LMFDB - Embedded newform 650.3.f.k.499.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,3,Mod(99,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.99"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	650.f (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-12,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$17.7112171834$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} + 92x^{10} + 3284x^{8} + 58196x^{6} + 540184x^{4} + 2488032x^{2} + 4435236 $ x^12 + 92x^10 + 3284x^8 + 58196x^6 + 540184x^4 + 2488032*x^2 + 4435236
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			499.6
Root			$4.70114i$ of defining polynomial
Character	$\chi$	$=$	650.499
Dual form			650.3.f.k.99.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +4.70114i q^{3} +2.00000i q^{4} +(4.70114 - 4.70114i) q^{6} +(1.86993 - 1.86993i) q^{7} +(2.00000 - 2.00000i) q^{8} -13.1007 q^{9} +(-1.50121 - 1.50121i) q^{11} -9.40228 q^{12} +(10.1766 - 8.08933i) q^{13} -3.73986 q^{14} -4.00000 q^{16} +19.8411 q^{17} +(13.1007 + 13.1007i) q^{18} +(20.7120 - 20.7120i) q^{19} +(8.79080 + 8.79080i) q^{21} +3.00242i q^{22} +44.1807 q^{23} +(9.40228 + 9.40228i) q^{24} +(-18.2659 - 2.08724i) q^{26} -19.2781i q^{27} +(3.73986 + 3.73986i) q^{28} -24.1625 q^{29} +(-9.97901 + 9.97901i) q^{31} +(4.00000 + 4.00000i) q^{32} +(7.05740 - 7.05740i) q^{33} +(-19.8411 - 19.8411i) q^{34} -26.2015i q^{36} +(15.0444 - 15.0444i) q^{37} -41.4240 q^{38} +(38.0291 + 47.8415i) q^{39} +(-17.5307 + 17.5307i) q^{41} -17.5816i q^{42} -49.6545 q^{43} +(3.00242 - 3.00242i) q^{44} +(-44.1807 - 44.1807i) q^{46} +(11.8184 - 11.8184i) q^{47} -18.8046i q^{48} +42.0067i q^{49} +93.2758i q^{51} +(16.1787 + 20.3531i) q^{52} -17.1636i q^{53} +(-19.2781 + 19.2781i) q^{54} -7.47972i q^{56} +(97.3700 + 97.3700i) q^{57} +(24.1625 + 24.1625i) q^{58} +(18.4313 + 18.4313i) q^{59} +16.9508 q^{61} +19.9580 q^{62} +(-24.4974 + 24.4974i) q^{63} -8.00000i q^{64} -14.1148 q^{66} +(17.6595 + 17.6595i) q^{67} +39.6822i q^{68} +207.700i q^{69} +(74.4471 - 74.4471i) q^{71} +(-26.2015 + 26.2015i) q^{72} +(-11.4832 + 11.4832i) q^{73} -30.0888 q^{74} +(41.4240 + 41.4240i) q^{76} -5.61431 q^{77} +(9.81241 - 85.8706i) q^{78} -144.652 q^{79} -27.2774 q^{81} +35.0613 q^{82} +(85.5928 + 85.5928i) q^{83} +(-17.5816 + 17.5816i) q^{84} +(49.6545 + 49.6545i) q^{86} -113.591i q^{87} -6.00484 q^{88} +(103.371 + 103.371i) q^{89} +(3.90299 - 34.1560i) q^{91} +88.3615i q^{92} +(-46.9127 - 46.9127i) q^{93} -23.6367 q^{94} +(-18.8046 + 18.8046i) q^{96} +(113.064 + 113.064i) q^{97} +(42.0067 - 42.0067i) q^{98} +(19.6670 + 19.6670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 8 q^{7} + 24 q^{8} - 76 q^{9} - 16 q^{11} - 44 q^{13} + 16 q^{14} - 48 q^{16} + 32 q^{17} + 76 q^{18} + 68 q^{19} - 44 q^{21} - 16 q^{23} + 24 q^{26} - 16 q^{28} - 216 q^{29} + 64 q^{31}+ \cdots - 484 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 - 8 * q^7 + 24 * q^8 - 76 * q^9 - 16 * q^11 - 44 * q^13 + 16 * q^14 - 48 * q^16 + 32 * q^17 + 76 * q^18 + 68 * q^19 - 44 * q^21 - 16 * q^23 + 24 * q^26 - 16 * q^28 - 216 * q^29 + 64 * q^31 + 48 * q^32 - 52 * q^33 - 32 * q^34 - 28 * q^37 - 136 * q^38 - 140 * q^39 - 160 * q^43 + 32 * q^44 + 16 * q^46 - 104 * q^47 + 40 * q^52 + 96 * q^54 + 100 * q^57 + 216 * q^58 + 108 * q^59 + 88 * q^61 - 128 * q^62 - 312 * q^63 + 104 * q^66 - 240 * q^67 + 12 * q^71 - 152 * q^72 + 164 * q^73 + 56 * q^74 + 136 * q^76 - 336 * q^77 + 160 * q^78 - 392 * q^79 - 204 * q^81 + 536 * q^83 + 88 * q^84 + 160 * q^86 - 64 * q^88 + 364 * q^89 - 244 * q^91 - 236 * q^93 + 208 * q^94 - 192 * q^97 - 484 * q^98 - 484 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$			4.70114i			1.56705i	0.621362	+	0.783524i	$0.286580\pi$
$3$			4.70114i			1.56705i	−0.621362	+	0.783524i	$0.713420\pi$
$4$			2.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	4.70114	−	4.70114i	0.783524	−	0.783524i
$7$	1.86993	−	1.86993i	0.267133	−	0.267133i	−0.560811	−	0.827944i	$-0.689511\pi$
$7$	1.86993	−	1.86993i	0.267133	−	0.267133i	0.827944	+	0.560811i	$0.189511\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	−13.1007			−1.45564
$10$		0			0
$11$	−1.50121	−	1.50121i	−0.136474	−	0.136474i	0.635570	−	0.772043i	$-0.280765\pi$
$11$	−1.50121	−	1.50121i	−0.136474	−	0.136474i	−0.772043	+	0.635570i	$0.780765\pi$
$12$	−9.40228			−0.783524
$13$	10.1766	−	8.08933i	0.782813	−	0.622256i
$13$	10.1766	−	8.08933i	0.782813	−	0.622256i
$14$	−3.73986			−0.267133
$15$		0			0
$16$	−4.00000			−0.250000
$17$	19.8411			1.16712			0.583562	−	0.812069i	$-0.301659\pi$
$17$	19.8411			1.16712			0.583562	+	0.812069i	$0.301659\pi$
$18$	13.1007	+	13.1007i	0.727819	+	0.727819i
$19$	20.7120	−	20.7120i	1.09010	−	1.09010i	0.0945880	−	0.995517i	$-0.469847\pi$
$19$	20.7120	−	20.7120i	1.09010	−	1.09010i	0.995517	−	0.0945880i	$-0.0301534\pi$
$20$		0			0
$21$	8.79080	+	8.79080i	0.418610	+	0.418610i
$22$			3.00242i			0.136474i
$23$	44.1807			1.92090			0.960451	−	0.278449i	$-0.0898203\pi$
$23$	44.1807			1.92090			0.960451	+	0.278449i	$0.0898203\pi$
$24$	9.40228	+	9.40228i	0.391762	+	0.391762i
$25$		0			0
$26$	−18.2659	−	2.08724i	−0.702535	−	0.0802785i
$27$		−	19.2781i		−	0.714005i
$28$	3.73986	+	3.73986i	0.133566	+	0.133566i
$29$	−24.1625			−0.833189			−0.416595	−	0.909092i	$-0.636777\pi$
$29$	−24.1625			−0.833189			−0.416595	+	0.909092i	$0.636777\pi$
$30$		0			0
$31$	−9.97901	+	9.97901i	−0.321903	+	0.321903i	−0.849497	−	0.527594i	$-0.823094\pi$
$31$	−9.97901	+	9.97901i	−0.321903	+	0.321903i	0.527594	+	0.849497i	$0.323094\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	7.05740	−	7.05740i	0.213861	−	0.213861i
$34$	−19.8411	−	19.8411i	−0.583562	−	0.583562i
$35$		0			0
$36$		−	26.2015i		−	0.727819i
$37$	15.0444	−	15.0444i	0.406606	−	0.406606i	−0.473947	−	0.880553i	$-0.657171\pi$
$37$	15.0444	−	15.0444i	0.406606	−	0.406606i	0.880553	+	0.473947i	$0.157171\pi$
$38$	−41.4240			−1.09010
$39$	38.0291	+	47.8415i	0.975105	+	1.22671i
$40$		0			0
$41$	−17.5307	+	17.5307i	−0.427577	+	0.427577i	−0.887802	−	0.460225i	$-0.847769\pi$
$41$	−17.5307	+	17.5307i	−0.427577	+	0.427577i	0.460225	+	0.887802i	$0.347769\pi$
$42$		−	17.5816i		−	0.418610i
$43$	−49.6545			−1.15475			−0.577377	−	0.816477i	$-0.695924\pi$
$43$	−49.6545			−1.15475			−0.577377	+	0.816477i	$0.695924\pi$
$44$	3.00242	−	3.00242i	0.0682368	−	0.0682368i
$45$		0			0
$46$	−44.1807	−	44.1807i	−0.960451	−	0.960451i
$47$	11.8184	−	11.8184i	0.251455	−	0.251455i	−0.570112	−	0.821567i	$-0.693100\pi$
$47$	11.8184	−	11.8184i	0.251455	−	0.251455i	0.821567	+	0.570112i	$0.193100\pi$
$48$		−	18.8046i		−	0.391762i
$49$			42.0067i			0.857280i
$50$		0			0
$51$			93.2758i			1.82894i
$52$	16.1787	+	20.3531i	0.311128	+	0.391407i
$53$		−	17.1636i		−	0.323842i	−0.986804	−	0.161921i	$-0.948231\pi$
$53$		−	17.1636i		−	0.323842i	0.986804	−	0.161921i	$-0.0517689\pi$
$54$	−19.2781	+	19.2781i	−0.357003	+	0.357003i
$55$		0			0
$56$		−	7.47972i		−	0.133566i
$57$	97.3700	+	97.3700i	1.70825	+	1.70825i
$58$	24.1625	+	24.1625i	0.416595	+	0.416595i
$59$	18.4313	+	18.4313i	0.312395	+	0.312395i	0.845837	−	0.533442i	$-0.179102\pi$
$59$	18.4313	+	18.4313i	0.312395	+	0.312395i	−0.533442	+	0.845837i	$0.679102\pi$
$60$		0			0
$61$	16.9508			0.277882			0.138941	−	0.990301i	$-0.455630\pi$
$61$	16.9508			0.277882			0.138941	+	0.990301i	$0.455630\pi$
$62$	19.9580			0.321903
$63$	−24.4974	+	24.4974i	−0.388848	+	0.388848i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−14.1148			−0.213861
$67$	17.6595	+	17.6595i	0.263574	+	0.263574i	0.826504	−	0.562930i	$-0.190326\pi$
$67$	17.6595	+	17.6595i	0.263574	+	0.263574i	−0.562930	+	0.826504i	$0.690326\pi$
$68$			39.6822i			0.583562i
$69$			207.700i			3.01014i
$70$		0			0
$71$	74.4471	−	74.4471i	1.04855	−	1.04855i	0.0497912	−	0.998760i	$-0.484144\pi$
$71$	74.4471	−	74.4471i	1.04855	−	1.04855i	0.998760	−	0.0497912i	$-0.0158556\pi$
$72$	−26.2015	+	26.2015i	−0.363909	+	0.363909i
$73$	−11.4832	+	11.4832i	−0.157304	+	0.157304i	−0.781371	−	0.624067i	$-0.785479\pi$
$73$	−11.4832	+	11.4832i	−0.157304	+	0.157304i	0.624067	+	0.781371i	$0.285479\pi$
$74$	−30.0888			−0.406606
$75$		0			0
$76$	41.4240	+	41.4240i	0.545052	+	0.545052i
$77$	−5.61431			−0.0729132
$78$	9.81241	−	85.8706i	0.125800	−	1.10091i
$79$	−144.652			−1.83103			−0.915517	−	0.402280i	$-0.868218\pi$
$79$	−144.652			−1.83103			−0.915517	+	0.402280i	$0.868218\pi$
$80$		0			0
$81$	−27.2774			−0.336758
$82$	35.0613			0.427577
$83$	85.5928	+	85.5928i	1.03124	+	1.03124i	0.999496	+	0.0317424i	$0.0101056\pi$
$83$	85.5928	+	85.5928i	1.03124	+	1.03124i	0.0317424	+	0.999496i	$0.489894\pi$
$84$	−17.5816	+	17.5816i	−0.209305	+	0.209305i
$85$		0			0
$86$	49.6545	+	49.6545i	0.577377	+	0.577377i
$87$		−	113.591i		−	1.30565i
$88$	−6.00484			−0.0682368
$89$	103.371	+	103.371i	1.16147	+	1.16147i	0.984153	+	0.177321i	$0.0567430\pi$
$89$	103.371	+	103.371i	1.16147	+	1.16147i	0.177321	+	0.984153i	$0.443257\pi$
$90$		0			0
$91$	3.90299	−	34.1560i	0.0428900	−	0.375340i
$92$			88.3615i			0.960451i
$93$	−46.9127	−	46.9127i	−0.504438	−	0.504438i
$94$	−23.6367			−0.251455
$95$		0			0
$96$	−18.8046	+	18.8046i	−0.195881	+	0.195881i
$97$	113.064	+	113.064i	1.16560	+	1.16560i	0.983229	+	0.182375i	$0.0583785\pi$
$97$	113.064	+	113.064i	1.16560	+	1.16560i	0.182375	+	0.983229i	$0.441621\pi$
$98$	42.0067	−	42.0067i	0.428640	−	0.428640i
$99$	19.6670	+	19.6670i	0.198656	+	0.198656i
$100$		0			0
$101$		−	125.556i		−	1.24313i	−0.783364	−	0.621564i	$-0.786498\pi$
$101$		−	125.556i		−	1.24313i	0.783364	−	0.621564i	$-0.213502\pi$
$102$	93.2758	−	93.2758i	0.914469	−	0.914469i
$103$	−24.9195			−0.241937			−0.120969	−	0.992656i	$-0.538600\pi$
$103$	−24.9195			−0.241937			−0.120969	+	0.992656i	$0.538600\pi$
$104$	4.17448	−	36.5318i	0.0401392	−	0.351267i
$105$		0			0
$106$	−17.1636	+	17.1636i	−0.161921	+	0.161921i
$107$		−	158.069i		−	1.47728i	−0.674097	−	0.738642i	$-0.735467\pi$
$107$		−	158.069i		−	1.47728i	0.674097	−	0.738642i	$-0.264533\pi$
$108$	38.5563			0.357003
$109$	−8.59537	+	8.59537i	−0.0788566	+	0.0788566i	−0.745435	−	0.666578i	$-0.767758\pi$
$109$	−8.59537	+	8.59537i	−0.0788566	+	0.0788566i	0.666578	+	0.745435i	$0.267758\pi$
$110$		0			0
$111$	70.7259	+	70.7259i	0.637170	+	0.637170i
$112$	−7.47972	+	7.47972i	−0.0667832	+	0.0667832i
$113$			168.579i			1.49185i	0.666028	+	0.745927i	$0.267993\pi$
$113$			168.579i			1.49185i	−0.666028	+	0.745927i	$0.732007\pi$
$114$		−	194.740i		−	1.70825i
$115$		0			0
$116$		−	48.3250i		−	0.416595i
$117$	−133.321	+	105.976i	−1.13949	+	0.905780i
$118$		−	36.8626i		−	0.312395i
$119$	37.1014	−	37.1014i	0.311777	−	0.311777i
$120$		0			0
$121$		−	116.493i		−	0.962750i
$122$	−16.9508	−	16.9508i	−0.138941	−	0.138941i
$123$	−82.4141	−	82.4141i	−0.670034	−	0.670034i
$124$	−19.9580	−	19.9580i	−0.160952	−	0.160952i
$125$		0			0
$126$	48.9949			0.388848
$127$	−2.40010			−0.0188984			−0.00944920	−	0.999955i	$-0.503008\pi$
$127$	−2.40010			−0.0188984			−0.00944920	+	0.999955i	$0.503008\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	233.433i		−	1.80956i
$130$		0			0
$131$	54.9647			0.419578			0.209789	−	0.977747i	$-0.432722\pi$
$131$	54.9647			0.419578			0.209789	+	0.977747i	$0.432722\pi$
$132$	14.1148	+	14.1148i	0.106930	+	0.106930i
$133$		−	77.4599i		−	0.582405i
$134$		−	35.3189i		−	0.263574i
$135$		0			0
$136$	39.6822	−	39.6822i	0.291781	−	0.291781i
$137$	−6.42401	+	6.42401i	−0.0468906	+	0.0468906i	−0.730163	−	0.683273i	$-0.760556\pi$
$137$	−6.42401	+	6.42401i	−0.0468906	+	0.0468906i	0.683273	+	0.730163i	$0.260556\pi$
$138$	207.700	−	207.700i	1.50507	−	1.50507i
$139$	168.602			1.21296			0.606481	−	0.795098i	$-0.292581\pi$
$139$	168.602			1.21296			0.606481	+	0.795098i	$0.292581\pi$
$140$		0			0
$141$	55.5599	+	55.5599i	0.394041	+	0.394041i
$142$	−148.894			−1.04855
$143$	−27.4210	−	3.13339i	−0.191755	−	0.0219118i
$144$	52.4029			0.363909
$145$		0			0
$146$	22.9664			0.157304
$147$	−197.480			−1.34340
$148$	30.0888	+	30.0888i	0.203303	+	0.203303i
$149$	56.6920	−	56.6920i	0.380483	−	0.380483i	−0.490793	−	0.871276i	$-0.663293\pi$
$149$	56.6920	−	56.6920i	0.380483	−	0.380483i	0.871276	+	0.490793i	$0.163293\pi$
$150$		0			0
$151$	−94.4664	−	94.4664i	−0.625605	−	0.625605i	0.321354	−	0.946959i	$-0.395862\pi$
$151$	−94.4664	−	94.4664i	−0.625605	−	0.625605i	−0.946959	+	0.321354i	$0.895862\pi$
$152$		−	82.8479i		−	0.545052i
$153$	−259.933			−1.69891
$154$	5.61431	+	5.61431i	0.0364566	+	0.0364566i
$155$		0			0
$156$	−95.6830	+	76.0582i	−0.613353	+	0.487553i
$157$			231.256i			1.47297i	0.676455	+	0.736484i	$0.263515\pi$
$157$			231.256i			1.47297i	−0.676455	+	0.736484i	$0.736485\pi$
$158$	144.652	+	144.652i	0.915517	+	0.915517i
$159$	80.6885			0.507475
$160$		0			0
$161$	82.6149	−	82.6149i	0.513136	−	0.513136i
$162$	27.2774	+	27.2774i	0.168379	+	0.168379i
$163$	−150.313	+	150.313i	−0.922167	+	0.922167i	−0.997182	−	0.0750153i	$-0.976099\pi$
$163$	−150.313	+	150.313i	−0.922167	+	0.922167i	0.0750153	+	0.997182i	$0.476099\pi$
$164$	−35.0613	−	35.0613i	−0.213789	−	0.213789i
$165$		0			0
$166$		−	171.186i		−	1.03124i
$167$	180.532	−	180.532i	1.08103	−	1.08103i	0.0846176	−	0.996413i	$-0.473033\pi$
$167$	180.532	−	180.532i	1.08103	−	1.08103i	0.996413	−	0.0846176i	$-0.0269669\pi$
$168$	35.1632			0.209305
$169$	38.1253	−	164.643i	0.225594	−	0.974221i
$170$		0			0
$171$	−271.342	+	271.342i	−1.58680	+	1.58680i
$172$		−	99.3089i		−	0.577377i
$173$	232.945			1.34650			0.673251	−	0.739414i	$-0.264897\pi$
$173$	232.945			1.34650			0.673251	+	0.739414i	$0.264897\pi$
$174$	−113.591	+	113.591i	−0.652823	+	0.652823i
$175$		0			0
$176$	6.00484	+	6.00484i	0.0341184	+	0.0341184i
$177$	−86.6481	+	86.6481i	−0.489537	+	0.489537i
$178$		−	206.742i		−	1.16147i
$179$		−	125.287i		−	0.699926i	−0.936763	−	0.349963i	$-0.886194\pi$
$179$		−	125.287i		−	0.699926i	0.936763	−	0.349963i	$-0.113806\pi$
$180$		0			0
$181$			220.820i			1.22000i	0.792402	+	0.609999i	$0.208830\pi$
$181$			220.820i			1.22000i	−0.792402	+	0.609999i	$0.791170\pi$
$182$	−38.0589	+	30.2530i	−0.209115	+	0.166225i
$183$			79.6882i			0.435455i
$184$	88.3615	−	88.3615i	0.480226	−	0.480226i
$185$		0			0
$186$			93.8255i			0.504438i
$187$	−29.7857	−	29.7857i	−0.159282	−	0.159282i
$188$	23.6367	+	23.6367i	0.125727	+	0.125727i
$189$	−36.0488	−	36.0488i	−0.190734	−	0.190734i
$190$		0			0
$191$	−292.765			−1.53280			−0.766400	−	0.642364i	$-0.777954\pi$
$191$	−292.765			−1.53280			−0.766400	+	0.642364i	$0.777954\pi$
$192$	37.6091			0.195881
$193$	−33.9482	+	33.9482i	−0.175897	+	0.175897i	−0.789565	−	0.613667i	$-0.789694\pi$
$193$	−33.9482	+	33.9482i	−0.175897	+	0.175897i	0.613667	+	0.789565i	$0.289694\pi$
$194$		−	226.127i		−	1.16560i
$195$		0			0
$196$	−84.0135			−0.428640
$197$	113.364	+	113.364i	0.575454	+	0.575454i	0.933647	−	0.358194i	$-0.116607\pi$
$197$	113.364	+	113.364i	0.575454	+	0.575454i	−0.358194	+	0.933647i	$0.616607\pi$
$198$		−	39.3339i		−	0.198656i
$199$			98.5552i			0.495252i	0.968856	+	0.247626i	$0.0796505\pi$
$199$			98.5552i			0.495252i	−0.968856	+	0.247626i	$0.920350\pi$
$200$		0			0
$201$	−83.0197	+	83.0197i	−0.413033	+	0.413033i
$202$	−125.556	+	125.556i	−0.621564	+	0.621564i
$203$	−45.1821	+	45.1821i	−0.222572	+	0.222572i
$204$	−186.552			−0.914469
$205$		0			0
$206$	24.9195	+	24.9195i	0.120969	+	0.120969i
$207$	−578.800			−2.79614
$208$	−40.7063	+	32.3573i	−0.195703	+	0.155564i
$209$	−62.1861			−0.297541
$210$		0			0
$211$	255.221			1.20958			0.604788	−	0.796387i	$-0.293258\pi$
$211$	255.221			1.20958			0.604788	+	0.796387i	$0.293258\pi$
$212$	34.3272			0.161921
$213$	349.986	+	349.986i	1.64313	+	1.64313i
$214$	−158.069	+	158.069i	−0.738642	+	0.738642i
$215$		0			0
$216$	−38.5563	−	38.5563i	−0.178501	−	0.178501i
$217$			37.3201i			0.171982i
$218$	17.1907			0.0788566
$219$	−53.9842	−	53.9842i	−0.246503	−	0.246503i
$220$		0			0
$221$	201.914	−	160.501i	0.913640	−	0.726250i
$222$		−	141.452i		−	0.637170i
$223$	−301.837	−	301.837i	−1.35353	−	1.35353i	−0.881676	−	0.471855i	$-0.843585\pi$
$223$	−301.837	−	301.837i	−1.35353	−	1.35353i	−0.471855	−	0.881676i	$-0.656415\pi$
$224$	14.9594			0.0667832
$225$		0			0
$226$	168.579	−	168.579i	0.745927	−	0.745927i
$227$	−155.443	−	155.443i	−0.684770	−	0.684770i	0.276301	−	0.961071i	$-0.410891\pi$
$227$	−155.443	−	155.443i	−0.684770	−	0.684770i	−0.961071	+	0.276301i	$0.910891\pi$
$228$	−194.740	+	194.740i	−0.854123	+	0.854123i
$229$	20.9147	+	20.9147i	0.0913307	+	0.0913307i	0.751296	−	0.659965i	$-0.229429\pi$
$229$	20.9147	+	20.9147i	0.0913307	+	0.0913307i	−0.659965	+	0.751296i	$0.729429\pi$
$230$		0			0
$231$		−	26.3937i		−	0.114258i
$232$	−48.3250	+	48.3250i	−0.208297	+	0.208297i
$233$	−335.555			−1.44015			−0.720075	−	0.693896i	$-0.755893\pi$
$233$	−335.555			−1.44015			−0.720075	+	0.693896i	$0.755893\pi$
$234$	239.297	+	27.3444i	1.02264	+	0.116856i
$235$		0			0
$236$	−36.8626	+	36.8626i	−0.156197	+	0.156197i
$237$		−	680.028i		−	2.86932i
$238$	−74.2029			−0.311777
$239$	−156.914	+	156.914i	−0.656545	+	0.656545i	−0.954561	−	0.298016i	$-0.903675\pi$
$239$	−156.914	+	156.914i	−0.656545	+	0.656545i	0.298016	+	0.954561i	$0.403675\pi$
$240$		0			0
$241$	−105.359	−	105.359i	−0.437176	−	0.437176i	0.453885	−	0.891060i	$-0.350038\pi$
$241$	−105.359	−	105.359i	−0.437176	−	0.437176i	−0.891060	+	0.453885i	$0.850038\pi$
$242$	−116.493	+	116.493i	−0.481375	+	0.481375i
$243$		−	301.738i		−	1.24172i
$244$			33.9017i			0.138941i
$245$		0			0
$246$			164.828i			0.670034i
$247$	43.2309	−	378.323i	0.175024	−	1.53167i
$248$			39.9160i			0.160952i
$249$	−402.384	+	402.384i	−1.61600	+	1.61600i
$250$		0			0
$251$			169.558i			0.675530i	0.941231	+	0.337765i	$0.109671\pi$
$251$			169.558i			0.675530i	−0.941231	+	0.337765i	$0.890329\pi$
$252$	−48.9949	−	48.9949i	−0.194424	−	0.194424i
$253$	−66.3246	−	66.3246i	−0.262153	−	0.262153i
$254$	2.40010	+	2.40010i	0.00944920	+	0.00944920i
$255$		0			0
$256$	16.0000			0.0625000
$257$	83.4951			0.324884			0.162442	−	0.986718i	$-0.448063\pi$
$257$	83.4951			0.324884			0.162442	+	0.986718i	$0.448063\pi$
$258$	−233.433	+	233.433i	−0.904778	+	0.904778i
$259$		−	56.2640i		−	0.217235i
$260$		0			0
$261$	316.546			1.21282
$262$	−54.9647	−	54.9647i	−0.209789	−	0.209789i
$263$		−	83.7827i		−	0.318565i	−0.987233	−	0.159283i	$-0.949082\pi$
$263$		−	83.7827i		−	0.318565i	0.987233	−	0.159283i	$-0.0509181\pi$
$264$		−	28.2296i		−	0.106930i
$265$		0			0
$266$	−77.4599	+	77.4599i	−0.291203	+	0.291203i
$267$	−485.963	+	485.963i	−1.82008	+	1.82008i
$268$	−35.3189	+	35.3189i	−0.131787	+	0.131787i
$269$	112.184			0.417040			0.208520	−	0.978018i	$-0.433135\pi$
$269$	112.184			0.417040			0.208520	+	0.978018i	$0.433135\pi$
$270$		0			0
$271$	−268.430	−	268.430i	−0.990517	−	0.990517i	0.00943804	−	0.999955i	$-0.496996\pi$
$271$	−268.430	−	268.430i	−0.990517	−	0.990517i	−0.999955	+	0.00943804i	$0.996996\pi$
$272$	−79.3644			−0.291781
$273$	160.572	+	18.3485i	0.588176	+	0.0672107i
$274$	12.8480			0.0468906
$275$		0			0
$276$	−415.400			−1.50507
$277$	278.287			1.00465			0.502324	−	0.864680i	$-0.332479\pi$
$277$	278.287			1.00465			0.502324	+	0.864680i	$0.332479\pi$
$278$	−168.602	−	168.602i	−0.606481	−	0.606481i
$279$	130.732	−	130.732i	0.468575	−	0.468575i
$280$		0			0
$281$	175.880	+	175.880i	0.625907	+	0.625907i	0.947036	−	0.321129i	$-0.104062\pi$
$281$	175.880	+	175.880i	0.625907	+	0.625907i	−0.321129	+	0.947036i	$0.604062\pi$
$282$		−	111.120i		−	0.394041i
$283$	−465.647			−1.64539			−0.822697	−	0.568480i	$-0.807532\pi$
$283$	−465.647			−1.64539			−0.822697	+	0.568480i	$0.807532\pi$
$284$	148.894	+	148.894i	0.524275	+	0.524275i
$285$		0			0
$286$	24.2876	+	30.5544i	0.0849216	+	0.106833i
$287$			65.5622i			0.228440i
$288$	−52.4029	−	52.4029i	−0.181955	−	0.181955i
$289$	104.669			0.362177
$290$		0			0
$291$	−531.528	+	531.528i	−1.82656	+	1.82656i
$292$	−22.9664	−	22.9664i	−0.0786522	−	0.0786522i
$293$	241.334	−	241.334i	0.823667	−	0.823667i	−0.162965	−	0.986632i	$-0.552106\pi$
$293$	241.334	−	241.334i	0.823667	−	0.823667i	0.986632	+	0.162965i	$0.0521057\pi$
$294$	197.480	+	197.480i	0.671699	+	0.671699i
$295$		0			0
$296$		−	60.1776i		−	0.203303i
$297$	−28.9405	+	28.9405i	−0.0974429	+	0.0974429i
$298$	−113.384			−0.380483
$299$	449.609	−	357.393i	1.50371	−	1.19529i
$300$		0			0
$301$	−92.8503	+	92.8503i	−0.308473	+	0.308473i
$302$			188.933i			0.625605i
$303$	590.256			1.94804
$304$	−82.8479	+	82.8479i	−0.272526	+	0.272526i
$305$		0			0
$306$	259.933	+	259.933i	0.849454	+	0.849454i
$307$	280.203	−	280.203i	0.912715	−	0.912715i	−0.0837701	−	0.996485i	$-0.526696\pi$
$307$	280.203	−	280.203i	0.912715	−	0.912715i	0.996485	+	0.0837701i	$0.0266961\pi$
$308$		−	11.2286i		−	0.0364566i
$309$		−	117.150i		−	0.379127i
$310$		0			0
$311$			13.7375i			0.0441719i	0.999756	+	0.0220859i	$0.00703075\pi$
$311$			13.7375i			0.0441719i	−0.999756	+	0.0220859i	$0.992969\pi$
$312$	171.741	+	19.6248i	0.550453	+	0.0629001i
$313$		−	84.5828i		−	0.270233i	−0.990830	−	0.135116i	$-0.956859\pi$
$313$		−	84.5828i		−	0.270233i	0.990830	−	0.135116i	$-0.0431408\pi$
$314$	231.256	−	231.256i	0.736484	−	0.736484i
$315$		0			0
$316$		−	289.303i		−	0.915517i
$317$	438.576	+	438.576i	1.38352	+	1.38352i	0.838282	+	0.545237i	$0.183560\pi$
$317$	438.576	+	438.576i	1.38352	+	1.38352i	0.545237	+	0.838282i	$0.316440\pi$
$318$	−80.6885	−	80.6885i	−0.253737	−	0.253737i
$319$	36.2730	+	36.2730i	0.113708	+	0.113708i
$320$		0			0
$321$	743.107			2.31498
$322$	−165.230			−0.513136
$323$	410.948	−	410.948i	1.27229	−	1.27229i
$324$		−	54.5547i		−	0.168379i
$325$		0			0
$326$	300.626			0.922167
$327$	−40.4081	−	40.4081i	−0.123572	−	0.123572i
$328$			70.1226i			0.213789i
$329$		−	44.1990i		−	0.134344i
$330$		0			0
$331$	21.7454	−	21.7454i	0.0656962	−	0.0656962i	−0.673495	−	0.739191i	$-0.735208\pi$
$331$	21.7454	−	21.7454i	0.0656962	−	0.0656962i	0.739191	+	0.673495i	$0.235208\pi$
$332$	−171.186	+	171.186i	−0.515619	+	0.515619i
$333$	−197.093	+	197.093i	−0.591870	+	0.591870i
$334$	−361.064			−1.08103
$335$		0			0
$336$	−35.1632	−	35.1632i	−0.104652	−	0.104652i
$337$	−364.125			−1.08049			−0.540245	−	0.841508i	$-0.681669\pi$
$337$	−364.125			−1.08049			−0.540245	+	0.841508i	$0.681669\pi$
$338$	−202.769	+	126.518i	−0.599908	+	0.374314i
$339$	−792.516			−2.33780
$340$		0			0
$341$	29.9612			0.0878627
$342$	542.684			1.58680
$343$	170.176	+	170.176i	0.496140	+	0.496140i
$344$	−99.3089	+	99.3089i	−0.288689	+	0.288689i
$345$		0			0
$346$	−232.945	−	232.945i	−0.673251	−	0.673251i
$347$			185.153i			0.533582i	0.963754	+	0.266791i	$0.0859634\pi$
$347$			185.153i			0.533582i	−0.963754	+	0.266791i	$0.914037\pi$
$348$	227.183			0.652823
$349$	−139.886	−	139.886i	−0.400820	−	0.400820i	0.477702	−	0.878522i	$-0.341470\pi$
$349$	−139.886	−	139.886i	−0.400820	−	0.400820i	−0.878522	+	0.477702i	$0.841470\pi$
$350$		0			0
$351$	−155.947	−	196.185i	−0.444294	−	0.558933i
$352$		−	12.0097i		−	0.0341184i
$353$	193.983	+	193.983i	0.549528	+	0.549528i	0.926304	−	0.376776i	$-0.122967\pi$
$353$	193.983	+	193.983i	0.549528	+	0.549528i	−0.376776	+	0.926304i	$0.622967\pi$
$354$	173.296			0.489537
$355$		0			0
$356$	−206.742	+	206.742i	−0.580737	+	0.580737i
$357$	174.419	+	174.419i	0.488569	+	0.488569i
$358$	−125.287	+	125.287i	−0.349963	+	0.349963i
$359$	108.050	+	108.050i	0.300975	+	0.300975i	0.841395	−	0.540420i	$-0.181735\pi$
$359$	108.050	+	108.050i	0.300975	+	0.300975i	−0.540420	+	0.841395i	$0.681735\pi$
$360$		0			0
$361$		−	496.973i		−	1.37666i
$362$	220.820	−	220.820i	0.609999	−	0.609999i
$363$	547.649			1.50867
$364$	68.3119	+	7.80598i	0.187670	+	0.0214450i
$365$		0			0
$366$	79.6882	−	79.6882i	0.217727	−	0.217727i
$367$			35.1926i			0.0958927i	0.998850	+	0.0479464i	$0.0152677\pi$
$367$			35.1926i			0.0958927i	−0.998850	+	0.0479464i	$0.984732\pi$
$368$	−176.723			−0.480226
$369$	229.665	−	229.665i	0.622397	−	0.622397i
$370$		0			0
$371$	−32.0947	−	32.0947i	−0.0865087	−	0.0865087i
$372$	93.8255	−	93.8255i	0.252219	−	0.252219i
$373$		−	666.073i		−	1.78572i	−0.450337	−	0.892859i	$-0.648696\pi$
$373$		−	666.073i		−	1.78572i	0.450337	−	0.892859i	$-0.351304\pi$
$374$			59.5713i			0.159282i
$375$		0			0
$376$		−	47.2735i		−	0.125727i
$377$	−245.891	+	195.458i	−0.652232	+	0.518457i
$378$			72.0975i			0.190734i
$379$	−263.815	+	263.815i	−0.696081	+	0.696081i	−0.963563	−	0.267482i	$-0.913808\pi$
$379$	−263.815	+	263.815i	−0.696081	+	0.696081i	0.267482	+	0.963563i	$0.413808\pi$
$380$		0			0
$381$		−	11.2832i		−	0.0296147i
$382$	292.765	+	292.765i	0.766400	+	0.766400i
$383$	350.886	+	350.886i	0.916151	+	0.916151i	0.996747	−	0.0805958i	$-0.0256823\pi$
$383$	350.886	+	350.886i	0.916151	+	0.916151i	−0.0805958	+	0.996747i	$0.525682\pi$
$384$	−37.6091	−	37.6091i	−0.0979405	−	0.0979405i
$385$		0			0
$386$	67.8964			0.175897
$387$	650.510			1.68090
$388$	−226.127	+	226.127i	−0.582802	+	0.582802i
$389$		−	563.670i		−	1.44902i	−0.689262	−	0.724512i	$-0.742065\pi$
$389$		−	563.670i		−	1.44902i	0.689262	−	0.724512i	$-0.257935\pi$
$390$		0			0
$391$	876.594			2.24193
$392$	84.0135	+	84.0135i	0.214320	+	0.214320i
$393$			258.397i			0.657499i
$394$		−	226.729i		−	0.575454i
$395$		0			0
$396$	−39.3339	+	39.3339i	−0.0993281	+	0.0993281i
$397$	−76.5969	+	76.5969i	−0.192939	+	0.192939i	−0.796965	−	0.604026i	$-0.793562\pi$
$397$	−76.5969	+	76.5969i	−0.192939	+	0.192939i	0.604026	+	0.796965i	$0.293562\pi$
$398$	98.5552	−	98.5552i	0.247626	−	0.247626i
$399$	364.150			0.912657
$400$		0			0
$401$	−484.409	−	484.409i	−1.20800	−	1.20800i	−0.971673	−	0.236329i	$-0.924056\pi$
$401$	−484.409	−	484.409i	−1.20800	−	1.20800i	−0.236329	−	0.971673i	$-0.575944\pi$
$402$	166.039			0.413033
$403$	−20.8286	+	182.276i	−0.0516838	+	0.452297i
$404$	251.112			0.621564
$405$		0			0
$406$	90.3643			0.222572
$407$	−45.1696			−0.110982
$408$	186.552	+	186.552i	0.457234	+	0.457234i
$409$	−309.379	+	309.379i	−0.756428	+	0.756428i	−0.975670	−	0.219242i	$-0.929641\pi$
$409$	−309.379	+	309.379i	−0.756428	+	0.756428i	0.219242	+	0.975670i	$0.429641\pi$
$410$		0			0
$411$	−30.2002	−	30.2002i	−0.0734798	−	0.0734798i
$412$		−	49.8391i		−	0.120969i
$413$	68.9304			0.166902
$414$	578.800	+	578.800i	1.39807	+	1.39807i
$415$		0			0
$416$	73.0636	+	8.34896i	0.175634	+	0.0200696i
$417$			792.620i			1.90077i
$418$	62.1861	+	62.1861i	0.148771	+	0.148771i
$419$	−147.503			−0.352037			−0.176018	−	0.984387i	$-0.556322\pi$
$419$	−147.503			−0.352037			−0.176018	+	0.984387i	$0.556322\pi$
$420$		0			0
$421$	157.123	−	157.123i	0.373215	−	0.373215i	−0.495432	−	0.868647i	$-0.664990\pi$
$421$	157.123	−	157.123i	0.373215	−	0.373215i	0.868647	+	0.495432i	$0.164990\pi$
$422$	−255.221	−	255.221i	−0.604788	−	0.604788i
$423$	−154.829	+	154.829i	−0.366027	+	0.366027i
$424$	−34.3272	−	34.3272i	−0.0809604	−	0.0809604i
$425$		0			0
$426$		−	699.973i		−	1.64313i
$427$	31.6968	−	31.6968i	0.0742315	−	0.0742315i
$428$	316.139			0.738642
$429$	14.7305	−	128.910i	0.0343368	−	0.300489i
$430$		0			0
$431$	−102.789	+	102.789i	−0.238491	+	0.238491i	−0.816225	−	0.577734i	$-0.803937\pi$
$431$	−102.789	+	102.789i	−0.238491	+	0.238491i	0.577734	+	0.816225i	$0.303937\pi$
$432$			77.1125i			0.178501i
$433$	−423.761			−0.978663			−0.489332	−	0.872098i	$-0.662759\pi$
$433$	−423.761			−0.978663			−0.489332	+	0.872098i	$0.662759\pi$
$434$	37.3201	−	37.3201i	0.0859910	−	0.0859910i
$435$		0			0
$436$	−17.1907	−	17.1907i	−0.0394283	−	0.0394283i
$437$	915.071	−	915.071i	2.09398	−	2.09398i
$438$			107.968i			0.246503i
$439$			175.599i			0.399998i	0.979796	+	0.199999i	$0.0640939\pi$
$439$			175.599i			0.399998i	−0.979796	+	0.199999i	$0.935906\pi$
$440$		0			0
$441$		−	550.319i		−	1.24789i
$442$	−362.416	−	41.4131i	−0.819945	−	0.0936949i
$443$		−	97.0515i		−	0.219078i	−0.993983	−	0.109539i	$-0.965063\pi$
$443$		−	97.0515i		−	0.219078i	0.993983	−	0.109539i	$-0.0349374\pi$
$444$	−141.452	+	141.452i	−0.318585	+	0.318585i
$445$		0			0
$446$			603.675i			1.35353i
$447$	266.517	+	266.517i	0.596235	+	0.596235i
$448$	−14.9594	−	14.9594i	−0.0333916	−	0.0333916i
$449$	284.200	+	284.200i	0.632962	+	0.632962i	0.948810	−	0.315848i	$-0.102289\pi$
$449$	284.200	+	284.200i	0.632962	+	0.632962i	−0.315848	+	0.948810i	$0.602289\pi$
$450$		0			0
$451$	52.6344			0.116706
$452$	−337.159			−0.745927
$453$	444.100	−	444.100i	0.980353	−	0.980353i
$454$			310.886i			0.684770i
$455$		0			0
$456$	389.480			0.854123
$457$	−285.388	−	285.388i	−0.624482	−	0.624482i	0.322192	−	0.946674i	$-0.395580\pi$
$457$	−285.388	−	285.388i	−0.624482	−	0.624482i	−0.946674	+	0.322192i	$0.895580\pi$
$458$		−	41.8295i		−	0.0913307i
$459$		−	382.499i		−	0.833332i
$460$		0			0
$461$	−197.058	+	197.058i	−0.427458	+	0.427458i	−0.887762	−	0.460303i	$-0.847741\pi$
$461$	−197.058	+	197.058i	−0.427458	+	0.427458i	0.460303	+	0.887762i	$0.347741\pi$
$462$	−26.3937	+	26.3937i	−0.0571292	+	0.0571292i
$463$	120.626	−	120.626i	0.260531	−	0.260531i	−0.564738	−	0.825270i	$-0.691023\pi$
$463$	120.626	−	120.626i	0.260531	−	0.260531i	0.825270	+	0.564738i	$0.191023\pi$
$464$	96.6499			0.208297
$465$		0			0
$466$	335.555	+	335.555i	0.720075	+	0.720075i
$467$	537.485			1.15093			0.575466	−	0.817826i	$-0.304821\pi$
$467$	537.485			1.15093			0.575466	+	0.817826i	$0.304821\pi$
$468$	−211.952	−	266.641i	−0.452890	−	0.569746i
$469$	66.0439			0.140819
$470$		0			0
$471$	−1087.17			−2.30821
$472$	73.7251			0.156197
$473$	74.5418	+	74.5418i	0.157594	+	0.157594i
$474$	−680.028	+	680.028i	−1.43466	+	1.43466i
$475$		0			0
$476$	74.2029	+	74.2029i	0.155888	+	0.155888i
$477$			224.856i			0.471396i
$478$	313.829			0.656545
$479$	−144.980	−	144.980i	−0.302672	−	0.302672i	0.539387	−	0.842058i	$-0.318656\pi$
$479$	−144.980	−	144.980i	−0.302672	−	0.302672i	−0.842058	+	0.539387i	$0.818656\pi$
$480$		0			0
$481$	31.4013	−	274.800i	0.0652834	−	0.571309i
$482$			210.719i			0.437176i
$483$	388.384	+	388.384i	0.804108	+	0.804108i
$484$	232.985			0.481375
$485$		0			0
$486$	−301.738	+	301.738i	−0.620860	+	0.620860i
$487$	−661.857	−	661.857i	−1.35905	−	1.35905i	−0.875091	−	0.483958i	$-0.839199\pi$
$487$	−661.857	−	661.857i	−1.35905	−	1.35905i	−0.483958	−	0.875091i	$-0.660801\pi$
$488$	33.9017	−	33.9017i	0.0694706	−	0.0694706i
$489$	−706.644	−	706.644i	−1.44508	−	1.44508i
$490$		0			0
$491$		−	53.9981i		−	0.109976i	−0.998487	−	0.0549879i	$-0.982488\pi$
$491$		−	53.9981i		−	0.109976i	0.998487	−	0.0549879i	$-0.0175120\pi$
$492$	164.828	−	164.828i	0.335017	−	0.335017i
$493$	−479.410			−0.972434
$494$	−421.554	+	335.092i	−0.853348	+	0.678325i
$495$		0			0
$496$	39.9160	−	39.9160i	0.0804759	−	0.0804759i
$497$		−	278.422i		−	0.560205i
$498$	804.768			1.61600
$499$	−403.192	+	403.192i	−0.808001	+	0.808001i	−0.984331	−	0.176330i	$-0.943577\pi$
$499$	−403.192	+	403.192i	−0.808001	+	0.808001i	0.176330	+	0.984331i	$0.443577\pi$
$500$		0			0
$501$	848.707	+	848.707i	1.69403	+	1.69403i
$502$	169.558	−	169.558i	0.337765	−	0.337765i
$503$			624.707i			1.24196i	0.783825	+	0.620981i	$0.213266\pi$
$503$			624.707i			1.24196i	−0.783825	+	0.620981i	$0.786734\pi$
$504$			97.9898i			0.194424i
$505$		0			0
$506$			132.649i			0.262153i
$507$	774.012	+	179.233i	1.52665	+	0.353516i
$508$		−	4.80019i		−	0.00944920i
$509$	−61.2684	+	61.2684i	−0.120370	+	0.120370i	−0.764726	−	0.644356i	$-0.777126\pi$
$509$	−61.2684	+	61.2684i	−0.120370	+	0.120370i	0.644356	+	0.764726i	$0.277126\pi$
$510$		0			0
$511$			42.9456i			0.0840423i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−399.288	−	399.288i	−0.778340	−	0.778340i
$514$	−83.4951	−	83.4951i	−0.162442	−	0.162442i
$515$		0			0
$516$	466.865			0.904778
$517$	−35.4837			−0.0686339
$518$	−56.2640	+	56.2640i	−0.108618	+	0.108618i
$519$			1095.11i			2.11003i
$520$		0			0
$521$	−481.059			−0.923337			−0.461669	−	0.887052i	$-0.652749\pi$
$521$	−481.059			−0.923337			−0.461669	+	0.887052i	$0.652749\pi$
$522$	−316.546	−	316.546i	−0.606411	−	0.606411i
$523$		−	345.672i		−	0.660942i	−0.943816	−	0.330471i	$-0.892792\pi$
$523$		−	345.672i		−	0.660942i	0.943816	−	0.330471i	$-0.107208\pi$
$524$			109.929i			0.209789i
$525$		0			0
$526$	−83.7827	+	83.7827i	−0.159283	+	0.159283i
$527$	−197.994	+	197.994i	−0.375701	+	0.375701i
$528$	−28.2296	+	28.2296i	−0.0534652	+	0.0534652i
$529$	1422.94			2.68986
$530$		0			0
$531$	−241.463	−	241.463i	−0.454733	−	0.454733i
$532$	154.920			0.291203
$533$	−36.5907	+	320.213i	−0.0686505	+	0.600776i
$534$	971.925			1.82008
$535$		0			0
$536$	70.6379			0.131787
$537$	588.991			1.09682
$538$	−112.184	−	112.184i	−0.208520	−	0.208520i
$539$	63.0609	−	63.0609i	0.116996	−	0.116996i
$540$		0			0
$541$	79.8003	+	79.8003i	0.147505	+	0.147505i	0.777003	−	0.629497i	$-0.216739\pi$
$541$	79.8003	+	79.8003i	0.147505	+	0.147505i	−0.629497	+	0.777003i	$0.716739\pi$
$542$			536.860i			0.990517i
$543$	−1038.10			−1.91179
$544$	79.3644	+	79.3644i	0.145890	+	0.145890i
$545$		0			0
$546$	−142.223	−	178.921i	−0.260483	−	0.327693i
$547$			411.476i			0.752241i	0.926571	+	0.376120i	$0.122742\pi$
$547$			411.476i			0.752241i	−0.926571	+	0.376120i	$0.877258\pi$
$548$	−12.8480	−	12.8480i	−0.0234453	−	0.0234453i
$549$	−222.068			−0.404496
$550$		0			0
$551$	−500.453	+	500.453i	−0.908263	+	0.908263i
$552$	415.400	+	415.400i	0.752536	+	0.752536i
$553$	−270.488	+	270.488i	−0.489129	+	0.489129i
$554$	−278.287	−	278.287i	−0.502324	−	0.502324i
$555$		0			0
$556$			337.203i			0.606481i
$557$	−446.024	+	446.024i	−0.800761	+	0.800761i	−0.983214	−	0.182454i	$-0.941596\pi$
$557$	−446.024	+	446.024i	−0.800761	+	0.800761i	0.182454	+	0.983214i	$0.441596\pi$
$558$	−261.465			−0.468575
$559$	−505.312	+	401.672i	−0.903958	+	0.718554i
$560$		0			0
$561$	140.027	−	140.027i	0.249602	−	0.249602i
$562$		−	351.760i		−	0.625907i
$563$	−628.339			−1.11606			−0.558028	−	0.829822i	$-0.688442\pi$
$563$	−628.339			−1.11606			−0.558028	+	0.829822i	$0.688442\pi$
$564$	−111.120	+	111.120i	−0.197021	+	0.197021i
$565$		0			0
$566$	465.647	+	465.647i	0.822697	+	0.822697i
$567$	−51.0067	+	51.0067i	−0.0899590	+	0.0899590i
$568$		−	297.788i		−	0.524275i
$569$			808.201i			1.42039i	0.704006	+	0.710194i	$0.251393\pi$
$569$			808.201i			1.42039i	−0.704006	+	0.710194i	$0.748607\pi$
$570$		0			0
$571$		−	317.754i		−	0.556487i	−0.960511	−	0.278244i	$-0.910248\pi$
$571$		−	317.754i		−	0.556487i	0.960511	−	0.278244i	$-0.0897523\pi$
$572$	6.26677	−	54.8419i	0.0109559	−	0.0958775i
$573$		−	1376.33i		−	2.40197i
$574$	65.5622	−	65.5622i	0.114220	−	0.114220i
$575$		0			0
$576$			104.806i			0.181955i
$577$	−610.160	−	610.160i	−1.05747	−	1.05747i	−0.998245	−	0.0592249i	$-0.981137\pi$
$577$	−610.160	−	610.160i	−1.05747	−	1.05747i	−0.0592249	−	0.998245i	$-0.518863\pi$
$578$	−104.669	−	104.669i	−0.181088	−	0.181088i
$579$	−159.595	−	159.595i	−0.275639	−	0.275639i
$580$		0			0
$581$	320.105			0.550955
$582$	1063.06			1.82656
$583$	−25.7662	+	25.7662i	−0.0441958	+	0.0441958i
$584$			45.9329i			0.0786522i
$585$		0			0
$586$	−482.669			−0.823667
$587$	−126.380	−	126.380i	−0.215299	−	0.215299i	0.591215	−	0.806514i	$-0.298648\pi$
$587$	−126.380	−	126.380i	−0.215299	−	0.215299i	−0.806514	+	0.591215i	$0.798648\pi$
$588$		−	394.959i		−	0.671699i
$589$			413.370i			0.701817i
$590$		0			0
$591$	−532.942	+	532.942i	−0.901763	+	0.901763i
$592$	−60.1776	+	60.1776i	−0.101651	+	0.101651i
$593$	357.867	−	357.867i	0.603486	−	0.603486i	−0.337750	−	0.941236i	$-0.609666\pi$
$593$	357.867	−	357.867i	0.603486	−	0.603486i	0.941236	+	0.337750i	$0.109666\pi$
$594$	57.8811			0.0974429
$595$		0			0
$596$	113.384	+	113.384i	0.190241	+	0.190241i
$597$	−463.322			−0.776084
$598$	−807.002	−	92.2158i	−1.34950	−	0.154207i
$599$	−388.454			−0.648505			−0.324252	−	0.945971i	$-0.605113\pi$
$599$	−388.454			−0.648505			−0.324252	+	0.945971i	$0.605113\pi$
$600$		0			0
$601$	−761.564			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$601$	−761.564			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$602$	185.701			0.308473
$603$	−231.352	−	231.352i	−0.383668	−	0.383668i
$604$	188.933	−	188.933i	0.312803	−	0.312803i
$605$		0			0
$606$	−590.256	−	590.256i	−0.974020	−	0.974020i
$607$			674.936i			1.11192i	0.831209	+	0.555961i	$0.187649\pi$
$607$			674.936i			1.11192i	−0.831209	+	0.555961i	$0.812351\pi$
$608$	165.696			0.272526
$609$	−212.408	−	212.408i	−0.348781	−	0.348781i
$610$		0			0
$611$	24.6678	−	215.873i	0.0403728	−	0.353312i
$612$		−	519.866i		−	0.849454i
$613$	498.707	+	498.707i	0.813552	+	0.813552i	0.985165	−	0.171613i	$-0.0548977\pi$
$613$	498.707	+	498.707i	0.813552	+	0.813552i	−0.171613	+	0.985165i	$0.554898\pi$
$614$	−560.407			−0.912715
$615$		0			0
$616$	−11.2286	+	11.2286i	−0.0182283	+	0.0182283i
$617$	52.0030	+	52.0030i	0.0842836	+	0.0842836i	0.747992	−	0.663708i	$-0.231018\pi$
$617$	52.0030	+	52.0030i	0.0842836	+	0.0842836i	−0.663708	+	0.747992i	$0.731018\pi$
$618$	−117.150	+	117.150i	−0.189563	+	0.189563i
$619$	−95.1831	−	95.1831i	−0.153769	−	0.153769i	0.626030	−	0.779799i	$-0.284679\pi$
$619$	−95.1831	−	95.1831i	−0.153769	−	0.153769i	−0.779799	+	0.626030i	$0.784679\pi$
$620$		0			0
$621$		−	851.722i		−	1.37153i
$622$	13.7375	−	13.7375i	0.0220859	−	0.0220859i
$623$	386.594			0.620535
$624$	−152.116	−	191.366i	−0.243776	−	0.306676i
$625$		0			0
$626$	−84.5828	+	84.5828i	−0.135116	+	0.135116i
$627$		−	292.346i		−	0.466261i
$628$	−462.512			−0.736484
$629$	298.498	−	298.498i	0.474559	−	0.474559i
$630$		0			0
$631$	477.880	+	477.880i	0.757337	+	0.757337i	0.975837	−	0.218500i	$-0.0701163\pi$
$631$	477.880	+	477.880i	0.757337	+	0.757337i	−0.218500	+	0.975837i	$0.570116\pi$
$632$	−289.303	+	289.303i	−0.457758	+	0.457758i
$633$			1199.83i			1.89546i
$634$		−	877.151i		−	1.38352i
$635$		0			0
$636$			161.377i			0.253737i
$637$	339.806	+	427.485i	0.533448	+	0.671090i
$638$		−	72.5459i		−	0.113708i
$639$	−975.312	+	975.312i	−1.52631	+	1.52631i
$640$		0			0
$641$			104.344i			0.162783i	0.996682	+	0.0813916i	$0.0259364\pi$
$641$			104.344i			0.162783i	−0.996682	+	0.0813916i	$0.974064\pi$
$642$	−743.107	−	743.107i	−1.15749	−	1.15749i
$643$	208.375	+	208.375i	0.324066	+	0.324066i	0.850325	−	0.526258i	$-0.176405\pi$
$643$	208.375	+	208.375i	0.324066	+	0.324066i	−0.526258	+	0.850325i	$0.676405\pi$
$644$	165.230	+	165.230i	0.256568	+	0.256568i
$645$		0			0
$646$	−821.897			−1.27229
$647$	31.5847			0.0488171			0.0244085	−	0.999702i	$-0.492230\pi$
$647$	31.5847			0.0488171			0.0244085	+	0.999702i	$0.492230\pi$
$648$	−54.5547	+	54.5547i	−0.0841894	+	0.0841894i
$649$		−	55.3385i		−	0.0852673i
$650$		0			0
$651$	−175.447			−0.269504
$652$	−300.626	−	300.626i	−0.461084	−	0.461084i
$653$		−	468.398i		−	0.717302i	−0.933472	−	0.358651i	$-0.883237\pi$
$653$		−	468.398i		−	0.717302i	0.933472	−	0.358651i	$-0.116763\pi$
$654$			80.8161i			0.123572i
$655$		0			0
$656$	70.1226	−	70.1226i	0.106894	−	0.106894i
$657$	150.439	−	150.439i	0.228978	−	0.228978i
$658$	−44.1990	+	44.1990i	−0.0671718	+	0.0671718i
$659$	−252.033			−0.382447			−0.191224	−	0.981546i	$-0.561246\pi$
$659$	−252.033			−0.382447			−0.191224	+	0.981546i	$0.561246\pi$
$660$		0			0
$661$	93.5969	+	93.5969i	0.141599	+	0.141599i	0.774353	−	0.632754i	$-0.218076\pi$
$661$	93.5969	+	93.5969i	0.141599	+	0.141599i	−0.632754	+	0.774353i	$0.718076\pi$
$662$	−43.4909			−0.0656962
$663$	754.539	+	949.228i	1.13807	+	1.43172i
$664$	342.371			0.515619
$665$		0			0
$666$	394.186			0.591870
$667$	−1067.52			−1.60047
$668$	361.064	+	361.064i	0.540516	+	0.540516i
$669$	1418.98	−	1418.98i	2.12105	−	2.12105i
$670$		0			0
$671$	−25.4468	−	25.4468i	−0.0379236	−	0.0379236i
$672$			70.3264i			0.104652i
$673$	41.0765			0.0610348			0.0305174	−	0.999534i	$-0.490284\pi$
$673$	41.0765			0.0610348			0.0305174	+	0.999534i	$0.490284\pi$
$674$	364.125	+	364.125i	0.540245	+	0.540245i
$675$		0			0
$676$	329.287	+	76.2507i	0.487111	+	0.112797i
$677$		−	980.144i		−	1.44778i	−0.689918	−	0.723888i	$-0.742353\pi$
$677$		−	980.144i		−	1.44778i	0.689918	−	0.723888i	$-0.257647\pi$
$678$	792.516	+	792.516i	1.16890	+	1.16890i
$679$	422.842			0.622742
$680$		0			0
$681$	730.759	−	730.759i	1.07307	−	1.07307i
$682$	−29.9612	−	29.9612i	−0.0439313	−	0.0439313i
$683$	351.524	−	351.524i	0.514676	−	0.514676i	−0.401279	−	0.915956i	$-0.631434\pi$
$683$	351.524	−	351.524i	0.514676	−	0.514676i	0.915956	+	0.401279i	$0.131434\pi$
$684$	−542.684	−	542.684i	−0.793398	−	0.793398i
$685$		0			0
$686$		−	340.352i		−	0.496140i
$687$	−98.3231	+	98.3231i	−0.143120	+	0.143120i
$688$	198.618			0.288689
$689$	−138.842	−	174.667i	−0.201512	−	0.253507i
$690$		0			0
$691$	−612.276	+	612.276i	−0.886072	+	0.886072i	−0.994143	−	0.108071i	$-0.965533\pi$
$691$	−612.276	+	612.276i	−0.886072	+	0.886072i	0.108071	+	0.994143i	$0.465533\pi$
$692$			465.890i			0.673251i
$693$	73.5516			0.106135
$694$	185.153	−	185.153i	0.266791	−	0.266791i
$695$		0			0
$696$	−227.183	−	227.183i	−0.326412	−	0.326412i
$697$	−347.828	+	347.828i	−0.499035	+	0.499035i
$698$			279.772i			0.400820i
$699$		−	1577.49i		−	2.25678i
$700$		0			0
$701$			1039.77i			1.48327i	0.670804	+	0.741635i	$0.265949\pi$
$701$			1039.77i			1.48327i	−0.670804	+	0.741635i	$0.734051\pi$
$702$	−40.2381	+	352.133i	−0.0573192	+	0.501614i
$703$		−	623.199i		−	0.886485i
$704$	−12.0097	+	12.0097i	−0.0170592	+	0.0170592i
$705$		0			0
$706$		−	387.967i		−	0.549528i
$707$	−234.781	−	234.781i	−0.332080	−	0.332080i
$708$	−173.296	−	173.296i	−0.244769	−	0.244769i
$709$	336.761	+	336.761i	0.474981	+	0.474981i	0.903522	−	0.428542i	$-0.140972\pi$
$709$	336.761	+	336.761i	0.474981	+	0.474981i	−0.428542	+	0.903522i	$0.640972\pi$
$710$		0			0
$711$	1895.04			2.66532
$712$	413.485			0.580737
$713$	−440.880	+	440.880i	−0.618345	+	0.618345i
$714$		−	348.838i		−	0.488569i
$715$		0			0
$716$	250.574			0.349963
$717$	−737.677	−	737.677i	−1.02884	−	1.02884i
$718$		−	216.100i		−	0.300975i
$719$		−	25.7066i		−	0.0357533i	−0.999840	−	0.0178766i	$-0.994309\pi$
$719$		−	25.7066i		−	0.0357533i	0.999840	−	0.0178766i	$-0.00569062\pi$
$720$		0			0
$721$	−46.5978	+	46.5978i	−0.0646293	+	0.0646293i
$722$	−496.973	+	496.973i	−0.688328	+	0.688328i
$723$	495.309	−	495.309i	0.685075	−	0.685075i
$724$	−441.639			−0.609999
$725$		0			0
$726$	−547.649	−	547.649i	−0.754337	−	0.754337i
$727$	−98.7160			−0.135785			−0.0678927	−	0.997693i	$-0.521628\pi$
$727$	−98.7160			−0.135785			−0.0678927	+	0.997693i	$0.521628\pi$
$728$	−60.5059	−	76.1179i	−0.0831125	−	0.104558i
$729$	1173.02			1.60908
$730$		0			0
$731$	−985.199			−1.34774
$732$	−159.376			−0.217727
$733$	−70.0366	−	70.0366i	−0.0955479	−	0.0955479i	0.657717	−	0.753265i	$-0.271522\pi$
$733$	−70.0366	−	70.0366i	−0.0955479	−	0.0955479i	−0.753265	+	0.657717i	$0.771522\pi$
$734$	35.1926	−	35.1926i	0.0479464	−	0.0479464i
$735$		0			0
$736$	176.723	+	176.723i	0.240113	+	0.240113i
$737$		−	53.0212i		−	0.0719419i
$738$	−459.329			−0.622397
$739$	−884.117	−	884.117i	−1.19637	−	1.19637i	−0.975246	−	0.221124i	$-0.929028\pi$
$739$	−884.117	−	884.117i	−1.19637	−	1.19637i	−0.221124	−	0.975246i	$-0.570972\pi$
$740$		0			0
$741$	1778.55	+	203.235i	2.40020	+	0.274271i
$742$			64.1894i			0.0865087i
$743$	−236.735	−	236.735i	−0.318621	−	0.318621i	0.529617	−	0.848237i	$-0.322336\pi$
$743$	−236.735	−	236.735i	−0.318621	−	0.318621i	−0.848237	+	0.529617i	$0.822336\pi$
$744$	−187.651			−0.252219
$745$		0			0
$746$	−666.073	+	666.073i	−0.892859	+	0.892859i
$747$	−1121.33	−	1121.33i	−1.50111	−	1.50111i
$748$	59.5713	−	59.5713i	0.0796408	−	0.0796408i
$749$	−295.579	−	295.579i	−0.394631	−	0.394631i
$750$		0			0
$751$		−	1099.03i		−	1.46343i	−0.681612	−	0.731714i	$-0.738721\pi$
$751$		−	1099.03i		−	1.46343i	0.681612	−	0.731714i	$-0.261279\pi$
$752$	−47.2735	+	47.2735i	−0.0628637	+	0.0628637i
$753$	−797.116			−1.05859
$754$	441.350	+	50.4329i	0.585344	+	0.0668871i
$755$		0			0
$756$	72.0975	−	72.0975i	0.0953671	−	0.0953671i
$757$			718.877i			0.949639i	0.880083	+	0.474819i	$0.157487\pi$
$757$			718.877i			0.949639i	−0.880083	+	0.474819i	$0.842513\pi$
$758$	527.629			0.696081
$759$	311.801	−	311.801i	0.410805	−	0.410805i
$760$		0			0
$761$	−2.13237	−	2.13237i	−0.00280207	−	0.00280207i	0.705704	−	0.708506i	$-0.250631\pi$
$761$	−2.13237	−	2.13237i	−0.00280207	−	0.00280207i	−0.708506	+	0.705704i	$0.750631\pi$
$762$	−11.2832	+	11.2832i	−0.0148073	+	0.0148073i
$763$			32.1455i			0.0421304i
$764$		−	585.529i		−	0.766400i
$765$		0			0
$766$		−	701.772i		−	0.916151i
$767$	336.664	+	38.4705i	0.438936	+	0.0501571i
$768$			75.2183i			0.0979405i
$769$	788.894	−	788.894i	1.02587	−	1.02587i	0.0262133	−	0.999656i	$-0.491655\pi$
$769$	788.894	−	788.894i	1.02587	−	1.02587i	0.999656	−	0.0262133i	$-0.00834492\pi$
$770$		0			0
$771$			392.522i			0.509108i
$772$	−67.8964	−	67.8964i	−0.0879487	−	0.0879487i
$773$	777.339	+	777.339i	1.00561	+	1.00561i	0.999984	+	0.00562865i	$0.00179166\pi$
$773$	777.339	+	777.339i	1.00561	+	1.00561i	0.00562865	+	0.999984i	$0.498208\pi$
$774$	−650.510	−	650.510i	−0.840452	−	0.840452i
$775$		0			0
$776$	452.254			0.582802
$777$	264.505			0.340418
$778$	−563.670	+	563.670i	−0.724512	+	0.724512i
$779$			726.190i			0.932207i
$780$		0			0
$781$	−223.522			−0.286199
$782$	−876.594	−	876.594i	−1.12096	−	1.12096i
$783$			465.808i			0.594901i
$784$		−	168.027i		−	0.214320i
$785$		0			0
$786$	258.397	−	258.397i	0.328749	−	0.328749i
$787$	924.344	−	924.344i	1.17452	−	1.17452i	0.193395	−	0.981121i	$-0.438050\pi$
$787$	924.344	−	924.344i	1.17452	−	1.17452i	0.981121	−	0.193395i	$-0.0619499\pi$
$788$	−226.729	+	226.729i	−0.287727	+	0.287727i
$789$	393.874			0.499207
$790$		0			0
$791$	315.232	+	315.232i	0.398523	+	0.398523i
$792$	78.6678			0.0993281
$793$	172.501	−	137.121i	0.217530	−	0.172914i
$794$	153.194			0.192939
$795$		0			0
$796$	−197.110			−0.247626
$797$	−619.505			−0.777297			−0.388648	−	0.921386i	$-0.627058\pi$
$797$	−619.505			−0.777297			−0.388648	+	0.921386i	$0.627058\pi$
$798$	−364.150	−	364.150i	−0.456328	−	0.456328i
$799$	234.489	−	234.489i	0.293479	−	0.293479i
$800$		0			0
$801$	−1354.24	−	1354.24i	−1.69068	−	1.69068i
$802$			968.818i			1.20800i
$803$	34.4775			0.0429358
$804$	−166.039	−	166.039i	−0.206517	−	0.206517i
$805$		0			0
$806$	203.104	−	161.447i	0.251990	−	0.200307i
$807$			527.392i			0.653521i
$808$	−251.112	−	251.112i	−0.310782	−	0.310782i
$809$	−834.817			−1.03191			−0.515956	−	0.856615i	$-0.672563\pi$
$809$	−834.817			−1.03191			−0.515956	+	0.856615i	$0.672563\pi$
$810$		0			0
$811$	171.743	−	171.743i	0.211766	−	0.211766i	−0.593251	−	0.805018i	$-0.702156\pi$
$811$	171.743	−	171.743i	0.211766	−	0.211766i	0.805018	+	0.593251i	$0.202156\pi$
$812$	−90.3643	−	90.3643i	−0.111286	−	0.111286i
$813$	1261.93	−	1261.93i	1.55219	−	1.55219i
$814$	45.1696	+	45.1696i	0.0554910	+	0.0554910i
$815$		0			0
$816$		−	373.103i		−	0.457234i
$817$	−1028.44	+	1028.44i	−1.25880	+	1.25880i
$818$	618.758			0.756428
$819$	−51.1321	+	447.468i	−0.0624323	+	0.546359i
$820$		0			0
$821$	−196.299	+	196.299i	−0.239097	+	0.239097i	−0.816476	−	0.577379i	$-0.804075\pi$
$821$	−196.299	+	196.299i	−0.239097	+	0.239097i	0.577379	+	0.816476i	$0.304075\pi$
$822$			60.4004i			0.0734798i
$823$	−782.315			−0.950565			−0.475282	−	0.879833i	$-0.657654\pi$
$823$	−782.315			−0.950565			−0.475282	+	0.879833i	$0.657654\pi$
$824$	−49.8391	+	49.8391i	−0.0604843	+	0.0604843i
$825$		0			0
$826$	−68.9304	−	68.9304i	−0.0834508	−	0.0834508i
$827$	574.071	−	574.071i	0.694161	−	0.694161i	−0.268984	−	0.963145i	$-0.586688\pi$
$827$	574.071	−	574.071i	0.694161	−	0.694161i	0.963145	+	0.268984i	$0.0866879\pi$
$828$		−	1157.60i		−	1.39807i
$829$			646.610i			0.779988i	0.920817	+	0.389994i	$0.127523\pi$
$829$			646.610i			0.779988i	−0.920817	+	0.389994i	$0.872477\pi$
$830$		0			0
$831$			1308.27i			1.57433i
$832$	−64.7147	−	81.4126i	−0.0777821	−	0.0978517i
$833$			833.459i			1.00055i
$834$	792.620	−	792.620i	0.950384	−	0.950384i
$835$		0			0
$836$		−	124.372i		−	0.148771i
$837$	192.377	+	192.377i	0.229841	+	0.229841i
$838$	147.503	+	147.503i	0.176018	+	0.176018i
$839$	48.7532	+	48.7532i	0.0581087	+	0.0581087i	0.735564	−	0.677455i	$-0.236917\pi$
$839$	48.7532	+	48.7532i	0.0581087	+	0.0581087i	−0.677455	+	0.735564i	$0.736917\pi$
$840$		0			0
$841$	−257.174			−0.305796
$842$	−314.247			−0.373215
$843$	−826.836	+	826.836i	−0.980825	+	0.980825i
$844$			510.441i			0.604788i
$845$		0			0
$846$	309.659			0.366027
$847$	−217.833	−	217.833i	−0.257182	−	0.257182i
$848$			68.6544i			0.0809604i
$849$		−	2189.07i		−	2.57841i
$850$		0			0
$851$	664.673	−	664.673i	0.781050	−	0.781050i
$852$	−699.973	+	699.973i	−0.821564	+	0.821564i
$853$	−189.455	+	189.455i	−0.222104	+	0.222104i	−0.809384	−	0.587280i	$-0.800199\pi$
$853$	−189.455	+	189.455i	−0.222104	+	0.222104i	0.587280	+	0.809384i	$0.300199\pi$
$854$	−63.3937			−0.0742315
$855$		0			0
$856$	−316.139	−	316.139i	−0.369321	−	0.369321i
$857$	644.425			0.751954			0.375977	−	0.926629i	$-0.377307\pi$
$857$	644.425			0.751954			0.375977	+	0.926629i	$0.377307\pi$
$858$	−143.640	+	114.179i	−0.167413	+	0.133076i
$859$	78.4060			0.0912759			0.0456379	−	0.998958i	$-0.485468\pi$
$859$	78.4060			0.0912759			0.0456379	+	0.998958i	$0.485468\pi$
$860$		0			0
$861$	−308.217			−0.357976
$862$	205.579			0.238491
$863$	−255.051	−	255.051i	−0.295540	−	0.295540i	0.543724	−	0.839264i	$-0.317014\pi$
$863$	−255.051	−	255.051i	−0.295540	−	0.295540i	−0.839264	+	0.543724i	$0.817014\pi$
$864$	77.1125	−	77.1125i	0.0892506	−	0.0892506i
$865$		0			0
$866$	423.761	+	423.761i	0.489332	+	0.489332i
$867$			492.064i			0.567548i
$868$	−74.6402			−0.0859910
$869$	217.153	+	217.153i	0.249888	+	0.249888i
$870$		0			0
$871$	322.566	+	36.8595i	0.370340	+	0.0423187i
$872$			34.3815i			0.0394283i
$873$	−1481.22	−	1481.22i	−1.69670	−	1.69670i
$874$	−1830.14			−2.09398
$875$		0			0
$876$	107.968	−	107.968i	0.123252	−	0.123252i
$877$	473.757	+	473.757i	0.540202	+	0.540202i	0.923588	−	0.383386i	$-0.125242\pi$
$877$	473.757	+	473.757i	0.540202	+	0.540202i	−0.383386	+	0.923588i	$0.625242\pi$
$878$	175.599	−	175.599i	0.199999	−	0.199999i
$879$	1134.55	+	1134.55i	1.29073	+	1.29073i
$880$		0			0
$881$		−	181.000i		−	0.205448i	−0.994710	−	0.102724i	$-0.967244\pi$
$881$		−	181.000i		−	0.205448i	0.994710	−	0.102724i	$-0.0327559\pi$
$882$	−550.319	+	550.319i	−0.623944	+	0.623944i
$883$	−211.169			−0.239150			−0.119575	−	0.992825i	$-0.538153\pi$
$883$	−211.169			−0.239150			−0.119575	+	0.992825i	$0.538153\pi$
$884$	321.002	+	403.829i	0.363125	+	0.456820i
$885$		0			0
$886$	−97.0515	+	97.0515i	−0.109539	+	0.109539i
$887$		−	86.2904i		−	0.0972835i	−0.998816	−	0.0486417i	$-0.984511\pi$
$887$		−	86.2904i		−	0.0972835i	0.998816	−	0.0486417i	$-0.0154893\pi$
$888$	282.904			0.318585
$889$	−4.48801	+	4.48801i	−0.00504838	+	0.00504838i
$890$		0			0
$891$	40.9491	+	40.9491i	0.0459585	+	0.0459585i
$892$	603.675	−	603.675i	0.676766	−	0.676766i
$893$		−	489.564i		−	0.548224i
$894$		−	533.034i		−	0.596235i
$895$		0			0
$896$			29.9189i			0.0333916i
$897$	1680.15	+	2113.67i	1.87308	+	2.35638i
$898$		−	568.400i		−	0.632962i
$899$	241.118	−	241.118i	0.268206	−	0.268206i
$900$		0			0
$901$		−	340.545i		−	0.377963i
$902$	−52.6344	−	52.6344i	−0.0583530	−	0.0583530i
$903$	−436.503	−	436.503i	−0.483392	−	0.483392i
$904$	337.159	+	337.159i	0.372963	+	0.372963i
$905$		0			0
$906$	−888.200			−0.980353
$907$	737.549			0.813175			0.406587	−	0.913612i	$-0.366719\pi$
$907$	737.549			0.813175			0.406587	+	0.913612i	$0.366719\pi$
$908$	310.886	−	310.886i	0.342385	−	0.342385i
$909$			1644.87i			1.80954i
$910$		0			0
$911$	1267.14			1.39094			0.695469	−	0.718556i	$-0.255197\pi$
$911$	1267.14			1.39094			0.695469	+	0.718556i	$0.255197\pi$
$912$	−389.480	−	389.480i	−0.427061	−	0.427061i
$913$		−	256.986i		−	0.281474i
$914$			570.776i			0.624482i
$915$		0			0
$916$	−41.8295	+	41.8295i	−0.0456653	+	0.0456653i
$917$	102.780	−	102.780i	0.112083	−	0.112083i
$918$	−382.499	+	382.499i	−0.416666	+	0.416666i
$919$	−275.951			−0.300273			−0.150137	−	0.988665i	$-0.547971\pi$
$919$	−275.951			−0.300273			−0.150137	+	0.988665i	$0.547971\pi$
$920$		0			0
$921$	1317.28	+	1317.28i	1.43027	+	1.43027i
$922$	394.116			0.427458
$923$	155.389	−	1359.84i	0.168352	−	1.47329i
$924$	52.7874			0.0571292
$925$		0			0
$926$	−241.252			−0.260531
$927$	326.464			0.352173
$928$	−96.6499	−	96.6499i	−0.104149	−	0.104149i
$929$	−757.514	+	757.514i	−0.815408	+	0.815408i	−0.985439	−	0.170031i	$-0.945613\pi$
$929$	−757.514	+	757.514i	−0.815408	+	0.815408i	0.170031	+	0.985439i	$0.445613\pi$
$930$		0			0
$931$	870.043	+	870.043i	0.934525	+	0.934525i
$932$		−	671.110i		−	0.720075i
$933$	−64.5817			−0.0692194
$934$	−537.485	−	537.485i	−0.575466	−	0.575466i
$935$		0			0
$936$	−54.6888	+	478.594i	−0.0584282	+	0.511318i
$937$		−	57.6262i		−	0.0615007i	−0.999527	−	0.0307504i	$-0.990210\pi$
$937$		−	57.6262i		−	0.0615007i	0.999527	−	0.0307504i	$-0.00978969\pi$
$938$	−66.0439	−	66.0439i	−0.0704093	−	0.0704093i
$939$	397.636			0.423467
$940$		0			0
$941$	−902.679	+	902.679i	−0.959277	+	0.959277i	−0.999203	−	0.0399261i	$-0.987288\pi$
$941$	−902.679	+	902.679i	−0.959277	+	0.959277i	0.0399261	+	0.999203i	$0.487288\pi$
$942$	1087.17	+	1087.17i	1.15411	+	1.15411i
$943$	−774.518	+	774.518i	−0.821334	+	0.821334i
$944$	−73.7251	−	73.7251i	−0.0780986	−	0.0780986i
$945$		0			0
$946$		−	149.084i		−	0.157594i
$947$	−341.194	+	341.194i	−0.360289	+	0.360289i	−0.863919	−	0.503630i	$-0.831997\pi$
$947$	−341.194	+	341.194i	−0.360289	+	0.360289i	0.503630	+	0.863919i	$0.331997\pi$
$948$	1360.06			1.43466
$949$	−23.9682	+	209.751i	−0.0252563	+	0.221024i
$950$		0			0
$951$	−2061.81	+	2061.81i	−2.16804	+	2.16804i
$952$		−	148.406i		−	0.155888i
$953$	−1754.80			−1.84134			−0.920672	−	0.390337i	$-0.872359\pi$
$953$	−1754.80			−1.84134			−0.920672	+	0.390337i	$0.872359\pi$
$954$	224.856	−	224.856i	0.235698	−	0.235698i
$955$		0			0
$956$	−313.829	−	313.829i	−0.328273	−	0.328273i
$957$	−170.524	+	170.524i	−0.178186	+	0.178186i
$958$			289.959i			0.302672i
$959$			24.0249i			0.0250520i
$960$		0			0
$961$			761.839i			0.792756i
$962$	−306.201	+	243.399i	−0.318296	+	0.253013i
$963$			2070.83i			2.15039i
$964$	210.719	−	210.719i	0.218588	−	0.218588i
$965$		0			0
$966$		−	776.768i		−	0.804108i
$967$	−1265.44	−	1265.44i	−1.30863	−	1.30863i	−0.922408	−	0.386217i	$-0.873781\pi$
$967$	−1265.44	−	1265.44i	−1.30863	−	1.30863i	−0.386217	−	0.922408i	$-0.626219\pi$
$968$	−232.985	−	232.985i	−0.240687	−	0.240687i
$969$	1931.93	+	1931.93i	1.99373	+	1.99373i
$970$		0			0
$971$	−23.0027			−0.0236897			−0.0118448	−	0.999930i	$-0.503770\pi$
$971$	−23.0027			−0.0236897			−0.0118448	+	0.999930i	$0.503770\pi$
$972$	603.476			0.620860
$973$	315.273	−	315.273i	0.324022	−	0.324022i
$974$			1323.71i			1.35905i
$975$		0			0
$976$	−67.8033			−0.0694706
$977$	−79.6072	−	79.6072i	−0.0814812	−	0.0814812i	0.665192	−	0.746673i	$-0.268350\pi$
$977$	−79.6072	−	79.6072i	−0.0814812	−	0.0814812i	−0.746673	+	0.665192i	$0.768350\pi$
$978$			1413.29i			1.44508i
$979$		−	310.364i		−	0.317021i
$980$		0			0
$981$	112.606	−	112.606i	0.114787	−	0.114787i
$982$	−53.9981	+	53.9981i	−0.0549879	+	0.0549879i
$983$	−1001.39	+	1001.39i	−1.01870	+	1.01870i	−0.0188828	+	0.999822i	$0.506011\pi$
$983$	−1001.39	+	1001.39i	−1.01870	+	1.01870i	−0.999822	+	0.0188828i	$0.993989\pi$
$984$	−329.657			−0.335017
$985$		0			0
$986$	479.410	+	479.410i	0.486217	+	0.486217i
$987$	207.786			0.210523
$988$	756.647	+	86.4618i	0.765837	+	0.0875119i
$989$	−2193.77			−2.21817
$990$		0			0
$991$	997.813			1.00688			0.503438	−	0.864032i	$-0.332068\pi$
$991$	997.813			1.00688			0.503438	+	0.864032i	$0.332068\pi$
$992$	−79.8321			−0.0804759
$993$	102.228	+	102.228i	0.102949	+	0.102949i
$994$	−278.422	+	278.422i	−0.280102	+	0.280102i
$995$		0			0
$996$	−804.768	−	804.768i	−0.808000	−	0.808000i
$997$		−	1138.16i		−	1.14158i	−0.821095	−	0.570792i	$-0.806636\pi$
$997$		−	1138.16i		−	1.14158i	0.821095	−	0.570792i	$-0.193364\pi$
$998$	806.385			0.808001
$999$	−290.028	−	290.028i	−0.290318	−	0.290318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.3.f.k.499.6		12
5.2	odd	4		130.3.k.b.31.6	yes	12
5.3	odd	4		650.3.k.j.551.1		12
5.4	even	2		650.3.f.n.499.1		12
13.8	odd	4		650.3.f.n.99.6		12
15.2	even	4		1170.3.r.a.811.5		12
65.8	even	4		650.3.k.j.151.1		12
65.34	odd	4	inner	650.3.f.k.99.1		12
65.47	even	4		130.3.k.b.21.6	✓	12
195.47	odd	4		1170.3.r.a.541.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.k.b.21.6	✓	12	65.47	even	4
130.3.k.b.31.6	yes	12	5.2	odd	4
650.3.f.k.99.1		12	65.34	odd	4	inner
650.3.f.k.499.6		12	1.1	even	1	trivial
650.3.f.n.99.6		12	13.8	odd	4
650.3.f.n.499.1		12	5.4	even	2
650.3.k.j.151.1		12	65.8	even	4
650.3.k.j.551.1		12	5.3	odd	4
1170.3.r.a.541.5		12	195.47	odd	4
1170.3.r.a.811.5		12	15.2	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	650.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +4.70114i q^{3} +2.00000i q^{4} +(4.70114 - 4.70114i) q^{6} +(1.86993 - 1.86993i) q^{7} +(2.00000 - 2.00000i) q^{8} -13.1007 q^{9} +(-1.50121 - 1.50121i) q^{11} -9.40228 q^{12} +(10.1766 - 8.08933i) q^{13} -3.73986 q^{14} -4.00000 q^{16} +19.8411 q^{17} +(13.1007 + 13.1007i) q^{18} +(20.7120 - 20.7120i) q^{19} +(8.79080 + 8.79080i) q^{21} +3.00242i q^{22} +44.1807 q^{23} +(9.40228 + 9.40228i) q^{24} +(-18.2659 - 2.08724i) q^{26} -19.2781i q^{27} +(3.73986 + 3.73986i) q^{28} -24.1625 q^{29} +(-9.97901 + 9.97901i) q^{31} +(4.00000 + 4.00000i) q^{32} +(7.05740 - 7.05740i) q^{33} +(-19.8411 - 19.8411i) q^{34} -26.2015i q^{36} +(15.0444 - 15.0444i) q^{37} -41.4240 q^{38} +(38.0291 + 47.8415i) q^{39} +(-17.5307 + 17.5307i) q^{41} -17.5816i q^{42} -49.6545 q^{43} +(3.00242 - 3.00242i) q^{44} +(-44.1807 - 44.1807i) q^{46} +(11.8184 - 11.8184i) q^{47} -18.8046i q^{48} +42.0067i q^{49} +93.2758i q^{51} +(16.1787 + 20.3531i) q^{52} -17.1636i q^{53} +(-19.2781 + 19.2781i) q^{54} -7.47972i q^{56} +(97.3700 + 97.3700i) q^{57} +(24.1625 + 24.1625i) q^{58} +(18.4313 + 18.4313i) q^{59} +16.9508 q^{61} +19.9580 q^{62} +(-24.4974 + 24.4974i) q^{63} -8.00000i q^{64} -14.1148 q^{66} +(17.6595 + 17.6595i) q^{67} +39.6822i q^{68} +207.700i q^{69} +(74.4471 - 74.4471i) q^{71} +(-26.2015 + 26.2015i) q^{72} +(-11.4832 + 11.4832i) q^{73} -30.0888 q^{74} +(41.4240 + 41.4240i) q^{76} -5.61431 q^{77} +(9.81241 - 85.8706i) q^{78} -144.652 q^{79} -27.2774 q^{81} +35.0613 q^{82} +(85.5928 + 85.5928i) q^{83} +(-17.5816 + 17.5816i) q^{84} +(49.6545 + 49.6545i) q^{86} -113.591i q^{87} -6.00484 q^{88} +(103.371 + 103.371i) q^{89} +(3.90299 - 34.1560i) q^{91} +88.3615i q^{92} +(-46.9127 - 46.9127i) q^{93} -23.6367 q^{94} +(-18.8046 + 18.8046i) q^{96} +(113.064 + 113.064i) q^{97} +(42.0067 - 42.0067i) q^{98} +(19.6670 + 19.6670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 8 q^{7} + 24 q^{8} - 76 q^{9} - 16 q^{11} - 44 q^{13} + 16 q^{14} - 48 q^{16} + 32 q^{17} + 76 q^{18} + 68 q^{19} - 44 q^{21} - 16 q^{23} + 24 q^{26} - 16 q^{28} - 216 q^{29} + 64 q^{31}+ \cdots - 484 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 8 * q^7 + 24 * q^8 - 76 * q^9 - 16 * q^11 - 44 * q^13 + 16 * q^14 - 48 * q^16 + 32 * q^17 + 76 * q^18 + 68 * q^19 - 44 * q^21 - 16 * q^23 + 24 * q^26 - 16 * q^28 - 216 * q^29 + 64 * q^31 + 48 * q^32 - 52 * q^33 - 32 * q^34 - 28 * q^37 - 136 * q^38 - 140 * q^39 - 160 * q^43 + 32 * q^44 + 16 * q^46 - 104 * q^47 + 40 * q^52 + 96 * q^54 + 100 * q^57 + 216 * q^58 + 108 * q^59 + 88 * q^61 - 128 * q^62 - 312 * q^63 + 104 * q^66 - 240 * q^67 + 12 * q^71 - 152 * q^72 + 164 * q^73 + 56 * q^74 + 136 * q^76 - 336 * q^77 + 160 * q^78 - 392 * q^79 - 204 * q^81 + 536 * q^83 + 88 * q^84 + 160 * q^86 - 64 * q^88 + 364 * q^89 - 244 * q^91 - 236 * q^93 + 208 * q^94 - 192 * q^97 - 484 * q^98 - 484 * q^99

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