LMFDB - Embedded newform 460.2.s.a.449.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			449.6
Character	$\chi$	$=$	460.449
Dual form			460.2.s.a.209.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.678118 - 0.0974986i) q^{3} +(-0.379538 + 2.20362i) q^{5} +(-0.330568 + 0.286439i) q^{7} +(-2.42814 - 0.712967i) q^{9} +O(q^{10})$	\(q+(-0.678118 - 0.0974986i) q^{3} +(-0.379538 + 2.20362i) q^{5} +(-0.330568 + 0.286439i) q^{7} +(-2.42814 - 0.712967i) q^{9} +(-4.82496 - 3.10081i) q^{11} +(1.83954 + 1.59397i) q^{13} +(0.472222 - 1.45731i) q^{15} +(-4.13868 + 1.89007i) q^{17} +(0.683283 - 1.49618i) q^{19} +(0.252092 - 0.162009i) q^{21} +(-1.39222 - 4.58931i) q^{23} +(-4.71190 - 1.67272i) q^{25} +(3.44659 + 1.57401i) q^{27} +(-2.82510 - 6.18610i) q^{29} +(0.516021 + 3.58901i) q^{31} +(2.96957 + 2.57314i) q^{33} +(-0.505740 - 0.837162i) q^{35} +(-2.55002 + 8.68456i) q^{37} +(-1.09201 - 1.26025i) q^{39} +(-5.57870 + 1.63806i) q^{41} +(-10.5454 - 1.51620i) q^{43} +(2.49268 - 5.08011i) q^{45} +12.5068i q^{47} +(-0.968976 + 6.73937i) q^{49} +(2.99079 - 0.878175i) q^{51} +(3.36925 - 2.91947i) q^{53} +(8.66428 - 9.45551i) q^{55} +(-0.609222 + 0.947968i) q^{57} +(4.68637 - 5.40835i) q^{59} +(0.569827 + 3.96324i) q^{61} +(1.00689 - 0.459830i) q^{63} +(-4.21068 + 3.44867i) q^{65} +(-2.50406 - 3.89639i) q^{67} +(0.496637 + 3.24783i) q^{69} +(10.9929 - 7.06473i) q^{71} +(11.0494 + 5.04610i) q^{73} +(3.03214 + 1.59370i) q^{75} +(2.48317 - 0.357026i) q^{77} +(3.98573 - 4.59978i) q^{79} +(4.20302 + 2.70112i) q^{81} +(2.41993 - 8.24153i) q^{83} +(-2.59422 - 9.83744i) q^{85} +(1.31261 + 4.47035i) q^{87} +(-0.877218 + 6.10119i) q^{89} -1.06467 q^{91} -2.48408i q^{93} +(3.03769 + 2.07356i) q^{95} +(0.138860 + 0.472913i) q^{97} +(9.50490 + 10.9692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{10}{11}\right)$

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
$3$	−0.678118	−	0.0974986i	−0.391511	−	0.0562909i	−0.0562518	−	0.998417i	$-0.517915\pi$
$3$	−0.678118	−	0.0974986i	−0.391511	−	0.0562909i	−0.335260	+	0.942126i	$0.608824\pi$
$4$		0			0
$5$	−0.379538	+	2.20362i	−0.169735	+	0.985490i
$5$	−0.379538	+	2.20362i	−0.169735	+	0.985490i
$6$		0			0
$7$	−0.330568	+	0.286439i	−0.124943	+	0.108264i	−0.715091	−	0.699031i	$-0.753615\pi$
$7$	−0.330568	+	0.286439i	−0.124943	+	0.108264i	0.590148	+	0.807295i	$0.299069\pi$
$8$		0			0
$9$	−2.42814	−	0.712967i	−0.809380	−	0.237656i
$10$		0			0
$11$	−4.82496	−	3.10081i	−1.45478	−	0.934930i	−0.998994	−	0.0448405i	$-0.985722\pi$
$11$	−4.82496	−	3.10081i	−1.45478	−	0.934930i	−0.455786	−	0.890090i	$-0.650642\pi$
$12$		0			0
$13$	1.83954	+	1.59397i	0.510195	+	0.442087i	0.871525	−	0.490351i	$-0.163132\pi$
$13$	1.83954	+	1.59397i	0.510195	+	0.442087i	−0.361329	+	0.932438i	$0.617677\pi$
$14$		0			0
$15$	0.472222	−	1.45731i	0.121927	−	0.376276i
$16$		0			0
$17$	−4.13868	+	1.89007i	−1.00378	+	0.458410i	−0.848349	−	0.529438i	$-0.822403\pi$
$17$	−4.13868	+	1.89007i	−1.00378	+	0.458410i	−0.155428	+	0.987847i	$0.549676\pi$
$18$		0			0
$19$	0.683283	−	1.49618i	0.156756	−	0.343247i	−0.814917	−	0.579578i	$-0.803217\pi$
$19$	0.683283	−	1.49618i	0.156756	−	0.343247i	0.971673	+	0.236330i	$0.0759448\pi$
$20$		0			0
$21$	0.252092	−	0.162009i	0.0550109	−	0.0353533i
$22$		0			0
$23$	−1.39222	−	4.58931i	−0.290297	−	0.956936i
$23$	−1.39222	−	4.58931i	−0.290297	−	0.956936i
$24$		0			0
$25$	−4.71190	−	1.67272i	−0.942380	−	0.334544i
$26$		0			0
$27$	3.44659	+	1.57401i	0.663297	+	0.302918i
$28$		0			0
$29$	−2.82510	−	6.18610i	−0.524608	−	1.14873i	−0.967665	−	0.252237i	$-0.918834\pi$
$29$	−2.82510	−	6.18610i	−0.524608	−	1.14873i	0.443058	−	0.896493i	$-0.353894\pi$
$30$		0			0
$31$	0.516021	+	3.58901i	0.0926802	+	0.644605i	0.982218	+	0.187744i	$0.0601174\pi$
$31$	0.516021	+	3.58901i	0.0926802	+	0.644605i	−0.889538	+	0.456861i	$0.848974\pi$
$32$		0			0
$33$	2.96957	+	2.57314i	0.516935	+	0.447927i
$34$		0			0
$35$	−0.505740	−	0.837162i	−0.0854856	−	0.141506i
$36$		0			0
$37$	−2.55002	+	8.68456i	−0.419220	+	1.42773i	0.431499	+	0.902113i	$0.357985\pi$
$37$	−2.55002	+	8.68456i	−0.419220	+	1.42773i	−0.850720	+	0.525620i	$0.823833\pi$
$38$		0			0
$39$	−1.09201	−	1.26025i	−0.174862	−	0.201801i
$40$		0			0
$41$	−5.57870	+	1.63806i	−0.871247	+	0.255821i	−0.686646	−	0.726992i	$-0.740918\pi$
$41$	−5.57870	+	1.63806i	−0.871247	+	0.255821i	−0.184602	+	0.982813i	$0.559099\pi$
$42$		0			0
$43$	−10.5454	−	1.51620i	−1.60815	−	0.231218i	−0.721083	−	0.692849i	$-0.756355\pi$
$43$	−10.5454	−	1.51620i	−1.60815	−	0.231218i	−0.887072	+	0.461632i	$0.847264\pi$
$44$		0			0
$45$	2.49268	−	5.08011i	0.371587	−	0.757298i
$46$		0			0
$47$			12.5068i			1.82431i	0.409845	+	0.912155i	$0.365583\pi$
$47$			12.5068i			1.82431i	−0.409845	+	0.912155i	$0.634417\pi$
$48$		0			0
$49$	−0.968976	+	6.73937i	−0.138425	+	0.962768i
$50$		0			0
$51$	2.99079	−	0.878175i	0.418794	−	0.122969i
$52$		0			0
$53$	3.36925	−	2.91947i	0.462803	−	0.401021i	−0.392007	−	0.919962i	$-0.628219\pi$
$53$	3.36925	−	2.91947i	0.462803	−	0.401021i	0.854810	+	0.518941i	$0.173674\pi$
$54$		0			0
$55$	8.66428	−	9.45551i	1.16829	−	1.27498i
$56$		0			0
$57$	−0.609222	+	0.947968i	−0.0806934	+	0.125561i
$58$		0			0
$59$	4.68637	−	5.40835i	0.610113	−	0.704108i	−0.363685	−	0.931522i	$-0.618482\pi$
$59$	4.68637	−	5.40835i	0.610113	−	0.704108i	0.973798	+	0.227414i	$0.0730271\pi$
$60$		0			0
$61$	0.569827	+	3.96324i	0.0729589	+	0.507440i	0.993230	+	0.116160i	$0.0370586\pi$
$61$	0.569827	+	3.96324i	0.0729589	+	0.507440i	−0.920272	+	0.391280i	$0.872032\pi$
$62$		0			0
$63$	1.00689	−	0.459830i	0.126856	−	0.0579331i
$64$		0			0
$65$	−4.21068	+	3.44867i	−0.522270	+	0.427755i
$66$		0			0
$67$	−2.50406	−	3.89639i	−0.305919	−	0.476020i	0.653922	−	0.756562i	$-0.273122\pi$
$67$	−2.50406	−	3.89639i	−0.305919	−	0.476020i	−0.959842	+	0.280542i	$0.909486\pi$
$68$		0			0
$69$	0.496637	+	3.24783i	0.0597880	+	0.390993i
$70$		0			0
$71$	10.9929	−	7.06473i	1.30462	−	0.838429i	0.310914	−	0.950438i	$-0.399365\pi$
$71$	10.9929	−	7.06473i	1.30462	−	0.838429i	0.993707	+	0.112009i	$0.0357286\pi$
$72$		0			0
$73$	11.0494	+	5.04610i	1.29324	+	0.590602i	0.938795	−	0.344476i	$-0.111943\pi$
$73$	11.0494	+	5.04610i	1.29324	+	0.590602i	0.354443	+	0.935078i	$0.384671\pi$
$74$		0			0
$75$	3.03214	+	1.59370i	0.350121	+	0.184025i
$76$		0			0
$77$	2.48317	−	0.357026i	0.282984	−	0.0406869i
$78$		0			0
$79$	3.98573	−	4.59978i	0.448430	−	0.517516i	−0.485857	−	0.874038i	$-0.661492\pi$
$79$	3.98573	−	4.59978i	0.448430	−	0.517516i	0.934287	+	0.356523i	$0.116038\pi$
$80$		0			0
$81$	4.20302	+	2.70112i	0.467002	+	0.300124i
$82$		0			0
$83$	2.41993	−	8.24153i	0.265622	−	0.904626i	−0.713380	−	0.700777i	$-0.752837\pi$
$83$	2.41993	−	8.24153i	0.265622	−	0.904626i	0.979002	−	0.203849i	$-0.0653451\pi$
$84$		0			0
$85$	−2.59422	−	9.83744i	−0.281382	−	1.06702i
$86$		0			0
$87$	1.31261	+	4.47035i	0.140727	+	0.479272i
$88$		0			0
$89$	−0.877218	+	6.10119i	−0.0929849	+	0.646725i	0.889020	+	0.457869i	$0.151387\pi$
$89$	−0.877218	+	6.10119i	−0.0929849	+	0.646725i	−0.982005	+	0.188856i	$0.939522\pi$
$90$		0			0
$91$	−1.06467			−0.111607
$92$		0			0
$93$		−	2.48408i		−	0.257587i
$94$		0			0
$95$	3.03769	+	2.07356i	0.311660	+	0.212742i
$96$		0			0
$97$	0.138860	+	0.472913i	0.0140991	+	0.0480170i	0.966242	−	0.257636i	$-0.0829435\pi$
$97$	0.138860	+	0.472913i	0.0140991	+	0.0480170i	−0.952143	+	0.305653i	$0.901125\pi$
$98$		0			0
$99$	9.50490	+	10.9692i	0.955279	+	1.10245i
$100$		0			0
$101$	−12.6961	−	3.72790i	−1.26331	−	0.370940i	−0.419582	−	0.907717i	$-0.637823\pi$
$101$	−12.6961	−	3.72790i	−1.26331	−	0.370940i	−0.843724	+	0.536777i	$0.819642\pi$
$102$		0			0
$103$	0.0660724	−	0.102811i	0.00651031	−	0.0101302i	−0.837983	−	0.545696i	$-0.816265\pi$
$103$	0.0660724	−	0.102811i	0.00651031	−	0.0101302i	0.844493	+	0.535566i	$0.179902\pi$
$104$		0			0
$105$	0.261329	+	0.617003i	0.0255031	+	0.0602133i
$106$		0			0
$107$	−3.19202	+	0.458943i	−0.308584	+	0.0443677i	−0.294867	−	0.955538i	$-0.595275\pi$
$107$	−3.19202	+	0.458943i	−0.308584	+	0.0443677i	−0.0137167	+	0.999906i	$0.504366\pi$
$108$		0			0
$109$	2.57860	+	5.64635i	0.246985	+	0.540822i	0.992002	−	0.126224i	$-0.0402858\pi$
$109$	2.57860	+	5.64635i	0.246985	+	0.540822i	−0.745017	+	0.667046i	$0.767559\pi$
$110$		0			0
$111$	2.57594	−	5.64053i	0.244498	−	0.535376i
$112$		0			0
$113$	−6.84237	−	10.6469i	−0.643676	−	1.00158i	−0.997794	−	0.0663788i	$-0.978855\pi$
$113$	−6.84237	−	10.6469i	−0.643676	−	1.00158i	0.354119	−	0.935201i	$-0.384781\pi$
$114$		0			0
$115$	10.6415	−	1.32610i	0.992325	−	0.123660i
$116$		0			0
$117$	−3.33021	−	5.18190i	−0.307878	−	0.479067i
$118$		0			0
$119$	0.826725	−	1.81028i	0.0757858	−	0.165948i
$120$		0			0
$121$	9.09562	+	19.9166i	0.826875	+	1.81060i
$122$		0			0
$123$	3.94273	−	0.566879i	0.355504	−	0.0511137i
$124$		0			0
$125$	5.47439	−	9.74839i	0.489644	−	0.871922i
$126$		0			0
$127$	−2.83553	+	4.41218i	−0.251613	+	0.391517i	−0.943967	−	0.330041i	$-0.892937\pi$
$127$	−2.83553	+	4.41218i	−0.251613	+	0.391517i	0.692354	+	0.721558i	$0.256574\pi$
$128$		0			0
$129$	7.00318	+	2.05632i	0.616595	+	0.181049i
$130$		0			0
$131$	7.57205	+	8.73861i	0.661573	+	0.763496i	0.983033	−	0.183427i	$-0.0587191\pi$
$131$	7.57205	+	8.73861i	0.661573	+	0.763496i	−0.321460	+	0.946923i	$0.604174\pi$
$132$		0			0
$133$	0.202693	+	0.690309i	0.0175757	+	0.0598573i
$134$		0			0
$135$	−4.77663	+	6.99760i	−0.411107	+	0.602257i
$136$		0			0
$137$			19.2933i			1.64834i	0.566346	+	0.824168i	$0.308357\pi$
$137$			19.2933i			1.64834i	−0.566346	+	0.824168i	$0.691643\pi$
$138$		0			0
$139$	−1.60190			−0.135871			−0.0679357	−	0.997690i	$-0.521641\pi$
$139$	−1.60190			−0.135871			−0.0679357	+	0.997690i	$0.521641\pi$
$140$		0			0
$141$	1.21940	−	8.48111i	0.102692	−	0.714239i
$142$		0			0
$143$	−3.93309	−	13.3949i	−0.328902	−	1.12014i
$144$		0			0
$145$	14.7041	−	3.87759i	1.22111	−	0.322016i
$146$		0			0
$147$	1.31416	−	4.47562i	0.108390	−	0.369143i
$148$		0			0
$149$	−10.2209	−	6.56856i	−0.837326	−	0.538117i	0.0502718	−	0.998736i	$-0.483991\pi$
$149$	−10.2209	−	6.56856i	−0.837326	−	0.538117i	−0.887598	+	0.460619i	$0.847628\pi$
$150$		0			0
$151$	−6.03776	+	6.96794i	−0.491346	+	0.567043i	−0.946225	−	0.323510i	$-0.895137\pi$
$151$	−6.03776	+	6.96794i	−0.491346	+	0.567043i	0.454879	+	0.890553i	$0.349682\pi$
$152$		0			0
$153$	11.3969	−	1.63862i	0.921381	−	0.132475i
$154$		0			0
$155$	−8.10467	−	0.225050i	−0.650983	−	0.0180764i
$156$		0			0
$157$	−2.58299	−	1.17961i	−0.206145	−	0.0941432i	0.309667	−	0.950845i	$-0.399782\pi$
$157$	−2.58299	−	1.17961i	−0.206145	−	0.0941432i	−0.515812	+	0.856702i	$0.672510\pi$
$158$		0			0
$159$	−2.56940	+	1.65125i	−0.203766	+	0.130953i
$160$		0			0
$161$	1.77478	+	1.11829i	0.139872	+	0.0881338i
$162$		0			0
$163$	−1.45916	−	2.27050i	−0.114291	−	0.177840i	0.779396	−	0.626532i	$-0.215526\pi$
$163$	−1.45916	−	2.27050i	−0.114291	−	0.177840i	−0.893686	+	0.448692i	$0.851890\pi$
$164$		0			0
$165$	−6.79730	+	5.56719i	−0.529169	+	0.433405i
$166$		0			0
$167$	−19.9515	+	9.11155i	−1.54389	+	0.705073i	−0.991692	−	0.128637i	$-0.958940\pi$
$167$	−19.9515	+	9.11155i	−1.54389	+	0.705073i	−0.552203	+	0.833710i	$0.686213\pi$
$168$		0			0
$169$	−1.00693	−	7.00336i	−0.0774562	−	0.538720i
$170$		0			0
$171$	−2.72583	+	3.14578i	−0.208450	+	0.240564i
$172$		0			0
$173$	−12.2667	+	19.0873i	−0.932616	+	1.45118i	−0.0406000	+	0.999175i	$0.512927\pi$
$173$	−12.2667	+	19.0873i	−0.932616	+	1.45118i	−0.892016	+	0.452004i	$0.850709\pi$
$174$		0			0
$175$	2.03674	−	0.796725i	0.153963	−	0.0602267i
$176$		0			0
$177$	−3.70521	+	3.21059i	−0.278501	+	0.241322i
$178$		0			0
$179$	−9.22053	+	2.70739i	−0.689175	+	0.202360i	−0.607525	−	0.794301i	$-0.707837\pi$
$179$	−9.22053	+	2.70739i	−0.689175	+	0.202360i	−0.0816506	+	0.996661i	$0.526019\pi$
$180$		0			0
$181$	3.16076	−	21.9836i	0.234937	−	1.63402i	−0.441313	−	0.897353i	$-0.645487\pi$
$181$	3.16076	−	21.9836i	0.234937	−	1.63402i	0.676251	−	0.736672i	$-0.263604\pi$
$182$		0			0
$183$		−	2.74310i		−	0.202776i
$184$		0			0
$185$	−18.1697	−	8.91540i	−1.33586	−	0.655473i
$186$		0			0
$187$	25.8297	+	3.71375i	1.88886	+	0.271576i
$188$		0			0
$189$	−1.59019	+	0.466922i	−0.115669	+	0.0339636i
$190$		0			0
$191$	−12.2948	−	14.1890i	−0.889624	−	1.02668i	−0.999464	−	0.0327317i	$-0.989579\pi$
$191$	−12.2948	−	14.1890i	−0.889624	−	1.02668i	0.109840	−	0.993949i	$-0.464966\pi$
$192$		0			0
$193$	3.15245	−	10.7363i	0.226918	−	0.772813i	−0.764787	−	0.644283i	$-0.777156\pi$
$193$	3.15245	−	10.7363i	0.226918	−	0.772813i	0.991706	−	0.128530i	$-0.0410258\pi$
$194$		0			0
$195$	3.19157	−	1.92807i	0.228553	−	0.138072i
$196$		0			0
$197$	16.2472	+	14.0783i	1.15757	+	1.00304i	0.999879	+	0.0155486i	$0.00494946\pi$
$197$	16.2472	+	14.0783i	1.15757	+	1.00304i	0.157688	+	0.987489i	$0.449596\pi$
$198$		0			0
$199$	0.600380	+	4.17573i	0.0425598	+	0.296010i	0.999973	+	0.00729010i	$0.00232053\pi$
$199$	0.600380	+	4.17573i	0.0425598	+	0.296010i	−0.957414	+	0.288720i	$0.906770\pi$
$200$		0			0
$201$	1.31815	+	2.88635i	0.0929754	+	0.203588i
$202$		0			0
$203$	2.70583	+	1.23571i	0.189912	+	0.0867299i
$204$		0			0
$205$	−1.49232	−	12.9151i	−0.104228	−	0.902027i
$206$		0			0
$207$	0.108479	+	12.1361i	0.00753983	+	0.843516i
$208$		0			0
$209$	−7.93619	+	5.10028i	−0.548958	+	0.352794i
$210$		0			0
$211$	6.67557	−	14.6175i	0.459565	−	1.00631i	−0.528021	−	0.849231i	$-0.677066\pi$
$211$	6.67557	−	14.6175i	0.459565	−	1.00631i	0.987586	−	0.157076i	$-0.0502069\pi$
$212$		0			0
$213$	−8.14330	+	3.71892i	−0.557970	+	0.254816i
$214$		0			0
$215$	7.34350	−	22.6626i	0.500822	−	1.54557i
$216$		0			0
$217$	−1.19861	−	1.03860i	−0.0813671	−	0.0705050i
$218$		0			0
$219$	−7.00083	−	4.49916i	−0.473072	−	0.304025i
$220$		0			0
$221$	−10.6260	−	3.12006i	−0.714779	−	0.209878i
$222$		0			0
$223$	−3.59678	+	3.11662i	−0.240858	+	0.208705i	−0.766922	−	0.641740i	$-0.778213\pi$
$223$	−3.59678	+	3.11662i	−0.240858	+	0.208705i	0.526064	+	0.850445i	$0.323667\pi$
$224$		0			0
$225$	10.2486	+	7.42102i	0.683238	+	0.494735i
$226$		0			0
$227$	−19.8240	−	2.85026i	−1.31577	−	0.189179i	−0.551552	−	0.834141i	$-0.685964\pi$
$227$	−19.8240	−	2.85026i	−1.31577	−	0.189179i	−0.764215	+	0.644962i	$0.776873\pi$
$228$		0			0
$229$	11.0559			0.730592			0.365296	−	0.930891i	$-0.380968\pi$
$229$	11.0559			0.730592			0.365296	+	0.930891i	$0.380968\pi$
$230$		0			0
$231$	−1.71869			−0.113082
$232$		0			0
$233$	21.6414	+	3.11156i	1.41777	+	0.203845i	0.808211	−	0.588893i	$-0.200436\pi$
$233$	21.6414	+	3.11156i	1.41777	+	0.203845i	0.609562	+	0.792738i	$0.291345\pi$
$234$		0			0
$235$	−27.5604	−	4.74683i	−1.79784	−	0.309649i
$236$		0			0
$237$	−3.15127	+	2.73059i	−0.204697	+	0.177371i
$238$		0			0
$239$	1.26551	+	0.371586i	0.0818587	+	0.0240359i	0.322405	−	0.946602i	$-0.395509\pi$
$239$	1.26551	+	0.371586i	0.0818587	+	0.0240359i	−0.240547	+	0.970638i	$0.577327\pi$
$240$		0			0
$241$	−4.28196	−	2.75185i	−0.275826	−	0.177262i	0.395414	−	0.918503i	$-0.370601\pi$
$241$	−4.28196	−	2.75185i	−0.275826	−	0.177262i	−0.671239	+	0.741241i	$0.734238\pi$
$242$		0			0
$243$	−11.1774	−	9.68526i	−0.717030	−	0.621310i
$244$		0			0
$245$	−14.4833	−	4.69311i	−0.925302	−	0.299832i
$246$		0			0
$247$	3.64179	−	1.66315i	0.231721	−	0.105824i
$248$		0			0
$249$	−2.44454	+	5.35279i	−0.154916	+	0.339219i
$250$		0			0
$251$	−11.4076	+	7.33121i	−0.720041	+	0.462742i	−0.848651	−	0.528953i	$-0.822585\pi$
$251$	−11.4076	+	7.33121i	−0.720041	+	0.462742i	0.128610	+	0.991695i	$0.458948\pi$
$252$		0			0
$253$	−7.51318	+	26.4602i	−0.472350	+	1.66354i
$254$		0			0
$255$	0.800047	+	6.92387i	0.0501009	+	0.433590i
$256$		0			0
$257$	2.66771	+	1.21830i	0.166407	+	0.0759955i	0.496877	−	0.867821i	$-0.334480\pi$
$257$	2.66771	+	1.21830i	0.166407	+	0.0759955i	−0.330470	+	0.943816i	$0.607207\pi$
$258$		0			0
$259$	−1.64464	−	3.60126i	−0.102193	−	0.223772i
$260$		0			0
$261$	2.44925	+	17.0349i	0.151605	+	1.05444i
$262$		0			0
$263$	6.04034	+	5.23399i	0.372464	+	0.322742i	0.820899	−	0.571074i	$-0.193473\pi$
$263$	6.04034	+	5.23399i	0.372464	+	0.322742i	−0.448435	+	0.893815i	$0.648018\pi$
$264$		0			0
$265$	5.15466	+	8.53261i	0.316648	+	0.524154i
$266$		0			0
$267$	1.18971	−	4.05180i	0.0728093	−	0.247966i
$268$		0			0
$269$	−12.1896	−	14.0675i	−0.743213	−	0.857714i	0.250679	−	0.968070i	$-0.419346\pi$
$269$	−12.1896	−	14.0675i	−0.743213	−	0.857714i	−0.993892	+	0.110357i	$0.964801\pi$
$270$		0			0
$271$	−12.6722	+	3.72090i	−0.769783	+	0.226029i	−0.642963	−	0.765897i	$-0.722295\pi$
$271$	−12.6722	+	3.72090i	−0.769783	+	0.226029i	−0.126820	+	0.991926i	$0.540477\pi$
$272$		0			0
$273$	0.721969	+	0.103803i	0.0436955	+	0.00628247i
$274$		0			0
$275$	17.5479	+	22.6815i	1.05818	+	1.36775i
$276$		0			0
$277$		−	17.4002i		−	1.04548i	−0.852493	−	0.522739i	$-0.824910\pi$
$277$		−	17.4002i		−	1.04548i	0.852493	−	0.522739i	$-0.175090\pi$
$278$		0			0
$279$	1.30587	−	9.08253i	0.0781804	−	0.543757i
$280$		0			0
$281$	3.01952	−	0.886612i	0.180130	−	0.0528909i	−0.190424	−	0.981702i	$-0.560986\pi$
$281$	3.01952	−	0.886612i	0.180130	−	0.0528909i	0.370553	+	0.928811i	$0.379168\pi$
$282$		0			0
$283$	−9.32257	+	8.07805i	−0.554169	+	0.480191i	−0.886344	−	0.463027i	$-0.846763\pi$
$283$	−9.32257	+	8.07805i	−0.554169	+	0.480191i	0.332175	+	0.943218i	$0.392218\pi$
$284$		0			0
$285$	−1.85774	−	1.70228i	−0.110043	−	0.100835i
$286$		0			0
$287$	1.37494	−	2.13945i	0.0811601	−	0.126288i
$288$		0			0
$289$	2.42366	−	2.79705i	0.142568	−	0.164533i
$290$		0			0
$291$	−0.0480549	−	0.334229i	−0.00281703	−	0.0195929i
$292$		0			0
$293$	−8.53083	+	3.89590i	−0.498377	+	0.227601i	−0.648712	−	0.761034i	$-0.724692\pi$
$293$	−8.53083	+	3.89590i	−0.498377	+	0.227601i	0.150335	+	0.988635i	$0.451965\pi$
$294$		0			0
$295$	10.1393	+	12.3797i	0.590334	+	0.720772i
$296$		0			0
$297$	−11.7490	−	18.2818i	−0.681745	−	1.06082i
$298$		0			0
$299$	4.75417	−	10.6613i	0.274941	−	0.616561i
$300$		0			0
$301$	3.92026	−	2.51940i	0.225960	−	0.145216i
$302$		0			0
$303$	8.24597	+	3.76581i	0.473718	+	0.216340i
$304$		0			0
$305$	−8.94975	−	0.248516i	−0.512461	−	0.0142300i
$306$		0			0
$307$	0.233018	−	0.0335029i	0.0132990	−	0.00191211i	−0.135662	−	0.990755i	$-0.543316\pi$
$307$	0.233018	−	0.0335029i	0.0132990	−	0.00191211i	0.148961	+	0.988843i	$0.452407\pi$
$308$		0			0
$309$	−0.0548288	+	0.0632758i	−0.00311910	+	0.00359963i
$310$		0			0
$311$	14.4571	+	9.29102i	0.819787	+	0.526845i	0.882018	−	0.471217i	$-0.156185\pi$
$311$	14.4571	+	9.29102i	0.819787	+	0.526845i	−0.0622304	+	0.998062i	$0.519821\pi$
$312$		0			0
$313$	−2.67898	+	9.12377i	−0.151425	+	0.515706i	−0.999909	−	0.0135154i	$-0.995698\pi$
$313$	−2.67898	+	9.12377i	−0.151425	+	0.515706i	0.848484	+	0.529222i	$0.177516\pi$
$314$		0			0
$315$	0.631139	+	2.39332i	0.0355607	+	0.134848i
$316$		0			0
$317$	−9.00398	−	30.6647i	−0.505714	−	1.72230i	−0.675993	−	0.736908i	$-0.736285\pi$
$317$	−9.00398	−	30.6647i	−0.505714	−	1.72230i	0.170279	−	0.985396i	$-0.445533\pi$
$318$		0			0
$319$	−5.55096	+	38.6078i	−0.310794	+	2.16162i
$320$		0			0
$321$	2.20931			0.123312
$322$		0			0
$323$			7.48367i			0.416402i
$324$		0			0
$325$	−6.00145	−	10.5876i	−0.332901	−	0.587297i
$326$		0			0
$327$	−1.19808	−	4.08030i	−0.0662542	−	0.225641i
$328$		0			0
$329$	−3.58245	−	4.13436i	−0.197507	−	0.227935i
$330$		0			0
$331$	−32.9124	−	9.66396i	−1.80903	−	0.531179i	−0.810519	−	0.585712i	$-0.800815\pi$
$331$	−32.9124	−	9.66396i	−1.80903	−	0.531179i	−0.998512	+	0.0545327i	$0.982633\pi$
$332$		0			0
$333$	12.3836	−	19.2693i	0.678617	−	1.05595i
$334$		0			0
$335$	9.53656	−	4.03917i	0.521038	−	0.220683i
$336$		0			0
$337$	4.23269	−	0.608569i	0.230569	−	0.0331508i	−0.0260617	−	0.999660i	$-0.508297\pi$
$337$	4.23269	−	0.608569i	0.230569	−	0.0331508i	0.256631	+	0.966509i	$0.417388\pi$
$338$		0			0
$339$	3.60187	+	7.88700i	0.195627	+	0.428363i
$340$		0			0
$341$	8.63906	−	18.9169i	0.467831	−	1.02441i
$342$		0			0
$343$	−3.26546	−	5.08115i	−0.176318	−	0.274356i
$344$		0			0
$345$	−7.34548	−	0.138276i	−0.395467	−	0.00744455i
$346$		0			0
$347$	1.50611	+	2.34355i	0.0808520	+	0.125808i	0.879324	−	0.476223i	$-0.157995\pi$
$347$	1.50611	+	2.34355i	0.0808520	+	0.125808i	−0.798472	+	0.602031i	$0.794358\pi$
$348$		0			0
$349$	11.9869	−	26.2477i	0.641646	−	1.40501i	−0.257034	−	0.966402i	$-0.582745\pi$
$349$	11.9869	−	26.2477i	0.641646	−	1.40501i	0.898680	−	0.438606i	$-0.144528\pi$
$350$		0			0
$351$	3.83122	+	8.38920i	0.204495	+	0.447782i
$352$		0			0
$353$	22.7719	−	3.27410i	1.21202	−	0.174263i	0.493488	−	0.869752i	$-0.335722\pi$
$353$	22.7719	−	3.27410i	1.21202	−	0.174263i	0.718536	+	0.695490i	$0.244813\pi$
$354$		0			0
$355$	11.3958	+	26.9056i	0.604824	+	1.42800i
$356$		0			0
$357$	−0.737117	+	1.14698i	−0.0390123	+	0.0607044i
$358$		0			0
$359$	−13.0867	−	3.84259i	−0.690687	−	0.202804i	−0.0824923	−	0.996592i	$-0.526288\pi$
$359$	−13.0867	−	3.84259i	−0.690687	−	0.202804i	−0.608195	+	0.793788i	$0.708106\pi$
$360$		0			0
$361$	10.6707	+	12.3146i	0.561614	+	0.648137i
$362$		0			0
$363$	−4.22606	−	14.3926i	−0.221811	−	0.755417i
$364$		0			0
$365$	−15.3134	+	22.4336i	−0.801539	+	1.17423i
$366$		0			0
$367$		−	11.2424i		−	0.586848i	−0.955982	−	0.293424i	$-0.905205\pi$
$367$		−	11.2424i		−	0.586848i	0.955982	−	0.293424i	$-0.0947948\pi$
$368$		0			0
$369$	14.7138			0.765968
$370$		0			0
$371$	−0.277517	+	1.93017i	−0.0144079	+	0.100209i
$372$		0			0
$373$	0.789728	+	2.68957i	0.0408905	+	0.139260i	0.977408	−	0.211360i	$-0.0677891\pi$
$373$	0.789728	+	2.68957i	0.0408905	+	0.139260i	−0.936518	+	0.350620i	$0.885971\pi$
$374$		0			0
$375$	−4.66273	+	6.07681i	−0.240783	+	0.313805i
$376$		0			0
$377$	4.66357	−	15.8827i	0.240186	−	0.817999i
$378$		0			0
$379$	−5.61895	−	3.61108i	−0.288626	−	0.185489i	0.388313	−	0.921527i	$-0.373058\pi$
$379$	−5.61895	−	3.61108i	−0.288626	−	0.185489i	−0.676940	+	0.736039i	$0.736694\pi$
$380$		0			0
$381$	2.35301	−	2.71551i	0.120548	−	0.139120i
$382$		0			0
$383$	−34.2208	+	4.92020i	−1.74860	+	0.251411i	−0.941021	−	0.338349i	$-0.890131\pi$
$383$	−34.2208	+	4.92020i	−1.74860	+	0.251411i	−0.807579	+	0.589760i	$0.799222\pi$
$384$		0			0
$385$	−0.155708	+	5.60748i	−0.00793562	+	0.285783i
$386$		0			0
$387$	24.5247	+	11.2000i	1.24666	+	0.569330i
$388$		0			0
$389$	−4.69272	+	3.01583i	−0.237930	+	0.152908i	−0.654173	−	0.756345i	$-0.726983\pi$
$389$	−4.69272	+	3.01583i	−0.237930	+	0.152908i	0.416243	+	0.909254i	$0.363347\pi$
$390$		0			0
$391$	14.4361	+	16.3623i	0.730063	+	0.827476i
$392$		0			0
$393$	−4.28274	−	6.66407i	−0.216036	−	0.336158i
$394$		0			0
$395$	8.62344	+	10.5288i	0.433892	+	0.529763i
$396$		0			0
$397$	−2.34262	+	1.06984i	−0.117573	+	0.0536938i	−0.473333	−	0.880884i	$-0.656949\pi$
$397$	−2.34262	+	1.06984i	−0.117573	+	0.0536938i	0.355760	+	0.934577i	$0.384222\pi$
$398$		0			0
$399$	−0.0701455	−	0.487873i	−0.00351167	−	0.0244242i
$400$		0			0
$401$	−7.21405	+	8.32546i	−0.360253	+	0.415754i	−0.906724	−	0.421724i	$-0.861425\pi$
$401$	−7.21405	+	8.32546i	−0.360253	+	0.415754i	0.546472	+	0.837478i	$0.315971\pi$
$402$		0			0
$403$	−4.77152	+	7.42463i	−0.237686	+	0.369847i
$404$		0			0
$405$	−7.54745	+	8.23669i	−0.375036	+	0.409285i
$406$		0			0
$407$	39.2329	−	33.9955i	1.94470	−	1.68510i
$408$		0			0
$409$	28.6318	−	8.40706i	1.41575	−	0.415702i	0.517689	−	0.855569i	$-0.326792\pi$
$409$	28.6318	−	8.40706i	1.41575	−	0.415702i	0.898063	+	0.439867i	$0.144974\pi$
$410$		0			0
$411$	1.88107	−	13.0831i	0.0927862	−	0.645342i
$412$		0			0
$413$			3.13019i			0.154026i
$414$		0			0
$415$	17.2428	+	8.46059i	0.846414	+	0.415314i
$416$		0			0
$417$	1.08628	+	0.156183i	0.0531952	+	0.00764832i
$418$		0			0
$419$	25.3067	−	7.43071i	1.23631	−	0.363014i	0.402684	−	0.915339i	$-0.368078\pi$
$419$	25.3067	−	7.43071i	1.23631	−	0.363014i	0.833629	+	0.552325i	$0.186259\pi$
$420$		0			0
$421$	14.3375	+	16.5463i	0.698765	+	0.806418i	0.988585	−	0.150663i	$-0.0481408\pi$
$421$	14.3375	+	16.5463i	0.698765	+	0.806418i	−0.289820	+	0.957081i	$0.593595\pi$
$422$		0			0
$423$	8.91696	−	30.3684i	0.433558	−	1.47656i
$424$		0			0
$425$	22.6626	−	1.98299i	1.09930	−	0.0961889i
$426$		0			0
$427$	−1.32359	−	1.14690i	−0.0640531	−	0.0555023i
$428$		0			0
$429$	1.36112	+	9.46678i	0.0657153	+	0.457060i
$430$		0			0
$431$	−0.656166	−	1.43680i	−0.0316064	−	0.0692084i	0.893170	−	0.449719i	$-0.148476\pi$
$431$	−0.656166	−	1.43680i	−0.0316064	−	0.0692084i	−0.924777	+	0.380510i	$0.875748\pi$
$432$		0			0
$433$	−4.04652	−	1.84799i	−0.194464	−	0.0888085i	0.315803	−	0.948825i	$-0.397726\pi$
$433$	−4.04652	−	1.84799i	−0.194464	−	0.0888085i	−0.510267	+	0.860016i	$0.670453\pi$
$434$		0			0
$435$	−10.3491	+	1.19583i	−0.496204	+	0.0573358i
$436$		0			0
$437$	−7.81771	−	1.05278i	−0.373972	−	0.0503615i
$438$		0			0
$439$	−7.85683	+	5.04928i	−0.374986	+	0.240989i	−0.714535	−	0.699599i	$-0.753362\pi$
$439$	−7.85683	+	5.04928i	−0.374986	+	0.240989i	0.339549	+	0.940588i	$0.389725\pi$
$440$		0			0
$441$	7.15776	−	15.6733i	0.340846	−	0.746348i
$442$		0			0
$443$	0.0519299	−	0.0237156i	0.00246727	−	0.00112676i	−0.414181	−	0.910195i	$-0.635932\pi$
$443$	0.0519299	−	0.0237156i	0.00246727	−	0.00112676i	0.416648	+	0.909068i	$0.363205\pi$
$444$		0			0
$445$	−13.1118	−	4.24869i	−0.621558	−	0.201407i
$446$		0			0
$447$	6.29053	+	5.45077i	0.297532	+	0.257813i
$448$		0			0
$449$	11.4449	+	7.35518i	0.540117	+	0.347112i	0.782085	−	0.623172i	$-0.214156\pi$
$449$	11.4449	+	7.35518i	0.540117	+	0.347112i	−0.241968	+	0.970284i	$0.577793\pi$
$450$		0			0
$451$	31.9963	+	9.39497i	1.50665	+	0.442392i
$452$		0			0
$453$	4.77367	−	4.13641i	0.224287	−	0.194346i
$454$		0			0
$455$	0.404082	−	2.34612i	0.0189436	−	0.109988i
$456$		0			0
$457$	−29.4254	−	4.23074i	−1.37646	−	0.197905i	−0.585948	−	0.810349i	$-0.699278\pi$
$457$	−29.4254	−	4.23074i	−1.37646	−	0.197905i	−0.790515	+	0.612443i	$0.790187\pi$
$458$		0			0
$459$	−17.2393			−0.804663
$460$		0			0
$461$	10.1353			0.472050			0.236025	−	0.971747i	$-0.424155\pi$
$461$	10.1353			0.472050			0.236025	+	0.971747i	$0.424155\pi$
$462$		0			0
$463$	−5.82149	−	0.837003i	−0.270547	−	0.0388988i	0.00570584	−	0.999984i	$-0.498184\pi$
$463$	−5.82149	−	0.837003i	−0.270547	−	0.0388988i	−0.276253	+	0.961085i	$0.589093\pi$
$464$		0			0
$465$	5.47398	+	0.942804i	0.253850	+	0.0437215i
$466$		0			0
$467$	1.12283	−	0.972938i	0.0519584	−	0.0450222i	−0.628495	−	0.777814i	$-0.716329\pi$
$467$	1.12283	−	0.972938i	0.0519584	−	0.0450222i	0.680453	+	0.732792i	$0.261783\pi$
$468$		0			0
$469$	1.94384	+	0.570763i	0.0897582	+	0.0263554i
$470$		0			0
$471$	1.63656	+	1.05175i	0.0754087	+	0.0484622i
$472$		0			0
$473$	46.1795	+	40.0148i	2.12334	+	1.83988i
$474$		0			0
$475$	−5.72225	+	5.90692i	−0.262555	+	0.271028i
$476$		0			0
$477$	−10.2625	+	4.68673i	−0.469888	+	0.214591i
$478$		0			0
$479$	−7.39973	+	16.2031i	−0.338102	+	0.740341i	−0.999957	−	0.00929159i	$-0.997042\pi$
$479$	−7.39973	+	16.2031i	−0.338102	+	0.740341i	0.661855	+	0.749632i	$0.269770\pi$
$480$		0			0
$481$	−18.5338	+	11.9109i	−0.845066	+	0.543091i
$482$		0			0
$483$	−1.09448	−	0.931373i	−0.0498004	−	0.0423789i
$484$		0			0
$485$	−1.09482	+	0.126506i	−0.0497134	+	0.00574433i
$486$		0			0
$487$	25.2360	+	11.5249i	1.14355	+	0.522243i	0.894863	−	0.446341i	$-0.147273\pi$
$487$	25.2360	+	11.5249i	1.14355	+	0.522243i	0.248689	+	0.968583i	$0.420000\pi$
$488$		0			0
$489$	0.768114	+	1.68194i	0.0347353	+	0.0760597i
$490$		0			0
$491$	1.77621	+	12.3538i	0.0801591	+	0.557519i	0.989837	+	0.142205i	$0.0454192\pi$
$491$	1.77621	+	12.3538i	0.0801591	+	0.557519i	−0.909678	+	0.415314i	$0.863672\pi$
$492$		0			0
$493$	23.3844	+	20.2627i	1.05318	+	0.912584i
$494$		0			0
$495$	−27.7795	+	16.7820i	−1.24860	+	0.754293i
$496$		0			0
$497$	−1.61030	+	5.48418i	−0.0722318	+	0.245999i
$498$		0			0
$499$	4.88935	+	5.64261i	0.218877	+	0.252598i	0.854560	−	0.519353i	$-0.173827\pi$
$499$	4.88935	+	5.64261i	0.218877	+	0.252598i	−0.635683	+	0.771950i	$0.719281\pi$
$500$		0			0
$501$	14.4178	−	4.23346i	0.644142	−	0.189137i
$502$		0			0
$503$	−23.4967	−	3.37831i	−1.04766	−	0.150631i	−0.403080	−	0.915165i	$-0.632061\pi$
$503$	−23.4967	−	3.37831i	−1.04766	−	0.150631i	−0.644584	+	0.764533i	$0.722970\pi$
$504$		0			0
$505$	13.0335	−	26.5625i	0.579985	−	1.18201i
$506$		0			0
$507$			4.84728i			0.215275i
$508$		0			0
$509$	−0.964959	+	6.71144i	−0.0427711	+	0.297479i	0.957197	+	0.289439i	$0.0934686\pi$
$509$	−0.964959	+	6.71144i	−0.0427711	+	0.297479i	−0.999968	+	0.00804077i	$0.997441\pi$
$510$		0			0
$511$	−5.09799	+	1.49690i	−0.225522	+	0.0662192i
$512$		0			0
$513$	4.71000	−	4.08124i	0.207951	−	0.180191i
$514$		0			0
$515$	0.201479	+	0.184619i	0.00887822	+	0.00813529i
$516$		0			0
$517$	38.7814	−	60.3450i	1.70560	−	2.65397i
$518$		0			0
$519$	10.1792	−	11.7474i	0.446818	−	0.515655i
$520$		0			0
$521$	−3.07635	−	21.3965i	−0.134777	−	0.937396i	−0.939208	−	0.343349i	$-0.888439\pi$
$521$	−3.07635	−	21.3965i	−0.134777	−	0.937396i	0.804431	−	0.594047i	$-0.202471\pi$
$522$		0			0
$523$	−26.5331	+	12.1173i	−1.16021	+	0.529852i	−0.900082	−	0.435722i	$-0.856493\pi$
$523$	−26.5331	+	12.1173i	−1.16021	+	0.529852i	−0.260132	+	0.965573i	$0.583766\pi$
$524$		0			0
$525$	−1.45883	+	0.341694i	−0.0636684	+	0.0149128i
$526$		0			0
$527$	−8.91913	−	13.8784i	−0.388523	−	0.604554i
$528$		0			0
$529$	−19.1235	+	12.7786i	−0.831455	+	0.555592i
$530$		0			0
$531$	−15.2351	+	9.79103i	−0.661149	+	0.424894i
$532$		0			0
$533$	−12.8732	−	5.87901i	−0.557602	−	0.254648i
$534$		0			0
$535$	0.200156	−	7.20818i	0.00865352	−	0.311637i
$536$		0			0
$537$	6.51658	−	0.936942i	0.281211	−	0.0404320i
$538$		0			0
$539$	25.5728	−	29.5126i	1.10150	−	1.27120i
$540$		0			0
$541$	−1.43124	−	0.919800i	−0.0615337	−	0.0395453i	0.509512	−	0.860463i	$-0.329826\pi$
$541$	−1.43124	−	0.919800i	−0.0615337	−	0.0395453i	−0.571046	+	0.820918i	$0.693462\pi$
$542$		0			0
$543$	−4.28673	+	14.5993i	−0.183961	+	0.626515i
$544$		0			0
$545$	−13.4211	+	3.53925i	−0.574896	+	0.151605i
$546$		0			0
$547$	−5.31095	−	18.0874i	−0.227080	−	0.773362i	−0.991665	−	0.128840i	$-0.958875\pi$
$547$	−5.31095	−	18.0874i	−0.227080	−	0.773362i	0.764586	−	0.644522i	$-0.222944\pi$
$548$		0			0
$549$	1.44203	−	10.0296i	0.0615445	−	0.428051i
$550$		0			0
$551$	−11.1859			−0.476534
$552$		0			0
$553$			2.66221i			0.113209i
$554$		0			0
$555$	11.4519	+	7.81721i	0.486107	+	0.331822i
$556$		0			0
$557$	−5.19492	−	17.6923i	−0.220116	−	0.749646i	−0.993310	−	0.115477i	$-0.963160\pi$
$557$	−5.19492	−	17.6923i	−0.220116	−	0.749646i	0.773194	−	0.634169i	$-0.218658\pi$
$558$		0			0
$559$	−16.9818	−	19.5981i	−0.718255	−	0.828910i
$560$		0			0
$561$	−17.1535	−	5.03672i	−0.724221	−	0.212651i
$562$		0			0
$563$	12.7888	−	19.8998i	0.538984	−	0.838676i	−0.459798	−	0.888024i	$-0.652078\pi$
$563$	12.7888	−	19.8998i	0.538984	−	0.838676i	0.998782	+	0.0493481i	$0.0157144\pi$
$564$		0			0
$565$	26.0588	−	11.0371i	1.09630	−	0.464333i
$566$		0			0
$567$	−2.16309	+	0.311005i	−0.0908413	+	0.0130610i
$568$		0			0
$569$	15.3824	+	33.6828i	0.644864	+	1.41206i	0.895978	+	0.444098i	$0.146476\pi$
$569$	15.3824	+	33.6828i	0.644864	+	1.41206i	−0.251114	+	0.967957i	$0.580797\pi$
$570$		0			0
$571$	−4.94438	+	10.8267i	−0.206916	+	0.453082i	−0.984429	−	0.175785i	$-0.943754\pi$
$571$	−4.94438	+	10.8267i	−0.206916	+	0.453082i	0.777513	+	0.628867i	$0.216481\pi$
$572$		0			0
$573$	6.95395	+	10.8206i	0.290505	+	0.452035i
$574$		0			0
$575$	−1.11662	+	23.9531i	−0.0465664	+	0.998915i
$576$		0			0
$577$	−7.06373	−	10.9914i	−0.294067	−	0.457577i	0.662512	−	0.749052i	$-0.269490\pi$
$577$	−7.06373	−	10.9914i	−0.294067	−	0.457577i	−0.956579	+	0.291475i	$0.905854\pi$
$578$		0			0
$579$	−3.18450	+	6.97309i	−0.132343	+	0.289792i
$580$		0			0
$581$	1.56074	+	3.41755i	0.0647505	+	0.141784i
$582$		0			0
$583$	−25.3093	+	3.63892i	−1.04820	+	0.150709i
$584$		0			0
$585$	12.6829	−	5.37179i	0.524373	−	0.222096i
$586$		0			0
$587$	4.42761	−	6.88949i	0.182747	−	0.284360i	−0.737778	−	0.675043i	$-0.764125\pi$
$587$	4.42761	−	6.88949i	0.182747	−	0.284360i	0.920525	+	0.390684i	$0.127761\pi$
$588$		0			0
$589$	5.72239	+	1.68025i	0.235787	+	0.0692334i
$590$		0			0
$591$	−9.64492	−	11.1308i	−0.396739	−	0.457861i
$592$		0			0
$593$	2.06408	+	7.02959i	0.0847614	+	0.288671i	0.990955	−	0.134191i	$-0.0428436\pi$
$593$	2.06408	+	7.02959i	0.0847614	+	0.288671i	−0.906194	+	0.422862i	$0.861025\pi$
$594$		0			0
$595$	3.67539	+	2.50886i	0.150676	+	0.102853i
$596$		0			0
$597$		−	2.89018i		−	0.118287i
$598$		0			0
$599$	0.300949			0.0122964			0.00614821	−	0.999981i	$-0.498043\pi$
$599$	0.300949			0.0122964			0.00614821	+	0.999981i	$0.498043\pi$
$600$		0			0
$601$	6.13219	−	42.6503i	0.250137	−	1.73974i	−0.347236	−	0.937778i	$-0.612880\pi$
$601$	6.13219	−	42.6503i	0.250137	−	1.73974i	0.597373	−	0.801964i	$-0.296211\pi$
$602$		0			0
$603$	3.30221	+	11.2463i	0.134476	+	0.457985i
$604$		0			0
$605$	−47.3409	+	12.4842i	−1.92468	+	0.507554i
$606$		0			0
$607$	9.00701	−	30.6751i	0.365583	−	1.24506i	−0.547332	−	0.836915i	$-0.684357\pi$
$607$	9.00701	−	30.6751i	0.365583	−	1.24506i	0.912916	−	0.408148i	$-0.133825\pi$
$608$		0			0
$609$	−1.71439	−	1.10177i	−0.0694706	−	0.0446460i
$610$		0			0
$611$	−19.9355	+	23.0068i	−0.806504	+	0.930755i
$612$		0			0
$613$	−7.93290	+	1.14058i	−0.320407	+	0.0460676i	−0.300642	−	0.953737i	$-0.597201\pi$
$613$	−7.93290	+	1.14058i	−0.320407	+	0.0460676i	−0.0197650	+	0.999805i	$0.506292\pi$
$614$		0			0
$615$	−0.247230	+	8.90343i	−0.00996928	+	0.359021i
$616$		0			0
$617$	−9.48776	−	4.33291i	−0.381963	−	0.174437i	0.215175	−	0.976576i	$-0.430968\pi$
$617$	−9.48776	−	4.33291i	−0.381963	−	0.174437i	−0.597137	+	0.802139i	$0.703695\pi$
$618$		0			0
$619$	−14.2094	+	9.13183i	−0.571124	+	0.367039i	−0.794102	−	0.607784i	$-0.792059\pi$
$619$	−14.2094	+	9.13183i	−0.571124	+	0.367039i	0.222978	+	0.974823i	$0.428422\pi$
$620$		0			0
$621$	2.42519	−	18.0088i	0.0973195	−	0.722670i
$622$		0			0
$623$	−1.45764	−	2.26813i	−0.0583990	−	0.0908706i
$624$		0			0
$625$	19.4040	+	15.7634i	0.776161	+	0.630535i
$626$		0			0
$627$	5.87894	−	2.68482i	0.234782	−	0.107221i
$628$		0			0
$629$	−5.86074	−	40.7623i	−0.233683	−	1.62530i
$630$		0			0
$631$	10.1529	−	11.7171i	0.404180	−	0.466448i	−0.516773	−	0.856122i	$-0.672867\pi$
$631$	10.1529	−	11.7171i	0.404180	−	0.466448i	0.920953	+	0.389674i	$0.127412\pi$
$632$		0			0
$633$	−5.95201	+	9.26150i	−0.236571	+	0.368112i
$634$		0			0
$635$	−8.64657	−	7.92303i	−0.343129	−	0.314416i
$636$		0			0
$637$	−12.5248	+	10.8528i	−0.496251	+	0.430004i
$638$		0			0
$639$	−31.7293	+	9.31656i	−1.25519	+	0.368558i
$640$		0			0
$641$	−5.88988	+	40.9650i	−0.232636	+	1.61802i	0.453988	+	0.891008i	$0.350001\pi$
$641$	−5.88988	+	40.9650i	−0.232636	+	1.61802i	−0.686624	+	0.727012i	$0.740908\pi$
$642$		0			0
$643$			40.6401i			1.60269i	0.598204	+	0.801344i	$0.295881\pi$
$643$			40.6401i			1.60269i	−0.598204	+	0.801344i	$0.704119\pi$
$644$		0			0
$645$	−7.18932	+	14.6519i	−0.283079	+	0.576918i
$646$		0			0
$647$	−11.5767	−	1.66448i	−0.455129	−	0.0654376i	−0.0890617	−	0.996026i	$-0.528387\pi$
$647$	−11.5767	−	1.66448i	−0.455129	−	0.0654376i	−0.366067	+	0.930588i	$0.619296\pi$
$648$		0			0
$649$	−39.3818	+	11.5635i	−1.54587	+	0.453909i
$650$		0			0
$651$	0.711538	+	0.821158i	0.0278874	+	0.0321837i
$652$		0			0
$653$	0.386421	−	1.31603i	0.0151218	−	0.0515003i	−0.951586	−	0.307381i	$-0.900547\pi$
$653$	0.386421	−	1.31603i	0.0151218	−	0.0515003i	0.966708	+	0.255881i	$0.0823655\pi$
$654$		0			0
$655$	−22.1305	+	13.3693i	−0.864709	+	0.522382i
$656$		0			0
$657$	−23.2319	−	20.1305i	−0.906362	−	0.785367i
$658$		0			0
$659$	3.00106	+	20.8728i	0.116905	+	0.813089i	0.960931	+	0.276788i	$0.0892699\pi$
$659$	3.00106	+	20.8728i	0.116905	+	0.813089i	−0.844026	+	0.536301i	$0.819821\pi$
$660$		0			0
$661$	−3.86449	−	8.46204i	−0.150311	−	0.329135i	0.819466	−	0.573128i	$-0.194270\pi$
$661$	−3.86449	−	8.46204i	−0.150311	−	0.329135i	−0.969777	+	0.243992i	$0.921543\pi$
$662$		0			0
$663$	6.90145	+	3.15179i	0.268030	+	0.122405i
$664$		0			0
$665$	−1.59811	+	0.184660i	−0.0619720	+	0.00716080i
$666$		0			0
$667$	−24.4568	+	21.5776i	−0.946970	+	0.835490i
$668$		0			0
$669$	2.74290	−	1.76276i	0.106047	−	0.0681522i
$670$		0			0
$671$	9.53986	−	20.8894i	0.368282	−	0.806425i
$672$		0			0
$673$	−37.1171	+	16.9508i	−1.43076	+	0.653407i	−0.971963	−	0.235134i	$-0.924447\pi$
$673$	−37.1171	+	16.9508i	−1.43076	+	0.653407i	−0.458798	+	0.888541i	$0.651720\pi$
$674$		0			0
$675$	−13.6071	−	13.1817i	−0.523739	−	0.507366i
$676$		0			0
$677$	18.5402	+	16.0652i	0.712559	+	0.617435i	0.933805	−	0.357782i	$-0.116467\pi$
$677$	18.5402	+	16.0652i	0.712559	+	0.617435i	−0.221246	+	0.975218i	$0.571013\pi$
$678$		0			0
$679$	−0.181363	−	0.116555i	−0.00696008	−	0.00447297i
$680$		0			0
$681$	13.1651	+	3.86563i	0.504489	+	0.148131i
$682$		0			0
$683$	31.4548	−	27.2557i	1.20358	−	1.04291i	0.205653	−	0.978625i	$-0.434068\pi$
$683$	31.4548	−	27.2557i	1.20358	−	1.04291i	0.997931	−	0.0642872i	$-0.0204774\pi$
$684$		0			0
$685$	−42.5151	−	7.32254i	−1.62442	−	0.279780i
$686$		0			0
$687$	−7.49718	−	1.07793i	−0.286035	−	0.0411257i
$688$		0			0
$689$	10.8514			0.413406
$690$		0			0
$691$	10.9577			0.416852			0.208426	−	0.978038i	$-0.433166\pi$
$691$	10.9577			0.416852			0.208426	+	0.978038i	$0.433166\pi$
$692$		0			0
$693$	−6.28404	−	0.903508i	−0.238711	−	0.0343214i
$694$		0			0
$695$	0.607983	−	3.52998i	0.0230621	−	0.133900i
$696$		0			0
$697$	19.9924	−	17.3235i	0.757267	−	0.656176i
$698$		0			0
$699$	−14.3720	−	4.22001i	−0.543600	−	0.159615i
$700$		0			0
$701$	−22.2991	−	14.3308i	−0.842226	−	0.541266i	0.0469150	−	0.998899i	$-0.485061\pi$
$701$	−22.2991	−	14.3308i	−0.842226	−	0.541266i	−0.889141	+	0.457633i	$0.848697\pi$
$702$		0			0
$703$	11.2513	+	9.74930i	0.424350	+	0.367702i
$704$		0			0
$705$	18.2264	+	5.90600i	0.686444	+	0.222433i
$706$		0			0
$707$	5.26473	−	2.40432i	0.198001	−	0.0904239i
$708$		0			0
$709$	10.9935	−	24.0724i	0.412869	−	0.904058i	−0.582932	−	0.812521i	$-0.698095\pi$
$709$	10.9935	−	24.0724i	0.412869	−	0.904058i	0.995802	−	0.0915371i	$-0.0291780\pi$
$710$		0			0
$711$	−12.9574	+	8.32722i	−0.485941	+	0.312295i
$712$		0			0
$713$	15.7526	−	7.36486i	0.589941	−	0.275816i
$714$		0			0
$715$	31.0100	−	3.58318i	1.15971	−	0.134003i
$716$		0			0
$717$	−0.821933	−	0.375364i	−0.0306956	−	0.0140182i
$718$		0			0
$719$	7.87587	+	17.2457i	0.293720	+	0.643158i	0.997752	−	0.0670105i	$-0.0213461\pi$
$719$	7.87587	+	17.2457i	0.293720	+	0.643158i	−0.704032	+	0.710168i	$0.748619\pi$
$720$		0			0
$721$	0.00760754	+	0.0529116i	0.000283320	+	0.00197053i
$722$		0			0
$723$	2.63537	+	2.28356i	0.0980106	+	0.0849267i
$724$		0			0
$725$	2.96398	+	33.8739i	0.110079	+	1.25805i
$726$		0			0
$727$	−3.31274	+	11.2821i	−0.122863	+	0.418432i	−0.997837	−	0.0657377i	$-0.979060\pi$
$727$	−3.31274	+	11.2821i	−0.122863	+	0.418432i	0.874974	+	0.484169i	$0.160878\pi$
$728$		0			0
$729$	−3.18004	−	3.66997i	−0.117779	−	0.135925i
$730$		0			0
$731$	46.5096	−	13.6565i	1.72022	−	0.505102i
$732$		0			0
$733$	−10.8262	−	1.55657i	−0.399873	−	0.0574931i	−0.0605553	−	0.998165i	$-0.519287\pi$
$733$	−10.8262	−	1.55657i	−0.399873	−	0.0574931i	−0.339318	+	0.940672i	$0.610196\pi$
$734$		0			0
$735$	9.36379	+	4.59458i	0.345389	+	0.169474i
$736$		0			0
$737$			26.5645i			0.978517i
$738$		0			0
$739$	2.11568	−	14.7149i	0.0778265	−	0.541295i	−0.913188	−	0.407539i	$-0.866387\pi$
$739$	2.11568	−	14.7149i	0.0778265	−	0.541295i	0.991014	−	0.133756i	$-0.0427039\pi$
$740$		0			0
$741$	−2.63171	+	0.772741i	−0.0966784	+	0.0283874i
$742$		0			0
$743$	1.95527	−	1.69425i	0.0717318	−	0.0621560i	−0.618257	−	0.785976i	$-0.712161\pi$
$743$	1.95527	−	1.69425i	0.0717318	−	0.0621560i	0.689989	+	0.723820i	$0.257615\pi$
$744$		0			0
$745$	18.3538	−	20.0299i	0.672432	−	0.733840i
$746$		0			0
$747$	−11.7519	+	18.2863i	−0.429979	+	0.669060i
$748$		0			0
$749$	0.923720	−	1.06603i	0.0337520	−	0.0389519i
$750$		0			0
$751$	−4.22170	−	29.3626i	−0.154052	−	1.07146i	−0.909337	−	0.416060i	$-0.863411\pi$
$751$	−4.22170	−	29.3626i	−0.154052	−	1.07146i	0.755285	−	0.655396i	$-0.227498\pi$
$752$		0			0
$753$	8.45047	−	3.85920i	0.307952	−	0.140637i
$754$		0			0
$755$	−13.0632	−	15.9495i	−0.475417	−	0.580463i
$756$		0			0
$757$	10.9067	+	16.9711i	0.396410	+	0.616827i	0.980886	−	0.194585i	$-0.0623360\pi$
$757$	10.9067	+	16.9711i	0.396410	+	0.616827i	−0.584475	+	0.811412i	$0.698700\pi$
$758$		0			0
$759$	7.67466	−	17.2106i	0.278572	−	0.624706i
$760$		0			0
$761$	−40.3076	+	25.9041i	−1.46115	+	0.939023i	−0.462523	+	0.886607i	$0.653056\pi$
$761$	−40.3076	+	25.9041i	−1.46115	+	0.939023i	−0.998625	+	0.0524161i	$0.983308\pi$
$762$		0			0
$763$	−2.46974	−	1.12789i	−0.0894105	−	0.0408324i
$764$		0			0
$765$	−0.714644	+	25.7363i	−0.0258380	+	0.930497i
$766$		0			0
$767$	17.2415	−	2.47895i	0.622554	−	0.0895097i
$768$		0			0
$769$	−16.3907	+	18.9159i	−0.591064	+	0.682124i	−0.969946	−	0.243321i	$-0.921763\pi$
$769$	−16.3907	+	18.9159i	−0.591064	+	0.682124i	0.378882	+	0.925445i	$0.376309\pi$
$770$		0			0
$771$	−1.69024	−	1.08625i	−0.0608724	−	0.0391203i
$772$		0			0
$773$	2.09630	−	7.13933i	0.0753986	−	0.256784i	−0.913165	−	0.407591i	$-0.866369\pi$
$773$	2.09630	−	7.13933i	0.0753986	−	0.256784i	0.988563	+	0.150807i	$0.0481871\pi$
$774$		0			0
$775$	3.57196	−	17.7742i	0.128309	−	0.638469i
$776$		0			0
$777$	0.764143	+	2.60243i	0.0274135	+	0.0933617i
$778$		0			0
$779$	−1.36101	+	9.46601i	−0.0487631	+	0.339155i
$780$		0			0
$781$	−74.9468			−2.68181
$782$		0			0
$783$		−	25.7677i		−	0.920863i
$784$		0			0
$785$	3.57976	−	5.24422i	0.127767	−	0.187174i
$786$		0			0
$787$	−2.48569	−	8.46548i	−0.0886052	−	0.301762i	0.903253	−	0.429108i	$-0.141172\pi$
$787$	−2.48569	−	8.46548i	−0.0886052	−	0.301762i	−0.991858	+	0.127347i	$0.959354\pi$
$788$		0			0
$789$	−3.58576	−	4.13819i	−0.127656	−	0.147323i
$790$		0			0
$791$	5.31157	+	1.55962i	0.188858	+	0.0554536i
$792$		0			0
$793$	−5.26905	+	8.19880i	−0.187109	+	0.291148i
$794$		0			0
$795$	−2.66355	−	6.28869i	−0.0944663	−	0.223037i
$796$		0			0
$797$	37.2357	−	5.35368i	1.31896	−	0.189637i	0.553351	−	0.832948i	$-0.313349\pi$
$797$	37.2357	−	5.35368i	1.31896	−	0.189637i	0.765605	+	0.643311i	$0.222440\pi$
$798$		0			0
$799$	−23.6388	−	51.7618i	−0.836282	−	1.83120i
$800$		0			0
$801$	6.47995	−	14.1891i	0.228958	−	0.501348i
$802$		0			0
$803$	−37.6660	−	58.6095i	−1.32920	−	2.06828i
$804$		0			0
$805$	−3.13789	+	3.48651i	−0.110596	+	0.122883i
$806$		0			0
$807$	6.89442	+	10.7279i	0.242695	+	0.377641i
$808$		0			0
$809$	−10.6896	+	23.4071i	−0.375828	+	0.822948i	0.623332	+	0.781958i	$0.285779\pi$
$809$	−10.6896	+	23.4071i	−0.375828	+	0.822948i	−0.999160	+	0.0409906i	$0.986949\pi$
$810$		0			0
$811$	−8.23740	−	18.0374i	−0.289254	−	0.633378i	0.708097	−	0.706115i	$-0.249554\pi$
$811$	−8.23740	−	18.0374i	−0.289254	−	0.633378i	−0.997351	+	0.0727369i	$0.976827\pi$
$812$		0			0
$813$	8.95604	−	1.28768i	0.314102	−	0.0451611i
$814$		0			0
$815$	5.55714	−	2.35370i	0.194658	−	0.0824466i
$816$		0			0
$817$	−9.47398	+	14.7418i	−0.331452	+	0.515750i
$818$		0			0
$819$	2.58516	+	0.759071i	0.0903328	+	0.0265241i
$820$		0			0
$821$	8.88934	+	10.2588i	0.310240	+	0.358036i	0.889361	−	0.457205i	$-0.151150\pi$
$821$	8.88934	+	10.2588i	0.310240	+	0.358036i	−0.579121	+	0.815242i	$0.696604\pi$
$822$		0			0
$823$	9.37724	+	31.9360i	0.326870	+	1.11322i	0.944981	+	0.327126i	$0.106080\pi$
$823$	9.37724	+	31.9360i	0.326870	+	1.11322i	−0.618110	+	0.786091i	$0.712102\pi$
$824$		0			0
$825$	−9.68815	−	17.0916i	−0.337298	−	0.595055i
$826$		0			0
$827$			53.7978i			1.87073i	0.353680	+	0.935366i	$0.384930\pi$
$827$			53.7978i			1.87073i	−0.353680	+	0.935366i	$0.615070\pi$
$828$		0			0
$829$	−14.6707			−0.509535			−0.254767	−	0.967002i	$-0.581999\pi$
$829$	−14.6707			−0.509535			−0.254767	+	0.967002i	$0.581999\pi$
$830$		0			0
$831$	−1.69650	+	11.7994i	−0.0588509	+	0.409317i
$832$		0			0
$833$	−8.72762	−	29.7235i	−0.302394	−	1.02986i
$834$		0			0
$835$	−12.5061	−	47.4238i	−0.432790	−	1.64117i
$836$		0			0
$837$	−3.87061	+	13.1821i	−0.133788	+	0.455639i
$838$		0			0
$839$	41.6615	+	26.7742i	1.43832	+	0.924349i	0.999670	+	0.0256891i	$0.00817801\pi$
$839$	41.6615	+	26.7742i	1.43832	+	0.924349i	0.438646	+	0.898660i	$0.355458\pi$
$840$		0			0
$841$	−11.2957	+	13.0360i	−0.389508	+	0.449516i
$842$		0			0
$843$	−2.13404	+	0.306828i	−0.0735001	+	0.0105677i
$844$		0			0
$845$	15.8149	+	0.439148i	0.544050	+	0.0151072i
$846$		0			0
$847$	−8.71162	−	3.97846i	−0.299335	−	0.136702i
$848$		0			0
$849$	7.10940	−	4.56893i	0.243994	−	0.156805i
$850$		0			0
$851$	43.4063	−	0.387990i	1.48795	−	0.0133001i
$852$		0			0
$853$	8.48814	+	13.2078i	0.290628	+	0.452226i	0.955611	−	0.294633i	$-0.0951973\pi$
$853$	8.48814	+	13.2078i	0.290628	+	0.452226i	−0.664982	+	0.746859i	$0.731561\pi$
$854$		0			0
$855$	−5.89755	−	7.20065i	−0.201692	−	0.246257i
$856$		0			0
$857$	−22.5499	+	10.2982i	−0.770289	+	0.351779i	−0.761485	−	0.648182i	$-0.775530\pi$
$857$	−22.5499	+	10.2982i	−0.770289	+	0.351779i	−0.00880362	+	0.999961i	$0.502802\pi$
$858$		0			0
$859$	5.40729	+	37.6085i	0.184494	+	1.28319i	0.845975	+	0.533223i	$0.179019\pi$
$859$	5.40729	+	37.6085i	0.184494	+	1.28319i	−0.661481	+	0.749962i	$0.730072\pi$
$860$		0			0
$861$	−1.14096	+	1.31674i	−0.0388839	+	0.0448745i
$862$		0			0
$863$	7.40760	−	11.5265i	0.252158	−	0.392365i	−0.691980	−	0.721917i	$-0.743261\pi$
$863$	7.40760	−	11.5265i	0.252158	−	0.392365i	0.944137	+	0.329552i	$0.106898\pi$
$864$		0			0
$865$	−37.4055	−	34.2754i	−1.27182	−	1.16540i
$866$		0			0
$867$	−1.91624	+	1.66043i	−0.0650788	+	0.0563911i
$868$		0			0
$869$	−33.4940	+	9.83474i	−1.13621	+	0.333621i
$870$		0			0
$871$	1.60441	−	11.1589i	0.0543635	−	0.378106i
$872$		0			0
$873$		−	1.24730i		−	0.0422147i
$874$		0			0
$875$	0.982660	+	4.79058i	0.0332200	+	0.161951i
$876$		0			0
$877$	57.5959	+	8.28104i	1.94488	+	0.279631i	0.998992	−	0.0448781i	$-0.0142899\pi$
$877$	57.5959	+	8.28104i	1.94488	+	0.279631i	0.945883	+	0.324509i	$0.105199\pi$
$878$		0			0
$879$	6.16475	−	1.81013i	0.207932	−	0.0610543i
$880$		0			0
$881$	33.4690	+	38.6252i	1.12760	+	1.30132i	0.948248	+	0.317532i	$0.102854\pi$
$881$	33.4690	+	38.6252i	1.12760	+	1.30132i	0.179350	+	0.983785i	$0.442601\pi$
$882$		0			0
$883$	8.88973	−	30.2757i	0.299163	−	1.01886i	−0.663505	−	0.748172i	$-0.730932\pi$
$883$	8.88973	−	30.2757i	0.299163	−	1.01886i	0.962668	−	0.270685i	$-0.0872501\pi$
$884$		0			0
$885$	−5.66865	−	9.38343i	−0.190550	−	0.315421i
$886$		0			0
$887$	−19.8056	−	17.1616i	−0.665006	−	0.576231i	0.255572	−	0.966790i	$-0.417736\pi$
$887$	−19.8056	−	17.1616i	−0.665006	−	0.576231i	−0.920578	+	0.390559i	$0.872282\pi$
$888$		0			0
$889$	−0.326482	−	2.27073i	−0.0109499	−	0.0761579i
$890$		0			0
$891$	−11.9037	−	26.0656i	−0.398790	−	0.873229i
$892$		0			0
$893$	18.7125	+	8.54571i	0.626190	+	0.285971i
$894$		0			0
$895$	−2.46653	−	21.3461i	−0.0824468	−	0.713523i
$896$		0			0
$897$	−4.26335	+	6.76612i	−0.142349	+	0.225914i
$898$		0			0
$899$	20.7442	−	13.3315i	0.691857	−	0.444629i
$900$		0			0
$901$	−8.42624	+	18.4509i	−0.280719	+	0.614689i
$902$		0			0
$903$	−2.90404	+	1.32623i	−0.0966403	+	0.0441341i
$904$		0			0
$905$	47.2438	+	15.3087i	1.57044	+	0.508879i
$906$		0			0
$907$	−11.4494	−	9.92099i	−0.380172	−	0.329421i	0.443722	−	0.896164i	$-0.353658\pi$
$907$	−11.4494	−	9.92099i	−0.380172	−	0.329421i	−0.823894	+	0.566743i	$0.808203\pi$
$908$		0			0
$909$	28.1700	+	18.1038i	0.934340	+	0.600464i
$910$		0			0
$911$	51.7980	+	15.2093i	1.71615	+	0.503906i	0.984140	−	0.177393i	$-0.0567664\pi$
$911$	51.7980	+	15.2093i	1.71615	+	0.503906i	0.732005	+	0.681299i	$0.238585\pi$
$912$		0			0
$913$	−37.2315	+	32.2613i	−1.23218	+	1.06769i
$914$		0			0
$915$	6.04475	+	1.04111i	0.199833	+	0.0344181i
$916$		0			0
$917$	−5.00616	−	0.719777i	−0.165318	−	0.0237691i
$918$		0			0
$919$	51.9324			1.71309			0.856546	−	0.516070i	$-0.172606\pi$
$919$	51.9324			1.71309			0.856546	+	0.516070i	$0.172606\pi$
$920$		0			0
$921$	−0.161280			−0.00531436
$922$		0			0
$923$	31.4828	+	4.52655i	1.03627	+	0.148993i
$924$		0			0
$925$	26.5423	−	36.6553i	0.872704	−	1.20522i
$926$		0			0
$927$	−0.233734	+	0.202531i	−0.00767682	+	0.00665200i
$928$		0			0
$929$	3.89966	+	1.14504i	0.127944	+	0.0375676i	0.345078	−	0.938574i	$-0.387853\pi$
$929$	3.89966	+	1.14504i	0.127944	+	0.0375676i	−0.217134	+	0.976142i	$0.569671\pi$
$930$		0			0
$931$	9.42124	+	6.05466i	0.308769	+	0.198434i
$932$		0			0
$933$	−8.89776	−	7.70995i	−0.291299	−	0.252412i
$934$		0			0
$935$	−17.9871	+	55.5094i	−0.588240	+	1.81535i
$936$		0			0
$937$	−46.0707	+	21.0398i	−1.50506	+	0.687339i	−0.985900	−	0.167335i	$-0.946484\pi$
$937$	−46.0707	+	21.0398i	−1.50506	+	0.687339i	−0.519163	+	0.854675i	$0.673756\pi$
$938$		0			0
$939$	2.70622	−	5.92580i	0.0883142	−	0.193381i
$940$		0			0
$941$	27.7688	−	17.8460i	0.905238	−	0.581761i	−0.00310103	−	0.999995i	$-0.500987\pi$
$941$	27.7688	−	17.8460i	0.905238	−	0.581761i	0.908339	+	0.418234i	$0.137351\pi$
$942$		0			0
$943$	15.2843	+	23.3219i	0.497726	+	0.759464i
$944$		0			0
$945$	−0.425382	−	3.68140i	−0.0138377	−	0.119756i
$946$		0			0
$947$	−4.39242	−	2.00595i	−0.142734	−	0.0651847i	0.342767	−	0.939420i	$-0.388636\pi$
$947$	−4.39242	−	2.00595i	−0.142734	−	0.0651847i	−0.485502	+	0.874236i	$0.661363\pi$
$948$		0			0
$949$	12.2825	+	26.8949i	0.398707	+	0.873046i
$950$		0			0
$951$	3.11599	+	21.6722i	0.101043	+	0.702769i
$952$		0			0
$953$	−40.4334	−	35.0357i	−1.30977	−	1.13492i	−0.981735	−	0.190252i	$-0.939069\pi$
$953$	−40.4334	−	35.0357i	−1.30977	−	1.13492i	−0.328031	−	0.944667i	$-0.606385\pi$
$954$		0			0
$955$	35.9336	−	21.7079i	1.16278	−	0.702452i
$956$		0			0
$957$	7.52841	−	25.6394i	0.243359	−	0.828805i
$958$		0			0
$959$	−5.52634	−	6.37774i	−0.178455	−	0.205948i
$960$		0			0
$961$	17.1296	−	5.02970i	0.552567	−	0.162248i
$962$		0			0
$963$	8.07788	+	1.16142i	0.260306	+	0.0374263i
$964$		0			0
$965$	22.4622	+	11.0216i	0.723083	+	0.354799i
$966$		0			0
$967$		−	48.9778i		−	1.57502i	−0.616302	−	0.787510i	$-0.711370\pi$
$967$		−	48.9778i		−	1.57502i	0.616302	−	0.787510i	$-0.288630\pi$
$968$		0			0
$969$	0.729647	−	5.07481i	0.0234396	−	0.163026i
$970$		0			0
$971$	−38.9055	+	11.4237i	−1.24854	+	0.366603i	−0.838216	−	0.545339i	$-0.816401\pi$
$971$	−38.9055	+	11.4237i	−1.24854	+	0.366603i	−0.410320	+	0.911942i	$0.634583\pi$
$972$		0			0
$973$	0.529537	−	0.458847i	0.0169762	−	0.0147099i
$974$		0			0
$975$	3.03741	+	7.76480i	0.0972750	+	0.248673i
$976$		0			0
$977$	−11.0498	+	17.1938i	−0.353514	+	0.550078i	−0.971780	−	0.235891i	$-0.924199\pi$
$977$	−11.0498	+	17.1938i	−0.353514	+	0.550078i	0.618266	+	0.785969i	$0.287836\pi$
$978$		0			0
$979$	23.1512	−	26.7179i	0.739915	−	0.853907i
$980$		0			0
$981$	−2.23555	−	15.5486i	−0.0713756	−	0.496428i
$982$		0			0
$983$	11.3260	−	5.17239i	0.361242	−	0.164974i	−0.226522	−	0.974006i	$-0.572736\pi$
$983$	11.3260	−	5.17239i	0.361242	−	0.164974i	0.587764	+	0.809032i	$0.300008\pi$
$984$		0			0
$985$	−37.1897	+	30.4595i	−1.18496	+	0.970520i
$986$		0			0
$987$	2.02623	+	3.15287i	0.0644955	+	0.100357i
$988$		0			0
$989$	7.72317	+	50.5068i	0.245582	+	1.60602i
$990$		0			0
$991$	−23.5408	+	15.1288i	−0.747799	+	0.480581i	−0.858206	−	0.513305i	$-0.828421\pi$
$991$	−23.5408	+	15.1288i	−0.747799	+	0.480581i	0.110407	+	0.993886i	$0.464784\pi$
$992$		0			0
$993$	21.3763	+	9.76222i	0.678356	+	0.309795i
$994$		0			0
$995$	−9.42961	−	0.261841i	−0.298939	−	0.00830091i
$996$		0			0
$997$	3.76863	−	0.541848i	0.119354	−	0.0171605i	−0.0823790	−	0.996601i	$-0.526252\pi$
$997$	3.76863	−	0.541848i	0.119354	−	0.0171605i	0.201733	+	0.979441i	$0.435343\pi$
$998$		0			0
$999$	−22.4584	+	25.9184i	−0.710553	+	0.820022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.449.6	yes	120
5.4	even	2	inner	460.2.s.a.449.7	yes	120
23.2	even	11	inner	460.2.s.a.209.7	yes	120
115.94	even	22	inner	460.2.s.a.209.6	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.209.6	✓	120	115.94	even	22	inner
460.2.s.a.209.7	yes	120	23.2	even	11	inner
460.2.s.a.449.6	yes	120	1.1	even	1	trivial
460.2.s.a.449.7	yes	120	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.678118 - 0.0974986i) q^{3} +(-0.379538 + 2.20362i) q^{5} +(-0.330568 + 0.286439i) q^{7} +(-2.42814 - 0.712967i) q^{9} +O(q^{10})\)	\(q+(-0.678118 - 0.0974986i) q^{3} +(-0.379538 + 2.20362i) q^{5} +(-0.330568 + 0.286439i) q^{7} +(-2.42814 - 0.712967i) q^{9} +(-4.82496 - 3.10081i) q^{11} +(1.83954 + 1.59397i) q^{13} +(0.472222 - 1.45731i) q^{15} +(-4.13868 + 1.89007i) q^{17} +(0.683283 - 1.49618i) q^{19} +(0.252092 - 0.162009i) q^{21} +(-1.39222 - 4.58931i) q^{23} +(-4.71190 - 1.67272i) q^{25} +(3.44659 + 1.57401i) q^{27} +(-2.82510 - 6.18610i) q^{29} +(0.516021 + 3.58901i) q^{31} +(2.96957 + 2.57314i) q^{33} +(-0.505740 - 0.837162i) q^{35} +(-2.55002 + 8.68456i) q^{37} +(-1.09201 - 1.26025i) q^{39} +(-5.57870 + 1.63806i) q^{41} +(-10.5454 - 1.51620i) q^{43} +(2.49268 - 5.08011i) q^{45} +12.5068i q^{47} +(-0.968976 + 6.73937i) q^{49} +(2.99079 - 0.878175i) q^{51} +(3.36925 - 2.91947i) q^{53} +(8.66428 - 9.45551i) q^{55} +(-0.609222 + 0.947968i) q^{57} +(4.68637 - 5.40835i) q^{59} +(0.569827 + 3.96324i) q^{61} +(1.00689 - 0.459830i) q^{63} +(-4.21068 + 3.44867i) q^{65} +(-2.50406 - 3.89639i) q^{67} +(0.496637 + 3.24783i) q^{69} +(10.9929 - 7.06473i) q^{71} +(11.0494 + 5.04610i) q^{73} +(3.03214 + 1.59370i) q^{75} +(2.48317 - 0.357026i) q^{77} +(3.98573 - 4.59978i) q^{79} +(4.20302 + 2.70112i) q^{81} +(2.41993 - 8.24153i) q^{83} +(-2.59422 - 9.83744i) q^{85} +(1.31261 + 4.47035i) q^{87} +(-0.877218 + 6.10119i) q^{89} -1.06467 q^{91} -2.48408i q^{93} +(3.03769 + 2.07356i) q^{95} +(0.138860 + 0.472913i) q^{97} +(9.50490 + 10.9692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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