LMFDB - Embedded newform 650.3.k.j.551.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,3,Mod(151,650)] 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("650.151"); 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([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	650.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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			551.1
Root			$4.70114i$ of defining polynomial
Character	$\chi$	$=$	650.551
Dual form			650.3.k.j.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} -4.70114 q^{3} -2.00000i q^{4} +(4.70114 - 4.70114i) q^{6} +(-1.86993 - 1.86993i) q^{7} +(2.00000 + 2.00000i) q^{8} +13.1007 q^{9} +(-1.50121 - 1.50121i) q^{11} +9.40228i q^{12} +(8.08933 + 10.1766i) q^{13} +3.73986 q^{14} -4.00000 q^{16} -19.8411i q^{17} +(-13.1007 + 13.1007i) q^{18} +(-20.7120 + 20.7120i) q^{19} +(8.79080 + 8.79080i) q^{21} +3.00242 q^{22} +44.1807i q^{23} +(-9.40228 - 9.40228i) q^{24} +(-18.2659 - 2.08724i) q^{26} -19.2781 q^{27} +(-3.73986 + 3.73986i) q^{28} +24.1625 q^{29} +(-9.97901 + 9.97901i) q^{31} +(4.00000 - 4.00000i) q^{32} +(7.05740 + 7.05740i) q^{33} +(19.8411 + 19.8411i) q^{34} -26.2015i q^{36} +(-15.0444 - 15.0444i) q^{37} -41.4240i q^{38} +(-38.0291 - 47.8415i) q^{39} +(-17.5307 + 17.5307i) q^{41} -17.5816 q^{42} -49.6545i q^{43} +(-3.00242 + 3.00242i) q^{44} +(-44.1807 - 44.1807i) q^{46} +(-11.8184 - 11.8184i) q^{47} +18.8046 q^{48} -42.0067i q^{49} +93.2758i q^{51} +(20.3531 - 16.1787i) q^{52} +17.1636 q^{53} +(19.2781 - 19.2781i) q^{54} -7.47972i q^{56} +(97.3700 - 97.3700i) q^{57} +(-24.1625 + 24.1625i) q^{58} +(-18.4313 - 18.4313i) q^{59} +16.9508 q^{61} -19.9580i q^{62} +(-24.4974 - 24.4974i) q^{63} +8.00000i q^{64} -14.1148 q^{66} +(17.6595 - 17.6595i) q^{67} -39.6822 q^{68} -207.700i q^{69} +(74.4471 - 74.4471i) q^{71} +(26.2015 + 26.2015i) q^{72} +(-11.4832 - 11.4832i) q^{73} +30.0888 q^{74} +(41.4240 + 41.4240i) q^{76} +5.61431i q^{77} +(85.8706 + 9.81241i) q^{78} +144.652 q^{79} -27.2774 q^{81} -35.0613i q^{82} +(-85.5928 + 85.5928i) q^{83} +(17.5816 - 17.5816i) q^{84} +(49.6545 + 49.6545i) q^{86} -113.591 q^{87} -6.00484i q^{88} +(-103.371 - 103.371i) q^{89} +(3.90299 - 34.1560i) q^{91} +88.3615 q^{92} +(46.9127 - 46.9127i) q^{93} +23.6367 q^{94} +(-18.8046 + 18.8046i) q^{96} +(113.064 - 113.064i) q^{97} +(42.0067 + 42.0067i) q^{98} +(-19.6670 - 19.6670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 8 q^{7} + 24 q^{8} + 76 q^{9} - 16 q^{11} + 20 q^{13} - 16 q^{14} - 48 q^{16} - 76 q^{18} - 68 q^{19} - 44 q^{21} + 32 q^{22} + 24 q^{26} + 96 q^{27} + 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 + 20 * q^13 - 16 * q^14 - 48 * q^16 - 76 * q^18 - 68 * q^19 - 44 * q^21 + 32 * q^22 + 24 * q^26 + 96 * q^27 + 16 * q^28 + 216 * q^29 + 64 * q^31 + 48 * q^32 - 52 * q^33 + 32 * q^34 + 28 * q^37 + 140 * q^39 + 88 * q^42 - 32 * q^44 + 16 * q^46 + 104 * q^47 - 88 * q^52 + 424 * q^53 - 96 * q^54 + 100 * q^57 - 216 * q^58 - 108 * q^59 + 88 * q^61 - 312 * q^63 + 104 * q^66 - 240 * q^67 - 64 * q^68 + 12 * q^71 + 152 * q^72 + 164 * q^73 - 56 * q^74 + 136 * q^76 - 120 * q^78 + 392 * q^79 - 204 * q^81 - 536 * q^83 - 88 * q^84 + 160 * q^86 + 672 * q^87 - 364 * q^89 - 244 * q^91 - 32 * q^92 + 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
$3$	−4.70114			−1.56705			−0.783524	−	0.621362i	$-0.786580\pi$
$3$	−4.70114			−1.56705			−0.783524	+	0.621362i	$0.786580\pi$
$4$		−	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	$-0.310489\pi$
$7$	−1.86993	−	1.86993i	−0.267133	−	0.267133i	−0.827944	+	0.560811i	$0.810489\pi$
$8$	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	$0.780765\pi$
$12$			9.40228i			0.783524i
$13$	8.08933	+	10.1766i	0.622256	+	0.782813i
$13$	8.08933	+	10.1766i	0.622256	+	0.782813i
$14$	3.73986			0.267133
$15$		0			0
$16$	−4.00000			−0.250000
$17$		−	19.8411i		−	1.16712i	−0.812069	−	0.583562i	$-0.801659\pi$
$17$		−	19.8411i		−	1.16712i	0.812069	−	0.583562i	$-0.198341\pi$
$18$	−13.1007	+	13.1007i	−0.727819	+	0.727819i
$19$	−20.7120	+	20.7120i	−1.09010	+	1.09010i	−0.0945880	+	0.995517i	$0.530153\pi$
$19$	−20.7120	+	20.7120i	−1.09010	+	1.09010i	−0.995517	+	0.0945880i	$0.969847\pi$
$20$		0			0
$21$	8.79080	+	8.79080i	0.418610	+	0.418610i
$22$	3.00242			0.136474
$23$			44.1807i			1.92090i	0.278449	+	0.960451i	$0.410180\pi$
$23$			44.1807i			1.92090i	−0.278449	+	0.960451i	$0.589820\pi$
$24$	−9.40228	−	9.40228i	−0.391762	−	0.391762i
$25$		0			0
$26$	−18.2659	−	2.08724i	−0.702535	−	0.0802785i
$27$	−19.2781			−0.714005
$28$	−3.73986	+	3.73986i	−0.133566	+	0.133566i
$29$	24.1625			0.833189			0.416595	−	0.909092i	$-0.363223\pi$
$29$	24.1625			0.833189			0.416595	+	0.909092i	$0.363223\pi$
$30$		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	$-0.342829\pi$
$37$	−15.0444	−	15.0444i	−0.406606	−	0.406606i	−0.880553	+	0.473947i	$0.842829\pi$
$38$		−	41.4240i		−	1.09010i
$39$	−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	$0.347769\pi$
$42$	−17.5816			−0.418610
$43$		−	49.6545i		−	1.15475i	−0.816477	−	0.577377i	$-0.804076\pi$
$43$		−	49.6545i		−	1.15475i	0.816477	−	0.577377i	$-0.195924\pi$
$44$	−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	$-0.306900\pi$
$47$	−11.8184	−	11.8184i	−0.251455	−	0.251455i	−0.821567	+	0.570112i	$0.806900\pi$
$48$	18.8046			0.391762
$49$		−	42.0067i		−	0.857280i
$50$		0			0
$51$			93.2758i			1.82894i
$52$	20.3531	−	16.1787i	0.391407	−	0.311128i
$53$	17.1636			0.323842			0.161921	−	0.986804i	$-0.448231\pi$
$53$	17.1636			0.323842			0.161921	+	0.986804i	$0.448231\pi$
$54$	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	0.533442	−	0.845837i	$-0.320898\pi$
$59$	−18.4313	−	18.4313i	−0.312395	−	0.312395i	−0.845837	+	0.533442i	$0.820898\pi$
$60$		0			0
$61$	16.9508			0.277882			0.138941	−	0.990301i	$-0.455630\pi$
$61$	16.9508			0.277882			0.138941	+	0.990301i	$0.455630\pi$
$62$		−	19.9580i		−	0.321903i
$63$	−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	−0.562930	−	0.826504i	$-0.690326\pi$
$67$	17.6595	−	17.6595i	0.263574	−	0.263574i	0.826504	+	0.562930i	$0.190326\pi$
$68$	−39.6822			−0.583562
$69$		−	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	0.624067	−	0.781371i	$-0.285479\pi$
$73$	−11.4832	−	11.4832i	−0.157304	−	0.157304i	−0.781371	+	0.624067i	$0.785479\pi$
$74$	30.0888			0.406606
$75$		0			0
$76$	41.4240	+	41.4240i	0.545052	+	0.545052i
$77$			5.61431i			0.0729132i
$78$	85.8706	+	9.81241i	1.10091	+	0.125800i
$79$	144.652			1.83103			0.915517	−	0.402280i	$-0.131782\pi$
$79$	144.652			1.83103			0.915517	+	0.402280i	$0.131782\pi$
$80$		0			0
$81$	−27.2774			−0.336758
$82$		−	35.0613i		−	0.427577i
$83$	−85.5928	+	85.5928i	−1.03124	+	1.03124i	−0.0317424	+	0.999496i	$0.510106\pi$
$83$	−85.5928	+	85.5928i	−1.03124	+	1.03124i	−0.999496	+	0.0317424i	$0.989894\pi$
$84$	17.5816	−	17.5816i	0.209305	−	0.209305i
$85$		0			0
$86$	49.6545	+	49.6545i	0.577377	+	0.577377i
$87$	−113.591			−1.30565
$88$		−	6.00484i		−	0.0682368i
$89$	−103.371	−	103.371i	−1.16147	−	1.16147i	−0.984153	−	0.177321i	$-0.943257\pi$
$89$	−103.371	−	103.371i	−1.16147	−	1.16147i	−0.177321	−	0.984153i	$-0.556743\pi$
$90$		0			0
$91$	3.90299	−	34.1560i	0.0428900	−	0.375340i
$92$	88.3615			0.960451
$93$	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	0.182375	−	0.983229i	$-0.441621\pi$
$97$	113.064	−	113.064i	1.16560	−	1.16560i	0.983229	−	0.182375i	$-0.0583785\pi$
$98$	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
$103$		−	24.9195i		−	0.241937i	−0.992656	−	0.120969i	$-0.961400\pi$
$103$		−	24.9195i		−	0.241937i	0.992656	−	0.120969i	$-0.0386000\pi$
$104$	−4.17448	+	36.5318i	−0.0401392	+	0.351267i
$105$		0			0
$106$	−17.1636	+	17.1636i	−0.161921	+	0.161921i
$107$	−158.069			−1.47728			−0.738642	−	0.674097i	$-0.764533\pi$
$107$	−158.069			−1.47728			−0.738642	+	0.674097i	$0.764533\pi$
$108$			38.5563i			0.357003i
$109$	8.59537	−	8.59537i	0.0788566	−	0.0788566i	−0.666578	−	0.745435i	$-0.732242\pi$
$109$	8.59537	−	8.59537i	0.0788566	−	0.0788566i	0.745435	+	0.666578i	$0.232242\pi$
$110$		0			0
$111$	70.7259	+	70.7259i	0.637170	+	0.637170i
$112$	7.47972	+	7.47972i	0.0667832	+	0.0667832i
$113$	−168.579			−1.49185			−0.745927	−	0.666028i	$-0.767993\pi$
$113$	−168.579			−1.49185			−0.745927	+	0.666028i	$0.767993\pi$
$114$			194.740i			1.70825i
$115$		0			0
$116$		−	48.3250i		−	0.416595i
$117$	105.976	+	133.321i	0.905780	+	1.13949i
$118$	36.8626			0.312395
$119$	−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
$127$			2.40010i			0.0188984i	0.999955	+	0.00944920i	$0.00300782\pi$
$127$			2.40010i			0.0188984i	−0.999955	+	0.00944920i	$0.996992\pi$
$128$	−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
$133$	77.4599			0.582405
$134$			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	$-0.239444\pi$
$137$	6.42401	+	6.42401i	0.0468906	+	0.0468906i	−0.683273	+	0.730163i	$0.739444\pi$
$138$	207.700	+	207.700i	1.50507	+	1.50507i
$139$	−168.602			−1.21296			−0.606481	−	0.795098i	$-0.707419\pi$
$139$	−168.602			−1.21296			−0.606481	+	0.795098i	$0.707419\pi$
$140$		0			0
$141$	55.5599	+	55.5599i	0.394041	+	0.394041i
$142$			148.894i			1.04855i
$143$	3.13339	−	27.4210i	0.0219118	−	0.191755i
$144$	−52.4029			−0.363909
$145$		0			0
$146$	22.9664			0.157304
$147$			197.480i			1.34340i
$148$	−30.0888	+	30.0888i	−0.203303	+	0.203303i
$149$	−56.6920	+	56.6920i	−0.380483	+	0.380483i	−0.871276	−	0.490793i	$-0.836707\pi$
$149$	−56.6920	+	56.6920i	−0.380483	+	0.380483i	0.490793	+	0.871276i	$0.336707\pi$
$150$		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	$0.895862\pi$
$152$	−82.8479			−0.545052
$153$		−	259.933i		−	1.69891i
$154$	−5.61431	−	5.61431i	−0.0364566	−	0.0364566i
$155$		0			0
$156$	−95.6830	+	76.0582i	−0.613353	+	0.487553i
$157$	231.256			1.47297			0.736484	−	0.676455i	$-0.236485\pi$
$157$	231.256			1.47297			0.736484	+	0.676455i	$0.236485\pi$
$158$	−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	0.0750153	−	0.997182i	$-0.476099\pi$
$163$	−150.313	−	150.313i	−0.922167	−	0.922167i	−0.997182	+	0.0750153i	$0.976099\pi$
$164$	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	−0.996413	−	0.0846176i	$-0.973033\pi$
$167$	−180.532	−	180.532i	−1.08103	−	1.08103i	−0.0846176	−	0.996413i	$-0.526967\pi$
$168$			35.1632i			0.209305i
$169$	−38.1253	+	164.643i	−0.225594	+	0.974221i
$170$		0			0
$171$	−271.342	+	271.342i	−1.58680	+	1.58680i
$172$	−99.3089			−0.577377
$173$			232.945i			1.34650i	0.739414	+	0.673251i	$0.235103\pi$
$173$			232.945i			1.34650i	−0.739414	+	0.673251i	$0.764897\pi$
$174$	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
$178$	206.742			1.16147
$179$			125.287i			0.699926i	0.936763	+	0.349963i	$0.113806\pi$
$179$			125.287i			0.699926i	−0.936763	+	0.349963i	$0.886194\pi$
$180$		0			0
$181$			220.820i			1.22000i	0.792402	+	0.609999i	$0.208830\pi$
$181$			220.820i			1.22000i	−0.792402	+	0.609999i	$0.791170\pi$
$182$	30.2530	+	38.0589i	0.166225	+	0.209115i
$183$	−79.6882			−0.435455
$184$	−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	$0.777954\pi$
$192$		−	37.6091i		−	0.195881i
$193$	−33.9482	−	33.9482i	−0.175897	−	0.175897i	0.613667	−	0.789565i	$-0.289694\pi$
$193$	−33.9482	−	33.9482i	−0.175897	−	0.175897i	−0.789565	+	0.613667i	$0.789694\pi$
$194$			226.127i			1.16560i
$195$		0			0
$196$	−84.0135			−0.428640
$197$	113.364	−	113.364i	0.575454	−	0.575454i	−0.358194	−	0.933647i	$-0.616607\pi$
$197$	113.364	−	113.364i	0.575454	−	0.575454i	0.933647	+	0.358194i	$0.116607\pi$
$198$	39.3339			0.198656
$199$		−	98.5552i		−	0.495252i	−0.968856	−	0.247626i	$-0.920350\pi$
$199$		−	98.5552i		−	0.495252i	0.968856	−	0.247626i	$-0.0796505\pi$
$200$		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
$207$			578.800i			2.79614i
$208$	−32.3573	−	40.7063i	−0.155564	−	0.195703i
$209$	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	$0.293258\pi$
$212$		−	34.3272i		−	0.161921i
$213$	−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
$217$	37.3201			0.171982
$218$			17.1907i			0.0788566i
$219$	53.9842	+	53.9842i	0.246503	+	0.246503i
$220$		0			0
$221$	201.914	−	160.501i	0.913640	−	0.726250i
$222$	−141.452			−0.637170
$223$	301.837	−	301.837i	1.35353	−	1.35353i	0.471855	−	0.881676i	$-0.343585\pi$
$223$	301.837	−	301.837i	1.35353	−	1.35353i	0.881676	−	0.471855i	$-0.156415\pi$
$224$	−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	−0.961071	−	0.276301i	$-0.910891\pi$
$227$	−155.443	+	155.443i	−0.684770	+	0.684770i	0.276301	+	0.961071i	$0.410891\pi$
$228$	−194.740	−	194.740i	−0.854123	−	0.854123i
$229$	−20.9147	−	20.9147i	−0.0913307	−	0.0913307i	0.659965	−	0.751296i	$-0.270571\pi$
$229$	−20.9147	−	20.9147i	−0.0913307	−	0.0913307i	−0.751296	+	0.659965i	$0.770571\pi$
$230$		0			0
$231$		−	26.3937i		−	0.114258i
$232$	48.3250	+	48.3250i	0.208297	+	0.208297i
$233$		−	335.555i		−	1.44015i	−0.693896	−	0.720075i	$-0.744107\pi$
$233$		−	335.555i		−	1.44015i	0.693896	−	0.720075i	$-0.255893\pi$
$234$	−239.297	−	27.3444i	−1.02264	−	0.116856i
$235$		0			0
$236$	−36.8626	+	36.8626i	−0.156197	+	0.156197i
$237$	−680.028			−2.86932
$238$		−	74.2029i		−	0.311777i
$239$	156.914	−	156.914i	0.656545	−	0.656545i	−0.298016	−	0.954561i	$-0.596325\pi$
$239$	156.914	−	156.914i	0.656545	−	0.656545i	0.954561	+	0.298016i	$0.0963247\pi$
$240$		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
$243$	301.738			1.24172
$244$		−	33.9017i		−	0.138941i
$245$		0			0
$246$			164.828i			0.670034i
$247$	−378.323	−	43.2309i	−1.53167	−	0.175024i
$248$	−39.9160			−0.160952
$249$	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
$257$		−	83.4951i		−	0.324884i	−0.986718	−	0.162442i	$-0.948063\pi$
$257$		−	83.4951i		−	0.324884i	0.986718	−	0.162442i	$-0.0519370\pi$
$258$	−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
$263$	83.7827			0.318565			0.159283	−	0.987233i	$-0.449082\pi$
$263$	83.7827			0.318565			0.159283	+	0.987233i	$0.449082\pi$
$264$			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	$-0.566865\pi$
$269$	−112.184			−0.417040			−0.208520	+	0.978018i	$0.566865\pi$
$270$		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	$0.996996\pi$
$272$			79.3644i			0.291781i
$273$	−18.3485	+	160.572i	−0.0672107	+	0.588176i
$274$	−12.8480			−0.0468906
$275$		0			0
$276$	−415.400			−1.50507
$277$		−	278.287i		−	1.00465i	−0.864680	−	0.502324i	$-0.832479\pi$
$277$		−	278.287i		−	1.00465i	0.864680	−	0.502324i	$-0.167521\pi$
$278$	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	$0.604062\pi$
$282$	−111.120			−0.394041
$283$		−	465.647i		−	1.64539i	−0.568480	−	0.822697i	$-0.692468\pi$
$283$		−	465.647i		−	1.64539i	0.568480	−	0.822697i	$-0.307532\pi$
$284$	−148.894	−	148.894i	−0.524275	−	0.524275i
$285$		0			0
$286$	24.2876	+	30.5544i	0.0849216	+	0.106833i
$287$	65.5622			0.228440
$288$	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	0.986632	−	0.162965i	$-0.0521057\pi$
$293$	241.334	+	241.334i	0.823667	+	0.823667i	−0.162965	+	0.986632i	$0.552106\pi$
$294$	−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
$298$		−	113.384i		−	0.380483i
$299$	−449.609	+	357.393i	−1.50371	+	1.19529i
$300$		0			0
$301$	−92.8503	+	92.8503i	−0.308473	+	0.308473i
$302$	188.933			0.625605
$303$			590.256i			1.94804i
$304$	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	$-0.473304\pi$
$307$	−280.203	−	280.203i	−0.912715	−	0.912715i	−0.996485	+	0.0837701i	$0.973304\pi$
$308$	11.2286			0.0364566
$309$			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	$0.992969\pi$
$312$	19.6248	−	171.741i	0.0629001	−	0.550453i
$313$	84.5828			0.270233			0.135116	−	0.990830i	$-0.456859\pi$
$313$	84.5828			0.270233			0.135116	+	0.990830i	$0.456859\pi$
$314$	−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	0.545237	−	0.838282i	$-0.316440\pi$
$317$	438.576	−	438.576i	1.38352	−	1.38352i	0.838282	−	0.545237i	$-0.183560\pi$
$318$	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
$322$			165.230i			0.513136i
$323$	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
$328$	−70.1226			−0.213789
$329$			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
$337$			364.125i			1.08049i	0.841508	+	0.540245i	$0.181669\pi$
$337$			364.125i			1.08049i	−0.841508	+	0.540245i	$0.818331\pi$
$338$	−126.518	−	202.769i	−0.374314	−	0.599908i
$339$	792.516			2.33780
$340$		0			0
$341$	29.9612			0.0878627
$342$		−	542.684i		−	1.58680i
$343$	−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
$347$	185.153			0.533582			0.266791	−	0.963754i	$-0.414037\pi$
$347$	185.153			0.533582			0.266791	+	0.963754i	$0.414037\pi$
$348$			227.183i			0.652823i
$349$	139.886	+	139.886i	0.400820	+	0.400820i	0.878522	−	0.477702i	$-0.158530\pi$
$349$	139.886	+	139.886i	0.400820	+	0.400820i	−0.477702	+	0.878522i	$0.658530\pi$
$350$		0			0
$351$	−155.947	−	196.185i	−0.444294	−	0.558933i
$352$	−12.0097			−0.0341184
$353$	−193.983	+	193.983i	−0.549528	+	0.549528i	−0.926304	−	0.376776i	$-0.877033\pi$
$353$	−193.983	+	193.983i	−0.549528	+	0.549528i	0.376776	+	0.926304i	$0.377033\pi$
$354$	−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	0.540420	−	0.841395i	$-0.318265\pi$
$359$	−108.050	−	108.050i	−0.300975	−	0.300975i	−0.841395	+	0.540420i	$0.818265\pi$
$360$		0			0
$361$		−	496.973i		−	1.37666i
$362$	−220.820	−	220.820i	−0.609999	−	0.609999i
$363$			547.649i			1.50867i
$364$	−68.3119	−	7.80598i	−0.187670	−	0.0214450i
$365$		0			0
$366$	79.6882	−	79.6882i	0.217727	−	0.217727i
$367$	35.1926			0.0958927			0.0479464	−	0.998850i	$-0.484732\pi$
$367$	35.1926			0.0958927			0.0479464	+	0.998850i	$0.484732\pi$
$368$		−	176.723i		−	0.480226i
$369$	−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
$373$	666.073			1.78572			0.892859	−	0.450337i	$-0.148696\pi$
$373$	666.073			1.78572			0.892859	+	0.450337i	$0.148696\pi$
$374$		−	59.5713i		−	0.159282i
$375$		0			0
$376$		−	47.2735i		−	0.125727i
$377$	195.458	+	245.891i	0.518457	+	0.652232i
$378$	−72.0975			−0.190734
$379$	263.815	−	263.815i	0.696081	−	0.696081i	−0.267482	−	0.963563i	$-0.586192\pi$
$379$	263.815	−	263.815i	0.696081	−	0.696081i	0.963563	+	0.267482i	$0.0861916\pi$
$380$		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	$-0.974318\pi$
$383$	−350.886	+	350.886i	−0.916151	+	0.916151i	0.0805958	+	0.996747i	$0.474318\pi$
$384$	37.6091	+	37.6091i	0.0979405	+	0.0979405i
$385$		0			0
$386$	67.8964			0.175897
$387$		−	650.510i		−	1.68090i
$388$	−226.127	−	226.127i	−0.582802	−	0.582802i
$389$			563.670i			1.44902i	0.689262	+	0.724512i	$0.257935\pi$
$389$			563.670i			1.44902i	−0.689262	+	0.724512i	$0.742065\pi$
$390$		0			0
$391$	876.594			2.24193
$392$	84.0135	−	84.0135i	0.214320	−	0.214320i
$393$	−258.397			−0.657499
$394$			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	$-0.206438\pi$
$397$	76.5969	+	76.5969i	0.192939	+	0.192939i	−0.604026	+	0.796965i	$0.706438\pi$
$398$	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	$-0.575944\pi$
$402$		−	166.039i		−	0.413033i
$403$	−182.276	−	20.8286i	−0.452297	−	0.0516838i
$404$	−251.112			−0.621564
$405$		0			0
$406$	90.3643			0.222572
$407$			45.1696i			0.110982i
$408$	−186.552	+	186.552i	−0.457234	+	0.457234i
$409$	309.379	−	309.379i	0.756428	−	0.756428i	−0.219242	−	0.975670i	$-0.570359\pi$
$409$	309.379	−	309.379i	0.756428	−	0.756428i	0.975670	+	0.219242i	$0.0703586\pi$
$410$		0			0
$411$	−30.2002	−	30.2002i	−0.0734798	−	0.0734798i
$412$	−49.8391			−0.120969
$413$			68.9304i			0.166902i
$414$	−578.800	−	578.800i	−1.39807	−	1.39807i
$415$		0			0
$416$	73.0636	+	8.34896i	0.175634	+	0.0200696i
$417$	792.620			1.90077
$418$	−62.1861	+	62.1861i	−0.148771	+	0.148771i
$419$	147.503			0.352037			0.176018	−	0.984387i	$-0.443678\pi$
$419$	147.503			0.352037			0.176018	+	0.984387i	$0.443678\pi$
$420$		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
$428$			316.139i			0.738642i
$429$	−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	$0.303937\pi$
$432$	77.1125			0.178501
$433$		−	423.761i		−	0.978663i	−0.872098	−	0.489332i	$-0.837241\pi$
$433$		−	423.761i		−	0.978663i	0.872098	−	0.489332i	$-0.162759\pi$
$434$	−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
$438$	−107.968			−0.246503
$439$		−	175.599i		−	0.399998i	−0.979796	−	0.199999i	$-0.935906\pi$
$439$		−	175.599i		−	0.399998i	0.979796	−	0.199999i	$-0.0640939\pi$
$440$		0			0
$441$		−	550.319i		−	1.24789i
$442$	−41.4131	+	362.416i	−0.0936949	+	0.819945i
$443$	97.0515			0.219078			0.109539	−	0.993983i	$-0.465063\pi$
$443$	97.0515			0.219078			0.109539	+	0.993983i	$0.465063\pi$
$444$	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	0.315848	−	0.948810i	$-0.397711\pi$
$449$	−284.200	−	284.200i	−0.632962	−	0.632962i	−0.948810	+	0.315848i	$0.897711\pi$
$450$		0			0
$451$	52.6344			0.116706
$452$			337.159i			0.745927i
$453$	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	−0.946674	−	0.322192i	$-0.895580\pi$
$457$	−285.388	+	285.388i	−0.624482	+	0.624482i	0.322192	+	0.946674i	$0.395580\pi$
$458$	41.8295			0.0913307
$459$			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	0.825270	−	0.564738i	$-0.191023\pi$
$463$	120.626	+	120.626i	0.260531	+	0.260531i	−0.564738	+	0.825270i	$0.691023\pi$
$464$	−96.6499			−0.208297
$465$		0			0
$466$	335.555	+	335.555i	0.720075	+	0.720075i
$467$		−	537.485i		−	1.15093i	−0.817826	−	0.575466i	$-0.804821\pi$
$467$		−	537.485i		−	1.15093i	0.817826	−	0.575466i	$-0.195179\pi$
$468$	266.641	−	211.952i	0.569746	−	0.452890i
$469$	−66.0439			−0.140819
$470$		0			0
$471$	−1087.17			−2.30821
$472$		−	73.7251i		−	0.156197i
$473$	−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
$477$	224.856			0.471396
$478$			313.829i			0.656545i
$479$	144.980	+	144.980i	0.302672	+	0.302672i	0.842058	−	0.539387i	$-0.181344\pi$
$479$	144.980	+	144.980i	0.302672	+	0.302672i	−0.539387	+	0.842058i	$0.681344\pi$
$480$		0			0
$481$	31.4013	−	274.800i	0.0652834	−	0.571309i
$482$	210.719			0.437176
$483$	−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	−0.483958	+	0.875091i	$0.660801\pi$
$487$	−661.857	+	661.857i	−1.35905	+	1.35905i	−0.875091	+	0.483958i	$0.839199\pi$
$488$	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
$493$		−	479.410i		−	0.972434i
$494$	421.554	−	335.092i	0.853348	−	0.678325i
$495$		0			0
$496$	39.9160	−	39.9160i	0.0804759	−	0.0804759i
$497$	−278.422			−0.560205
$498$			804.768i			1.61600i
$499$	403.192	−	403.192i	0.808001	−	0.808001i	−0.176330	−	0.984331i	$-0.556423\pi$
$499$	403.192	−	403.192i	0.808001	−	0.808001i	0.984331	+	0.176330i	$0.0564227\pi$
$500$		0			0
$501$	848.707	+	848.707i	1.69403	+	1.69403i
$502$	−169.558	−	169.558i	−0.337765	−	0.337765i
$503$	−624.707			−1.24196			−0.620981	−	0.783825i	$-0.713266\pi$
$503$	−624.707			−1.24196			−0.620981	+	0.783825i	$0.713266\pi$
$504$		−	97.9898i		−	0.194424i
$505$		0			0
$506$			132.649i			0.262153i
$507$	179.233	−	774.012i	0.353516	−	1.52665i
$508$	4.80019			0.00944920
$509$	61.2684	−	61.2684i	0.120370	−	0.120370i	−0.644356	−	0.764726i	$-0.722874\pi$
$509$	61.2684	−	61.2684i	0.120370	−	0.120370i	0.764726	+	0.644356i	$0.222874\pi$
$510$		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
$517$			35.4837i			0.0686339i
$518$	−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
$523$	345.672			0.660942			0.330471	−	0.943816i	$-0.392792\pi$
$523$	345.672			0.660942			0.330471	+	0.943816i	$0.392792\pi$
$524$		−	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
$532$		−	154.920i		−	0.291203i
$533$	−320.213	−	36.5907i	−0.600776	−	0.0686505i
$534$	−971.925			−1.82008
$535$		0			0
$536$	70.6379			0.131787
$537$		−	588.991i		−	1.09682i
$538$	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	$0.716739\pi$
$542$	536.860			0.990517
$543$		−	1038.10i		−	1.91179i
$544$	−79.3644	−	79.3644i	−0.145890	−	0.145890i
$545$		0			0
$546$	−142.223	−	178.921i	−0.260483	−	0.327693i
$547$	411.476			0.752241			0.376120	−	0.926571i	$-0.377258\pi$
$547$	411.476			0.752241			0.376120	+	0.926571i	$0.377258\pi$
$548$	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	$-0.0584039\pi$
$557$	446.024	+	446.024i	0.800761	+	0.800761i	−0.182454	+	0.983214i	$0.558404\pi$
$558$		−	261.465i		−	0.468575i
$559$	505.312	−	401.672i	0.903958	−	0.718554i
$560$		0			0
$561$	140.027	−	140.027i	0.249602	−	0.249602i
$562$	−351.760			−0.625907
$563$		−	628.339i		−	1.11606i	−0.829822	−	0.558028i	$-0.811558\pi$
$563$		−	628.339i		−	1.11606i	0.829822	−	0.558028i	$-0.188442\pi$
$564$	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
$568$	297.788			0.524275
$569$		−	808.201i		−	1.42039i	−0.704006	−	0.710194i	$-0.748607\pi$
$569$		−	808.201i		−	1.42039i	0.704006	−	0.710194i	$-0.251393\pi$
$570$		0			0
$571$		−	317.754i		−	0.556487i	−0.960511	−	0.278244i	$-0.910248\pi$
$571$		−	317.754i		−	0.556487i	0.960511	−	0.278244i	$-0.0897523\pi$
$572$	−54.8419	−	6.26677i	−0.0958775	−	0.0109559i
$573$	1376.33			2.40197
$574$	−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	−0.0592249	+	0.998245i	$0.518863\pi$
$577$	−610.160	+	610.160i	−1.05747	+	1.05747i	−0.998245	+	0.0592249i	$0.981137\pi$
$578$	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
$582$		−	1063.06i		−	1.82656i
$583$	−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	−0.806514	−	0.591215i	$-0.798648\pi$
$587$	−126.380	+	126.380i	−0.215299	+	0.215299i	0.591215	+	0.806514i	$0.298648\pi$
$588$	394.959			0.671699
$589$		−	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	0.941236	−	0.337750i	$-0.109666\pi$
$593$	357.867	+	357.867i	0.603486	+	0.603486i	−0.337750	+	0.941236i	$0.609666\pi$
$594$	−57.8811			−0.0974429
$595$		0			0
$596$	113.384	+	113.384i	0.190241	+	0.190241i
$597$			463.322i			0.776084i
$598$	92.2158	−	807.002i	0.154207	−	1.34950i
$599$	388.454			0.648505			0.324252	−	0.945971i	$-0.394887\pi$
$599$	388.454			0.648505			0.324252	+	0.945971i	$0.394887\pi$
$600$		0			0
$601$	−761.564			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$601$	−761.564			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$602$		−	185.701i		−	0.308473i
$603$	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
$607$	674.936			1.11192			0.555961	−	0.831209i	$-0.312351\pi$
$607$	674.936			1.11192			0.555961	+	0.831209i	$0.312351\pi$
$608$			165.696i			0.272526i
$609$	212.408	+	212.408i	0.348781	+	0.348781i
$610$		0			0
$611$	24.6678	−	215.873i	0.0403728	−	0.353312i
$612$	−519.866			−0.849454
$613$	−498.707	+	498.707i	−0.813552	+	0.813552i	−0.985165	−	0.171613i	$-0.945102\pi$
$613$	−498.707	+	498.707i	−0.813552	+	0.813552i	0.171613	+	0.985165i	$0.445102\pi$
$614$	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	−0.663708	−	0.747992i	$-0.731018\pi$
$617$	52.0030	−	52.0030i	0.0842836	−	0.0842836i	0.747992	+	0.663708i	$0.231018\pi$
$618$	−117.150	−	117.150i	−0.189563	−	0.189563i
$619$	95.1831	+	95.1831i	0.153769	+	0.153769i	0.779799	−	0.626030i	$-0.215321\pi$
$619$	95.1831	+	95.1831i	0.153769	+	0.153769i	−0.626030	+	0.779799i	$0.715321\pi$
$620$		0			0
$621$		−	851.722i		−	1.37153i
$622$	−13.7375	−	13.7375i	−0.0220859	−	0.0220859i
$623$			386.594i			0.620535i
$624$	152.116	+	191.366i	0.243776	+	0.306676i
$625$		0			0
$626$	−84.5828	+	84.5828i	−0.135116	+	0.135116i
$627$	−292.346			−0.466261
$628$		−	462.512i		−	0.736484i
$629$	−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
$633$	−1199.83			−1.89546
$634$			877.151i			1.38352i
$635$		0			0
$636$			161.377i			0.253737i
$637$	427.485	−	339.806i	0.671090	−	0.533448i
$638$	72.5459			0.113708
$639$	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	$-0.823595\pi$
$643$	−208.375	+	208.375i	−0.324066	+	0.324066i	0.526258	+	0.850325i	$0.323595\pi$
$644$	−165.230	−	165.230i	−0.256568	−	0.256568i
$645$		0			0
$646$	−821.897			−1.27229
$647$		−	31.5847i		−	0.0488171i	−0.999702	−	0.0244085i	$-0.992230\pi$
$647$		−	31.5847i		−	0.0488171i	0.999702	−	0.0244085i	$-0.00777025\pi$
$648$	−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
$653$	468.398			0.717302			0.358651	−	0.933472i	$-0.383237\pi$
$653$	468.398			0.717302			0.358651	+	0.933472i	$0.383237\pi$
$654$		−	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	$-0.438754\pi$
$659$	252.033			0.382447			0.191224	+	0.981546i	$0.438754\pi$
$660$		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	$0.718076\pi$
$662$			43.4909i			0.0656962i
$663$	−949.228	+	754.539i	−1.43172	+	1.13807i
$664$	−342.371			−0.515619
$665$		0			0
$666$	394.186			0.591870
$667$			1067.52i			1.60047i
$668$	−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
$672$	70.3264			0.104652
$673$			41.0765i			0.0610348i	0.999534	+	0.0305174i	$0.00971551\pi$
$673$			41.0765i			0.0610348i	−0.999534	+	0.0305174i	$0.990284\pi$
$674$	−364.125	−	364.125i	−0.540245	−	0.540245i
$675$		0			0
$676$	329.287	+	76.2507i	0.487111	+	0.112797i
$677$	−980.144			−1.44778			−0.723888	−	0.689918i	$-0.757647\pi$
$677$	−980.144			−1.44778			−0.723888	+	0.689918i	$0.757647\pi$
$678$	−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	0.915956	−	0.401279i	$-0.131434\pi$
$683$	351.524	+	351.524i	0.514676	+	0.514676i	−0.401279	+	0.915956i	$0.631434\pi$
$684$	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
$688$			198.618i			0.288689i
$689$	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	$0.465533\pi$
$692$	465.890			0.673251
$693$			73.5516i			0.106135i
$694$	−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
$698$	−279.772			−0.400820
$699$			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	$0.734051\pi$
$702$	352.133	+	40.2381i	0.501614	+	0.0573192i
$703$	623.199			0.886485
$704$	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	0.428542	−	0.903522i	$-0.359028\pi$
$709$	−336.761	−	336.761i	−0.474981	−	0.474981i	−0.903522	+	0.428542i	$0.859028\pi$
$710$		0			0
$711$	1895.04			2.66532
$712$		−	413.485i		−	0.580737i
$713$	−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
$718$	216.100			0.300975
$719$			25.7066i			0.0357533i	0.999840	+	0.0178766i	$0.00569062\pi$
$719$			25.7066i			0.0357533i	−0.999840	+	0.0178766i	$0.994309\pi$
$720$		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
$727$			98.7160i			0.135785i	0.997693	+	0.0678927i	$0.0216276\pi$
$727$			98.7160i			0.135785i	−0.997693	+	0.0678927i	$0.978372\pi$
$728$	76.1179	−	60.5059i	0.104558	−	0.0831125i
$729$	−1173.02			−1.60908
$730$		0			0
$731$	−985.199			−1.34774
$732$			159.376i			0.217727i
$733$	70.0366	−	70.0366i	0.0955479	−	0.0955479i	−0.657717	−	0.753265i	$-0.728478\pi$
$733$	70.0366	−	70.0366i	0.0955479	−	0.0955479i	0.753265	+	0.657717i	$0.228478\pi$
$734$	−35.1926	+	35.1926i	−0.0479464	+	0.0479464i
$735$		0			0
$736$	176.723	+	176.723i	0.240113	+	0.240113i
$737$	−53.0212			−0.0719419
$738$		−	459.329i		−	0.622397i
$739$	884.117	+	884.117i	1.19637	+	1.19637i	0.975246	+	0.221124i	$0.0709724\pi$
$739$	884.117	+	884.117i	1.19637	+	1.19637i	0.221124	+	0.975246i	$0.429028\pi$
$740$		0			0
$741$	1778.55	+	203.235i	2.40020	+	0.274271i
$742$	64.1894			0.0865087
$743$	236.735	−	236.735i	0.318621	−	0.318621i	−0.529617	−	0.848237i	$-0.677664\pi$
$743$	236.735	−	236.735i	0.318621	−	0.318621i	0.848237	+	0.529617i	$0.177664\pi$
$744$	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
$753$		−	797.116i		−	1.05859i
$754$	−441.350	−	50.4329i	−0.585344	−	0.0668871i
$755$		0			0
$756$	72.0975	−	72.0975i	0.0953671	−	0.0953671i
$757$	718.877			0.949639			0.474819	−	0.880083i	$-0.342513\pi$
$757$	718.877			0.949639			0.474819	+	0.880083i	$0.342513\pi$
$758$			527.629i			0.696081i
$759$	−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
$763$	−32.1455			−0.0421304
$764$			585.529i			0.766400i
$765$		0			0
$766$		−	701.772i		−	0.916151i
$767$	38.4705	−	336.664i	0.0501571	−	0.438936i
$768$	−75.2183			−0.0979405
$769$	−788.894	+	788.894i	−1.02587	+	1.02587i	−0.0262133	+	0.999656i	$0.508345\pi$
$769$	−788.894	+	788.894i	−1.02587	+	1.02587i	−0.999656	+	0.0262133i	$0.991655\pi$
$770$		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	−0.00562865	+	0.999984i	$0.501792\pi$
$773$	−777.339	+	777.339i	−1.00561	+	1.00561i	−0.999984	+	0.00562865i	$0.998208\pi$
$774$	650.510	+	650.510i	0.840452	+	0.840452i
$775$		0			0
$776$	452.254			0.582802
$777$		−	264.505i		−	0.340418i
$778$	−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
$783$	−465.808			−0.594901
$784$			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	−0.981121	−	0.193395i	$-0.938050\pi$
$787$	−924.344	−	924.344i	−1.17452	−	1.17452i	−0.193395	−	0.981121i	$-0.561950\pi$
$788$	−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
$792$		−	78.6678i		−	0.0993281i
$793$	137.121	+	172.501i	0.172914	+	0.217530i
$794$	−153.194			−0.192939
$795$		0			0
$796$	−197.110			−0.247626
$797$			619.505i			0.777297i	0.921386	+	0.388648i	$0.127058\pi$
$797$			619.505i			0.777297i	−0.921386	+	0.388648i	$0.872942\pi$
$798$	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
$802$	968.818			1.20800
$803$			34.4775i			0.0429358i
$804$	166.039	+	166.039i	0.206517	+	0.206517i
$805$		0			0
$806$	203.104	−	161.447i	0.251990	−	0.200307i
$807$	527.392			0.653521
$808$	251.112	−	251.112i	0.310782	−	0.310782i
$809$	834.817			1.03191			0.515956	−	0.856615i	$-0.327437\pi$
$809$	834.817			1.03191			0.515956	+	0.856615i	$0.327437\pi$
$810$		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
$818$			618.758i			0.756428i
$819$	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	$0.304075\pi$
$822$	60.4004			0.0734798
$823$		−	782.315i		−	0.950565i	−0.879833	−	0.475282i	$-0.842346\pi$
$823$		−	782.315i		−	0.950565i	0.879833	−	0.475282i	$-0.157654\pi$
$824$	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	$-0.413312\pi$
$827$	−574.071	−	574.071i	−0.694161	−	0.694161i	−0.963145	+	0.268984i	$0.913312\pi$
$828$	1157.60			1.39807
$829$		−	646.610i		−	0.779988i	−0.920817	−	0.389994i	$-0.872477\pi$
$829$		−	646.610i		−	0.779988i	0.920817	−	0.389994i	$-0.127523\pi$
$830$		0			0
$831$			1308.27i			1.57433i
$832$	−81.4126	+	64.7147i	−0.0978517	+	0.0777821i
$833$	−833.459			−1.00055
$834$	−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	0.677455	−	0.735564i	$-0.263083\pi$
$839$	−48.7532	−	48.7532i	−0.0581087	−	0.0581087i	−0.735564	+	0.677455i	$0.763083\pi$
$840$		0			0
$841$	−257.174			−0.305796
$842$			314.247i			0.373215i
$843$	−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
$848$	−68.6544			−0.0809604
$849$			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	0.587280	−	0.809384i	$-0.300199\pi$
$853$	−189.455	−	189.455i	−0.222104	−	0.222104i	−0.809384	+	0.587280i	$0.800199\pi$
$854$	63.3937			0.0742315
$855$		0			0
$856$	−316.139	−	316.139i	−0.369321	−	0.369321i
$857$		−	644.425i		−	0.751954i	−0.926629	−	0.375977i	$-0.877307\pi$
$857$		−	644.425i		−	0.751954i	0.926629	−	0.375977i	$-0.122693\pi$
$858$	−114.179	−	143.640i	−0.133076	−	0.167413i
$859$	−78.4060			−0.0912759			−0.0456379	−	0.998958i	$-0.514532\pi$
$859$	−78.4060			−0.0912759			−0.0456379	+	0.998958i	$0.514532\pi$
$860$		0			0
$861$	−308.217			−0.357976
$862$		−	205.579i		−	0.238491i
$863$	255.051	−	255.051i	0.295540	−	0.295540i	−0.543724	−	0.839264i	$-0.682986\pi$
$863$	255.051	−	255.051i	0.295540	−	0.295540i	0.839264	+	0.543724i	$0.182986\pi$
$864$	−77.1125	+	77.1125i	−0.0892506	+	0.0892506i
$865$		0			0
$866$	423.761	+	423.761i	0.489332	+	0.489332i
$867$	492.064			0.567548
$868$		−	74.6402i		−	0.0859910i
$869$	−217.153	−	217.153i	−0.249888	−	0.249888i
$870$		0			0
$871$	322.566	+	36.8595i	0.370340	+	0.0423187i
$872$	34.3815			0.0394283
$873$	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	−0.383386	−	0.923588i	$-0.625242\pi$
$877$	473.757	−	473.757i	0.540202	−	0.540202i	0.923588	+	0.383386i	$0.125242\pi$
$878$	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
$883$		−	211.169i		−	0.239150i	−0.992825	−	0.119575i	$-0.961847\pi$
$883$		−	211.169i		−	0.239150i	0.992825	−	0.119575i	$-0.0381532\pi$
$884$	−321.002	−	403.829i	−0.363125	−	0.456820i
$885$		0			0
$886$	−97.0515	+	97.0515i	−0.109539	+	0.109539i
$887$	−86.2904			−0.0972835			−0.0486417	−	0.998816i	$-0.515489\pi$
$887$	−86.2904			−0.0972835			−0.0486417	+	0.998816i	$0.515489\pi$
$888$			282.904i			0.318585i
$889$	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
$893$	489.564			0.548224
$894$			533.034i			0.596235i
$895$		0			0
$896$			29.9189i			0.0333916i
$897$	2113.67	−	1680.15i	2.35638	−	1.87308i
$898$	568.400			0.632962
$899$	−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
$907$		−	737.549i		−	0.813175i	−0.913612	−	0.406587i	$-0.866719\pi$
$907$		−	737.549i		−	0.813175i	0.913612	−	0.406587i	$-0.133281\pi$
$908$	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
$913$	256.986			0.281474
$914$		−	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	$-0.452029\pi$
$919$	275.951			0.300273			0.150137	+	0.988665i	$0.452029\pi$
$920$		0			0
$921$	1317.28	+	1317.28i	1.43027	+	1.43027i
$922$		−	394.116i		−	0.427458i
$923$	1359.84	+	155.389i	1.47329	+	0.168352i
$924$	−52.7874			−0.0571292
$925$		0			0
$926$	−241.252			−0.260531
$927$		−	326.464i		−	0.352173i
$928$	96.6499	−	96.6499i	0.104149	−	0.104149i
$929$	757.514	−	757.514i	0.815408	−	0.815408i	−0.170031	−	0.985439i	$-0.554387\pi$
$929$	757.514	−	757.514i	0.815408	−	0.815408i	0.985439	+	0.170031i	$0.0543867\pi$
$930$		0			0
$931$	870.043	+	870.043i	0.934525	+	0.934525i
$932$	−671.110			−0.720075
$933$		−	64.5817i		−	0.0692194i
$934$	537.485	+	537.485i	0.575466	+	0.575466i
$935$		0			0
$936$	−54.6888	+	478.594i	−0.0584282	+	0.511318i
$937$	−57.6262			−0.0615007			−0.0307504	−	0.999527i	$-0.509790\pi$
$937$	−57.6262			−0.0615007			−0.0307504	+	0.999527i	$0.509790\pi$
$938$	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	$-0.168003\pi$
$947$	341.194	+	341.194i	0.360289	+	0.360289i	−0.503630	+	0.863919i	$0.668003\pi$
$948$			1360.06i			1.43466i
$949$	23.9682	−	209.751i	0.0252563	−	0.221024i
$950$		0			0
$951$	−2061.81	+	2061.81i	−2.16804	+	2.16804i
$952$	−148.406			−0.155888
$953$		−	1754.80i		−	1.84134i	−0.390337	−	0.920672i	$-0.627641\pi$
$953$		−	1754.80i		−	1.84134i	0.390337	−	0.920672i	$-0.372359\pi$
$954$	−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
$958$	−289.959			−0.302672
$959$		−	24.0249i		−	0.0250520i
$960$		0			0
$961$			761.839i			0.792756i
$962$	243.399	+	306.201i	0.253013	+	0.318296i
$963$	−2070.83			−2.15039
$964$	−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	−0.386217	+	0.922408i	$0.626219\pi$
$967$	−1265.44	+	1265.44i	−1.30863	+	1.30863i	−0.922408	+	0.386217i	$0.873781\pi$
$968$	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	$0.503770\pi$
$972$		−	603.476i		−	0.620860i
$973$	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	−0.746673	−	0.665192i	$-0.768350\pi$
$977$	−79.6072	+	79.6072i	−0.0814812	+	0.0814812i	0.665192	+	0.746673i	$0.268350\pi$
$978$	−1413.29			−1.44508
$979$			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	−0.999822	−	0.0188828i	$-0.993989\pi$
$983$	−1001.39	−	1001.39i	−1.01870	−	1.01870i	−0.0188828	−	0.999822i	$-0.506011\pi$
$984$	329.657			0.335017
$985$		0			0
$986$	479.410	+	479.410i	0.486217	+	0.486217i
$987$		−	207.786i		−	0.210523i
$988$	−86.4618	+	756.647i	−0.0875119	+	0.765837i
$989$	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	$0.332068\pi$
$992$			79.8321i			0.0804759i
$993$	−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
$997$	−1138.16			−1.14158			−0.570792	−	0.821095i	$-0.693364\pi$
$997$	−1138.16			−1.14158			−0.570792	+	0.821095i	$0.693364\pi$
$998$			806.385i			0.808001i
$999$	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.k.j.551.1		12
5.2	odd	4		650.3.f.k.499.6		12
5.3	odd	4		650.3.f.n.499.1		12
5.4	even	2		130.3.k.b.31.6	yes	12
13.8	odd	4	inner	650.3.k.j.151.1		12
15.14	odd	2		1170.3.r.a.811.5		12
65.8	even	4		650.3.f.k.99.1		12
65.34	odd	4		130.3.k.b.21.6	✓	12
65.47	even	4		650.3.f.n.99.6		12
195.164	even	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	65.34	odd	4
130.3.k.b.31.6	yes	12	5.4	even	2
650.3.f.k.99.1		12	65.8	even	4
650.3.f.k.499.6		12	5.2	odd	4
650.3.f.n.99.6		12	65.47	even	4
650.3.f.n.499.1		12	5.3	odd	4
650.3.k.j.151.1		12	13.8	odd	4	inner
650.3.k.j.551.1		12	1.1	even	1	trivial
1170.3.r.a.541.5		12	195.164	even	4
1170.3.r.a.811.5		12	15.14	odd	2

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -4.70114 q^{3} -2.00000i q^{4} +(4.70114 - 4.70114i) q^{6} +(-1.86993 - 1.86993i) q^{7} +(2.00000 + 2.00000i) q^{8} +13.1007 q^{9} +(-1.50121 - 1.50121i) q^{11} +9.40228i q^{12} +(8.08933 + 10.1766i) q^{13} +3.73986 q^{14} -4.00000 q^{16} -19.8411i q^{17} +(-13.1007 + 13.1007i) q^{18} +(-20.7120 + 20.7120i) q^{19} +(8.79080 + 8.79080i) q^{21} +3.00242 q^{22} +44.1807i q^{23} +(-9.40228 - 9.40228i) q^{24} +(-18.2659 - 2.08724i) q^{26} -19.2781 q^{27} +(-3.73986 + 3.73986i) q^{28} +24.1625 q^{29} +(-9.97901 + 9.97901i) q^{31} +(4.00000 - 4.00000i) q^{32} +(7.05740 + 7.05740i) q^{33} +(19.8411 + 19.8411i) q^{34} -26.2015i q^{36} +(-15.0444 - 15.0444i) q^{37} -41.4240i q^{38} +(-38.0291 - 47.8415i) q^{39} +(-17.5307 + 17.5307i) q^{41} -17.5816 q^{42} -49.6545i q^{43} +(-3.00242 + 3.00242i) q^{44} +(-44.1807 - 44.1807i) q^{46} +(-11.8184 - 11.8184i) q^{47} +18.8046 q^{48} -42.0067i q^{49} +93.2758i q^{51} +(20.3531 - 16.1787i) q^{52} +17.1636 q^{53} +(19.2781 - 19.2781i) q^{54} -7.47972i q^{56} +(97.3700 - 97.3700i) q^{57} +(-24.1625 + 24.1625i) q^{58} +(-18.4313 - 18.4313i) q^{59} +16.9508 q^{61} -19.9580i q^{62} +(-24.4974 - 24.4974i) q^{63} +8.00000i q^{64} -14.1148 q^{66} +(17.6595 - 17.6595i) q^{67} -39.6822 q^{68} -207.700i q^{69} +(74.4471 - 74.4471i) q^{71} +(26.2015 + 26.2015i) q^{72} +(-11.4832 - 11.4832i) q^{73} +30.0888 q^{74} +(41.4240 + 41.4240i) q^{76} +5.61431i q^{77} +(85.8706 + 9.81241i) q^{78} +144.652 q^{79} -27.2774 q^{81} -35.0613i q^{82} +(-85.5928 + 85.5928i) q^{83} +(17.5816 - 17.5816i) q^{84} +(49.6545 + 49.6545i) q^{86} -113.591 q^{87} -6.00484i q^{88} +(-103.371 - 103.371i) q^{89} +(3.90299 - 34.1560i) q^{91} +88.3615 q^{92} +(46.9127 - 46.9127i) q^{93} +23.6367 q^{94} +(-18.8046 + 18.8046i) q^{96} +(113.064 - 113.064i) q^{97} +(42.0067 + 42.0067i) q^{98} +(-19.6670 - 19.6670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 8 q^{7} + 24 q^{8} + 76 q^{9} - 16 q^{11} + 20 q^{13} - 16 q^{14} - 48 q^{16} - 76 q^{18} - 68 q^{19} - 44 q^{21} + 32 q^{22} + 24 q^{26} + 96 q^{27} + 16 q^{28} + 216 q^{29} + 64 q^{31}+ \cdots + 484 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 8 * q^7 + 24 * q^8 + 76 * q^9 - 16 * q^11 + 20 * q^13 - 16 * q^14 - 48 * q^16 - 76 * q^18 - 68 * q^19 - 44 * q^21 + 32 * q^22 + 24 * q^26 + 96 * q^27 + 16 * q^28 + 216 * q^29 + 64 * q^31 + 48 * q^32 - 52 * q^33 + 32 * q^34 + 28 * q^37 + 140 * q^39 + 88 * q^42 - 32 * q^44 + 16 * q^46 + 104 * q^47 - 88 * q^52 + 424 * q^53 - 96 * q^54 + 100 * q^57 - 216 * q^58 - 108 * q^59 + 88 * q^61 - 312 * q^63 + 104 * q^66 - 240 * q^67 - 64 * q^68 + 12 * q^71 + 152 * q^72 + 164 * q^73 - 56 * q^74 + 136 * q^76 - 120 * q^78 + 392 * q^79 - 204 * q^81 - 536 * q^83 - 88 * q^84 + 160 * q^86 + 672 * q^87 - 364 * q^89 - 244 * q^91 - 32 * q^92 + 236 * q^93 - 208 * q^94 - 192 * q^97 - 484 * q^98 + 484 * q^99

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