LMFDB - Embedded newform 555.2.g.a.184.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(184,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("555.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			184.6
Character	$\chi$	$=$	555.184
Dual form			555.2.g.a.184.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46809 q^{2} +1.00000i q^{3} +4.09146 q^{4} +(-1.94703 - 1.09958i) q^{5} -2.46809i q^{6} -1.91769i q^{7} -5.16192 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.46809 q^{2} +1.00000i q^{3} +4.09146 q^{4} +(-1.94703 - 1.09958i) q^{5} -2.46809i q^{6} -1.91769i q^{7} -5.16192 q^{8} -1.00000 q^{9} +(4.80544 + 2.71386i) q^{10} -3.25824 q^{11} +4.09146i q^{12} +0.160612 q^{13} +4.73304i q^{14} +(1.09958 - 1.94703i) q^{15} +4.55716 q^{16} +1.85492 q^{17} +2.46809 q^{18} +3.64999i q^{19} +(-7.96621 - 4.49889i) q^{20} +1.91769 q^{21} +8.04162 q^{22} +4.23161 q^{23} -5.16192i q^{24} +(2.58185 + 4.28183i) q^{25} -0.396404 q^{26} -1.00000i q^{27} -7.84617i q^{28} +4.15490i q^{29} +(-2.71386 + 4.80544i) q^{30} -4.23836i q^{31} -0.923622 q^{32} -3.25824i q^{33} -4.57810 q^{34} +(-2.10865 + 3.73381i) q^{35} -4.09146 q^{36} +(-5.15526 + 3.22851i) q^{37} -9.00850i q^{38} +0.160612i q^{39} +(10.0504 + 5.67594i) q^{40} +0.101625 q^{41} -4.73304 q^{42} +0.344898 q^{43} -13.3310 q^{44} +(1.94703 + 1.09958i) q^{45} -10.4440 q^{46} +8.46641i q^{47} +4.55716i q^{48} +3.32245 q^{49} +(-6.37225 - 10.5679i) q^{50} +1.85492i q^{51} +0.657137 q^{52} +2.83582i q^{53} +2.46809i q^{54} +(6.34388 + 3.58269i) q^{55} +9.89898i q^{56} -3.64999 q^{57} -10.2547i q^{58} +9.33509i q^{59} +(4.49889 - 7.96621i) q^{60} +12.6863i q^{61} +10.4607i q^{62} +1.91769i q^{63} -6.83473 q^{64} +(-0.312716 - 0.176605i) q^{65} +8.04162i q^{66} +7.49943i q^{67} +7.58933 q^{68} +4.23161i q^{69} +(5.20434 - 9.21537i) q^{70} +2.80907 q^{71} +5.16192 q^{72} +5.66300i q^{73} +(12.7236 - 7.96825i) q^{74} +(-4.28183 + 2.58185i) q^{75} +14.9338i q^{76} +6.24829i q^{77} -0.396404i q^{78} +8.03998i q^{79} +(-8.87292 - 5.01095i) q^{80} +1.00000 q^{81} -0.250819 q^{82} -14.8176i q^{83} +7.84617 q^{84} +(-3.61158 - 2.03963i) q^{85} -0.851239 q^{86} -4.15490 q^{87} +16.8188 q^{88} -1.54104i q^{89} +(-4.80544 - 2.71386i) q^{90} -0.308004i q^{91} +17.3135 q^{92} +4.23836 q^{93} -20.8959i q^{94} +(4.01345 - 7.10664i) q^{95} -0.923622i q^{96} -18.2175 q^{97} -8.20012 q^{98} +3.25824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) $ 40 * q + 44 * q^4 - 40 * q^9	$ 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.46809			−1.74520			−0.872601	−	0.488433i	$-0.837569\pi$
$2$	−2.46809			−1.74520			−0.872601	+	0.488433i	$0.837569\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	4.09146			2.04573
$5$	−1.94703	−	1.09958i	−0.870738	−	0.491746i
$5$	−1.94703	−	1.09958i	−0.870738	−	0.491746i
$6$		−	2.46809i		−	1.00759i
$7$		−	1.91769i		−	0.724820i	−0.932019	−	0.362410i	$-0.881954\pi$
$7$		−	1.91769i		−	0.724820i	0.932019	−	0.362410i	$-0.118046\pi$
$8$	−5.16192			−1.82502
$9$	−1.00000			−0.333333
$10$	4.80544	+	2.71386i	1.51962	+	0.858197i
$11$	−3.25824			−0.982395			−0.491197	−	0.871048i	$-0.663441\pi$
$11$	−3.25824			−0.982395			−0.491197	+	0.871048i	$0.663441\pi$
$12$			4.09146i			1.18110i
$13$	0.160612			0.0445456			0.0222728	−	0.999752i	$-0.492910\pi$
$13$	0.160612			0.0445456			0.0222728	+	0.999752i	$0.492910\pi$
$14$			4.73304i			1.26496i
$15$	1.09958	−	1.94703i	0.283910	−	0.502721i
$16$	4.55716			1.13929
$17$	1.85492			0.449884			0.224942	−	0.974372i	$-0.427781\pi$
$17$	1.85492			0.449884			0.224942	+	0.974372i	$0.427781\pi$
$18$	2.46809			0.581734
$19$			3.64999i			0.837365i	0.908133	+	0.418683i	$0.137508\pi$
$19$			3.64999i			0.837365i	−0.908133	+	0.418683i	$0.862492\pi$
$20$	−7.96621	−	4.49889i	−1.78130	−	1.00598i
$21$	1.91769			0.418475
$22$	8.04162			1.71448
$23$	4.23161			0.882352			0.441176	−	0.897421i	$-0.354561\pi$
$23$	4.23161			0.882352			0.441176	+	0.897421i	$0.354561\pi$
$24$		−	5.16192i		−	1.05367i
$25$	2.58185	+	4.28183i	0.516371	+	0.856365i
$26$	−0.396404			−0.0777412
$27$		−	1.00000i		−	0.192450i
$28$		−	7.84617i		−	1.48279i
$29$			4.15490i			0.771546i	0.922594	+	0.385773i	$0.126065\pi$
$29$			4.15490i			0.771546i	−0.922594	+	0.385773i	$0.873935\pi$
$30$	−2.71386	+	4.80544i	−0.495480	+	0.877350i
$31$		−	4.23836i		−	0.761232i	−0.924733	−	0.380616i	$-0.875712\pi$
$31$		−	4.23836i		−	0.761232i	0.924733	−	0.380616i	$-0.124288\pi$
$32$	−0.923622			−0.163275
$33$		−	3.25824i		−	0.567186i
$34$	−4.57810			−0.785138
$35$	−2.10865	+	3.73381i	−0.356427	+	0.631128i
$36$	−4.09146			−0.681911
$37$	−5.15526	+	3.22851i	−0.847520	+	0.530764i
$37$	−5.15526	+	3.22851i	−0.847520	+	0.530764i
$38$		−	9.00850i		−	1.46137i
$39$			0.160612i			0.0257184i
$40$	10.0504	+	5.67594i	1.58911	+	0.897445i
$41$	0.101625			0.0158711			0.00793556	−	0.999969i	$-0.497474\pi$
$41$	0.101625			0.0158711			0.00793556	+	0.999969i	$0.497474\pi$
$42$	−4.73304			−0.730323
$43$	0.344898			0.0525964			0.0262982	−	0.999654i	$-0.491628\pi$
$43$	0.344898			0.0525964			0.0262982	+	0.999654i	$0.491628\pi$
$44$	−13.3310			−2.00972
$45$	1.94703	+	1.09958i	0.290246	+	0.163915i
$46$	−10.4440			−1.53988
$47$			8.46641i			1.23495i	0.786589	+	0.617477i	$0.211845\pi$
$47$			8.46641i			1.23495i	−0.786589	+	0.617477i	$0.788155\pi$
$48$			4.55716i			0.657769i
$49$	3.32245			0.474636
$50$	−6.37225	−	10.5679i	−0.901172	−	1.49453i
$51$			1.85492i			0.259740i
$52$	0.657137			0.0911285
$53$			2.83582i			0.389530i	0.980850	+	0.194765i	$0.0623943\pi$
$53$			2.83582i			0.389530i	−0.980850	+	0.194765i	$0.937606\pi$
$54$			2.46809i			0.335864i
$55$	6.34388	+	3.58269i	0.855409	+	0.483089i
$56$			9.89898i			1.32281i
$57$	−3.64999			−0.483453
$58$		−	10.2547i		−	1.34650i
$59$			9.33509i			1.21533i	0.794195	+	0.607663i	$0.207893\pi$
$59$			9.33509i			1.21533i	−0.794195	+	0.607663i	$0.792107\pi$
$60$	4.49889	−	7.96621i	0.580804	−	1.02843i
$61$			12.6863i			1.62431i	0.583439	+	0.812157i	$0.301707\pi$
$61$			12.6863i			1.62431i	−0.583439	+	0.812157i	$0.698293\pi$
$62$			10.4607i			1.32850i
$63$			1.91769i			0.241607i
$64$	−6.83473			−0.854341
$65$	−0.312716	−	0.176605i	−0.0387876	−	0.0219052i
$66$			8.04162i			0.989855i
$67$			7.49943i			0.916201i	0.888900	+	0.458101i	$0.151470\pi$
$67$			7.49943i			0.916201i	−0.888900	+	0.458101i	$0.848530\pi$
$68$	7.58933			0.920341
$69$			4.23161i			0.509426i
$70$	5.20434	−	9.21537i	0.622038	−	1.10145i
$71$	2.80907			0.333375			0.166687	−	0.986010i	$-0.446693\pi$
$71$	2.80907			0.333375			0.166687	+	0.986010i	$0.446693\pi$
$72$	5.16192			0.608338
$73$			5.66300i			0.662804i	0.943490	+	0.331402i	$0.107522\pi$
$73$			5.66300i			0.662804i	−0.943490	+	0.331402i	$0.892478\pi$
$74$	12.7236	−	7.96825i	1.47909	−	0.926290i
$75$	−4.28183	+	2.58185i	−0.494423	+	0.298127i
$76$			14.9338i			1.71302i
$77$			6.24829i			0.712059i
$78$		−	0.396404i		−	0.0448839i
$79$			8.03998i			0.904568i	0.891874	+	0.452284i	$0.149391\pi$
$79$			8.03998i			0.904568i	−0.891874	+	0.452284i	$0.850609\pi$
$80$	−8.87292	−	5.01095i	−0.992023	−	0.560241i
$81$	1.00000			0.111111
$82$	−0.250819			−0.0276983
$83$		−	14.8176i		−	1.62644i	−0.581955	−	0.813221i	$-0.697712\pi$
$83$		−	14.8176i		−	1.62644i	0.581955	−	0.813221i	$-0.302288\pi$
$84$	7.84617			0.856088
$85$	−3.61158	−	2.03963i	−0.391731	−	0.221229i
$86$	−0.851239			−0.0917914
$87$	−4.15490			−0.445452
$88$	16.8188			1.79289
$89$		−	1.54104i		−	0.163350i	−0.996659	−	0.0816750i	$-0.973973\pi$
$89$		−	1.54104i		−	0.163350i	0.996659	−	0.0816750i	$-0.0260269\pi$
$90$	−4.80544	−	2.71386i	−0.506538	−	0.286066i
$91$		−	0.308004i		−	0.0322876i
$92$	17.3135			1.80506
$93$	4.23836			0.439498
$94$		−	20.8959i		−	2.15524i
$95$	4.01345	−	7.10664i	0.411771	−	0.729126i
$96$		−	0.923622i		−	0.0942668i
$97$	−18.2175			−1.84971			−0.924855	−	0.380320i	$-0.875814\pi$
$97$	−18.2175			−1.84971			−0.924855	+	0.380320i	$0.875814\pi$
$98$	−8.20012			−0.828337
$99$	3.25824			0.327465
$100$	10.5636	+	17.5189i	1.05636	+	1.75189i
$101$	−10.0606			−1.00107			−0.500534	−	0.865717i	$-0.666863\pi$
$101$	−10.0606			−1.00107			−0.500534	+	0.865717i	$0.666863\pi$
$102$		−	4.57810i		−	0.453300i
$103$	14.0747			1.38682			0.693412	−	0.720542i	$-0.256107\pi$
$103$	14.0747			1.38682			0.693412	+	0.720542i	$0.256107\pi$
$104$	−0.829065			−0.0812965
$105$	−3.73381	−	2.10865i	−0.364382	−	0.205783i
$106$		−	6.99905i		−	0.679808i
$107$			17.7781i			1.71867i	0.511411	+	0.859336i	$0.329123\pi$
$107$			17.7781i			1.71867i	−0.511411	+	0.859336i	$0.670877\pi$
$108$		−	4.09146i		−	0.393701i
$109$		−	7.88688i		−	0.755426i	−0.925923	−	0.377713i	$-0.876711\pi$
$109$		−	7.88688i		−	0.755426i	0.925923	−	0.377713i	$-0.123289\pi$
$110$	−15.6573	−	8.84239i	−1.49286	−	0.843089i
$111$	−3.22851	−	5.15526i	−0.306437	−	0.489316i
$112$		−	8.73922i		−	0.825779i
$113$	4.05935			0.381872			0.190936	−	0.981603i	$-0.438848\pi$
$113$	4.05935			0.381872			0.190936	+	0.981603i	$0.438848\pi$
$114$	9.00850			0.843723
$115$	−8.23908	−	4.65299i	−0.768298	−	0.433894i
$116$			16.9996i			1.57838i
$117$	−0.160612			−0.0148485
$118$		−	23.0398i		−	2.12099i
$119$		−	3.55716i		−	0.326084i
$120$	−5.67594	+	10.0504i	−0.518140	+	0.917474i
$121$	−0.383902			−0.0349002
$122$		−	31.3109i		−	2.83476i
$123$			0.101625i			0.00916319i
$124$		−	17.3411i		−	1.55728i
$125$	−0.318747	−	11.1758i	−0.0285096	−	0.999594i
$126$		−	4.73304i		−	0.421652i
$127$		−	13.1627i		−	1.16800i	−0.811753	−	0.584001i	$-0.801487\pi$
$127$		−	13.1627i		−	1.16800i	0.811753	−	0.584001i	$-0.198513\pi$
$128$	18.7160			1.65427
$129$			0.344898i			0.0303666i
$130$	0.771810	+	0.435877i	0.0676922	+	0.0382289i
$131$		−	0.781638i		−	0.0682920i	−0.999417	−	0.0341460i	$-0.989129\pi$
$131$		−	0.781638i		−	0.0682920i	0.999417	−	0.0341460i	$-0.0108711\pi$
$132$		−	13.3310i		−	1.16031i
$133$	6.99956			0.606939
$134$		−	18.5093i		−	1.59896i
$135$	−1.09958	+	1.94703i	−0.0946366	+	0.167574i
$136$	−9.57494			−0.821044
$137$			3.69964i			0.316082i	0.987433	+	0.158041i	$0.0505178\pi$
$137$			3.69964i			0.316082i	−0.987433	+	0.158041i	$0.949482\pi$
$138$		−	10.4440i		−	0.889052i
$139$	−7.46494			−0.633168			−0.316584	−	0.948564i	$-0.602536\pi$
$139$	−7.46494			−0.633168			−0.316584	+	0.948564i	$0.602536\pi$
$140$	−8.62748	+	15.2767i	−0.729155	+	1.29112i
$141$	−8.46641			−0.713001
$142$	−6.93303			−0.581807
$143$	−0.523310			−0.0437614
$144$	−4.55716			−0.379763
$145$	4.56864	−	8.08972i	0.379405	−	0.671815i
$146$		−	13.9768i		−	1.15673i
$147$			3.32245i			0.274031i
$148$	−21.0926	+	13.2093i	−1.73380	+	1.08580i
$149$	22.9555			1.88059			0.940296	−	0.340359i	$-0.110549\pi$
$149$	22.9555			1.88059			0.940296	+	0.340359i	$0.110549\pi$
$150$	10.5679	−	6.37225i	0.862868	−	0.520292i
$151$	14.7687			1.20186			0.600931	−	0.799301i	$-0.294797\pi$
$151$	14.7687			1.20186			0.600931	+	0.799301i	$0.294797\pi$
$152$		−	18.8410i		−	1.52820i
$153$	−1.85492			−0.149961
$154$		−	15.4213i		−	1.24269i
$155$	−4.66041	+	8.25222i	−0.374333	+	0.662834i
$156$			0.657137i			0.0526130i
$157$		−	2.19178i		−	0.174923i	−0.996168	−	0.0874616i	$-0.972124\pi$
$157$		−	2.19178i		−	0.174923i	0.996168	−	0.0874616i	$-0.0278755\pi$
$158$		−	19.8434i		−	1.57865i
$159$	−2.83582			−0.224895
$160$	1.79832	+	1.01560i	0.142170	+	0.0802898i
$161$		−	8.11493i		−	0.639546i
$162$	−2.46809			−0.193911
$163$	−15.4284			−1.20845			−0.604224	−	0.796815i	$-0.706517\pi$
$163$	−15.4284			−1.20845			−0.604224	+	0.796815i	$0.706517\pi$
$164$	0.415794			0.0324680
$165$	−3.58269	+	6.34388i	−0.278912	+	0.493871i
$166$			36.5711i			2.83847i
$167$	18.4894			1.43075			0.715376	−	0.698740i	$-0.246255\pi$
$167$	18.4894			1.43075			0.715376	+	0.698740i	$0.246255\pi$
$168$	−9.89898			−0.763723
$169$	−12.9742			−0.998016
$170$	8.91370	+	5.03398i	0.683650	+	0.386089i
$171$		−	3.64999i		−	0.279122i
$172$	1.41114			0.107598
$173$			24.4913i			1.86204i	0.364968	+	0.931020i	$0.381080\pi$
$173$			24.4913i			1.86204i	−0.364968	+	0.931020i	$0.618920\pi$
$174$	10.2547			0.777404
$175$	8.21122	−	4.95120i	0.620710	−	0.374276i
$176$	−14.8483			−1.11923
$177$	−9.33509			−0.701668
$178$			3.80343i			0.285079i
$179$		−	21.5527i		−	1.61092i	−0.592649	−	0.805461i	$-0.701918\pi$
$179$		−	21.5527i		−	1.61092i	0.592649	−	0.805461i	$-0.298082\pi$
$180$	7.96621	+	4.49889i	0.593766	+	0.335327i
$181$	23.2257			1.72635			0.863175	−	0.504904i	$-0.168472\pi$
$181$	23.2257			1.72635			0.863175	+	0.504904i	$0.168472\pi$
$182$			0.760181i			0.0563483i
$183$	−12.6863			−0.937798
$184$	−21.8433			−1.61031
$185$	13.5875	−	0.617391i	0.998969	−	0.0453915i
$186$	−10.4607			−0.767012
$187$	−6.04376			−0.441963
$188$			34.6400i			2.52638i
$189$	−1.91769			−0.139492
$190$	−9.90555	+	17.5398i	−0.718624	+	1.27247i
$191$		−	8.14176i		−	0.589117i	−0.955633	−	0.294559i	$-0.904827\pi$
$191$		−	8.14176i		−	0.589117i	0.955633	−	0.294559i	$-0.0951726\pi$
$192$		−	6.83473i		−	0.493254i
$193$	−14.4396			−1.03939			−0.519694	−	0.854353i	$-0.673954\pi$
$193$	−14.4396			−1.03939			−0.519694	+	0.854353i	$0.673954\pi$
$194$	44.9625			3.22812
$195$	0.176605	−	0.312716i	0.0126469	−	0.0223940i
$196$	13.5937			0.970979
$197$			11.9277i			0.849811i	0.905238	+	0.424905i	$0.139693\pi$
$197$			11.9277i			0.849811i	−0.905238	+	0.424905i	$0.860307\pi$
$198$	−8.04162			−0.571493
$199$			5.39451i			0.382407i	0.981550	+	0.191203i	$0.0612390\pi$
$199$			5.39451i			0.382407i	−0.981550	+	0.191203i	$0.938761\pi$
$200$	−13.3273	−	22.1024i	−0.942385	−	1.56288i
$201$	−7.49943			−0.528969
$202$	24.8305			1.74707
$203$	7.96782			0.559232
$204$			7.58933i			0.531359i
$205$	−0.197866	−	0.111744i	−0.0138196	−	0.00780456i
$206$	−34.7377			−2.42029
$207$	−4.23161			−0.294117
$208$	0.731932			0.0507504
$209$		−	11.8925i		−	0.822623i
$210$	9.21537	+	5.20434i	0.635921	+	0.359134i
$211$	19.3328			1.33093			0.665463	−	0.746431i	$-0.268234\pi$
$211$	19.3328			1.33093			0.665463	+	0.746431i	$0.268234\pi$
$212$			11.6026i			0.796873i
$213$			2.80907i			0.192474i
$214$		−	43.8779i		−	2.99943i
$215$	−0.671526	−	0.379242i	−0.0457977	−	0.0258641i
$216$			5.16192i			0.351224i
$217$	−8.12787			−0.551756
$218$			19.4655i			1.31837i
$219$	−5.66300			−0.382670
$220$	25.9558	+	14.6584i	1.74994	+	0.988271i
$221$	0.297921			0.0200404
$222$	7.96825	+	12.7236i	0.534794	+	0.853955i
$223$		−	14.0238i		−	0.939106i	−0.882904	−	0.469553i	$-0.844415\pi$
$223$		−	14.0238i		−	0.939106i	0.882904	−	0.469553i	$-0.155585\pi$
$224$			1.77122i			0.118345i
$225$	−2.58185	−	4.28183i	−0.172124	−	0.285455i
$226$	−10.0188			−0.666443
$227$	−4.83369			−0.320823			−0.160412	−	0.987050i	$-0.551282\pi$
$227$	−4.83369			−0.320823			−0.160412	+	0.987050i	$0.551282\pi$
$228$	−14.9338			−0.989015
$229$	2.48827			0.164430			0.0822149	−	0.996615i	$-0.473801\pi$
$229$	2.48827			0.164430			0.0822149	+	0.996615i	$0.473801\pi$
$230$	20.3348	+	11.4840i	1.34084	+	0.757232i
$231$	−6.24829			−0.411108
$232$		−	21.4473i		−	1.40808i
$233$			8.02623i			0.525816i	0.964821	+	0.262908i	$0.0846815\pi$
$233$			8.02623i			0.525816i	−0.964821	+	0.262908i	$0.915319\pi$
$234$	0.396404			0.0259137
$235$	9.30949	−	16.4844i	0.607284	−	1.07532i
$236$			38.1942i			2.48623i
$237$	−8.03998			−0.522253
$238$			8.77939i			0.569084i
$239$			28.7939i			1.86252i	0.364353	+	0.931261i	$0.381290\pi$
$239$			28.7939i			1.86252i	−0.364353	+	0.931261i	$0.618710\pi$
$240$	5.01095	−	8.87292i	0.323455	−	0.572745i
$241$			27.4478i			1.76807i	0.467424	+	0.884033i	$0.345182\pi$
$241$			27.4478i			1.76807i	−0.467424	+	0.884033i	$0.654818\pi$
$242$	0.947505			0.0609079
$243$			1.00000i			0.0641500i
$244$			51.9055i			3.32291i
$245$	−6.46892	−	3.65330i	−0.413284	−	0.233401i
$246$		−	0.250819i		−	0.0159916i
$247$			0.586231i			0.0373010i
$248$			21.8781i			1.38926i
$249$	14.8176			0.939027
$250$	0.786697	+	27.5829i	0.0497551	+	1.74449i
$251$			0.0892217i			0.00563162i	0.999996	+	0.00281581i	$0.000896302\pi$
$251$			0.0892217i			0.00563162i	−0.999996	+	0.00281581i	$0.999104\pi$
$252$			7.84617i			0.494262i
$253$	−13.7876			−0.866818
$254$			32.4867i			2.03840i
$255$	2.03963	−	3.61158i	0.127726	−	0.226166i
$256$	−32.5232			−2.03270
$257$	−0.196416			−0.0122521			−0.00612606	−	0.999981i	$-0.501950\pi$
$257$	−0.196416			−0.0122521			−0.00612606	+	0.999981i	$0.501950\pi$
$258$		−	0.851239i		−	0.0529958i
$259$	6.19129	+	9.88621i	0.384708	+	0.614299i
$260$	−1.27947	−	0.722573i	−0.0793491	−	0.0448121i
$261$		−	4.15490i		−	0.257182i
$262$			1.92915i			0.119183i
$263$		−	8.71844i		−	0.537602i	−0.963196	−	0.268801i	$-0.913373\pi$
$263$		−	8.71844i		−	0.537602i	0.963196	−	0.268801i	$-0.0866274\pi$
$264$			16.8188i			1.03512i
$265$	3.11820	−	5.52142i	0.191550	−	0.339178i
$266$	−17.2755			−1.05923
$267$	1.54104			0.0943101
$268$			30.6837i			1.87430i
$269$	−26.8140			−1.63488			−0.817440	−	0.576014i	$-0.804607\pi$
$269$	−26.8140			−1.63488			−0.817440	+	0.576014i	$0.804607\pi$
$270$	2.71386	−	4.80544i	0.165160	−	0.292450i
$271$	1.24258			0.0754813			0.0377406	−	0.999288i	$-0.487984\pi$
$271$	1.24258			0.0754813			0.0377406	+	0.999288i	$0.487984\pi$
$272$	8.45315			0.512547
$273$	0.308004			0.0186412
$274$		−	9.13105i		−	0.551627i
$275$	−8.41229	−	13.9512i	−0.507280	−	0.841289i
$276$			17.3135i			1.04215i
$277$	4.08138			0.245226			0.122613	−	0.992455i	$-0.460873\pi$
$277$	4.08138			0.245226			0.122613	+	0.992455i	$0.460873\pi$
$278$	18.4242			1.10501
$279$			4.23836i			0.253744i
$280$	10.8847	−	19.2736i	0.650486	−	1.15182i
$281$		−	12.5169i		−	0.746698i	−0.927691	−	0.373349i	$-0.878209\pi$
$281$		−	12.5169i		−	0.746698i	0.927691	−	0.373349i	$-0.121791\pi$
$282$	20.8959			1.24433
$283$	19.9252			1.18443			0.592215	−	0.805780i	$-0.298253\pi$
$283$	19.9252			1.18443			0.592215	+	0.805780i	$0.298253\pi$
$284$	11.4932			0.681996
$285$	7.10664	+	4.01345i	0.420961	+	0.237736i
$286$	1.29158			0.0763725
$287$		−	0.194885i		−	0.0115037i
$288$	0.923622			0.0544250
$289$	−13.5593			−0.797605
$290$	−11.2758	+	19.9661i	−0.662138	+	1.17245i
$291$		−	18.2175i		−	1.06793i
$292$			23.1700i			1.35592i
$293$		−	7.53011i		−	0.439914i	−0.975510	−	0.219957i	$-0.929408\pi$
$293$		−	7.53011i		−	0.439914i	0.975510	−	0.219957i	$-0.0705917\pi$
$294$		−	8.20012i		−	0.478240i
$295$	10.2647	−	18.1757i	0.597632	−	1.05823i
$296$	26.6111	−	16.6653i	1.54674	−	0.968652i
$297$			3.25824i			0.189062i
$298$	−56.6563			−3.28201
$299$	0.679646			0.0393049
$300$	−17.5189	+	10.5636i	−1.01146	+	0.609888i
$301$		−	0.661408i		−	0.0381229i
$302$	−36.4506			−2.09749
$303$		−	10.0606i		−	0.577967i
$304$			16.6336i			0.954001i
$305$	13.9496	−	24.7006i	0.798750	−	1.41435i
$306$	4.57810			0.261713
$307$		−	22.0180i		−	1.25663i	−0.777957	−	0.628317i	$-0.783744\pi$
$307$		−	22.0180i		−	1.25663i	0.777957	−	0.628317i	$-0.216256\pi$
$308$			25.5647i			1.45668i
$309$			14.0747i			0.800683i
$310$	11.5023	−	20.3672i	0.653287	−	1.15678i
$311$		−	18.3210i		−	1.03889i	−0.854505	−	0.519443i	$-0.826139\pi$
$311$		−	18.3210i		−	1.03889i	0.854505	−	0.519443i	$-0.173861\pi$
$312$		−	0.829065i		−	0.0469365i
$313$	16.3043			0.921572			0.460786	−	0.887511i	$-0.347568\pi$
$313$	16.3043			0.921572			0.460786	+	0.887511i	$0.347568\pi$
$314$			5.40951i			0.305276i
$315$	2.10865	−	3.73381i	0.118809	−	0.210376i
$316$			32.8953i			1.85050i
$317$		−	5.52814i		−	0.310491i	−0.987876	−	0.155246i	$-0.950383\pi$
$317$		−	5.52814i		−	0.310491i	0.987876	−	0.155246i	$-0.0496169\pi$
$318$	6.99905			0.392487
$319$		−	13.5376i		−	0.757963i
$320$	13.3074	+	7.51532i	0.743908	+	0.420119i
$321$	−17.7781			−0.992276
$322$			20.0284i			1.11614i
$323$			6.77043i			0.376717i
$324$	4.09146			0.227304
$325$	0.414676	+	0.687711i	0.0230021	+	0.0381473i
$326$	38.0787			2.10899
$327$	7.88688			0.436145
$328$	−0.524579			−0.0289650
$329$	16.2360			0.895119
$330$	8.84239	−	15.6573i	0.486757	−	0.861904i
$331$		−	14.1823i		−	0.779532i	−0.920914	−	0.389766i	$-0.872556\pi$
$331$		−	14.1823i		−	0.779532i	0.920914	−	0.389766i	$-0.127444\pi$
$332$		−	60.6257i		−	3.32727i
$333$	5.15526	−	3.22851i	0.282507	−	0.176921i
$334$	−45.6335			−2.49695
$335$	8.24621	−	14.6016i	0.450539	−	0.797772i
$336$	8.73922			0.476764
$337$			32.0002i			1.74316i	0.490252	+	0.871581i	$0.336905\pi$
$337$			32.0002i			1.74316i	−0.490252	+	0.871581i	$0.663095\pi$
$338$	32.0215			1.74174
$339$			4.05935i			0.220474i
$340$	−14.7767	−	8.34506i	−0.801377	−	0.452575i
$341$			13.8096i			0.747830i
$342$			9.00850i			0.487124i
$343$		−	19.7953i		−	1.06885i
$344$	−1.78034			−0.0959893
$345$	4.65299	−	8.23908i	0.250509	−	0.443577i
$346$		−	60.4467i		−	3.24964i
$347$	−19.8930			−1.06791			−0.533956	−	0.845512i	$-0.679295\pi$
$347$	−19.8930			−1.06791			−0.533956	+	0.845512i	$0.679295\pi$
$348$	−16.9996			−0.911276
$349$	−20.3204			−1.08772			−0.543862	−	0.839174i	$-0.683039\pi$
$349$	−20.3204			−1.08772			−0.543862	+	0.839174i	$0.683039\pi$
$350$	−20.2660	+	12.2200i	−1.08327	+	0.653187i
$351$		−	0.160612i		−	0.00857281i
$352$	3.00938			0.160400
$353$	−5.17147			−0.275250			−0.137625	−	0.990484i	$-0.543947\pi$
$353$	−5.17147			−0.275250			−0.137625	+	0.990484i	$0.543947\pi$
$354$	23.0398			1.22455
$355$	−5.46934	−	3.08879i	−0.290282	−	0.163936i
$356$		−	6.30511i		−	0.334170i
$357$	3.55716			0.188265
$358$			53.1939i			2.81138i
$359$	−17.0401			−0.899343			−0.449672	−	0.893194i	$-0.648459\pi$
$359$	−17.0401			−0.899343			−0.449672	+	0.893194i	$0.648459\pi$
$360$	−10.0504	−	5.67594i	−0.529704	−	0.299148i
$361$	5.67757			0.298820
$362$	−57.3230			−3.01283
$363$		−	0.383902i		−	0.0201496i
$364$		−	1.26019i		−	0.0660517i
$365$	6.22691	−	11.0260i	0.325931	−	0.577129i
$366$	31.3109			1.63665
$367$		−	6.30201i		−	0.328962i	−0.986380	−	0.164481i	$-0.947405\pi$
$367$		−	6.30201i		−	0.328962i	0.986380	−	0.164481i	$-0.0525949\pi$
$368$	19.2841			1.00525
$369$	−0.101625			−0.00529037
$370$	−33.5350	+	1.52378i	−1.74340	+	0.0792173i
$371$	5.43823			0.282339
$372$	17.3411			0.899094
$373$			26.5425i			1.37432i	0.726508	+	0.687158i	$0.241142\pi$
$373$			26.5425i			1.37432i	−0.726508	+	0.687158i	$0.758858\pi$
$374$	14.9165			0.771316
$375$	11.1758	−	0.318747i	0.577116	−	0.0164600i
$376$		−	43.7030i		−	2.25381i
$377$			0.667325i			0.0343690i
$378$	4.73304			0.243441
$379$	−18.7796			−0.964645			−0.482323	−	0.875994i	$-0.660207\pi$
$379$	−18.7796			−0.964645			−0.482323	+	0.875994i	$0.660207\pi$
$380$	16.4209	−	29.0766i	0.842374	−	1.49160i
$381$	13.1627			0.674346
$382$			20.0946i			1.02813i
$383$	−22.8606			−1.16812			−0.584062	−	0.811709i	$-0.698537\pi$
$383$	−22.8606			−1.16812			−0.584062	+	0.811709i	$0.698537\pi$
$384$			18.7160i			0.955095i
$385$	6.87049	−	12.1656i	0.350153	−	0.620017i
$386$	35.6383			1.81394
$387$	−0.344898			−0.0175321
$388$	−74.5364			−3.78401
$389$			16.0868i			0.815635i	0.913064	+	0.407817i	$0.133710\pi$
$389$			16.0868i			0.815635i	−0.913064	+	0.407817i	$0.866290\pi$
$390$	−0.435877	+	0.771810i	−0.0220715	+	0.0390821i
$391$	7.84929			0.396956
$392$	−17.1503			−0.866219
$393$	0.781638			0.0394284
$394$		−	29.4385i		−	1.48309i
$395$	8.84059	−	15.6541i	0.444818	−	0.787642i
$396$	13.3310			0.669906
$397$			35.8828i			1.80090i	0.434955	+	0.900452i	$0.356764\pi$
$397$			35.8828i			1.80090i	−0.434955	+	0.900452i	$0.643236\pi$
$398$		−	13.3141i		−	0.667377i
$399$			6.99956i			0.350416i
$400$	11.7659	+	19.5129i	0.588296	+	0.975647i
$401$		−	6.73236i		−	0.336198i	−0.985770	−	0.168099i	$-0.946237\pi$
$401$		−	6.73236i		−	0.336198i	0.985770	−	0.168099i	$-0.0537629\pi$
$402$	18.5093			0.923158
$403$		−	0.680730i		−	0.0339096i
$404$	−41.1627			−2.04792
$405$	−1.94703	−	1.09958i	−0.0967487	−	0.0546385i
$406$	−19.6653			−0.975972
$407$	16.7971	−	10.5192i	0.832599	−	0.521420i
$408$		−	9.57494i		−	0.474030i
$409$			10.3100i			0.509795i	0.966968	+	0.254898i	$0.0820418\pi$
$409$			10.3100i			0.509795i	−0.966968	+	0.254898i	$0.917958\pi$
$410$	0.488352	+	0.275795i	0.0241180	+	0.0136205i
$411$	−3.69964			−0.182490
$412$	57.5862			2.83707
$413$	17.9018			0.880892
$414$	10.4440			0.513294
$415$	−16.2931	+	28.8503i	−0.799797	+	1.41621i
$416$	−0.148344			−0.00727319
$417$		−	7.46494i		−	0.365560i
$418$			29.3518i			1.43564i
$419$	−12.9809			−0.634159			−0.317080	−	0.948399i	$-0.602702\pi$
$419$	−12.9809			−0.634159			−0.317080	+	0.948399i	$0.602702\pi$
$420$	−15.2767	−	8.62748i	−0.745428	−	0.420978i
$421$		−	11.1021i		−	0.541082i	−0.962708	−	0.270541i	$-0.912797\pi$
$421$		−	11.1021i		−	0.541082i	0.962708	−	0.270541i	$-0.0872026\pi$
$422$	−47.7151			−2.32273
$423$		−	8.46641i		−	0.411651i
$424$		−	14.6383i		−	0.710897i
$425$	4.78913	+	7.94243i	0.232307	+	0.385265i
$426$		−	6.93303i		−	0.335906i
$427$	24.3284			1.17733
$428$			72.7384i			3.51594i
$429$		−	0.523310i		−	0.0252657i
$430$	1.65739	+	0.936003i	0.0799263	+	0.0451381i
$431$			9.56678i			0.460816i	0.973094	+	0.230408i	$0.0740060\pi$
$431$			9.56678i			0.460816i	−0.973094	+	0.230408i	$0.925994\pi$
$432$		−	4.55716i		−	0.219256i
$433$		−	35.9670i		−	1.72847i	−0.503092	−	0.864233i	$-0.667804\pi$
$433$		−	35.9670i		−	1.72847i	0.503092	−	0.864233i	$-0.332196\pi$
$434$	20.0603			0.962926
$435$	8.08972	+	4.56864i	0.387872	+	0.219049i
$436$		−	32.2689i		−	1.54540i
$437$			15.4453i			0.738851i
$438$	13.9768			0.667837
$439$			29.8373i			1.42406i	0.702151	+	0.712028i	$0.252223\pi$
$439$			29.8373i			1.42406i	−0.702151	+	0.712028i	$0.747777\pi$
$440$	−32.7466	−	18.4935i	−1.56113	−	0.881645i
$441$	−3.32245			−0.158212
$442$	−0.735296			−0.0349745
$443$		−	12.9518i		−	0.615357i	−0.951490	−	0.307678i	$-0.900448\pi$
$443$		−	12.9518i		−	0.615357i	0.951490	−	0.307678i	$-0.0995521\pi$
$444$	−13.2093	−	21.0926i	−0.626887	−	1.00101i
$445$	−1.69449	+	3.00045i	−0.0803267	+	0.142235i
$446$			34.6121i			1.63893i
$447$			22.9555i			1.08576i
$448$			13.1069i			0.619243i
$449$			18.9294i			0.893333i	0.894701	+	0.446666i	$0.147389\pi$
$449$			18.9294i			0.893333i	−0.894701	+	0.446666i	$0.852611\pi$
$450$	6.37225	+	10.5679i	0.300391	+	0.498177i
$451$	−0.331117			−0.0155917
$452$	16.6087			0.781207
$453$			14.7687i			0.693896i
$454$	11.9300			0.559902
$455$	−0.338674	+	0.599692i	−0.0158773	+	0.0281140i
$456$	18.8410			0.882309
$457$	−25.6766			−1.20110			−0.600550	−	0.799587i	$-0.705052\pi$
$457$	−25.6766			−1.20110			−0.600550	+	0.799587i	$0.705052\pi$
$458$	−6.14128			−0.286963
$459$		−	1.85492i		−	0.0865801i
$460$	−33.7099	−	19.0375i	−1.57173	−	0.887630i
$461$			14.9902i			0.698162i	0.937093	+	0.349081i	$0.113506\pi$
$461$			14.9902i			0.698162i	−0.937093	+	0.349081i	$0.886494\pi$
$462$	15.4213			0.717466
$463$	3.91544			0.181966			0.0909830	−	0.995852i	$-0.470999\pi$
$463$	3.91544			0.181966			0.0909830	+	0.995852i	$0.470999\pi$
$464$			18.9345i			0.879014i
$465$	−8.25222	−	4.66041i	−0.382687	−	0.216121i
$466$		−	19.8094i		−	0.917655i
$467$	−9.49418			−0.439338			−0.219669	−	0.975574i	$-0.570498\pi$
$467$	−9.49418			−0.439338			−0.219669	+	0.975574i	$0.570498\pi$
$468$	−0.657137			−0.0303762
$469$	14.3816			0.664081
$470$	−22.9766	+	40.6849i	−1.05983	+	1.87665i
$471$	2.19178			0.100992
$472$		−	48.1870i		−	2.21799i
$473$	−1.12376			−0.0516705
$474$	19.8434			0.911437
$475$	−15.6286	+	9.42374i	−0.717090	+	0.432391i
$476$		−	14.5540i		−	0.667082i
$477$		−	2.83582i		−	0.129843i
$478$		−	71.0659i		−	3.25048i
$479$		−	24.0544i		−	1.09907i	−0.835469	−	0.549537i	$-0.814804\pi$
$479$		−	24.0544i		−	1.09907i	0.835469	−	0.549537i	$-0.185196\pi$
$480$	−1.01560	+	1.79832i	−0.0463554	+	0.0820817i
$481$	−0.827995	+	0.518536i	−0.0377533	+	0.0236432i
$482$		−	67.7435i		−	3.08563i
$483$	8.11493			0.369242
$484$	−1.57072			−0.0713965
$485$	35.4701	+	20.0316i	1.61061	+	0.909588i
$486$		−	2.46809i		−	0.111955i
$487$	−4.04086			−0.183109			−0.0915544	−	0.995800i	$-0.529184\pi$
$487$	−4.04086			−0.183109			−0.0915544	+	0.995800i	$0.529184\pi$
$488$		−	65.4857i		−	2.96440i
$489$		−	15.4284i		−	0.697697i
$490$	15.9659	+	9.01667i	0.721265	+	0.407332i
$491$	−42.0127			−1.89601			−0.948003	−	0.318261i	$-0.896901\pi$
$491$	−42.0127			−1.89601			−0.948003	+	0.318261i	$0.896901\pi$
$492$			0.415794i			0.0187454i
$493$			7.70700i			0.347106i
$494$		−	1.44687i		−	0.0650977i
$495$	−6.34388	−	3.58269i	−0.285136	−	0.161030i
$496$		−	19.3149i		−	0.867263i
$497$		−	5.38693i		−	0.241637i
$498$	−36.5711			−1.63879
$499$		−	26.2454i		−	1.17491i	−0.809258	−	0.587454i	$-0.800130\pi$
$499$		−	26.2454i		−	1.17491i	0.809258	−	0.587454i	$-0.199870\pi$
$500$	−1.30414	−	45.7254i	−0.0583231	−	2.04490i
$501$			18.4894i			0.826045i
$502$		−	0.220207i		−	0.00982833i
$503$	−2.48182			−0.110659			−0.0553294	−	0.998468i	$-0.517621\pi$
$503$	−2.48182			−0.110659			−0.0553294	+	0.998468i	$0.517621\pi$
$504$		−	9.89898i		−	0.440936i
$505$	19.5883	+	11.0624i	0.871669	+	0.492272i
$506$	34.0290			1.51277
$507$		−	12.9742i		−	0.576205i
$508$		−	53.8547i		−	2.38942i
$509$	−0.310206			−0.0137496			−0.00687481	−	0.999976i	$-0.502188\pi$
$509$	−0.310206			−0.0137496			−0.00687481	+	0.999976i	$0.502188\pi$
$510$	−5.03398	+	8.91370i	−0.222908	+	0.394705i
$511$	10.8599			0.480413
$512$	42.8383			1.89320
$513$	3.64999			0.161151
$514$	0.484773			0.0213824
$515$	−27.4039	−	15.4763i	−1.20756	−	0.681965i
$516$			1.41114i			0.0621218i
$517$		−	27.5856i		−	1.21321i
$518$	−15.2807	−	24.4000i	−0.671393	−	1.07208i
$519$	−24.4913			−1.07505
$520$	1.61421	+	0.911621i	0.0707880	+	0.0399772i
$521$	15.5254			0.680182			0.340091	−	0.940393i	$-0.389542\pi$
$521$	15.5254			0.680182			0.340091	+	0.940393i	$0.389542\pi$
$522$			10.2547i			0.448835i
$523$	−0.260734			−0.0114011			−0.00570055	−	0.999984i	$-0.501815\pi$
$523$	−0.260734			−0.0114011			−0.00570055	+	0.999984i	$0.501815\pi$
$524$		−	3.19804i		−	0.139707i
$525$	4.95120	+	8.21122i	0.216088	+	0.358367i
$526$			21.5179i			0.938224i
$527$		−	7.86181i		−	0.342466i
$528$		−	14.8483i		−	0.646189i
$529$	−5.09345			−0.221455
$530$	−7.69601	+	13.6274i	−0.334293	+	0.591935i
$531$		−	9.33509i		−	0.405108i
$532$	28.6384			1.24163
$533$	0.0163221			0.000706989
$534$	−3.80343			−0.164590
$535$	19.5484	−	34.6145i	0.845151	−	1.49651i
$536$		−	38.7115i		−	1.67208i
$537$	21.5527			0.930066
$538$	66.1794			2.85320
$539$	−10.8253			−0.466280
$540$	−4.49889	+	7.96621i	−0.193601	+	0.342811i
$541$			24.9793i			1.07394i	0.843600	+	0.536971i	$0.180432\pi$
$541$			24.9793i			1.07394i	−0.843600	+	0.536971i	$0.819568\pi$
$542$	−3.06680			−0.131730
$543$			23.2257i			0.996709i
$544$	−1.71324			−0.0734547
$545$	−8.67224	+	15.3560i	−0.371478	+	0.657778i
$546$	−0.760181			−0.0325327
$547$	39.0492			1.66962			0.834811	−	0.550536i	$-0.185577\pi$
$547$	39.0492			1.66962			0.834811	+	0.550536i	$0.185577\pi$
$548$			15.1370i			0.646619i
$549$		−	12.6863i		−	0.541438i
$550$	20.7623	+	34.4328i	0.885307	+	1.46822i
$551$	−15.1653			−0.646066
$552$		−	21.8433i		−	0.929711i
$553$	15.4182			0.655649
$554$	−10.0732			−0.427970
$555$	0.617391	+	13.5875i	0.0262068	+	0.576755i
$556$	−30.5426			−1.29529
$557$	−13.1039			−0.555230			−0.277615	−	0.960692i	$-0.589544\pi$
$557$	−13.1039			−0.555230			−0.277615	+	0.960692i	$0.589544\pi$
$558$		−	10.4607i		−	0.442835i
$559$	0.0553946			0.00234294
$560$	−9.60946	+	17.0155i	−0.406074	+	0.719038i
$561$		−	6.04376i		−	0.255168i
$562$			30.8929i			1.30314i
$563$	−5.39617			−0.227422			−0.113711	−	0.993514i	$-0.536274\pi$
$563$	−5.39617			−0.227422			−0.113711	+	0.993514i	$0.536274\pi$
$564$	−34.6400			−1.45861
$565$	−7.90368	−	4.46357i	−0.332510	−	0.187784i
$566$	−49.1772			−2.06707
$567$		−	1.91769i		−	0.0805355i
$568$	−14.5002			−0.608414
$569$			34.8653i			1.46163i	0.682575	+	0.730815i	$0.260860\pi$
$569$			34.8653i			1.46163i	−0.682575	+	0.730815i	$0.739140\pi$
$570$	−17.5398	−	9.90555i	−0.734662	−	0.414898i
$571$	0.312308			0.0130697			0.00653484	−	0.999979i	$-0.497920\pi$
$571$	0.312308			0.0130697			0.00653484	+	0.999979i	$0.497920\pi$
$572$	−2.14111			−0.0895241
$573$	8.14176			0.340127
$574$			0.480993i			0.0200763i
$575$	10.9254	+	18.1190i	0.455621	+	0.755616i
$576$	6.83473			0.284780
$577$	4.78834			0.199341			0.0996706	−	0.995020i	$-0.468221\pi$
$577$	4.78834			0.199341			0.0996706	+	0.995020i	$0.468221\pi$
$578$	33.4655			1.39198
$579$		−	14.4396i		−	0.600091i
$580$	18.6924	−	33.0988i	0.776161	−	1.37435i
$581$	−28.4156			−1.17888
$582$			44.9625i			1.86376i
$583$		−	9.23976i		−	0.382672i
$584$		−	29.2320i		−	1.20963i
$585$	0.312716	+	0.176605i	0.0129292	+	0.00730172i
$586$			18.5850i			0.767739i
$587$	13.6113			0.561799			0.280899	−	0.959737i	$-0.409367\pi$
$587$	13.6113			0.561799			0.280899	+	0.959737i	$0.409367\pi$
$588$			13.5937i			0.560595i
$589$	15.4700			0.637429
$590$	−25.3341	+	44.8593i	−1.04299	+	1.84683i
$591$	−11.9277			−0.490639
$592$	−23.4933	+	14.7128i	−0.965570	+	0.604693i
$593$		−	36.7432i		−	1.50886i	−0.656378	−	0.754432i	$-0.727912\pi$
$593$		−	36.7432i		−	1.50886i	0.656378	−	0.754432i	$-0.272088\pi$
$594$		−	8.04162i		−	0.329952i
$595$	−3.91138	+	6.92590i	−0.160351	+	0.283934i
$596$	93.9218			3.84719
$597$	−5.39451			−0.220783
$598$	−1.67743			−0.0685951
$599$	−6.17128			−0.252152			−0.126076	−	0.992021i	$-0.540238\pi$
$599$	−6.17128			−0.252152			−0.126076	+	0.992021i	$0.540238\pi$
$600$	22.1024	−	13.3273i	0.902329	−	0.544086i
$601$	−8.93177			−0.364334			−0.182167	−	0.983268i	$-0.558311\pi$
$601$	−8.93177			−0.364334			−0.182167	+	0.983268i	$0.558311\pi$
$602$			1.63241i			0.0665322i
$603$		−	7.49943i		−	0.305400i
$604$	60.4258			2.45869
$605$	0.747469	+	0.422130i	0.0303889	+	0.0171620i
$606$			24.8305i			1.00867i
$607$	32.6682			1.32596			0.662981	−	0.748637i	$-0.269291\pi$
$607$	32.6682			1.32596			0.662981	+	0.748637i	$0.269291\pi$
$608$		−	3.37121i		−	0.136721i
$609$			7.96782i			0.322872i
$610$	−34.4288	+	60.9633i	−1.39398	+	2.46833i
$611$			1.35980i			0.0550118i
$612$	−7.58933			−0.306780
$613$			25.8793i			1.04525i	0.852562	+	0.522627i	$0.175048\pi$
$613$			25.8793i			1.04525i	−0.852562	+	0.522627i	$0.824952\pi$
$614$			54.3424i			2.19308i
$615$	0.111744	−	0.197866i	0.00450597	−	0.00797874i
$616$		−	32.2532i		−	1.29952i
$617$		−	18.3543i		−	0.738917i	−0.929247	−	0.369459i	$-0.879543\pi$
$617$		−	18.3543i		−	0.738917i	0.929247	−	0.369459i	$-0.120457\pi$
$618$		−	34.7377i		−	1.39735i
$619$	30.1957			1.21367			0.606835	−	0.794828i	$-0.292439\pi$
$619$	30.1957			1.21367			0.606835	+	0.794828i	$0.292439\pi$
$620$	−19.0679	+	33.7637i	−0.765785	+	1.35598i
$621$		−	4.23161i		−	0.169809i
$622$			45.2178i			1.81307i
$623$	−2.95524			−0.118399
$624$			0.731932i			0.0293007i
$625$	−11.6681	+	22.1101i	−0.466722	+	0.884404i
$626$	−40.2404			−1.60833
$627$	11.8925			0.474942
$628$		−	8.96760i		−	0.357846i
$629$	−9.56259	+	5.98862i	−0.381285	+	0.238782i
$630$	−5.20434	+	9.21537i	−0.207346	+	0.367149i
$631$			25.2935i			1.00692i	0.864020	+	0.503458i	$0.167939\pi$
$631$			25.2935i			1.00692i	−0.864020	+	0.503458i	$0.832061\pi$
$632$		−	41.5017i		−	1.65085i
$633$			19.3328i			0.768410i
$634$			13.6439i			0.541870i
$635$	−14.4734	+	25.6282i	−0.574360	+	1.01702i
$636$	−11.6026			−0.460075
$637$	0.533625			0.0211430
$638$			33.4121i			1.32280i
$639$	−2.80907			−0.111125
$640$	−36.4406	−	20.5797i	−1.44044	−	0.813483i
$641$	26.9540			1.06462			0.532309	−	0.846550i	$-0.321324\pi$
$641$	26.9540			1.06462			0.532309	+	0.846550i	$0.321324\pi$
$642$	43.8779			1.73172
$643$	42.5227			1.67693			0.838466	−	0.544954i	$-0.183453\pi$
$643$	42.5227			1.67693			0.838466	+	0.544954i	$0.183453\pi$
$644$		−	33.2020i		−	1.30834i
$645$	0.379242	−	0.671526i	0.0149326	−	0.0264413i
$646$		−	16.7100i		−	0.657447i
$647$	−28.7393			−1.12986			−0.564929	−	0.825139i	$-0.691097\pi$
$647$	−28.7393			−1.12986			−0.564929	+	0.825139i	$0.691097\pi$
$648$	−5.16192			−0.202779
$649$		−	30.4159i		−	1.19393i
$650$	−1.02346	−	1.69733i	−0.0401433	−	0.0665748i
$651$		−	8.12787i		−	0.318556i
$652$	−63.1249			−2.47216
$653$	−9.09821			−0.356040			−0.178020	−	0.984027i	$-0.556969\pi$
$653$	−9.09821			−0.356040			−0.178020	+	0.984027i	$0.556969\pi$
$654$	−19.4655			−0.761162
$655$	−0.859472	+	1.52187i	−0.0335824	+	0.0594645i
$656$	0.463120			0.0180818
$657$		−	5.66300i		−	0.220935i
$658$	−40.0719			−1.56216
$659$	−32.0286			−1.24766			−0.623829	−	0.781561i	$-0.714424\pi$
$659$	−32.0286			−1.24766			−0.623829	+	0.781561i	$0.714424\pi$
$660$	−14.6584	+	25.9558i	−0.570579	+	1.01033i
$661$			6.98256i			0.271590i	0.990737	+	0.135795i	$0.0433589\pi$
$661$			6.98256i			0.271590i	−0.990737	+	0.135795i	$0.956641\pi$
$662$			35.0033i			1.36044i
$663$			0.297921i			0.0115703i
$664$			76.4873i			2.96828i
$665$	−13.6284	−	7.69656i	−0.528485	−	0.298460i
$666$	−12.7236	+	7.96825i	−0.493031	+	0.308763i
$667$			17.5819i			0.680775i
$668$	75.6487			2.92694
$669$	14.0238			0.542193
$670$	−20.3524	+	36.0381i	−0.786281	+	1.39227i
$671$		−	41.3349i		−	1.59572i
$672$	−1.77122			−0.0683264
$673$		−	16.4223i		−	0.633034i	−0.948587	−	0.316517i	$-0.897487\pi$
$673$		−	16.4223i		−	0.633034i	0.948587	−	0.316517i	$-0.102513\pi$
$674$		−	78.9793i		−	3.04217i
$675$	4.28183	−	2.58185i	0.164808	−	0.0993756i
$676$	−53.0835			−2.04167
$677$			1.87980i			0.0722466i	0.999347	+	0.0361233i	$0.0115009\pi$
$677$			1.87980i			0.0722466i	−0.999347	+	0.0361233i	$0.988499\pi$
$678$		−	10.0188i		−	0.384771i
$679$			34.9356i			1.34071i
$680$	18.6427	+	10.5284i	0.714915	+	0.403746i
$681$		−	4.83369i		−	0.185227i
$682$		−	34.0833i		−	1.30512i
$683$	−8.35053			−0.319524			−0.159762	−	0.987156i	$-0.551073\pi$
$683$	−8.35053			−0.319524			−0.159762	+	0.987156i	$0.551073\pi$
$684$		−	14.9338i		−	0.571008i
$685$	4.06805	−	7.20332i	0.155432	−	0.275225i
$686$			48.8566i			1.86535i
$687$			2.48827i			0.0949335i
$688$	1.57175			0.0599225
$689$			0.455465i			0.0173518i
$690$	−11.4840	+	20.3348i	−0.437188	+	0.774132i
$691$	4.98372			0.189590			0.0947948	−	0.995497i	$-0.469781\pi$
$691$	4.98372			0.189590			0.0947948	+	0.995497i	$0.469781\pi$
$692$			100.205i			3.80924i
$693$		−	6.24829i		−	0.237353i
$694$	49.0977			1.86372
$695$	14.5345	+	8.20829i	0.551324	+	0.311358i
$696$	21.4473			0.812957
$697$	0.188505			0.00714015
$698$	50.1525			1.89830
$699$	−8.02623			−0.303580
$700$	33.5959	−	20.2577i	1.26981	−	0.765668i
$701$			31.2957i			1.18202i	0.806664	+	0.591011i	$0.201271\pi$
$701$			31.2957i			1.18202i	−0.806664	+	0.591011i	$0.798729\pi$
$702$			0.396404i			0.0149613i
$703$	−11.7840	−	18.8167i	−0.444443	−	0.709684i
$704$	22.2692			0.839300
$705$	16.4844	+	9.30949i	0.620837	+	0.350616i
$706$	12.7637			0.480366
$707$			19.2932i			0.725594i
$708$	−38.1942			−1.43543
$709$			27.0071i			1.01427i	0.861866	+	0.507137i	$0.169296\pi$
$709$			27.0071i			1.01427i	−0.861866	+	0.507137i	$0.830704\pi$
$710$	13.4988	+	7.62341i	0.506601	+	0.286101i
$711$		−	8.03998i		−	0.301523i
$712$			7.95473i			0.298116i
$713$		−	17.9351i		−	0.671675i
$714$	−8.77939			−0.328561
$715$	1.01890	+	0.575421i	0.0381047	+	0.0215195i
$716$		−	88.1819i		−	3.29551i
$717$	−28.7939			−1.07533
$718$	42.0565			1.56954
$719$	−20.2055			−0.753539			−0.376770	−	0.926307i	$-0.622965\pi$
$719$	−20.2055			−0.753539			−0.376770	+	0.926307i	$0.622965\pi$
$720$	8.87292	+	5.01095i	0.330674	+	0.186747i
$721$		−	26.9910i		−	1.00520i
$722$	−14.0128			−0.521501
$723$	−27.4478			−1.02079
$724$	95.0270			3.53165
$725$	−17.7906	+	10.7274i	−0.660725	+	0.398404i
$726$			0.947505i			0.0351652i
$727$	−32.6455			−1.21075			−0.605377	−	0.795939i	$-0.706977\pi$
$727$	−32.6455			−1.21075			−0.605377	+	0.795939i	$0.706977\pi$
$728$			1.58989i			0.0589253i
$729$	−1.00000			−0.0370370
$730$	−15.3686	+	27.2132i	−0.568816	+	1.00721i
$731$	0.639757			0.0236623
$732$	−51.9055			−1.91848
$733$		−	45.9219i		−	1.69617i	−0.529863	−	0.848083i	$-0.677757\pi$
$733$		−	45.9219i		−	1.69617i	0.529863	−	0.848083i	$-0.322243\pi$
$734$			15.5539i			0.574106i
$735$	3.65330	−	6.46892i	0.134754	−	0.238610i
$736$	−3.90841			−0.144066
$737$		−	24.4349i		−	0.900071i
$738$	0.250819			0.00923277
$739$	−24.0511			−0.884735			−0.442368	−	0.896834i	$-0.645861\pi$
$739$	−24.0511			−0.884735			−0.442368	+	0.896834i	$0.645861\pi$
$740$	55.5926	−	2.52603i	2.04362	−	0.0928588i
$741$	−0.586231			−0.0215357
$742$	−13.4220			−0.492738
$743$			48.7620i			1.78890i	0.447164	+	0.894452i	$0.352434\pi$
$743$			48.7620i			1.78890i	−0.447164	+	0.894452i	$0.647566\pi$
$744$	−21.8781			−0.802090
$745$	−44.6951	−	25.2414i	−1.63750	−	0.924774i
$746$		−	65.5092i		−	2.39846i
$747$			14.8176i			0.542147i
$748$	−24.7278			−0.904139
$749$	34.0929			1.24573
$750$	−27.5829	+	0.786697i	−1.00718	+	0.0287261i
$751$	22.4964			0.820904			0.410452	−	0.911882i	$-0.365371\pi$
$751$	22.4964			0.820904			0.410452	+	0.911882i	$0.365371\pi$
$752$			38.5828i			1.40697i
$753$	−0.0892217			−0.00325142
$754$		−	1.64702i		−	0.0599809i
$755$	−28.7552	−	16.2394i	−1.04651	−	0.591012i
$756$	−7.84617			−0.285363
$757$	17.8264			0.647912			0.323956	−	0.946072i	$-0.394987\pi$
$757$	17.8264			0.647912			0.323956	+	0.946072i	$0.394987\pi$
$758$	46.3498			1.68350
$759$		−	13.7876i		−	0.500458i
$760$	−20.7171	+	36.6839i	−0.751489	+	1.33067i
$761$	−39.1998			−1.42099			−0.710496	−	0.703701i	$-0.751529\pi$
$761$	−39.1998			−1.42099			−0.710496	+	0.703701i	$0.751529\pi$
$762$	−32.4867			−1.17687
$763$	−15.1246			−0.547548
$764$		−	33.3117i		−	1.20518i
$765$	3.61158	+	2.03963i	0.130577	+	0.0737429i
$766$	56.4221			2.03861
$767$			1.49932i			0.0541374i
$768$		−	32.5232i		−	1.17358i
$769$		−	3.06875i		−	0.110662i	−0.998468	−	0.0553309i	$-0.982379\pi$
$769$		−	3.06875i		−	0.110662i	0.998468	−	0.0553309i	$-0.0176214\pi$
$770$	−16.9570	+	30.0258i	−0.611087	+	1.08206i
$771$		−	0.196416i		−	0.00707376i
$772$	−59.0793			−2.12631
$773$			18.5199i			0.666114i	0.942907	+	0.333057i	$0.108080\pi$
$773$			18.5199i			0.666114i	−0.942907	+	0.333057i	$0.891920\pi$
$774$	0.851239			0.0305971
$775$	18.1479	−	10.9428i	0.651892	−	0.393078i
$776$	94.0375			3.37575
$777$	−9.88621	+	6.19129i	−0.354666	+	0.222111i
$778$		−	39.7037i		−	1.42345i
$779$			0.370929i			0.0132899i
$780$	0.722573	−	1.27947i	0.0258723	−	0.0458122i
$781$	−9.15260			−0.327506
$782$	−19.3728			−0.692768
$783$	4.15490			0.148484
$784$	15.1409			0.540748
$785$	−2.41004	+	4.26746i	−0.0860178	+	0.152312i
$786$	−1.92915			−0.0688106
$787$		−	6.49476i		−	0.231513i	−0.993278	−	0.115757i	$-0.963071\pi$
$787$		−	6.49476i		−	0.231513i	0.993278	−	0.115757i	$-0.0369293\pi$
$788$			48.8016i			1.73849i
$789$	8.71844			0.310385
$790$	−21.8194	+	38.6357i	−0.776298	+	1.37460i
$791$		−	7.78459i		−	0.276788i
$792$	−16.8188			−0.597629
$793$			2.03757i			0.0723561i
$794$		−	88.5619i		−	3.14294i
$795$	5.52142	+	3.11820i	0.195825	+	0.110591i
$796$			22.0715i			0.782302i
$797$	−32.6929			−1.15804			−0.579022	−	0.815312i	$-0.696565\pi$
$797$	−32.6929			−1.15804			−0.579022	+	0.815312i	$0.696565\pi$
$798$		−	17.2755i		−	0.611547i
$799$			15.7045i			0.555585i
$800$	−2.38466	−	3.95479i	−0.0843104	−	0.139823i
$801$			1.54104i			0.0544500i
$802$			16.6161i			0.586734i
$803$		−	18.4514i		−	0.651135i
$804$	−30.6837			−1.08213
$805$	−8.92300	+	15.8000i	−0.314495	+	0.556878i
$806$			1.68010i			0.0591791i
$807$		−	26.8140i		−	0.943898i
$808$	51.9321			1.82697
$809$			19.6653i			0.691396i	0.938346	+	0.345698i	$0.112358\pi$
$809$			19.6653i			0.691396i	−0.938346	+	0.345698i	$0.887642\pi$
$810$	4.80544	+	2.71386i	0.168846	+	0.0953552i
$811$	37.1956			1.30611			0.653057	−	0.757309i	$-0.273486\pi$
$811$	37.1956			1.30611			0.653057	+	0.757309i	$0.273486\pi$
$812$	32.6001			1.14404
$813$			1.24258i			0.0435791i
$814$	−41.4566	+	25.9624i	−1.45305	+	0.909983i
$815$	30.0396	+	16.9648i	1.05224	+	0.594250i
$816$			8.45315i			0.295919i
$817$			1.25887i			0.0440424i
$818$		−	25.4459i		−	0.889696i
$819$			0.308004i			0.0107625i
$820$	−0.809563	−	0.457198i	−0.0282712	−	0.0159660i
$821$	37.0614			1.29345			0.646727	−	0.762722i	$-0.276137\pi$
$821$	37.0614			1.29345			0.646727	+	0.762722i	$0.276137\pi$
$822$	9.13105			0.318482
$823$			12.2101i			0.425619i	0.977094	+	0.212809i	$0.0682613\pi$
$823$			12.2101i			0.425619i	−0.977094	+	0.212809i	$0.931739\pi$
$824$	−72.6526			−2.53097
$825$	13.9512	−	8.41229i	0.485718	−	0.292878i
$826$	−44.1833			−1.53733
$827$	51.8534			1.80312			0.901560	−	0.432655i	$-0.142423\pi$
$827$	51.8534			1.80312			0.901560	+	0.432655i	$0.142423\pi$
$828$	−17.3135			−0.601686
$829$		−	12.1497i		−	0.421975i	−0.977489	−	0.210988i	$-0.932332\pi$
$829$		−	12.1497i		−	0.421975i	0.977489	−	0.210988i	$-0.0676680\pi$
$830$	40.2128	−	71.2051i	1.39581	−	2.47157i
$831$			4.08138i			0.141582i
$832$	−1.09774			−0.0380572
$833$	6.16288			0.213531
$834$			18.4242i			0.637976i
$835$	−35.9994	−	20.3305i	−1.24581	−	0.703567i
$836$		−	48.6579i		−	1.68287i
$837$	−4.23836			−0.146499
$838$	32.0381			1.10674
$839$	24.2373			0.836764			0.418382	−	0.908271i	$-0.362597\pi$
$839$	24.2373			0.836764			0.418382	+	0.908271i	$0.362597\pi$
$840$	19.2736	+	10.8847i	0.665003	+	0.375558i
$841$	11.7368			0.404717
$842$			27.4009i			0.944298i
$843$	12.5169			0.431106
$844$	79.0995			2.72272
$845$	25.2612	+	14.2662i	0.869011	+	0.490771i
$846$			20.8959i			0.718415i
$847$			0.736206i			0.0252963i
$848$			12.9233i			0.443787i
$849$			19.9252i			0.683831i
$850$	−11.8200	−	19.6026i	−0.405422	−	0.672365i
$851$	−21.8151	+	13.6618i	−0.747811	+	0.468320i
$852$			11.4932i			0.393750i
$853$	−20.6067			−0.705559			−0.352780	−	0.935706i	$-0.614763\pi$
$853$	−20.6067			−0.705559			−0.352780	+	0.935706i	$0.614763\pi$
$854$	−60.0447			−2.05469
$855$	−4.01345	+	7.10664i	−0.137257	+	0.243042i
$856$		−	91.7691i		−	3.13660i
$857$	27.5193			0.940041			0.470021	−	0.882655i	$-0.344246\pi$
$857$	27.5193			0.940041			0.470021	+	0.882655i	$0.344246\pi$
$858$			1.29158i			0.0440937i
$859$		−	20.7359i		−	0.707499i	−0.935340	−	0.353749i	$-0.884907\pi$
$859$		−	20.7359i		−	0.707499i	0.935340	−	0.353749i	$-0.115093\pi$
$860$	−2.74753	−	1.55166i	−0.0936899	−	0.0529110i
$861$	0.194885			0.00664166
$862$		−	23.6117i		−	0.804217i
$863$		−	27.0552i		−	0.920970i	−0.887667	−	0.460485i	$-0.847676\pi$
$863$		−	27.0552i		−	0.920970i	0.887667	−	0.460485i	$-0.152324\pi$
$864$			0.923622i			0.0314223i
$865$	26.9301	−	47.6853i	0.915651	−	1.62135i
$866$			88.7699i			3.01652i
$867$		−	13.5593i		−	0.460497i
$868$	−33.2549			−1.12875
$869$		−	26.1961i		−	0.888643i
$870$	−19.9661	−	11.2758i	−0.676916	−	0.382286i
$871$			1.20450i			0.0408128i
$872$			40.7115i			1.37866i
$873$	18.2175			0.616570
$874$		−	38.1205i		−	1.28944i
$875$	−21.4317	+	0.611259i	−0.724525	+	0.0206643i
$876$	−23.1700			−0.782840
$877$		−	10.4699i		−	0.353542i	−0.984252	−	0.176771i	$-0.943435\pi$
$877$		−	10.4699i		−	0.353542i	0.984252	−	0.176771i	$-0.0565652\pi$
$878$		−	73.6411i		−	2.48527i
$879$	7.53011			0.253984
$880$	28.9101	+	16.3269i	0.974558	+	0.550378i
$881$	−3.29840			−0.111126			−0.0555630	−	0.998455i	$-0.517695\pi$
$881$	−3.29840			−0.111126			−0.0555630	+	0.998455i	$0.517695\pi$
$882$	8.20012			0.276112
$883$	−13.9081			−0.468046			−0.234023	−	0.972231i	$-0.575189\pi$
$883$	−13.9081			−0.468046			−0.234023	+	0.972231i	$0.575189\pi$
$884$	1.21893			0.0409972
$885$	18.1757	+	10.2647i	0.610970	+	0.345043i
$886$			31.9661i			1.07392i
$887$		−	3.56498i		−	0.119700i	−0.998207	−	0.0598502i	$-0.980938\pi$
$887$		−	3.56498i		−	0.119700i	0.998207	−	0.0598502i	$-0.0190623\pi$
$888$	16.6653	+	26.6111i	0.559251	+	0.893009i
$889$	−25.2420			−0.846590
$890$	4.18216	−	7.40538i	0.140186	−	0.248229i
$891$	−3.25824			−0.109155
$892$		−	57.3781i		−	1.92116i
$893$	−30.9023			−1.03411
$894$		−	56.6563i		−	1.89487i
$895$	−23.6988	+	41.9637i	−0.792165	+	1.40269i
$896$		−	35.8915i		−	1.19905i
$897$			0.679646i			0.0226927i
$898$		−	46.7194i		−	1.55905i
$899$	17.6100			0.587325
$900$	−10.5636	−	17.5189i	−0.352119	−	0.583965i
$901$			5.26021i			0.175243i
$902$	0.817227			0.0272107
$903$	0.661408			0.0220103
$904$	−20.9540			−0.696921
$905$	−45.2211	−	25.5385i	−1.50320	−	0.848927i
$906$		−	36.4506i		−	1.21099i
$907$	−53.3011			−1.76984			−0.884918	−	0.465747i	$-0.845786\pi$
$907$	−53.3011			−1.76984			−0.884918	+	0.465747i	$0.845786\pi$
$908$	−19.7769			−0.656319
$909$	10.0606			0.333690
$910$	0.835878	−	1.48009i	0.0277091	−	0.0490647i
$911$		−	16.6865i		−	0.552849i	−0.961036	−	0.276425i	$-0.910850\pi$
$911$		−	16.6865i		−	0.552849i	0.961036	−	0.276425i	$-0.0891496\pi$
$912$	−16.6336			−0.550793
$913$			48.2792i			1.59781i
$914$	63.3721			2.09616
$915$	24.7006	+	13.9496i	0.816577	+	0.461159i
$916$	10.1807			0.336379
$917$	−1.49894			−0.0494994
$918$			4.57810i			0.151100i
$919$			19.3345i			0.637786i	0.947791	+	0.318893i	$0.103311\pi$
$919$			19.3345i			0.637786i	−0.947791	+	0.318893i	$0.896689\pi$
$920$	42.5295	+	24.0184i	1.40216	+	0.791862i
$921$	22.0180			0.725518
$922$		−	36.9971i		−	1.21843i
$923$	0.451169			0.0148504
$924$	−25.5647			−0.841016
$925$	−27.1341	−	13.7384i	−0.892162	−	0.451715i
$926$	−9.66366			−0.317567
$927$	−14.0747			−0.462275
$928$		−	3.83756i		−	0.125974i
$929$	−18.4972			−0.606873			−0.303436	−	0.952852i	$-0.598134\pi$
$929$	−18.4972			−0.606873			−0.303436	+	0.952852i	$0.598134\pi$
$930$	20.3672	+	11.5023i	0.667867	+	0.377176i
$931$			12.1269i			0.397444i
$932$			32.8390i			1.07568i
$933$	18.3210			0.599802
$934$	23.4325			0.766734
$935$	11.7674	+	6.64559i	0.384834	+	0.217334i
$936$	0.829065			0.0270988
$937$		−	42.2346i		−	1.37974i	−0.723932	−	0.689871i	$-0.757667\pi$
$937$		−	42.2346i		−	1.37974i	0.723932	−	0.689871i	$-0.242333\pi$
$938$	−35.4951			−1.15896
$939$			16.3043i			0.532070i
$940$	38.0894	−	67.4452i	1.24234	−	2.19982i
$941$	−7.45305			−0.242963			−0.121481	−	0.992594i	$-0.538764\pi$
$941$	−7.45305			−0.242963			−0.121481	+	0.992594i	$0.538764\pi$
$942$	−5.40951			−0.176251
$943$	0.430036			0.0140039
$944$			42.5415i			1.38461i
$945$	3.73381	+	2.10865i	0.121461	+	0.0685945i
$946$	2.77354			0.0901754
$947$	6.47683			0.210469			0.105234	−	0.994447i	$-0.466441\pi$
$947$	6.47683			0.210469			0.105234	+	0.994447i	$0.466441\pi$
$948$	−32.8953			−1.06839
$949$			0.909543i			0.0295250i
$950$	38.5728	−	23.2586i	1.25147	−	0.754610i
$951$	5.52814			0.179262
$952$			18.3618i			0.595109i
$953$		−	13.3359i		−	0.431992i	−0.976394	−	0.215996i	$-0.930700\pi$
$953$		−	13.3359i		−	0.431992i	0.976394	−	0.215996i	$-0.0692998\pi$
$954$			6.99905i			0.226603i
$955$	−8.95250	+	15.8523i	−0.289696	+	0.512967i
$956$			117.809i			3.81022i
$957$	13.5376			0.437610
$958$			59.3684i			1.91811i
$959$	7.09478			0.229102
$960$	−7.51532	+	13.3074i	−0.242556	+	0.429495i
$961$	13.0363			0.420526
$962$	2.04357	−	1.27979i	0.0658872	−	0.0412622i
$963$		−	17.7781i		−	0.572891i
$964$			112.302i			3.61699i
$965$	28.1144	+	15.8775i	0.905035	+	0.511115i
$966$	−20.0284			−0.644403
$967$	12.5830			0.404643			0.202321	−	0.979319i	$-0.435151\pi$
$967$	12.5830			0.404643			0.202321	+	0.979319i	$0.435151\pi$
$968$	1.98167			0.0636934
$969$	−6.77043			−0.217498
$970$	−87.5433	−	49.4398i	−2.81085	−	1.58742i
$971$	10.0748			0.323315			0.161658	−	0.986847i	$-0.448316\pi$
$971$	10.0748			0.323315			0.161658	+	0.986847i	$0.448316\pi$
$972$			4.09146i			0.131234i
$973$			14.3155i			0.458933i
$974$	9.97320			0.319562
$975$	−0.687711	+	0.414676i	−0.0220244	+	0.0132803i
$976$			57.8134i			1.85056i
$977$	46.4552			1.48623			0.743117	−	0.669162i	$-0.233347\pi$
$977$	46.4552			1.48623			0.743117	+	0.669162i	$0.233347\pi$
$978$			38.0787i			1.21762i
$979$			5.02107i			0.160474i
$980$	−26.4674	−	14.9473i	−0.845469	−	0.477475i
$981$			7.88688i			0.251809i
$982$	103.691			3.30892
$983$			14.8732i			0.474382i	0.971463	+	0.237191i	$0.0762268\pi$
$983$			14.8732i			0.474382i	−0.971463	+	0.237191i	$0.923773\pi$
$984$		−	0.524579i		−	0.0167230i
$985$	13.1154	−	23.2235i	0.417891	−	0.739963i
$986$		−	19.0216i		−	0.605770i
$987$			16.2360i			0.516797i
$988$			2.39854i			0.0763078i
$989$	1.45947			0.0464086
$990$	15.6573	+	8.84239i	0.497621	+	0.281030i
$991$			2.13548i			0.0678358i	0.999425	+	0.0339179i	$0.0107985\pi$
$991$			2.13548i			0.0678358i	−0.999425	+	0.0339179i	$0.989202\pi$
$992$			3.91464i			0.124290i
$993$	14.1823			0.450063
$994$			13.2954i			0.421705i
$995$	5.93169	−	10.5033i	0.188047	−	0.332976i
$996$	60.6257			1.92100
$997$	−28.7022			−0.909007			−0.454504	−	0.890745i	$-0.650183\pi$
$997$	−28.7022			−0.909007			−0.454504	+	0.890745i	$0.650183\pi$
$998$			64.7761i			2.05045i
$999$	3.22851	+	5.15526i	0.102146	+	0.163105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.g.a.184.6	yes	40
3.2	odd	2		1665.2.g.e.739.36		40
5.4	even	2	inner	555.2.g.a.184.35	yes	40
15.14	odd	2		1665.2.g.e.739.5		40
37.36	even	2	inner	555.2.g.a.184.36	yes	40
111.110	odd	2		1665.2.g.e.739.6		40
185.184	even	2	inner	555.2.g.a.184.5	✓	40
555.554	odd	2		1665.2.g.e.739.35		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.g.a.184.5	✓	40	185.184	even	2	inner
555.2.g.a.184.6	yes	40	1.1	even	1	trivial
555.2.g.a.184.35	yes	40	5.4	even	2	inner
555.2.g.a.184.36	yes	40	37.36	even	2	inner
1665.2.g.e.739.5		40	15.14	odd	2
1665.2.g.e.739.6		40	111.110	odd	2
1665.2.g.e.739.35		40	555.554	odd	2
1665.2.g.e.739.36		40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.46809 q^{2} +1.00000i q^{3} +4.09146 q^{4} +(-1.94703 - 1.09958i) q^{5} -2.46809i q^{6} -1.91769i q^{7} -5.16192 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.46809 q^{2} +1.00000i q^{3} +4.09146 q^{4} +(-1.94703 - 1.09958i) q^{5} -2.46809i q^{6} -1.91769i q^{7} -5.16192 q^{8} -1.00000 q^{9} +(4.80544 + 2.71386i) q^{10} -3.25824 q^{11} +4.09146i q^{12} +0.160612 q^{13} +4.73304i q^{14} +(1.09958 - 1.94703i) q^{15} +4.55716 q^{16} +1.85492 q^{17} +2.46809 q^{18} +3.64999i q^{19} +(-7.96621 - 4.49889i) q^{20} +1.91769 q^{21} +8.04162 q^{22} +4.23161 q^{23} -5.16192i q^{24} +(2.58185 + 4.28183i) q^{25} -0.396404 q^{26} -1.00000i q^{27} -7.84617i q^{28} +4.15490i q^{29} +(-2.71386 + 4.80544i) q^{30} -4.23836i q^{31} -0.923622 q^{32} -3.25824i q^{33} -4.57810 q^{34} +(-2.10865 + 3.73381i) q^{35} -4.09146 q^{36} +(-5.15526 + 3.22851i) q^{37} -9.00850i q^{38} +0.160612i q^{39} +(10.0504 + 5.67594i) q^{40} +0.101625 q^{41} -4.73304 q^{42} +0.344898 q^{43} -13.3310 q^{44} +(1.94703 + 1.09958i) q^{45} -10.4440 q^{46} +8.46641i q^{47} +4.55716i q^{48} +3.32245 q^{49} +(-6.37225 - 10.5679i) q^{50} +1.85492i q^{51} +0.657137 q^{52} +2.83582i q^{53} +2.46809i q^{54} +(6.34388 + 3.58269i) q^{55} +9.89898i q^{56} -3.64999 q^{57} -10.2547i q^{58} +9.33509i q^{59} +(4.49889 - 7.96621i) q^{60} +12.6863i q^{61} +10.4607i q^{62} +1.91769i q^{63} -6.83473 q^{64} +(-0.312716 - 0.176605i) q^{65} +8.04162i q^{66} +7.49943i q^{67} +7.58933 q^{68} +4.23161i q^{69} +(5.20434 - 9.21537i) q^{70} +2.80907 q^{71} +5.16192 q^{72} +5.66300i q^{73} +(12.7236 - 7.96825i) q^{74} +(-4.28183 + 2.58185i) q^{75} +14.9338i q^{76} +6.24829i q^{77} -0.396404i q^{78} +8.03998i q^{79} +(-8.87292 - 5.01095i) q^{80} +1.00000 q^{81} -0.250819 q^{82} -14.8176i q^{83} +7.84617 q^{84} +(-3.61158 - 2.03963i) q^{85} -0.851239 q^{86} -4.15490 q^{87} +16.8188 q^{88} -1.54104i q^{89} +(-4.80544 - 2.71386i) q^{90} -0.308004i q^{91} +17.3135 q^{92} +4.23836 q^{93} -20.8959i q^{94} +(4.01345 - 7.10664i) q^{95} -0.923622i q^{96} -18.2175 q^{97} -8.20012 q^{98} +3.25824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 40 q^{9}+O(q^{10}) \) 40 * q + 44 * q^4 - 40 * q^9	\( 40 q + 44 q^{4} - 40 q^{9} + 4 q^{10} + 8 q^{11} + 52 q^{16} - 16 q^{21} + 8 q^{25} - 16 q^{26} + 16 q^{30} - 32 q^{34} - 44 q^{36} - 28 q^{40} + 8 q^{41} + 16 q^{44} - 8 q^{46} - 24 q^{49} + 92 q^{64} - 48 q^{65} - 56 q^{70} + 24 q^{71} - 68 q^{74} + 8 q^{75} + 40 q^{81} - 16 q^{84} - 64 q^{85} + 80 q^{86} - 4 q^{90} + 32 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 40 * q^9 + 4 * q^10 + 8 * q^11 + 52 * q^16 - 16 * q^21 + 8 * q^25 - 16 * q^26 + 16 * q^30 - 32 * q^34 - 44 * q^36 - 28 * q^40 + 8 * q^41 + 16 * q^44 - 8 * q^46 - 24 * q^49 + 92 * q^64 - 48 * q^65 - 56 * q^70 + 24 * q^71 - 68 * q^74 + 8 * q^75 + 40 * q^81 - 16 * q^84 - 64 * q^85 + 80 * q^86 - 4 * q^90 + 32 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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