LMFDB - Embedded newform 324.4.b.c.323.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,4,Mod(323,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("324.323");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	324.b (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:	$19.1166188419$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.5
Character	$\chi$	$=$	324.323
Dual form			324.4.b.c.323.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36704 - 1.54827i) q^{2} +(3.20572 + 7.32962i) q^{4} +1.43006i q^{5} -27.5763i q^{7} +(3.76017 - 22.3128i) q^{8} +O(q^{10})$	\(q+(-2.36704 - 1.54827i) q^{2} +(3.20572 + 7.32962i) q^{4} +1.43006i q^{5} -27.5763i q^{7} +(3.76017 - 22.3128i) q^{8} +(2.21411 - 3.38499i) q^{10} -22.2175 q^{11} +69.1930 q^{13} +(-42.6956 + 65.2742i) q^{14} +(-43.4467 + 46.9935i) q^{16} +31.4507i q^{17} +11.4986i q^{19} +(-10.4818 + 4.58436i) q^{20} +(52.5896 + 34.3987i) q^{22} -145.362 q^{23} +122.955 q^{25} +(-163.782 - 107.129i) q^{26} +(202.124 - 88.4021i) q^{28} -108.194i q^{29} -118.703i q^{31} +(175.598 - 43.9681i) q^{32} +(48.6942 - 74.4450i) q^{34} +39.4357 q^{35} -300.439 q^{37} +(17.8029 - 27.2176i) q^{38} +(31.9085 + 5.37725i) q^{40} -398.202i q^{41} -200.065i q^{43} +(-71.2231 - 162.846i) q^{44} +(344.077 + 225.060i) q^{46} -303.539 q^{47} -417.454 q^{49} +(-291.039 - 190.367i) q^{50} +(221.814 + 507.159i) q^{52} +243.342i q^{53} -31.7722i q^{55} +(-615.305 - 103.692i) q^{56} +(-167.513 + 256.099i) q^{58} -83.8393 q^{59} -398.436 q^{61} +(-183.784 + 280.974i) q^{62} +(-483.722 - 167.800i) q^{64} +98.9499i q^{65} -355.375i q^{67} +(-230.522 + 100.822i) q^{68} +(-93.3457 - 61.0571i) q^{70} -866.235 q^{71} +64.6645 q^{73} +(711.149 + 465.160i) q^{74} +(-84.2802 + 36.8613i) q^{76} +612.677i q^{77} -409.798i q^{79} +(-67.2033 - 62.1312i) q^{80} +(-616.524 + 942.559i) q^{82} +159.798 q^{83} -44.9763 q^{85} +(-309.754 + 473.561i) q^{86} +(-83.5415 + 495.734i) q^{88} -1493.47i q^{89} -1908.09i q^{91} +(-465.990 - 1065.45i) q^{92} +(718.488 + 469.960i) q^{94} -16.4436 q^{95} -1400.23 q^{97} +(988.129 + 646.332i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4}+O(q^{10}) $ 24 * q + 24 * q^4	$ 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64} - 1128 q^{70} - 4776 q^{73} + 1200 q^{76} - 4104 q^{82} - 1440 q^{85} - 3912 q^{88} + 2376 q^{94} - 1176 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.36704	−	1.54827i	−0.836874	−	0.547396i
$2$	−2.36704	−	1.54827i	−0.836874	−	0.547396i
$3$		0			0
$3$		0			0
$4$	3.20572	+	7.32962i	0.400715	+	0.916203i
$5$			1.43006i			0.127908i	0.997953	+	0.0639540i	$0.0203711\pi$
$5$			1.43006i			0.127908i	−0.997953	+	0.0639540i	$0.979629\pi$
$6$		0			0
$7$		−	27.5763i		−	1.48898i	−0.667632	−	0.744491i	$-0.732692\pi$
$7$		−	27.5763i		−	1.48898i	0.667632	−	0.744491i	$-0.267308\pi$
$8$	3.76017	−	22.3128i	0.166177	−	0.986096i
$9$		0			0
$10$	2.21411	−	3.38499i	0.0700164	−	0.107043i
$11$	−22.2175			−0.608984			−0.304492	−	0.952515i	$-0.598487\pi$
$11$	−22.2175			−0.608984			−0.304492	+	0.952515i	$0.598487\pi$
$12$		0			0
$13$	69.1930			1.47621			0.738103	−	0.674688i	$-0.235722\pi$
$13$	69.1930			1.47621			0.738103	+	0.674688i	$0.235722\pi$
$14$	−42.6956	+	65.2742i	−0.815063	+	1.24609i
$15$		0			0
$16$	−43.4467	+	46.9935i	−0.678854	+	0.734273i
$17$			31.4507i			0.448701i	0.974509	+	0.224351i	$0.0720261\pi$
$17$			31.4507i			0.448701i	−0.974509	+	0.224351i	$0.927974\pi$
$18$		0			0
$19$			11.4986i			0.138840i	0.997588	+	0.0694199i	$0.0221148\pi$
$19$			11.4986i			0.138840i	−0.997588	+	0.0694199i	$0.977885\pi$
$20$	−10.4818	+	4.58436i	−0.117190	+	0.0512547i
$21$		0			0
$22$	52.5896	+	34.3987i	0.509643	+	0.333355i
$23$	−145.362			−1.31783			−0.658914	−	0.752218i	$-0.728984\pi$
$23$	−145.362			−1.31783			−0.658914	+	0.752218i	$0.728984\pi$
$24$		0			0
$25$	122.955			0.983640
$26$	−163.782	−	107.129i	−1.23540	−	0.808070i
$27$		0			0
$28$	202.124	−	88.4021i	1.36421	−	0.596658i
$29$		−	108.194i		−	0.692796i	−0.938088	−	0.346398i	$-0.887405\pi$
$29$		−	108.194i		−	0.692796i	0.938088	−	0.346398i	$-0.112595\pi$
$30$		0			0
$31$		−	118.703i		−	0.687731i	−0.939019	−	0.343865i	$-0.888264\pi$
$31$		−	118.703i		−	0.687731i	0.939019	−	0.343865i	$-0.111736\pi$
$32$	175.598	−	43.9681i	0.970053	−	0.242891i
$33$		0			0
$34$	48.6942	−	74.4450i	0.245617	−	0.375506i
$35$	39.4357			0.190453
$36$		0			0
$37$	−300.439			−1.33491			−0.667457	−	0.744649i	$-0.732617\pi$
$37$	−300.439			−1.33491			−0.667457	+	0.744649i	$0.732617\pi$
$38$	17.8029	−	27.2176i	0.0760003	−	0.116191i
$39$		0			0
$40$	31.9085	+	5.37725i	0.126130	+	0.0212554i
$41$		−	398.202i		−	1.51680i	−0.651791	−	0.758399i	$-0.725982\pi$
$41$		−	398.202i		−	1.51680i	0.651791	−	0.758399i	$-0.274018\pi$
$42$		0			0
$43$		−	200.065i		−	0.709525i	−0.934956	−	0.354763i	$-0.884562\pi$
$43$		−	200.065i		−	0.709525i	0.934956	−	0.354763i	$-0.115438\pi$
$44$	−71.2231	−	162.846i	−0.244029	−	0.557953i
$45$		0			0
$46$	344.077	+	225.060i	1.10286	+	0.721374i
$47$	−303.539			−0.942037			−0.471018	−	0.882123i	$-0.656113\pi$
$47$	−303.539			−0.942037			−0.471018	+	0.882123i	$0.656113\pi$
$48$		0			0
$49$	−417.454			−1.21707
$50$	−291.039	−	190.367i	−0.823182	−	0.538440i
$51$		0			0
$52$	221.814	+	507.159i	0.591539	+	1.35250i
$53$			243.342i			0.630673i	0.948980	+	0.315336i	$0.102117\pi$
$53$			243.342i			0.630673i	−0.948980	+	0.315336i	$0.897883\pi$
$54$		0			0
$55$		−	31.7722i		−	0.0778940i
$56$	−615.305	−	103.692i	−1.46828	−	0.247435i
$57$		0			0
$58$	−167.513	+	256.099i	−0.379234	+	0.579783i
$59$	−83.8393			−0.184999			−0.0924996	−	0.995713i	$-0.529486\pi$
$59$	−83.8393			−0.184999			−0.0924996	+	0.995713i	$0.529486\pi$
$60$		0			0
$61$	−398.436			−0.836302			−0.418151	−	0.908377i	$-0.637322\pi$
$61$	−398.436			−0.836302			−0.418151	+	0.908377i	$0.637322\pi$
$62$	−183.784	+	280.974i	−0.376461	+	0.575544i
$63$		0			0
$64$	−483.722	−	167.800i	−0.944770	−	0.327734i
$65$			98.9499i			0.188819i
$66$		0			0
$67$		−	355.375i		−	0.647999i	−0.946057	−	0.323999i	$-0.894972\pi$
$67$		−	355.375i		−	0.647999i	0.946057	−	0.323999i	$-0.105028\pi$
$68$	−230.522	+	100.822i	−0.411101	+	0.179801i
$69$		0			0
$70$	−93.3457	−	61.0571i	−0.159385	−	0.104253i
$71$	−866.235			−1.44793			−0.723966	−	0.689836i	$-0.757683\pi$
$71$	−866.235			−1.44793			−0.723966	+	0.689836i	$0.757683\pi$
$72$		0			0
$73$	64.6645			0.103677			0.0518384	−	0.998655i	$-0.483492\pi$
$73$	64.6645			0.103677			0.0518384	+	0.998655i	$0.483492\pi$
$74$	711.149	+	465.160i	1.11715	+	0.730726i
$75$		0			0
$76$	−84.2802	+	36.8613i	−0.127205	+	0.0556352i
$77$			612.677i			0.906766i
$78$		0			0
$79$		−	409.798i		−	0.583619i	−0.956476	−	0.291809i	$-0.905743\pi$
$79$		−	409.798i		−	0.583619i	0.956476	−	0.291809i	$-0.0942573\pi$
$80$	−67.2033	−	62.1312i	−0.0939194	−	0.0868310i
$81$		0			0
$82$	−616.524	+	942.559i	−0.830289	+	1.26937i
$83$	159.798			0.211327			0.105663	−	0.994402i	$-0.466303\pi$
$83$	159.798			0.211327			0.105663	+	0.994402i	$0.466303\pi$
$84$		0			0
$85$	−44.9763			−0.0573925
$86$	−309.754	+	473.561i	−0.388391	+	0.593783i
$87$		0			0
$88$	−83.5415	+	495.734i	−0.101199	+	0.600517i
$89$		−	1493.47i		−	1.77873i	−0.457195	−	0.889366i	$-0.651146\pi$
$89$		−	1493.47i		−	1.77873i	0.457195	−	0.889366i	$-0.348854\pi$
$90$		0			0
$91$		−	1908.09i		−	2.19805i
$92$	−465.990	−	1065.45i	−0.528074	−	1.20740i
$93$		0			0
$94$	718.488	+	469.960i	0.788366	+	0.515667i
$95$	−16.4436			−0.0177587
$96$		0			0
$97$	−1400.23			−1.46569			−0.732844	−	0.680397i	$-0.761807\pi$
$97$	−1400.23			−1.46569			−0.732844	+	0.680397i	$0.761807\pi$
$98$	988.129	+	646.332i	1.01853	+	0.666218i
$99$		0			0
$100$	394.159	+	901.213i	0.394159	+	0.901213i
$101$		−	239.418i		−	0.235871i	−0.993021	−	0.117936i	$-0.962372\pi$
$101$		−	239.418i		−	0.235871i	0.993021	−	0.117936i	$-0.0376276\pi$
$102$		0			0
$103$		−	582.049i		−	0.556806i	−0.960464	−	0.278403i	$-0.910195\pi$
$103$		−	582.049i		−	0.556806i	0.960464	−	0.278403i	$-0.0898051\pi$
$104$	260.177	−	1543.89i	0.245312	−	1.45568i
$105$		0			0
$106$	376.760	−	576.000i	0.345228	−	0.527793i
$107$	1470.35			1.32845			0.664224	−	0.747533i	$-0.268762\pi$
$107$	1470.35			1.32845			0.664224	+	0.747533i	$0.268762\pi$
$108$		0			0
$109$	−1.40399			−0.00123374			−0.000616870	−	1.00000i	$-0.500196\pi$
$109$	−1.40399			−0.00123374			−0.000616870		1.00000i	$0.500196\pi$
$110$	−49.1920	+	75.2061i	−0.0426388	+	0.0651874i
$111$		0			0
$112$	1295.91	+	1198.10i	1.09332	+	1.01080i
$113$			1356.51i			1.12929i	0.825333	+	0.564646i	$0.190987\pi$
$113$			1356.51i			1.12929i	−0.825333	+	0.564646i	$0.809013\pi$
$114$		0			0
$115$		−	207.876i		−	0.168561i
$116$	793.020	−	346.840i	0.634742	−	0.277614i
$117$		0			0
$118$	198.451	+	129.806i	0.154821	+	0.101268i
$119$	867.295			0.668108
$120$		0			0
$121$	−837.383			−0.629138
$122$	943.111	+	616.886i	0.699879	+	0.457789i
$123$		0			0
$124$	870.047	−	380.528i	0.630101	−	0.275584i
$125$			354.589i			0.253724i
$126$		0			0
$127$			547.847i			0.382784i	0.981514	+	0.191392i	$0.0613002\pi$
$127$			547.847i			0.382784i	−0.981514	+	0.191392i	$0.938700\pi$
$128$	885.189	+	1146.12i	0.611253	+	0.791435i
$129$		0			0
$130$	153.201	−	234.218i	0.103359	−	0.158017i
$131$	1863.22			1.24267			0.621336	−	0.783544i	$-0.286590\pi$
$131$	1863.22			1.24267			0.621336	+	0.783544i	$0.286590\pi$
$132$		0			0
$133$	317.089			0.206730
$134$	−550.216	+	841.185i	−0.354712	+	0.542293i
$135$		0			0
$136$	701.754	+	118.260i	0.442462	+	0.0745640i
$137$			1447.95i			0.902966i	0.892280	+	0.451483i	$0.149105\pi$
$137$			1447.95i			0.902966i	−0.892280	+	0.451483i	$0.850895\pi$
$138$		0			0
$139$			374.274i			0.228385i	0.993459	+	0.114193i	$0.0364281\pi$
$139$			374.274i			0.228385i	−0.993459	+	0.114193i	$0.963572\pi$
$140$	126.420	+	289.049i	0.0763174	+	0.174493i
$141$		0			0
$142$	2050.41	+	1341.16i	1.21174	+	0.792592i
$143$	−1537.29			−0.898986
$144$		0			0
$145$	154.723			0.0886143
$146$	−153.063	−	100.118i	−0.0867644	−	0.0567523i
$147$		0			0
$148$	−963.123	−	2202.10i	−0.534920	−	1.22305i
$149$		−	2469.10i		−	1.35756i	−0.734342	−	0.678779i	$-0.762509\pi$
$149$		−	2469.10i		−	1.35756i	0.734342	−	0.678779i	$-0.237491\pi$
$150$		0			0
$151$		−	606.741i		−	0.326992i	−0.986544	−	0.163496i	$-0.947723\pi$
$151$		−	606.741i		−	0.326992i	0.986544	−	0.163496i	$-0.0522772\pi$
$152$	256.566	+	43.2366i	0.136909	+	0.0230720i
$153$		0			0
$154$	948.589	−	1450.23i	0.496360	−	0.758849i
$155$	169.752			0.0879663
$156$		0			0
$157$	−74.3398			−0.0377895			−0.0188948	−	0.999821i	$-0.506015\pi$
$157$	−74.3398			−0.0377895			−0.0188948	+	0.999821i	$0.506015\pi$
$158$	−634.478	+	970.007i	−0.319471	+	0.488415i
$159$		0			0
$160$	62.8768	+	251.116i	0.0310678	+	0.124078i
$161$			4008.55i			1.96222i
$162$		0			0
$163$			40.4850i			0.0194542i	0.999953	+	0.00972709i	$0.00309628\pi$
$163$			40.4850i			0.0194542i	−0.999953	+	0.00972709i	$0.996904\pi$
$164$	2918.67	−	1276.53i	1.38969	−	0.607804i
$165$		0			0
$166$	−378.248	−	247.410i	−0.176854	−	0.115679i
$167$	−41.1229			−0.0190550			−0.00952750	−	0.999955i	$-0.503033\pi$
$167$	−41.1229			−0.0190550			−0.00952750	+	0.999955i	$0.503033\pi$
$168$		0			0
$169$	2590.67			1.17919
$170$	106.460	+	69.6354i	0.0480303	+	0.0314164i
$171$		0			0
$172$	1466.40	−	641.352i	0.650069	−	0.284318i
$173$		−	1099.81i		−	0.483334i	−0.970359	−	0.241667i	$-0.922306\pi$
$173$		−	1099.81i		−	0.483334i	0.970359	−	0.241667i	$-0.0776941\pi$
$174$		0			0
$175$		−	3390.65i		−	1.46462i
$176$	965.276	−	1044.08i	0.413412	−	0.447160i
$177$		0			0
$178$	−2312.29	+	3535.09i	−0.973671	+	1.48857i
$179$	3849.91			1.60757			0.803787	−	0.594917i	$-0.202815\pi$
$179$	3849.91			1.60757			0.803787	+	0.594917i	$0.202815\pi$
$180$		0			0
$181$	−1091.65			−0.448296			−0.224148	−	0.974555i	$-0.571960\pi$
$181$	−1091.65			−0.448296			−0.224148	+	0.974555i	$0.571960\pi$
$182$	−2954.24	+	4516.52i	−1.20320	+	1.83949i
$183$		0			0
$184$	−546.585	+	3243.43i	−0.218993	+	1.29951i
$185$		−	429.644i		−	0.170746i
$186$		0			0
$187$		−	698.756i		−	0.273252i
$188$	−973.062	−	2224.83i	−0.377489	−	0.863097i
$189$		0			0
$190$	38.9226	+	25.4591i	0.0148618	+	0.00972105i
$191$	639.347			0.242207			0.121103	−	0.992640i	$-0.461357\pi$
$191$	639.347			0.242207			0.121103	+	0.992640i	$0.461357\pi$
$192$		0			0
$193$	1748.21			0.652014			0.326007	−	0.945367i	$-0.394297\pi$
$193$	1748.21			0.652014			0.326007	+	0.945367i	$0.394297\pi$
$194$	3314.39	+	2167.93i	1.22660	+	0.802312i
$195$		0			0
$196$	−1338.24	−	3059.78i	−0.487698	−	1.11508i
$197$		−	2079.55i		−	0.752089i	−0.926602	−	0.376044i	$-0.877284\pi$
$197$		−	2079.55i		−	0.752089i	0.926602	−	0.376044i	$-0.122716\pi$
$198$		0			0
$199$			1834.81i			0.653598i	0.945094	+	0.326799i	$0.105970\pi$
$199$			1834.81i			0.653598i	−0.945094	+	0.326799i	$0.894030\pi$
$200$	462.331	−	2743.47i	0.163459	−	0.969963i
$201$		0			0
$202$	−370.684	+	566.711i	−0.129115	+	0.197394i
$203$	−2983.59			−1.03156
$204$		0			0
$205$	569.451			0.194011
$206$	−901.169	+	1377.73i	−0.304793	+	0.465976i
$207$		0			0
$208$	−3006.21	+	3251.62i	−1.00213	+	1.08394i
$209$		−	255.470i		−	0.0845512i
$210$		0			0
$211$			4973.70i			1.62277i	0.584514	+	0.811383i	$0.301285\pi$
$211$			4973.70i			1.62277i	−0.584514	+	0.811383i	$0.698715\pi$
$212$	−1783.61	+	780.088i	−0.577824	+	0.252720i
$213$		0			0
$214$	−3480.37	−	2276.50i	−1.11174	−	0.727188i
$215$	286.104			0.0907540
$216$		0			0
$217$	−3273.39			−1.02402
$218$	3.32329	+	2.17375i	0.00103248	+	0.000675344i
$219$		0			0
$220$	232.878	−	101.853i	0.0713667	−	0.0312133i
$221$			2176.17i			0.662376i
$222$		0			0
$223$		−	706.670i		−	0.212207i	−0.994355	−	0.106103i	$-0.966163\pi$
$223$		−	706.670i		−	0.212207i	0.994355	−	0.106103i	$-0.0338375\pi$
$224$	−1212.48	−	4842.36i	−0.361661	−	1.44439i
$225$		0			0
$226$	2100.25	−	3210.92i	0.618170	−	0.945075i
$227$	−3209.60			−0.938454			−0.469227	−	0.883078i	$-0.655467\pi$
$227$	−3209.60			−0.938454			−0.469227	+	0.883078i	$0.655467\pi$
$228$		0			0
$229$	1463.65			0.422362			0.211181	−	0.977447i	$-0.432269\pi$
$229$	1463.65			0.422362			0.211181	+	0.977447i	$0.432269\pi$
$230$	−321.848	+	492.049i	−0.0922696	+	0.141064i
$231$		0			0
$232$	−2414.11	−	406.827i	−0.683164	−	0.115127i
$233$			1324.13i			0.372303i	0.982521	+	0.186152i	$0.0596015\pi$
$233$			1324.13i			0.372303i	−0.982521	+	0.186152i	$0.940398\pi$
$234$		0			0
$235$		−	434.078i		−	0.120494i
$236$	−268.766	−	614.510i	−0.0741320	−	0.169497i
$237$		0			0
$238$	−2052.92	−	1342.81i	−0.559122	−	0.365720i
$239$	789.055			0.213555			0.106778	−	0.994283i	$-0.465947\pi$
$239$	789.055			0.213555			0.106778	+	0.994283i	$0.465947\pi$
$240$		0			0
$241$	−2340.77			−0.625654			−0.312827	−	0.949810i	$-0.601276\pi$
$241$	−2340.77			−0.625654			−0.312827	+	0.949810i	$0.601276\pi$
$242$	1982.12	+	1296.50i	0.526509	+	0.344388i
$243$		0			0
$244$	−1277.27	−	2920.38i	−0.335119	−	0.766222i
$245$		−	596.983i		−	0.155673i
$246$		0			0
$247$			795.621i			0.204956i
$248$	−2648.59	−	446.342i	−0.678168	−	0.114285i
$249$		0			0
$250$	549.000	−	839.326i	0.138887	−	0.212335i
$251$	−938.044			−0.235892			−0.117946	−	0.993020i	$-0.537631\pi$
$251$	−938.044			−0.235892			−0.117946	+	0.993020i	$0.537631\pi$
$252$		0			0
$253$	3229.58			0.802537
$254$	848.215	−	1296.77i	0.209534	−	0.320342i
$255$		0			0
$256$	−320.771	−	4083.42i	−0.0783132	−	0.996929i
$257$		−	165.995i		−	0.0402898i	−0.999797	−	0.0201449i	$-0.993587\pi$
$257$		−	165.995i		−	0.0402898i	0.999797	−	0.0201449i	$-0.00641275\pi$
$258$		0			0
$259$			8285.00i			1.98766i
$260$	−725.265	+	317.206i	−0.172996	+	0.0756626i
$261$		0			0
$262$	−4410.31	−	2884.76i	−1.03996	−	0.680234i
$263$	4831.74			1.13284			0.566422	−	0.824115i	$-0.308327\pi$
$263$	4831.74			1.13284			0.566422	+	0.824115i	$0.308327\pi$
$264$		0			0
$265$	−347.993			−0.0806681
$266$	−750.561	−	490.939i	−0.173007	−	0.113163i
$267$		0			0
$268$	2604.76	−	1139.23i	0.593698	−	0.259663i
$269$		−	5581.42i		−	1.26508i	−0.774529	−	0.632538i	$-0.782013\pi$
$269$		−	5581.42i		−	1.26508i	0.774529	−	0.632538i	$-0.217987\pi$
$270$		0			0
$271$			8094.32i			1.81437i	0.420729	+	0.907186i	$0.361774\pi$
$271$			8094.32i			1.81437i	−0.420729	+	0.907186i	$0.638226\pi$
$272$	−1477.98	−	1366.43i	−0.329469	−	0.304603i
$273$		0			0
$274$	2241.81	−	3427.34i	0.494280	−	0.755669i
$275$	−2731.75			−0.599021
$276$		0			0
$277$	−1845.68			−0.400348			−0.200174	−	0.979760i	$-0.564151\pi$
$277$	−1845.68			−0.400348			−0.200174	+	0.979760i	$0.564151\pi$
$278$	579.477	−	885.921i	0.125017	−	0.191130i
$279$		0			0
$280$	148.285	−	879.921i	0.0316490	−	0.187805i
$281$		−	2534.56i		−	0.538076i	−0.963130	−	0.269038i	$-0.913294\pi$
$281$		−	2534.56i		−	0.538076i	0.963130	−	0.269038i	$-0.0867057\pi$
$282$		0			0
$283$			3107.90i			0.652811i	0.945230	+	0.326405i	$0.105837\pi$
$283$			3107.90i			0.652811i	−0.945230	+	0.326405i	$0.894163\pi$
$284$	−2776.91	−	6349.17i	−0.580208	−	1.32660i
$285$		0			0
$286$	3638.83	+	2380.15i	0.752338	+	0.492101i
$287$	−10981.0			−2.25848
$288$		0			0
$289$	3923.85			0.798667
$290$	−366.236	−	239.553i	−0.0741589	−	0.0485071i
$291$		0			0
$292$	207.296	+	473.966i	0.0415449	+	0.0949889i
$293$		−	5570.68i		−	1.11073i	−0.831608	−	0.555363i	$-0.812580\pi$
$293$		−	5570.68i		−	1.11073i	0.831608	−	0.555363i	$-0.187420\pi$
$294$		0			0
$295$		−	119.895i		−	0.0236629i
$296$	−1129.70	+	6703.63i	−0.221833	+	1.31635i
$297$		0			0
$298$	−3822.83	+	5844.44i	−0.743122	+	1.13610i
$299$	−10058.0			−1.94539
$300$		0			0
$301$	−5517.05			−1.05647
$302$	−939.398	+	1436.18i	−0.178994	+	0.273651i
$303$		0			0
$304$	−540.358	−	499.575i	−0.101946	−	0.0942520i
$305$		−	569.785i		−	0.106970i
$306$		0			0
$307$		−	7746.70i		−	1.44016i	−0.693893	−	0.720078i	$-0.744106\pi$
$307$		−	7746.70i		−	1.44016i	0.693893	−	0.720078i	$-0.255894\pi$
$308$	−4490.69	+	1964.07i	−0.830782	+	0.363355i
$309$		0			0
$310$	−401.808	−	262.821i	−0.0736167	−	0.0481524i
$311$	5813.08			1.05990			0.529951	−	0.848028i	$-0.322210\pi$
$311$	5813.08			1.05990			0.529951	+	0.848028i	$0.322210\pi$
$312$		0			0
$313$	2735.47			0.493986			0.246993	−	0.969017i	$-0.420558\pi$
$313$	2735.47			0.493986			0.246993	+	0.969017i	$0.420558\pi$
$314$	175.965	+	115.098i	0.0316251	+	0.0206858i
$315$		0			0
$316$	3003.67	−	1313.70i	0.534713	−	0.233865i
$317$			6275.17i			1.11183i	0.831241	+	0.555913i	$0.187631\pi$
$317$			6275.17i			1.11183i	−0.831241	+	0.555913i	$0.812369\pi$
$318$		0			0
$319$			2403.80i			0.421902i
$320$	239.963	−	691.750i	0.0419198	−	0.120844i
$321$		0			0
$322$	6206.32	−	9488.38i	1.07411	−	1.64213i
$323$	−361.639			−0.0622976
$324$		0			0
$325$	8507.62			1.45206
$326$	62.6817	−	95.8295i	0.0106491	−	0.0162807i
$327$		0			0
$328$	−8885.00	−	1497.31i	−1.49571	−	0.252058i
$329$			8370.50i			1.40268i
$330$		0			0
$331$		−	349.149i		−	0.0579787i	−0.999580	−	0.0289893i	$-0.990771\pi$
$331$		−	349.149i		−	0.0579787i	0.999580	−	0.0289893i	$-0.00922888\pi$
$332$	512.268	+	1171.26i	0.0846818	+	0.193618i
$333$		0			0
$334$	97.3394	+	63.6693i	0.0159466	+	0.0104306i
$335$	508.205			0.0828843
$336$		0			0
$337$	9326.08			1.50749			0.753744	−	0.657168i	$-0.228246\pi$
$337$	9326.08			1.50749			0.753744	+	0.657168i	$0.228246\pi$
$338$	−6132.22	−	4011.06i	−0.986830	−	0.645482i
$339$		0			0
$340$	−144.181	−	329.659i	−0.0229981	−	0.0525832i
$341$			2637.28i			0.418817i
$342$		0			0
$343$			2053.18i			0.323210i
$344$	−4464.01	−	752.277i	−0.699660	−	0.117907i
$345$		0			0
$346$	−1702.80	+	2603.28i	−0.264575	+	0.404489i
$347$	−5561.31			−0.860365			−0.430183	−	0.902742i	$-0.641551\pi$
$347$	−5561.31			−0.860365			−0.430183	+	0.902742i	$0.641551\pi$
$348$		0			0
$349$	10672.2			1.63688			0.818439	−	0.574593i	$-0.194840\pi$
$349$	10672.2			1.63688			0.818439	+	0.574593i	$0.194840\pi$
$350$	−5249.64	+	8025.78i	−0.801728	+	1.22570i
$351$		0			0
$352$	−3901.36	+	976.860i	−0.590747	+	0.147917i
$353$			403.742i			0.0608754i	0.999537	+	0.0304377i	$0.00969012\pi$
$353$			403.742i			0.0608754i	−0.999537	+	0.0304377i	$0.990310\pi$
$354$		0			0
$355$		−	1238.76i		−	0.185202i
$356$	10946.6	−	4787.64i	1.62968	−	0.712766i
$357$		0			0
$358$	−9112.87	−	5960.70i	−1.34534	−	0.879979i
$359$	6398.10			0.940609			0.470305	−	0.882504i	$-0.344144\pi$
$359$	6398.10			0.940609			0.470305	+	0.882504i	$0.344144\pi$
$360$		0			0
$361$	6726.78			0.980724
$362$	2583.97	+	1690.17i	0.375167	+	0.245396i
$363$		0			0
$364$	13985.6	−	6116.81i	2.01386	−	0.880790i
$365$			92.4738i			0.0132611i
$366$		0			0
$367$			11054.6i			1.57233i	0.618015	+	0.786166i	$0.287937\pi$
$367$			11054.6i			1.57233i	−0.618015	+	0.786166i	$0.712063\pi$
$368$	6315.50	−	6831.06i	0.894614	−	0.967646i
$369$		0			0
$370$	−665.205	+	1016.98i	−0.0934658	+	0.142893i
$371$	6710.49			0.939060
$372$		0			0
$373$	3512.37			0.487570			0.243785	−	0.969829i	$-0.421611\pi$
$373$	3512.37			0.487570			0.243785	+	0.969829i	$0.421611\pi$
$374$	−1081.86	+	1653.98i	−0.149577	+	0.228677i
$375$		0			0
$376$	−1141.36	+	6772.81i	−0.156545	+	0.928939i
$377$		−	7486.26i		−	1.02271i
$378$		0			0
$379$			1238.70i			0.167883i	0.996471	+	0.0839413i	$0.0267508\pi$
$379$			1238.70i			0.167883i	−0.996471	+	0.0839413i	$0.973249\pi$
$380$	−52.7137	−	120.525i	−0.00711619	−	0.0162706i
$381$		0			0
$382$	−1513.36	−	989.881i	−0.202697	−	0.132583i
$383$	−1708.00			−0.227871			−0.113936	−	0.993488i	$-0.536346\pi$
$383$	−1708.00			−0.227871			−0.113936	+	0.993488i	$0.536346\pi$
$384$		0			0
$385$	−876.162			−0.115983
$386$	−4138.07	−	2706.69i	−0.545653	−	0.356910i
$387$		0			0
$388$	−4488.75	−	10263.1i	−0.587324	−	1.34287i
$389$		−	8951.01i		−	1.16667i	−0.812232	−	0.583334i	$-0.801748\pi$
$389$		−	8951.01i		−	1.16667i	0.812232	−	0.583334i	$-0.198252\pi$
$390$		0			0
$391$		−	4571.74i		−	0.591311i
$392$	−1569.70	+	9314.57i	−0.202249	+	1.20015i
$393$		0			0
$394$	−3219.70	+	4922.36i	−0.411690	+	0.629403i
$395$	586.034			0.0746496
$396$		0			0
$397$	−9391.26			−1.18724			−0.593619	−	0.804746i	$-0.702302\pi$
$397$	−9391.26			−1.18724			−0.593619	+	0.804746i	$0.702302\pi$
$398$	2840.78	−	4343.06i	0.357777	−	0.546979i
$399$		0			0
$400$	−5341.98	+	5778.08i	−0.667748	+	0.722260i
$401$		−	4074.64i		−	0.507426i	−0.967279	−	0.253713i	$-0.918348\pi$
$401$		−	4074.64i		−	0.507426i	0.967279	−	0.253713i	$-0.0816519\pi$
$402$		0			0
$403$		−	8213.40i		−	1.01523i
$404$	1754.84	−	767.508i	0.216106	−	0.0945172i
$405$		0			0
$406$	7062.27	+	4619.40i	0.863287	+	0.564673i
$407$	6674.99			0.812941
$408$		0			0
$409$	−671.431			−0.0811739			−0.0405869	−	0.999176i	$-0.512923\pi$
$409$	−671.431			−0.0811739			−0.0405869	+	0.999176i	$0.512923\pi$
$410$	−1347.91	−	881.664i	−0.162362	−	0.106201i
$411$		0			0
$412$	4266.20	−	1865.89i	0.510147	−	0.223121i
$413$			2311.98i			0.275460i
$414$		0			0
$415$			228.520i			0.0270304i
$416$	12150.2	−	3042.28i	1.43200	−	0.358558i
$417$		0			0
$418$	−395.536	+	604.706i	−0.0462830	+	0.0707587i
$419$	9407.15			1.09682			0.548412	−	0.836208i	$-0.315233\pi$
$419$	9407.15			1.09682			0.548412	+	0.836208i	$0.315233\pi$
$420$		0			0
$421$	−12312.4			−1.42534			−0.712671	−	0.701499i	$-0.752515\pi$
$421$	−12312.4			−1.42534			−0.712671	+	0.701499i	$0.752515\pi$
$422$	7700.63	−	11772.9i	0.888296	−	1.35805i
$423$		0			0
$424$	5429.65	+	915.008i	0.621904	+	0.104804i
$425$			3867.02i			0.441360i
$426$		0			0
$427$			10987.4i			1.24524i
$428$	4713.53	+	10777.1i	0.532330	+	1.21713i
$429$		0			0
$430$	−677.218	−	442.966i	−0.0759497	−	0.0496784i
$431$	7647.49			0.854679			0.427340	−	0.904091i	$-0.359451\pi$
$431$	7647.49			0.854679			0.427340	+	0.904091i	$0.359451\pi$
$432$		0			0
$433$	−13985.2			−1.55216			−0.776082	−	0.630632i	$-0.782796\pi$
$433$	−13985.2			−1.55216			−0.776082	+	0.630632i	$0.782796\pi$
$434$	7748.23	+	5068.09i	0.856974	+	0.560544i
$435$		0			0
$436$	−4.50079	−	10.2907i	−0.000494378	−	0.00113036i
$437$		−	1671.46i		−	0.182967i
$438$		0			0
$439$		−	13517.7i		−	1.46962i	−0.678272	−	0.734811i	$-0.737271\pi$
$439$		−	13517.7i		−	1.46962i	0.678272	−	0.734811i	$-0.262729\pi$
$440$	−708.928	−	119.469i	−0.0768109	−	0.0129442i
$441$		0			0
$442$	3369.30	−	5151.07i	0.362582	−	0.554325i
$443$	−6541.00			−0.701518			−0.350759	−	0.936466i	$-0.614076\pi$
$443$	−6541.00			−0.701518			−0.350759	+	0.936466i	$0.614076\pi$
$444$		0			0
$445$	2135.74			0.227514
$446$	−1094.12	+	1672.71i	−0.116161	+	0.177590i
$447$		0			0
$448$	−4627.30	+	13339.3i	−0.487990	+	1.40675i
$449$			17599.7i			1.84984i	0.380158	+	0.924921i	$0.375870\pi$
$449$			17599.7i			1.84984i	−0.380158	+	0.924921i	$0.624130\pi$
$450$		0			0
$451$			8847.05i			0.923706i
$452$	−9942.73	+	4348.60i	−1.03466	+	0.452525i
$453$		0			0
$454$	7597.25	+	4969.33i	0.785367	+	0.513706i
$455$	2728.67			0.281148
$456$		0			0
$457$	−2398.99			−0.245558			−0.122779	−	0.992434i	$-0.539181\pi$
$457$	−2398.99			−0.245558			−0.122779	+	0.992434i	$0.539181\pi$
$458$	−3464.52	−	2266.13i	−0.353463	−	0.231199i
$459$		0			0
$460$	1523.65	−	666.392i	0.154436	−	0.0675450i
$461$		−	3738.60i		−	0.377709i	−0.982005	−	0.188855i	$-0.939522\pi$
$461$		−	3738.60i		−	0.377709i	0.982005	−	0.188855i	$-0.0604775\pi$
$462$		0			0
$463$		−	2503.05i		−	0.251245i	−0.992078	−	0.125623i	$-0.959907\pi$
$463$		−	2503.05i		−	0.251245i	0.992078	−	0.125623i	$-0.0400928\pi$
$464$	5084.40	+	4700.66i	0.508702	+	0.470308i
$465$		0			0
$466$	2050.11	−	3134.26i	0.203797	−	0.311571i
$467$	5361.30			0.531245			0.265622	−	0.964077i	$-0.414423\pi$
$467$	5361.30			0.531245			0.265622	+	0.964077i	$0.414423\pi$
$468$		0			0
$469$	−9799.93			−0.964859
$470$	−672.069	+	1027.48i	−0.0659580	+	0.100838i
$471$		0			0
$472$	−315.250	+	1870.69i	−0.0307427	+	0.182427i
$473$			4444.94i			0.432090i
$474$		0			0
$475$			1413.81i			0.136568i
$476$	2780.31	+	6356.95i	0.267721	+	0.612122i
$477$		0			0
$478$	−1867.72	−	1221.67i	−0.178719	−	0.116899i
$479$	1219.85			0.116360			0.0581799	−	0.998306i	$-0.481470\pi$
$479$	1219.85			0.116360			0.0581799	+	0.998306i	$0.481470\pi$
$480$		0			0
$481$	−20788.3			−1.97061
$482$	5540.70	+	3624.15i	0.523593	+	0.342480i
$483$		0			0
$484$	−2684.42	−	6137.70i	−0.252105	−	0.576418i
$485$		−	2002.41i		−	0.187473i
$486$		0			0
$487$			1483.03i			0.137993i	0.997617	+	0.0689964i	$0.0219797\pi$
$487$			1483.03i			0.137993i	−0.997617	+	0.0689964i	$0.978020\pi$
$488$	−1498.18	+	8890.21i	−0.138975	+	0.824674i
$489$		0			0
$490$	−924.290	+	1413.08i	−0.0852147	+	0.130278i
$491$	−13884.7			−1.27619			−0.638094	−	0.769958i	$-0.720277\pi$
$491$	−13884.7			−1.27619			−0.638094	+	0.769958i	$0.720277\pi$
$492$		0			0
$493$	3402.77			0.310859
$494$	1231.84	−	1883.26i	0.112192	−	0.171522i
$495$		0			0
$496$	5578.26	+	5157.24i	0.504982	+	0.466869i
$497$			23887.6i			2.15594i
$498$		0			0
$499$		−	20199.4i		−	1.81213i	−0.423143	−	0.906063i	$-0.639073\pi$
$499$		−	20199.4i		−	1.81213i	0.423143	−	0.906063i	$-0.360927\pi$
$500$	−2599.01	+	1136.72i	−0.232462	+	0.101671i
$501$		0			0
$502$	2220.38	+	1452.34i	0.197411	+	0.129126i
$503$	388.562			0.0344436			0.0172218	−	0.999852i	$-0.494518\pi$
$503$	388.562			0.0344436			0.0172218	+	0.999852i	$0.494518\pi$
$504$		0			0
$505$	342.381			0.0301698
$506$	−7644.53	−	5000.26i	−0.671622	−	0.439305i
$507$		0			0
$508$	−4015.51	+	1756.25i	−0.350708	+	0.153387i
$509$		−	6760.52i		−	0.588712i	−0.955696	−	0.294356i	$-0.904895\pi$
$509$		−	6760.52i		−	0.588712i	0.955696	−	0.294356i	$-0.0951052\pi$
$510$		0			0
$511$		−	1783.21i		−	0.154373i
$512$	−5562.96	+	10162.2i	−0.480177	+	0.877172i
$513$		0			0
$514$	−257.005	+	392.916i	−0.0220545	+	0.0337175i
$515$	832.363			0.0712200
$516$		0			0
$517$	6743.88			0.573685
$518$	12827.4	−	19610.9i	1.08804	−	1.66342i
$519$		0			0
$520$	2207.85	+	372.068i	0.186193	+	0.0313774i
$521$			17324.6i			1.45683i	0.685139	+	0.728413i	$0.259742\pi$
$521$			17324.6i			1.45683i	−0.685139	+	0.728413i	$0.740258\pi$
$522$		0			0
$523$		−	16119.4i		−	1.34771i	−0.738864	−	0.673855i	$-0.764637\pi$
$523$		−	16119.4i		−	1.34771i	0.738864	−	0.673855i	$-0.235363\pi$
$524$	5972.96	+	13656.7i	0.497958	+	1.13854i
$525$		0			0
$526$	−11436.9	−	7480.84i	−0.948047	−	0.620114i
$527$	3733.29			0.308586
$528$		0			0
$529$	8963.10			0.736673
$530$	823.712	+	538.787i	0.0675090	+	0.0441574i
$531$		0			0
$532$	1016.50	+	2324.14i	0.0828398	+	0.189406i
$533$		−	27552.8i		−	2.23911i
$534$		0			0
$535$			2102.68i			0.169919i
$536$	−7929.40	−	1336.27i	−0.638989	−	0.107683i
$537$		0			0
$538$	−8641.55	+	13211.4i	−0.692497	+	1.05871i
$539$	9274.78			0.741175
$540$		0			0
$541$	−4412.42			−0.350655			−0.175328	−	0.984510i	$-0.556099\pi$
$541$	−4412.42			−0.350655			−0.175328	+	0.984510i	$0.556099\pi$
$542$	12532.2	−	19159.6i	0.993180	−	1.51840i
$543$		0			0
$544$	1382.83	+	5522.70i	0.108986	+	0.435264i
$545$		−	2.00778i		−	0.000157805i
$546$		0			0
$547$			6911.97i			0.540282i	0.962821	+	0.270141i	$0.0870704\pi$
$547$			6911.97i			0.540282i	−0.962821	+	0.270141i	$0.912930\pi$
$548$	−10612.9	+	4641.71i	−0.827300	+	0.361832i
$549$		0			0
$550$	6466.15	+	4229.49i	0.501305	+	0.327902i
$551$	1244.08			0.0961877
$552$		0			0
$553$	−11300.7			−0.868998
$554$	4368.80	+	2857.62i	0.335041	+	0.219149i
$555$		0			0
$556$	−2743.29	+	1199.82i	−0.209247	+	0.0915174i
$557$		−	17257.6i		−	1.31280i	−0.754415	−	0.656398i	$-0.772079\pi$
$557$		−	17257.6i		−	1.31280i	0.754415	−	0.656398i	$-0.227921\pi$
$558$		0			0
$559$		−	13843.1i		−	1.04741i
$560$	−1713.35	+	1853.22i	−0.129290	+	0.139844i
$561$		0			0
$562$	−3924.19	+	5999.40i	−0.294541	+	0.450302i
$563$	25109.1			1.87961			0.939805	−	0.341711i	$-0.111006\pi$
$563$	25109.1			1.87961			0.939805	+	0.341711i	$0.111006\pi$
$564$		0			0
$565$	−1939.89			−0.144446
$566$	4811.86	−	7356.51i	0.357346	−	0.546320i
$567$		0			0
$568$	−3257.19	+	19328.1i	−0.240614	+	1.42780i
$569$			17105.2i			1.26026i	0.776490	+	0.630129i	$0.216998\pi$
$569$			17105.2i			1.26026i	−0.776490	+	0.630129i	$0.783002\pi$
$570$		0			0
$571$		−	5558.85i		−	0.407409i	−0.979032	−	0.203705i	$-0.934702\pi$
$571$		−	5558.85i		−	0.407409i	0.979032	−	0.203705i	$-0.0652982\pi$
$572$	−4928.14	−	11267.8i	−0.360238	−	0.823654i
$573$		0			0
$574$	25992.3	+	17001.5i	1.89007	+	1.23629i
$575$	−17873.0			−1.29627
$576$		0			0
$577$	19014.3			1.37188			0.685939	−	0.727659i	$-0.259392\pi$
$577$	19014.3			1.37188			0.685939	+	0.727659i	$0.259392\pi$
$578$	−9287.90	−	6075.18i	−0.668384	−	0.437187i
$579$		0			0
$580$	496.000	+	1134.06i	0.0355091	+	0.0811886i
$581$		−	4406.64i		−	0.314662i
$582$		0			0
$583$		−	5406.46i		−	0.384070i
$584$	243.149	−	1442.85i	0.0172287	−	0.102235i
$585$		0			0
$586$	−8624.91	+	13186.0i	−0.608006	+	0.929537i
$587$	25194.3			1.77152			0.885759	−	0.464146i	$-0.153639\pi$
$587$	25194.3			1.77152			0.885759	+	0.464146i	$0.153639\pi$
$588$		0			0
$589$	1364.91			0.0954844
$590$	−185.630	+	283.796i	−0.0129530	+	0.0198028i
$591$		0			0
$592$	13053.1	−	14118.6i	0.906212	−	0.980191i
$593$		−	17307.5i		−	1.19854i	−0.800548	−	0.599269i	$-0.795458\pi$
$593$		−	17307.5i		−	1.19854i	0.800548	−	0.599269i	$-0.204542\pi$
$594$		0			0
$595$			1240.28i			0.0854564i
$596$	18097.5	−	7915.24i	1.24380	−	0.543994i
$597$		0			0
$598$	23807.7	+	15572.5i	1.62804	+	1.06490i
$599$	−21481.5			−1.46529			−0.732647	−	0.680609i	$-0.761715\pi$
$599$	−21481.5			−1.46529			−0.732647	+	0.680609i	$0.761715\pi$
$600$		0			0
$601$	−5433.48			−0.368779			−0.184390	−	0.982853i	$-0.559031\pi$
$601$	−5433.48			−0.368779			−0.184390	+	0.982853i	$0.559031\pi$
$602$	13059.1	+	8541.89i	0.884133	+	0.578308i
$603$		0			0
$604$	4447.18	−	1945.04i	0.299591	−	0.131031i
$605$		−	1197.50i		−	0.0804719i
$606$		0			0
$607$		−	13492.4i		−	0.902206i	−0.892472	−	0.451103i	$-0.851031\pi$
$607$		−	13492.4i		−	0.902206i	0.892472	−	0.451103i	$-0.148969\pi$
$608$	505.570	+	2019.13i	0.0337230	+	0.134682i
$609$		0			0
$610$	−882.181	+	1348.70i	−0.0585548	+	0.0895202i
$611$	−21002.8			−1.39064
$612$		0			0
$613$	8330.79			0.548903			0.274451	−	0.961601i	$-0.411504\pi$
$613$	8330.79			0.548903			0.274451	+	0.961601i	$0.411504\pi$
$614$	−11994.0	+	18336.7i	−0.788335	+	1.20523i
$615$		0			0
$616$	13670.5	+	2303.77i	0.894159	+	0.150684i
$617$			19799.8i			1.29191i	0.763375	+	0.645955i	$0.223541\pi$
$617$			19799.8i			1.29191i	−0.763375	+	0.645955i	$0.776459\pi$
$618$		0			0
$619$		−	26180.8i		−	1.69999i	−0.526788	−	0.849997i	$-0.676604\pi$
$619$		−	26180.8i		−	1.69999i	0.526788	−	0.849997i	$-0.323396\pi$
$620$	544.177	+	1244.22i	0.0352494	+	0.0805950i
$621$		0			0
$622$	−13759.8	−	9000.22i	−0.887005	−	0.580186i
$623$	−41184.4			−2.64850
$624$		0			0
$625$	14862.3			0.951186
$626$	−6474.95	−	4235.24i	−0.413404	−	0.270406i
$627$		0			0
$628$	−238.313	−	544.882i	−0.0151429	−	0.0346229i
$629$		−	9449.01i		−	0.598977i
$630$		0			0
$631$		−	24489.4i		−	1.54502i	−0.635004	−	0.772509i	$-0.719001\pi$
$631$		−	24489.4i		−	1.54502i	0.635004	−	0.772509i	$-0.280999\pi$
$632$	−9143.74	−	1540.91i	−0.575504	−	0.0969843i
$633$		0			0
$634$	9715.66	−	14853.6i	0.608609	−	0.930458i
$635$	−783.452			−0.0489612
$636$		0			0
$637$	−28884.9			−1.79664
$638$	3721.72	−	5689.87i	0.230947	−	0.353079i
$639$		0			0
$640$	−1639.02	+	1265.87i	−0.101231	+	0.0781842i
$641$		−	23417.0i		−	1.44293i	−0.692453	−	0.721463i	$-0.743470\pi$
$641$		−	23417.0i		−	1.44293i	0.692453	−	0.721463i	$-0.256530\pi$
$642$		0			0
$643$		−	1600.14i		−	0.0981388i	−0.998795	−	0.0490694i	$-0.984374\pi$
$643$		−	1600.14i		−	0.0981388i	0.998795	−	0.0490694i	$-0.0156255\pi$
$644$	−29381.2	+	12850.3i	−1.79779	+	0.786293i
$645$		0			0
$646$	856.012	+	559.914i	0.0521352	+	0.0341014i
$647$	19887.1			1.20841			0.604206	−	0.796828i	$-0.293491\pi$
$647$	19887.1			1.20841			0.604206	+	0.796828i	$0.293491\pi$
$648$		0			0
$649$	1862.70			0.112662
$650$	−20137.9	−	13172.1i	−1.21519	−	0.794849i
$651$		0			0
$652$	−296.740	+	129.784i	−0.0178240	+	0.00779559i
$653$		−	4537.86i		−	0.271945i	−0.990713	−	0.135973i	$-0.956584\pi$
$653$		−	4537.86i		−	0.271945i	0.990713	−	0.135973i	$-0.0434159\pi$
$654$		0			0
$655$			2664.51i			0.158948i
$656$	18712.9	+	17300.6i	1.11374	+	1.02968i
$657$		0			0
$658$	12959.8	−	19813.3i	0.767819	−	1.17386i
$659$	1760.97			0.104093			0.0520467	−	0.998645i	$-0.483426\pi$
$659$	1760.97			0.104093			0.0520467	+	0.998645i	$0.483426\pi$
$660$		0			0
$661$	−7897.92			−0.464741			−0.232370	−	0.972627i	$-0.574648\pi$
$661$	−7897.92			−0.464741			−0.232370	+	0.972627i	$0.574648\pi$
$662$	−540.576	+	826.447i	−0.0317373	+	0.0485208i
$663$		0			0
$664$	600.867	−	3565.54i	0.0351177	−	0.208388i
$665$			453.455i			0.0264424i
$666$		0			0
$667$			15727.3i			0.912987i
$668$	−131.829	−	301.415i	−0.00763563	−	0.0174582i
$669$		0			0
$670$	−1202.94	−	786.839i	−0.0693637	−	0.0453705i
$671$	8852.24			0.509295
$672$		0			0
$673$	−16057.8			−0.919734			−0.459867	−	0.887988i	$-0.652103\pi$
$673$	−16057.8			−0.919734			−0.459867	+	0.887988i	$0.652103\pi$
$674$	−22075.2	−	14439.3i	−1.26158	−	0.825193i
$675$		0			0
$676$	8304.98	+	18988.6i	0.472518	+	1.08037i
$677$			19067.2i			1.08244i	0.840880	+	0.541221i	$0.182038\pi$
$677$			19067.2i			1.08244i	−0.840880	+	0.541221i	$0.817962\pi$
$678$		0			0
$679$			38613.2i			2.18238i
$680$	−169.118	+	1003.55i	−0.00953734	+	0.0565945i
$681$		0			0
$682$	4083.22	−	6242.53i	0.229259	−	0.350497i
$683$	−15166.6			−0.849682			−0.424841	−	0.905268i	$-0.639670\pi$
$683$	−15166.6			−0.849682			−0.424841	+	0.905268i	$0.639670\pi$
$684$		0			0
$685$	−2070.64			−0.115497
$686$	3178.87	−	4859.94i	0.176924	−	0.270486i
$687$		0			0
$688$	9401.74	+	8692.15i	0.520985	+	0.481664i
$689$			16837.6i			0.931003i
$690$		0			0
$691$			10037.6i			0.552601i	0.961071	+	0.276301i	$0.0891085\pi$
$691$			10037.6i			0.552601i	−0.961071	+	0.276301i	$0.910891\pi$
$692$	8061.16	−	3525.67i	0.442832	−	0.193679i
$693$		0			0
$694$	13163.8	+	8610.41i	0.720017	+	0.470961i
$695$	−535.233			−0.0292123
$696$		0			0
$697$	12523.7			0.680589
$698$	−25261.5	−	16523.5i	−1.36986	−	0.896020i
$699$		0			0
$700$	24852.2	−	10869.5i	1.34189	−	0.586896i
$701$		−	13222.0i		−	0.712394i	−0.934411	−	0.356197i	$-0.884073\pi$
$701$		−	13222.0i		−	0.712394i	0.934411	−	0.356197i	$-0.115927\pi$
$702$		0			0
$703$		−	3454.62i		−	0.185339i
$704$	10747.1	+	3728.09i	0.575350	+	0.199585i
$705$		0			0
$706$	625.101	−	955.672i	0.0333229	−	0.0509450i
$707$	−6602.27			−0.351208
$708$		0			0
$709$	23584.5			1.24927			0.624636	−	0.780916i	$-0.285247\pi$
$709$	23584.5			1.24927			0.624636	+	0.780916i	$0.285247\pi$
$710$	−1917.94	+	2932.20i	−0.101379	+	0.154991i
$711$		0			0
$712$	−33323.4	−	5615.69i	−1.75400	−	0.295585i
$713$			17254.9i			0.906311i
$714$		0			0
$715$		−	2198.42i		−	0.114988i
$716$	12341.7	+	28218.4i	0.644179	+	1.47286i
$717$		0			0
$718$	−15144.5	−	9905.98i	−0.787171	−	0.514886i
$719$	−19376.4			−1.00503			−0.502517	−	0.864567i	$-0.667593\pi$
$719$	−19376.4			−1.00503			−0.502517	+	0.864567i	$0.667593\pi$
$720$		0			0
$721$	−16050.8			−0.829074
$722$	−15922.5	−	10414.9i	−0.820742	−	0.536844i
$723$		0			0
$724$	−3499.52	−	8001.37i	−0.179639	−	0.410730i
$725$		−	13303.0i		−	0.681462i
$726$		0			0
$727$			22163.1i			1.13065i	0.824868	+	0.565325i	$0.191249\pi$
$727$			22163.1i			1.13065i	−0.824868	+	0.565325i	$0.808751\pi$
$728$	−42574.8	−	7174.74i	−2.16748	−	0.365266i
$729$		0			0
$730$	143.174	−	218.889i	0.00725907	−	0.0110979i
$731$	6292.18			0.318365
$732$		0			0
$733$	−29668.5			−1.49499			−0.747497	−	0.664265i	$-0.768745\pi$
$733$	−29668.5			−1.49499			−0.747497	+	0.664265i	$0.768745\pi$
$734$	17115.5	−	26166.7i	0.860689	−	1.31584i
$735$		0			0
$736$	−25525.3	+	6391.28i	−1.27836	+	0.320089i
$737$			7895.53i			0.394621i
$738$		0			0
$739$			14616.0i			0.727549i	0.931487	+	0.363774i	$0.118512\pi$
$739$			14616.0i			0.727549i	−0.931487	+	0.363774i	$0.881488\pi$
$740$	3149.13	−	1377.32i	0.156438	−	0.0684206i
$741$		0			0
$742$	−15884.0	−	10389.6i	−0.785875	−	0.514038i
$743$	−35897.8			−1.77249			−0.886246	−	0.463214i	$-0.846696\pi$
$743$	−35897.8			−1.77249			−0.886246	+	0.463214i	$0.846696\pi$
$744$		0			0
$745$	3530.94			0.173643
$746$	−8313.90	−	5438.09i	−0.408034	−	0.266894i
$747$		0			0
$748$	5121.62	−	2240.02i	0.250354	−	0.109496i
$749$		−	40546.8i		−	1.97804i
$750$		0			0
$751$		−	26780.7i		−	1.30125i	−0.759397	−	0.650627i	$-0.774506\pi$
$751$		−	26780.7i		−	1.30125i	0.759397	−	0.650627i	$-0.225494\pi$
$752$	13187.8	−	14264.4i	0.639506	−	0.691712i
$753$		0			0
$754$	−11590.7	+	17720.2i	−0.559828	+	0.855880i
$755$	867.673			0.0418250
$756$		0			0
$757$	1805.80			0.0867016			0.0433508	−	0.999060i	$-0.486197\pi$
$757$	1805.80			0.0867016			0.0433508	+	0.999060i	$0.486197\pi$
$758$	1917.83	−	2932.04i	0.0918982	−	0.140497i
$759$		0			0
$760$	−61.8307	+	366.903i	−0.00295110	+	0.0175118i
$761$			4354.06i			0.207404i	0.994608	+	0.103702i	$0.0330688\pi$
$761$			4354.06i			0.207404i	−0.994608	+	0.103702i	$0.966931\pi$
$762$		0			0
$763$			38.7168i			0.00183702i
$764$	2049.57	+	4686.17i	0.0970560	+	0.221910i
$765$		0			0
$766$	4042.89	+	2644.44i	0.190699	+	0.124736i
$767$	−5801.10			−0.273097
$768$		0			0
$769$	2781.37			0.130428			0.0652138	−	0.997871i	$-0.479227\pi$
$769$	2781.37			0.130428			0.0652138	+	0.997871i	$0.479227\pi$
$770$	2073.91	+	1356.54i	0.0970629	+	0.0634885i
$771$		0			0
$772$	5604.26	+	12813.7i	0.261272	+	0.597377i
$773$			7776.95i			0.361860i	0.983496	+	0.180930i	$0.0579107\pi$
$773$			7776.95i			0.361860i	−0.983496	+	0.180930i	$0.942089\pi$
$774$		0			0
$775$		−	14595.1i		−	0.676479i
$776$	−5265.10	+	31243.0i	−0.243564	+	1.44531i
$777$		0			0
$778$	−13858.6	+	21187.4i	−0.638630	+	0.976354i
$779$	4578.76			0.210592
$780$		0			0
$781$	19245.6			0.881767
$782$	−7078.28	+	10821.5i	−0.323681	+	0.494853i
$783$		0			0
$784$	18137.0	−	19617.6i	0.826212	−	0.893660i
$785$		−	106.310i		−	0.00483359i
$786$		0			0
$787$		−	33714.5i		−	1.52705i	−0.645775	−	0.763527i	$-0.723466\pi$
$787$		−	33714.5i		−	1.52705i	0.645775	−	0.763527i	$-0.276534\pi$
$788$	15242.3	−	6666.44i	0.689066	−	0.301373i
$789$		0			0
$790$	−1387.16	−	907.339i	−0.0624723	−	0.0408629i
$791$	37407.7			1.68150
$792$		0			0
$793$	−27569.0			−1.23456
$794$	22229.5	+	14540.2i	0.993569	+	0.649890i
$795$		0			0
$796$	−13448.4	+	5881.88i	−0.598828	+	0.261907i
$797$		−	43993.9i		−	1.95526i	−0.210329	−	0.977631i	$-0.567453\pi$
$797$		−	43993.9i		−	1.95526i	0.210329	−	0.977631i	$-0.432547\pi$
$798$		0			0
$799$		−	9546.52i		−	0.422693i
$800$	21590.7	−	5406.09i	0.954183	−	0.238918i
$801$		0			0
$802$	−6308.65	+	9644.83i	−0.277763	+	0.424652i
$803$	−1436.68			−0.0631375
$804$		0			0
$805$	−5732.45			−0.250984
$806$	−12716.6	+	19441.4i	−0.555734	+	0.849622i
$807$		0			0
$808$	−5342.09	−	900.252i	−0.232592	−	0.0391965i
$809$			43059.9i			1.87133i	0.352893	+	0.935664i	$0.385198\pi$
$809$			43059.9i			1.87133i	−0.352893	+	0.935664i	$0.614802\pi$
$810$		0			0
$811$			17269.7i			0.747743i	0.927480	+	0.373872i	$0.121970\pi$
$811$			17269.7i			0.747743i	−0.927480	+	0.373872i	$0.878030\pi$
$812$	−9564.56	−	21868.6i	−0.413362	−	0.945119i
$813$		0			0
$814$	−15799.9	−	10334.7i	−0.680329	−	0.445001i
$815$	−57.8958			−0.00248835
$816$		0			0
$817$	2300.46			0.0985103
$818$	1589.30	+	1039.56i	0.0679323	+	0.0444342i
$819$		0			0
$820$	1825.50	+	4173.86i	0.0777430	+	0.177753i
$821$			29180.4i			1.24044i	0.784426	+	0.620222i	$0.212958\pi$
$821$			29180.4i			1.24044i	−0.784426	+	0.620222i	$0.787042\pi$
$822$		0			0
$823$			37538.1i			1.58991i	0.606670	+	0.794954i	$0.292505\pi$
$823$			37538.1i			1.58991i	−0.606670	+	0.794954i	$0.707495\pi$
$824$	−12987.2	−	2188.60i	−0.549064	−	0.0925287i
$825$		0			0
$826$	3579.57	−	5472.54i	0.150786	−	0.230526i
$827$	−14426.3			−0.606594			−0.303297	−	0.952896i	$-0.598087\pi$
$827$	−14426.3			−0.606594			−0.303297	+	0.952896i	$0.598087\pi$
$828$		0			0
$829$	22149.2			0.927956			0.463978	−	0.885847i	$-0.346422\pi$
$829$	22149.2			0.927956			0.463978	+	0.885847i	$0.346422\pi$
$830$	353.811	−	540.915i	0.0147963	−	0.0226210i
$831$		0			0
$832$	−33470.2	−	11610.6i	−1.39468	−	0.483803i
$833$		−	13129.2i		−	0.546100i
$834$		0			0
$835$		−	58.8080i		−	0.00243729i
$836$	1872.49	−	818.965i	0.0774660	−	0.0338810i
$837$		0			0
$838$	−22267.1	−	14564.8i	−0.917903	−	0.600397i
$839$	−16049.0			−0.660398			−0.330199	−	0.943911i	$-0.607116\pi$
$839$	−16049.0			−0.660398			−0.330199	+	0.943911i	$0.607116\pi$
$840$		0			0
$841$	12683.1			0.520033
$842$	29143.8	+	19062.9i	1.19283	+	0.780226i
$843$		0			0
$844$	−36455.3	+	15944.3i	−1.48678	+	0.650267i
$845$			3704.81i			0.150827i
$846$		0			0
$847$			23092.0i			0.936776i
$848$	−11435.5	−	10572.4i	−0.463086	−	0.428135i
$849$		0			0
$850$	5987.19	−	9153.38i	0.241599	−	0.369363i
$851$	43672.3			1.75919
$852$		0			0
$853$	24293.6			0.975142			0.487571	−	0.873083i	$-0.337883\pi$
$853$	24293.6			0.975142			0.487571	+	0.873083i	$0.337883\pi$
$854$	17011.4	−	26007.6i	0.681639	−	1.04211i
$855$		0			0
$856$	5528.76	−	32807.6i	0.220758	−	1.30998i
$857$		−	5896.50i		−	0.235030i	−0.993071	−	0.117515i	$-0.962507\pi$
$857$		−	5896.50i		−	0.235030i	0.993071	−	0.117515i	$-0.0374928\pi$
$858$		0			0
$859$			36950.1i			1.46766i	0.679332	+	0.733831i	$0.262270\pi$
$859$			36950.1i			1.46766i	−0.679332	+	0.733831i	$0.737730\pi$
$860$	917.169	+	2097.03i	0.0363665	+	0.0831491i
$861$		0			0
$862$	−18101.9	−	11840.4i	−0.715259	−	0.467848i
$863$	33898.3			1.33709			0.668546	−	0.743671i	$-0.266917\pi$
$863$	33898.3			1.33709			0.668546	+	0.743671i	$0.266917\pi$
$864$		0			0
$865$	1572.78			0.0618223
$866$	33103.5	+	21652.9i	1.29897	+	0.849648i
$867$		0			0
$868$	−10493.6	−	23992.7i	−0.410340	−	0.938209i
$869$			9104.68i			0.355415i
$870$		0			0
$871$		−	24589.4i		−	0.956580i
$872$	−5.27923	+	31.3269i	−0.000205020	+	0.00121659i
$873$		0			0
$874$	−2587.86	+	3956.40i	−0.100155	+	0.153120i
$875$	9778.28			0.377790
$876$		0			0
$877$	41700.0			1.60560			0.802800	−	0.596249i	$-0.203343\pi$
$877$	41700.0			1.60560			0.802800	+	0.596249i	$0.203343\pi$
$878$	−20929.0	+	31996.8i	−0.804465	+	1.22989i
$879$		0			0
$880$	1493.09	+	1380.40i	0.0571954	+	0.0528787i
$881$			15865.5i			0.606723i	0.952876	+	0.303361i	$0.0981090\pi$
$881$			15865.5i			0.606723i	−0.952876	+	0.303361i	$0.901891\pi$
$882$		0			0
$883$			41172.6i			1.56916i	0.620027	+	0.784581i	$0.287122\pi$
$883$			41172.6i			1.56916i	−0.620027	+	0.784581i	$0.712878\pi$
$884$	−15950.5	+	6976.20i	−0.606870	+	0.265424i
$885$		0			0
$886$	15482.8	+	10127.2i	0.587082	+	0.384008i
$887$	18435.9			0.697876			0.348938	−	0.937146i	$-0.386542\pi$
$887$	18435.9			0.697876			0.348938	+	0.937146i	$0.386542\pi$
$888$		0			0
$889$	15107.6			0.569959
$890$	−5055.38	−	3306.70i	−0.190401	−	0.124540i
$891$		0			0
$892$	5179.63	−	2265.39i	0.194425	−	0.0850346i
$893$		−	3490.27i		−	0.130792i
$894$		0			0
$895$			5505.58i			0.205622i
$896$	31605.8	−	24410.3i	1.17843	−	0.910145i
$897$		0			0
$898$	27249.0	−	41659.0i	1.01260	−	1.54809i
$899$	−12842.9			−0.476457
$900$		0			0
$901$	−7653.29			−0.282983
$902$	13697.6	−	20941.3i	0.505633	−	0.773025i
$903$		0			0
$904$	30267.6	+	5100.72i	1.11359	+	0.187663i
$905$		−	1561.12i		−	0.0573407i
$906$		0			0
$907$			8478.35i			0.310385i	0.987884	+	0.155192i	$0.0495998\pi$
$907$			8478.35i			0.310385i	−0.987884	+	0.155192i	$0.950400\pi$
$908$	−10289.1	−	23525.2i	−0.376053	−	0.859814i
$909$		0			0
$910$	−6458.87	−	4224.72i	−0.235285	−	0.153899i
$911$	33611.2			1.22238			0.611190	−	0.791484i	$-0.290691\pi$
$911$	33611.2			1.22238			0.611190	+	0.791484i	$0.290691\pi$
$912$		0			0
$913$	−3550.31			−0.128695
$914$	5678.50	+	3714.29i	0.205501	+	0.134418i
$915$		0			0
$916$	4692.06	+	10728.0i	0.169247	+	0.386969i
$917$		−	51380.7i		−	1.85032i
$918$		0			0
$919$			4323.08i			0.155174i	0.996986	+	0.0775871i	$0.0247216\pi$
$919$			4323.08i			0.155174i	−0.996986	+	0.0775871i	$0.975278\pi$
$920$	−4638.29	−	781.647i	−0.166217	−	0.0280110i
$921$		0			0
$922$	−5788.36	+	8849.40i	−0.206757	+	0.316095i
$923$	−59937.4			−2.13745
$924$		0			0
$925$	−36940.4			−1.31307
$926$	−3875.39	+	5924.81i	−0.137531	+	0.210261i
$927$		0			0
$928$	−4757.07	−	18998.7i	−0.168274	−	0.672050i
$929$		−	15176.2i		−	0.535967i	−0.963423	−	0.267984i	$-0.913643\pi$
$929$		−	15176.2i		−	0.535967i	0.963423	−	0.267984i	$-0.0863573\pi$
$930$		0			0
$931$		−	4800.13i		−	0.168977i
$932$	−9705.37	+	4244.79i	−0.341105	+	0.149188i
$933$		0			0
$934$	−12690.4	−	8300.73i	−0.444585	−	0.290801i
$935$	999.260			0.0349511
$936$		0			0
$937$	13144.0			0.458266			0.229133	−	0.973395i	$-0.426411\pi$
$937$	13144.0			0.458266			0.229133	+	0.973395i	$0.426411\pi$
$938$	23196.8	+	15172.9i	0.807465	+	0.528160i
$939$		0			0
$940$	3181.63	−	1391.53i	0.110397	−	0.0482838i
$941$			34198.4i			1.18474i	0.805668	+	0.592368i	$0.201807\pi$
$941$			34198.4i			1.18474i	−0.805668	+	0.592368i	$0.798193\pi$
$942$		0			0
$943$			57883.4i			1.99888i
$944$	3642.54	−	3939.90i	0.125588	−	0.135840i
$945$		0			0
$946$	6881.96	−	10521.3i	0.236524	−	0.361604i
$947$	19148.4			0.657065			0.328532	−	0.944493i	$-0.393446\pi$
$947$	19148.4			0.657065			0.328532	+	0.944493i	$0.393446\pi$
$948$		0			0
$949$	4474.33			0.153048
$950$	2188.95	−	3346.53i	0.0747569	−	0.114290i
$951$		0			0
$952$	3261.18	−	19351.8i	0.111025	−	0.658818i
$953$			12906.3i			0.438696i	0.975647	+	0.219348i	$0.0703930\pi$
$953$			12906.3i			0.438696i	−0.975647	+	0.219348i	$0.929607\pi$
$954$		0			0
$955$			914.301i			0.0309802i
$956$	2529.49	+	5783.48i	0.0855749	+	0.195660i
$957$		0			0
$958$	−2887.43	−	1888.66i	−0.0973785	−	0.0636949i
$959$	39929.0			1.34450
$960$		0			0
$961$	15700.6			0.527026
$962$	49206.5	+	32185.8i	1.64915	+	1.07870i
$963$		0			0
$964$	−7503.88	−	17157.0i	−0.250709	−	0.573226i
$965$			2500.03i			0.0833978i
$966$		0			0
$967$			13887.5i			0.461831i	0.972974	+	0.230916i	$0.0741721\pi$
$967$			13887.5i			0.461831i	−0.972974	+	0.230916i	$0.925828\pi$
$968$	−3148.70	+	18684.4i	−0.104549	+	0.620391i
$969$		0			0
$970$	−3100.26	+	4739.77i	−0.102622	+	0.156891i
$971$	42722.6			1.41198			0.705990	−	0.708222i	$-0.250502\pi$
$971$	42722.6			1.41198			0.705990	+	0.708222i	$0.250502\pi$
$972$		0			0
$973$	10321.1			0.340061
$974$	2296.13	−	3510.39i	0.0755367	−	0.115483i
$975$		0			0
$976$	17310.7	−	18723.9i	0.567728	−	0.614074i
$977$			48997.8i			1.60448i	0.597000	+	0.802242i	$0.296359\pi$
$977$			48997.8i			1.60448i	−0.597000	+	0.802242i	$0.703641\pi$
$978$		0			0
$979$			33181.1i			1.08322i
$980$	4375.66	−	1913.76i	0.142628	−	0.0623805i
$981$		0			0
$982$	32865.6	+	21497.3i	1.06801	+	0.698580i
$983$	−11567.3			−0.375319			−0.187660	−	0.982234i	$-0.560090\pi$
$983$	−11567.3			−0.375319			−0.187660	+	0.982234i	$0.560090\pi$
$984$		0			0
$985$	2973.87			0.0961982
$986$	−8054.49	−	5268.41i	−0.260149	−	0.170163i
$987$		0			0
$988$	−5831.60	+	2550.54i	−0.187781	+	0.0821291i
$989$			29081.8i			0.935033i
$990$		0			0
$991$		−	47618.2i		−	1.52638i	−0.646174	−	0.763190i	$-0.723632\pi$
$991$		−	47618.2i		−	1.52638i	0.646174	−	0.763190i	$-0.276368\pi$
$992$	−5219.13	−	20844.0i	−0.167044	−	0.667136i
$993$		0			0
$994$	36984.4	−	56542.8i	1.18016	−	1.80425i
$995$	−2623.88			−0.0836005
$996$		0			0
$997$	−6894.27			−0.219001			−0.109500	−	0.993987i	$-0.534925\pi$
$997$	−6894.27			−0.219001			−0.109500	+	0.993987i	$0.534925\pi$
$998$	−31274.2	+	47812.8i	−0.991950	+	1.51652i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.4.b.c.323.5		24
3.2	odd	2	inner	324.4.b.c.323.20		24
4.3	odd	2	inner	324.4.b.c.323.19		24
9.2	odd	6		108.4.h.b.71.7		24
9.4	even	3		108.4.h.b.35.11		24
9.5	odd	6		36.4.h.b.11.2	✓	24
9.7	even	3		36.4.h.b.23.6	yes	24
12.11	even	2	inner	324.4.b.c.323.6		24
36.7	odd	6		36.4.h.b.23.2	yes	24
36.11	even	6		108.4.h.b.71.11		24
36.23	even	6		36.4.h.b.11.6	yes	24
36.31	odd	6		108.4.h.b.35.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.2	✓	24	9.5	odd	6
36.4.h.b.11.6	yes	24	36.23	even	6
36.4.h.b.23.2	yes	24	36.7	odd	6
36.4.h.b.23.6	yes	24	9.7	even	3
108.4.h.b.35.7		24	36.31	odd	6
108.4.h.b.35.11		24	9.4	even	3
108.4.h.b.71.7		24	9.2	odd	6
108.4.h.b.71.11		24	36.11	even	6
324.4.b.c.323.5		24	1.1	even	1	trivial
324.4.b.c.323.6		24	12.11	even	2	inner
324.4.b.c.323.19		24	4.3	odd	2	inner
324.4.b.c.323.20		24	3.2	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	324.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.36704 - 1.54827i) q^{2} +(3.20572 + 7.32962i) q^{4} +1.43006i q^{5} -27.5763i q^{7} +(3.76017 - 22.3128i) q^{8} +O(q^{10})\)	\(q+(-2.36704 - 1.54827i) q^{2} +(3.20572 + 7.32962i) q^{4} +1.43006i q^{5} -27.5763i q^{7} +(3.76017 - 22.3128i) q^{8} +(2.21411 - 3.38499i) q^{10} -22.2175 q^{11} +69.1930 q^{13} +(-42.6956 + 65.2742i) q^{14} +(-43.4467 + 46.9935i) q^{16} +31.4507i q^{17} +11.4986i q^{19} +(-10.4818 + 4.58436i) q^{20} +(52.5896 + 34.3987i) q^{22} -145.362 q^{23} +122.955 q^{25} +(-163.782 - 107.129i) q^{26} +(202.124 - 88.4021i) q^{28} -108.194i q^{29} -118.703i q^{31} +(175.598 - 43.9681i) q^{32} +(48.6942 - 74.4450i) q^{34} +39.4357 q^{35} -300.439 q^{37} +(17.8029 - 27.2176i) q^{38} +(31.9085 + 5.37725i) q^{40} -398.202i q^{41} -200.065i q^{43} +(-71.2231 - 162.846i) q^{44} +(344.077 + 225.060i) q^{46} -303.539 q^{47} -417.454 q^{49} +(-291.039 - 190.367i) q^{50} +(221.814 + 507.159i) q^{52} +243.342i q^{53} -31.7722i q^{55} +(-615.305 - 103.692i) q^{56} +(-167.513 + 256.099i) q^{58} -83.8393 q^{59} -398.436 q^{61} +(-183.784 + 280.974i) q^{62} +(-483.722 - 167.800i) q^{64} +98.9499i q^{65} -355.375i q^{67} +(-230.522 + 100.822i) q^{68} +(-93.3457 - 61.0571i) q^{70} -866.235 q^{71} +64.6645 q^{73} +(711.149 + 465.160i) q^{74} +(-84.2802 + 36.8613i) q^{76} +612.677i q^{77} -409.798i q^{79} +(-67.2033 - 62.1312i) q^{80} +(-616.524 + 942.559i) q^{82} +159.798 q^{83} -44.9763 q^{85} +(-309.754 + 473.561i) q^{86} +(-83.5415 + 495.734i) q^{88} -1493.47i q^{89} -1908.09i q^{91} +(-465.990 - 1065.45i) q^{92} +(718.488 + 469.960i) q^{94} -16.4436 q^{95} -1400.23 q^{97} +(988.129 + 646.332i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4}+O(q^{10}) \) 24 * q + 24 * q^4	\( 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64} - 1128 q^{70} - 4776 q^{73} + 1200 q^{76} - 4104 q^{82} - 1440 q^{85} - 3912 q^{88} + 2376 q^{94} - 1176 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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