LMFDB - Embedded newform 560.3.bx.c.481.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,3,Mod(241,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("560.241");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	560.bx (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:	$15.2588948042$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 19 x^{10} - 26 x^{9} + 244 x^{8} - 338 x^{7} + 1249 x^{6} - 986 x^{5} + 3532 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 19x^10 - 26x^9 + 244x^8 - 338x^7 + 1249x^6 - 986x^5 + 3532x^4 - 3618x^3 + 3579x^2 - 1386*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			481.5
Root			$1.77870 + 3.08079i$ of defining polynomial
Character	$\chi$	$=$	560.481
Dual form			560.3.bx.c.241.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10717 - 1.21658i) q^{3} +(1.93649 + 1.11803i) q^{5} +(5.39402 - 4.46146i) q^{7} +(-1.53989 + 2.66717i) q^{9} +O(q^{10})$	\(q+(2.10717 - 1.21658i) q^{3} +(1.93649 + 1.11803i) q^{5} +(5.39402 - 4.46146i) q^{7} +(-1.53989 + 2.66717i) q^{9} +(-6.95056 - 12.0387i) q^{11} -0.702771i q^{13} +5.44069 q^{15} +(23.6124 - 13.6326i) q^{17} +(-2.21652 - 1.27971i) q^{19} +(5.93841 - 15.9633i) q^{21} +(16.4777 - 28.5402i) q^{23} +(2.50000 + 4.33013i) q^{25} +29.3919i q^{27} +3.39850 q^{29} +(-20.7530 + 11.9818i) q^{31} +(-29.2920 - 16.9118i) q^{33} +(15.4335 - 2.60888i) q^{35} +(11.9080 - 20.6253i) q^{37} +(-0.854973 - 1.48086i) q^{39} +25.1015i q^{41} +25.1201 q^{43} +(-5.96397 + 3.44330i) q^{45} +(5.59742 + 3.23167i) q^{47} +(9.19081 - 48.1303i) q^{49} +(33.1702 - 57.4524i) q^{51} +(18.0214 + 31.2139i) q^{53} -31.0838i q^{55} -6.22744 q^{57} +(32.0135 - 18.4830i) q^{59} +(-30.3577 - 17.5270i) q^{61} +(3.59326 + 21.2569i) q^{63} +(0.785721 - 1.36091i) q^{65} +(-22.8634 - 39.6006i) q^{67} -80.1854i q^{69} -80.4090 q^{71} +(77.7901 - 44.9121i) q^{73} +(10.5359 + 6.08288i) q^{75} +(-91.2017 - 33.9274i) q^{77} +(0.0415972 - 0.0720485i) q^{79} +(21.8985 + 37.9293i) q^{81} +95.3085i q^{83} +60.9668 q^{85} +(7.16122 - 4.13453i) q^{87} +(104.811 + 60.5126i) q^{89} +(-3.13538 - 3.79076i) q^{91} +(-29.1534 + 50.4952i) q^{93} +(-2.86151 - 4.95628i) q^{95} -0.362083i q^{97} +42.8124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 2 q^{7} + 14 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 2 * q^7 + 14 * q^9	$ 12 q + 6 q^{3} + 2 q^{7} + 14 q^{9} + 14 q^{11} + 20 q^{15} + 48 q^{17} + 30 q^{19} - 84 q^{21} + 14 q^{23} + 30 q^{25} + 64 q^{29} - 132 q^{31} - 192 q^{33} - 30 q^{35} + 44 q^{37} + 24 q^{39} + 4 q^{43} - 180 q^{45} - 204 q^{47} - 24 q^{49} + 132 q^{51} + 196 q^{53} - 48 q^{57} - 72 q^{59} + 72 q^{61} - 536 q^{63} + 30 q^{65} + 138 q^{67} + 8 q^{71} - 528 q^{73} + 30 q^{75} - 176 q^{77} + 12 q^{79} - 310 q^{81} - 138 q^{87} + 204 q^{89} + 480 q^{91} + 84 q^{93} - 60 q^{95} + 44 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 2 * q^7 + 14 * q^9 + 14 * q^11 + 20 * q^15 + 48 * q^17 + 30 * q^19 - 84 * q^21 + 14 * q^23 + 30 * q^25 + 64 * q^29 - 132 * q^31 - 192 * q^33 - 30 * q^35 + 44 * q^37 + 24 * q^39 + 4 * q^43 - 180 * q^45 - 204 * q^47 - 24 * q^49 + 132 * q^51 + 196 * q^53 - 48 * q^57 - 72 * q^59 + 72 * q^61 - 536 * q^63 + 30 * q^65 + 138 * q^67 + 8 * q^71 - 528 * q^73 + 30 * q^75 - 176 * q^77 + 12 * q^79 - 310 * q^81 - 138 * q^87 + 204 * q^89 + 480 * q^91 + 84 * q^93 - 60 * q^95 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.10717	−	1.21658i	0.702390	−	0.405525i	−0.105847	−	0.994382i	$-0.533755\pi$
$3$	2.10717	−	1.21658i	0.702390	−	0.405525i	0.808237	+	0.588857i	$0.200422\pi$
$4$		0			0
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$		0			0
$7$	5.39402	−	4.46146i	0.770574	−	0.637351i
$7$	5.39402	−	4.46146i	0.770574	−	0.637351i
$8$		0			0
$9$	−1.53989	+	2.66717i	−0.171099	+	0.296352i
$10$		0			0
$11$	−6.95056	−	12.0387i	−0.631869	−	1.09443i	−0.987169	−	0.159677i	$-0.948955\pi$
$11$	−6.95056	−	12.0387i	−0.631869	−	1.09443i	0.355300	−	0.934752i	$-0.384379\pi$
$12$		0			0
$13$		−	0.702771i		−	0.0540593i	−0.999635	−	0.0270296i	$-0.991395\pi$
$13$		−	0.702771i		−	0.0540593i	0.999635	−	0.0270296i	$-0.00860485\pi$
$14$		0			0
$15$	5.44069			0.362713
$16$		0			0
$17$	23.6124	−	13.6326i	1.38896	−	0.801918i	0.395764	−	0.918352i	$-0.370480\pi$
$17$	23.6124	−	13.6326i	1.38896	−	0.801918i	0.993198	+	0.116435i	$0.0371466\pi$
$18$		0			0
$19$	−2.21652	−	1.27971i	−0.116659	−	0.0673530i	0.440535	−	0.897735i	$-0.354789\pi$
$19$	−2.21652	−	1.27971i	−0.116659	−	0.0673530i	−0.557194	+	0.830382i	$0.688122\pi$
$20$		0			0
$21$	5.93841	−	15.9633i	0.282782	−	0.760156i
$22$		0			0
$23$	16.4777	−	28.5402i	0.716422	−	1.24088i	−0.245987	−	0.969273i	$-0.579112\pi$
$23$	16.4777	−	28.5402i	0.716422	−	1.24088i	0.962409	−	0.271605i	$-0.0875546\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$		0			0
$27$			29.3919i			1.08859i
$28$		0			0
$29$	3.39850			0.117190			0.0585949	−	0.998282i	$-0.481338\pi$
$29$	3.39850			0.117190			0.0585949	+	0.998282i	$0.481338\pi$
$30$		0			0
$31$	−20.7530	+	11.9818i	−0.669452	+	0.386508i	−0.795869	−	0.605469i	$-0.792986\pi$
$31$	−20.7530	+	11.9818i	−0.669452	+	0.386508i	0.126417	+	0.991977i	$0.459652\pi$
$32$		0			0
$33$	−29.2920	−	16.9118i	−0.887637	−	0.512478i
$34$		0			0
$35$	15.4335	−	2.60888i	0.440958	−	0.0745394i
$36$		0			0
$37$	11.9080	−	20.6253i	0.321838	−	0.557440i	−0.659029	−	0.752117i	$-0.729033\pi$
$37$	11.9080	−	20.6253i	0.321838	−	0.557440i	0.980867	+	0.194677i	$0.0623659\pi$
$38$		0			0
$39$	−0.854973	−	1.48086i	−0.0219224	−	0.0379707i
$40$		0			0
$41$			25.1015i			0.612231i	0.951994	+	0.306116i	$0.0990295\pi$
$41$			25.1015i			0.612231i	−0.951994	+	0.306116i	$0.900971\pi$
$42$		0			0
$43$	25.1201			0.584189			0.292094	−	0.956390i	$-0.405648\pi$
$43$	25.1201			0.584189			0.292094	+	0.956390i	$0.405648\pi$
$44$		0			0
$45$	−5.96397	+	3.44330i	−0.132533	+	0.0765177i
$46$		0			0
$47$	5.59742	+	3.23167i	0.119094	+	0.0687590i	0.558364	−	0.829596i	$-0.311429\pi$
$47$	5.59742	+	3.23167i	0.119094	+	0.0687590i	−0.439270	+	0.898355i	$0.644763\pi$
$48$		0			0
$49$	9.19081	−	48.1303i	0.187568	−	0.982252i
$50$		0			0
$51$	33.1702	−	57.4524i	0.650395	−	1.12652i
$52$		0			0
$53$	18.0214	+	31.2139i	0.340026	+	0.588942i	0.984437	−	0.175737i	$-0.0562309\pi$
$53$	18.0214	+	31.2139i	0.340026	+	0.588942i	−0.644412	+	0.764679i	$0.722898\pi$
$54$		0			0
$55$		−	31.0838i		−	0.565161i
$56$		0			0
$57$	−6.22744			−0.109253
$58$		0			0
$59$	32.0135	−	18.4830i	0.542602	−	0.313272i	−0.203531	−	0.979069i	$-0.565242\pi$
$59$	32.0135	−	18.4830i	0.542602	−	0.313272i	0.746133	+	0.665797i	$0.231908\pi$
$60$		0			0
$61$	−30.3577	−	17.5270i	−0.497667	−	0.287328i	0.230083	−	0.973171i	$-0.426100\pi$
$61$	−30.3577	−	17.5270i	−0.497667	−	0.287328i	−0.727750	+	0.685843i	$0.759434\pi$
$62$		0			0
$63$	3.59326	+	21.2569i	0.0570359	+	0.337411i
$64$		0			0
$65$	0.785721	−	1.36091i	0.0120880	−	0.0209371i
$66$		0			0
$67$	−22.8634	−	39.6006i	−0.341245	−	0.591053i	0.643419	−	0.765514i	$-0.277515\pi$
$67$	−22.8634	−	39.6006i	−0.341245	−	0.591053i	−0.984664	+	0.174461i	$0.944182\pi$
$68$		0			0
$69$		−	80.1854i		−	1.16211i
$70$		0			0
$71$	−80.4090			−1.13252			−0.566261	−	0.824226i	$-0.691611\pi$
$71$	−80.4090			−1.13252			−0.566261	+	0.824226i	$0.691611\pi$
$72$		0			0
$73$	77.7901	−	44.9121i	1.06562	−	0.615235i	0.138637	−	0.990343i	$-0.455728\pi$
$73$	77.7901	−	44.9121i	1.06562	−	0.615235i	0.926981	+	0.375109i	$0.122395\pi$
$74$		0			0
$75$	10.5359	+	6.08288i	0.140478	+	0.0811050i
$76$		0			0
$77$	−91.2017	−	33.9274i	−1.18444	−	0.440616i
$78$		0			0
$79$	0.0415972	−	0.0720485i	0.000526547	−	0.000912006i	−0.865762	−	0.500456i	$-0.833166\pi$
$79$	0.0415972	−	0.0720485i	0.000526547	−	0.000912006i	0.866289	+	0.499544i	$0.166499\pi$
$80$		0			0
$81$	21.8985	+	37.9293i	0.270352	+	0.468263i
$82$		0			0
$83$			95.3085i			1.14830i	0.818752	+	0.574148i	$0.194666\pi$
$83$			95.3085i			1.14830i	−0.818752	+	0.574148i	$0.805334\pi$
$84$		0			0
$85$	60.9668			0.717257
$86$		0			0
$87$	7.16122	−	4.13453i	0.0823129	−	0.0475234i
$88$		0			0
$89$	104.811	+	60.5126i	1.17765	+	0.679917i	0.955470	−	0.295089i	$-0.0953493\pi$
$89$	104.811	+	60.5126i	1.17765	+	0.679917i	0.222180	+	0.975006i	$0.428683\pi$
$90$		0			0
$91$	−3.13538	−	3.79076i	−0.0344547	−	0.0416567i
$92$		0			0
$93$	−29.1534	+	50.4952i	−0.313477	+	0.542959i
$94$		0			0
$95$	−2.86151	−	4.95628i	−0.0301212	−	0.0521714i
$96$		0			0
$97$		−	0.362083i		−	0.00373282i	−0.999998	−	0.00186641i	$-0.999406\pi$
$97$		−	0.362083i		−	0.00373282i	0.999998	−	0.00186641i	$-0.000594097\pi$
$98$		0			0
$99$	42.8124			0.432448
$100$		0			0
$101$	−139.134	+	80.3290i	−1.37756	+	0.795336i	−0.991866	−	0.127289i	$-0.959372\pi$
$101$	−139.134	+	80.3290i	−1.37756	+	0.795336i	−0.385697	+	0.922625i	$0.626039\pi$
$102$		0			0
$103$	−124.234	−	71.7266i	−1.20616	−	0.696375i	−0.244239	−	0.969715i	$-0.578538\pi$
$103$	−124.234	−	71.7266i	−1.20616	−	0.696375i	−0.961917	+	0.273340i	$0.911871\pi$
$104$		0			0
$105$	29.3472	−	24.2734i	0.279497	−	0.231175i
$106$		0			0
$107$	−31.7317	+	54.9609i	−0.296558	+	0.513653i	−0.975346	−	0.220681i	$-0.929172\pi$
$107$	−31.7317	+	54.9609i	−0.296558	+	0.513653i	0.678788	+	0.734334i	$0.262505\pi$
$108$		0			0
$109$	−28.3546	−	49.1115i	−0.260134	−	0.450565i	0.706144	−	0.708069i	$-0.250433\pi$
$109$	−28.3546	−	49.1115i	−0.260134	−	0.450565i	−0.966277	+	0.257504i	$0.917100\pi$
$110$		0			0
$111$		−	57.9480i		−	0.522054i
$112$		0			0
$113$	53.1456			0.470315			0.235157	−	0.971957i	$-0.424439\pi$
$113$	53.1456			0.470315			0.235157	+	0.971957i	$0.424439\pi$
$114$		0			0
$115$	63.8178	−	36.8452i	0.554938	−	0.320393i
$116$		0			0
$117$	1.87441	+	1.08219i	0.0160206	+	0.00924948i
$118$		0			0
$119$	66.5442	−	178.880i	0.559195	−	1.50319i
$120$		0			0
$121$	−36.1206	+	62.5627i	−0.298517	+	0.517047i
$122$		0			0
$123$	30.5379	+	52.8931i	0.248275	+	0.430025i
$124$		0			0
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	39.1961			0.308630			0.154315	−	0.988022i	$-0.450683\pi$
$127$	39.1961			0.308630			0.154315	+	0.988022i	$0.450683\pi$
$128$		0			0
$129$	52.9323	−	30.5605i	0.410328	−	0.236903i
$130$		0			0
$131$	46.8501	+	27.0489i	0.357634	+	0.206480i	0.668043	−	0.744123i	$-0.267132\pi$
$131$	46.8501	+	27.0489i	0.357634	+	0.206480i	−0.310408	+	0.950603i	$0.600466\pi$
$132$		0			0
$133$	−17.6653	+	2.98614i	−0.132822	+	0.0224521i
$134$		0			0
$135$	−32.8612	+	56.9172i	−0.243416	+	0.421609i
$136$		0			0
$137$	41.3341	+	71.5927i	0.301708	+	0.522574i	0.976523	−	0.215413i	$-0.0691098\pi$
$137$	41.3341	+	71.5927i	0.301708	+	0.522574i	−0.674815	+	0.737987i	$0.735776\pi$
$138$		0			0
$139$			98.5453i			0.708959i	0.935064	+	0.354480i	$0.115342\pi$
$139$			98.5453i			0.708959i	−0.935064	+	0.354480i	$0.884658\pi$
$140$		0			0
$141$	15.7263			0.111534
$142$		0			0
$143$	−8.46046	+	4.88465i	−0.0591641	+	0.0341584i
$144$		0			0
$145$	6.58117	+	3.79964i	0.0453874	+	0.0262044i
$146$		0			0
$147$	−39.1876	−	112.600i	−0.266582	−	0.765987i
$148$		0			0
$149$	−37.5964	+	65.1189i	−0.252325	+	0.437040i	−0.964166	−	0.265301i	$-0.914529\pi$
$149$	−37.5964	+	65.1189i	−0.252325	+	0.437040i	0.711841	+	0.702341i	$0.247862\pi$
$150$		0			0
$151$	77.4963	+	134.227i	0.513220	+	0.888923i	0.999882	+	0.0153332i	$0.00488092\pi$
$151$	77.4963	+	134.227i	0.513220	+	0.888923i	−0.486662	+	0.873590i	$0.661786\pi$
$152$		0			0
$153$			83.9708i			0.548829i
$154$		0			0
$155$	−53.5840			−0.345703
$156$		0			0
$157$	−100.478	+	58.0108i	−0.639985	+	0.369495i	−0.784609	−	0.619991i	$-0.787136\pi$
$157$	−100.478	+	58.0108i	−0.639985	+	0.369495i	0.144624	+	0.989487i	$0.453803\pi$
$158$		0			0
$159$	75.9481	+	43.8487i	0.477661	+	0.275778i
$160$		0			0
$161$	−38.4499	−	227.461i	−0.238819	−	1.41280i
$162$		0			0
$163$	−95.0947	+	164.709i	−0.583403	+	1.01048i	0.411669	+	0.911333i	$0.364946\pi$
$163$	−95.0947	+	164.709i	−0.583403	+	1.01048i	−0.995072	+	0.0991507i	$0.968387\pi$
$164$		0			0
$165$	−37.8158	−	65.4990i	−0.229187	−	0.396963i
$166$		0			0
$167$			259.403i			1.55331i	0.629925	+	0.776656i	$0.283086\pi$
$167$			259.403i			1.55331i	−0.629925	+	0.776656i	$0.716914\pi$
$168$		0			0
$169$	168.506			0.997078
$170$		0			0
$171$	6.82638	−	3.94121i	0.0399204	−	0.0230480i
$172$		0			0
$173$	−196.181	−	113.265i	−1.13399	−	0.654710i	−0.189056	−	0.981966i	$-0.560543\pi$
$173$	−196.181	−	113.265i	−1.13399	−	0.654710i	−0.944936	+	0.327256i	$0.893876\pi$
$174$		0			0
$175$	32.8037	+	12.2031i	0.187450	+	0.0697322i
$176$		0			0
$177$	44.9720	−	77.8938i	0.254079	−	0.440078i
$178$		0			0
$179$	93.5046	+	161.955i	0.522372	+	0.904775i	0.999661	+	0.0260288i	$0.00828615\pi$
$179$	93.5046	+	161.955i	0.522372	+	0.904775i	−0.477289	+	0.878746i	$0.658381\pi$
$180$		0			0
$181$			183.025i			1.01119i	0.862771	+	0.505595i	$0.168727\pi$
$181$			183.025i			1.01119i	−0.862771	+	0.505595i	$0.831273\pi$
$182$		0			0
$183$	−85.2917			−0.466075
$184$		0			0
$185$	46.1196	−	26.6271i	0.249295	−	0.143930i
$186$		0			0
$187$	−328.238	−	189.508i	−1.75528	−	1.01341i
$188$		0			0
$189$	131.131	+	158.540i	0.693814	+	0.838839i
$190$		0			0
$191$	−98.7648	+	171.066i	−0.517093	+	0.895631i	0.482710	+	0.875780i	$0.339653\pi$
$191$	−98.7648	+	171.066i	−0.517093	+	0.895631i	−0.999803	+	0.0198511i	$0.993681\pi$
$192$		0			0
$193$	42.3264	+	73.3116i	0.219308	+	0.379853i	0.954597	−	0.297902i	$-0.0962867\pi$
$193$	42.3264	+	73.3116i	0.219308	+	0.379853i	−0.735289	+	0.677754i	$0.762953\pi$
$194$		0			0
$195$		−	3.82356i		−	0.0196080i
$196$		0			0
$197$	−247.330			−1.25548			−0.627742	−	0.778421i	$-0.716021\pi$
$197$	−247.330			−1.25548			−0.627742	+	0.778421i	$0.716021\pi$
$198$		0			0
$199$	106.101	−	61.2572i	0.533169	−	0.307825i	−0.209137	−	0.977886i	$-0.567065\pi$
$199$	106.101	−	61.2572i	0.533169	−	0.307825i	0.742306	+	0.670061i	$0.233732\pi$
$200$		0			0
$201$	−96.3541	−	55.6301i	−0.479374	−	0.276767i
$202$		0			0
$203$	18.3316	−	15.1623i	0.0903033	−	0.0746910i
$204$		0			0
$205$	−28.0643	+	48.6088i	−0.136899	+	0.237116i
$206$		0			0
$207$	50.7477	+	87.8975i	0.245158	+	0.424626i
$208$		0			0
$209$			35.5787i			0.170233i
$210$		0			0
$211$	−410.851			−1.94716			−0.973580	−	0.228348i	$-0.926668\pi$
$211$	−410.851			−1.94716			−0.973580	+	0.228348i	$0.926668\pi$
$212$		0			0
$213$	−169.436	+	97.8237i	−0.795472	+	0.459266i
$214$		0			0
$215$	48.6449	+	28.0851i	0.226255	+	0.130629i
$216$		0			0
$217$	−58.4860	+	157.218i	−0.269521	+	0.724509i
$218$		0			0
$219$	109.278	−	189.275i	0.498986	−	0.864269i
$220$		0			0
$221$	−9.58059	−	16.5941i	−0.0433511	−	0.0750863i
$222$		0			0
$223$		−	69.8903i		−	0.313409i	−0.987646	−	0.156705i	$-0.949913\pi$
$223$		−	69.8903i		−	0.313409i	0.987646	−	0.156705i	$-0.0500871\pi$
$224$		0			0
$225$	−15.3989			−0.0684395
$226$		0			0
$227$	89.7377	−	51.8101i	0.395320	−	0.228238i	−0.289142	−	0.957286i	$-0.593370\pi$
$227$	89.7377	−	51.8101i	0.395320	−	0.228238i	0.684463	+	0.729048i	$0.260037\pi$
$228$		0			0
$229$	−262.717	−	151.680i	−1.14724	−	0.662358i	−0.199025	−	0.979994i	$-0.563778\pi$
$229$	−262.717	−	151.680i	−1.14724	−	0.662358i	−0.948213	+	0.317636i	$0.897111\pi$
$230$		0			0
$231$	−233.453	+	39.4628i	−1.01062	+	0.170835i
$232$		0			0
$233$	−214.222	+	371.043i	−0.919406	+	1.59246i	−0.119087	+	0.992884i	$0.537997\pi$
$233$	−214.222	+	371.043i	−0.919406	+	1.59246i	−0.800319	+	0.599574i	$0.795337\pi$
$234$		0			0
$235$	7.22624	+	12.5162i	0.0307499	+	0.0532605i
$236$		0			0
$237$		−	0.202425i		−	0.000854112i
$238$		0			0
$239$	−109.615			−0.458641			−0.229320	−	0.973351i	$-0.573650\pi$
$239$	−109.615			−0.458641			−0.229320	+	0.973351i	$0.573650\pi$
$240$		0			0
$241$	247.622	−	142.965i	1.02748	−	0.593215i	0.111217	−	0.993796i	$-0.464525\pi$
$241$	247.622	−	142.965i	1.02748	−	0.593215i	0.916261	+	0.400581i	$0.131192\pi$
$242$		0			0
$243$	−136.800	−	78.9813i	−0.562962	−	0.325026i
$244$		0			0
$245$	71.6093	−	82.9283i	0.292283	−	0.338483i
$246$		0			0
$247$	−0.899340	+	1.55770i	−0.00364105	+	0.00630649i
$248$		0			0
$249$	115.950	+	200.831i	0.465663	+	0.806551i
$250$		0			0
$251$			101.215i			0.403248i	0.979463	+	0.201624i	$0.0646219\pi$
$251$			101.215i			0.403248i	−0.979463	+	0.201624i	$0.935378\pi$
$252$		0			0
$253$	−458.117			−1.81074
$254$		0			0
$255$	128.468	−	74.1707i	0.503794	−	0.290866i
$256$		0			0
$257$	438.580	+	253.214i	1.70654	+	0.985269i	0.938773	+	0.344536i	$0.111964\pi$
$257$	438.580	+	253.214i	1.70654	+	0.985269i	0.767763	+	0.640733i	$0.221370\pi$
$258$		0			0
$259$	−27.7868	−	164.380i	−0.107285	−	0.634673i
$260$		0			0
$261$	−5.23332	+	9.06437i	−0.0200510	+	0.0347294i
$262$		0			0
$263$	−27.2892	−	47.2663i	−0.103761	−	0.179720i	0.809470	−	0.587161i	$-0.199754\pi$
$263$	−27.2892	−	47.2663i	−0.103761	−	0.179720i	−0.913231	+	0.407441i	$0.866421\pi$
$264$		0			0
$265$			80.5940i			0.304128i
$266$		0			0
$267$	294.472			1.10289
$268$		0			0
$269$	423.694	−	244.620i	1.57507	−	0.909368i	0.579540	−	0.814944i	$-0.303232\pi$
$269$	423.694	−	244.620i	1.57507	−	0.909368i	0.995532	−	0.0944245i	$-0.0301011\pi$
$270$		0			0
$271$	422.146	+	243.726i	1.55773	+	0.899357i	0.997473	+	0.0710401i	$0.0226318\pi$
$271$	422.146	+	243.726i	1.55773	+	0.899357i	0.560259	+	0.828317i	$0.310702\pi$
$272$		0			0
$273$	−11.2185	−	4.17334i	−0.0410935	−	0.0152870i
$274$		0			0
$275$	34.7528	−	60.1936i	0.126374	−	0.218886i
$276$		0			0
$277$	152.488	+	264.116i	0.550497	+	0.953488i	0.998239	+	0.0593253i	$0.0188949\pi$
$277$	152.488	+	264.116i	0.550497	+	0.953488i	−0.447742	+	0.894163i	$0.647772\pi$
$278$		0			0
$279$		−	73.8023i		−	0.264524i
$280$		0			0
$281$	−110.177			−0.392089			−0.196044	−	0.980595i	$-0.562810\pi$
$281$	−110.177			−0.392089			−0.196044	+	0.980595i	$0.562810\pi$
$282$		0			0
$283$	−230.563	+	133.116i	−0.814710	+	0.470373i	−0.848589	−	0.529053i	$-0.822547\pi$
$283$	−230.563	+	133.116i	−0.814710	+	0.470373i	0.0338789	+	0.999426i	$0.489214\pi$
$284$		0			0
$285$	−12.0594	−	6.96249i	−0.0423136	−	0.0244298i
$286$		0			0
$287$	111.989	+	135.398i	0.390206	+	0.471769i
$288$		0			0
$289$	227.196	−	393.514i	0.786144	−	1.36164i
$290$		0			0
$291$	−0.440502	−	0.762971i	−0.00151375	−	0.00262189i
$292$		0			0
$293$			8.79423i			0.0300145i	0.999887	+	0.0150072i	$0.00477713\pi$
$293$			8.79423i			0.0300145i	−0.999887	+	0.0150072i	$0.995223\pi$
$294$		0			0
$295$	82.6586			0.280199
$296$		0			0
$297$	353.841	−	204.290i	1.19138	−	0.687846i
$298$		0			0
$299$	−20.0572	−	11.5800i	−0.0670810	−	0.0387292i
$300$		0			0
$301$	135.498	−	112.072i	0.450160	−	0.372333i
$302$		0			0
$303$	−195.452	+	338.534i	−0.645058	+	1.11727i
$304$		0			0
$305$	−39.1916	−	67.8818i	−0.128497	−	0.222563i
$306$		0			0
$307$		−	447.196i		−	1.45667i	−0.685224	−	0.728333i	$-0.740296\pi$
$307$		−	447.196i		−	1.45667i	0.685224	−	0.728333i	$-0.259704\pi$
$308$		0			0
$309$	−349.043			−1.12959
$310$		0			0
$311$	194.895	−	112.523i	0.626671	−	0.361809i	−0.152790	−	0.988259i	$-0.548826\pi$
$311$	194.895	−	112.523i	0.626671	−	0.361809i	0.779462	+	0.626450i	$0.215493\pi$
$312$		0			0
$313$	−291.069	−	168.049i	−0.929934	−	0.536898i	−0.0431435	−	0.999069i	$-0.513737\pi$
$313$	−291.069	−	168.049i	−0.929934	−	0.536898i	−0.886791	+	0.462171i	$0.847071\pi$
$314$		0			0
$315$	−16.8076	+	45.1812i	−0.0533575	+	0.143432i
$316$		0			0
$317$	41.2173	−	71.3905i	0.130023	−	0.225207i	−0.793662	−	0.608359i	$-0.791828\pi$
$317$	41.2173	−	71.3905i	0.130023	−	0.225207i	0.923685	+	0.383152i	$0.125161\pi$
$318$		0			0
$319$	−23.6215	−	40.9136i	−0.0740486	−	0.128256i
$320$		0			0
$321$			154.416i			0.481046i
$322$		0			0
$323$	−69.7829			−0.216046
$324$		0			0
$325$	3.04309	−	1.75693i	0.00936334	−	0.00540593i
$326$		0			0
$327$	−119.496	−	68.9909i	−0.365431	−	0.210981i
$328$		0			0
$329$	44.6105	−	7.54095i	0.135594	−	0.0229208i
$330$		0			0
$331$	−47.3818	+	82.0677i	−0.143147	+	0.247939i	−0.928680	−	0.370881i	$-0.879056\pi$
$331$	−47.3818	+	82.0677i	−0.143147	+	0.247939i	0.785533	+	0.618820i	$0.212389\pi$
$332$		0			0
$333$	36.6741	+	63.5213i	0.110132	+	0.190755i
$334$		0			0
$335$		−	102.248i		−	0.305219i
$336$		0			0
$337$	−362.615			−1.07601			−0.538005	−	0.842942i	$-0.680822\pi$
$337$	−362.615			−1.07601			−0.538005	+	0.842942i	$0.680822\pi$
$338$		0			0
$339$	111.987	−	64.6556i	0.330345	−	0.190725i
$340$		0			0
$341$	288.490	+	166.560i	0.846012	+	0.488445i
$342$		0			0
$343$	−165.156	−	300.620i	−0.481504	−	0.876444i
$344$		0			0
$345$	89.6500	−	155.278i	0.259855	−	0.450082i
$346$		0			0
$347$	193.996	+	336.011i	0.559066	+	0.968330i	0.997575	+	0.0696035i	$0.0221734\pi$
$347$	193.996	+	336.011i	0.559066	+	0.968330i	−0.438509	+	0.898727i	$0.644493\pi$
$348$		0			0
$349$		−	445.741i		−	1.27719i	−0.769541	−	0.638597i	$-0.779515\pi$
$349$		−	445.741i		−	1.27719i	0.769541	−	0.638597i	$-0.220485\pi$
$350$		0			0
$351$	20.6558			0.0588484
$352$		0			0
$353$	247.732	−	143.028i	0.701790	−	0.405179i	−0.106224	−	0.994342i	$-0.533876\pi$
$353$	247.732	−	143.028i	0.701790	−	0.405179i	0.808014	+	0.589163i	$0.200543\pi$
$354$		0			0
$355$	−155.711	−	89.9001i	−0.438624	−	0.253240i
$356$		0			0
$357$	−77.4010	−	457.886i	−0.216810	−	1.28260i
$358$		0			0
$359$	215.089	−	372.546i	0.599135	−	1.03773i	−0.393814	−	0.919190i	$-0.628845\pi$
$359$	215.089	−	372.546i	0.599135	−	1.03773i	0.992949	−	0.118542i	$-0.0378220\pi$
$360$		0			0
$361$	−177.225	−	306.962i	−0.490927	−	0.850311i
$362$		0			0
$363$			175.774i			0.484225i
$364$		0			0
$365$	200.853			0.550283
$366$		0			0
$367$	289.182	−	166.959i	0.787961	−	0.454930i	−0.0512831	−	0.998684i	$-0.516331\pi$
$367$	289.182	−	166.959i	0.787961	−	0.454930i	0.839244	+	0.543755i	$0.182998\pi$
$368$		0			0
$369$	−66.9499	−	38.6535i	−0.181436	−	0.104752i
$370$		0			0
$371$	236.467	+	87.9668i	0.637377	+	0.237107i
$372$		0			0
$373$	24.6405	−	42.6786i	0.0660603	−	0.114420i	−0.831104	−	0.556118i	$-0.812290\pi$
$373$	24.6405	−	42.6786i	0.0660603	−	0.114420i	0.897164	+	0.441698i	$0.145624\pi$
$374$		0			0
$375$	13.6017	+	23.5589i	0.0362713	+	0.0628237i
$376$		0			0
$377$		−	2.38837i		−	0.00633519i
$378$		0			0
$379$	635.496			1.67677			0.838385	−	0.545078i	$-0.183500\pi$
$379$	635.496			1.67677			0.838385	+	0.545078i	$0.183500\pi$
$380$		0			0
$381$	82.5928	−	47.6850i	0.216779	−	0.125157i
$382$		0			0
$383$	84.4675	+	48.7673i	0.220542	+	0.127330i	0.606201	−	0.795311i	$-0.292693\pi$
$383$	84.4675	+	48.7673i	0.220542	+	0.127330i	−0.385659	+	0.922641i	$0.626026\pi$
$384$		0			0
$385$	−138.679	−	167.667i	−0.360206	−	0.435498i
$386$		0			0
$387$	−38.6822	+	66.9995i	−0.0999540	+	0.173125i
$388$		0			0
$389$	335.431	+	580.983i	0.862289	+	1.49353i	0.869714	+	0.493557i	$0.164303\pi$
$389$	335.431	+	580.983i	0.862289	+	1.49353i	−0.00742425	+	0.999972i	$0.502363\pi$
$390$		0			0
$391$		−	898.535i		−	2.29804i
$392$		0			0
$393$	131.628			0.334932
$394$		0			0
$395$	0.161105	−	0.0930142i	0.000407861	−	0.000235479i
$396$		0			0
$397$	−482.681	−	278.676i	−1.21582	−	0.701954i	−0.251799	−	0.967780i	$-0.581022\pi$
$397$	−482.681	−	278.676i	−1.21582	−	0.701954i	−0.964021	+	0.265825i	$0.914356\pi$
$398$		0			0
$399$	−33.5909	+	27.7834i	−0.0841877	+	0.0696327i
$400$		0			0
$401$	−297.504	+	515.293i	−0.741906	+	1.28502i	0.209720	+	0.977762i	$0.432745\pi$
$401$	−297.504	+	515.293i	−0.741906	+	1.28502i	−0.951626	+	0.307258i	$0.900589\pi$
$402$		0			0
$403$	8.42042	+	14.5846i	0.0208944	+	0.0361901i
$404$		0			0
$405$			97.9330i			0.241810i
$406$		0			0
$407$	−331.070			−0.813439
$408$		0			0
$409$	394.822	−	227.951i	0.965336	−	0.557337i	0.0675247	−	0.997718i	$-0.478490\pi$
$409$	394.822	−	227.951i	0.965336	−	0.557337i	0.897811	+	0.440381i	$0.145157\pi$
$410$		0			0
$411$	174.196	+	100.572i	0.423834	+	0.244701i
$412$		0			0
$413$	90.2203	−	242.525i	0.218451	−	0.587227i
$414$		0			0
$415$	−106.558	+	184.564i	−0.256767	+	0.444733i
$416$		0			0
$417$	119.888	+	207.652i	0.287501	+	0.497966i
$418$		0			0
$419$		−	120.662i		−	0.287977i	−0.989579	−	0.143989i	$-0.954007\pi$
$419$		−	120.662i		−	0.287977i	0.989579	−	0.143989i	$-0.0459929\pi$
$420$		0			0
$421$	−206.898			−0.491444			−0.245722	−	0.969340i	$-0.579025\pi$
$421$	−206.898			−0.491444			−0.245722	+	0.969340i	$0.579025\pi$
$422$		0			0
$423$	−17.2388	+	9.95283i	−0.0407537	+	0.0235292i
$424$		0			0
$425$	118.062	+	68.1630i	0.277792	+	0.160384i
$426$		0			0
$427$	−241.946	+	40.8985i	−0.566618	+	0.0957810i
$428$		0			0
$429$	−11.8851	+	20.5856i	−0.0277042	+	0.0479850i
$430$		0			0
$431$	−134.929	−	233.704i	−0.313060	−	0.542236i	0.665963	−	0.745985i	$-0.268021\pi$
$431$	−134.929	−	233.704i	−0.313060	−	0.542236i	−0.979023	+	0.203749i	$0.934687\pi$
$432$		0			0
$433$			8.67846i			0.0200426i	0.999950	+	0.0100213i	$0.00318994\pi$
$433$			8.67846i			0.0200426i	−0.999950	+	0.0100213i	$0.996810\pi$
$434$		0			0
$435$	18.4902			0.0425062
$436$		0			0
$437$	−73.0462	+	42.1732i	−0.167154	+	0.0965063i
$438$		0			0
$439$	−3.11208	−	1.79676i	−0.00708901	−	0.00409284i	0.496451	−	0.868065i	$-0.334636\pi$
$439$	−3.11208	−	1.79676i	−0.00708901	−	0.00409284i	−0.503540	+	0.863972i	$0.667969\pi$
$440$		0			0
$441$	114.219	+	98.6288i	0.258999	+	0.223648i
$442$		0			0
$443$	202.201	−	350.223i	0.456437	−	0.790571i	−0.542333	−	0.840164i	$-0.682459\pi$
$443$	202.201	−	350.223i	0.456437	−	0.790571i	0.998770	+	0.0495923i	$0.0157922\pi$
$444$		0			0
$445$	135.310	+	234.364i	0.304068	+	0.526661i
$446$		0			0
$447$			182.955i			0.409296i
$448$		0			0
$449$	339.672			0.756508			0.378254	−	0.925702i	$-0.376525\pi$
$449$	339.672			0.756508			0.378254	+	0.925702i	$0.376525\pi$
$450$		0			0
$451$	302.190	−	174.469i	0.670044	−	0.386850i
$452$		0			0
$453$	326.596	+	188.560i	0.720962	+	0.416247i
$454$		0			0
$455$	−1.83344	−	10.8462i	−0.00402955	−	0.0238379i
$456$		0			0
$457$	318.139	−	551.033i	0.696147	−	1.20576i	−0.273646	−	0.961831i	$-0.588230\pi$
$457$	318.139	−	551.033i	0.696147	−	1.20576i	0.969793	−	0.243931i	$-0.0784370\pi$
$458$		0			0
$459$	400.688	+	694.012i	0.872959	+	1.51201i
$460$		0			0
$461$		−	483.724i		−	1.04929i	−0.851321	−	0.524646i	$-0.824198\pi$
$461$		−	483.724i		−	1.04929i	0.851321	−	0.524646i	$-0.175802\pi$
$462$		0			0
$463$	−409.737			−0.884961			−0.442480	−	0.896778i	$-0.645901\pi$
$463$	−409.737			−0.884961			−0.442480	+	0.896778i	$0.645901\pi$
$464$		0			0
$465$	−112.911	+	65.1890i	−0.242819	+	0.140191i
$466$		0			0
$467$	−317.491	−	183.303i	−0.679851	−	0.392512i	0.119948	−	0.992780i	$-0.461727\pi$
$467$	−317.491	−	183.303i	−0.679851	−	0.392512i	−0.799799	+	0.600268i	$0.795061\pi$
$468$		0			0
$469$	−300.002	−	111.602i	−0.639663	−	0.237957i
$470$		0			0
$471$	−141.149	+	244.477i	−0.299679	+	0.519060i
$472$		0			0
$473$	−174.599	−	302.414i	−0.369131	−	0.639353i
$474$		0			0
$475$		−	12.7971i		−	0.0269412i
$476$		0			0
$477$	−111.004			−0.232712
$478$		0			0
$479$	73.5403	−	42.4585i	0.153529	−	0.0886399i	−0.421267	−	0.906936i	$-0.638415\pi$
$479$	73.5403	−	42.4585i	0.153529	−	0.0886399i	0.574796	+	0.818297i	$0.305081\pi$
$480$		0			0
$481$	−14.4948	−	8.36861i	−0.0301348	−	0.0173983i
$482$		0			0
$483$	−357.744	−	432.521i	−0.740670	−	0.895490i
$484$		0			0
$485$	0.404821	−	0.701171i	0.000834683	−	0.00144571i
$486$		0			0
$487$	−16.3728	−	28.3585i	−0.0336197	−	0.0582311i	0.848726	−	0.528833i	$-0.177370\pi$
$487$	−16.3728	−	28.3585i	−0.0336197	−	0.0582311i	−0.882346	+	0.470602i	$0.844037\pi$
$488$		0			0
$489$			462.760i			0.946339i
$490$		0			0
$491$	−522.932			−1.06503			−0.532517	−	0.846419i	$-0.678754\pi$
$491$	−522.932			−1.06503			−0.532517	+	0.846419i	$0.678754\pi$
$492$		0			0
$493$	80.2466	−	46.3304i	0.162772	−	0.0939765i
$494$		0			0
$495$	82.9058	+	47.8657i	0.167486	+	0.0966984i
$496$		0			0
$497$	−433.728	+	358.741i	−0.872692	+	0.721814i
$498$		0			0
$499$	−30.4582	+	52.7551i	−0.0610384	+	0.105722i	−0.894930	−	0.446207i	$-0.852775\pi$
$499$	−30.4582	+	52.7551i	−0.0610384	+	0.105722i	0.833891	+	0.551929i	$0.186108\pi$
$500$		0			0
$501$	315.583	+	546.606i	0.629907	+	1.09103i
$502$		0			0
$503$			523.122i			1.04000i	0.854165	+	0.520002i	$0.174069\pi$
$503$			523.122i			1.04000i	−0.854165	+	0.520002i	$0.825931\pi$
$504$		0			0
$505$	−359.242			−0.711370
$506$		0			0
$507$	355.071	−	205.000i	0.700337	−	0.404340i
$508$		0			0
$509$	−10.9283	−	6.30945i	−0.0214701	−	0.0123958i	0.489227	−	0.872157i	$-0.337279\pi$
$509$	−10.9283	−	6.30945i	−0.0214701	−	0.0123958i	−0.510697	+	0.859761i	$0.670612\pi$
$510$		0			0
$511$	219.227	−	589.314i	0.429017	−	1.15326i
$512$		0			0
$513$	37.6130	−	65.1477i	0.0733198	−	0.126994i
$514$		0			0
$515$	−160.386	−	277.796i	−0.311428	−	0.539410i
$516$		0			0
$517$		−	89.8477i		−	0.173787i
$518$		0			0
$519$	−551.181			−1.06201
$520$		0			0
$521$	−216.848	+	125.197i	−0.416215	+	0.240302i	−0.693456	−	0.720499i	$-0.743913\pi$
$521$	−216.848	+	125.197i	−0.416215	+	0.240302i	0.277242	+	0.960800i	$0.410580\pi$
$522$		0			0
$523$	303.166	+	175.033i	0.579667	+	0.334671i	0.761001	−	0.648751i	$-0.224708\pi$
$523$	303.166	+	175.033i	0.579667	+	0.334671i	−0.181334	+	0.983422i	$0.558042\pi$
$524$		0			0
$525$	83.9690	−	14.1941i	0.159941	−	0.0270364i
$526$		0			0
$527$	−326.685	+	565.835i	−0.619895	+	1.07369i
$528$		0			0
$529$	−278.529	−	482.426i	−0.526520	−	0.911959i
$530$		0			0
$531$			113.847i			0.214402i
$532$		0			0
$533$	17.6406			0.0330968
$534$		0			0
$535$	−122.896	+	70.9542i	−0.229713	+	0.132625i
$536$		0			0
$537$	394.060	+	227.511i	0.733818	+	0.423670i
$538$		0			0
$539$	−643.309	+	223.887i	−1.19352	+	0.415375i
$540$		0			0
$541$	−204.673	+	354.504i	−0.378324	+	0.655276i	−0.990819	−	0.135199i	$-0.956833\pi$
$541$	−204.673	+	354.504i	−0.378324	+	0.655276i	0.612495	+	0.790475i	$0.290166\pi$
$542$		0			0
$543$	222.664	+	385.665i	0.410063	+	0.710250i
$544$		0			0
$545$		−	126.805i		−	0.232671i
$546$		0			0
$547$	−189.589			−0.346598			−0.173299	−	0.984869i	$-0.555443\pi$
$547$	−189.589			−0.346598			−0.173299	+	0.984869i	$0.555443\pi$
$548$		0			0
$549$	93.4949	−	53.9793i	0.170300	−	0.0983230i
$550$		0			0
$551$	−7.53284	−	4.34908i	−0.0136712	−	0.00789308i
$552$		0			0
$553$	−0.0970651	−	0.574215i	−0.000175525	−	0.00103836i
$554$		0			0
$555$	64.7878	−	112.216i	0.116735	−	0.202191i
$556$		0			0
$557$	−61.6991	−	106.866i	−0.110770	−	0.191860i	0.805311	−	0.592853i	$-0.201998\pi$
$557$	−61.6991	−	106.866i	−0.110770	−	0.191860i	−0.916081	+	0.400993i	$0.868665\pi$
$558$		0			0
$559$		−	17.6537i		−	0.0315808i
$560$		0			0
$561$	−922.205			−1.64386
$562$		0			0
$563$	373.460	−	215.617i	0.663339	−	0.382979i	−0.130209	−	0.991487i	$-0.541565\pi$
$563$	373.460	−	215.617i	0.663339	−	0.382979i	0.793548	+	0.608507i	$0.208231\pi$
$564$		0			0
$565$	102.916	+	59.4186i	0.182152	+	0.105166i
$566$		0			0
$567$	287.341	+	106.892i	0.506773	+	0.188522i
$568$		0			0
$569$	−430.759	+	746.097i	−0.757046	+	1.31124i	0.187304	+	0.982302i	$0.440025\pi$
$569$	−430.759	+	746.097i	−0.757046	+	1.31124i	−0.944351	+	0.328941i	$0.893308\pi$
$570$		0			0
$571$	214.469	+	371.472i	0.375603	+	0.650563i	0.990417	−	0.138109i	$-0.0441024\pi$
$571$	214.469	+	371.472i	0.375603	+	0.650563i	−0.614814	+	0.788672i	$0.710769\pi$
$572$		0			0
$573$			480.619i			0.838777i
$574$		0			0
$575$	164.777			0.286569
$576$		0			0
$577$	−156.886	+	90.5781i	−0.271899	+	0.156981i	−0.629750	−	0.776798i	$-0.716843\pi$
$577$	−156.886	+	90.5781i	−0.271899	+	0.156981i	0.357851	+	0.933779i	$0.383509\pi$
$578$		0			0
$579$	178.378	+	102.987i	0.308080	+	0.177870i
$580$		0			0
$581$	425.215	+	514.096i	0.731867	+	0.884846i
$582$		0			0
$583$	250.517	−	433.908i	0.429703	−	0.744268i
$584$		0			0
$585$	2.41985	+	4.19130i	0.00413649	+	0.00716461i
$586$		0			0
$587$			104.998i			0.178872i	0.995993	+	0.0894359i	$0.0285064\pi$
$587$			104.998i			0.178872i	−0.995993	+	0.0894359i	$0.971494\pi$
$588$		0			0
$589$	61.3325			0.104130
$590$		0			0
$591$	−521.167	+	300.896i	−0.881840	+	0.509130i
$592$		0			0
$593$	−27.5368	−	15.8984i	−0.0464365	−	0.0268101i	0.476602	−	0.879119i	$-0.341868\pi$
$593$	−27.5368	−	15.8984i	−0.0464365	−	0.0268101i	−0.523039	+	0.852309i	$0.675202\pi$
$594$		0			0
$595$	328.856	−	272.001i	0.552699	−	0.457144i
$596$		0			0
$597$	149.048	−	258.159i	0.249662	−	0.432427i
$598$		0			0
$599$	−58.9176	−	102.048i	−0.0983600	−	0.170365i	0.812646	−	0.582758i	$-0.198026\pi$
$599$	−58.9176	−	102.048i	−0.0983600	−	0.170365i	−0.911006	+	0.412393i	$0.864693\pi$
$600$		0			0
$601$		−	1044.07i		−	1.73722i	−0.495494	−	0.868611i	$-0.665013\pi$
$601$		−	1044.07i		−	1.73722i	0.495494	−	0.868611i	$-0.334987\pi$
$602$		0			0
$603$	140.828			0.233546
$604$		0			0
$605$	−139.894	+	80.7680i	−0.231230	+	0.133501i
$606$		0			0
$607$	251.794	+	145.373i	0.414817	+	0.239495i	0.692857	−	0.721075i	$-0.256352\pi$
$607$	251.794	+	145.373i	0.414817	+	0.239495i	−0.278040	+	0.960569i	$0.589685\pi$
$608$		0			0
$609$	20.1817	−	54.2512i	0.0331391	−	0.0890824i
$610$		0			0
$611$	2.27112	−	3.93370i	0.00371706	−	0.00643814i
$612$		0			0
$613$	93.0624	+	161.189i	0.151815	+	0.262951i	0.931895	−	0.362729i	$-0.118155\pi$
$613$	93.0624	+	161.189i	0.151815	+	0.262951i	−0.780080	+	0.625680i	$0.784822\pi$
$614$		0			0
$615$			136.569i			0.222064i
$616$		0			0
$617$	386.307			0.626105			0.313053	−	0.949736i	$-0.398648\pi$
$617$	386.307			0.626105			0.313053	+	0.949736i	$0.398648\pi$
$618$		0			0
$619$	−30.9861	+	17.8898i	−0.0500583	+	0.0289012i	−0.524820	−	0.851213i	$-0.675867\pi$
$619$	−30.9861	+	17.8898i	−0.0500583	+	0.0289012i	0.474762	+	0.880114i	$0.342534\pi$
$620$		0			0
$621$	838.851	+	484.311i	1.35081	+	0.779889i
$622$		0			0
$623$	835.326	−	141.203i	1.34081	−	0.226651i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	43.2842	+	74.9704i	0.0690338	+	0.119570i
$628$		0			0
$629$		−	649.349i		−	1.03235i
$630$		0			0
$631$	−888.207			−1.40762			−0.703809	−	0.710389i	$-0.748519\pi$
$631$	−888.207			−1.40762			−0.703809	+	0.710389i	$0.748519\pi$
$632$		0			0
$633$	−865.732	+	499.831i	−1.36767	+	0.789622i
$634$		0			0
$635$	75.9029	+	43.8225i	0.119532	+	0.0690119i
$636$		0			0
$637$	−33.8246	−	6.45903i	−0.0530998	−	0.0101398i
$638$		0			0
$639$	123.821	−	214.464i	0.193773	−	0.335625i
$640$		0			0
$641$	−322.467	−	558.528i	−0.503068	−	0.871339i	−0.999994	−	0.00354621i	$-0.998871\pi$
$641$	−322.467	−	558.528i	−0.503068	−	0.871339i	0.496926	−	0.867793i	$-0.334462\pi$
$642$		0			0
$643$			466.160i			0.724976i	0.931988	+	0.362488i	$0.118073\pi$
$643$			466.160i			0.724976i	−0.931988	+	0.362488i	$0.881927\pi$
$644$		0			0
$645$	136.671			0.211893
$646$		0			0
$647$	457.087	−	263.899i	0.706471	−	0.407881i	−0.103282	−	0.994652i	$-0.532934\pi$
$647$	457.087	−	263.899i	0.706471	−	0.407881i	0.809753	+	0.586771i	$0.199601\pi$
$648$		0			0
$649$	−445.024	−	256.935i	−0.685707	−	0.395893i
$650$		0			0
$651$	68.0281	+	402.438i	0.104498	+	0.618185i
$652$		0			0
$653$	220.560	−	382.021i	0.337764	−	0.585025i	−0.646248	−	0.763128i	$-0.723663\pi$
$653$	220.560	−	382.021i	0.337764	−	0.585025i	0.984012	+	0.178103i	$0.0569960\pi$
$654$		0			0
$655$	60.4832	+	104.760i	0.0923408	+	0.159939i
$656$		0			0
$657$			276.639i			0.421064i
$658$		0			0
$659$	−884.354			−1.34196			−0.670982	−	0.741474i	$-0.734127\pi$
$659$	−884.354			−1.34196			−0.670982	+	0.741474i	$0.734127\pi$
$660$		0			0
$661$	631.224	−	364.437i	0.954953	−	0.551342i	0.0603369	−	0.998178i	$-0.480782\pi$
$661$	631.224	−	364.437i	0.954953	−	0.551342i	0.894616	+	0.446836i	$0.147449\pi$
$662$		0			0
$663$	−40.3759	−	23.3110i	−0.0608987	−	0.0351599i
$664$		0			0
$665$	−37.5473	−	13.9678i	−0.0564621	−	0.0210041i
$666$		0			0
$667$	55.9995	−	96.9939i	0.0839572	−	0.145418i
$668$		0			0
$669$	−85.0268	−	147.271i	−0.127095	−	0.220136i
$670$		0			0
$671$			487.290i			0.726215i
$672$		0			0
$673$	1042.57			1.54914			0.774571	−	0.632487i	$-0.217966\pi$
$673$	1042.57			1.54914			0.774571	+	0.632487i	$0.217966\pi$
$674$		0			0
$675$	−127.271	+	73.4798i	−0.188549	+	0.108859i
$676$		0			0
$677$	−706.342	−	407.806i	−1.04334	−	0.602373i	−0.122563	−	0.992461i	$-0.539111\pi$
$677$	−706.342	−	407.806i	−1.04334	−	0.602373i	−0.920778	+	0.390088i	$0.872445\pi$
$678$		0			0
$679$	−1.61542	−	1.95308i	−0.00237911	−	0.00287641i
$680$		0			0
$681$	126.062	−	218.345i	0.185113	−	0.320625i
$682$		0			0
$683$	356.071	+	616.734i	0.521334	+	0.902977i	0.999692	+	0.0248124i	$0.00789885\pi$
$683$	356.071	+	616.734i	0.521334	+	0.902977i	−0.478358	+	0.878165i	$0.658768\pi$
$684$		0			0
$685$			184.852i			0.269856i
$686$		0			0
$687$	−738.121			−1.07441
$688$		0			0
$689$	21.9362	−	12.6649i	0.0318378	−	0.0183815i
$690$		0			0
$691$	−875.286	−	505.346i	−1.26669	−	0.731326i	−0.292333	−	0.956317i	$-0.594432\pi$
$691$	−875.286	−	505.346i	−1.26669	−	0.731326i	−0.974361	+	0.224990i	$0.927765\pi$
$692$		0			0
$693$	230.931	−	191.006i	0.333233	−	0.275621i
$694$		0			0
$695$	−110.177	+	190.832i	−0.158528	+	0.274579i
$696$		0			0
$697$	342.199	+	592.705i	0.490959	+	0.850366i
$698$		0			0
$699$			1042.47i			1.49137i
$700$		0			0
$701$	60.6890			0.0865748			0.0432874	−	0.999063i	$-0.486217\pi$
$701$	60.6890			0.0865748			0.0432874	+	0.999063i	$0.486217\pi$
$702$		0			0
$703$	−52.7886	+	30.4775i	−0.0750905	+	0.0433535i
$704$		0			0
$705$	30.4538	+	17.5825i	0.0431969	+	0.0249397i
$706$		0			0
$707$	−392.106	+	1054.04i	−0.554605	+	1.49086i
$708$		0			0
$709$	−324.501	+	562.052i	−0.457688	+	0.792740i	−0.998838	−	0.0481865i	$-0.984656\pi$
$709$	−324.501	+	562.052i	−0.457688	+	0.792740i	0.541150	+	0.840926i	$0.317989\pi$
$710$		0			0
$711$	0.128110	+	0.221893i	0.000180183	+	0.000312086i
$712$		0			0
$713$			789.727i			1.10761i
$714$		0			0
$715$	−21.8448			−0.0305522
$716$		0			0
$717$	−230.978	+	133.355i	−0.322145	+	0.185990i
$718$		0			0
$719$	182.027	+	105.093i	0.253167	+	0.146166i	0.621213	−	0.783641i	$-0.286640\pi$
$719$	182.027	+	105.093i	0.253167	+	0.146166i	−0.368047	+	0.929807i	$0.619973\pi$
$720$		0			0
$721$	−990.126	+	167.371i	−1.37327	+	0.232137i
$722$		0			0
$723$	347.855	−	602.502i	0.481127	−	0.833336i
$724$		0			0
$725$	8.49625	+	14.7159i	0.0117190	+	0.0202979i
$726$		0			0
$727$		−	743.893i		−	1.02324i	−0.859213	−	0.511618i	$-0.829046\pi$
$727$		−	743.893i		−	1.02324i	0.859213	−	0.511618i	$-0.170954\pi$
$728$		0			0
$729$	−778.520			−1.06793
$730$		0			0
$731$	593.145	−	342.452i	0.811416	−	0.468471i
$732$		0			0
$733$	−306.576	−	177.002i	−0.418248	−	0.241476i	0.276079	−	0.961135i	$-0.410965\pi$
$733$	−306.576	−	177.002i	−0.418248	−	0.241476i	−0.694328	+	0.719659i	$0.744298\pi$
$734$		0			0
$735$	50.0044	−	261.862i	0.0680332	−	0.356275i
$736$		0			0
$737$	−317.827	+	550.492i	−0.431244	+	0.746937i
$738$		0			0
$739$	−619.606	−	1073.19i	−0.838438	−	1.45222i	−0.891200	−	0.453610i	$-0.850136\pi$
$739$	−619.606	−	1073.19i	−0.838438	−	1.45222i	0.0527626	−	0.998607i	$-0.483197\pi$
$740$		0			0
$741$			4.37646i			0.00590615i
$742$		0			0
$743$	1060.01			1.42666			0.713328	−	0.700830i	$-0.247187\pi$
$743$	1060.01			1.42666			0.713328	+	0.700830i	$0.247187\pi$
$744$		0			0
$745$	−145.610	+	84.0681i	−0.195450	+	0.112843i
$746$		0			0
$747$	−254.204	−	146.765i	−0.340299	−	0.196472i
$748$		0			0
$749$	74.0444	+	438.029i	0.0988576	+	0.584819i
$750$		0			0
$751$	−509.992	+	883.332i	−0.679084	+	1.17621i	0.296173	+	0.955134i	$0.404289\pi$
$751$	−509.992	+	883.332i	−0.679084	+	1.17621i	−0.975257	+	0.221073i	$0.929044\pi$
$752$		0			0
$753$	123.136	+	213.278i	0.163527	+	0.283237i
$754$		0			0
$755$			346.574i			0.459038i
$756$		0			0
$757$	1023.43			1.35196			0.675978	−	0.736921i	$-0.263721\pi$
$757$	1023.43			1.35196			0.675978	+	0.736921i	$0.263721\pi$
$758$		0			0
$759$	−965.330	+	557.334i	−1.27184	+	0.734300i
$760$		0			0
$761$	−388.132	−	224.088i	−0.510028	−	0.294465i	0.222817	−	0.974860i	$-0.428475\pi$
$761$	−388.132	−	224.088i	−0.510028	−	0.294465i	−0.732845	+	0.680395i	$0.761808\pi$
$762$		0			0
$763$	−372.054	−	138.406i	−0.487620	−	0.181397i
$764$		0			0
$765$	−93.8822	+	162.609i	−0.122722	+	0.212560i
$766$		0			0
$767$	−12.9893	−	22.4982i	−0.0169352	−	0.0293327i
$768$		0			0
$769$			1383.52i			1.79912i	0.436798	+	0.899560i	$0.356112\pi$
$769$			1383.52i			1.79912i	−0.436798	+	0.899560i	$0.643888\pi$
$770$		0			0
$771$	1232.22			1.59821
$772$		0			0
$773$	264.759	−	152.858i	0.342508	−	0.197747i	−0.318873	−	0.947798i	$-0.603304\pi$
$773$	264.759	−	152.858i	0.342508	−	0.197747i	0.661381	+	0.750051i	$0.269971\pi$
$774$		0			0
$775$	−103.765	−	59.9088i	−0.133890	−	0.0773016i
$776$		0			0
$777$	−258.532	−	312.572i	−0.332732	−	0.402281i
$778$		0			0
$779$	32.1225	−	55.6379i	0.0412356	−	0.0714222i
$780$		0			0
$781$	558.888	+	968.022i	0.715606	+	1.23947i
$782$		0			0
$783$			99.8885i			0.127571i
$784$		0			0
$785$	−259.432			−0.330487
$786$		0			0
$787$	−486.720	+	281.008i	−0.618450	+	0.357062i	−0.776265	−	0.630406i	$-0.782888\pi$
$787$	−486.720	+	281.008i	−0.618450	+	0.357062i	0.157815	+	0.987469i	$0.449555\pi$
$788$		0			0
$789$	−115.006	−	66.3988i	−0.145762	−	0.0841557i
$790$		0			0
$791$	286.668	−	237.107i	0.362412	−	0.299756i
$792$		0			0
$793$	−12.3175	+	21.3345i	−0.0155327	+	0.0269035i
$794$		0			0
$795$	98.0486	+	169.825i	0.123332	+	0.213617i
$796$		0			0
$797$			1187.30i			1.48971i	0.667226	+	0.744855i	$0.267482\pi$
$797$			1187.30i			1.48971i	−0.667226	+	0.744855i	$0.732518\pi$
$798$		0			0
$799$	176.224			0.220556
$800$		0			0
$801$	−322.794	+	186.365i	−0.402989	+	0.232666i
$802$		0			0
$803$	−1081.37	−	624.329i	−1.34666	−	0.777495i
$804$		0			0
$805$	179.851	−	483.464i	0.223417	−	0.600577i
$806$		0			0
$807$	595.197	−	1030.91i	0.737543	−	1.27746i
$808$		0			0
$809$	54.8294	+	94.9673i	0.0677743	+	0.117389i	0.897921	−	0.440156i	$-0.145077\pi$
$809$	54.8294	+	94.9673i	0.0677743	+	0.117389i	−0.830147	+	0.557545i	$0.811744\pi$
$810$		0			0
$811$			343.153i			0.423123i	0.977365	+	0.211561i	$0.0678549\pi$
$811$			343.153i			0.423123i	−0.977365	+	0.211561i	$0.932145\pi$
$812$		0			0
$813$	1186.04			1.45885
$814$		0			0
$815$	−368.300	+	212.638i	−0.451902	+	0.260906i
$816$		0			0
$817$	−55.6791	−	32.1464i	−0.0681507	−	0.0393468i
$818$		0			0
$819$	14.9387	−	2.52524i	0.0182402	−	0.00308332i
$820$		0			0
$821$	236.282	−	409.252i	0.287797	−	0.498480i	−0.685486	−	0.728086i	$-0.740410\pi$
$821$	236.282	−	409.252i	0.287797	−	0.498480i	0.973284	+	0.229606i	$0.0737437\pi$
$822$		0			0
$823$	−767.466	−	1329.29i	−0.932523	−	1.61518i	−0.778992	−	0.627033i	$-0.784269\pi$
$823$	−767.466	−	1329.29i	−0.932523	−	1.61518i	−0.153530	−	0.988144i	$-0.549064\pi$
$824$		0			0
$825$		−	169.118i		−	0.204991i
$826$		0			0
$827$	421.191			0.509299			0.254650	−	0.967033i	$-0.418040\pi$
$827$	421.191			0.509299			0.254650	+	0.967033i	$0.418040\pi$
$828$		0			0
$829$	−1175.23	+	678.517i	−1.41764	+	0.818477i	−0.996091	−	0.0883274i	$-0.971848\pi$
$829$	−1175.23	+	678.517i	−1.41764	+	0.818477i	−0.421552	+	0.906804i	$0.638515\pi$
$830$		0			0
$831$	642.634	+	371.025i	0.773327	+	0.446480i
$832$		0			0
$833$	−439.125	−	1261.77i	−0.527161	−	1.51472i
$834$		0			0
$835$	−290.021	+	502.332i	−0.347331	+	0.601595i
$836$		0			0
$837$	−352.167	−	609.971i	−0.420749	−	0.728758i
$838$		0			0
$839$			45.8593i			0.0546595i	0.999626	+	0.0273297i	$0.00870041\pi$
$839$			45.8593i			0.0546595i	−0.999626	+	0.0273297i	$0.991300\pi$
$840$		0			0
$841$	−829.450			−0.986267
$842$		0			0
$843$	−232.162	+	134.039i	−0.275399	+	0.159002i
$844$		0			0
$845$	326.311	+	188.396i	0.386166	+	0.222953i
$846$		0			0
$847$	84.2857	+	498.614i	0.0995108	+	0.588683i
$848$		0			0
$849$	−323.890	+	560.994i	−0.381496	+	0.660771i
$850$		0			0
$851$	−392.433	−	679.715i	−0.461144	−	0.798725i
$852$		0			0
$853$		−	713.413i		−	0.836358i	−0.908365	−	0.418179i	$-0.862668\pi$
$853$		−	713.413i		−	0.836358i	0.908365	−	0.418179i	$-0.137332\pi$
$854$		0			0
$855$	17.6256			0.0206148
$856$		0			0
$857$	149.029	−	86.0417i	0.173896	−	0.100399i	−0.410526	−	0.911849i	$-0.634655\pi$
$857$	149.029	−	86.0417i	0.173896	−	0.100399i	0.584421	+	0.811450i	$0.301322\pi$
$858$		0			0
$859$	−225.787	−	130.358i	−0.262849	−	0.151756i	0.362785	−	0.931873i	$-0.381826\pi$
$859$	−225.787	−	130.358i	−0.262849	−	0.151756i	−0.625633	+	0.780117i	$0.715159\pi$
$860$		0			0
$861$	400.702	+	149.063i	0.465391	+	0.173128i
$862$		0			0
$863$	−545.050	+	944.055i	−0.631576	+	1.09392i	0.355653	+	0.934618i	$0.384258\pi$
$863$	−545.050	+	944.055i	−0.631576	+	1.09392i	−0.987230	+	0.159304i	$0.949075\pi$
$864$		0			0
$865$	−253.268	−	438.673i	−0.292795	−	0.507136i
$866$		0			0
$867$		−	1105.60i		−	1.27520i
$868$		0			0
$869$	−1.15650			−0.00133083
$870$		0			0
$871$	−27.8301	+	16.0677i	−0.0319519	+	0.0184474i
$872$		0			0
$873$	0.965736	+	0.557568i	0.00110623	+	0.000638681i
$874$		0			0
$875$	49.8806	+	60.3069i	0.0570064	+	0.0689222i
$876$		0			0
$877$	325.559	−	563.884i	0.371219	−	0.642970i	−0.618535	−	0.785758i	$-0.712273\pi$
$877$	325.559	−	563.884i	0.371219	−	0.642970i	0.989753	+	0.142788i	$0.0456067\pi$
$878$		0			0
$879$	10.6988	+	18.5309i	0.0121716	+	0.0210819i
$880$		0			0
$881$		−	1649.45i		−	1.87225i	−0.351671	−	0.936123i	$-0.614387\pi$
$881$		−	1649.45i		−	1.87225i	0.351671	−	0.936123i	$-0.385613\pi$
$882$		0			0
$883$	1487.78			1.68492			0.842460	−	0.538759i	$-0.181107\pi$
$883$	1487.78			1.68492			0.842460	+	0.538759i	$0.181107\pi$
$884$		0			0
$885$	174.176	−	100.560i	0.196809	−	0.113628i
$886$		0			0
$887$	−133.291	−	76.9555i	−0.150271	−	0.0867592i	0.422979	−	0.906140i	$-0.360984\pi$
$887$	−133.291	−	76.9555i	−0.150271	−	0.0867592i	−0.573250	+	0.819380i	$0.694318\pi$
$888$		0			0
$889$	211.424	−	174.872i	0.237823	−	0.196706i
$890$		0			0
$891$	304.413	−	527.259i	0.341654	−	0.591761i
$892$		0			0
$893$	−8.27118	−	14.3261i	−0.00926224	−	0.0160427i
$894$		0			0
$895$			418.165i			0.467224i
$896$		0			0
$897$	−56.3520			−0.0628227
$898$		0			0
$899$	−70.5291	+	40.7200i	−0.0784528	+	0.0452948i
$900$		0			0
$901$	851.053	+	491.356i	0.944565	+	0.545345i
$902$		0			0
$903$	149.174	−	400.999i	0.165198	−	0.444074i
$904$		0			0
$905$	−204.629	+	354.427i	−0.226109	+	0.391632i
$906$		0			0
$907$	525.953	+	910.978i	0.579883	+	1.00439i	0.995492	+	0.0948429i	$0.0302349\pi$
$907$	525.953	+	910.978i	0.579883	+	1.00439i	−0.415610	+	0.909543i	$0.636432\pi$
$908$		0			0
$909$		−	494.791i		−	0.544324i
$910$		0			0
$911$	1305.28			1.43279			0.716397	−	0.697693i	$-0.245790\pi$
$911$	1305.28			1.43279			0.716397	+	0.697693i	$0.245790\pi$
$912$		0			0
$913$	1147.39	−	662.447i	1.25673	−	0.725572i
$914$		0			0
$915$	−165.167	−	95.3590i	−0.180510	−	0.104218i
$916$		0			0
$917$	373.388	−	63.1174i	0.407184	−	0.0688303i
$918$		0			0
$919$	−854.848	+	1480.64i	−0.930194	+	1.61114i	−0.147205	+	0.989106i	$0.547028\pi$
$919$	−854.848	+	1480.64i	−0.930194	+	1.61114i	−0.782988	+	0.622037i	$0.786306\pi$
$920$		0			0
$921$	−544.048	−	942.319i	−0.590714	−	1.02315i
$922$		0			0
$923$			56.5091i			0.0612233i
$924$		0			0
$925$	119.080			0.128735
$926$		0			0
$927$	382.614	−	220.902i	0.412744	−	0.238298i
$928$		0			0
$929$	−703.298	−	406.049i	−0.757048	−	0.437082i	0.0711866	−	0.997463i	$-0.477321\pi$
$929$	−703.298	−	406.049i	−0.757048	−	0.437082i	−0.828235	+	0.560381i	$0.810655\pi$
$930$		0			0
$931$	−81.9643	+	94.9201i	−0.0880390	+	0.101955i
$932$		0			0
$933$	273.784	−	474.208i	0.293445	−	0.508262i
$934$		0			0
$935$	−423.754	−	733.963i	−0.453212	−	0.784987i
$936$		0			0
$937$		−	996.727i		−	1.06374i	−0.846825	−	0.531871i	$-0.821489\pi$
$937$		−	996.727i		−	1.06374i	0.846825	−	0.531871i	$-0.178511\pi$
$938$		0			0
$939$	−817.777			−0.870902
$940$		0			0
$941$	1330.08	−	767.920i	1.41347	−	0.816068i	0.417757	−	0.908559i	$-0.362816\pi$
$941$	1330.08	−	767.920i	1.41347	−	0.816068i	0.995714	+	0.0924907i	$0.0294828\pi$
$942$		0			0
$943$	716.402	+	413.615i	0.759705	+	0.438616i
$944$		0			0
$945$	76.6800	+	453.621i	0.0811429	+	0.480022i
$946$		0			0
$947$	597.863	−	1035.53i	0.631323	−	1.09348i	−0.355959	−	0.934502i	$-0.615846\pi$
$947$	597.863	−	1035.53i	0.631323	−	1.09348i	0.987282	−	0.158981i	$-0.0508210\pi$
$948$		0			0
$949$	−31.5629	−	54.6686i	−0.0332591	−	0.0576065i
$950$		0			0
$951$		−	200.576i		−	0.210911i
$952$		0			0
$953$	770.228			0.808214			0.404107	−	0.914712i	$-0.367582\pi$
$953$	770.228			0.808214			0.404107	+	0.914712i	$0.367582\pi$
$954$		0			0
$955$	−382.514	+	220.845i	−0.400539	+	0.231251i
$956$		0			0
$957$	−99.5490	−	57.4746i	−0.104022	−	0.0600571i
$958$		0			0
$959$	542.364	+	201.762i	0.565552	+	0.210388i
$960$		0			0
$961$	−193.375	+	334.936i	−0.201223	+	0.348528i
$962$		0			0
$963$	−97.7265	−	169.267i	−0.101481	−	0.175771i
$964$		0			0
$965$			189.290i			0.196155i
$966$		0			0
$967$	628.771			0.650229			0.325114	−	0.945675i	$-0.394597\pi$
$967$	628.771			0.650229			0.325114	+	0.945675i	$0.394597\pi$
$968$		0			0
$969$	−147.044	+	84.8962i	−0.151749	+	0.0876121i
$970$		0			0
$971$	584.383	+	337.394i	0.601837	+	0.347471i	0.769764	−	0.638329i	$-0.220374\pi$
$971$	584.383	+	337.394i	0.601837	+	0.347471i	−0.167927	+	0.985799i	$0.553707\pi$
$972$		0			0
$973$	439.656	+	531.555i	0.451856	+	0.546305i
$974$		0			0
$975$	4.27487	−	7.40429i	0.00438448	−	0.00759414i
$976$		0			0
$977$	577.502	+	1000.26i	0.591098	+	1.02381i	0.994085	+	0.108605i	$0.0346385\pi$
$977$	577.502	+	1000.26i	0.591098	+	1.02381i	−0.402987	+	0.915206i	$0.632028\pi$
$978$		0			0
$979$		−	1682.39i		−	1.71847i
$980$		0			0
$981$	174.652			0.178034
$982$		0			0
$983$	−207.193	+	119.623i	−0.210776	+	0.121692i	−0.601672	−	0.798743i	$-0.705499\pi$
$983$	−207.193	+	119.623i	−0.210776	+	0.121692i	0.390896	+	0.920435i	$0.372165\pi$
$984$		0			0
$985$	−478.953	−	276.524i	−0.486247	−	0.280735i
$986$		0			0
$987$	84.8278	−	70.1621i	0.0859451	−	0.0710863i
$988$		0			0
$989$	413.922	−	716.933i	0.418525	−	0.724907i
$990$		0			0
$991$	−356.230	−	617.008i	−0.359465	−	0.622612i	0.628407	−	0.777885i	$-0.283707\pi$
$991$	−356.230	−	617.008i	−0.359465	−	0.622612i	−0.987872	+	0.155273i	$0.950374\pi$
$992$		0			0
$993$			230.574i			0.232199i
$994$		0			0
$995$	273.951			0.275327
$996$		0			0
$997$	−1208.64	+	697.807i	−1.21227	+	0.699906i	−0.963254	−	0.268592i	$-0.913442\pi$
$997$	−1208.64	+	697.807i	−1.21227	+	0.699906i	−0.249019	+	0.968499i	$0.580108\pi$
$998$		0			0
$999$	606.217	+	349.999i	0.606824	+	0.350350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.3.bx.c.481.5		12
4.3	odd	2		35.3.h.a.26.1	✓	12
7.3	odd	6	inner	560.3.bx.c.241.5		12
12.11	even	2		315.3.w.c.271.6		12
20.3	even	4		175.3.j.b.124.12		24
20.7	even	4		175.3.j.b.124.1		24
20.19	odd	2		175.3.i.d.26.6		12
28.3	even	6		35.3.h.a.31.1	yes	12
28.11	odd	6		245.3.h.c.31.1		12
28.19	even	6		245.3.d.a.146.12		12
28.23	odd	6		245.3.d.a.146.11		12
28.27	even	2		245.3.h.c.166.1		12
84.59	odd	6		315.3.w.c.136.6		12
140.3	odd	12		175.3.j.b.24.1		24
140.59	even	6		175.3.i.d.101.6		12
140.87	odd	12		175.3.j.b.24.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.h.a.26.1	✓	12	4.3	odd	2
35.3.h.a.31.1	yes	12	28.3	even	6
175.3.i.d.26.6		12	20.19	odd	2
175.3.i.d.101.6		12	140.59	even	6
175.3.j.b.24.1		24	140.3	odd	12
175.3.j.b.24.12		24	140.87	odd	12
175.3.j.b.124.1		24	20.7	even	4
175.3.j.b.124.12		24	20.3	even	4
245.3.d.a.146.11		12	28.23	odd	6
245.3.d.a.146.12		12	28.19	even	6
245.3.h.c.31.1		12	28.11	odd	6
245.3.h.c.166.1		12	28.27	even	2
315.3.w.c.136.6		12	84.59	odd	6
315.3.w.c.271.6		12	12.11	even	2
560.3.bx.c.241.5		12	7.3	odd	6	inner
560.3.bx.c.481.5		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	560.bx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.10717 - 1.21658i) q^{3} +(1.93649 + 1.11803i) q^{5} +(5.39402 - 4.46146i) q^{7} +(-1.53989 + 2.66717i) q^{9} +O(q^{10})\)	\(q+(2.10717 - 1.21658i) q^{3} +(1.93649 + 1.11803i) q^{5} +(5.39402 - 4.46146i) q^{7} +(-1.53989 + 2.66717i) q^{9} +(-6.95056 - 12.0387i) q^{11} -0.702771i q^{13} +5.44069 q^{15} +(23.6124 - 13.6326i) q^{17} +(-2.21652 - 1.27971i) q^{19} +(5.93841 - 15.9633i) q^{21} +(16.4777 - 28.5402i) q^{23} +(2.50000 + 4.33013i) q^{25} +29.3919i q^{27} +3.39850 q^{29} +(-20.7530 + 11.9818i) q^{31} +(-29.2920 - 16.9118i) q^{33} +(15.4335 - 2.60888i) q^{35} +(11.9080 - 20.6253i) q^{37} +(-0.854973 - 1.48086i) q^{39} +25.1015i q^{41} +25.1201 q^{43} +(-5.96397 + 3.44330i) q^{45} +(5.59742 + 3.23167i) q^{47} +(9.19081 - 48.1303i) q^{49} +(33.1702 - 57.4524i) q^{51} +(18.0214 + 31.2139i) q^{53} -31.0838i q^{55} -6.22744 q^{57} +(32.0135 - 18.4830i) q^{59} +(-30.3577 - 17.5270i) q^{61} +(3.59326 + 21.2569i) q^{63} +(0.785721 - 1.36091i) q^{65} +(-22.8634 - 39.6006i) q^{67} -80.1854i q^{69} -80.4090 q^{71} +(77.7901 - 44.9121i) q^{73} +(10.5359 + 6.08288i) q^{75} +(-91.2017 - 33.9274i) q^{77} +(0.0415972 - 0.0720485i) q^{79} +(21.8985 + 37.9293i) q^{81} +95.3085i q^{83} +60.9668 q^{85} +(7.16122 - 4.13453i) q^{87} +(104.811 + 60.5126i) q^{89} +(-3.13538 - 3.79076i) q^{91} +(-29.1534 + 50.4952i) q^{93} +(-2.86151 - 4.95628i) q^{95} -0.362083i q^{97} +42.8124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 2 q^{7} + 14 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 2 * q^7 + 14 * q^9	\( 12 q + 6 q^{3} + 2 q^{7} + 14 q^{9} + 14 q^{11} + 20 q^{15} + 48 q^{17} + 30 q^{19} - 84 q^{21} + 14 q^{23} + 30 q^{25} + 64 q^{29} - 132 q^{31} - 192 q^{33} - 30 q^{35} + 44 q^{37} + 24 q^{39} + 4 q^{43} - 180 q^{45} - 204 q^{47} - 24 q^{49} + 132 q^{51} + 196 q^{53} - 48 q^{57} - 72 q^{59} + 72 q^{61} - 536 q^{63} + 30 q^{65} + 138 q^{67} + 8 q^{71} - 528 q^{73} + 30 q^{75} - 176 q^{77} + 12 q^{79} - 310 q^{81} - 138 q^{87} + 204 q^{89} + 480 q^{91} + 84 q^{93} - 60 q^{95} + 44 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 2 * q^7 + 14 * q^9 + 14 * q^11 + 20 * q^15 + 48 * q^17 + 30 * q^19 - 84 * q^21 + 14 * q^23 + 30 * q^25 + 64 * q^29 - 132 * q^31 - 192 * q^33 - 30 * q^35 + 44 * q^37 + 24 * q^39 + 4 * q^43 - 180 * q^45 - 204 * q^47 - 24 * q^49 + 132 * q^51 + 196 * q^53 - 48 * q^57 - 72 * q^59 + 72 * q^61 - 536 * q^63 + 30 * q^65 + 138 * q^67 + 8 * q^71 - 528 * q^73 + 30 * q^75 - 176 * q^77 + 12 * q^79 - 310 * q^81 - 138 * q^87 + 204 * q^89 + 480 * q^91 + 84 * q^93 - 60 * q^95 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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