LMFDB - Embedded newform 175.2.x.a.103.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.10
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.000942774 + 4.94087e-5i) q^{2} +(1.67776 + 2.07186i) q^{3} +(-1.98904 - 0.209057i) q^{4} +(2.16354 + 0.564890i) q^{5} +(0.00147938 + 0.00203619i) q^{6} +(-2.21008 + 1.45449i) q^{7} +(-0.00372978 - 0.000590739i) q^{8} +(-0.853997 + 4.01774i) q^{9} +(0.00201182 + 0.000639461i) q^{10} +(4.83530 - 1.02777i) q^{11} +(-2.90400 - 4.47177i) q^{12} +(-4.82554 - 2.45874i) q^{13} +(-0.00215547 + 0.00126206i) q^{14} +(2.45953 + 5.43031i) q^{15} +(3.91259 + 0.831646i) q^{16} +(0.276678 + 0.720771i) q^{17} +(-0.00100364 + 0.00374563i) q^{18} +(0.101132 + 0.962206i) q^{19} +(-4.18528 - 1.57589i) q^{20} +(-6.72150 - 2.13869i) q^{21} +(0.00460937 - 0.000730053i) q^{22} +(0.143592 - 2.73990i) q^{23} +(-0.00503375 - 0.00871871i) q^{24} +(4.36180 + 2.44432i) q^{25} +(-0.00442791 - 0.00255646i) q^{26} +(-2.63077 + 1.34044i) q^{27} +(4.70001 - 2.43102i) q^{28} +(2.32212 - 3.19613i) q^{29} +(0.00205047 + 0.00524107i) q^{30} +(3.67313 - 8.24998i) q^{31} +(0.0109428 + 0.00293211i) q^{32} +(10.2419 + 8.29371i) q^{33} +(0.000225232 + 0.000693194i) q^{34} +(-5.60322 + 1.89840i) q^{35} +(2.53857 - 7.81292i) q^{36} +(-1.77525 + 1.15286i) q^{37} +(4.78032e-5 + 0.000912139i) q^{38} +(-3.00194 - 14.1230i) q^{39} +(-0.00773582 - 0.00338500i) q^{40} +(-6.23478 + 2.02580i) q^{41} +(-0.00623118 - 0.00234840i) q^{42} +(-2.74386 - 2.74386i) q^{43} +(-9.83248 + 1.03344i) q^{44} +(-4.11724 + 8.21012i) q^{45} +(0.000270749 - 0.00257601i) q^{46} +(-4.18090 - 1.60490i) q^{47} +(4.84133 + 9.50164i) q^{48} +(2.76889 - 6.42909i) q^{49} +(0.00399142 + 0.00251995i) q^{50} +(-1.02914 + 1.78252i) q^{51} +(9.08419 + 5.89934i) q^{52} +(-0.179681 + 0.145503i) q^{53} +(-0.00254645 + 0.00113375i) q^{54} +(11.0419 + 0.507781i) q^{55} +(0.00910233 - 0.00411936i) q^{56} +(-1.82388 + 1.82388i) q^{57} +(0.00234715 - 0.00289849i) q^{58} +(2.95382 - 3.28055i) q^{59} +(-3.75686 - 11.3153i) q^{60} +(-9.04162 + 8.14111i) q^{61} +(0.00387055 - 0.00759638i) q^{62} +(-3.95638 - 10.1217i) q^{63} +(-7.60843 - 2.47213i) q^{64} +(-9.05133 - 8.04547i) q^{65} +(0.00924600 + 0.00832513i) q^{66} +(0.672823 - 0.258273i) q^{67} +(-0.399642 - 1.49149i) q^{68} +(5.91760 - 4.29939i) q^{69} +(-0.00537637 + 0.00151292i) q^{70} +(3.49220 + 2.53723i) q^{71} +(0.00555865 - 0.0144808i) q^{72} +(0.442460 - 0.681329i) q^{73} +(-0.00173062 + 0.000999174i) q^{74} +(2.25376 + 13.1380i) q^{75} -1.93501i q^{76} +(-9.19150 + 9.30437i) q^{77} +(-0.00213235 - 0.0134631i) q^{78} +(2.01057 + 4.51581i) q^{79} +(7.99524 + 4.00948i) q^{80} +(4.06615 + 1.81036i) q^{81} +(-0.00597808 + 0.00160182i) q^{82} +(-2.09559 + 13.2310i) q^{83} +(12.9222 + 5.65911i) q^{84} +(0.191447 + 1.71571i) q^{85} +(-0.00245127 - 0.00272241i) q^{86} +(10.5179 - 0.551220i) q^{87} +(-0.0186417 + 0.000976972i) q^{88} +(-7.76599 - 8.62500i) q^{89} +(-0.00428727 + 0.00753686i) q^{90} +(14.2410 - 1.58472i) q^{91} +(-0.858405 + 5.41975i) q^{92} +(23.2555 - 6.23128i) q^{93} +(-0.00386235 - 0.00171963i) q^{94} +(-0.324737 + 2.13890i) q^{95} +(0.0122845 + 0.0275913i) q^{96} +(2.13624 + 13.4877i) q^{97} +(0.00292809 - 0.00592437i) q^{98} +20.3047i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	0.000942774	0	4.94087e-5i	0.000666642	0	3.49372e-5i	0.0526693	−	0.998612i	$-0.483227\pi$
$2$	0.000942774	0	4.94087e-5i	0.000666642	0	3.49372e-5i	−0.0520026	+	0.998647i	$0.516560\pi$
$3$	1.67776	+	2.07186i	0.968656	+	1.19619i	0.980552	+	0.196261i	$0.0628801\pi$
$3$	1.67776	+	2.07186i	0.968656	+	1.19619i	−0.0118956	+	0.999929i	$0.503787\pi$
$4$	−1.98904	−	0.209057i	−0.994521	−	0.104528i
$5$	2.16354	+	0.564890i	0.967564	+	0.252626i
$5$	2.16354	+	0.564890i	0.967564	+	0.252626i
$6$	0.00147938	+	0.00203619i	0.000603955	+	0.000831273i
$7$	−2.21008	+	1.45449i	−0.835331	+	0.549747i
$7$	−2.21008	+	1.45449i	−0.835331	+	0.549747i
$8$	−0.00372978		0.000590739i	−0.00131868		0.000208858i
$9$	−0.853997	+	4.01774i	−0.284666	+	1.33925i
$10$	0.00201182		0.000639461i	0.000636192		0.000202215i
$11$	4.83530	−	1.02777i	1.45790	−	0.309886i	0.590312	−	0.807175i	$-0.299005\pi$
$11$	4.83530	−	1.02777i	1.45790	−	0.309886i	0.867585	+	0.497289i	$0.165671\pi$
$12$	−2.90400	−	4.47177i	−0.838313	−	1.29089i
$13$	−4.82554	−	2.45874i	−1.33836	−	0.681931i	−0.369432	−	0.929258i	$-0.620448\pi$
$13$	−4.82554	−	2.45874i	−1.33836	−	0.681931i	−0.968932	+	0.247327i	$0.920448\pi$
$14$	−0.00215547	+	0.00126206i	−0.000576073	+	0.000337300i
$15$	2.45953	+	5.43031i	0.635047	+	1.40210i
$16$	3.91259	+	0.831646i	0.978146	+	0.207911i
$17$	0.276678	+	0.720771i	0.0671043	+	0.174813i	0.963032	−	0.269388i	$-0.0868213\pi$
$17$	0.276678	+	0.720771i	0.0671043	+	0.174813i	−0.895928	+	0.444200i	$0.853488\pi$
$18$	−0.00100364	+	0.00374563i	−0.000236560	+	0.000882852i
$19$	0.101132	+	0.962206i	0.0232013	+	0.220745i	0.999979	+	0.00648984i	$0.00206580\pi$
$19$	0.101132	+	0.962206i	0.0232013	+	0.220745i	−0.976778	+	0.214255i	$0.931268\pi$
$20$	−4.18528	−	1.57589i	−0.935856	−	0.352380i
$21$	−6.72150	−	2.13869i	−1.46675	−	0.466699i
$22$	0.00460937		0.000730053i	0.000982722		0.000155648i
$23$	0.143592	−	2.73990i	0.0299410	−	0.571308i	−0.941932	−	0.335803i	$-0.890992\pi$
$23$	0.143592	−	2.73990i	0.0299410	−	0.571308i	0.971873	−	0.235505i	$-0.0756744\pi$
$24$	−0.00503375	−	0.00871871i	−0.00102751	−	0.00177970i
$25$	4.36180	+	2.44432i	0.872360	+	0.488864i
$26$	−0.00442791	−	0.00255646i	−0.000868385	−	0.000501362i
$27$	−2.63077	+	1.34044i	−0.506292	+	0.257968i
$28$	4.70001	−	2.43102i	0.888219	−	0.459419i
$29$	2.32212	−	3.19613i	0.431207	−	0.593506i	−0.537023	−	0.843568i	$-0.680451\pi$
$29$	2.32212	−	3.19613i	0.431207	−	0.593506i	0.968230	+	0.250062i	$0.0804511\pi$
$30$	0.00205047	+	0.00524107i	0.000374364	+	0.000956884i
$31$	3.67313	−	8.24998i	0.659713	−	1.48174i	−0.204631	−	0.978839i	$-0.565600\pi$
$31$	3.67313	−	8.24998i	0.659713	−	1.48174i	0.864344	−	0.502901i	$-0.167734\pi$
$32$	0.0109428	+	0.00293211i	0.00193443	+	0.000518329i
$33$	10.2419	+	8.29371i	1.78288	+	1.44375i
$34$	0.000225232	0	0.000693194i	3.86270e−5	0	0.000118882i
$35$	−5.60322	+	1.89840i	−0.947117	+	0.320889i
$36$	2.53857	−	7.81292i	0.423095	−	1.30215i
$37$	−1.77525	+	1.15286i	−0.291849	+	0.189529i	−0.682256	−	0.731113i	$-0.739001\pi$
$37$	−1.77525	+	1.15286i	−0.291849	+	0.189529i	0.390407	+	0.920642i	$0.372334\pi$
$38$	4.78032e−5	0	0.000912139i	7.75470e−6	0	0.000147969i
$39$	−3.00194	−	14.1230i	−0.480696	−	2.26150i
$40$	−0.00773582	−	0.00338500i	−0.00122314	−	0.000535215i
$41$	−6.23478	+	2.02580i	−0.973710	+	0.316377i	−0.752313	−	0.658806i	$-0.771062\pi$
$41$	−6.23478	+	2.02580i	−0.973710	+	0.316377i	−0.221397	+	0.975184i	$0.571062\pi$
$42$	−0.00623118	−	0.00234840i	−0.000961492	−	0.000362366i
$43$	−2.74386	−	2.74386i	−0.418435	−	0.418435i	0.466229	−	0.884664i	$-0.345612\pi$
$43$	−2.74386	−	2.74386i	−0.418435	−	0.418435i	−0.884664	+	0.466229i	$0.845612\pi$
$44$	−9.83248	+	1.03344i	−1.48230	+	0.155796i
$45$	−4.11724	+	8.21012i	−0.613761	+	1.22389i
$46$	0.000270749	−	0.00257601i	3.99198e−5	−	0.000379812i
$47$	−4.18090	−	1.60490i	−0.609847	−	0.234098i	0.0337904	−	0.999429i	$-0.489242\pi$
$47$	−4.18090	−	1.60490i	−0.609847	−	0.234098i	−0.643637	+	0.765331i	$0.722575\pi$
$48$	4.84133	+	9.50164i	0.698786	+	1.37144i
$49$	2.76889	−	6.42909i	0.395556	−	0.918442i
$50$	0.00399142	+	0.00251995i	0.000564472	+	0.000356375i
$51$	−1.02914	+	1.78252i	−0.144108	+	0.249603i
$52$	9.08419	+	5.89934i	1.25975	+	0.818092i
$53$	−0.179681	+	0.145503i	−0.0246811	+	0.0199863i	−0.641582	−	0.767055i	$-0.721721\pi$
$53$	−0.179681	+	0.145503i	−0.0246811	+	0.0199863i	0.616901	+	0.787041i	$0.288388\pi$
$54$	−0.00254645	+	0.00113375i	−0.000346528	+	0.000154284i
$55$	11.0419	+	0.507781i	1.48889	+	0.0684692i
$56$	0.00910233	−	0.00411936i	0.00121635	−	0.000550473i
$57$	−1.82388	+	1.82388i	−0.241579	+	0.241579i
$58$	0.00234715	−	0.00289849i	0.000308196	−	0.000380590i
$59$	2.95382	−	3.28055i	0.384554	−	0.427091i	−0.519525	−	0.854455i	$-0.673891\pi$
$59$	2.95382	−	3.28055i	0.384554	−	0.427091i	0.904079	+	0.427364i	$0.140558\pi$
$60$	−3.75686	−	11.3153i	−0.485009	−	1.46080i
$61$	−9.04162	+	8.14111i	−1.15766	+	1.04236i	−0.159180	+	0.987250i	$0.550885\pi$
$61$	−9.04162	+	8.14111i	−1.15766	+	1.04236i	−0.998480	+	0.0551126i	$0.982448\pi$
$62$	0.00387055	−	0.00759638i	0.000491560	−	0.000964741i
$63$	−3.95638	−	10.1217i	−0.498457	−	1.27521i
$64$	−7.60843	−	2.47213i	−0.951054	−	0.309016i
$65$	−9.05133	−	8.04547i	−1.12268	−	0.997918i
$66$	0.00924600	+	0.00832513i	0.00113810	+	0.00102475i
$67$	0.672823	−	0.258273i	0.0821984	−	0.0315530i	−0.316921	−	0.948452i	$-0.602649\pi$
$67$	0.672823	−	0.258273i	0.0821984	−	0.0315530i	0.399120	+	0.916899i	$0.369316\pi$
$68$	−0.399642	−	1.49149i	−0.0484637	−	0.180869i
$69$	5.91760	−	4.29939i	0.712396	−	0.517586i
$70$	−0.00537637	+	0.00151292i	−0.000642599	+	0.000180828i
$71$	3.49220	+	2.53723i	0.414447	+	0.301114i	0.775400	−	0.631471i	$-0.217548\pi$
$71$	3.49220	+	2.53723i	0.414447	+	0.301114i	−0.360952	+	0.932584i	$0.617548\pi$
$72$	0.00555865	−	0.0144808i	0.000655094	−	0.00170658i
$73$	0.442460	−	0.681329i	0.0517860	−	0.0797435i	−0.811829	−	0.583895i	$-0.801528\pi$
$73$	0.442460	−	0.681329i	0.0517860	−	0.0797435i	0.863615	+	0.504151i	$0.168195\pi$
$74$	−0.00173062		0.000999174i	−0.000201181		0.000116152i
$75$	2.25376	+	13.1380i	0.260242	+	1.51705i
$76$		−	1.93501i		−	0.221961i
$77$	−9.19150	+	9.30437i	−1.04747	+	1.06033i
$78$	−0.00213235	−	0.0134631i	−0.000241441	−	0.00152440i
$79$	2.01057	+	4.51581i	0.226207	+	0.508069i	0.990618	−	0.136660i	$-0.0436369\pi$
$79$	2.01057	+	4.51581i	0.226207	+	0.508069i	−0.764411	+	0.644729i	$0.776970\pi$
$80$	7.99524	+	4.00948i	0.893895	+	0.448273i
$81$	4.06615	+	1.81036i	0.451794	+	0.201152i
$82$	−0.00597808	+	0.00160182i	−0.000660169	+	0.000176892i
$83$	−2.09559	+	13.2310i	−0.230020	+	1.45229i	0.554497	+	0.832186i	$0.312911\pi$
$83$	−2.09559	+	13.2310i	−0.230020	+	1.45229i	−0.784518	+	0.620106i	$0.787089\pi$
$84$	12.9222	+	5.65911i	1.40993	+	0.617460i
$85$	0.191447	+	1.71571i	0.0207654	+	0.186095i
$86$	−0.00245127	−	0.00272241i	−0.000264327	−	0.000293565i
$87$	10.5179	−	0.551220i	1.12764	−	0.0590970i
$88$	−0.0186417		0.000976972i	−0.00198722		0.000104146i
$89$	−7.76599	−	8.62500i	−0.823193	−	0.914249i	0.174323	−	0.984689i	$-0.444226\pi$
$89$	−7.76599	−	8.62500i	−0.823193	−	0.914249i	−0.997516	+	0.0704400i	$0.977560\pi$
$90$	−0.00428727	+	0.00753686i	−0.000451918	+	0.000794455i
$91$	14.2410	−	1.58472i	1.49287	−	0.166124i
$92$	−0.858405	+	5.41975i	−0.0894949	+	0.565048i
$93$	23.2555	−	6.23128i	2.41148	−	0.646154i
$94$	−0.00386235	−	0.00171963i	−0.000398371	−	0.000177366i
$95$	−0.324737	+	2.13890i	−0.0333174	+	0.219446i
$96$	0.0122845	+	0.0275913i	0.00125378	+	0.00281603i
$97$	2.13624	+	13.4877i	0.216902	+	1.36947i	0.820258	+	0.571994i	$0.193830\pi$
$97$	2.13624	+	13.4877i	0.216902	+	1.36947i	−0.603355	+	0.797472i	$0.706170\pi$
$98$	0.00292809	−	0.00592437i	0.000295782	−	0.000598452i
$99$			20.3047i			2.04070i
$100$	−8.16480	−	5.77372i	−0.816480	−	0.577372i
$101$	−10.5363	+	6.08311i	−1.04840	+	0.605292i	−0.922200	−	0.386713i	$-0.873610\pi$
$101$	−10.5363	+	6.08311i	−1.04840	+	0.605292i	−0.126197	+	0.992005i	$0.540277\pi$
$102$	−0.00105832	+	0.00162966i	−0.000104789	+	0.000161361i
$103$	1.40808	−	3.66819i	0.138743	−	0.361437i	−0.846551	−	0.532308i	$-0.821325\pi$
$103$	1.40808	−	3.66819i	0.138743	−	0.361437i	0.985293	+	0.170871i	$0.0546581\pi$
$104$	0.0165457	+	0.0120212i	0.00162244	+	0.00117877i
$105$	−13.3341	−	8.42403i	−1.30127	−	0.822101i
$106$	−0.000176588	0	0.000128298i	−1.71517e−5	0	1.24614e-5i
$107$	0.0184739	+	0.0689457i	0.00178594	+	0.00666523i	0.966813	−	0.255485i	$-0.0822351\pi$
$107$	0.0184739	+	0.0689457i	0.00178594	+	0.00666523i	−0.965027	+	0.262150i	$0.915568\pi$
$108$	5.51294	−	2.11622i	0.530483	−	0.203633i
$109$	7.26066	+	6.53753i	0.695445	+	0.626182i	0.939085	−	0.343684i	$-0.111675\pi$
$109$	7.26066	+	6.53753i	0.695445	+	0.626182i	−0.243640	+	0.969866i	$0.578342\pi$
$110$	0.0103850	+	0.00102429i	0.000990167	+	9.76622e-5i
$111$	−5.36702	−	1.74385i	−0.509415	−	0.165519i
$112$	−9.85674	+	3.85283i	−0.931375	+	0.364058i
$113$	−7.83452	+	15.3761i	−0.737009	+	1.44646i	0.151908	+	0.988395i	$0.451458\pi$
$113$	−7.83452	+	15.3761i	−0.737009	+	1.44646i	−0.888917	+	0.458068i	$0.848542\pi$
$114$	−0.00180963	+	0.00162939i	−0.000169487	+	0.000152607i
$115$	1.85841	−	5.84676i	0.173297	−	0.545213i
$116$	−5.28697	+	5.87178i	−0.490883	+	0.545181i
$117$	13.9996	−	17.2880i	1.29426	−	1.59828i
$118$	0.00294687	−	0.00294687i	0.000271281	−	0.000271281i
$119$	−1.65984	−	1.19053i	−0.152157	−	0.109136i
$120$	−0.00596560	−	0.0217068i	−0.000544582	−	0.00198155i
$121$	12.2748	−	5.46509i	1.11589	−	0.496826i
$122$	−0.00892644	+	0.00722849i	−0.000808162	+	0.000654437i
$123$	−14.6577	−	9.51880i	−1.32164	−	0.858281i
$124$	−9.03072	+	15.6417i	−0.810983	+	1.40466i
$125$	8.05615	+	7.75232i	0.720564	+	0.693389i
$126$	−0.00322987	−	0.00973791i	−0.000287740	−	0.000867522i
$127$	−7.97116	−	15.6443i	−0.707326	−	1.38821i	−0.912335	−	0.409445i	$-0.865722\pi$
$127$	−7.97116	−	15.6443i	−0.707326	−	1.38821i	0.205009	−	0.978760i	$-0.434278\pi$
$128$	−0.0282036	−	0.0108263i	−0.00249287	−	0.000956922i
$129$	1.08136	−	10.2884i	0.0952084	−	0.905847i
$130$	−0.00813584	−	0.00803227i	−0.000713561	−	0.000704477i
$131$	2.88542	−	0.303269i	0.252100	−	0.0264968i	0.0223645	−	0.999750i	$-0.492881\pi$
$131$	2.88542	−	0.303269i	0.252100	−	0.0264968i	0.229735	+	0.973253i	$0.426214\pi$
$132$	−18.6377	−	18.6377i	−1.62220	−	1.62220i
$133$	−1.62303	−	1.97945i	−0.140735	−	0.171641i
$134$	0.000647081	0	0.000210249i	5.58993e−5	0	1.81628e-5i
$135$	−6.44897	+	1.41401i	−0.555039	+	0.121698i
$136$	−0.000606160	−	0.00285176i	−5.19778e−5	−	0.000244536i
$137$	−1.08686	−	20.7386i	−0.0928568	−	1.77181i	−0.507329	−	0.861752i	$-0.669367\pi$
$137$	−1.08686	−	20.7386i	−0.0928568	−	1.77181i	0.414473	−	0.910062i	$-0.363966\pi$
$138$	0.00579139	−	0.00376097i	0.000492996	−	0.000320155i
$139$	−0.653905	+	2.01251i	−0.0554635	+	0.170699i	−0.974951	−	0.222421i	$-0.928604\pi$
$139$	−0.653905	+	2.01251i	−0.0554635	+	0.170699i	0.919487	+	0.393120i	$0.128604\pi$
$140$	11.5419	−	2.60461i	0.975470	−	0.220130i
$141$	−3.68943	−	11.3549i	−0.310706	−	0.956254i
$142$	0.00316699	+	0.00256458i	0.000265768	+	0.000215215i
$143$	−25.8600	−	6.92916i	−2.16252	−	0.579445i
$144$	−6.68267	+	15.0095i	−0.556889	+	1.25079i
$145$	6.82946	−	5.60320i	0.567156	−	0.465320i
$146$	0.000450803	0	0.000620477i	3.73087e−5	0	5.13511e-5i
$147$	17.9657	−	5.04971i	1.48179	−	0.416493i
$148$	3.77206	−	1.92196i	0.310062	−	0.157984i
$149$	−9.34465	−	5.39514i	−0.765543	−	0.441987i	0.0657390	−	0.997837i	$-0.479060\pi$
$149$	−9.34465	−	5.39514i	−0.765543	−	0.441987i	−0.831283	+	0.555850i	$0.812393\pi$
$150$	0.00147565	+	0.0124976i	0.000120486	+	0.00102042i
$151$	−3.46356	−	5.99906i	−0.281861	−	0.488197i	0.689982	−	0.723826i	$-0.257618\pi$
$151$	−3.46356	−	5.99906i	−0.281861	−	0.488197i	−0.971843	+	0.235629i	$0.924285\pi$
$152$	0.000191213	−	0.00364856i	1.55094e−5	−	0.000295937i
$153$	−3.13215	+	0.496084i	−0.253219	+	0.0401060i
$154$	−0.00912522	+	0.00831778i	−0.000735331	+	0.000670266i
$155$	12.6073	−	15.7742i	1.01264	−	1.26702i
$156$	3.01848	+	28.7189i	0.241672	+	2.29935i
$157$	−4.51732	+	16.8589i	−0.360521	+	1.34548i	0.512871	+	0.858466i	$0.328582\pi$
$157$	−4.51732	+	16.8589i	−0.360521	+	1.34548i	−0.873392	+	0.487018i	$0.838085\pi$
$158$	0.00167239	+	0.00435673i	0.000133048	+	0.000346603i
$159$	−0.602923	−	0.128155i	−0.0478149	−	0.0101634i
$160$	0.0220188	+	0.0125252i	0.00174074	+	0.000990204i
$161$	3.66781	+	6.26424i	0.289064	+	0.493691i
$162$	0.00374401	+	0.00190767i	0.000294157	+	0.000149880i
$163$	−4.39358	−	6.76552i	−0.344132	−	0.529916i	0.623651	−	0.781703i	$-0.285649\pi$
$163$	−4.39358	−	6.76552i	−0.344132	−	0.529916i	−0.967783	+	0.251786i	$0.918982\pi$
$164$	12.8248	−	2.72599i	1.00145	−	0.212864i
$165$	17.4737	+	23.7293i	1.36032	+	1.84732i
$166$	−0.00262939	+	0.0123703i	−0.000204080	+	0.000960122i
$167$	5.27411	+	0.835336i	0.408123	+	0.0646403i	0.357121	−	0.934058i	$-0.383759\pi$
$167$	5.27411	+	0.835336i	0.408123	+	0.0646403i	0.0510020	+	0.998699i	$0.483759\pi$
$168$	0.0238063	+	0.0119475i	0.00183669	+	0.000921767i
$169$	9.59926	+	13.2122i	0.738405	+	1.01633i
$170$	9.57208e−5		0.00162698i	7.34145e−6		0.000124784i
$171$	−3.95226	−	0.415399i	−0.302237	−	0.0317664i
$172$	4.88403	+	6.03128i	0.372404	+	0.459881i
$173$	−3.82057	−	0.200228i	−0.290473	−	0.0152230i	−0.0934568	−	0.995623i	$-0.529792\pi$
$173$	−3.82057	−	0.200228i	−0.290473	−	0.0152230i	−0.197016	+	0.980400i	$0.563125\pi$
$174$	0.00994323			0.000753795
$175$	−13.1952	+	0.942068i	−0.997461	+	0.0712137i
$176$	19.7733			1.49047
$177$	11.7526	+	0.615930i	0.883382	+	0.0462961i
$178$	−0.00689542	−	0.00851513i	−0.000516834	−	0.000638236i
$179$	7.80326	+	0.820156i	0.583243	+	0.0613013i	0.391555	−	0.920155i	$-0.371937\pi$
$179$	7.80326	+	0.820156i	0.583243	+	0.0613013i	0.191688	+	0.981456i	$0.438604\pi$
$180$	9.90574	−	15.4695i	0.738330	−	1.15303i
$181$	−13.0808	−	18.0042i	−0.972287	−	1.33824i	−0.940883	−	0.338732i	$-0.890002\pi$
$181$	−13.0808	−	18.0042i	−0.972287	−	1.33824i	−0.0314040	−	0.999507i	$-0.509998\pi$
$182$	0.0135044		0.000790403i	0.00100101		5.85885e-5i
$183$	−32.0369	−	5.07415i	−2.36824	−	0.375092i
$184$	−0.00215413	+	0.0101344i	−0.000158805	+	0.000747117i
$185$	−4.49206	+	1.49144i	−0.330263	+	0.109653i
$186$	0.0222325	−	0.00472567i	0.00163017	−	0.000346503i
$187$	2.07861	+	3.20078i	0.152003	+	0.234064i
$188$	7.98048	+	4.06626i	0.582036	+	0.296562i
$189$	3.86454	−	6.78892i	0.281104	−	0.493821i
$190$	−0.000411834		0.00200045i	−2.98776e−5		0.000145128i
$191$	−10.1894	−	2.16582i	−0.737279	−	0.156713i	−0.176058	−	0.984380i	$-0.556335\pi$
$191$	−10.1894	−	2.16582i	−0.737279	−	0.156713i	−0.561221	+	0.827666i	$0.689668\pi$
$192$	−7.64322	−	19.9113i	−0.551602	−	1.43697i
$193$	−1.73551	+	6.47700i	−0.124925	+	0.466225i	−0.999837	−	0.0180564i	$-0.994252\pi$
$193$	−1.73551	+	6.47700i	−0.124925	+	0.466225i	0.874912	+	0.484281i	$0.160919\pi$
$194$	0.00134758	+	0.0128214i	9.67507e−5	+	0.000920522i
$195$	1.48314	−	32.2515i	0.106210	−	2.30958i
$196$	−6.85150	+	12.2089i	−0.489393	+	0.872063i
$197$	24.8565	−	3.93688i	1.77095	−	0.280491i	0.816172	−	0.577809i	$-0.196092\pi$
$197$	24.8565	−	3.93688i	1.77095	−	0.280491i	0.954779	+	0.297318i	$0.0960922\pi$
$198$	−0.00100323	+	0.0191427i	−7.12963e−5	+	0.00136041i
$199$	0.330685	+	0.572764i	0.0234417	+	0.0406022i	0.877508	−	0.479562i	$-0.159204\pi$
$199$	0.330685	+	0.572764i	0.0234417	+	0.0406022i	−0.854067	+	0.520164i	$0.825871\pi$
$200$	−0.0148246	−	0.0116935i	−0.00104826	−	0.000826852i
$201$	1.66394	+	0.960678i	0.117365	+	0.0677610i
$202$	−0.0102339	+	0.00521442i	−0.000720052	+	0.000366885i
$203$	−0.483325	+	10.4412i	−0.0339227	+	0.732829i
$204$	2.41965	−	3.33036i	0.169409	−	0.233172i
$205$	−14.6336	+	0.860940i	−1.02205	+	0.0601307i
$206$	0.00150875	−	0.00338870i	0.000105119	−	0.000236102i
$207$	10.8856	+	2.91678i	0.756599	+	0.202730i
$208$	−16.8355	−	13.6332i	−1.16734	−	0.945289i
$209$	1.47793	+	4.54861i	0.102231	+	0.314634i
$210$	−0.0121548	−	0.00860078i	−0.000838762	−	0.000593510i
$211$	1.58569	−	4.88026i	0.109164	−	0.335971i	−0.881521	−	0.472144i	$-0.843480\pi$
$211$	1.58569	−	4.88026i	0.109164	−	0.335971i	0.990685	+	0.136173i	$0.0434803\pi$
$212$	0.387811	−	0.251848i	0.0266350	−	0.0172970i
$213$	0.602282	+	11.4922i	0.0412676	+	0.787434i
$214$	1.40102e−5	0	6.59130e-5i	9.57720e−7	0	4.50572e-6i
$215$	−4.38647	−	7.48643i	−0.299155	−	0.510570i
$216$	0.0106040	−	0.00344546i	0.000721513	−	0.000234434i
$217$	3.88164	+	23.5756i	0.263503	+	1.60042i
$218$	0.00652215	+	0.00652215i	0.000441736	+	0.000441736i
$219$	2.15396	−	0.226390i	0.145551	−	0.0152981i
$220$	−21.8567	−	3.31839i	−1.47358	−	0.223726i
$221$	0.437064	−	4.15839i	0.0294001	−	0.279723i
$222$	−0.00497372	−	0.00190923i	−0.000333814	−	0.000128139i
$223$	−3.09117	−	6.06675i	−0.207000	−	0.406260i	0.764043	−	0.645165i	$-0.223211\pi$
$223$	−3.09117	−	6.06675i	−0.207000	−	0.406260i	−0.971043	+	0.238905i	$0.923211\pi$
$224$	−0.0284492	+	0.00943602i	−0.00190084	+	0.000630471i
$225$	−13.5456	+	15.4371i	−0.903041	+	1.02914i
$226$	−0.00814589	+	0.0141091i	−0.000541857	+	0.000938523i
$227$	−3.37972	−	2.19482i	−0.224320	−	0.145675i	0.427587	−	0.903974i	$-0.359364\pi$
$227$	−3.37972	−	2.19482i	−0.224320	−	0.145675i	−0.651907	+	0.758299i	$0.726031\pi$
$228$	4.00908	−	3.24649i	0.265508	−	0.215004i
$229$	12.8764	−	5.73293i	0.850894	−	0.378843i	0.0655106	−	0.997852i	$-0.479132\pi$
$229$	12.8764	−	5.73293i	0.850894	−	0.378843i	0.785384	+	0.619009i	$0.212466\pi$
$230$	0.00204094	−	0.00542035i	0.000134575	−	0.000357407i
$231$	−34.6985	−	3.43300i	−2.28300	−	0.225875i
$232$	−0.0105491	+	0.0105491i	−0.000692580	+	0.000692580i
$233$	4.41194	−	5.44829i	0.289036	−	0.356929i	−0.611859	−	0.790967i	$-0.709578\pi$
$233$	4.41194	−	5.44829i	0.289036	−	0.356929i	0.900895	+	0.434037i	$0.142911\pi$
$234$	0.0140526	−	0.0156070i	0.000918647	−	0.00102026i
$235$	−8.13895	−	5.83400i	−0.530927	−	0.380569i
$236$	−6.56109	+	5.90763i	−0.427090	+	0.384554i
$237$	−5.98289	+	11.7421i	−0.388630	+	0.762730i
$238$	−0.00150603	−	0.00120441i	−9.76213e−5	−	7.80706e-5i
$239$	−6.46280	−	2.09989i	−0.418044	−	0.135831i	0.0924397	−	0.995718i	$-0.470533\pi$
$239$	−6.46280	−	2.09989i	−0.418044	−	0.135831i	−0.510483	+	0.859888i	$0.670533\pi$
$240$	5.10702	+	23.2920i	0.329657	+	1.50349i
$241$	11.5537	+	10.4030i	0.744239	+	0.670116i	0.951319	−	0.308208i	$-0.0997293\pi$
$241$	11.5537	+	10.4030i	0.744239	+	0.670116i	−0.207080	+	0.978324i	$0.566396\pi$
$242$	0.0118424	−	0.00454586i	0.000761256	−	0.000292219i
$243$	5.36375	+	20.0178i	0.344084	+	1.28414i
$244$	19.6861	−	14.3028i	1.26027	−	0.915643i
$245$	9.62234	−	12.3455i	0.614749	−	0.788723i
$246$	−0.0133486	−	0.00969829i	−0.000851073	−	0.000618340i
$247$	1.87779	−	4.89182i	0.119481	−	0.311259i
$248$	−0.0185735	+	0.0286007i	−0.00117942	+	0.00181615i
$249$	−30.9287	+	17.8567i	−1.96003	+	1.13162i
$250$	0.00721209	+	0.00770673i	0.000456133	+	0.000487416i
$251$		−	19.2636i		−	1.21591i	−0.793972	−	0.607955i	$-0.791990\pi$
$251$		−	19.2636i		−	1.21591i	0.793972	−	0.607955i	$-0.208010\pi$
$252$	5.75341	+	20.9595i	0.362430	+	1.32033i
$253$	−2.12169	−	13.3958i	−0.133389	−	0.842187i
$254$	−0.00674204	−	0.0151429i	−0.000423033	−	0.000950148i
$255$	−3.23351	+	3.27520i	−0.202490	+	0.205101i
$256$	14.6167	+	6.50776i	0.913541	+	0.406735i
$257$	−4.39708	+	1.17819i	−0.274282	+	0.0734937i	−0.393338	−	0.919394i	$-0.628680\pi$
$257$	−4.39708	+	1.17819i	−0.274282	+	0.0734937i	0.119056	+	0.992888i	$0.462013\pi$
$258$	0.00152782	−	0.00964625i	9.51176e−5	−	0.000600549i
$259$	2.24661	−	5.13000i	0.139598	−	0.318763i
$260$	16.3215	+	17.8950i	1.01222	+	1.10980i
$261$	10.8581	+	12.0592i	0.672101	+	0.746443i
$262$	0.00273528		0.000143350i	0.000168986		8.85619e-6i
$263$	26.8485	−	1.40707i	1.65555	−	0.0867635i	0.798497	−	0.601998i	$-0.205629\pi$
$263$	26.8485	−	1.40707i	1.65555	−	0.0867635i	0.857049	+	0.515235i	$0.172295\pi$
$264$	−0.0333005	−	0.0369840i	−0.00204951	−	0.00227621i
$265$	−0.470940	+	0.213301i	−0.0289296	+	0.0131030i
$266$	−0.00143235	−	0.00194637i	−8.78230e−5	−	0.000119340i
$267$	4.84035	−	30.5608i	0.296225	−	1.87029i
$268$	−1.39227	+	0.373057i	−0.0850463	+	0.0227881i
$269$	−8.58299	−	3.82140i	−0.523314	−	0.232995i	0.128039	−	0.991769i	$-0.459132\pi$
$269$	−8.58299	−	3.82140i	−0.523314	−	0.232995i	−0.651353	+	0.758775i	$0.725798\pi$
$270$	−0.00614979	+	0.00101445i	−0.000374264	+	6.17377e-5i
$271$	6.62606	+	14.8824i	0.402505	+	0.904040i	0.995131	+	0.0985625i	$0.0314244\pi$
$271$	6.62606	+	14.8824i	0.402505	+	0.904040i	−0.592626	+	0.805478i	$0.701909\pi$
$272$	0.483100	+	3.05017i	0.0292923	+	0.184944i
$273$	27.1764	+	26.8467i	1.64479	+	1.62484i
$274$		−	0.0196055i		−	0.00118441i
$275$	23.6028	+	7.33608i	1.42330	+	0.442382i
$276$	−12.6692	+	7.31456i	−0.762595	+	0.440285i
$277$	−9.57066	+	14.7375i	−0.575045	+	0.885492i	−0.999804	−	0.0198145i	$-0.993692\pi$
$277$	−9.57066	+	14.7375i	−0.575045	+	0.885492i	0.424758	+	0.905307i	$0.360359\pi$
$278$	−0.000715920		0.00186504i	−4.29380e−5		0.000111857i
$279$	30.0094	+	21.8031i	1.79662	+	1.30532i
$280$	0.0220202	−	0.00377058i	0.00131596	−	0.000225335i
$281$	−16.5863	+	12.0506i	−0.989455	+	0.718881i	−0.959802	−	0.280679i	$-0.909440\pi$
$281$	−16.5863	+	12.0506i	−0.989455	+	0.718881i	−0.0296530	+	0.999560i	$0.509440\pi$
$282$	−0.00291726	−	0.0108874i	−0.000173721	−	0.000648334i
$283$	18.9946	−	7.29133i	1.12911	−	0.433424i	0.279136	−	0.960251i	$-0.409952\pi$
$283$	18.9946	−	7.29133i	1.12911	−	0.433424i	0.849972	+	0.526827i	$0.176618\pi$
$284$	−6.41570	−	5.77672i	−0.380702	−	0.342786i
$285$	−4.97634	+	2.91575i	−0.294773	+	0.172714i
$286$	−0.0240377	−	0.00781033i	−0.00142138	−	0.000461835i
$287$	10.8328	−	13.5456i	0.639442	−	0.799574i
$288$	−0.0211256	+	0.0414613i	−0.00124484	+	0.00244313i
$289$	12.1905	−	10.9764i	0.717088	−	0.645669i
$290$	0.00671548	−	0.00494511i	0.000394347	−	0.000290387i
$291$	−24.3605	+	27.0551i	−1.42804	+	1.58600i
$292$	−1.02251	+	1.26269i	−0.0598378	+	0.0738935i
$293$	−1.07980	+	1.07980i	−0.0630827	+	0.0630827i	−0.737944	−	0.674862i	$-0.764203\pi$
$293$	−1.07980	+	1.07980i	−0.0630827	+	0.0630827i	0.674862	+	0.737944i	$0.264203\pi$
$294$	0.0171871	−	0.00387307i	0.00100237	−	0.000225882i
$295$	8.24384	−	5.42901i	0.479975	−	0.316089i
$296$	0.00730233	−	0.00325121i	0.000424439	−	0.000188972i
$297$	−11.3429	+	9.18528i	−0.658180	+	0.532984i
$298$	−0.00854332	−	0.00554810i	−0.000494901	−	0.000321393i
$299$	−7.42959	+	12.8684i	−0.429665	+	0.744201i
$300$	−1.73623	−	26.6033i	−0.100241	−	1.53594i
$301$	10.0551	+	2.07322i	0.579565	+	0.119498i
$302$	−0.00296895	−	0.00582689i	−0.000170844	−	0.000335300i
$303$	−30.2807	−	11.6237i	−1.73958	−	0.667763i
$304$	−0.404527	+	3.84882i	−0.0232012	+	0.220745i
$305$	−24.1607	+	12.5061i	−1.38344	+	0.716096i
$306$	−0.00297742		0.000312940i	−0.000170208		1.78896e-5i
$307$	4.76575	+	4.76575i	0.271996	+	0.271996i	0.829903	−	0.557908i	$-0.188396\pi$
$307$	4.76575	+	4.76575i	0.271996	+	0.271996i	−0.557908	+	0.829903i	$0.688396\pi$
$308$	20.2274	−	16.5853i	1.15256	−	0.945033i
$309$	9.96241	−	3.23698i	0.566742	−	0.184146i
$310$	0.0126652	−	0.0142486i	0.000719335	−	0.000809268i
$311$	4.33352	+	20.3876i	0.245731	+	1.15607i	0.911945	+	0.410313i	$0.134581\pi$
$311$	4.33352	+	20.3876i	0.245731	+	1.15607i	−0.666213	+	0.745761i	$0.732086\pi$
$312$	0.00285356	+	0.0544491i	0.000161551	+	0.00308258i
$313$	2.97190	−	1.92997i	0.167982	−	0.109089i	−0.457910	−	0.888999i	$-0.651402\pi$
$313$	2.97190	−	1.92997i	0.167982	−	0.109089i	0.625892	+	0.779910i	$0.284735\pi$
$314$	−0.00509178	+	0.0156709i	−0.000287346	+	0.000884360i
$315$	−2.84216	−	24.1335i	−0.160138	−	1.35977i
$316$	−3.05505	−	9.40247i	−0.171860	−	0.528930i
$317$	9.43807	+	7.64280i	0.530095	+	0.429262i	0.856636	−	0.515921i	$-0.172550\pi$
$317$	9.43807	+	7.64280i	0.530095	+	0.429262i	−0.326542	+	0.945183i	$0.605883\pi$
$318$	−0.000562088	0	0.000150611i	−3.15204e−5	0	8.44585e-6i
$319$	7.94325	−	17.8408i	0.444737	−	0.998895i
$320$	−15.0647	−	9.64647i	−0.842140	−	0.539254i
$321$	−0.111851	+	0.153950i	−0.00624292	+	0.00859265i
$322$	0.00314841	+	0.00608699i	0.000175454	+	0.000339214i
$323$	−0.665549	+	0.339114i	−0.0370321	+	0.0188688i
$324$	−7.70927	−	4.45095i	−0.428293	−	0.247275i
$325$	−15.0381	−	22.5197i	−0.834164	−	1.24917i
$326$	−0.00380788	−	0.00659544i	−0.000210899	−	0.000365287i
$327$	−1.36321	+	26.0115i	−0.0753854	+	1.43844i
$328$	0.0244511	−	0.00387267i	0.00135008	−	0.000213832i
$329$	11.5744	−	2.53415i	0.638119	−	0.139712i
$330$	0.0153013	+	0.0232347i	0.000842308	+	0.00127903i
$331$	−0.354346	−	3.37137i	−0.0194766	−	0.185307i	0.980458	−	0.196728i	$-0.0630314\pi$
$331$	−0.354346	−	3.37137i	−0.0194766	−	0.185307i	−0.999935	+	0.0114201i	$0.996365\pi$
$332$	6.93424	−	25.8789i	0.380566	−	1.42029i
$333$	−3.11584	−	8.11703i	−0.170747	−	0.444811i
$334$	0.00493102	+	0.00104812i	0.000269813	+	5.73506e-5i
$335$	1.60157	−	0.178712i	0.0875034	−	0.00976407i
$336$	−24.5198	−	13.9577i	−1.33766	−	0.761455i
$337$	−27.4074	−	13.9648i	−1.49298	−	0.760710i	−0.498623	−	0.866819i	$-0.666161\pi$
$337$	−27.4074	−	13.9648i	−1.49298	−	0.760710i	−0.994354	+	0.106109i	$0.966161\pi$
$338$	0.00839713	+	0.0129304i	0.000456744	+	0.000703324i
$339$	−45.0016	+	9.56539i	−2.44415	+	0.519521i
$340$	−0.0221168	−	3.45264i	−0.00119945	−	0.187246i
$341$	9.28155	−	43.6662i	0.502624	−	2.36466i
$342$	−0.00370556		0.000586903i	−0.000200374		3.17361e-5i
$343$	3.23160	+	18.2361i	0.174490	+	0.984659i
$344$	0.00861308	+	0.0118549i	0.000464386	+	0.000639173i
$345$	15.2316	−	5.95911i	0.820044	−	0.320827i
$346$	−0.00359204		0.000377539i	−0.000193109		2.02966e-5i
$347$	6.48906	+	8.01332i	0.348351	+	0.430177i	0.920964	−	0.389648i	$-0.127403\pi$
$347$	6.48906	+	8.01332i	0.348351	+	0.430177i	−0.572613	+	0.819826i	$0.694070\pi$
$348$	−21.0358	−	1.10244i	−1.12764	−	0.0590969i
$349$	2.01795			0.108019			0.0540093	−	0.998540i	$-0.482800\pi$
$349$	2.01795			0.108019			0.0540093	+	0.998540i	$0.482800\pi$
$350$	−0.0124866		0.000236201i	−0.000667437		1.26255e-5i
$351$	15.9907			0.853519
$352$	0.0559252	+	0.00293091i	0.00298082	+	0.000156218i
$353$	12.4874	+	15.4207i	0.664638	+	0.820760i	0.992277	−	0.124043i	$-0.0395862\pi$
$353$	12.4874	+	15.4207i	0.664638	+	0.820760i	−0.327639	+	0.944803i	$0.606253\pi$
$354$	0.0110496	+	0.00116136i	0.000587282	+	6.17258e-5i
$355$	6.12225	+	7.46210i	0.324935	+	0.396047i
$356$	13.6438	+	18.7790i	0.723118	+	0.995287i
$357$	−0.318188	−	5.43638i	−0.0168403	−	0.287724i
$358$	0.00731619	+	0.00115877i	0.000386673	+	6.12429e-5i
$359$	2.69470	−	12.6776i	0.142221	−	0.669096i	−0.848047	−	0.529921i	$-0.822222\pi$
$359$	2.69470	−	12.6776i	0.142221	−	0.669096i	0.990268	−	0.139175i	$-0.0444450\pi$
$360$	0.0202064	−	0.0281897i	0.00106497	−	0.00148573i
$361$	17.6692	−	3.75570i	0.929957	−	0.197669i
$362$	−0.0114427	−	0.0176202i	−0.000601413	−	0.000926095i
$363$	31.9171	+	16.2626i	1.67521	+	0.853563i
$364$	−28.6573	+	0.174891i	−1.50205	+	0.00916679i
$365$	1.34215	−	1.22414i	0.0702516	−	0.0640744i
$366$	−0.0299529	−	0.00636668i	−0.00156566	−	0.000332792i
$367$	1.44163	+	3.75556i	0.0752522	+	0.196039i	0.966047	−	0.258368i	$-0.0831847\pi$
$367$	1.44163	+	3.75556i	0.0752522	+	0.196039i	−0.890794	+	0.454407i	$0.849851\pi$
$368$	2.84044	−	10.6007i	0.148068	−	0.552598i
$369$	−2.81467	−	26.7798i	−0.146526	−	1.39410i
$370$	−0.00430869	+	0.00118414i	−0.000223998	+	6.15606e-5i
$371$	0.185476	−	0.582917i	0.00962944	−	0.0302636i
$372$	−47.5588	+	7.53257i	−2.46581	+	0.390546i
$373$	0.668325	−	12.7524i	0.0346045	−	0.660294i	−0.925175	−	0.379540i	$-0.876082\pi$
$373$	0.668325	−	12.7524i	0.0346045	−	0.660294i	0.959780	−	0.280754i	$-0.0905845\pi$
$374$	0.00180151	+	0.00312031i	9.31540e−5	+	0.000161347i
$375$	−2.54545	+	29.6978i	−0.131446	+	1.53359i
$376$	0.0146458	+	0.00845573i	0.000755297	+	0.000436071i
$377$	−19.0639	+	9.71355i	−0.981842	+	0.500274i
$378$	0.00397882	−	0.00620948i	0.000204648	−	0.000319381i
$379$	−18.7383	+	25.7910i	−0.962519	+	1.32479i	−0.0167829	+	0.999859i	$0.505342\pi$
$379$	−18.7383	+	25.7910i	−0.962519	+	1.32479i	−0.945736	+	0.324935i	$0.894658\pi$
$380$	1.09307	−	4.18647i	0.0560732	−	0.214761i
$381$	19.0391	−	42.7625i	0.975403	−	2.19079i
$382$	−0.00949929	−	0.00254533i	−0.000486026	−	0.000130230i
$383$	−17.3449	−	14.0456i	−0.886281	−	0.717696i	0.0738434	−	0.997270i	$-0.476474\pi$
$383$	−17.3449	−	14.0456i	−0.886281	−	0.717696i	−0.960124	+	0.279574i	$0.909807\pi$
$384$	−0.0248882	−	0.0765980i	−0.00127007	−	0.00390887i
$385$	−25.1421	+	14.9382i	−1.28136	+	0.761321i
$386$	−0.00195621	+	0.00602060i	−9.95685e−5	+	0.000306440i
$387$	13.3674	−	8.68087i	0.679501	−	0.441273i
$388$	−1.42938	−	27.2742i	−0.0725657	−	1.38464i
$389$	3.10708	+	14.6177i	0.157535	+	0.741146i	0.984002	+	0.178160i	$0.0570143\pi$
$389$	3.10708	+	14.6177i	0.157535	+	0.741146i	−0.826466	+	0.562986i	$0.809652\pi$
$390$	0.00299177	−	0.0303326i	0.000151494	−	0.00153595i
$391$	2.01457	−	0.654572i	0.101881	−	0.0331031i
$392$	−0.0141253	+	0.0223434i	−0.000713434	+	0.00112851i
$393$	5.46937	+	5.46937i	0.275893	+	0.275893i
$394$	0.0236285	−	0.00248346i	0.00119039	−	0.000125115i
$395$	1.79901	+	10.9059i	0.0905179	+	0.548735i
$396$	4.24483	−	40.3869i	0.213311	−	2.02952i
$397$	−6.55175	−	2.51498i	−0.328823	−	0.126223i	0.188356	−	0.982101i	$-0.439684\pi$
$397$	−6.55175	−	2.51498i	−0.328823	−	0.126223i	−0.517178	+	0.855878i	$0.673018\pi$
$398$	0.000283462	0	0.000556326i	1.42087e−5	0	2.78861e-5i
$399$	1.37810	−	6.68375i	0.0689912	−	0.334606i
$400$	15.0331	+	13.1911i	0.751655	+	0.659554i
$401$	−3.16906	+	5.48898i	−0.158255	+	0.274106i	−0.934240	−	0.356646i	$-0.883920\pi$
$401$	−3.16906	+	5.48898i	−0.158255	+	0.274106i	0.775984	+	0.630752i	$0.217254\pi$
$402$	0.00152126		0.000987915i	7.58733e−5		4.92727e-5i
$403$	−38.0093	+	30.7794i	−1.89338	+	1.53323i
$404$	22.2288	−	9.89689i	1.10592	−	0.492389i
$405$	7.77461	+	6.21372i	0.386323	+	0.308762i
$406$	−0.000971552		0.00981981i	−4.82173e−5		0.000487349i
$407$	−7.39898	+	7.39898i	−0.366754	+	0.366754i
$408$	0.00489146	−	0.00604045i	0.000242163	−	0.000299047i
$409$	4.52973	−	5.03077i	0.223981	−	0.248756i	−0.620672	−	0.784070i	$-0.713140\pi$
$409$	4.52973	−	5.03077i	0.223981	−	0.248756i	0.844653	+	0.535314i	$0.179807\pi$
$410$	−0.0138387		8.86471e-5i	−0.000683443		4.37797e-6i
$411$	41.1439	−	37.0462i	2.02948	−	1.82735i
$412$	−3.56760	+	7.00181i	−0.175763	+	0.344954i
$413$	−1.75663	+	11.5466i	−0.0864382	+	0.568170i
$414$	0.0101185	+	0.00328770i	0.000497298	+	0.000161582i
$415$	−12.0079	+	27.4420i	−0.589447	+	1.34708i
$416$	−0.0455956	−	0.0410544i	−0.00223551	−	0.00201286i
$417$	−5.26675	+	2.02171i	−0.257914	+	0.0990038i
$418$	0.00116862	+	0.00436133i	5.71589e−5	+	0.000213320i
$419$	−21.9666	+	15.9597i	−1.07314	+	0.779681i	−0.976474	−	0.215636i	$-0.930817\pi$
$419$	−21.9666	+	15.9597i	−1.07314	+	0.779681i	−0.0966645	+	0.995317i	$0.530817\pi$
$420$	24.7610	+	19.5433i	1.20821	+	0.953618i
$421$	14.9220	+	10.8415i	0.727255	+	0.528382i	0.888694	−	0.458501i	$-0.151613\pi$
$421$	14.9220	+	10.8415i	0.727255	+	0.528382i	−0.161439	+	0.986883i	$0.551613\pi$
$422$	0.00173608	−	0.00452263i	8.45109e−5	−	0.000220158i
$423$	10.0185	−	15.4272i	0.487118	−	0.750096i
$424$	0.000756124	0	0.000436548i	3.67206e−5	0	2.12007e-5i
$425$	−0.554982	+	3.82015i	−0.0269206	+	0.185304i
$426$			0.0108643i			0.000526378i
$427$	8.14149	−	31.1435i	0.393994	−	1.50714i
$428$	−0.0223319	−	0.140998i	−0.00107945	−	0.00681540i
$429$	−29.0306	−	65.2038i	−1.40161	−	3.14807i
$430$	−0.00376555	−	0.00727474i	−0.000181591	−	0.000350819i
$431$	20.1770	+	8.98338i	0.971892	+	0.432714i	0.830365	−	0.557220i	$-0.188132\pi$
$431$	20.1770	+	8.98338i	0.971892	+	0.432714i	0.141527	+	0.989934i	$0.454799\pi$
$432$	−11.4079	+	3.05673i	−0.548862	+	0.147067i
$433$	−0.188692	+	1.19136i	−0.00906797	+	0.0572529i	−0.991807	−	0.127742i	$-0.959227\pi$
$433$	−0.188692	+	1.19136i	−0.00906797	+	0.0572529i	0.982739	+	0.184995i	$0.0592270\pi$
$434$	0.00249467	+	0.0224183i	0.000119748	+	0.00107611i
$435$	23.0673	+	4.74887i	1.10599	+	0.227691i
$436$	−13.0751	−	14.5213i	−0.626182	−	0.695445i
$437$	2.65087	−	0.138926i	0.126808	−	0.00664573i
$438$	0.00204188		0.000107011i	9.75650e−5		5.11317e-6i
$439$	17.4276	+	19.3553i	0.831774	+	0.923779i	0.998058	−	0.0622991i	$-0.0198433\pi$
$439$	17.4276	+	19.3553i	0.831774	+	0.923779i	−0.166283	+	0.986078i	$0.553177\pi$
$440$	−0.0408840	−	0.00841681i	−0.00194907	−	0.000401256i
$441$	23.4658	+	16.6151i	1.11742	+	0.791196i
$442$	0.000617513	−	0.00389882i	2.93721e−5	−	0.000185448i
$443$	3.65513	−	0.979388i	0.173660	−	0.0465321i	−0.170941	−	0.985281i	$-0.554681\pi$
$443$	3.65513	−	0.979388i	0.173660	−	0.0465321i	0.344601	+	0.938749i	$0.388014\pi$
$444$	10.3107	+	4.59060i	0.489322	+	0.217860i
$445$	−11.9298	−	23.0475i	−0.565529	−	1.09255i
$446$	−0.00261452	−	0.00587231i	−0.000123801	−	0.000278062i
$447$	−4.50011	−	28.4126i	−0.212848	−	1.34387i
$448$	20.4109	−	5.60282i	0.964326	−	0.264708i
$449$			17.0058i			0.802554i	0.915957	+	0.401277i	$0.131433\pi$
$449$			17.0058i			0.802554i	−0.915957	+	0.401277i	$0.868567\pi$
$450$	−0.0135332	+	0.0138845i	−0.000637960	+	0.000654519i
$451$	−28.0650	+	16.2033i	−1.32153	+	0.762984i
$452$	18.7977	−	28.9459i	0.884168	−	1.36150i
$453$	6.61821	−	17.2410i	0.310951	−	0.810054i
$454$	−0.00307787	−	0.00223620i	−0.000144452	−	0.000104950i
$455$	31.7062	+	4.61601i	1.48641	+	0.216402i
$456$	0.00788012	−	0.00572524i	0.000369020	−	0.000268109i
$457$	0.357319	+	1.33353i	0.0167147	+	0.0623800i	0.973779	−	0.227494i	$-0.0730532\pi$
$457$	0.357319	+	1.33353i	0.0167147	+	0.0623800i	−0.957065	+	0.289874i	$0.906387\pi$
$458$	0.0124228	−	0.00476865i	0.000580477	−	0.000222824i
$459$	−1.69403	−	1.52531i	−0.0790704	−	0.0711953i
$460$	−4.91876	+	11.2409i	−0.229338	+	0.524112i
$461$	−33.9089	−	11.0177i	−1.57930	−	0.513145i	−0.617421	−	0.786633i	$-0.711823\pi$
$461$	−33.9089	−	11.0177i	−1.57930	−	0.513145i	−0.961875	+	0.273488i	$0.911823\pi$
$462$	−0.0325432	−	0.00495095i	−0.00151405	−	0.000230339i
$463$	−2.27863	+	4.47206i	−0.105897	+	0.207834i	−0.937874	−	0.346975i	$-0.887209\pi$
$463$	−2.27863	+	4.47206i	−0.105897	+	0.207834i	0.831977	+	0.554809i	$0.187209\pi$
$464$	11.7435	−	10.5739i	0.545180	−	0.490882i
$465$	53.8341	−	0.344848i	2.49649	−	0.0159919i
$466$	0.00442865	−	0.00491852i	0.000205153	−	0.000227846i
$467$	−12.0843	+	14.9229i	−0.559197	+	0.690551i	−0.975832	−	0.218523i	$-0.929876\pi$
$467$	−12.0843	+	14.9229i	−0.559197	+	0.690551i	0.416635	+	0.909074i	$0.363209\pi$
$468$	−31.4599	+	31.4599i	−1.45423	+	1.45423i
$469$	−1.11134	+	1.54942i	−0.0513167	+	0.0715456i
$470$	−0.00738494	−	0.00590228i	−0.000340642	−	0.000272252i
$471$	−42.5082	+	18.9259i	−1.95868	+	0.872058i
$472$	−0.0129550	+	0.0104908i	−0.000596303	+	0.000482877i
$473$	−16.0874	−	10.4473i	−0.739702	−	0.480368i
$474$	−0.00622067	+	0.0107745i	−0.000285725	+	0.000494890i
$475$	−1.91082	+	4.44415i	−0.0876746	+	0.203911i
$476$	3.05260	+	2.71502i	0.139916	+	0.124443i
$477$	−0.431145	−	0.846170i	−0.0197408	−	0.0387435i
$478$	−0.00598920	−	0.00229904i	−0.000273940	−	0.000105156i
$479$	−3.57101	+	33.9759i	−0.163163	+	1.55240i	0.540182	+	0.841548i	$0.318355\pi$
$479$	−3.57101	+	33.9759i	−0.163163	+	1.55240i	−0.703346	+	0.710848i	$0.748311\pi$
$480$	0.0109918	+	0.0666343i	0.000501706	+	0.00304142i
$481$	11.4011	−	1.19831i	0.519846	−	0.0546381i
$482$	0.0103785	+	0.0103785i	0.000472729	+	0.000472729i
$483$	−6.82493	+	18.1091i	−0.310545	+	0.823993i
$484$	−25.5576	+	8.30417i	−1.16171	+	0.377462i
$485$	−2.99722	+	30.3879i	−0.136097	+	1.37984i
$486$	0.00406775	+	0.0191372i	0.000184517	+	0.000868083i
$487$	−1.35222	−	25.8018i	−0.0612748	−	1.16919i	−0.840272	−	0.542165i	$-0.817605\pi$
$487$	−1.35222	−	25.8018i	−0.0612748	−	1.16919i	0.778997	−	0.627027i	$-0.215728\pi$
$488$	0.0385325	−	0.0250233i	0.00174428	−	0.00113275i
$489$	6.64585	−	20.4538i	0.300536	−	0.924954i
$490$	0.00968166	−	0.0111636i	0.000437373	−	0.000504318i
$491$	−11.4055	−	35.1024i	−0.514721	−	1.58415i	−0.783789	−	0.621027i	$-0.786716\pi$
$491$	−11.4055	−	35.1024i	−0.514721	−	1.58415i	0.269068	−	0.963121i	$-0.413284\pi$
$492$	27.1648	+	21.9976i	1.22468	+	0.991728i
$493$	2.94615	+	0.789419i	0.132688	+	0.0355537i
$494$	0.00201203	−	0.00451910i	9.05257e−5	−	0.000203324i
$495$	−11.4699	+	43.9300i	−0.515534	+	1.97451i
$496$	21.2325	−	29.2240i	0.953366	−	1.31220i
$497$	−11.4084	−	0.528097i	−0.511737	−	0.0236884i
$498$	−0.0300411	+	0.0153067i	−0.00134617	+	0.000685909i
$499$	31.2169	+	18.0231i	1.39746	+	0.806823i	0.994126	−	0.108231i	$-0.0345185\pi$
$499$	31.2169	+	18.0231i	1.39746	+	0.806823i	0.403333	+	0.915053i	$0.367852\pi$
$500$	−14.4034	−	17.1039i	−0.644137	−	0.764909i
$501$	7.11799	+	12.3287i	0.318008	+	0.550807i
$502$	0.000951790	−	0.0181612i	4.24805e−5	−	0.000810576i
$503$	19.7617	−	3.12995i	0.881132	−	0.139558i	0.300557	−	0.953764i	$-0.402828\pi$
$503$	19.7617	−	3.12995i	0.881132	−	0.139558i	0.580576	+	0.814206i	$0.302828\pi$
$504$	0.00877716	+	0.0400887i	0.000390966	+	0.00178569i
$505$	−26.2319	+	7.20922i	−1.16730	+	0.320806i
$506$	−0.00133840	−	0.0127340i	−5.94992e−5	−	0.000566097i
$507$	−11.2687	+	42.0554i	−0.500460	+	1.86774i
$508$	12.5844	+	32.7836i	0.558344	+	1.45454i
$509$	−20.0991	−	4.27220i	−0.890877	−	0.189362i	−0.260337	−	0.965518i	$-0.583834\pi$
$509$	−20.0991	−	4.27220i	−0.890877	−	0.189362i	−0.630541	+	0.776156i	$0.717167\pi$
$510$	−0.00321029	+	0.00292801i	−0.000142154	+	0.000129654i
$511$	0.0131171	+	2.14935i	0.000580267	+	0.0950814i
$512$	0.0672935	+	0.0342878i	0.00297398	+	0.00151532i
$513$	−1.55584	−	2.39578i	−0.0686919	−	0.105776i
$514$	−0.00420366		0.000893516i	−0.000185416		3.94113e-5i
$515$	5.11857	−	7.14085i	0.225551	−	0.314663i
$516$	−4.30174	+	20.2381i	−0.189373	+	0.890932i
$517$	−21.8654	−	3.46313i	−0.961638	−	0.152308i
$518$	0.00237151	−	0.00472543i	0.000104198	−	0.000207623i
$519$	−5.99516	−	8.25163i	−0.263158	−	0.362206i
$520$	0.0290067	+	0.0353548i	0.00127203	+	0.00155041i
$521$	−19.4555	−	2.04486i	−0.852363	−	0.0895869i	−0.331737	−	0.943372i	$-0.607635\pi$
$521$	−19.4555	−	2.04486i	−0.852363	−	0.0895869i	−0.520626	+	0.853785i	$0.674301\pi$
$522$	0.00964092	+	0.0119055i	0.000421972	+	0.000521092i
$523$	−2.52086	−	0.132113i	−0.110230	−	0.00577689i	−0.00285867	−	0.999996i	$-0.500910\pi$
$523$	−2.52086	−	0.132113i	−0.110230	−	0.00577689i	−0.107371	+	0.994219i	$0.534243\pi$
$524$	−5.80262			−0.253488
$525$	−24.0902	−	25.7580i	−1.05138	−	1.12417i
$526$	0.0253815			0.00110669
$527$	6.96262	+	0.364895i	0.303296	+	0.0158951i
$528$	33.1748	+	40.9675i	1.44375	+	1.78288i
$529$	15.3876	+	1.61730i	0.669025	+	0.0703174i
$530$	−0.000454528	0	0.000177826i	−1.97435e−5	0	7.72427e-6i
$531$	10.6578	+	14.6692i	0.462510	+	0.636591i
$532$	2.81446	+	4.27653i	0.122022	+	0.185411i
$533$	35.0671	+	5.55409i	1.51893	+	0.240574i
$534$	0.00607332	−	0.0285727i	0.000262818	−	0.00123646i
$535$	0.00102237	+	0.159602i	4.42011e−5	+	0.00690022i
$536$	−0.00266205		0.000565837i	−0.000114983		2.44404e-5i
$537$	11.3928	+	17.5433i	0.491634	+	0.757050i
$538$	−0.00790301	−	0.00402679i	−0.000340723	−	0.000173607i
$539$	6.78077	−	33.9324i	0.292069	−	1.46157i
$540$	13.1229	−	1.46432i	0.564719	−	0.0630143i
$541$	−11.8244	−	2.51335i	−0.508370	−	0.108057i	−0.0534158	−	0.998572i	$-0.517011\pi$
$541$	−11.8244	−	2.51335i	−0.508370	−	0.108057i	−0.454954	+	0.890515i	$0.650344\pi$
$542$	0.00551156	+	0.0143581i	0.000236742	+	0.000616733i
$543$	15.3557	−	57.3083i	0.658976	−	2.45933i
$544$	0.000914248		0.00869849i	3.91981e−5		0.000372945i
$545$	12.0157	+	18.2457i	0.514698	+	0.781559i
$546$	0.0242947	+	0.0266531i	0.00103972	+	0.00114065i
$547$	25.8593	−	4.09571i	1.10566	−	0.175120i	0.423198	−	0.906037i	$-0.360907\pi$
$547$	25.8593	−	4.09571i	1.10566	−	0.175120i	0.682466	+	0.730917i	$0.260907\pi$
$548$	−2.17372	+	41.4771i	−0.0928568	+	1.77181i
$549$	−24.9873	−	43.2793i	−1.06643	−	1.84712i
$550$	0.0218896	+	0.00808245i	0.000933378	+	0.000344637i
$551$	3.31017	+	1.91113i	0.141018	+	0.0814168i
$552$	−0.0246112	+	0.0125400i	−0.00104752	+	0.000533738i
$553$	−11.0117	−	7.05594i	−0.468267	−	0.300049i
$554$	−0.00975113	+	0.0134213i	−0.000414286	+	0.000570216i
$555$	−10.6267	−	6.80466i	−0.451077	−	0.288842i
$556$	1.72137	−	3.86627i	0.0730026	−	0.163966i
$557$	−30.0108	−	8.04137i	−1.27160	−	0.340724i	−0.440955	−	0.897529i	$-0.645360\pi$
$557$	−30.0108	−	8.04137i	−1.27160	−	0.340724i	−0.830643	+	0.556806i	$0.812027\pi$
$558$	0.0272148	+	0.0220381i	0.00115210	+	0.000932949i
$559$	6.49418	+	19.9870i	0.274675	+	0.845362i
$560$	−23.5019	+	2.76777i	−0.993135	+	0.116960i
$561$	−3.14416	+	9.67674i	−0.132747	+	0.408552i
$562$	−0.0162325	+	0.0105415i	−0.000684727	+	0.000444667i
$563$	−1.61325	−	30.7827i	−0.0679905	−	1.29734i	−0.793265	−	0.608877i	$-0.791620\pi$
$563$	−1.61325	−	30.7827i	−0.0679905	−	1.29734i	0.725274	−	0.688460i	$-0.241713\pi$
$564$	4.96461	+	23.3567i	0.209048	+	0.983493i
$565$	−25.6361	+	28.8412i	−1.07852	+	1.21336i
$566$	0.0182678	−	0.00593557i	0.000767854	−	0.000249491i
$567$	−11.6197	+	1.91314i	−0.487980	+	0.0803442i
$568$	−0.0115263	−	0.0115263i	−0.000483632	−	0.000483632i
$569$	−25.1774	+	2.64625i	−1.05549	+	0.110937i	−0.616343	−	0.787477i	$-0.711387\pi$
$569$	−25.1774	+	2.64625i	−1.05549	+	0.110937i	−0.439149	+	0.898414i	$0.644720\pi$
$570$	−0.00483562	+	0.00250302i	−0.000202542	+	0.000104840i
$571$	1.90443	−	18.1194i	0.0796978	−	0.758274i	−0.879569	−	0.475772i	$-0.842169\pi$
$571$	1.90443	−	18.1194i	0.0796978	−	0.758274i	0.959267	−	0.282502i	$-0.0911644\pi$
$572$	49.9880	+	19.1886i	2.09010	+	0.802315i
$573$	−12.6081	−	24.7448i	−0.526711	−	1.03373i
$574$	0.0108822	−	0.0122352i	0.000454214	−	0.000510689i
$575$	7.32351	−	11.5999i	0.305411	−	0.483749i
$576$	16.4300	−	28.4575i	0.684581	−	1.18573i
$577$	−11.1900	−	7.26686i	−0.465845	−	0.302523i	0.290290	−	0.956939i	$-0.406248\pi$
$577$	−11.1900	−	7.26686i	−0.465845	−	0.302523i	−0.756135	+	0.654415i	$0.772915\pi$
$578$	0.0120352	−	0.00974592i	0.000500599	−	0.000405377i
$579$	−16.3312	+	7.27113i	−0.678703	+	0.302178i
$580$	−14.7555	+	9.71726i	−0.612688	+	0.403487i
$581$	−14.6130	−	32.2896i	−0.606250	−	1.33960i
$582$	−0.0243032	+	0.0243032i	−0.00100740	+	0.00100740i
$583$	−0.719267	+	0.888221i	−0.0297890	+	0.0367863i
$584$	−0.00205276	+	0.00227983i	−8.49440e−5	+	9.43399e-5i
$585$	40.0544	−	29.4951i	1.65605	−	1.21947i
$586$	−0.00107136		0.000964657i	−4.42575e−5		3.98496e-5i
$587$	−16.5752	+	32.5308i	−0.684134	+	1.34269i	0.243757	+	0.969836i	$0.421620\pi$
$587$	−16.5752	+	32.5308i	−0.684134	+	1.34269i	−0.927891	+	0.372852i	$0.878380\pi$
$588$	−36.7903	+	6.28824i	−1.51721	+	0.259322i
$589$	8.30965	+	2.69997i	0.342393	+	0.111250i
$590$	0.00804032	−	0.00471101i	0.000331015	−	0.000193949i
$591$	49.8599	+	44.8941i	2.05096	+	1.84669i
$592$	−7.90459	+	3.03429i	−0.324877	+	0.124708i
$593$	5.46046	+	20.3787i	0.224234	+	0.836854i	0.982710	+	0.185152i	$0.0592778\pi$
$593$	5.46046	+	20.3787i	0.224234	+	0.836854i	−0.758476	+	0.651701i	$0.774056\pi$
$594$	−0.0111476	+	0.00809920i	−0.000457391	+	0.000332314i
$595$	−2.91860	−	3.51339i	−0.119651	−	0.144035i
$596$	17.4590	+	12.6847i	0.715149	+	0.519586i
$597$	−0.631877	+	1.64610i	−0.0258610	+	0.0673702i
$598$	−0.00764024	+	0.0117649i	−0.000312433	+	0.000481104i
$599$	33.8887	−	19.5656i	1.38465	−	0.799430i	0.391947	−	0.919988i	$-0.371802\pi$
$599$	33.8887	−	19.5656i	1.38465	−	0.799430i	0.992706	+	0.120558i	$0.0384684\pi$
$600$	−0.000644873	−	0.0503333i	−2.63268e−5	−	0.00205485i
$601$		−	16.9750i		−	0.692423i	−0.938157	−	0.346211i	$-0.887468\pi$
$601$		−	16.9750i		−	0.692423i	0.938157	−	0.346211i	$-0.112532\pi$
$602$	0.00937723	+	0.00245138i	0.000382187	+	9.99109e-5i
$603$	0.463083	+	2.92379i	0.0188582	+	0.119066i
$604$	5.63503	+	12.6565i	0.229286	+	0.514985i
$605$	29.6441	−	4.89003i	1.20521	−	0.198808i
$606$	−0.0279735	−	0.0124546i	−0.00113635	−	0.000505934i
$607$	−4.36034	+	1.16835i	−0.176981	+	0.0474218i	−0.346221	−	0.938153i	$-0.612535\pi$
$607$	−4.36034	+	1.16835i	−0.176981	+	0.0474218i	0.169240	+	0.985575i	$0.445869\pi$
$608$	−0.00171463	+	0.0108257i	−6.95374e−5	+	0.000439042i
$609$	−22.4436	+	16.5165i	−0.909462	+	0.669281i
$610$	−0.0233960	+	0.0105967i	−0.000947276	+	0.000429046i
$611$	16.2291	+	18.0242i	0.656559	+	0.729182i
$612$	6.33369	−	0.331935i	0.256024	−	0.0134177i
$613$	13.9317	−	0.730131i	0.562698	−	0.0294897i	0.231133	−	0.972922i	$-0.425757\pi$
$613$	13.9317	−	0.730131i	0.562698	−	0.0294897i	0.331565	+	0.943432i	$0.392423\pi$
$614$	0.00425755	+	0.00472849i	0.000171821	+	0.000190826i
$615$	−26.3354	−	28.8743i	−1.06194	−	1.16432i
$616$	0.0397787	−	0.0292735i	0.00160273	−	0.00117946i
$617$	1.84942	−	11.6768i	0.0744549	−	0.470090i	−0.922086	−	0.386985i	$-0.873516\pi$
$617$	1.84942	−	11.6768i	0.0744549	−	0.470090i	0.996541	−	0.0831047i	$-0.0264836\pi$
$618$	0.00955223	−	0.00255951i	0.000384247	−	0.000102959i
$619$	34.6537	+	15.4288i	1.39285	+	0.620137i	0.959659	−	0.281165i	$-0.0907208\pi$
$619$	34.6537	+	15.4288i	1.39285	+	0.620137i	0.433191	+	0.901302i	$0.357387\pi$
$620$	−28.3741	+	28.7400i	−1.13953	+	1.15423i
$621$	3.29492	+	7.40051i	0.132221	+	0.296972i
$622$	0.00307820	+	0.0194350i	0.000123425	+	0.000779273i
$623$	29.7085	+	7.76635i	1.19024	+	0.311152i
$624$		−	57.7541i		−	2.31202i
$625$	13.0506	+	21.3233i	0.522023	+	0.852931i
$626$	0.00289719	−	0.00167269i	0.000115795	−	6.68542e-5i
$627$	−6.94448	+	10.6936i	−0.277336	+	0.427060i
$628$	12.5096	−	32.5886i	0.499187	−	1.30043i
$629$	−1.32212	−	0.960577i	−0.0527164	−	0.0383007i
$630$	−0.00148711	−	0.0228929i	−5.92478e−5	−	0.000912074i
$631$	16.6746	−	12.1148i	0.663803	−	0.482281i	−0.204142	−	0.978941i	$-0.565440\pi$
$631$	16.6746	−	12.1148i	0.663803	−	0.482281i	0.867945	+	0.496660i	$0.165440\pi$
$632$	−0.00483131	−	0.0180307i	−0.000192179	−	0.000717222i
$633$	12.7716	−	4.90257i	0.507627	−	0.194860i
$634$	0.00852034	+	0.00767175i	0.000338386	+	0.000304684i
$635$	−8.40862	−	38.3498i	−0.333686	−	1.52187i
$636$	1.17245	+	0.380952i	0.0464906	+	0.0151057i
$637$	−29.1689	+	24.2159i	−1.15571	+	0.959468i
$638$	0.00837018	−	0.0164274i	0.000331379	−	0.000650367i
$639$	−13.1763	+	11.8640i	−0.521244	+	0.469331i
$640$	−0.0549039	−	0.0393551i	−0.00217027	−	0.00155565i
$641$	−10.7676	+	11.9586i	−0.425293	+	0.472335i	−0.917266	−	0.398275i	$-0.869609\pi$
$641$	−10.7676	+	11.9586i	−0.425293	+	0.472335i	0.491973	+	0.870610i	$0.336276\pi$
$642$	−0.000113057	0	0.000139614i	−4.46200e−6	0	5.51011e-6i
$643$	9.53067	−	9.53067i	0.375853	−	0.375853i	−0.493751	−	0.869604i	$-0.664374\pi$
$643$	9.53067	−	9.53067i	0.375853	−	0.375853i	0.869604	+	0.493751i	$0.164374\pi$
$644$	−5.98586	−	13.2266i	−0.235876	−	0.521202i
$645$	8.15140	−	21.6486i	0.320961	−	0.852413i
$646$	−0.000644217	0	0.000286824i	−2.53464e−5	0	1.12849e-5i
$647$	−3.44618	+	2.79066i	−0.135483	+	0.109712i	−0.694667	−	0.719332i	$-0.744448\pi$
$647$	−3.44618	+	2.79066i	−0.135483	+	0.109712i	0.559183	+	0.829044i	$0.311115\pi$
$648$	−0.0140964	−	0.00915429i	−0.000553757	−	0.000359614i
$649$	10.9109	−	18.8983i	0.428291	−	0.741822i
$650$	−0.0130649	−	0.0219740i	−0.000512446	−	0.000861891i
$651$	−42.3330	+	47.5965i	−1.65916	+	1.86546i
$652$	7.32464	+	14.3754i	0.286855	+	0.562985i
$653$	2.60858	+	1.00134i	0.102082	+	0.0391854i	0.408873	−	0.912591i	$-0.365922\pi$
$653$	2.60858	+	1.00134i	0.102082	+	0.0391854i	−0.306791	+	0.951777i	$0.599255\pi$
$654$	−0.00257039	+	0.0244556i	−0.000100510	+	0.000956290i
$655$	6.41402	+	0.973807i	0.250617	+	0.0380498i
$656$	−26.0789	+	2.74100i	−1.01821	+	0.107018i
$657$	2.35954	+	2.35954i	0.0920545	+	0.0920545i
$658$	0.0110373	−	0.00181725i	0.000430278	−	7.08437e-5i
$659$	24.9611	−	8.11036i	0.972347	−	0.315935i	0.220584	−	0.975368i	$-0.429204\pi$
$659$	24.9611	−	8.11036i	0.972347	−	0.315935i	0.751763	+	0.659433i	$0.229204\pi$
$660$	−29.7951	−	50.8516i	−1.15977	−	1.97940i
$661$	3.78516	+	17.8078i	0.147226	+	0.692643i	0.988399	+	0.151878i	$0.0485319\pi$
$661$	3.78516	+	17.8078i	0.147226	+	0.692643i	−0.841174	+	0.540765i	$0.818135\pi$
$662$	−0.000167493	−	0.00319595i	−6.50979e−6	−	0.000124214i
$663$	9.34890	−	6.07124i	0.363081	−	0.235788i
$664$	0.0156321	−	0.0481108i	0.000606645	−	0.00186706i
$665$	−2.39332	−	5.19946i	−0.0928089	−	0.201626i
$666$	−0.00253648	−	0.00780647i	−9.82865e−5	−	0.000302495i
$667$	−8.42362	−	6.82131i	−0.326164	−	0.264122i
$668$	−10.3158	−	2.76411i	−0.399130	−	0.106947i
$669$	7.38324	−	16.5830i	0.285453	−	0.641137i
$670$	0.00151875		8.93532e-5i	5.86745e−5		3.45202e-6i
$671$	−35.3517	+	48.6574i	−1.36474	+	1.87840i
$672$	−0.0672810	−	0.0431113i	−0.00259542	−	0.00166306i
$673$	2.22212	−	1.13223i	0.0856564	−	0.0436441i	−0.410638	−	0.911799i	$-0.634694\pi$
$673$	2.22212	−	1.13223i	0.0856564	−	0.0436441i	0.496294	+	0.868155i	$0.334694\pi$
$674$	−0.0251490	−	0.0145198i	−0.000968704	−	0.000559281i
$675$	−14.7514	−	0.583699i	−0.567780	−	0.0224666i
$676$	−16.3312	−	28.2865i	−0.628124	−	1.08794i
$677$	2.07721	−	39.6355i	0.0798335	−	1.52331i	−0.605947	−	0.795505i	$-0.707205\pi$
$677$	2.07721	−	39.6355i	0.0798335	−	1.52331i	0.685780	−	0.727809i	$-0.259461\pi$
$678$	−0.0428990	+	0.00679453i	−0.00164753	+	0.000260942i
$679$	−24.3390	−	26.7017i	−0.934046	−	1.02472i
$680$	0.000299479	−	0.00651230i	1.14845e−5	−	0.000249735i
$681$	−1.12301	−	10.6847i	−0.0430337	−	0.409439i
$682$	0.0109079	−	0.0407088i	0.000417685	−	0.00155882i
$683$	6.73991	+	17.5581i	0.257896	+	0.671841i	0.999999	+	0.00155541i	$0.000495102\pi$
$683$	6.73991	+	17.5581i	0.257896	+	0.671841i	−0.742103	+	0.670286i	$0.766172\pi$
$684$	7.77437	+	1.65249i	0.297261	+	0.0631847i
$685$	9.36353	−	45.4826i	0.357762	−	1.73780i
$686$	0.00214565	+	0.0173522i	8.19212e−5	+	0.000662511i
$687$	33.4813	+	17.0596i	1.27739	+	0.650864i
$688$	−8.45367	−	13.0175i	−0.322293	−	0.496288i
$689$	1.22481	−	0.260342i	0.0466616	−	0.00991822i
$690$	0.0146544	−	0.00486551i	0.000557885	−	0.000185227i
$691$	−1.23547	+	5.81245i	−0.0469997	+	0.221116i	−0.995379	−	0.0960214i	$-0.969388\pi$
$691$	−1.23547	+	5.81245i	−0.0469997	+	0.221116i	0.948380	+	0.317137i	$0.102722\pi$
$692$	7.55742	+	1.19698i	0.287290	+	0.0455023i
$693$	−29.5330	−	44.8750i	−1.12187	−	1.70466i
$694$	0.00572179	+	0.00787536i	0.000217196	+	0.000298945i
$695$	−2.55160	+	3.98477i	−0.0967876	+	0.151151i
$696$	−0.0395551	−	0.00415740i	−0.00149933	−	0.000157586i
$697$	−3.18517	−	3.93335i	−0.120647	−	0.148986i
$698$	0.00190247		9.97045e-5i	7.20097e−5		3.77387e-6i
$699$	18.6903			0.706931
$700$	26.4427	+	0.884727i	0.999440	+	0.0334395i
$701$	−14.1559			−0.534661			−0.267331	−	0.963605i	$-0.586142\pi$
$701$	−14.1559			−0.534661			−0.267331	+	0.963605i	$0.586142\pi$
$702$	0.0150756		0.000790078i	0.000568992		2.98196e-5i
$703$	−1.28882	−	1.59156i	−0.0486089	−	0.0600270i
$704$	−39.3298	−	4.13373i	−1.48230	−	0.155796i
$705$	−1.56796	−	26.6509i	−0.0590527	−	1.00373i
$706$	0.0110109	+	0.0151552i	0.000414400	+	0.000570373i
$707$	14.4381	−	28.7691i	0.543001	−	1.08197i
$708$	−23.2477	−	3.68208i	−0.873704	−	0.138381i
$709$	−8.85674	+	41.6677i	−0.332622	+	1.56486i	0.420694	+	0.907203i	$0.361787\pi$
$709$	−8.85674	+	41.6677i	−0.332622	+	1.56486i	−0.753315	+	0.657659i	$0.771547\pi$
$710$	0.00540320	+	0.00733756i	0.000202779	+	0.000275374i
$711$	−19.8604	+	4.22145i	−0.744822	+	0.158317i
$712$	0.0238703	+	0.0367570i	0.000894577	+	0.00137753i
$713$	−22.0767	−	11.2486i	−0.826777	−	0.421264i
$714$	−3.13747e−5	−	0.00514100i	−1.17417e−6	−	0.000192397i
$715$	−52.0348	−	29.5995i	−1.94599	−	1.10696i
$716$	−15.3496	−	3.26265i	−0.573640	−	0.121931i
$717$	−6.49235	−	16.9131i	−0.242461	−	0.631633i
$718$	0.00316687	−	0.0118189i	0.000118187	−	0.000441078i
$719$	3.00240	+	28.5659i	0.111971	+	1.06533i	0.895832	+	0.444393i	$0.146581\pi$
$719$	3.00240	+	28.5659i	0.111971	+	1.06533i	−0.783861	+	0.620936i	$0.786753\pi$
$720$	−22.9369	+	28.6987i	−0.854810	+	1.06954i
$721$	2.22338	+	10.1550i	0.0828029	+	0.378193i
$722$	0.0168436	−	0.00266777i	0.000626854	−	9.92840e-5i
$723$	−2.16923	+	41.3914i	−0.0806746	+	1.53936i
$724$	22.2544	+	38.5457i	0.827076	+	1.43254i
$725$	17.9410	−	8.26485i	0.666311	−	0.306949i
$726$	0.0292871	+	0.0169089i	0.00108695	+	0.000627548i
$727$	3.71652	−	1.89366i	0.137838	−	0.0702320i	−0.383711	−	0.923453i	$-0.625354\pi$
$727$	3.71652	−	1.89366i	0.137838	−	0.0702320i	0.521549	+	0.853221i	$0.325354\pi$
$728$	−0.0540521	−	0.00250208i	−0.00200330	−	9.27332e-5i
$729$	−24.6264	+	33.8953i	−0.912088	+	1.25538i
$730$	0.00132583	−	0.00108777i	4.90712e−5	−	4.02603e-5i
$731$	1.21853	−	2.73686i	0.0450689	−	0.101226i
$732$	62.6621	+	16.7902i	2.31606	+	0.620585i
$733$	9.79535	+	7.93211i	0.361799	+	0.292979i	0.792933	−	0.609309i	$-0.208553\pi$
$733$	9.79535	+	7.93211i	0.361799	+	0.292979i	−0.431134	+	0.902288i	$0.641886\pi$
$734$	0.00117357	+	0.00361188i	4.33172e−5	+	0.000133317i
$735$	41.7221	−	0.776588i	1.53894	−	0.0286449i
$736$	0.00960498	−	0.0295611i	0.000354044	−	0.00108964i
$737$	2.98786	−	1.94034i	0.110059	−	0.0714732i
$738$	−0.00133044	−	0.0253863i	−4.89742e−5	−	0.000934484i
$739$	−3.45433	−	16.2514i	−0.127070	−	0.597816i	−0.994892	−	0.100942i	$-0.967814\pi$
$739$	−3.45433	−	16.2514i	−0.127070	−	0.597816i	0.867823	−	0.496874i	$-0.165519\pi$
$740$	9.24670	−	2.02744i	0.339915	−	0.0745301i
$741$	13.2857	−	4.31678i	0.488061	−	0.158581i
$742$	0.000203663	0	0.000540395i	7.47671e−6	0	1.98385e-5i
$743$	−2.71850	−	2.71850i	−0.0997323	−	0.0997323i	0.655480	−	0.755212i	$-0.272466\pi$
$743$	−2.71850	−	2.71850i	−0.0997323	−	0.0997323i	−0.755212	+	0.655480i	$0.772466\pi$
$744$	−0.0904187	+	0.00950339i	−0.00331491	+	0.000348411i
$745$	−17.1699	−	16.9513i	−0.629055	−	0.621047i
$746$	0.00126016	−	0.0119896i	4.61377e−5	−	0.000438971i
$747$	−51.3691	−	19.7188i	−1.87950	−	0.721472i
$748$	−3.46530	−	6.80103i	−0.126704	−	0.248670i
$749$	−0.141110	−	0.125505i	−0.00515605	−	0.00458586i
$750$	−0.00386711	+	0.0278725i	−0.000141207	+	0.00101776i
$751$	5.06756	−	8.77727i	0.184918	−	0.320287i	−0.758631	−	0.651521i	$-0.774131\pi$
$751$	5.06756	−	8.77727i	0.184918	−	0.320287i	0.943549	+	0.331233i	$0.107465\pi$
$752$	−15.0234	−	9.75632i	−0.547848	−	0.355777i
$753$	39.9116	−	32.3198i	1.45446	−	1.17780i
$754$	−0.0184529	+	0.00821576i	−0.000672015	+	0.000299200i
$755$	−4.10474	−	14.9357i	−0.149387	−	0.543567i
$756$	−9.10600	+	12.6955i	−0.331182	+	0.461733i
$757$	28.7244	−	28.7244i	1.04401	−	1.04401i	0.0450200	−	0.998986i	$-0.485665\pi$
$757$	28.7244	−	28.7244i	1.04401	−	1.04401i	0.998986	−	0.0450200i	$-0.0143352\pi$
$758$	−0.0189402	+	0.0233892i	−0.000687940	+	0.000849535i
$759$	24.1946	−	26.8708i	0.878208	−	0.975348i
$760$	0.00247473	−	0.00778578i	8.97678e−5	−	0.000282420i
$761$	−23.2704	+	20.9527i	−0.843550	+	0.759536i	−0.972694	−	0.232090i	$-0.925444\pi$
$761$	−23.2704	+	20.9527i	−0.843550	+	0.759536i	0.129144	+	0.991626i	$0.458777\pi$
$762$	0.0200624	−	0.0393747i	0.000726784	−	0.00142639i
$763$	−25.5554	−	3.88786i	−0.925169	−	0.140750i
$764$	19.8144	+	6.43808i	0.716859	+	0.232922i
$765$	−7.05676	−	0.696023i	−0.255138	−	0.0251648i
$766$	−0.0156583	−	0.0140988i	−0.000565758	−	0.000509410i
$767$	−22.3198	+	8.56775i	−0.805920	+	0.309364i
$768$	11.0401	+	41.2022i	0.398375	+	1.48676i
$769$	−19.4789	+	14.1523i	−0.702429	+	0.510344i	−0.880722	−	0.473633i	$-0.842942\pi$
$769$	−19.4789	+	14.1523i	−0.702429	+	0.510344i	0.178294	+	0.983977i	$0.442942\pi$
$770$	−0.0244414	+	0.0128411i	−0.000880807	+	0.000462761i
$771$	−9.81830	−	7.13341i	−0.353597	−	0.256904i
$772$	4.80606	−	12.5202i	0.172974	−	0.450612i
$773$	−21.1130	+	32.5112i	−0.759381	+	1.16934i	0.221580	+	0.975142i	$0.428879\pi$
$773$	−21.1130	+	32.5112i	−0.759381	+	1.16934i	−0.980961	+	0.194203i	$0.937788\pi$
$774$	0.0130313	−	0.00752363i	0.000468401	−	0.000270431i
$775$	36.1870	−	27.0064i	1.29988	−	0.970100i
$776$		−	0.0515680i		−	0.00185118i
$777$	14.3979	−	3.95225i	0.516523	−	0.141786i
$778$	0.00220704	+	0.0139347i	7.91261e−5	+	0.000499583i
$779$	−2.57978	−	5.79427i	−0.0924301	−	0.207601i
$780$	−9.69242	+	63.8396i	−0.347044	+	2.28582i
$781$	19.4935	+	8.67907i	0.697533	+	0.310561i
$782$	0.00193162		0.000517577i	6.90747e−5		1.85085e-5i
$783$	−1.82474	+	11.5209i	−0.0652108	+	0.411725i
$784$	16.1803	−	22.8516i	0.577866	−	0.816130i
$785$	−19.2968	+	33.9230i	−0.688732	+	1.21076i
$786$	0.00488615	+	0.00542662i	0.000174283	+	0.000193561i
$787$	39.0282	−	2.04538i	1.39120	−	0.0729099i	0.658051	−	0.752973i	$-0.271381\pi$
$787$	39.0282	−	2.04538i	1.39120	−	0.0729099i	0.733153	+	0.680063i	$0.238048\pi$
$788$	−50.2636	+	2.63421i	−1.79057	+	0.0938397i
$789$	47.9605	+	53.2656i	1.70744	+	1.89630i
$790$	0.00115721	+	0.0103707i	4.11718e−5	+	0.000368972i
$791$	−5.04956	−	45.3777i	−0.179542	−	1.61344i
$792$	0.0119948	−	0.0757320i	0.000426215	−	0.00269102i
$793$	63.6475	−	17.0543i	2.26019	−	0.605616i
$794$	−0.00605255	−	0.00269477i	−0.000214797	−	9.56338e-5i
$795$	−1.23205	−	0.617854i	−0.0436965	−	0.0219130i
$796$	−0.538007	−	1.20838i	−0.0190692	−	0.0428300i
$797$	−2.66839	−	16.8476i	−0.0945193	−	0.596771i	−0.988798	−	0.149261i	$-0.952311\pi$
$797$	−2.66839	−	16.8476i	−0.0945193	−	0.596771i	0.894279	−	0.447511i	$-0.147689\pi$
$798$	0.00162947	−	0.00623318i	5.76826e−5	−	0.000220652i
$799$		−	3.45751i		−	0.122318i
$800$	0.0405632	+	0.0395370i	0.00143413	+	0.00139784i
$801$	41.2852	−	23.8360i	1.45874	−	0.842203i
$802$	−0.00325891	+	0.00501828i	−0.000115076	+	0.000177202i
$803$	1.43917	−	3.74918i	0.0507873	−	0.132306i
$804$	−3.10882	−	2.25869i	−0.109640	−	0.0796578i
$805$	4.39685	+	15.6248i	0.154969	+	0.550703i
$806$	−0.0373550	+	0.0271400i	−0.00131577	+	0.000955965i
$807$	−6.48281	−	24.1942i	−0.228206	−	0.851675i
$808$	0.0428914	−	0.0164645i	0.00150892	−	0.000579218i
$809$	−24.1206	−	21.7183i	−0.848036	−	0.763575i	0.125504	−	0.992093i	$-0.459945\pi$
$809$	−24.1206	−	21.7183i	−0.848036	−	0.763575i	−0.973540	+	0.228518i	$0.926612\pi$
$810$	0.00702268	+	0.00624226i	0.000246752	+	0.000219331i
$811$	28.6458	+	9.30758i	1.00589	+	0.326833i	0.765216	−	0.643773i	$-0.222632\pi$
$811$	28.6458	+	9.30758i	1.00589	+	0.326833i	0.240673	+	0.970606i	$0.422632\pi$
$812$	3.14416	−	20.6670i	0.110338	−	0.725268i
$813$	−19.7173	+	38.6974i	−0.691516	+	1.35718i
$814$	−0.00734114	+	0.00660999i	−0.000257307	+	0.000231680i
$815$	−5.68391	−	17.1194i	−0.199099	−	0.599665i
$816$	−5.50902	+	6.11838i	−0.192854	+	0.214186i
$817$	2.36267	−	2.91765i	0.0826592	−	0.102076i
$818$	0.00451907	−	0.00451907i	0.000158006	−	0.000158006i
$819$	−5.79481	+	58.5702i	−0.202487	+	2.04661i
$820$	29.2867	+	1.34680i	1.02274	+	0.0470322i
$821$	29.1606	−	12.9831i	1.01771	−	0.453114i	0.171059	−	0.985261i	$-0.445281\pi$
$821$	29.1606	−	12.9831i	1.01771	−	0.453114i	0.846652	+	0.532147i	$0.178615\pi$
$822$	0.0406198	−	0.0328933i	0.00141678	−	0.00114729i
$823$	−15.3988	−	10.0001i	−0.536769	−	0.348582i	0.247614	−	0.968859i	$-0.420354\pi$
$823$	−15.3988	−	10.0001i	−0.536769	−	0.348582i	−0.784383	+	0.620277i	$0.787020\pi$
$824$	−0.00741878	+	0.0128497i	−0.000258446	+	0.000447641i
$825$	24.4005	+	61.2100i	0.849518	+	2.13106i
$826$	−0.00222661	+	0.0107990i	−7.74736e−5	+	0.000375746i
$827$	13.7590	+	27.0035i	0.478447	+	0.939005i	0.996495	+	0.0836537i	$0.0266590\pi$
$827$	13.7590	+	27.0035i	0.478447	+	0.939005i	−0.518048	+	0.855352i	$0.673341\pi$
$828$	−21.0421	−	8.07730i	−0.731263	−	0.280706i
$829$	2.01687	−	19.1892i	0.0700487	−	0.666469i	−0.902007	−	0.431720i	$-0.857907\pi$
$829$	2.01687	−	19.1892i	0.0700487	−	0.666469i	0.972056	−	0.234748i	$-0.0754266\pi$
$830$	−0.0126766	+	0.0252783i	−0.000440013	+	0.000877423i
$831$	−46.5914	+	4.89696i	−1.61624	+	0.169874i
$832$	30.6365	+	30.6365i	1.06213	+	1.06213i
$833$	5.39999	+	0.216950i	0.187099	+	0.00751687i
$834$	−0.00506524	+	0.00164580i	−0.000175395	+	5.69893e-5i
$835$	10.9389	+	4.78657i	0.378555	+	0.165646i
$836$	−1.98875	−	9.35636i	−0.0687825	−	0.323596i
$837$	1.39548	+	26.6274i	0.0482349	+	0.920377i
$838$	−0.0214981	+	0.0139610i	−0.000742639	+	0.000482275i
$839$	−9.65006	+	29.6998i	−0.333157	+	1.02535i	0.634465	+	0.772951i	$0.281220\pi$
$839$	−9.65006	+	29.6998i	−0.333157	+	1.02535i	−0.967623	+	0.252401i	$0.918780\pi$
$840$	0.0447568	+	0.0392967i	0.00154426	+	0.00135587i
$841$	4.13852	+	12.7371i	0.142708	+	0.439209i
$842$	0.0135324	+	0.0109584i	0.000466359	+	0.000377650i
$843$	−52.7951	−	14.1464i	−1.81836	−	0.487228i
$844$	−4.17426	+	9.37555i	−0.143684	+	0.322720i
$845$	13.3049	+	34.0077i	0.457703	+	1.16990i
$846$	0.0102075	−	0.0140494i	0.000350939	−	0.000483027i
$847$	−19.1793	+	29.9319i	−0.659009	+	1.02847i
$848$	−0.824024	+	0.419861i	−0.0282971	+	0.0144181i
$849$	46.9750	+	27.1210i	1.61218	+	0.930790i
$850$	−0.000711971		0.00357411i	−2.44204e−5		0.000122591i
$851$	2.90381	+	5.02954i	0.0995413	+	0.172411i
$852$	1.20456	−	22.9844i	0.0412676	−	0.787433i
$853$	−8.52083	+	1.34957i	−0.291748	+	0.0462083i	−0.300593	−	0.953753i	$-0.597185\pi$
$853$	−8.52083	+	1.34957i	−0.291748	+	0.0462083i	0.00884499	+	0.999961i	$0.497185\pi$
$854$	0.00921434	−	0.0289590i	0.000315308	−	0.000990956i
$855$	−8.31621	−	3.13132i	−0.284408	−	0.107089i
$856$	−2.81748e−5	0	0.000268065i	−9.62995e−7	0	9.16229e-6i
$857$	9.78746	−	36.5273i	0.334333	−	1.24775i	−0.570257	−	0.821466i	$-0.693156\pi$
$857$	9.78746	−	36.5273i	0.334333	−	1.24775i	0.904590	−	0.426282i	$-0.140177\pi$
$858$	−0.0241476	−	0.0629068i	−0.000824387	−	0.00214760i
$859$	−2.69697	−	0.573259i	−0.0920195	−	0.0195594i	0.161672	−	0.986845i	$-0.448311\pi$
$859$	−2.69697	−	0.573259i	−0.0920195	−	0.0195594i	−0.253691	+	0.967285i	$0.581645\pi$
$860$	7.15979	+	15.8078i	0.244147	+	0.539043i
$861$	46.2396	−	0.282193i	1.57584	−	0.00961712i
$862$	0.0185785	+	0.00946622i	0.000632786	+	0.000322421i
$863$	−16.4800	−	25.3770i	−0.560987	−	0.863844i	0.438403	−	0.898778i	$-0.355544\pi$
$863$	−16.4800	−	25.3770i	−0.560987	−	0.863844i	−0.999390	+	0.0349349i	$0.988878\pi$
$864$	−0.0327183	+	0.00695448i	−0.00111310	+	0.000236596i
$865$	−8.15284	−	2.59140i	−0.277205	−	0.0881103i
$866$	−0.000236757		0.00111386i	−8.04535e−6		3.78504e-5i
$867$	43.1943	+	6.84131i	1.46696	+	0.232343i
$868$	−2.79211	−	47.7044i	−0.0947704	−	1.61919i
$869$	14.3629	+	19.7689i	0.487229	+	0.670613i
$870$	0.0215126	+	0.00561683i	0.000729345	+	0.000190428i
$871$	−3.88176	−	0.407990i	−0.131528	−	0.0138242i
$872$	−0.0232187	−	0.0286727i	−0.000786284	−	0.000970980i
$873$	−56.0144	−	2.93559i	−1.89580	−	0.0993546i
$874$	0.00250603			8.47678e−5
$875$	−29.0804	−	5.41562i	−0.983098	−	0.183081i
$876$	−4.33165			−0.146353
$877$	−9.26366	−	0.485488i	−0.312812	−	0.0163938i	−0.104716	−	0.994502i	$-0.533393\pi$
$877$	−9.26366	−	0.485488i	−0.312812	−	0.0163938i	−0.208096	+	0.978108i	$0.566727\pi$
$878$	0.0154740	+	0.0191088i	0.000522221	+	0.000644889i
$879$	−4.04885	−	0.425551i	−0.136564	−	0.0143535i
$880$	42.7802	+	11.1697i	1.44212	+	0.376531i
$881$	2.03919	+	2.80671i	0.0687022	+	0.0945604i	0.841985	−	0.539500i	$-0.181387\pi$
$881$	2.03919	+	2.80671i	0.0687022	+	0.0945604i	−0.773283	+	0.634061i	$0.781387\pi$
$882$	0.0213020	+	0.0168237i	0.000717276	+	0.000566484i
$883$	−50.8737	−	8.05760i	−1.71204	−	0.271160i	−0.777981	−	0.628288i	$-0.783756\pi$
$883$	−50.8737	−	8.05760i	−1.71204	−	0.271160i	−0.934056	+	0.357128i	$0.883756\pi$
$884$	−1.73868	+	8.17984i	−0.0584781	+	0.275118i
$885$	25.0794	+	7.97153i	0.843033	+	0.267960i
$886$	0.00349435		0.000742747i	0.000117395		2.49531e-5i
$887$	−8.04618	−	12.3900i	−0.270164	−	0.416016i	0.677384	−	0.735630i	$-0.263114\pi$
$887$	−8.04618	−	12.3900i	−0.270164	−	0.416016i	−0.947548	+	0.319613i	$0.896447\pi$
$888$	0.0189876	+	0.00967467i	0.000637183	+	0.000324661i
$889$	40.3714	+	22.9811i	1.35401	+	0.770761i
$890$	−0.0101084	−	0.0223180i	−0.000338834	−	0.000748100i
$891$	21.5217	+	4.57457i	0.721003	+	0.153254i
$892$	4.88016	+	12.7133i	0.163400	+	0.425672i
$893$	1.12142	−	4.18519i	0.0375269	−	0.140052i
$894$	−0.00283876	−	0.0270090i	−9.49423e−5	−	0.000903315i
$895$	16.4194	+	6.18242i	0.548839	+	0.206656i
$896$	0.0780790	−	0.0170949i	0.00260844	−	0.000571100i
$897$	−39.1267	+	6.19706i	−1.30640	+	0.206914i
$898$	−0.000840234		0.0160326i	−2.80390e−5		0.000535016i
$899$	−17.8385	−	30.8972i	−0.594948	−	1.03048i
$900$	30.1700	−	27.8733i	1.00567	−	0.929110i
$901$	−0.154588	−	0.0892513i	−0.00515007	−	0.00297339i
$902$	−0.0272595	+	0.0138894i	−0.000907642	+	0.000462467i
$903$	12.5746	+	24.3111i	0.418456	+	0.809023i
$904$	0.0383043	−	0.0527213i	0.00127398	−	0.00175348i
$905$	−18.1304	−	46.3419i	−0.602676	−	1.54046i
$906$	0.00709133	−	0.0159274i	0.000235594	−	0.000529152i
$907$	−9.81060	−	2.62874i	−0.325755	−	0.0872859i	0.0922352	−	0.995737i	$-0.470599\pi$
$907$	−9.81060	−	2.62874i	−0.325755	−	0.0872859i	−0.417991	+	0.908451i	$0.637266\pi$
$908$	6.26357	+	5.07214i	0.207864	+	0.168325i
$909$	−15.4424	−	47.5269i	−0.512193	−	1.57637i
$910$	0.0296637	+	0.00591842i	0.000983343	+	0.000196194i
$911$	−14.3699	+	44.2260i	−0.476096	+	1.46527i	0.368378	+	0.929676i	$0.379913\pi$
$911$	−14.3699	+	44.2260i	−0.476096	+	1.46527i	−0.844474	+	0.535596i	$0.820087\pi$
$912$	−8.65292	+	5.61927i	−0.286527	+	0.186073i
$913$	3.46571	+	66.1297i	0.114698	+	2.18857i
$914$	0.000270983		0.00127487i	8.96331e−6		4.21691e-5i
$915$	−66.4468	−	29.0755i	−2.19666	−	0.961205i
$916$	−26.8102	+	8.71115i	−0.885832	+	0.287824i
$917$	−5.93589	+	4.86707i	−0.196020	+	0.160725i
$918$	−0.00152172	−	0.00152172i	−5.02243e−5	−	5.02243e-5i
$919$	−21.8717	+	2.29881i	−0.721481	+	0.0758307i	−0.458150	−	0.888875i	$-0.651488\pi$
$919$	−21.8717	+	2.29881i	−0.721481	+	0.0758307i	−0.263331	+	0.964706i	$0.584821\pi$
$920$	−0.0103854	+	0.0207093i	−0.000342395	+	0.000682765i
$921$	−1.87819	+	17.8698i	−0.0618884	+	0.588829i
$922$	−0.0314241	−	0.0120626i	−0.00103490	−	0.000397260i
$923$	−10.6134	−	20.8299i	−0.349343	−	0.685624i
$924$	68.2992	+	14.0823i	2.24688	+	0.463275i
$925$	−10.5612	+	0.689265i	−0.347252	+	0.0226629i
$926$	−0.00236919	+	0.00410356i	−7.78565e−5	+	0.000134851i
$927$	13.5353	+	8.78994i	0.444558	+	0.288699i
$928$	0.0347819	−	0.0281658i	0.00114177	−	0.000924588i
$929$	−29.8800	+	13.3034i	−0.980330	+	0.436471i	−0.833397	−	0.552675i	$-0.813607\pi$
$929$	−29.8800	+	13.3034i	−0.980330	+	0.436471i	−0.146933	+	0.989146i	$0.546940\pi$
$930$	0.0507704	+	0.00233476i	0.00166483	+	7.65597e-5i
$931$	6.46613	+	2.01406i	0.211919	+	0.0660082i
$932$	−9.91453	+	9.91453i	−0.324761	+	0.324761i
$933$	−34.9697	+	43.1840i	−1.14486	+	1.41378i
$934$	−0.0121301	+	0.0134719i	−0.000396910	+	0.000440813i
$935$	2.68907	+	8.09919i	0.0879419	+	0.264872i
$936$	−0.0624280	+	0.0562104i	−0.00204052	+	0.00183729i
$937$	13.2091	−	25.9243i	0.431522	−	0.846910i	−0.568190	−	0.822898i	$-0.692356\pi$
$937$	13.2091	−	25.9243i	0.431522	−	0.846910i	0.999712	−	0.0240121i	$-0.00764402\pi$
$938$	−0.00112429	+	0.00140584i	−3.67095e−5	+	4.59024e-5i
$939$	8.98478	+	2.91933i	0.293207	+	0.0952688i
$940$	14.9691	+	13.3056i	0.488238	+	0.433980i
$941$	−13.1885	−	11.8750i	−0.429933	−	0.387113i	0.425558	−	0.904931i	$-0.360078\pi$
$941$	−13.1885	−	11.8750i	−0.429933	−	0.387113i	−0.855491	+	0.517818i	$0.826744\pi$
$942$	−0.0410107	+	0.0157425i	−0.00133620	+	0.000512920i
$943$	4.65523	+	17.3736i	0.151595	+	0.565761i
$944$	14.2853	−	10.3789i	0.464947	−	0.337804i
$945$	12.1961	−	12.5051i	0.396738	−	0.406790i
$946$	−0.0146506	−	0.0106443i	−0.000476333	−	0.000346076i
$947$	−3.98955	+	10.3931i	−0.129643	+	0.337731i	−0.983003	−	0.183591i	$-0.941228\pi$
$947$	−3.98955	+	10.3931i	−0.129643	+	0.337731i	0.853360	+	0.521322i	$0.174561\pi$
$948$	14.3550	−	22.1047i	0.466228	−	0.717928i
$949$	−3.81032	+	2.19989i	−0.123688	+	0.0714114i
$950$	−0.00202105	+	0.00409541i	−6.55716e−5	+	0.000132873i
$951$			32.3772i			1.04990i
$952$	0.00548753	+	0.00542095i	0.000177852	+	0.000175694i
$953$	−0.154306	−	0.974249i	−0.00499846	−	0.0315590i	0.985063	−	0.172194i	$-0.0550856\pi$
$953$	−0.154306	−	0.974249i	−0.00499846	−	0.0315590i	−0.990062	+	0.140635i	$0.955086\pi$
$954$	−0.000364664	0	0.000819049i	−1.18064e−5	0	2.65177e-5i
$955$	−20.8217	−	10.4417i	−0.673775	−	0.337886i
$956$	12.4158	+	5.52786i	0.401555	+	0.178784i
$957$	50.2907	−	13.4753i	1.62567	−	0.435596i
$958$	−0.00504535	+	0.0318551i	−0.000163008	+	0.00102919i
$959$	32.5661	+	44.2530i	1.05162	+	1.42900i
$960$	−5.28873	−	47.3964i	−0.170693	−	1.52971i
$961$	−33.8272	−	37.5689i	−1.09120	−	1.21190i
$962$	0.0108079		0.000566417i	0.000348460		1.82620e-5i
$963$	−0.292783	+	0.0153441i	−0.00943479	+	0.000494456i
$964$	−20.8060	−	23.1074i	−0.670116	−	0.744239i
$965$	−7.41363	+	13.0329i	−0.238653	+	0.419543i
$966$	−0.00732911	+	0.0167356i	−0.000235810	+	0.000538459i
$967$	−6.08079	+	38.3926i	−0.195545	+	1.23462i	0.673237	+	0.739427i	$0.264903\pi$
$967$	−6.08079	+	38.3926i	−0.195545	+	1.23462i	−0.868782	+	0.495195i	$0.835097\pi$
$968$	−0.0490107	+	0.0131324i	−0.00157526	+	0.000422090i
$969$	−1.81923	−	0.809973i	−0.0584421	−	0.0260201i
$970$	−0.00432712	+	0.0285008i	−0.000138936	+	0.000915105i
$971$	−13.4299	−	30.1639i	−0.430985	−	0.968007i	−0.990286	−	0.139043i	$-0.955597\pi$
$971$	−13.4299	−	30.1639i	−0.430985	−	0.968007i	0.559302	−	0.828964i	$-0.311069\pi$
$972$	−6.48387	−	40.9375i	−0.207970	−	1.31307i
$973$	−1.48201	−	5.39891i	−0.0475109	−	0.173081i
$974$		−	0.0243921i		−	0.000781573i
$975$	21.4274	−	68.9396i	0.686225	−	2.20783i
$976$	−42.1466	+	24.3334i	−1.34908	+	0.778892i
$977$	4.64739	−	7.15636i	0.148683	−	0.228952i	−0.756479	−	0.654018i	$-0.773082\pi$
$977$	4.64739	−	7.15636i	0.148683	−	0.228952i	0.905163	+	0.425065i	$0.139749\pi$
$978$	0.00727613	−	0.0189550i	0.000232665	−	0.000606113i
$979$	−46.4154	−	33.7228i	−1.48344	−	1.07778i
$980$	−21.7201	+	22.5441i	−0.693825	+	0.720143i
$981$	−32.4667	+	23.5884i	−1.03658	+	0.753120i
$982$	−0.00901840	−	0.0336571i	−0.000287789	−	0.00107404i
$983$	−34.0217	+	13.0597i	−1.08512	+	0.416540i	−0.834198	−	0.551466i	$-0.814069\pi$
$983$	−34.0217	+	13.0597i	−1.08512	+	0.416540i	−0.250927	+	0.968006i	$0.580735\pi$
$984$	0.0490467	+	0.0441619i	0.00156355	+	0.00140783i
$985$	56.0018	+	5.52358i	1.78437	+	0.175996i
$986$	0.00273855		0.000889809i	8.72133e−5		2.83373e-5i
$987$	24.6695	+	19.7289i	0.785240	+	0.627979i
$988$	−4.75768	+	9.33748i	−0.151362	+	0.297065i
$989$	−7.91189	+	7.12390i	−0.251583	+	0.226527i
$990$	−0.0129841	+	0.0408493i	−0.000412660	+	0.00129828i
$991$	−11.9528	+	13.2749i	−0.379692	+	0.421691i	−0.902453	−	0.430788i	$-0.858236\pi$
$991$	−11.9528	+	13.2749i	−0.379692	+	0.421691i	0.522761	+	0.852480i	$0.324902\pi$
$992$	0.0643841	−	0.0795077i	0.00204420	−	0.00252437i
$993$	6.39051	−	6.39051i	0.202797	−	0.202797i
$994$	−0.0107295	−	0.00106155i	−0.000340318	−	3.36703e-5i
$995$	0.391902	+	1.42600i	0.0124241	+	0.0452072i
$996$	65.2516	−	29.0519i	2.06758	−	0.920545i
$997$	36.4893	−	29.5484i	1.15563	−	0.935809i	0.156970	−	0.987603i	$-0.449827\pi$
$997$	36.4893	−	29.5484i	1.15563	−	0.935809i	0.998658	+	0.0517946i	$0.0164941\pi$
$998$	0.0285399	+	0.0185341i	0.000903416	+	0.000586685i
$999$	3.12493	−	5.41253i	0.0988683	−	0.171245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.103.10	yes	288
5.2	odd	4		875.2.bb.b.257.9		288
5.3	odd	4		875.2.bb.a.257.10		288
5.4	even	2		875.2.bb.c.243.9		288
7.3	odd	6	inner	175.2.x.a.3.9	✓	288
25.6	even	5		875.2.bb.b.768.9		288
25.8	odd	20		875.2.bb.c.607.10		288
25.17	odd	20	inner	175.2.x.a.117.9	yes	288
25.19	even	10		875.2.bb.a.768.10		288
35.3	even	12		875.2.bb.a.507.10		288
35.17	even	12		875.2.bb.b.507.9		288
35.24	odd	6		875.2.bb.c.493.10		288
175.17	even	60	inner	175.2.x.a.17.10	yes	288
175.31	odd	30		875.2.bb.b.143.9		288
175.94	odd	30		875.2.bb.a.143.10		288
175.108	even	60		875.2.bb.c.857.9		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.9	✓	288	7.3	odd	6	inner
175.2.x.a.17.10	yes	288	175.17	even	60	inner
175.2.x.a.103.10	yes	288	1.1	even	1	trivial
175.2.x.a.117.9	yes	288	25.17	odd	20	inner
875.2.bb.a.143.10		288	175.94	odd	30
875.2.bb.a.257.10		288	5.3	odd	4
875.2.bb.a.507.10		288	35.3	even	12
875.2.bb.a.768.10		288	25.19	even	10
875.2.bb.b.143.9		288	175.31	odd	30
875.2.bb.b.257.9		288	5.2	odd	4
875.2.bb.b.507.9		288	35.17	even	12
875.2.bb.b.768.9		288	25.6	even	5
875.2.bb.c.243.9		288	5.4	even	2
875.2.bb.c.493.10		288	35.24	odd	6
875.2.bb.c.607.10		288	25.8	odd	20
875.2.bb.c.857.9		288	175.108	even	60

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.000942774 + 4.94087e-5i) q^{2} +(1.67776 + 2.07186i) q^{3} +(-1.98904 - 0.209057i) q^{4} +(2.16354 + 0.564890i) q^{5} +(0.00147938 + 0.00203619i) q^{6} +(-2.21008 + 1.45449i) q^{7} +(-0.00372978 - 0.000590739i) q^{8} +(-0.853997 + 4.01774i) q^{9} +(0.00201182 + 0.000639461i) q^{10} +(4.83530 - 1.02777i) q^{11} +(-2.90400 - 4.47177i) q^{12} +(-4.82554 - 2.45874i) q^{13} +(-0.00215547 + 0.00126206i) q^{14} +(2.45953 + 5.43031i) q^{15} +(3.91259 + 0.831646i) q^{16} +(0.276678 + 0.720771i) q^{17} +(-0.00100364 + 0.00374563i) q^{18} +(0.101132 + 0.962206i) q^{19} +(-4.18528 - 1.57589i) q^{20} +(-6.72150 - 2.13869i) q^{21} +(0.00460937 - 0.000730053i) q^{22} +(0.143592 - 2.73990i) q^{23} +(-0.00503375 - 0.00871871i) q^{24} +(4.36180 + 2.44432i) q^{25} +(-0.00442791 - 0.00255646i) q^{26} +(-2.63077 + 1.34044i) q^{27} +(4.70001 - 2.43102i) q^{28} +(2.32212 - 3.19613i) q^{29} +(0.00205047 + 0.00524107i) q^{30} +(3.67313 - 8.24998i) q^{31} +(0.0109428 + 0.00293211i) q^{32} +(10.2419 + 8.29371i) q^{33} +(0.000225232 + 0.000693194i) q^{34} +(-5.60322 + 1.89840i) q^{35} +(2.53857 - 7.81292i) q^{36} +(-1.77525 + 1.15286i) q^{37} +(4.78032e-5 + 0.000912139i) q^{38} +(-3.00194 - 14.1230i) q^{39} +(-0.00773582 - 0.00338500i) q^{40} +(-6.23478 + 2.02580i) q^{41} +(-0.00623118 - 0.00234840i) q^{42} +(-2.74386 - 2.74386i) q^{43} +(-9.83248 + 1.03344i) q^{44} +(-4.11724 + 8.21012i) q^{45} +(0.000270749 - 0.00257601i) q^{46} +(-4.18090 - 1.60490i) q^{47} +(4.84133 + 9.50164i) q^{48} +(2.76889 - 6.42909i) q^{49} +(0.00399142 + 0.00251995i) q^{50} +(-1.02914 + 1.78252i) q^{51} +(9.08419 + 5.89934i) q^{52} +(-0.179681 + 0.145503i) q^{53} +(-0.00254645 + 0.00113375i) q^{54} +(11.0419 + 0.507781i) q^{55} +(0.00910233 - 0.00411936i) q^{56} +(-1.82388 + 1.82388i) q^{57} +(0.00234715 - 0.00289849i) q^{58} +(2.95382 - 3.28055i) q^{59} +(-3.75686 - 11.3153i) q^{60} +(-9.04162 + 8.14111i) q^{61} +(0.00387055 - 0.00759638i) q^{62} +(-3.95638 - 10.1217i) q^{63} +(-7.60843 - 2.47213i) q^{64} +(-9.05133 - 8.04547i) q^{65} +(0.00924600 + 0.00832513i) q^{66} +(0.672823 - 0.258273i) q^{67} +(-0.399642 - 1.49149i) q^{68} +(5.91760 - 4.29939i) q^{69} +(-0.00537637 + 0.00151292i) q^{70} +(3.49220 + 2.53723i) q^{71} +(0.00555865 - 0.0144808i) q^{72} +(0.442460 - 0.681329i) q^{73} +(-0.00173062 + 0.000999174i) q^{74} +(2.25376 + 13.1380i) q^{75} -1.93501i q^{76} +(-9.19150 + 9.30437i) q^{77} +(-0.00213235 - 0.0134631i) q^{78} +(2.01057 + 4.51581i) q^{79} +(7.99524 + 4.00948i) q^{80} +(4.06615 + 1.81036i) q^{81} +(-0.00597808 + 0.00160182i) q^{82} +(-2.09559 + 13.2310i) q^{83} +(12.9222 + 5.65911i) q^{84} +(0.191447 + 1.71571i) q^{85} +(-0.00245127 - 0.00272241i) q^{86} +(10.5179 - 0.551220i) q^{87} +(-0.0186417 + 0.000976972i) q^{88} +(-7.76599 - 8.62500i) q^{89} +(-0.00428727 + 0.00753686i) q^{90} +(14.2410 - 1.58472i) q^{91} +(-0.858405 + 5.41975i) q^{92} +(23.2555 - 6.23128i) q^{93} +(-0.00386235 - 0.00171963i) q^{94} +(-0.324737 + 2.13890i) q^{95} +(0.0122845 + 0.0275913i) q^{96} +(2.13624 + 13.4877i) q^{97} +(0.00292809 - 0.00592437i) q^{98} +20.3047i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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