LMFDB - Embedded newform 108.4.h.b.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	108.71
Dual form			108.4.h.b.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66543 + 0.946295i) q^{2} +(6.20905 - 5.04457i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +O(q^{10})$	\(q+(-2.66543 + 0.946295i) q^{2} +(6.20905 - 5.04457i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +(6.70190 + 1.23654i) q^{10} +(-24.1428 - 41.8166i) q^{11} +(-20.3570 + 35.2594i) q^{13} +(-4.88158 + 5.72493i) q^{14} +(13.1046 - 62.6440i) q^{16} -36.3729i q^{17} -125.173i q^{19} +(-19.0336 + 3.04606i) q^{20} +(103.922 + 88.6131i) q^{22} +(97.0560 - 168.106i) q^{23} +(-59.5972 - 103.225i) q^{25} +(20.8944 - 113.245i) q^{26} +(7.59405 - 19.8788i) q^{28} +(-153.593 + 88.6772i) q^{29} +(-152.058 - 87.7909i) q^{31} +(24.3503 + 179.374i) q^{32} +(34.4195 + 96.9496i) q^{34} -6.40918 q^{35} +199.364 q^{37} +(118.451 + 333.641i) q^{38} +(47.8502 - 26.1304i) q^{40} +(201.816 + 116.518i) q^{41} +(-252.553 + 145.812i) q^{43} +(-360.851 - 137.851i) q^{44} +(-99.6182 + 539.918i) q^{46} +(30.9476 + 53.6029i) q^{47} +(-167.962 + 290.919i) q^{49} +(256.534 + 218.744i) q^{50} +(51.4707 + 321.620i) q^{52} -352.175i q^{53} +116.343i q^{55} +(-1.43018 + 60.1718i) q^{56} +(325.478 - 381.708i) q^{58} +(-70.7911 + 122.614i) q^{59} +(-7.71518 - 13.3631i) q^{61} +(488.377 + 90.1086i) q^{62} +(-234.645 - 455.067i) q^{64} +(84.9565 - 49.0496i) q^{65} +(131.657 + 76.0120i) q^{67} +(-183.486 - 225.841i) q^{68} +(17.0832 - 6.06498i) q^{70} -28.0331 q^{71} +124.499 q^{73} +(-531.392 + 188.657i) q^{74} +(-631.445 - 777.207i) q^{76} +(-111.232 - 64.2199i) q^{77} +(648.411 - 374.360i) q^{79} +(-102.814 + 114.929i) q^{80} +(-648.187 - 119.595i) q^{82} +(174.444 + 302.146i) q^{83} +(-43.8198 + 75.8981i) q^{85} +(535.182 - 627.641i) q^{86} +(1092.27 + 25.9614i) q^{88} +416.864i q^{89} +108.299i q^{91} +(-245.397 - 1533.38i) q^{92} +(-133.213 - 113.589i) q^{94} +(-150.801 + 261.195i) q^{95} +(-752.565 - 1303.48i) q^{97} +(172.396 - 934.367i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) $ 24 * q - 12 * q^4 + 72 * q^5	$ 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−2.66543	+	0.946295i	−0.942372	+	0.334566i
$2$	−2.66543	+	0.946295i	−0.942372	+	0.334566i
$3$		0			0
$3$		0			0
$4$	6.20905	−	5.04457i	0.776131	−	0.630571i
$5$	−2.08666	−	1.20474i	−0.186637	−	0.107755i	0.403770	−	0.914860i	$-0.367699\pi$
$5$	−2.08666	−	1.20474i	−0.186637	−	0.107755i	−0.590407	+	0.807106i	$0.701033\pi$
$6$		0			0
$7$	2.30362	−	1.33000i	0.124384	−	0.0718131i	−0.436517	−	0.899696i	$-0.643788\pi$
$7$	2.30362	−	1.33000i	0.124384	−	0.0718131i	0.560901	+	0.827883i	$0.310455\pi$
$8$	−11.7761	+	19.3216i	−0.520437	+	0.853900i
$9$		0			0
$10$	6.70190	+	1.23654i	0.211933	+	0.0391029i
$11$	−24.1428	−	41.8166i	−0.661758	−	1.14620i	−0.980153	−	0.198241i	$-0.936477\pi$
$11$	−24.1428	−	41.8166i	−0.661758	−	1.14620i	0.318395	−	0.947958i	$-0.396856\pi$
$12$		0			0
$13$	−20.3570	+	35.2594i	−0.434309	+	0.752245i	−0.997239	−	0.0742593i	$-0.976341\pi$
$13$	−20.3570	+	35.2594i	−0.434309	+	0.752245i	0.562930	+	0.826505i	$0.309674\pi$
$14$	−4.88158	+	5.72493i	−0.0931898	+	0.109289i
$15$		0			0
$16$	13.1046	−	62.6440i	0.204759	−	0.978812i
$17$		−	36.3729i		−	0.518925i	−0.965753	−	0.259463i	$-0.916455\pi$
$17$		−	36.3729i		−	0.518925i	0.965753	−	0.259463i	$-0.0835455\pi$
$18$		0			0
$19$		−	125.173i		−	1.51141i	−0.654914	−	0.755703i	$-0.727295\pi$
$19$		−	125.173i		−	1.51141i	0.654914	−	0.755703i	$-0.272705\pi$
$20$	−19.0336	+	3.04606i	−0.212802	+	0.0340560i
$21$		0			0
$22$	103.922	+	88.6131i	1.00710	+	0.858745i
$23$	97.0560	−	168.106i	0.879894	−	1.52402i	0.0284384	−	0.999596i	$-0.490947\pi$
$23$	97.0560	−	168.106i	0.879894	−	1.52402i	0.851456	−	0.524426i	$-0.175720\pi$
$24$		0			0
$25$	−59.5972	−	103.225i	−0.476778	−	0.825803i
$26$	20.8944	−	113.245i	0.157605	−	0.854200i
$27$		0			0
$28$	7.59405	−	19.8788i	0.0512550	−	0.134169i
$29$	−153.593	+	88.6772i	−0.983503	+	0.567826i	−0.903326	−	0.428955i	$-0.858882\pi$
$29$	−153.593	+	88.6772i	−0.983503	+	0.567826i	−0.0801773	+	0.996781i	$0.525549\pi$
$30$		0			0
$31$	−152.058	−	87.7909i	−0.880983	−	0.508636i	−0.0100006	−	0.999950i	$-0.503183\pi$
$31$	−152.058	−	87.7909i	−0.880983	−	0.508636i	−0.870982	+	0.491314i	$0.836517\pi$
$32$	24.3503	+	179.374i	0.134518	+	0.990911i
$33$		0			0
$34$	34.4195	+	96.9496i	0.173615	+	0.489021i
$35$	−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	$0.353946\pi$
$38$	118.451	+	333.641i	0.505665	+	1.42431i
$39$		0			0
$40$	47.8502	−	26.1304i	0.189145	−	0.103290i
$41$	201.816	+	116.518i	0.768740	+	0.443832i	0.832425	−	0.554138i	$-0.186952\pi$
$41$	201.816	+	116.518i	0.768740	+	0.443832i	−0.0636849	+	0.997970i	$0.520285\pi$
$42$		0			0
$43$	−252.553	+	145.812i	−0.895674	+	0.517118i	−0.875794	−	0.482685i	$-0.839662\pi$
$43$	−252.553	+	145.812i	−0.895674	+	0.517118i	−0.0198798	+	0.999802i	$0.506328\pi$
$44$	−360.851	−	137.851i	−1.23637	−	0.472315i
$45$		0			0
$46$	−99.6182	+	539.918i	−0.319302	+	1.73058i
$47$	30.9476	+	53.6029i	0.0960463	+	0.166357i	0.910045	−	0.414510i	$-0.136047\pi$
$47$	30.9476	+	53.6029i	0.0960463	+	0.166357i	−0.813998	+	0.580867i	$0.802714\pi$
$48$		0			0
$49$	−167.962	+	290.919i	−0.489686	+	0.848161i
$50$	256.534	+	218.744i	0.725588	+	0.618701i
$51$		0			0
$52$	51.4707	+	321.620i	0.137264	+	0.857704i
$53$		−	352.175i		−	0.912735i	−0.889791	−	0.456367i	$-0.849150\pi$
$53$		−	352.175i		−	0.912735i	0.889791	−	0.456367i	$-0.150850\pi$
$54$		0			0
$55$			116.343i			0.285231i
$56$	−1.43018	+	60.1718i	−0.00341278	+	0.143586i
$57$		0			0
$58$	325.478	−	381.708i	0.736851	−	0.864150i
$59$	−70.7911	+	122.614i	−0.156207	+	0.270559i	−0.933498	−	0.358583i	$-0.883260\pi$
$59$	−70.7911	+	122.614i	−0.156207	+	0.270559i	0.777291	+	0.629141i	$0.216593\pi$
$60$		0			0
$61$	−7.71518	−	13.3631i	−0.0161939	−	0.0280486i	0.857815	−	0.513959i	$-0.171822\pi$
$61$	−7.71518	−	13.3631i	−0.0161939	−	0.0280486i	−0.874009	+	0.485910i	$0.838488\pi$
$62$	488.377	+	90.1086i	1.00039	+	0.184577i
$63$		0			0
$64$	−234.645	−	455.067i	−0.458291	−	0.888802i
$65$	84.9565	−	49.0496i	0.162116	−	0.0935978i
$66$		0			0
$67$	131.657	+	76.0120i	0.240066	+	0.138602i	0.615207	−	0.788366i	$-0.289072\pi$
$67$	131.657	+	76.0120i	0.240066	+	0.138602i	−0.375141	+	0.926968i	$0.622406\pi$
$68$	−183.486	−	225.841i	−0.327220	−	0.402754i
$69$		0			0
$70$	17.0832	−	6.06498i	0.0291691	−	0.0103558i
$71$	−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	$0.468178\pi$
$74$	−531.392	+	188.657i	−0.834771	+	0.296365i
$75$		0			0
$76$	−631.445	−	777.207i	−0.953049	−	1.17305i
$77$	−111.232	−	64.2199i	−0.164624	−	0.0950459i
$78$		0			0
$79$	648.411	−	374.360i	0.923443	−	0.533150i	0.0387108	−	0.999250i	$-0.487675\pi$
$79$	648.411	−	374.360i	0.923443	−	0.533150i	0.884732	+	0.466101i	$0.154342\pi$
$80$	−102.814	+	114.929i	−0.143687	+	0.160619i
$81$		0			0
$82$	−648.187	−	119.595i	−0.872931	−	0.161061i
$83$	174.444	+	302.146i	0.230695	+	0.399576i	0.958013	−	0.286725i	$-0.0925667\pi$
$83$	174.444	+	302.146i	0.230695	+	0.399576i	−0.727318	+	0.686301i	$0.759233\pi$
$84$		0			0
$85$	−43.8198	+	75.8981i	−0.0559167	+	0.0968506i
$86$	535.182	−	627.641i	0.671048	−	0.786979i
$87$		0			0
$88$	1092.27	+	25.9614i	1.32314	+	0.0314488i
$89$			416.864i			0.496488i	0.968698	+	0.248244i	$0.0798535\pi$
$89$			416.864i			0.496488i	−0.968698	+	0.248244i	$0.920146\pi$
$90$		0			0
$91$			108.299i			0.124756i
$92$	−245.397	−	1533.38i	−0.278091	−	1.73768i
$93$		0			0
$94$	−133.213	−	113.589i	−0.146169	−	0.124637i
$95$	−150.801	+	261.195i	−0.162861	+	0.282084i
$96$		0			0
$97$	−752.565	−	1303.48i	−0.787747	−	1.36442i	−0.927344	−	0.374209i	$-0.877914\pi$
$97$	−752.565	−	1303.48i	−0.787747	−	1.36442i	0.139598	−	0.990208i	$-0.455419\pi$
$98$	172.396	−	934.367i	0.177701	−	0.963115i
$99$		0			0
$100$	−890.770	−	340.289i	−0.890770	−	0.340289i
$101$	−377.088	+	217.712i	−0.371502	+	0.214487i	−0.674114	−	0.738627i	$-0.735474\pi$
$101$	−377.088	+	217.712i	−0.371502	+	0.214487i	0.302613	+	0.953114i	$0.402141\pi$
$102$		0			0
$103$	1511.52	+	872.679i	1.44597	+	0.834831i	0.998238	−	0.0593366i	$-0.0188985\pi$
$103$	1511.52	+	872.679i	1.44597	+	0.834831i	0.447732	+	0.894168i	$0.352232\pi$
$104$	−441.539	−	808.548i	−0.416312	−	0.762353i
$105$		0			0
$106$	333.261	+	938.698i	0.305370	+	0.860136i
$107$	−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	$0.255389\pi$
$110$	−110.095	−	310.104i	−0.0954285	−	0.268794i
$111$		0			0
$112$	−53.1283	−	161.737i	−0.0448228	−	0.136453i
$113$	384.367	+	221.914i	0.319984	+	0.184743i	0.651386	−	0.758747i	$-0.274188\pi$
$113$	384.367	+	221.914i	0.319984	+	0.184743i	−0.331401	+	0.943490i	$0.607521\pi$
$114$		0			0
$115$	−405.046	+	233.854i	−0.328442	+	0.189626i
$116$	−506.331	+	1325.41i	−0.405273	+	1.06088i
$117$		0			0
$118$	72.6600	−	393.808i	0.0566855	−	0.307228i
$119$	−48.3759	−	83.7895i	−0.0372657	−	0.0645460i
$120$		0			0
$121$	−500.254	+	866.466i	−0.375848	+	0.650989i
$122$	33.2097	+	28.3175i	0.0246448	+	0.0210143i
$123$		0			0
$124$	−1387.00	+	221.971i	−1.00449	+	0.160755i
$125$			588.380i			0.421010i
$126$		0			0
$127$			425.829i			0.297529i	0.988873	+	0.148765i	$0.0475297\pi$
$127$			425.829i			0.297529i	−0.988873	+	0.148765i	$0.952470\pi$
$128$	1056.06	+	990.906i	0.729244	+	0.684254i
$129$		0			0
$130$	−180.030	+	211.132i	−0.121459	+	0.142443i
$131$	−871.836	+	1510.06i	−0.581471	+	1.00714i	0.413835	+	0.910352i	$0.364189\pi$
$131$	−871.836	+	1510.06i	−0.581471	+	1.00714i	−0.995305	+	0.0967846i	$0.969144\pi$
$132$		0			0
$133$	−166.480	−	288.352i	−0.108539	−	0.187995i
$134$	−422.851	−	78.0187i	−0.272603	−	0.0502969i
$135$		0			0
$136$	702.782	+	428.333i	0.443110	+	0.270068i
$137$	1274.32	−	735.731i	0.794692	−	0.458816i	−0.0469195	−	0.998899i	$-0.514940\pi$
$137$	1274.32	−	735.731i	0.794692	−	0.458816i	0.841612	+	0.540083i	$0.181607\pi$
$138$		0			0
$139$	−1107.04	−	639.151i	−0.675526	−	0.390015i	0.122641	−	0.992451i	$-0.460864\pi$
$139$	−1107.04	−	639.151i	−0.675526	−	0.390015i	−0.798167	+	0.602436i	$0.794197\pi$
$140$	−39.7949	+	32.3316i	−0.0240235	+	0.0195180i
$141$		0			0
$142$	74.7204	−	26.5276i	0.0441577	−	0.0156771i
$143$	1965.90			1.14963
$144$		0			0
$145$	427.331			0.244744
$146$	−331.843	+	117.813i	−0.188106	+	0.0667825i
$147$		0			0
$148$	1237.86	−	1005.71i	0.687511	−	0.558572i
$149$	−1861.15	−	1074.53i	−1.02330	−	0.590800i	−0.108239	−	0.994125i	$-0.534521\pi$
$149$	−1861.15	−	1074.53i	−1.02330	−	0.590800i	−0.915057	+	0.403325i	$0.867854\pi$
$150$		0			0
$151$	−828.626	+	478.407i	−0.446574	+	0.257829i	−0.706382	−	0.707831i	$-0.749674\pi$
$151$	−828.626	+	478.407i	−0.446574	+	0.257829i	0.259808	+	0.965660i	$0.416341\pi$
$152$	2418.54	+	1474.06i	1.29059	+	0.786592i
$153$		0			0
$154$	357.252	+	65.9152i	0.186936	+	0.0344909i
$155$	211.530	+	366.380i	0.109616	+	0.189860i
$156$		0			0
$157$	−1046.60	+	1812.77i	−0.532024	+	0.921493i	0.467277	+	0.884111i	$0.345235\pi$
$157$	−1046.60	+	1812.77i	−0.532024	+	0.921493i	−0.999301	+	0.0373822i	$0.988098\pi$
$158$	−1374.04	+	1611.42i	−0.691853	+	0.811378i
$159$		0			0
$160$	165.288	−	403.629i	0.0816696	−	0.199436i
$161$		−	516.337i		−	0.252752i
$162$		0			0
$163$		−	1468.60i		−	0.705703i	−0.935679	−	0.352851i	$-0.885212\pi$
$163$		−	1468.60i		−	0.705703i	0.935679	−	0.352851i	$-0.114788\pi$
$164$	1840.87	−	294.606i	0.876511	−	0.140273i
$165$		0			0
$166$	−750.887	−	640.273i	−0.351085	−	0.299366i
$167$	1524.19	−	2639.98i	0.706261	−	1.22328i	−0.259974	−	0.965616i	$-0.583714\pi$
$167$	1524.19	−	2639.98i	0.706261	−	1.22328i	0.966235	−	0.257664i	$-0.0829527\pi$
$168$		0			0
$169$	269.685	+	467.108i	0.122751	+	0.212612i
$170$	44.9766	−	243.768i	0.0202915	−	0.109977i
$171$		0			0
$172$	−832.558	+	2179.37i	−0.369081	+	0.966137i
$173$	2403.71	−	1387.79i	1.05636	−	0.609892i	0.131940	−	0.991258i	$-0.457879\pi$
$173$	2403.71	−	1387.79i	1.05636	−	0.609892i	0.924424	+	0.381365i	$0.124546\pi$
$174$		0			0
$175$	−274.579	−	158.528i	−0.118607	−	0.0684778i
$176$	−2935.94	+	964.414i	−1.25742	+	0.413042i
$177$		0			0
$178$	−394.476	−	1111.12i	−0.166108	−	0.467877i
$179$	−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	$0.548048\pi$
$182$	−102.483	−	288.664i	−0.0417392	−	0.117567i
$183$		0			0
$184$	2105.12	+	3854.91i	0.843433	+	1.54450i
$185$	−416.006	−	240.181i	−0.165326	−	0.0954512i
$186$		0			0
$187$	−1520.99	+	878.146i	−0.594792	+	0.343403i
$188$	462.559	+	176.705i	0.179445	+	0.0685509i
$189$		0			0
$190$	154.782	−	838.898i	0.0591003	−	0.320316i
$191$	−1543.00	−	2672.55i	−0.584542	−	1.01246i	−0.994932	−	0.100546i	$-0.967941\pi$
$191$	−1543.00	−	2672.55i	−0.584542	−	1.01246i	0.410391	−	0.911910i	$-0.365392\pi$
$192$		0			0
$193$	817.160	−	1415.36i	0.304769	−	0.527876i	−0.672441	−	0.740151i	$-0.734754\pi$
$193$	817.160	−	1415.36i	0.304769	−	0.527876i	0.977210	+	0.212275i	$0.0680873\pi$
$194$	3239.39	+	2762.19i	1.19884	+	1.02224i
$195$		0			0
$196$	424.676	+	2653.63i	0.154765	+	0.967066i
$197$			3350.67i			1.21181i	0.795539	+	0.605903i	$0.207188\pi$
$197$			3350.67i			1.21181i	−0.795539	+	0.605903i	$0.792812\pi$
$198$		0			0
$199$		−	1046.61i		−	0.372826i	−0.982471	−	0.186413i	$-0.940314\pi$
$199$		−	1046.61i		−	0.372826i	0.982471	−	0.186413i	$-0.0596863\pi$
$200$	2696.30	+	64.0864i	0.953286	+	0.0226580i
$201$		0			0
$202$	799.083	−	937.133i	0.278333	−	0.326418i
$203$	−235.881	+	408.558i	−0.0815547	+	0.141257i
$204$		0			0
$205$	−280.748	−	486.270i	−0.0956502	−	0.165671i
$206$	−4854.68	−	895.718i	−1.64195	−	0.302950i
$207$		0			0
$208$	1942.02	+	1737.30i	0.647378	+	0.579136i
$209$	−5234.33	+	3022.04i	−1.73237	+	1.00019i
$210$		0			0
$211$	−4570.77	−	2638.94i	−1.49130	−	0.861004i	−0.491352	−	0.870961i	$-0.663497\pi$
$211$	−4570.77	−	2638.94i	−1.49130	−	0.861004i	−0.999950	+	0.00995667i	$0.996831\pi$
$212$	−1776.57	−	2186.67i	−0.575544	−	0.708402i
$213$		0			0
$214$	2089.18	−	741.711i	0.667352	−	0.236927i
$215$	702.658			0.222888
$216$		0			0
$217$	−467.047			−0.146107
$218$	−4216.42	+	1496.94i	−1.30996	+	0.465070i
$219$		0			0
$220$	586.901	+	722.380i	0.179858	+	0.221377i
$221$	1282.49	+	740.444i	0.390359	+	0.225374i
$222$		0			0
$223$	4122.02	−	2379.85i	1.23781	−	0.714648i	0.269161	−	0.963095i	$-0.413254\pi$
$223$	4122.02	−	2379.85i	1.23781	−	0.714648i	0.968645	+	0.248447i	$0.0799202\pi$
$224$	294.661	+	380.824i	0.0878923	+	0.113593i
$225$		0			0
$226$	−1234.50	−	227.773i	−0.363353	−	0.0670409i
$227$	−1115.23	−	1931.63i	−0.326080	−	0.564788i	0.655650	−	0.755065i	$-0.272395\pi$
$227$	−1115.23	−	1931.63i	−0.326080	−	0.564788i	−0.981730	+	0.190277i	$0.939061\pi$
$228$		0			0
$229$	2917.29	−	5052.89i	0.841833	−	1.45810i	−0.0465095	−	0.998918i	$-0.514810\pi$
$229$	2917.29	−	5052.89i	0.841833	−	1.45810i	0.888343	−	0.459181i	$-0.151857\pi$
$230$	858.329	−	1006.61i	0.246072	−	0.288583i
$231$		0			0
$232$	95.3568	−	4011.94i	0.0269848	−	1.13533i
$233$		−	3080.09i		−	0.866022i	−0.901389	−	0.433011i	$-0.857451\pi$
$233$		−	3080.09i		−	0.866022i	0.901389	−	0.433011i	$-0.142549\pi$
$234$		0			0
$235$		−	149.135i		−	0.0413978i
$236$	178.988	+	1118.43i	0.0493693	+	0.308489i
$237$		0			0
$238$	208.232	+	177.557i	0.0567130	+	0.0483586i
$239$	2645.73	−	4582.53i	0.716058	−	1.24025i	−0.246492	−	0.969145i	$-0.579278\pi$
$239$	2645.73	−	4582.53i	0.716058	−	1.24025i	0.962550	−	0.271104i	$-0.0873887\pi$
$240$		0			0
$241$	2501.61	+	4332.91i	0.668642	+	1.15812i	0.978284	+	0.207268i	$0.0664573\pi$
$241$	2501.61	+	4332.91i	0.668642	+	1.15812i	−0.309642	+	0.950853i	$0.600209\pi$
$242$	513.461	−	2782.89i	0.136391	−	0.739220i
$243$		0			0
$244$	−115.315	−	44.0523i	−0.0302553	−	0.0115580i
$245$	700.961	−	404.700i	0.182787	−	0.105532i
$246$		0			0
$247$	4413.53	+	2548.15i	1.13695	+	0.656417i
$248$	3486.92	−	1904.16i	0.892820	−	0.487559i
$249$		0			0
$250$	−556.781	−	1568.29i	−0.140856	−	0.396748i
$251$	−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
$254$	−402.960	−	1135.02i	−0.0995432	−	0.280383i
$255$		0			0
$256$	−3752.54	−	1641.85i	−0.916147	−	0.400842i
$257$	753.933	+	435.283i	0.182992	+	0.105651i	0.588698	−	0.808353i	$-0.299641\pi$
$257$	753.933	+	435.283i	0.182992	+	0.105651i	−0.405705	+	0.914004i	$0.632974\pi$
$258$		0			0
$259$	459.260	−	265.154i	0.110182	−	0.0636134i
$260$	280.065	−	733.121i	0.0668033	−	0.174870i
$261$		0			0
$262$	894.852	−	4849.99i	0.211008	−	1.14364i
$263$	2155.19	+	3732.90i	0.505304	+	0.875212i	0.999981	+	0.00613515i	$0.00195289\pi$
$263$	2155.19	+	3732.90i	0.505304	+	0.875212i	−0.494677	+	0.869077i	$0.664714\pi$
$264$		0			0
$265$	−424.278	+	734.871i	−0.0983516	+	0.170350i
$266$	716.608	+	611.043i	0.165181	+	0.140848i
$267$		0			0
$268$	1200.91	−	192.189i	0.273721	−	0.0438052i
$269$		−	5603.52i		−	1.27008i	−0.772478	−	0.635042i	$-0.780983\pi$
$269$		−	5603.52i		−	1.27008i	0.772478	−	0.635042i	$-0.219017\pi$
$270$		0			0
$271$			2149.22i			0.481756i	0.970555	+	0.240878i	$0.0774353\pi$
$271$			2149.22i			0.481756i	−0.970555	+	0.240878i	$0.922565\pi$
$272$	−2278.55	−	476.653i	−0.507931	−	0.106255i
$273$		0			0
$274$	−2700.40	+	3166.93i	−0.595392	+	0.698252i
$275$	−2877.69	+	4984.31i	−0.631023	+	1.09296i
$276$		0			0
$277$	1604.99	+	2779.93i	0.348140	+	0.602995i	0.985919	−	0.167224i	$-0.0534802\pi$
$277$	1604.99	+	2779.93i	0.348140	+	0.602995i	−0.637779	+	0.770219i	$0.720147\pi$
$278$	3555.57	+	656.025i	0.767083	+	0.141531i
$279$		0			0
$280$	75.4755	−	123.835i	0.0161090	−	0.0264306i
$281$	814.389	−	470.188i	0.172891	−	0.0998187i	−0.411057	−	0.911610i	$-0.634840\pi$
$281$	814.389	−	470.188i	0.172891	−	0.0998187i	0.583948	+	0.811791i	$0.301507\pi$
$282$		0			0
$283$	−1775.44	−	1025.05i	−0.372929	−	0.215310i	0.301809	−	0.953369i	$-0.402410\pi$
$283$	−1775.44	−	1025.05i	−0.372929	−	0.215310i	−0.674737	+	0.738058i	$0.735743\pi$
$284$	−174.059	+	141.415i	−0.0363680	+	0.0295473i
$285$		0			0
$286$	−5239.98	+	1860.33i	−1.08338	+	0.384627i
$287$	619.877			0.127492
$288$		0			0
$289$	3590.01			0.730716
$290$	−1139.02	+	404.381i	−0.230640	+	0.0818830i
$291$		0			0
$292$	773.020	−	628.043i	0.154923	−	0.125868i
$293$	3842.30	+	2218.35i	0.766108	+	0.442312i	0.831484	−	0.555548i	$-0.187492\pi$
$293$	3842.30	+	2218.35i	0.766108	+	0.442312i	−0.0653767	+	0.997861i	$0.520825\pi$
$294$		0			0
$295$	295.434	−	170.569i	0.0583080	−	0.0336641i
$296$	−2347.74	+	3852.03i	−0.461013	+	0.756400i
$297$		0			0
$298$	5977.58	+	1102.90i	1.16199	+	0.214394i
$299$	3951.54	+	6844.26i	0.764292	+	1.32379i
$300$		0			0
$301$	−387.858	+	671.790i	−0.0742716	+	0.128642i
$302$	1755.93	−	2059.29i	0.334578	−	0.392380i
$303$		0			0
$304$	−7841.35	−	1640.35i	−1.47938	−	0.309475i
$305$			37.1790i			0.00697988i
$306$		0			0
$307$			7392.80i			1.37436i	0.726486	+	0.687181i	$0.241152\pi$
$307$			7392.80i			1.37436i	−0.726486	+	0.687181i	$0.758848\pi$
$308$	−1014.61	+	162.374i	−0.187703	+	0.0300393i
$309$		0			0
$310$	−910.522	−	776.392i	−0.166820	−	0.142245i
$311$	−2448.25	+	4240.50i	−0.446391	+	0.773172i	−0.998148	−	0.0608332i	$-0.980624\pi$
$311$	−2448.25	+	4240.50i	−0.446391	+	0.773172i	0.551757	+	0.834005i	$0.313958\pi$
$312$		0			0
$313$	−340.861	−	590.388i	−0.0615546	−	0.106616i	0.833606	−	0.552360i	$-0.186273\pi$
$313$	−340.861	−	590.388i	−0.0615546	−	0.106616i	−0.895160	+	0.445744i	$0.852939\pi$
$314$	1074.23	−	5822.20i	0.193065	−	1.04639i
$315$		0			0
$316$	2137.53	−	5595.38i	0.380524	−	0.996091i
$317$	−1344.13	+	776.034i	−0.238151	+	0.137497i	−0.614327	−	0.789052i	$-0.710572\pi$
$317$	−1344.13	+	776.034i	−0.238151	+	0.137497i	0.376176	+	0.926548i	$0.377239\pi$
$318$		0			0
$319$	7416.37	+	4281.84i	1.30168	+	0.751527i
$320$	−58.6103	+	1232.26i	−0.0102388	+	0.215266i
$321$		0			0
$322$	488.607	+	1376.26i	0.0845621	+	0.238186i
$323$	−4552.92			−0.784307
$324$		0			0
$325$	4852.88			0.828276
$326$	1389.73	+	3914.45i	0.236104	+	0.665035i
$327$		0			0
$328$	−4627.93	+	2527.26i	−0.779069	+	0.425441i
$329$	142.583	+	82.3206i	0.0238932	+	0.0137948i
$330$		0			0
$331$	−6410.22	+	3700.94i	−1.06446	+	0.614569i	−0.926664	−	0.375891i	$-0.877337\pi$
$331$	−6410.22	+	3700.94i	−1.06446	+	0.614569i	−0.137801	+	0.990460i	$0.544003\pi$
$332$	2607.33	+	996.043i	0.431011	+	0.164653i
$333$		0			0
$334$	−1564.43	+	8479.02i	−0.256293	+	1.38908i
$335$	−183.149	−	317.223i	−0.0298701	−	0.0517365i
$336$		0			0
$337$	4871.58	−	8437.83i	0.787454	−	1.36391i	−0.140068	−	0.990142i	$-0.544732\pi$
$337$	4871.58	−	8437.83i	0.787454	−	1.36391i	0.927522	−	0.373769i	$-0.121935\pi$
$338$	−1160.85	−	989.842i	−0.186810	−	0.159291i
$339$		0			0
$340$	110.794	+	692.307i	0.0176725	+	0.110428i
$341$			8478.09i			1.34638i
$342$		0			0
$343$			1805.94i			0.284290i
$344$	156.795	−	6596.82i	0.0245750	−	1.03394i
$345$		0			0
$346$	−5093.68	+	5973.67i	−0.791439	+	0.928169i
$347$	−3523.75	+	6103.31i	−0.545143	+	0.944216i	0.453455	+	0.891279i	$0.350191\pi$
$347$	−3523.75	+	6103.31i	−0.545143	+	0.944216i	−0.998598	+	0.0529363i	$0.983142\pi$
$348$		0			0
$349$	603.773	+	1045.77i	0.0926052	+	0.160397i	0.908607	−	0.417653i	$-0.137147\pi$
$349$	603.773	+	1045.77i	0.0926052	+	0.160397i	−0.816001	+	0.578050i	$0.803814\pi$
$350$	881.886	+	162.713i	0.134682	+	0.0248497i
$351$		0			0
$352$	6912.94	−	5348.85i	1.04676	−	0.809928i
$353$	−1316.47	+	760.063i	−0.198494	+	0.114601i	−0.595953	−	0.803019i	$-0.703226\pi$
$353$	−1316.47	+	760.063i	−0.198494	+	0.114601i	0.397459	+	0.917620i	$0.369892\pi$
$354$		0			0
$355$	58.4957	+	33.7725i	0.00874544	+	0.00504918i
$356$	2102.90	+	2588.33i	0.313071	+	0.385340i
$357$		0			0
$358$	1273.06	−	451.968i	0.187942	−	0.0667241i
$359$	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
$362$	1952.03	−	693.020i	0.283415	−	0.100620i
$363$		0			0
$364$	546.322	+	672.434i	0.0786678	+	0.0968273i
$365$	−259.787	−	149.988i	−0.0372545	−	0.0215089i
$366$		0			0
$367$	3492.35	−	2016.31i	0.496729	−	0.286786i	−0.230633	−	0.973041i	$-0.574080\pi$
$367$	3492.35	−	2016.31i	0.496729	−	0.286786i	0.727362	+	0.686254i	$0.240746\pi$
$368$	−9258.94	−	8282.93i	−1.31156	−	1.17331i
$369$		0			0
$370$	1336.12	+	246.522i	0.187734	+	0.0346380i
$371$	−468.392	−	811.278i	−0.0655463	−	0.113530i
$372$		0			0
$373$	−1227.68	+	2126.40i	−0.170420	+	0.295176i	−0.938567	−	0.345098i	$-0.887846\pi$
$373$	−1227.68	+	2126.40i	−0.170420	+	0.295176i	0.768147	+	0.640274i	$0.221179\pi$
$374$	3223.12	−	3779.95i	0.445624	−	0.522611i
$375$		0			0
$376$	−1400.14	−	33.2788i	−0.192038	−	0.00456442i
$377$		−	7220.81i		−	0.986448i
$378$		0			0
$379$		−	9518.27i		−	1.29003i	−0.764171	−	0.645014i	$-0.776851\pi$
$379$		−	9518.27i		−	1.29003i	0.764171	−	0.645014i	$-0.223149\pi$
$380$	381.285	+	2382.50i	0.0514724	+	0.321630i
$381$		0			0
$382$	6641.78	+	5663.37i	0.889589	+	0.758543i
$383$	4727.72	−	8188.65i	0.630744	−	1.09248i	−0.356655	−	0.934236i	$-0.616083\pi$
$383$	4727.72	−	8188.65i	0.630744	−	1.09248i	0.987400	−	0.158245i	$-0.0505837\pi$
$384$		0			0
$385$	154.736	+	268.011i	0.0204833	+	0.0354781i
$386$	−838.733	+	4545.83i	−0.110597	+	0.599421i
$387$		0			0
$388$	−11248.2	−	4297.01i	−1.47176	−	0.562236i
$389$	2568.69	−	1483.04i	0.334802	−	0.193298i	−0.323169	−	0.946341i	$-0.604748\pi$
$389$	2568.69	−	1483.04i	0.334802	−	0.193298i	0.657971	+	0.753043i	$0.271415\pi$
$390$		0			0
$391$	−6114.50	−	3530.21i	−0.790854	−	0.456600i
$392$	−3643.06	−	6671.20i	−0.469394	−	0.859557i
$393$		0			0
$394$	−3170.73	−	8930.99i	−0.405429	−	1.14197i
$395$	−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	$0.473878\pi$
$398$	990.405	+	2789.68i	0.124735	+	0.351341i
$399$		0			0
$400$	−7247.45	+	2380.68i	−0.905931	+	0.297585i
$401$	1782.15	+	1028.93i	0.221936	+	0.128135i	0.606847	−	0.794819i	$-0.292434\pi$
$401$	1782.15	+	1028.93i	0.221936	+	0.128135i	−0.384910	+	0.922954i	$0.625768\pi$
$402$		0			0
$403$	6190.90	−	3574.32i	0.765238	−	0.441810i
$404$	−1243.10	+	3254.03i	−0.153085	+	0.400728i
$405$		0			0
$406$	242.108	−	1312.20i	0.0295951	−	0.160402i
$407$	−4813.22	−	8336.74i	−0.586198	−	1.01532i
$408$		0			0
$409$	−2897.54	+	5018.69i	−0.350304	+	0.606744i	−0.986303	−	0.164946i	$-0.947255\pi$
$409$	−2897.54	+	5018.69i	−0.350304	+	0.606744i	0.635999	+	0.771690i	$0.280588\pi$
$410$	1208.47	+	1030.45i	0.145566	+	0.124122i
$411$		0			0
$412$	13787.4	−	2206.48i	1.64868	−	0.263849i
$413$			376.608i			0.0448709i
$414$		0			0
$415$		−	840.635i		−	0.0994341i
$416$	−6820.32	−	2792.94i	−0.803830	−	0.329171i
$417$		0			0
$418$	11092.0	−	13008.3i	1.29791	−	1.52214i
$419$	7052.61	−	12215.5i	0.822298	−	1.42426i	−0.0816695	−	0.996659i	$-0.526025\pi$
$419$	7052.61	−	12215.5i	0.822298	−	1.42426i	0.903967	−	0.427602i	$-0.140641\pi$
$420$		0			0
$421$	−3210.43	−	5560.63i	−0.371655	−	0.643726i	0.618165	−	0.786048i	$-0.287876\pi$
$421$	−3210.43	−	5560.63i	−0.371655	−	0.643726i	−0.989820	+	0.142323i	$0.954543\pi$
$422$	14680.3	+	2708.60i	1.69343	+	0.312447i
$423$		0			0
$424$	6804.57	+	4147.26i	0.779384	+	0.475021i
$425$	−3754.61	+	2167.73i	−0.428530	+	0.247412i
$426$		0			0
$427$	−35.5457	−	20.5223i	−0.00402852	−	0.00232587i
$428$	−4866.68	+	3953.96i	−0.549626	+	0.446546i
$429$		0			0
$430$	−1872.89	+	664.922i	−0.210043	+	0.0745707i
$431$	−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	$0.505296\pi$
$434$	1244.88	−	441.964i	0.137687	−	0.0488824i
$435$		0			0
$436$	9822.04	−	7979.96i	1.07888	−	0.876539i
$437$	−21042.4	−	12148.8i	−2.30342	−	1.32988i
$438$		0			0
$439$	2090.02	−	1206.67i	0.227224	−	0.131188i	−0.382067	−	0.924135i	$-0.624788\pi$
$439$	2090.02	−	1206.67i	0.227224	−	0.131188i	0.609291	+	0.792947i	$0.291454\pi$
$440$	−2247.93	−	1370.07i	−0.243559	−	0.148445i
$441$		0			0
$442$	−4119.06	−	759.992i	−0.443266	−	0.0817853i
$443$	−2409.36	−	4173.14i	−0.258402	−	0.447566i	0.707412	−	0.706802i	$-0.249863\pi$
$443$	−2409.36	−	4173.14i	−0.258402	−	0.447566i	−0.965814	+	0.259236i	$0.916529\pi$
$444$		0			0
$445$	502.211	−	869.854i	0.0534990	−	0.0926630i
$446$	−8734.92	+	10244.0i	−0.927378	+	1.08759i
$447$		0			0
$448$	−1145.77	−	736.225i	−0.120832	−	0.0776415i
$449$			8677.13i			0.912024i	0.889974	+	0.456012i	$0.150723\pi$
$449$			8677.13i			0.912024i	−0.889974	+	0.456012i	$0.849277\pi$
$450$		0			0
$451$		−	11252.3i		−	1.17484i
$452$	3506.02	−	561.089i	0.364843	−	0.0583881i
$453$		0			0
$454$	4800.46	+	4093.29i	0.496248	+	0.423145i
$455$	130.472	−	225.984i	0.0134431	−	0.0232841i
$456$		0			0
$457$	3460.04	+	5992.97i	0.354166	+	0.613434i	0.986975	−	0.160874i	$-0.0514313\pi$
$457$	3460.04	+	5992.97i	0.354166	+	0.613434i	−0.632809	+	0.774308i	$0.718098\pi$
$458$	−2994.30	+	16228.8i	−0.305491	+	1.65572i
$459$		0			0
$460$	−1335.26	+	3495.29i	−0.135341	+	0.354280i
$461$	13470.8	−	7777.39i	1.36095	−	0.785747i	0.371203	−	0.928552i	$-0.378945\pi$
$461$	13470.8	−	7777.39i	1.36095	−	0.785747i	0.989751	+	0.142805i	$0.0456121\pi$
$462$		0			0
$463$	−9994.39	−	5770.27i	−1.00319	−	0.579194i	−0.0940023	−	0.995572i	$-0.529966\pi$
$463$	−9994.39	−	5770.27i	−1.00319	−	0.579194i	−0.909192	+	0.416378i	$0.863299\pi$
$464$	3542.31	+	10783.8i	0.354413	+	1.07893i
$465$		0			0
$466$	2914.67	+	8209.76i	0.289742	+	0.816116i
$467$	−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
$470$	141.126	+	397.509i	0.0138503	+	0.0390122i
$471$		0			0
$472$	−1535.44	−	2811.71i	−0.149734	−	0.274194i
$473$	12194.7	+	7040.61i	1.18544	+	0.684414i
$474$		0			0
$475$	−12921.1	+	7459.98i	−1.24812	+	0.720605i
$476$	−723.051	−	276.218i	−0.0696239	−	0.0265975i
$477$		0			0
$478$	−2715.57	+	14718.1i	−0.259848	+	1.40834i
$479$	−2830.70	−	4902.92i	−0.270017	−	0.467683i	0.698849	−	0.715269i	$-0.253696\pi$
$479$	−2830.70	−	4902.92i	−0.270017	−	0.467683i	−0.968866	+	0.247586i	$0.920363\pi$
$480$		0			0
$481$	−4058.46	+	7029.46i	−0.384719	+	0.666353i
$482$	−10768.1	−	9181.81i	−1.01758	−	0.867677i
$483$		0			0
$484$	1264.84	+	7903.50i	0.118787	+	0.742252i
$485$			3626.57i			0.339534i
$486$		0			0
$487$			9082.26i			0.845085i	0.906343	+	0.422542i	$0.138862\pi$
$487$			9082.26i			0.845085i	−0.906343	+	0.422542i	$0.861138\pi$
$488$	349.051	+	8.29632i	0.0323786	+	0.000769584i
$489$		0			0
$490$	−1485.40	+	1742.02i	−0.136946	+	0.160605i
$491$	−5098.79	+	8831.36i	−0.468646	+	0.811718i	−0.999358	−	0.0358342i	$-0.988591\pi$
$491$	−5098.79	+	8831.36i	−0.468646	+	0.811718i	0.530712	+	0.847552i	$0.321925\pi$
$492$		0			0
$493$	3225.45	+	5586.65i	0.294659	+	0.510365i
$494$	−14175.3	−	2615.42i	−1.29104	−	0.238205i
$495$		0			0
$496$	−7492.24	+	8375.07i	−0.678249	+	0.758169i
$497$	−64.5778	+	37.2840i	−0.00582839	+	0.00336502i
$498$		0			0
$499$	−2353.15	−	1358.59i	−0.211105	−	0.121881i	0.390720	−	0.920510i	$-0.372226\pi$
$499$	−2353.15	−	1358.59i	−0.211105	−	0.121881i	−0.601825	+	0.798628i	$0.705559\pi$
$500$	2968.12	+	3653.28i	0.265477	+	0.326759i
$501$		0			0
$502$	6870.64	−	2439.25i	0.610860	−	0.216871i
$503$	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
$506$	24982.6	−	8869.47i	2.19489	−	0.779241i
$507$		0			0
$508$	2148.13	+	2643.99i	0.187613	+	0.230922i
$509$	−2866.64	−	1655.05i	−0.249629	−	0.144124i	0.369965	−	0.929046i	$-0.379370\pi$
$509$	−2866.64	−	1655.05i	−0.249629	−	0.144124i	−0.619595	+	0.784922i	$0.712703\pi$
$510$		0			0
$511$	286.798	−	165.583i	0.0248282	−	0.0143346i
$512$	11555.8	+	825.228i	0.997460	+	0.0712310i
$513$		0			0
$514$	−2421.46	−	446.775i	−0.207794	−	0.0383393i
$515$	−2102.70	−	3641.98i	−0.179914	−	0.311621i
$516$		0			0
$517$	1494.33	−	2588.25i	0.127119	−	0.220176i
$518$	−973.212	+	1141.35i	−0.0825492	+	0.0968105i
$519$		0			0
$520$	−52.7443	+	2219.11i	−0.00444806	+	0.187143i
$521$		−	5030.71i		−	0.423031i	−0.977375	−	0.211516i	$-0.932160\pi$
$521$		−	5030.71i		−	0.423031i	0.977375	−	0.211516i	$-0.0678400\pi$
$522$		0			0
$523$			9680.16i			0.809338i	0.914463	+	0.404669i	$0.132613\pi$
$523$			9680.16i			0.809338i	−0.914463	+	0.404669i	$0.867387\pi$
$524$	2204.35	+	13774.1i	0.183774	+	1.14833i
$525$		0			0
$526$	−9276.95	−	7910.35i	−0.769000	−	0.655718i
$527$	−3193.21	+	5530.81i	−0.263944	+	0.457164i
$528$		0			0
$529$	−12756.2	−	22094.4i	−1.04843	−	1.81593i
$530$	435.479	−	2360.24i	0.0356905	−	0.193438i
$531$		0			0
$532$	−2488.30	−	950.571i	−0.202784	−	0.0774671i
$533$	−8216.73	+	4743.93i	−0.667742	+	0.385521i
$534$		0			0
$535$	1635.54	+	944.278i	0.132169	+	0.0763078i
$536$	−3019.08	+	1648.68i	−0.243291	+	0.132859i
$537$		0			0
$538$	5302.58	+	14935.8i	0.424927	+	1.19689i
$539$	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	$0.234139\pi$
$542$	−2033.80	−	5728.60i	−0.161179	−	0.453993i
$543$		0			0
$544$	6524.36	−	885.691i	0.514209	−	0.0698046i
$545$	−3300.88	−	1905.76i	−0.259438	−	0.149787i
$546$		0			0
$547$	3928.78	−	2268.28i	0.307098	−	0.177303i	−0.338529	−	0.940956i	$-0.609929\pi$
$547$	3928.78	−	2268.28i	0.307098	−	0.177303i	0.645627	+	0.763653i	$0.276596\pi$
$548$	4200.89	−	10996.6i	0.327469	−	0.857212i
$549$		0			0
$550$	2953.66	−	16008.5i	0.228990	−	1.24110i
$551$	11100.0	+	19225.8i	0.858216	+	1.48647i
$552$		0			0
$553$	995.797	−	1724.77i	0.0765743	−	0.132631i
$554$	−6908.63	−	5890.91i	−0.529819	−	0.451771i
$555$		0			0
$556$	−10097.9	+	1616.03i	−0.770229	+	0.123264i
$557$			17657.1i			1.34319i	0.740918	+	0.671596i	$0.234391\pi$
$557$			17657.1i			1.34319i	−0.740918	+	0.671596i	$0.765609\pi$
$558$		0			0
$559$		−	11873.1i		−	0.898355i
$560$	−83.9898	+	401.497i	−0.00633789	+	0.0302970i
$561$		0			0
$562$	−1725.76	+	2023.91i	−0.129532	+	0.151910i
$563$	4972.47	−	8612.57i	0.372229	−	0.644719i	−0.617679	−	0.786430i	$-0.711927\pi$
$563$	4972.47	−	8612.57i	0.372229	−	0.644719i	0.989908	+	0.141711i	$0.0452604\pi$
$564$		0			0
$565$	−534.697	−	926.122i	−0.0398139	−	0.0689597i
$566$	5702.30	+	1052.11i	0.423473	+	0.0781334i
$567$		0			0
$568$	330.122	−	541.643i	0.0243866	−	0.0400121i
$569$	4084.02	−	2357.91i	0.300898	−	0.173724i	−0.341948	−	0.939719i	$-0.611087\pi$
$569$	4084.02	−	2357.91i	0.300898	−	0.173724i	0.642846	+	0.765995i	$0.277753\pi$
$570$		0			0
$571$	7993.20	+	4614.88i	0.585823	+	0.338225i	0.763444	−	0.645874i	$-0.223507\pi$
$571$	7993.20	+	4614.88i	0.585823	+	0.338225i	−0.177621	+	0.984099i	$0.556840\pi$
$572$	12206.4	−	9917.14i	0.892264	−	0.724924i
$573$		0			0
$574$	−1652.24	+	586.587i	−0.120145	+	0.0426545i
$575$	−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	$0.453021\pi$
$578$	−9568.92	+	3397.21i	−0.688607	+	0.244473i
$579$		0			0
$580$	2653.32	−	2155.70i	0.189953	−	0.154329i
$581$	803.706	+	464.020i	0.0573896	+	0.0331339i
$582$		0			0
$583$	−14726.8	+	8502.51i	−1.04618	+	0.604010i
$584$	−1466.12	+	2405.51i	−0.103884	+	0.170447i
$585$		0			0
$586$	−12340.6	−	2276.92i	−0.869941	−	0.160509i
$587$	4317.74	+	7478.55i	0.303599	+	0.525848i	0.976948	−	0.213476i	$-0.0684785\pi$
$587$	4317.74	+	7478.55i	0.303599	+	0.525848i	−0.673350	+	0.739324i	$0.735145\pi$
$588$		0			0
$589$	−10989.1	+	19033.6i	−0.768755	+	1.33152i
$590$	−626.052	+	734.209i	−0.0436850	+	0.0512320i
$591$		0			0
$592$	2612.59	−	12489.0i	0.181380	−	0.867050i
$593$		−	24260.9i		−	1.68006i	−0.542537	−	0.840032i	$-0.682536\pi$
$593$		−	24260.9i		−	1.68006i	0.542537	−	0.840032i	$-0.317464\pi$
$594$		0			0
$595$			233.121i			0.0160622i
$596$	−16976.5	+	2716.85i	−1.16675	+	0.186723i
$597$		0			0
$598$	−17009.2	−	14503.6i	−1.16314	−	0.991800i
$599$	−7549.02	+	13075.3i	−0.514932	+	0.891889i	0.484917	+	0.874560i	$0.338850\pi$
$599$	−7549.02	+	13075.3i	−0.514932	+	0.891889i	−0.999850	+	0.0173291i	$0.994484\pi$
$600$		0			0
$601$	−2964.13	−	5134.03i	−0.201180	−	0.348455i	0.747729	−	0.664004i	$-0.231144\pi$
$601$	−2964.13	−	5134.03i	−0.201180	−	0.348455i	−0.948909	+	0.315550i	$0.897811\pi$
$602$	398.097	−	2157.64i	0.0269522	−	0.146078i
$603$		0			0
$604$	−2731.62	+	7150.52i	−0.184020	+	0.481706i
$605$	2087.73	−	1205.35i	0.140294	−	0.0809990i
$606$		0			0
$607$	16115.3	+	9304.20i	1.07760	+	0.622151i	0.930247	−	0.366933i	$-0.119592\pi$
$607$	16115.3	+	9304.20i	1.07760	+	0.622151i	0.147350	+	0.989084i	$0.452926\pi$
$608$	22452.8	−	3048.00i	1.49767	−	0.203311i
$609$		0			0
$610$	−35.1823	−	99.0981i	−0.00233523	−	0.00657765i
$611$	−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	$0.415766\pi$
$614$	−6995.77	−	19705.0i	−0.459815	−	1.29516i
$615$		0			0
$616$	2550.71	−	1392.91i	0.166836	−	0.0911073i
$617$	25269.7	+	14589.5i	1.64882	+	0.951946i	0.977542	+	0.210740i	$0.0675873\pi$
$617$	25269.7	+	14589.5i	1.64882	+	0.951946i	0.671277	+	0.741206i	$0.265746\pi$
$618$		0			0
$619$	14117.6	−	8150.83i	0.916698	−	0.529256i	0.0341179	−	0.999418i	$-0.489138\pi$
$619$	14117.6	−	8150.83i	0.916698	−	0.529256i	0.882580	+	0.470162i	$0.155804\pi$
$620$	3161.63	+	1207.80i	0.204797	+	0.0782359i
$621$		0			0
$622$	2512.88	−	13619.5i	0.161990	−	0.877963i
$623$	554.427	+	960.297i	0.0356544	+	0.0617552i
$624$		0			0
$625$	−6740.81	+	11675.4i	−0.431412	+	0.747227i
$626$	1467.22	+	1251.08i	0.0936774	+	0.0798776i
$627$		0			0
$628$	2646.23	+	16535.2i	0.168147	+	1.05068i
$629$		−	7251.46i		−	0.459674i
$630$		0			0
$631$		−	2517.83i		−	0.158848i	−0.996841	−	0.0794242i	$-0.974692\pi$
$631$		−	2517.83i		−	0.158848i	0.996841	−	0.0794242i	$-0.0253082\pi$
$632$	−402.559	+	16936.8i	−0.0253369	+	1.06600i
$633$		0			0
$634$	2848.33	−	3340.41i	0.178425	−	0.209250i
$635$	513.012	−	888.562i	0.0320602	−	0.0555300i
$636$		0			0
$637$	−6838.42	−	11844.5i	−0.425350	−	0.736728i
$638$	−23819.7	−	4394.88i	−1.47811	−	0.272720i
$639$		0			0
$640$	−1009.86	−	3339.96i	−0.0623720	−	0.206287i
$641$	−14572.0	+	8413.13i	−0.897907	+	0.518407i	−0.876520	−	0.481365i	$-0.840141\pi$
$641$	−14572.0	+	8413.13i	−0.897907	+	0.518407i	−0.0213863	+	0.999771i	$0.506808\pi$
$642$		0			0
$643$	17687.6	+	10211.9i	1.08481	+	0.626313i	0.932189	−	0.361973i	$-0.117897\pi$
$643$	17687.6	+	10211.9i	1.08481	+	0.626313i	0.152617	+	0.988285i	$0.451230\pi$
$644$	−2604.70	−	3205.96i	−0.159378	−	0.196169i
$645$		0			0
$646$	12135.5	−	4308.41i	0.739109	−	0.262402i
$647$	−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
$650$	−12935.0	+	4592.26i	−0.780544	+	0.277113i
$651$		0			0
$652$	−7408.45	−	9118.60i	−0.444996	−	0.547718i
$653$	−21836.5	−	12607.3i	−1.30862	−	0.755533i	−0.326756	−	0.945109i	$-0.605955\pi$
$653$	−21836.5	−	12607.3i	−1.30862	−	0.755533i	−0.981866	+	0.189576i	$0.939289\pi$
$654$		0			0
$655$	3638.46	−	2100.66i	0.217048	−	0.125313i
$656$	9943.90	−	11115.6i	0.591835	−	0.661573i
$657$		0			0
$658$	−457.946	−	84.4938i	−0.0271316	−	0.00500595i
$659$	−6865.03	−	11890.6i	−0.405802	−	0.702870i	0.588612	−	0.808416i	$-0.299675\pi$
$659$	−6865.03	−	11890.6i	−0.405802	−	0.702870i	−0.994415	+	0.105545i	$0.966341\pi$
$660$		0			0
$661$	−772.039	+	1337.21i	−0.0454294	+	0.0786860i	−0.887846	−	0.460141i	$-0.847799\pi$
$661$	−772.039	+	1337.21i	−0.0454294	+	0.0786860i	0.842417	+	0.538827i	$0.181132\pi$
$662$	13583.8	−	15930.6i	0.797508	−	0.935286i
$663$		0			0
$664$	−7892.20	−	187.584i	−0.461260	−	0.0109633i
$665$			802.258i			0.0467823i
$666$		0			0
$667$			34426.6i			1.99851i
$668$	−3853.77	−	24080.7i	−0.223214	−	1.39477i
$669$		0			0
$670$	788.357	+	672.223i	0.0454580	+	0.0387616i
$671$	−372.533	+	645.246i	−0.0214329	+	0.0371229i
$672$		0			0
$673$	2684.11	+	4649.02i	0.153737	+	0.266280i	0.932598	−	0.360916i	$-0.117536\pi$
$673$	2684.11	+	4649.02i	0.153737	+	0.266280i	−0.778861	+	0.627196i	$0.784202\pi$
$674$	−5000.19	+	27100.4i	−0.285757	+	1.54877i
$675$		0			0
$676$	4030.84	+	1539.85i	0.229338	+	0.0876110i
$677$	16713.8	−	9649.71i	0.948838	−	0.547812i	0.0561181	−	0.998424i	$-0.482128\pi$
$677$	16713.8	−	9649.71i	0.948838	−	0.547812i	0.892720	+	0.450612i	$0.148794\pi$
$678$		0			0
$679$	−3467.25	−	2001.82i	−0.195966	−	0.113141i
$680$	−950.441	−	1740.45i	−0.0535996	−	0.0981520i
$681$		0			0
$682$	−8022.78	−	22597.8i	−0.450452	−	1.26879i
$683$	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
$686$	−1708.95	−	4813.60i	−0.0951136	−	0.267907i
$687$		0			0
$688$	5824.61	+	17731.7i	0.322763	+	0.982581i
$689$	12417.5	+	7169.23i	0.686600	+	0.396409i
$690$		0			0
$691$	20587.2	−	11886.0i	1.13339	−	0.654364i	0.188606	−	0.982053i	$-0.439603\pi$
$691$	20587.2	−	11886.0i	1.13339	−	0.654364i	0.944786	+	0.327689i	$0.106270\pi$
$692$	7924.00	−	20742.5i	0.435297	−	1.13947i
$693$		0			0
$694$	3616.77	−	19602.5i	0.197825	−	1.07219i
$695$	1540.02	+	2667.39i	0.0840520	+	0.145582i
$696$		0			0
$697$	4238.12	−	7340.64i	0.230316	−	0.398919i
$698$	−2598.92	−	2216.07i	−0.140932	−	0.120171i
$699$		0			0
$700$	−2504.58	+	400.823i	−0.135235	+	0.0216424i
$701$			3501.89i			0.188680i	0.995540	+	0.0943399i	$0.0300740\pi$
$701$			3501.89i			0.188680i	−0.995540	+	0.0943399i	$0.969926\pi$
$702$		0			0
$703$		−	24955.1i		−	1.33883i
$704$	−13364.4	+	20798.7i	−0.715467	+	1.11346i
$705$		0			0
$706$	2789.71	−	3271.66i	0.148714	−	0.174406i
$707$	−579.113	+	1003.05i	−0.0308059	+	0.0533574i
$708$		0			0
$709$	−2079.38	−	3601.59i	−0.110145	−	0.190777i	0.805684	−	0.592346i	$-0.201798\pi$
$709$	−2079.38	−	3601.59i	−0.110145	−	0.190777i	−0.915829	+	0.401569i	$0.868465\pi$
$710$	−187.875	−	34.6641i	−0.00993074	−	0.00183228i
$711$		0			0
$712$	−8054.45	−	4909.04i	−0.423951	−	0.258391i
$713$	−29516.3	+	17041.3i	−1.55034	+	0.895091i
$714$		0			0
$715$	−4102.18	−	2368.40i	−0.214564	−	0.123878i
$716$	−2965.55	+	2409.38i	−0.154788	+	0.125758i
$717$		0			0
$718$	−17365.8	+	6165.30i	−0.902627	+	0.320455i
$719$	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
$722$	23480.7	−	8336.24i	1.21033	−	0.429699i
$723$		0			0
$724$	−4547.20	+	3694.39i	−0.233419	+	0.189642i
$725$	18307.5	+	10569.8i	0.937825	+	0.541454i
$726$		0			0
$727$	−31220.9	+	18025.4i	−1.59274	+	0.919566i	−0.599900	+	0.800075i	$0.704793\pi$
$727$	−31220.9	+	18025.4i	−1.59274	+	0.919566i	−0.992835	+	0.119491i	$0.961874\pi$
$728$	−2092.51	−	1275.35i	−0.106529	−	0.0649278i
$729$		0			0
$730$	834.378	+	153.948i	0.0423037	+	0.00780530i
$731$	5303.59	+	9186.10i	0.268345	+	0.464788i
$732$		0			0
$733$	10850.9	−	18794.4i	0.546779	−	0.947049i	−0.451714	−	0.892163i	$-0.649187\pi$
$733$	10850.9	−	18794.4i	0.546779	−	0.947049i	0.998493	−	0.0548859i	$-0.0174795\pi$
$734$	−7400.60	+	8679.14i	−0.372154	+	0.436448i
$735$		0			0
$736$	32517.2	+	13315.9i	1.62853	+	0.666889i
$737$		−	7340.58i		−	0.366884i
$738$		0			0
$739$		−	26112.0i		−	1.29979i	−0.760024	−	0.649895i	$-0.774813\pi$
$739$		−	26112.0i		−	1.29979i	0.760024	−	0.649895i	$-0.225187\pi$
$740$	−3794.61	+	607.275i	−0.188504	+	0.0301674i
$741$		0			0
$742$	2016.18	+	1719.17i	0.0997522	+	0.0850576i
$743$	−2806.43	+	4860.88i	−0.138570	+	0.240011i	−0.926956	−	0.375171i	$-0.877584\pi$
$743$	−2806.43	+	4860.88i	−0.138570	+	0.240011i	0.788385	+	0.615182i	$0.210917\pi$
$744$		0			0
$745$	2589.06	+	4484.38i	0.127323	+	0.220530i
$746$	1260.09	−	6829.51i	0.0618432	−	0.335182i
$747$		0			0
$748$	−5014.06	+	13125.2i	−0.245096	+	0.641585i
$749$	−1805.59	+	1042.46i	−0.0880839	+	0.0508553i
$750$		0			0
$751$	−24027.9	−	13872.5i	−1.16750	−	0.674056i	−0.214409	−	0.976744i	$-0.568783\pi$
$751$	−24027.9	−	13872.5i	−1.16750	−	0.674056i	−0.953090	+	0.302688i	$0.902116\pi$
$752$	3763.46	−	1236.24i	0.182499	−	0.0599481i
$753$		0			0
$754$	6833.02	+	19246.6i	0.330032	+	0.929601i
$755$	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	$0.684294\pi$
$758$	9007.10	+	25370.3i	0.431600	+	1.21569i
$759$		0			0
$760$	−3270.83	−	5989.57i	−0.156113	−	0.285874i
$761$	−27979.1	−	16153.7i	−1.33277	−	0.769477i	−0.347049	−	0.937847i	$-0.612816\pi$
$761$	−27979.1	−	16153.7i	−1.33277	−	0.769477i	−0.985724	+	0.168370i	$0.946150\pi$
$762$		0			0
$763$	3644.08	−	2103.91i	0.172902	−	0.0998253i
$764$	−23062.4	−	8810.24i	−1.09211	−	0.417203i
$765$		0			0
$766$	−4852.53	+	26300.1i	−0.228889	+	1.24055i
$767$	−2882.19	−	4992.10i	−0.135684	−	0.235012i
$768$		0			0
$769$	1200.97	−	2080.14i	0.0563174	−	0.0975446i	−0.836492	−	0.547979i	$-0.815397\pi$
$769$	1200.97	−	2080.14i	0.0563174	−	0.0975446i	0.892810	+	0.450434i	$0.148731\pi$
$770$	−666.055	−	567.938i	−0.0311727	−	0.0265806i
$771$		0			0
$772$	−2066.11	−	12910.3i	−0.0963224	−	0.601880i
$773$			21135.4i			0.983424i	0.870758	+	0.491712i	$0.163629\pi$
$773$			21135.4i			0.983424i	−0.870758	+	0.491712i	$0.836371\pi$
$774$		0			0
$775$			20928.4i			0.970025i
$776$	34047.6	+	809.252i	1.57505	+	0.0374362i
$777$		0			0
$778$	−5443.29	+	6383.68i	−0.250837	+	0.294172i
$779$	14585.0	−	25262.0i	0.670811	−	1.16188i
$780$		0			0
$781$	676.799	+	1172.25i	0.0310087	+	0.0537086i
$782$	19638.4	+	3623.41i	0.898041	+	0.165694i
$783$		0			0
$784$	16023.3	+	14334.2i	0.729922	+	0.652979i
$785$	4367.81	−	2521.76i	0.198591	−	0.114656i
$786$		0			0
$787$	3776.51	+	2180.37i	0.171052	+	0.0987570i	0.583082	−	0.812413i	$-0.301847\pi$
$787$	3776.51	+	2180.37i	0.171052	+	0.0987570i	−0.412030	+	0.911170i	$0.635180\pi$
$788$	16902.7	+	20804.5i	0.764130	+	0.940520i
$789$		0			0
$790$	4808.50	−	1707.14i	0.216555	−	0.0768826i
$791$	1180.58			0.0530679
$792$		0			0
$793$	628.232			0.0281326
$794$	−3456.65	+	1227.20i	−0.154499	+	0.0548510i
$795$		0			0
$796$	−5279.71	−	6498.47i	−0.235094	−	0.289362i
$797$	17755.1	+	10250.9i	0.789106	+	0.455590i	0.839648	−	0.543132i	$-0.182762\pi$
$797$	17755.1	+	10250.9i	0.789106	+	0.455590i	−0.0505420	+	0.998722i	$0.516095\pi$
$798$		0			0
$799$	1949.69	−	1125.66i	0.0863270	−	0.0498409i
$800$	17064.8	−	13203.8i	0.754163	−	0.583530i
$801$		0			0
$802$	−5723.88	−	1056.09i	−0.252016	−	0.0464985i
$803$	−3005.76	−	5206.12i	−0.132093	−	0.228792i
$804$		0			0
$805$	−622.050	+	1077.42i	−0.0272352	+	0.0471728i
$806$	−13119.1	+	15385.5i	−0.573324	+	0.672372i
$807$		0			0
$808$	234.111	−	9849.74i	0.0101931	−	0.428852i
$809$		−	34550.7i		−	1.50153i	−0.660568	−	0.750766i	$-0.729685\pi$
$809$		−	34550.7i		−	1.50153i	0.660568	−	0.750766i	$-0.270315\pi$
$810$		0			0
$811$			19709.5i			0.853384i	0.904397	+	0.426692i	$0.140321\pi$
$811$			19709.5i			0.853384i	−0.904397	+	0.426692i	$0.859679\pi$
$812$	596.402	+	3726.68i	0.0257754	+	0.161060i
$813$		0			0
$814$	20718.3	+	17666.3i	0.892109	+	0.760692i
$815$	−1769.27	+	3064.47i	−0.0760429	+	0.131710i
$816$		0			0
$817$	18251.7	+	31612.9i	0.781575	+	1.35373i
$818$	2974.03	−	16118.9i	0.127121	−	0.688978i
$819$		0			0
$820$	−4196.20	−	1603.02i	−0.178704	−	0.0682682i
$821$	28891.8	−	16680.7i	1.22817	−	0.709086i	0.261526	−	0.965196i	$-0.415774\pi$
$821$	28891.8	−	16680.7i	1.22817	−	0.709086i	0.966648	+	0.256110i	$0.0824409\pi$
$822$		0			0
$823$	−36540.4	−	21096.6i	−1.54765	−	0.893537i	−0.998321	−	0.0579313i	$-0.981550\pi$
$823$	−36540.4	−	21096.6i	−1.54765	−	0.893537i	−0.549330	−	0.835605i	$-0.685117\pi$
$824$	−34661.4	+	18928.2i	−1.46540	+	0.800237i
$825$		0			0
$826$	−356.382	−	1003.82i	−0.0150123	−	0.0422851i
$827$	−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	$0.663488\pi$
$830$	795.489	+	2240.66i	0.0332673	+	0.0937039i
$831$		0			0
$832$	20822.0	+	990.366i	0.867637	+	0.0412678i
$833$	10581.6	+	6109.28i	0.440132	+	0.254110i
$834$		0			0
$835$	−6360.95	+	3672.50i	−0.263629	+	0.152206i
$836$	−17255.3	+	45168.9i	−0.713860	+	1.86866i
$837$		0			0
$838$	−7238.80	+	39233.4i	−0.298401	+	1.61730i
$839$	4579.55	+	7932.02i	0.188443	+	0.326393i	0.944731	−	0.327846i	$-0.106323\pi$
$839$	4579.55	+	7932.02i	0.188443	+	0.326393i	−0.756288	+	0.654238i	$0.772989\pi$
$840$		0			0
$841$	3532.81	−	6119.00i	0.144852	−	0.250892i
$842$	13819.2	+	11783.5i	0.565606	+	0.482286i
$843$		0			0
$844$	−41692.5	+	6672.30i	−1.70037	+	0.272121i
$845$		−	1299.60i		−	0.0529082i
$846$		0			0
$847$			2661.35i			0.107963i
$848$	−22061.6	−	4615.11i	−0.893396	−	0.186891i
$849$		0			0
$850$	7956.35	−	9330.90i	0.321059	−	0.376526i
$851$	19349.5	−	33514.3i	0.779427	−	1.35001i
$852$		0			0
$853$	16740.3	+	28995.1i	0.671955	+	1.16386i	0.977349	+	0.211634i	$0.0678784\pi$
$853$	16740.3	+	28995.1i	0.671955	+	1.16386i	−0.305394	+	0.952226i	$0.598788\pi$
$854$	114.165	+	21.0641i	0.00457452	+	0.000844028i
$855$		0			0
$856$	9230.20	−	15144.3i	0.368553	−	0.604699i
$857$	−26803.0	+	15474.7i	−1.06835	+	0.616811i	−0.927730	−	0.373253i	$-0.878242\pi$
$857$	−26803.0	+	15474.7i	−1.06835	+	0.616811i	−0.140618	+	0.990064i	$0.544909\pi$
$858$		0			0
$859$	−5321.93	−	3072.62i	−0.211388	−	0.122045i	0.390568	−	0.920574i	$-0.372278\pi$
$859$	−5321.93	−	3072.62i	−0.211388	−	0.122045i	−0.601956	+	0.798529i	$0.705612\pi$
$860$	4362.84	−	3544.61i	0.172990	−	0.140547i
$861$		0			0
$862$	2984.56	−	1059.59i	0.117929	−	0.0418676i
$863$	−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
$866$	799.185	−	283.731i	0.0313596	−	0.0111335i
$867$		0			0
$868$	−2899.92	+	2356.05i	−0.113398	+	0.0921308i
$869$	−31309.0	−	18076.3i	−1.22219	−	0.705633i
$870$		0			0
$871$	−5360.27	+	3094.75i	−0.208526	+	0.120392i
$872$	−18628.6	+	30564.6i	−0.723444	+	1.18698i
$873$		0			0
$874$	67583.3	+	12469.5i	2.61561	+	0.482595i
$875$	782.544	+	1355.41i	0.0302341	+	0.0523669i
$876$		0			0
$877$	2574.73	−	4459.56i	0.0991361	−	0.171709i	−0.812191	−	0.583391i	$-0.801725\pi$
$877$	2574.73	−	4459.56i	0.0991361	−	0.171709i	0.911327	+	0.411683i	$0.135059\pi$
$878$	−4428.94	+	5194.08i	−0.170238	+	0.199649i
$879$		0			0
$880$	7288.19	+	1524.63i	0.279187	+	0.0584037i
$881$			26936.4i			1.03009i	0.857162	+	0.515046i	$0.172225\pi$
$881$			26936.4i			1.03009i	−0.857162	+	0.515046i	$0.827775\pi$
$882$		0			0
$883$		−	37301.8i		−	1.42164i	−0.703376	−	0.710818i	$-0.748325\pi$
$883$		−	37301.8i		−	1.42164i	0.703376	−	0.710818i	$-0.251675\pi$
$884$	11698.2	−	1872.14i	0.445084	−	0.0712295i
$885$		0			0
$886$	10371.0	+	8843.25i	0.393252	+	0.335321i
$887$	−17421.8	+	30175.4i	−0.659488	+	1.14227i	0.321261	+	0.946991i	$0.395893\pi$
$887$	−17421.8	+	30175.4i	−0.659488	+	1.14227i	−0.980748	+	0.195276i	$0.937440\pi$
$888$		0			0
$889$	566.352	+	980.950i	0.0213665	+	0.0370079i
$890$	−515.469	+	2793.78i	−0.0194141	+	0.105222i
$891$		0			0
$892$	13588.5	−	35570.4i	0.510064	−	1.33519i
$893$	6709.65	−	3873.82i	0.251433	−	0.145165i
$894$		0			0
$895$	996.628	+	575.404i	0.0372219	+	0.0214901i
$896$	3750.66	+	878.120i	0.139845	+	0.0327410i
$897$		0			0
$898$	−8211.12	−	23128.3i	−0.305132	−	0.859466i
$899$	31140.2			1.15527
$900$		0			0
$901$	−12809.6			−0.473641
$902$	10648.0	+	29992.4i	0.393061	+	1.10714i
$903$		0			0
$904$	−8814.09	+	4813.27i	−0.324284	+	0.177087i
$905$	1528.17	+	882.289i	0.0561304	+	0.0324069i
$906$		0			0
$907$	−7693.07	+	4441.59i	−0.281636	+	0.162603i	−0.634164	−	0.773199i	$-0.718656\pi$
$907$	−7693.07	+	4441.59i	−0.281636	+	0.162603i	0.352528	+	0.935801i	$0.385322\pi$
$908$	−16668.8	−	6367.75i	−0.609220	−	0.232732i
$909$		0			0
$910$	−133.916	+	725.809i	−0.00487833	+	0.0264399i
$911$	−22256.0	−	38548.6i	−0.809413	−	1.40194i	−0.913271	−	0.407352i	$-0.866452\pi$
$911$	−22256.0	−	38548.6i	−0.809413	−	1.40194i	0.103858	−	0.994592i	$-0.466881\pi$
$912$		0			0
$913$	8423.14	−	14589.3i	0.305329	−	0.528845i
$914$	−14893.6	−	12699.6i	−0.538991	−	0.459591i
$915$		0			0
$916$	−7376.08	−	46090.1i	−0.266062	−	1.66251i
$917$			4638.16i			0.167029i
$918$		0			0
$919$		−	7223.63i		−	0.259288i	−0.991561	−	0.129644i	$-0.958617\pi$
$919$		−	7223.63i		−	0.259288i	0.991561	−	0.129644i	$-0.0413834\pi$
$920$	251.469	−	10580.0i	0.00901160	−	0.379145i
$921$		0			0
$922$	−28545.9	+	33477.5i	−1.01964	+	1.19579i
$923$	570.670	−	988.430i	0.0203509	−	0.0352487i
$924$		0			0
$925$	−11881.6	−	20579.5i	−0.422339	−	0.731512i
$926$	32099.7	+	5922.60i	1.13916	+	0.210182i
$927$		0			0
$928$	−19646.4	−	25391.4i	−0.694964	−	0.898182i
$929$	30912.2	−	17847.2i	1.09171	−	0.630298i	0.157677	−	0.987491i	$-0.449599\pi$
$929$	30912.2	−	17847.2i	1.09171	−	0.630298i	0.934031	+	0.357193i	$0.116266\pi$
$930$		0			0
$931$	36415.3	+	21024.4i	1.28192	+	0.740114i
$932$	−15537.7	−	19124.4i	−0.546089	−	0.672147i
$933$		0			0
$934$	18.6919	−	6.63610i	0.000654837	−	0.000232484i
$935$	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	$0.525875\pi$
$938$	−1077.85	+	382.666i	−0.0375194	+	0.0133203i
$939$		0			0
$940$	−752.322	−	925.987i	−0.0261043	−	0.0321302i
$941$	−22129.9	−	12776.7i	−0.766645	−	0.442623i	0.0650314	−	0.997883i	$-0.479285\pi$
$941$	−22129.9	−	12776.7i	−0.766645	−	0.442623i	−0.831676	+	0.555260i	$0.812619\pi$
$942$		0			0
$943$	39174.9	−	22617.6i	1.35282	−	0.781051i
$944$	6753.33	+	6041.44i	0.232841	+	0.208297i
$945$		0			0
$946$	−39166.6	−	7226.48i	−1.34611	−	0.248365i
$947$	−26469.6	−	45846.6i	−0.908285	−	1.57319i	−0.816447	−	0.577421i	$-0.804059\pi$
$947$	−26469.6	−	45846.6i	−0.908285	−	1.57319i	−0.0918380	−	0.995774i	$-0.529274\pi$
$948$		0			0
$949$	−2534.42	+	4389.75i	−0.0866922	+	0.150155i
$950$	27380.9	−	32111.2i	0.935108	−	1.09666i
$951$		0			0
$952$	2188.63	+	52.0198i	0.0745103	+	0.00177098i
$953$			744.138i			0.0252938i	0.999920	+	0.0126469i	$0.00402574\pi$
$953$			744.138i			0.0252938i	−0.999920	+	0.0126469i	$0.995974\pi$
$954$		0			0
$955$			7435.63i			0.251949i
$956$	−6689.46	−	41799.7i	−0.226310	−	1.41412i
$957$		0			0
$958$	12184.7	+	10389.7i	0.410927	+	0.350393i
$959$	1957.04	−	3389.70i	0.0658980	−	0.114139i
$960$		0			0
$961$	518.981	+	898.901i	0.0174207	+	0.0301736i
$962$	4165.60	−	22577.0i	0.139610	−	0.756666i
$963$		0			0
$964$	37390.3	+	14283.7i	1.24923	+	0.477228i
$965$	−3410.28	+	1968.92i	−0.113762	+	0.0656807i
$966$		0			0
$967$	−14044.5	−	8108.61i	−0.467054	−	0.269654i	0.247952	−	0.968772i	$-0.420243\pi$
$967$	−14044.5	−	8108.61i	−0.467054	−	0.269654i	−0.715006	+	0.699119i	$0.753576\pi$
$968$	−10850.4	−	19869.3i	−0.360274	−	0.659736i
$969$		0			0
$970$	−3431.81	−	9666.37i	−0.113597	−	0.319968i
$971$	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
$974$	−8594.50	−	24208.1i	−0.282737	−	0.796385i
$975$		0			0
$976$	−938.221	+	308.192i	−0.0307702	+	0.0101076i
$977$	−18376.3	−	10609.6i	−0.601751	−	0.347421i	0.167979	−	0.985791i	$-0.446276\pi$
$977$	−18376.3	−	10609.6i	−0.601751	−	0.347421i	−0.769730	+	0.638369i	$0.779609\pi$
$978$		0			0
$979$	17431.8	−	10064.3i	0.569074	−	0.328555i
$980$	2310.77	−	6048.85i	0.0753211	−	0.197167i
$981$		0			0
$982$	5233.39	−	28364.3i	0.170065	−	0.921733i
$983$	19149.3	+	33167.6i	0.621331	+	1.07618i	0.989238	+	0.146314i	$0.0467411\pi$
$983$	19149.3	+	33167.6i	0.621331	+	1.07618i	−0.367907	+	0.929862i	$0.619926\pi$
$984$		0			0
$985$	4036.68	−	6991.73i	0.130578	−	0.226168i
$986$	−13883.8	−	11838.6i	−0.448429	−	0.382371i
$987$		0			0
$988$	40258.2	−	6442.76i	1.29634	−	0.207461i
$989$			56607.5i			1.82004i
$990$		0			0
$991$		−	17803.2i		−	0.570674i	−0.958427	−	0.285337i	$-0.907894\pi$
$991$		−	17803.2i		−	0.570674i	0.958427	−	0.285337i	$-0.0921055\pi$
$992$	12044.7	−	29413.0i	0.385505	−	0.941396i
$993$		0			0
$994$	136.846	−	160.488i	0.00436669	−	0.00512108i
$995$	−1260.89	+	2183.93i	−0.0401738	+	0.0695831i
$996$		0			0
$997$	−4517.89	−	7825.21i	−0.143513	−	0.248573i	0.785304	−	0.619110i	$-0.212507\pi$
$997$	−4517.89	−	7825.21i	−0.143513	−	0.248573i	−0.928817	+	0.370538i	$0.879173\pi$
$998$	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	108.4.h.b.71.2		24
3.2	odd	2		36.4.h.b.23.11	yes	24
4.3	odd	2	inner	108.4.h.b.71.3		24
9.2	odd	6	inner	108.4.h.b.35.3		24
9.4	even	3		324.4.b.c.323.13		24
9.5	odd	6		324.4.b.c.323.12		24
9.7	even	3		36.4.h.b.11.10	✓	24
12.11	even	2		36.4.h.b.23.10	yes	24
36.7	odd	6		36.4.h.b.11.11	yes	24
36.11	even	6	inner	108.4.h.b.35.2		24
36.23	even	6		324.4.b.c.323.14		24
36.31	odd	6		324.4.b.c.323.11		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.66543 + 0.946295i) q^{2} +(6.20905 - 5.04457i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +O(q^{10})\)	\(q+(-2.66543 + 0.946295i) q^{2} +(6.20905 - 5.04457i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(2.30362 - 1.33000i) q^{7} +(-11.7761 + 19.3216i) q^{8} +(6.70190 + 1.23654i) q^{10} +(-24.1428 - 41.8166i) q^{11} +(-20.3570 + 35.2594i) q^{13} +(-4.88158 + 5.72493i) q^{14} +(13.1046 - 62.6440i) q^{16} -36.3729i q^{17} -125.173i q^{19} +(-19.0336 + 3.04606i) q^{20} +(103.922 + 88.6131i) q^{22} +(97.0560 - 168.106i) q^{23} +(-59.5972 - 103.225i) q^{25} +(20.8944 - 113.245i) q^{26} +(7.59405 - 19.8788i) q^{28} +(-153.593 + 88.6772i) q^{29} +(-152.058 - 87.7909i) q^{31} +(24.3503 + 179.374i) q^{32} +(34.4195 + 96.9496i) q^{34} -6.40918 q^{35} +199.364 q^{37} +(118.451 + 333.641i) q^{38} +(47.8502 - 26.1304i) q^{40} +(201.816 + 116.518i) q^{41} +(-252.553 + 145.812i) q^{43} +(-360.851 - 137.851i) q^{44} +(-99.6182 + 539.918i) q^{46} +(30.9476 + 53.6029i) q^{47} +(-167.962 + 290.919i) q^{49} +(256.534 + 218.744i) q^{50} +(51.4707 + 321.620i) q^{52} -352.175i q^{53} +116.343i q^{55} +(-1.43018 + 60.1718i) q^{56} +(325.478 - 381.708i) q^{58} +(-70.7911 + 122.614i) q^{59} +(-7.71518 - 13.3631i) q^{61} +(488.377 + 90.1086i) q^{62} +(-234.645 - 455.067i) q^{64} +(84.9565 - 49.0496i) q^{65} +(131.657 + 76.0120i) q^{67} +(-183.486 - 225.841i) q^{68} +(17.0832 - 6.06498i) q^{70} -28.0331 q^{71} +124.499 q^{73} +(-531.392 + 188.657i) q^{74} +(-631.445 - 777.207i) q^{76} +(-111.232 - 64.2199i) q^{77} +(648.411 - 374.360i) q^{79} +(-102.814 + 114.929i) q^{80} +(-648.187 - 119.595i) q^{82} +(174.444 + 302.146i) q^{83} +(-43.8198 + 75.8981i) q^{85} +(535.182 - 627.641i) q^{86} +(1092.27 + 25.9614i) q^{88} +416.864i q^{89} +108.299i q^{91} +(-245.397 - 1533.38i) q^{92} +(-133.213 - 113.589i) q^{94} +(-150.801 + 261.195i) q^{95} +(-752.565 - 1303.48i) q^{97} +(172.396 - 934.367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 24 * q - 12 * q^4 + 72 * q^5	\( 24 q - 12 q^{4} + 72 q^{5} + 96 q^{10} - 216 q^{13} + 36 q^{14} - 72 q^{16} + 540 q^{20} - 192 q^{22} + 252 q^{25} - 672 q^{28} - 576 q^{29} - 360 q^{32} - 660 q^{34} + 1248 q^{37} + 144 q^{38} + 636 q^{40} - 1116 q^{41} + 960 q^{46} + 348 q^{49} + 648 q^{50} + 132 q^{52} + 1692 q^{56} + 516 q^{58} - 264 q^{61} + 960 q^{64} + 2592 q^{65} - 5688 q^{68} + 564 q^{70} - 4776 q^{73} - 5652 q^{74} - 600 q^{76} - 648 q^{77} - 4104 q^{82} + 720 q^{85} + 9540 q^{86} + 1956 q^{88} + 7416 q^{92} - 1188 q^{94} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 + 72 * q^5 + 96 * q^10 - 216 * q^13 + 36 * q^14 - 72 * q^16 + 540 * q^20 - 192 * q^22 + 252 * q^25 - 672 * q^28 - 576 * q^29 - 360 * q^32 - 660 * q^34 + 1248 * q^37 + 144 * q^38 + 636 * q^40 - 1116 * q^41 + 960 * q^46 + 348 * q^49 + 648 * q^50 + 132 * q^52 + 1692 * q^56 + 516 * q^58 - 264 * q^61 + 960 * q^64 + 2592 * q^65 - 5688 * q^68 + 564 * q^70 - 4776 * q^73 - 5652 * q^74 - 600 * q^76 - 648 * q^77 - 4104 * q^82 + 720 * q^85 + 9540 * q^86 + 1956 * q^88 + 7416 * q^92 - 1188 * q^94 + 588 * q^97

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