LMFDB - Embedded newform 324.4.b.c.323.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("324.323");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	324.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.1166188419$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.14
Character	$\chi$	$=$	324.323
Dual form			324.4.b.c.323.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.513200 + 2.78148i) q^{2} +(-7.47325 + 2.85491i) q^{4} -2.40947i q^{5} -2.66000i q^{7} +(-11.7761 - 19.3216i) q^{8} +O(q^{10})$	\(q+(0.513200 + 2.78148i) q^{2} +(-7.47325 + 2.85491i) q^{4} -2.40947i q^{5} -2.66000i q^{7} +(-11.7761 - 19.3216i) q^{8} +(6.70190 - 1.23654i) q^{10} +48.2857 q^{11} +40.7140 q^{13} +(7.39872 - 1.36511i) q^{14} +(47.6990 - 42.6709i) q^{16} +36.3729i q^{17} +125.173i q^{19} +(6.87883 + 18.0066i) q^{20} +(24.7802 + 134.306i) q^{22} -194.112 q^{23} +119.194 q^{25} +(20.8944 + 113.245i) q^{26} +(7.59405 + 19.8788i) q^{28} +177.354i q^{29} -175.582i q^{31} +(143.167 + 110.775i) q^{32} +(-101.171 + 18.6666i) q^{34} -6.40918 q^{35} +199.364 q^{37} +(-348.167 + 64.2389i) q^{38} +(-46.5547 + 28.3743i) q^{40} +233.037i q^{41} +291.623i q^{43} +(-360.851 + 137.851i) q^{44} +(-99.6182 - 539.918i) q^{46} -61.8953 q^{47} +335.924 q^{49} +(61.1706 + 331.537i) q^{50} +(-304.266 + 116.235i) q^{52} +352.175i q^{53} -116.343i q^{55} +(-51.3952 + 31.3245i) q^{56} +(-493.308 + 91.0183i) q^{58} +141.582 q^{59} +15.4304 q^{61} +(488.377 - 90.1086i) q^{62} +(-234.645 + 455.067i) q^{64} -98.0993i q^{65} +152.024i q^{67} +(-103.841 - 271.824i) q^{68} +(-3.28919 - 17.8270i) q^{70} -28.0331 q^{71} +124.499 q^{73} +(102.314 + 554.527i) q^{74} +(-357.358 - 935.451i) q^{76} -128.440i q^{77} -748.721i q^{79} +(-102.814 - 114.929i) q^{80} +(-648.187 + 119.595i) q^{82} -348.888 q^{83} +87.6396 q^{85} +(-811.144 + 149.661i) q^{86} +(-568.619 - 932.955i) q^{88} -416.864i q^{89} -108.299i q^{91} +(1450.65 - 554.172i) q^{92} +(-31.7647 - 172.160i) q^{94} +301.601 q^{95} +1505.13 q^{97} +(172.396 + 934.367i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4}+O(q^{10}) $ 24 * q + 24 * q^4	$ 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64} - 1128 q^{70} - 4776 q^{73} + 1200 q^{76} - 4104 q^{82} - 1440 q^{85} - 3912 q^{88} + 2376 q^{94} - 1176 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.513200	+	2.78148i	0.181444	+	0.983401i
$2$	0.513200	+	2.78148i	0.181444	+	0.983401i
$3$		0			0
$3$		0			0
$4$	−7.47325	+	2.85491i	−0.934156	+	0.356864i
$5$		−	2.40947i		−	0.215510i	−0.994177	−	0.107755i	$-0.965634\pi$
$5$		−	2.40947i		−	0.215510i	0.994177	−	0.107755i	$-0.0343662\pi$
$6$		0			0
$7$		−	2.66000i		−	0.143626i	−0.997418	−	0.0718131i	$-0.977121\pi$
$7$		−	2.66000i		−	0.143626i	0.997418	−	0.0718131i	$-0.0228785\pi$
$8$	−11.7761	−	19.3216i	−0.520437	−	0.853900i
$9$		0			0
$10$	6.70190	−	1.23654i	0.211933	−	0.0391029i
$11$	48.2857			1.32352			0.661758	−	0.749717i	$-0.269810\pi$
$11$	48.2857			1.32352			0.661758	+	0.749717i	$0.269810\pi$
$12$		0			0
$13$	40.7140			0.868618			0.434309	−	0.900764i	$-0.356993\pi$
$13$	40.7140			0.868618			0.434309	+	0.900764i	$0.356993\pi$
$14$	7.39872	−	1.36511i	0.141242	−	0.0260601i
$15$		0			0
$16$	47.6990	−	42.6709i	0.745297	−	0.666733i
$17$			36.3729i			0.518925i	0.965753	+	0.259463i	$0.0835455\pi$
$17$			36.3729i			0.518925i	−0.965753	+	0.259463i	$0.916455\pi$
$18$		0			0
$19$			125.173i			1.51141i	0.654914	+	0.755703i	$0.272705\pi$
$19$			125.173i			1.51141i	−0.654914	+	0.755703i	$0.727295\pi$
$20$	6.87883	+	18.0066i	0.0769076	+	0.201320i
$21$		0			0
$22$	24.7802	+	134.306i	0.240144	+	1.30155i
$23$	−194.112			−1.75979			−0.879894	−	0.475169i	$-0.842387\pi$
$23$	−194.112			−1.75979			−0.879894	+	0.475169i	$0.842387\pi$
$24$		0			0
$25$	119.194			0.953556
$26$	20.8944	+	113.245i	0.157605	+	0.854200i
$27$		0			0
$28$	7.59405	+	19.8788i	0.0512550	+	0.134169i
$29$			177.354i			1.13565i	0.823149	+	0.567826i	$0.192215\pi$
$29$			177.354i			1.13565i	−0.823149	+	0.567826i	$0.807785\pi$
$30$		0			0
$31$		−	175.582i		−	1.01727i	−0.860982	−	0.508636i	$-0.830150\pi$
$31$		−	175.582i		−	1.01727i	0.860982	−	0.508636i	$-0.169850\pi$
$32$	143.167	+	110.775i	0.790895	+	0.611951i
$33$		0			0
$34$	−101.171	+	18.6666i	−0.510312	+	0.0941557i
$35$	−6.40918			−0.0309529
$36$		0			0
$37$	199.364			0.885818			0.442909	−	0.896566i	$-0.353946\pi$
$37$	199.364			0.885818			0.442909	+	0.896566i	$0.353946\pi$
$38$	−348.167	+	64.2389i	−1.48632	+	0.274235i
$39$		0			0
$40$	−46.5547	+	28.3743i	−0.184024	+	0.112159i
$41$			233.037i			0.887665i	0.896110	+	0.443832i	$0.146381\pi$
$41$			233.037i			0.887665i	−0.896110	+	0.443832i	$0.853619\pi$
$42$		0			0
$43$			291.623i			1.03424i	0.855914	+	0.517118i	$0.172995\pi$
$43$			291.623i			1.03424i	−0.855914	+	0.517118i	$0.827005\pi$
$44$	−360.851	+	137.851i	−1.23637	+	0.472315i
$45$		0			0
$46$	−99.6182	−	539.918i	−0.319302	−	1.73058i
$47$	−61.8953			−0.192093			−0.0960463	−	0.995377i	$-0.530620\pi$
$47$	−61.8953			−0.192093			−0.0960463	+	0.995377i	$0.530620\pi$
$48$		0			0
$49$	335.924			0.979372
$50$	61.1706	+	331.537i	0.173017	+	0.937728i
$51$		0			0
$52$	−304.266	+	116.235i	−0.811425	+	0.309978i
$53$			352.175i			0.912735i	0.889791	+	0.456367i	$0.150850\pi$
$53$			352.175i			0.912735i	−0.889791	+	0.456367i	$0.849150\pi$
$54$		0			0
$55$		−	116.343i		−	0.285231i
$56$	−51.3952	+	31.3245i	−0.122642	+	0.0747484i
$57$		0			0
$58$	−493.308	+	91.0183i	−1.11680	+	0.206057i
$59$	141.582			0.312414			0.156207	−	0.987724i	$-0.450073\pi$
$59$	141.582			0.312414			0.156207	+	0.987724i	$0.450073\pi$
$60$		0			0
$61$	15.4304			0.0323878			0.0161939	−	0.999869i	$-0.494845\pi$
$61$	15.4304			0.0323878			0.0161939	+	0.999869i	$0.494845\pi$
$62$	488.377	−	90.1086i	1.00039	−	0.184577i
$63$		0			0
$64$	−234.645	+	455.067i	−0.458291	+	0.888802i
$65$		−	98.0993i		−	0.187196i
$66$		0			0
$67$			152.024i			0.277204i	0.990348	+	0.138602i	$0.0442609\pi$
$67$			152.024i			0.277204i	−0.990348	+	0.138602i	$0.955739\pi$
$68$	−103.841	−	271.824i	−0.185186	−	0.484758i
$69$		0			0
$70$	−3.28919	−	17.8270i	−0.00561620	−	0.0304391i
$71$	−28.0331			−0.0468580			−0.0234290	−	0.999726i	$-0.507458\pi$
$71$	−28.0331			−0.0468580			−0.0234290	+	0.999726i	$0.507458\pi$
$72$		0			0
$73$	124.499			0.199609			0.0998047	−	0.995007i	$-0.468178\pi$
$73$	124.499			0.199609			0.0998047	+	0.995007i	$0.468178\pi$
$74$	102.314	+	554.527i	0.160726	+	0.871115i
$75$		0			0
$76$	−357.358	−	935.451i	−0.539366	−	1.41189i
$77$		−	128.440i		−	0.190092i
$78$		0			0
$79$		−	748.721i		−	1.06630i	−0.846021	−	0.533150i	$-0.821008\pi$
$79$		−	748.721i		−	1.06630i	0.846021	−	0.533150i	$-0.178992\pi$
$80$	−102.814	−	114.929i	−0.143687	−	0.160619i
$81$		0			0
$82$	−648.187	+	119.595i	−0.872931	+	0.161061i
$83$	−348.888			−0.461390			−0.230695	−	0.973026i	$-0.574100\pi$
$83$	−348.888			−0.461390			−0.230695	+	0.973026i	$0.574100\pi$
$84$		0			0
$85$	87.6396			0.111833
$86$	−811.144	+	149.661i	−1.01707	+	0.187655i
$87$		0			0
$88$	−568.619	−	932.955i	−0.688807	−	1.13015i
$89$		−	416.864i		−	0.496488i	−0.968698	−	0.248244i	$-0.920146\pi$
$89$		−	416.864i		−	0.496488i	0.968698	−	0.248244i	$-0.0798535\pi$
$90$		0			0
$91$		−	108.299i		−	0.124756i
$92$	1450.65	−	554.172i	1.64392	−	0.628005i
$93$		0			0
$94$	−31.7647	−	172.160i	−0.0348540	−	0.188904i
$95$	301.601			0.325723
$96$		0			0
$97$	1505.13			1.57549			0.787747	−	0.615999i	$-0.211248\pi$
$97$	1505.13			1.57549			0.787747	+	0.615999i	$0.211248\pi$
$98$	172.396	+	934.367i	0.177701	+	0.963115i
$99$		0			0
$100$	−890.770	+	340.289i	−0.890770	+	0.340289i
$101$			435.424i			0.428973i	0.976727	+	0.214487i	$0.0688078\pi$
$101$			435.424i			0.428973i	−0.976727	+	0.214487i	$0.931192\pi$
$102$		0			0
$103$			1745.36i			1.66966i	0.550506	+	0.834831i	$0.314435\pi$
$103$			1745.36i			1.66966i	−0.550506	+	0.834831i	$0.685565\pi$
$104$	−479.454	−	786.658i	−0.452061	−	0.741713i
$105$		0			0
$106$	−979.567	+	180.736i	−0.897585	+	0.165610i
$107$	−783.805			−0.708161			−0.354081	−	0.935215i	$-0.615206\pi$
$107$	−783.805			−0.708161			−0.354081	+	0.935215i	$0.615206\pi$
$108$		0			0
$109$	1581.89			1.39007			0.695035	−	0.718976i	$-0.255389\pi$
$109$	1581.89			1.39007			0.695035	+	0.718976i	$0.255389\pi$
$110$	323.606	−	59.7072i	0.280496	−	0.0517533i
$111$		0			0
$112$	−113.504	−	126.879i	−0.0957604	−	0.107044i
$113$			443.829i			0.369486i	0.982787	+	0.184743i	$0.0591453\pi$
$113$			443.829i			0.369486i	−0.982787	+	0.184743i	$0.940855\pi$
$114$		0			0
$115$			467.707i			0.379252i
$116$	−506.331	−	1325.41i	−0.405273	−	1.06088i
$117$		0			0
$118$	72.6600	+	393.808i	0.0566855	+	0.307228i
$119$	96.7518			0.0745313
$120$		0			0
$121$	1000.51			0.751697
$122$	7.91886	+	42.9192i	0.00587656	+	0.0318502i
$123$		0			0
$124$	501.270	+	1312.17i	0.363027	+	0.950291i
$125$		−	588.380i		−	0.421010i
$126$		0			0
$127$		−	425.829i		−	0.297529i	−0.988873	−	0.148765i	$-0.952470\pi$
$127$		−	425.829i		−	0.297529i	0.988873	−	0.148765i	$-0.0475297\pi$
$128$	−1386.18	−	419.120i	−0.957203	−	0.289416i
$129$		0			0
$130$	272.861	−	50.3445i	0.184088	−	0.0339654i
$131$	1743.67			1.16294			0.581471	−	0.813567i	$-0.302478\pi$
$131$	1743.67			1.16294			0.581471	+	0.813567i	$0.302478\pi$
$132$		0			0
$133$	332.960			0.217078
$134$	−422.851	+	78.0187i	−0.272603	+	0.0502969i
$135$		0			0
$136$	702.782	−	428.333i	0.443110	−	0.270068i
$137$		−	1471.46i		−	0.917632i	−0.888531	−	0.458816i	$-0.848274\pi$
$137$		−	1471.46i		−	0.917632i	0.888531	−	0.458816i	$-0.151726\pi$
$138$		0			0
$139$		−	1278.30i		−	0.780030i	−0.920809	−	0.390015i	$-0.872470\pi$
$139$		−	1278.30i		−	0.780030i	0.920809	−	0.390015i	$-0.127530\pi$
$140$	47.8974	−	18.2976i	0.0289148	−	0.0110459i
$141$		0			0
$142$	−14.3866	−	77.9735i	−0.00850209	−	0.0460802i
$143$	1965.90			1.14963
$144$		0			0
$145$	427.331			0.244744
$146$	63.8928	+	346.291i	0.0362179	+	0.196296i
$147$		0			0
$148$	−1489.90	+	569.167i	−0.827493	+	0.316116i
$149$		−	2149.07i		−	1.18160i	−0.806818	−	0.590800i	$-0.798812\pi$
$149$		−	2149.07i		−	1.18160i	0.806818	−	0.590800i	$-0.201188\pi$
$150$		0			0
$151$			956.815i			0.515659i	0.966190	+	0.257829i	$0.0830073\pi$
$151$			956.815i			0.515659i	−0.966190	+	0.257829i	$0.916993\pi$
$152$	2418.54	−	1474.06i	1.29059	−	0.786592i
$153$		0			0
$154$	357.252	−	65.9152i	0.186936	−	0.0344909i
$155$	−423.059			−0.219232
$156$		0			0
$157$	2093.20			1.06405			0.532024	−	0.846729i	$-0.321431\pi$
$157$	2093.20			1.06405			0.532024	+	0.846729i	$0.321431\pi$
$158$	2082.55	−	384.243i	1.04860	−	0.193473i
$159$		0			0
$160$	266.909	−	344.958i	0.131881	−	0.170446i
$161$			516.337i			0.252752i
$162$		0			0
$163$			1468.60i			0.705703i	0.935679	+	0.352851i	$0.114788\pi$
$163$			1468.60i			0.705703i	−0.935679	+	0.352851i	$0.885212\pi$
$164$	−665.299	−	1741.54i	−0.316775	−	0.829218i
$165$		0			0
$166$	−179.049	−	970.424i	−0.0837163	−	0.453732i
$167$	−3048.38			−1.41252			−0.706261	−	0.707952i	$-0.749619\pi$
$167$	−3048.38			−1.41252			−0.706261	+	0.707952i	$0.749619\pi$
$168$		0			0
$169$	−539.369			−0.245503
$170$	44.9766	+	243.768i	0.0202915	+	0.109977i
$171$		0			0
$172$	−832.558	−	2179.37i	−0.369081	−	0.966137i
$173$		−	2775.57i		−	1.21978i	−0.792484	−	0.609892i	$-0.791213\pi$
$173$		−	2775.57i		−	1.21978i	0.792484	−	0.609892i	$-0.208787\pi$
$174$		0			0
$175$		−	317.057i		−	0.136956i
$176$	2303.18	−	2060.39i	0.986413	−	0.882432i
$177$		0			0
$178$	1159.50	−	213.934i	0.488247	−	0.0900846i
$179$	−477.618			−0.199435			−0.0997174	−	0.995016i	$-0.531794\pi$
$179$	−477.618			−0.199435			−0.0997174	+	0.995016i	$0.531794\pi$
$180$		0			0
$181$	−732.350			−0.300747			−0.150373	−	0.988629i	$-0.548048\pi$
$181$	−732.350			−0.300747			−0.150373	+	0.988629i	$0.548048\pi$
$182$	301.232	−	55.5791i	0.122686	−	0.0226362i
$183$		0			0
$184$	2285.89	+	3750.54i	0.915859	+	1.50268i
$185$		−	480.363i		−	0.190902i
$186$		0			0
$187$			1756.29i			0.686807i
$188$	462.559	−	176.705i	0.179445	−	0.0685509i
$189$		0			0
$190$	154.782	+	838.898i	0.0591003	+	0.320316i
$191$	3086.00			1.16908			0.584542	−	0.811364i	$-0.301274\pi$
$191$	3086.00			1.16908			0.584542	+	0.811364i	$0.301274\pi$
$192$		0			0
$193$	−1634.32			−0.609539			−0.304769	−	0.952426i	$-0.598579\pi$
$193$	−1634.32			−0.609539			−0.304769	+	0.952426i	$0.598579\pi$
$194$	772.433	+	4186.49i	0.285863	+	1.54934i
$195$		0			0
$196$	−2510.45	+	959.034i	−0.914886	+	0.349502i
$197$		−	3350.67i		−	1.21181i	−0.795539	−	0.605903i	$-0.792812\pi$
$197$		−	3350.67i		−	1.21181i	0.795539	−	0.605903i	$-0.207188\pi$
$198$		0			0
$199$			1046.61i			0.372826i	0.982471	+	0.186413i	$0.0596863\pi$
$199$			1046.61i			0.372826i	−0.982471	+	0.186413i	$0.940314\pi$
$200$	−1403.65	−	2303.02i	−0.496266	−	0.814241i
$201$		0			0
$202$	−1211.12	+	223.459i	−0.421853	+	0.0778344i
$203$	471.762			0.163109
$204$		0			0
$205$	561.496			0.191300
$206$	−4854.68	+	895.718i	−1.64195	+	0.302950i
$207$		0			0
$208$	1942.02	−	1737.30i	0.647378	−	0.579136i
$209$			6044.08i			2.00037i
$210$		0			0
$211$		−	5277.87i		−	1.72201i	−0.508598	−	0.861004i	$-0.669836\pi$
$211$		−	5277.87i		−	1.72201i	0.508598	−	0.861004i	$-0.330164\pi$
$212$	−1005.43	−	2631.89i	−0.325722	−	0.852637i
$213$		0			0
$214$	−402.249	−	2180.14i	−0.128491	−	0.696407i
$215$	702.658			0.222888
$216$		0			0
$217$	−467.047			−0.146107
$218$	811.826	+	4400.00i	0.252219	+	1.36700i
$219$		0			0
$220$	332.149	+	869.461i	0.101789	+	0.266450i
$221$			1480.89i			0.450748i
$222$		0			0
$223$		−	4759.70i		−	1.42930i	−0.699484	−	0.714648i	$-0.746587\pi$
$223$		−	4759.70i		−	1.42930i	0.699484	−	0.714648i	$-0.253413\pi$
$224$	294.661	−	380.824i	0.0878923	−	0.113593i
$225$		0			0
$226$	−1234.50	+	227.773i	−0.363353	+	0.0670409i
$227$	2230.45			0.652161			0.326080	−	0.945342i	$-0.394272\pi$
$227$	2230.45			0.652161			0.326080	+	0.945342i	$0.394272\pi$
$228$		0			0
$229$	−5834.58			−1.68367			−0.841833	−	0.539737i	$-0.818524\pi$
$229$	−5834.58			−1.68367			−0.841833	+	0.539737i	$0.818524\pi$
$230$	−1300.92	+	240.027i	−0.372957	+	0.0688128i
$231$		0			0
$232$	3426.76	−	2088.55i	0.969733	−	0.591035i
$233$			3080.09i			0.866022i	0.901389	+	0.433011i	$0.142549\pi$
$233$			3080.09i			0.866022i	−0.901389	+	0.433011i	$0.857451\pi$
$234$		0			0
$235$			149.135i			0.0413978i
$236$	−1058.08	+	404.204i	−0.291844	+	0.111489i
$237$		0			0
$238$	49.6530	+	269.113i	0.0135232	+	0.0732942i
$239$	−5291.45			−1.43212			−0.716058	−	0.698041i	$-0.754055\pi$
$239$	−5291.45			−1.43212			−0.716058	+	0.698041i	$0.754055\pi$
$240$		0			0
$241$	−5003.21			−1.33728			−0.668642	−	0.743585i	$-0.733124\pi$
$241$	−5003.21			−1.33728			−0.668642	+	0.743585i	$0.733124\pi$
$242$	513.461	+	2782.89i	0.136391	+	0.739220i
$243$		0			0
$244$	−115.315	+	44.0523i	−0.0302553	+	0.0115580i
$245$		−	809.401i		−	0.211064i
$246$		0			0
$247$			5096.31i			1.31283i
$248$	−3392.51	+	2067.68i	−0.868648	+	0.529426i
$249$		0			0
$250$	1636.57	−	301.956i	0.414022	−	0.0763896i
$251$	−2577.68			−0.648215			−0.324107	−	0.946020i	$-0.605064\pi$
$251$	−2577.68			−0.648215			−0.324107	+	0.946020i	$0.605064\pi$
$252$		0			0
$253$	−9372.83			−2.32911
$254$	1184.43	−	218.535i	0.292591	−	0.0539848i
$255$		0			0
$256$	454.386	−	4070.72i	0.110934	−	0.993828i
$257$			870.567i			0.211301i	0.994403	+	0.105651i	$0.0336925\pi$
$257$			870.567i			0.211301i	−0.994403	+	0.105651i	$0.966307\pi$
$258$		0			0
$259$		−	530.308i		−	0.127227i
$260$	280.065	+	733.121i	0.0668033	+	0.174870i
$261$		0			0
$262$	894.852	+	4849.99i	0.211008	+	1.14364i
$263$	−4310.39			−1.01061			−0.505304	−	0.862942i	$-0.668620\pi$
$263$	−4310.39			−1.01061			−0.505304	+	0.862942i	$0.668620\pi$
$264$		0			0
$265$	848.556			0.196703
$266$	170.875	+	926.122i	0.0393873	+	0.213474i
$267$		0			0
$268$	−434.015	−	1136.11i	−0.0989241	−	0.258952i
$269$			5603.52i			1.27008i	0.772478	+	0.635042i	$0.219017\pi$
$269$			5603.52i			1.27008i	−0.772478	+	0.635042i	$0.780983\pi$
$270$		0			0
$271$		−	2149.22i		−	0.481756i	−0.970555	−	0.240878i	$-0.922565\pi$
$271$		−	2149.22i		−	0.481756i	0.970555	−	0.240878i	$-0.0774353\pi$
$272$	1552.07	+	1734.95i	0.345985	+	0.386753i
$273$		0			0
$274$	4092.84	−	755.155i	0.902400	−	0.166498i
$275$	5755.39			1.26205
$276$		0			0
$277$	−3209.99			−0.696279			−0.348140	−	0.937443i	$-0.613186\pi$
$277$	−3209.99			−0.696279			−0.348140	+	0.937443i	$0.613186\pi$
$278$	3555.57	−	656.025i	0.767083	−	0.141531i
$279$		0			0
$280$	75.4755	+	123.835i	0.0161090	+	0.0264306i
$281$		−	940.375i		−	0.199637i	−0.995006	−	0.0998187i	$-0.968174\pi$
$281$		−	940.375i		−	0.199637i	0.995006	−	0.0998187i	$-0.0318263\pi$
$282$		0			0
$283$		−	2050.10i		−	0.430621i	−0.976546	−	0.215310i	$-0.930924\pi$
$283$		−	2050.10i		−	0.430621i	0.976546	−	0.215310i	$-0.0690763\pi$
$284$	209.499	−	80.0320i	0.0437727	−	0.0167219i
$285$		0			0
$286$	1008.90	+	5468.12i	0.208593	+	1.13055i
$287$	619.877			0.127492
$288$		0			0
$289$	3590.01			0.730716
$290$	219.306	+	1188.61i	0.0444072	+	0.240682i
$291$		0			0
$292$	−930.411	+	355.433i	−0.186466	+	0.0712334i
$293$			4436.71i			0.884625i	0.896861	+	0.442312i	$0.145842\pi$
$293$			4436.71i			0.884625i	−0.896861	+	0.442312i	$0.854158\pi$
$294$		0			0
$295$		−	341.138i		−	0.0673283i
$296$	−2347.74	−	3852.03i	−0.461013	−	0.756400i
$297$		0			0
$298$	5977.58	−	1102.90i	1.16199	−	0.214394i
$299$	−7903.08			−1.52858
$300$		0			0
$301$	775.716			0.148543
$302$	−2661.36	+	491.037i	−0.507100	+	0.0935630i
$303$		0			0
$304$	5341.26	+	5970.64i	1.00770	+	1.12645i
$305$		−	37.1790i		−	0.00697988i
$306$		0			0
$307$		−	7392.80i		−	1.37436i	−0.726486	−	0.687181i	$-0.758848\pi$
$307$		−	7392.80i		−	1.37436i	0.726486	−	0.687181i	$-0.241152\pi$
$308$	366.684	+	959.862i	0.0678368	+	0.177575i
$309$		0			0
$310$	−217.114	−	1176.73i	−0.0397782	−	0.215593i
$311$	4896.50			0.892782			0.446391	−	0.894838i	$-0.352709\pi$
$311$	4896.50			0.892782			0.446391	+	0.894838i	$0.352709\pi$
$312$		0			0
$313$	681.722			0.123109			0.0615546	−	0.998104i	$-0.480394\pi$
$313$	681.722			0.123109			0.0615546	+	0.998104i	$0.480394\pi$
$314$	1074.23	+	5822.20i	0.193065	+	1.04639i
$315$		0			0
$316$	2137.53	+	5595.38i	0.380524	+	0.996091i
$317$			1552.07i			0.274993i	0.990502	+	0.137497i	$0.0439056\pi$
$317$			1552.07i			0.274993i	−0.990502	+	0.137497i	$0.956094\pi$
$318$		0			0
$319$			8563.69i			1.50305i
$320$	1096.47	+	565.370i	0.191546	+	0.0987661i
$321$		0			0
$322$	−1436.18	+	264.984i	−0.248556	+	0.0458602i
$323$	−4552.92			−0.784307
$324$		0			0
$325$	4852.88			0.828276
$326$	−4084.88	+	753.685i	−0.693989	+	0.128045i
$327$		0			0
$328$	4502.63	−	2744.28i	0.757977	−	0.461973i
$329$			164.641i			0.0275895i
$330$		0			0
$331$			7401.89i			1.22914i	0.788863	+	0.614569i	$0.210670\pi$
$331$			7401.89i			1.22914i	−0.788863	+	0.614569i	$0.789330\pi$
$332$	2607.33	−	996.043i	0.431011	−	0.164653i
$333$		0			0
$334$	−1564.43	−	8479.02i	−0.256293	−	1.38908i
$335$	366.297			0.0597402
$336$		0			0
$337$	−9743.17			−1.57491			−0.787454	−	0.616373i	$-0.788601\pi$
$337$	−9743.17			−1.57491			−0.787454	+	0.616373i	$0.788601\pi$
$338$	−276.804	−	1500.24i	−0.0445449	−	0.241428i
$339$		0			0
$340$	−654.953	+	250.203i	−0.104470	+	0.0399093i
$341$		−	8478.09i		−	1.34638i
$342$		0			0
$343$		−	1805.94i		−	0.284290i
$344$	5634.61	−	3434.20i	0.883134	−	0.538254i
$345$		0			0
$346$	7720.19	−	1424.42i	1.19954	−	0.221322i
$347$	7047.49			1.09029			0.545143	−	0.838343i	$-0.316475\pi$
$347$	7047.49			1.09029			0.545143	+	0.838343i	$0.316475\pi$
$348$		0			0
$349$	−1207.55			−0.185210			−0.0926052	−	0.995703i	$-0.529519\pi$
$349$	−1207.55			−0.185210			−0.0926052	+	0.995703i	$0.529519\pi$
$350$	881.886	−	162.713i	0.134682	−	0.0248497i
$351$		0			0
$352$	6912.94	+	5348.85i	1.04676	+	0.809928i
$353$			1520.13i			0.229201i	0.993412	+	0.114601i	$0.0365589\pi$
$353$			1520.13i			0.229201i	−0.993412	+	0.114601i	$0.963441\pi$
$354$		0			0
$355$			67.5450i			0.0100984i
$356$	1190.11	+	3115.33i	0.177179	+	0.463798i
$357$		0			0
$358$	−245.114	−	1328.48i	−0.0361862	−	0.196125i
$359$	6515.20			0.957825			0.478912	−	0.877863i	$-0.341031\pi$
$359$	6515.20			0.957825			0.478912	+	0.877863i	$0.341031\pi$
$360$		0			0
$361$	−8809.35			−1.28435
$362$	−375.842	−	2037.02i	−0.0545686	−	0.295755i
$363$		0			0
$364$	309.184	+	809.346i	0.0445210	+	0.116542i
$365$		−	299.977i		−	0.0430178i
$366$		0			0
$367$		−	4032.62i		−	0.573573i	−0.957995	−	0.286786i	$-0.907413\pi$
$367$		−	4032.62i		−	0.573573i	0.957995	−	0.286786i	$-0.0925870\pi$
$368$	−9258.94	+	8282.93i	−1.31156	+	1.17331i
$369$		0			0
$370$	1336.12	−	246.522i	0.187734	−	0.0346380i
$371$	936.784			0.131093
$372$		0			0
$373$	2455.35			0.340840			0.170420	−	0.985372i	$-0.445488\pi$
$373$	2455.35			0.340840			0.170420	+	0.985372i	$0.445488\pi$
$374$	−4885.09	+	901.329i	−0.675407	+	0.124617i
$375$		0			0
$376$	728.888	+	1195.91i	0.0999721	+	0.164028i
$377$			7220.81i			0.986448i
$378$		0			0
$379$			9518.27i			1.29003i	0.764171	+	0.645014i	$0.223149\pi$
$379$			9518.27i			1.29003i	−0.764171	+	0.645014i	$0.776851\pi$
$380$	−2253.94	+	861.045i	−0.304276	+	0.116239i
$381$		0			0
$382$	1583.73	+	8583.64i	0.212123	+	1.14968i
$383$	−9455.44			−1.26149			−0.630744	−	0.775991i	$-0.717250\pi$
$383$	−9455.44			−1.26149			−0.630744	+	0.775991i	$0.717250\pi$
$384$		0			0
$385$	−309.472			−0.0409666
$386$	−838.733	−	4545.83i	−0.110597	−	0.599421i
$387$		0			0
$388$	−11248.2	+	4297.01i	−1.47176	+	0.562236i
$389$		−	2966.07i		−	0.386596i	−0.981140	−	0.193298i	$-0.938082\pi$
$389$		−	2966.07i		−	0.386596i	0.981140	−	0.193298i	$-0.0619184\pi$
$390$		0			0
$391$		−	7060.42i		−	0.913199i
$392$	−3955.89	−	6490.58i	−0.509701	−	0.836285i
$393$		0			0
$394$	9319.83	−	1719.57i	1.19169	−	0.219874i
$395$	−1804.02			−0.229798
$396$		0			0
$397$	1296.85			0.163947			0.0819733	−	0.996635i	$-0.473878\pi$
$397$	1296.85			0.163947			0.0819733	+	0.996635i	$0.473878\pi$
$398$	−2911.13	+	537.122i	−0.366638	+	0.0676469i
$399$		0			0
$400$	5685.45	−	5086.14i	0.710682	−	0.635767i
$401$			2057.85i			0.256270i	0.991757	+	0.128135i	$0.0408991\pi$
$401$			2057.85i			0.256270i	−0.991757	+	0.128135i	$0.959101\pi$
$402$		0			0
$403$		−	7148.64i		−	0.883620i
$404$	−1243.10	−	3254.03i	−0.153085	−	0.400728i
$405$		0			0
$406$	242.108	+	1312.20i	0.0295951	+	0.160402i
$407$	9626.44			1.17240
$408$		0			0
$409$	5795.08			0.700607			0.350304	−	0.936636i	$-0.386078\pi$
$409$	5795.08			0.700607			0.350304	+	0.936636i	$0.386078\pi$
$410$	288.160	+	1561.79i	0.0347102	+	0.188125i
$411$		0			0
$412$	−4982.84	−	13043.5i	−0.595842	−	1.55973i
$413$		−	376.608i		−	0.0448709i
$414$		0			0
$415$			840.635i			0.0994341i
$416$	5828.92	+	4510.09i	0.686986	+	0.531552i
$417$		0			0
$418$	−16811.5	+	3101.82i	−1.96717	+	0.362955i
$419$	−14105.2			−1.64460			−0.822298	−	0.569058i	$-0.807308\pi$
$419$	−14105.2			−1.64460			−0.822298	+	0.569058i	$0.807308\pi$
$420$		0			0
$421$	6420.86			0.743310			0.371655	−	0.928371i	$-0.378790\pi$
$421$	6420.86			0.743310			0.371655	+	0.928371i	$0.378790\pi$
$422$	14680.3	−	2708.60i	1.69343	−	0.312447i
$423$		0			0
$424$	6804.57	−	4147.26i	0.779384	−	0.475021i
$425$			4335.45i			0.494824i
$426$		0			0
$427$		−	41.0447i		−	0.00465174i
$428$	5857.57	−	2237.69i	0.661534	−	0.252717i
$429$		0			0
$430$	360.604	+	1954.43i	0.0404415	+	0.219188i
$431$	−1119.73			−0.125140			−0.0625700	−	0.998041i	$-0.519930\pi$
$431$	−1119.73			−0.125140			−0.0625700	+	0.998041i	$0.519930\pi$
$432$		0			0
$433$	−299.833			−0.0332773			−0.0166387	−	0.999862i	$-0.505296\pi$
$433$	−299.833			−0.0332773			−0.0166387	+	0.999862i	$0.505296\pi$
$434$	−239.688	−	1299.08i	−0.0265102	−	0.143682i
$435$		0			0
$436$	−11821.9	+	4516.16i	−1.29854	+	0.496066i
$437$		−	24297.6i		−	2.65976i
$438$		0			0
$439$		−	2413.35i		−	0.262375i	−0.991358	−	0.131188i	$-0.958121\pi$
$439$		−	2413.35i		−	0.262375i	0.991358	−	0.131188i	$-0.0418791\pi$
$440$	−2247.93	+	1370.07i	−0.243559	+	0.148445i
$441$		0			0
$442$	−4119.06	+	759.992i	−0.443266	+	0.0817853i
$443$	4818.73			0.516805			0.258402	−	0.966037i	$-0.416804\pi$
$443$	4818.73			0.516805			0.258402	+	0.966037i	$0.416804\pi$
$444$		0			0
$445$	−1004.42			−0.106998
$446$	13239.0	−	2442.68i	1.40557	−	0.259337i
$447$		0			0
$448$	1210.48	+	624.154i	0.127655	+	0.0658226i
$449$		−	8677.13i		−	0.912024i	−0.889974	−	0.456012i	$-0.849277\pi$
$449$		−	8677.13i		−	0.912024i	0.889974	−	0.456012i	$-0.150723\pi$
$450$		0			0
$451$			11252.3i			1.17484i
$452$	−1267.09	−	3316.85i	−0.131856	−	0.345158i
$453$		0			0
$454$	1144.67	+	6203.96i	0.118330	+	0.641336i
$455$	−260.944			−0.0268862
$456$		0			0
$457$	−6920.09			−0.708333			−0.354166	−	0.935182i	$-0.615235\pi$
$457$	−6920.09			−0.708333			−0.354166	+	0.935182i	$0.615235\pi$
$458$	−2994.30	−	16228.8i	−0.305491	−	1.65572i
$459$		0			0
$460$	−1335.26	−	3495.29i	−0.135341	−	0.354280i
$461$		−	15554.8i		−	1.57149i	−0.618548	−	0.785747i	$-0.712279\pi$
$461$		−	15554.8i		−	1.57149i	0.618548	−	0.785747i	$-0.287721\pi$
$462$		0			0
$463$		−	11540.5i		−	1.15839i	−0.815189	−	0.579194i	$-0.803367\pi$
$463$		−	11540.5i		−	1.15839i	0.815189	−	0.579194i	$-0.196633\pi$
$464$	7567.88	+	8459.63i	0.757177	+	0.846397i
$465$		0			0
$466$	−8567.20	+	1580.70i	−0.851648	+	0.157134i
$467$	−7.01271			−0.000694881			−0.000347441	−	1.00000i	$-0.500111\pi$
$467$	−7.01271			−0.000694881			−0.000347441		1.00000i	$0.500111\pi$
$468$		0			0
$469$	404.383			0.0398138
$470$	−414.816	+	76.5361i	−0.0407107	+	0.00751137i
$471$		0			0
$472$	−1667.29	−	2735.59i	−0.162592	−	0.266770i
$473$			14081.2i			1.36883i
$474$		0			0
$475$			14920.0i			1.44121i
$476$	−723.051	+	276.218i	−0.0696239	+	0.0265975i
$477$		0			0
$478$	−2715.57	−	14718.1i	−0.259848	−	1.40834i
$479$	5661.41			0.540034			0.270017	−	0.962856i	$-0.412971\pi$
$479$	5661.41			0.540034			0.270017	+	0.962856i	$0.412971\pi$
$480$		0			0
$481$	8116.92			0.769438
$482$	−2567.65	−	13916.3i	−0.242641	−	1.31509i
$483$		0			0
$484$	−7477.05	+	2856.36i	−0.702203	+	0.268253i
$485$		−	3626.57i		−	0.339534i
$486$		0			0
$487$		−	9082.26i		−	0.845085i	−0.906343	−	0.422542i	$-0.861138\pi$
$487$		−	9082.26i		−	0.845085i	0.906343	−	0.422542i	$-0.138862\pi$
$488$	−181.710	−	298.139i	−0.0168558	−	0.0276559i
$489$		0			0
$490$	2251.33	−	415.384i	0.207561	−	0.0382962i
$491$	10197.6			0.937291			0.468646	−	0.883386i	$-0.344742\pi$
$491$	10197.6			0.937291			0.468646	+	0.883386i	$0.344742\pi$
$492$		0			0
$493$	−6450.90			−0.589319
$494$	−14175.3	+	2615.42i	−1.29104	+	0.238205i
$495$		0			0
$496$	−7492.24	−	8375.07i	−0.678249	−	0.758169i
$497$			74.5680i			0.00673004i
$498$		0			0
$499$		−	2717.18i		−	0.243763i	−0.992545	−	0.121881i	$-0.961107\pi$
$499$		−	2717.18i		−	0.243763i	0.992545	−	0.121881i	$-0.0388928\pi$
$500$	1679.77	+	4397.11i	0.150243	+	0.393289i
$501$		0			0
$502$	−1322.87	−	7169.77i	−0.117614	−	0.637455i
$503$	8294.45			0.735251			0.367626	−	0.929974i	$-0.380171\pi$
$503$	8294.45			0.735251			0.367626	+	0.929974i	$0.380171\pi$
$504$		0			0
$505$	1049.14			0.0924479
$506$	−4810.14	−	26070.3i	−0.422602	−	2.29045i
$507$		0			0
$508$	1215.70	+	3182.33i	0.106177	+	0.277939i
$509$		−	3310.11i		−	0.288247i	−0.989560	−	0.144124i	$-0.953964\pi$
$509$		−	3310.11i		−	0.288247i	0.989560	−	0.144124i	$-0.0460363\pi$
$510$		0			0
$511$		−	331.166i		−	0.0286692i
$512$	11555.8	−	825.228i	0.997460	−	0.0712310i
$513$		0			0
$514$	−2421.46	+	446.775i	−0.207794	+	0.0383393i
$515$	4205.39			0.359829
$516$		0			0
$517$	−2988.66			−0.254238
$518$	1475.04	−	272.154i	0.125115	−	0.0230845i
$519$		0			0
$520$	−1895.43	+	1155.23i	−0.159846	+	0.0974235i
$521$			5030.71i			0.423031i	0.977375	+	0.211516i	$0.0678400\pi$
$521$			5030.71i			0.423031i	−0.977375	+	0.211516i	$0.932160\pi$
$522$		0			0
$523$		−	9680.16i		−	0.809338i	−0.914463	−	0.404669i	$-0.867387\pi$
$523$		−	9680.16i		−	0.809338i	0.914463	−	0.404669i	$-0.132613\pi$
$524$	−13030.9	+	4978.02i	−1.08637	+	0.415012i
$525$		0			0
$526$	−2212.09	−	11989.2i	−0.183368	−	0.993833i
$527$	6386.42			0.527888
$528$		0			0
$529$	25512.4			2.09686
$530$	435.479	+	2360.24i	0.0356905	+	0.193438i
$531$		0			0
$532$	−2488.30	+	950.571i	−0.202784	+	0.0774671i
$533$			9487.87i			0.771041i
$534$		0			0
$535$			1888.56i			0.152616i
$536$	2937.34	−	1790.26i	0.236705	−	0.144267i
$537$		0			0
$538$	−15586.1	+	2875.73i	−1.24900	+	0.230449i
$539$	16220.3			1.29621
$540$		0			0
$541$	18659.8			1.48290			0.741449	−	0.671009i	$-0.234139\pi$
$541$	18659.8			1.48290			0.741449	+	0.671009i	$0.234139\pi$
$542$	5978.01	−	1102.98i	0.473759	−	0.0874115i
$543$		0			0
$544$	−4029.21	+	5207.42i	−0.317557	+	0.410416i
$545$		−	3811.52i		−	0.299574i
$546$		0			0
$547$		−	4536.56i		−	0.354606i	−0.984156	−	0.177303i	$-0.943263\pi$
$547$		−	4536.56i		−	0.354606i	0.984156	−	0.177303i	$-0.0567372\pi$
$548$	4200.89	+	10996.6i	0.327469	+	0.857212i
$549$		0			0
$550$	2953.66	+	16008.5i	0.228990	+	1.24110i
$551$	−22200.0			−1.71643
$552$		0			0
$553$	−1991.59			−0.153149
$554$	−1647.36	−	8928.51i	−0.126335	−	0.684722i
$555$		0			0
$556$	3649.44	+	9553.07i	0.278364	+	0.728670i
$557$		−	17657.1i		−	1.34319i	−0.740918	−	0.671596i	$-0.765609\pi$
$557$		−	17657.1i		−	1.34319i	0.740918	−	0.671596i	$-0.234391\pi$
$558$		0			0
$559$			11873.1i			0.898355i
$560$	−305.712	+	273.486i	−0.0230691	+	0.0206373i
$561$		0			0
$562$	2615.63	−	482.601i	0.196324	−	0.0362229i
$563$	−9944.94			−0.744457			−0.372229	−	0.928141i	$-0.621406\pi$
$563$	−9944.94			−0.744457			−0.372229	+	0.928141i	$0.621406\pi$
$564$		0			0
$565$	1069.39			0.0796278
$566$	5702.30	−	1052.11i	0.423473	−	0.0781334i
$567$		0			0
$568$	330.122	+	541.643i	0.0243866	+	0.0400121i
$569$		−	4715.82i		−	0.347447i	−0.984794	−	0.173724i	$-0.944420\pi$
$569$		−	4715.82i		−	0.347447i	0.984794	−	0.173724i	$-0.0555799\pi$
$570$		0			0
$571$			9229.75i			0.676450i	0.941065	+	0.338225i	$0.109827\pi$
$571$			9229.75i			0.676450i	−0.941065	+	0.338225i	$0.890173\pi$
$572$	−14691.7	+	5612.48i	−1.07393	+	0.410261i
$573$		0			0
$574$	318.121	+	1724.17i	0.0231326	+	0.125376i
$575$	−23137.1			−1.67806
$576$		0			0
$577$	4076.34			0.294108			0.147054	−	0.989128i	$-0.453021\pi$
$577$	4076.34			0.294108			0.147054	+	0.989128i	$0.453021\pi$
$578$	1842.39	+	9985.54i	0.132584	+	0.718587i
$579$		0			0
$580$	−3193.55	+	1219.99i	−0.228629	+	0.0873403i
$581$			928.039i			0.0662677i
$582$		0			0
$583$			17005.0i			1.20802i
$584$	−1466.12	−	2405.51i	−0.103884	−	0.170447i
$585$		0			0
$586$	−12340.6	+	2276.92i	−0.869941	+	0.160509i
$587$	−8635.49			−0.607197			−0.303599	−	0.952800i	$-0.598188\pi$
$587$	−8635.49			−0.607197			−0.303599	+	0.952800i	$0.598188\pi$
$588$		0			0
$589$	21978.1			1.53751
$590$	948.869	−	175.072i	0.0662107	−	0.0122163i
$591$		0			0
$592$	9509.47	−	8507.05i	0.660197	−	0.590604i
$593$			24260.9i			1.68006i	0.542537	+	0.840032i	$0.317464\pi$
$593$			24260.9i			1.68006i	−0.542537	+	0.840032i	$0.682536\pi$
$594$		0			0
$595$		−	233.121i		−	0.0160622i
$596$	6135.39	+	16060.5i	0.421670	+	1.10380i
$597$		0			0
$598$	−4055.86	−	21982.2i	−0.277352	−	1.50321i
$599$	15098.0			1.02986			0.514932	−	0.857231i	$-0.327817\pi$
$599$	15098.0			1.02986			0.514932	+	0.857231i	$0.327817\pi$
$600$		0			0
$601$	5928.26			0.402361			0.201180	−	0.979554i	$-0.435522\pi$
$601$	5928.26			0.402361			0.201180	+	0.979554i	$0.435522\pi$
$602$	398.097	+	2157.64i	0.0269522	+	0.146078i
$603$		0			0
$604$	−2731.62	−	7150.52i	−0.184020	−	0.481706i
$605$		−	2410.70i		−	0.161998i
$606$		0			0
$607$			18608.4i			1.24430i	0.782897	+	0.622151i	$0.213741\pi$
$607$			18608.4i			1.24430i	−0.782897	+	0.622151i	$0.786259\pi$
$608$	−13866.1	+	17920.7i	−0.924907	+	1.19536i
$609$		0			0
$610$	103.413	−	19.0803i	0.00686403	−	0.00126645i
$611$	−2520.01			−0.166855
$612$		0			0
$613$	7939.25			0.523105			0.261552	−	0.965189i	$-0.415766\pi$
$613$	7939.25			0.523105			0.261552	+	0.965189i	$0.415766\pi$
$614$	20562.9	−	3793.98i	1.35155	−	0.249369i
$615$		0			0
$616$	−2481.65	+	1512.52i	−0.162319	+	0.0989308i
$617$			29179.0i			1.90389i	0.306265	+	0.951946i	$0.400921\pi$
$617$			29179.0i			1.90389i	−0.306265	+	0.951946i	$0.599079\pi$
$618$		0			0
$619$		−	16301.7i		−	1.05851i	−0.848462	−	0.529256i	$-0.822471\pi$
$619$		−	16301.7i		−	1.05851i	0.848462	−	0.529256i	$-0.177529\pi$
$620$	3161.63	−	1207.80i	0.204797	−	0.0782359i
$621$		0			0
$622$	2512.88	+	13619.5i	0.161990	+	0.877963i
$623$	−1108.85			−0.0713087
$624$		0			0
$625$	13481.6			0.862824
$626$	349.860	+	1896.19i	0.0223374	+	0.121066i
$627$		0			0
$628$	−15643.0	+	5975.90i	−0.993988	+	0.379720i
$629$			7251.46i			0.459674i
$630$		0			0
$631$			2517.83i			0.158848i	0.996841	+	0.0794242i	$0.0253082\pi$
$631$			2517.83i			0.158848i	−0.996841	+	0.0794242i	$0.974692\pi$
$632$	−14466.4	+	8817.04i	−0.910513	+	0.554942i
$633$		0			0
$634$	−4317.05	+	796.521i	−0.270429	+	0.0498958i
$635$	−1026.02			−0.0641205
$636$		0			0
$637$	13676.8			0.850700
$638$	−23819.7	+	4394.88i	−1.47811	+	0.272720i
$639$		0			0
$640$	−1009.86	+	3339.96i	−0.0623720	+	0.206287i
$641$			16826.3i			1.03681i	0.855134	+	0.518407i	$0.173475\pi$
$641$			16826.3i			1.03681i	−0.855134	+	0.518407i	$0.826525\pi$
$642$		0			0
$643$			20423.8i			1.25263i	0.779572	+	0.626313i	$0.215437\pi$
$643$			20423.8i			1.25263i	−0.779572	+	0.626313i	$0.784563\pi$
$644$	−1474.09	−	3858.71i	−0.0901979	−	0.236110i
$645$		0			0
$646$	−2336.56	−	12663.8i	−0.142307	−	0.771289i
$647$	−21477.2			−1.30503			−0.652515	−	0.757776i	$-0.726286\pi$
$647$	−21477.2			−1.30503			−0.652515	+	0.757776i	$0.726286\pi$
$648$		0			0
$649$	6836.40			0.413485
$650$	2490.50	+	13498.2i	0.150285	+	0.814527i
$651$		0			0
$652$	−4192.72	−	10975.2i	−0.251840	−	0.659237i
$653$		−	25214.7i		−	1.51107i	−0.655111	−	0.755533i	$-0.727378\pi$
$653$		−	25214.7i		−	1.51107i	0.655111	−	0.755533i	$-0.272622\pi$
$654$		0			0
$655$		−	4201.33i		−	0.250625i
$656$	9943.90	+	11115.6i	0.591835	+	0.661573i
$657$		0			0
$658$	−457.946	+	84.4938i	−0.0271316	+	0.00500595i
$659$	13730.1			0.811605			0.405802	−	0.913961i	$-0.366992\pi$
$659$	13730.1			0.811605			0.405802	+	0.913961i	$0.366992\pi$
$660$		0			0
$661$	1544.08			0.0908588			0.0454294	−	0.998968i	$-0.485534\pi$
$661$	1544.08			0.0908588			0.0454294	+	0.998968i	$0.485534\pi$
$662$	−20588.2	+	3798.65i	−1.20874	+	0.223019i
$663$		0			0
$664$	4108.55	+	6741.05i	0.240125	+	0.393981i
$665$		−	802.258i		−	0.0467823i
$666$		0			0
$667$		−	34426.6i		−	1.99851i
$668$	22781.3	−	8702.86i	1.31952	−	0.504078i
$669$		0			0
$670$	187.984	+	1018.85i	0.0108395	+	0.0587486i
$671$	745.066			0.0428658
$672$		0			0
$673$	−5368.23			−0.307474			−0.153737	−	0.988112i	$-0.549131\pi$
$673$	−5368.23			−0.307474			−0.153737	+	0.988112i	$0.549131\pi$
$674$	−5000.19	−	27100.4i	−0.285757	−	1.54877i
$675$		0			0
$676$	4030.84	−	1539.85i	0.229338	−	0.0876110i
$677$		−	19299.4i		−	1.09562i	−0.836602	−	0.547812i	$-0.815461\pi$
$677$		−	19299.4i		−	1.09562i	0.836602	−	0.547812i	$-0.184539\pi$
$678$		0			0
$679$		−	4003.64i		−	0.226282i
$680$	−1032.06	−	1693.33i	−0.0582023	−	0.0954946i
$681$		0			0
$682$	23581.6	−	4350.95i	1.32403	−	0.244291i
$683$	7466.11			0.418276			0.209138	−	0.977886i	$-0.432934\pi$
$683$	7466.11			0.418276			0.209138	+	0.977886i	$0.432934\pi$
$684$		0			0
$685$	−3545.45			−0.197759
$686$	5023.17	−	926.806i	0.279571	−	0.0515825i
$687$		0			0
$688$	12443.8	+	13910.1i	0.689559	+	0.770812i
$689$			14338.5i			0.792818i
$690$		0			0
$691$		−	23772.0i		−	1.30873i	−0.756180	−	0.654364i	$-0.772937\pi$
$691$		−	23772.0i		−	1.30873i	0.756180	−	0.654364i	$-0.227063\pi$
$692$	7924.00	+	20742.5i	0.435297	+	1.13947i
$693$		0			0
$694$	3616.77	+	19602.5i	0.197825	+	1.07219i
$695$	−3080.03			−0.168104
$696$		0			0
$697$	−8476.24			−0.460632
$698$	−619.713	−	3358.76i	−0.0336052	−	0.182136i
$699$		0			0
$700$	905.168	+	2369.44i	0.0488745	+	0.127938i
$701$		−	3501.89i		−	0.188680i	−0.995540	−	0.0943399i	$-0.969926\pi$
$701$		−	3501.89i		−	0.188680i	0.995540	−	0.0943399i	$-0.0300740\pi$
$702$		0			0
$703$			24955.1i			1.33883i
$704$	−11330.0	+	21973.2i	−0.606556	+	1.17634i
$705$		0			0
$706$	−4228.20	+	780.128i	−0.225397	+	0.0415871i
$707$	1158.23			0.0616118
$708$		0			0
$709$	4158.76			0.220290			0.110145	−	0.993916i	$-0.464869\pi$
$709$	4158.76			0.220290			0.110145	+	0.993916i	$0.464869\pi$
$710$	−187.875	+	34.6641i	−0.00993074	+	0.00183228i
$711$		0			0
$712$	−8054.45	+	4909.04i	−0.423951	+	0.258391i
$713$			34082.5i			1.79018i
$714$		0			0
$715$		−	4736.79i		−	0.247757i
$716$	3569.36	−	1363.56i	0.186303	−	0.0711711i
$717$		0			0
$718$	3343.60	+	18121.9i	0.173791	+	0.941926i
$719$	20077.1			1.04137			0.520687	−	0.853748i	$-0.325676\pi$
$719$	20077.1			1.04137			0.520687	+	0.853748i	$0.325676\pi$
$720$		0			0
$721$	4642.64			0.239807
$722$	−4520.96	−	24503.0i	−0.233037	−	1.26303i
$723$		0			0
$724$	5473.04	−	2090.79i	0.280945	−	0.107326i
$725$			21139.7i			1.08291i
$726$		0			0
$727$			36050.8i			1.83913i	0.392935	+	0.919566i	$0.371460\pi$
$727$			36050.8i			1.83913i	−0.392935	+	0.919566i	$0.628540\pi$
$728$	−2092.51	+	1275.35i	−0.106529	+	0.0649278i
$729$		0			0
$730$	834.378	−	153.948i	0.0423037	−	0.00780530i
$731$	−10607.2			−0.536691
$732$		0			0
$733$	−21701.9			−1.09356			−0.546779	−	0.837277i	$-0.684146\pi$
$733$	−21701.9			−1.09356			−0.546779	+	0.837277i	$0.684146\pi$
$734$	11216.7	−	2069.54i	0.564052	−	0.104071i
$735$		0			0
$736$	−27790.5	−	21502.8i	−1.39181	−	1.07690i
$737$			7340.58i			0.366884i
$738$		0			0
$739$			26112.0i			1.29979i	0.760024	+	0.649895i	$0.225187\pi$
$739$			26112.0i			1.29979i	−0.760024	+	0.649895i	$0.774813\pi$
$740$	1371.39	+	3589.87i	0.0681262	+	0.178333i
$741$		0			0
$742$	480.757	+	2605.64i	0.0237859	+	0.128917i
$743$	5612.86			0.277141			0.138570	−	0.990353i	$-0.455749\pi$
$743$	5612.86			0.277141			0.138570	+	0.990353i	$0.455749\pi$
$744$		0			0
$745$	−5178.11			−0.254646
$746$	1260.09	+	6829.51i	0.0618432	+	0.335182i
$747$		0			0
$748$	−5014.06	−	13125.2i	−0.245096	−	0.641585i
$749$			2084.92i			0.101711i
$750$		0			0
$751$		−	27745.1i		−	1.34811i	−0.738681	−	0.674056i	$-0.764551\pi$
$751$		−	27745.1i		−	1.34811i	0.738681	−	0.674056i	$-0.235449\pi$
$752$	−2952.34	+	2641.13i	−0.143166	+	0.128075i
$753$		0			0
$754$	−20084.5	+	3705.72i	−0.970074	+	0.178985i
$755$	2305.42			0.111129
$756$		0			0
$757$	−22792.6			−1.09433			−0.547167	−	0.837023i	$-0.684294\pi$
$757$	−22792.6			−1.09433			−0.547167	+	0.837023i	$0.684294\pi$
$758$	−26474.9	+	4884.78i	−1.26862	+	0.234067i
$759$		0			0
$760$	−3551.70	−	5827.41i	−0.169518	−	0.278135i
$761$		−	32307.4i		−	1.53895i	−0.638675	−	0.769477i	$-0.720517\pi$
$761$		−	32307.4i		−	1.53895i	0.638675	−	0.769477i	$-0.279483\pi$
$762$		0			0
$763$		−	4207.82i		−	0.199651i
$764$	−23062.4	+	8810.24i	−1.09211	+	0.417203i
$765$		0			0
$766$	−4852.53	−	26300.1i	−0.228889	−	1.24055i
$767$	5764.38			0.271369
$768$		0			0
$769$	−2401.94			−0.112635			−0.0563174	−	0.998413i	$-0.517936\pi$
$769$	−2401.94			−0.112635			−0.0563174	+	0.998413i	$0.517936\pi$
$770$	−158.821	−	860.790i	−0.00743313	−	0.0402866i
$771$		0			0
$772$	12213.7	−	4665.84i	0.569404	−	0.217522i
$773$		−	21135.4i		−	0.983424i	−0.870758	−	0.491712i	$-0.836371\pi$
$773$		−	21135.4i		−	0.983424i	0.870758	−	0.491712i	$-0.163629\pi$
$774$		0			0
$775$		−	20928.4i		−	0.970025i
$776$	−17724.6	−	29081.5i	−0.819945	−	1.34531i
$777$		0			0
$778$	8250.07	−	1522.19i	0.380179	−	0.0701454i
$779$	−29170.0			−1.34162
$780$		0			0
$781$	−1353.60			−0.0620174
$782$	19638.4	−	3623.41i	0.898041	−	0.165694i
$783$		0			0
$784$	16023.3	−	14334.2i	0.729922	−	0.652979i
$785$		−	5043.51i		−	0.229313i
$786$		0			0
$787$			4360.74i			0.197514i	0.995112	+	0.0987570i	$0.0314867\pi$
$787$			4360.74i			0.197514i	−0.995112	+	0.0987570i	$0.968513\pi$
$788$	9565.87	+	25040.4i	0.432449	+	1.13202i
$789$		0			0
$790$	−925.824	−	5017.85i	−0.0416954	−	0.225984i
$791$	1180.58			0.0530679
$792$		0			0
$793$	628.232			0.0281326
$794$	665.541	+	3607.15i	0.0297471	+	0.161225i
$795$		0			0
$796$	−2987.99	−	7821.60i	−0.133048	−	0.348278i
$797$			20501.8i			0.911181i	0.890190	+	0.455590i	$0.150572\pi$
$797$			20501.8i			0.911181i	−0.890190	+	0.455590i	$0.849428\pi$
$798$		0			0
$799$		−	2251.31i		−	0.0996818i
$800$	17064.8	+	13203.8i	0.754163	+	0.583530i
$801$		0			0
$802$	−5723.88	+	1056.09i	−0.252016	+	0.0464985i
$803$	6011.51			0.264186
$804$		0			0
$805$	1244.10			0.0544705
$806$	19883.8	−	3668.68i	0.868954	−	0.160327i
$807$		0			0
$808$	8413.07	−	5127.61i	0.366300	−	0.223253i
$809$			34550.7i			1.50153i	0.660568	+	0.750766i	$0.270315\pi$
$809$			34550.7i			1.50153i	−0.660568	+	0.750766i	$0.729685\pi$
$810$		0			0
$811$		−	19709.5i		−	0.853384i	−0.904397	−	0.426692i	$-0.859679\pi$
$811$		−	19709.5i		−	0.853384i	0.904397	−	0.426692i	$-0.140321\pi$
$812$	−3525.60	+	1346.84i	−0.152370	+	0.0582078i
$813$		0			0
$814$	4940.29	+	26775.7i	0.212724	+	1.15294i
$815$	3538.55			0.152086
$816$		0			0
$817$	−36503.4			−1.56315
$818$	2974.03	+	16118.9i	0.127121	+	0.688978i
$819$		0			0
$820$	−4196.20	+	1603.02i	−0.178704	+	0.0682682i
$821$		−	33361.4i		−	1.41817i	−0.705122	−	0.709086i	$-0.749108\pi$
$821$		−	33361.4i		−	1.41817i	0.705122	−	0.709086i	$-0.250892\pi$
$822$		0			0
$823$		−	42193.2i		−	1.78707i	−0.448990	−	0.893537i	$-0.648216\pi$
$823$		−	42193.2i		−	1.78707i	0.448990	−	0.893537i	$-0.351784\pi$
$824$	33723.0	−	20553.6i	1.42572	−	0.868954i
$825$		0			0
$826$	1047.53	−	193.275i	0.0441261	−	0.00814153i
$827$	−13992.0			−0.588329			−0.294165	−	0.955755i	$-0.595041\pi$
$827$	−13992.0			−0.588329			−0.294165	+	0.955755i	$0.595041\pi$
$828$		0			0
$829$	−23454.8			−0.982653			−0.491327	−	0.870975i	$-0.663488\pi$
$829$	−23454.8			−0.982653			−0.491327	+	0.870975i	$0.663488\pi$
$830$	−2338.21	+	431.414i	−0.0977836	+	0.0180417i
$831$		0			0
$832$	−9553.33	+	18527.6i	−0.398080	+	0.772030i
$833$			12218.6i			0.508221i
$834$		0			0
$835$			7345.00i			0.304412i
$836$	−17255.3	−	45168.9i	−0.713860	−	1.86866i
$837$		0			0
$838$	−7238.80	−	39233.4i	−0.298401	−	1.61730i
$839$	−9159.10			−0.376886			−0.188443	−	0.982084i	$-0.560344\pi$
$839$	−9159.10			−0.376886			−0.188443	+	0.982084i	$0.560344\pi$
$840$		0			0
$841$	−7065.62			−0.289705
$842$	3295.19	+	17859.5i	0.134869	+	0.730973i
$843$		0			0
$844$	15067.8	+	39442.9i	0.614522	+	1.60863i
$845$			1299.60i			0.0529082i
$846$		0			0
$847$		−	2661.35i		−	0.107963i
$848$	15027.6	+	16798.4i	0.608550	+	0.680258i
$849$		0			0
$850$	−12059.0	+	2224.95i	−0.486611	+	0.0897827i
$851$	−38699.0			−1.55885
$852$		0			0
$853$	−33480.6			−1.34391			−0.671955	−	0.740592i	$-0.734545\pi$
$853$	−33480.6			−1.34391			−0.671955	+	0.740592i	$0.734545\pi$
$854$	114.165	−	21.0641i	0.00457452	−	0.000844028i
$855$		0			0
$856$	9230.20	+	15144.3i	0.368553	+	0.604699i
$857$			30949.5i			1.23362i	0.787111	+	0.616811i	$0.211576\pi$
$857$			30949.5i			1.23362i	−0.787111	+	0.616811i	$0.788424\pi$
$858$		0			0
$859$		−	6145.24i		−	0.244089i	−0.992525	−	0.122045i	$-0.961055\pi$
$859$		−	6145.24i		−	0.244089i	0.992525	−	0.122045i	$-0.0389451\pi$
$860$	−5251.14	+	2006.02i	−0.208212	+	0.0795405i
$861$		0			0
$862$	−574.644	−	3114.50i	−0.0227059	−	0.123063i
$863$	−13685.9			−0.539830			−0.269915	−	0.962884i	$-0.586996\pi$
$863$	−13685.9			−0.539830			−0.269915	+	0.962884i	$0.586996\pi$
$864$		0			0
$865$	−6687.66			−0.262875
$866$	−153.874	−	833.980i	−0.00603795	−	0.0327249i
$867$		0			0
$868$	3490.36	−	1333.38i	0.136487	−	0.0521402i
$869$		−	36152.5i		−	1.41127i
$870$		0			0
$871$			6189.50i			0.240785i
$872$	−18628.6	−	30564.6i	−0.723444	−	1.18698i
$873$		0			0
$874$	67583.3	−	12469.5i	2.61561	−	0.482595i
$875$	−1565.09			−0.0604681
$876$		0			0
$877$	−5149.46			−0.198272			−0.0991361	−	0.995074i	$-0.531608\pi$
$877$	−5149.46			−0.198272			−0.0991361	+	0.995074i	$0.531608\pi$
$878$	6712.68	−	1238.53i	0.258020	−	0.0476063i
$879$		0			0
$880$	−4964.46	−	5549.44i	−0.190173	−	0.212582i
$881$		−	26936.4i		−	1.03009i	−0.857162	−	0.515046i	$-0.827775\pi$
$881$		−	26936.4i		−	1.03009i	0.857162	−	0.515046i	$-0.172225\pi$
$882$		0			0
$883$			37301.8i			1.42164i	0.703376	+	0.710818i	$0.251675\pi$
$883$			37301.8i			1.42164i	−0.703376	+	0.710818i	$0.748325\pi$
$884$	−4227.80	−	11067.0i	−0.160856	−	0.421069i
$885$		0			0
$886$	2472.97	+	13403.2i	0.0937709	+	0.508227i
$887$	34843.5			1.31898			0.659488	−	0.751715i	$-0.270773\pi$
$887$	34843.5			1.31898			0.659488	+	0.751715i	$0.270773\pi$
$888$		0			0
$889$	−1132.70			−0.0427330
$890$	−515.469	−	2793.78i	−0.0194141	−	0.105222i
$891$		0			0
$892$	13588.5	+	35570.4i	0.510064	+	1.33519i
$893$		−	7747.64i		−	0.290330i
$894$		0			0
$895$			1150.81i			0.0429802i
$896$	−1114.86	+	3687.23i	−0.0415678	+	0.137480i
$897$		0			0
$898$	24135.2	−	4453.10i	0.896886	−	0.165481i
$899$	31140.2			1.15527
$900$		0			0
$901$	−12809.6			−0.473641
$902$	−31298.2	+	5774.70i	−1.15534	+	0.213167i
$903$		0			0
$904$	8575.46	−	5226.59i	0.315504	−	0.192294i
$905$			1764.58i			0.0648139i
$906$		0			0
$907$			8883.19i			0.325206i	0.986692	+	0.162603i	$0.0519889\pi$
$907$			8883.19i			0.325206i	−0.986692	+	0.162603i	$0.948011\pi$
$908$	−16668.8	+	6367.75i	−0.609220	+	0.232732i
$909$		0			0
$910$	−133.916	−	725.809i	−0.00487833	−	0.0264399i
$911$	44512.1			1.61883			0.809413	−	0.587240i	$-0.199785\pi$
$911$	44512.1			1.61883			0.809413	+	0.587240i	$0.199785\pi$
$912$		0			0
$913$	−16846.3			−0.610658
$914$	−3551.39	−	19248.1i	−0.128522	−	0.696575i
$915$		0			0
$916$	43603.3	−	16657.2i	1.57281	−	0.600840i
$917$		−	4638.16i		−	0.167029i
$918$		0			0
$919$			7223.63i			0.259288i	0.991561	+	0.129644i	$0.0413834\pi$
$919$			7223.63i			0.259288i	−0.991561	+	0.129644i	$0.958617\pi$
$920$	9036.83	−	5507.79i	0.323843	−	0.197377i
$921$		0			0
$922$	43265.3	−	7982.72i	1.54541	−	0.285137i
$923$	−1141.34			−0.0407017
$924$		0			0
$925$	23763.1			0.844677
$926$	32099.7	−	5922.60i	1.13916	−	0.210182i
$927$		0			0
$928$	−19646.4	+	25391.4i	−0.694964	+	0.898182i
$929$		−	35694.3i		−	1.26060i	−0.776353	−	0.630298i	$-0.782933\pi$
$929$		−	35694.3i		−	1.26060i	0.776353	−	0.630298i	$-0.217067\pi$
$930$		0			0
$931$			42048.8i			1.48023i
$932$	−8793.37	−	23018.3i	−0.309052	−	0.809000i
$933$		0			0
$934$	−3.59892	−	19.5057i	−0.000126082	−	0.000683347i
$935$	4231.74			0.148014
$936$		0			0
$937$	−4657.90			−0.162398			−0.0811991	−	0.996698i	$-0.525875\pi$
$937$	−4657.90			−0.162398			−0.0811991	+	0.996698i	$0.525875\pi$
$938$	207.529	+	1124.78i	0.00722396	+	0.0391529i
$939$		0			0
$940$	−425.767	−	1114.52i	−0.0147734	−	0.0386721i
$941$		−	25553.4i		−	0.885245i	−0.896708	−	0.442623i	$-0.854048\pi$
$941$		−	25553.4i		−	0.885245i	0.896708	−	0.442623i	$-0.145952\pi$
$942$		0			0
$943$		−	45235.2i		−	1.56210i
$944$	6753.33	−	6041.44i	0.232841	−	0.208297i
$945$		0			0
$946$	−39166.6	+	7226.48i	−1.34611	+	0.248365i
$947$	52939.1			1.81657			0.908285	−	0.418353i	$-0.137392\pi$
$947$	52939.1			1.81657			0.908285	+	0.418353i	$0.137392\pi$
$948$		0			0
$949$	5068.85			0.173384
$950$	−41499.5	+	7656.92i	−1.41729	+	0.261498i
$951$		0			0
$952$	−1139.36	−	1869.40i	−0.0387888	−	0.0636423i
$953$		−	744.138i		−	0.0252938i	−0.999920	−	0.0126469i	$-0.995974\pi$
$953$		−	744.138i		−	0.0252938i	0.999920	−	0.0126469i	$-0.00402574\pi$
$954$		0			0
$955$		−	7435.63i		−	0.251949i
$956$	39544.4	−	15106.6i	1.33782	−	0.511070i
$957$		0			0
$958$	2905.43	+	15747.1i	0.0979857	+	0.531070i
$959$	−3914.08			−0.131796
$960$		0			0
$961$	−1037.96			−0.0348414
$962$	4165.60	+	22577.0i	0.139610	+	0.756666i
$963$		0			0
$964$	37390.3	−	14283.7i	1.24923	−	0.477228i
$965$			3937.85i			0.131361i
$966$		0			0
$967$		−	16217.2i		−	0.539308i	−0.962957	−	0.269654i	$-0.913091\pi$
$967$		−	16217.2i		−	0.539308i	0.962957	−	0.269654i	$-0.0869093\pi$
$968$	−11782.1	−	19331.4i	−0.391211	−	0.641874i
$969$		0			0
$970$	10087.2	−	1861.16i	0.333898	−	0.0616063i
$971$	33620.7			1.11116			0.555582	−	0.831462i	$-0.312496\pi$
$971$	33620.7			1.11116			0.555582	+	0.831462i	$0.312496\pi$
$972$		0			0
$973$	−3400.28			−0.112033
$974$	25262.1	−	4661.01i	0.831058	−	0.153335i
$975$		0			0
$976$	736.012	−	658.428i	0.0241385	−	0.0215940i
$977$		−	21219.2i		−	0.694843i	−0.937709	−	0.347421i	$-0.887057\pi$
$977$		−	21219.2i		−	0.694843i	0.937709	−	0.347421i	$-0.112943\pi$
$978$		0			0
$979$		−	20128.5i		−	0.657110i
$980$	2310.77	+	6048.85i	0.0753211	+	0.197167i
$981$		0			0
$982$	5233.39	+	28364.3i	0.170065	+	0.921733i
$983$	−38298.6			−1.24266			−0.621331	−	0.783548i	$-0.713408\pi$
$983$	−38298.6			−1.24266			−0.621331	+	0.783548i	$0.713408\pi$
$984$		0			0
$985$	−8073.35			−0.261156
$986$	−3310.60	−	17943.1i	−0.106928	−	0.579537i
$987$		0			0
$988$	−14549.5	−	38086.0i	−0.468503	−	1.22639i
$989$		−	56607.5i		−	1.82004i
$990$		0			0
$991$			17803.2i			0.570674i	0.958427	+	0.285337i	$0.0921055\pi$
$991$			17803.2i			0.570674i	−0.958427	+	0.285337i	$0.907894\pi$
$992$	19450.1	−	25137.6i	0.622521	−	0.804555i
$993$		0			0
$994$	−207.409	+	38.2683i	−0.00661833	+	0.00122112i
$995$	2521.78			0.0803477
$996$		0			0
$997$	9035.77			0.287027			0.143513	−	0.989648i	$-0.454160\pi$
$997$	9035.77			0.287027			0.143513	+	0.989648i	$0.454160\pi$
$998$	7557.78	−	1394.46i	0.239717	−	0.0442292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.4.b.c.323.14		24
3.2	odd	2	inner	324.4.b.c.323.11		24
4.3	odd	2	inner	324.4.b.c.323.12		24
9.2	odd	6		108.4.h.b.71.3		24
9.4	even	3		108.4.h.b.35.2		24
9.5	odd	6		36.4.h.b.11.11	yes	24
9.7	even	3		36.4.h.b.23.10	yes	24
12.11	even	2	inner	324.4.b.c.323.13		24
36.7	odd	6		36.4.h.b.23.11	yes	24
36.11	even	6		108.4.h.b.71.2		24
36.23	even	6		36.4.h.b.11.10	✓	24
36.31	odd	6		108.4.h.b.35.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.10	✓	24	36.23	even	6
36.4.h.b.11.11	yes	24	9.5	odd	6
36.4.h.b.23.10	yes	24	9.7	even	3
36.4.h.b.23.11	yes	24	36.7	odd	6
108.4.h.b.35.2		24	9.4	even	3
108.4.h.b.35.3		24	36.31	odd	6
108.4.h.b.71.2		24	36.11	even	6
108.4.h.b.71.3		24	9.2	odd	6
324.4.b.c.323.11		24	3.2	odd	2	inner
324.4.b.c.323.12		24	4.3	odd	2	inner
324.4.b.c.323.13		24	12.11	even	2	inner
324.4.b.c.323.14		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	324.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.513200 + 2.78148i) q^{2} +(-7.47325 + 2.85491i) q^{4} -2.40947i q^{5} -2.66000i q^{7} +(-11.7761 - 19.3216i) q^{8} +O(q^{10})\)	\(q+(0.513200 + 2.78148i) q^{2} +(-7.47325 + 2.85491i) q^{4} -2.40947i q^{5} -2.66000i q^{7} +(-11.7761 - 19.3216i) q^{8} +(6.70190 - 1.23654i) q^{10} +48.2857 q^{11} +40.7140 q^{13} +(7.39872 - 1.36511i) q^{14} +(47.6990 - 42.6709i) q^{16} +36.3729i q^{17} +125.173i q^{19} +(6.87883 + 18.0066i) q^{20} +(24.7802 + 134.306i) q^{22} -194.112 q^{23} +119.194 q^{25} +(20.8944 + 113.245i) q^{26} +(7.59405 + 19.8788i) q^{28} +177.354i q^{29} -175.582i q^{31} +(143.167 + 110.775i) q^{32} +(-101.171 + 18.6666i) q^{34} -6.40918 q^{35} +199.364 q^{37} +(-348.167 + 64.2389i) q^{38} +(-46.5547 + 28.3743i) q^{40} +233.037i q^{41} +291.623i q^{43} +(-360.851 + 137.851i) q^{44} +(-99.6182 - 539.918i) q^{46} -61.8953 q^{47} +335.924 q^{49} +(61.1706 + 331.537i) q^{50} +(-304.266 + 116.235i) q^{52} +352.175i q^{53} -116.343i q^{55} +(-51.3952 + 31.3245i) q^{56} +(-493.308 + 91.0183i) q^{58} +141.582 q^{59} +15.4304 q^{61} +(488.377 - 90.1086i) q^{62} +(-234.645 + 455.067i) q^{64} -98.0993i q^{65} +152.024i q^{67} +(-103.841 - 271.824i) q^{68} +(-3.28919 - 17.8270i) q^{70} -28.0331 q^{71} +124.499 q^{73} +(102.314 + 554.527i) q^{74} +(-357.358 - 935.451i) q^{76} -128.440i q^{77} -748.721i q^{79} +(-102.814 - 114.929i) q^{80} +(-648.187 + 119.595i) q^{82} -348.888 q^{83} +87.6396 q^{85} +(-811.144 + 149.661i) q^{86} +(-568.619 - 932.955i) q^{88} -416.864i q^{89} -108.299i q^{91} +(1450.65 - 554.172i) q^{92} +(-31.7647 - 172.160i) q^{94} +301.601 q^{95} +1505.13 q^{97} +(172.396 + 934.367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4}+O(q^{10}) \) 24 * q + 24 * q^4	\( 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64} - 1128 q^{70} - 4776 q^{73} + 1200 q^{76} - 4104 q^{82} - 1440 q^{85} - 3912 q^{88} + 2376 q^{94} - 1176 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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