LMFDB - Embedded newform 650.3.k.l.551.6

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 = [14,-14,0] 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:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 84x^{12} + 2668x^{10} + 40556x^{8} + 303080x^{6} + 1000960x^{4} + 1045476x^{2} + 193600 $ x^14 + 84x^12 + 2668x^10 + 40556x^8 + 303080x^6 + 1000960x^4 + 1045476x^2 + 193600
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			551.6
Root			$3.84840i$ of defining polynomial
Character	$\chi$	$=$	650.551
Dual form			650.3.k.l.151.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} +3.84840 q^{3} -2.00000i q^{4} +(-3.84840 + 3.84840i) q^{6} +(-2.44952 - 2.44952i) q^{7} +(2.00000 + 2.00000i) q^{8} +5.81016 q^{9} +(-4.31164 - 4.31164i) q^{11} -7.69679i q^{12} +(-9.48115 - 8.89425i) q^{13} +4.89903 q^{14} -4.00000 q^{16} -11.8592i q^{17} +(-5.81016 + 5.81016i) q^{18} +(9.71168 - 9.71168i) q^{19} +(-9.42671 - 9.42671i) q^{21} +8.62329 q^{22} -10.6797i q^{23} +(7.69679 + 7.69679i) q^{24} +(18.3754 - 0.586903i) q^{26} -12.2758 q^{27} +(-4.89903 + 4.89903i) q^{28} -21.5195 q^{29} +(39.8823 - 39.8823i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-16.5929 - 16.5929i) q^{33} +(11.8592 + 11.8592i) q^{34} -11.6203i q^{36} +(18.6605 + 18.6605i) q^{37} +19.4234i q^{38} +(-36.4872 - 34.2286i) q^{39} +(40.3015 - 40.3015i) q^{41} +18.8534 q^{42} +52.7965i q^{43} +(-8.62329 + 8.62329i) q^{44} +(10.6797 + 10.6797i) q^{46} +(-40.6800 - 40.6800i) q^{47} -15.3936 q^{48} -36.9997i q^{49} -45.6388i q^{51} +(-17.7885 + 18.9623i) q^{52} -42.2147 q^{53} +(12.2758 - 12.2758i) q^{54} -9.79806i q^{56} +(37.3744 - 37.3744i) q^{57} +(21.5195 - 21.5195i) q^{58} +(5.34862 + 5.34862i) q^{59} -72.6777 q^{61} +79.7646i q^{62} +(-14.2321 - 14.2321i) q^{63} +8.00000i q^{64} +33.1858 q^{66} +(-48.5284 + 48.5284i) q^{67} -23.7183 q^{68} -41.0996i q^{69} +(56.4982 - 56.4982i) q^{71} +(11.6203 + 11.6203i) q^{72} +(54.1769 + 54.1769i) q^{73} -37.3210 q^{74} +(-19.4234 - 19.4234i) q^{76} +21.1229i q^{77} +(70.7159 - 2.25863i) q^{78} +38.8202 q^{79} -99.5335 q^{81} +80.6030i q^{82} +(-32.3864 + 32.3864i) q^{83} +(-18.8534 + 18.8534i) q^{84} +(-52.7965 - 52.7965i) q^{86} -82.8156 q^{87} -17.2466i q^{88} +(44.0147 + 44.0147i) q^{89} +(1.43763 + 45.0109i) q^{91} -21.3593 q^{92} +(153.483 - 153.483i) q^{93} +81.3601 q^{94} +(15.3936 - 15.3936i) q^{96} +(49.9858 - 49.9858i) q^{97} +(36.9997 + 36.9997i) q^{98} +(-25.0513 - 25.0513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 28 q^{8} + 42 q^{9} + 8 q^{11} - 2 q^{13} - 56 q^{16} - 42 q^{18} - 44 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{26} - 120 q^{27} - 72 q^{29} - 64 q^{31} + 56 q^{32} - 56 q^{33} - 96 q^{34}+ \cdots - 292 q^{99}+O(q^{100}) $ 14 * q - 14 * q^2 + 28 * q^8 + 42 * q^9 + 8 * q^11 - 2 * q^13 - 56 * q^16 - 42 * q^18 - 44 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^26 - 120 * q^27 - 72 * q^29 - 64 * q^31 + 56 * q^32 - 56 * q^33 - 96 * q^34 + 98 * q^37 + 144 * q^39 + 138 * q^41 - 8 * q^42 + 16 * q^44 + 8 * q^46 - 40 * q^47 - 16 * q^52 - 176 * q^53 + 120 * q^54 + 264 * q^57 + 72 * q^58 + 20 * q^59 - 180 * q^61 + 160 * q^63 + 112 * q^66 - 8 * q^67 + 192 * q^68 - 100 * q^71 + 84 * q^72 + 54 * q^73 - 196 * q^74 + 88 * q^76 - 264 * q^78 - 344 * q^79 + 38 * q^81 + 296 * q^83 + 8 * q^84 - 120 * q^86 - 496 * q^87 + 398 * q^89 + 48 * q^91 - 16 * q^92 + 120 * q^93 + 80 * q^94 + 162 * q^97 - 130 * q^98 - 292 * 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
$3$	3.84840			1.28280			0.641399	−	0.767207i	$-0.278354\pi$
$3$	3.84840			1.28280			0.641399	+	0.767207i	$0.278354\pi$
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−3.84840	+	3.84840i	−0.641399	+	0.641399i
$7$	−2.44952	−	2.44952i	−0.349931	−	0.349931i	0.510153	−	0.860084i	$-0.329589\pi$
$7$	−2.44952	−	2.44952i	−0.349931	−	0.349931i	−0.860084	+	0.510153i	$0.829589\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	5.81016			0.645573
$10$		0			0
$11$	−4.31164	−	4.31164i	−0.391968	−	0.391968i	0.483421	−	0.875388i	$-0.339394\pi$
$11$	−4.31164	−	4.31164i	−0.391968	−	0.391968i	−0.875388	+	0.483421i	$0.839394\pi$
$12$		−	7.69679i		−	0.641399i
$13$	−9.48115	−	8.89425i	−0.729320	−	0.684173i
$13$	−9.48115	−	8.89425i	−0.729320	−	0.684173i
$14$	4.89903			0.349931
$15$		0			0
$16$	−4.00000			−0.250000
$17$		−	11.8592i		−	0.697598i	−0.937198	−	0.348799i	$-0.886590\pi$
$17$		−	11.8592i		−	0.697598i	0.937198	−	0.348799i	$-0.113410\pi$
$18$	−5.81016	+	5.81016i	−0.322787	+	0.322787i
$19$	9.71168	−	9.71168i	0.511141	−	0.511141i	−0.403735	−	0.914876i	$-0.632288\pi$
$19$	9.71168	−	9.71168i	0.511141	−	0.511141i	0.914876	+	0.403735i	$0.132288\pi$
$20$		0			0
$21$	−9.42671	−	9.42671i	−0.448891	−	0.448891i
$22$	8.62329			0.391968
$23$		−	10.6797i		−	0.464333i	−0.972676	−	0.232167i	$-0.925419\pi$
$23$		−	10.6797i		−	0.464333i	0.972676	−	0.232167i	$-0.0745815\pi$
$24$	7.69679	+	7.69679i	0.320700	+	0.320700i
$25$		0			0
$26$	18.3754	−	0.586903i	0.706746	−	0.0225732i
$27$	−12.2758			−0.454658
$28$	−4.89903	+	4.89903i	−0.174965	+	0.174965i
$29$	−21.5195			−0.742052			−0.371026	−	0.928622i	$-0.620994\pi$
$29$	−21.5195			−0.742052			−0.371026	+	0.928622i	$0.620994\pi$
$30$		0			0
$31$	39.8823	−	39.8823i	1.28653	−	1.28653i	0.349643	−	0.936883i	$-0.386303\pi$
$31$	39.8823	−	39.8823i	1.28653	−	1.28653i	0.936883	−	0.349643i	$-0.113697\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−16.5929	−	16.5929i	−0.502816	−	0.502816i
$34$	11.8592	+	11.8592i	0.348799	+	0.348799i
$35$		0			0
$36$		−	11.6203i		−	0.322787i
$37$	18.6605	+	18.6605i	0.504338	+	0.504338i	0.912783	−	0.408445i	$-0.133929\pi$
$37$	18.6605	+	18.6605i	0.504338	+	0.504338i	−0.408445	+	0.912783i	$0.633929\pi$
$38$			19.4234i			0.511141i
$39$	−36.4872	−	34.2286i	−0.935570	−	0.877657i
$40$		0			0
$41$	40.3015	−	40.3015i	0.982963	−	0.982963i	−0.0168942	−	0.999857i	$-0.505378\pi$
$41$	40.3015	−	40.3015i	0.982963	−	0.982963i	0.999857	+	0.0168942i	$0.00537784\pi$
$42$	18.8534			0.448891
$43$			52.7965i			1.22782i	0.789374	+	0.613912i	$0.210405\pi$
$43$			52.7965i			1.22782i	−0.789374	+	0.613912i	$0.789595\pi$
$44$	−8.62329	+	8.62329i	−0.195984	+	0.195984i
$45$		0			0
$46$	10.6797	+	10.6797i	0.232167	+	0.232167i
$47$	−40.6800	−	40.6800i	−0.865533	−	0.865533i	0.126441	−	0.991974i	$-0.459644\pi$
$47$	−40.6800	−	40.6800i	−0.865533	−	0.865533i	−0.991974	+	0.126441i	$0.959644\pi$
$48$	−15.3936			−0.320700
$49$		−	36.9997i		−	0.755097i
$50$		0			0
$51$		−	45.6388i		−	0.894878i
$52$	−17.7885	+	18.9623i	−0.342087	+	0.364660i
$53$	−42.2147			−0.796503			−0.398252	−	0.917276i	$-0.630383\pi$
$53$	−42.2147			−0.796503			−0.398252	+	0.917276i	$0.630383\pi$
$54$	12.2758	−	12.2758i	0.227329	−	0.227329i
$55$		0			0
$56$		−	9.79806i		−	0.174965i
$57$	37.3744	−	37.3744i	0.655691	−	0.655691i
$58$	21.5195	−	21.5195i	0.371026	−	0.371026i
$59$	5.34862	+	5.34862i	0.0906546	+	0.0906546i	0.750980	−	0.660325i	$-0.229582\pi$
$59$	5.34862	+	5.34862i	0.0906546	+	0.0906546i	−0.660325	+	0.750980i	$0.729582\pi$
$60$		0			0
$61$	−72.6777			−1.19144			−0.595719	−	0.803193i	$-0.703133\pi$
$61$	−72.6777			−1.19144			−0.595719	+	0.803193i	$0.703133\pi$
$62$			79.7646i			1.28653i
$63$	−14.2321	−	14.2321i	−0.225906	−	0.225906i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	33.1858			0.502816
$67$	−48.5284	+	48.5284i	−0.724305	+	0.724305i	−0.969479	−	0.245174i	$-0.921155\pi$
$67$	−48.5284	+	48.5284i	−0.724305	+	0.724305i	0.245174	+	0.969479i	$0.421155\pi$
$68$	−23.7183			−0.348799
$69$		−	41.0996i		−	0.595646i
$70$		0			0
$71$	56.4982	−	56.4982i	0.795749	−	0.795749i	−0.186673	−	0.982422i	$-0.559771\pi$
$71$	56.4982	−	56.4982i	0.795749	−	0.795749i	0.982422	+	0.186673i	$0.0597705\pi$
$72$	11.6203	+	11.6203i	0.161393	+	0.161393i
$73$	54.1769	+	54.1769i	0.742149	+	0.742149i	0.972991	−	0.230842i	$-0.0741482\pi$
$73$	54.1769	+	54.1769i	0.742149	+	0.742149i	−0.230842	+	0.972991i	$0.574148\pi$
$74$	−37.3210			−0.504338
$75$		0			0
$76$	−19.4234	−	19.4234i	−0.255570	−	0.255570i
$77$			21.1229i			0.274323i
$78$	70.7159	−	2.25863i	0.906613	−	0.0289568i
$79$	38.8202			0.491395			0.245698	−	0.969347i	$-0.420983\pi$
$79$	38.8202			0.491395			0.245698	+	0.969347i	$0.420983\pi$
$80$		0			0
$81$	−99.5335			−1.22881
$82$			80.6030i			0.982963i
$83$	−32.3864	+	32.3864i	−0.390198	+	0.390198i	−0.874758	−	0.484560i	$-0.838980\pi$
$83$	−32.3864	+	32.3864i	−0.390198	+	0.390198i	0.484560	+	0.874758i	$0.338980\pi$
$84$	−18.8534	+	18.8534i	−0.224445	+	0.224445i
$85$		0			0
$86$	−52.7965	−	52.7965i	−0.613912	−	0.613912i
$87$	−82.8156			−0.951904
$88$		−	17.2466i		−	0.195984i
$89$	44.0147	+	44.0147i	0.494547	+	0.494547i	0.909735	−	0.415189i	$-0.136284\pi$
$89$	44.0147	+	44.0147i	0.494547	+	0.494547i	−0.415189	+	0.909735i	$0.636284\pi$
$90$		0			0
$91$	1.43763	+	45.0109i	0.0157981	+	0.494625i
$92$	−21.3593			−0.232167
$93$	153.483	−	153.483i	1.65035	−	1.65035i
$94$	81.3601			0.865533
$95$		0			0
$96$	15.3936	−	15.3936i	0.160350	−	0.160350i
$97$	49.9858	−	49.9858i	0.515317	−	0.515317i	−0.400833	−	0.916151i	$-0.631279\pi$
$97$	49.9858	−	49.9858i	0.515317	−	0.515317i	0.916151	+	0.400833i	$0.131279\pi$
$98$	36.9997	+	36.9997i	0.377548	+	0.377548i
$99$	−25.0513	−	25.0513i	−0.253044	−	0.253044i
$100$		0			0
$101$			85.1995i			0.843560i	0.906698	+	0.421780i	$0.138594\pi$
$101$			85.1995i			0.843560i	−0.906698	+	0.421780i	$0.861406\pi$
$102$	45.6388	+	45.6388i	0.447439	+	0.447439i
$103$			11.4074i			0.110752i	0.998466	+	0.0553758i	$0.0176357\pi$
$103$			11.4074i			0.110752i	−0.998466	+	0.0553758i	$0.982364\pi$
$104$	−1.17381	−	36.7508i	−0.0112866	−	0.353373i
$105$		0			0
$106$	42.2147	−	42.2147i	0.398252	−	0.398252i
$107$	62.1056			0.580426			0.290213	−	0.956962i	$-0.406274\pi$
$107$	62.1056			0.580426			0.290213	+	0.956962i	$0.406274\pi$
$108$			24.5516i			0.227329i
$109$	133.664	−	133.664i	1.22627	−	1.22627i	0.260909	−	0.965363i	$-0.415978\pi$
$109$	133.664	−	133.664i	1.22627	−	1.22627i	0.965363	−	0.260909i	$-0.0840221\pi$
$110$		0			0
$111$	71.8130	+	71.8130i	0.646964	+	0.646964i
$112$	9.79806	+	9.79806i	0.0874827	+	0.0874827i
$113$	−148.138			−1.31096			−0.655478	−	0.755214i	$-0.727533\pi$
$113$	−148.138			−1.31096			−0.655478	+	0.755214i	$0.727533\pi$
$114$			74.7488i			0.655691i
$115$		0			0
$116$			43.0390i			0.371026i
$117$	−55.0870	−	51.6770i	−0.470829	−	0.441684i
$118$	−10.6972			−0.0906546
$119$	−29.0492	+	29.0492i	−0.244111	+	0.244111i
$120$		0			0
$121$		−	83.8195i		−	0.692723i
$122$	72.6777	−	72.6777i	0.595719	−	0.595719i
$123$	155.096	−	155.096i	1.26094	−	1.26094i
$124$	−79.7646	−	79.7646i	−0.643263	−	0.643263i
$125$		0			0
$126$	28.4641			0.225906
$127$		−	230.518i		−	1.81511i	−0.419938	−	0.907553i	$-0.637948\pi$
$127$		−	230.518i		−	1.81511i	0.419938	−	0.907553i	$-0.362052\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			203.182i			1.57505i
$130$		0			0
$131$	214.401			1.63665			0.818326	−	0.574755i	$-0.194903\pi$
$131$	214.401			1.63665			0.818326	+	0.574755i	$0.194903\pi$
$132$	−33.1858	+	33.1858i	−0.251408	+	0.251408i
$133$	−47.5778			−0.357728
$134$		−	97.0568i		−	0.724305i
$135$		0			0
$136$	23.7183	−	23.7183i	0.174399	−	0.174399i
$137$	−101.847	−	101.847i	−0.743408	−	0.743408i	0.229824	−	0.973232i	$-0.426185\pi$
$137$	−101.847	−	101.847i	−0.743408	−	0.743408i	−0.973232	+	0.229824i	$0.926185\pi$
$138$	41.0996	+	41.0996i	0.297823	+	0.297823i
$139$	75.7601			0.545037			0.272519	−	0.962151i	$-0.412143\pi$
$139$	75.7601			0.545037			0.272519	+	0.962151i	$0.412143\pi$
$140$		0			0
$141$	−156.553	−	156.553i	−1.11030	−	1.11030i
$142$			112.996i			0.795749i
$143$	2.53052	+	79.2282i	0.0176959	+	0.554043i
$144$	−23.2406			−0.161393
$145$		0			0
$146$	−108.354			−0.742149
$147$		−	142.390i		−	0.968637i
$148$	37.3210	−	37.3210i	0.252169	−	0.252169i
$149$	−111.435	+	111.435i	−0.747883	+	0.747883i	−0.974081	−	0.226198i	$-0.927370\pi$
$149$	−111.435	+	111.435i	−0.747883	+	0.747883i	0.226198	+	0.974081i	$0.427370\pi$
$150$		0			0
$151$	135.707	+	135.707i	0.898722	+	0.898722i	0.995323	−	0.0966013i	$-0.0307972\pi$
$151$	135.707	+	135.707i	0.898722	+	0.898722i	−0.0966013	+	0.995323i	$0.530797\pi$
$152$	38.8467			0.255570
$153$		−	68.9036i		−	0.450350i
$154$	−21.1229	−	21.1229i	−0.137162	−	0.137162i
$155$		0			0
$156$	−68.4572	+	72.9745i	−0.438828	+	0.467785i
$157$	172.878			1.10114			0.550568	−	0.834790i	$-0.314411\pi$
$157$	172.878			1.10114			0.550568	+	0.834790i	$0.314411\pi$
$158$	−38.8202	+	38.8202i	−0.245698	+	0.245698i
$159$	−162.459			−1.02175
$160$		0			0
$161$	−26.1600	+	26.1600i	−0.162485	+	0.162485i
$162$	99.5335	−	99.5335i	0.614404	−	0.614404i
$163$	−55.5819	−	55.5819i	−0.340993	−	0.340993i	0.515747	−	0.856741i	$-0.327514\pi$
$163$	−55.5819	−	55.5819i	−0.340993	−	0.340993i	−0.856741	+	0.515747i	$0.827514\pi$
$164$	−80.6030	−	80.6030i	−0.491482	−	0.491482i
$165$		0			0
$166$		−	64.7728i		−	0.390198i
$167$	92.0373	+	92.0373i	0.551121	+	0.551121i	0.926764	−	0.375643i	$-0.122578\pi$
$167$	92.0373	+	92.0373i	0.551121	+	0.551121i	−0.375643	+	0.926764i	$0.622578\pi$
$168$		−	37.7068i		−	0.224445i
$169$	10.7846	+	168.656i	0.0638140	+	0.997962i
$170$		0			0
$171$	56.4264	−	56.4264i	0.329979	−	0.329979i
$172$	105.593			0.613912
$173$			86.3308i			0.499022i	0.968372	+	0.249511i	$0.0802699\pi$
$173$			86.3308i			0.499022i	−0.968372	+	0.249511i	$0.919730\pi$
$174$	82.8156	−	82.8156i	0.475952	−	0.475952i
$175$		0			0
$176$	17.2466	+	17.2466i	0.0979919	+	0.0979919i
$177$	20.5836	+	20.5836i	0.116292	+	0.116292i
$178$	−88.0293			−0.494547
$179$			223.879i			1.25072i	0.780336	+	0.625361i	$0.215048\pi$
$179$			223.879i			1.25072i	−0.780336	+	0.625361i	$0.784952\pi$
$180$		0			0
$181$			305.729i			1.68911i	0.535468	+	0.844555i	$0.320135\pi$
$181$			305.729i			1.68911i	−0.535468	+	0.844555i	$0.679865\pi$
$182$	−46.4485	−	43.5732i	−0.255211	−	0.239413i
$183$	−279.693			−1.52838
$184$	21.3593	−	21.3593i	0.116083	−	0.116083i
$185$		0			0
$186$			306.966i			1.65035i
$187$	−51.1325	+	51.1325i	−0.273436	+	0.273436i
$188$	−81.3601	+	81.3601i	−0.432766	+	0.432766i
$189$	30.0697	+	30.0697i	0.159099	+	0.159099i
$190$		0			0
$191$	−288.933			−1.51274			−0.756368	−	0.654146i	$-0.773028\pi$
$191$	−288.933			−1.51274			−0.756368	+	0.654146i	$0.773028\pi$
$192$			30.7872i			0.160350i
$193$	116.591	+	116.591i	0.604098	+	0.604098i	0.941397	−	0.337299i	$-0.109513\pi$
$193$	116.591	+	116.591i	0.604098	+	0.604098i	−0.337299	+	0.941397i	$0.609513\pi$
$194$			99.9716i			0.515317i
$195$		0			0
$196$	−73.9995			−0.377548
$197$	−104.376	+	104.376i	−0.529827	+	0.529827i	−0.920521	−	0.390694i	$-0.872235\pi$
$197$	−104.376	+	104.376i	−0.529827	+	0.529827i	0.390694	+	0.920521i	$0.372235\pi$
$198$	50.1027			0.253044
$199$		−	194.443i		−	0.977101i	−0.872536	−	0.488551i	$-0.837526\pi$
$199$		−	194.443i		−	0.977101i	0.872536	−	0.488551i	$-0.162474\pi$
$200$		0			0
$201$	−186.757	+	186.757i	−0.929137	+	0.929137i
$202$	−85.1995	−	85.1995i	−0.421780	−	0.421780i
$203$	52.7124	+	52.7124i	0.259667	+	0.259667i
$204$	−91.2775			−0.447439
$205$		0			0
$206$	−11.4074	−	11.4074i	−0.0553758	−	0.0553758i
$207$		−	62.0506i		−	0.299761i
$208$	37.9246	+	35.5770i	0.182330	+	0.171043i
$209$	−83.7466			−0.400701
$210$		0			0
$211$	−103.472			−0.490389			−0.245195	−	0.969474i	$-0.578852\pi$
$211$	−103.472			−0.490389			−0.245195	+	0.969474i	$0.578852\pi$
$212$			84.4293i			0.398252i
$213$	217.427	−	217.427i	1.02079	−	1.02079i
$214$	−62.1056	+	62.1056i	−0.290213	+	0.290213i
$215$		0			0
$216$	−24.5516	−	24.5516i	−0.113665	−	0.113665i
$217$	−195.385			−0.900390
$218$			267.327i			1.22627i
$219$	208.494	+	208.494i	0.952028	+	0.952028i
$220$		0			0
$221$	−105.478	+	112.439i	−0.477278	+	0.508772i
$222$	−143.626			−0.646964
$223$	−14.2146	+	14.2146i	−0.0637428	+	0.0637428i	−0.738260	−	0.674517i	$-0.764352\pi$
$223$	−14.2146	+	14.2146i	−0.0637428	+	0.0637428i	0.674517	+	0.738260i	$0.264352\pi$
$224$	−19.5961			−0.0874827
$225$		0			0
$226$	148.138	−	148.138i	0.655478	−	0.655478i
$227$	−283.524	+	283.524i	−1.24900	+	1.24900i	−0.292842	+	0.956161i	$0.594601\pi$
$227$	−283.524	+	283.524i	−1.24900	+	1.24900i	−0.956161	+	0.292842i	$0.905399\pi$
$228$	−74.7488	−	74.7488i	−0.327845	−	0.327845i
$229$	−303.668	−	303.668i	−1.32606	−	1.32606i	−0.908774	−	0.417288i	$-0.862981\pi$
$229$	−303.668	−	303.668i	−1.32606	−	1.32606i	−0.417288	−	0.908774i	$-0.637019\pi$
$230$		0			0
$231$			81.2892i			0.351901i
$232$	−43.0390	−	43.0390i	−0.185513	−	0.185513i
$233$		−	134.811i		−	0.578588i	−0.957240	−	0.289294i	$-0.906580\pi$
$233$		−	134.811i		−	0.578588i	0.957240	−	0.289294i	$-0.0934204\pi$
$234$	106.764	−	3.41000i	0.456256	−	0.0145726i
$235$		0			0
$236$	10.6972	−	10.6972i	0.0453273	−	0.0453273i
$237$	149.396			0.630361
$238$		−	58.0984i		−	0.244111i
$239$	204.968	−	204.968i	0.857606	−	0.857606i	−0.133449	−	0.991056i	$-0.542605\pi$
$239$	204.968	−	204.968i	0.857606	−	0.857606i	0.991056	+	0.133449i	$0.0426054\pi$
$240$		0			0
$241$	264.576	+	264.576i	1.09782	+	1.09782i	0.994665	+	0.103160i	$0.0328953\pi$
$241$	264.576	+	264.576i	1.09782	+	1.09782i	0.103160	+	0.994665i	$0.467105\pi$
$242$	83.8195	+	83.8195i	0.346361	+	0.346361i
$243$	−272.562			−1.12166
$244$			145.355i			0.595719i
$245$		0			0
$246$			310.192i			1.26094i
$247$	−178.456	+	5.69981i	−0.722494	+	0.0230761i
$248$	159.529			0.643263
$249$	−124.636	+	124.636i	−0.500545	+	0.500545i
$250$		0			0
$251$		−	89.6680i		−	0.357243i	−0.983918	−	0.178621i	$-0.942836\pi$
$251$		−	89.6680i		−	0.357243i	0.983918	−	0.178621i	$-0.0571638\pi$
$252$	−28.4641	+	28.4641i	−0.112953	+	0.112953i
$253$	−46.0469	+	46.0469i	−0.182004	+	0.182004i
$254$	230.518	+	230.518i	0.907553	+	0.907553i
$255$		0			0
$256$	16.0000			0.0625000
$257$			209.326i			0.814497i	0.913317	+	0.407248i	$0.133512\pi$
$257$			209.326i			0.814497i	−0.913317	+	0.407248i	$0.866488\pi$
$258$	−203.182	−	203.182i	−0.787526	−	0.787526i
$259$		−	91.4184i		−	0.352967i
$260$		0			0
$261$	−125.032			−0.479049
$262$	−214.401	+	214.401i	−0.818326	+	0.818326i
$263$	−135.381			−0.514756			−0.257378	−	0.966311i	$-0.582859\pi$
$263$	−135.381			−0.514756			−0.257378	+	0.966311i	$0.582859\pi$
$264$		−	66.3717i		−	0.251408i
$265$		0			0
$266$	47.5778	−	47.5778i	0.178864	−	0.178864i
$267$	169.386	+	169.386i	0.634404	+	0.634404i
$268$	97.0568	+	97.0568i	0.362152	+	0.362152i
$269$	−65.9632			−0.245217			−0.122608	−	0.992455i	$-0.539126\pi$
$269$	−65.9632			−0.245217			−0.122608	+	0.992455i	$0.539126\pi$
$270$		0			0
$271$	−290.080	−	290.080i	−1.07040	−	1.07040i	−0.997326	−	0.0730788i	$-0.976718\pi$
$271$	−290.080	−	290.080i	−1.07040	−	1.07040i	−0.0730788	−	0.997326i	$-0.523282\pi$
$272$			47.4367i			0.174399i
$273$	5.53256	+	173.220i	0.0202658	+	0.634504i
$274$	203.694			0.743408
$275$		0			0
$276$	−82.1992			−0.297823
$277$		−	191.294i		−	0.690593i	−0.938494	−	0.345296i	$-0.887778\pi$
$277$		−	191.294i		−	0.690593i	0.938494	−	0.345296i	$-0.112222\pi$
$278$	−75.7601	+	75.7601i	−0.272519	+	0.272519i
$279$	231.722	−	231.722i	0.830546	−	0.830546i
$280$		0			0
$281$	131.638	+	131.638i	0.468464	+	0.468464i	0.901417	−	0.432953i	$-0.142528\pi$
$281$	131.638	+	131.638i	0.468464	+	0.468464i	−0.432953	+	0.901417i	$0.642528\pi$
$282$	313.106			1.11030
$283$			380.847i			1.34575i	0.739756	+	0.672875i	$0.234941\pi$
$283$			380.847i			1.34575i	−0.739756	+	0.672875i	$0.765059\pi$
$284$	−112.996	−	112.996i	−0.397874	−	0.397874i
$285$		0			0
$286$	−81.7587	−	76.6977i	−0.285870	−	0.268174i
$287$	−197.438			−0.687938
$288$	23.2406	−	23.2406i	0.0806966	−	0.0806966i
$289$	148.360			0.513357
$290$		0			0
$291$	192.365	−	192.365i	0.661049	−	0.661049i
$292$	108.354	−	108.354i	0.371074	−	0.371074i
$293$	−33.0661	−	33.0661i	−0.112854	−	0.112854i	0.648425	−	0.761279i	$-0.275428\pi$
$293$	−33.0661	−	33.0661i	−0.112854	−	0.112854i	−0.761279	+	0.648425i	$0.775428\pi$
$294$	142.390	+	142.390i	0.484319	+	0.484319i
$295$		0			0
$296$			74.6420i			0.252169i
$297$	52.9288	+	52.9288i	0.178211	+	0.178211i
$298$		−	222.869i		−	0.747883i
$299$	−94.9877	+	101.256i	−0.317684	+	0.338647i
$300$		0			0
$301$	129.326	−	129.326i	0.429654	−	0.429654i
$302$	−271.414			−0.898722
$303$			327.882i			1.08212i
$304$	−38.8467	+	38.8467i	−0.127785	+	0.127785i
$305$		0			0
$306$	68.9036	+	68.9036i	0.225175	+	0.225175i
$307$	365.876	+	365.876i	1.19178	+	1.19178i	0.976568	+	0.215210i	$0.0690437\pi$
$307$	365.876	+	365.876i	1.19178	+	1.19178i	0.215210	+	0.976568i	$0.430956\pi$
$308$	42.2458			0.137162
$309$			43.9002i			0.142072i
$310$		0			0
$311$			315.994i			1.01606i	0.861340	+	0.508028i	$0.169626\pi$
$311$			315.994i			1.01606i	−0.861340	+	0.508028i	$0.830374\pi$
$312$	−4.51727	−	141.432i	−0.0144784	−	0.453307i
$313$	65.8042			0.210237			0.105118	−	0.994460i	$-0.466478\pi$
$313$	65.8042			0.210237			0.105118	+	0.994460i	$0.466478\pi$
$314$	−172.878	+	172.878i	−0.550568	+	0.550568i
$315$		0			0
$316$		−	77.6405i		−	0.245698i
$317$	169.512	−	169.512i	0.534739	−	0.534739i	−0.387240	−	0.921979i	$-0.626571\pi$
$317$	169.512	−	169.512i	0.534739	−	0.534739i	0.921979	+	0.387240i	$0.126571\pi$
$318$	162.459	−	162.459i	0.510877	−	0.510877i
$319$	92.7845	+	92.7845i	0.290861	+	0.290861i
$320$		0			0
$321$	239.007			0.744570
$322$		−	52.3200i		−	0.162485i
$323$	−115.172	−	115.172i	−0.356571	−	0.356571i
$324$			199.067i			0.614404i
$325$		0			0
$326$	111.164			0.340993
$327$	514.391	−	514.391i	1.57306	−	1.57306i
$328$	161.206			0.491482
$329$			199.293i			0.605753i
$330$		0			0
$331$	140.641	−	140.641i	0.424896	−	0.424896i	−0.461989	−	0.886886i	$-0.652864\pi$
$331$	140.641	−	140.641i	0.424896	−	0.424896i	0.886886	+	0.461989i	$0.152864\pi$
$332$	64.7728	+	64.7728i	0.195099	+	0.195099i
$333$	108.420	+	108.420i	0.325587	+	0.325587i
$334$	−184.075			−0.551121
$335$		0			0
$336$	37.7068	+	37.7068i	0.112223	+	0.112223i
$337$		−	275.256i		−	0.816784i	−0.912807	−	0.408392i	$-0.866090\pi$
$337$		−	275.256i		−	0.816784i	0.912807	−	0.408392i	$-0.133910\pi$
$338$	−179.440	−	157.871i	−0.530888	−	0.467074i
$339$	−570.094			−1.68169
$340$		0			0
$341$	−343.917			−1.00855
$342$			112.853i			0.329979i
$343$	−210.658	+	210.658i	−0.614163	+	0.614163i
$344$	−105.593	+	105.593i	−0.306956	+	0.306956i
$345$		0			0
$346$	−86.3308	−	86.3308i	−0.249511	−	0.249511i
$347$	−539.829			−1.55570			−0.777851	−	0.628448i	$-0.783690\pi$
$347$	−539.829			−1.55570			−0.777851	+	0.628448i	$0.783690\pi$
$348$			165.631i			0.475952i
$349$	−387.267	−	387.267i	−1.10965	−	1.10965i	−0.993196	−	0.116452i	$-0.962848\pi$
$349$	−387.267	−	387.267i	−1.10965	−	1.10965i	−0.116452	−	0.993196i	$-0.537152\pi$
$350$		0			0
$351$	116.389	+	109.184i	0.331591	+	0.311065i
$352$	−34.4932			−0.0979919
$353$	440.861	−	440.861i	1.24890	−	1.24890i	0.292693	−	0.956207i	$-0.405449\pi$
$353$	440.861	−	440.861i	1.24890	−	1.24890i	0.956207	−	0.292693i	$-0.0945512\pi$
$354$	−41.1673			−0.116292
$355$		0			0
$356$	88.0293	−	88.0293i	0.247273	−	0.247273i
$357$	−111.793	+	111.793i	−0.313145	+	0.313145i
$358$	−223.879	−	223.879i	−0.625361	−	0.625361i
$359$	122.211	+	122.211i	0.340421	+	0.340421i	0.856525	−	0.516105i	$-0.172618\pi$
$359$	122.211	+	122.211i	0.340421	+	0.340421i	−0.516105	+	0.856525i	$0.672618\pi$
$360$		0			0
$361$			172.367i			0.477470i
$362$	−305.729	−	305.729i	−0.844555	−	0.844555i
$363$		−	322.571i		−	0.888624i
$364$	90.0217	−	2.87525i	0.247312	−	0.00789905i
$365$		0			0
$366$	279.693	−	279.693i	0.764188	−	0.764188i
$367$	460.229			1.25403			0.627015	−	0.779007i	$-0.284277\pi$
$367$	460.229			1.25403			0.627015	+	0.779007i	$0.284277\pi$
$368$			42.7187i			0.116083i
$369$	234.158	−	234.158i	0.634575	−	0.634575i
$370$		0			0
$371$	103.406	+	103.406i	0.278721	+	0.278721i
$372$	−306.966	−	306.966i	−0.825177	−	0.825177i
$373$	550.843			1.47679			0.738395	−	0.674369i	$-0.235584\pi$
$373$	550.843			1.47679			0.738395	+	0.674369i	$0.235584\pi$
$374$		−	102.265i		−	0.273436i
$375$		0			0
$376$		−	162.720i		−	0.432766i
$377$	204.030	+	191.400i	0.541193	+	0.507692i
$378$	−60.1394			−0.159099
$379$	318.854	−	318.854i	0.841303	−	0.841303i	−0.147726	−	0.989028i	$-0.547195\pi$
$379$	318.854	−	318.854i	0.841303	−	0.841303i	0.989028	+	0.147726i	$0.0471953\pi$
$380$		0			0
$381$		−	887.126i		−	2.32842i
$382$	288.933	−	288.933i	0.756368	−	0.756368i
$383$	−87.4053	+	87.4053i	−0.228212	+	0.228212i	−0.811946	−	0.583733i	$-0.801591\pi$
$383$	−87.4053	+	87.4053i	−0.228212	+	0.228212i	0.583733	+	0.811946i	$0.301591\pi$
$384$	−30.7872	−	30.7872i	−0.0801749	−	0.0801749i
$385$		0			0
$386$	−233.182			−0.604098
$387$			306.756i			0.792651i
$388$	−99.9716	−	99.9716i	−0.257659	−	0.257659i
$389$		−	221.342i		−	0.569004i	−0.958675	−	0.284502i	$-0.908172\pi$
$389$		−	221.342i		−	0.569004i	0.958675	−	0.284502i	$-0.0918282\pi$
$390$		0			0
$391$	−126.652			−0.323918
$392$	73.9995	−	73.9995i	0.188774	−	0.188774i
$393$	825.101			2.09949
$394$		−	208.752i		−	0.529827i
$395$		0			0
$396$	−50.1027	+	50.1027i	−0.126522	+	0.126522i
$397$	−2.99158	−	2.99158i	−0.00753545	−	0.00753545i	0.703329	−	0.710864i	$-0.251696\pi$
$397$	−2.99158	−	2.99158i	−0.00753545	−	0.00753545i	−0.710864	+	0.703329i	$0.751696\pi$
$398$	194.443	+	194.443i	0.488551	+	0.488551i
$399$	−183.098			−0.458893
$400$		0			0
$401$	27.4281	+	27.4281i	0.0683993	+	0.0683993i	0.740479	−	0.672080i	$-0.234599\pi$
$401$	27.4281	+	27.4281i	0.0683993	+	0.0683993i	−0.672080	+	0.740479i	$0.734599\pi$
$402$		−	373.513i		−	0.929137i
$403$	−732.853	+	23.4070i	−1.81850	+	0.0580820i
$404$	170.399			0.421780
$405$		0			0
$406$	−105.425			−0.259667
$407$		−	160.915i		−	0.395368i
$408$	91.2775	−	91.2775i	0.223719	−	0.223719i
$409$	226.925	−	226.925i	0.554828	−	0.554828i	−0.373002	−	0.927830i	$-0.621672\pi$
$409$	226.925	−	226.925i	0.554828	−	0.554828i	0.927830	+	0.373002i	$0.121672\pi$
$410$		0			0
$411$	−391.947	−	391.947i	−0.953643	−	0.953643i
$412$	22.8148			0.0553758
$413$		−	26.2031i		−	0.0634457i
$414$	62.0506	+	62.0506i	0.149881	+	0.149881i
$415$		0			0
$416$	−73.5016	+	2.34761i	−0.176687	+	0.00564329i
$417$	291.555			0.699173
$418$	83.7466	−	83.7466i	0.200351	−	0.200351i
$419$	−146.384			−0.349364			−0.174682	−	0.984625i	$-0.555890\pi$
$419$	−146.384			−0.349364			−0.174682	+	0.984625i	$0.555890\pi$
$420$		0			0
$421$	465.756	−	465.756i	1.10631	−	1.10631i	0.112676	−	0.993632i	$-0.464058\pi$
$421$	465.756	−	465.756i	1.10631	−	1.10631i	0.993632	−	0.112676i	$-0.0359423\pi$
$422$	103.472	−	103.472i	0.245195	−	0.245195i
$423$	−236.357	−	236.357i	−0.558765	−	0.558765i
$424$	−84.4293	−	84.4293i	−0.199126	−	0.199126i
$425$		0			0
$426$			434.855i			1.02079i
$427$	178.025	+	178.025i	0.416921	+	0.416921i
$428$		−	124.211i		−	0.290213i
$429$	9.73843	+	304.902i	0.0227003	+	0.710726i
$430$		0			0
$431$	−412.642	+	412.642i	−0.957406	+	0.957406i	−0.999129	−	0.0417231i	$-0.986715\pi$
$431$	−412.642	+	412.642i	−0.957406	+	0.957406i	0.0417231	+	0.999129i	$0.486715\pi$
$432$	49.1031			0.113665
$433$		−	490.129i		−	1.13194i	−0.824427	−	0.565968i	$-0.808502\pi$
$433$		−	490.129i		−	1.13194i	0.824427	−	0.565968i	$-0.191498\pi$
$434$	195.385	−	195.385i	0.450195	−	0.450195i
$435$		0			0
$436$	−267.327	−	267.327i	−0.613136	−	0.613136i
$437$	−103.717	−	103.717i	−0.237340	−	0.237340i
$438$	−416.988			−0.952028
$439$			32.6479i			0.0743687i	0.999308	+	0.0371844i	$0.0118389\pi$
$439$			32.6479i			0.0743687i	−0.999308	+	0.0371844i	$0.988161\pi$
$440$		0			0
$441$		−	214.974i		−	0.487470i
$442$	−6.96017	−	217.917i	−0.0157470	−	0.493025i
$443$	458.868			1.03582			0.517909	−	0.855436i	$-0.326711\pi$
$443$	458.868			1.03582			0.517909	+	0.855436i	$0.326711\pi$
$444$	143.626	−	143.626i	0.323482	−	0.323482i
$445$		0			0
$446$		−	28.4293i		−	0.0637428i
$447$	−428.845	+	428.845i	−0.959384	+	0.959384i
$448$	19.5961	−	19.5961i	0.0437414	−	0.0437414i
$449$	290.072	+	290.072i	0.646041	+	0.646041i	0.952034	−	0.305993i	$-0.0989883\pi$
$449$	290.072	+	290.072i	0.646041	+	0.646041i	−0.305993	+	0.952034i	$0.598988\pi$
$450$		0			0
$451$	−347.531			−0.770579
$452$			296.276i			0.655478i
$453$	522.254	+	522.254i	1.15288	+	1.15288i
$454$		−	567.047i		−	1.24900i
$455$		0			0
$456$	149.498			0.327845
$457$	338.468	−	338.468i	0.740631	−	0.740631i	−0.232068	−	0.972699i	$-0.574549\pi$
$457$	338.468	−	338.468i	0.740631	−	0.740631i	0.972699	+	0.232068i	$0.0745493\pi$
$458$	607.337			1.32606
$459$			145.580i			0.317169i
$460$		0			0
$461$	351.781	−	351.781i	0.763082	−	0.763082i	−0.213796	−	0.976878i	$-0.568583\pi$
$461$	351.781	−	351.781i	0.763082	−	0.763082i	0.976878	+	0.213796i	$0.0685828\pi$
$462$	−81.2892	−	81.2892i	−0.175951	−	0.175951i
$463$	−283.858	−	283.858i	−0.613085	−	0.613085i	0.330664	−	0.943749i	$-0.392727\pi$
$463$	−283.858	−	283.858i	−0.613085	−	0.613085i	−0.943749	+	0.330664i	$0.892727\pi$
$464$	86.0781			0.185513
$465$		0			0
$466$	134.811	+	134.811i	0.289294	+	0.289294i
$467$			267.631i			0.573085i	0.958067	+	0.286543i	$0.0925060\pi$
$467$			267.631i			0.573085i	−0.958067	+	0.286543i	$0.907494\pi$
$468$	−103.354	+	110.174i	−0.220842	+	0.235415i
$469$	237.742			0.506913
$470$		0			0
$471$	665.304			1.41254
$472$			21.3945i			0.0453273i
$473$	227.640	−	227.640i	0.481268	−	0.481268i
$474$	−149.396	+	149.396i	−0.315181	+	0.315181i
$475$		0			0
$476$	58.0984	+	58.0984i	0.122056	+	0.122056i
$477$	−245.274			−0.514201
$478$			409.936i			0.857606i
$479$	226.465	+	226.465i	0.472788	+	0.472788i	0.902816	−	0.430028i	$-0.141496\pi$
$479$	226.465	+	226.465i	0.472788	+	0.472788i	−0.430028	+	0.902816i	$0.641496\pi$
$480$		0			0
$481$	−10.9519	−	342.894i	−0.0227690	−	0.712878i
$482$	−529.151			−1.09782
$483$	−100.674	+	100.674i	−0.208435	+	0.208435i
$484$	−167.639			−0.346361
$485$		0			0
$486$	272.562	−	272.562i	0.560828	−	0.560828i
$487$	−127.792	+	127.792i	−0.262406	+	0.262406i	−0.826031	−	0.563625i	$-0.809406\pi$
$487$	−127.792	+	127.792i	−0.262406	+	0.262406i	0.563625	+	0.826031i	$0.309406\pi$
$488$	−145.355	−	145.355i	−0.297860	−	0.297860i
$489$	−213.901	−	213.901i	−0.437426	−	0.437426i
$490$		0			0
$491$		−	430.146i		−	0.876060i	−0.898960	−	0.438030i	$-0.855676\pi$
$491$		−	430.146i		−	0.876060i	0.898960	−	0.438030i	$-0.144324\pi$
$492$	−310.192	−	310.192i	−0.630472	−	0.630472i
$493$			255.204i			0.517654i
$494$	172.756	−	184.156i	0.349709	−	0.372785i
$495$		0			0
$496$	−159.529	+	159.529i	−0.321631	+	0.321631i
$497$	−276.786			−0.556914
$498$		−	249.271i		−	0.500545i
$499$	−270.521	+	270.521i	−0.542127	+	0.542127i	−0.924152	−	0.382025i	$-0.875227\pi$
$499$	−270.521	+	270.521i	−0.542127	+	0.542127i	0.382025	+	0.924152i	$0.375227\pi$
$500$		0			0
$501$	354.196	+	354.196i	0.706978	+	0.706978i
$502$	89.6680	+	89.6680i	0.178621	+	0.178621i
$503$	−455.762			−0.906088			−0.453044	−	0.891488i	$-0.649662\pi$
$503$	−455.762			−0.906088			−0.453044	+	0.891488i	$0.649662\pi$
$504$		−	56.9283i		−	0.112953i
$505$		0			0
$506$		−	92.0939i		−	0.182004i
$507$	41.5033	+	649.053i	0.0818606	+	1.28018i
$508$	−461.037			−0.907553
$509$	169.114	−	169.114i	0.332248	−	0.332248i	−0.521192	−	0.853440i	$-0.674512\pi$
$509$	169.114	−	169.114i	0.332248	−	0.332248i	0.853440	+	0.521192i	$0.174512\pi$
$510$		0			0
$511$		−	265.414i		−	0.519402i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−119.218	+	119.218i	−0.232395	+	0.232395i
$514$	−209.326	−	209.326i	−0.407248	−	0.407248i
$515$		0			0
$516$	406.363			0.787526
$517$			350.796i			0.678522i
$518$	91.4184	+	91.4184i	0.176483	+	0.176483i
$519$			332.235i			0.640145i
$520$		0			0
$521$	388.553			0.745782			0.372891	−	0.927875i	$-0.378366\pi$
$521$	388.553			0.745782			0.372891	+	0.927875i	$0.378366\pi$
$522$	125.032	−	125.032i	0.239525	−	0.239525i
$523$	508.158			0.971622			0.485811	−	0.874064i	$-0.338524\pi$
$523$	508.158			0.971622			0.485811	+	0.874064i	$0.338524\pi$
$524$		−	428.803i		−	0.818326i
$525$		0			0
$526$	135.381	−	135.381i	0.257378	−	0.257378i
$527$	−472.971	−	472.971i	−0.897478	−	0.897478i
$528$	66.3717	+	66.3717i	0.125704	+	0.125704i
$529$	414.945			0.784395
$530$		0			0
$531$	31.0763	+	31.0763i	0.0585242	+	0.0585242i
$532$			95.1556i			0.178864i
$533$	−740.556	+	23.6530i	−1.38941	+	0.0443772i
$534$	−338.772			−0.634404
$535$		0			0
$536$	−194.114			−0.362152
$537$			861.576i			1.60442i
$538$	65.9632	−	65.9632i	0.122608	−	0.122608i
$539$	−159.530	+	159.530i	−0.295973	+	0.295973i
$540$		0			0
$541$	−154.103	−	154.103i	−0.284849	−	0.284849i	0.550190	−	0.835039i	$-0.314555\pi$
$541$	−154.103	−	154.103i	−0.284849	−	0.284849i	−0.835039	+	0.550190i	$0.814555\pi$
$542$	580.159			1.07040
$543$			1176.57i			2.16679i
$544$	−47.4367	−	47.4367i	−0.0871997	−	0.0871997i
$545$		0			0
$546$	−178.752	−	167.687i	−0.327385	−	0.307119i
$547$	164.591			0.300898			0.150449	−	0.988618i	$-0.451928\pi$
$547$	164.591			0.300898			0.150449	+	0.988618i	$0.451928\pi$
$548$	−203.694	+	203.694i	−0.371704	+	0.371704i
$549$	−422.269			−0.769160
$550$		0			0
$551$	−208.991	+	208.991i	−0.379293	+	0.379293i
$552$	82.1992	−	82.1992i	0.148912	−	0.148912i
$553$	−95.0908	−	95.0908i	−0.171954	−	0.171954i
$554$	191.294	+	191.294i	0.345296	+	0.345296i
$555$		0			0
$556$		−	151.520i		−	0.272519i
$557$	551.903	+	551.903i	0.990850	+	0.990850i	0.999959	−	0.00910881i	$-0.00289946\pi$
$557$	551.903	+	551.903i	0.990850	+	0.990850i	−0.00910881	+	0.999959i	$0.502899\pi$
$558$			463.445i			0.830546i
$559$	469.585	−	500.571i	0.840045	−	0.895477i
$560$		0			0
$561$	−196.778	+	196.778i	−0.350763	+	0.350763i
$562$	−263.277			−0.468464
$563$			128.247i			0.227792i	0.993493	+	0.113896i	$0.0363331\pi$
$563$			128.247i			0.227792i	−0.993493	+	0.113896i	$0.963667\pi$
$564$	−313.106	+	313.106i	−0.555152	+	0.555152i
$565$		0			0
$566$	−380.847	−	380.847i	−0.672875	−	0.672875i
$567$	243.809	+	243.809i	0.429998	+	0.429998i
$568$	225.993			0.397874
$569$			758.893i			1.33373i	0.745178	+	0.666865i	$0.232364\pi$
$569$			758.893i			1.33373i	−0.745178	+	0.666865i	$0.767636\pi$
$570$		0			0
$571$		−	87.8635i		−	0.153877i	−0.997036	−	0.0769383i	$-0.975486\pi$
$571$		−	87.8635i		−	0.153877i	0.997036	−	0.0769383i	$-0.0245144\pi$
$572$	158.456	−	5.06103i	0.277022	−	0.00884796i
$573$	−1111.93			−1.94054
$574$	197.438	−	197.438i	0.343969	−	0.343969i
$575$		0			0
$576$			46.4813i			0.0806966i
$577$	−297.465	+	297.465i	−0.515537	+	0.515537i	−0.916218	−	0.400681i	$-0.868774\pi$
$577$	−297.465	+	297.465i	−0.515537	+	0.515537i	0.400681	+	0.916218i	$0.368774\pi$
$578$	−148.360	+	148.360i	−0.256679	+	0.256679i
$579$	448.688	+	448.688i	0.774936	+	0.774936i
$580$		0			0
$581$	158.662			0.273084
$582$			384.730i			0.661049i
$583$	182.015	+	182.015i	0.312203	+	0.312203i
$584$			216.707i			0.371074i
$585$		0			0
$586$	66.1323			0.112854
$587$	132.481	−	132.481i	0.225692	−	0.225692i	−0.585198	−	0.810890i	$-0.698983\pi$
$587$	132.481	−	132.481i	0.225692	−	0.225692i	0.810890	+	0.585198i	$0.198983\pi$
$588$	−284.779			−0.484319
$589$		−	774.648i		−	1.31519i
$590$		0			0
$591$	−401.680	+	401.680i	−0.679662	+	0.679662i
$592$	−74.6420	−	74.6420i	−0.126085	−	0.126085i
$593$	−94.7444	−	94.7444i	−0.159771	−	0.159771i	0.622694	−	0.782465i	$-0.286038\pi$
$593$	−94.7444	−	94.7444i	−0.159771	−	0.159771i	−0.782465	+	0.622694i	$0.786038\pi$
$594$	−105.858			−0.178211
$595$		0			0
$596$	222.869	+	222.869i	0.373942	+	0.373942i
$597$		−	748.294i		−	1.25342i
$598$	−6.26793	−	196.243i	−0.0104815	−	0.328166i
$599$	−1004.01			−1.67615			−0.838076	−	0.545554i	$-0.816319\pi$
$599$	−1004.01			−1.67615			−0.838076	+	0.545554i	$0.816319\pi$
$600$		0			0
$601$	1002.31			1.66773			0.833867	−	0.551965i	$-0.186122\pi$
$601$	1002.31			1.66773			0.833867	+	0.551965i	$0.186122\pi$
$602$			258.652i			0.429654i
$603$	−281.958	+	281.958i	−0.467592	+	0.467592i
$604$	271.414	−	271.414i	0.449361	−	0.449361i
$605$		0			0
$606$	−327.882	−	327.882i	−0.541059	−	0.541059i
$607$	−238.427			−0.392796			−0.196398	−	0.980524i	$-0.562924\pi$
$607$	−238.427			−0.392796			−0.196398	+	0.980524i	$0.562924\pi$
$608$		−	77.6934i		−	0.127785i
$609$	202.858	+	202.858i	0.333101	+	0.333101i
$610$		0			0
$611$	23.8752	+	747.512i	0.0390757	+	1.22342i
$612$	−137.807			−0.225175
$613$	580.531	−	580.531i	0.947033	−	0.947033i	−0.0516332	−	0.998666i	$-0.516443\pi$
$613$	580.531	−	580.531i	0.947033	−	0.947033i	0.998666	+	0.0516332i	$0.0164427\pi$
$614$	−731.752			−1.19178
$615$		0			0
$616$	−42.2458	+	42.2458i	−0.0685808	+	0.0685808i
$617$	567.878	−	567.878i	0.920385	−	0.920385i	−0.0766713	−	0.997056i	$-0.524429\pi$
$617$	567.878	−	567.878i	0.920385	−	0.920385i	0.997056	+	0.0766713i	$0.0244292\pi$
$618$	−43.9002	−	43.9002i	−0.0710360	−	0.0710360i
$619$	26.0583	+	26.0583i	0.0420973	+	0.0420973i	0.727842	−	0.685745i	$-0.240523\pi$
$619$	26.0583	+	26.0583i	0.0420973	+	0.0420973i	−0.685745	+	0.727842i	$0.740523\pi$
$620$		0			0
$621$			131.101i			0.211113i
$622$	−315.994	−	315.994i	−0.508028	−	0.508028i
$623$		−	215.629i		−	0.346114i
$624$	145.949	+	136.914i	0.233893	+	0.219414i
$625$		0			0
$626$	−65.8042	+	65.8042i	−0.105118	+	0.105118i
$627$	−322.290			−0.514019
$628$		−	345.757i		−	0.550568i
$629$	221.298	−	221.298i	0.351825	−	0.351825i
$630$		0			0
$631$	−407.417	−	407.417i	−0.645668	−	0.645668i	0.306275	−	0.951943i	$-0.400917\pi$
$631$	−407.417	−	407.417i	−0.645668	−	0.645668i	−0.951943	+	0.306275i	$0.900917\pi$
$632$	77.6405	+	77.6405i	0.122849	+	0.122849i
$633$	−398.202			−0.629071
$634$			339.025i			0.534739i
$635$		0			0
$636$			324.918i			0.510877i
$637$	−329.085	+	350.800i	−0.516617	+	0.550707i
$638$	−185.569			−0.290861
$639$	328.263	−	328.263i	0.513714	−	0.513714i
$640$		0			0
$641$		−	144.048i		−	0.224724i	−0.993667	−	0.112362i	$-0.964158\pi$
$641$		−	144.048i		−	0.224724i	0.993667	−	0.112362i	$-0.0358416\pi$
$642$	−239.007	+	239.007i	−0.372285	+	0.372285i
$643$	82.2042	−	82.2042i	0.127845	−	0.127845i	−0.640289	−	0.768134i	$-0.721185\pi$
$643$	82.2042	−	82.2042i	0.127845	−	0.127845i	0.768134	+	0.640289i	$0.221185\pi$
$644$	52.3200	+	52.3200i	0.0812423	+	0.0812423i
$645$		0			0
$646$	230.345			0.356571
$647$		−	657.369i		−	1.01603i	−0.861349	−	0.508013i	$-0.830380\pi$
$647$		−	657.369i		−	1.01603i	0.861349	−	0.508013i	$-0.169620\pi$
$648$	−199.067	−	199.067i	−0.307202	−	0.307202i
$649$		−	46.1227i		−	0.0710674i
$650$		0			0
$651$	−751.918			−1.15502
$652$	−111.164	+	111.164i	−0.170497	+	0.170497i
$653$	792.552			1.21371			0.606854	−	0.794813i	$-0.292431\pi$
$653$	792.552			1.21371			0.606854	+	0.794813i	$0.292431\pi$
$654$			1028.78i			1.57306i
$655$		0			0
$656$	−161.206	+	161.206i	−0.245741	+	0.245741i
$657$	314.776	+	314.776i	0.479111	+	0.479111i
$658$	−199.293	−	199.293i	−0.302877	−	0.302877i
$659$	−617.958			−0.937722			−0.468861	−	0.883272i	$-0.655335\pi$
$659$	−617.958			−0.937722			−0.468861	+	0.883272i	$0.655335\pi$
$660$		0			0
$661$	206.874	+	206.874i	0.312971	+	0.312971i	0.846059	−	0.533089i	$-0.178969\pi$
$661$	206.874	+	206.874i	0.312971	+	0.312971i	−0.533089	+	0.846059i	$0.678969\pi$
$662$			281.281i			0.424896i
$663$	−405.923	+	432.708i	−0.612251	+	0.652652i
$664$	−129.546			−0.195099
$665$		0			0
$666$	−216.841			−0.325587
$667$			229.821i			0.344560i
$668$	184.075	−	184.075i	0.275561	−	0.275561i
$669$	−54.7036	+	54.7036i	−0.0817691	+	0.0817691i
$670$		0			0
$671$	313.361	+	313.361i	0.467005	+	0.467005i
$672$	−75.4137			−0.112223
$673$			1124.43i			1.67077i	0.549663	+	0.835386i	$0.314756\pi$
$673$			1124.43i			1.67077i	−0.549663	+	0.835386i	$0.685244\pi$
$674$	275.256	+	275.256i	0.408392	+	0.408392i
$675$		0			0
$676$	337.311	−	21.5691i	0.498981	−	0.0319070i
$677$	446.105			0.658943			0.329472	−	0.944165i	$-0.393129\pi$
$677$	446.105			0.658943			0.329472	+	0.944165i	$0.393129\pi$
$678$	570.094	−	570.094i	0.840847	−	0.840847i
$679$	−244.882			−0.360651
$680$		0			0
$681$	−1091.11	+	1091.11i	−1.60222	+	1.60222i
$682$	343.917	−	343.917i	0.504276	−	0.504276i
$683$	−897.278	−	897.278i	−1.31373	−	1.31373i	−0.918644	−	0.395086i	$-0.870715\pi$
$683$	−897.278	−	897.278i	−1.31373	−	1.31373i	−0.395086	−	0.918644i	$-0.629285\pi$
$684$	−112.853	−	112.853i	−0.164989	−	0.164989i
$685$		0			0
$686$		−	421.315i		−	0.614163i
$687$	−1168.64	−	1168.64i	−1.70107	−	1.70107i
$688$		−	211.186i		−	0.306956i
$689$	400.244	+	375.468i	0.580905	+	0.544946i
$690$		0			0
$691$	−447.025	+	447.025i	−0.646924	+	0.646924i	−0.952249	−	0.305324i	$-0.901235\pi$
$691$	−447.025	+	447.025i	−0.646924	+	0.646924i	0.305324	+	0.952249i	$0.401235\pi$
$692$	172.662			0.249511
$693$			122.727i			0.177096i
$694$	539.829	−	539.829i	0.777851	−	0.777851i
$695$		0			0
$696$	−165.631	−	165.631i	−0.237976	−	0.237976i
$697$	−477.942	−	477.942i	−0.685713	−	0.685713i
$698$	774.535			1.10965
$699$		−	518.806i		−	0.742212i
$700$		0			0
$701$		−	182.818i		−	0.260795i	−0.991462	−	0.130398i	$-0.958375\pi$
$701$		−	182.818i		−	0.260795i	0.991462	−	0.130398i	$-0.0416254\pi$
$702$	−225.572	+	7.20469i	−0.321328	+	0.0102631i
$703$	362.450			0.515576
$704$	34.4932	−	34.4932i	0.0489960	−	0.0489960i
$705$		0			0
$706$			881.723i			1.24890i
$707$	208.698	−	208.698i	0.295188	−	0.295188i
$708$	41.1673	−	41.1673i	0.0581458	−	0.0581458i
$709$	−16.2875	−	16.2875i	−0.0229726	−	0.0229726i	0.695527	−	0.718500i	$-0.255171\pi$
$709$	−16.2875	−	16.2875i	−0.0229726	−	0.0229726i	−0.718500	+	0.695527i	$0.755171\pi$
$710$		0			0
$711$	225.552			0.317232
$712$			176.059i			0.247273i
$713$	−425.930	−	425.930i	−0.597377	−	0.597377i
$714$		−	223.586i		−	0.313145i
$715$		0			0
$716$	447.758			0.625361
$717$	788.798	−	788.798i	1.10014	−	1.10014i
$718$	−244.422			−0.340421
$719$		−	60.4508i		−	0.0840762i	−0.999116	−	0.0420381i	$-0.986615\pi$
$719$		−	60.4508i		−	0.0840762i	0.999116	−	0.0420381i	$-0.0133851\pi$
$720$		0			0
$721$	27.9426	−	27.9426i	0.0387554	−	0.0387554i
$722$	−172.367	−	172.367i	−0.238735	−	0.238735i
$723$	1018.19	+	1018.19i	1.40829	+	1.40829i
$724$	611.458			0.844555
$725$		0			0
$726$	322.571	+	322.571i	0.444312	+	0.444312i
$727$		−	149.229i		−	0.205266i	−0.994719	−	0.102633i	$-0.967273\pi$
$727$		−	149.229i		−	0.205266i	0.994719	−	0.102633i	$-0.0327268\pi$
$728$	−87.1464	+	92.8970i	−0.119707	+	0.127606i
$729$	−153.127			−0.210050
$730$		0			0
$731$	626.122			0.856528
$732$			559.386i			0.764188i
$733$	894.559	−	894.559i	1.22041	−	1.22041i	0.252921	−	0.967487i	$-0.418609\pi$
$733$	894.559	−	894.559i	1.22041	−	1.22041i	0.967487	−	0.252921i	$-0.0813914\pi$
$734$	−460.229	+	460.229i	−0.627015	+	0.627015i
$735$		0			0
$736$	−42.7187	−	42.7187i	−0.0580417	−	0.0580417i
$737$	418.474			0.567808
$738$			468.316i			0.634575i
$739$	−113.697	−	113.697i	−0.153852	−	0.153852i	0.625984	−	0.779836i	$-0.284698\pi$
$739$	−113.697	−	113.697i	−0.153852	−	0.153852i	−0.779836	+	0.625984i	$0.784698\pi$
$740$		0			0
$741$	−686.770	+	21.9351i	−0.926814	+	0.0296021i
$742$	−206.811			−0.278721
$743$	387.099	−	387.099i	0.520994	−	0.520994i	−0.396877	−	0.917872i	$-0.629906\pi$
$743$	387.099	−	387.099i	0.520994	−	0.520994i	0.917872	+	0.396877i	$0.129906\pi$
$744$	613.932			0.825177
$745$		0			0
$746$	−550.843	+	550.843i	−0.738395	+	0.738395i
$747$	−188.170	+	188.170i	−0.251901	+	0.251901i
$748$	102.265	+	102.265i	0.136718	+	0.136718i
$749$	−152.129	−	152.129i	−0.203109	−	0.203109i
$750$		0			0
$751$			342.334i			0.455837i	0.973680	+	0.227919i	$0.0731920\pi$
$751$			342.334i			0.455837i	−0.973680	+	0.227919i	$0.926808\pi$
$752$	162.720	+	162.720i	0.216383	+	0.216383i
$753$		−	345.078i		−	0.458271i
$754$	−395.430	+	12.6299i	−0.524443	+	0.0167505i
$755$		0			0
$756$	60.1394	−	60.1394i	0.0795495	−	0.0795495i
$757$	−243.161			−0.321217			−0.160608	−	0.987018i	$-0.551346\pi$
$757$	−243.161			−0.321217			−0.160608	+	0.987018i	$0.551346\pi$
$758$			637.707i			0.841303i
$759$	−177.207	+	177.207i	−0.233474	+	0.233474i
$760$		0			0
$761$	−419.621	−	419.621i	−0.551407	−	0.551407i	0.375440	−	0.926847i	$-0.377492\pi$
$761$	−419.621	−	419.621i	−0.551407	−	0.551407i	−0.926847	+	0.375440i	$0.877492\pi$
$762$	887.126	+	887.126i	1.16421	+	1.16421i
$763$	−654.823			−0.858221
$764$			577.866i			0.756368i
$765$		0			0
$766$		−	174.811i		−	0.228212i
$767$	−3.13912	−	98.2831i	−0.00409273	−	0.128140i
$768$	61.5743			0.0801749
$769$	−80.4079	+	80.4079i	−0.104562	+	0.104562i	−0.757452	−	0.652891i	$-0.773556\pi$
$769$	−80.4079	+	80.4079i	−0.104562	+	0.104562i	0.652891	+	0.757452i	$0.273556\pi$
$770$		0			0
$771$			805.568i			1.04484i
$772$	233.182	−	233.182i	0.302049	−	0.302049i
$773$	714.523	−	714.523i	0.924351	−	0.924351i	−0.0729822	−	0.997333i	$-0.523252\pi$
$773$	714.523	−	714.523i	0.924351	−	0.924351i	0.997333	+	0.0729822i	$0.0232516\pi$
$774$	−306.756	−	306.756i	−0.396325	−	0.396325i
$775$		0			0
$776$	199.943			0.257659
$777$		−	351.814i		−	0.452786i
$778$	221.342	+	221.342i	0.284502	+	0.284502i
$779$		−	782.790i		−	1.00487i
$780$		0			0
$781$	−487.200			−0.623816
$782$	126.652	−	126.652i	0.161959	−	0.161959i
$783$	264.169			0.337380
$784$			147.999i			0.188774i
$785$		0			0
$786$	−825.101	+	825.101i	−1.04975	+	1.04975i
$787$	72.2015	+	72.2015i	0.0917428	+	0.0917428i	0.751489	−	0.659746i	$-0.229336\pi$
$787$	72.2015	+	72.2015i	0.0917428	+	0.0917428i	−0.659746	+	0.751489i	$0.729336\pi$
$788$	208.752	+	208.752i	0.264914	+	0.264914i
$789$	−520.999			−0.660328
$790$		0			0
$791$	362.867	+	362.867i	0.458744	+	0.458744i
$792$		−	100.205i		−	0.126522i
$793$	689.069	+	646.414i	0.868939	+	0.815150i
$794$	5.98315			0.00753545
$795$		0			0
$796$	−388.886			−0.488551
$797$		−	1012.42i		−	1.27029i	−0.772392	−	0.635146i	$-0.780940\pi$
$797$		−	1012.42i		−	1.27029i	0.772392	−	0.635146i	$-0.219060\pi$
$798$	183.098	−	183.098i	0.229447	−	0.229447i
$799$	−482.431	+	482.431i	−0.603794	+	0.603794i
$800$		0			0
$801$	255.732	+	255.732i	0.319266	+	0.319266i
$802$	−54.8562			−0.0683993
$803$		−	467.183i		−	0.581797i
$804$	373.513	+	373.513i	0.464569	+	0.464569i
$805$		0			0
$806$	709.446	−	756.261i	0.880207	−	0.938288i
$807$	−253.853			−0.314563
$808$	−170.399	+	170.399i	−0.210890	+	0.210890i
$809$	1107.04			1.36840			0.684202	−	0.729293i	$-0.260151\pi$
$809$	1107.04			1.36840			0.684202	+	0.729293i	$0.260151\pi$
$810$		0			0
$811$	3.44353	−	3.44353i	0.00424603	−	0.00424603i	−0.704981	−	0.709227i	$-0.749044\pi$
$811$	3.44353	−	3.44353i	0.00424603	−	0.00424603i	0.709227	+	0.704981i	$0.249044\pi$
$812$	105.425	−	105.425i	0.129834	−	0.129834i
$813$	−1116.34	−	1116.34i	−1.37311	−	1.37311i
$814$	160.915	+	160.915i	0.197684	+	0.197684i
$815$		0			0
$816$			182.555i			0.223719i
$817$	512.742	+	512.742i	0.627591	+	0.627591i
$818$			453.849i			0.554828i
$819$	8.35284	+	261.520i	0.0101988	+	0.319316i
$820$		0			0
$821$	67.6867	−	67.6867i	0.0824442	−	0.0824442i	−0.664682	−	0.747126i	$-0.731433\pi$
$821$	67.6867	−	67.6867i	0.0824442	−	0.0824442i	0.747126	+	0.664682i	$0.231433\pi$
$822$	783.894			0.953643
$823$		−	975.932i		−	1.18582i	−0.805268	−	0.592911i	$-0.797978\pi$
$823$		−	975.932i		−	1.18582i	0.805268	−	0.592911i	$-0.202022\pi$
$824$	−22.8148	+	22.8148i	−0.0276879	+	0.0276879i
$825$		0			0
$826$	26.2031	+	26.2031i	0.0317229	+	0.0317229i
$827$	−629.158	−	629.158i	−0.760772	−	0.760772i	0.215690	−	0.976462i	$-0.430800\pi$
$827$	−629.158	−	629.158i	−0.760772	−	0.760772i	−0.976462	+	0.215690i	$0.930800\pi$
$828$	−124.101			−0.149881
$829$		−	989.174i		−	1.19321i	−0.802534	−	0.596607i	$-0.796515\pi$
$829$		−	989.174i		−	1.19321i	0.802534	−	0.596607i	$-0.203485\pi$
$830$		0			0
$831$		−	736.176i		−	0.885892i
$832$	71.1540	−	75.8492i	0.0855217	−	0.0911649i
$833$	−438.786			−0.526754
$834$	−291.555	+	291.555i	−0.349586	+	0.349586i
$835$		0			0
$836$			167.493i			0.200351i
$837$	−489.586	+	489.586i	−0.584930	+	0.584930i
$838$	146.384	−	146.384i	0.174682	−	0.174682i
$839$	−309.990	−	309.990i	−0.369476	−	0.369476i	0.497810	−	0.867286i	$-0.334138\pi$
$839$	−309.990	−	309.990i	−0.369476	−	0.369476i	−0.867286	+	0.497810i	$0.834138\pi$
$840$		0			0
$841$	−377.910			−0.449358
$842$			931.511i			1.10631i
$843$	506.597	+	506.597i	0.600945	+	0.600945i
$844$			206.944i			0.245195i
$845$		0			0
$846$	472.715			0.558765
$847$	−205.317	+	205.317i	−0.242405	+	0.242405i
$848$	168.859			0.199126
$849$			1465.65i			1.72633i
$850$		0			0
$851$	199.288	−	199.288i	0.234181	−	0.234181i
$852$	−434.855	−	434.855i	−0.510393	−	0.510393i
$853$	16.3492	+	16.3492i	0.0191667	+	0.0191667i	0.716625	−	0.697459i	$-0.245686\pi$
$853$	16.3492	+	16.3492i	0.0191667	+	0.0191667i	−0.697459	+	0.716625i	$0.745686\pi$
$854$	−356.051			−0.416921
$855$		0			0
$856$	124.211	+	124.211i	0.145107	+	0.145107i
$857$		−	173.877i		−	0.202890i	−0.994841	−	0.101445i	$-0.967653\pi$
$857$		−	173.877i		−	0.202890i	0.994841	−	0.101445i	$-0.0323466\pi$
$858$	−314.640	−	295.163i	−0.366713	−	0.344013i
$859$	516.287			0.601033			0.300516	−	0.953777i	$-0.402841\pi$
$859$	516.287			0.601033			0.300516	+	0.953777i	$0.402841\pi$
$860$		0			0
$861$	−759.821			−0.882486
$862$		−	825.284i		−	0.957406i
$863$	−490.757	+	490.757i	−0.568664	+	0.568664i	−0.931754	−	0.363090i	$-0.881722\pi$
$863$	−490.757	+	490.757i	−0.568664	+	0.568664i	0.363090	+	0.931754i	$0.381722\pi$
$864$	−49.1031	+	49.1031i	−0.0568323	+	0.0568323i
$865$		0			0
$866$	490.129	+	490.129i	0.565968	+	0.565968i
$867$	570.949			0.658534
$868$			390.769i			0.450195i
$869$	−167.379	−	167.379i	−0.192611	−	0.192611i
$870$		0			0
$871$	891.729	−	28.4815i	1.02380	−	0.0326997i
$872$	534.655			0.613136
$873$	290.425	−	290.425i	0.332675	−	0.332675i
$874$	207.435			0.237340
$875$		0			0
$876$	416.988	−	416.988i	0.476014	−	0.476014i
$877$	−36.7229	+	36.7229i	−0.0418733	+	0.0418733i	−0.727733	−	0.685860i	$-0.759426\pi$
$877$	−36.7229	+	36.7229i	−0.0418733	+	0.0418733i	0.685860	+	0.727733i	$0.259426\pi$
$878$	−32.6479	−	32.6479i	−0.0371844	−	0.0371844i
$879$	−127.252	−	127.252i	−0.144769	−	0.144769i
$880$		0			0
$881$		−	144.572i		−	0.164100i	−0.996628	−	0.0820501i	$-0.973853\pi$
$881$		−	144.572i		−	0.164100i	0.996628	−	0.0820501i	$-0.0261468\pi$
$882$	214.974	+	214.974i	0.243735	+	0.243735i
$883$		−	221.400i		−	0.250736i	−0.992110	−	0.125368i	$-0.959989\pi$
$883$		−	221.400i		−	0.250736i	0.992110	−	0.125368i	$-0.0400112\pi$
$884$	224.877	+	210.957i	0.254386	+	0.238639i
$885$		0			0
$886$	−458.868	+	458.868i	−0.517909	+	0.517909i
$887$	867.086			0.977549			0.488774	−	0.872410i	$-0.337444\pi$
$887$	867.086			0.977549			0.488774	+	0.872410i	$0.337444\pi$
$888$			287.252i			0.323482i
$889$	−564.659	+	564.659i	−0.635161	+	0.635161i
$890$		0			0
$891$	429.153	+	429.153i	0.481653	+	0.481653i
$892$	28.4293	+	28.4293i	0.0318714	+	0.0318714i
$893$	−790.143			−0.884818
$894$		−	857.689i		−	0.959384i
$895$		0			0
$896$			39.1923i			0.0437414i
$897$	−365.550	+	389.672i	−0.407525	+	0.434417i
$898$	−580.145			−0.646041
$899$	−858.248	+	858.248i	−0.954670	+	0.954670i
$900$		0			0
$901$			500.631i			0.555639i
$902$	347.531	−	347.531i	0.385290	−	0.385290i
$903$	497.697	−	497.697i	0.551159	−	0.551159i
$904$	−296.276	−	296.276i	−0.327739	−	0.327739i
$905$		0			0
$906$	−1044.51			−1.15288
$907$			214.025i			0.235970i	0.993015	+	0.117985i	$0.0376435\pi$
$907$			214.025i			0.235970i	−0.993015	+	0.117985i	$0.962356\pi$
$908$	567.047	+	567.047i	0.624501	+	0.624501i
$909$			495.023i			0.544579i
$910$		0			0
$911$	−1755.52			−1.92702			−0.963511	−	0.267669i	$-0.913747\pi$
$911$	−1755.52			−1.92702			−0.963511	+	0.267669i	$0.913747\pi$
$912$	−149.498	+	149.498i	−0.163923	+	0.163923i
$913$	279.277			0.305890
$914$			676.937i			0.740631i
$915$		0			0
$916$	−607.337	+	607.337i	−0.663031	+	0.663031i
$917$	−525.179	−	525.179i	−0.572715	−	0.572715i
$918$	−145.580	−	145.580i	−0.158584	−	0.158584i
$919$	917.734			0.998623			0.499311	−	0.866423i	$-0.333586\pi$
$919$	917.734			0.998623			0.499311	+	0.866423i	$0.333586\pi$
$920$		0			0
$921$	1408.04	+	1408.04i	1.52881	+	1.52881i
$922$			703.562i			0.763082i
$923$	−1038.18	+	33.1589i	−1.12479	+	0.0359252i
$924$	162.578			0.175951
$925$		0			0
$926$	567.716			0.613085
$927$			66.2789i			0.0714982i
$928$	−86.0781	+	86.0781i	−0.0927566	+	0.0927566i
$929$	−471.906	+	471.906i	−0.507972	+	0.507972i	−0.913903	−	0.405932i	$-0.866947\pi$
$929$	−471.906	+	471.906i	−0.507972	+	0.507972i	0.405932	+	0.913903i	$0.366947\pi$
$930$		0			0
$931$	−359.330	−	359.330i	−0.385961	−	0.385961i
$932$	−269.622			−0.289294
$933$			1216.07i			1.30340i
$934$	−267.631	−	267.631i	−0.286543	−	0.286543i
$935$		0			0
$936$	−6.81999	−	213.528i	−0.00728632	−	0.228128i
$937$	−1133.03			−1.20921			−0.604607	−	0.796524i	$-0.706670\pi$
$937$	−1133.03			−1.20921			−0.604607	+	0.796524i	$0.706670\pi$
$938$	−237.742	+	237.742i	−0.253457	+	0.253457i
$939$	253.241			0.269692
$940$		0			0
$941$	−965.320	+	965.320i	−1.02584	+	1.02584i	−0.0261879	+	0.999657i	$0.508337\pi$
$941$	−965.320	+	965.320i	−1.02584	+	1.02584i	−0.999657	+	0.0261879i	$0.991663\pi$
$942$	−665.304	+	665.304i	−0.706268	+	0.706268i
$943$	−430.406	−	430.406i	−0.456423	−	0.456423i
$944$	−21.3945	−	21.3945i	−0.0226637	−	0.0226637i
$945$		0			0
$946$			455.279i			0.481268i
$947$	766.185	+	766.185i	0.809065	+	0.809065i	0.984492	−	0.175427i	$-0.0561307\pi$
$947$	766.185	+	766.185i	0.809065	+	0.809065i	−0.175427	+	0.984492i	$0.556131\pi$
$948$		−	298.791i		−	0.315181i
$949$	−31.7965	−	995.522i	−0.0335053	−	1.04902i
$950$		0			0
$951$	652.351	−	652.351i	0.685963	−	0.685963i
$952$	−116.197			−0.122056
$953$			743.766i			0.780447i	0.920720	+	0.390223i	$0.127602\pi$
$953$			743.766i			0.780447i	−0.920720	+	0.390223i	$0.872398\pi$
$954$	245.274	−	245.274i	0.257100	−	0.257100i
$955$		0			0
$956$	−409.936	−	409.936i	−0.428803	−	0.428803i
$957$	357.072	+	357.072i	0.373116	+	0.373116i
$958$	−452.931			−0.472788
$959$			498.951i			0.520283i
$960$		0			0
$961$		−	2220.20i		−	2.31030i
$962$	353.846	+	331.942i	0.367824	+	0.345055i
$963$	360.844			0.374708
$964$	529.151	−	529.151i	0.548912	−	0.548912i
$965$		0			0
$966$		−	201.348i		−	0.208435i
$967$	228.660	−	228.660i	0.236463	−	0.236463i	−0.578921	−	0.815384i	$-0.696526\pi$
$967$	228.660	−	228.660i	0.236463	−	0.236463i	0.815384	+	0.578921i	$0.196526\pi$
$968$	167.639	−	167.639i	0.173181	−	0.173181i
$969$	−443.229	−	443.229i	−0.457409	−	0.457409i
$970$		0			0
$971$	1063.56			1.09532			0.547662	−	0.836699i	$-0.315518\pi$
$971$	1063.56			1.09532			0.547662	+	0.836699i	$0.315518\pi$
$972$			545.125i			0.560828i
$973$	−185.576	−	185.576i	−0.190725	−	0.190725i
$974$		−	255.583i		−	0.262406i
$975$		0			0
$976$	290.711			0.297860
$977$	347.768	−	347.768i	0.355955	−	0.355955i	−0.506364	−	0.862320i	$-0.669011\pi$
$977$	347.768	−	347.768i	0.355955	−	0.355955i	0.862320	+	0.506364i	$0.169011\pi$
$978$	427.803			0.437426
$979$		−	379.551i		−	0.387693i
$980$		0			0
$981$	776.607	−	776.607i	0.791648	−	0.791648i
$982$	430.146	+	430.146i	0.438030	+	0.438030i
$983$	1187.00	+	1187.00i	1.20753	+	1.20753i	0.971825	+	0.235705i	$0.0757400\pi$
$983$	1187.00	+	1187.00i	1.20753	+	1.20753i	0.235705	+	0.971825i	$0.424260\pi$
$984$	620.384			0.630472
$985$		0			0
$986$	−255.204	−	255.204i	−0.258827	−	0.258827i
$987$			766.958i			0.777060i
$988$	11.3996	+	356.912i	0.0115381	+	0.361247i
$989$	563.849			0.570120
$990$		0			0
$991$	566.323			0.571466			0.285733	−	0.958309i	$-0.407763\pi$
$991$	566.323			0.571466			0.285733	+	0.958309i	$0.407763\pi$
$992$		−	319.058i		−	0.321631i
$993$	541.241	−	541.241i	0.545057	−	0.545057i
$994$	276.786	−	276.786i	0.278457	−	0.278457i
$995$		0			0
$996$	249.271	+	249.271i	0.250273	+	0.250273i
$997$	−1051.32			−1.05448			−0.527242	−	0.849715i	$-0.676774\pi$
$997$	−1051.32			−1.05448			−0.527242	+	0.849715i	$0.676774\pi$
$998$		−	541.043i		−	0.542127i
$999$	−229.072	−	229.072i	−0.229302	−	0.229302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.3.k.l.551.6		14
5.2	odd	4		130.3.f.a.109.2	yes	14
5.3	odd	4		130.3.f.b.109.6	yes	14
5.4	even	2		650.3.k.m.551.2		14
13.8	odd	4	inner	650.3.k.l.151.6		14
65.8	even	4		130.3.f.a.99.6	✓	14
65.34	odd	4		650.3.k.m.151.2		14
65.47	even	4		130.3.f.b.99.2	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.3.f.a.99.6	✓	14	65.8	even	4
130.3.f.a.109.2	yes	14	5.2	odd	4
130.3.f.b.99.2	yes	14	65.47	even	4
130.3.f.b.109.6	yes	14	5.3	odd	4
650.3.k.l.151.6		14	13.8	odd	4	inner
650.3.k.l.551.6		14	1.1	even	1	trivial
650.3.k.m.151.2		14	65.34	odd	4
650.3.k.m.551.2		14	5.4	even	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +3.84840 q^{3} -2.00000i q^{4} +(-3.84840 + 3.84840i) q^{6} +(-2.44952 - 2.44952i) q^{7} +(2.00000 + 2.00000i) q^{8} +5.81016 q^{9} +(-4.31164 - 4.31164i) q^{11} -7.69679i q^{12} +(-9.48115 - 8.89425i) q^{13} +4.89903 q^{14} -4.00000 q^{16} -11.8592i q^{17} +(-5.81016 + 5.81016i) q^{18} +(9.71168 - 9.71168i) q^{19} +(-9.42671 - 9.42671i) q^{21} +8.62329 q^{22} -10.6797i q^{23} +(7.69679 + 7.69679i) q^{24} +(18.3754 - 0.586903i) q^{26} -12.2758 q^{27} +(-4.89903 + 4.89903i) q^{28} -21.5195 q^{29} +(39.8823 - 39.8823i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-16.5929 - 16.5929i) q^{33} +(11.8592 + 11.8592i) q^{34} -11.6203i q^{36} +(18.6605 + 18.6605i) q^{37} +19.4234i q^{38} +(-36.4872 - 34.2286i) q^{39} +(40.3015 - 40.3015i) q^{41} +18.8534 q^{42} +52.7965i q^{43} +(-8.62329 + 8.62329i) q^{44} +(10.6797 + 10.6797i) q^{46} +(-40.6800 - 40.6800i) q^{47} -15.3936 q^{48} -36.9997i q^{49} -45.6388i q^{51} +(-17.7885 + 18.9623i) q^{52} -42.2147 q^{53} +(12.2758 - 12.2758i) q^{54} -9.79806i q^{56} +(37.3744 - 37.3744i) q^{57} +(21.5195 - 21.5195i) q^{58} +(5.34862 + 5.34862i) q^{59} -72.6777 q^{61} +79.7646i q^{62} +(-14.2321 - 14.2321i) q^{63} +8.00000i q^{64} +33.1858 q^{66} +(-48.5284 + 48.5284i) q^{67} -23.7183 q^{68} -41.0996i q^{69} +(56.4982 - 56.4982i) q^{71} +(11.6203 + 11.6203i) q^{72} +(54.1769 + 54.1769i) q^{73} -37.3210 q^{74} +(-19.4234 - 19.4234i) q^{76} +21.1229i q^{77} +(70.7159 - 2.25863i) q^{78} +38.8202 q^{79} -99.5335 q^{81} +80.6030i q^{82} +(-32.3864 + 32.3864i) q^{83} +(-18.8534 + 18.8534i) q^{84} +(-52.7965 - 52.7965i) q^{86} -82.8156 q^{87} -17.2466i q^{88} +(44.0147 + 44.0147i) q^{89} +(1.43763 + 45.0109i) q^{91} -21.3593 q^{92} +(153.483 - 153.483i) q^{93} +81.3601 q^{94} +(15.3936 - 15.3936i) q^{96} +(49.9858 - 49.9858i) q^{97} +(36.9997 + 36.9997i) q^{98} +(-25.0513 - 25.0513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 28 q^{8} + 42 q^{9} + 8 q^{11} - 2 q^{13} - 56 q^{16} - 42 q^{18} - 44 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{26} - 120 q^{27} - 72 q^{29} - 64 q^{31} + 56 q^{32} - 56 q^{33} - 96 q^{34}+ \cdots - 292 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 28 * q^8 + 42 * q^9 + 8 * q^11 - 2 * q^13 - 56 * q^16 - 42 * q^18 - 44 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^26 - 120 * q^27 - 72 * q^29 - 64 * q^31 + 56 * q^32 - 56 * q^33 - 96 * q^34 + 98 * q^37 + 144 * q^39 + 138 * q^41 - 8 * q^42 + 16 * q^44 + 8 * q^46 - 40 * q^47 - 16 * q^52 - 176 * q^53 + 120 * q^54 + 264 * q^57 + 72 * q^58 + 20 * q^59 - 180 * q^61 + 160 * q^63 + 112 * q^66 - 8 * q^67 + 192 * q^68 - 100 * q^71 + 84 * q^72 + 54 * q^73 - 196 * q^74 + 88 * q^76 - 264 * q^78 - 344 * q^79 + 38 * q^81 + 296 * q^83 + 8 * q^84 - 120 * q^86 - 496 * q^87 + 398 * q^89 + 48 * q^91 - 16 * q^92 + 120 * q^93 + 80 * q^94 + 162 * q^97 - 130 * q^98 - 292 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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