})$	\(q+(1.05294 - 1.82374i) q^{3} -1.00000i q^{5} +(2.22378 - 1.28390i) q^{7} +(-0.717351 - 1.24249i) q^{9} +(-0.677514 - 0.391163i) q^{11} +(-3.60555 - 0.00176922i) q^{13} +(-1.82374 - 1.05294i) q^{15} +(-2.71490 - 4.70235i) q^{17} +(2.95402 - 1.70551i) q^{19} -5.40747i q^{21} +(1.35081 - 2.33967i) q^{23} -1.00000 q^{25} +3.29632 q^{27} +(1.43503 - 2.48554i) q^{29} +4.66733i q^{31} +(-1.42676 + 0.823740i) q^{33} +(-1.28390 - 2.22378i) q^{35} +(-4.67176 - 2.69724i) q^{37} +(-3.79964 + 6.57372i) q^{39} +(3.54167 + 2.04478i) q^{41} +(2.06587 + 3.57819i) q^{43} +(-1.24249 + 0.717351i) q^{45} +1.17711i q^{47} +(-0.203187 + 0.351931i) q^{49} -11.4345 q^{51} -7.43470 q^{53} +(-0.391163 + 0.677514i) q^{55} -7.18316i q^{57} +(11.6397 - 6.72021i) q^{59} +(0.200883 + 0.347939i) q^{61} +(-3.19047 - 1.84202i) q^{63} +(-0.00176922 + 3.60555i) q^{65} +(-11.8624 - 6.84877i) q^{67} +(-2.84464 - 4.92706i) q^{69} +(-4.07512 + 2.35277i) q^{71} +7.33154i q^{73} +(-1.05294 + 1.82374i) q^{75} -2.00886 q^{77} +8.10451 q^{79} +(5.62287 - 9.73909i) q^{81} -14.2887i q^{83} +(-4.70235 + 2.71490i) q^{85} +(-3.02198 - 5.23423i) q^{87} +(11.5196 + 6.65086i) q^{89} +(-8.02024 + 4.62524i) q^{91} +(8.51199 + 4.91440i) q^{93} +(-1.70551 - 2.95402i) q^{95} +(2.98650 - 1.72426i) q^{97} +1.12241i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 12 * q - 6 * q^7 + 2 * q^9	$ 12 q - 6 q^{7} + 2 q^{9} - 2 q^{13} - 8 q^{17} + 24 q^{19} + 2 q^{23} - 12 q^{25} + 12 q^{27} + 12 q^{29} + 4 q^{35} + 24 q^{37} - 28 q^{39} + 24 q^{41} + 18 q^{43} - 12 q^{45} + 24 q^{49} - 68 q^{53} - 2 q^{55} + 48 q^{59} + 18 q^{61} + 36 q^{63} + 16 q^{65} - 18 q^{67} - 8 q^{69} + 64 q^{77} + 12 q^{79} + 14 q^{81} - 18 q^{87} + 30 q^{89} - 76 q^{91} - 12 q^{93} + 10 q^{95} - 84 q^{97}+O(q^{100}) $ 12 * q - 6 * q^7 + 2 * q^9 - 2 * q^13 - 8 * q^17 + 24 * q^19 + 2 * q^23 - 12 * q^25 + 12 * q^27 + 12 * q^29 + 4 * q^35 + 24 * q^37 - 28 * q^39 + 24 * q^41 + 18 * q^43 - 12 * q^45 + 24 * q^49 - 68 * q^53 - 2 * q^55 + 48 * q^59 + 18 * q^61 + 36 * q^63 + 16 * q^65 - 18 * q^67 - 8 * q^69 + 64 * q^77 + 12 * q^79 + 14 * q^81 - 18 * q^87 + 30 * q^89 - 76 * q^91 - 12 * q^93 + 10 * q^95 - 84 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.05294	−	1.82374i	0.607913	−	1.05294i	−0.383670	−	0.923470i	$-0.625340\pi$
$3$	1.05294	−	1.82374i	0.607913	−	1.05294i	0.991584	−	0.129467i	$-0.0413265\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	2.22378	−	1.28390i	0.840512	−	0.485270i	−0.0169265	−	0.999857i	$-0.505388\pi$
$7$	2.22378	−	1.28390i	0.840512	−	0.485270i	0.857438	+	0.514587i	$0.172055\pi$
$8$		0			0
$9$	−0.717351	−	1.24249i	−0.239117	−	0.414163i
$10$		0			0
$11$	−0.677514	−	0.391163i	−0.204278	−	0.117940i	0.394371	−	0.918951i	$-0.370962\pi$
$11$	−0.677514	−	0.391163i	−0.204278	−	0.117940i	−0.598649	+	0.801011i	$0.704296\pi$
$12$		0			0
$13$	−3.60555	−	0.00176922i	−1.00000	−	0.000490694i
$13$	−3.60555	−	0.00176922i	−1.00000	−	0.000490694i
$14$		0			0
$15$	−1.82374	−	1.05294i	−0.470888	−	0.271867i
$16$		0			0
$17$	−2.71490	−	4.70235i	−0.658461	−	1.14049i	−0.981014	−	0.193936i	$-0.937875\pi$
$17$	−2.71490	−	4.70235i	−0.658461	−	1.14049i	0.322553	−	0.946551i	$-0.395459\pi$
$18$		0			0
$19$	2.95402	−	1.70551i	0.677699	−	0.391270i	−0.121288	−	0.992617i	$-0.538703\pi$
$19$	2.95402	−	1.70551i	0.677699	−	0.391270i	0.798988	+	0.601347i	$0.205369\pi$
$20$		0			0
$21$		−	5.40747i		−	1.18001i
$22$		0			0
$23$	1.35081	−	2.33967i	0.281664	−	0.487856i	−0.690131	−	0.723684i	$-0.742447\pi$
$23$	1.35081	−	2.33967i	0.281664	−	0.487856i	0.971795	+	0.235829i	$0.0757805\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	3.29632			0.634377
$28$		0			0
$29$	1.43503	−	2.48554i	0.266478	−	0.461553i	−0.701472	−	0.712697i	$-0.747474\pi$
$29$	1.43503	−	2.48554i	0.266478	−	0.461553i	0.967950	+	0.251144i	$0.0808069\pi$
$30$		0			0
$31$			4.66733i			0.838276i	0.907922	+	0.419138i	$0.137668\pi$
$31$			4.66733i			0.838276i	−0.907922	+	0.419138i	$0.862332\pi$
$32$		0			0
$33$	−1.42676	+	0.823740i	−0.248367	+	0.143395i
$34$		0			0
$35$	−1.28390	−	2.22378i	−0.217019	−	0.375888i
$36$		0			0
$37$	−4.67176	−	2.69724i	−0.768032	−	0.443424i	0.0641401	−	0.997941i	$-0.479570\pi$
$37$	−4.67176	−	2.69724i	−0.768032	−	0.443424i	−0.832172	+	0.554517i	$0.812903\pi$
$38$		0			0
$39$	−3.79964	+	6.57372i	−0.608430	+	1.05264i
$40$		0			0
$41$	3.54167	+	2.04478i	0.553116	+	0.319341i	0.750378	−	0.661009i	$-0.229872\pi$
$41$	3.54167	+	2.04478i	0.553116	+	0.319341i	−0.197262	+	0.980351i	$0.563205\pi$
$42$		0			0
$43$	2.06587	+	3.57819i	0.315042	+	0.545668i	0.979446	−	0.201705i	$-0.0646481\pi$
$43$	2.06587	+	3.57819i	0.315042	+	0.545668i	−0.664405	+	0.747373i	$0.731315\pi$
$44$		0			0
$45$	−1.24249	+	0.717351i	−0.185219	+	0.106936i
$46$		0			0
$47$			1.17711i			0.171699i	0.996308	+	0.0858497i	$0.0273605\pi$
$47$			1.17711i			0.171699i	−0.996308	+	0.0858497i	$0.972640\pi$
$48$		0			0
$49$	−0.203187	+	0.351931i	−0.0290268	+	0.0502758i
$50$		0			0
$51$	−11.4345			−1.60115
$52$		0			0
$53$	−7.43470			−1.02123			−0.510617	−	0.859808i	$-0.670583\pi$
$53$	−7.43470			−1.02123			−0.510617	+	0.859808i	$0.670583\pi$
$54$		0			0
$55$	−0.391163	+	0.677514i	−0.0527444	+	0.0913560i
$56$		0			0
$57$		−	7.18316i		−	0.951433i
$58$		0			0
$59$	11.6397	−	6.72021i	1.51536	−	0.874896i	0.515527	−	0.856873i	$-0.327596\pi$
$59$	11.6397	−	6.72021i	1.51536	−	0.874896i	0.999838	−	0.0180229i	$-0.00573719\pi$
$60$		0			0
$61$	0.200883	+	0.347939i	0.0257204	+	0.0445490i	0.878599	−	0.477560i	$-0.158479\pi$
$61$	0.200883	+	0.347939i	0.0257204	+	0.0445490i	−0.852879	+	0.522109i	$0.825145\pi$
$62$		0			0
$63$	−3.19047	−	1.84202i	−0.401961	−	0.232073i
$64$		0			0
$65$	−0.00176922	+	3.60555i	−0.000219445	+	0.447214i
$66$		0			0
$67$	−11.8624	−	6.84877i	−1.44922	−	0.836710i	−0.450789	−	0.892630i	$-0.648857\pi$
$67$	−11.8624	−	6.84877i	−1.44922	−	0.836710i	−0.998435	+	0.0559202i	$0.982191\pi$
$68$		0			0
$69$	−2.84464	−	4.92706i	−0.342454	−	0.593148i
$70$		0			0
$71$	−4.07512	+	2.35277i	−0.483628	+	0.279223i	−0.721927	−	0.691969i	$-0.756743\pi$
$71$	−4.07512	+	2.35277i	−0.483628	+	0.279223i	0.238299	+	0.971192i	$0.423410\pi$
$72$		0			0
$73$			7.33154i			0.858092i	0.903283	+	0.429046i	$0.141150\pi$
$73$			7.33154i			0.858092i	−0.903283	+	0.429046i	$0.858850\pi$
$74$		0			0
$75$	−1.05294	+	1.82374i	−0.121583	+	0.210587i
$76$		0			0
$77$	−2.00886			−0.228931
$78$		0			0
$79$	8.10451			0.911829			0.455915	−	0.890024i	$-0.349312\pi$
$79$	8.10451			0.911829			0.455915	+	0.890024i	$0.349312\pi$
$80$		0			0
$81$	5.62287	−	9.73909i	0.624763	−	1.08212i
$82$		0			0
$83$		−	14.2887i		−	1.56839i	−0.620514	−	0.784195i	$-0.713076\pi$
$83$		−	14.2887i		−	1.56839i	0.620514	−	0.784195i	$-0.286924\pi$
$84$		0			0
$85$	−4.70235	+	2.71490i	−0.510041	+	0.294473i
$86$		0			0
$87$	−3.02198	−	5.23423i	−0.323990	−	0.561168i
$88$		0			0
$89$	11.5196	+	6.65086i	1.22108	+	0.704990i	0.965148	−	0.261706i	$-0.0842849\pi$
$89$	11.5196	+	6.65086i	1.22108	+	0.704990i	0.255930	+	0.966695i	$0.417618\pi$
$90$		0			0
$91$	−8.02024	+	4.62524i	−0.840750	+	0.484857i
$92$		0			0
$93$	8.51199	+	4.91440i	0.882652	+	0.509599i
$94$		0			0
$95$	−1.70551	−	2.95402i	−0.174981	−	0.303076i
$96$		0			0
$97$	2.98650	−	1.72426i	0.303233	−	0.175072i	−0.340661	−	0.940186i	$-0.610651\pi$
$97$	2.98650	−	1.72426i	0.303233	−	0.175072i	0.643894	+	0.765114i	$0.277318\pi$
$98$		0			0
$99$			1.12241i			0.112806i
$100$		0			0
$101$	−7.30757	+	12.6571i	−0.727130	+	1.25943i	0.230961	+	0.972963i	$0.425813\pi$
$101$	−7.30757	+	12.6571i	−0.727130	+	1.25943i	−0.958091	+	0.286463i	$0.907520\pi$
$102$		0			0
$103$	3.13207			0.308612			0.154306	−	0.988023i	$-0.450686\pi$
$103$	3.13207			0.308612			0.154306	+	0.988023i	$0.450686\pi$
$104$		0			0
$105$	−5.40747			−0.527715
$106$		0			0
$107$	4.46395	−	7.73179i	0.431546	−	0.747460i	−0.565460	−	0.824775i	$-0.691302\pi$
$107$	4.46395	−	7.73179i	0.431546	−	0.747460i	0.997007	+	0.0773155i	$0.0246349\pi$
$108$		0			0
$109$			8.61181i			0.824862i	0.910989	+	0.412431i	$0.135320\pi$
$109$			8.61181i			0.824862i	−0.910989	+	0.412431i	$0.864680\pi$
$110$		0			0
$111$	−9.83813	+	5.68005i	−0.933794	+	0.539126i
$112$		0			0
$113$	8.53990	+	14.7915i	0.803366	+	1.39147i	0.917389	+	0.397992i	$0.130293\pi$
$113$	8.53990	+	14.7915i	0.803366	+	1.39147i	−0.114023	+	0.993478i	$0.536374\pi$
$114$		0			0
$115$	−2.33967	−	1.35081i	−0.218176	−	0.125964i
$116$		0			0
$117$	2.58425	+	4.48113i	0.238914	+	0.414280i
$118$		0			0
$119$	−12.0747	−	6.97134i	−1.10689	−	0.639062i
$120$		0			0
$121$	−5.19398	−	8.99624i	−0.472180	−	0.817840i
$122$		0			0
$123$	7.45830	−	4.30605i	0.672493	−	0.388264i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−7.36957	+	12.7645i	−0.653944	+	1.13266i	0.328213	+	0.944604i	$0.393553\pi$
$127$	−7.36957	+	12.7645i	−0.653944	+	1.13266i	−0.982157	+	0.188061i	$0.939780\pi$
$128$		0			0
$129$	8.70091			0.766072
$130$		0			0
$131$	6.43889			0.562568			0.281284	−	0.959625i	$-0.409240\pi$
$131$	6.43889			0.562568			0.281284	+	0.959625i	$0.409240\pi$
$132$		0			0
$133$	4.37941	−	7.58536i	0.379743	−	0.657734i
$134$		0			0
$135$		−	3.29632i		−	0.283702i
$136$		0			0
$137$	7.28500	−	4.20600i	0.622400	−	0.359343i	−0.155403	−	0.987851i	$-0.549668\pi$
$137$	7.28500	−	4.20600i	0.622400	−	0.359343i	0.777803	+	0.628509i	$0.216334\pi$
$138$		0			0
$139$	3.44535	+	5.96753i	0.292231	+	0.506159i	0.974337	−	0.225094i	$-0.0722690\pi$
$139$	3.44535	+	5.96753i	0.292231	+	0.506159i	−0.682106	+	0.731253i	$0.738936\pi$
$140$		0			0
$141$	2.14675	+	1.23942i	0.180789	+	0.104378i
$142$		0			0
$143$	2.44212	+	1.41156i	0.204220	+	0.118040i
$144$		0			0
$145$	−2.48554	−	1.43503i	−0.206413	−	0.119172i
$146$		0			0
$147$	0.427887	+	0.741122i	0.0352915	+	0.0611267i
$148$		0			0
$149$	2.11623	−	1.22181i	0.173369	−	0.100094i	−0.410805	−	0.911723i	$-0.634752\pi$
$149$	2.11623	−	1.22181i	0.173369	−	0.100094i	0.584173	+	0.811629i	$0.301419\pi$
$150$		0			0
$151$			16.4786i			1.34101i	0.741907	+	0.670503i	$0.233922\pi$
$151$			16.4786i			1.34101i	−0.741907	+	0.670503i	$0.766078\pi$
$152$		0			0
$153$	−3.89508	+	6.74647i	−0.314898	+	0.545420i
$154$		0			0
$155$	4.66733			0.374889
$156$		0			0
$157$	11.9282			0.951977			0.475988	−	0.879452i	$-0.342090\pi$
$157$	11.9282			0.951977			0.475988	+	0.879452i	$0.342090\pi$
$158$		0			0
$159$	−7.82827	+	13.5590i	−0.620822	+	1.07530i
$160$		0			0
$161$		−	6.93724i		−	0.546731i
$162$		0			0
$163$	15.9387	−	9.20224i	1.24842	−	0.720775i	0.277625	−	0.960690i	$-0.410453\pi$
$163$	15.9387	−	9.20224i	1.24842	−	0.720775i	0.970794	+	0.239914i	$0.0771194\pi$
$164$		0			0
$165$	0.823740	+	1.42676i	0.0641281	+	0.111073i
$166$		0			0
$167$	5.50406	+	3.17777i	0.425917	+	0.245903i	0.697606	−	0.716482i	$-0.254249\pi$
$167$	5.50406	+	3.17777i	0.425917	+	0.245903i	−0.271689	+	0.962385i	$0.587582\pi$
$168$		0			0
$169$	13.0000	+	0.0127581i	1.00000	+	0.000981389i
$170$		0			0
$171$	−4.23814	−	2.44689i	−0.324099	−	0.187119i
$172$		0			0
$173$	−12.5546	−	21.7452i	−0.954508	−	1.65326i	−0.735489	−	0.677536i	$-0.763048\pi$
$173$	−12.5546	−	21.7452i	−0.954508	−	1.65326i	−0.219019	−	0.975721i	$-0.570286\pi$
$174$		0			0
$175$	−2.22378	+	1.28390i	−0.168102	+	0.0970539i
$176$		0			0
$177$		−	28.3038i		−	2.12744i
$178$		0			0
$179$	1.70344	−	2.95044i	0.127321	−	0.220526i	−0.795317	−	0.606194i	$-0.792696\pi$
$179$	1.70344	−	2.95044i	0.127321	−	0.220526i	0.922638	+	0.385668i	$0.126029\pi$
$180$		0			0
$181$	−22.3717			−1.66288			−0.831438	−	0.555618i	$-0.812482\pi$
$181$	−22.3717			−1.66288			−0.831438	+	0.555618i	$0.812482\pi$
$182$		0			0
$183$	0.846067			0.0625431
$184$		0			0
$185$	−2.69724	+	4.67176i	−0.198305	+	0.343474i
$186$		0			0
$187$			4.24788i			0.310636i
$188$		0			0
$189$	7.33030	−	4.23215i	0.533201	−	0.307844i
$190$		0			0
$191$	0.230620	+	0.399446i	0.0166871	+	0.0289029i	0.874248	−	0.485479i	$-0.161355\pi$
$191$	0.230620	+	0.399446i	0.0166871	+	0.0289029i	−0.857561	+	0.514382i	$0.828021\pi$
$192$		0			0
$193$	20.4971	+	11.8340i	1.47542	+	0.851831i	0.999616	−	0.0277223i	$-0.00882541\pi$
$193$	20.4971	+	11.8340i	1.47542	+	0.851831i	0.475800	+	0.879554i	$0.342159\pi$
$194$		0			0
$195$	6.57372	+	3.79964i	0.470754	+	0.272098i
$196$		0			0
$197$	22.8821	+	13.2110i	1.63029	+	0.941246i	0.984004	+	0.178146i	$0.0570101\pi$
$197$	22.8821	+	13.2110i	1.63029	+	0.941246i	0.646281	+	0.763099i	$0.276323\pi$
$198$		0			0
$199$	−1.37998	−	2.39019i	−0.0978240	−	0.169436i	0.812960	−	0.582320i	$-0.197855\pi$
$199$	−1.37998	−	2.39019i	−0.0978240	−	0.169436i	−0.910784	+	0.412884i	$0.864522\pi$
$200$		0			0
$201$	−24.9807	+	14.4226i	−1.76201	+	1.01729i
$202$		0			0
$203$		−	7.36973i		−	0.517254i
$204$		0			0
$205$	2.04478	−	3.54167i	0.142814	−	0.247361i
$206$		0			0
$207$	−3.87602			−0.269402
$208$		0			0
$209$	−2.66852			−0.184586
$210$		0			0
$211$	−1.89842	+	3.28817i	−0.130693	+	0.226367i	−0.923944	−	0.382528i	$-0.875054\pi$
$211$	−1.89842	+	3.28817i	−0.130693	+	0.226367i	0.793251	+	0.608895i	$0.208387\pi$
$212$		0			0
$213$			9.90928i			0.678973i
$214$		0			0
$215$	3.57819	−	2.06587i	0.244030	−	0.140891i
$216$		0			0
$217$	5.99239	+	10.3791i	0.406790	+	0.704581i
$218$		0			0
$219$	13.3708	+	7.71965i	0.903516	+	0.521645i
$220$		0			0
$221$	9.78040	+	16.9594i	0.657901	+	1.14081i
$222$		0			0
$223$	12.0602	+	6.96294i	0.807609	+	0.466273i	0.846125	−	0.532985i	$-0.178930\pi$
$223$	12.0602	+	6.96294i	0.807609	+	0.466273i	−0.0385161	+	0.999258i	$0.512263\pi$
$224$		0			0
$225$	0.717351	+	1.24249i	0.0478234	+	0.0828326i
$226$		0			0
$227$	19.1499	−	11.0562i	1.27102	−	0.733826i	0.295844	−	0.955236i	$-0.404399\pi$
$227$	19.1499	−	11.0562i	1.27102	−	0.733826i	0.975181	+	0.221410i	$0.0710660\pi$
$228$		0			0
$229$		−	10.4426i		−	0.690063i	−0.938591	−	0.345032i	$-0.887868\pi$
$229$		−	10.4426i		−	0.690063i	0.938591	−	0.345032i	$-0.112132\pi$
$230$		0			0
$231$	−2.11520	+	3.66364i	−0.139170	+	0.241050i
$232$		0			0
$233$	−25.6199			−1.67842			−0.839208	−	0.543811i	$-0.816981\pi$
$233$	−25.6199			−1.67842			−0.839208	+	0.543811i	$0.816981\pi$
$234$		0			0
$235$	1.17711			0.0767863
$236$		0			0
$237$	8.53354	−	14.7805i	0.554313	−	0.960098i
$238$		0			0
$239$		−	10.2447i		−	0.662674i	−0.943513	−	0.331337i	$-0.892500\pi$
$239$		−	10.2447i		−	0.662674i	0.943513	−	0.331337i	$-0.107500\pi$
$240$		0			0
$241$	−6.59926	+	3.81008i	−0.425096	+	0.245429i	−0.697255	−	0.716823i	$-0.745596\pi$
$241$	−6.59926	+	3.81008i	−0.425096	+	0.245429i	0.272159	+	0.962252i	$0.412262\pi$
$242$		0			0
$243$	−6.89657	−	11.9452i	−0.442415	−	0.766286i
$244$		0			0
$245$	0.351931	+	0.203187i	0.0224840	+	0.0129812i
$246$		0			0
$247$	−10.6539	+	6.14406i	−0.677891	+	0.390937i
$248$		0			0
$249$	−26.0589	−	15.0451i	−1.65142	−	0.953445i
$250$		0			0
$251$	6.18307	+	10.7094i	0.390272	+	0.675971i	0.992485	−	0.122364i	$-0.0390477\pi$
$251$	6.18307	+	10.7094i	0.390272	+	0.675971i	−0.602213	+	0.798335i	$0.705714\pi$
$252$		0			0
$253$	−1.83039	+	1.05677i	−0.115075	+	0.0664388i
$254$		0			0
$255$			11.4345i			0.716055i
$256$		0			0
$257$	−5.22772	+	9.05468i	−0.326096	+	0.564816i	−0.981734	−	0.190260i	$-0.939067\pi$
$257$	−5.22772	+	9.05468i	−0.326096	+	0.564816i	0.655637	+	0.755076i	$0.272400\pi$
$258$		0			0
$259$	−13.8520			−0.860720
$260$		0			0
$261$	−4.11767			−0.254877
$262$		0			0
$263$	−1.01088	+	1.75090i	−0.0623338	+	0.107965i	−0.895508	−	0.445045i	$-0.853188\pi$
$263$	−1.01088	+	1.75090i	−0.0623338	+	0.107965i	0.833174	+	0.553010i	$0.186521\pi$
$264$		0			0
$265$			7.43470i			0.456710i
$266$		0			0
$267$	24.2589	−	14.0059i	1.48462	−	0.857145i
$268$		0			0
$269$	6.64696	+	11.5129i	0.405272	+	0.701952i	0.994353	−	0.106122i	$-0.0338434\pi$
$269$	6.64696	+	11.5129i	0.405272	+	0.701952i	−0.589081	+	0.808074i	$0.700510\pi$
$270$		0			0
$271$	21.8301	+	12.6036i	1.32608	+	0.765613i	0.984691	−	0.174308i	$-0.0557690\pi$
$271$	21.8301	+	12.6036i	1.32608	+	0.765613i	0.341390	+	0.939922i	$0.389102\pi$
$272$		0			0
$273$	−0.00956703	+	19.4969i	−0.000579023	+	1.18001i
$274$		0			0
$275$	0.677514	+	0.391163i	0.0408556	+	0.0235880i
$276$		0			0
$277$	2.77755	+	4.81086i	0.166887	+	0.289057i	0.937324	−	0.348460i	$-0.113295\pi$
$277$	2.77755	+	4.81086i	0.166887	+	0.289057i	−0.770437	+	0.637516i	$0.779962\pi$
$278$		0			0
$279$	5.79910	−	3.34811i	0.347183	−	0.200446i
$280$		0			0
$281$		−	13.8493i		−	0.826182i	−0.910690	−	0.413091i	$-0.864449\pi$
$281$		−	13.8493i		−	0.826182i	0.910690	−	0.413091i	$-0.135551\pi$
$282$		0			0
$283$	−16.1966	+	28.0533i	−0.962787	+	1.66760i	−0.247340	+	0.968929i	$0.579556\pi$
$283$	−16.1966	+	28.0533i	−0.962787	+	1.66760i	−0.715447	+	0.698667i	$0.753777\pi$
$284$		0			0
$285$	−7.18316			−0.425494
$286$		0			0
$287$	10.5012			0.619867
$288$		0			0
$289$	−6.24140	+	10.8104i	−0.367141	+	0.635907i
$290$		0			0
$291$		−	7.26213i		−	0.425714i
$292$		0			0
$293$	20.2278	−	11.6785i	1.18172	−	0.682265i	0.225307	−	0.974288i	$-0.427662\pi$
$293$	20.2278	−	11.6785i	1.18172	−	0.682265i	0.956411	+	0.292023i	$0.0943282\pi$
$294$		0			0
$295$	−6.72021	−	11.6397i	−0.391265	−	0.677692i
$296$		0			0
$297$	−2.23330	−	1.28940i	−0.129589	−	0.0748184i
$298$		0			0
$299$	−4.87456	+	8.43342i	−0.281903	+	0.487717i
$300$		0			0
$301$	9.18809	+	5.30474i	0.529593	+	0.305760i
$302$		0			0
$303$	15.3888	+	26.6542i	0.884064	+	1.53124i
$304$		0			0
$305$	0.347939	−	0.200883i	0.0199229	−	0.0115025i
$306$		0			0
$307$			7.01204i			0.400198i	0.979776	+	0.200099i	$0.0641264\pi$
$307$			7.01204i			0.400198i	−0.979776	+	0.200099i	$0.935874\pi$
$308$		0			0
$309$	3.29787	−	5.71209i	0.187610	−	0.324949i
$310$		0			0
$311$	−20.8628			−1.18302			−0.591511	−	0.806297i	$-0.701468\pi$
$311$	−20.8628			−1.18302			−0.591511	+	0.806297i	$0.701468\pi$
$312$		0			0
$313$	−17.6009			−0.994859			−0.497430	−	0.867504i	$-0.665723\pi$
$313$	−17.6009			−0.994859			−0.497430	+	0.867504i	$0.665723\pi$
$314$		0			0
$315$	−1.84202	+	3.19047i	−0.103786	+	0.179763i
$316$		0			0
$317$			10.3994i			0.584091i	0.956404	+	0.292045i	$0.0943358\pi$
$317$			10.3994i			0.584091i	−0.956404	+	0.292045i	$0.905664\pi$
$318$		0			0
$319$	−1.94450	+	1.12266i	−0.108871	+	0.0628568i
$320$		0			0
$321$	−9.40051	−	16.2822i	−0.524685	−	0.908782i
$322$		0			0
$323$	−16.0398	−	9.26057i	−0.892477	−	0.515272i
$324$		0			0
$325$	3.60555	+	0.00176922i	0.200000	+	9.81389e-5i
$326$		0			0
$327$	15.7057	+	9.06770i	0.868528	+	0.501445i
$328$		0			0
$329$	1.51130	+	2.61764i	0.0833205	+	0.144315i
$330$		0			0
$331$	3.70785	−	2.14073i	0.203802	−	0.117665i	−0.394626	−	0.918842i	$-0.629126\pi$
$331$	3.70785	−	2.14073i	0.203802	−	0.117665i	0.598428	+	0.801177i	$0.295792\pi$
$332$		0			0
$333$			7.73947i			0.424121i
$334$		0			0
$335$	−6.84877	+	11.8624i	−0.374188	+	0.648113i
$336$		0			0
$337$	20.4848			1.11588			0.557939	−	0.829882i	$-0.311592\pi$
$337$	20.4848			1.11588			0.557939	+	0.829882i	$0.311592\pi$
$338$		0			0
$339$	35.9679			1.95351
$340$		0			0
$341$	1.82569	−	3.16218i	0.0988664	−	0.171242i
$342$		0			0
$343$			19.0181i			1.02688i
$344$		0			0
$345$	−4.92706	+	2.84464i	−0.265264	+	0.153150i
$346$		0			0
$347$	12.9047	+	22.3517i	0.692763	+	1.19990i	0.970929	+	0.239368i	$0.0769401\pi$
$347$	12.9047	+	22.3517i	0.692763	+	1.19990i	−0.278166	+	0.960533i	$0.589727\pi$
$348$		0			0
$349$	−9.54436	−	5.51044i	−0.510898	−	0.294967i	0.222305	−	0.974977i	$-0.428642\pi$
$349$	−9.54436	−	5.51044i	−0.510898	−	0.294967i	−0.733203	+	0.680010i	$0.761975\pi$
$350$		0			0
$351$	−11.8850	−	0.00583192i	−0.634377	−	0.000311285i
$352$		0			0
$353$	−0.830929	−	0.479737i	−0.0442259	−	0.0255338i	0.477724	−	0.878510i	$-0.341462\pi$
$353$	−0.830929	−	0.479737i	−0.0442259	−	0.0255338i	−0.521950	+	0.852976i	$0.674795\pi$
$354$		0			0
$355$	2.35277	+	4.07512i	0.124872	+	0.216285i
$356$		0			0
$357$	−25.4278	+	14.6808i	−1.34578	+	0.776988i
$358$		0			0
$359$		−	26.3599i		−	1.39122i	−0.718418	−	0.695612i	$-0.755133\pi$
$359$		−	26.3599i		−	1.39122i	0.718418	−	0.695612i	$-0.244867\pi$
$360$		0			0
$361$	−3.68250	+	6.37828i	−0.193816	+	0.335699i
$362$		0			0
$363$	−21.8757			−1.14818
$364$		0			0
$365$	7.33154			0.383750
$366$		0			0
$367$	0.412460	−	0.714402i	0.0215302	−	0.0372915i	−0.855060	−	0.518530i	$-0.826480\pi$
$367$	0.412460	−	0.714402i	0.0215302	−	0.0372915i	0.876590	+	0.481238i	$0.159813\pi$
$368$		0			0
$369$		−	5.86731i		−	0.305440i
$370$		0			0
$371$	−16.5332	+	9.54544i	−0.858360	+	0.495574i
$372$		0			0
$373$	−15.1821	−	26.2962i	−0.786100	−	1.36157i	−0.928340	−	0.371733i	$-0.878764\pi$
$373$	−15.1821	−	26.2962i	−0.786100	−	1.36157i	0.142239	−	0.989832i	$-0.454570\pi$
$374$		0			0
$375$	1.82374	+	1.05294i	0.0941775	+	0.0543734i
$376$		0			0
$377$	−5.17845	+	8.95919i	−0.266704	+	0.461422i
$378$		0			0
$379$	2.34824	+	1.35576i	0.120621	+	0.0696407i	0.559097	−	0.829102i	$-0.311148\pi$
$379$	2.34824	+	1.35576i	0.120621	+	0.0696407i	−0.438475	+	0.898743i	$0.644481\pi$
$380$		0			0
$381$	15.5194	+	26.8804i	0.795083	+	1.37712i
$382$		0			0
$383$	9.25885	−	5.34560i	0.473105	−	0.273147i	−0.244433	−	0.969666i	$-0.578602\pi$
$383$	9.25885	−	5.34560i	0.473105	−	0.273147i	0.717539	+	0.696519i	$0.245269\pi$
$384$		0			0
$385$			2.00886i			0.102381i
$386$		0			0
$387$	2.96390	−	5.13363i	0.150664	−	0.260957i
$388$		0			0
$389$	1.70818			0.0866083			0.0433041	−	0.999062i	$-0.486212\pi$
$389$	1.70818			0.0866083			0.0433041	+	0.999062i	$0.486212\pi$
$390$		0			0
$391$	−14.6693			−0.741857
$392$		0			0
$393$	6.77974	−	11.7429i	0.341993	−	0.592349i
$394$		0			0
$395$		−	8.10451i		−	0.407782i
$396$		0			0
$397$	20.8779	−	12.0538i	1.04783	−	0.604965i	0.125789	−	0.992057i	$-0.459854\pi$
$397$	20.8779	−	12.0538i	1.04783	−	0.604965i	0.922041	+	0.387092i	$0.126520\pi$
$398$		0			0
$399$	−9.22248	−	15.9738i	−0.461701	−	0.799690i
$400$		0			0
$401$	−3.26997	−	1.88792i	−0.163294	−	0.0942781i	0.416126	−	0.909307i	$-0.363388\pi$
$401$	−3.26997	−	1.88792i	−0.163294	−	0.0942781i	−0.579420	+	0.815029i	$0.696721\pi$
$402$		0			0
$403$	0.00825754	−	16.8283i	0.000411338	−	0.838276i
$404$		0			0
$405$	−9.73909	−	5.62287i	−0.483939	−	0.279403i
$406$		0			0
$407$	2.11012	+	3.65484i	0.104595	+	0.181164i
$408$		0			0
$409$	−15.5273	+	8.96468i	−0.767775	+	0.443275i	−0.832080	−	0.554655i	$-0.812850\pi$
$409$	−15.5273	+	8.96468i	−0.767775	+	0.443275i	0.0643055	+	0.997930i	$0.479517\pi$
$410$		0			0
$411$		−	17.7146i		−	0.873797i
$412$		0			0
$413$	17.2562	−	29.8886i	0.849121	−	1.47072i
$414$		0			0
$415$	−14.2887			−0.701405
$416$		0			0
$417$	14.5110			0.710605
$418$		0			0
$419$	−2.82726	+	4.89695i	−0.138121	+	0.239232i	−0.926785	−	0.375592i	$-0.877439\pi$
$419$	−2.82726	+	4.89695i	−0.138121	+	0.239232i	0.788665	+	0.614824i	$0.210773\pi$
$420$		0			0
$421$			13.7210i			0.668723i	0.942445	+	0.334361i	$0.108521\pi$
$421$			13.7210i			0.668723i	−0.942445	+	0.334361i	$0.891479\pi$
$422$		0			0
$423$	1.46255	−	0.844403i	0.0711116	−	0.0410563i
$424$		0			0
$425$	2.71490	+	4.70235i	0.131692	+	0.228097i
$426$		0			0
$427$	0.893440	+	0.515828i	0.0432366	+	0.0249627i
$428$		0			0
$429$	5.14571	−	2.96751i	0.248437	−	0.143273i
$430$		0			0
$431$	−13.4739	−	7.77918i	−0.649017	−	0.374710i	0.139063	−	0.990284i	$-0.455591\pi$
$431$	−13.4739	−	7.77918i	−0.649017	−	0.374710i	−0.788079	+	0.615574i	$0.788924\pi$
$432$		0			0
$433$	−10.8581	−	18.8068i	−0.521806	−	0.903795i	−0.999678	−	0.0253654i	$-0.991925\pi$
$433$	−10.8581	−	18.8068i	−0.521806	−	0.903795i	0.477872	−	0.878429i	$-0.341408\pi$
$434$		0			0
$435$	−5.23423	+	3.02198i	−0.250962	+	0.144893i
$436$		0			0
$437$		−	9.21526i		−	0.440826i
$438$		0			0
$439$	−9.79190	+	16.9601i	−0.467342	+	0.809460i	−0.999304	−	0.0373084i	$-0.988122\pi$
$439$	−9.79190	+	16.9601i	−0.467342	+	0.809460i	0.531962	+	0.846768i	$0.321455\pi$
$440$		0			0
$441$	0.583027			0.0277632
$442$		0			0
$443$	−31.2961			−1.48692			−0.743461	−	0.668779i	$-0.766817\pi$
$443$	−31.2961			−1.48692			−0.743461	+	0.668779i	$0.766817\pi$
$444$		0			0
$445$	6.65086	−	11.5196i	0.315281	−	0.546083i
$446$		0			0
$447$		−	5.14595i		−	0.243395i
$448$		0			0
$449$	6.64176	−	3.83462i	0.313444	−	0.180967i	−0.335023	−	0.942210i	$-0.608744\pi$
$449$	6.64176	−	3.83462i	0.313444	−	0.180967i	0.648467	+	0.761243i	$0.275411\pi$
$450$		0			0
$451$	−1.59969	−	2.77074i	−0.0753263	−	0.130469i
$452$		0			0
$453$	30.0526	+	17.3509i	1.41200	+	0.815216i
$454$		0			0
$455$	4.62524	+	8.02024i	0.216835	+	0.375995i
$456$		0			0
$457$	−17.6132	−	10.1690i	−0.823910	−	0.475685i	0.0278531	−	0.999612i	$-0.491133\pi$
$457$	−17.6132	−	10.1690i	−0.823910	−	0.475685i	−0.851763	+	0.523927i	$0.824466\pi$
$458$		0			0
$459$	−8.94918	−	15.5004i	−0.417712	−	0.723499i
$460$		0			0
$461$	−21.1013	+	12.1828i	−0.982784	+	0.567411i	−0.903110	−	0.429410i	$-0.858722\pi$
$461$	−21.1013	+	12.1828i	−0.982784	+	0.567411i	−0.0796748	+	0.996821i	$0.525388\pi$
$462$		0			0
$463$		−	13.2963i		−	0.617933i	−0.951073	−	0.308966i	$-0.900017\pi$
$463$		−	13.2963i		−	0.617933i	0.951073	−	0.308966i	$-0.0999830\pi$
$464$		0			0
$465$	4.91440	−	8.51199i	0.227900	−	0.394734i
$466$		0			0
$467$	−2.81786			−0.130395			−0.0651975	−	0.997872i	$-0.520768\pi$
$467$	−2.81786			−0.130395			−0.0651975	+	0.997872i	$0.520768\pi$
$468$		0			0
$469$	−35.1726			−1.62412
$470$		0			0
$471$	12.5597	−	21.7540i	0.578719	−	1.00237i
$472$		0			0
$473$		−	3.23236i		−	0.148624i
$474$		0			0
$475$	−2.95402	+	1.70551i	−0.135540	+	0.0782540i
$476$		0			0
$477$	5.33329	+	9.23754i	0.244195	+	0.422958i
$478$		0			0
$479$	3.55596	+	2.05304i	0.162476	+	0.0938056i	0.579033	−	0.815304i	$-0.303430\pi$
$479$	3.55596	+	2.05304i	0.162476	+	0.0938056i	−0.416557	+	0.909109i	$0.636763\pi$
$480$		0			0
$481$	16.8395	+	9.73330i	0.767814	+	0.443800i
$482$		0			0
$483$	−12.6517	−	7.30447i	−0.575673	−	0.332365i
$484$		0			0
$485$	−1.72426	−	2.98650i	−0.0782944	−	0.135610i
$486$		0			0
$487$	35.4824	−	20.4858i	1.60786	−	0.928299i	0.618012	−	0.786168i	$-0.287938\pi$
$487$	35.4824	−	20.4858i	1.60786	−	0.928299i	0.989848	−	0.142130i	$-0.0453951\pi$
$488$		0			0
$489$		−	38.7575i		−	1.75267i
$490$		0			0
$491$	15.8231	−	27.4063i	0.714085	−	1.23683i	−0.249227	−	0.968445i	$-0.580176\pi$
$491$	15.8231	−	27.4063i	0.714085	−	1.23683i	0.963311	−	0.268386i	$-0.0864903\pi$
$492$		0			0
$493$	−15.5838			−0.701860
$494$		0			0
$495$	1.12241			0.0504484
$496$		0			0
$497$	−6.04146	+	10.4641i	−0.270997	+	0.469380i
$498$		0			0
$499$		−	21.2455i		−	0.951080i	−0.879694	−	0.475540i	$-0.842253\pi$
$499$		−	21.2455i		−	0.951080i	0.879694	−	0.475540i	$-0.157747\pi$
$500$		0			0
$501$	11.5908	−	6.69198i	0.517841	−	0.298976i
$502$		0			0
$503$	−15.5141	−	26.8711i	−0.691737	−	1.19812i	−0.971268	−	0.237988i	$-0.923512\pi$
$503$	−15.5141	−	26.8711i	−0.691737	−	1.19812i	0.279531	−	0.960137i	$-0.409821\pi$
$504$		0			0
$505$	12.6571	+	7.30757i	0.563233	+	0.325182i
$506$		0			0
$507$	13.7114	−	23.6952i	0.608946	−	1.05234i
$508$		0			0
$509$	14.8638	+	8.58160i	0.658825	+	0.380373i	0.791829	−	0.610743i	$-0.209129\pi$
$509$	14.8638	+	8.58160i	0.658825	+	0.380373i	−0.133004	+	0.991115i	$0.542462\pi$
$510$		0			0
$511$	9.41298	+	16.3038i	0.416406	+	0.721236i
$512$		0			0
$513$	9.73740	−	5.62189i	0.429917	−	0.248212i
$514$		0			0
$515$		−	3.13207i		−	0.138016i
$516$		0			0
$517$	0.460443	−	0.797510i	0.0202503	−	0.0350745i
$518$		0			0
$519$	−52.8768			−2.32103
$520$		0			0
$521$	22.0185			0.964647			0.482323	−	0.875993i	$-0.339793\pi$
$521$	22.0185			0.964647			0.482323	+	0.875993i	$0.339793\pi$
$522$		0			0
$523$	11.4763	−	19.8776i	0.501824	−	0.869185i	−0.498173	−	0.867077i	$-0.665996\pi$
$523$	11.4763	−	19.8776i	0.501824	−	0.869185i	0.999998	−	0.00210800i	$-0.000670996\pi$
$524$		0			0
$525$			5.40747i			0.236001i
$526$		0			0
$527$	21.9474	−	12.6713i	0.956044	−	0.551972i
$528$		0			0
$529$	7.85062	+	13.5977i	0.341331	+	0.591203i
$530$		0			0
$531$	−16.6996	−	9.64150i	−0.724699	−	0.418405i
$532$		0			0
$533$	−12.7660	−	7.37883i	−0.552959	−	0.319613i
$534$		0			0
$535$	−7.73179	−	4.46395i	−0.334274	−	0.192993i
$536$		0			0
$537$	−3.58722	−	6.21325i	−0.154800	−	0.268122i
$538$		0			0
$539$	0.275325	−	0.158959i	0.0118591	−	0.00684684i
$540$		0			0
$541$			16.7908i			0.721892i	0.932587	+	0.360946i	$0.117546\pi$
$541$			16.7908i			0.721892i	−0.932587	+	0.360946i	$0.882454\pi$
$542$		0			0
$543$	−23.5560	+	40.8002i	−1.01088	+	1.75090i
$544$		0			0
$545$	8.61181			0.368890
$546$		0			0
$547$	−43.9155			−1.87769			−0.938846	−	0.344337i	$-0.888104\pi$
$547$	−43.9155			−1.87769			−0.938846	+	0.344337i	$0.888104\pi$
$548$		0			0
$549$	0.288207	−	0.499189i	0.0123004	−	0.0213049i
$550$		0			0
$551$		−	9.78978i		−	0.417058i
$552$		0			0
$553$	18.0227	−	10.4054i	0.766403	−	0.442483i
$554$		0			0
$555$	5.68005	+	9.83813i	0.241105	+	0.417605i
$556$		0			0
$557$	−14.6118	−	8.43611i	−0.619120	−	0.357449i	0.157406	−	0.987534i	$-0.449687\pi$
$557$	−14.6118	−	8.43611i	−0.619120	−	0.357449i	−0.776526	+	0.630085i	$0.783020\pi$
$558$		0			0
$559$	−7.44226	−	12.9050i	−0.314774	−	0.545823i
$560$		0			0
$561$	7.74703	+	4.47275i	0.327080	+	0.188840i
$562$		0			0
$563$	11.4958	+	19.9112i	0.484488	+	0.839158i	0.999841	−	0.0178197i	$-0.00567248\pi$
$563$	11.4958	+	19.9112i	0.484488	+	0.839158i	−0.515353	+	0.856978i	$0.672339\pi$
$564$		0			0
$565$	14.7915	−	8.53990i	0.622285	−	0.359276i
$566$		0			0
$567$		−	28.8769i		−	1.21271i
$568$		0			0
$569$	6.78715	−	11.7557i	0.284532	−	0.492824i	−0.687963	−	0.725745i	$-0.741495\pi$
$569$	6.78715	−	11.7557i	0.284532	−	0.492824i	0.972496	+	0.232921i	$0.0748284\pi$
$570$		0			0
$571$	−45.8554			−1.91899			−0.959495	−	0.281727i	$-0.909093\pi$
$571$	−45.8554			−1.91899			−0.959495	+	0.281727i	$0.909093\pi$
$572$		0			0
$573$	0.971314			0.0405772
$574$		0			0
$575$	−1.35081	+	2.33967i	−0.0563327	+	0.0975711i
$576$		0			0
$577$			31.9150i			1.32864i	0.747449	+	0.664319i	$0.231278\pi$
$577$			31.9150i			1.32864i	−0.747449	+	0.664319i	$0.768722\pi$
$578$		0			0
$579$	43.1643	−	24.9209i	1.79385	−	1.03568i
$580$		0			0
$581$	−18.3453	−	31.7750i	−0.761092	−	1.31825i
$582$		0			0
$583$	5.03712	+	2.90818i	0.208616	+	0.120445i
$584$		0			0
$585$	4.48113	−	2.58425i	0.185272	−	0.106846i
$586$		0			0
$587$	−17.7194	−	10.2303i	−0.731358	−	0.422250i	0.0875608	−	0.996159i	$-0.472093\pi$
$587$	−17.7194	−	10.2303i	−0.731358	−	0.422250i	−0.818919	+	0.573909i	$0.805426\pi$
$588$		0			0
$589$	7.96015	+	13.7874i	0.327992	+	0.568099i
$590$		0			0
$591$	48.1869	−	27.8207i	1.98214	−	1.14439i
$592$		0			0
$593$		−	1.21152i		−	0.0497511i	−0.999691	−	0.0248755i	$-0.992081\pi$
$593$		−	1.21152i		−	0.0497511i	0.999691	−	0.0248755i	$-0.00791894\pi$
$594$		0			0
$595$	−6.97134	+	12.0747i	−0.285797	+	0.495015i
$596$		0			0
$597$	−5.81211			−0.237874
$598$		0			0
$599$	−11.6944			−0.477821			−0.238910	−	0.971042i	$-0.576790\pi$
$599$	−11.6944			−0.477821			−0.238910	+	0.971042i	$0.576790\pi$
$600$		0			0
$601$	−16.9720	+	29.3964i	−0.692303	+	1.19910i	0.278778	+	0.960356i	$0.410071\pi$
$601$	−16.9720	+	29.3964i	−0.692303	+	1.19910i	−0.971081	+	0.238749i	$0.923263\pi$
$602$		0			0
$603$			19.6519i			0.800287i
$604$		0			0
$605$	−8.99624	+	5.19398i	−0.365749	+	0.211165i
$606$		0			0
$607$	11.1499	+	19.3122i	0.452560	+	0.783857i	0.998544	−	0.0539382i	$-0.0171774\pi$
$607$	11.1499	+	19.3122i	0.452560	+	0.783857i	−0.545984	+	0.837796i	$0.683844\pi$
$608$		0			0
$609$	−13.4405	−	7.75986i	−0.544635	−	0.314445i
$610$		0			0
$611$	0.00208257	−	4.24414i	8.42520e−5	−	0.171699i
$612$		0			0
$613$	−32.3554	−	18.6804i	−1.30682	−	0.754494i	−0.325258	−	0.945625i	$-0.605451\pi$
$613$	−32.3554	−	18.6804i	−1.30682	−	0.754494i	−0.981564	+	0.191131i	$0.938784\pi$
$614$		0			0
$615$	−4.30605	−	7.45830i	−0.173637	−	0.300748i
$616$		0			0
$617$	19.9910	−	11.5418i	0.804809	−	0.464657i	−0.0403411	−	0.999186i	$-0.512844\pi$
$617$	19.9910	−	11.5418i	0.804809	−	0.464657i	0.845150	+	0.534529i	$0.179511\pi$
$618$		0			0
$619$			19.8138i			0.796383i	0.917302	+	0.398192i	$0.130362\pi$
$619$			19.8138i			0.796383i	−0.917302	+	0.398192i	$0.869638\pi$
$620$		0			0
$621$	4.45270	−	7.71231i	0.178681	−	0.309484i
$622$		0			0
$623$	34.1562			1.36844
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−2.80979	+	4.86669i	−0.112212	+	0.194357i
$628$		0			0
$629$			29.2910i			1.16791i
$630$		0			0
$631$	−21.2273	+	12.2556i	−0.845046	+	0.487888i	−0.858976	−	0.512015i	$-0.828899\pi$
$631$	−21.2273	+	12.2556i	−0.845046	+	0.487888i	0.0139300	+	0.999903i	$0.495566\pi$
$632$		0			0
$633$	3.99784	+	6.92447i	0.158900	+	0.275223i
$634$		0			0
$635$	12.7645	+	7.36957i	0.506543	+	0.292453i
$636$		0			0
$637$	0.733225	−	1.26855i	0.0290514	−	0.0502616i
$638$		0			0
$639$	5.84659	+	3.37553i	0.231287	+	0.133534i
$640$		0			0
$641$	−1.02860	−	1.78159i	−0.0406273	−	0.0703686i	0.844997	−	0.534771i	$-0.179602\pi$
$641$	−1.02860	−	1.78159i	−0.0406273	−	0.0703686i	−0.885624	+	0.464403i	$0.846269\pi$
$642$		0			0
$643$	−27.5893	+	15.9287i	−1.08801	+	0.628165i	−0.933047	−	0.359755i	$-0.882860\pi$
$643$	−27.5893	+	15.9287i	−1.08801	+	0.628165i	−0.154967	+	0.987920i	$0.549527\pi$
$644$		0			0
$645$		−	8.70091i		−	0.342598i
$646$		0			0
$647$	8.25459	−	14.2974i	0.324521	−	0.562088i	−0.656894	−	0.753983i	$-0.728130\pi$
$647$	8.25459	−	14.2974i	0.324521	−	0.562088i	0.981415	+	0.191895i	$0.0614634\pi$
$648$		0			0
$649$	−10.5148			−0.412741
$650$		0			0
$651$	25.2384			0.989172
$652$		0			0
$653$	22.3370	−	38.6888i	0.874113	−	1.51401i	0.0164083	−	0.999865i	$-0.494777\pi$
$653$	22.3370	−	38.6888i	0.874113	−	1.51401i	0.857705	−	0.514143i	$-0.171890\pi$
$654$		0			0
$655$		−	6.43889i		−	0.251588i
$656$		0			0
$657$	9.10936	−	5.25929i	0.355390	−	0.205184i
$658$		0			0
$659$	20.4956	+	35.4994i	0.798395	+	1.38286i	0.920661	+	0.390363i	$0.127651\pi$
$659$	20.4956	+	35.4994i	0.798395	+	1.38286i	−0.122266	+	0.992497i	$0.539016\pi$
$660$		0			0
$661$	−27.1203	−	15.6579i	−1.05486	−	0.609022i	−0.130852	−	0.991402i	$-0.541771\pi$
$661$	−27.1203	−	15.6579i	−1.05486	−	0.609022i	−0.924005	+	0.382379i	$0.875105\pi$
$662$		0			0
$663$	41.2276	+	0.0202302i	1.60115	+	0.000785674i
$664$		0			0
$665$	−7.58536	−	4.37941i	−0.294147	−	0.169826i
$666$		0			0
$667$	−3.87690	−	6.71498i	−0.150114	−	0.260005i
$668$		0			0
$669$	25.3972	−	14.6631i	0.981912	−	0.566907i
$670$		0			0
$671$		−	0.314312i		−	0.0121339i
$672$		0			0
$673$	1.91053	−	3.30914i	0.0736457	−	0.127558i	−0.826851	−	0.562421i	$-0.809870\pi$
$673$	1.91053	−	3.30914i	0.0736457	−	0.127558i	0.900497	+	0.434863i	$0.143203\pi$
$674$		0			0
$675$	−3.29632			−0.126875
$676$		0			0
$677$	−40.7735			−1.56705			−0.783527	−	0.621358i	$-0.786581\pi$
$677$	−40.7735			−1.56705			−0.783527	+	0.621358i	$0.786581\pi$
$678$		0			0
$679$	4.42755	−	7.66875i	0.169914	−	0.294300i
$680$		0			0
$681$		−	46.5659i		−	1.78441i
$682$		0			0
$683$	−16.5699	+	9.56663i	−0.634029	+	0.366057i	−0.782311	−	0.622888i	$-0.785959\pi$
$683$	−16.5699	+	9.56663i	−0.634029	+	0.366057i	0.148282	+	0.988945i	$0.452626\pi$
$684$		0			0
$685$	−4.20600	−	7.28500i	−0.160703	−	0.278346i
$686$		0			0
$687$	−19.0445	−	10.9953i	−0.726593	−	0.419499i
$688$		0			0
$689$	26.8062	+	0.0131537i	1.02123	+	0.000501114i
$690$		0			0
$691$	16.2164	+	9.36256i	0.616902	+	0.356169i	0.775662	−	0.631149i	$-0.217416\pi$
$691$	16.2164	+	9.36256i	0.616902	+	0.356169i	−0.158760	+	0.987317i	$0.550750\pi$
$692$		0			0
$693$	1.44106	+	2.49599i	0.0547413	+	0.0948147i
$694$		0			0
$695$	5.96753	−	3.44535i	0.226361	−	0.130690i
$696$		0			0
$697$		−	22.2055i		−	0.841095i
$698$		0			0
$699$	−26.9761	+	46.7240i	−1.02033	+	1.76727i
$700$		0			0
$701$	−38.5192			−1.45485			−0.727425	−	0.686187i	$-0.759283\pi$
$701$	−38.5192			−1.45485			−0.727425	+	0.686187i	$0.759283\pi$
$702$		0			0
$703$	−18.4006			−0.693993
$704$		0			0
$705$	1.23942	−	2.14675i	0.0466794	−	0.0808511i
$706$		0			0
$707$			37.5288i			1.41142i
$708$		0			0
$709$	−45.6308	+	26.3450i	−1.71370	+	0.989407i	−0.784266	+	0.620425i	$0.786960\pi$
$709$	−45.6308	+	26.3450i	−1.71370	+	0.989407i	−0.929437	+	0.368982i	$0.879707\pi$
$710$		0			0
$711$	−5.81378	−	10.0698i	−0.218034	−	0.377646i
$712$		0			0
$713$	10.9200	+	6.30467i	0.408958	+	0.236112i
$714$		0			0
$715$	1.41156	−	2.44212i	0.0527892	−	0.0913301i
$716$		0			0
$717$	−18.6836	−	10.7870i	−0.697753	−	0.402848i
$718$		0			0
$719$	−13.3279	−	23.0845i	−0.497046	−	0.860908i	0.502949	−	0.864316i	$-0.332248\pi$
$719$	−13.3279	−	23.0845i	−0.497046	−	0.860908i	−0.999994	+	0.00340819i	$0.998915\pi$
$720$		0			0
$721$	6.96506	−	4.02128i	0.259392	−	0.149760i
$722$		0			0
$723$			16.0471i			0.596798i
$724$		0			0
$725$	−1.43503	+	2.48554i	−0.0532955	+	0.0923105i
$726$		0			0
$727$	−17.0407			−0.632003			−0.316002	−	0.948759i	$-0.602340\pi$
$727$	−17.0407			−0.632003			−0.316002	+	0.948759i	$0.602340\pi$
$728$		0			0
$729$	4.69060			0.173726
$730$		0			0
$731$	11.2173	−	19.4289i	0.414885	−	0.718602i
$732$		0			0
$733$			46.6560i			1.72328i	0.507523	+	0.861638i	$0.330561\pi$
$733$			46.6560i			1.72328i	−0.507523	+	0.861638i	$0.669439\pi$
$734$		0			0
$735$	0.741122	−	0.427887i	0.0273367	−	0.0157828i
$736$		0			0
$737$	5.35797	+	9.28028i	0.197363	+	0.341843i
$738$		0			0
$739$	25.0308	+	14.4516i	0.920774	+	0.531609i	0.883882	−	0.467710i	$-0.154921\pi$
$739$	25.0308	+	14.4516i	0.920774	+	0.531609i	0.0368919	+	0.999319i	$0.488254\pi$
$740$		0			0
$741$	−0.0127086	+	25.8992i	−0.000466863	+	0.951433i
$742$		0			0
$743$	−19.8017	−	11.4325i	−0.726453	−	0.419418i	0.0906700	−	0.995881i	$-0.471099\pi$
$743$	−19.8017	−	11.4325i	−0.726453	−	0.419418i	−0.817123	+	0.576463i	$0.804432\pi$
$744$		0			0
$745$	−1.22181	−	2.11623i	−0.0447636	−	0.0775328i
$746$		0			0
$747$	−17.7536	+	10.2500i	−0.649569	+	0.375029i
$748$		0			0
$749$		−	22.9251i		−	0.837665i
$750$		0			0
$751$	25.9536	−	44.9530i	0.947062	−	1.64036i	0.195493	−	0.980705i	$-0.437369\pi$
$751$	25.9536	−	44.9530i	0.947062	−	1.64036i	0.751569	−	0.659654i	$-0.229297\pi$
$752$		0			0
$753$	26.0415			0.949006
$754$		0			0
$755$	16.4786			0.599716
$756$		0			0
$757$	−11.8400	+	20.5075i	−0.430332	+	0.745357i	−0.996902	−	0.0786571i	$-0.974937\pi$
$757$	−11.8400	+	20.5075i	−0.430332	+	0.745357i	0.566570	+	0.824014i	$0.308270\pi$
$758$		0			0
$759$			4.45087i			0.161556i
$760$		0			0
$761$	−43.3551	+	25.0311i	−1.57162	+	0.907375i	−0.575649	+	0.817697i	$0.695251\pi$
$761$	−43.3551	+	25.0311i	−1.57162	+	0.907375i	−0.995971	+	0.0896784i	$0.971416\pi$
$762$		0			0
$763$	11.0567	+	19.1508i	0.400281	+	0.693306i
$764$		0			0
$765$	6.74647	+	3.89508i	0.243919	+	0.140827i
$766$		0			0
$767$	−41.9796	+	24.2094i	−1.51579	+	0.874153i
$768$		0			0
$769$	−39.3644	−	22.7271i	−1.41952	−	0.819559i	−0.423261	−	0.906008i	$-0.639115\pi$
$769$	−39.3644	−	22.7271i	−1.41952	−	0.819559i	−0.996256	+	0.0864489i	$0.972448\pi$
$770$		0			0
$771$	11.0089	+	19.0680i	0.396477	+	0.686718i
$772$		0			0
$773$	−8.59375	+	4.96161i	−0.309096	+	0.178457i	−0.646522	−	0.762896i	$-0.723777\pi$
$773$	−8.59375	+	4.96161i	−0.309096	+	0.178457i	0.337426	+	0.941352i	$0.390444\pi$
$774$		0			0
$775$		−	4.66733i		−	0.167655i
$776$		0			0
$777$	−14.5853	+	25.2624i	−0.523243	+	0.906284i
$778$		0			0
$779$	13.9496			0.499795
$780$		0			0
$781$	3.68127			0.131726
$782$		0			0
$783$	4.73030	−	8.19312i	0.169047	−	0.292798i
$784$		0			0
$785$		−	11.9282i		−	0.425737i
$786$		0			0
$787$	−46.9679	+	27.1170i	−1.67423	+	0.966615i	−0.708996	+	0.705212i	$0.750852\pi$
$787$	−46.9679	+	27.1170i	−1.67423	+	0.966615i	−0.965230	+	0.261403i	$0.915815\pi$
$788$		0			0
$789$	2.12879	+	3.68718i	0.0757871	+	0.131267i
$790$		0			0
$791$	37.9818	+	21.9288i	1.35048	+	0.779698i
$792$		0			0
$793$	−0.723677	−	1.25487i	−0.0256985	−	0.0445616i
$794$		0			0
$795$	13.5590	+	7.82827i	0.480887	+	0.277640i
$796$		0			0
$797$	−11.6972	−	20.2601i	−0.414336	−	0.717650i	0.581023	−	0.813887i	$-0.302653\pi$
$797$	−11.6972	−	20.2601i	−0.414336	−	0.717650i	−0.995358	+	0.0962370i	$0.969319\pi$
$798$		0			0
$799$	5.53519	−	3.19575i	0.195821	−	0.113057i
$800$		0			0
$801$		−	19.0840i		−	0.674300i
$802$		0			0
$803$	2.86783	−	4.96722i	0.101203	−	0.175289i
$804$		0			0
$805$	−6.93724			−0.244506
$806$		0			0
$807$	27.9953			0.985482
$808$		0			0
$809$	2.26162	−	3.91724i	0.0795144	−	0.137723i	−0.823526	−	0.567278i	$-0.807996\pi$
$809$	2.26162	−	3.91724i	0.0795144	−	0.137723i	0.903041	+	0.429555i	$0.141330\pi$
$810$		0			0
$811$			2.66035i			0.0934176i	0.998909	+	0.0467088i	$0.0148733\pi$
$811$			2.66035i			0.0934176i	−0.998909	+	0.0467088i	$0.985127\pi$
$812$		0			0
$813$	45.9713	−	26.5416i	1.61228	−	0.930853i
$814$		0			0
$815$	−9.20224	−	15.9387i	−0.322340	−	0.558310i
$816$		0			0
$817$	12.2052	+	7.04670i	0.427007	+	0.246533i
$818$		0			0
$819$	11.5001	+	6.64714i	0.401848	+	0.232270i
$820$		0			0
$821$	24.2386	+	13.9941i	0.845931	+	0.488399i	0.859276	−	0.511512i	$-0.170915\pi$
$821$	24.2386	+	13.9941i	0.845931	+	0.488399i	−0.0133446	+	0.999911i	$0.504248\pi$
$822$		0			0
$823$	22.9653	+	39.7770i	0.800519	+	1.38654i	0.919275	+	0.393617i	$0.128776\pi$
$823$	22.9653	+	39.7770i	0.800519	+	1.38654i	−0.118755	+	0.992924i	$0.537890\pi$
$824$		0			0
$825$	1.42676	−	0.823740i	0.0496734	−	0.0286789i
$826$		0			0
$827$		−	24.3812i		−	0.847817i	−0.905705	−	0.423908i	$-0.860658\pi$
$827$		−	24.3812i		−	0.847817i	0.905705	−	0.423908i	$-0.139342\pi$
$828$		0			0
$829$	−12.3511	+	21.3928i	−0.428972	+	0.743001i	−0.996782	−	0.0801582i	$-0.974457\pi$
$829$	−12.3511	+	21.3928i	−0.428972	+	0.743001i	0.567810	+	0.823160i	$0.307791\pi$
$830$		0			0
$831$	11.6983			0.405811
$832$		0			0
$833$	2.20654			0.0764520
$834$		0			0
$835$	3.17777	−	5.50406i	0.109971	−	0.190476i
$836$		0			0
$837$			15.3850i			0.531783i
$838$		0			0
$839$	−8.26271	+	4.77048i	−0.285261	+	0.164695i	−0.635803	−	0.771852i	$-0.719331\pi$
$839$	−8.26271	+	4.77048i	−0.285261	+	0.164695i	0.350542	+	0.936547i	$0.385997\pi$
$840$		0			0
$841$	10.3814	+	17.9811i	0.357979	+	0.620039i
$842$		0			0
$843$	−25.2576	−	14.5825i	−0.869917	−	0.502247i
$844$		0			0
$845$	0.0127581	−	13.0000i	0.000438890	−	0.447213i
$846$		0			0
$847$	−23.1006	−	13.3371i	−0.793746	−	0.458269i
$848$		0			0
$849$	34.1079	+	59.0767i	1.17058	+	2.02751i
$850$		0			0
$851$	−12.6213	+	7.28692i	−0.432653	+	0.249792i
$852$		0			0
$853$			14.7920i			0.506469i	0.967405	+	0.253234i	$0.0814944\pi$
$853$			14.7920i			0.506469i	−0.967405	+	0.253234i	$0.918506\pi$
$854$		0			0
$855$	−2.44689	+	4.23814i	−0.0836820	+	0.144941i
$856$		0			0
$857$	−57.1318			−1.95159			−0.975793	−	0.218696i	$-0.929820\pi$
$857$	−57.1318			−1.95159			−0.975793	+	0.218696i	$0.929820\pi$
$858$		0			0
$859$	−3.04858			−0.104016			−0.0520081	−	0.998647i	$-0.516562\pi$
$859$	−3.04858			−0.104016			−0.0520081	+	0.998647i	$0.516562\pi$
$860$		0			0
$861$	11.0571	−	19.1515i	0.376825	−	0.652680i
$862$		0			0
$863$			34.9154i			1.18853i	0.804268	+	0.594267i	$0.202558\pi$
$863$			34.9154i			1.18853i	−0.804268	+	0.594267i	$0.797442\pi$
$864$		0			0
$865$	−21.7452	+	12.5546i	−0.739359	+	0.426869i
$866$		0			0
$867$	13.1436	+	22.7654i	0.446380	+	0.773152i
$868$		0			0
$869$	−5.49092	−	3.17019i	−0.186267	−	0.107541i
$870$		0			0
$871$	42.7584	+	24.7146i	1.44881	+	0.837421i
$872$		0			0
$873$	−4.28474	−	2.47380i	−0.145016	−	0.0837253i
$874$		0			0
$875$	1.28390	+	2.22378i	0.0434038	+	0.0751776i
$876$		0			0
$877$	13.4930	−	7.79018i	0.455626	−	0.263056i	−0.254577	−	0.967052i	$-0.581936\pi$
$877$	13.4930	−	7.79018i	0.455626	−	0.263056i	0.710203	+	0.703997i	$0.248603\pi$
$878$		0			0
$879$		−	49.1869i		−	1.65903i
$880$		0			0
$881$	−4.73006	+	8.19271i	−0.159360	+	0.276019i	−0.934638	−	0.355601i	$-0.884276\pi$
$881$	−4.73006	+	8.19271i	−0.159360	+	0.276019i	0.775278	+	0.631620i	$0.217610\pi$
$882$		0			0
$883$	40.6231			1.36708			0.683538	−	0.729915i	$-0.260440\pi$
$883$	40.6231			1.36708			0.683538	+	0.729915i	$0.260440\pi$
$884$		0			0
$885$	−28.3038			−0.951422
$886$		0			0
$887$	−6.05566	+	10.4887i	−0.203329	+	0.352177i	−0.949599	−	0.313467i	$-0.898510\pi$
$887$	−6.05566	+	10.4887i	−0.203329	+	0.352177i	0.746270	+	0.665643i	$0.231843\pi$
$888$		0			0
$889$			37.8473i			1.26936i
$890$		0			0
$891$	−7.61915	+	4.39892i	−0.255251	+	0.147369i
$892$		0			0
$893$	2.00757	+	3.47722i	0.0671808	+	0.116361i
$894$		0			0
$895$	−2.95044	−	1.70344i	−0.0986223	−	0.0569396i
$896$		0			0
$897$	10.2478	+	17.7698i	0.342163	+	0.593316i
$898$		0			0
$899$	11.6008	+	6.69773i	0.386909	+	0.223382i
$900$		0			0
$901$	20.1845	+	34.9606i	0.672443	+	1.16471i
$902$		0			0
$903$	19.3489	−	11.1711i	0.643893	−	0.371752i
$904$		0			0
$905$			22.3717i			0.743661i
$906$		0			0
$907$	4.21672	−	7.30357i	0.140014	−	0.242511i	−0.787488	−	0.616330i	$-0.788619\pi$
$907$	4.21672	−	7.30357i	0.140014	−	0.242511i	0.927502	+	0.373819i	$0.121952\pi$
$908$		0			0
$909$	20.9684			0.695477
$910$		0			0
$911$	5.84235			0.193566			0.0967828	−	0.995306i	$-0.469145\pi$
$911$	5.84235			0.193566			0.0967828	+	0.995306i	$0.469145\pi$
$912$		0			0
$913$	−5.58922	+	9.68081i	−0.184976	+	0.320388i
$914$		0			0
$915$		−	0.846067i		−	0.0279701i
$916$		0			0
$917$	14.3187	−	8.26690i	0.472845	−	0.272997i
$918$		0			0
$919$	3.12946	+	5.42039i	0.103231	+	0.178802i	0.913014	−	0.407928i	$-0.133748\pi$
$919$	3.12946	+	5.42039i	0.103231	+	0.178802i	−0.809783	+	0.586730i	$0.800415\pi$
$920$		0			0
$921$	12.7881	+	7.38323i	0.421383	+	0.243286i
$922$		0			0
$923$	14.6972	−	8.47583i	0.483765	−	0.278985i
$924$		0			0
$925$	4.67176	+	2.69724i	0.153606	+	0.0886847i
$926$		0			0
$927$	−2.24680	−	3.89157i	−0.0737945	−	0.127816i
$928$		0			0
$929$	47.6289	−	27.4986i	1.56266	−	0.902199i	0.565668	−	0.824633i	$-0.308618\pi$
$929$	47.6289	−	27.4986i	1.56266	−	0.902199i	0.996987	−	0.0775662i	$-0.0247149\pi$
$930$		0			0
$931$			1.38615i			0.0454292i
$932$		0			0
$933$	−21.9672	+	38.0483i	−0.719174	+	1.24565i
$934$		0			0
$935$	4.24788			0.138920
$936$		0			0
$937$	−27.5445			−0.899840			−0.449920	−	0.893069i	$-0.648547\pi$
$937$	−27.5445			−0.899840			−0.449920	+	0.893069i	$0.648547\pi$
$938$		0			0
$939$	−18.5326	+	32.0994i	−0.604788	+	1.04752i
$940$		0			0
$941$		−	23.0134i		−	0.750215i	−0.926981	−	0.375108i	$-0.877606\pi$
$941$		−	23.0134i		−	0.750215i	0.926981	−	0.375108i	$-0.122394\pi$
$942$		0			0
$943$	9.56825	−	5.52423i	0.311585	−	0.179894i
$944$		0			0
$945$	−4.23215	−	7.33030i	−0.137672	−	0.238455i
$946$		0			0
$947$	−27.2600	−	15.7386i	−0.885831	−	0.511435i	−0.0132543	−	0.999912i	$-0.504219\pi$
$947$	−27.2600	−	15.7386i	−0.885831	−	0.511435i	−0.872576	+	0.488478i	$0.837552\pi$
$948$		0			0
$949$	0.0129711	−	26.4342i	0.000421061	−	0.858092i
$950$		0			0
$951$	18.9659	+	10.9500i	0.615011	+	0.355077i
$952$		0			0
$953$	−20.2729	−	35.1137i	−0.656705	−	1.13745i	−0.981464	−	0.191649i	$-0.938616\pi$
$953$	−20.2729	−	35.1137i	−0.656705	−	1.13745i	0.324759	−	0.945797i	$-0.394717\pi$
$954$		0			0
$955$	0.399446	−	0.230620i	0.0129258	−	0.00746270i
$956$		0			0
$957$			4.72835i			0.152846i
$958$		0			0
$959$	10.8002	−	18.7065i	0.348756	−	0.604063i
$960$		0			0
$961$	9.21607			0.297293
$962$		0			0
$963$	−12.8089			−0.412760
$964$		0			0
$965$	11.8340	−	20.4971i	0.380951	−	0.659826i
$966$		0			0
$967$			14.0952i			0.453271i	0.973980	+	0.226636i	$0.0727727\pi$
$967$			14.0952i			0.453271i	−0.973980	+	0.226636i	$0.927227\pi$
$968$		0			0
$969$	−33.7777	+	19.5016i	−1.08510	+	0.626481i
$970$		0			0
$971$	17.1083	+	29.6325i	0.549032	+	0.950951i	0.998341	+	0.0575747i	$0.0183367\pi$
$971$	17.1083	+	29.6325i	0.549032	+	0.950951i	−0.449309	+	0.893376i	$0.648330\pi$
$972$		0			0
$973$	15.3235	+	8.84700i	0.491247	+	0.283622i
$974$		0			0
$975$	3.79964	−	6.57372i	0.121686	−	0.210528i
$976$		0			0
$977$	−5.39032	−	3.11210i	−0.172452	−	0.0995650i	0.411290	−	0.911505i	$-0.365078\pi$
$977$	−5.39032	−	3.11210i	−0.172452	−	0.0995650i	−0.583741	+	0.811940i	$0.698412\pi$
$978$		0			0
$979$	−5.20314	−	9.01210i	−0.166293	−	0.288028i
$980$		0			0
$981$	10.7001	−	6.17770i	0.341627	−	0.197239i
$982$		0			0
$983$			14.6295i			0.466608i	0.972404	+	0.233304i	$0.0749538\pi$
$983$			14.6295i			0.466608i	−0.972404	+	0.233304i	$0.925046\pi$
$984$		0			0
$985$	13.2110	−	22.8821i	0.420938	−	0.729086i
$986$		0			0
$987$	6.36520			0.202607
$988$		0			0
$989$	11.1624			0.354943
$990$		0			0
$991$	10.7471	−	18.6144i	0.341392	−	0.591307i	−0.643300	−	0.765614i	$-0.722435\pi$
$991$	10.7471	−	18.6144i	0.341392	−	0.591307i	0.984691	+	0.174307i	$0.0557685\pi$
$992$		0			0
$993$		−	9.01620i		−	0.286121i
$994$		0			0
$995$	−2.39019	+	1.37998i	−0.0757741	+	0.0437482i
$996$		0			0
$997$	6.90978	+	11.9681i	0.218835	+	0.379033i	0.954452	−	0.298364i	$-0.0964410\pi$
$997$	6.90978	+	11.9681i	0.218835	+	0.379033i	−0.735617	+	0.677398i	$0.763108\pi$
$998$		0			0
$999$	−15.3996	−	8.89096i	−0.487222	−	0.281298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.e.641.6		12
4.3	odd	2		520.2.bu.a.121.1	✓	12
13.10	even	6	inner	1040.2.da.e.881.6		12
52.7	even	12		6760.2.a.bj.1.6		6
52.19	even	12		6760.2.a.bg.1.6		6
52.23	odd	6		520.2.bu.a.361.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.a.121.1	✓	12	4.3	odd	2
520.2.bu.a.361.1	yes	12	52.23	odd	6
1040.2.da.e.641.6		12	1.1	even	1	trivial
1040.2.da.e.881.6		12	13.10	even	6	inner
6760.2.a.bg.1.6		6	52.19	even	12
6760.2.a.bj.1.6		6	52.7	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05294 - 1.82374i) q^{3} -1.00000i q^{5} +(2.22378 - 1.28390i) q^{7} +(-0.717351 - 1.24249i) q^{9} +O(q^{10})\)	\(q+(1.05294 - 1.82374i) q^{3} -1.00000i q^{5} +(2.22378 - 1.28390i) q^{7} +(-0.717351 - 1.24249i) q^{9} +(-0.677514 - 0.391163i) q^{11} +(-3.60555 - 0.00176922i) q^{13} +(-1.82374 - 1.05294i) q^{15} +(-2.71490 - 4.70235i) q^{17} +(2.95402 - 1.70551i) q^{19} -5.40747i q^{21} +(1.35081 - 2.33967i) q^{23} -1.00000 q^{25} +3.29632 q^{27} +(1.43503 - 2.48554i) q^{29} +4.66733i q^{31} +(-1.42676 + 0.823740i) q^{33} +(-1.28390 - 2.22378i) q^{35} +(-4.67176 - 2.69724i) q^{37} +(-3.79964 + 6.57372i) q^{39} +(3.54167 + 2.04478i) q^{41} +(2.06587 + 3.57819i) q^{43} +(-1.24249 + 0.717351i) q^{45} +1.17711i q^{47} +(-0.203187 + 0.351931i) q^{49} -11.4345 q^{51} -7.43470 q^{53} +(-0.391163 + 0.677514i) q^{55} -7.18316i q^{57} +(11.6397 - 6.72021i) q^{59} +(0.200883 + 0.347939i) q^{61} +(-3.19047 - 1.84202i) q^{63} +(-0.00176922 + 3.60555i) q^{65} +(-11.8624 - 6.84877i) q^{67} +(-2.84464 - 4.92706i) q^{69} +(-4.07512 + 2.35277i) q^{71} +7.33154i q^{73} +(-1.05294 + 1.82374i) q^{75} -2.00886 q^{77} +8.10451 q^{79} +(5.62287 - 9.73909i) q^{81} -14.2887i q^{83} +(-4.70235 + 2.71490i) q^{85} +(-3.02198 - 5.23423i) q^{87} +(11.5196 + 6.65086i) q^{89} +(-8.02024 + 4.62524i) q^{91} +(8.51199 + 4.91440i) q^{93} +(-1.70551 - 2.95402i) q^{95} +(2.98650 - 1.72426i) q^{97} +1.12241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 12 * q - 6 * q^7 + 2 * q^9	\( 12 q - 6 q^{7} + 2 q^{9} - 2 q^{13} - 8 q^{17} + 24 q^{19} + 2 q^{23} - 12 q^{25} + 12 q^{27} + 12 q^{29} + 4 q^{35} + 24 q^{37} - 28 q^{39} + 24 q^{41} + 18 q^{43} - 12 q^{45} + 24 q^{49} - 68 q^{53} - 2 q^{55} + 48 q^{59} + 18 q^{61} + 36 q^{63} + 16 q^{65} - 18 q^{67} - 8 q^{69} + 64 q^{77} + 12 q^{79} + 14 q^{81} - 18 q^{87} + 30 q^{89} - 76 q^{91} - 12 q^{93} + 10 q^{95} - 84 q^{97}+O(q^{100}) \) 12 * q - 6 * q^7 + 2 * q^9 - 2 * q^13 - 8 * q^17 + 24 * q^19 + 2 * q^23 - 12 * q^25 + 12 * q^27 + 12 * q^29 + 4 * q^35 + 24 * q^37 - 28 * q^39 + 24 * q^41 + 18 * q^43 - 12 * q^45 + 24 * q^49 - 68 * q^53 - 2 * q^55 + 48 * q^59 + 18 * q^61 + 36 * q^63 + 16 * q^65 - 18 * q^67 - 8 * q^69 + 64 * q^77 + 12 * q^79 + 14 * q^81 - 18 * q^87 + 30 * q^89 - 76 * q^91 - 12 * q^93 + 10 * q^95 - 84 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more