LMFDB - Embedded newform 294.4.d.b.293.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(293,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.293");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.5
Character	$\chi$	$=$	294.293
Dual form			294.4.d.b.293.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +(-4.92023 + 1.67071i) q^{3} -4.00000 q^{4} +21.7262 q^{5} +(3.34143 + 9.84047i) q^{6} +8.00000i q^{8} +(21.4174 - 16.4406i) q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +(-4.92023 + 1.67071i) q^{3} -4.00000 q^{4} +21.7262 q^{5} +(3.34143 + 9.84047i) q^{6} +8.00000i q^{8} +(21.4174 - 16.4406i) q^{9} -43.4525i q^{10} +48.6690i q^{11} +(19.6809 - 6.68286i) q^{12} -13.5281i q^{13} +(-106.898 + 36.2983i) q^{15} +16.0000 q^{16} -61.2540 q^{17} +(-32.8812 - 42.8348i) q^{18} +27.4217i q^{19} -86.9049 q^{20} +97.3380 q^{22} +139.599i q^{23} +(-13.3657 - 39.3619i) q^{24} +347.029 q^{25} -27.0563 q^{26} +(-77.9112 + 116.674i) q^{27} +82.4366i q^{29} +(72.5967 + 213.796i) q^{30} -123.758i q^{31} -32.0000i q^{32} +(-81.3120 - 239.463i) q^{33} +122.508i q^{34} +(-85.6697 + 65.7625i) q^{36} +44.9998 q^{37} +54.8434 q^{38} +(22.6017 + 66.5617i) q^{39} +173.810i q^{40} +418.462 q^{41} +223.323 q^{43} -194.676i q^{44} +(465.320 - 357.193i) q^{45} +279.197 q^{46} +282.148 q^{47} +(-78.7238 + 26.7314i) q^{48} -694.058i q^{50} +(301.384 - 102.338i) q^{51} +54.1126i q^{52} +648.059i q^{53} +(233.348 + 155.822i) q^{54} +1057.39i q^{55} +(-45.8138 - 134.921i) q^{57} +164.873 q^{58} +190.334 q^{59} +(427.593 - 145.193i) q^{60} -674.695i q^{61} -247.515 q^{62} -64.0000 q^{64} -293.916i q^{65} +(-478.926 + 162.624i) q^{66} -204.894 q^{67} +245.016 q^{68} +(-233.229 - 686.858i) q^{69} +688.830i q^{71} +(131.525 + 171.339i) q^{72} +201.684i q^{73} -89.9995i q^{74} +(-1707.46 + 579.786i) q^{75} -109.687i q^{76} +(133.123 - 45.2034i) q^{78} +317.046 q^{79} +347.620 q^{80} +(188.412 - 704.231i) q^{81} -836.925i q^{82} -360.449 q^{83} -1330.82 q^{85} -446.647i q^{86} +(-137.728 - 405.608i) q^{87} -389.352 q^{88} -203.018 q^{89} +(-714.385 - 930.640i) q^{90} -558.394i q^{92} +(206.764 + 608.917i) q^{93} -564.296i q^{94} +595.770i q^{95} +(53.4629 + 157.448i) q^{96} -361.361i q^{97} +(800.148 + 1042.36i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 96 q^{4} + 128 q^{9}+O(q^{10}) $ 24 * q - 96 * q^4 + 128 * q^9	$ 24 q - 96 q^{4} + 128 q^{9} - 336 q^{15} + 384 q^{16} + 32 q^{18} + 288 q^{22} + 456 q^{25} + 544 q^{30} - 512 q^{36} - 432 q^{37} + 2656 q^{39} + 624 q^{43} - 1344 q^{46} + 3696 q^{51} + 176 q^{57} - 96 q^{58} + 1344 q^{60} - 1536 q^{64} - 528 q^{67} - 128 q^{72} - 5216 q^{78} - 7488 q^{79} + 336 q^{81} - 1728 q^{85} - 1152 q^{88} + 7392 q^{93} + 5656 q^{99}+O(q^{100}) $ 24 * q - 96 * q^4 + 128 * q^9 - 336 * q^15 + 384 * q^16 + 32 * q^18 + 288 * q^22 + 456 * q^25 + 544 * q^30 - 512 * q^36 - 432 * q^37 + 2656 * q^39 + 624 * q^43 - 1344 * q^46 + 3696 * q^51 + 176 * q^57 - 96 * q^58 + 1344 * q^60 - 1536 * q^64 - 528 * q^67 - 128 * q^72 - 5216 * q^78 - 7488 * q^79 + 336 * q^81 - 1728 * q^85 - 1152 * q^88 + 7392 * q^93 + 5656 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	−4.92023	+	1.67071i	−0.946900	+	0.321529i
$3$	−4.92023	+	1.67071i	−0.946900	+	0.321529i
$4$	−4.00000			−0.500000
$5$	21.7262			1.94325			0.971626	−	0.236521i	$-0.0760071\pi$
$5$	21.7262			1.94325			0.971626	+	0.236521i	$0.0760071\pi$
$6$	3.34143	+	9.84047i	0.227355	+	0.669559i
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	21.4174	−	16.4406i	0.793238	−	0.608912i
$10$		−	43.4525i		−	1.37409i
$11$			48.6690i			1.33402i	0.745048	+	0.667011i	$0.232427\pi$
$11$			48.6690i			1.33402i	−0.745048	+	0.667011i	$0.767573\pi$
$12$	19.6809	−	6.68286i	0.473450	−	0.160765i
$13$		−	13.5281i		−	0.288618i	−0.989533	−	0.144309i	$-0.953904\pi$
$13$		−	13.5281i		−	0.288618i	0.989533	−	0.144309i	$-0.0460959\pi$
$14$		0			0
$15$	−106.898	+	36.2983i	−1.84007	+	0.624813i
$16$	16.0000			0.250000
$17$	−61.2540			−0.873898			−0.436949	−	0.899486i	$-0.643941\pi$
$17$	−61.2540			−0.873898			−0.436949	+	0.899486i	$0.643941\pi$
$18$	−32.8812	−	42.8348i	−0.430566	−	0.560904i
$19$			27.4217i			0.331104i	0.986201	+	0.165552i	$0.0529405\pi$
$19$			27.4217i			0.331104i	−0.986201	+	0.165552i	$0.947060\pi$
$20$	−86.9049			−0.971626
$21$		0			0
$22$	97.3380			0.943297
$23$			139.599i			1.26558i	0.774324	+	0.632789i	$0.218090\pi$
$23$			139.599i			1.26558i	−0.774324	+	0.632789i	$0.781910\pi$
$24$	−13.3657	−	39.3619i	−0.113678	−	0.334780i
$25$	347.029			2.77623
$26$	−27.0563			−0.204084
$27$	−77.9112	+	116.674i	−0.555334	+	0.831628i
$28$		0			0
$29$			82.4366i			0.527865i	0.964541	+	0.263933i	$0.0850197\pi$
$29$			82.4366i			0.527865i	−0.964541	+	0.263933i	$0.914980\pi$
$30$	72.5967	+	213.796i	0.441809	+	1.30112i
$31$		−	123.758i		−	0.717017i	−0.933526	−	0.358509i	$-0.883285\pi$
$31$		−	123.758i		−	0.717017i	0.933526	−	0.358509i	$-0.116715\pi$
$32$		−	32.0000i		−	0.176777i
$33$	−81.3120	−	239.463i	−0.428927	−	1.26319i
$34$			122.508i			0.617940i
$35$		0			0
$36$	−85.6697	+	65.7625i	−0.396619	+	0.304456i
$37$	44.9998			0.199944			0.0999718	−	0.994990i	$-0.468125\pi$
$37$	44.9998			0.199944			0.0999718	+	0.994990i	$0.468125\pi$
$38$	54.8434			0.234126
$39$	22.6017	+	66.5617i	0.0927991	+	0.273292i
$40$			173.810i			0.687044i
$41$	418.462			1.59397			0.796986	−	0.603998i	$-0.206426\pi$
$41$	418.462			1.59397			0.796986	+	0.603998i	$0.206426\pi$
$42$		0			0
$43$	223.323			0.792012			0.396006	−	0.918248i	$-0.370396\pi$
$43$	223.323			0.792012			0.396006	+	0.918248i	$0.370396\pi$
$44$		−	194.676i		−	0.667011i
$45$	465.320	−	357.193i	1.54146	−	1.18327i
$46$	279.197			0.894899
$47$	282.148			0.875650			0.437825	−	0.899060i	$-0.355749\pi$
$47$	282.148			0.875650			0.437825	+	0.899060i	$0.355749\pi$
$48$	−78.7238	+	26.7314i	−0.236725	+	0.0803823i
$49$		0			0
$50$		−	694.058i		−	1.96309i
$51$	301.384	−	102.338i	0.827494	−	0.280984i
$52$			54.1126i			0.144309i
$53$			648.059i			1.67958i	0.542912	+	0.839790i	$0.317322\pi$
$53$			648.059i			1.67958i	−0.542912	+	0.839790i	$0.682678\pi$
$54$	233.348	+	155.822i	0.588049	+	0.392680i
$55$			1057.39i			2.59234i
$56$		0			0
$57$	−45.8138	−	134.921i	−0.106459	−	0.313522i
$58$	164.873			0.373257
$59$	190.334			0.419990			0.209995	−	0.977702i	$-0.432655\pi$
$59$	190.334			0.419990			0.209995	+	0.977702i	$0.432655\pi$
$60$	427.593	−	145.193i	0.920033	−	0.312406i
$61$		−	674.695i		−	1.41616i	−0.706132	−	0.708080i	$-0.749562\pi$
$61$		−	674.695i		−	1.41616i	0.706132	−	0.708080i	$-0.250438\pi$
$62$	−247.515			−0.507008
$63$		0			0
$64$	−64.0000			−0.125000
$65$		−	293.916i		−	0.560858i
$66$	−478.926	+	162.624i	−0.893207	+	0.303297i
$67$	−204.894			−0.373609			−0.186804	−	0.982397i	$-0.559813\pi$
$67$	−204.894			−0.373609			−0.186804	+	0.982397i	$0.559813\pi$
$68$	245.016			0.436949
$69$	−233.229	−	686.858i	−0.406920	−	1.19838i
$70$		0			0
$71$			688.830i			1.15140i	0.817663	+	0.575698i	$0.195270\pi$
$71$			688.830i			1.15140i	−0.817663	+	0.575698i	$0.804730\pi$
$72$	131.525	+	171.339i	0.215283	+	0.280452i
$73$			201.684i			0.323361i	0.986843	+	0.161680i	$0.0516914\pi$
$73$			201.684i			0.323361i	−0.986843	+	0.161680i	$0.948309\pi$
$74$		−	89.9995i		−	0.141381i
$75$	−1707.46	+	579.786i	−2.62881	+	0.892640i
$76$		−	109.687i		−	0.165552i
$77$		0			0
$78$	133.123	−	45.2034i	0.193247	−	0.0656189i
$79$	317.046			0.451524			0.225762	−	0.974182i	$-0.427513\pi$
$79$	317.046			0.451524			0.225762	+	0.974182i	$0.427513\pi$
$80$	347.620			0.485813
$81$	188.412	−	704.231i	0.258453	−	0.966024i
$82$		−	836.925i		−	1.12711i
$83$	−360.449			−0.476680			−0.238340	−	0.971182i	$-0.576603\pi$
$83$	−360.449			−0.476680			−0.238340	+	0.971182i	$0.576603\pi$
$84$		0			0
$85$	−1330.82			−1.69821
$86$		−	446.647i		−	0.560037i
$87$	−137.728	−	405.608i	−0.169724	−	0.499836i
$88$	−389.352			−0.471648
$89$	−203.018			−0.241797			−0.120898	−	0.992665i	$-0.538577\pi$
$89$	−203.018			−0.241797			−0.120898	+	0.992665i	$0.538577\pi$
$90$	−714.385	−	930.640i	−0.836698	−	1.08998i
$91$		0			0
$92$		−	558.394i		−	0.632789i
$93$	206.764	+	608.917i	0.230542	+	0.678943i
$94$		−	564.296i		−	0.619178i
$95$			595.770i			0.643418i
$96$	53.4629	+	157.448i	0.0568389	+	0.167390i
$97$		−	361.361i		−	0.378254i	−0.981953	−	0.189127i	$-0.939434\pi$
$97$		−	361.361i		−	0.378254i	0.981953	−	0.189127i	$-0.0605658\pi$
$98$		0			0
$99$	800.148	+	1042.36i	0.812302	+	1.05820i
$100$	−1388.12			−1.38812
$101$	−404.006			−0.398021			−0.199011	−	0.979997i	$-0.563773\pi$
$101$	−404.006			−0.398021			−0.199011	+	0.979997i	$0.563773\pi$
$102$	−204.676	−	602.768i	−0.198686	−	0.585127i
$103$			1232.70i			1.17924i	0.807681	+	0.589620i	$0.200722\pi$
$103$			1232.70i			1.17924i	−0.807681	+	0.589620i	$0.799278\pi$
$104$	108.225			0.102042
$105$		0			0
$106$	1296.12			1.18764
$107$		−	1088.36i		−	0.983328i	−0.870785	−	0.491664i	$-0.836389\pi$
$107$		−	1088.36i		−	0.983328i	0.870785	−	0.491664i	$-0.163611\pi$
$108$	311.645	−	466.696i	0.277667	−	0.415814i
$109$	−793.844			−0.697582			−0.348791	−	0.937201i	$-0.613408\pi$
$109$	−793.844			−0.697582			−0.348791	+	0.937201i	$0.613408\pi$
$110$	2114.79			1.83306
$111$	−221.409	+	75.1818i	−0.189327	+	0.0642877i
$112$		0			0
$113$			584.946i			0.486966i	0.969905	+	0.243483i	$0.0782900\pi$
$113$			584.946i			0.486966i	−0.969905	+	0.243483i	$0.921710\pi$
$114$	−269.842	+	91.6277i	−0.221693	+	0.0752782i
$115$			3032.95i			2.45934i
$116$		−	329.747i		−	0.263933i
$117$	−222.411	−	289.738i	−0.175743	−	0.228943i
$118$		−	380.668i		−	0.296978i
$119$		0			0
$120$	−290.387	−	855.185i	−0.220905	−	0.650561i
$121$	−1037.67			−0.779617
$122$	−1349.39			−1.00138
$123$	−2058.93	+	699.131i	−1.50933	+	0.512509i
$124$			495.031i			0.358509i
$125$	4823.85			3.45167
$126$		0			0
$127$	447.085			0.312381			0.156190	−	0.987727i	$-0.450079\pi$
$127$	447.085			0.312381			0.156190	+	0.987727i	$0.450079\pi$
$128$			128.000i			0.0883883i
$129$	−1098.80	+	373.110i	−0.749956	+	0.254655i
$130$	−587.831			−0.396586
$131$	2202.28			1.46881			0.734405	−	0.678711i	$-0.237461\pi$
$131$	2202.28			1.46881			0.734405	+	0.678711i	$0.237461\pi$
$132$	325.248	+	957.851i	0.214464	+	0.631593i
$133$		0			0
$134$			409.788i			0.264181i
$135$	−1692.72	+	2534.89i	−1.07915	+	1.61606i
$136$		−	490.032i		−	0.308970i
$137$			355.722i			0.221835i	0.993830	+	0.110917i	$0.0353789\pi$
$137$			355.722i			0.221835i	−0.993830	+	0.110917i	$0.964621\pi$
$138$	−1373.72	+	466.459i	−0.847380	+	0.287736i
$139$		−	1857.98i		−	1.13376i	−0.823802	−	0.566878i	$-0.808151\pi$
$139$		−	1857.98i		−	1.13376i	0.823802	−	0.566878i	$-0.191849\pi$
$140$		0			0
$141$	−1388.23	+	471.389i	−0.829152	+	0.281547i
$142$	1377.66			0.814160
$143$	658.401			0.385023
$144$	342.679	−	263.050i	0.198309	−	0.152228i
$145$			1791.04i			1.02578i
$146$	403.368			0.228651
$147$		0			0
$148$	−179.999			−0.0999718
$149$		−	1412.62i		−	0.776686i	−0.921515	−	0.388343i	$-0.873048\pi$
$149$		−	1412.62i		−	0.776686i	0.921515	−	0.388343i	$-0.126952\pi$
$150$	1159.57	+	3414.93i	0.631192	+	1.85885i
$151$	−169.505			−0.0913519			−0.0456760	−	0.998956i	$-0.514544\pi$
$151$	−169.505			−0.0913519			−0.0456760	+	0.998956i	$0.514544\pi$
$152$	−219.374			−0.117063
$153$	−1311.90	+	1007.05i	−0.693209	+	0.532127i
$154$		0			0
$155$		−	2688.79i		−	1.39335i
$156$	−90.4067	−	266.247i	−0.0463995	−	0.136646i
$157$		−	1736.20i		−	0.882573i	−0.897366	−	0.441286i	$-0.854522\pi$
$157$		−	1736.20i		−	0.882573i	0.897366	−	0.441286i	$-0.145478\pi$
$158$		−	634.092i		−	0.319276i
$159$	−1082.72	−	3188.60i	−0.540034	−	1.59039i
$160$		−	695.239i		−	0.343522i
$161$		0			0
$162$	−1408.46	−	376.824i	−0.683082	−	0.182754i
$163$	−2991.62			−1.43756			−0.718778	−	0.695240i	$-0.755298\pi$
$163$	−2991.62			−1.43756			−0.718778	+	0.695240i	$0.755298\pi$
$164$	−1673.85			−0.796986
$165$	−1766.60	−	5202.62i	−0.833514	−	2.45469i
$166$			720.899i			0.337064i
$167$	−2158.27			−1.00007			−0.500036	−	0.866004i	$-0.666680\pi$
$167$	−2158.27			−1.00007			−0.500036	+	0.866004i	$0.666680\pi$
$168$		0			0
$169$	2013.99			0.916700
$170$			2661.64i			1.20081i
$171$	450.830	+	587.302i	0.201613	+	0.262644i
$172$	−893.294			−0.396006
$173$	−1626.35			−0.714735			−0.357367	−	0.933964i	$-0.616326\pi$
$173$	−1626.35			−0.714735			−0.357367	+	0.933964i	$0.616326\pi$
$174$	−811.215	+	275.456i	−0.353437	+	0.120013i
$175$		0			0
$176$			778.704i			0.333506i
$177$	−936.489	+	317.994i	−0.397688	+	0.135039i
$178$			406.037i			0.170976i
$179$			1967.54i			0.821570i	0.911732	+	0.410785i	$0.134745\pi$
$179$			1967.54i			0.821570i	−0.911732	+	0.410785i	$0.865255\pi$
$180$	−1861.28	+	1428.77i	−0.770731	+	0.591635i
$181$		−	2783.32i		−	1.14300i	−0.820603	−	0.571499i	$-0.806362\pi$
$181$		−	2783.32i		−	1.14300i	0.820603	−	0.571499i	$-0.193638\pi$
$182$		0			0
$183$	1127.22	+	3319.66i	0.455337	+	1.34096i
$184$	−1116.79			−0.447450
$185$	977.675			0.388541
$186$	1217.83	−	413.527i	0.480085	−	0.163018i
$187$		−	2981.17i		−	1.16580i
$188$	−1128.59			−0.437825
$189$		0			0
$190$	1191.54			0.454965
$191$		−	2821.24i		−	1.06878i	−0.845237	−	0.534392i	$-0.820541\pi$
$191$		−	2821.24i		−	1.06878i	0.845237	−	0.534392i	$-0.179459\pi$
$192$	314.895	−	106.926i	0.118362	−	0.0401912i
$193$	1214.08			0.452804			0.226402	−	0.974034i	$-0.427304\pi$
$193$	1214.08			0.452804			0.226402	+	0.974034i	$0.427304\pi$
$194$	−722.722			−0.267466
$195$	491.049	+	1446.13i	0.180332	+	0.531076i
$196$		0			0
$197$		−	5.68871i		−	0.00205738i	−0.999999	−	0.00102869i	$-0.999673\pi$
$197$		−	5.68871i		−	0.00205738i	0.999999	−	0.00102869i	$-0.000327442\pi$
$198$	2084.73	−	1600.30i	0.748259	−	0.574384i
$199$		−	1137.21i		−	0.405098i	−0.979272	−	0.202549i	$-0.935077\pi$
$199$		−	1137.21i		−	0.405098i	0.979272	−	0.202549i	$-0.0649225\pi$
$200$			2776.23i			0.981546i
$201$	1008.13	−	342.320i	0.353770	−	0.120126i
$202$			808.012i			0.281443i
$203$		0			0
$204$	−1205.54	+	409.352i	−0.413747	+	0.140492i
$205$	9091.61			3.09749
$206$	2465.40			0.833849
$207$	2295.09	+	2989.84i	0.770626	+	1.00390i
$208$		−	216.450i		−	0.0721545i
$209$	−1334.59			−0.441700
$210$		0			0
$211$	−5612.13			−1.83107			−0.915533	−	0.402243i	$-0.868231\pi$
$211$	−5612.13			−1.83107			−0.915533	+	0.402243i	$0.868231\pi$
$212$		−	2592.23i		−	0.839790i
$213$	−1150.84	−	3389.21i	−0.370207	−	1.09026i
$214$	−2176.73			−0.695318
$215$	4851.98			1.53908
$216$	−933.393	−	623.289i	−0.294025	−	0.196340i
$217$		0			0
$218$			1587.69i			0.493265i
$219$	−336.957	−	992.333i	−0.103970	−	0.306190i
$220$		−	4229.57i		−	1.29617i
$221$			828.653i			0.252223i
$222$	150.364	+	442.819i	0.0454583	+	0.133874i
$223$		−	1737.80i		−	0.521846i	−0.965360	−	0.260923i	$-0.915973\pi$
$223$		−	1737.80i		−	0.521846i	0.965360	−	0.260923i	$-0.0840268\pi$
$224$		0			0
$225$	7432.47	−	5705.37i	2.20221	−	1.69048i
$226$	1169.89			0.344337
$227$	−2305.05			−0.673972			−0.336986	−	0.941510i	$-0.609408\pi$
$227$	−2305.05			−0.673972			−0.336986	+	0.941510i	$0.609408\pi$
$228$	183.255	+	539.685i	0.0532297	+	0.156761i
$229$			5434.63i			1.56826i	0.620599	+	0.784128i	$0.286889\pi$
$229$			5434.63i			1.56826i	−0.620599	+	0.784128i	$0.713111\pi$
$230$	6065.90			1.73902
$231$		0			0
$232$	−659.493			−0.186629
$233$		−	3847.42i		−	1.08177i	−0.841096	−	0.540885i	$-0.818089\pi$
$233$		−	3847.42i		−	1.08177i	0.841096	−	0.540885i	$-0.181911\pi$
$234$	−579.476	+	444.822i	−0.161887	+	0.124269i
$235$	6130.01			1.70161
$236$	−761.336			−0.209995
$237$	−1559.94	+	529.693i	−0.427548	+	0.145178i
$238$		0			0
$239$		−	6913.12i		−	1.87101i	−0.353308	−	0.935507i	$-0.614943\pi$
$239$		−	6913.12i		−	1.87101i	0.353308	−	0.935507i	$-0.385057\pi$
$240$	−1710.37	+	580.773i	−0.460016	+	0.156203i
$241$			5125.57i			1.36999i	0.728548	+	0.684994i	$0.240195\pi$
$241$			5125.57i			1.36999i	−0.728548	+	0.684994i	$0.759805\pi$
$242$			2075.34i			0.551272i
$243$	249.538	+	3779.77i	0.0658761	+	0.997828i
$244$			2698.78i			0.708080i
$245$		0			0
$246$	1398.26	+	4117.87i	0.362398	+	1.06726i
$247$	370.965			0.0955624
$248$	990.061			0.253504
$249$	1773.50	−	602.208i	0.451368	−	0.153267i
$250$		−	9647.70i		−	2.44070i
$251$	−4752.99			−1.19524			−0.597622	−	0.801778i	$-0.703888\pi$
$251$	−4752.99			−1.19524			−0.597622	+	0.801778i	$0.703888\pi$
$252$		0			0
$253$	−6794.12			−1.68831
$254$		−	894.170i		−	0.220887i
$255$	6547.94	−	2223.42i	1.60803	−	0.546023i
$256$	256.000			0.0625000
$257$	−2684.79			−0.651644			−0.325822	−	0.945431i	$-0.605641\pi$
$257$	−2684.79			−0.651644			−0.325822	+	0.945431i	$0.605641\pi$
$258$	746.220	+	2197.61i	0.180068	+	0.530299i
$259$		0			0
$260$			1175.66i			0.280429i
$261$	1355.31	+	1765.58i	0.321424	+	0.418723i
$262$		−	4404.56i		−	1.03861i
$263$		−	1936.11i		−	0.453937i	−0.973902	−	0.226968i	$-0.927119\pi$
$263$		−	1936.11i		−	0.453937i	0.973902	−	0.226968i	$-0.0728814\pi$
$264$	1915.70	−	650.496i	0.446604	−	0.151649i
$265$			14079.9i			3.26385i
$266$		0			0
$267$	998.898	−	339.186i	0.228957	−	0.0777447i
$268$	819.577			0.186804
$269$	−2558.15			−0.579826			−0.289913	−	0.957053i	$-0.593626\pi$
$269$	−2558.15			−0.579826			−0.289913	+	0.957053i	$0.593626\pi$
$270$	5069.78	+	3385.43i	1.14273	+	0.763077i
$271$		−	1869.65i		−	0.419090i	−0.977799	−	0.209545i	$-0.932802\pi$
$271$		−	1869.65i		−	0.419090i	0.977799	−	0.209545i	$-0.0671983\pi$
$272$	−980.064			−0.218475
$273$		0			0
$274$	711.444			0.156861
$275$			16889.5i			3.70356i
$276$	932.917	+	2747.43i	0.203460	+	0.599188i
$277$	3239.48			0.702677			0.351338	−	0.936249i	$-0.385727\pi$
$277$	3239.48			0.702677			0.351338	+	0.936249i	$0.385727\pi$
$278$	−3715.96			−0.801686
$279$	−2034.65	−	2650.57i	−0.436600	−	0.568765i
$280$		0			0
$281$			7733.03i			1.64169i	0.571153	+	0.820843i	$0.306496\pi$
$281$			7733.03i			1.64169i	−0.571153	+	0.820843i	$0.693504\pi$
$282$	942.778	+	2776.47i	0.199084	+	0.586299i
$283$		−	1550.02i		−	0.325580i	−0.986661	−	0.162790i	$-0.947951\pi$
$283$		−	1550.02i		−	0.325580i	0.986661	−	0.162790i	$-0.0520493\pi$
$284$		−	2755.32i		−	0.575698i
$285$	−995.362	−	2931.33i	−0.206878	−	0.609252i
$286$		−	1316.80i		−	0.272252i
$287$		0			0
$288$	−526.100	−	685.358i	−0.107641	−	0.140226i
$289$	−1160.95			−0.236301
$290$	3582.07			0.725333
$291$	603.731	+	1777.98i	0.121620	+	0.358169i
$292$		−	806.736i		−	0.161680i
$293$	1754.65			0.349856			0.174928	−	0.984581i	$-0.444031\pi$
$293$	1754.65			0.349856			0.174928	+	0.984581i	$0.444031\pi$
$294$		0			0
$295$	4135.24			0.816146
$296$			359.998i			0.0706907i
$297$	−5678.41	−	3791.86i	−1.10941	−	0.740828i
$298$	−2825.24			−0.549200
$299$	1888.51			0.365269
$300$	6829.86	−	2319.15i	1.31441	−	0.446320i
$301$		0			0
$302$			339.011i			0.0645956i
$303$	1987.81	−	674.979i	0.376886	−	0.127975i
$304$			438.747i			0.0827759i
$305$		−	14658.6i		−	2.75196i
$306$	2014.11	+	2623.81i	0.376271	+	0.490173i
$307$		−	3328.40i		−	0.618768i	−0.950937	−	0.309384i	$-0.899877\pi$
$307$		−	3328.40i		−	0.618768i	0.950937	−	0.309384i	$-0.100123\pi$
$308$		0			0
$309$	−2059.49	−	6065.18i	−0.379160	−	1.11662i
$310$	−5377.57			−0.985244
$311$	6516.09			1.18808			0.594041	−	0.804435i	$-0.297532\pi$
$311$	6516.09			1.18808			0.594041	+	0.804435i	$0.297532\pi$
$312$	−532.493	+	180.813i	−0.0966234	+	0.0328094i
$313$		−	2138.94i		−	0.386262i	−0.981173	−	0.193131i	$-0.938136\pi$
$313$		−	2138.94i		−	0.386262i	0.981173	−	0.193131i	$-0.0618642\pi$
$314$	−3472.40			−0.624073
$315$		0			0
$316$	−1268.18			−0.225762
$317$			2800.51i			0.496190i	0.968736	+	0.248095i	$0.0798045\pi$
$317$			2800.51i			0.496190i	−0.968736	+	0.248095i	$0.920195\pi$
$318$	−6377.20	+	2165.44i	−1.12458	+	0.381862i
$319$	−4012.11			−0.704184
$320$	−1390.48			−0.242907
$321$	1818.34	+	5355.00i	0.316169	+	0.931113i
$322$		0			0
$323$		−	1679.69i		−	0.289351i
$324$	−753.648	+	2816.93i	−0.129226	+	0.483012i
$325$		−	4694.66i		−	0.801270i
$326$			5983.24i			1.01651i
$327$	3905.90	−	1326.29i	0.660540	−	0.224293i
$328$			3347.70i			0.563554i
$329$		0			0
$330$	−10405.2	+	3533.21i	−1.73573	+	0.589384i
$331$	3547.29			0.589054			0.294527	−	0.955643i	$-0.404838\pi$
$331$	3547.29			0.589054			0.294527	+	0.955643i	$0.404838\pi$
$332$	1441.80			0.238340
$333$	963.779	−	739.824i	0.158603	−	0.121748i
$334$			4316.54i			0.707158i
$335$	−4451.58			−0.726017
$336$		0			0
$337$	9536.10			1.54144			0.770719	−	0.637175i	$-0.219897\pi$
$337$	9536.10			1.54144			0.770719	+	0.637175i	$0.219897\pi$
$338$		−	4027.98i		−	0.648205i
$339$	−977.278	−	2878.07i	−0.156574	−	0.461108i
$340$	5323.27			0.849103
$341$	6023.16			0.956517
$342$	1174.60	−	901.659i	0.185717	−	0.142562i
$343$		0			0
$344$			1786.59i			0.280018i
$345$	−5067.19	−	14922.8i	−0.790749	−	2.32875i
$346$			3252.70i			0.505394i
$347$			11462.9i			1.77338i	0.462368	+	0.886688i	$0.347000\pi$
$347$			11462.9i			1.77338i	−0.462368	+	0.886688i	$0.653000\pi$
$348$	550.912	+	1622.43i	0.0848621	+	0.249918i
$349$		−	6414.25i		−	0.983802i	−0.870651	−	0.491901i	$-0.836302\pi$
$349$		−	6414.25i		−	0.983802i	0.870651	−	0.491901i	$-0.163698\pi$
$350$		0			0
$351$	1578.38	+	1053.99i	0.240023	+	0.160279i
$352$	1557.41			0.235824
$353$	−9432.88			−1.42227			−0.711135	−	0.703055i	$-0.751819\pi$
$353$	−9432.88			−1.42227			−0.711135	+	0.703055i	$0.751819\pi$
$354$	635.988	+	1872.98i	0.0954870	+	0.281208i
$355$			14965.7i			2.23745i
$356$	812.073			0.120898
$357$		0			0
$358$	3935.09			0.580938
$359$			2187.42i			0.321582i	0.986988	+	0.160791i	$0.0514045\pi$
$359$			2187.42i			0.321582i	−0.986988	+	0.160791i	$0.948596\pi$
$360$	2857.54	+	3722.56i	0.418349	+	0.544989i
$361$	6107.05			0.890370
$362$	−5566.65			−0.808222
$363$	5105.58	−	1733.65i	0.738219	−	0.250670i
$364$		0			0
$365$			4381.83i			0.628372i
$366$	6639.31	−	2254.44i	0.948203	−	0.321972i
$367$			6596.58i			0.938253i	0.883131	+	0.469127i	$0.155431\pi$
$367$			6596.58i			0.938253i	−0.883131	+	0.469127i	$0.844569\pi$
$368$			2233.58i			0.316395i
$369$	8962.39	−	6879.78i	1.26440	−	0.970588i
$370$		−	1955.35i		−	0.274740i
$371$		0			0
$372$	−827.055	−	2435.67i	−0.115271	−	0.339472i
$373$	−9102.50			−1.26356			−0.631782	−	0.775146i	$-0.717676\pi$
$373$	−9102.50			−1.26356			−0.631782	+	0.775146i	$0.717676\pi$
$374$	−5962.34			−0.824345
$375$	−23734.5	+	8059.28i	−3.26838	+	1.10981i
$376$			2257.18i			0.309589i
$377$	1115.21			0.152351
$378$		0			0
$379$	−2129.23			−0.288578			−0.144289	−	0.989536i	$-0.546090\pi$
$379$	−2129.23			−0.288578			−0.144289	+	0.989536i	$0.546090\pi$
$380$		−	2383.08i		−	0.321709i
$381$	−2199.76	+	746.951i	−0.295793	+	0.100440i
$382$	−5642.48			−0.755745
$383$	−8599.66			−1.14732			−0.573658	−	0.819095i	$-0.694476\pi$
$383$	−8599.66			−1.14732			−0.573658	+	0.819095i	$0.694476\pi$
$384$	−213.852	−	629.790i	−0.0284194	−	0.0836949i
$385$		0			0
$386$		−	2428.16i		−	0.320181i
$387$	4783.01	−	3671.58i	0.628254	−	0.482265i
$388$			1445.44i			0.189127i
$389$		−	8528.65i		−	1.11162i	−0.831310	−	0.555809i	$-0.812409\pi$
$389$		−	8528.65i		−	1.11162i	0.831310	−	0.555809i	$-0.187591\pi$
$390$	2892.27	−	982.098i	0.375527	−	0.127514i
$391$		−	8550.97i		−	1.10599i
$392$		0			0
$393$	−10835.7	+	3679.38i	−1.39082	+	0.472265i
$394$	−11.3774			−0.00145479
$395$	6888.21			0.877426
$396$	−3200.59	−	4169.46i	−0.406151	−	0.529099i
$397$		−	3008.62i		−	0.380349i	−0.981750	−	0.190174i	$-0.939095\pi$
$397$		−	3008.62i		−	0.380349i	0.981750	−	0.190174i	$-0.0609053\pi$
$398$	−2274.42			−0.286448
$399$		0			0
$400$	5552.46			0.694058
$401$		−	8292.05i		−	1.03263i	−0.856398	−	0.516316i	$-0.827303\pi$
$401$		−	8292.05i		−	1.03263i	0.856398	−	0.516316i	$-0.172697\pi$
$402$	−684.639	−	2016.25i	−0.0849421	−	0.250153i
$403$	−1674.21			−0.206944
$404$	1616.02			0.199011
$405$	4093.48	−	15300.3i	0.502239	−	1.87723i
$406$		0			0
$407$			2190.09i			0.266729i
$408$	818.704	+	2411.07i	0.0993428	+	0.292563i
$409$			11599.6i			1.40236i	0.712984	+	0.701180i	$0.247343\pi$
$409$			11599.6i			1.40236i	−0.712984	+	0.701180i	$0.752657\pi$
$410$		−	18183.2i		−	2.19026i
$411$	−594.310	−	1750.24i	−0.0713264	−	0.210055i
$412$		−	4930.81i		−	0.589620i
$413$		0			0
$414$	5979.68	−	4590.17i	0.709868	−	0.544915i
$415$	−7831.20			−0.926310
$416$	−432.901			−0.0510209
$417$	3104.16	+	9141.71i	0.364535	+	1.07355i
$418$			2669.17i			0.312329i
$419$	−11271.3			−1.31417			−0.657085	−	0.753816i	$-0.728211\pi$
$419$	−11271.3			−1.31417			−0.657085	+	0.753816i	$0.728211\pi$
$420$		0			0
$421$	1344.95			0.155697			0.0778487	−	0.996965i	$-0.475195\pi$
$421$	1344.95			0.155697			0.0778487	+	0.996965i	$0.475195\pi$
$422$			11224.3i			1.29476i
$423$	6042.89	−	4638.69i	0.694598	−	0.533193i
$424$	−5184.47			−0.593821
$425$	−21256.9			−2.42614
$426$	−6778.41	+	2301.68i	−0.770927	+	0.261776i
$427$		0			0
$428$			4353.45i			0.491664i
$429$	−3239.49	+	1100.00i	−0.364578	+	0.123796i
$430$		−	9703.95i		−	1.08829i
$431$		−	15201.0i		−	1.69885i	−0.527707	−	0.849427i	$-0.676948\pi$
$431$		−	15201.0i		−	1.69885i	0.527707	−	0.849427i	$-0.323052\pi$
$432$	−1246.58	+	1866.79i	−0.138833	+	0.207907i
$433$		−	953.542i		−	0.105830i	−0.998599	−	0.0529149i	$-0.983149\pi$
$433$		−	953.542i		−	0.105830i	0.998599	−	0.0529149i	$-0.0168512\pi$
$434$		0			0
$435$	−2992.31	−	8812.32i	−0.329817	−	0.971307i
$436$	3175.37			0.348791
$437$	−3828.03			−0.419038
$438$	−1984.67	+	673.913i	−0.216509	+	0.0735179i
$439$		−	7267.08i		−	0.790066i	−0.918667	−	0.395033i	$-0.870733\pi$
$439$		−	7267.08i		−	0.790066i	0.918667	−	0.395033i	$-0.129267\pi$
$440$	−8459.15			−0.916532
$441$		0			0
$442$	1657.31			0.178348
$443$		−	158.197i		−	0.0169665i	−0.999964	−	0.00848326i	$-0.997300\pi$
$443$		−	158.197i		−	0.0169665i	0.999964	−	0.00848326i	$-0.00270034\pi$
$444$	885.637	−	300.727i	0.0946633	−	0.0321439i
$445$	−4410.82			−0.469872
$446$	−3475.60			−0.369001
$447$	2360.08	+	6950.42i	0.249727	+	0.735444i
$448$		0			0
$449$		−	5856.97i		−	0.615606i	−0.951450	−	0.307803i	$-0.900406\pi$
$449$		−	5856.97i		−	0.615606i	0.951450	−	0.307803i	$-0.0995938\pi$
$450$	−11410.7	−	14864.9i	−1.19535	−	1.55720i
$451$			20366.1i			2.12639i
$452$		−	2339.79i		−	0.243483i
$453$	834.006	−	283.195i	0.0865011	−	0.0293723i
$454$			4610.10i			0.476570i
$455$		0			0
$456$	1079.37	−	366.511i	0.110847	−	0.0376391i
$457$	−9973.38			−1.02086			−0.510432	−	0.859918i	$-0.670515\pi$
$457$	−9973.38			−1.02086			−0.510432	+	0.859918i	$0.670515\pi$
$458$	10869.3			1.10892
$459$	4772.37	−	7146.76i	0.485305	−	0.726758i
$460$		−	12131.8i		−	1.22967i
$461$	12159.0			1.22842			0.614209	−	0.789144i	$-0.289475\pi$
$461$	12159.0			1.22842			0.614209	+	0.789144i	$0.289475\pi$
$462$		0			0
$463$	−5686.12			−0.570748			−0.285374	−	0.958416i	$-0.592118\pi$
$463$	−5686.12			−0.570748			−0.285374	+	0.958416i	$0.592118\pi$
$464$			1318.99i			0.131966i
$465$	4492.20	+	13229.5i	0.448001	+	1.31936i
$466$	−7694.83			−0.764928
$467$	−13467.8			−1.33451			−0.667254	−	0.744830i	$-0.732531\pi$
$467$	−13467.8			−1.33451			−0.667254	+	0.744830i	$0.732531\pi$
$468$	889.644	+	1158.95i	0.0878714	+	0.114471i
$469$		0			0
$470$		−	12260.0i		−	1.20322i
$471$	2900.70	+	8542.52i	0.283773	+	0.835708i
$472$			1522.67i			0.148489i
$473$			10868.9i			1.05656i
$474$	1059.39	+	3119.88i	0.102657	+	0.302322i
$475$			9516.12i			0.919220i
$476$		0			0
$477$	10654.5	+	13879.7i	1.02272	+	1.33231i
$478$	−13826.2			−1.32301
$479$	−902.528			−0.0860910			−0.0430455	−	0.999073i	$-0.513706\pi$
$479$	−902.528			−0.0860910			−0.0430455	+	0.999073i	$0.513706\pi$
$480$	1161.55	+	3420.74i	0.110452	+	0.325281i
$481$		−	608.763i		−	0.0577073i
$482$	10251.1			0.968728
$483$		0			0
$484$	4150.68			0.389808
$485$		−	7851.01i		−	0.735044i
$486$	7559.53	−	499.076i	0.705571	−	0.0465814i
$487$	−10707.8			−0.996341			−0.498170	−	0.867079i	$-0.665995\pi$
$487$	−10707.8			−0.996341			−0.498170	+	0.867079i	$0.665995\pi$
$488$	5397.56			0.500688
$489$	14719.5	−	4998.14i	1.36122	−	0.462216i
$490$		0			0
$491$			4248.26i			0.390471i	0.980756	+	0.195236i	$0.0625472\pi$
$491$			4248.26i			0.390471i	−0.980756	+	0.195236i	$0.937453\pi$
$492$	8235.73	−	2796.53i	0.754666	−	0.256254i
$493$		−	5049.57i		−	0.461301i
$494$		−	741.929i		−	0.0675728i
$495$	17384.2	+	22646.6i	1.57851	+	2.05635i
$496$		−	1980.12i		−	0.179254i
$497$		0			0
$498$	−1204.42	−	3546.99i	−0.108376	−	0.319166i
$499$	13120.7			1.17708			0.588542	−	0.808467i	$-0.299702\pi$
$499$	13120.7			1.17708			0.588542	+	0.808467i	$0.299702\pi$
$500$	−19295.4			−1.72583
$501$	10619.2	−	3605.86i	0.946968	−	0.321553i
$502$			9505.99i			0.845165i
$503$	12220.6			1.08328			0.541639	−	0.840611i	$-0.317804\pi$
$503$	12220.6			1.08328			0.541639	+	0.840611i	$0.317804\pi$
$504$		0			0
$505$	−8777.53			−0.773456
$506$			13588.2i			1.19382i
$507$	−9909.30	+	3364.80i	−0.868023	+	0.294746i
$508$	−1788.34			−0.156190
$509$	4376.04			0.381070			0.190535	−	0.981680i	$-0.438978\pi$
$509$	4376.04			0.381070			0.190535	+	0.981680i	$0.438978\pi$
$510$	−4446.84	−	13095.9i	−0.386096	−	1.13705i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$	−3199.40	−	2136.46i	−0.275355	−	0.183873i
$514$			5369.57i			0.460782i
$515$			26782.0i			2.29156i
$516$	4395.21	−	1492.44i	0.374978	−	0.127327i
$517$			13731.9i			1.16814i
$518$		0			0
$519$	8002.02	−	2717.17i	0.676782	−	0.229808i
$520$	2351.32			0.198293
$521$	10723.9			0.901772			0.450886	−	0.892582i	$-0.351108\pi$
$521$	10723.9			0.901772			0.450886	+	0.892582i	$0.351108\pi$
$522$	3531.16	−	2710.62i	0.296082	−	0.227281i
$523$		−	9119.08i		−	0.762427i	−0.924487	−	0.381214i	$-0.875506\pi$
$523$		−	9119.08i		−	0.762427i	0.924487	−	0.381214i	$-0.124494\pi$
$524$	−8809.12			−0.734405
$525$		0			0
$526$	−3872.21			−0.320982
$527$			7580.65i			0.626600i
$528$	−1300.99	−	3831.41i	−0.107232	−	0.315796i
$529$	−7320.75			−0.601689
$530$	28159.7			2.30789
$531$	4076.47	−	3129.21i	0.333152	−	0.255737i
$532$		0			0
$533$		−	5661.02i		−	0.460049i
$534$	−678.371	−	1997.80i	−0.0549738	−	0.161897i
$535$		−	23646.0i		−	1.91085i
$536$		−	1639.15i		−	0.132091i
$537$	−3287.20	−	9680.77i	−0.264159	−	0.777944i
$538$			5116.30i			0.409999i
$539$		0			0
$540$	6770.86	−	10139.6i	0.539577	−	0.808031i
$541$	19220.5			1.52746			0.763728	−	0.645539i	$-0.223367\pi$
$541$	19220.5			1.52746			0.763728	+	0.645539i	$0.223367\pi$
$542$	−3739.31			−0.296341
$543$	4650.14	+	13694.6i	0.367507	+	1.08231i
$544$			1960.13i			0.154485i
$545$	−17247.2			−1.35558
$546$		0			0
$547$	−10042.0			−0.784946			−0.392473	−	0.919764i	$-0.628380\pi$
$547$	−10042.0			−0.784946			−0.392473	+	0.919764i	$0.628380\pi$
$548$		−	1422.89i		−	0.110917i
$549$	−11092.4	−	14450.2i	−0.862317	−	1.12335i
$550$	33779.1			2.61881
$551$	−2260.55			−0.174778
$552$	5494.86	−	1865.83i	0.423690	−	0.143868i
$553$		0			0
$554$		−	6478.96i		−	0.496868i
$555$	−4810.39	+	1633.42i	−0.367909	+	0.124927i
$556$			7431.93i			0.566878i
$557$		−	17628.0i		−	1.34098i	−0.741920	−	0.670488i	$-0.766085\pi$
$557$		−	17628.0i		−	1.34098i	0.741920	−	0.670488i	$-0.233915\pi$
$558$	−5301.14	+	4069.30i	−0.402178	+	0.308723i
$559$		−	3021.15i		−	0.228589i
$560$		0			0
$561$	4980.68	+	14668.1i	0.374839	+	1.10390i
$562$	15466.1			1.16085
$563$	19043.6			1.42556			0.712782	−	0.701386i	$-0.247435\pi$
$563$	19043.6			1.42556			0.712782	+	0.701386i	$0.247435\pi$
$564$	5552.94	−	1885.56i	0.414576	−	0.140773i
$565$			12708.7i			0.946297i
$566$	−3100.04			−0.230220
$567$		0			0
$568$	−5510.64			−0.407080
$569$			8296.20i			0.611239i	0.952154	+	0.305619i	$0.0988635\pi$
$569$			8296.20i			0.611239i	−0.952154	+	0.305619i	$0.901136\pi$
$570$	−5862.66	+	1990.72i	−0.430806	+	0.146285i
$571$	−1386.13			−0.101589			−0.0507947	−	0.998709i	$-0.516175\pi$
$571$	−1386.13			−0.101589			−0.0507947	+	0.998709i	$0.516175\pi$
$572$	−2633.60			−0.192511
$573$	4713.49	+	13881.2i	0.343645	+	1.01203i
$574$		0			0
$575$			48444.7i			3.51354i
$576$	−1370.72	+	1052.20i	−0.0991547	+	0.0761140i
$577$		−	14971.8i		−	1.08022i	−0.841595	−	0.540108i	$-0.818383\pi$
$577$		−	14971.8i		−	1.08022i	0.841595	−	0.540108i	$-0.181617\pi$
$578$			2321.90i			0.167090i
$579$	−5973.55	+	2028.38i	−0.428760	+	0.145590i
$580$		−	7164.15i		−	0.512888i
$581$		0			0
$582$	3555.96	−	1207.46i	0.253264	−	0.0859982i
$583$	−31540.4			−2.24060
$584$	−1613.47			−0.114325
$585$	−4832.15	−	6294.92i	−0.341513	−	0.444894i
$586$		−	3509.30i		−	0.247386i
$587$	−4416.35			−0.310532			−0.155266	−	0.987873i	$-0.549623\pi$
$587$	−4416.35			−0.310532			−0.155266	+	0.987873i	$0.549623\pi$
$588$		0			0
$589$	3393.64			0.237407
$590$		−	8270.48i		−	0.577102i
$591$	9.50422	+	27.9898i	0.000661508	+	0.00194813i
$592$	719.996			0.0499859
$593$	−5548.49			−0.384231			−0.192116	−	0.981372i	$-0.561535\pi$
$593$	−5548.49			−0.384231			−0.192116	+	0.981372i	$0.561535\pi$
$594$	−7583.71	+	11356.8i	−0.523844	+	0.784471i
$595$		0			0
$596$			5650.47i			0.388343i
$597$	1899.95	+	5595.33i	0.130251	+	0.383587i
$598$		−	3777.02i		−	0.258284i
$599$			2016.74i			0.137566i	0.997632	+	0.0687829i	$0.0219116\pi$
$599$			2016.74i			0.137566i	−0.997632	+	0.0687829i	$0.978088\pi$
$600$	−4638.29	−	13659.7i	−0.315596	−	0.929426i
$601$			5439.16i			0.369165i	0.982817	+	0.184582i	$0.0590933\pi$
$601$			5439.16i			0.369165i	−0.982817	+	0.184582i	$0.940907\pi$
$602$		0			0
$603$	−4388.30	+	3368.59i	−0.296361	+	0.227495i
$604$	678.021			0.0456760
$605$	−22544.6			−1.51499
$606$	−1349.96	−	3975.61i	−0.0904923	−	0.266499i
$607$		−	22433.8i		−	1.50010i	−0.661381	−	0.750050i	$-0.730029\pi$
$607$		−	22433.8i		−	1.50010i	0.661381	−	0.750050i	$-0.269971\pi$
$608$	877.494			0.0585314
$609$		0			0
$610$	−29317.1			−1.94593
$611$		−	3816.94i		−	0.252728i
$612$	5247.61	−	4028.21i	0.346605	−	0.266064i
$613$	3599.69			0.237178			0.118589	−	0.992943i	$-0.462163\pi$
$613$	3599.69			0.237178			0.118589	+	0.992943i	$0.462163\pi$
$614$	−6656.79			−0.437535
$615$	−44732.9	+	15189.5i	−2.93301	+	0.995934i
$616$		0			0
$617$		−	21419.4i		−	1.39759i	−0.715321	−	0.698796i	$-0.753720\pi$
$617$		−	21419.4i		−	1.39759i	0.715321	−	0.698796i	$-0.246280\pi$
$618$	−12130.4	+	4118.99i	−0.789571	+	0.268107i
$619$		−	18366.9i		−	1.19262i	−0.802756	−	0.596308i	$-0.796634\pi$
$619$		−	18366.9i		−	1.19262i	0.802756	−	0.596308i	$-0.203366\pi$
$620$			10755.1i			0.696673i
$621$	−16287.5	−	10876.3i	−1.05249	−	0.702818i
$622$		−	13032.2i		−	0.840101i
$623$		0			0
$624$	361.627	+	1064.99i	0.0231998	+	0.0683231i
$625$	61425.5			3.93123
$626$	−4277.88			−0.273128
$627$	6566.48	−	2229.71i	0.418245	−	0.142019i
$628$			6944.80i			0.441286i
$629$	−2756.41			−0.174730
$630$		0			0
$631$	21152.9			1.33452			0.667262	−	0.744823i	$-0.267466\pi$
$631$	21152.9			1.33452			0.667262	+	0.744823i	$0.267466\pi$
$632$			2536.37i			0.159638i
$633$	27613.0	−	9376.27i	1.73384	−	0.588741i
$634$	5601.02			0.350859
$635$	9713.47			0.607035
$636$	4330.88	+	12754.4i	0.270017	+	0.795197i
$637$		0			0
$638$			8024.21i			0.497934i
$639$	11324.8	+	14753.0i	0.701098	+	0.913331i
$640$			2780.96i			0.171761i
$641$		−	2450.79i		−	0.151014i	−0.997145	−	0.0755072i	$-0.975942\pi$
$641$		−	2450.79i		−	0.151014i	0.997145	−	0.0755072i	$-0.0240576\pi$
$642$	10710.0	−	3636.69i	0.658396	−	0.223565i
$643$		−	15343.8i		−	0.941056i	−0.882385	−	0.470528i	$-0.844063\pi$
$643$		−	15343.8i		−	0.941056i	0.882385	−	0.470528i	$-0.155937\pi$
$644$		0			0
$645$	−23872.9	+	8106.27i	−1.45735	+	0.494859i
$646$	−3359.38			−0.204602
$647$	5712.58			0.347117			0.173558	−	0.984824i	$-0.444473\pi$
$647$	5712.58			0.347117			0.173558	+	0.984824i	$0.444473\pi$
$648$	5633.85	+	1507.30i	0.341541	+	0.0913769i
$649$			9263.37i			0.560276i
$650$	−9389.32			−0.566584
$651$		0			0
$652$	11966.5			0.718778
$653$			15033.5i			0.900930i	0.892794	+	0.450465i	$0.148742\pi$
$653$			15033.5i			0.900930i	−0.892794	+	0.450465i	$0.851258\pi$
$654$	−2652.57	−	7811.79i	−0.158599	−	0.467072i
$655$	47847.2			2.85427
$656$	6695.40			0.398493
$657$	3315.81	+	4319.55i	0.196898	+	0.256502i
$658$		0			0
$659$		−	24135.6i		−	1.42669i	−0.700813	−	0.713345i	$-0.747179\pi$
$659$		−	24135.6i		−	1.42669i	0.700813	−	0.713345i	$-0.252821\pi$
$660$	7066.41	+	20810.5i	0.416757	+	1.22734i
$661$		−	3739.96i		−	0.220072i	−0.993928	−	0.110036i	$-0.964903\pi$
$661$		−	3739.96i		−	0.220072i	0.993928	−	0.110036i	$-0.0350966\pi$
$662$		−	7094.59i		−	0.416524i
$663$	−1384.44	−	4077.17i	−0.0810970	−	0.238830i
$664$		−	2883.59i		−	0.168532i
$665$		0			0
$666$	−1479.65	−	1927.56i	−0.0860889	−	0.112149i
$667$	−11508.0			−0.668055
$668$	8633.09			0.500036
$669$	2903.37	+	8550.38i	0.167789	+	0.494136i
$670$			8903.15i			0.513371i
$671$	32836.7			1.88919
$672$		0			0
$673$	−11803.0			−0.676037			−0.338018	−	0.941140i	$-0.609757\pi$
$673$	−11803.0			−0.676037			−0.338018	+	0.941140i	$0.609757\pi$
$674$		−	19072.2i		−	1.08996i
$675$	−27037.4	+	40489.3i	−1.54174	+	2.30879i
$676$	−8055.96			−0.458350
$677$	30670.1			1.74113			0.870567	−	0.492050i	$-0.163752\pi$
$677$	30670.1			1.74113			0.870567	+	0.492050i	$0.163752\pi$
$678$	−5756.15	+	1954.56i	−0.326052	+	0.110714i
$679$		0			0
$680$		−	10646.5i		−	0.600406i
$681$	11341.4	−	3851.08i	0.638184	−	0.216702i
$682$		−	12046.3i		−	0.676360i
$683$			14007.5i			0.784747i	0.919806	+	0.392374i	$0.128346\pi$
$683$			14007.5i			0.784747i	−0.919806	+	0.392374i	$0.871654\pi$
$684$	−1803.32	−	2349.21i	−0.100806	−	0.131322i
$685$			7728.49i			0.431081i
$686$		0			0
$687$	−9079.72	−	26739.7i	−0.504240	−	1.48498i
$688$	3573.17			0.198003
$689$	8767.03			0.484757
$690$	−29845.6	+	10134.4i	−1.64667	+	0.559144i
$691$		−	9461.83i		−	0.520905i	−0.965487	−	0.260452i	$-0.916128\pi$
$691$		−	9461.83i		−	0.520905i	0.965487	−	0.260452i	$-0.0838717\pi$
$692$	6505.40			0.357367
$693$		0			0
$694$	22925.8			1.25397
$695$		−	40366.9i		−	2.20317i
$696$	3244.86	−	1101.82i	0.176719	−	0.0600066i
$697$	−25632.5			−1.39297
$698$	−12828.5			−0.695653
$699$	6427.94	+	18930.2i	0.347821	+	1.02433i
$700$		0			0
$701$			8147.43i			0.438979i	0.975615	+	0.219489i	$0.0704391\pi$
$701$			8147.43i			0.438979i	−0.975615	+	0.219489i	$0.929561\pi$
$702$	2107.99	−	3156.77i	0.113335	−	0.169722i
$703$			1233.97i			0.0662020i
$704$		−	3114.81i		−	0.166753i
$705$	−30161.1	+	10241.5i	−1.61125	+	0.547117i
$706$			18865.8i			1.00570i
$707$		0			0
$708$	3745.95	−	1271.98i	0.198844	−	0.0675195i
$709$	−28097.3			−1.48831			−0.744157	−	0.668005i	$-0.767149\pi$
$709$	−28097.3			−1.48831			−0.744157	+	0.668005i	$0.767149\pi$
$710$	29931.4			1.58212
$711$	6790.30	−	5212.43i	0.358166	−	0.274939i
$712$		−	1624.15i		−	0.0854880i
$713$	17276.4			0.907441
$714$		0			0
$715$	14304.6			0.748197
$716$		−	7870.17i		−	0.410785i
$717$	11549.8	+	34014.2i	0.601586	+	1.77166i
$718$	4374.85			0.227393
$719$	21857.1			1.13370			0.566851	−	0.823821i	$-0.308162\pi$
$719$	21857.1			1.13370			0.566851	+	0.823821i	$0.308162\pi$
$720$	7445.12	−	5715.08i	0.385365	−	0.295817i
$721$		0			0
$722$		−	12214.1i		−	0.629587i
$723$	−8563.37	−	25219.0i	−0.440491	−	1.29724i
$724$			11133.3i			0.571499i
$725$			28607.9i			1.46548i
$726$	−3467.30	−	10211.2i	−0.177250	−	0.521999i
$727$			29.7842i			0.00151944i	1.00000		0.000759722i	$0.000241827\pi$
$727$			29.7842i			0.00151944i	−1.00000		0.000759722i	$0.999758\pi$
$728$		0			0
$729$	−7542.70	−	18180.4i	−0.383209	−	0.923662i
$730$	8763.67			0.444326
$731$	−13679.5			−0.692138
$732$	−4508.89	−	13278.6i	−0.227668	−	0.670481i
$733$			33848.6i			1.70563i	0.522213	+	0.852815i	$0.325107\pi$
$733$			33848.6i			1.70563i	−0.522213	+	0.852815i	$0.674893\pi$
$734$	13193.2			0.663445
$735$		0			0
$736$	4467.15			0.223725
$737$		−	9971.99i		−	0.498403i
$738$	−13759.6	−	17924.8i	−0.686310	−	0.894065i
$739$	25275.2			1.25814			0.629068	−	0.777350i	$-0.283437\pi$
$739$	25275.2			1.25814			0.629068	+	0.777350i	$0.283437\pi$
$740$	−3910.70			−0.194270
$741$	−1825.23	+	619.776i	−0.0904880	+	0.0307261i
$742$		0			0
$743$		−	9958.69i		−	0.491721i	−0.969305	−	0.245861i	$-0.920929\pi$
$743$		−	9958.69i		−	0.491721i	0.969305	−	0.245861i	$-0.0790705\pi$
$744$	−4871.33	+	1654.11i	−0.240043	+	0.0815089i
$745$		−	30690.9i		−	1.50930i
$746$			18205.0i			0.893475i
$747$	−7719.89	+	5926.01i	−0.378121	+	0.290256i
$748$			11924.7i			0.582900i
$749$		0			0
$750$	16118.6	+	47469.0i	0.784756	+	2.31110i
$751$	13112.3			0.637119			0.318559	−	0.947903i	$-0.396801\pi$
$751$	13112.3			0.637119			0.318559	+	0.947903i	$0.396801\pi$
$752$	4514.37			0.218912
$753$	23385.8	−	7940.90i	1.13178	−	0.384306i
$754$		−	2230.43i		−	0.107729i
$755$	−3682.71			−0.177520
$756$		0			0
$757$	28844.1			1.38488			0.692442	−	0.721473i	$-0.256535\pi$
$757$	28844.1			1.38488			0.692442	+	0.721473i	$0.256535\pi$
$758$			4258.46i			0.204056i
$759$	33428.7	−	11351.0i	1.59866	−	0.542841i
$760$	−4766.16			−0.227483
$761$	17175.4			0.818144			0.409072	−	0.912502i	$-0.365853\pi$
$761$	17175.4			0.818144			0.409072	+	0.912502i	$0.365853\pi$
$762$	1493.90	+	4399.53i	0.0710215	+	0.209157i
$763$		0			0
$764$			11285.0i			0.534392i
$765$	−28502.7	+	21879.5i	−1.34708	+	1.03406i
$766$			17199.3i			0.811275i
$767$		−	2574.87i		−	0.121217i
$768$	−1259.58	+	427.703i	−0.0591812	+	0.0200956i
$769$		−	34779.8i		−	1.63094i	−0.578800	−	0.815470i	$-0.696479\pi$
$769$		−	34779.8i		−	1.63094i	0.578800	−	0.815470i	$-0.303521\pi$
$770$		0			0
$771$	13209.8	−	4485.51i	0.617041	−	0.209522i
$772$	−4856.31			−0.226402
$773$	16923.2			0.787432			0.393716	−	0.919232i	$-0.371189\pi$
$773$	16923.2			0.787432			0.393716	+	0.919232i	$0.371189\pi$
$774$	−7343.15	−	9566.02i	−0.341013	−	0.444242i
$775$		−	42947.5i		−	1.99061i
$776$	2890.89			0.133733
$777$		0			0
$778$	−17057.3			−0.786033
$779$			11474.9i			0.527770i
$780$	−1964.20	−	5784.54i	−0.0901661	−	0.265538i
$781$	−33524.7			−1.53599
$782$	−17101.9			−0.782051
$783$	−9618.22	−	6422.73i	−0.438987	−	0.293141i
$784$		0			0
$785$		−	37721.1i		−	1.71506i
$786$	7358.76	+	21671.5i	0.333942	+	0.983455i
$787$			39489.6i			1.78863i	0.447436	+	0.894316i	$0.352337\pi$
$787$			39489.6i			1.78863i	−0.447436	+	0.894316i	$0.647663\pi$
$788$			22.7548i			0.00102869i
$789$	3234.68	+	9526.09i	0.145954	+	0.429833i
$790$		−	13776.4i		−	0.620434i
$791$		0			0
$792$	−8338.91	+	6401.19i	−0.374129	+	0.287192i
$793$	−9127.37			−0.408729
$794$	−6017.24			−0.268947
$795$	−23523.4	−	69276.3i	−1.04942	−	3.09054i
$796$			4548.83i			0.202549i
$797$	−32760.9			−1.45602			−0.728012	−	0.685565i	$-0.759555\pi$
$797$	−32760.9			−1.45602			−0.728012	+	0.685565i	$0.759555\pi$
$798$		0			0
$799$	−17282.7			−0.765229
$800$		−	11104.9i		−	0.490773i
$801$	−4348.13	+	3337.75i	−0.191802	+	0.147233i
$802$	−16584.1			−0.730180
$803$	−9815.76			−0.431371
$804$	−4032.51	+	1369.28i	−0.176885	+	0.0600631i
$805$		0			0
$806$			3348.42i			0.146331i
$807$	12586.7	−	4273.94i	0.549037	−	0.186431i
$808$		−	3232.05i		−	0.140722i
$809$		−	24216.1i		−	1.05240i	−0.850360	−	0.526201i	$-0.823616\pi$
$809$		−	24216.1i		−	1.05240i	0.850360	−	0.526201i	$-0.176384\pi$
$810$	−30600.6	−	8186.97i	−1.32740	−	0.355137i
$811$		−	27676.9i		−	1.19836i	−0.800615	−	0.599179i	$-0.795494\pi$
$811$		−	27676.9i		−	1.19836i	0.800615	−	0.599179i	$-0.204506\pi$
$812$		0			0
$813$	3123.66	+	9199.13i	0.134750	+	0.396836i
$814$	4380.18			0.188606
$815$	−64996.6			−2.79353
$816$	4822.14	−	1637.41i	0.206874	−	0.0702460i
$817$			6123.91i			0.262238i
$818$	23199.3			0.991618
$819$		0			0
$820$	−36366.4			−1.54875
$821$			36666.3i			1.55866i	0.626612	+	0.779331i	$0.284441\pi$
$821$			36666.3i			1.55866i	−0.626612	+	0.779331i	$0.715559\pi$
$822$	−3500.47	+	1188.62i	−0.148532	+	0.0504354i
$823$	−39504.0			−1.67318			−0.836588	−	0.547833i	$-0.815453\pi$
$823$	−39504.0			−1.67318			−0.836588	+	0.547833i	$0.815453\pi$
$824$	−9861.61			−0.416924
$825$	−28217.6	−	83100.5i	−1.19080	−	3.50690i
$826$		0			0
$827$			36665.1i			1.54168i	0.637029	+	0.770840i	$0.280163\pi$
$827$			36665.1i			1.54168i	−0.637029	+	0.770840i	$0.719837\pi$
$828$	−9180.35	−	11959.4i	−0.385313	−	0.501952i
$829$			17217.1i			0.721320i	0.932697	+	0.360660i	$0.117449\pi$
$829$			17217.1i			0.721320i	−0.932697	+	0.360660i	$0.882551\pi$
$830$			15662.4i			0.655000i
$831$	−15939.0	+	5412.25i	−0.665365	+	0.225931i
$832$			865.801i			0.0360772i
$833$		0			0
$834$	18283.4	−	6208.32i	0.759116	−	0.257766i
$835$	−46891.1			−1.94339
$836$	5338.34			0.220850
$837$	14439.3	+	9642.10i	0.596291	+	0.398184i
$838$			22542.5i			0.929259i
$839$	8274.08			0.340468			0.170234	−	0.985404i	$-0.445548\pi$
$839$	8274.08			0.340468			0.170234	+	0.985404i	$0.445548\pi$
$840$		0			0
$841$	17593.2			0.721358
$842$		−	2689.89i		−	0.110095i
$843$	−12919.7	−	38048.3i	−0.527850	−	1.55451i
$844$	22448.5			0.915533
$845$	43756.4			1.78138
$846$	−9277.38	−	12085.8i	−0.377025	−	0.491155i
$847$		0			0
$848$			10368.9i			0.419895i
$849$	2589.64	+	7626.46i	0.104683	+	0.308292i
$850$			42513.8i			1.71554i
$851$			6281.90i			0.253044i
$852$	4603.35	+	13556.8i	0.185104	+	0.545128i
$853$			45421.2i			1.82320i	0.411075	+	0.911601i	$0.365153\pi$
$853$			45421.2i			1.82320i	−0.411075	+	0.911601i	$0.634847\pi$
$854$		0			0
$855$	9794.83	+	12759.9i	0.391785	+	0.510383i
$856$	8706.91			0.347659
$857$	−3995.75			−0.159267			−0.0796337	−	0.996824i	$-0.525375\pi$
$857$	−3995.75			−0.159267			−0.0796337	+	0.996824i	$0.525375\pi$
$858$	2200.00	+	6478.98i	0.0875371	+	0.257796i
$859$		−	8676.84i		−	0.344645i	−0.985041	−	0.172323i	$-0.944873\pi$
$859$		−	8676.84i		−	0.344645i	0.985041	−	0.172323i	$-0.0551271\pi$
$860$	−19407.9			−0.769540
$861$		0			0
$862$	−30402.0			−1.20127
$863$		−	32022.9i		−	1.26312i	−0.775328	−	0.631559i	$-0.782415\pi$
$863$		−	32022.9i		−	1.26312i	0.775328	−	0.631559i	$-0.217585\pi$
$864$	3733.57	+	2493.16i	0.147012	+	0.0981701i
$865$	−35334.5			−1.38891
$866$	−1907.08			−0.0748330
$867$	5712.14	−	1939.61i	0.223754	−	0.0759778i
$868$		0			0
$869$			15430.3i			0.602344i
$870$	−17624.6	+	5984.62i	−0.686818	+	0.233216i
$871$			2771.84i			0.107830i
$872$		−	6350.75i		−	0.246632i
$873$	−5941.00	−	7739.42i	−0.230323	−	0.300046i
$874$			7656.06i			0.296304i
$875$		0			0
$876$	1347.83	+	3969.33i	0.0519850	+	0.153095i
$877$	−14787.5			−0.569372			−0.284686	−	0.958621i	$-0.591889\pi$
$877$	−14787.5			−0.569372			−0.284686	+	0.958621i	$0.591889\pi$
$878$	−14534.2			−0.558661
$879$	−8633.30	+	2931.52i	−0.331279	+	0.112489i
$880$			16918.3i			0.648086i
$881$	10308.3			0.394206			0.197103	−	0.980383i	$-0.436847\pi$
$881$	10308.3			0.394206			0.197103	+	0.980383i	$0.436847\pi$
$882$		0			0
$883$	−30917.7			−1.17833			−0.589165	−	0.808013i	$-0.700543\pi$
$883$	−30917.7			−1.17833			−0.589165	+	0.808013i	$0.700543\pi$
$884$		−	3314.61i		−	0.126111i
$885$	−20346.4	+	6908.81i	−0.772808	+	0.262415i
$886$	−316.394			−0.0119971
$887$	7802.14			0.295344			0.147672	−	0.989036i	$-0.452822\pi$
$887$	7802.14			0.295344			0.147672	+	0.989036i	$0.452822\pi$
$888$	−601.454	−	1771.27i	−0.0227291	−	0.0669370i
$889$		0			0
$890$			8821.64i			0.332250i
$891$	34274.2	+	9169.82i	1.28870	+	0.344782i
$892$			6951.19i			0.260923i
$893$			7736.98i			0.289931i
$894$	13900.8	−	4720.17i	0.520037	−	0.176584i
$895$			42747.3i			1.59652i
$896$		0			0
$897$	−9291.91	+	3155.16i	−0.345873	+	0.117445i
$898$	−11713.9			−0.435299
$899$	10202.2			0.378489
$900$	−29729.9	+	22821.5i	−1.10111	+	0.845240i
$901$		−	39696.2i		−	1.46778i
$902$	40732.3			1.50359
$903$		0			0
$904$	−4679.57			−0.172168
$905$		−	60471.1i		−	2.22114i
$906$	−566.390	−	1668.01i	−0.0207694	−	0.0611655i
$907$	−27721.8			−1.01487			−0.507435	−	0.861690i	$-0.669406\pi$
$907$	−27721.8			−1.01487			−0.507435	+	0.861690i	$0.669406\pi$
$908$	9220.21			0.336986
$909$	−8652.77	+	6642.11i	−0.315725	+	0.242360i
$910$		0			0
$911$		−	49080.0i		−	1.78495i	−0.451094	−	0.892476i	$-0.648966\pi$
$911$		−	49080.0i		−	1.78495i	0.451094	−	0.892476i	$-0.351034\pi$
$912$	−733.021	−	2158.74i	−0.0266149	−	0.0783805i
$913$		−	17542.7i		−	0.635902i
$914$			19946.8i			0.721860i
$915$	24490.3	+	72123.6i	0.884835	+	2.60583i
$916$		−	21738.5i		−	0.784128i
$917$		0			0
$918$	−14293.5	−	9544.74i	−0.513896	−	0.343163i
$919$	7603.45			0.272921			0.136461	−	0.990645i	$-0.456427\pi$
$919$	7603.45			0.272921			0.136461	+	0.990645i	$0.456427\pi$
$920$	−24263.6			−0.869508
$921$	5560.80	+	16376.5i	0.198952	+	0.585911i
$922$		−	24318.0i		−	0.868622i
$923$	9318.59			0.332313
$924$		0			0
$925$	15616.2			0.555090
$926$			11372.2i			0.403580i
$927$	20266.4	+	26401.3i	0.718053	+	0.935418i
$928$	2637.97			0.0933143
$929$	4956.43			0.175043			0.0875216	−	0.996163i	$-0.472105\pi$
$929$	4956.43			0.175043			0.0875216	+	0.996163i	$0.472105\pi$
$930$	26458.9	−	8984.39i	0.932927	−	0.316785i
$931$		0			0
$932$			15389.7i			0.540885i
$933$	−32060.7	+	10886.5i	−1.12499	+	0.382003i
$934$			26935.6i			0.943640i
$935$		−	64769.6i		−	2.26545i
$936$	2317.90	−	1779.29i	0.0809435	−	0.0621345i
$937$		−	30085.4i		−	1.04893i	−0.851433	−	0.524464i	$-0.824266\pi$
$937$		−	30085.4i		−	1.04893i	0.851433	−	0.524464i	$-0.175734\pi$
$938$		0			0
$939$	3573.56	+	10524.1i	0.124194	+	0.365751i
$940$	−24520.1			−0.850804
$941$	−35955.2			−1.24560			−0.622799	−	0.782382i	$-0.714004\pi$
$941$	−35955.2			−1.24560			−0.622799	+	0.782382i	$0.714004\pi$
$942$	17085.0	−	5801.39i	0.590935	−	0.200658i
$943$			58416.7i			2.01730i
$944$	3045.35			0.104997
$945$		0			0
$946$	21737.8			0.747102
$947$			21321.7i			0.731639i	0.930686	+	0.365819i	$0.119211\pi$
$947$			21321.7i			0.731639i	−0.930686	+	0.365819i	$0.880789\pi$
$948$	6239.76	−	2118.77i	0.213774	−	0.0725892i
$949$	2728.41			0.0933277
$950$	19032.2			0.649987
$951$	−4678.85	−	13779.2i	−0.159540	−	0.469842i
$952$		0			0
$953$		−	25987.9i		−	0.883347i	−0.897176	−	0.441674i	$-0.854385\pi$
$953$		−	25987.9i		−	0.883347i	0.897176	−	0.441674i	$-0.145615\pi$
$954$	27759.5	−	21309.0i	0.942083	−	0.723169i
$955$		−	61294.9i		−	2.07692i
$956$			27652.5i			0.935507i
$957$	19740.5	−	6703.09i	0.666792	−	0.226416i
$958$			1805.06i			0.0608755i
$959$		0			0
$960$	6841.48	−	2323.09i	0.230008	−	0.0781016i
$961$	14475.0			0.485886
$962$	−1217.53			−0.0408052
$963$	−17893.4	−	23309.9i	−0.598760	−	0.780013i
$964$		−	20502.3i		−	0.684994i
$965$	26377.3			0.879913
$966$		0			0
$967$	44652.9			1.48494			0.742471	−	0.669878i	$-0.233653\pi$
$967$	44652.9			1.48494			0.742471	+	0.669878i	$0.233653\pi$
$968$		−	8301.36i		−	0.275636i
$969$	2806.28	+	8264.46i	0.0930348	+	0.273986i
$970$	−15702.0			−0.519754
$971$	26384.2			0.871997			0.435998	−	0.899947i	$-0.356395\pi$
$971$	26384.2			0.871997			0.435998	+	0.899947i	$0.356395\pi$
$972$	−998.153	−	15119.1i	−0.0329380	−	0.498914i
$973$		0			0
$974$			21415.7i			0.704519i
$975$	7843.44	+	23098.8i	0.257632	+	0.758723i
$976$		−	10795.1i		−	0.354040i
$977$			30645.4i			1.00351i	0.865009	+	0.501756i	$0.167313\pi$
$977$			30645.4i			1.00351i	−0.865009	+	0.501756i	$0.832687\pi$
$978$	−9996.28	−	29438.9i	−0.326836	−	0.962529i
$979$		−	9880.69i		−	0.322562i
$980$		0			0
$981$	−17002.1	+	13051.3i	−0.553348	+	0.424766i
$982$	8496.53			0.276105
$983$	−546.210			−0.0177227			−0.00886134	−	0.999961i	$-0.502821\pi$
$983$	−546.210			−0.0177227			−0.00886134	+	0.999961i	$0.502821\pi$
$984$	−5593.05	−	16471.5i	−0.181199	−	0.533629i
$985$		−	123.594i		−	0.00399801i
$986$	−10099.1			−0.326189
$987$		0			0
$988$	−1483.86			−0.0477812
$989$			31175.6i			1.00235i
$990$	45293.3	−	34768.4i	1.45406	−	1.11617i
$991$	15440.5			0.494938			0.247469	−	0.968896i	$-0.420401\pi$
$991$	15440.5			0.494938			0.247469	+	0.968896i	$0.420401\pi$
$992$	−3960.24			−0.126752
$993$	−17453.5	+	5926.52i	−0.557775	+	0.189398i
$994$		0			0
$995$		−	24707.2i		−	0.787208i
$996$	−7093.98	+	2408.83i	−0.225684	+	0.0766333i
$997$			53069.1i			1.68577i	0.538092	+	0.842886i	$0.319145\pi$
$997$			53069.1i			1.68577i	−0.538092	+	0.842886i	$0.680855\pi$
$998$		−	26241.5i		−	0.832324i
$999$	−3505.98	+	5250.31i	−0.111035	+	0.166279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.d.b.293.5	✓	24
3.2	odd	2	inner	294.4.d.b.293.20	yes	24
7.2	even	3		294.4.f.c.227.12		48
7.3	odd	6		294.4.f.c.215.13		48
7.4	even	3		294.4.f.c.215.15		48
7.5	odd	6		294.4.f.c.227.10		48
7.6	odd	2	inner	294.4.d.b.293.19	yes	24
21.2	odd	6		294.4.f.c.227.13		48
21.5	even	6		294.4.f.c.227.15		48
21.11	odd	6		294.4.f.c.215.10		48
21.17	even	6		294.4.f.c.215.12		48
21.20	even	2	inner	294.4.d.b.293.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.d.b.293.5	✓	24	1.1	even	1	trivial
294.4.d.b.293.6	yes	24	21.20	even	2	inner
294.4.d.b.293.19	yes	24	7.6	odd	2	inner
294.4.d.b.293.20	yes	24	3.2	odd	2	inner
294.4.f.c.215.10		48	21.11	odd	6
294.4.f.c.215.12		48	21.17	even	6
294.4.f.c.215.13		48	7.3	odd	6
294.4.f.c.215.15		48	7.4	even	3
294.4.f.c.227.10		48	7.5	odd	6
294.4.f.c.227.12		48	7.2	even	3
294.4.f.c.227.13		48	21.2	odd	6
294.4.f.c.227.15		48	21.5	even	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +(-4.92023 + 1.67071i) q^{3} -4.00000 q^{4} +21.7262 q^{5} +(3.34143 + 9.84047i) q^{6} +8.00000i q^{8} +(21.4174 - 16.4406i) q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +(-4.92023 + 1.67071i) q^{3} -4.00000 q^{4} +21.7262 q^{5} +(3.34143 + 9.84047i) q^{6} +8.00000i q^{8} +(21.4174 - 16.4406i) q^{9} -43.4525i q^{10} +48.6690i q^{11} +(19.6809 - 6.68286i) q^{12} -13.5281i q^{13} +(-106.898 + 36.2983i) q^{15} +16.0000 q^{16} -61.2540 q^{17} +(-32.8812 - 42.8348i) q^{18} +27.4217i q^{19} -86.9049 q^{20} +97.3380 q^{22} +139.599i q^{23} +(-13.3657 - 39.3619i) q^{24} +347.029 q^{25} -27.0563 q^{26} +(-77.9112 + 116.674i) q^{27} +82.4366i q^{29} +(72.5967 + 213.796i) q^{30} -123.758i q^{31} -32.0000i q^{32} +(-81.3120 - 239.463i) q^{33} +122.508i q^{34} +(-85.6697 + 65.7625i) q^{36} +44.9998 q^{37} +54.8434 q^{38} +(22.6017 + 66.5617i) q^{39} +173.810i q^{40} +418.462 q^{41} +223.323 q^{43} -194.676i q^{44} +(465.320 - 357.193i) q^{45} +279.197 q^{46} +282.148 q^{47} +(-78.7238 + 26.7314i) q^{48} -694.058i q^{50} +(301.384 - 102.338i) q^{51} +54.1126i q^{52} +648.059i q^{53} +(233.348 + 155.822i) q^{54} +1057.39i q^{55} +(-45.8138 - 134.921i) q^{57} +164.873 q^{58} +190.334 q^{59} +(427.593 - 145.193i) q^{60} -674.695i q^{61} -247.515 q^{62} -64.0000 q^{64} -293.916i q^{65} +(-478.926 + 162.624i) q^{66} -204.894 q^{67} +245.016 q^{68} +(-233.229 - 686.858i) q^{69} +688.830i q^{71} +(131.525 + 171.339i) q^{72} +201.684i q^{73} -89.9995i q^{74} +(-1707.46 + 579.786i) q^{75} -109.687i q^{76} +(133.123 - 45.2034i) q^{78} +317.046 q^{79} +347.620 q^{80} +(188.412 - 704.231i) q^{81} -836.925i q^{82} -360.449 q^{83} -1330.82 q^{85} -446.647i q^{86} +(-137.728 - 405.608i) q^{87} -389.352 q^{88} -203.018 q^{89} +(-714.385 - 930.640i) q^{90} -558.394i q^{92} +(206.764 + 608.917i) q^{93} -564.296i q^{94} +595.770i q^{95} +(53.4629 + 157.448i) q^{96} -361.361i q^{97} +(800.148 + 1042.36i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 96 q^{4} + 128 q^{9}+O(q^{10}) \) 24 * q - 96 * q^4 + 128 * q^9	\( 24 q - 96 q^{4} + 128 q^{9} - 336 q^{15} + 384 q^{16} + 32 q^{18} + 288 q^{22} + 456 q^{25} + 544 q^{30} - 512 q^{36} - 432 q^{37} + 2656 q^{39} + 624 q^{43} - 1344 q^{46} + 3696 q^{51} + 176 q^{57} - 96 q^{58} + 1344 q^{60} - 1536 q^{64} - 528 q^{67} - 128 q^{72} - 5216 q^{78} - 7488 q^{79} + 336 q^{81} - 1728 q^{85} - 1152 q^{88} + 7392 q^{93} + 5656 q^{99}+O(q^{100}) \) 24 * q - 96 * q^4 + 128 * q^9 - 336 * q^15 + 384 * q^16 + 32 * q^18 + 288 * q^22 + 456 * q^25 + 544 * q^30 - 512 * q^36 - 432 * q^37 + 2656 * q^39 + 624 * q^43 - 1344 * q^46 + 3696 * q^51 + 176 * q^57 - 96 * q^58 + 1344 * q^60 - 1536 * q^64 - 528 * q^67 - 128 * q^72 - 5216 * q^78 - 7488 * q^79 + 336 * q^81 - 1728 * q^85 - 1152 * q^88 + 7392 * q^93 + 5656 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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