LMFDB - Embedded newform 108.4.h.b.71.3

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			71.3
Character	$\chi$	$=$	108.71
Dual form			108.4.h.b.35.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15223 + 1.83518i) q^{2} +(1.26420 - 7.89948i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(-2.30362 + 1.33000i) q^{7} +(11.7761 + 19.3216i) q^{8} +O(q^{10})$	\(q+(-2.15223 + 1.83518i) q^{2} +(1.26420 - 7.89948i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(-2.30362 + 1.33000i) q^{7} +(11.7761 + 19.3216i) q^{8} +(6.70190 - 1.23654i) q^{10} +(24.1428 + 41.8166i) q^{11} +(-20.3570 + 35.2594i) q^{13} +(2.51714 - 7.09003i) q^{14} +(-60.8036 - 19.9731i) q^{16} -36.3729i q^{17} +125.173i q^{19} +(-12.1548 + 14.9605i) q^{20} +(-128.702 - 45.6925i) q^{22} +(-97.0560 + 168.106i) q^{23} +(-59.5972 - 103.225i) q^{25} +(-20.8944 - 113.245i) q^{26} +(7.59405 + 19.8788i) q^{28} +(-153.593 + 88.6772i) q^{29} +(152.058 + 87.7909i) q^{31} +(167.518 - 68.5991i) q^{32} +(66.7510 + 78.2830i) q^{34} +6.40918 q^{35} +199.364 q^{37} +(-229.716 - 269.402i) q^{38} +(-1.29548 - 54.5047i) q^{40} +(201.816 + 116.518i) q^{41} +(252.553 - 145.812i) q^{43} +(360.851 - 137.851i) q^{44} +(-99.6182 - 539.918i) q^{46} +(-30.9476 - 53.6029i) q^{47} +(-167.962 + 290.919i) q^{49} +(317.705 + 112.793i) q^{50} +(252.795 + 205.385i) q^{52} -352.175i q^{53} -116.343i q^{55} +(-52.8254 - 28.8473i) q^{56} +(167.830 - 472.726i) q^{58} +(70.7911 - 122.614i) q^{59} +(-7.71518 - 13.3631i) q^{61} +(-488.377 + 90.1086i) q^{62} +(-234.645 + 455.067i) q^{64} +(84.9565 - 49.0496i) q^{65} +(-131.657 - 76.0120i) q^{67} +(-287.327 - 45.9827i) q^{68} +(-13.7940 + 11.7620i) q^{70} +28.0331 q^{71} +124.499 q^{73} +(-429.078 + 365.870i) q^{74} +(988.804 + 158.244i) q^{76} +(-111.232 - 64.2199i) q^{77} +(-648.411 + 374.360i) q^{79} +(102.814 + 114.929i) q^{80} +(-648.187 + 119.595i) q^{82} +(-174.444 - 302.146i) q^{83} +(-43.8198 + 75.8981i) q^{85} +(-275.962 + 777.302i) q^{86} +(-523.653 + 958.916i) q^{88} +416.864i q^{89} -108.299i q^{91} +(1205.25 + 979.212i) q^{92} +(164.978 + 58.5712i) q^{94} +(150.801 - 261.195i) q^{95} +(-752.565 - 1303.48i) q^{97} +(-172.396 - 934.367i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.15223	+	1.83518i	−0.760929	+	0.648835i
$2$	−2.15223	+	1.83518i	−0.760929	+	0.648835i
$3$		0			0
$3$		0			0
$4$	1.26420	−	7.89948i	0.158025	−	0.987435i
$5$	−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	−0.560901	−	0.827883i	$-0.689545\pi$
$7$	−2.30362	+	1.33000i	−0.124384	+	0.0718131i	0.436517	+	0.899696i	$0.356212\pi$
$8$	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	$0.0635229\pi$
$11$	24.1428	+	41.8166i	0.661758	+	1.14620i	−0.318395	+	0.947958i	$0.603144\pi$
$12$		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	$0.309674\pi$
$14$	2.51714	−	7.09003i	0.0480524	−	0.135349i
$15$		0			0
$16$	−60.8036	−	19.9731i	−0.950056	−	0.312079i
$17$		−	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	$0.272705\pi$
$19$			125.173i			1.51141i	−0.654914	+	0.755703i	$0.727295\pi$
$20$	−12.1548	+	14.9605i	−0.135894	+	0.167264i
$21$		0			0
$22$	−128.702	−	45.6925i	−1.24725	−	0.442804i
$23$	−97.0560	+	168.106i	−0.879894	+	1.52402i	−0.0284384	+	0.999596i	$0.509053\pi$
$23$	−97.0560	+	168.106i	−0.879894	+	1.52402i	−0.851456	+	0.524426i	$0.824280\pi$
$24$		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	0.870982	−	0.491314i	$-0.163483\pi$
$31$	152.058	+	87.7909i	0.880983	+	0.508636i	0.0100006	+	0.999950i	$0.496817\pi$
$32$	167.518	−	68.5991i	0.925413	−	0.378960i
$33$		0			0
$34$	66.7510	+	78.2830i	0.336697	+	0.394865i
$35$	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	$0.353946\pi$
$38$	−229.716	−	269.402i	−0.980654	−	1.15007i
$39$		0			0
$40$	−1.29548	−	54.5047i	−0.00512084	−	0.215449i
$41$	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	0.0198798	−	0.999802i	$-0.493672\pi$
$43$	252.553	−	145.812i	0.895674	−	0.517118i	0.875794	+	0.482685i	$0.160338\pi$
$44$	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	0.813998	−	0.580867i	$-0.197286\pi$
$47$	−30.9476	−	53.6029i	−0.0960463	−	0.166357i	−0.910045	+	0.414510i	$0.863953\pi$
$48$		0			0
$49$	−167.962	+	290.919i	−0.489686	+	0.848161i
$50$	317.705	+	112.793i	0.898604	+	0.319027i
$51$		0			0
$52$	252.795	+	205.385i	0.674162	+	0.547726i
$53$		−	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
$56$	−52.8254	−	28.8473i	−0.126055	−	0.0688373i
$57$		0			0
$58$	167.830	−	472.726i	0.379950	−	1.07021i
$59$	70.7911	−	122.614i	0.156207	−	0.270559i	−0.777291	−	0.629141i	$-0.783407\pi$
$59$	70.7911	−	122.614i	0.156207	−	0.270559i	0.933498	+	0.358583i	$0.116740\pi$
$60$		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	0.375141	−	0.926968i	$-0.377594\pi$
$67$	−131.657	−	76.0120i	−0.240066	−	0.138602i	−0.615207	+	0.788366i	$0.710928\pi$
$68$	−287.327	−	45.9827i	−0.512405	−	0.0820033i
$69$		0			0
$70$	−13.7940	+	11.7620i	−0.0235529	+	0.0200833i
$71$	28.0331			0.0468580			0.0234290	−	0.999726i	$-0.492542\pi$
$71$	28.0331			0.0468580			0.0234290	+	0.999726i	$0.492542\pi$
$72$		0			0
$73$	124.499			0.199609			0.0998047	−	0.995007i	$-0.468178\pi$
$73$	124.499			0.199609			0.0998047	+	0.995007i	$0.468178\pi$
$74$	−429.078	+	365.870i	−0.674045	+	0.574750i
$75$		0			0
$76$	988.804	+	158.244i	1.49242	+	0.238840i
$77$	−111.232	−	64.2199i	−0.164624	−	0.0950459i
$78$		0			0
$79$	−648.411	+	374.360i	−0.923443	+	0.533150i	−0.884732	−	0.466101i	$-0.845658\pi$
$79$	−648.411	+	374.360i	−0.923443	+	0.533150i	−0.0387108	+	0.999250i	$0.512325\pi$
$80$	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	0.727318	−	0.686301i	$-0.240767\pi$
$83$	−174.444	−	302.146i	−0.230695	−	0.399576i	−0.958013	+	0.286725i	$0.907433\pi$
$84$		0			0
$85$	−43.8198	+	75.8981i	−0.0559167	+	0.0968506i
$86$	−275.962	+	777.302i	−0.346020	+	0.974635i
$87$		0			0
$88$	−523.653	+	958.916i	−0.634336	+	1.16160i
$89$			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
$92$	1205.25	+	979.212i	1.36583	+	1.10967i
$93$		0			0
$94$	164.978	+	58.5712i	0.181023	+	0.0642677i
$95$	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	−0.447732	−	0.894168i	$-0.647768\pi$
$103$	−1511.52	−	872.679i	−1.44597	−	0.834831i	−0.998238	+	0.0593366i	$0.981101\pi$
$104$	−920.993	+	21.8904i	−0.868373	+	0.0206397i
$105$		0			0
$106$	646.306	+	757.962i	0.592215	+	0.694526i
$107$	783.805			0.708161			0.354081	−	0.935215i	$-0.384794\pi$
$107$	783.805			0.708161			0.354081	+	0.935215i	$0.384794\pi$
$108$		0			0
$109$	1581.89			1.39007			0.695035	−	0.718976i	$-0.255389\pi$
$109$	1581.89			1.39007			0.695035	+	0.718976i	$0.255389\pi$
$110$	213.511	+	250.397i	0.185068	+	0.217040i
$111$		0			0
$112$	166.633	−	34.8582i	0.140583	−	0.0294088i
$113$	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
$122$	41.1286	+	14.6017i	0.0305214	+	0.0108359i
$123$		0			0
$124$	885.735	−	1090.20i	0.641462	−	0.789536i
$125$			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	$-0.0475297\pi$
$128$	−330.121	−	1410.03i	−0.227960	−	0.973671i
$129$		0			0
$130$	−92.8309	+	261.477i	−0.0626293	+	0.176408i
$131$	871.836	−	1510.06i	0.581471	−	1.00714i	−0.413835	−	0.910352i	$-0.635811\pi$
$131$	871.836	−	1510.06i	0.581471	−	1.00714i	0.995305	−	0.0967846i	$-0.0308558\pi$
$132$		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	0.798167	−	0.602436i	$-0.205803\pi$
$139$	1107.04	+	639.151i	0.675526	+	0.390015i	−0.122641	+	0.992451i	$0.539136\pi$
$140$	8.10250	−	50.6292i	0.00489133	−	0.0305639i
$141$		0			0
$142$	−60.3338	+	51.4459i	−0.0356556	+	0.0304031i
$143$	−1965.90			−1.14963
$144$		0			0
$145$	427.331			0.244744
$146$	−267.950	+	228.478i	−0.151889	+	0.129514i
$147$		0			0
$148$	252.037	−	1574.87i	0.139982	−	0.874688i
$149$	−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	−0.259808	−	0.965660i	$-0.583659\pi$
$151$	828.626	−	478.407i	0.446574	−	0.257829i	0.706382	+	0.707831i	$0.250326\pi$
$152$	−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	$0.988098\pi$
$158$	708.511	−	1995.66i	0.356748	−	1.00485i
$159$		0			0
$160$	−432.197	−	58.6713i	−0.213551	−	0.0289899i
$161$		−	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	$0.885212\pi$
$164$	1175.57	−	1446.94i	0.559736	−	0.688944i
$165$		0			0
$166$	929.936	+	330.151i	0.434801	+	0.154365i
$167$	−1524.19	+	2639.98i	−0.706261	+	1.22328i	0.259974	+	0.965616i	$0.416286\pi$
$167$	−1524.19	+	2639.98i	−0.706261	+	1.22328i	−0.966235	+	0.257664i	$0.917047\pi$
$168$		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
$176$	−632.765	−	3024.81i	−0.271003	−	1.29547i
$177$		0			0
$178$	−765.021	−	897.187i	−0.322139	−	0.377792i
$179$	477.618			0.199435			0.0997174	−	0.995016i	$-0.468206\pi$
$179$	477.618			0.199435			0.0997174	+	0.995016i	$0.468206\pi$
$180$		0			0
$181$	−732.350			−0.300747			−0.150373	−	0.988629i	$-0.548048\pi$
$181$	−732.350			−0.300747			−0.150373	+	0.988629i	$0.548048\pi$
$182$	198.749	+	233.085i	0.0809463	+	0.0949307i
$183$		0			0
$184$	−4391.01	+	104.367i	−1.75929	+	0.0418153i
$185$	−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	$0.0320590\pi$
$191$	1543.00	+	2672.55i	0.584542	+	1.01246i	−0.410391	+	0.911910i	$0.634608\pi$
$192$		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	$0.0680873\pi$
$194$	4011.82	+	1424.30i	1.48470	+	0.527106i
$195$		0			0
$196$	2085.77	+	1694.59i	0.760121	+	0.617564i
$197$			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	$0.0596863\pi$
$199$			1046.61i			0.372826i	−0.982471	+	0.186413i	$0.940314\pi$
$200$	1292.65	−	2367.11i	0.457021	−	0.836899i
$201$		0			0
$202$	412.040	−	1160.59i	0.143520	−	0.404252i
$203$	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	0.999950	−	0.00995667i	$-0.00316936\pi$
$211$	4570.77	+	2638.94i	1.49130	+	0.861004i	0.491352	+	0.870961i	$0.336503\pi$
$212$	−2782.00	−	445.220i	−0.901266	−	0.144235i
$213$		0			0
$214$	−1686.93	+	1438.43i	−0.538860	+	0.459480i
$215$	−702.658			−0.222888
$216$		0			0
$217$	−467.047			−0.146107
$218$	−3404.60	+	2903.06i	−1.05774	+	0.901927i
$219$		0			0
$220$	−919.050	−	147.081i	−0.281647	−	0.0450737i
$221$	1282.49	+	740.444i	0.390359	+	0.225374i
$222$		0			0
$223$	−4122.02	+	2379.85i	−1.23781	+	0.714648i	−0.968645	−	0.248447i	$-0.920080\pi$
$223$	−4122.02	+	2379.85i	−1.23781	+	0.714648i	−0.269161	+	0.963095i	$0.586746\pi$
$224$	−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	0.981730	−	0.190277i	$-0.0609387\pi$
$227$	1115.23	+	1931.63i	0.326080	+	0.564788i	−0.655650	+	0.755065i	$0.727605\pi$
$228$		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	$-0.151857\pi$
$230$	−442.589	+	1246.64i	−0.126885	+	0.357396i
$231$		0			0
$232$	−3522.12	−	1923.39i	−0.996718	−	0.544296i
$233$		−	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
$236$	−879.091	−	714.221i	−0.242474	−	0.196999i
$237$		0			0
$238$	−257.885	−	91.5558i	−0.0702362	−	0.0249356i
$239$	−2645.73	+	4582.53i	−0.716058	+	1.24025i	0.246492	+	0.969145i	$0.420722\pi$
$239$	−2645.73	+	4582.53i	−0.716058	+	1.24025i	−0.962550	+	0.271104i	$0.912611\pi$
$240$		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
$248$	94.4037	+	3971.84i	0.0241719	+	1.01698i
$249$		0			0
$250$	−1079.78	−	1266.33i	−0.273166	−	0.320359i
$251$	2577.68			0.648215			0.324107	−	0.946020i	$-0.394936\pi$
$251$	2577.68			0.648215			0.324107	+	0.946020i	$0.394936\pi$
$252$		0			0
$253$	−9372.83			−2.32911
$254$	781.475	+	916.483i	0.193048	+	0.226399i
$255$		0			0
$256$	3298.15	+	2428.87i	0.805213	+	0.592986i
$257$	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	$-0.998047\pi$
$263$	−2155.19	−	3732.90i	−0.505304	−	0.875212i	0.494677	−	0.869077i	$-0.335286\pi$
$264$		0			0
$265$	−424.278	+	734.871i	−0.0983516	+	0.170350i
$266$	887.483	+	315.079i	0.204568	+	0.0726268i
$267$		0			0
$268$	−766.896	+	943.924i	−0.174797	+	0.215147i
$269$		−	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	$-0.922565\pi$
$271$		−	2149.22i		−	0.481756i	0.970555	−	0.240878i	$-0.0774353\pi$
$272$	−726.479	+	2211.60i	−0.161946	+	0.493008i
$273$		0			0
$274$	−1392.44	+	3922.08i	−0.307008	+	0.864751i
$275$	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	0.674737	−	0.738058i	$-0.264257\pi$
$283$	1775.44	+	1025.05i	0.372929	+	0.215310i	−0.301809	+	0.953369i	$0.597590\pi$
$284$	35.4395	−	221.447i	0.00740475	−	0.0462693i
$285$		0			0
$286$	4231.08	−	3607.80i	0.874787	−	0.745921i
$287$	−619.877			−0.127492
$288$		0			0
$289$	3590.01			0.730716
$290$	−919.715	+	784.230i	−0.186233	+	0.158799i
$291$		0			0
$292$	157.392	−	983.476i	0.0315433	−	0.197101i
$293$	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
$302$	−905.429	+	2550.32i	−0.172522	+	0.485943i
$303$		0			0
$304$	2500.09	−	7610.98i	0.471678	−	1.43592i
$305$			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	$-0.241152\pi$
$308$	−647.923	+	797.489i	−0.119866	+	0.147536i
$309$		0			0
$310$	1127.64	+	400.339i	0.206598	+	0.0733475i
$311$	2448.25	−	4240.50i	0.446391	−	0.773172i	−0.551757	−	0.834005i	$-0.686042\pi$
$311$	2448.25	−	4240.50i	0.446391	−	0.773172i	0.998148	+	0.0608332i	$0.0193758\pi$
$312$		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
$320$	1037.86	−	666.886i	0.181307	−	0.116500i
$321$		0			0
$322$	947.573	+	1111.28i	0.163994	+	0.192326i
$323$	4552.92			0.784307
$324$		0			0
$325$	4852.88			0.828276
$326$	−2695.15	−	3160.76i	−0.457885	−	0.536990i
$327$		0			0
$328$	125.295	+	5271.53i	0.0210923	+	0.887414i
$329$	142.583	+	82.3206i	0.0238932	+	0.0137948i
$330$		0			0
$331$	6410.22	−	3700.94i	1.06446	−	0.614569i	0.137801	−	0.990460i	$-0.455997\pi$
$331$	6410.22	−	3700.94i	1.06446	−	0.614569i	0.926664	+	0.375891i	$0.122663\pi$
$332$	−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	$-0.121935\pi$
$338$	−1437.65	−	510.403i	−0.231355	−	0.0821368i
$339$		0			0
$340$	544.158	+	442.104i	0.0867975	+	0.0705190i
$341$			8478.09i			1.34638i
$342$		0			0
$343$		−	1805.94i		−	0.284290i
$344$	5791.41	+	3162.62i	0.907709	+	0.495689i
$345$		0			0
$346$	−2626.51	+	7398.09i	−0.408098	+	1.14949i
$347$	3523.75	−	6103.31i	0.545143	−	0.944216i	−0.453455	−	0.891279i	$-0.649809\pi$
$347$	3523.75	−	6103.31i	0.545143	−	0.944216i	0.998598	−	0.0529363i	$-0.0168580\pi$
$348$		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
$356$	3293.01	+	527.000i	0.490250	+	0.0784576i
$357$		0			0
$358$	−1027.94	+	876.517i	−0.151756	+	0.129400i
$359$	−6515.20			−0.957825			−0.478912	−	0.877863i	$-0.658969\pi$
$359$	−6515.20			−0.957825			−0.478912	+	0.877863i	$0.658969\pi$
$360$		0			0
$361$	−8809.35			−1.28435
$362$	1576.19	−	1344.00i	0.228847	−	0.195135i
$363$		0			0
$364$	−855.506	−	136.912i	−0.123189	−	0.0197146i
$365$	−259.787	−	149.988i	−0.0372545	−	0.0215089i
$366$		0			0
$367$	−3492.35	+	2016.31i	−0.496729	+	0.286786i	−0.727362	−	0.686254i	$-0.759254\pi$
$367$	−3492.35	+	2016.31i	−0.496729	+	0.286786i	0.230633	+	0.973041i	$0.425920\pi$
$368$	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	$0.221179\pi$
$374$	−1661.97	+	4681.28i	−0.229782	+	0.647228i
$375$		0			0
$376$	671.247	−	1229.19i	0.0920663	−	0.168592i
$377$		−	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	$0.776851\pi$
$380$	−1872.66	−	1521.45i	−0.252804	−	0.205391i
$381$		0			0
$382$	−8225.52	−	2920.27i	−1.10171	−	0.391136i
$383$	−4727.72	+	8188.65i	−0.630744	+	1.09248i	0.356655	+	0.934236i	$0.383917\pi$
$383$	−4727.72	+	8188.65i	−0.630744	+	1.09248i	−0.987400	+	0.158245i	$0.949416\pi$
$384$		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
$392$	−7598.96	+	180.614i	−0.979095	+	0.0232714i
$393$		0			0
$394$	−6149.10	−	7211.43i	−0.786262	−	0.922097i
$395$	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	$0.473878\pi$
$398$	−1920.73	−	2252.55i	−0.241903	−	0.283694i
$399$		0			0
$400$	1562.00	+	7466.82i	0.195250	+	0.933352i
$401$	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	$0.280588\pi$
$410$	1496.63	+	531.341i	0.180276	+	0.0640026i
$411$		0			0
$412$	−8804.58	+	10837.0i	−1.05284	+	1.29588i
$413$			376.608i			0.0448709i
$414$		0			0
$415$			840.635i			0.0994341i
$416$	−991.398	+	7303.04i	−0.116844	+	0.860723i
$417$		0			0
$418$	5719.48	−	16110.1i	0.669256	−	1.88509i
$419$	−7052.61	+	12215.5i	−0.822298	+	1.42426i	0.0816695	+	0.996659i	$0.473975\pi$
$419$	−7052.61	+	12215.5i	−0.822298	+	1.42426i	−0.903967	+	0.427602i	$0.859359\pi$
$420$		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
$428$	990.887	−	6191.65i	0.111907	−	0.699263i
$429$		0			0
$430$	1512.28	−	1289.51i	0.169602	−	0.144617i
$431$	1119.73			0.125140			0.0625700	−	0.998041i	$-0.480070\pi$
$431$	1119.73			0.125140			0.0625700	+	0.998041i	$0.480070\pi$
$432$		0			0
$433$	−299.833			−0.0332773			−0.0166387	−	0.999862i	$-0.505296\pi$
$433$	−299.833			−0.0332773			−0.0166387	+	0.999862i	$0.505296\pi$
$434$	1005.19	−	857.116i	0.111177	−	0.0947993i
$435$		0			0
$436$	1999.83	−	12496.1i	0.219666	−	1.37260i
$437$	−21042.4	−	12148.8i	−2.30342	−	1.32988i
$438$		0			0
$439$	−2090.02	+	1206.67i	−0.227224	+	0.131188i	−0.609291	−	0.792947i	$-0.708546\pi$
$439$	−2090.02	+	1206.67i	−0.227224	+	0.131188i	0.382067	+	0.924135i	$0.375212\pi$
$440$	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	0.965814	−	0.259236i	$-0.0834706\pi$
$443$	2409.36	+	4173.14i	0.258402	+	0.447566i	−0.707412	+	0.706802i	$0.750137\pi$
$444$		0			0
$445$	502.211	−	869.854i	0.0534990	−	0.0926630i
$446$	4504.08	−	12686.7i	0.478194	−	1.34693i
$447$		0			0
$448$	−64.7043	−	1360.38i	−0.00682364	−	0.143464i
$449$			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
$452$	2238.93	−	2755.76i	0.232987	−	0.286770i
$453$		0			0
$454$	−5945.12	−	2110.67i	−0.614578	−	0.218191i
$455$	−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	0.909192	−	0.416378i	$-0.136701\pi$
$463$	9994.39	+	5770.27i	1.00319	+	0.579194i	0.0940023	+	0.995572i	$0.470034\pi$
$464$	11110.2	−	2324.16i	1.11159	−	0.232535i
$465$		0			0
$466$	5652.53	+	6629.06i	0.561906	+	0.658981i
$467$	7.01271			0.000694881			0.000347441	−	1.00000i	$-0.499889\pi$
$467$	7.01271			0.000694881			0.000347441		1.00000i	$0.499889\pi$
$468$		0			0
$469$	404.383			0.0398138
$470$	−273.690	−	320.973i	−0.0268604	−	0.0315008i
$471$		0			0
$472$	3202.73	−	76.1234i	0.312326	−	0.00742344i
$473$	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	0.968866	−	0.247586i	$-0.0796373\pi$
$479$	2830.70	+	4902.92i	0.270017	+	0.467683i	−0.698849	+	0.715269i	$0.746304\pi$
$480$		0			0
$481$	−4058.46	+	7029.46i	−0.384719	+	0.666353i
$482$	−13335.7	−	4734.52i	−1.26022	−	0.447409i
$483$		0			0
$484$	6212.21	+	5047.14i	0.583415	+	0.473999i
$485$			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	$-0.138862\pi$
$488$	167.340	−	306.435i	0.0155228	−	0.0284255i
$489$		0			0
$490$	−765.932	+	2157.40i	−0.0706149	+	0.198901i
$491$	5098.79	−	8831.36i	0.468646	−	0.811718i	−0.530712	−	0.847552i	$-0.678075\pi$
$491$	5098.79	−	8831.36i	0.468646	−	0.811718i	0.999358	+	0.0358342i	$0.0114088\pi$
$492$		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	0.601825	−	0.798628i	$-0.294441\pi$
$499$	2353.15	+	1358.59i	0.211105	+	0.121881i	−0.390720	+	0.920510i	$0.627774\pi$
$500$	4647.89	+	743.831i	0.415720	+	0.0665302i
$501$		0			0
$502$	−5547.77	+	4730.52i	−0.493245	+	0.420585i
$503$	−8294.45			−0.735251			−0.367626	−	0.929974i	$-0.619829\pi$
$503$	−8294.45			−0.735251			−0.367626	+	0.929974i	$0.619829\pi$
$504$		0			0
$505$	1049.14			0.0924479
$506$	20172.5	−	17200.9i	1.77229	−	1.51121i
$507$		0			0
$508$	−3363.83	−	538.334i	−0.293791	−	0.0470171i
$509$	−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
$518$	501.828	−	1413.50i	0.0425657	−	0.119895i
$519$		0			0
$520$	1948.17	+	1063.88i	0.164294	+	0.0897193i
$521$		−	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	$-0.867387\pi$
$523$		−	9680.16i		−	0.809338i	0.914463	−	0.404669i	$-0.132613\pi$
$524$	−10826.5	−	8796.08i	−0.902595	−	0.733317i
$525$		0			0
$526$	11489.0	+	4078.90i	0.952369	+	0.338115i
$527$	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
$536$	−81.7376	−	3438.94i	−0.00658680	−	0.277126i
$537$		0			0
$538$	10283.5	+	12060.1i	0.824076	+	0.966443i
$539$	−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	$0.234139\pi$
$542$	3944.21	+	4625.62i	0.312580	+	0.366582i
$543$		0			0
$544$	−2495.15	−	6093.11i	−0.196652	−	0.480220i
$545$	−3300.88	−	1905.76i	−0.259438	−	0.149787i
$546$		0			0
$547$	−3928.78	+	2268.28i	−0.307098	+	0.177303i	−0.645627	−	0.763653i	$-0.723404\pi$
$547$	−3928.78	+	2268.28i	−0.307098	+	0.177303i	0.338529	+	0.940956i	$0.390071\pi$
$548$	−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
$554$	−8556.00	−	3037.59i	−0.656154	−	0.232951i
$555$		0			0
$556$	6448.49	−	7937.04i	0.491865	−	0.605406i
$557$			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
$560$	−389.701	−	128.011i	−0.0294069	−	0.00965974i
$561$		0			0
$562$	−889.873	+	2506.51i	−0.0667919	+	0.188133i
$563$	−4972.47	+	8612.57i	−0.372229	+	0.644719i	−0.989908	−	0.141711i	$-0.954740\pi$
$563$	−4972.47	+	8612.57i	−0.372229	+	0.644719i	0.617679	+	0.786430i	$0.288073\pi$
$564$		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	0.177621	−	0.984099i	$-0.443160\pi$
$571$	−7993.20	−	4614.88i	−0.585823	−	0.338225i	−0.763444	+	0.645874i	$0.776493\pi$
$572$	−2485.30	+	15529.6i	−0.181671	+	1.13519i
$573$		0			0
$574$	1334.12	−	1137.59i	0.0970123	−	0.0827213i
$575$	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	$0.453021\pi$
$578$	−7726.53	+	6588.33i	−0.556023	+	0.474115i
$579$		0			0
$580$	540.232	−	3375.69i	0.0386757	−	0.241669i
$581$	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	0.673350	−	0.739324i	$-0.264855\pi$
$587$	−4317.74	−	7478.55i	−0.303599	−	0.525848i	−0.976948	+	0.213476i	$0.931522\pi$
$588$		0			0
$589$	−10989.1	+	19033.6i	−0.768755	+	1.33152i
$590$	322.818	−	909.281i	0.0225258	−	0.0634483i
$591$		0			0
$592$	−12122.1	−	3981.92i	−0.841577	−	0.276446i
$593$		−	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
$596$	−10841.1	+	13343.7i	−0.745083	+	0.917076i
$597$		0			0
$598$	21065.1	+	7478.64i	1.44050	+	0.511412i
$599$	7549.02	−	13075.3i	0.514932	−	0.891889i	−0.484917	−	0.874560i	$-0.661150\pi$
$599$	7549.02	−	13075.3i	0.514932	−	0.891889i	0.999850	−	0.0173291i	$-0.00551631\pi$
$600$		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	−0.147350	−	0.989084i	$-0.547074\pi$
$607$	−16115.3	−	9304.20i	−1.07760	−	0.622151i	−0.930247	+	0.366933i	$0.880408\pi$
$608$	8586.77	+	20968.7i	0.572762	+	1.39867i
$609$		0			0
$610$	−68.2303	−	80.0179i	−0.00452880	−	0.00531119i
$611$	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	$0.415766\pi$
$614$	13567.1	+	15911.0i	0.891735	+	1.04579i
$615$		0			0
$616$	−69.0572	−	2905.44i	−0.00451687	−	0.190038i
$617$	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	−0.882580	−	0.470162i	$-0.844196\pi$
$619$	−14117.6	+	8150.83i	−0.916698	+	0.529256i	−0.0341179	+	0.999418i	$0.510862\pi$
$620$	−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
$626$	1817.08	+	645.110i	0.116015	+	0.0411882i
$627$		0			0
$628$	12996.8	+	10559.3i	0.825842	+	0.670959i
$629$		−	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	$0.974692\pi$
$632$	−14869.0	−	8119.79i	−0.935850	−	0.511057i
$633$		0			0
$634$	1468.72	−	4136.93i	0.0920034	−	0.259146i
$635$	−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	−0.152617	−	0.988285i	$-0.548770\pi$
$643$	−17687.6	−	10211.9i	−1.08481	−	0.626313i	−0.932189	+	0.361973i	$0.882103\pi$
$644$	−4078.79	−	652.754i	−0.249576	−	0.0399412i
$645$		0			0
$646$	−9798.94	+	8355.44i	−0.596802	+	0.508886i
$647$	21477.2			1.30503			0.652515	−	0.757776i	$-0.273714\pi$
$647$	21477.2			1.30503			0.652515	+	0.757776i	$0.273714\pi$
$648$		0			0
$649$	6836.40			0.413485
$650$	−10444.5	+	8905.93i	−0.630259	+	0.537415i
$651$		0			0
$652$	11601.2	+	1856.61i	0.696836	+	0.111519i
$653$	−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	0.994415	−	0.105545i	$-0.0336588\pi$
$659$	6865.03	+	11890.6i	0.405802	+	0.702870i	−0.588612	+	0.808416i	$0.700325\pi$
$660$		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	$0.181132\pi$
$662$	−7004.37	+	19729.2i	−0.411228	+	1.15831i
$663$		0			0
$664$	3783.65	−	6928.64i	0.221135	−	0.404945i
$665$			802.258i			0.0467823i
$666$		0			0
$667$		−	34426.6i		−	1.99851i
$668$	18927.6	+	15377.8i	1.09630	+	0.890696i
$669$		0			0
$670$	−976.341	−	346.626i	−0.0562975	−	0.0199870i
$671$	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
$680$	−1982.50	+	47.1205i	−0.111802	+	0.00265734i
$681$		0			0
$682$	−15558.9	−	18246.8i	−0.873576	−	1.02450i
$683$	−7466.11			−0.418276			−0.209138	−	0.977886i	$-0.567066\pi$
$683$	−7466.11			−0.418276			−0.209138	+	0.977886i	$0.567066\pi$
$684$		0			0
$685$	−3545.45			−0.197759
$686$	3314.22	+	3886.79i	0.184457	+	0.216324i
$687$		0			0
$688$	−18268.4	+	3821.61i	−1.01232	+	0.211769i
$689$	12417.5	+	7169.23i	0.686600	+	0.396409i
$690$		0			0
$691$	−20587.2	+	11886.0i	−1.13339	+	0.654364i	−0.944786	−	0.327689i	$-0.893730\pi$
$691$	−20587.2	+	11886.0i	−1.13339	+	0.654364i	−0.188606	+	0.982053i	$0.560397\pi$
$692$	−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
$698$	−3218.63	−	1142.70i	−0.174537	−	0.0619651i
$699$		0			0
$700$	1599.41	−	1968.62i	0.0863603	−	0.106296i
$701$			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
$704$	−24694.4	+	1174.55i	−1.32202	+	0.0628799i
$705$		0			0
$706$	1438.49	−	4051.79i	0.0766830	−	0.215993i
$707$	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
$716$	603.805	−	3772.93i	0.0315157	−	0.196929i
$717$		0			0
$718$	14022.2	−	11956.6i	0.728836	−	0.621470i
$719$	−20077.1			−1.04137			−0.520687	−	0.853748i	$-0.674324\pi$
$719$	−20077.1			−1.04137			−0.520687	+	0.853748i	$0.674324\pi$
$720$		0			0
$721$	4642.64			0.239807
$722$	18959.8	−	16166.8i	0.977298	−	0.833331i
$723$		0			0
$724$	−925.838	+	5785.19i	−0.0475256	+	0.296968i
$725$	18307.5	+	10569.8i	0.937825	+	0.541454i
$726$		0			0
$727$	31220.9	−	18025.4i	1.59274	−	0.919566i	0.599900	−	0.800075i	$-0.295207\pi$
$727$	31220.9	−	18025.4i	1.59274	−	0.919566i	0.992835	−	0.119491i	$-0.0381263\pi$
$728$	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	$-0.0174795\pi$
$734$	3816.05	−	10748.7i	0.191898	−	0.540519i
$735$		0			0
$736$	−4726.68	+	34818.7i	−0.236723	+	1.74379i
$737$		−	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	$0.774813\pi$
$740$	−2423.22	+	2982.60i	−0.120378	+	0.148165i
$741$		0			0
$742$	−2496.93	−	886.474i	−0.123538	−	0.0438591i
$743$	2806.43	−	4860.88i	0.138570	−	0.240011i	−0.788385	−	0.615182i	$-0.789083\pi$
$743$	2806.43	−	4860.88i	0.138570	−	0.240011i	0.926956	+	0.375171i	$0.122416\pi$
$744$		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	0.953090	−	0.302688i	$-0.0978841\pi$
$751$	24027.9	+	13872.5i	1.16750	+	0.674056i	0.214409	+	0.976744i	$0.431217\pi$
$752$	811.113	+	3877.37i	0.0393328	+	0.188023i
$753$		0			0
$754$	13251.5	+	15540.9i	0.640042	+	0.750616i
$755$	−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	$0.684294\pi$
$758$	−17467.8	−	20485.5i	−0.837016	−	0.981620i
$759$		0			0
$760$	6822.54	−	162.160i	0.325631	−	0.00773968i
$761$	−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	$0.148731\pi$
$770$	−824.876	−	292.852i	−0.0386058	−	0.0137060i
$771$		0			0
$772$	−10147.6	−	8244.44i	−0.473082	−	0.384358i
$773$			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
$776$	16323.0	−	29890.7i	0.755103	−	1.38275i
$777$		0			0
$778$	−2806.78	+	7905.87i	−0.129342	+	0.364318i
$779$	−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	0.412030	−	0.911170i	$-0.364820\pi$
$787$	−3776.51	−	2180.37i	−0.171052	−	0.0987570i	−0.583082	+	0.812413i	$0.698153\pi$
$788$	26468.6	+	4235.93i	1.19658	+	0.191496i
$789$		0			0
$790$	−3882.67	+	3310.71i	−0.174860	+	0.149101i
$791$	−1180.58			−0.0530679
$792$		0			0
$793$	628.232			0.0281326
$794$	−2791.11	+	2379.95i	−0.124752	+	0.106374i
$795$		0			0
$796$	8267.70	+	1323.13i	0.368142	+	0.0589159i
$797$	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
$806$	6764.72	−	19054.2i	0.295629	−	0.832699i
$807$		0			0
$808$	−8647.18	−	4722.12i	−0.376493	−	0.205599i
$809$		−	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	$-0.859679\pi$
$811$		−	19709.5i		−	0.853384i	0.904397	−	0.426692i	$-0.140321\pi$
$812$	−2929.19	−	2379.84i	−0.126594	−	0.102852i
$813$		0			0
$814$	−25658.6	−	9109.46i	−1.10483	−	0.392244i
$815$	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	$0.0184504\pi$
$823$	36540.4	+	21096.6i	1.54765	+	0.893537i	0.549330	+	0.835605i	$0.314883\pi$
$824$	−938.413	−	39481.8i	−0.0396738	−	1.66919i
$825$		0			0
$826$	−691.145	−	810.548i	−0.0291138	−	0.0341435i
$827$	13992.0			0.588329			0.294165	−	0.955755i	$-0.404959\pi$
$827$	13992.0			0.588329			0.294165	+	0.955755i	$0.404959\pi$
$828$		0			0
$829$	−23454.8			−0.982653			−0.491327	−	0.870975i	$-0.663488\pi$
$829$	−23454.8			−0.982653			−0.491327	+	0.870975i	$0.663488\pi$
$830$	−1542.72	−	1809.24i	−0.0645164	−	0.0756623i
$831$		0			0
$832$	−11268.7	−	17537.2i	−0.469558	−	0.730762i
$833$	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	0.756288	−	0.654238i	$-0.227011\pi$
$839$	−4579.55	−	7932.02i	−0.188443	−	0.326393i	−0.944731	+	0.327846i	$0.893677\pi$
$840$		0			0
$841$	3532.81	−	6119.00i	0.144852	−	0.250892i
$842$	17114.4	+	6076.03i	0.700475	+	0.248686i
$843$		0			0
$844$	26624.6	−	32770.6i	1.08585	−	1.33650i
$845$		−	1299.60i		−	0.0529082i
$846$		0			0
$847$		−	2661.35i		−	0.107963i
$848$	−7034.01	+	21413.5i	−0.284846	+	0.867149i
$849$		0			0
$850$	4102.62	−	11555.8i	0.165551	−	0.466309i
$851$	−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	0.601956	−	0.798529i	$-0.294388\pi$
$859$	5321.93	+	3072.62i	0.211388	+	0.122045i	−0.390568	+	0.920574i	$0.627722\pi$
$860$	−888.301	+	5550.63i	−0.0352219	+	0.220087i
$861$		0			0
$862$	−2409.91	+	2054.91i	−0.0952227	+	0.0811953i
$863$	13685.9			0.539830			0.269915	−	0.962884i	$-0.413004\pi$
$863$	13685.9			0.539830			0.269915	+	0.962884i	$0.413004\pi$
$864$		0			0
$865$	−6687.66			−0.262875
$866$	645.311	−	550.249i	0.0253217	−	0.0215915i
$867$		0			0
$868$	−590.441	+	3689.43i	−0.0230886	+	0.144271i
$869$	−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	$0.135059\pi$
$878$	2283.74	−	6432.61i	0.0877819	−	0.247255i
$879$		0			0
$880$	−2323.73	+	7074.07i	−0.0890146	+	0.270985i
$881$			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	$0.251675\pi$
$883$			37301.8i			1.42164i	−0.703376	+	0.710818i	$0.748325\pi$
$884$	7470.44	−	9194.91i	0.284229	−	0.349840i
$885$		0			0
$886$	−12844.0	−	4559.94i	−0.487023	−	0.172905i
$887$	17421.8	−	30175.4i	0.659488	−	1.14227i	−0.321261	−	0.946991i	$-0.604107\pi$
$887$	17421.8	−	30175.4i	0.659488	−	1.14227i	0.980748	−	0.195276i	$-0.0625601\pi$
$888$		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
$896$	2635.80	+	2809.11i	0.0982769	+	0.104739i
$897$		0			0
$898$	−15924.1	−	18675.2i	−0.591754	−	0.693985i
$899$	−31140.2			−1.15527
$900$		0			0
$901$	−12809.6			−0.473641
$902$	−20650.1	−	24217.7i	−0.762277	−	0.893969i
$903$		0			0
$904$	238.630	+	10039.9i	0.00877956	+	0.369382i
$905$	1528.17	+	882.289i	0.0561304	+	0.0324069i
$906$		0			0
$907$	7693.07	−	4441.59i	0.281636	−	0.162603i	−0.352528	−	0.935801i	$-0.614678\pi$
$907$	7693.07	−	4441.59i	0.281636	−	0.162603i	0.634164	+	0.773199i	$0.281344\pi$
$908$	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	$0.133548\pi$
$911$	22256.0	+	38548.6i	0.809413	+	1.40194i	−0.103858	+	0.994592i	$0.533119\pi$
$912$		0			0
$913$	8423.14	−	14589.3i	0.305329	−	0.528845i
$914$	−18445.0	−	6548.45i	−0.667513	−	0.236984i
$915$		0			0
$916$	−36227.2	−	29432.9i	−1.30675	−	1.06167i
$917$			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	$0.958617\pi$
$920$	9288.30	+	5072.23i	0.332855	+	0.181768i
$921$		0			0
$922$	−14719.4	+	41460.2i	−0.525768	+	1.48093i
$923$	−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
$932$	−24331.1	−	3893.85i	−0.855141	−	0.136853i
$933$		0			0
$934$	−15.0930	+	12.8696i	−0.000528755	+	0.000450864i
$935$	−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	$0.525875\pi$
$938$	−870.326	+	742.117i	−0.0302955	+	0.0258326i
$939$		0			0
$940$	1178.09	+	188.537i	0.0408777	+	0.00654190i
$941$	−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	$0.195941\pi$
$947$	26469.6	+	45846.6i	0.908285	+	1.57319i	0.0918380	+	0.995774i	$0.470726\pi$
$948$		0			0
$949$	−2534.42	+	4389.75i	−0.0866922	+	0.150155i
$950$	−14118.7	+	39768.1i	−0.482180	+	1.35816i
$951$		0			0
$952$	−1049.26	+	1921.42i	−0.0357214	+	0.0654133i
$953$			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
$956$	32854.9	+	26693.1i	1.11151	+	0.903051i
$957$		0			0
$958$	−15090.1	−	5357.36i	−0.508913	−	0.180677i
$959$	−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	0.715006	−	0.699119i	$-0.246424\pi$
$967$	14044.5	+	8108.61i	0.467054	+	0.269654i	−0.247952	+	0.968772i	$0.579757\pi$
$968$	−22632.5	+	537.936i	−0.751485	+	0.0178615i
$969$		0			0
$970$	−6655.42	−	7805.22i	−0.220302	−	0.258361i
$971$	−33620.7			−1.11116			−0.555582	−	0.831462i	$-0.687504\pi$
$971$	−33620.7			−1.11116			−0.555582	+	0.831462i	$0.687504\pi$
$972$		0			0
$973$	−3400.28			−0.112033
$974$	16667.6	+	19547.1i	0.548321	+	0.643049i
$975$		0			0
$976$	202.209	+	966.619i	0.00663171	+	0.0317016i
$977$	−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	$-0.953259\pi$
$983$	−19149.3	−	33167.6i	−0.621331	−	1.07618i	0.367907	−	0.929862i	$-0.380074\pi$
$984$		0			0
$985$	4036.68	−	6991.73i	0.130578	−	0.226168i
$986$	−17194.4	−	6104.46i	−0.555358	−	0.197166i
$987$		0			0
$988$	−25708.7	+	31643.2i	−0.827836	+	1.01893i
$989$			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	$0.907894\pi$
$992$	31494.8	+	4275.47i	1.00803	+	0.136841i
$993$		0			0
$994$	70.5633	−	198.756i	0.00225164	−	0.00634220i
$995$	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.71.3		24
3.2	odd	2		36.4.h.b.23.10	yes	24
4.3	odd	2	inner	108.4.h.b.71.2		24
9.2	odd	6	inner	108.4.h.b.35.2		24
9.4	even	3		324.4.b.c.323.11		24
9.5	odd	6		324.4.b.c.323.14		24
9.7	even	3		36.4.h.b.11.11	yes	24
12.11	even	2		36.4.h.b.23.11	yes	24
36.7	odd	6		36.4.h.b.11.10	✓	24
36.11	even	6	inner	108.4.h.b.35.3		24
36.23	even	6		324.4.b.c.323.12		24
36.31	odd	6		324.4.b.c.323.13		24

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

\(f(q)\)	\(=\)	\(q+(-2.15223 + 1.83518i) q^{2} +(1.26420 - 7.89948i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(-2.30362 + 1.33000i) q^{7} +(11.7761 + 19.3216i) q^{8} +O(q^{10})\)	\(q+(-2.15223 + 1.83518i) q^{2} +(1.26420 - 7.89948i) q^{4} +(-2.08666 - 1.20474i) q^{5} +(-2.30362 + 1.33000i) q^{7} +(11.7761 + 19.3216i) q^{8} +(6.70190 - 1.23654i) q^{10} +(24.1428 + 41.8166i) q^{11} +(-20.3570 + 35.2594i) q^{13} +(2.51714 - 7.09003i) q^{14} +(-60.8036 - 19.9731i) q^{16} -36.3729i q^{17} +125.173i q^{19} +(-12.1548 + 14.9605i) q^{20} +(-128.702 - 45.6925i) q^{22} +(-97.0560 + 168.106i) q^{23} +(-59.5972 - 103.225i) q^{25} +(-20.8944 - 113.245i) q^{26} +(7.59405 + 19.8788i) q^{28} +(-153.593 + 88.6772i) q^{29} +(152.058 + 87.7909i) q^{31} +(167.518 - 68.5991i) q^{32} +(66.7510 + 78.2830i) q^{34} +6.40918 q^{35} +199.364 q^{37} +(-229.716 - 269.402i) q^{38} +(-1.29548 - 54.5047i) q^{40} +(201.816 + 116.518i) q^{41} +(252.553 - 145.812i) q^{43} +(360.851 - 137.851i) q^{44} +(-99.6182 - 539.918i) q^{46} +(-30.9476 - 53.6029i) q^{47} +(-167.962 + 290.919i) q^{49} +(317.705 + 112.793i) q^{50} +(252.795 + 205.385i) q^{52} -352.175i q^{53} -116.343i q^{55} +(-52.8254 - 28.8473i) q^{56} +(167.830 - 472.726i) q^{58} +(70.7911 - 122.614i) q^{59} +(-7.71518 - 13.3631i) q^{61} +(-488.377 + 90.1086i) q^{62} +(-234.645 + 455.067i) q^{64} +(84.9565 - 49.0496i) q^{65} +(-131.657 - 76.0120i) q^{67} +(-287.327 - 45.9827i) q^{68} +(-13.7940 + 11.7620i) q^{70} +28.0331 q^{71} +124.499 q^{73} +(-429.078 + 365.870i) q^{74} +(988.804 + 158.244i) q^{76} +(-111.232 - 64.2199i) q^{77} +(-648.411 + 374.360i) q^{79} +(102.814 + 114.929i) q^{80} +(-648.187 + 119.595i) q^{82} +(-174.444 - 302.146i) q^{83} +(-43.8198 + 75.8981i) q^{85} +(-275.962 + 777.302i) q^{86} +(-523.653 + 958.916i) q^{88} +416.864i q^{89} -108.299i q^{91} +(1205.25 + 979.212i) q^{92} +(164.978 + 58.5712i) q^{94} +(150.801 - 261.195i) q^{95} +(-752.565 - 1303.48i) q^{97} +(-172.396 - 934.367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 72 q^{5}+O(q^{10}) \) 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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