LMFDB - Embedded newform 684.3.g.d.343.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.4
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83969 + 0.784567i) q^{2} +(2.76891 - 2.88672i) q^{4} -6.85656 q^{5} +3.48151i q^{7} +(-2.82911 + 7.48306i) q^{8} +O(q^{10})$	\(q+(-1.83969 + 0.784567i) q^{2} +(2.76891 - 2.88672i) q^{4} -6.85656 q^{5} +3.48151i q^{7} +(-2.82911 + 7.48306i) q^{8} +(12.6139 - 5.37943i) q^{10} +1.50468i q^{11} +0.937697 q^{13} +(-2.73148 - 6.40489i) q^{14} +(-0.666287 - 15.9861i) q^{16} -17.5278 q^{17} +4.35890i q^{19} +(-18.9852 + 19.7930i) q^{20} +(-1.18053 - 2.76815i) q^{22} +9.27180i q^{23} +22.0124 q^{25} +(-1.72507 + 0.735686i) q^{26} +(10.0501 + 9.63998i) q^{28} -4.00078 q^{29} +21.0627i q^{31} +(13.7679 + 28.8867i) q^{32} +(32.2457 - 13.7517i) q^{34} -23.8712i q^{35} -13.0995 q^{37} +(-3.41985 - 8.01902i) q^{38} +(19.3979 - 51.3080i) q^{40} +30.0397 q^{41} -50.7290i q^{43} +(4.34360 + 4.16633i) q^{44} +(-7.27435 - 17.0572i) q^{46} -74.1179i q^{47} +36.8791 q^{49} +(-40.4959 + 17.2702i) q^{50} +(2.59640 - 2.70687i) q^{52} +18.4542 q^{53} -10.3170i q^{55} +(-26.0523 - 9.84955i) q^{56} +(7.36019 - 3.13888i) q^{58} -13.0255i q^{59} +12.7314 q^{61} +(-16.5251 - 38.7488i) q^{62} +(-47.9923 - 42.3407i) q^{64} -6.42937 q^{65} -48.1521i q^{67} +(-48.5328 + 50.5978i) q^{68} +(18.7285 + 43.9155i) q^{70} +20.6631i q^{71} -53.9322 q^{73} +(24.0989 - 10.2774i) q^{74} +(12.5829 + 12.0694i) q^{76} -5.23857 q^{77} -111.084i q^{79} +(4.56844 + 109.610i) q^{80} +(-55.2636 + 23.5681i) q^{82} -107.836i q^{83} +120.180 q^{85} +(39.8003 + 93.3255i) q^{86} +(-11.2596 - 4.25691i) q^{88} +136.537 q^{89} +3.26460i q^{91} +(26.7651 + 25.6728i) q^{92} +(58.1505 + 136.354i) q^{94} -29.8870i q^{95} +70.1306 q^{97} +(-67.8461 + 28.9341i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4}+O(q^{10}) $ 36 * q - 12 * q^4	$ 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) $ 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.83969	+	0.784567i	−0.919844	+	0.392284i
$2$	−1.83969	+	0.784567i	−0.919844	+	0.392284i
$3$		0			0
$3$		0			0
$4$	2.76891	−	2.88672i	0.692227	−	0.721680i
$5$	−6.85656			−1.37131			−0.685656	−	0.727926i	$-0.740484\pi$
$5$	−6.85656			−1.37131			−0.685656	+	0.727926i	$0.740484\pi$
$6$		0			0
$7$			3.48151i			0.497358i	0.968586	+	0.248679i	$0.0799965\pi$
$7$			3.48151i			0.497358i	−0.968586	+	0.248679i	$0.920004\pi$
$8$	−2.82911	+	7.48306i	−0.353638	+	0.935382i
$9$		0			0
$10$	12.6139	−	5.37943i	1.26139	−	0.537943i
$11$			1.50468i			0.136789i	0.997658	+	0.0683947i	$0.0217877\pi$
$11$			1.50468i			0.136789i	−0.997658	+	0.0683947i	$0.978212\pi$
$12$		0			0
$13$	0.937697			0.0721305			0.0360653	−	0.999349i	$-0.488518\pi$
$13$	0.937697			0.0721305			0.0360653	+	0.999349i	$0.488518\pi$
$14$	−2.73148	−	6.40489i	−0.195105	−	0.457492i
$15$		0			0
$16$	−0.666287	−	15.9861i	−0.0416429	−	0.999133i
$17$	−17.5278			−1.03105			−0.515523	−	0.856876i	$-0.672402\pi$
$17$	−17.5278			−1.03105			−0.515523	+	0.856876i	$0.672402\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−18.9852	+	19.7930i	−0.949259	+	0.989648i
$21$		0			0
$22$	−1.18053	−	2.76815i	−0.0536603	−	0.125825i
$23$			9.27180i			0.403122i	0.979476	+	0.201561i	$0.0646014\pi$
$23$			9.27180i			0.403122i	−0.979476	+	0.201561i	$0.935399\pi$
$24$		0			0
$25$	22.0124			0.880495
$26$	−1.72507	+	0.735686i	−0.0663488	+	0.0282956i
$27$		0			0
$28$	10.0501	+	9.63998i	0.358933	+	0.344285i
$29$	−4.00078			−0.137958			−0.0689790	−	0.997618i	$-0.521974\pi$
$29$	−4.00078			−0.137958			−0.0689790	+	0.997618i	$0.521974\pi$
$30$		0			0
$31$			21.0627i			0.679442i	0.940526	+	0.339721i	$0.110333\pi$
$31$			21.0627i			0.679442i	−0.940526	+	0.339721i	$0.889667\pi$
$32$	13.7679	+	28.8867i	0.430248	+	0.902711i
$33$		0			0
$34$	32.2457	−	13.7517i	0.948402	−	0.404462i
$35$		−	23.8712i		−	0.682033i
$36$		0			0
$37$	−13.0995			−0.354040			−0.177020	−	0.984207i	$-0.556646\pi$
$37$	−13.0995			−0.354040			−0.177020	+	0.984207i	$0.556646\pi$
$38$	−3.41985	−	8.01902i	−0.0899960	−	0.211027i
$39$		0			0
$40$	19.3979	−	51.3080i	0.484948	−	1.28270i
$41$	30.0397			0.732675			0.366337	−	0.930482i	$-0.380612\pi$
$41$	30.0397			0.732675			0.366337	+	0.930482i	$0.380612\pi$
$42$		0			0
$43$		−	50.7290i		−	1.17974i	−0.807497	−	0.589872i	$-0.799178\pi$
$43$		−	50.7290i		−	1.17974i	0.807497	−	0.589872i	$-0.200822\pi$
$44$	4.34360	+	4.16633i	0.0987182	+	0.0946894i
$45$		0			0
$46$	−7.27435	−	17.0572i	−0.158138	−	0.370809i
$47$		−	74.1179i		−	1.57698i	−0.615049	−	0.788489i	$-0.710864\pi$
$47$		−	74.1179i		−	1.57698i	0.615049	−	0.788489i	$-0.289136\pi$
$48$		0			0
$49$	36.8791			0.752635
$50$	−40.4959	+	17.2702i	−0.809918	+	0.345404i
$51$		0			0
$52$	2.59640	−	2.70687i	0.0499307	−	0.0520551i
$53$	18.4542			0.348192			0.174096	−	0.984729i	$-0.444300\pi$
$53$	18.4542			0.348192			0.174096	+	0.984729i	$0.444300\pi$
$54$		0			0
$55$		−	10.3170i		−	0.187581i
$56$	−26.0523	−	9.84955i	−0.465220	−	0.175885i
$57$		0			0
$58$	7.36019	−	3.13888i	0.126900	−	0.0541187i
$59$		−	13.0255i		−	0.220771i	−0.993889	−	0.110386i	$-0.964791\pi$
$59$		−	13.0255i		−	0.220771i	0.993889	−	0.110386i	$-0.0352086\pi$
$60$		0			0
$61$	12.7314			0.208711			0.104356	−	0.994540i	$-0.466722\pi$
$61$	12.7314			0.208711			0.104356	+	0.994540i	$0.466722\pi$
$62$	−16.5251	−	38.7488i	−0.266534	−	0.624981i
$63$		0			0
$64$	−47.9923	−	42.3407i	−0.749880	−	0.661574i
$65$	−6.42937			−0.0989134
$66$		0			0
$67$		−	48.1521i		−	0.718688i	−0.933205	−	0.359344i	$-0.883000\pi$
$67$		−	48.1521i		−	0.718688i	0.933205	−	0.359344i	$-0.117000\pi$
$68$	−48.5328	+	50.5978i	−0.713718	+	0.744085i
$69$		0			0
$70$	18.7285	+	43.9155i	0.267550	+	0.627364i
$71$			20.6631i			0.291030i	0.989356	+	0.145515i	$0.0464839\pi$
$71$			20.6631i			0.291030i	−0.989356	+	0.145515i	$0.953516\pi$
$72$		0			0
$73$	−53.9322			−0.738797			−0.369399	−	0.929271i	$-0.620436\pi$
$73$	−53.9322			−0.738797			−0.369399	+	0.929271i	$0.620436\pi$
$74$	24.0989	−	10.2774i	0.325661	−	0.138884i
$75$		0			0
$76$	12.5829	+	12.0694i	0.165565	+	0.158808i
$77$	−5.23857			−0.0680334
$78$		0			0
$79$		−	111.084i		−	1.40613i	−0.711128	−	0.703063i	$-0.751815\pi$
$79$		−	111.084i		−	1.40613i	0.711128	−	0.703063i	$-0.248185\pi$
$80$	4.56844	+	109.610i	0.0571054	+	1.37012i
$81$		0			0
$82$	−55.2636	+	23.5681i	−0.673947	+	0.287416i
$83$		−	107.836i		−	1.29923i	−0.760262	−	0.649616i	$-0.774930\pi$
$83$		−	107.836i		−	1.29923i	0.760262	−	0.649616i	$-0.225070\pi$
$84$		0			0
$85$	120.180			1.41389
$86$	39.8003	+	93.3255i	0.462794	+	1.08518i
$87$		0			0
$88$	−11.2596	−	4.25691i	−0.127950	−	0.0483740i
$89$	136.537			1.53412			0.767060	−	0.641575i	$-0.221719\pi$
$89$	136.537			1.53412			0.767060	+	0.641575i	$0.221719\pi$
$90$		0			0
$91$			3.26460i			0.0358747i
$92$	26.7651	+	25.6728i	0.290925	+	0.279052i
$93$		0			0
$94$	58.1505	+	136.354i	0.618622	+	1.45057i
$95$		−	29.8870i		−	0.314600i
$96$		0			0
$97$	70.1306			0.722996			0.361498	−	0.932373i	$-0.382265\pi$
$97$	70.1306			0.722996			0.361498	+	0.932373i	$0.382265\pi$
$98$	−67.8461	+	28.9341i	−0.692307	+	0.295246i
$99$		0			0
$100$	60.9503	−	63.5435i	0.609503	−	0.635435i
$101$	106.813			1.05755			0.528777	−	0.848761i	$-0.322651\pi$
$101$	106.813			1.05755			0.528777	+	0.848761i	$0.322651\pi$
$102$		0			0
$103$		−	136.543i		−	1.32566i	−0.748768	−	0.662832i	$-0.769354\pi$
$103$		−	136.543i		−	1.32566i	0.748768	−	0.662832i	$-0.230646\pi$
$104$	−2.65284	+	7.01684i	−0.0255081	+	0.0674696i
$105$		0			0
$106$	−33.9499	+	14.4785i	−0.320282	+	0.136590i
$107$		−	65.2362i		−	0.609684i	−0.952403	−	0.304842i	$-0.901396\pi$
$107$		−	65.2362i		−	0.609684i	0.952403	−	0.304842i	$-0.0986036\pi$
$108$		0			0
$109$	15.7329			0.144339			0.0721694	−	0.997392i	$-0.477008\pi$
$109$	15.7329			0.144339			0.0721694	+	0.997392i	$0.477008\pi$
$110$	8.09434	+	18.9800i	0.0735849	+	0.172545i
$111$		0			0
$112$	55.6558	−	2.31968i	0.496927	−	0.0207115i
$113$	−15.7564			−0.139437			−0.0697185	−	0.997567i	$-0.522210\pi$
$113$	−15.7564			−0.139437			−0.0697185	+	0.997567i	$0.522210\pi$
$114$		0			0
$115$		−	63.5726i		−	0.552806i
$116$	−11.0778	+	11.5491i	−0.0954983	+	0.0995615i
$117$		0			0
$118$	10.2194	+	23.9629i	0.0866049	+	0.203075i
$119$		−	61.0231i		−	0.512799i
$120$		0			0
$121$	118.736			0.981289
$122$	−23.4218	+	9.98864i	−0.191982	+	0.0818741i
$123$		0			0
$124$	60.8021	+	58.3207i	0.490340	+	0.470328i
$125$	20.4848			0.163879
$126$		0			0
$127$			115.630i			0.910475i	0.890370	+	0.455237i	$0.150446\pi$
$127$			115.630i			0.910475i	−0.890370	+	0.455237i	$0.849554\pi$
$128$	121.510	+	40.2406i	0.949297	+	0.314379i
$129$		0			0
$130$	11.8280	−	5.04427i	0.0909849	−	0.0388021i
$131$		−	191.396i		−	1.46104i	−0.682893	−	0.730518i	$-0.739279\pi$
$131$		−	191.396i		−	1.46104i	0.682893	−	0.730518i	$-0.260721\pi$
$132$		0			0
$133$	−15.1755			−0.114102
$134$	37.7786	+	88.5849i	0.281930	+	0.661082i
$135$		0			0
$136$	49.5880	−	131.161i	0.364617	−	0.964422i
$137$	−51.8540			−0.378497			−0.189248	−	0.981929i	$-0.560605\pi$
$137$	−51.8540			−0.378497			−0.189248	+	0.981929i	$0.560605\pi$
$138$		0			0
$139$			95.1434i			0.684485i	0.939612	+	0.342243i	$0.111186\pi$
$139$			95.1434i			0.684485i	−0.939612	+	0.342243i	$0.888814\pi$
$140$	−68.9093	−	66.0971i	−0.492209	−	0.472122i
$141$		0			0
$142$	−16.2116	−	38.0137i	−0.114166	−	0.267702i
$143$			1.41094i			0.00986669i
$144$		0			0
$145$	27.4316			0.189183
$146$	99.2185	−	42.3134i	0.679579	−	0.289818i
$147$		0			0
$148$	−36.2712	+	37.8145i	−0.245076	+	0.255503i
$149$	134.656			0.903731			0.451866	−	0.892086i	$-0.350759\pi$
$149$	134.656			0.903731			0.451866	+	0.892086i	$0.350759\pi$
$150$		0			0
$151$			197.754i			1.30963i	0.755789	+	0.654816i	$0.227254\pi$
$151$			197.754i			1.30963i	−0.755789	+	0.654816i	$0.772746\pi$
$152$	−32.6179	−	12.3318i	−0.214591	−	0.0811302i
$153$		0			0
$154$	9.63734	−	4.11001i	0.0625801	−	0.0266884i
$155$		−	144.418i		−	0.931727i
$156$		0			0
$157$	−153.626			−0.978508			−0.489254	−	0.872141i	$-0.662731\pi$
$157$	−153.626			−0.978508			−0.489254	+	0.872141i	$0.662731\pi$
$158$	87.1528	+	204.360i	0.551600	+	1.29342i
$159$		0			0
$160$	−94.4007	−	198.064i	−0.590004	−	1.23790i
$161$	−32.2799			−0.200496
$162$		0			0
$163$			91.8571i			0.563540i	0.959482	+	0.281770i	$0.0909216\pi$
$163$			91.8571i			0.563540i	−0.959482	+	0.281770i	$0.909078\pi$
$164$	83.1771	−	86.7161i	0.507178	−	0.528757i
$165$		0			0
$166$	84.6048	+	198.385i	0.509667	+	1.19509i
$167$		−	90.1229i		−	0.539658i	−0.962908	−	0.269829i	$-0.913033\pi$
$167$		−	90.1229i		−	0.539658i	0.962908	−	0.269829i	$-0.0869672\pi$
$168$		0			0
$169$	−168.121			−0.994797
$170$	−221.094	+	94.2895i	−1.30055	+	0.554644i
$171$		0			0
$172$	−146.440	−	140.464i	−0.851397	−	0.816650i
$173$	174.970			1.01139			0.505694	−	0.862713i	$-0.331237\pi$
$173$	174.970			1.01139			0.505694	+	0.862713i	$0.331237\pi$
$174$		0			0
$175$			76.6363i			0.437921i
$176$	24.0541	−	1.00255i	0.136671	−	0.00569631i
$177$		0			0
$178$	−251.185	+	107.122i	−1.41115	+	0.601810i
$179$		−	337.723i		−	1.88672i	−0.331773	−	0.943359i	$-0.607647\pi$
$179$		−	337.723i		−	1.88672i	0.331773	−	0.943359i	$-0.392353\pi$
$180$		0			0
$181$	−354.420			−1.95812			−0.979061	−	0.203566i	$-0.934747\pi$
$181$	−354.420			−1.95812			−0.979061	+	0.203566i	$0.934747\pi$
$182$	−2.56130	−	6.00584i	−0.0140731	−	0.0329991i
$183$		0			0
$184$	−69.3814	−	26.2309i	−0.377073	−	0.142559i
$185$	89.8172			0.485499
$186$		0			0
$187$		−	26.3738i		−	0.141036i
$188$	−213.958	−	205.226i	−1.13807	−	1.09163i
$189$		0			0
$190$	23.4484	+	54.9828i	0.123413	+	0.289383i
$191$			252.341i			1.32116i	0.750757	+	0.660579i	$0.229689\pi$
$191$			252.341i			1.32116i	−0.750757	+	0.660579i	$0.770311\pi$
$192$		0			0
$193$	−76.1396			−0.394506			−0.197253	−	0.980353i	$-0.563202\pi$
$193$	−76.1396			−0.394506			−0.197253	+	0.980353i	$0.563202\pi$
$194$	−129.019	+	55.0222i	−0.665044	+	0.283619i
$195$		0			0
$196$	102.115	−	106.460i	0.520994	−	0.543161i
$197$	−189.204			−0.960429			−0.480214	−	0.877151i	$-0.659441\pi$
$197$	−189.204			−0.960429			−0.480214	+	0.877151i	$0.659441\pi$
$198$		0			0
$199$			248.391i			1.24820i	0.781346	+	0.624098i	$0.214533\pi$
$199$			248.391i			1.24820i	−0.781346	+	0.624098i	$0.785467\pi$
$200$	−62.2753	+	164.720i	−0.311377	+	0.823599i
$201$		0			0
$202$	−196.502	+	83.8019i	−0.972785	+	0.414861i
$203$		−	13.9288i		−	0.0686145i
$204$		0			0
$205$	−205.969			−1.00473
$206$	107.127	+	251.197i	0.520036	+	1.21940i
$207$		0			0
$208$	−0.624775	−	14.9901i	−0.00300373	−	0.0720679i
$209$	−6.55877			−0.0313817
$210$		0			0
$211$		−	198.497i		−	0.940742i	−0.882469	−	0.470371i	$-0.844120\pi$
$211$		−	198.497i		−	0.940742i	0.882469	−	0.470371i	$-0.155880\pi$
$212$	51.0979	−	53.2720i	0.241028	−	0.251283i
$213$		0			0
$214$	51.1821	+	120.014i	0.239169	+	0.560814i
$215$			347.826i			1.61780i
$216$		0			0
$217$	−73.3300			−0.337926
$218$	−28.9437	+	12.3435i	−0.132769	+	0.0566217i
$219$		0			0
$220$	−29.7821	−	28.5667i	−0.135373	−	0.129849i
$221$	−16.4357			−0.0743699
$222$		0			0
$223$			69.7435i			0.312751i	0.987698	+	0.156376i	$0.0499810\pi$
$223$			69.7435i			0.312751i	−0.987698	+	0.156376i	$0.950019\pi$
$224$	−100.569	+	47.9332i	−0.448971	+	0.213988i
$225$		0			0
$226$	28.9868	−	12.3619i	0.128260	−	0.0546988i
$227$		−	136.171i		−	0.599871i	−0.953960	−	0.299935i	$-0.903035\pi$
$227$		−	136.171i		−	0.599871i	0.953960	−	0.299935i	$-0.0969651\pi$
$228$		0			0
$229$	297.925			1.30098			0.650492	−	0.759513i	$-0.274563\pi$
$229$	297.925			1.30098			0.650492	+	0.759513i	$0.274563\pi$
$230$	49.8770	+	116.954i	0.216857	+	0.508495i
$231$		0			0
$232$	11.3186	−	29.9381i	0.0487872	−	0.129043i
$233$	−195.861			−0.840607			−0.420304	−	0.907384i	$-0.638076\pi$
$233$	−195.861			−0.840607			−0.420304	+	0.907384i	$0.638076\pi$
$234$		0			0
$235$			508.194i			2.16253i
$236$	−37.6009	−	36.0664i	−0.159326	−	0.152824i
$237$		0			0
$238$	47.8767	+	112.264i	0.201163	+	0.471696i
$239$			59.6836i			0.249722i	0.992174	+	0.124861i	$0.0398485\pi$
$239$			59.6836i			0.249722i	−0.992174	+	0.124861i	$0.960151\pi$
$240$		0			0
$241$	38.2215			0.158595			0.0792977	−	0.996851i	$-0.474732\pi$
$241$	38.2215			0.158595			0.0792977	+	0.996851i	$0.474732\pi$
$242$	−218.437	+	93.1563i	−0.902633	+	0.384943i
$243$		0			0
$244$	35.2521	−	36.7520i	0.144476	−	0.150623i
$245$	−252.864			−1.03210
$246$		0			0
$247$			4.08733i			0.0165479i
$248$	−157.613	−	59.5886i	−0.635538	−	0.240277i
$249$		0			0
$250$	−37.6857	+	16.0717i	−0.150743	+	0.0642868i
$251$			65.6105i			0.261396i	0.991422	+	0.130698i	$0.0417219\pi$
$251$			65.6105i			0.261396i	−0.991422	+	0.130698i	$0.958278\pi$
$252$		0			0
$253$	−13.9511			−0.0551428
$254$	−90.7197	−	212.724i	−0.357164	−	0.837495i
$255$		0			0
$256$	−255.112	+	21.3027i	−0.996532	+	0.0832136i
$257$	267.641			1.04141			0.520703	−	0.853738i	$-0.325670\pi$
$257$	267.641			1.04141			0.520703	+	0.853738i	$0.325670\pi$
$258$		0			0
$259$		−	45.6059i		−	0.176085i
$260$	−17.8023	+	18.5598i	−0.0684705	+	0.0713838i
$261$		0			0
$262$	150.163	+	352.109i	0.573141	+	1.34393i
$263$			354.015i			1.34607i	0.739613	+	0.673033i	$0.235009\pi$
$263$			354.015i			1.34607i	−0.739613	+	0.673033i	$0.764991\pi$
$264$		0			0
$265$	−126.532			−0.477479
$266$	27.9183	−	11.9062i	0.104956	−	0.0447603i
$267$		0			0
$268$	−139.002	−	133.329i	−0.518663	−	0.497496i
$269$	−392.148			−1.45780			−0.728900	−	0.684621i	$-0.759968\pi$
$269$	−392.148			−1.45780			−0.728900	+	0.684621i	$0.759968\pi$
$270$		0			0
$271$			69.1456i			0.255150i	0.991829	+	0.127575i	$0.0407193\pi$
$271$			69.1456i			0.255150i	−0.991829	+	0.127575i	$0.959281\pi$
$272$	11.6785	+	280.201i	0.0429358	+	1.03015i
$273$		0			0
$274$	95.3953	−	40.6830i	0.348158	−	0.148478i
$275$			33.1217i			0.120442i
$276$		0			0
$277$	−295.659			−1.06736			−0.533680	−	0.845687i	$-0.679191\pi$
$277$	−295.659			−1.06736			−0.533680	+	0.845687i	$0.679191\pi$
$278$	−74.6464	−	175.034i	−0.268512	−	0.629620i
$279$		0			0
$280$	178.629	+	67.5340i	0.637962	+	0.241193i
$281$	−114.200			−0.406405			−0.203203	−	0.979137i	$-0.565135\pi$
$281$	−114.200			−0.406405			−0.203203	+	0.979137i	$0.565135\pi$
$282$		0			0
$283$		−	422.450i		−	1.49276i	−0.665523	−	0.746378i	$-0.731791\pi$
$283$		−	422.450i		−	1.49276i	0.665523	−	0.746378i	$-0.268209\pi$
$284$	59.6487	+	57.2144i	0.210031	+	0.201459i
$285$		0			0
$286$	−1.10697	−	2.59569i	−0.00387054	−	0.00907582i
$287$			104.583i			0.364402i
$288$		0			0
$289$	18.2232			0.0630561
$290$	−50.4656	+	21.5219i	−0.174019	+	0.0742135i
$291$		0			0
$292$	−149.333	+	155.687i	−0.511416	+	0.533175i
$293$	14.8354			0.0506329			0.0253164	−	0.999679i	$-0.491941\pi$
$293$	14.8354			0.0506329			0.0253164	+	0.999679i	$0.491941\pi$
$294$		0			0
$295$			89.3101i			0.302746i
$296$	37.0598	−	98.0241i	0.125202	−	0.331162i
$297$		0			0
$298$	−247.725	+	105.647i	−0.831292	+	0.354519i
$299$			8.69414i			0.0290774i
$300$		0			0
$301$	176.613			0.586755
$302$	−155.152	−	363.806i	−0.513747	−	1.20466i
$303$		0			0
$304$	69.6819	−	2.90428i	0.229217	−	0.00955355i
$305$	−87.2936			−0.286208
$306$		0			0
$307$		−	23.7714i		−	0.0774312i	−0.999250	−	0.0387156i	$-0.987673\pi$
$307$		−	23.7714i		−	0.0774312i	0.999250	−	0.0387156i	$-0.0123266\pi$
$308$	−14.5051	+	15.1223i	−0.0470945	+	0.0490983i
$309$		0			0
$310$	113.305	+	265.684i	0.365501	+	0.857044i
$311$		−	524.800i		−	1.68746i	−0.536767	−	0.843730i	$-0.680355\pi$
$311$		−	524.800i		−	1.68746i	0.536767	−	0.843730i	$-0.319645\pi$
$312$		0			0
$313$	565.393			1.80637			0.903184	−	0.429254i	$-0.141224\pi$
$313$	565.393			1.80637			0.903184	+	0.429254i	$0.141224\pi$
$314$	282.624	−	120.530i	0.900075	−	0.383853i
$315$		0			0
$316$	−320.668	−	307.581i	−1.01477	−	0.973358i
$317$	121.835			0.384337			0.192169	−	0.981362i	$-0.438448\pi$
$317$	121.835			0.384337			0.192169	+	0.981362i	$0.438448\pi$
$318$		0			0
$319$		−	6.01991i		−	0.0188712i
$320$	329.062	+	290.312i	1.02832	+	0.907224i
$321$		0			0
$322$	59.3849	−	25.3257i	0.184425	−	0.0786513i
$323$		−	76.4018i		−	0.236538i
$324$		0			0
$325$	20.6409			0.0635106
$326$	−72.0680	−	168.988i	−0.221068	−	0.518369i
$327$		0			0
$328$	−84.9854	+	224.789i	−0.259102	+	0.685331i
$329$	258.042			0.784323
$330$		0			0
$331$		−	635.110i		−	1.91876i	−0.282114	−	0.959381i	$-0.591036\pi$
$331$		−	635.110i		−	1.91876i	0.282114	−	0.959381i	$-0.408964\pi$
$332$	−311.293	−	298.589i	−0.937629	−	0.899364i
$333$		0			0
$334$	70.7075	+	165.798i	0.211699	+	0.496402i
$335$			330.158i			0.985546i
$336$		0			0
$337$	−391.693			−1.16229			−0.581147	−	0.813799i	$-0.697396\pi$
$337$	−391.693			−1.16229			−0.581147	+	0.813799i	$0.697396\pi$
$338$	309.290	−	131.902i	0.915059	−	0.390243i
$339$		0			0
$340$	332.768	−	346.927i	0.978730	−	1.02037i
$341$	−31.6927			−0.0929405
$342$		0			0
$343$			298.989i			0.871687i
$344$	379.608	+	143.518i	1.10351	+	0.417202i
$345$		0			0
$346$	−321.891	+	137.276i	−0.930319	+	0.396751i
$347$			265.028i			0.763770i	0.924210	+	0.381885i	$0.124725\pi$
$347$			265.028i			0.763770i	−0.924210	+	0.381885i	$0.875275\pi$
$348$		0			0
$349$	570.851			1.63568			0.817838	−	0.575448i	$-0.195172\pi$
$349$	570.851			1.63568			0.817838	+	0.575448i	$0.195172\pi$
$350$	−60.1263	−	140.987i	−0.171789	−	0.402820i
$351$		0			0
$352$	−43.4654	+	20.7164i	−0.123481	+	0.0588534i
$353$	−194.344			−0.550549			−0.275274	−	0.961366i	$-0.588769\pi$
$353$	−194.344			−0.550549			−0.275274	+	0.961366i	$0.588769\pi$
$354$		0			0
$355$		−	141.678i		−	0.399093i
$356$	378.058	−	394.143i	1.06196	−	1.10714i
$357$		0			0
$358$	264.966	+	621.304i	0.740129	+	1.73549i
$359$			152.638i			0.425174i	0.977142	+	0.212587i	$0.0681890\pi$
$359$			152.638i			0.425174i	−0.977142	+	0.212587i	$0.931811\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	652.023	−	278.066i	1.80117	−	0.768139i
$363$		0			0
$364$	9.42398	+	9.03938i	0.0258900	+	0.0248334i
$365$	369.789			1.01312
$366$		0			0
$367$		−	420.698i		−	1.14632i	−0.819445	−	0.573158i	$-0.805718\pi$
$367$		−	420.698i		−	1.14632i	0.819445	−	0.573158i	$-0.194282\pi$
$368$	148.220	−	6.17768i	0.402772	−	0.0167872i
$369$		0			0
$370$	−165.236	+	70.4677i	−0.446583	+	0.190453i
$371$			64.2483i			0.173176i
$372$		0			0
$373$	272.769			0.731285			0.365642	−	0.930755i	$-0.380849\pi$
$373$	272.769			0.731285			0.365642	+	0.930755i	$0.380849\pi$
$374$	20.6920	+	48.5195i	0.0553262	+	0.129731i
$375$		0			0
$376$	554.629	+	209.687i	1.47508	+	0.557679i
$377$	−3.75152			−0.00995098
$378$		0			0
$379$		−	441.727i		−	1.16551i	−0.812649	−	0.582753i	$-0.801975\pi$
$379$		−	441.727i		−	1.16551i	0.812649	−	0.582753i	$-0.198025\pi$
$380$	−86.2755	−	82.7545i	−0.227041	−	0.217775i
$381$		0			0
$382$	−197.978	−	464.229i	−0.518268	−	1.21526i
$383$		−	420.975i		−	1.09915i	−0.835444	−	0.549575i	$-0.814790\pi$
$383$		−	420.975i		−	1.09915i	0.835444	−	0.549575i	$-0.185210\pi$
$384$		0			0
$385$	35.9185			0.0932949
$386$	140.073	−	59.7366i	0.362884	−	0.154758i
$387$		0			0
$388$	194.185	−	202.447i	0.500478	−	0.521772i
$389$	236.495			0.607957			0.303979	−	0.952679i	$-0.401685\pi$
$389$	236.495			0.607957			0.303979	+	0.952679i	$0.401685\pi$
$390$		0			0
$391$		−	162.514i		−	0.415637i
$392$	−104.335	+	275.968i	−0.266160	+	0.704001i
$393$		0			0
$394$	348.077	−	148.444i	0.883445	−	0.376760i
$395$			761.653i			1.92824i
$396$		0			0
$397$	−263.186			−0.662938			−0.331469	−	0.943466i	$-0.607544\pi$
$397$	−263.186			−0.662938			−0.331469	+	0.943466i	$0.607544\pi$
$398$	−194.879	−	456.962i	−0.489647	−	1.14815i
$399$		0			0
$400$	−14.6666	−	351.893i	−0.0366664	−	0.879731i
$401$	−42.5636			−0.106144			−0.0530718	−	0.998591i	$-0.516901\pi$
$401$	−42.5636			−0.106144			−0.0530718	+	0.998591i	$0.516901\pi$
$402$		0			0
$403$			19.7504i			0.0490085i
$404$	295.755	−	308.339i	0.732067	−	0.763215i
$405$		0			0
$406$	10.9280	+	25.6246i	0.0269164	+	0.0631147i
$407$		−	19.7106i		−	0.0484289i
$408$		0			0
$409$	61.9100			0.151369			0.0756846	−	0.997132i	$-0.475886\pi$
$409$	61.9100			0.151369			0.0756846	+	0.997132i	$0.475886\pi$
$410$	378.918	−	161.596i	0.924191	−	0.394137i
$411$		0			0
$412$	−394.162	−	378.076i	−0.956705	−	0.917661i
$413$	45.3484			0.109802
$414$		0			0
$415$			739.386i			1.78165i
$416$	12.9102	+	27.0870i	0.0310340	+	0.0651130i
$417$		0			0
$418$	12.0661	−	5.14579i	0.0288662	−	0.0123105i
$419$		−	261.846i		−	0.624931i	−0.949929	−	0.312465i	$-0.898845\pi$
$419$		−	261.846i		−	0.624931i	0.949929	−	0.312465i	$-0.101155\pi$
$420$		0			0
$421$	669.316			1.58983			0.794913	−	0.606724i	$-0.207517\pi$
$421$	669.316			1.58983			0.794913	+	0.606724i	$0.207517\pi$
$422$	155.734	+	365.172i	0.369038	+	0.865336i
$423$		0			0
$424$	−52.2088	+	138.094i	−0.123134	+	0.325692i
$425$	−385.828			−0.907831
$426$		0			0
$427$			44.3245i			0.103804i
$428$	−188.318	−	180.633i	−0.439996	−	0.422040i
$429$		0			0
$430$	−272.893	−	639.892i	−0.634634	−	1.48812i
$431$			696.465i			1.61593i	0.589231	+	0.807965i	$0.299431\pi$
$431$			696.465i			1.61593i	−0.589231	+	0.807965i	$0.700569\pi$
$432$		0			0
$433$	−783.325			−1.80907			−0.904533	−	0.426405i	$-0.859780\pi$
$433$	−783.325			−1.80907			−0.904533	+	0.426405i	$0.859780\pi$
$434$	134.904	−	57.5323i	0.310840	−	0.132563i
$435$		0			0
$436$	43.5630	−	45.4165i	0.0999152	−	0.104166i
$437$	−40.4148			−0.0924825
$438$		0			0
$439$		−	127.605i		−	0.290673i	−0.989382	−	0.145336i	$-0.953574\pi$
$439$		−	127.605i		−	0.290673i	0.989382	−	0.145336i	$-0.0464264\pi$
$440$	77.2023	+	29.1877i	0.175460	+	0.0663358i
$441$		0			0
$442$	30.2367	−	12.8949i	0.0684087	−	0.0291741i
$443$			449.837i			1.01543i	0.861524	+	0.507717i	$0.169510\pi$
$443$			449.837i			1.01543i	−0.861524	+	0.507717i	$0.830490\pi$
$444$		0			0
$445$	−936.172			−2.10376
$446$	−54.7185	−	128.306i	−0.122687	−	0.287682i
$447$		0			0
$448$	147.410	−	167.086i	0.329039	−	0.372959i
$449$	270.045			0.601437			0.300719	−	0.953713i	$-0.402773\pi$
$449$	270.045			0.601437			0.300719	+	0.953713i	$0.402773\pi$
$450$		0			0
$451$			45.2002i			0.100222i
$452$	−43.6280	+	45.4842i	−0.0965221	+	0.100629i
$453$		0			0
$454$	106.835	+	250.512i	0.235319	+	0.551788i
$455$		−	22.3839i		−	0.0491954i
$456$		0			0
$457$	747.133			1.63487			0.817433	−	0.576024i	$-0.195397\pi$
$457$	747.133			1.63487			0.817433	+	0.576024i	$0.195397\pi$
$458$	−548.090	+	233.742i	−1.19670	+	0.510355i
$459$		0			0
$460$	−183.516	−	176.027i	−0.398949	−	0.382667i
$461$	−418.026			−0.906780			−0.453390	−	0.891312i	$-0.649786\pi$
$461$	−418.026			−0.906780			−0.453390	+	0.891312i	$0.649786\pi$
$462$		0			0
$463$			740.964i			1.60035i	0.599764	+	0.800177i	$0.295261\pi$
$463$			740.964i			1.60035i	−0.599764	+	0.800177i	$0.704739\pi$
$464$	2.66567	+	63.9570i	0.00574498	+	0.137838i
$465$		0			0
$466$	360.324	−	153.666i	0.773228	−	0.329756i
$467$		−	171.991i		−	0.368289i	−0.982899	−	0.184145i	$-0.941049\pi$
$467$		−	171.991i		−	0.368289i	0.982899	−	0.184145i	$-0.0589514\pi$
$468$		0			0
$469$	167.642			0.357446
$470$	−398.712	−	934.918i	−0.848324	−	1.98919i
$471$		0			0
$472$	97.4706	+	36.8505i	0.206505	+	0.0780731i
$473$	76.3310			0.161376
$474$		0			0
$475$			95.9497i			0.201999i
$476$	−176.157	−	168.967i	−0.370077	−	0.354974i
$477$		0			0
$478$	−46.8258	−	109.799i	−0.0979619	−	0.229706i
$479$			659.966i			1.37780i	0.724857	+	0.688899i	$0.241906\pi$
$479$			659.966i			1.37780i	−0.724857	+	0.688899i	$0.758094\pi$
$480$		0			0
$481$	−12.2833			−0.0255371
$482$	−70.3157	+	29.9873i	−0.145883	+	0.0622144i
$483$		0			0
$484$	328.769	−	342.757i	0.679275	−	0.708176i
$485$	−480.855			−0.991453
$486$		0			0
$487$		−	497.308i		−	1.02117i	−0.859829	−	0.510583i	$-0.829430\pi$
$487$		−	497.308i		−	1.02117i	0.859829	−	0.510583i	$-0.170570\pi$
$488$	−36.0185	+	95.2698i	−0.0738083	+	0.195225i
$489$		0			0
$490$	465.190	−	198.389i	0.949368	−	0.404875i
$491$			359.256i			0.731682i	0.930677	+	0.365841i	$0.119219\pi$
$491$			359.256i			0.731682i	−0.930677	+	0.365841i	$0.880781\pi$
$492$		0			0
$493$	70.1248			0.142241
$494$	−3.20678	−	7.51941i	−0.00649146	−	0.0152215i
$495$		0			0
$496$	336.711	−	14.0338i	0.678853	−	0.0282940i
$497$	−71.9389			−0.144746
$498$		0			0
$499$			89.9655i			0.180292i	0.995929	+	0.0901458i	$0.0287333\pi$
$499$			89.9655i			0.180292i	−0.995929	+	0.0901458i	$0.971267\pi$
$500$	56.7206	−	59.1339i	0.113441	−	0.118268i
$501$		0			0
$502$	−51.4758	−	120.703i	−0.102542	−	0.240444i
$503$		−	426.179i		−	0.847275i	−0.905832	−	0.423637i	$-0.860753\pi$
$503$		−	426.179i		−	0.847275i	0.905832	−	0.423637i	$-0.139247\pi$
$504$		0			0
$505$	−732.369			−1.45024
$506$	25.6657	−	10.9456i	0.0507228	−	0.0216316i
$507$		0			0
$508$	333.792	+	320.170i	0.657071	+	0.630256i
$509$	241.872			0.475191			0.237595	−	0.971364i	$-0.423641\pi$
$509$	241.872			0.475191			0.237595	+	0.971364i	$0.423641\pi$
$510$		0			0
$511$		−	187.765i		−	0.367447i
$512$	452.613	−	239.343i	0.884011	−	0.467467i
$513$		0			0
$514$	−492.377	+	209.983i	−0.957931	+	0.408526i
$515$			936.218i			1.81790i
$516$		0			0
$517$	111.524			0.215714
$518$	35.7809	+	83.9006i	0.0690751	+	0.161970i
$519$		0			0
$520$	18.1894	−	48.1114i	0.0349796	−	0.0925218i
$521$	−766.199			−1.47063			−0.735315	−	0.677725i	$-0.762966\pi$
$521$	−766.199			−1.47063			−0.735315	+	0.677725i	$0.762966\pi$
$522$		0			0
$523$		−	510.839i		−	0.976748i	−0.872635	−	0.488374i	$-0.837590\pi$
$523$		−	510.839i		−	0.976748i	0.872635	−	0.488374i	$-0.162410\pi$
$524$	−552.506	−	529.958i	−1.05440	−	1.01137i
$525$		0			0
$526$	−277.749	−	651.278i	−0.528039	−	1.23817i
$527$		−	369.183i		−	0.700536i
$528$		0			0
$529$	443.034			0.837493
$530$	232.779	−	99.2728i	0.439207	−	0.187307i
$531$		0			0
$532$	−42.0197	+	43.8075i	−0.0789844	+	0.0823449i
$533$	28.1681			0.0528482
$534$		0			0
$535$			447.295i			0.836066i
$536$	360.325	+	136.227i	0.672248	+	0.254156i
$537$		0			0
$538$	721.430	−	307.666i	1.34095	−	0.571871i
$539$			55.4914i			0.102952i
$540$		0			0
$541$	794.504			1.46858			0.734292	−	0.678834i	$-0.237514\pi$
$541$	794.504			1.46858			0.734292	+	0.678834i	$0.237514\pi$
$542$	−54.2493	−	127.206i	−0.100091	−	0.234698i
$543$		0			0
$544$	−241.322	−	506.321i	−0.443606	−	0.930736i
$545$	−107.874			−0.197933
$546$		0			0
$547$		−	554.142i		−	1.01306i	−0.862223	−	0.506529i	$-0.830928\pi$
$547$		−	554.142i		−	1.01306i	0.862223	−	0.506529i	$-0.169072\pi$
$548$	−143.579	+	149.688i	−0.262006	+	0.273153i
$549$		0			0
$550$	−25.9862	−	60.9336i	−0.0472476	−	0.110788i
$551$		−	17.4390i		−	0.0316497i
$552$		0			0
$553$	386.740			0.699348
$554$	543.920	−	231.964i	0.981804	−	0.418708i
$555$		0			0
$556$	274.652	+	263.443i	0.493979	+	0.473819i
$557$	−135.483			−0.243236			−0.121618	−	0.992577i	$-0.538808\pi$
$557$	−135.483			−0.243236			−0.121618	+	0.992577i	$0.538808\pi$
$558$		0			0
$559$		−	47.5684i		−	0.0850955i
$560$	−381.607	+	15.9050i	−0.681441	+	0.0284019i
$561$		0			0
$562$	210.092	−	89.5975i	0.373830	−	0.159426i
$563$			572.058i			1.01609i	0.861331	+	0.508044i	$0.169631\pi$
$563$			572.058i			1.01609i	−0.861331	+	0.508044i	$0.830369\pi$
$564$		0			0
$565$	108.034			0.191211
$566$	331.440	+	777.176i	0.585583	+	1.37310i
$567$		0			0
$568$	−154.623	−	58.4582i	−0.272224	−	0.102919i
$569$	906.370			1.59292			0.796459	−	0.604693i	$-0.206704\pi$
$569$	906.370			1.59292			0.796459	+	0.604693i	$0.206704\pi$
$570$		0			0
$571$			68.6359i			0.120203i	0.998192	+	0.0601015i	$0.0191424\pi$
$571$			68.6359i			0.120203i	−0.998192	+	0.0601015i	$0.980858\pi$
$572$	4.07298	+	3.90676i	0.00712059	+	0.00682999i
$573$		0			0
$574$	−82.0527	−	192.401i	−0.142949	−	0.335193i
$575$			204.094i			0.354947i
$576$		0			0
$577$	703.422			1.21910			0.609551	−	0.792747i	$-0.291350\pi$
$577$	703.422			1.21910			0.609551	+	0.792747i	$0.291350\pi$
$578$	−33.5250	+	14.2973i	−0.0580018	+	0.0247359i
$579$		0			0
$580$	75.9556	−	79.1873i	0.130958	−	0.136530i
$581$	375.433			0.646184
$582$		0			0
$583$			27.7677i			0.0476289i
$584$	152.580	−	403.578i	0.261267	−	0.691058i
$585$		0			0
$586$	−27.2926	+	11.6394i	−0.0465744	+	0.0198624i
$587$			531.287i			0.905089i	0.891742	+	0.452545i	$0.149484\pi$
$587$			531.287i			0.905089i	−0.891742	+	0.452545i	$0.850516\pi$
$588$		0			0
$589$	−91.8102			−0.155875
$590$	−70.0697	−	164.303i	−0.118762	−	0.278479i
$591$		0			0
$592$	8.72800	+	209.410i	0.0147433	+	0.353733i
$593$	226.762			0.382398			0.191199	−	0.981551i	$-0.438762\pi$
$593$	226.762			0.382398			0.191199	+	0.981551i	$0.438762\pi$
$594$		0			0
$595$			418.408i			0.703208i
$596$	372.850	−	388.714i	0.625587	−	0.652204i
$597$		0			0
$598$	−6.82113	−	15.9945i	−0.0114066	−	0.0267467i
$599$		−	1036.25i		−	1.72996i	−0.501806	−	0.864980i	$-0.667331\pi$
$599$		−	1036.25i		−	1.72996i	0.501806	−	0.864980i	$-0.332669\pi$
$600$		0			0
$601$	300.972			0.500785			0.250393	−	0.968144i	$-0.419440\pi$
$601$	300.972			0.500785			0.250393	+	0.968144i	$0.419440\pi$
$602$	−324.913	+	138.565i	−0.539723	+	0.230174i
$603$		0			0
$604$	570.861	+	547.564i	0.945134	+	0.906562i
$605$	−814.120			−1.34565
$606$		0			0
$607$			289.792i			0.477417i	0.971091	+	0.238708i	$0.0767240\pi$
$607$			289.792i			0.477417i	−0.971091	+	0.238708i	$0.923276\pi$
$608$	−125.914	+	60.0131i	−0.207096	+	0.0987057i
$609$		0			0
$610$	160.593	−	68.4877i	0.263267	−	0.112275i
$611$		−	69.5001i		−	0.113748i
$612$		0			0
$613$	−324.124			−0.528750			−0.264375	−	0.964420i	$-0.585166\pi$
$613$	−324.124			−0.528750			−0.264375	+	0.964420i	$0.585166\pi$
$614$	18.6503	+	43.7320i	0.0303750	+	0.0712247i
$615$		0			0
$616$	14.8205	−	39.2005i	0.0240592	−	0.0636372i
$617$	−148.214			−0.240217			−0.120109	−	0.992761i	$-0.538324\pi$
$617$	−148.214			−0.240217			−0.120109	+	0.992761i	$0.538324\pi$
$618$		0			0
$619$		−	1207.62i		−	1.95092i	−0.220184	−	0.975458i	$-0.570666\pi$
$619$		−	1207.62i		−	1.95092i	0.220184	−	0.975458i	$-0.429334\pi$
$620$	−416.893	−	399.879i	−0.672408	−	0.644967i
$621$		0			0
$622$	411.741	+	965.469i	0.661963	+	1.55220i
$623$			475.354i			0.763008i
$624$		0			0
$625$	−690.765			−1.10522
$626$	−1040.15	+	443.589i	−1.66158	+	0.708608i
$627$		0			0
$628$	−425.376	+	443.474i	−0.677350	+	0.706169i
$629$	229.605			0.365031
$630$		0			0
$631$		−	211.122i		−	0.334583i	−0.985908	−	0.167291i	$-0.946498\pi$
$631$		−	211.122i		−	0.334583i	0.985908	−	0.167291i	$-0.0535020\pi$
$632$	831.247	+	314.268i	1.31526	+	0.497260i
$633$		0			0
$634$	−224.138	+	95.5876i	−0.353530	+	0.150769i
$635$		−	792.826i		−	1.24854i
$636$		0			0
$637$	34.5814			0.0542879
$638$	4.72303	+	11.0748i	0.00740286	+	0.0173586i
$639$		0			0
$640$	−833.141	−	275.912i	−1.30178	−	0.431112i
$641$	−1052.61			−1.64213			−0.821067	−	0.570832i	$-0.806621\pi$
$641$	−1052.61			−1.64213			−0.821067	+	0.570832i	$0.806621\pi$
$642$		0			0
$643$		−	59.1355i		−	0.0919681i	−0.998942	−	0.0459840i	$-0.985358\pi$
$643$		−	59.1355i		−	0.0919681i	0.998942	−	0.0459840i	$-0.0146423\pi$
$644$	−89.3800	+	93.1828i	−0.138789	+	0.144694i
$645$		0			0
$646$	59.9424	+	140.556i	0.0927900	+	0.217578i
$647$		−	281.614i		−	0.435261i	−0.976031	−	0.217630i	$-0.930167\pi$
$647$		−	281.614i		−	0.435261i	0.976031	−	0.217630i	$-0.0698327\pi$
$648$		0			0
$649$	19.5993			0.0301992
$650$	−37.9729	+	16.1942i	−0.0584198	+	0.0249141i
$651$		0			0
$652$	265.166	+	254.344i	0.406696	+	0.390098i
$653$	−647.492			−0.991565			−0.495783	−	0.868447i	$-0.665119\pi$
$653$	−647.492			−0.991565			−0.495783	+	0.868447i	$0.665119\pi$
$654$		0			0
$655$			1312.32i			2.00354i
$656$	−20.0150	−	480.218i	−0.0305107	−	0.732039i
$657$		0			0
$658$	−474.717	+	202.451i	−0.721455	+	0.307677i
$659$		−	611.308i		−	0.927630i	−0.885932	−	0.463815i	$-0.846480\pi$
$659$		−	611.308i		−	0.927630i	0.885932	−	0.463815i	$-0.153520\pi$
$660$		0			0
$661$	116.510			0.176263			0.0881316	−	0.996109i	$-0.471910\pi$
$661$	116.510			0.176263			0.0881316	+	0.996109i	$0.471910\pi$
$662$	498.287	+	1168.41i	0.752699	+	1.76496i
$663$		0			0
$664$	806.945	+	305.080i	1.21528	+	0.459458i
$665$	104.052			0.156469
$666$		0			0
$667$		−	37.0945i		−	0.0556139i
$668$	−260.160	−	249.542i	−0.389460	−	0.373566i
$669$		0			0
$670$	−259.031	−	607.388i	−0.386613	−	0.906549i
$671$			19.1567i			0.0285495i
$672$		0			0
$673$	−725.082			−1.07739			−0.538694	−	0.842502i	$-0.681082\pi$
$673$	−725.082			−1.07739			−0.538694	+	0.842502i	$0.681082\pi$
$674$	720.593	−	307.309i	1.06913	−	0.455949i
$675$		0			0
$676$	−465.511	+	485.317i	−0.688626	+	0.717925i
$677$	−338.180			−0.499528			−0.249764	−	0.968307i	$-0.580353\pi$
$677$	−338.180			−0.499528			−0.249764	+	0.968307i	$0.580353\pi$
$678$		0			0
$679$			244.160i			0.359588i
$680$	−340.003	+	899.316i	−0.500004	+	1.32252i
$681$		0			0
$682$	58.3047	−	24.8651i	0.0854908	−	0.0364590i
$683$			942.769i			1.38033i	0.723650	+	0.690167i	$0.242463\pi$
$683$			942.769i			1.38033i	−0.723650	+	0.690167i	$0.757537\pi$
$684$		0			0
$685$	355.540			0.519037
$686$	−234.577	−	550.046i	−0.341949	−	0.801817i
$687$		0			0
$688$	−810.959	+	33.8000i	−1.17872	+	0.0491280i
$689$	17.3044			0.0251152
$690$		0			0
$691$		−	757.759i		−	1.09661i	−0.836278	−	0.548306i	$-0.815273\pi$
$691$		−	757.759i		−	1.09661i	0.836278	−	0.548306i	$-0.184727\pi$
$692$	484.476	−	505.089i	0.700110	−	0.729898i
$693$		0			0
$694$	−207.932	−	487.569i	−0.299614	−	0.702550i
$695$		−	652.356i		−	0.938642i
$696$		0			0
$697$	−526.529			−0.755422
$698$	−1050.19	+	447.871i	−1.50457	+	0.641649i
$699$		0			0
$700$	221.227	+	212.199i	0.316039	+	0.303141i
$701$	452.743			0.645853			0.322926	−	0.946424i	$-0.395333\pi$
$701$	452.743			0.645853			0.322926	+	0.946424i	$0.395333\pi$
$702$		0			0
$703$		−	57.0993i		−	0.0812223i
$704$	63.7094	−	72.2133i	0.0904963	−	0.102576i
$705$		0			0
$706$	357.532	−	152.476i	0.506419	−	0.215971i
$707$			371.870i			0.525983i
$708$		0			0
$709$	−244.125			−0.344323			−0.172161	−	0.985069i	$-0.555075\pi$
$709$	−244.125			−0.344323			−0.172161	+	0.985069i	$0.555075\pi$
$710$	111.156	+	260.643i	0.156558	+	0.367103i
$711$		0			0
$712$	−386.277	+	1021.71i	−0.542524	+	1.43499i
$713$	−195.289			−0.273898
$714$		0			0
$715$		−	9.67417i		−	0.0135303i
$716$	−974.910	−	935.123i	−1.36161	−	1.30604i
$717$		0			0
$718$	−119.754	−	280.806i	−0.166789	−	0.391094i
$719$			91.5730i			0.127362i	0.997970	+	0.0636808i	$0.0202839\pi$
$719$			91.5730i			0.127362i	−0.997970	+	0.0636808i	$0.979716\pi$
$720$		0			0
$721$	475.377			0.659330
$722$	34.9541	−	14.9068i	0.0484129	−	0.0206465i
$723$		0			0
$724$	−981.357	+	1023.11i	−1.35547	+	1.41314i
$725$	−88.0667			−0.121471
$726$		0			0
$727$		−	170.479i		−	0.234497i	−0.993103	−	0.117248i	$-0.962593\pi$
$727$		−	170.479i		−	0.234497i	0.993103	−	0.117248i	$-0.0374074\pi$
$728$	−24.4292	−	9.23589i	−0.0335566	−	0.0126867i
$729$		0			0
$730$	−680.297	+	290.125i	−0.931914	+	0.397431i
$731$			889.166i			1.21637i
$732$		0			0
$733$	−705.909			−0.963040			−0.481520	−	0.876435i	$-0.659915\pi$
$733$	−705.909			−0.963040			−0.481520	+	0.876435i	$0.659915\pi$
$734$	330.066	+	773.953i	0.449681	+	1.05443i
$735$		0			0
$736$	−267.832	+	127.654i	−0.363902	+	0.173442i
$737$	72.4537			0.0983090
$738$		0			0
$739$		−	211.437i		−	0.286113i	−0.989715	−	0.143056i	$-0.954307\pi$
$739$		−	211.437i		−	0.286113i	0.989715	−	0.143056i	$-0.0456930\pi$
$740$	248.696	−	259.277i	0.336075	−	0.350374i
$741$		0			0
$742$	−50.4071	−	118.197i	−0.0679341	−	0.159295i
$743$		−	30.0792i		−	0.0404834i	−0.999795	−	0.0202417i	$-0.993556\pi$
$743$		−	30.0792i		−	0.0404834i	0.999795	−	0.0202417i	$-0.00644357\pi$
$744$		0			0
$745$	−923.276			−1.23930
$746$	−501.811	+	214.006i	−0.672668	+	0.286871i
$747$		0			0
$748$	−76.1337	−	73.0266i	−0.101783	−	0.0976291i
$749$	227.120			0.303231
$750$		0			0
$751$		−	422.495i		−	0.562576i	−0.959623	−	0.281288i	$-0.909238\pi$
$751$		−	422.495i		−	0.562576i	0.959623	−	0.281288i	$-0.0907617\pi$
$752$	−1184.86	+	49.3838i	−1.57561	+	0.0656700i
$753$		0			0
$754$	6.90163	−	2.94332i	0.00915335	−	0.00390361i
$755$		−	1355.91i		−	1.79591i
$756$		0			0
$757$	−337.192			−0.445432			−0.222716	−	0.974883i	$-0.571492\pi$
$757$	−337.192			−0.445432			−0.222716	+	0.974883i	$0.571492\pi$
$758$	346.564	+	812.640i	0.457209	+	1.07208i
$759$		0			0
$760$	223.646	+	84.5536i	0.294272	+	0.111255i
$761$	−653.091			−0.858202			−0.429101	−	0.903257i	$-0.641169\pi$
$761$	−653.091			−0.858202			−0.429101	+	0.903257i	$0.641169\pi$
$762$		0			0
$763$			54.7743i			0.0717881i
$764$	728.437	+	698.709i	0.953452	+	0.914541i
$765$		0			0
$766$	330.283	+	774.462i	0.431179	+	1.01105i
$767$		−	12.2140i		−	0.0159243i
$768$		0			0
$769$	963.693			1.25318			0.626588	−	0.779350i	$-0.284451\pi$
$769$	963.693			1.25318			0.626588	+	0.779350i	$0.284451\pi$
$770$	−66.0789	+	28.1805i	−0.0858168	+	0.0365981i
$771$		0			0
$772$	−210.824	+	219.794i	−0.273088	+	0.284707i
$773$	124.091			0.160531			0.0802656	−	0.996774i	$-0.474423\pi$
$773$	124.091			0.160531			0.0802656	+	0.996774i	$0.474423\pi$
$774$		0			0
$775$			463.640i			0.598246i
$776$	−198.407	+	524.792i	−0.255679	+	0.676278i
$777$		0			0
$778$	−435.078	+	185.546i	−0.559226	+	0.238492i
$779$			130.940i			0.168087i
$780$		0			0
$781$	−31.0915			−0.0398099
$782$	127.503	+	298.975i	0.163048	+	0.382322i
$783$		0			0
$784$	−24.5721	−	589.554i	−0.0313419	−	0.751982i
$785$	1053.34			1.34184
$786$		0			0
$787$		−	1063.88i		−	1.35182i	−0.736983	−	0.675911i	$-0.763750\pi$
$787$		−	1063.88i		−	1.35182i	0.736983	−	0.675911i	$-0.236250\pi$
$788$	−523.890	+	546.180i	−0.664835	+	0.693122i
$789$		0			0
$790$	−597.568	−	1401.20i	−0.756415	−	1.77368i
$791$		−	54.8559i		−	0.0693501i
$792$		0			0
$793$	11.9382			0.0150545
$794$	484.181	−	206.487i	0.609800	−	0.260060i
$795$		0			0
$796$	717.035	+	687.772i	0.900797	+	0.864035i
$797$	1224.07			1.53585			0.767926	−	0.640538i	$-0.221289\pi$
$797$	1224.07			1.53585			0.767926	+	0.640538i	$0.221289\pi$
$798$		0			0
$799$			1299.12i			1.62594i
$800$	303.065	+	635.866i	0.378831	+	0.794832i
$801$		0			0
$802$	78.3038	−	33.3940i	0.0976356	−	0.0416384i
$803$		−	81.1509i		−	0.101060i
$804$		0			0
$805$	221.329			0.274942
$806$	−15.4955	−	36.3346i	−0.0192252	−	0.0450802i
$807$		0			0
$808$	−302.185	+	799.287i	−0.373991	+	0.989217i
$809$	154.498			0.190974			0.0954868	−	0.995431i	$-0.469559\pi$
$809$	154.498			0.190974			0.0954868	+	0.995431i	$0.469559\pi$
$810$		0			0
$811$		−	894.012i		−	1.10236i	−0.834387	−	0.551179i	$-0.814178\pi$
$811$		−	894.012i		−	1.10236i	0.834387	−	0.551179i	$-0.185822\pi$
$812$	−40.2084	−	38.5674i	−0.0495177	−	0.0474969i
$813$		0			0
$814$	15.4643	+	36.2613i	0.0189979	+	0.0445470i
$815$		−	629.823i		−	0.772789i
$816$		0			0
$817$	221.122			0.270652
$818$	−113.895	+	48.5726i	−0.139236	+	0.0593797i
$819$		0			0
$820$	−570.309	+	594.574i	−0.695498	+	0.725090i
$821$	254.571			0.310074			0.155037	−	0.987909i	$-0.450450\pi$
$821$	254.571			0.310074			0.155037	+	0.987909i	$0.450450\pi$
$822$		0			0
$823$			1424.52i			1.73088i	0.501010	+	0.865442i	$0.332962\pi$
$823$			1424.52i			1.73088i	−0.501010	+	0.865442i	$0.667038\pi$
$824$	1021.76	+	386.296i	1.24000	+	0.468806i
$825$		0			0
$826$	−83.4269	+	35.5788i	−0.101001	+	0.0430737i
$827$		−	895.259i		−	1.08254i	−0.840849	−	0.541269i	$-0.817944\pi$
$827$		−	895.259i		−	1.08254i	0.840849	−	0.541269i	$-0.182056\pi$
$828$		0			0
$829$	−922.874			−1.11324			−0.556619	−	0.830768i	$-0.687902\pi$
$829$	−922.874			−1.11324			−0.556619	+	0.830768i	$0.687902\pi$
$830$	−580.098	−	1360.24i	−0.698913	−	1.63884i
$831$		0			0
$832$	−45.0022	−	39.7028i	−0.0540892	−	0.0477197i
$833$	−646.409			−0.776001
$834$		0			0
$835$			617.933i			0.740040i
$836$	−18.1606	+	18.9333i	−0.0217232	+	0.0226475i
$837$		0			0
$838$	205.436	+	481.715i	0.245150	+	0.574839i
$839$		−	982.947i		−	1.17157i	−0.810467	−	0.585785i	$-0.800786\pi$
$839$		−	982.947i		−	1.17157i	0.810467	−	0.585785i	$-0.199214\pi$
$840$		0			0
$841$	−824.994			−0.980968
$842$	−1231.33	+	525.124i	−1.46239	+	0.623662i
$843$		0			0
$844$	−573.004	−	549.619i	−0.678915	−	0.651207i
$845$	1152.73			1.36418
$846$		0			0
$847$			413.380i			0.488052i
$848$	−12.2958	−	295.010i	−0.0144997	−	0.347890i
$849$		0			0
$850$	709.804	−	302.708i	0.835063	−	0.356127i
$851$		−	121.456i		−	0.142721i
$852$		0			0
$853$	176.279			0.206658			0.103329	−	0.994647i	$-0.467051\pi$
$853$	176.279			0.206658			0.103329	+	0.994647i	$0.467051\pi$
$854$	−34.7755	−	81.5432i	−0.0407207	−	0.0954838i
$855$		0			0
$856$	488.166	+	184.560i	0.570287	+	0.215607i
$857$	664.405			0.775268			0.387634	−	0.921813i	$-0.373292\pi$
$857$	664.405			0.775268			0.387634	+	0.921813i	$0.373292\pi$
$858$		0			0
$859$		−	149.631i		−	0.174193i	−0.996200	−	0.0870963i	$-0.972241\pi$
$859$		−	149.631i		−	0.174193i	0.996200	−	0.0870963i	$-0.0277588\pi$
$860$	1004.08	+	963.098i	1.16753	+	1.11988i
$861$		0			0
$862$	−546.424	−	1281.28i	−0.633902	−	1.48640i
$863$		−	728.738i		−	0.844424i	−0.906497	−	0.422212i	$-0.861254\pi$
$863$		−	728.738i		−	0.844424i	0.906497	−	0.422212i	$-0.138746\pi$
$864$		0			0
$865$	−1199.69			−1.38693
$866$	1441.07	−	614.571i	1.66406	−	0.709667i
$867$		0			0
$868$	−203.044	+	211.683i	−0.233922	+	0.243874i
$869$	167.146			0.192343
$870$		0			0
$871$		−	45.1521i		−	0.0518394i
$872$	−44.5101	+	117.730i	−0.0510437	+	0.135012i
$873$		0			0
$874$	74.3507	−	31.7082i	0.0850695	−	0.0362794i
$875$			71.3180i			0.0815063i
$876$		0			0
$877$	−432.174			−0.492786			−0.246393	−	0.969170i	$-0.579245\pi$
$877$	−432.174			−0.492786			−0.246393	+	0.969170i	$0.579245\pi$
$878$	100.115	+	234.754i	0.114026	+	0.267374i
$879$		0			0
$880$	−164.928	+	6.87405i	−0.187418	+	0.00781142i
$881$	286.819			0.325560			0.162780	−	0.986662i	$-0.447954\pi$
$881$	286.819			0.325560			0.162780	+	0.986662i	$0.447954\pi$
$882$		0			0
$883$			1291.98i			1.46317i	0.681752	+	0.731583i	$0.261218\pi$
$883$			1291.98i			1.46317i	−0.681752	+	0.731583i	$0.738782\pi$
$884$	−45.5091	+	47.4454i	−0.0514809	+	0.0536712i
$885$		0			0
$886$	−352.928	−	827.560i	−0.398338	−	0.934041i
$887$		−	1271.13i		−	1.43306i	−0.697554	−	0.716532i	$-0.745728\pi$
$887$		−	1271.13i		−	1.43306i	0.697554	−	0.716532i	$-0.254272\pi$
$888$		0			0
$889$	−402.568			−0.452832
$890$	1722.26	−	734.490i	1.93513	−	0.825269i
$891$		0			0
$892$	201.330	+	193.113i	0.225706	+	0.216495i
$893$	323.073			0.361783
$894$		0			0
$895$			2315.61i			2.58728i
$896$	−140.098	+	423.038i	−0.156359	+	0.472141i
$897$		0			0
$898$	−496.799	+	211.869i	−0.553229	+	0.235934i
$899$		−	84.2673i		−	0.0937345i
$900$		0			0
$901$	−323.460			−0.359002
$902$	−35.4626	−	83.1543i	−0.0393155	−	0.0921888i
$903$		0			0
$904$	44.5765	−	117.906i	0.0493102	−	0.130427i
$905$	2430.10			2.68520
$906$		0			0
$907$			312.469i			0.344508i	0.985053	+	0.172254i	$0.0551050\pi$
$907$			312.469i			0.344508i	−0.985053	+	0.172254i	$0.944895\pi$
$908$	−393.086	−	377.044i	−0.432914	−	0.415247i
$909$		0			0
$910$	17.5617	+	41.1794i	0.0192985	+	0.0452521i
$911$			466.009i			0.511536i	0.966738	+	0.255768i	$0.0823283\pi$
$911$			466.009i			0.511536i	−0.966738	+	0.255768i	$0.917672\pi$
$912$		0			0
$913$	162.260			0.177721
$914$	−1374.49	+	586.176i	−1.50382	+	0.641331i
$915$		0			0
$916$	824.928	−	860.027i	0.900577	−	0.938894i
$917$	666.346			0.726659
$918$		0			0
$919$		−	661.858i		−	0.720194i	−0.932915	−	0.360097i	$-0.882744\pi$
$919$		−	661.858i		−	0.720194i	0.932915	−	0.360097i	$-0.117256\pi$
$920$	475.718	+	179.854i	0.517085	+	0.195493i
$921$		0			0
$922$	769.037	−	327.969i	0.834097	−	0.355715i
$923$			19.3758i			0.0209922i
$924$		0			0
$925$	−288.350			−0.311730
$926$	−581.336	−	1363.14i	−0.627793	−	1.47208i
$927$		0			0
$928$	−55.0825	−	115.570i	−0.0593562	−	0.124536i
$929$	1168.40			1.25769			0.628846	−	0.777530i	$-0.283528\pi$
$929$	1168.40			1.25769			0.628846	+	0.777530i	$0.283528\pi$
$930$		0			0
$931$			160.752i			0.172666i
$932$	−542.323	+	565.397i	−0.581891	+	0.606649i
$933$		0			0
$934$	134.938	+	316.410i	0.144474	+	0.338769i
$935$			180.833i			0.193405i
$936$		0			0
$937$	1544.67			1.64852			0.824262	−	0.566209i	$-0.191591\pi$
$937$	1544.67			1.64852			0.824262	+	0.566209i	$0.191591\pi$
$938$	−308.409	+	131.526i	−0.328794	+	0.140220i
$939$		0			0
$940$	1467.01	+	1407.14i	1.56065	+	1.49696i
$941$	−1418.34			−1.50727			−0.753633	−	0.657295i	$-0.771700\pi$
$941$	−1418.34			−1.50727			−0.753633	+	0.657295i	$0.771700\pi$
$942$		0			0
$943$			278.522i			0.295357i
$944$	−208.227	+	8.67872i	−0.220580	+	0.00919356i
$945$		0			0
$946$	−140.425	+	59.8868i	−0.148441	+	0.0633053i
$947$		−	764.011i		−	0.806770i	−0.915030	−	0.403385i	$-0.867834\pi$
$947$		−	764.011i		−	0.806770i	0.915030	−	0.403385i	$-0.132166\pi$
$948$		0			0
$949$	−50.5721			−0.0532898
$950$	−75.2790	−	176.518i	−0.0792410	−	0.185808i
$951$		0			0
$952$	456.640	+	172.641i	0.479663	+	0.181345i
$953$	−1093.95			−1.14790			−0.573951	−	0.818890i	$-0.694590\pi$
$953$	−1093.95			−1.14790			−0.573951	+	0.818890i	$0.694590\pi$
$954$		0			0
$955$		−	1730.19i		−	1.81172i
$956$	172.290	+	165.258i	0.180219	+	0.172865i
$957$		0			0
$958$	−517.787	−	1214.13i	−0.540488	−	1.26736i
$959$		−	180.530i		−	0.188248i
$960$		0			0
$961$	517.362			0.538358
$962$	22.5975	−	9.63709i	0.0234901	−	0.0100178i
$963$		0			0
$964$	105.832	−	110.335i	0.109784	−	0.114455i
$965$	522.056			0.540990
$966$		0			0
$967$			1292.92i			1.33705i	0.743692	+	0.668523i	$0.233073\pi$
$967$			1292.92i			1.33705i	−0.743692	+	0.668523i	$0.766927\pi$
$968$	−335.917	+	888.508i	−0.347021	+	0.917880i
$969$		0			0
$970$	884.623	−	377.263i	0.911982	−	0.388931i
$971$		−	551.716i		−	0.568194i	−0.958796	−	0.284097i	$-0.908306\pi$
$971$		−	551.716i		−	0.568194i	0.958796	−	0.284097i	$-0.0916938\pi$
$972$		0			0
$973$	−331.243			−0.340434
$974$	390.171	+	914.891i	0.400587	+	0.939314i
$975$		0			0
$976$	−8.48277	−	203.526i	−0.00869136	−	0.208530i
$977$	−1185.71			−1.21362			−0.606812	−	0.794845i	$-0.707552\pi$
$977$	−1185.71			−1.21362			−0.606812	+	0.794845i	$0.707552\pi$
$978$		0			0
$979$			205.445i			0.209852i
$980$	−700.157	+	729.946i	−0.714445	+	0.744843i
$981$		0			0
$982$	−281.860	−	660.919i	−0.287027	−	0.673033i
$983$		−	1302.58i		−	1.32510i	−0.749016	−	0.662552i	$-0.769473\pi$
$983$		−	1302.58i		−	1.32510i	0.749016	−	0.662552i	$-0.230527\pi$
$984$		0			0
$985$	1297.29			1.31705
$986$	−129.008	+	55.0176i	−0.130840	+	0.0557988i
$987$		0			0
$988$	11.7990	+	11.3174i	0.0119423	+	0.0114549i
$989$	470.349			0.475580
$990$		0			0
$991$			638.120i			0.643915i	0.946754	+	0.321958i	$0.104341\pi$
$991$			638.120i			0.643915i	−0.946754	+	0.321958i	$0.895659\pi$
$992$	−608.433	+	289.990i	−0.613340	+	0.292329i
$993$		0			0
$994$	132.345	−	56.4409i	0.133144	−	0.0567816i
$995$		−	1703.11i		−	1.71166i
$996$		0			0
$997$	560.429			0.562115			0.281058	−	0.959691i	$-0.409315\pi$
$997$	560.429			0.562115			0.281058	+	0.959691i	$0.409315\pi$
$998$	−70.5840	−	165.508i	−0.0707254	−	0.165840i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.4	yes	36
3.2	odd	2	inner	684.3.g.d.343.33	yes	36
4.3	odd	2	inner	684.3.g.d.343.3	✓	36
12.11	even	2	inner	684.3.g.d.343.34	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.3	✓	36	4.3	odd	2	inner
684.3.g.d.343.4	yes	36	1.1	even	1	trivial
684.3.g.d.343.33	yes	36	3.2	odd	2	inner
684.3.g.d.343.34	yes	36	12.11	even	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83969 + 0.784567i) q^{2} +(2.76891 - 2.88672i) q^{4} -6.85656 q^{5} +3.48151i q^{7} +(-2.82911 + 7.48306i) q^{8} +O(q^{10})\)	\(q+(-1.83969 + 0.784567i) q^{2} +(2.76891 - 2.88672i) q^{4} -6.85656 q^{5} +3.48151i q^{7} +(-2.82911 + 7.48306i) q^{8} +(12.6139 - 5.37943i) q^{10} +1.50468i q^{11} +0.937697 q^{13} +(-2.73148 - 6.40489i) q^{14} +(-0.666287 - 15.9861i) q^{16} -17.5278 q^{17} +4.35890i q^{19} +(-18.9852 + 19.7930i) q^{20} +(-1.18053 - 2.76815i) q^{22} +9.27180i q^{23} +22.0124 q^{25} +(-1.72507 + 0.735686i) q^{26} +(10.0501 + 9.63998i) q^{28} -4.00078 q^{29} +21.0627i q^{31} +(13.7679 + 28.8867i) q^{32} +(32.2457 - 13.7517i) q^{34} -23.8712i q^{35} -13.0995 q^{37} +(-3.41985 - 8.01902i) q^{38} +(19.3979 - 51.3080i) q^{40} +30.0397 q^{41} -50.7290i q^{43} +(4.34360 + 4.16633i) q^{44} +(-7.27435 - 17.0572i) q^{46} -74.1179i q^{47} +36.8791 q^{49} +(-40.4959 + 17.2702i) q^{50} +(2.59640 - 2.70687i) q^{52} +18.4542 q^{53} -10.3170i q^{55} +(-26.0523 - 9.84955i) q^{56} +(7.36019 - 3.13888i) q^{58} -13.0255i q^{59} +12.7314 q^{61} +(-16.5251 - 38.7488i) q^{62} +(-47.9923 - 42.3407i) q^{64} -6.42937 q^{65} -48.1521i q^{67} +(-48.5328 + 50.5978i) q^{68} +(18.7285 + 43.9155i) q^{70} +20.6631i q^{71} -53.9322 q^{73} +(24.0989 - 10.2774i) q^{74} +(12.5829 + 12.0694i) q^{76} -5.23857 q^{77} -111.084i q^{79} +(4.56844 + 109.610i) q^{80} +(-55.2636 + 23.5681i) q^{82} -107.836i q^{83} +120.180 q^{85} +(39.8003 + 93.3255i) q^{86} +(-11.2596 - 4.25691i) q^{88} +136.537 q^{89} +3.26460i q^{91} +(26.7651 + 25.6728i) q^{92} +(58.1505 + 136.354i) q^{94} -29.8870i q^{95} +70.1306 q^{97} +(-67.8461 + 28.9341i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 36 * q - 12 * q^4	\( 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) \) 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more