LMFDB - Embedded newform 504.4.i.b.125.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,4,Mod(125,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("504.125");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	504.i (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:	$29.7369626429$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.14
Character	$\chi$	$=$	504.125
Dual form			504.4.i.b.125.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45064 - 1.41222i) q^{2} +(4.01126 + 6.92169i) q^{4} -21.1851i q^{5} +(7.58217 + 16.8971i) q^{7} +(-0.0551907 - 22.6273i) q^{8} +O(q^{10})$	\(q+(-2.45064 - 1.41222i) q^{2} +(4.01126 + 6.92169i) q^{4} -21.1851i q^{5} +(7.58217 + 16.8971i) q^{7} +(-0.0551907 - 22.6273i) q^{8} +(-29.9180 + 51.9170i) q^{10} -34.6846 q^{11} +40.0348 q^{13} +(5.28124 - 52.1163i) q^{14} +(-31.8196 + 55.5294i) q^{16} -76.5612 q^{17} +3.05838 q^{19} +(146.637 - 84.9789i) q^{20} +(84.9993 + 48.9823i) q^{22} +181.651i q^{23} -323.808 q^{25} +(-98.1109 - 56.5380i) q^{26} +(-86.5422 + 120.260i) q^{28} -79.6686 q^{29} +25.5766i q^{31} +(156.398 - 91.1462i) q^{32} +(187.624 + 108.121i) q^{34} +(357.966 - 160.629i) q^{35} -162.762i q^{37} +(-7.49499 - 4.31911i) q^{38} +(-479.362 + 1.16922i) q^{40} +191.358 q^{41} -385.956i q^{43} +(-139.129 - 240.076i) q^{44} +(256.532 - 445.162i) q^{46} -199.255 q^{47} +(-228.021 + 256.233i) q^{49} +(793.537 + 457.289i) q^{50} +(160.590 + 277.109i) q^{52} -490.879 q^{53} +734.795i q^{55} +(381.917 - 172.497i) q^{56} +(195.239 + 112.510i) q^{58} +811.088i q^{59} -165.593 q^{61} +(36.1198 - 62.6789i) q^{62} +(-511.994 + 2.49764i) q^{64} -848.141i q^{65} +632.062i q^{67} +(-307.107 - 529.933i) q^{68} +(-1104.09 - 111.884i) q^{70} +618.163i q^{71} -279.677i q^{73} +(-229.856 + 398.870i) q^{74} +(12.2680 + 21.1692i) q^{76} +(-262.984 - 586.067i) q^{77} +598.872 q^{79} +(1176.40 + 674.101i) q^{80} +(-468.949 - 270.240i) q^{82} +52.2938i q^{83} +1621.96i q^{85} +(-545.055 + 945.838i) q^{86} +(1.91426 + 784.819i) q^{88} +1287.23 q^{89} +(303.551 + 676.471i) q^{91} +(-1257.33 + 728.651i) q^{92} +(488.303 + 281.393i) q^{94} -64.7921i q^{95} +1821.05i q^{97} +(920.656 - 305.917i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q+O(q^{10}) $ 88 * q	$ 88 q - 128 q^{16} - 1312 q^{22} - 3400 q^{25} + 584 q^{28} - 208 q^{46} - 2024 q^{49} - 3200 q^{58} - 1440 q^{64} - 2856 q^{70} - 10832 q^{79} - 272 q^{88}+O(q^{100}) $ 88 * q - 128 * q^16 - 1312 * q^22 - 3400 * q^25 + 584 * q^28 - 208 * q^46 - 2024 * q^49 - 3200 * q^58 - 1440 * q^64 - 2856 * q^70 - 10832 * q^79 - 272 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.45064	−	1.41222i	−0.866432	−	0.499296i
$2$	−2.45064	−	1.41222i	−0.866432	−	0.499296i
$3$		0			0
$3$		0			0
$4$	4.01126	+	6.92169i	0.501408	+	0.865211i
$5$		−	21.1851i		−	1.89485i	−0.319975	−	0.947426i	$-0.603674\pi$
$5$		−	21.1851i		−	1.89485i	0.319975	−	0.947426i	$-0.396326\pi$
$6$		0			0
$7$	7.58217	+	16.8971i	0.409399	+	0.912356i
$7$	7.58217	+	16.8971i	0.409399	+	0.912356i
$8$	−0.0551907	−	22.6273i	−0.00243911	−	0.999997i
$9$		0			0
$10$	−29.9180	+	51.9170i	−0.946092	+	1.64176i
$11$	−34.6846			−0.950708			−0.475354	−	0.879795i	$-0.657680\pi$
$11$	−34.6846			−0.950708			−0.475354	+	0.879795i	$0.657680\pi$
$12$		0			0
$13$	40.0348			0.854128			0.427064	−	0.904221i	$-0.359548\pi$
$13$	40.0348			0.854128			0.427064	+	0.904221i	$0.359548\pi$
$14$	5.28124	−	52.1163i	0.100819	−	0.994905i
$15$		0			0
$16$	−31.8196	+	55.5294i	−0.497181	+	0.867647i
$17$	−76.5612			−1.09228			−0.546142	−	0.837693i	$-0.683904\pi$
$17$	−76.5612			−1.09228			−0.546142	+	0.837693i	$0.683904\pi$
$18$		0			0
$19$	3.05838			0.0369285			0.0184642	−	0.999830i	$-0.494122\pi$
$19$	3.05838			0.0369285			0.0184642	+	0.999830i	$0.494122\pi$
$20$	146.637	−	84.9789i	1.63945	−	0.950093i
$21$		0			0
$22$	84.9993	+	48.9823i	0.823723	+	0.474684i
$23$			181.651i			1.64682i	0.567445	+	0.823411i	$0.307932\pi$
$23$			181.651i			1.64682i	−0.567445	+	0.823411i	$0.692068\pi$
$24$		0			0
$25$	−323.808			−2.59046
$26$	−98.1109	−	56.5380i	−0.740043	−	0.426462i
$27$		0			0
$28$	−86.5422	+	120.260i	−0.584105	+	0.811678i
$29$	−79.6686			−0.510141			−0.255070	−	0.966922i	$-0.582099\pi$
$29$	−79.6686			−0.510141			−0.255070	+	0.966922i	$0.582099\pi$
$30$		0			0
$31$			25.5766i			0.148183i	0.997251	+	0.0740917i	$0.0236058\pi$
$31$			25.5766i			0.148183i	−0.997251	+	0.0740917i	$0.976394\pi$
$32$	156.398	−	91.1462i	0.863986	−	0.503516i
$33$		0			0
$34$	187.624	+	108.121i	0.946389	+	0.545373i
$35$	357.966	−	160.629i	1.72878	−	0.775750i
$36$		0			0
$37$		−	162.762i		−	0.723185i	−0.932336	−	0.361593i	$-0.882233\pi$
$37$		−	162.762i		−	0.723185i	0.932336	−	0.361593i	$-0.117767\pi$
$38$	−7.49499	−	4.31911i	−0.0319960	−	0.0184382i
$39$		0			0
$40$	−479.362	+	1.16922i	−1.89485	+	0.00462175i
$41$	191.358			0.728905			0.364452	−	0.931222i	$-0.381256\pi$
$41$	191.358			0.728905			0.364452	+	0.931222i	$0.381256\pi$
$42$		0			0
$43$		−	385.956i		−	1.36878i	−0.729115	−	0.684392i	$-0.760068\pi$
$43$		−	385.956i		−	1.36878i	0.729115	−	0.684392i	$-0.239932\pi$
$44$	−139.129	−	240.076i	−0.476692	−	0.822563i
$45$		0			0
$46$	256.532	−	445.162i	0.822252	−	1.42686i
$47$	−199.255			−0.618391			−0.309195	−	0.950999i	$-0.600060\pi$
$47$	−199.255			−0.618391			−0.309195	+	0.950999i	$0.600060\pi$
$48$		0			0
$49$	−228.021	+	256.233i	−0.664786	+	0.747034i
$50$	793.537	+	457.289i	2.24446	+	1.29341i
$51$		0			0
$52$	160.590	+	277.109i	0.428266	+	0.739001i
$53$	−490.879			−1.27222			−0.636108	−	0.771600i	$-0.719457\pi$
$53$	−490.879			−1.27222			−0.636108	+	0.771600i	$0.719457\pi$
$54$		0			0
$55$			734.795i			1.80145i
$56$	381.917	−	172.497i	0.911354	−	0.411623i
$57$		0			0
$58$	195.239	+	112.510i	0.442002	+	0.254711i
$59$			811.088i			1.78974i	0.446327	+	0.894870i	$0.352732\pi$
$59$			811.088i			1.78974i	−0.446327	+	0.894870i	$0.647268\pi$
$60$		0			0
$61$	−165.593			−0.347575			−0.173787	−	0.984783i	$-0.555601\pi$
$61$	−165.593			−0.347575			−0.173787	+	0.984783i	$0.555601\pi$
$62$	36.1198	−	62.6789i	0.0739874	−	0.128391i
$63$		0			0
$64$	−511.994	+	2.49764i	−0.999988	+	0.00487820i
$65$		−	848.141i		−	1.61845i
$66$		0			0
$67$			632.062i			1.15252i	0.817268	+	0.576258i	$0.195488\pi$
$67$			632.062i			1.15252i	−0.817268	+	0.576258i	$0.804512\pi$
$68$	−307.107	−	529.933i	−0.547679	−	0.945056i
$69$		0			0
$70$	−1104.09	−	111.884i	−1.88520	−	0.191038i
$71$			618.163i			1.03327i	0.856205	+	0.516637i	$0.172816\pi$
$71$			618.163i			1.03327i	−0.856205	+	0.516637i	$0.827184\pi$
$72$		0			0
$73$		−	279.677i		−	0.448407i	−0.974542	−	0.224203i	$-0.928022\pi$
$73$		−	279.677i		−	0.448407i	0.974542	−	0.224203i	$-0.0719780\pi$
$74$	−229.856	+	398.870i	−0.361083	+	0.626591i
$75$		0			0
$76$	12.2680	+	21.1692i	0.0185162	+	0.0319509i
$77$	−262.984	−	586.067i	−0.389218	−	0.867384i
$78$		0			0
$79$	598.872			0.852891			0.426445	−	0.904513i	$-0.359766\pi$
$79$	598.872			0.852891			0.426445	+	0.904513i	$0.359766\pi$
$80$	1176.40	+	674.101i	1.64406	+	0.942084i
$81$		0			0
$82$	−468.949	−	270.240i	−0.631546	−	0.363939i
$83$			52.2938i			0.0691565i	0.999402	+	0.0345783i	$0.0110088\pi$
$83$			52.2938i			0.0691565i	−0.999402	+	0.0345783i	$0.988991\pi$
$84$		0			0
$85$			1621.96i			2.06972i
$86$	−545.055	+	945.838i	−0.683428	+	1.18596i
$87$		0			0
$88$	1.91426	+	784.819i	0.00231888	+	0.950705i
$89$	1287.23			1.53310			0.766552	−	0.642183i	$-0.221971\pi$
$89$	1287.23			1.53310			0.766552	+	0.642183i	$0.221971\pi$
$90$		0			0
$91$	303.551	+	676.471i	0.349679	+	0.779268i
$92$	−1257.33	+	728.651i	−1.42485	+	0.825729i
$93$		0			0
$94$	488.303	+	281.393i	0.535793	+	0.308760i
$95$		−	64.7921i		−	0.0699740i
$96$		0			0
$97$			1821.05i			1.90618i	0.302681	+	0.953092i	$0.402118\pi$
$97$			1821.05i			1.90618i	−0.302681	+	0.953092i	$0.597882\pi$
$98$	920.656	−	305.917i	0.948982	−	0.315329i
$99$		0			0
$100$	−1298.88	−	2241.30i	−1.29888	−	2.24130i
$101$			1598.46i			1.57478i	0.616453	+	0.787392i	$0.288569\pi$
$101$			1598.46i			1.57478i	−0.616453	+	0.787392i	$0.711431\pi$
$102$		0			0
$103$			598.346i			0.572396i	0.958171	+	0.286198i	$0.0923915\pi$
$103$			598.346i			0.572396i	−0.958171	+	0.286198i	$0.907608\pi$
$104$	−2.20955	−	905.882i	−0.00208331	−	0.854125i
$105$		0			0
$106$	1202.97	+	693.230i	1.10229	+	0.635212i
$107$	−692.414			−0.625591			−0.312795	−	0.949821i	$-0.601265\pi$
$107$	−692.414			−0.625591			−0.312795	+	0.949821i	$0.601265\pi$
$108$		0			0
$109$		−	1210.00i		−	1.06327i	−0.846972	−	0.531637i	$-0.821577\pi$
$109$		−	1210.00i		−	1.06327i	0.846972	−	0.531637i	$-0.178423\pi$
$110$	1037.69	−	1800.72i	0.899457	−	1.56083i
$111$		0			0
$112$	−1179.55	−	116.624i	−0.995148	−	0.0983924i
$113$		−	738.014i		−	0.614394i	−0.951646	−	0.307197i	$-0.900609\pi$
$113$		−	738.014i		−	0.614394i	0.951646	−	0.307197i	$-0.0993911\pi$
$114$		0			0
$115$	3848.30			3.12049
$116$	−319.571	−	551.441i	−0.255788	−	0.441379i
$117$		0			0
$118$	1145.44	−	1987.68i	0.893609	−	1.55069i
$119$	−580.500	−	1293.66i	−0.447179	−	0.996551i
$120$		0			0
$121$	−127.982			−0.0961547
$122$	405.809	+	233.854i	0.301150	+	0.173542i
$123$		0			0
$124$	−177.033	+	102.594i	−0.128210	+	0.0743003i
$125$			4211.77i			3.01369i
$126$		0			0
$127$	−166.510			−0.116341			−0.0581707	−	0.998307i	$-0.518527\pi$
$127$	−166.510			−0.116341			−0.0581707	+	0.998307i	$0.518527\pi$
$128$	1258.24	+	716.928i	0.868857	+	0.495063i
$129$		0			0
$130$	−1197.76	+	2078.49i	−0.808083	+	1.40227i
$131$			414.302i			0.276319i	0.990410	+	0.138159i	$0.0441186\pi$
$131$			414.302i			0.276319i	−0.990410	+	0.138159i	$0.955881\pi$
$132$		0			0
$133$	23.1892	+	51.6777i	0.0151185	+	0.0336919i
$134$	892.611	−	1548.95i	0.575447	−	0.998577i
$135$		0			0
$136$	4.22547	+	1732.38i	0.00266420	+	1.09228i
$137$			2462.32i			1.53555i	0.640722	+	0.767773i	$0.278635\pi$
$137$			2462.32i			1.53555i	−0.640722	+	0.767773i	$0.721365\pi$
$138$		0			0
$139$	−332.412			−0.202840			−0.101420	−	0.994844i	$-0.532339\pi$
$139$	−332.412			−0.202840			−0.101420	+	0.994844i	$0.532339\pi$
$140$	2547.72	+	1833.40i	1.53801	+	1.10679i
$141$		0			0
$142$	872.983	−	1514.89i	0.515909	−	0.895261i
$143$	−1388.59			−0.812026
$144$		0			0
$145$			1687.79i			0.966641i
$146$	−394.966	+	685.387i	−0.223888	+	0.388514i
$147$		0			0
$148$	1126.59	−	652.879i	0.625708	−	0.362611i
$149$	812.037			0.446474			0.223237	−	0.974764i	$-0.428338\pi$
$149$	812.037			0.446474			0.223237	+	0.974764i	$0.428338\pi$
$150$		0			0
$151$	−893.543			−0.481559			−0.240780	−	0.970580i	$-0.577403\pi$
$151$	−893.543			−0.481559			−0.240780	+	0.970580i	$0.577403\pi$
$152$	−0.168794	−	69.2031i	−9.00724e−5	−	0.0369283i
$153$		0			0
$154$	−183.178	+	1807.63i	−0.0958498	+	0.945864i
$155$	541.842			0.280786
$156$		0			0
$157$	894.542			0.454728			0.227364	−	0.973810i	$-0.426989\pi$
$157$	894.542			0.454728			0.227364	+	0.973810i	$0.426989\pi$
$158$	−1467.62	−	845.740i	−0.738971	−	0.425845i
$159$		0			0
$160$	−1930.94	−	3313.31i	−0.954089	−	1.63713i
$161$	−3069.37	+	1377.31i	−1.50249	+	0.674207i
$162$		0			0
$163$		−	1039.42i		−	0.499473i	−0.968314	−	0.249736i	$-0.919656\pi$
$163$		−	1039.42i		−	0.499473i	0.968314	−	0.249736i	$-0.0803439\pi$
$164$	767.587	+	1324.52i	0.365478	+	0.630657i
$165$		0			0
$166$	73.8504	−	128.153i	0.0345295	−	0.0599194i
$167$	2025.47			0.938537			0.469269	−	0.883055i	$-0.344518\pi$
$167$	2025.47			0.938537			0.469269	+	0.883055i	$0.344518\pi$
$168$		0			0
$169$	−594.214			−0.270466
$170$	2290.56	−	3974.83i	1.03340	−	1.79327i
$171$		0			0
$172$	2671.46	−	1548.17i	1.18429	−	0.686318i
$173$			678.349i			0.298115i	0.988829	+	0.149058i	$0.0476240\pi$
$173$			678.349i			0.298115i	−0.988829	+	0.149058i	$0.952376\pi$
$174$		0			0
$175$	−2455.17	−	5471.41i	−1.06053	−	2.36342i
$176$	1103.65	−	1926.01i	0.472674	−	0.824879i
$177$		0			0
$178$	−3154.54	−	1817.85i	−1.32833	−	0.765472i
$179$	−3481.81			−1.45387			−0.726936	−	0.686706i	$-0.759056\pi$
$179$	−3481.81			−1.45387			−0.726936	+	0.686706i	$0.759056\pi$
$180$		0			0
$181$	−1541.69			−0.633109			−0.316555	−	0.948574i	$-0.602526\pi$
$181$	−1541.69			−0.633109			−0.316555	+	0.948574i	$0.602526\pi$
$182$	211.434	−	2086.47i	0.0861127	−	0.849776i
$183$		0			0
$184$	4110.29	−	10.0255i	1.64682	−	0.00401678i
$185$	−3448.12			−1.37033
$186$		0			0
$187$	2655.49			1.03844
$188$	−799.265	−	1379.18i	−0.310066	−	0.535039i
$189$		0			0
$190$	−91.5008	+	158.782i	−0.0349377	+	0.0606277i
$191$		−	3772.38i		−	1.42911i	−0.699580	−	0.714554i	$-0.746630\pi$
$191$		−	3772.38i		−	1.42911i	0.699580	−	0.714554i	$-0.253370\pi$
$192$		0			0
$193$	1514.61			0.564891			0.282445	−	0.959283i	$-0.408854\pi$
$193$	1514.61			0.564891			0.282445	+	0.959283i	$0.408854\pi$
$194$	2571.73	−	4462.74i	0.951749	−	1.65158i
$195$		0			0
$196$	−2688.22	−	550.478i	−0.979671	−	0.200611i
$197$	−3631.15			−1.31324			−0.656621	−	0.754220i	$-0.728015\pi$
$197$	−3631.15			−1.31324			−0.656621	+	0.754220i	$0.728015\pi$
$198$		0			0
$199$		−	2271.88i		−	0.809293i	−0.914473	−	0.404646i	$-0.867395\pi$
$199$		−	2271.88i		−	0.809293i	0.914473	−	0.404646i	$-0.132605\pi$
$200$	17.8712	+	7326.92i	0.00631842	+	2.59046i
$201$		0			0
$202$	2257.39	−	3917.26i	0.786283	−	1.36444i
$203$	−604.060	−	1346.16i	−0.208851	−	0.465430i
$204$		0			0
$205$		−	4053.94i		−	1.38117i
$206$	844.997	−	1466.33i	0.285795	−	0.495942i
$207$		0			0
$208$	−1273.89	+	2223.11i	−0.424656	+	0.741081i
$209$	−106.079			−0.0351082
$210$		0			0
$211$			5972.67i			1.94870i	0.225037	+	0.974350i	$0.427750\pi$
$211$			5972.67i			1.94870i	−0.225037	+	0.974350i	$0.572250\pi$
$212$	−1969.05	−	3397.71i	−0.637899	−	1.10074i
$213$		0			0
$214$	1696.86	+	977.842i	0.542032	+	0.312355i
$215$	−8176.50			−2.59364
$216$		0			0
$217$	−432.169	+	193.926i	−0.135196	+	0.0606661i
$218$	−1708.79	+	2965.27i	−0.530888	+	0.921254i
$219$		0			0
$220$	−5086.03	+	2947.46i	−1.55864	+	0.903261i
$221$	−3065.11			−0.932950
$222$		0			0
$223$			404.511i			0.121471i	0.998154	+	0.0607356i	$0.0193446\pi$
$223$			404.511i			0.121471i	−0.998154	+	0.0607356i	$0.980655\pi$
$224$	2725.94	+	1951.58i	0.813101	+	0.582123i
$225$		0			0
$226$	−1042.24	+	1808.61i	−0.306764	+	0.532330i
$227$		−	3627.98i		−	1.06078i	−0.847754	−	0.530390i	$-0.822045\pi$
$227$		−	3627.98i		−	1.06078i	0.847754	−	0.530390i	$-0.177955\pi$
$228$		0			0
$229$	−5078.24			−1.46541			−0.732707	−	0.680544i	$-0.761743\pi$
$229$	−5078.24			−1.46541			−0.732707	+	0.680544i	$0.761743\pi$
$230$	−9430.79	−	5434.65i	−2.70369	−	1.55805i
$231$		0			0
$232$	4.39696	+	1802.69i	0.00124429	+	0.510139i
$233$			1456.59i			0.409548i	0.978809	+	0.204774i	$0.0656459\pi$
$233$			1456.59i			0.409548i	−0.978809	+	0.204774i	$0.934354\pi$
$234$		0			0
$235$			4221.24i			1.17176i
$236$	−5614.10	+	3253.48i	−1.54850	+	0.897389i
$237$		0			0
$238$	−404.339	+	3990.09i	−0.110123	+	1.08672i
$239$		−	5261.69i		−	1.42406i	−0.702149	−	0.712030i	$-0.747776\pi$
$239$		−	5261.69i		−	1.42406i	0.702149	−	0.712030i	$-0.252224\pi$
$240$		0			0
$241$		−	4776.22i		−	1.27661i	−0.769783	−	0.638306i	$-0.779635\pi$
$241$		−	4776.22i		−	1.27661i	0.769783	−	0.638306i	$-0.220365\pi$
$242$	313.637	+	180.739i	0.0833114	+	0.0480096i
$243$		0			0
$244$	−664.238	−	1146.19i	−0.174276	−	0.300725i
$245$	5428.31	+	4830.66i	1.41552	+	1.25967i
$246$		0			0
$247$	122.442			0.0315416
$248$	578.730	−	1.41159i	0.148183	−	0.000361435i
$249$		0			0
$250$	5947.95	−	10321.5i	1.50472	−	2.61116i
$251$		−	2707.08i		−	0.680754i	−0.940289	−	0.340377i	$-0.889445\pi$
$251$		−	2707.08i		−	0.680754i	0.940289	−	0.340377i	$-0.110555\pi$
$252$		0			0
$253$		−	6300.50i		−	1.56565i
$254$	408.056	+	235.149i	0.100802	+	0.0580888i
$255$		0			0
$256$	−2071.03	−	3533.84i	−0.505622	−	0.862755i
$257$	6235.13			1.51337			0.756686	−	0.653778i	$-0.226817\pi$
$257$	6235.13			1.51337			0.756686	+	0.653778i	$0.226817\pi$
$258$		0			0
$259$	2750.19	−	1234.09i	0.659802	−	0.296071i
$260$	5870.57	−	3402.11i	1.40030	−	0.811501i
$261$		0			0
$262$	585.087	−	1015.31i	0.137965	−	0.239411i
$263$			401.960i			0.0942431i	0.998889	+	0.0471215i	$0.0150048\pi$
$263$			401.960i			0.0942431i	−0.998889	+	0.0471215i	$0.984995\pi$
$264$		0			0
$265$			10399.3i			2.41066i
$266$	16.1521	−	159.391i	0.00372311	−	0.0367403i
$267$		0			0
$268$	−4374.93	+	2535.36i	−0.997170	+	0.577881i
$269$		−	3612.69i		−	0.818847i	−0.912345	−	0.409423i	$-0.865730\pi$
$269$		−	3612.69i		−	0.818847i	0.912345	−	0.409423i	$-0.134270\pi$
$270$		0			0
$271$			2392.24i			0.536229i	0.963387	+	0.268115i	$0.0864006\pi$
$271$			2392.24i			0.536229i	−0.963387	+	0.268115i	$0.913599\pi$
$272$	2436.15	−	4251.40i	0.543063	−	0.947717i
$273$		0			0
$274$	3477.34	−	6034.25i	0.766692	−	1.33045i
$275$	11231.1			2.46277
$276$		0			0
$277$			7905.15i			1.71471i	0.514726	+	0.857355i	$0.327894\pi$
$277$			7905.15i			1.71471i	−0.514726	+	0.857355i	$0.672106\pi$
$278$	814.622	+	469.439i	0.175747	+	0.101277i
$279$		0			0
$280$	−3654.36	−	8090.95i	−0.779964	−	1.72688i
$281$		−	6507.60i		−	1.38153i	−0.723078	−	0.690767i	$-0.757273\pi$
$281$		−	6507.60i		−	1.38153i	0.723078	−	0.690767i	$-0.242727\pi$
$282$		0			0
$283$	2385.57			0.501086			0.250543	−	0.968106i	$-0.419391\pi$
$283$	2385.57			0.501086			0.250543	+	0.968106i	$0.419391\pi$
$284$	−4278.73	+	2479.61i	−0.894000	+	0.518091i
$285$		0			0
$286$	3402.93	+	1961.00i	0.703565	+	0.405441i
$287$	1450.91	+	3233.39i	0.298413	+	0.665020i
$288$		0			0
$289$	948.621			0.193084
$290$	2383.53	−	4136.15i	0.482640	−	0.837529i
$291$		0			0
$292$	1935.84	−	1121.86i	0.387967	−	0.224835i
$293$			4825.82i			0.962210i	0.876663	+	0.481105i	$0.159764\pi$
$293$			4825.82i			0.962210i	−0.876663	+	0.481105i	$0.840236\pi$
$294$		0			0
$295$	17183.0			3.39129
$296$	−3682.87	+	8.98293i	−0.723183	+	0.00176393i
$297$		0			0
$298$	−1990.01	−	1146.78i	−0.386839	−	0.222923i
$299$			7272.38i			1.40660i
$300$		0			0
$301$	6521.52	−	2926.38i	1.24882	−	0.560378i
$302$	2189.75	+	1261.88i	0.417238	+	0.240441i
$303$		0			0
$304$	−97.3164	+	169.830i	−0.0183601	+	0.0320409i
$305$			3508.11i			0.658602i
$306$		0			0
$307$	414.961			0.0771435			0.0385718	−	0.999256i	$-0.487719\pi$
$307$	414.961			0.0771435			0.0385718	+	0.999256i	$0.487719\pi$
$308$	3001.68	−	4171.16i	0.555313	−	0.771669i
$309$		0			0
$310$	−1327.86	−	765.201i	−0.243282	−	0.140195i
$311$	−9767.89			−1.78099			−0.890493	−	0.454998i	$-0.849640\pi$
$311$	−9767.89			−1.78099			−0.890493	+	0.454998i	$0.849640\pi$
$312$		0			0
$313$		−	7636.60i		−	1.37906i	−0.724257	−	0.689531i	$-0.757817\pi$
$313$		−	7636.60i		−	1.37906i	0.724257	−	0.689531i	$-0.242183\pi$
$314$	−2192.20	−	1263.29i	−0.393990	−	0.227044i
$315$		0			0
$316$	2402.23	+	4145.21i	0.427646	+	0.737931i
$317$	−2580.26			−0.457168			−0.228584	−	0.973524i	$-0.573409\pi$
$317$	−2580.26			−0.457168			−0.228584	+	0.973524i	$0.573409\pi$
$318$		0			0
$319$	2763.27			0.484995
$320$	52.9127	+	10846.6i	0.00924346	+	1.89483i
$321$		0			0
$322$	9466.99	+	959.345i	1.63843	+	0.166032i
$323$	−234.153			−0.0403364
$324$		0			0
$325$	−12963.6			−2.21259
$326$	−1467.90	+	2547.25i	−0.249385	+	0.432759i
$327$		0			0
$328$	−10.5612	−	4329.92i	−0.00177788	−	0.728903i
$329$	−1510.79	−	3366.83i	−0.253168	−	0.564192i
$330$		0			0
$331$		−	3338.88i		−	0.554445i	−0.960806	−	0.277223i	$-0.910586\pi$
$331$		−	3338.88i		−	0.554445i	0.960806	−	0.277223i	$-0.0894140\pi$
$332$	−361.961	+	209.764i	−0.0598350	+	0.0346756i
$333$		0			0
$334$	−4963.70	−	2860.42i	−0.813178	−	0.468608i
$335$	13390.3			2.18385
$336$		0			0
$337$	619.770			0.100181			0.0500906	−	0.998745i	$-0.484049\pi$
$337$	619.770			0.100181			0.0500906	+	0.998745i	$0.484049\pi$
$338$	1456.20	+	839.162i	0.234340	+	0.135043i
$339$		0			0
$340$	−11226.7	+	6506.09i	−1.79074	+	1.03777i
$341$		−	887.112i		−	0.140879i
$342$		0			0
$343$	−6058.48	−	1910.09i	−0.953723	−	0.300686i
$344$	−8733.15	+	21.3011i	−1.36878	+	0.00333861i
$345$		0			0
$346$	957.979	−	1662.39i	0.148848	−	0.258296i
$347$	5312.40			0.821858			0.410929	−	0.911667i	$-0.365204\pi$
$347$	5312.40			0.821858			0.410929	+	0.911667i	$0.365204\pi$
$348$		0			0
$349$	−8996.20			−1.37982			−0.689908	−	0.723897i	$-0.742349\pi$
$349$	−8996.20			−1.37982			−0.689908	+	0.723897i	$0.742349\pi$
$350$	−1710.11	+	16875.7i	−0.261169	+	2.57727i
$351$		0			0
$352$	−5424.60	+	3161.37i	−0.821398	+	0.478697i
$353$	11852.7			1.78713			0.893566	−	0.448932i	$-0.148195\pi$
$353$	11852.7			1.78713			0.893566	+	0.448932i	$0.148195\pi$
$354$		0			0
$355$	13095.8			1.95790
$356$	5163.42	+	8909.81i	0.768709	+	1.32646i
$357$		0			0
$358$	8532.67	+	4917.09i	1.25968	+	0.725912i
$359$			9168.52i			1.34790i	0.738777	+	0.673950i	$0.235404\pi$
$359$			9168.52i			1.34790i	−0.738777	+	0.673950i	$0.764596\pi$
$360$		0			0
$361$	−6849.65			−0.998636
$362$	3778.12	+	2177.21i	0.548546	+	0.316109i
$363$		0			0
$364$	−3464.70	+	4814.58i	−0.498900	+	0.693277i
$365$	−5924.98			−0.849665
$366$		0			0
$367$		−	4679.82i		−	0.665625i	−0.942993	−	0.332813i	$-0.892002\pi$
$367$		−	4679.82i		−	0.665625i	0.942993	−	0.332813i	$-0.107998\pi$
$368$	−10087.0	−	5780.07i	−1.42886	−	0.818769i
$369$		0			0
$370$	8450.10	+	4869.51i	1.18730	+	0.684199i
$371$	−3721.93	−	8294.42i	−0.520844	−	1.16071i
$372$		0			0
$373$			3237.88i			0.449467i	0.974420	+	0.224734i	$0.0721512\pi$
$373$			3237.88i			0.449467i	−0.974420	+	0.224734i	$0.927849\pi$
$374$	−6507.65	−	3750.14i	−0.899740	−	0.518490i
$375$		0			0
$376$	10.9970	+	4508.62i	0.00150832	+	0.618389i
$377$	−3189.52			−0.435725
$378$		0			0
$379$		−	2473.40i		−	0.335224i	−0.985853	−	0.167612i	$-0.946394\pi$
$379$		−	2473.40i		−	0.335224i	0.985853	−	0.167612i	$-0.0536055\pi$
$380$	448.471	−	259.898i	0.0605423	−	0.0350855i
$381$		0			0
$382$	−5327.43	+	9244.73i	−0.713547	+	1.23822i
$383$	−8396.19			−1.12017			−0.560085	−	0.828435i	$-0.689232\pi$
$383$	−8396.19			−1.12017			−0.560085	+	0.828435i	$0.689232\pi$
$384$		0			0
$385$	−12415.9	+	5571.34i	−1.64356	+	0.737511i
$386$	−3711.76	−	2138.96i	−0.489439	−	0.282048i
$387$		0			0
$388$	−12604.8	+	7304.71i	−1.64925	+	0.955775i
$389$	−1094.01			−0.142593			−0.0712966	−	0.997455i	$-0.522714\pi$
$389$	−1094.01			−0.142593			−0.0712966	+	0.997455i	$0.522714\pi$
$390$		0			0
$391$		−	13907.4i		−	1.79880i
$392$	5810.45	+	5145.38i	0.748653	+	0.662962i
$393$		0			0
$394$	8898.64	+	5127.99i	1.13783	+	0.655696i
$395$		−	12687.2i		−	1.61610i
$396$		0			0
$397$	−9534.52			−1.20535			−0.602675	−	0.797987i	$-0.705899\pi$
$397$	−9534.52			−1.20535			−0.602675	+	0.797987i	$0.705899\pi$
$398$	−3208.40	+	5567.56i	−0.404076	+	0.701197i
$399$		0			0
$400$	10303.4	−	17980.9i	1.28793	−	2.24761i
$401$		−	2554.19i		−	0.318081i	−0.987272	−	0.159040i	$-0.949160\pi$
$401$		−	2554.19i		−	0.318081i	0.987272	−	0.159040i	$-0.0508400\pi$
$402$		0			0
$403$			1023.95i			0.126568i
$404$	−11064.1	+	6411.86i	−1.36252	+	0.789609i
$405$		0			0
$406$	−420.749	+	4152.03i	−0.0514321	+	0.507541i
$407$			5645.32i			0.687538i
$408$		0			0
$409$			5080.09i			0.614167i	0.951683	+	0.307084i	$0.0993532\pi$
$409$			5080.09i			0.614167i	−0.951683	+	0.307084i	$0.900647\pi$
$410$	−5725.06	+	9934.73i	−0.689611	+	1.19669i
$411$		0			0
$412$	−4141.57	+	2400.12i	−0.495243	+	0.287004i
$413$	−13705.0	+	6149.80i	−1.63288	+	0.732717i
$414$		0			0
$415$	1107.85			0.131041
$416$	6261.37	−	3649.02i	0.737954	−	0.430067i
$417$		0			0
$418$	259.960	+	149.806i	0.0304188	+	0.0175294i
$419$		−	9210.28i		−	1.07387i	−0.843623	−	0.536935i	$-0.819582\pi$
$419$		−	9210.28i		−	1.07387i	0.843623	−	0.536935i	$-0.180418\pi$
$420$		0			0
$421$			9284.04i			1.07477i	0.843338	+	0.537383i	$0.180587\pi$
$421$			9284.04i			1.07477i	−0.843338	+	0.537383i	$0.819413\pi$
$422$	8434.74	−	14636.9i	0.972978	−	1.68842i
$423$		0			0
$424$	27.0920	+	11107.3i	0.00310307	+	1.27221i
$425$	24791.1			2.82952
$426$		0			0
$427$	−1255.56	−	2798.04i	−0.142297	−	0.317112i
$428$	−2777.45	−	4792.68i	−0.313676	−	0.541268i
$429$		0			0
$430$	20037.7	+	11547.0i	2.24721	+	1.29499i
$431$			14348.9i			1.60363i	0.597574	+	0.801814i	$0.296131\pi$
$431$			14348.9i			1.60363i	−0.597574	+	0.801814i	$0.703869\pi$
$432$		0			0
$433$			7019.84i			0.779104i	0.921004	+	0.389552i	$0.127370\pi$
$433$			7019.84i			0.779104i	−0.921004	+	0.389552i	$0.872630\pi$
$434$	1332.96	+	135.076i	0.147428	+	0.0149398i
$435$		0			0
$436$	8375.24	−	4853.62i	0.919957	−	0.533134i
$437$			555.559i			0.0608146i
$438$		0			0
$439$			13744.5i			1.49428i	0.664667	+	0.747139i	$0.268573\pi$
$439$			13744.5i			1.49428i	−0.664667	+	0.747139i	$0.731427\pi$
$440$	16626.5	−	40.5539i	1.80145	−	0.00439393i
$441$		0			0
$442$	7511.49	+	4328.62i	0.808337	+	0.465818i
$443$	4282.17			0.459259			0.229630	−	0.973278i	$-0.426249\pi$
$443$	4282.17			0.459259			0.229630	+	0.973278i	$0.426249\pi$
$444$		0			0
$445$		−	27270.1i		−	2.90500i
$446$	571.259	−	991.311i	0.0606500	−	0.105246i
$447$		0			0
$448$	−3924.23	−	8632.26i	−0.413844	−	0.910348i
$449$			239.688i			0.0251929i	0.999921	+	0.0125964i	$0.00400967\pi$
$449$			239.688i			0.0251929i	−0.999921	+	0.0125964i	$0.995990\pi$
$450$		0			0
$451$	−6637.17			−0.692975
$452$	5108.30	−	2960.37i	0.531581	−	0.308062i
$453$		0			0
$454$	−5123.51	+	8890.86i	−0.529643	+	0.919094i
$455$	14331.1	−	6430.75i	1.47660	−	0.662589i
$456$		0			0
$457$	−4705.34			−0.481633			−0.240817	−	0.970571i	$-0.577415\pi$
$457$	−4705.34			−0.481633			−0.240817	+	0.970571i	$0.577415\pi$
$458$	12444.9	+	7171.61i	1.26968	+	0.731675i
$459$		0			0
$460$	15436.5	+	26636.7i	1.56463	+	2.69988i
$461$		−	8816.96i		−	0.890774i	−0.895338	−	0.445387i	$-0.853066\pi$
$461$		−	8816.96i		−	0.890774i	0.895338	−	0.445387i	$-0.146934\pi$
$462$		0			0
$463$	−13333.2			−1.33833			−0.669166	−	0.743113i	$-0.733349\pi$
$463$	−13333.2			−1.33833			−0.669166	+	0.743113i	$0.733349\pi$
$464$	2535.02	−	4423.95i	0.253632	−	0.442622i
$465$		0			0
$466$	2057.03	−	3569.59i	0.204485	−	0.354845i
$467$		−	6893.25i		−	0.683044i	−0.939874	−	0.341522i	$-0.889058\pi$
$467$		−	6893.25i		−	0.683044i	0.939874	−	0.341522i	$-0.110942\pi$
$468$		0			0
$469$	−10680.0	+	4792.40i	−1.05151	+	0.471839i
$470$	5961.33	−	10344.7i	0.585054	−	1.01525i
$471$		0			0
$472$	18352.8	−	44.7645i	1.78973	−	0.00436536i
$473$			13386.7i			1.30131i
$474$		0			0
$475$	−990.328			−0.0956619
$476$	6625.78	−	9207.25i	0.638008	−	0.886583i
$477$		0			0
$478$	−7430.67	+	12894.5i	−0.711027	+	1.23385i
$479$	6071.06			0.579110			0.289555	−	0.957161i	$-0.406493\pi$
$479$	6071.06			0.579110			0.289555	+	0.957161i	$0.406493\pi$
$480$		0			0
$481$		−	6516.13i		−	0.617692i
$482$	−6745.09	+	11704.8i	−0.637407	+	1.10610i
$483$		0			0
$484$	−513.369	−	885.851i	−0.0482127	−	0.0831941i
$485$	38579.2			3.61194
$486$		0			0
$487$	−10085.1			−0.938397			−0.469198	−	0.883093i	$-0.655457\pi$
$487$	−10085.1			−0.938397			−0.469198	+	0.883093i	$0.655457\pi$
$488$	9.13920	+	3746.94i	0.000847771	+	0.347573i
$489$		0			0
$490$	−6480.88	−	19504.2i	−0.597503	−	1.79818i
$491$	−11027.2			−1.01354			−0.506772	−	0.862080i	$-0.669161\pi$
$491$	−11027.2			−1.01354			−0.506772	+	0.862080i	$0.669161\pi$
$492$		0			0
$493$	6099.52			0.557218
$494$	−300.060	−	172.915i	−0.0273287	−	0.0157486i
$495$		0			0
$496$	−1420.25	−	813.836i	−0.128571	−	0.0736740i
$497$	−10445.1	+	4687.01i	−0.942713	+	0.423021i
$498$		0			0
$499$		−	3102.73i		−	0.278352i	−0.990268	−	0.139176i	$-0.955555\pi$
$499$		−	3102.73i		−	0.278352i	0.990268	−	0.139176i	$-0.0444453\pi$
$500$	−29152.5	+	16894.5i	−2.60748	+	1.51109i
$501$		0			0
$502$	−3822.99	+	6634.07i	−0.339898	+	0.589827i
$503$	−5879.25			−0.521158			−0.260579	−	0.965452i	$-0.583913\pi$
$503$	−5879.25			−0.521158			−0.260579	+	0.965452i	$0.583913\pi$
$504$		0			0
$505$	33863.6			2.98398
$506$	−8897.70	+	15440.2i	−0.781721	+	1.35653i
$507$		0			0
$508$	−667.915	−	1152.53i	−0.0583345	−	0.100660i
$509$		−	20971.1i		−	1.82618i	−0.407756	−	0.913091i	$-0.633689\pi$
$509$		−	20971.1i		−	1.82618i	0.407756	−	0.913091i	$-0.366311\pi$
$510$		0			0
$511$	4725.72	−	2120.56i	0.409107	−	0.183577i
$512$	84.7722	+	11584.9i	0.00731726	+	0.999973i
$513$		0			0
$514$	−15280.1	−	8805.39i	−1.31123	−	0.755621i
$515$	12676.0			1.08461
$516$		0			0
$517$	6911.08			0.587909
$518$	−8482.54	−	859.584i	−0.719500	−	0.0729111i
$519$		0			0
$520$	−19191.2	+	46.8095i	−1.61844	+	0.00394756i
$521$	18346.9			1.54278			0.771392	−	0.636360i	$-0.219561\pi$
$521$	18346.9			1.54278			0.771392	+	0.636360i	$0.219561\pi$
$522$		0			0
$523$	2876.39			0.240489			0.120245	−	0.992744i	$-0.461632\pi$
$523$	2876.39			0.240489			0.120245	+	0.992744i	$0.461632\pi$
$524$	−2867.67	+	1661.87i	−0.239074	+	0.138548i
$525$		0			0
$526$	567.657	−	985.059i	0.0470552	−	0.0816552i
$527$		−	1958.17i		−	0.161858i
$528$		0			0
$529$	−20830.2			−1.71202
$530$	14686.2	−	25485.0i	1.20363	−	2.08867i
$531$		0			0
$532$	−264.679	+	367.801i	−0.0215701	+	0.0299740i
$533$	7660.98			0.622578
$534$		0			0
$535$			14668.9i			1.18540i
$536$	14301.9	−	34.8839i	1.15251	−	0.00281111i
$537$		0			0
$538$	−5101.92	+	8853.40i	−0.408847	+	0.709475i
$539$	7908.82	−	8887.32i	0.632017	−	0.710211i
$540$		0			0
$541$		−	14029.6i		−	1.11493i	−0.830200	−	0.557465i	$-0.811774\pi$
$541$		−	14029.6i		−	1.11493i	0.830200	−	0.557465i	$-0.188226\pi$
$542$	3378.37	−	5862.51i	0.267737	−	0.464606i
$543$		0			0
$544$	−11974.0	+	6978.26i	−0.943718	+	0.549983i
$545$	−25633.9			−2.01475
$546$		0			0
$547$		−	2660.42i		−	0.207955i	−0.994580	−	0.103977i	$-0.966843\pi$
$547$		−	2660.42i		−	0.207955i	0.994580	−	0.103977i	$-0.0331570\pi$
$548$	−17043.4	+	9876.99i	−1.32857	+	0.769934i
$549$		0			0
$550$	−27523.5	−	15860.9i	−2.13383	−	1.22965i
$551$	−243.657			−0.0188387
$552$		0			0
$553$	4540.75	+	10119.2i	0.349172	+	0.778140i
$554$	11163.8	−	19372.7i	0.856147	−	1.48568i
$555$		0			0
$556$	−1333.39	−	2300.85i	−0.101706	−	0.175500i
$557$	−8706.57			−0.662315			−0.331157	−	0.943576i	$-0.607439\pi$
$557$	−8706.57			−0.662315			−0.331157	+	0.943576i	$0.607439\pi$
$558$		0			0
$559$		−	15451.7i		−	1.16912i
$560$	−2470.69	+	24988.8i	−0.186439	+	1.88566i
$561$		0			0
$562$	−9190.17	+	15947.8i	−0.689794	+	1.19700i
$563$			25257.4i			1.89071i	0.326041	+	0.945356i	$0.394285\pi$
$563$			25257.4i			1.89071i	−0.326041	+	0.945356i	$0.605715\pi$
$564$		0			0
$565$	−15634.9			−1.16419
$566$	−5846.16	−	3368.95i	−0.434156	−	0.250190i
$567$		0			0
$568$	13987.4	−	34.1168i	1.03327	−	0.00252026i
$569$			18513.7i			1.36403i	0.731336	+	0.682017i	$0.238897\pi$
$569$			18513.7i			1.36403i	−0.731336	+	0.682017i	$0.761103\pi$
$570$		0			0
$571$			15952.0i			1.16913i	0.811348	+	0.584564i	$0.198734\pi$
$571$			15952.0i			1.16913i	−0.811348	+	0.584564i	$0.801266\pi$
$572$	−5569.99	−	9611.39i	−0.407156	−	0.702574i
$573$		0			0
$574$	1010.61	−	9972.87i	0.0734878	−	0.725191i
$575$		−	58820.2i		−	4.26604i
$576$		0			0
$577$			17649.3i			1.27339i	0.771114	+	0.636697i	$0.219700\pi$
$577$			17649.3i			1.27339i	−0.771114	+	0.636697i	$0.780300\pi$
$578$	−2324.73	−	1339.66i	−0.167294	−	0.0964059i
$579$		0			0
$580$	−11682.3	+	6770.15i	−0.836349	+	0.484681i
$581$	−883.612	+	396.500i	−0.0630953	+	0.0283126i
$582$		0			0
$583$	17025.9			1.20951
$584$	−6328.35	+	15.4356i	−0.448406	+	0.00109371i
$585$		0			0
$586$	6815.13	−	11826.4i	0.480428	−	0.833690i
$587$		−	20281.0i		−	1.42604i	−0.701142	−	0.713021i	$-0.747326\pi$
$587$		−	20281.0i		−	1.42604i	0.701142	−	0.713021i	$-0.252674\pi$
$588$		0			0
$589$			78.2229i			0.00547219i
$590$	−42109.2	−	24266.2i	−2.93832	−	1.69326i
$591$		0			0
$592$	9038.06	+	5179.01i	0.627469	+	0.359554i
$593$	−2821.24			−0.195370			−0.0976852	−	0.995217i	$-0.531144\pi$
$593$	−2821.24			−0.195370			−0.0976852	+	0.995217i	$0.531144\pi$
$594$		0			0
$595$	−27406.3	+	12297.9i	−1.88832	+	0.847339i
$596$	3257.29	+	5620.67i	0.223865	+	0.386294i
$597$		0			0
$598$	10270.2	−	17822.0i	0.702308	−	1.21872i
$599$		−	10804.1i		−	0.736965i	−0.929635	−	0.368483i	$-0.879877\pi$
$599$		−	10804.1i		−	0.736965i	0.929635	−	0.368483i	$-0.120123\pi$
$600$		0			0
$601$		−	20731.4i		−	1.40707i	−0.710660	−	0.703536i	$-0.751604\pi$
$601$		−	20731.4i		−	1.40707i	0.710660	−	0.703536i	$-0.248396\pi$
$602$	−20114.6	−	2038.33i	−1.36181	−	0.138000i
$603$		0			0
$604$	−3584.23	−	6184.82i	−0.241457	−	0.416651i
$605$			2711.31i			0.182199i
$606$		0			0
$607$		−	1910.79i		−	0.127770i	−0.997957	−	0.0638852i	$-0.979651\pi$
$607$		−	1910.79i		−	0.127770i	0.997957	−	0.0638852i	$-0.0203492\pi$
$608$	478.325	−	278.760i	0.0319057	−	0.0185941i
$609$		0			0
$610$	4954.23	−	8597.11i	0.328837	−	0.570634i
$611$	−7977.15			−0.528185
$612$		0			0
$613$			7113.05i			0.468668i	0.972156	+	0.234334i	$0.0752909\pi$
$613$			7113.05i			0.468668i	−0.972156	+	0.234334i	$0.924709\pi$
$614$	−1016.92	−	586.016i	−0.0668396	−	0.0385174i
$615$		0			0
$616$	−13246.6	+	5982.98i	−0.866432	+	0.391333i
$617$		−	8852.59i		−	0.577621i	−0.957386	−	0.288810i	$-0.906740\pi$
$617$		−	8852.59i		−	0.577621i	0.957386	−	0.288810i	$-0.0932597\pi$
$618$		0			0
$619$	−1652.28			−0.107287			−0.0536437	−	0.998560i	$-0.517084\pi$
$619$	−1652.28			−0.107287			−0.0536437	+	0.998560i	$0.517084\pi$
$620$	2173.47	+	3750.46i	0.140788	+	0.242939i
$621$		0			0
$622$	23937.6	+	13794.4i	1.54310	+	0.889238i
$623$	9760.00	+	21750.4i	0.627650	+	1.39874i
$624$		0			0
$625$	48750.6			3.12004
$626$	−10784.6	+	18714.5i	−0.688559	+	1.19486i
$627$		0			0
$628$	3588.24	+	6191.74i	0.228004	+	0.393435i
$629$			12461.2i			0.789923i
$630$		0			0
$631$	7993.10			0.504279			0.252140	−	0.967691i	$-0.418866\pi$
$631$	7993.10			0.504279			0.252140	+	0.967691i	$0.418866\pi$
$632$	−33.0521	−	13550.9i	−0.00208029	−	0.852888i
$633$		0			0
$634$	6323.30	+	3643.91i	0.396104	+	0.228262i
$635$			3527.53i			0.220450i
$636$		0			0
$637$	−9128.80	+	10258.2i	−0.567812	+	0.638062i
$638$	−6771.77	−	3902.35i	−0.420215	−	0.242156i
$639$		0			0
$640$	15188.2	−	26655.9i	0.938071	−	1.64636i
$641$			4622.24i			0.284817i	0.989808	+	0.142408i	$0.0454846\pi$
$641$			4622.24i			0.284817i	−0.989808	+	0.142408i	$0.954515\pi$
$642$		0			0
$643$	−4207.35			−0.258043			−0.129022	−	0.991642i	$-0.541184\pi$
$643$	−4207.35			−0.258043			−0.129022	+	0.991642i	$0.541184\pi$
$644$	−21845.4	−	15720.5i	−1.33669	−	0.961917i
$645$		0			0
$646$	573.825	+	330.676i	0.0349487	+	0.0201398i
$647$	13738.8			0.834822			0.417411	−	0.908718i	$-0.362938\pi$
$647$	13738.8			0.834822			0.417411	+	0.908718i	$0.362938\pi$
$648$		0			0
$649$		−	28132.2i		−	1.70152i
$650$	31769.1	+	18307.5i	1.91706	+	1.10474i
$651$		0			0
$652$	7194.58	−	4169.40i	0.432149	−	0.250439i
$653$	−1083.79			−0.0649492			−0.0324746	−	0.999473i	$-0.510339\pi$
$653$	−1083.79			−0.0649492			−0.0324746	+	0.999473i	$0.510339\pi$
$654$		0			0
$655$	8777.03			0.523583
$656$	−6088.93	+	10626.0i	−0.362398	+	0.632432i
$657$		0			0
$658$	−1052.32	+	10384.4i	−0.0623458	+	0.615240i
$659$	−13466.6			−0.796030			−0.398015	−	0.917379i	$-0.630301\pi$
$659$	−13466.6			−0.796030			−0.398015	+	0.917379i	$0.630301\pi$
$660$		0			0
$661$	8956.78			0.527048			0.263524	−	0.964653i	$-0.415115\pi$
$661$	8956.78			0.527048			0.263524	+	0.964653i	$0.415115\pi$
$662$	−4715.24	+	8182.39i	−0.276832	+	0.480389i
$663$		0			0
$664$	1183.27	−	2.88613i	0.0691563	−	0.000168680i
$665$	1094.80	−	491.264i	0.0638411	−	0.0286472i
$666$		0			0
$667$		−	14471.9i		−	0.840111i
$668$	8124.70	+	14019.7i	0.470590	+	0.812033i
$669$		0			0
$670$	−32814.7	−	18910.0i	−1.89216	−	1.09039i
$671$	5743.53			0.330442
$672$		0			0
$673$	−15097.9			−0.864755			−0.432377	−	0.901693i	$-0.642325\pi$
$673$	−15097.9			−0.864755			−0.432377	+	0.901693i	$0.642325\pi$
$674$	−1518.83	−	875.253i	−0.0868001	−	0.0500200i
$675$		0			0
$676$	−2383.55	−	4112.96i	−0.135614	−	0.234010i
$677$		−	6316.41i		−	0.358581i	−0.983796	−	0.179290i	$-0.942620\pi$
$677$		−	6316.41i		−	0.358581i	0.983796	−	0.179290i	$-0.0573802\pi$
$678$		0			0
$679$	−30770.4	+	13807.5i	−1.73912	+	0.780389i
$680$	36700.6	−	89.5169i	2.06971	−	0.00504826i
$681$		0			0
$682$	−1252.80	+	2173.99i	−0.0703404	+	0.122062i
$683$	7973.40			0.446696			0.223348	−	0.974739i	$-0.428301\pi$
$683$	7973.40			0.446696			0.223348	+	0.974739i	$0.428301\pi$
$684$		0			0
$685$	52164.4			2.90963
$686$	12149.7	+	13236.9i	0.676205	+	0.736714i
$687$		0			0
$688$	21431.9	+	12280.9i	1.18762	+	0.680533i
$689$	−19652.3			−1.08664
$690$		0			0
$691$	−21774.4			−1.19875			−0.599377	−	0.800467i	$-0.704585\pi$
$691$	−21774.4			−1.19875			−0.599377	+	0.800467i	$0.704585\pi$
$692$	−4695.32	+	2721.04i	−0.257933	+	0.149477i
$693$		0			0
$694$	−13018.8	−	7502.29i	−0.712084	−	0.410350i
$695$			7042.18i			0.384353i
$696$		0			0
$697$	−14650.6			−0.796171
$698$	22046.4	+	12704.6i	1.19552	+	0.688936i
$699$		0			0
$700$	28023.1	−	38941.1i	1.51310	−	2.10262i
$701$	−20650.6			−1.11264			−0.556320	−	0.830968i	$-0.687787\pi$
$701$	−20650.6			−1.11264			−0.556320	+	0.830968i	$0.687787\pi$
$702$		0			0
$703$		−	497.787i		−	0.0267061i
$704$	17758.3	−	86.6294i	0.950697	−	0.00463774i
$705$		0			0
$706$	−29046.8	−	16738.7i	−1.54843	−	0.892307i
$707$	−27009.4	+	12119.8i	−1.43676	+	0.644714i
$708$		0			0
$709$			2585.40i			0.136949i	0.997653	+	0.0684745i	$0.0218132\pi$
$709$			2585.40i			0.136949i	−0.997653	+	0.0684745i	$0.978187\pi$
$710$	−32093.2	−	18494.2i	−1.69639	−	0.977571i
$711$		0			0
$712$	−71.0431	−	29126.6i	−0.00373940	−	1.53310i
$713$	−4646.02			−0.244032
$714$		0			0
$715$			29417.4i			1.53867i
$716$	−13966.5	−	24100.0i	−0.728982	−	1.25791i
$717$		0			0
$718$	12948.0	−	22468.7i	0.673000	−	1.16786i
$719$	−28992.4			−1.50380			−0.751901	−	0.659276i	$-0.770863\pi$
$719$	−28992.4			−1.50380			−0.751901	+	0.659276i	$0.770863\pi$
$720$		0			0
$721$	−10110.3	+	4536.76i	−0.522229	+	0.234338i
$722$	16786.0	+	9673.22i	0.865250	+	0.498615i
$723$		0			0
$724$	−6184.11	−	10671.1i	−0.317446	−	0.547773i
$725$	25797.3			1.32150
$726$		0			0
$727$		−	26205.1i		−	1.33685i	−0.743779	−	0.668426i	$-0.766968\pi$
$727$		−	26205.1i		−	1.33685i	0.743779	−	0.668426i	$-0.233032\pi$
$728$	15290.0	−	6905.88i	0.778413	−	0.351578i
$729$		0			0
$730$	14520.0	+	8367.38i	0.736176	+	0.424234i
$731$			29549.2i			1.49510i
$732$		0			0
$733$	26682.9			1.34455			0.672275	−	0.740302i	$-0.265317\pi$
$733$	26682.9			1.34455			0.672275	+	0.740302i	$0.265317\pi$
$734$	−6608.94	+	11468.5i	−0.332344	+	0.576719i
$735$		0			0
$736$	16556.8	+	28409.9i	0.829202	+	1.42283i
$737$		−	21922.8i		−	1.09571i
$738$		0			0
$739$		−	37027.6i		−	1.84314i	−0.388207	−	0.921572i	$-0.626905\pi$
$739$		−	37027.6i		−	1.84314i	0.388207	−	0.921572i	$-0.373095\pi$
$740$	−13831.3	−	23866.8i	−0.687093	−	1.18562i
$741$		0			0
$742$	−2592.45	+	25582.8i	−0.128264	+	1.26573i
$743$			21843.7i			1.07856i	0.842127	+	0.539279i	$0.181303\pi$
$743$			21843.7i			1.07856i	−0.842127	+	0.539279i	$0.818697\pi$
$744$		0			0
$745$		−	17203.1i		−	0.846002i
$746$	4572.61	−	7934.88i	0.224417	−	0.389432i
$747$		0			0
$748$	10651.9	+	18380.5i	0.520683	+	0.898472i
$749$	−5250.00	−	11699.8i	−0.256116	−	0.570761i
$750$		0			0
$751$	−8792.87			−0.427239			−0.213619	−	0.976917i	$-0.568525\pi$
$751$	−8792.87			−0.427239			−0.213619	+	0.976917i	$0.568525\pi$
$752$	6340.22	−	11064.5i	0.307452	−	0.536545i
$753$		0			0
$754$	7816.35	+	4504.30i	0.377526	+	0.217556i
$755$			18929.8i			0.912484i
$756$		0			0
$757$		−	8034.47i		−	0.385757i	−0.981223	−	0.192878i	$-0.938218\pi$
$757$		−	8034.47i		−	0.385757i	0.981223	−	0.192878i	$-0.0617823\pi$
$758$	−3492.98	+	6061.40i	−0.167376	+	0.290449i
$759$		0			0
$760$	−1466.07	+	3.57592i	−0.0699738	+	0.000170674i
$761$	−27879.9			−1.32805			−0.664024	−	0.747711i	$-0.731153\pi$
$761$	−27879.9			−1.32805			−0.664024	+	0.747711i	$0.731153\pi$
$762$		0			0
$763$	20445.4	−	9174.41i	0.970084	−	0.435303i
$764$	26111.2	−	15132.0i	1.23648	−	0.716566i
$765$		0			0
$766$	20576.0	+	11857.3i	0.970551	+	0.559296i
$767$			32471.7i			1.52867i
$768$		0			0
$769$		−	19306.7i		−	0.905355i	−0.891674	−	0.452677i	$-0.850469\pi$
$769$		−	19306.7i		−	0.905355i	0.891674	−	0.452677i	$-0.149531\pi$
$770$	38294.8	+	3880.63i	1.79227	+	0.181621i
$771$		0			0
$772$	6075.49	+	10483.7i	0.283241	+	0.488750i
$773$			6350.02i			0.295465i	0.989027	+	0.147732i	$0.0471975\pi$
$773$			6350.02i			0.295465i	−0.989027	+	0.147732i	$0.952803\pi$
$774$		0			0
$775$		−	8281.90i		−	0.383864i
$776$	41205.6	−	100.505i	1.90618	−	0.00464938i
$777$		0			0
$778$	2681.03	+	1544.99i	0.123547	+	0.0711962i
$779$	585.246			0.0269173
$780$		0			0
$781$		−	21440.7i		−	0.982341i
$782$	−19640.4	+	34082.1i	−0.898132	+	1.55854i
$783$		0			0
$784$	−6972.90	−	20815.1i	−0.317643	−	0.948210i
$785$		−	18951.0i		−	0.861642i
$786$		0			0
$787$	22291.3			1.00965			0.504827	−	0.863221i	$-0.331556\pi$
$787$	22291.3			1.00965			0.504827	+	0.863221i	$0.331556\pi$
$788$	−14565.5	−	25133.7i	−0.658470	−	1.13623i
$789$		0			0
$790$	−17917.1	+	31091.6i	−0.806913	+	1.40024i
$791$	12470.3	−	5595.75i	0.560546	−	0.251532i
$792$		0			0
$793$	−6629.50			−0.296873
$794$	23365.7	+	13464.9i	1.04435	+	0.601826i
$795$		0			0
$796$	15725.2	−	9113.10i	0.700209	−	0.405786i
$797$			1865.27i			0.0828998i	0.999141	+	0.0414499i	$0.0131977\pi$
$797$			1865.27i			0.0828998i	−0.999141	+	0.0414499i	$0.986802\pi$
$798$		0			0
$799$	15255.2			0.675458
$800$	−50643.0	+	29513.9i	−2.23812	+	1.30434i
$801$		0			0
$802$	−3607.09	+	6259.41i	−0.158816	+	0.275595i
$803$			9700.47i			0.426304i
$804$		0			0
$805$	29178.5	+	65025.0i	1.27752	+	2.84699i
$806$	1446.05	−	2509.34i	0.0631946	−	0.109662i
$807$		0			0
$808$	36169.0	−	88.2203i	1.57478	−	0.00384107i
$809$		−	18548.4i		−	0.806089i	−0.915180	−	0.403045i	$-0.867952\pi$
$809$		−	18548.4i		−	0.806089i	0.915180	−	0.403045i	$-0.132048\pi$
$810$		0			0
$811$	17430.4			0.754704			0.377352	−	0.926070i	$-0.376835\pi$
$811$	17430.4			0.754704			0.377352	+	0.926070i	$0.376835\pi$
$812$	6894.69	−	9580.94i	0.297976	−	0.414070i
$813$		0			0
$814$	7972.44	−	13834.6i	0.343285	−	0.595705i
$815$	−22020.3			−0.946427
$816$		0			0
$817$		−	1180.40i		−	0.0505470i
$818$	7174.22	−	12449.5i	0.306651	−	0.532134i
$819$		0			0
$820$	28060.1	−	16261.4i	1.19500	−	0.692527i
$821$	−22238.3			−0.945335			−0.472668	−	0.881241i	$-0.656709\pi$
$821$	−22238.3			−0.945335			−0.472668	+	0.881241i	$0.656709\pi$
$822$		0			0
$823$	−13685.2			−0.579630			−0.289815	−	0.957083i	$-0.593594\pi$
$823$	−13685.2			−0.579630			−0.289815	+	0.957083i	$0.593594\pi$
$824$	13539.0	−	33.0231i	0.572394	−	0.00139613i
$825$		0			0
$826$	42270.9	+	4283.55i	1.78062	+	0.180441i
$827$	19942.6			0.838539			0.419270	−	0.907862i	$-0.362286\pi$
$827$	19942.6			0.838539			0.419270	+	0.907862i	$0.362286\pi$
$828$		0			0
$829$	−18891.1			−0.791455			−0.395728	−	0.918368i	$-0.629508\pi$
$829$	−18891.1			−0.791455			−0.395728	+	0.918368i	$0.629508\pi$
$830$	−2714.94	−	1564.53i	−0.113538	−	0.0654284i
$831$		0			0
$832$	−20497.6	+	99.9924i	−0.854117	+	0.00416660i
$833$	17457.6	−	19617.5i	0.726135	−	0.815973i
$834$		0			0
$835$		−	42909.8i		−	1.77839i
$836$	−425.509	−	734.243i	−0.0176035	−	0.0303760i
$837$		0			0
$838$	−13007.0	+	22571.1i	−0.536179	+	0.930436i
$839$	−33269.2			−1.36899			−0.684494	−	0.729018i	$-0.739977\pi$
$839$	−33269.2			−1.36899			−0.684494	+	0.729018i	$0.739977\pi$
$840$		0			0
$841$	−18041.9			−0.739756
$842$	13111.1	−	22751.8i	0.536626	−	0.931211i
$843$		0			0
$844$	−41341.0	+	23957.9i	−1.68604	+	0.977093i
$845$			12588.5i			0.512493i
$846$		0			0
$847$	−970.380	−	2162.52i	−0.0393656	−	0.0877272i
$848$	15619.6	−	27258.2i	0.632522	−	1.10383i
$849$		0			0
$850$	−60754.1	−	35010.6i	−2.45159	−	1.41277i
$851$	29565.9			1.19096
$852$		0			0
$853$	−17794.2			−0.714256			−0.357128	−	0.934055i	$-0.616244\pi$
$853$	−17794.2			−0.714256			−0.357128	+	0.934055i	$0.616244\pi$
$854$	−874.539	+	8630.11i	−0.0350423	+	0.345804i
$855$		0			0
$856$	38.2148	+	15667.5i	0.00152588	+	0.625589i
$857$	−2452.81			−0.0977671			−0.0488835	−	0.998804i	$-0.515566\pi$
$857$	−2452.81			−0.0977671			−0.0488835	+	0.998804i	$0.515566\pi$
$858$		0			0
$859$	−3783.50			−0.150281			−0.0751404	−	0.997173i	$-0.523941\pi$
$859$	−3783.50			−0.150281			−0.0751404	+	0.997173i	$0.523941\pi$
$860$	−32798.1	−	56595.2i	−1.30047	−	2.24405i
$861$		0			0
$862$	20263.9	−	35164.0i	0.800684	−	1.38943i
$863$			39332.7i			1.55145i	0.631070	+	0.775726i	$0.282616\pi$
$863$			39332.7i			1.55145i	−0.631070	+	0.775726i	$0.717384\pi$
$864$		0			0
$865$	14370.9			0.564884
$866$	9913.57	−	17203.1i	0.389003	−	0.675040i
$867$		0			0
$868$	−3075.84	−	2213.45i	−0.120277	−	0.0865547i
$869$	−20771.6			−0.810850
$870$		0			0
$871$			25304.5i			0.984396i
$872$	−27379.1	+	66.7807i	−1.06327	+	0.00259344i
$873$		0			0
$874$	784.572	−	1361.47i	0.0303645	−	0.0526917i
$875$	−71166.5	+	31934.3i	−2.74956	+	1.23380i
$876$		0			0
$877$			21948.9i			0.845110i	0.906337	+	0.422555i	$0.138867\pi$
$877$			21948.9i			0.845110i	−0.906337	+	0.422555i	$0.861133\pi$
$878$	19410.3	−	33682.8i	0.746087	−	1.29469i
$879$		0			0
$880$	−40802.7	−	23380.9i	−1.56302	−	0.895647i
$881$	2497.58			0.0955114			0.0477557	−	0.998859i	$-0.484793\pi$
$881$	2497.58			0.0955114			0.0477557	+	0.998859i	$0.484793\pi$
$882$		0			0
$883$			31080.3i			1.18452i	0.805746	+	0.592261i	$0.201765\pi$
$883$			31080.3i			1.18452i	−0.805746	+	0.592261i	$0.798235\pi$
$884$	−12295.0	−	21215.8i	−0.467788	−	0.807199i
$885$		0			0
$886$	−10494.0	−	6047.37i	−0.397917	−	0.229306i
$887$	−5232.45			−0.198071			−0.0990353	−	0.995084i	$-0.531576\pi$
$887$	−5232.45			−0.198071			−0.0990353	+	0.995084i	$0.531576\pi$
$888$		0			0
$889$	−1262.51	−	2813.53i	−0.0476300	−	0.106145i
$890$	−38511.4	+	66829.2i	−1.45046	+	2.51699i
$891$		0			0
$892$	−2799.90	+	1622.60i	−0.105098	+	0.0609066i
$893$	−609.399			−0.0228362
$894$		0			0
$895$			73762.5i			2.75487i
$896$	−2573.80	+	26696.4i	−0.0959649	+	0.995385i
$897$		0			0
$898$	338.493	−	587.389i	0.0125787	−	0.0218279i
$899$		−	2037.65i		−	0.0755944i
$900$		0			0
$901$	37582.3			1.38962
$902$	16265.3	+	9373.15i	0.600416	+	0.346000i
$903$		0			0
$904$	−16699.3	+	40.7315i	−0.614392	+	0.00149857i
$905$			32660.8i			1.19965i
$906$		0			0
$907$		−	19181.1i		−	0.702202i	−0.936338	−	0.351101i	$-0.885807\pi$
$907$		−	19181.1i		−	0.702202i	0.936338	−	0.351101i	$-0.114193\pi$
$908$	25111.7	−	14552.8i	0.917799	−	0.531883i
$909$		0			0
$910$	−44202.0	−	4479.24i	−1.61020	−	0.163171i
$911$		−	11163.6i		−	0.405999i	−0.979179	−	0.203000i	$-0.934931\pi$
$911$		−	11163.6i		−	0.405999i	0.979179	−	0.203000i	$-0.0650690\pi$
$912$		0			0
$913$		−	1813.79i		−	0.0657476i
$914$	11531.1	+	6644.98i	0.417302	+	0.240477i
$915$		0			0
$916$	−20370.2	−	35150.0i	−0.734770	−	1.26789i
$917$	−7000.49	+	3141.31i	−0.252101	+	0.113125i
$918$		0			0
$919$	16868.9			0.605497			0.302749	−	0.953070i	$-0.402096\pi$
$919$	16868.9			0.605497			0.302749	+	0.953070i	$0.402096\pi$
$920$	−212.390	−	87076.8i	−0.00761120	−	3.12048i
$921$		0			0
$922$	−12451.5	+	21607.2i	−0.444760	+	0.771795i
$923$			24748.0i			0.882548i
$924$		0			0
$925$			52703.5i			1.87339i
$926$	32674.9	+	18829.5i	1.15957	+	0.668224i
$927$		0			0
$928$	−12460.0	+	7261.49i	−0.440754	+	0.256864i
$929$	−2289.19			−0.0808460			−0.0404230	−	0.999183i	$-0.512871\pi$
$929$	−2289.19			−0.0808460			−0.0404230	+	0.999183i	$0.512871\pi$
$930$		0			0
$931$	−697.377	+	783.657i	−0.0245495	+	0.0275868i
$932$	−10082.1	+	5842.78i	−0.354345	+	0.205350i
$933$		0			0
$934$	−9734.80	+	16892.9i	−0.341041	+	0.591811i
$935$		−	56256.8i		−	1.96770i
$936$		0			0
$937$		−	27738.4i		−	0.967100i	−0.875317	−	0.483550i	$-0.839347\pi$
$937$		−	27738.4i		−	0.967100i	0.875317	−	0.483550i	$-0.160653\pi$
$938$	32940.7	+	3338.07i	1.14664	+	0.116196i
$939$		0			0
$940$	−29218.1	+	16932.5i	−1.01382	+	0.587529i
$941$		−	17456.0i		−	0.604729i	−0.953192	−	0.302365i	$-0.902224\pi$
$941$		−	17456.0i		−	0.604729i	0.953192	−	0.302365i	$-0.0977760\pi$
$942$		0			0
$943$			34760.4i			1.20038i
$944$	−45039.2	−	25808.5i	−1.55286	−	0.889824i
$945$		0			0
$946$	18905.0	−	32806.0i	0.649740	−	1.12750i
$947$	27608.2			0.947357			0.473679	−	0.880698i	$-0.342926\pi$
$947$	27608.2			0.947357			0.473679	+	0.880698i	$0.342926\pi$
$948$		0			0
$949$		−	11196.8i		−	0.382997i
$950$	2426.94	+	1398.56i	0.0828845	+	0.0477636i
$951$		0			0
$952$	−29240.1	+	13206.6i	−0.995458	+	0.449609i
$953$		−	29064.4i		−	0.987922i	−0.869484	−	0.493961i	$-0.835549\pi$
$953$		−	29064.4i		−	0.987922i	0.869484	−	0.493961i	$-0.164451\pi$
$954$		0			0
$955$	−79918.1			−2.70795
$956$	36419.8	−	21106.0i	1.23211	−	0.714035i
$957$		0			0
$958$	−14878.0	−	8573.68i	−0.501759	−	0.289147i
$959$	−41605.9	+	18669.7i	−1.40096	+	0.628650i
$960$		0			0
$961$	29136.8			0.978042
$962$	−9202.22	+	15968.7i	−0.308411	+	0.535188i
$963$		0			0
$964$	33059.5	−	19158.7i	1.10454	−	0.640103i
$965$		−	32087.1i		−	1.07038i
$966$		0			0
$967$	9916.78			0.329785			0.164892	−	0.986312i	$-0.447272\pi$
$967$	9916.78			0.329785			0.164892	+	0.986312i	$0.447272\pi$
$968$	7.06340	+	2895.89i	0.000234531	+	0.0961544i
$969$		0			0
$970$	−94543.6	−	54482.3i	−3.12950	−	1.80342i
$971$			44197.3i			1.46072i	0.683063	+	0.730359i	$0.260647\pi$
$971$			44197.3i			1.46072i	−0.683063	+	0.730359i	$0.739353\pi$
$972$		0			0
$973$	−2520.40	−	5616.79i	−0.0830426	−	0.185063i
$974$	24714.9	+	14242.4i	0.813057	+	0.468538i
$975$		0			0
$976$	5269.11	−	9195.30i	0.172807	−	0.301572i
$977$		−	23220.3i		−	0.760373i	−0.924910	−	0.380186i	$-0.875860\pi$
$977$		−	23220.3i		−	0.760373i	0.924910	−	0.380186i	$-0.124140\pi$
$978$		0			0
$979$	−44647.0			−1.45753
$980$	−11661.9	+	56950.1i	−0.380129	+	1.85633i
$981$		0			0
$982$	27023.7	+	15572.8i	0.878166	+	0.506058i
$983$	54837.1			1.77928			0.889640	−	0.456663i	$-0.150955\pi$
$983$	54837.1			1.77928			0.889640	+	0.456663i	$0.150955\pi$
$984$		0			0
$985$			76926.3i			2.48840i
$986$	−14947.7	−	8613.88i	−0.482792	−	0.278217i
$987$		0			0
$988$	491.146	+	847.503i	0.0158152	+	0.0272902i
$989$	70109.3			2.25414
$990$		0			0
$991$	18645.4			0.597670			0.298835	−	0.954305i	$-0.403402\pi$
$991$	18645.4			0.597670			0.298835	+	0.954305i	$0.403402\pi$
$992$	2331.21	+	4000.13i	0.0746128	+	0.128028i
$993$		0			0
$994$	32216.4	+	3264.67i	1.02801	+	0.104174i
$995$	−48130.0			−1.53349
$996$		0			0
$997$	38576.5			1.22541			0.612703	−	0.790313i	$-0.290082\pi$
$997$	38576.5			1.22541			0.612703	+	0.790313i	$0.290082\pi$
$998$	−4381.75	+	7603.68i	−0.138980	+	0.241173i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.4.i.b.125.14	yes	88
3.2	odd	2	inner	504.4.i.b.125.76	yes	88
4.3	odd	2		2016.4.i.b.881.9		88
7.6	odd	2	inner	504.4.i.b.125.13	✓	88
8.3	odd	2		2016.4.i.b.881.80		88
8.5	even	2	inner	504.4.i.b.125.73	yes	88
12.11	even	2		2016.4.i.b.881.54		88
21.20	even	2	inner	504.4.i.b.125.75	yes	88
24.5	odd	2	inner	504.4.i.b.125.15	yes	88
24.11	even	2		2016.4.i.b.881.35		88
28.27	even	2		2016.4.i.b.881.36		88
56.13	odd	2	inner	504.4.i.b.125.74	yes	88
56.27	even	2		2016.4.i.b.881.53		88
84.83	odd	2		2016.4.i.b.881.79		88
168.83	odd	2		2016.4.i.b.881.10		88
168.125	even	2	inner	504.4.i.b.125.16	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.4.i.b.125.13	✓	88	7.6	odd	2	inner
504.4.i.b.125.14	yes	88	1.1	even	1	trivial
504.4.i.b.125.15	yes	88	24.5	odd	2	inner
504.4.i.b.125.16	yes	88	168.125	even	2	inner
504.4.i.b.125.73	yes	88	8.5	even	2	inner
504.4.i.b.125.74	yes	88	56.13	odd	2	inner
504.4.i.b.125.75	yes	88	21.20	even	2	inner
504.4.i.b.125.76	yes	88	3.2	odd	2	inner
2016.4.i.b.881.9		88	4.3	odd	2
2016.4.i.b.881.10		88	168.83	odd	2
2016.4.i.b.881.35		88	24.11	even	2
2016.4.i.b.881.36		88	28.27	even	2
2016.4.i.b.881.53		88	56.27	even	2
2016.4.i.b.881.54		88	12.11	even	2
2016.4.i.b.881.79		88	84.83	odd	2
2016.4.i.b.881.80		88	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	504.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.45064 - 1.41222i) q^{2} +(4.01126 + 6.92169i) q^{4} -21.1851i q^{5} +(7.58217 + 16.8971i) q^{7} +(-0.0551907 - 22.6273i) q^{8} +O(q^{10})\)	\(q+(-2.45064 - 1.41222i) q^{2} +(4.01126 + 6.92169i) q^{4} -21.1851i q^{5} +(7.58217 + 16.8971i) q^{7} +(-0.0551907 - 22.6273i) q^{8} +(-29.9180 + 51.9170i) q^{10} -34.6846 q^{11} +40.0348 q^{13} +(5.28124 - 52.1163i) q^{14} +(-31.8196 + 55.5294i) q^{16} -76.5612 q^{17} +3.05838 q^{19} +(146.637 - 84.9789i) q^{20} +(84.9993 + 48.9823i) q^{22} +181.651i q^{23} -323.808 q^{25} +(-98.1109 - 56.5380i) q^{26} +(-86.5422 + 120.260i) q^{28} -79.6686 q^{29} +25.5766i q^{31} +(156.398 - 91.1462i) q^{32} +(187.624 + 108.121i) q^{34} +(357.966 - 160.629i) q^{35} -162.762i q^{37} +(-7.49499 - 4.31911i) q^{38} +(-479.362 + 1.16922i) q^{40} +191.358 q^{41} -385.956i q^{43} +(-139.129 - 240.076i) q^{44} +(256.532 - 445.162i) q^{46} -199.255 q^{47} +(-228.021 + 256.233i) q^{49} +(793.537 + 457.289i) q^{50} +(160.590 + 277.109i) q^{52} -490.879 q^{53} +734.795i q^{55} +(381.917 - 172.497i) q^{56} +(195.239 + 112.510i) q^{58} +811.088i q^{59} -165.593 q^{61} +(36.1198 - 62.6789i) q^{62} +(-511.994 + 2.49764i) q^{64} -848.141i q^{65} +632.062i q^{67} +(-307.107 - 529.933i) q^{68} +(-1104.09 - 111.884i) q^{70} +618.163i q^{71} -279.677i q^{73} +(-229.856 + 398.870i) q^{74} +(12.2680 + 21.1692i) q^{76} +(-262.984 - 586.067i) q^{77} +598.872 q^{79} +(1176.40 + 674.101i) q^{80} +(-468.949 - 270.240i) q^{82} +52.2938i q^{83} +1621.96i q^{85} +(-545.055 + 945.838i) q^{86} +(1.91426 + 784.819i) q^{88} +1287.23 q^{89} +(303.551 + 676.471i) q^{91} +(-1257.33 + 728.651i) q^{92} +(488.303 + 281.393i) q^{94} -64.7921i q^{95} +1821.05i q^{97} +(920.656 - 305.917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q+O(q^{10}) \) 88 * q	\( 88 q - 128 q^{16} - 1312 q^{22} - 3400 q^{25} + 584 q^{28} - 208 q^{46} - 2024 q^{49} - 3200 q^{58} - 1440 q^{64} - 2856 q^{70} - 10832 q^{79} - 272 q^{88}+O(q^{100}) \) 88 * q - 128 * q^16 - 1312 * q^22 - 3400 * q^25 + 584 * q^28 - 208 * q^46 - 2024 * q^49 - 3200 * q^58 - 1440 * q^64 - 2856 * q^70 - 10832 * q^79 - 272 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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