LMFDB - Embedded newform 345.3.d.a.229.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,3,Mod(229,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("345.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	345.d (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:	$9.40056912043$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.16
Character	$\chi$	$=$	345.229
Dual form			345.3.d.a.229.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.48820i q^{2} -1.73205i q^{3} +1.78525 q^{4} +(0.794027 - 4.93655i) q^{5} -2.57765 q^{6} +12.7168 q^{7} -8.60963i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.48820i q^{2} -1.73205i q^{3} +1.78525 q^{4} +(0.794027 - 4.93655i) q^{5} -2.57765 q^{6} +12.7168 q^{7} -8.60963i q^{8} -3.00000 q^{9} +(-7.34659 - 1.18167i) q^{10} -4.27531i q^{11} -3.09214i q^{12} +15.4363i q^{13} -18.9252i q^{14} +(-8.55035 - 1.37530i) q^{15} -5.67190 q^{16} +30.8454 q^{17} +4.46461i q^{18} +10.7704i q^{19} +(1.41754 - 8.81297i) q^{20} -22.0261i q^{21} -6.36253 q^{22} +(-7.86140 + 21.6148i) q^{23} -14.9123 q^{24} +(-23.7390 - 7.83951i) q^{25} +22.9724 q^{26} +5.19615i q^{27} +22.7026 q^{28} -26.8805 q^{29} +(-2.04672 + 12.7247i) q^{30} +0.696771 q^{31} -25.9976i q^{32} -7.40505 q^{33} -45.9042i q^{34} +(10.0975 - 62.7770i) q^{35} -5.35574 q^{36} -27.3072 q^{37} +16.0286 q^{38} +26.7365 q^{39} +(-42.5019 - 6.83628i) q^{40} -65.4795 q^{41} -32.7793 q^{42} -34.1462 q^{43} -7.63249i q^{44} +(-2.38208 + 14.8096i) q^{45} +(32.1672 + 11.6994i) q^{46} +64.8134i q^{47} +9.82401i q^{48} +112.716 q^{49} +(-11.6668 + 35.3285i) q^{50} -53.4257i q^{51} +27.5577i q^{52} -35.9160 q^{53} +7.73294 q^{54} +(-21.1053 - 3.39471i) q^{55} -109.487i q^{56} +18.6549 q^{57} +40.0037i q^{58} -26.3025 q^{59} +(-15.2645 - 2.45524i) q^{60} +81.6109i q^{61} -1.03694i q^{62} -38.1503 q^{63} -61.3773 q^{64} +(76.2022 + 12.2569i) q^{65} +11.0202i q^{66} -6.00979 q^{67} +55.0666 q^{68} +(37.4379 + 13.6163i) q^{69} +(-93.4250 - 15.0271i) q^{70} +37.9228 q^{71} +25.8289i q^{72} -90.5168i q^{73} +40.6387i q^{74} +(-13.5784 + 41.1172i) q^{75} +19.2279i q^{76} -54.3682i q^{77} -39.7894i q^{78} -53.2816i q^{79} +(-4.50364 + 27.9996i) q^{80} +9.00000 q^{81} +97.4468i q^{82} +85.0565 q^{83} -39.3221i q^{84} +(24.4921 - 152.270i) q^{85} +50.8165i q^{86} +46.5584i q^{87} -36.8088 q^{88} +5.80872i q^{89} +(22.0398 + 3.54502i) q^{90} +196.300i q^{91} +(-14.0346 + 38.5877i) q^{92} -1.20684i q^{93} +96.4556 q^{94} +(53.1687 + 8.55200i) q^{95} -45.0291 q^{96} +39.7405 q^{97} -167.745i q^{98} +12.8259i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9}+O(q^{10}) $ 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9	$ 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9} + 148 q^{16} - 12 q^{24} - 64 q^{25} + 136 q^{26} + 76 q^{29} - 68 q^{31} - 108 q^{35} + 276 q^{36} + 48 q^{39} + 20 q^{41} + 344 q^{46} + 412 q^{49} - 352 q^{50} - 36 q^{54} - 184 q^{55} - 396 q^{59} - 684 q^{64} - 144 q^{69} + 600 q^{70} + 156 q^{71} - 120 q^{75} + 432 q^{81} - 76 q^{85} + 112 q^{95} + 516 q^{96}+O(q^{100}) $ 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9 + 148 * q^16 - 12 * q^24 - 64 * q^25 + 136 * q^26 + 76 * q^29 - 68 * q^31 - 108 * q^35 + 276 * q^36 + 48 * q^39 + 20 * q^41 + 344 * q^46 + 412 * q^49 - 352 * q^50 - 36 * q^54 - 184 * q^55 - 396 * q^59 - 684 * q^64 - 144 * q^69 + 600 * q^70 + 156 * q^71 - 120 * q^75 + 432 * q^81 - 76 * q^85 + 112 * q^95 + 516 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	1.48820i		−	0.744102i	−0.928212	−	0.372051i	$-0.878655\pi$
$2$		−	1.48820i		−	0.744102i	0.928212	−	0.372051i	$-0.121345\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	1.78525			0.446312
$5$	0.794027	−	4.93655i	0.158805	−	0.987310i
$5$	0.794027	−	4.93655i	0.158805	−	0.987310i
$6$	−2.57765			−0.429608
$7$	12.7168			1.81668			0.908341	−	0.418230i	$-0.137349\pi$
$7$	12.7168			1.81668			0.908341	+	0.418230i	$0.137349\pi$
$8$		−	8.60963i		−	1.07620i
$9$	−3.00000			−0.333333
$10$	−7.34659	−	1.18167i	−0.734659	−	0.118167i
$11$		−	4.27531i		−	0.388664i	−0.980936	−	0.194332i	$-0.937746\pi$
$11$		−	4.27531i		−	0.388664i	0.980936	−	0.194332i	$-0.0622540\pi$
$12$		−	3.09214i		−	0.257678i
$13$			15.4363i			1.18741i	0.804683	+	0.593705i	$0.202335\pi$
$13$			15.4363i			1.18741i	−0.804683	+	0.593705i	$0.797665\pi$
$14$		−	18.9252i		−	1.35180i
$15$	−8.55035	−	1.37530i	−0.570024	−	0.0916864i
$16$	−5.67190			−0.354493
$17$	30.8454			1.81443			0.907216	−	0.420664i	$-0.138203\pi$
$17$	30.8454			1.81443			0.907216	+	0.420664i	$0.138203\pi$
$18$			4.46461i			0.248034i
$19$			10.7704i			0.566864i	0.958992	+	0.283432i	$0.0914730\pi$
$19$			10.7704i			0.566864i	−0.958992	+	0.283432i	$0.908527\pi$
$20$	1.41754	−	8.81297i	0.0708768	−	0.440648i
$21$		−	22.0261i		−	1.04886i
$22$	−6.36253			−0.289206
$23$	−7.86140	+	21.6148i	−0.341800	+	0.939773i
$23$	−7.86140	+	21.6148i	−0.341800	+	0.939773i
$24$	−14.9123			−0.621347
$25$	−23.7390	−	7.83951i	−0.949562	−	0.313580i
$26$	22.9724			0.883554
$27$			5.19615i			0.192450i
$28$	22.7026			0.810807
$29$	−26.8805			−0.926914			−0.463457	−	0.886120i	$-0.653391\pi$
$29$	−26.8805			−0.926914			−0.463457	+	0.886120i	$0.653391\pi$
$30$	−2.04672	+	12.7247i	−0.0682240	+	0.424156i
$31$	0.696771			0.0224765			0.0112382	−	0.999937i	$-0.496423\pi$
$31$	0.696771			0.0224765			0.0112382	+	0.999937i	$0.496423\pi$
$32$		−	25.9976i		−	0.812424i
$33$	−7.40505			−0.224396
$34$		−	45.9042i		−	1.35012i
$35$	10.0975	−	62.7770i	0.288499	−	1.79363i
$36$	−5.35574			−0.148771
$37$	−27.3072			−0.738032			−0.369016	−	0.929423i	$-0.620305\pi$
$37$	−27.3072			−0.738032			−0.369016	+	0.929423i	$0.620305\pi$
$38$	16.0286			0.421805
$39$	26.7365			0.685551
$40$	−42.5019	−	6.83628i	−1.06255	−	0.170907i
$41$	−65.4795			−1.59706			−0.798530	−	0.601955i	$-0.794389\pi$
$41$	−65.4795			−1.59706			−0.798530	+	0.601955i	$0.794389\pi$
$42$	−32.7793			−0.780461
$43$	−34.1462			−0.794097			−0.397049	−	0.917798i	$-0.629966\pi$
$43$	−34.1462			−0.794097			−0.397049	+	0.917798i	$0.629966\pi$
$44$		−	7.63249i		−	0.173466i
$45$	−2.38208	+	14.8096i	−0.0529352	+	0.329103i
$46$	32.1672	+	11.6994i	0.699287	+	0.254334i
$47$			64.8134i			1.37901i	0.724281	+	0.689504i	$0.242172\pi$
$47$			64.8134i			1.37901i	−0.724281	+	0.689504i	$0.757828\pi$
$48$			9.82401i			0.204667i
$49$	112.716			2.30034
$50$	−11.6668	+	35.3285i	−0.233336	+	0.706571i
$51$		−	53.4257i		−	1.04756i
$52$			27.5577i			0.529955i
$53$	−35.9160			−0.677661			−0.338830	−	0.940848i	$-0.610031\pi$
$53$	−35.9160			−0.677661			−0.338830	+	0.940848i	$0.610031\pi$
$54$	7.73294			0.143203
$55$	−21.1053	−	3.39471i	−0.383732	−	0.0617220i
$56$		−	109.487i		−	1.95512i
$57$	18.6549			0.327279
$58$			40.0037i			0.689718i
$59$	−26.3025			−0.445806			−0.222903	−	0.974841i	$-0.571553\pi$
$59$	−26.3025			−0.445806			−0.222903	+	0.974841i	$0.571553\pi$
$60$	−15.2645	−	2.45524i	−0.254408	−	0.0409207i
$61$			81.6109i			1.33788i	0.743315	+	0.668941i	$0.233252\pi$
$61$			81.6109i			1.33788i	−0.743315	+	0.668941i	$0.766748\pi$
$62$		−	1.03694i		−	0.0167248i
$63$	−38.1503			−0.605561
$64$	−61.3773			−0.959020
$65$	76.2022	+	12.2569i	1.17234	+	0.188567i
$66$			11.0202i			0.166973i
$67$	−6.00979			−0.0896983			−0.0448491	−	0.998994i	$-0.514281\pi$
$67$	−6.00979			−0.0896983			−0.0448491	+	0.998994i	$0.514281\pi$
$68$	55.0666			0.809803
$69$	37.4379	+	13.6163i	0.542578	+	0.197338i
$70$	−93.4250	−	15.0271i	−1.33464	−	0.214673i
$71$	37.9228			0.534124			0.267062	−	0.963679i	$-0.413947\pi$
$71$	37.9228			0.534124			0.267062	+	0.963679i	$0.413947\pi$
$72$			25.8289i			0.358735i
$73$		−	90.5168i		−	1.23996i	−0.784619	−	0.619978i	$-0.787142\pi$
$73$		−	90.5168i		−	1.23996i	0.784619	−	0.619978i	$-0.212858\pi$
$74$			40.6387i			0.549171i
$75$	−13.5784	+	41.1172i	−0.181046	+	0.548230i
$76$			19.2279i			0.252998i
$77$		−	54.3682i		−	0.706080i
$78$		−	39.7894i		−	0.510120i
$79$		−	53.2816i		−	0.674450i	−0.941424	−	0.337225i	$-0.890512\pi$
$79$		−	53.2816i		−	0.674450i	0.941424	−	0.337225i	$-0.109488\pi$
$80$	−4.50364	+	27.9996i	−0.0562955	+	0.349995i
$81$	9.00000			0.111111
$82$			97.4468i			1.18838i
$83$	85.0565			1.02478			0.512388	−	0.858754i	$-0.328761\pi$
$83$	85.0565			1.02478			0.512388	+	0.858754i	$0.328761\pi$
$84$		−	39.3221i		−	0.468120i
$85$	24.4921	−	152.270i	0.288142	−	1.79141i
$86$			50.8165i			0.590890i
$87$			46.5584i			0.535154i
$88$	−36.8088			−0.418282
$89$			5.80872i			0.0652665i	0.999467	+	0.0326333i	$0.0103893\pi$
$89$			5.80872i			0.0652665i	−0.999467	+	0.0326333i	$0.989611\pi$
$90$	22.0398	+	3.54502i	0.244886	+	0.0393892i
$91$			196.300i			2.15715i
$92$	−14.0346	+	38.5877i	−0.152549	+	0.419432i
$93$		−	1.20684i		−	0.0129768i
$94$	96.4556			1.02612
$95$	53.1687	+	8.55200i	0.559670	+	0.0900211i
$96$	−45.0291			−0.469054
$97$	39.7405			0.409696			0.204848	−	0.978794i	$-0.434330\pi$
$97$	39.7405			0.409696			0.204848	+	0.978794i	$0.434330\pi$
$98$		−	167.745i		−	1.71168i
$99$			12.8259i			0.129555i
$100$	−42.3801	−	13.9955i	−0.423801	−	0.139955i
$101$	−99.0469			−0.980663			−0.490331	−	0.871536i	$-0.663124\pi$
$101$	−99.0469			−0.980663			−0.490331	+	0.871536i	$0.663124\pi$
$102$	−79.5084			−0.779494
$103$	−29.4647			−0.286065			−0.143033	−	0.989718i	$-0.545685\pi$
$103$	−29.4647			−0.286065			−0.143033	+	0.989718i	$0.545685\pi$
$104$	132.901			1.27789
$105$	−108.733	−	17.4893i	−1.03555	−	0.166565i
$106$			53.4504i			0.504249i
$107$	64.3564			0.601462			0.300731	−	0.953709i	$-0.402769\pi$
$107$	64.3564			0.601462			0.300731	+	0.953709i	$0.402769\pi$
$108$			9.27642i			0.0858928i
$109$			78.7776i			0.722731i	0.932424	+	0.361365i	$0.117689\pi$
$109$			78.7776i			0.722731i	−0.932424	+	0.361365i	$0.882311\pi$
$110$	−5.05203	+	31.4090i	−0.0459275	+	0.285536i
$111$			47.2974i			0.426103i
$112$	−72.1282			−0.644002
$113$	141.420			1.25150			0.625751	−	0.780023i	$-0.284793\pi$
$113$	141.420			1.25150			0.625751	+	0.780023i	$0.284793\pi$
$114$		−	27.7623i		−	0.243529i
$115$	100.460	+	55.9709i	0.873567	+	0.486704i
$116$	−47.9884			−0.413693
$117$		−	46.3090i		−	0.395803i
$118$			39.1435i			0.331725i
$119$	392.254			3.29625
$120$	−11.8408	+	73.6154i	−0.0986732	+	0.613462i
$121$	102.722			0.848940
$122$	121.454			0.995521
$123$			113.414i			0.922063i
$124$	1.24391			0.0100315
$125$	−57.5496	+	110.964i	−0.460397	+	0.887713i
$126$			56.7755i			0.450599i
$127$			179.193i			1.41096i	0.708727	+	0.705482i	$0.249270\pi$
$127$			179.193i			1.41096i	−0.708727	+	0.705482i	$0.750730\pi$
$128$		−	12.6484i		−	0.0988155i
$129$			59.1429i			0.458472i
$130$	18.2407	−	113.404i	0.140313	−	0.872341i
$131$	−98.4288			−0.751365			−0.375682	−	0.926748i	$-0.622592\pi$
$131$	−98.4288			−0.751365			−0.375682	+	0.926748i	$0.622592\pi$
$132$	−13.2199			−0.100150
$133$			136.965i			1.02981i
$134$			8.94379i			0.0667447i
$135$	25.6511	+	4.12589i	0.190008	+	0.0305621i
$136$		−	265.567i		−	1.95270i
$137$	−105.119			−0.767295			−0.383648	−	0.923480i	$-0.625332\pi$
$137$	−105.119			−0.767295			−0.383648	+	0.923480i	$0.625332\pi$
$138$	20.2639	−	55.7152i	0.146840	−	0.403733i
$139$	84.8078			0.610128			0.305064	−	0.952332i	$-0.401322\pi$
$139$	84.8078			0.610128			0.305064	+	0.952332i	$0.401322\pi$
$140$	18.0265	−	112.073i	0.128761	−	0.800518i
$141$	112.260			0.796171
$142$		−	56.4368i		−	0.397443i
$143$	65.9950			0.461504
$144$	17.0157			0.118164
$145$	−21.3439	+	132.697i	−0.147199	+	0.915151i
$146$	−134.707			−0.922654
$147$		−	195.231i		−	1.32810i
$148$	−48.7501			−0.329393
$149$		−	140.350i		−	0.941949i	−0.882147	−	0.470974i	$-0.843902\pi$
$149$		−	140.350i		−	0.941949i	0.882147	−	0.470974i	$-0.156098\pi$
$150$	61.1908	+	20.2075i	0.407939	+	0.134717i
$151$	−214.230			−1.41874			−0.709372	−	0.704834i	$-0.751021\pi$
$151$	−214.230			−1.41874			−0.709372	+	0.704834i	$0.751021\pi$
$152$	92.7293			0.610061
$153$	−92.5361			−0.604811
$154$	−80.9109			−0.525396
$155$	0.553255	−	3.43965i	0.00356939	−	0.0221913i
$156$	47.7313			0.305970
$157$	217.731			1.38682			0.693412	−	0.720541i	$-0.256107\pi$
$157$	217.731			1.38682			0.693412	+	0.720541i	$0.256107\pi$
$158$	−79.2939			−0.501860
$159$			62.2084i			0.391248i
$160$	−128.338	−	20.6428i	−0.802115	−	0.129017i
$161$	−99.9717	+	274.870i	−0.620942	+	1.70727i
$162$		−	13.3938i		−	0.0826780i
$163$		−	96.6805i		−	0.593132i	−0.955012	−	0.296566i	$-0.904159\pi$
$163$		−	96.6805i		−	0.593132i	0.955012	−	0.296566i	$-0.0958415\pi$
$164$	−116.897			−0.712787
$165$	−5.87981	+	36.5554i	−0.0356352	+	0.221548i
$166$		−	126.581i		−	0.762539i
$167$		−	146.668i		−	0.878252i	−0.898426	−	0.439126i	$-0.855288\pi$
$167$		−	146.668i		−	0.878252i	0.898426	−	0.439126i	$-0.144712\pi$
$168$	−189.637			−1.12879
$169$	−69.2801			−0.409941
$170$	−226.608	−	36.4492i	−1.33299	−	0.214407i
$171$		−	32.3112i		−	0.188955i
$172$	−60.9594			−0.354415
$173$		−	6.56628i		−	0.0379554i	−0.999820	−	0.0189777i	$-0.993959\pi$
$173$		−	6.56628i		−	0.0379554i	0.999820	−	0.0189777i	$-0.00604115\pi$
$174$	69.2884			0.398209
$175$	−301.884	−	99.6933i	−1.72505	−	0.569676i
$176$			24.2491i			0.137779i
$177$			45.5573i			0.257386i
$178$	8.64456			0.0485649
$179$	69.6886			0.389322			0.194661	−	0.980871i	$-0.437639\pi$
$179$	69.6886			0.389322			0.194661	+	0.980871i	$0.437639\pi$
$180$	−4.25261	+	26.4389i	−0.0236256	+	0.146883i
$181$		−	122.019i		−	0.674137i	−0.941480	−	0.337068i	$-0.890565\pi$
$181$		−	122.019i		−	0.674137i	0.941480	−	0.337068i	$-0.109435\pi$
$182$	292.135			1.60514
$183$	141.354			0.772427
$184$	186.095	+	67.6838i	1.01139	+	0.367847i
$185$	−21.6827	+	134.803i	−0.117204	+	0.728666i
$186$	−1.79603			−0.00965607
$187$		−	131.873i		−	0.705205i
$188$			115.708i			0.615468i
$189$			66.0783i			0.349621i
$190$	12.7271	−	79.1258i	0.0669849	−	0.416452i
$191$			10.4188i			0.0545487i	0.999628	+	0.0272744i	$0.00868278\pi$
$191$			10.4188i			0.0545487i	−0.999628	+	0.0272744i	$0.991317\pi$
$192$			106.309i			0.553691i
$193$			350.458i			1.81584i	0.419140	+	0.907922i	$0.362332\pi$
$193$			350.458i			1.81584i	−0.419140	+	0.907922i	$0.637668\pi$
$194$		−	59.1420i		−	0.304856i
$195$	21.2295	−	131.986i	0.108869	−	0.676851i
$196$	201.227			1.02667
$197$		−	132.632i		−	0.673258i	−0.941637	−	0.336629i	$-0.890713\pi$
$197$		−	132.632i		−	0.673258i	0.941637	−	0.336629i	$-0.109287\pi$
$198$	19.0876			0.0964020
$199$		−	339.036i		−	1.70370i	−0.523788	−	0.851849i	$-0.675482\pi$
$199$		−	339.036i		−	1.70370i	0.523788	−	0.851849i	$-0.324518\pi$
$200$	−67.4953	+	204.384i	−0.337476	+	1.02192i
$201$			10.4093i			0.0517873i
$202$			147.402i			0.729713i
$203$	−341.833			−1.68391
$204$		−	95.3782i		−	0.467540i
$205$	−51.9925	+	323.243i	−0.253622	+	1.57679i
$206$			43.8496i			0.212862i
$207$	23.5842	−	64.8443i	0.113933	−	0.313258i
$208$		−	87.5532i		−	0.420929i
$209$	46.0468			0.220320
$210$	−26.0277	+	161.817i	−0.123941	+	0.770556i
$211$	−141.472			−0.670482			−0.335241	−	0.942132i	$-0.608818\pi$
$211$	−141.472			−0.670482			−0.335241	+	0.942132i	$0.608818\pi$
$212$	−64.1190			−0.302448
$213$		−	65.6842i		−	0.308376i
$214$		−	95.7755i		−	0.447549i
$215$	−27.1130	+	168.564i	−0.126107	+	0.784020i
$216$	44.7370			0.207116
$217$	8.86068			0.0408326
$218$	117.237			0.537785
$219$	−156.780			−0.715889
$220$	−37.6782	−	6.06040i	−0.171264	−	0.0275473i
$221$			476.139i			2.15447i
$222$	70.3882			0.317064
$223$		−	375.406i		−	1.68343i	−0.539920	−	0.841717i	$-0.681545\pi$
$223$		−	375.406i		−	1.68343i	0.539920	−	0.841717i	$-0.318455\pi$
$224$		−	330.605i		−	1.47592i
$225$	71.2171	+	23.5185i	0.316521	+	0.104527i
$226$		−	210.461i		−	0.931245i
$227$	−322.505			−1.42073			−0.710363	−	0.703836i	$-0.751469\pi$
$227$	−322.505			−1.42073			−0.710363	+	0.703836i	$0.751469\pi$
$228$	33.3036			0.146069
$229$			20.6760i			0.0902884i	0.998980	+	0.0451442i	$0.0143747\pi$
$229$			20.6760i			0.0902884i	−0.998980	+	0.0451442i	$0.985625\pi$
$230$	83.2962	−	149.505i	0.362157	−	0.650023i
$231$	−94.1684			−0.407655
$232$			231.431i			0.997548i
$233$			176.353i			0.756881i	0.925626	+	0.378440i	$0.123539\pi$
$233$			176.353i			0.756881i	−0.925626	+	0.378440i	$0.876461\pi$
$234$	−68.9172			−0.294518
$235$	319.955	+	51.4636i	1.36151	+	0.218994i
$236$	−46.9565			−0.198968
$237$	−92.2864			−0.389394
$238$		−	583.753i		−	2.45275i
$239$	318.851			1.33410			0.667052	−	0.745012i	$-0.267556\pi$
$239$	318.851			1.33410			0.667052	+	0.745012i	$0.267556\pi$
$240$	48.4967	+	7.80053i	0.202070	+	0.0325022i
$241$		−	232.825i		−	0.966077i	−0.875599	−	0.483039i	$-0.839533\pi$
$241$		−	232.825i		−	0.966077i	0.875599	−	0.483039i	$-0.160467\pi$
$242$		−	152.871i		−	0.631698i
$243$		−	15.5885i		−	0.0641500i
$244$			145.696i			0.597113i
$245$	89.4999	−	556.430i	0.365306	−	2.27114i
$246$	168.783			0.686109
$247$	−166.256			−0.673099
$248$		−	5.99894i		−	0.0241893i
$249$		−	147.322i		−	0.591655i
$250$	165.137	+	85.6455i	0.660549	+	0.342582i
$251$		−	388.651i		−	1.54841i	−0.632936	−	0.774205i	$-0.718150\pi$
$251$		−	388.651i		−	1.54841i	0.632936	−	0.774205i	$-0.281850\pi$
$252$	−68.1078			−0.270269
$253$	92.4098	+	33.6099i	0.365256	+	0.132846i
$254$	266.675			1.04990
$255$	−263.739	−	42.4215i	−1.03427	−	0.166359i
$256$	−264.333			−1.03255
$257$		−	49.0820i		−	0.190981i	−0.995430	−	0.0954904i	$-0.969558\pi$
$257$		−	49.0820i		−	0.190981i	0.995430	−	0.0954904i	$-0.0304419\pi$
$258$	88.0168			0.341150
$259$	−347.259			−1.34077
$260$	136.040	+	21.8815i	0.523230	+	0.0841598i
$261$	80.6415			0.308971
$262$			146.482i			0.559092i
$263$	−338.647			−1.28763			−0.643815	−	0.765181i	$-0.722650\pi$
$263$	−338.647			−1.28763			−0.643815	+	0.765181i	$0.722650\pi$
$264$			63.7548i			0.241495i
$265$	−28.5183	+	177.301i	−0.107616	+	0.669061i
$266$	203.832			0.766285
$267$	10.0610			0.0376816
$268$	−10.7290			−0.0400334
$269$	−156.589			−0.582114			−0.291057	−	0.956706i	$-0.594007\pi$
$269$	−156.589			−0.582114			−0.291057	+	0.956706i	$0.594007\pi$
$270$	6.14016	−	38.1740i	0.0227413	−	0.141385i
$271$	142.248			0.524901			0.262451	−	0.964945i	$-0.415469\pi$
$271$	142.248			0.524901			0.262451	+	0.964945i	$0.415469\pi$
$272$	−174.952			−0.643205
$273$	340.002			1.24543
$274$			156.439i			0.570946i
$275$	−33.5163	+	101.492i	−0.121878	+	0.369061i
$276$	66.8359	+	24.3086i	0.242159	+	0.0880745i
$277$			190.799i			0.688805i	0.938822	+	0.344403i	$0.111919\pi$
$277$			190.799i			0.688805i	−0.938822	+	0.344403i	$0.888081\pi$
$278$		−	126.211i		−	0.453997i
$279$	−2.09031			−0.00749216
$280$	−540.487	−	86.9355i	−1.93031	−	0.310484i
$281$		−	315.889i		−	1.12416i	−0.827083	−	0.562079i	$-0.810002\pi$
$281$		−	315.889i		−	1.12416i	0.827083	−	0.562079i	$-0.189998\pi$
$282$		−	167.066i		−	0.592433i
$283$	−208.215			−0.735742			−0.367871	−	0.929877i	$-0.619913\pi$
$283$	−208.215			−0.735742			−0.367871	+	0.929877i	$0.619913\pi$
$284$	67.7016			0.238386
$285$	14.8125	−	92.0908i	0.0519737	−	0.323126i
$286$		−	98.2141i		−	0.343406i
$287$	−832.688			−2.90135
$288$			77.9928i			0.270808i
$289$	662.436			2.29217
$290$	197.480	+	31.7640i	0.680966	+	0.109531i
$291$		−	68.8326i		−	0.236538i
$292$		−	161.595i		−	0.553407i
$293$	31.8358			0.108655			0.0543273	−	0.998523i	$-0.482699\pi$
$293$	31.8358			0.108655			0.0543273	+	0.998523i	$0.482699\pi$
$294$	−290.543			−0.988241
$295$	−20.8849	+	129.844i	−0.0707964	+	0.440148i
$296$			235.105i			0.794273i
$297$	22.2152			0.0747985
$298$	−208.870			−0.700906
$299$	−333.653	−	121.351i	−1.11590	−	0.405857i
$300$	−24.2409	+	73.4045i	−0.0808029	+	0.244682i
$301$	−434.229			−1.44262
$302$			318.819i			1.05569i
$303$			171.554i			0.566186i
$304$		−	61.0887i		−	0.200950i
$305$	402.876	+	64.8013i	1.32090	+	0.212463i
$306$			137.713i			0.450041i
$307$		−	246.986i		−	0.804515i	−0.915526	−	0.402258i	$-0.868226\pi$
$307$		−	246.986i		−	0.804515i	0.915526	−	0.402258i	$-0.131774\pi$
$308$		−	97.0606i		−	0.315132i
$309$			51.0344i			0.165160i
$310$	−5.11889	−	0.823357i	−0.0165126	−	0.00265599i
$311$	−422.720			−1.35923			−0.679614	−	0.733570i	$-0.737853\pi$
$311$	−422.720			−1.35923			−0.679614	+	0.733570i	$0.737853\pi$
$312$		−	230.191i		−	0.737793i
$313$	436.906			1.39587			0.697933	−	0.716163i	$-0.254103\pi$
$313$	436.906			1.39587			0.697933	+	0.716163i	$0.254103\pi$
$314$		−	324.029i		−	1.03194i
$315$	−30.2924	+	188.331i	−0.0961664	+	0.597876i
$316$		−	95.1208i		−	0.301015i
$317$		−	256.740i		−	0.809905i	−0.914338	−	0.404953i	$-0.867288\pi$
$317$		−	256.740i		−	0.809905i	0.914338	−	0.404953i	$-0.132712\pi$
$318$	92.5787			0.291128
$319$			114.922i			0.360258i
$320$	−48.7353	+	302.992i	−0.152298	+	0.946850i
$321$		−	111.469i		−	0.347254i
$322$	409.063	+	148.778i	1.27038	+	0.462044i
$323$			332.217i			1.02854i
$324$	16.0672			0.0495902
$325$	121.013	−	366.444i	0.372348	−	1.12752i
$326$	−143.880			−0.441351
$327$	136.447			0.417269
$328$			563.754i			1.71876i
$329$			824.218i			2.50522i
$330$	54.4019	+	8.75036i	0.164854	+	0.0265163i
$331$	585.027			1.76745			0.883727	−	0.468003i	$-0.155026\pi$
$331$	585.027			1.76745			0.883727	+	0.468003i	$0.155026\pi$
$332$	151.847			0.457370
$333$	81.9216			0.246011
$334$	−218.272			−0.653509
$335$	−4.77193	+	29.6676i	−0.0142446	+	0.0885600i
$336$			124.930i			0.371815i
$337$	386.269			1.14620			0.573099	−	0.819486i	$-0.305741\pi$
$337$	386.269			1.14620			0.573099	+	0.819486i	$0.305741\pi$
$338$			103.103i			0.305038i
$339$		−	244.946i		−	0.722555i
$340$	43.7244	−	271.839i	0.128601	−	0.799527i
$341$		−	2.97891i		−	0.00873581i
$342$	−48.0857			−0.140602
$343$	810.268			2.36230
$344$			293.986i			0.854611i
$345$	96.9445	−	174.002i	0.280998	−	0.504354i
$346$	−9.77197			−0.0282427
$347$			244.267i			0.703938i	0.936012	+	0.351969i	$0.114488\pi$
$347$			244.267i			0.703938i	−0.936012	+	0.351969i	$0.885512\pi$
$348$			83.1183i			0.238846i
$349$	309.800			0.887678			0.443839	−	0.896107i	$-0.353616\pi$
$349$	309.800			0.887678			0.443839	+	0.896107i	$0.353616\pi$
$350$	−148.364	+	449.265i	−0.423897	+	1.28361i
$351$	−80.2095			−0.228517
$352$	−111.148			−0.315761
$353$			547.232i			1.55023i	0.631818	+	0.775116i	$0.282309\pi$
$353$			547.232i			1.55023i	−0.631818	+	0.775116i	$0.717691\pi$
$354$	67.7986			0.191521
$355$	30.1117	−	187.208i	0.0848218	−	0.527346i
$356$			10.3700i			0.0291292i
$357$		−	679.403i		−	1.90309i
$358$		−	103.711i		−	0.289695i
$359$		−	505.030i		−	1.40677i	−0.710810	−	0.703384i	$-0.751671\pi$
$359$		−	505.030i		−	1.40677i	0.710810	−	0.703384i	$-0.248329\pi$
$360$	127.506	+	20.5088i	0.354182	+	0.0569690i
$361$	244.998			0.678665
$362$	−181.589			−0.501627
$363$		−	177.919i		−	0.490136i
$364$			350.445i			0.962760i
$365$	−446.841	−	71.8728i	−1.22422	−	0.196912i
$366$		−	210.364i		−	0.574765i
$367$	40.2534			0.109682			0.0548411	−	0.998495i	$-0.482535\pi$
$367$	40.2534			0.109682			0.0548411	+	0.998495i	$0.482535\pi$
$368$	44.5890	−	122.597i	0.121166	−	0.333143i
$369$	196.438			0.532354
$370$	200.615	+	32.2682i	0.542202	+	0.0872114i
$371$	−456.736			−1.23109
$372$		−	2.15451i		−	0.00579171i
$373$	−579.554			−1.55376			−0.776882	−	0.629646i	$-0.783200\pi$
$373$	−579.554			−1.55376			−0.776882	+	0.629646i	$0.783200\pi$
$374$	−196.255			−0.524745
$375$	192.196	+	99.6788i	0.512522	+	0.265810i
$376$	558.020			1.48409
$377$		−	414.936i		−	1.10063i
$378$	98.3380			0.260154
$379$		−	334.998i		−	0.883900i	−0.897040	−	0.441950i	$-0.854287\pi$
$379$		−	334.998i		−	0.883900i	0.897040	−	0.441950i	$-0.145713\pi$
$380$	94.9193	+	15.2674i	0.249788	+	0.0401775i
$381$	310.371			0.814621
$382$	15.5053			0.0405898
$383$	508.087			1.32660			0.663299	−	0.748354i	$-0.269156\pi$
$383$	508.087			1.32660			0.663299	+	0.748354i	$0.269156\pi$
$384$	−21.9076			−0.0570512
$385$	−268.391	−	43.1698i	−0.697120	−	0.112129i
$386$	521.553			1.35117
$387$	102.439			0.264699
$388$	70.9467			0.182852
$389$			370.320i			0.951979i	0.879451	+	0.475990i	$0.157910\pi$
$389$			370.320i			0.951979i	−0.879451	+	0.475990i	$0.842090\pi$
$390$	−196.422	−	31.5938i	−0.503647	−	0.0810099i
$391$	−242.488	+	666.715i	−0.620173	+	1.70515i
$392$		−	970.447i		−	2.47563i
$393$			170.484i			0.433801i
$394$	−197.383			−0.500972
$395$	−263.027	−	42.3070i	−0.665891	−	0.107106i
$396$			22.8975i			0.0578219i
$397$			242.477i			0.610773i	0.952228	+	0.305387i	$0.0987857\pi$
$397$			242.477i			0.610773i	−0.952228	+	0.305387i	$0.901214\pi$
$398$	−504.554			−1.26772
$399$	237.230			0.594562
$400$	134.645	+	44.4649i	0.336613	+	0.111162i
$401$			502.129i			1.25219i	0.779746	+	0.626096i	$0.215348\pi$
$401$			502.129i			1.25219i	−0.779746	+	0.626096i	$0.784652\pi$
$402$	15.4911			0.0385351
$403$			10.7556i			0.0266888i
$404$	−176.823			−0.437682
$405$	7.14625	−	44.4289i	0.0176451	−	0.109701i
$406$			508.718i			1.25300i
$407$			116.747i			0.286847i
$408$	−459.976			−1.12739
$409$	−165.369			−0.404325			−0.202163	−	0.979352i	$-0.564797\pi$
$409$	−165.369			−0.404325			−0.202163	+	0.979352i	$0.564797\pi$
$410$	481.051	+	77.3755i	1.17330	+	0.188721i
$411$			182.072i			0.442998i
$412$	−52.6019			−0.127674
$413$	−334.483			−0.809887
$414$	−96.5016	−	35.0981i	−0.233096	−	0.0847780i
$415$	67.5372	−	419.885i	0.162740	−	1.01177i
$416$	401.307			0.964681
$417$		−	146.891i		−	0.352257i
$418$		−	68.5271i		−	0.163940i
$419$			97.8982i			0.233647i	0.993153	+	0.116824i	$0.0372712\pi$
$419$			97.8982i			0.233647i	−0.993153	+	0.116824i	$0.962729\pi$
$420$	−194.115	−	31.2228i	−0.462179	−	0.0743400i
$421$			580.162i			1.37806i	0.724734	+	0.689029i	$0.241963\pi$
$421$			580.162i			1.37806i	−0.724734	+	0.689029i	$0.758037\pi$
$422$			210.539i			0.498907i
$423$		−	194.440i		−	0.459670i
$424$			309.224i			0.729301i
$425$	−732.239	−	241.813i	−1.72292	−	0.568971i
$426$	−97.7515			−0.229464
$427$			1037.83i			2.43051i
$428$	114.892			0.268440
$429$		−	114.307i		−	0.266449i
$430$	250.858	+	40.3497i	0.583391	+	0.0938365i
$431$		−	717.474i		−	1.66467i	−0.554271	−	0.832336i	$-0.687003\pi$
$431$		−	717.474i		−	1.66467i	0.554271	−	0.832336i	$-0.312997\pi$
$432$		−	29.4720i		−	0.0682223i
$433$	407.798			0.941797			0.470899	−	0.882187i	$-0.343930\pi$
$433$	407.798			0.941797			0.470899	+	0.882187i	$0.343930\pi$
$434$		−	13.1865i		−	0.0303837i
$435$	229.838	+	36.9686i	0.528363	+	0.0849854i
$436$			140.638i			0.322563i
$437$	−232.800	−	84.6705i	−0.532723	−	0.193754i
$438$			233.320i			0.532694i
$439$	−411.873			−0.938207			−0.469104	−	0.883143i	$-0.655423\pi$
$439$	−411.873			−0.938207			−0.469104	+	0.883143i	$0.655423\pi$
$440$	−29.2272	+	181.709i	−0.0664255	+	0.412974i
$441$	−338.149			−0.766778
$442$	708.592			1.60315
$443$			431.371i			0.973748i	0.873472	+	0.486874i	$0.161863\pi$
$443$			431.371i			0.973748i	−0.873472	+	0.486874i	$0.838137\pi$
$444$			84.4377i			0.190175i
$445$	28.6750	+	4.61228i	0.0644383	+	0.0103647i
$446$	−558.680			−1.25265
$447$	−243.094			−0.543834
$448$	−780.521			−1.74224
$449$	−428.495			−0.954331			−0.477166	−	0.878813i	$-0.658336\pi$
$449$	−428.495			−0.954331			−0.477166	+	0.878813i	$0.658336\pi$
$450$	35.0004	−	105.986i	0.0777786	−	0.235524i
$451$			279.945i			0.620721i
$452$	252.469			0.558560
$453$			371.058i			0.819113i
$454$			479.953i			1.05716i
$455$	969.046	+	155.868i	2.12977	+	0.342567i
$456$		−	160.612i		−	0.352219i
$457$	418.532			0.915826			0.457913	−	0.888997i	$-0.348597\pi$
$457$	418.532			0.915826			0.457913	+	0.888997i	$0.348597\pi$
$458$	30.7702			0.0671838
$459$			160.277i			0.349188i
$460$	179.346	+	99.9220i	0.389884	+	0.217222i
$461$	187.102			0.405860			0.202930	−	0.979193i	$-0.434954\pi$
$461$	187.102			0.405860			0.202930	+	0.979193i	$0.434954\pi$
$462$			140.142i			0.303337i
$463$		−	916.641i		−	1.97979i	−0.141814	−	0.989893i	$-0.545293\pi$
$463$		−	916.641i		−	1.97979i	0.141814	−	0.989893i	$-0.454707\pi$
$464$	152.463			0.328585
$465$	−5.95764	−	0.958266i	−0.0128121	−	0.00206079i
$466$	262.450			0.563197
$467$	−295.215			−0.632153			−0.316077	−	0.948734i	$-0.602366\pi$
$467$	−295.215			−0.632153			−0.316077	+	0.948734i	$0.602366\pi$
$468$		−	82.6730i		−	0.176652i
$469$	−76.4251			−0.162953
$470$	76.5884	−	476.158i	0.162954	−	1.01310i
$471$		−	377.122i		−	0.800683i
$472$			226.455i			0.479778i
$473$			145.986i			0.308637i
$474$			137.341i			0.289749i
$475$	84.4348	−	255.679i	0.177757	−	0.538272i
$476$	700.270			1.47116
$477$	107.748			0.225887
$478$		−	474.515i		−	0.992709i
$479$			473.694i			0.988923i	0.869200	+	0.494461i	$0.164635\pi$
$479$			473.694i			0.988923i	−0.869200	+	0.494461i	$0.835365\pi$
$480$	−35.7544	+	222.289i	−0.0744883	+	0.463101i
$481$		−	421.523i		−	0.876346i
$482$	−346.491			−0.718860
$483$	476.089	+	173.156i	0.985692	+	0.358501i
$484$	183.384			0.378892
$485$	31.5550	−	196.181i	0.0650620	−	0.404497i
$486$	−23.1988			−0.0477342
$487$			92.1170i			0.189152i	0.995518	+	0.0945760i	$0.0301495\pi$
$487$			92.1170i			0.189152i	−0.995518	+	0.0945760i	$0.969850\pi$
$488$	702.639			1.43983
$489$	−167.456			−0.342445
$490$	−828.082	−	133.194i	−1.68996	−	0.271825i
$491$	−197.753			−0.402756			−0.201378	−	0.979514i	$-0.564542\pi$
$491$	−197.753			−0.402756			−0.201378	+	0.979514i	$0.564542\pi$
$492$			202.472i			0.411528i
$493$	−829.138			−1.68182
$494$			247.422i			0.500855i
$495$	63.3158	+	10.1841i	0.127911	+	0.0205740i
$496$	−3.95201			−0.00796777
$497$	482.256			0.970333
$498$	−219.245			−0.440252
$499$	−872.447			−1.74839			−0.874195	−	0.485575i	$-0.838610\pi$
$499$	−872.447			−1.74839			−0.874195	+	0.485575i	$0.838610\pi$
$500$	−102.740	+	198.099i	−0.205481	+	0.396197i
$501$	−254.037			−0.507059
$502$	−578.392			−1.15217
$503$	199.518			0.396655			0.198328	−	0.980136i	$-0.436449\pi$
$503$	199.518			0.396655			0.198328	+	0.980136i	$0.436449\pi$
$504$			328.460i			0.651707i
$505$	−78.6460	+	488.950i	−0.155735	+	0.968218i
$506$	50.0184	−	137.525i	0.0988506	−	0.271788i
$507$			119.997i			0.236680i
$508$			319.903i			0.629731i
$509$	−179.473			−0.352599			−0.176299	−	0.984337i	$-0.556413\pi$
$509$	−179.473			−0.352599			−0.176299	+	0.984337i	$0.556413\pi$
$510$	−63.1318	+	392.497i	−0.123788	+	0.769602i
$511$		−	1151.08i		−	2.25261i
$512$			342.787i			0.669506i
$513$	−55.9647			−0.109093
$514$	−73.0441			−0.142109
$515$	−23.3958	+	145.454i	−0.0454288	+	0.282435i
$516$			105.585i			0.204622i
$517$	277.097			0.535972
$518$			516.793i			0.997670i
$519$	−11.3731			−0.0219136
$520$	105.527	−	656.073i	0.202937	−	1.26168i
$521$			137.997i			0.264870i	0.991192	+	0.132435i	$0.0422796\pi$
$521$			137.997i			0.264870i	−0.991192	+	0.132435i	$0.957720\pi$
$522$		−	120.011i		−	0.229906i
$523$	179.904			0.343985			0.171992	−	0.985098i	$-0.444980\pi$
$523$	179.904			0.343985			0.171992	+	0.985098i	$0.444980\pi$
$524$	−175.720			−0.335343
$525$	−172.674	+	522.879i	−0.328903	+	0.995959i
$526$			503.976i			0.958129i
$527$	21.4922			0.0407821
$528$	42.0007			0.0795468
$529$	−405.397	−	339.845i	−0.766345	−	0.642429i
$530$	263.860	+	42.4411i	0.497850	+	0.0800775i
$531$	78.9076			0.148602
$532$			244.516i			0.459617i
$533$		−	1010.76i		−	1.89636i
$534$		−	14.9728i		−	0.0280390i
$535$	51.1008	−	317.699i	0.0955155	−	0.593829i
$536$			51.7420i			0.0965336i
$537$		−	120.704i		−	0.224775i
$538$			233.036i			0.433152i
$539$		−	481.898i		−	0.894059i
$540$	45.7935	+	7.36573i	0.0848028	+	0.0136402i
$541$	−358.999			−0.663585			−0.331792	−	0.943352i	$-0.607653\pi$
$541$	−358.999			−0.663585			−0.331792	+	0.943352i	$0.607653\pi$
$542$		−	211.695i		−	0.390580i
$543$	−211.343			−0.389213
$544$		−	801.905i		−	1.47409i
$545$	388.890	+	62.5516i	0.713559	+	0.114774i
$546$		−	505.993i		−	0.926726i
$547$			70.3378i			0.128588i	0.997931	+	0.0642942i	$0.0204796\pi$
$547$			70.3378i			0.128588i	−0.997931	+	0.0642942i	$0.979520\pi$
$548$	−187.664			−0.342453
$549$		−	244.833i		−	0.445961i
$550$	151.040	+	49.8791i	0.274619	+	0.0906894i
$551$		−	289.514i		−	0.525434i
$552$	117.232	−	322.326i	0.212376	−	0.583925i
$553$		−	677.570i		−	1.22526i
$554$	283.948			0.512542
$555$	233.486	+	37.5555i	0.420696	+	0.0676675i
$556$	151.403			0.272307
$557$	797.478			1.43174			0.715869	−	0.698234i	$-0.246031\pi$
$557$	797.478			1.43174			0.715869	+	0.698234i	$0.246031\pi$
$558$			3.11081i			0.00557493i
$559$		−	527.092i		−	0.942919i
$560$	−57.2718	+	356.065i	−0.102271	+	0.635830i
$561$	−228.411			−0.407151
$562$	−470.107			−0.836489
$563$	−490.117			−0.870545			−0.435273	−	0.900299i	$-0.643348\pi$
$563$	−490.117			−0.870545			−0.435273	+	0.900299i	$0.643348\pi$
$564$	200.412			0.355341
$565$	112.291	−	698.125i	0.198745	−	1.23562i
$566$			309.866i			0.547467i
$567$	114.451			0.201854
$568$		−	326.501i		−	0.574826i
$569$			58.9176i			0.103546i	0.998659	+	0.0517729i	$0.0164872\pi$
$569$			58.9176i			0.103546i	−0.998659	+	0.0517729i	$0.983513\pi$
$570$	−137.050	−	22.0440i	−0.240439	−	0.0386737i
$571$		−	248.329i		−	0.434903i	−0.976071	−	0.217451i	$-0.930226\pi$
$571$		−	248.329i		−	0.434903i	0.976071	−	0.217451i	$-0.0697743\pi$
$572$	117.818			0.205975
$573$	18.0459			0.0314937
$574$			1239.21i			2.15890i
$575$	356.071	−	451.484i	0.619255	−	0.785190i
$576$	184.132			0.319673
$577$		−	261.919i		−	0.453933i	−0.973903	−	0.226966i	$-0.927119\pi$
$577$		−	261.919i		−	0.453933i	0.973903	−	0.226966i	$-0.0728808\pi$
$578$		−	985.840i		−	1.70561i
$579$	607.011			1.04838
$580$	−38.1041	+	236.897i	−0.0656967	+	0.408443i
$581$	1081.64			1.86169
$582$	−102.437			−0.176008
$583$			153.552i			0.263383i
$584$	−779.316			−1.33445
$585$	−228.607	−	36.7706i	−0.390780	−	0.0628557i
$586$		−	47.3782i		−	0.0808501i
$587$		−	346.649i		−	0.590543i	−0.955413	−	0.295272i	$-0.904590\pi$
$587$		−	346.649i		−	0.590543i	0.955413	−	0.295272i	$-0.0954101\pi$
$588$		−	348.535i		−	0.592747i
$589$			7.50451i			0.0127411i
$590$	193.234	+	31.0810i	0.327515	+	0.0526797i
$591$	−229.725			−0.388705
$592$	154.884			0.261628
$593$		−	27.2582i		−	0.0459667i	−0.999736	−	0.0229833i	$-0.992684\pi$
$593$		−	27.2582i		−	0.0459667i	0.999736	−	0.0229833i	$-0.00731647\pi$
$594$		−	33.0607i		−	0.0556577i
$595$	311.460	−	1936.38i	0.523462	−	3.25442i
$596$		−	250.560i		−	0.420403i
$597$	−587.227			−0.983630
$598$	−180.595	+	496.543i	−0.301999	+	0.830340i
$599$	−475.431			−0.793707			−0.396854	−	0.917882i	$-0.629898\pi$
$599$	−475.431			−0.793707			−0.396854	+	0.917882i	$0.629898\pi$
$600$	354.004	+	116.905i	0.590007	+	0.194842i
$601$	65.9612			0.109752			0.0548762	−	0.998493i	$-0.482524\pi$
$601$	65.9612			0.109752			0.0548762	+	0.998493i	$0.482524\pi$
$602$			646.222i			1.07346i
$603$	18.0294			0.0298994
$604$	−382.455			−0.633203
$605$	81.5639	−	507.091i	0.134816	−	0.838167i
$606$	255.308			0.421300
$607$			660.549i			1.08822i	0.839014	+	0.544110i	$0.183132\pi$
$607$			660.549i			1.08822i	−0.839014	+	0.544110i	$0.816868\pi$
$608$	280.005			0.460534
$609$			592.073i			0.972205i
$610$	96.4375	−	599.562i	0.158094	−	0.982888i
$611$	−1000.48			−1.63745
$612$	−165.200			−0.269934
$613$	408.810			0.666901			0.333450	−	0.942768i	$-0.391787\pi$
$613$	408.810			0.666901			0.333450	+	0.942768i	$0.391787\pi$
$614$	−367.566			−0.598642
$615$	559.873	+	90.0537i	0.910362	+	0.146429i
$616$	−468.090			−0.759886
$617$	721.912			1.17004			0.585018	−	0.811020i	$-0.301087\pi$
$617$	721.912			1.17004			0.585018	+	0.811020i	$0.301087\pi$
$618$	75.9497			0.122896
$619$		−	1152.86i		−	1.86245i	−0.364443	−	0.931226i	$-0.618741\pi$
$619$		−	1152.86i		−	1.86245i	0.364443	−	0.931226i	$-0.381259\pi$
$620$	0.987698	−	6.14062i	0.00159306	−	0.00990423i
$621$	−112.314	−	40.8490i	−0.180859	−	0.0657794i
$622$			629.093i			1.01140i
$623$			73.8682i			0.118569i
$624$	−151.647			−0.243023
$625$	502.084	+	372.205i	0.803335	+	0.595528i
$626$		−	650.206i		−	1.03867i
$627$		−	79.7555i		−	0.127202i
$628$	388.705			0.618956
$629$	−842.300			−1.33911
$630$	280.275	+	45.0813i	0.444881	+	0.0715576i
$631$			242.746i			0.384701i	0.981326	+	0.192350i	$0.0616110\pi$
$631$			242.746i			0.384701i	−0.981326	+	0.192350i	$0.938389\pi$
$632$	−458.735			−0.725846
$633$			245.036i			0.387103i
$634$	−382.081			−0.602652
$635$	884.593	+	142.284i	1.39306	+	0.224069i
$636$			111.057i			0.174618i
$637$			1739.93i			2.73144i
$638$	171.028			0.268069
$639$	−113.768			−0.178041
$640$	−62.4394	−	10.0432i	−0.0975615	−	0.0156924i
$641$			422.353i			0.658897i	0.944174	+	0.329448i	$0.106863\pi$
$641$			422.353i			0.658897i	−0.944174	+	0.329448i	$0.893137\pi$
$642$	−165.888			−0.258393
$643$	−746.759			−1.16137			−0.580683	−	0.814129i	$-0.697215\pi$
$643$	−746.759			−1.16137			−0.580683	+	0.814129i	$0.697215\pi$
$644$	−178.474	+	490.712i	−0.277134	+	0.761975i
$645$	291.962	+	46.9611i	0.452654	+	0.0728079i
$646$	494.407			0.765336
$647$			813.975i			1.25808i	0.777375	+	0.629038i	$0.216551\pi$
$647$			813.975i			1.25808i	−0.777375	+	0.629038i	$0.783449\pi$
$648$		−	77.4867i		−	0.119578i
$649$			112.451i			0.173269i
$650$	−545.343	−	180.092i	−0.838989	−	0.277065i
$651$		−	15.3472i		−	0.0235747i
$652$		−	172.599i		−	0.264722i
$653$			1014.21i			1.55316i	0.630018	+	0.776580i	$0.283047\pi$
$653$			1014.21i			1.55316i	−0.630018	+	0.776580i	$0.716953\pi$
$654$		−	203.061i		−	0.310491i
$655$	−78.1551	+	485.899i	−0.119321	+	0.741830i
$656$	371.393			0.566148
$657$			271.550i			0.413319i
$658$	1226.60			1.86414
$659$			364.372i			0.552917i	0.961026	+	0.276458i	$0.0891608\pi$
$659$			364.372i			0.552917i	−0.961026	+	0.276458i	$0.910839\pi$
$660$	−10.4969	+	65.2605i	−0.0159044	+	0.0988795i
$661$		−	420.665i		−	0.636408i	−0.948022	−	0.318204i	$-0.896920\pi$
$661$		−	420.665i		−	0.636408i	0.948022	−	0.318204i	$-0.103080\pi$
$662$		−	870.640i		−	1.31517i
$663$	824.697			1.24389
$664$		−	732.305i		−	1.10287i
$665$	676.134	+	108.754i	1.01674	+	0.163540i
$666$		−	121.916i		−	0.183057i
$667$	211.318	−	581.016i	0.316819	−	0.871088i
$668$		−	261.839i		−	0.391974i
$669$	−650.222			−0.971931
$670$	44.1515	+	7.10161i	0.0658977	+	0.0105994i
$671$	348.912			0.519987
$672$	−572.626			−0.852121
$673$		−	922.669i		−	1.37098i	−0.728082	−	0.685490i	$-0.759588\pi$
$673$		−	922.669i		−	1.37098i	0.728082	−	0.685490i	$-0.240412\pi$
$674$		−	574.847i		−	0.852889i
$675$	40.7353	−	123.352i	0.0603486	−	0.182743i
$676$	−123.682			−0.182962
$677$	401.668			0.593306			0.296653	−	0.954985i	$-0.404129\pi$
$677$	401.668			0.593306			0.296653	+	0.954985i	$0.404129\pi$
$678$	−364.530			−0.537654
$679$	505.371			0.744287
$680$	−1310.99	−	210.868i	−1.92792	−	0.310099i
$681$			558.594i			0.820256i
$682$	−4.43323			−0.00650034
$683$		−	159.499i		−	0.233527i	−0.993160	−	0.116763i	$-0.962748\pi$
$683$		−	159.499i		−	0.233527i	0.993160	−	0.116763i	$-0.0372519\pi$
$684$		−	57.6836i		−	0.0843327i
$685$	−83.4677	+	518.927i	−0.121851	+	0.757558i
$686$		−	1205.84i		−	1.75779i
$687$	35.8120			0.0521280
$688$	193.674			0.281502
$689$		−	554.411i		−	0.804661i
$690$	−258.951	−	144.273i	−0.375291	−	0.209092i
$691$	−936.445			−1.35520			−0.677601	−	0.735429i	$-0.736981\pi$
$691$	−936.445			−1.35520			−0.677601	+	0.735429i	$0.736981\pi$
$692$		−	11.7224i		−	0.0169400i
$693$			163.104i			0.235360i
$694$	363.519			0.523802
$695$	67.3397	−	418.658i	0.0968916	−	0.602385i
$696$	400.851			0.575935
$697$	−2019.74			−2.89776
$698$		−	461.045i		−	0.660523i
$699$	305.453			0.436985
$700$	−538.938	−	177.977i	−0.769912	−	0.254253i
$701$			98.0933i			0.139933i	0.997549	+	0.0699667i	$0.0222893\pi$
$701$			98.0933i			0.139933i	−0.997549	+	0.0699667i	$0.977711\pi$
$702$			119.368i			0.170040i
$703$		−	294.110i		−	0.418364i
$704$			262.407i			0.372737i
$705$	89.1376	−	554.178i	0.126436	−	0.786068i
$706$	814.393			1.15353
$707$	−1259.56			−1.78155
$708$			81.3311i			0.114874i
$709$			919.680i			1.29715i	0.761150	+	0.648576i	$0.224635\pi$
$709$			919.680i			1.29715i	−0.761150	+	0.648576i	$0.775365\pi$
$710$	−278.603	−	44.8124i	−0.392399	−	0.0631161i
$711$			159.845i			0.224817i
$712$	50.0109			0.0702401
$713$	−5.47760	+	15.0606i	−0.00768246	+	0.0211228i
$714$	−1011.09			−1.41609
$715$	52.4019	−	325.788i	0.0732893	−	0.455647i
$716$	124.411			0.173759
$717$		−	552.266i		−	0.770245i
$718$	−751.588			−1.04678
$719$	748.619			1.04119			0.520597	−	0.853802i	$-0.325709\pi$
$719$	748.619			1.04119			0.520597	+	0.853802i	$0.325709\pi$
$720$	13.5109	−	83.9988i	0.0187652	−	0.116665i
$721$	−374.697			−0.519690
$722$		−	364.607i		−	0.504996i
$723$	−403.264			−0.557765
$724$		−	217.834i		−	0.300875i
$725$	638.117	+	210.730i	0.880162	+	0.290662i
$726$	−264.780			−0.364711
$727$	37.0930			0.0510220			0.0255110	−	0.999675i	$-0.491879\pi$
$727$	37.0930			0.0510220			0.0255110	+	0.999675i	$0.491879\pi$
$728$	1690.07			2.32153
$729$	−27.0000			−0.0370370
$730$	−106.961	+	664.990i	−0.146522	+	0.910945i
$731$	−1053.25			−1.44084
$732$	252.352			0.344743
$733$	−1282.77			−1.75003			−0.875017	−	0.484093i	$-0.839150\pi$
$733$	−1282.77			−1.75003			−0.875017	+	0.484093i	$0.839150\pi$
$734$		−	59.9052i		−	0.0816148i
$735$	−963.765	−	155.018i	−1.31125	−	0.210909i
$736$	561.932	+	204.377i	0.763494	+	0.277687i
$737$			25.6937i			0.0348625i
$738$		−	292.341i		−	0.396125i
$739$	881.738			1.19315			0.596575	−	0.802557i	$-0.296528\pi$
$739$	881.738			1.19315			0.596575	+	0.802557i	$0.296528\pi$
$740$	−38.7089	+	240.657i	−0.0523094	+	0.325213i
$741$			287.963i			0.388614i
$742$			679.716i			0.916060i
$743$	−704.213			−0.947797			−0.473899	−	0.880579i	$-0.657154\pi$
$743$	−704.213			−0.947797			−0.473899	+	0.880579i	$0.657154\pi$
$744$	−10.3905			−0.0139657
$745$	−692.847	−	111.442i	−0.929995	−	0.149587i
$746$			862.495i			1.15616i
$747$	−255.169			−0.341592
$748$		−	235.427i		−	0.314742i
$749$	818.406			1.09267
$750$	148.342	−	286.026i	0.197790	−	0.381368i
$751$			705.883i			0.939924i	0.882687	+	0.469962i	$0.155732\pi$
$751$			705.883i			0.939924i	−0.882687	+	0.469962i	$0.844268\pi$
$752$		−	367.615i		−	0.488850i
$753$	−673.163			−0.893974
$754$	−617.510			−0.818978
$755$	−170.105	+	1057.56i	−0.225304	+	1.40074i
$756$			117.966i			0.156040i
$757$	1368.07			1.80722			0.903611	−	0.428355i	$-0.140907\pi$
$757$	1368.07			1.80722			0.903611	+	0.428355i	$0.140907\pi$
$758$	−498.546			−0.657712
$759$	58.2141	−	160.059i	0.0766984	−	0.210881i
$760$	73.6296	−	457.763i	0.0968810	−	0.602319i
$761$	698.938			0.918447			0.459223	−	0.888321i	$-0.348128\pi$
$761$	698.938			0.918447			0.459223	+	0.888321i	$0.348128\pi$
$762$		−	461.895i		−	0.606161i
$763$			1001.80i			1.31297i
$764$			18.6002i			0.0243458i
$765$	−73.4762	+	456.809i	−0.0960473	+	0.597136i
$766$		−	756.138i		−	0.987125i
$767$		−	406.014i		−	0.529354i
$768$			457.837i			0.596142i
$769$		−	299.988i		−	0.390101i	−0.980793	−	0.195050i	$-0.937513\pi$
$769$		−	299.988i		−	0.390101i	0.980793	−	0.195050i	$-0.0624871\pi$
$770$	−64.2455	+	399.421i	−0.0834357	+	0.518728i
$771$	−85.0126			−0.110263
$772$			625.654i			0.810433i
$773$	−1493.57			−1.93217			−0.966086	−	0.258219i	$-0.916864\pi$
$773$	−1493.57			−1.93217			−0.966086	+	0.258219i	$0.916864\pi$
$774$		−	152.449i		−	0.196963i
$775$	−16.5407	−	5.46235i	−0.0213428	−	0.00704819i
$776$		−	342.151i		−	0.440916i
$777$			601.471i			0.774094i
$778$	551.112			0.708370
$779$		−	705.241i		−	0.905316i
$780$	37.8999	−	235.628i	0.0485897	−	0.302087i
$781$		−	162.132i		−	0.207595i
$782$	992.209	+	360.871i	1.26881	+	0.461472i
$783$		−	139.675i		−	0.178385i
$784$	−639.316			−0.815454
$785$	172.885	−	1074.84i	0.220235	−	1.36923i
$786$	253.714			0.322792
$787$	97.7533			0.124210			0.0621050	−	0.998070i	$-0.480219\pi$
$787$	97.7533			0.124210			0.0621050	+	0.998070i	$0.480219\pi$
$788$		−	236.781i		−	0.300483i
$789$			586.554i			0.743414i
$790$	−62.9615	+	391.438i	−0.0796981	+	0.495491i
$791$	1798.40			2.27358
$792$	110.426			0.139427
$793$	−1259.77			−1.58861
$794$	360.855			0.454478
$795$	307.095	+	49.3951i	0.386283	+	0.0621323i
$796$		−	605.263i		−	0.760381i
$797$	230.206			0.288841			0.144420	−	0.989516i	$-0.453868\pi$
$797$	230.206			0.288841			0.144420	+	0.989516i	$0.453868\pi$
$798$		−	353.047i		−	0.442415i
$799$			1999.19i			2.50212i
$800$	−203.808	+	617.158i	−0.254760	+	0.771447i
$801$		−	17.4262i		−	0.0217555i
$802$	747.271			0.931759
$803$	−386.987			−0.481927
$804$			18.5831i			0.0231133i
$805$	1277.53	+	711.770i	1.58699	+	0.884186i
$806$	16.0065			0.0198592
$807$			271.220i			0.336084i
$808$			852.757i			1.05539i
$809$	−573.439			−0.708825			−0.354412	−	0.935089i	$-0.615319\pi$
$809$	−573.439			−0.708825			−0.354412	+	0.935089i	$0.615319\pi$
$810$	−66.1193	−	10.6351i	−0.0816288	−	0.0131297i
$811$	−667.428			−0.822969			−0.411485	−	0.911417i	$-0.634990\pi$
$811$	−667.428			−0.822969			−0.411485	+	0.911417i	$0.634990\pi$
$812$	−610.257			−0.751548
$813$		−	246.381i		−	0.303052i
$814$	173.743			0.213443
$815$	−477.268	−	76.7670i	−0.585605	−	0.0941926i
$816$			303.025i			0.371354i
$817$		−	367.769i		−	0.450145i
$818$			246.103i			0.300859i
$819$		−	588.901i		−	0.719049i
$820$	−92.8195	+	577.068i	−0.113195	+	0.703742i
$821$	260.045			0.316742			0.158371	−	0.987380i	$-0.449376\pi$
$821$	260.045			0.316742			0.158371	+	0.987380i	$0.449376\pi$
$822$	270.961			0.329636
$823$			1087.33i			1.32118i	0.750747	+	0.660590i	$0.229694\pi$
$823$			1087.33i			1.32118i	−0.750747	+	0.660590i	$0.770306\pi$
$824$			253.681i			0.307865i
$825$	175.789	+	58.0520i	0.213077	+	0.0703660i
$826$			497.780i			0.602639i
$827$	1253.20			1.51536			0.757681	−	0.652625i	$-0.226332\pi$
$827$	1253.20			1.51536			0.757681	+	0.652625i	$0.226332\pi$
$828$	42.1037	−	115.763i	0.0508498	−	0.139811i
$829$	−512.397			−0.618090			−0.309045	−	0.951047i	$-0.600009\pi$
$829$	−512.397			−0.618090			−0.309045	+	0.951047i	$0.600009\pi$
$830$	−624.875	−	100.509i	−0.752862	−	0.121095i
$831$	330.474			0.397682
$832$		−	947.440i		−	1.13875i
$833$	3476.78			4.17380
$834$	−218.604			−0.262115
$835$	−724.034	−	116.458i	−0.867107	−	0.139471i
$836$	82.2050			0.0983314
$837$			3.62053i			0.00432560i
$838$	145.693			0.173857
$839$			781.458i			0.931416i	0.884938	+	0.465708i	$0.154200\pi$
$839$			781.458i			0.931416i	−0.884938	+	0.465708i	$0.845800\pi$
$840$	−150.577	+	936.151i	−0.179258	+	1.11446i
$841$	−118.439			−0.140831
$842$	863.400			1.02542
$843$	−547.135			−0.649033
$844$	−252.562			−0.299244
$845$	−55.0103	+	342.004i	−0.0651009	+	0.404739i
$846$	−289.367			−0.342041
$847$	1306.29			1.54225
$848$	203.712			0.240226
$849$			360.639i			0.424781i
$850$	−359.866	+	1089.72i	−0.423372	+	1.28203i
$851$	214.673	−	590.239i	0.252259	−	0.693582i
$852$		−	117.263i		−	0.137632i
$853$		−	45.5152i		−	0.0533589i	−0.999644	−	0.0266795i	$-0.991507\pi$
$853$		−	45.5152i		−	0.0533589i	0.999644	−	0.0266795i	$-0.00849335\pi$
$854$	1544.50			1.80855
$855$	−159.506	−	25.6560i	−0.186557	−	0.0300070i
$856$		−	554.085i		−	0.647296i
$857$		−	766.778i		−	0.894724i	−0.894353	−	0.447362i	$-0.852364\pi$
$857$		−	766.778i		−	0.894724i	0.894353	−	0.447362i	$-0.147636\pi$
$858$	−170.112			−0.198266
$859$	1073.34			1.24952			0.624761	−	0.780816i	$-0.285196\pi$
$859$	1073.34			1.24952			0.624761	+	0.780816i	$0.285196\pi$
$860$	−48.4035	+	300.929i	−0.0562831	+	0.349918i
$861$			1442.26i			1.67510i
$862$	−1067.75			−1.23869
$863$		−	998.850i		−	1.15742i	−0.815535	−	0.578708i	$-0.803557\pi$
$863$		−	998.850i		−	1.15742i	0.815535	−	0.578708i	$-0.196443\pi$
$864$	135.087			0.156351
$865$	−32.4148	−	5.21381i	−0.0374737	−	0.00602753i
$866$		−	606.887i		−	0.700793i
$867$		−	1147.37i		−	1.32338i
$868$	15.8185			0.0182241
$869$	−227.795			−0.262135
$870$	55.0169	−	342.046i	0.0632378	−	0.393156i
$871$		−	92.7690i		−	0.106509i
$872$	678.246			0.777806
$873$	−119.222			−0.136565
$874$	−126.007	+	346.454i	−0.144173	+	0.396400i
$875$	−731.845	+	1411.11i	−0.836395	+	1.61269i
$876$	−279.891			−0.319510
$877$			147.510i			0.168198i	0.996457	+	0.0840991i	$0.0268012\pi$
$877$			147.510i			0.168198i	−0.996457	+	0.0840991i	$0.973199\pi$
$878$			612.951i			0.698122i
$879$		−	55.1412i		−	0.0627318i
$880$	119.707	+	19.2545i	0.136031	+	0.0218801i
$881$			1021.09i			1.15902i	0.814967	+	0.579508i	$0.196755\pi$
$881$			1021.09i			1.15902i	−0.814967	+	0.579508i	$0.803245\pi$
$882$			503.235i			0.570561i
$883$		−	1179.44i		−	1.33572i	−0.744288	−	0.667858i	$-0.767211\pi$
$883$		−	1179.44i		−	1.33572i	0.744288	−	0.667858i	$-0.232789\pi$
$884$			850.026i			0.961568i
$885$	224.896	+	36.1738i	0.254120	+	0.0408743i
$886$	641.967			0.724568
$887$			44.5648i			0.0502421i	0.999684	+	0.0251211i	$0.00799713\pi$
$887$			44.5648i			0.0502421i	−0.999684	+	0.0251211i	$0.992003\pi$
$888$	407.213			0.458574
$889$			2278.75i			2.56328i
$890$	6.86402	−	42.6743i	0.00771238	−	0.0479487i
$891$		−	38.4778i		−	0.0431849i
$892$		−	670.192i		−	0.751336i
$893$	−698.067			−0.781710
$894$			361.774i			0.404668i
$895$	55.3347	−	344.021i	0.0618264	−	0.384381i
$896$		−	160.847i		−	0.179516i
$897$	−210.186	+	577.903i	−0.234321	+	0.644262i
$898$			637.688i			0.710120i
$899$	−18.7296			−0.0208338
$900$	127.140	+	41.9864i	0.141267	+	0.0466516i
$901$	−1107.84			−1.22957
$902$	416.615			0.461880
$903$			752.108i			0.832899i
$904$		−	1217.57i		−	1.34687i
$905$	−602.352	−	96.8862i	−0.665582	−	0.107057i
$906$	552.210			0.609503
$907$	−909.225			−1.00245			−0.501227	−	0.865316i	$-0.667118\pi$
$907$	−909.225			−1.00245			−0.501227	+	0.865316i	$0.667118\pi$
$908$	−575.751			−0.634087
$909$	297.141			0.326888
$910$	231.963	−	1442.14i	0.254905	−	1.58477i
$911$			875.406i			0.960929i	0.877014	+	0.480464i	$0.159532\pi$
$911$			875.406i			0.960929i	−0.877014	+	0.480464i	$0.840468\pi$
$912$	−105.809			−0.116018
$913$		−	363.643i		−	0.398294i
$914$		−	622.862i		−	0.681468i
$915$	112.239	−	697.802i	0.122666	−	0.762625i
$916$			36.9119i			0.0402968i
$917$	−1251.70			−1.36499
$918$	238.525			0.259831
$919$		−	357.631i		−	0.389152i	−0.980887	−	0.194576i	$-0.937667\pi$
$919$		−	357.631i		−	0.389152i	0.980887	−	0.194576i	$-0.0623331\pi$
$920$	481.889	−	864.925i	0.523792	−	0.940136i
$921$	−427.793			−0.464487
$922$		−	278.445i		−	0.302001i
$923$			585.388i			0.634224i
$924$	−168.114			−0.181942
$925$	648.246	+	214.075i	0.700807	+	0.231432i
$926$	−1364.15			−1.47316
$927$	88.3942			0.0953552
$928$			698.828i			0.753047i
$929$	−833.634			−0.897346			−0.448673	−	0.893696i	$-0.648103\pi$
$929$	−833.634			−0.897346			−0.448673	+	0.893696i	$0.648103\pi$
$930$	−1.42610	+	8.86619i	−0.00153344	+	0.00953353i
$931$			1214.00i			1.30398i
$932$			314.834i			0.337805i
$933$			732.172i			0.784751i
$934$			439.341i			0.470386i
$935$	−651.000	−	104.711i	−0.696256	−	0.111990i
$936$	−398.703			−0.425965
$937$	405.050			0.432284			0.216142	−	0.976362i	$-0.430653\pi$
$937$	405.050			0.432284			0.216142	+	0.976362i	$0.430653\pi$
$938$			113.736i			0.121254i
$939$		−	756.744i		−	0.805904i
$940$	571.198	+	91.8754i	0.607658	+	0.0977397i
$941$			95.5436i			0.101534i	0.998711	+	0.0507670i	$0.0161666\pi$
$941$			95.5436i			0.101534i	−0.998711	+	0.0507670i	$0.983833\pi$
$942$	−561.234			−0.595790
$943$	514.760	−	1415.32i	0.545875	−	1.50087i
$944$	149.185			0.158035
$945$	326.199	+	52.4680i	0.345184	+	0.0555217i
$946$	217.256			0.229658
$947$		−	1280.55i		−	1.35222i	−0.736801	−	0.676109i	$-0.763665\pi$
$947$		−	1280.55i		−	1.35222i	0.736801	−	0.676109i	$-0.236335\pi$
$948$	−164.754			−0.173791
$949$	1397.25			1.47234
$950$	−380.503	−	125.656i	−0.400529	−	0.132270i
$951$	−444.687			−0.467599
$952$		−	3377.16i		−	3.54743i
$953$	1307.15			1.37162			0.685809	−	0.727782i	$-0.259449\pi$
$953$	1307.15			1.37162			0.685809	+	0.727782i	$0.259449\pi$
$954$		−	160.351i		−	0.168083i
$955$	51.4330	+	8.27282i	0.0538565	+	0.00866264i
$956$	569.228			0.595426
$957$	199.051			0.207995
$958$	704.953			0.735860
$959$	−1336.78			−1.39393
$960$	524.798	+	84.4119i	0.546664	+	0.0879291i
$961$	−960.515			−0.999495
$962$	−627.312			−0.652091
$963$	−193.069			−0.200487
$964$		−	415.650i		−	0.431172i
$965$	1730.05	+	278.273i	1.79280	+	0.288366i
$966$	257.692	−	708.518i	0.266761	−	0.733455i
$967$			599.640i			0.620103i	0.950720	+	0.310051i	$0.100346\pi$
$967$			599.640i			0.620103i	−0.950720	+	0.310051i	$0.899654\pi$
$968$		−	884.396i		−	0.913632i
$969$	575.417			0.593826
$970$	−291.957	−	46.9604i	−0.300987	−	0.0484127i
$971$			118.802i			0.122350i	0.998127	+	0.0611751i	$0.0194848\pi$
$971$			118.802i			0.122350i	−0.998127	+	0.0611751i	$0.980515\pi$
$972$		−	27.8293i		−	0.0286309i
$973$	1078.48			1.10841
$974$	137.089			0.140748
$975$	−634.699	−	209.601i	−0.650973	−	0.214975i
$976$		−	462.888i		−	0.474271i
$977$	−665.578			−0.681247			−0.340623	−	0.940200i	$-0.610638\pi$
$977$	−665.578			−0.681247			−0.340623	+	0.940200i	$0.610638\pi$
$978$			249.208i			0.254814i
$979$	24.8341			0.0253668
$980$	159.780	−	993.366i	0.163040	−	1.01364i
$981$		−	236.333i		−	0.240910i
$982$			294.297i			0.299691i
$983$	715.970			0.728352			0.364176	−	0.931330i	$-0.381351\pi$
$983$	715.970			0.728352			0.364176	+	0.931330i	$0.381351\pi$
$984$	976.451			0.992328
$985$	−654.743	−	105.313i	−0.664714	−	0.106917i
$986$			1233.93i			1.25145i
$987$	1427.59			1.44639
$988$	−296.807			−0.300412
$989$	268.437	−	738.062i	0.271423	−	0.746271i
$990$	15.1561	−	94.2269i	0.0153092	−	0.0951787i
$991$	1839.35			1.85606			0.928029	−	0.372507i	$-0.121502\pi$
$991$	1839.35			1.85606			0.928029	+	0.372507i	$0.121502\pi$
$992$		−	18.1144i		−	0.0182605i
$993$		−	1013.30i		−	1.02044i
$994$		−	717.695i		−	0.722027i
$995$	−1673.67	−	269.204i	−1.68208	−	0.270556i
$996$		−	263.007i		−	0.264063i
$997$			1310.89i			1.31483i	0.753528	+	0.657416i	$0.228350\pi$
$997$			1310.89i			1.31483i	−0.753528	+	0.657416i	$0.771650\pi$
$998$			1298.38i			1.30098i
$999$		−	141.892i		−	0.142034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.3.d.a.229.16	yes	48
5.4	even	2	inner	345.3.d.a.229.33	yes	48
23.22	odd	2	inner	345.3.d.a.229.15	✓	48
115.114	odd	2	inner	345.3.d.a.229.34	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.3.d.a.229.15	✓	48	23.22	odd	2	inner
345.3.d.a.229.16	yes	48	1.1	even	1	trivial
345.3.d.a.229.33	yes	48	5.4	even	2	inner
345.3.d.a.229.34	yes	48	115.114	odd	2	inner

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	345.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.48820i q^{2} -1.73205i q^{3} +1.78525 q^{4} +(0.794027 - 4.93655i) q^{5} -2.57765 q^{6} +12.7168 q^{7} -8.60963i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.48820i q^{2} -1.73205i q^{3} +1.78525 q^{4} +(0.794027 - 4.93655i) q^{5} -2.57765 q^{6} +12.7168 q^{7} -8.60963i q^{8} -3.00000 q^{9} +(-7.34659 - 1.18167i) q^{10} -4.27531i q^{11} -3.09214i q^{12} +15.4363i q^{13} -18.9252i q^{14} +(-8.55035 - 1.37530i) q^{15} -5.67190 q^{16} +30.8454 q^{17} +4.46461i q^{18} +10.7704i q^{19} +(1.41754 - 8.81297i) q^{20} -22.0261i q^{21} -6.36253 q^{22} +(-7.86140 + 21.6148i) q^{23} -14.9123 q^{24} +(-23.7390 - 7.83951i) q^{25} +22.9724 q^{26} +5.19615i q^{27} +22.7026 q^{28} -26.8805 q^{29} +(-2.04672 + 12.7247i) q^{30} +0.696771 q^{31} -25.9976i q^{32} -7.40505 q^{33} -45.9042i q^{34} +(10.0975 - 62.7770i) q^{35} -5.35574 q^{36} -27.3072 q^{37} +16.0286 q^{38} +26.7365 q^{39} +(-42.5019 - 6.83628i) q^{40} -65.4795 q^{41} -32.7793 q^{42} -34.1462 q^{43} -7.63249i q^{44} +(-2.38208 + 14.8096i) q^{45} +(32.1672 + 11.6994i) q^{46} +64.8134i q^{47} +9.82401i q^{48} +112.716 q^{49} +(-11.6668 + 35.3285i) q^{50} -53.4257i q^{51} +27.5577i q^{52} -35.9160 q^{53} +7.73294 q^{54} +(-21.1053 - 3.39471i) q^{55} -109.487i q^{56} +18.6549 q^{57} +40.0037i q^{58} -26.3025 q^{59} +(-15.2645 - 2.45524i) q^{60} +81.6109i q^{61} -1.03694i q^{62} -38.1503 q^{63} -61.3773 q^{64} +(76.2022 + 12.2569i) q^{65} +11.0202i q^{66} -6.00979 q^{67} +55.0666 q^{68} +(37.4379 + 13.6163i) q^{69} +(-93.4250 - 15.0271i) q^{70} +37.9228 q^{71} +25.8289i q^{72} -90.5168i q^{73} +40.6387i q^{74} +(-13.5784 + 41.1172i) q^{75} +19.2279i q^{76} -54.3682i q^{77} -39.7894i q^{78} -53.2816i q^{79} +(-4.50364 + 27.9996i) q^{80} +9.00000 q^{81} +97.4468i q^{82} +85.0565 q^{83} -39.3221i q^{84} +(24.4921 - 152.270i) q^{85} +50.8165i q^{86} +46.5584i q^{87} -36.8088 q^{88} +5.80872i q^{89} +(22.0398 + 3.54502i) q^{90} +196.300i q^{91} +(-14.0346 + 38.5877i) q^{92} -1.20684i q^{93} +96.4556 q^{94} +(53.1687 + 8.55200i) q^{95} -45.0291 q^{96} +39.7405 q^{97} -167.745i q^{98} +12.8259i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9}+O(q^{10}) \) 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9	\( 48 q - 92 q^{4} + 12 q^{6} - 144 q^{9} + 148 q^{16} - 12 q^{24} - 64 q^{25} + 136 q^{26} + 76 q^{29} - 68 q^{31} - 108 q^{35} + 276 q^{36} + 48 q^{39} + 20 q^{41} + 344 q^{46} + 412 q^{49} - 352 q^{50} - 36 q^{54} - 184 q^{55} - 396 q^{59} - 684 q^{64} - 144 q^{69} + 600 q^{70} + 156 q^{71} - 120 q^{75} + 432 q^{81} - 76 q^{85} + 112 q^{95} + 516 q^{96}+O(q^{100}) \) 48 * q - 92 * q^4 + 12 * q^6 - 144 * q^9 + 148 * q^16 - 12 * q^24 - 64 * q^25 + 136 * q^26 + 76 * q^29 - 68 * q^31 - 108 * q^35 + 276 * q^36 + 48 * q^39 + 20 * q^41 + 344 * q^46 + 412 * q^49 - 352 * q^50 - 36 * q^54 - 184 * q^55 - 396 * q^59 - 684 * q^64 - 144 * q^69 + 600 * q^70 + 156 * q^71 - 120 * q^75 + 432 * q^81 - 76 * q^85 + 112 * q^95 + 516 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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