LMFDB - Embedded newform 108.4.i.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	108.49
Dual form			108.4.i.a.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00857 + 5.09733i) q^{3} +(13.2490 - 4.82225i) q^{5} +(3.17294 + 17.9946i) q^{7} +(-24.9656 - 10.2821i) q^{9} +O(q^{10})$	\(q+(-1.00857 + 5.09733i) q^{3} +(13.2490 - 4.82225i) q^{5} +(3.17294 + 17.9946i) q^{7} +(-24.9656 - 10.2821i) q^{9} +(33.5576 + 12.2140i) q^{11} +(-6.15848 - 5.16757i) q^{13} +(11.2180 + 72.3982i) q^{15} +(-58.3572 + 101.078i) q^{17} +(39.9112 + 69.1281i) q^{19} +(-94.9247 - 1.97537i) q^{21} +(-15.4931 + 87.8657i) q^{23} +(56.5267 - 47.4316i) q^{25} +(77.5906 - 116.888i) q^{27} +(85.5671 - 71.7993i) q^{29} +(47.1052 - 267.147i) q^{31} +(-96.1038 + 158.735i) q^{33} +(128.813 + 223.110i) q^{35} +(180.562 - 312.742i) q^{37} +(32.5521 - 26.1799i) q^{39} +(-10.5230 - 8.82981i) q^{41} +(-383.698 - 139.655i) q^{43} +(-380.352 - 15.8370i) q^{45} +(14.3445 + 81.3518i) q^{47} +(8.57561 - 3.12127i) q^{49} +(-456.369 - 399.410i) q^{51} -28.8354 q^{53} +503.503 q^{55} +(-392.622 + 133.720i) q^{57} +(629.134 - 228.986i) q^{59} +(-16.7704 - 95.1097i) q^{61} +(105.808 - 481.870i) q^{63} +(-106.513 - 38.7676i) q^{65} +(514.271 + 431.525i) q^{67} +(-432.254 - 167.592i) q^{69} +(-47.7773 + 82.7527i) q^{71} +(-502.908 - 871.062i) q^{73} +(184.763 + 335.974i) q^{75} +(-113.309 + 642.610i) q^{77} +(780.366 - 654.805i) q^{79} +(517.559 + 513.395i) q^{81} +(-547.955 + 459.789i) q^{83} +(-285.754 + 1620.59i) q^{85} +(279.684 + 508.578i) q^{87} +(314.627 + 544.950i) q^{89} +(73.4481 - 127.216i) q^{91} +(1314.23 + 509.547i) q^{93} +(862.136 + 723.418i) q^{95} +(-1544.58 - 562.179i) q^{97} +(-712.199 - 649.969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 54 * q + 12 * q^5 - 48 * q^9	$ 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) $ 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.00857	+	5.09733i	−0.194100	+	0.980982i
$3$	−1.00857	+	5.09733i	−0.194100	+	0.980982i
$4$		0			0
$5$	13.2490	−	4.82225i	1.18503	−	0.431315i	0.327053	−	0.945006i	$-0.393945\pi$
$5$	13.2490	−	4.82225i	1.18503	−	0.431315i	0.857975	+	0.513691i	$0.171722\pi$
$6$		0			0
$7$	3.17294	+	17.9946i	0.171323	+	0.971618i	0.942303	+	0.334760i	$0.108655\pi$
$7$	3.17294	+	17.9946i	0.171323	+	0.971618i	−0.770981	+	0.636858i	$0.780234\pi$
$8$		0			0
$9$	−24.9656	−	10.2821i	−0.924650	−	0.380817i
$10$		0			0
$11$	33.5576	+	12.2140i	0.919817	+	0.334786i	0.758166	−	0.652062i	$-0.226096\pi$
$11$	33.5576	+	12.2140i	0.919817	+	0.334786i	0.161651	+	0.986848i	$0.448318\pi$
$12$		0			0
$13$	−6.15848	−	5.16757i	−0.131389	−	0.110248i	0.574725	−	0.818346i	$-0.305109\pi$
$13$	−6.15848	−	5.16757i	−0.131389	−	0.110248i	−0.706114	+	0.708098i	$0.749553\pi$
$14$		0			0
$15$	11.2180	+	72.3982i	0.193098	+	1.24621i
$16$		0			0
$17$	−58.3572	+	101.078i	−0.832570	+	1.44205i	0.0634231	+	0.997987i	$0.479798\pi$
$17$	−58.3572	+	101.078i	−0.832570	+	1.44205i	−0.895993	+	0.444067i	$0.853535\pi$
$18$		0			0
$19$	39.9112	+	69.1281i	0.481908	+	0.834689i	0.999784	−	0.0207667i	$-0.00661072\pi$
$19$	39.9112	+	69.1281i	0.481908	+	0.834689i	−0.517877	+	0.855455i	$0.673277\pi$
$20$		0			0
$21$	−94.9247	−	1.97537i	−0.986394	−	0.0205267i
$22$		0			0
$23$	−15.4931	+	87.8657i	−0.140458	+	0.796576i	0.830445	+	0.557101i	$0.188086\pi$
$23$	−15.4931	+	87.8657i	−0.140458	+	0.796576i	−0.970903	+	0.239475i	$0.923025\pi$
$24$		0			0
$25$	56.5267	−	47.4316i	0.452214	−	0.379453i
$26$		0			0
$27$	77.5906	−	116.888i	0.553049	−	0.833149i
$28$		0			0
$29$	85.5671	−	71.7993i	0.547911	−	0.459752i	−0.326322	−	0.945259i	$-0.605809\pi$
$29$	85.5671	−	71.7993i	0.547911	−	0.459752i	0.874233	+	0.485507i	$0.161365\pi$
$30$		0			0
$31$	47.1052	−	267.147i	0.272914	−	1.54777i	−0.472596	−	0.881279i	$-0.656683\pi$
$31$	47.1052	−	267.147i	0.272914	−	1.54777i	0.745511	−	0.666494i	$-0.232206\pi$
$32$		0			0
$33$	−96.1038	+	158.735i	−0.506955	+	0.837342i
$34$		0			0
$35$	128.813	+	223.110i	0.622095	+	1.07750i
$36$		0			0
$37$	180.562	−	312.742i	0.802275	−	1.38958i	−0.115841	−	0.993268i	$-0.536956\pi$
$37$	180.562	−	312.742i	0.802275	−	1.38958i	0.918115	−	0.396313i	$-0.129710\pi$
$38$		0			0
$39$	32.5521	−	26.1799i	0.133654	−	0.107491i
$40$		0			0
$41$	−10.5230	−	8.82981i	−0.0400832	−	0.0336338i	0.622526	−	0.782599i	$-0.286106\pi$
$41$	−10.5230	−	8.82981i	−0.0400832	−	0.0336338i	−0.662609	+	0.748965i	$0.730551\pi$
$42$		0			0
$43$	−383.698	−	139.655i	−1.36078	−	0.495282i	−0.444482	−	0.895788i	$-0.646612\pi$
$43$	−383.698	−	139.655i	−1.36078	−	0.495282i	−0.916294	+	0.400506i	$0.868834\pi$
$44$		0			0
$45$	−380.352	−	15.8370i	−1.25999	−	0.0524632i
$46$		0			0
$47$	14.3445	+	81.3518i	0.0445184	+	0.252476i	0.998942	−	0.0459775i	$-0.0146402\pi$
$47$	14.3445	+	81.3518i	0.0445184	+	0.252476i	−0.954424	+	0.298454i	$0.903529\pi$
$48$		0			0
$49$	8.57561	−	3.12127i	0.0250018	−	0.00909990i
$50$		0			0
$51$	−456.369	−	399.410i	−1.25303	−	1.09664i
$52$		0			0
$53$	−28.8354			−0.0747329			−0.0373665	−	0.999302i	$-0.511897\pi$
$53$	−28.8354			−0.0747329			−0.0373665	+	0.999302i	$0.511897\pi$
$54$		0			0
$55$	503.503			1.23441
$56$		0			0
$57$	−392.622	+	133.720i	−0.912353	+	0.310730i
$58$		0			0
$59$	629.134	−	228.986i	1.38824	−	0.505279i	0.463575	−	0.886058i	$-0.346566\pi$
$59$	629.134	−	228.986i	1.38824	−	0.505279i	0.924666	+	0.380779i	$0.124344\pi$
$60$		0			0
$61$	−16.7704	−	95.1097i	−0.0352005	−	0.199632i	0.962136	−	0.272570i	$-0.0878736\pi$
$61$	−16.7704	−	95.1097i	−0.0352005	−	0.199632i	−0.997336	+	0.0729379i	$0.976763\pi$
$62$		0			0
$63$	105.808	−	481.870i	0.211595	−	0.963650i
$64$		0			0
$65$	−106.513	−	38.7676i	−0.203251	−	0.0739773i
$66$		0			0
$67$	514.271	+	431.525i	0.937735	+	0.786853i	0.977190	−	0.212368i	$-0.0681176\pi$
$67$	514.271	+	431.525i	0.937735	+	0.786853i	−0.0394546	+	0.999221i	$0.512562\pi$
$68$		0			0
$69$	−432.254	−	167.592i	−0.754164	−	0.292402i
$70$		0			0
$71$	−47.7773	+	82.7527i	−0.0798609	+	0.138323i	−0.903190	−	0.429241i	$-0.858781\pi$
$71$	−47.7773	+	82.7527i	−0.0798609	+	0.138323i	0.823329	+	0.567565i	$0.192114\pi$
$72$		0			0
$73$	−502.908	−	871.062i	−0.806314	−	1.39658i	−0.915400	−	0.402545i	$-0.868126\pi$
$73$	−502.908	−	871.062i	−0.806314	−	1.39658i	0.109086	−	0.994032i	$-0.465207\pi$
$74$		0			0
$75$	184.763	+	335.974i	0.284461	+	0.517265i
$76$		0			0
$77$	−113.309	+	642.610i	−0.167699	+	0.951068i
$78$		0			0
$79$	780.366	−	654.805i	1.11137	−	0.932548i	0.113231	−	0.993569i	$-0.463880\pi$
$79$	780.366	−	654.805i	1.11137	−	0.932548i	0.998137	+	0.0610203i	$0.0194355\pi$
$80$		0			0
$81$	517.559	+	513.395i	0.709957	+	0.704245i
$82$		0			0
$83$	−547.955	+	459.789i	−0.724650	+	0.608053i	−0.928667	−	0.370914i	$-0.879044\pi$
$83$	−547.955	+	459.789i	−0.724650	+	0.608053i	0.204018	+	0.978967i	$0.434600\pi$
$84$		0			0
$85$	−285.754	+	1620.59i	−0.364640	+	2.06797i
$86$		0			0
$87$	279.684	+	508.578i	0.344659	+	0.626728i
$88$		0			0
$89$	314.627	+	544.950i	0.374724	+	0.649041i	0.990286	−	0.139048i	$-0.0444042\pi$
$89$	314.627	+	544.950i	0.374724	+	0.649041i	−0.615562	+	0.788089i	$0.711071\pi$
$90$		0			0
$91$	73.4481	−	127.216i	0.0846094	−	0.146548i
$92$		0			0
$93$	1314.23	+	509.547i	1.46536	+	0.568146i
$94$		0			0
$95$	862.136	+	723.418i	0.931088	+	0.781275i
$96$		0			0
$97$	−1544.58	−	562.179i	−1.61678	−	0.588461i	−0.634017	−	0.773319i	$-0.718595\pi$
$97$	−1544.58	−	562.179i	−1.61678	−	0.588461i	−0.982765	+	0.184858i	$0.940817\pi$
$98$		0			0
$99$	−712.199	−	649.969i	−0.723017	−	0.659842i
$100$		0			0
$101$	−221.812	−	1257.96i	−0.218526	−	1.23932i	−0.874683	−	0.484696i	$-0.838930\pi$
$101$	−221.812	−	1257.96i	−0.218526	−	1.23932i	0.656157	−	0.754624i	$-0.272181\pi$
$102$		0			0
$103$	−47.4842	+	17.2828i	−0.0454248	+	0.0165333i	−0.364633	−	0.931151i	$-0.618805\pi$
$103$	−47.4842	+	17.2828i	−0.0454248	+	0.0165333i	0.319208	+	0.947685i	$0.396583\pi$
$104$		0			0
$105$	−1267.18	+	431.579i	−1.17776	+	0.401121i
$106$		0			0
$107$	−1585.17			−1.43219			−0.716095	−	0.698003i	$-0.754072\pi$
$107$	−1585.17			−1.43219			−0.716095	+	0.698003i	$0.754072\pi$
$108$		0			0
$109$	201.612			0.177164			0.0885821	−	0.996069i	$-0.471766\pi$
$109$	201.612			0.177164			0.0885821	+	0.996069i	$0.471766\pi$
$110$		0			0
$111$	1412.04	+	1235.81i	1.20743	+	1.05673i
$112$		0			0
$113$	1453.68	−	529.095i	1.21018	−	0.440470i	0.343414	−	0.939184i	$-0.388417\pi$
$113$	1453.68	−	529.095i	1.21018	−	0.440470i	0.866766	+	0.498715i	$0.166194\pi$
$114$		0			0
$115$	218.442	+	1238.84i	0.177129	+	1.00455i
$116$		0			0
$117$	100.617	+	192.333i	0.0795043	+	0.151976i
$118$		0			0
$119$	−2004.02	−	729.403i	−1.54376	−	0.561884i
$120$		0			0
$121$	−42.6753	−	35.8088i	−0.0320626	−	0.0269037i
$122$		0			0
$123$	55.6216	−	44.7335i	0.0407743	−	0.0327925i
$124$		0			0
$125$	−361.010	+	625.287i	−0.258318	+	0.447419i
$126$		0			0
$127$	1112.61	+	1927.10i	0.777387	+	1.34647i	0.933443	+	0.358725i	$0.116788\pi$
$127$	1112.61	+	1927.10i	0.777387	+	1.34647i	−0.156056	+	0.987748i	$0.549878\pi$
$128$		0			0
$129$	1098.85	−	1814.98i	0.749989	−	1.23876i
$130$		0			0
$131$	215.838	−	1224.08i	0.143953	−	0.816397i	−0.824249	−	0.566227i	$-0.808402\pi$
$131$	215.838	−	1224.08i	0.143953	−	0.816397i	0.968202	−	0.250170i	$-0.0804865\pi$
$132$		0			0
$133$	−1117.30	+	937.525i	−0.728437	+	0.611231i
$134$		0			0
$135$	464.339	−	1922.81i	0.296029	−	1.22584i
$136$		0			0
$137$	2055.53	−	1724.79i	1.28187	−	1.07561i	0.288883	−	0.957364i	$-0.406716\pi$
$137$	2055.53	−	1724.79i	1.28187	−	1.07561i	0.992984	−	0.118250i	$-0.0377283\pi$
$138$		0			0
$139$	−261.289	+	1481.85i	−0.159441	+	0.904234i	0.795172	+	0.606384i	$0.207381\pi$
$139$	−261.289	+	1481.85i	−0.159441	+	0.904234i	−0.954613	+	0.297850i	$0.903731\pi$
$140$		0			0
$141$	−429.145	−	8.93045i	−0.256316	−	0.00533390i
$142$		0			0
$143$	−143.547	−	248.631i	−0.0839440	−	0.145395i
$144$		0			0
$145$	787.445	−	1363.90i	0.450992	−	0.781140i
$146$		0			0
$147$	7.26100	+	46.8607i	0.00407399	+	0.0262926i
$148$		0			0
$149$	−172.536	−	144.775i	−0.0948639	−	0.0796003i	0.594122	−	0.804375i	$-0.297500\pi$
$149$	−172.536	−	144.775i	−0.0948639	−	0.0796003i	−0.688986	+	0.724774i	$0.741944\pi$
$150$		0			0
$151$	−2151.99	−	783.262i	−1.15978	−	0.422126i	−0.310761	−	0.950488i	$-0.600584\pi$
$151$	−2151.99	−	783.262i	−1.15978	−	0.422126i	−0.849019	+	0.528362i	$0.822806\pi$
$152$		0			0
$153$	2496.21	−	1923.43i	1.31900	−	1.01634i
$154$		0			0
$155$	−664.150	−	3766.58i	−0.344167	−	1.95187i
$156$		0			0
$157$	−1002.97	+	365.052i	−0.509846	+	0.185569i	−0.584117	−	0.811669i	$-0.698559\pi$
$157$	−1002.97	+	365.052i	−0.509846	+	0.185569i	0.0742710	+	0.997238i	$0.476337\pi$
$158$		0			0
$159$	29.0826	−	146.984i	0.0145057	−	0.0733117i
$160$		0			0
$161$	−1630.27			−0.798032
$162$		0			0
$163$	565.717			0.271843			0.135921	−	0.990720i	$-0.456601\pi$
$163$	565.717			0.271843			0.135921	+	0.990720i	$0.456601\pi$
$164$		0			0
$165$	−507.820	+	2566.52i	−0.239598	+	1.21093i
$166$		0			0
$167$	−1411.33	+	513.682i	−0.653964	+	0.238023i	−0.647628	−	0.761956i	$-0.724239\pi$
$167$	−1411.33	+	513.682i	−0.653964	+	0.238023i	−0.00633579	+	0.999980i	$0.502017\pi$
$168$		0			0
$169$	−370.282	−	2099.97i	−0.168540	−	0.955837i
$170$		0			0
$171$	−285.625	−	2136.19i	−0.127733	−	0.955314i
$172$		0			0
$173$	−388.119	−	141.264i	−0.170567	−	0.0620814i	0.255325	−	0.966855i	$-0.417818\pi$
$173$	−388.119	−	141.264i	−0.170567	−	0.0620814i	−0.425892	+	0.904774i	$0.640040\pi$
$174$		0			0
$175$	1032.87	+	866.680i	0.446158	+	0.374371i
$176$		0			0
$177$	532.690	+	3437.85i	0.226212	+	1.45991i
$178$		0			0
$179$	−699.370	+	1211.34i	−0.292030	+	0.505811i	−0.974290	−	0.225299i	$-0.927664\pi$
$179$	−699.370	+	1211.34i	−0.292030	+	0.505811i	0.682260	+	0.731110i	$0.260997\pi$
$180$		0			0
$181$	−807.914	−	1399.35i	−0.331778	−	0.574656i	0.651083	−	0.759007i	$-0.274315\pi$
$181$	−807.914	−	1399.35i	−0.331778	−	0.574656i	−0.982860	+	0.184351i	$0.940982\pi$
$182$		0			0
$183$	501.720	+	10.4407i	0.202668	+	0.00421749i
$184$		0			0
$185$	884.145	−	5014.24i	0.351371	−	1.99272i
$186$		0			0
$187$	−3192.88	+	2679.15i	−1.24859	+	1.04769i
$188$		0			0
$189$	2349.54	+	1025.34i	0.904252	+	0.394615i
$190$		0			0
$191$	−1340.95	+	1125.19i	−0.507998	+	0.426261i	−0.860424	−	0.509579i	$-0.829801\pi$
$191$	−1340.95	+	1125.19i	−0.507998	+	0.426261i	0.352426	+	0.935840i	$0.385357\pi$
$192$		0			0
$193$	−212.711	+	1206.35i	−0.0793331	+	0.449920i	0.919103	+	0.394017i	$0.128915\pi$
$193$	−212.711	+	1206.35i	−0.0793331	+	0.449920i	−0.998436	+	0.0559032i	$0.982196\pi$
$194$		0			0
$195$	305.037	−	503.832i	0.112021	−	0.185027i
$196$		0			0
$197$	2719.89	+	4710.98i	0.983675	+	1.70377i	0.647683	+	0.761910i	$0.275738\pi$
$197$	2719.89	+	4710.98i	0.983675	+	1.70377i	0.335992	+	0.941865i	$0.390929\pi$
$198$		0			0
$199$	1103.11	−	1910.64i	0.392951	−	0.680611i	−0.599886	−	0.800085i	$-0.704788\pi$
$199$	1103.11	−	1910.64i	0.392951	−	0.680611i	0.992837	+	0.119474i	$0.0381209\pi$
$200$		0			0
$201$	−2718.31	+	2186.19i	−0.953903	+	0.767173i
$202$		0			0
$203$	1563.50	+	1311.93i	0.540572	+	0.453594i
$204$		0			0
$205$	−181.998	−	66.2420i	−0.0620064	−	0.0225685i
$206$		0			0
$207$	1290.23	−	2034.31i	0.433224	−	0.683066i
$208$		0			0
$209$	494.993	+	2807.25i	0.163825	+	0.929097i
$210$		0			0
$211$	−445.805	+	162.260i	−0.145453	+	0.0529404i	−0.413721	−	0.910404i	$-0.635771\pi$
$211$	−445.805	+	162.260i	−0.145453	+	0.0529404i	0.268268	+	0.963344i	$0.413549\pi$
$212$		0			0
$213$	−373.631	−	326.999i	−0.120191	−	0.105191i
$214$		0			0
$215$	−5757.06			−1.82618
$216$		0			0
$217$	4956.67			1.55060
$218$		0			0
$219$	4947.31	−	1684.96i	1.52652	−	0.519904i
$220$		0			0
$221$	881.717	−	320.919i	0.268374	−	0.0976803i
$222$		0			0
$223$	−257.186	−	1458.57i	−0.0772306	−	0.437996i	−0.998764	−	0.0496981i	$-0.984174\pi$
$223$	−257.186	−	1458.57i	−0.0772306	−	0.437996i	0.921534	−	0.388298i	$-0.126937\pi$
$224$		0			0
$225$	−1898.92	+	602.945i	−0.562642	+	0.178650i
$226$		0			0
$227$	1055.78	+	384.271i	0.308697	+	0.112357i	0.491723	−	0.870751i	$-0.336367\pi$
$227$	1055.78	+	384.271i	0.308697	+	0.112357i	−0.183026	+	0.983108i	$0.558589\pi$
$228$		0			0
$229$	2643.38	+	2218.06i	0.762793	+	0.640059i	0.938852	−	0.344321i	$-0.111891\pi$
$229$	2643.38	+	2218.06i	0.762793	+	0.640059i	−0.176060	+	0.984380i	$0.556335\pi$
$230$		0			0
$231$	−3161.32	−	1225.69i	−0.900430	−	0.349112i
$232$		0			0
$233$	3359.46	−	5818.75i	0.944572	−	1.63605i	0.187967	−	0.982175i	$-0.439810\pi$
$233$	3359.46	−	5818.75i	0.944572	−	1.63605i	0.756605	−	0.653872i	$-0.226857\pi$
$234$		0			0
$235$	582.350	+	1008.66i	0.161652	+	0.279990i
$236$		0			0
$237$	2550.70	+	4638.20i	0.699097	+	1.27124i
$238$		0			0
$239$	−1084.54	+	6150.74i	−0.293528	+	1.66468i	0.379598	+	0.925152i	$0.376062\pi$
$239$	−1084.54	+	6150.74i	−0.293528	+	1.66468i	−0.673126	+	0.739528i	$0.735049\pi$
$240$		0			0
$241$	−644.213	+	540.559i	−0.172189	+	0.144483i	−0.724809	−	0.688949i	$-0.758072\pi$
$241$	−644.213	+	540.559i	−0.172189	+	0.144483i	0.552621	+	0.833433i	$0.313628\pi$
$242$		0			0
$243$	−3138.94	+	2120.37i	−0.828654	+	0.559761i
$244$		0			0
$245$	98.5668	−	82.7074i	0.0257029	−	0.0215673i
$246$		0			0
$247$	111.433	−	631.968i	0.0287057	−	0.162798i
$248$		0			0
$249$	−1791.04	−	3256.84i	−0.455835	−	0.828891i
$250$		0			0
$251$	2582.47	+	4472.97i	0.649419	+	1.12483i	0.983262	+	0.182198i	$0.0583211\pi$
$251$	2582.47	+	4472.97i	0.649419	+	1.12483i	−0.333843	+	0.942629i	$0.608346\pi$
$252$		0			0
$253$	−1593.10	+	2759.33i	−0.395878	+	0.685681i
$254$		0			0
$255$	−7972.49	−	3091.07i	−1.95787	−	0.759098i
$256$		0			0
$257$	3334.32	+	2797.83i	0.809297	+	0.679081i	0.950440	−	0.310909i	$-0.100633\pi$
$257$	3334.32	+	2797.83i	0.809297	+	0.679081i	−0.141143	+	0.989989i	$0.545078\pi$
$258$		0			0
$259$	6200.59	+	2256.83i	1.48759	+	0.541438i
$260$		0			0
$261$	−2874.47	+	912.704i	−0.681707	+	0.216456i
$262$		0			0
$263$	−267.218	−	1515.47i	−0.0626517	−	0.355315i	−0.999976	−	0.00685846i	$-0.997817\pi$
$263$	−267.218	−	1515.47i	−0.0626517	−	0.355315i	0.937325	−	0.348457i	$-0.113294\pi$
$264$		0			0
$265$	−382.041	+	139.051i	−0.0885606	+	0.0322334i
$266$		0			0
$267$	−3095.12	+	1054.14i	−0.709431	+	0.241618i
$268$		0			0
$269$	3281.40			0.743757			0.371878	−	0.928281i	$-0.378714\pi$
$269$	3281.40			0.743757			0.371878	+	0.928281i	$0.378714\pi$
$270$		0			0
$271$	−4649.81			−1.04227			−0.521136	−	0.853474i	$-0.674492\pi$
$271$	−4649.81			−1.04227			−0.521136	+	0.853474i	$0.674492\pi$
$272$		0			0
$273$	574.383	+	502.696i	0.127338	+	0.111445i
$274$		0			0
$275$	2476.23	−	901.273i	0.542990	−	0.197632i
$276$		0			0
$277$	−1143.21	−	6483.47i	−0.247974	−	1.40633i	−0.813482	−	0.581590i	$-0.802431\pi$
$277$	−1143.21	−	6483.47i	−0.247974	−	1.40633i	0.565508	−	0.824743i	$-0.308680\pi$
$278$		0			0
$279$	−3922.82	+	6185.13i	−0.841768	+	1.32722i
$280$		0			0
$281$	−4066.26	−	1480.00i	−0.863249	−	0.314197i	−0.127819	−	0.991798i	$-0.540798\pi$
$281$	−4066.26	−	1480.00i	−0.863249	−	0.314197i	−0.735430	+	0.677601i	$0.763020\pi$
$282$		0			0
$283$	−954.503	−	800.923i	−0.200492	−	0.168233i	0.537014	−	0.843573i	$-0.319552\pi$
$283$	−954.503	−	800.923i	−0.200492	−	0.168233i	−0.737506	+	0.675340i	$0.763997\pi$
$284$		0			0
$285$	−4557.03	+	3664.97i	−0.947141	+	0.761735i
$286$		0			0
$287$	125.500	−	217.373i	0.0258120	−	0.0447078i
$288$		0			0
$289$	−4354.62	−	7542.42i	−0.886347	−	1.53520i
$290$		0			0
$291$	4423.43	−	7306.21i	0.891086	−	1.47181i
$292$		0			0
$293$	−584.021	+	3312.15i	−0.116447	+	0.660402i	0.869577	+	0.493797i	$0.164392\pi$
$293$	−584.021	+	3312.15i	−0.116447	+	0.660402i	−0.986024	+	0.166605i	$0.946720\pi$
$294$		0			0
$295$	7231.18	−	6067.68i	1.42717	−	1.19754i
$296$		0			0
$297$	4031.41	−	2974.77i	0.787631	−	0.581191i
$298$		0			0
$299$	549.466	−	461.057i	0.106276	−	0.0891759i
$300$		0			0
$301$	1295.58	−	7347.61i	0.248093	−	1.40701i
$302$		0			0
$303$	6635.93	+	138.093i	1.25817	+	0.0261823i
$304$		0			0
$305$	−680.834	−	1179.24i	−0.127818	−	0.221387i
$306$		0			0
$307$	1343.07	−	2326.27i	0.249685	−	0.432467i	−0.713753	−	0.700397i	$-0.753006\pi$
$307$	1343.07	−	2326.27i	0.249685	−	0.432467i	0.963438	+	0.267930i	$0.0863396\pi$
$308$		0			0
$309$	−40.2050	−	259.474i	−0.00740189	−	0.0477700i
$310$		0			0
$311$	607.838	+	510.037i	0.110827	+	0.0929953i	0.696517	−	0.717540i	$-0.254732\pi$
$311$	607.838	+	510.037i	0.110827	+	0.0929953i	−0.585690	+	0.810535i	$0.699176\pi$
$312$		0			0
$313$	1948.47	+	709.186i	0.351866	+	0.128069i	0.511905	−	0.859042i	$-0.328940\pi$
$313$	1948.47	+	709.186i	0.351866	+	0.128069i	−0.160039	+	0.987111i	$0.551162\pi$
$314$		0			0
$315$	−921.851	−	6894.54i	−0.164890	−	1.23322i
$316$		0			0
$317$	1177.45	+	6677.64i	0.208619	+	1.18314i	0.891643	+	0.452739i	$0.149553\pi$
$317$	1177.45	+	6677.64i	0.208619	+	1.18314i	−0.683024	+	0.730396i	$0.739336\pi$
$318$		0			0
$319$	3748.38	−	1364.30i	0.657896	−	0.239455i
$320$		0			0
$321$	1598.76	−	8080.14i	0.277988	−	1.40495i
$322$		0			0
$323$	−9316.41			−1.60489
$324$		0			0
$325$	−593.225			−0.101250
$326$		0			0
$327$	−203.340	+	1027.68i	−0.0343875	+	0.173795i
$328$		0			0
$329$	−1418.38	+	516.249i	−0.237684	+	0.0865098i
$330$		0			0
$331$	−300.134	−	1702.14i	−0.0498394	−	0.282653i	0.949695	−	0.313178i	$-0.101393\pi$
$331$	−300.134	−	1702.14i	−0.0498394	−	0.282653i	−0.999534	+	0.0305241i	$0.990282\pi$
$332$		0			0
$333$	−7723.46	+	5951.24i	−1.27100	+	0.979357i
$334$		0			0
$335$	8894.51	+	3237.34i	1.45062	+	0.527984i
$336$		0			0
$337$	−4592.96	−	3853.95i	−0.742417	−	0.622962i	0.191069	−	0.981577i	$-0.438805\pi$
$337$	−4592.96	−	3853.95i	−0.742417	−	0.622962i	−0.933486	+	0.358615i	$0.883249\pi$
$338$		0			0
$339$	1230.83	+	7943.50i	0.197197	+	1.27266i
$340$		0			0
$341$	4843.65	−	8389.45i	0.769204	−	1.33230i
$342$		0			0
$343$	3217.06	+	5572.11i	0.506429	+	0.877160i
$344$		0			0
$345$	−6535.12	−	135.995i	−1.01982	−	0.0212224i
$346$		0			0
$347$	550.059	−	3119.54i	0.0850971	−	0.482610i	−0.912238	−	0.409660i	$-0.865648\pi$
$347$	550.059	−	3119.54i	0.0850971	−	0.482610i	0.997336	−	0.0729501i	$-0.0232414\pi$
$348$		0			0
$349$	−5745.12	+	4820.73i	−0.881173	+	0.739392i	−0.966420	−	0.256968i	$-0.917276\pi$
$349$	−5745.12	+	4820.73i	−0.881173	+	0.739392i	0.0852471	+	0.996360i	$0.472832\pi$
$350$		0			0
$351$	−1081.86	+	318.894i	−0.164518	+	0.0484937i
$352$		0			0
$353$	−6735.79	+	5652.00i	−1.01561	+	0.852197i	−0.989069	−	0.147451i	$-0.952893\pi$
$353$	−6735.79	+	5652.00i	−1.01561	+	0.852197i	−0.0265392	+	0.999648i	$0.508449\pi$
$354$		0			0
$355$	−233.948	+	1326.79i	−0.0349766	+	0.198362i
$356$		0			0
$357$	5739.20	−	9479.48i	0.850843	−	1.40534i
$358$		0			0
$359$	3196.24	+	5536.04i	0.469891	+	0.813875i	0.999407	−	0.0344245i	$-0.0109598\pi$
$359$	3196.24	+	5536.04i	0.469891	+	0.813875i	−0.529516	+	0.848300i	$0.677626\pi$
$360$		0			0
$361$	243.700	−	422.101i	0.0355300	−	0.0615397i
$362$		0			0
$363$	225.570	−	181.414i	0.0326154	−	0.0262308i
$364$		0			0
$365$	−10863.5	−	9115.57i	−1.55787	−	1.30721i
$366$		0			0
$367$	10794.5	+	3928.89i	1.53534	+	0.558819i	0.964922	−	0.262535i	$-0.0845585\pi$
$367$	10794.5	+	3928.89i	1.53534	+	0.558819i	0.570419	+	0.821354i	$0.306781\pi$
$368$		0			0
$369$	171.923	+	328.639i	0.0242546	+	0.0463638i
$370$		0			0
$371$	−91.4929	−	518.882i	−0.0128034	−	0.0726119i
$372$		0			0
$373$	2603.65	−	947.652i	0.361426	−	0.131548i	−0.154923	−	0.987927i	$-0.549513\pi$
$373$	2603.65	−	947.652i	0.361426	−	0.131548i	0.516349	+	0.856378i	$0.327291\pi$
$374$		0			0
$375$	−2823.19	−	2470.83i	−0.388771	−	0.340249i
$376$		0			0
$377$	−897.991			−0.122676
$378$		0			0
$379$	−8765.55			−1.18801			−0.594005	−	0.804461i	$-0.702454\pi$
$379$	−8765.55			−1.18801			−0.594005	+	0.804461i	$0.702454\pi$
$380$		0			0
$381$	−10945.2	+	3727.72i	−1.47176	+	0.501252i
$382$		0			0
$383$	−3592.97	+	1307.73i	−0.479353	+	0.174470i	−0.570384	−	0.821378i	$-0.693206\pi$
$383$	−3592.97	+	1307.73i	−0.479353	+	0.174470i	0.0910317	+	0.995848i	$0.470984\pi$
$384$		0			0
$385$	1597.59	+	9060.36i	0.211482	+	1.19937i
$386$		0			0
$387$	8143.29	+	7431.76i	1.06963	+	0.976169i
$388$		0			0
$389$	8013.33	+	2916.61i	1.04445	+	0.380149i	0.806566	−	0.591144i	$-0.201323\pi$
$389$	8013.33	+	2916.61i	1.04445	+	0.380149i	0.237886	+	0.971293i	$0.423546\pi$
$390$		0			0
$391$	−7977.12	−	6693.60i	−1.03176	−	0.865754i
$392$		0			0
$393$	6021.83	+	2334.77i	0.772930	+	0.299678i
$394$		0			0
$395$	7181.45	−	12438.6i	0.914780	−	1.58445i
$396$		0			0
$397$	6081.30	+	10533.1i	0.768796	+	1.33159i	0.938216	+	0.346050i	$0.112477\pi$
$397$	6081.30	+	10533.1i	0.768796	+	1.33159i	−0.169420	+	0.985544i	$0.554190\pi$
$398$		0			0
$399$	−3652.00	−	6640.81i	−0.458217	−	0.833223i
$400$		0			0
$401$	−1077.38	+	6110.10i	−0.134168	+	0.760907i	0.841267	+	0.540620i	$0.181810\pi$
$401$	−1077.38	+	6110.10i	−0.134168	+	0.760907i	−0.975435	+	0.220287i	$0.929301\pi$
$402$		0			0
$403$	−1670.60	+	1401.80i	−0.206497	+	0.173272i
$404$		0			0
$405$	9332.86	+	4306.18i	1.14507	+	0.528335i
$406$		0			0
$407$	9879.03	−	8289.49i	1.20316	−	1.00957i
$408$		0			0
$409$	−773.536	+	4386.94i	−0.0935181	+	0.530367i	0.901673	+	0.432418i	$0.142339\pi$
$409$	−773.536	+	4386.94i	−0.0935181	+	0.530367i	−0.995191	+	0.0979494i	$0.968772\pi$
$410$		0			0
$411$	6718.70	+	12217.3i	0.806348	+	1.46626i
$412$		0			0
$413$	6116.72	+	10594.5i	0.728775	+	1.26228i
$414$		0			0
$415$	−5042.65	+	8734.13i	−0.596467	+	1.03311i
$416$		0			0
$417$	−7289.93	−	2826.43i	−0.856089	−	0.331920i
$418$		0			0
$419$	−9991.52	−	8383.88i	−1.16496	−	0.977517i	−0.164998	−	0.986294i	$-0.552762\pi$
$419$	−9991.52	−	8383.88i	−1.16496	−	0.977517i	−0.999961	+	0.00877723i	$0.997206\pi$
$420$		0			0
$421$	−15259.8	−	5554.12i	−1.76655	−	0.642972i	−1.00000		0.000788484i	$-0.999749\pi$
$421$	−15259.8	−	5554.12i	−1.76655	−	0.642972i	−0.766551	−	0.642183i	$-0.778029\pi$
$422$		0			0
$423$	478.345	−	2178.49i	0.0549833	−	0.250406i
$424$		0			0
$425$	1495.53	+	8481.56i	0.170691	+	0.968038i
$426$		0			0
$427$	1658.25	−	603.555i	0.187936	−	0.0684029i
$428$		0			0
$429$	1412.13	−	480.944i	0.158924	−	0.0541264i
$430$		0			0
$431$	−506.152			−0.0565672			−0.0282836	−	0.999600i	$-0.509004\pi$
$431$	−506.152			−0.0565672			−0.0282836	+	0.999600i	$0.509004\pi$
$432$		0			0
$433$	3810.53			0.422916			0.211458	−	0.977387i	$-0.432179\pi$
$433$	3810.53			0.422916			0.211458	+	0.977387i	$0.432179\pi$
$434$		0			0
$435$	6158.03	+	5389.46i	0.678747	+	0.594034i
$436$		0			0
$437$	−6692.34	+	2435.81i	−0.732581	+	0.266638i
$438$		0			0
$439$	2784.60	+	15792.2i	0.302737	+	1.71691i	0.633969	+	0.773358i	$0.281425\pi$
$439$	2784.60	+	15792.2i	0.302737	+	1.71691i	−0.331232	+	0.943549i	$0.607464\pi$
$440$		0			0
$441$	−246.188	−	10.2507i	−0.0265833	−	0.00110687i
$442$		0			0
$443$	−7142.68	−	2599.72i	−0.766048	−	0.278819i	−0.0707054	−	0.997497i	$-0.522525\pi$
$443$	−7142.68	−	2599.72i	−0.766048	−	0.278819i	−0.695342	+	0.718679i	$0.744747\pi$
$444$		0			0
$445$	6796.38	+	5702.84i	0.723999	+	0.607507i
$446$		0			0
$447$	911.982	−	733.458i	0.0964995	−	0.0776094i
$448$		0			0
$449$	7613.88	−	13187.6i	0.800270	−	1.38611i	−0.119168	−	0.992874i	$-0.538023\pi$
$449$	7613.88	−	13187.6i	0.800270	−	1.38611i	0.919438	−	0.393234i	$-0.128644\pi$
$450$		0			0
$451$	−245.278	−	424.834i	−0.0256091	−	0.0443562i
$452$		0			0
$453$	6162.99	−	10179.5i	0.639211	−	1.05579i
$454$		0			0
$455$	359.649	−	2039.67i	0.0370562	−	0.210156i
$456$		0			0
$457$	2349.87	−	1971.78i	0.240531	−	0.201829i	−0.514551	−	0.857460i	$-0.672042\pi$
$457$	2349.87	−	1971.78i	0.240531	−	0.201829i	0.755082	+	0.655630i	$0.227597\pi$
$458$		0			0
$459$	7286.74	+	14663.9i	0.740993	+	1.49118i
$460$		0			0
$461$	−4161.68	+	3492.06i	−0.420453	+	0.352802i	−0.828335	−	0.560233i	$-0.810712\pi$
$461$	−4161.68	+	3492.06i	−0.420453	+	0.352802i	0.407883	+	0.913034i	$0.366267\pi$
$462$		0			0
$463$	3055.02	−	17325.9i	0.306650	−	1.73910i	−0.308986	−	0.951067i	$-0.599989\pi$
$463$	3055.02	−	17325.9i	0.306650	−	1.73910i	0.615635	−	0.788031i	$-0.288899\pi$
$464$		0			0
$465$	19869.4	+	413.479i	1.98155	+	0.0412358i
$466$		0			0
$467$	761.856	+	1319.57i	0.0754914	+	0.130755i	0.901300	−	0.433196i	$-0.142614\pi$
$467$	761.856	+	1319.57i	0.0754914	+	0.130755i	−0.825808	+	0.563951i	$0.809281\pi$
$468$		0			0
$469$	−6133.38	+	10623.3i	−0.603866	+	1.04593i
$470$		0			0
$471$	−849.220	−	5480.66i	−0.0830786	−	0.536169i
$472$		0			0
$473$	−11170.2	−	9372.93i	−1.08585	−	0.911137i
$474$		0			0
$475$	5534.90	+	2014.54i	0.534650	+	0.194597i
$476$		0			0
$477$	719.892	+	296.487i	0.0691019	+	0.0284596i
$478$		0			0
$479$	17.9267	+	101.668i	0.00171001	+	0.00969793i	0.985651	−	0.168797i	$-0.0539883\pi$
$479$	17.9267	+	101.668i	0.00171001	+	0.00969793i	−0.983941	+	0.178495i	$0.942877\pi$
$480$		0			0
$481$	−2728.10	+	992.948i	−0.258609	+	0.0941259i
$482$		0			0
$483$	1644.24	−	8310.02i	0.154898	−	0.782855i
$484$		0			0
$485$	−23175.1			−2.16974
$486$		0			0
$487$	−6424.90			−0.597823			−0.298912	−	0.954281i	$-0.596624\pi$
$487$	−6424.90			−0.597823			−0.298912	+	0.954281i	$0.596624\pi$
$488$		0			0
$489$	−570.566	+	2883.64i	−0.0527646	+	0.266673i
$490$		0			0
$491$	−9033.50	+	3287.92i	−0.830297	+	0.302203i	−0.721981	−	0.691913i	$-0.756768\pi$
$491$	−9033.50	+	3287.92i	−0.830297	+	0.302203i	−0.108316	+	0.994116i	$0.534546\pi$
$492$		0			0
$493$	2263.85	+	12838.9i	0.206813	+	1.17289i
$494$		0			0
$495$	−12570.2	−	5177.05i	−1.14140	−	0.470083i
$496$		0			0
$497$	−1640.70	−	597.166i	−0.148079	−	0.0538964i
$498$		0			0
$499$	−15561.9	−	13058.0i	−1.39608	−	1.17145i	−0.962806	−	0.270192i	$-0.912913\pi$
$499$	−15561.9	−	13058.0i	−1.39608	−	1.17145i	−0.433277	−	0.901261i	$-0.642643\pi$
$500$		0			0
$501$	−1194.98	−	7712.10i	−0.106562	−	0.687727i
$502$		0			0
$503$	4198.74	−	7272.42i	0.372192	−	0.644655i	−0.617711	−	0.786405i	$-0.711940\pi$
$503$	4198.74	−	7272.42i	0.372192	−	0.644655i	0.989902	+	0.141751i	$0.0452731\pi$
$504$		0			0
$505$	−9004.96	−	15597.0i	−0.793496	−	1.37438i
$506$		0			0
$507$	11077.7	+	230.526i	0.970372	+	0.0201933i
$508$		0			0
$509$	1856.65	−	10529.6i	0.161679	−	0.916926i	−0.790744	−	0.612147i	$-0.790306\pi$
$509$	1856.65	−	10529.6i	0.161679	−	0.916926i	0.952423	−	0.304779i	$-0.0985827\pi$
$510$		0			0
$511$	14078.7	−	11813.5i	1.21880	−	1.02269i
$512$		0			0
$513$	11176.9	+	698.580i	0.961938	+	0.0601229i
$514$		0			0
$515$	−545.777	+	457.961i	−0.0466986	+	0.0391848i
$516$		0			0
$517$	−512.261	+	2905.17i	−0.0435768	+	0.247136i
$518$		0			0
$519$	1111.51	−	1835.90i	0.0940078	−	0.155273i
$520$		0			0
$521$	−8883.34	−	15386.4i	−0.746998	−	1.29384i	−0.949255	−	0.314506i	$-0.898161\pi$
$521$	−8883.34	−	15386.4i	−0.746998	−	1.29384i	0.202257	−	0.979332i	$-0.435172\pi$
$522$		0			0
$523$	−9911.83	+	17167.8i	−0.828708	+	1.43536i	0.0703449	+	0.997523i	$0.477590\pi$
$523$	−9911.83	+	17167.8i	−0.828708	+	1.43536i	−0.899052	+	0.437841i	$0.855743\pi$
$524$		0			0
$525$	−5459.48	+	4390.77i	−0.453850	+	0.365007i
$526$		0			0
$527$	24253.6	+	20351.2i	2.00475	+	1.68219i
$528$		0			0
$529$	3952.90	+	1438.74i	0.324887	+	0.118249i
$530$		0			0
$531$	−18061.1	−	752.026i	−1.47606	−	0.0614598i
$532$		0			0
$533$	19.1767	+	108.756i	0.00155841	+	0.00883820i
$534$		0			0
$535$	−21002.0	+	7644.09i	−1.69719	+	0.617725i
$536$		0			0
$537$	−5469.26	−	4786.65i	−0.439508	−	0.384654i
$538$		0			0
$539$	325.899			0.0260436
$540$		0			0
$541$	879.526			0.0698960			0.0349480	−	0.999389i	$-0.488873\pi$
$541$	879.526			0.0698960			0.0349480	+	0.999389i	$0.488873\pi$
$542$		0			0
$543$	7947.78	−	2706.86i	0.628125	−	0.213927i
$544$		0			0
$545$	2671.16	−	972.221i	0.209944	−	0.0764135i
$546$		0			0
$547$	−1578.98	−	8954.82i	−0.123423	−	0.699964i	−0.982232	−	0.187670i	$-0.939907\pi$
$547$	−1578.98	−	8954.82i	−0.123423	−	0.699964i	0.858810	−	0.512295i	$-0.171205\pi$
$548$		0			0
$549$	−559.241	+	2546.90i	−0.0434751	+	0.197995i
$550$		0			0
$551$	8378.43	+	3049.50i	0.647792	+	0.235777i
$552$		0			0
$553$	14259.0	+	11964.7i	1.09648	+	0.920059i
$554$		0			0
$555$	24667.5	+	9564.01i	1.88663	+	0.731476i
$556$		0			0
$557$	11427.3	−	19792.7i	0.869283	−	1.50564i	0.00655273	−	0.999979i	$-0.497914\pi$
$557$	11427.3	−	19792.7i	0.869283	−	1.50564i	0.862730	−	0.505664i	$-0.168752\pi$
$558$		0			0
$559$	1641.32	+	2842.85i	0.124187	+	0.215098i
$560$		0			0
$561$	−10436.2	−	18977.3i	−0.785416	−	1.42820i
$562$		0			0
$563$	999.815	−	5670.23i	0.0748440	−	0.424462i	−0.924245	−	0.381799i	$-0.875305\pi$
$563$	999.815	−	5670.23i	0.0748440	−	0.424462i	0.999090	−	0.0426629i	$-0.0135841\pi$
$564$		0			0
$565$	16708.4	−	14020.0i	1.24412	−	1.04394i
$566$		0			0
$567$	−7596.16	+	10942.2i	−0.562626	+	0.810460i
$568$		0			0
$569$	−912.392	+	765.588i	−0.0672223	+	0.0564062i	−0.675780	−	0.737104i	$-0.736193\pi$
$569$	−912.392	+	765.588i	−0.0672223	+	0.0564062i	0.608557	+	0.793510i	$0.291748\pi$
$570$		0			0
$571$	1268.54	−	7194.23i	0.0929713	−	0.527267i	−0.902379	−	0.430944i	$-0.858181\pi$
$571$	1268.54	−	7194.23i	0.0929713	−	0.527267i	0.995350	−	0.0963229i	$-0.0307081\pi$
$572$		0			0
$573$	−4383.02	−	7970.09i	−0.319552	−	0.581074i
$574$		0			0
$575$	3291.83	+	5701.62i	0.238746	+	0.413520i
$576$		0			0
$577$	5516.75	−	9555.29i	0.398033	−	0.689414i	−0.595450	−	0.803393i	$-0.703026\pi$
$577$	5516.75	−	9555.29i	0.398033	−	0.689414i	0.993483	+	0.113978i	$0.0363594\pi$
$578$		0			0
$579$	−5934.60	−	2300.95i	−0.425965	−	0.165154i
$580$		0			0
$581$	−10012.4	−	8401.37i	−0.714944	−	0.599910i
$582$		0			0
$583$	−967.646	−	352.194i	−0.0687406	−	0.0250195i
$584$		0			0
$585$	2260.55	+	2063.03i	0.159764	+	0.145805i
$586$		0			0
$587$	−1937.43	−	10987.7i	−0.136229	−	0.772593i	−0.973996	−	0.226565i	$-0.927250\pi$
$587$	−1937.43	−	10987.7i	−0.136229	−	0.772593i	0.837767	−	0.546028i	$-0.183861\pi$
$588$		0			0
$589$	20347.4	−	7405.84i	1.42343	−	0.518085i
$590$		0			0
$591$	−26756.6	+	9112.80i	−1.86230	+	0.634265i
$592$		0			0
$593$	9356.50			0.647935			0.323967	−	0.946068i	$-0.394983\pi$
$593$	9356.50			0.647935			0.323967	+	0.946068i	$0.394983\pi$
$594$		0			0
$595$	−30068.6			−2.07175
$596$		0			0
$597$	8626.59	+	7549.92i	0.591395	+	0.517584i
$598$		0			0
$599$	2260.98	−	822.930i	0.154226	−	0.0561335i	−0.263754	−	0.964590i	$-0.584961\pi$
$599$	2260.98	−	822.930i	0.154226	−	0.0561335i	0.417979	+	0.908457i	$0.362738\pi$
$600$		0			0
$601$	1862.04	+	10560.2i	0.126380	+	0.716736i	0.980479	+	0.196625i	$0.0629983\pi$
$601$	1862.04	+	10560.2i	0.126380	+	0.716736i	−0.854099	+	0.520111i	$0.825891\pi$
$602$		0			0
$603$	−8402.11	−	16061.0i	−0.567430	−	1.08467i
$604$		0			0
$605$	−738.084	−	268.641i	−0.0495990	−	0.0180526i
$606$		0			0
$607$	6535.29	+	5483.76i	0.437000	+	0.366687i	0.834585	−	0.550879i	$-0.185707\pi$
$607$	6535.29	+	5483.76i	0.437000	+	0.366687i	−0.397585	+	0.917565i	$0.630152\pi$
$608$		0			0
$609$	−8264.26	+	6646.50i	−0.549893	+	0.442249i
$610$		0			0
$611$	332.051	−	575.130i	0.0219859	−	0.0380806i
$612$		0			0
$613$	2670.34	+	4625.17i	0.175945	+	0.304745i	0.940488	−	0.339827i	$-0.110369\pi$
$613$	2670.34	+	4625.17i	0.175945	+	0.304745i	−0.764543	+	0.644573i	$0.777035\pi$
$614$		0			0
$615$	521.216	−	860.896i	0.0341747	−	0.0564466i
$616$		0			0
$617$	−3028.80	+	17177.2i	−0.197625	+	1.12079i	0.711005	+	0.703187i	$0.248240\pi$
$617$	−3028.80	+	17177.2i	−0.197625	+	1.12079i	−0.908630	+	0.417601i	$0.862871\pi$
$618$		0			0
$619$	−6065.97	+	5089.96i	−0.393881	+	0.330505i	−0.818123	−	0.575044i	$-0.804985\pi$
$619$	−6065.97	+	5089.96i	−0.393881	+	0.330505i	0.424242	+	0.905549i	$0.360541\pi$
$620$		0			0
$621$	9068.28	+	8628.50i	0.585986	+	0.557568i
$622$		0			0
$623$	−8807.88	+	7390.69i	−0.566421	+	0.475284i
$624$		0			0
$625$	−3369.43	+	19109.0i	−0.215644	+	1.22298i
$626$		0			0
$627$	−14808.7	−	308.167i	−0.943225	−	0.0196284i
$628$		0			0
$629$	21074.1	+	36501.5i	1.33590	+	2.31385i
$630$		0			0
$631$	8251.31	−	14291.7i	0.520570	−	0.901653i	−0.479144	−	0.877736i	$-0.659053\pi$
$631$	8251.31	−	14291.7i	0.520570	−	0.901653i	0.999714	−	0.0239171i	$-0.00761378\pi$
$632$		0			0
$633$	−377.465	−	2436.07i	−0.0237013	−	0.152962i
$634$		0			0
$635$	24033.9	+	20166.8i	1.50198	+	1.26031i
$636$		0			0
$637$	−68.9420	−	25.0928i	−0.00428820	−	0.00156078i
$638$		0			0
$639$	2043.66	−	1574.72i	0.126519	−	0.0974882i
$640$		0			0
$641$	3265.74	+	18520.9i	0.201231	+	1.14124i	0.903262	+	0.429089i	$0.141165\pi$
$641$	3265.74	+	18520.9i	0.201231	+	1.14124i	−0.702031	+	0.712146i	$0.747723\pi$
$642$		0			0
$643$	−955.782	+	347.876i	−0.0586195	+	0.0213358i	−0.371163	−	0.928568i	$-0.621041\pi$
$643$	−955.782	+	347.876i	−0.0586195	+	0.0213358i	0.312544	+	0.949903i	$0.398819\pi$
$644$		0			0
$645$	5806.42	−	29345.7i	0.354461	−	1.79145i
$646$		0			0
$647$	−20407.3			−1.24002			−0.620011	−	0.784593i	$-0.712872\pi$
$647$	−20407.3			−1.24002			−0.620011	+	0.784593i	$0.712872\pi$
$648$		0			0
$649$	23909.0			1.44609
$650$		0			0
$651$	−4999.16	+	25265.8i	−0.300971	+	1.52111i
$652$		0			0
$653$	−24273.6	+	8834.88i	−1.45467	+	0.529457i	−0.943892	−	0.330254i	$-0.892866\pi$
$653$	−24273.6	+	8834.88i	−1.45467	+	0.529457i	−0.510780	+	0.859711i	$0.670643\pi$
$654$		0			0
$655$	−3043.16	−	17258.6i	−0.181536	−	1.02954i
$656$		0			0
$657$	3599.07	+	26917.5i	0.213719	+	1.59840i
$658$		0			0
$659$	−11124.7	−	4049.07i	−0.657599	−	0.239347i	−0.00839966	−	0.999965i	$-0.502674\pi$
$659$	−11124.7	−	4049.07i	−0.657599	−	0.239347i	−0.649199	+	0.760618i	$0.724896\pi$
$660$		0			0
$661$	−5401.80	−	4532.65i	−0.317860	−	0.266717i	0.469871	−	0.882735i	$-0.344300\pi$
$661$	−5401.80	−	4532.65i	−0.317860	−	0.266717i	−0.787732	+	0.616018i	$0.788745\pi$
$662$		0			0
$663$	746.554	+	4818.07i	0.0437311	+	0.282230i
$664$		0			0
$665$	−10282.1	+	17809.2i	−0.599585	+	1.03851i
$666$		0			0
$667$	4982.99	+	8630.80i	0.289269	+	0.501028i
$668$		0			0
$669$	7694.21	+	160.116i	0.444657	+	0.00925326i
$670$		0			0
$671$	598.892	−	3396.48i	0.0344560	−	0.195410i
$672$		0			0
$673$	−17454.9	+	14646.4i	−0.999756	+	0.838895i	−0.986951	−	0.161023i	$-0.948521\pi$
$673$	−17454.9	+	14646.4i	−0.999756	+	0.838895i	−0.0128057	+	0.999918i	$0.504076\pi$
$674$		0			0
$675$	−1158.21	−	10287.5i	−0.0660440	−	0.586617i
$676$		0			0
$677$	−8712.25	+	7310.45i	−0.494592	+	0.415012i	−0.855669	−	0.517524i	$-0.826854\pi$
$677$	−8712.25	+	7310.45i	−0.494592	+	0.415012i	0.361076	+	0.932536i	$0.382409\pi$
$678$		0			0
$679$	5215.37	−	29577.8i	0.294768	−	1.67171i
$680$		0			0
$681$	−3023.58	+	4994.07i	−0.170138	+	0.281018i
$682$		0			0
$683$	−5758.82	−	9974.56i	−0.322628	−	0.558808i	0.658401	−	0.752667i	$-0.271233\pi$
$683$	−5758.82	−	9974.56i	−0.322628	−	0.558808i	−0.981029	+	0.193859i	$0.937900\pi$
$684$		0			0
$685$	18916.4	−	32764.1i	1.05512	−	1.82752i
$686$		0			0
$687$	−13972.2	+	11237.1i	−0.775944	+	0.624050i
$688$		0			0
$689$	177.582	+	149.009i	0.00981907	+	0.00823918i
$690$		0			0
$691$	−13056.2	−	4752.05i	−0.718784	−	0.261616i	−0.0433746	−	0.999059i	$-0.513811\pi$
$691$	−13056.2	−	4752.05i	−0.718784	−	0.261616i	−0.675410	+	0.737443i	$0.736033\pi$
$692$		0			0
$693$	9436.19	−	14878.1i	0.517245	−	0.815543i
$694$		0			0
$695$	3684.00	+	20893.0i	0.201068	+	1.14031i
$696$		0			0
$697$	1506.59	−	548.352i	0.0818738	−	0.0297996i
$698$		0			0
$699$	26271.8	+	22992.9i	1.42159	+	1.24416i
$700$		0			0
$701$	25381.5			1.36754			0.683771	−	0.729696i	$-0.260339\pi$
$701$	25381.5			1.36754			0.683771	+	0.729696i	$0.260339\pi$
$702$		0			0
$703$	28825.7			1.54649
$704$		0			0
$705$	−5728.81	+	1951.12i	−0.306042	+	0.104232i
$706$		0			0
$707$	21932.7	−	7982.83i	1.16671	−	0.424647i
$708$		0			0
$709$	−3197.43	−	18133.5i	−0.169368	−	0.960535i	−0.944445	−	0.328668i	$-0.893400\pi$
$709$	−3197.43	−	18133.5i	−0.169368	−	0.960535i	0.775077	−	0.631867i	$-0.217711\pi$
$710$		0			0
$711$	−26215.0	+	8323.81i	−1.38276	+	0.439054i
$712$		0			0
$713$	22743.2	+	8277.85i	1.19459	+	0.434794i
$714$		0			0
$715$	−3100.81	−	2601.89i	−0.162187	−	0.136091i
$716$		0			0
$717$	−30258.5	−	11731.7i	−1.57605	−	0.611060i
$718$		0			0
$719$	−4178.46	+	7237.30i	−0.216732	+	0.375391i	−0.953807	−	0.300420i	$-0.902873\pi$
$719$	−4178.46	+	7237.30i	−0.216732	+	0.375391i	0.737075	+	0.675811i	$0.236206\pi$
$720$		0			0
$721$	−461.662	−	799.623i	−0.0238463	−	0.0413031i
$722$		0			0
$723$	−2105.67	−	3828.96i	−0.108314	−	0.196958i
$724$		0			0
$725$	1431.27	−	8117.16i	0.0733189	−	0.415812i
$726$		0			0
$727$	−2910.27	+	2442.01i	−0.148468	+	0.124579i	−0.713996	−	0.700149i	$-0.753117\pi$
$727$	−2910.27	+	2442.01i	−0.148468	+	0.124579i	0.565528	+	0.824729i	$0.308672\pi$
$728$		0			0
$729$	−7642.39	−	18138.8i	−0.388274	−	0.921544i
$730$		0			0
$731$	36507.5	−	30633.4i	1.84716	−	1.54996i
$732$		0			0
$733$	−3398.64	+	19274.7i	−0.171257	+	0.971249i	0.771118	+	0.636692i	$0.219698\pi$
$733$	−3398.64	+	19274.7i	−0.171257	+	0.971249i	−0.942375	+	0.334557i	$0.891413\pi$
$734$		0			0
$735$	322.175	+	585.844i	0.0161682	+	0.0294002i
$736$		0			0
$737$	11987.1	+	20762.2i	0.599117	+	1.03770i
$738$		0			0
$739$	−3828.18	+	6630.60i	−0.190557	+	0.330055i	−0.945435	−	0.325811i	$-0.894363\pi$
$739$	−3828.18	+	6630.60i	−0.190557	+	0.330055i	0.754878	+	0.655866i	$0.227696\pi$
$740$		0			0
$741$	3108.96	+	1205.40i	0.154130	+	0.0597589i
$742$		0			0
$743$	−8817.80	−	7399.01i	−0.435388	−	0.365334i	0.398592	−	0.917128i	$-0.369499\pi$
$743$	−8817.80	−	7399.01i	−0.435388	−	0.365334i	−0.833980	+	0.551794i	$0.813943\pi$
$744$		0			0
$745$	−2984.08	−	1086.12i	−0.146749	−	0.0534123i
$746$		0			0
$747$	18407.6	−	5844.79i	0.901604	−	0.286278i
$748$		0			0
$749$	−5029.65	−	28524.6i	−0.245366	−	1.39154i
$750$		0			0
$751$	21813.3	−	7939.39i	1.05989	−	0.385769i	0.247504	−	0.968887i	$-0.420390\pi$
$751$	21813.3	−	7939.39i	1.05989	−	0.385769i	0.812387	+	0.583118i	$0.198168\pi$
$752$		0			0
$753$	−25404.8	+	8652.39i	−1.22949	+	0.418739i
$754$		0			0
$755$	−32288.9			−1.55644
$756$		0			0
$757$	−2092.13			−0.100449			−0.0502244	−	0.998738i	$-0.515994\pi$
$757$	−2092.13			−0.100449			−0.0502244	+	0.998738i	$0.515994\pi$
$758$		0			0
$759$	−12458.4	−	10903.5i	−0.595801	−	0.521440i
$760$		0			0
$761$	22912.8	−	8339.57i	1.09144	−	0.397253i	0.267288	−	0.963617i	$-0.413873\pi$
$761$	22912.8	−	8339.57i	1.09144	−	0.397253i	0.824155	+	0.566364i	$0.191650\pi$
$762$		0			0
$763$	639.701	+	3627.93i	0.0303522	+	0.172136i
$764$		0			0
$765$	23797.0	−	37520.8i	1.12468	−	1.77329i
$766$		0			0
$767$	−5057.81	−	1840.89i	−0.238105	−	0.0866633i
$768$		0			0
$769$	3200.87	+	2685.85i	0.150099	+	0.125948i	0.714745	−	0.699385i	$-0.246543\pi$
$769$	3200.87	+	2685.85i	0.150099	+	0.125948i	−0.564646	+	0.825333i	$0.690987\pi$
$770$		0			0
$771$	−17624.4	+	14174.3i	−0.823250	+	0.662096i
$772$		0			0
$773$	−7133.99	+	12356.4i	−0.331943	+	0.574942i	−0.982893	−	0.184179i	$-0.941037\pi$
$773$	−7133.99	+	12356.4i	−0.331943	+	0.574942i	0.650950	+	0.759121i	$0.274371\pi$
$774$		0			0
$775$	−10008.5	−	17335.2i	−0.463891	−	0.803482i
$776$		0			0
$777$	−17757.6	+	29330.3i	−0.819882	+	1.35421i
$778$		0			0
$779$	190.405	−	1079.84i	0.00875734	−	0.0496653i
$780$		0			0
$781$	−2614.03	+	2193.43i	−0.119766	+	0.100496i
$782$		0			0
$783$	−1753.24	−	15572.7i	−0.0800200	−	0.710756i
$784$		0			0
$785$	−11528.0	+	9673.16i	−0.524143	+	0.439809i
$786$		0			0
$787$	−3425.45	+	19426.7i	−0.155151	+	0.879908i	0.803496	+	0.595310i	$0.202971\pi$
$787$	−3425.45	+	19426.7i	−0.155151	+	0.879908i	−0.958647	+	0.284597i	$0.908140\pi$
$788$		0			0
$789$	7994.37	+	166.362i	0.360719	+	0.00750651i
$790$		0			0
$791$	14133.3	+	24479.6i	0.635300	+	1.10037i
$792$		0			0
$793$	−388.206	+	672.393i	−0.0173841	+	0.0301102i
$794$		0			0
$795$	−323.475	−	2087.63i	−0.0144308	−	0.0931329i
$796$		0			0
$797$	−7710.37	−	6469.77i	−0.342679	−	0.287542i	0.455163	−	0.890408i	$-0.349581\pi$
$797$	−7710.37	−	6469.77i	−0.342679	−	0.287542i	−0.797843	+	0.602866i	$0.794025\pi$
$798$		0			0
$799$	−9059.96	−	3297.55i	−0.401149	−	0.146006i
$800$		0			0
$801$	−2251.63	−	16840.0i	−0.0993229	−	0.742837i
$802$		0			0
$803$	−6237.25	−	35373.2i	−0.274107	−	1.55454i
$804$		0			0
$805$	−21599.4	+	7861.55i	−0.945690	+	0.344203i
$806$		0			0
$807$	−3309.53	+	16726.4i	−0.144363	+	0.729612i
$808$		0			0
$809$	−22978.1			−0.998601			−0.499300	−	0.866429i	$-0.666410\pi$
$809$	−22978.1			−0.998601			−0.499300	+	0.866429i	$0.666410\pi$
$810$		0			0
$811$	26002.0			1.12584			0.562919	−	0.826512i	$-0.309678\pi$
$811$	26002.0			1.12584			0.562919	+	0.826512i	$0.309678\pi$
$812$		0			0
$813$	4689.67	−	23701.6i	0.202305	−	1.02245i
$814$		0			0
$815$	7495.19	−	2728.03i	0.322141	−	0.117250i
$816$		0			0
$817$	−5659.76	−	32098.1i	−0.242362	−	1.37450i
$818$		0			0
$819$	−3141.71	+	2420.82i	−0.134042	+	0.103285i
$820$		0			0
$821$	−26141.6	−	9514.78i	−1.11127	−	0.404468i	−0.279809	−	0.960056i	$-0.590271\pi$
$821$	−26141.6	−	9514.78i	−1.11127	−	0.404468i	−0.831458	+	0.555588i	$0.812493\pi$
$822$		0			0
$823$	1726.87	+	1449.01i	0.0731407	+	0.0613723i	0.678625	−	0.734485i	$-0.262576\pi$
$823$	1726.87	+	1449.01i	0.0731407	+	0.0613723i	−0.605484	+	0.795857i	$0.707021\pi$
$824$		0			0
$825$	2096.63	+	13531.2i	0.0884792	+	0.571023i
$826$		0			0
$827$	821.250	−	1422.45i	0.0345316	−	0.0598105i	−0.848243	−	0.529607i	$-0.822339\pi$
$827$	821.250	−	1422.45i	0.0345316	−	0.0598105i	0.882775	+	0.469797i	$0.155673\pi$
$828$		0			0
$829$	−5372.26	−	9305.02i	−0.225074	−	0.389839i	0.731268	−	0.682090i	$-0.238929\pi$
$829$	−5372.26	−	9305.02i	−0.225074	−	0.389839i	−0.956342	+	0.292251i	$0.905596\pi$
$830$		0			0
$831$	34201.4	+	711.728i	1.42772	+	0.0297107i
$832$		0			0
$833$	−184.958	+	1048.95i	−0.00769318	+	0.0436302i
$834$		0			0
$835$	−16221.6	+	13611.6i	−0.672302	+	0.564129i
$836$		0			0
$837$	−27571.2	−	26234.1i	−1.13859	−	1.08337i
$838$		0			0
$839$	6016.97	−	5048.83i	0.247591	−	0.207753i	−0.510543	−	0.859852i	$-0.670556\pi$
$839$	6016.97	−	5048.83i	0.247591	−	0.207753i	0.758134	+	0.652099i	$0.226111\pi$
$840$		0			0
$841$	−2068.52	+	11731.2i	−0.0848137	+	0.481002i
$842$		0			0
$843$	11645.2	−	19234.4i	0.475778	−	0.785846i
$844$		0			0
$845$	−15032.5	−	26037.0i	−0.611991	−	1.06000i
$846$		0			0
$847$	508.960	−	881.545i	0.0206471	−	0.0357618i
$848$		0			0
$849$	5045.26	−	4057.63i	0.203949	−	0.164025i
$850$		0			0
$851$	24681.8	+	20710.5i	0.994221	+	0.834251i
$852$		0			0
$853$	21669.0	+	7886.87i	0.869792	+	0.316578i	0.738083	−	0.674710i	$-0.235731\pi$
$853$	21669.0	+	7886.87i	0.869792	+	0.316578i	0.131709	+	0.991288i	$0.457954\pi$
$854$		0			0
$855$	−14085.5	−	26925.1i	−0.563408	−	1.07698i
$856$		0			0
$857$	−3543.22	−	20094.6i	−0.141230	−	0.800955i	−0.970317	−	0.241836i	$-0.922250\pi$
$857$	−3543.22	−	20094.6i	−0.141230	−	0.800955i	0.829087	−	0.559119i	$-0.188861\pi$
$858$		0			0
$859$	9749.16	−	3548.41i	0.387238	−	0.140943i	−0.141062	−	0.990001i	$-0.545052\pi$
$859$	9749.16	−	3548.41i	0.387238	−	0.140943i	0.528300	+	0.849058i	$0.322830\pi$
$860$		0			0
$861$	981.446	+	858.954i	0.0388474	+	0.0339989i
$862$		0			0
$863$	−4579.50			−0.180635			−0.0903175	−	0.995913i	$-0.528788\pi$
$863$	−4579.50			−0.180635			−0.0903175	+	0.995913i	$0.528788\pi$
$864$		0			0
$865$	−5823.40			−0.228904
$866$		0			0
$867$	42838.2	−	14589.9i	1.67804	−	0.571508i
$868$		0			0
$869$	34185.0	−	12442.3i	1.33446	−	0.485703i
$870$		0			0
$871$	−937.191	−	5315.07i	−0.0364587	−	0.206767i
$872$		0			0
$873$	32780.8	+	29916.5i	1.27086	+	1.15982i
$874$		0			0
$875$	−12397.3	−	4512.24i	−0.478976	−	0.174333i
$876$		0			0
$877$	2605.11	+	2185.94i	0.100306	+	0.0841665i	0.691561	−	0.722318i	$-0.256923\pi$
$877$	2605.11	+	2185.94i	0.100306	+	0.0841665i	−0.591256	+	0.806484i	$0.701368\pi$
$878$		0			0
$879$	−16294.1	−	6317.49i	−0.625240	−	0.242416i
$880$		0			0
$881$	−12076.5	+	20917.0i	−0.461823	+	0.799902i	−0.999052	−	0.0435352i	$-0.986138\pi$
$881$	−12076.5	+	20917.0i	−0.461823	+	0.799902i	0.537228	+	0.843437i	$0.319471\pi$
$882$		0			0
$883$	9087.36	+	15739.8i	0.346335	+	0.599870i	0.985595	−	0.169120i	$-0.0540926\pi$
$883$	9087.36	+	15739.8i	0.346335	+	0.599870i	−0.639260	+	0.768991i	$0.720759\pi$
$884$		0			0
$885$	23635.8	+	42979.4i	0.897750	+	1.63247i
$886$		0			0
$887$	−4251.25	+	24110.0i	−0.160928	+	0.912667i	0.792237	+	0.610214i	$0.208917\pi$
$887$	−4251.25	+	24110.0i	−0.160928	+	0.912667i	−0.953164	+	0.302453i	$0.902195\pi$
$888$		0			0
$889$	−31147.1	+	26135.5i	−1.17507	+	0.986004i
$890$		0			0
$891$	11097.4	+	23549.7i	0.417259	+	0.885460i
$892$		0			0
$893$	−5051.20	+	4238.46i	−0.189285	+	0.158829i
$894$		0			0
$895$	−3424.56	+	19421.6i	−0.127900	+	0.725356i
$896$		0			0
$897$	1795.98	+	3265.82i	0.0668519	+	0.121564i
$898$		0			0
$899$	−15150.3	−	26241.1i	−0.562058	−	0.973514i
$900$		0			0
$901$	1682.75	−	2914.61i	0.0622204	−	0.107769i
$902$		0			0
$903$	36146.5	+	14014.6i	1.33209	+	0.516475i
$904$		0			0
$905$	−17452.1	−	14644.0i	−0.641023	−	0.537882i
$906$		0			0
$907$	6108.70	+	2223.38i	0.223634	+	0.0813961i	0.451407	−	0.892318i	$-0.350922\pi$
$907$	6108.70	+	2223.38i	0.223634	+	0.0813961i	−0.227773	+	0.973714i	$0.573144\pi$
$908$		0			0
$909$	−7396.73	+	33686.3i	−0.269894	+	1.22916i
$910$		0			0
$911$	−2777.96	−	15754.6i	−0.101029	−	0.572966i	−0.992732	−	0.120345i	$-0.961600\pi$
$911$	−2777.96	−	15754.6i	−0.101029	−	0.572966i	0.891703	−	0.452621i	$-0.149511\pi$
$912$		0			0
$913$	−24003.9	+	8736.70i	−0.870113	+	0.316695i
$914$		0			0
$915$	6697.64	−	2281.09i	0.241986	−	0.0824158i
$916$		0			0
$917$	22711.6			0.817889
$918$		0			0
$919$	11885.2			0.426611			0.213305	−	0.976986i	$-0.431577\pi$
$919$	11885.2			0.426611			0.213305	+	0.976986i	$0.431577\pi$
$920$		0			0
$921$	10503.2	+	9192.31i	0.375778	+	0.328878i
$922$		0			0
$923$	721.866	−	262.738i	0.0257427	−	0.00936958i
$924$		0			0
$925$	−4627.28	−	26242.6i	−0.164480	−	0.932813i
$926$		0			0
$927$	1363.17	+	56.7595i	0.0482982	+	0.00201103i
$928$		0			0
$929$	−16750.5	−	6096.69i	−0.591568	−	0.215313i	0.0288511	−	0.999584i	$-0.490815\pi$
$929$	−16750.5	−	6096.69i	−0.591568	−	0.215313i	−0.620419	+	0.784271i	$0.713037\pi$
$930$		0			0
$931$	558.030	+	468.242i	0.0196441	+	0.0164834i
$932$		0			0
$933$	−3212.87	+	2583.94i	−0.112738	+	0.0906693i
$934$		0			0
$935$	−29383.0	+	50892.9i	−1.02773	+	1.78008i
$936$		0			0
$937$	3408.22	+	5903.21i	0.118828	+	0.205816i	0.919303	−	0.393550i	$-0.128753\pi$
$937$	3408.22	+	5903.21i	0.118828	+	0.205816i	−0.800476	+	0.599365i	$0.795420\pi$
$938$		0			0
$939$	−5580.13	+	9216.74i	−0.193930	+	0.320316i
$940$		0			0
$941$	−512.291	+	2905.35i	−0.0177473	+	0.100650i	−0.992395	−	0.123096i	$-0.960718\pi$
$941$	−512.291	+	2905.35i	−0.0177473	+	0.100650i	0.974647	+	0.223746i	$0.0718287\pi$
$942$		0			0
$943$	938.870	−	787.805i	0.0324219	−	0.0272052i
$944$		0			0
$945$	36073.5	+	2254.66i	1.24177	+	0.0776128i
$946$		0			0
$947$	−5209.50	+	4371.29i	−0.178760	+	0.149998i	−0.727777	−	0.685813i	$-0.759447\pi$
$947$	−5209.50	+	4371.29i	−0.178760	+	0.149998i	0.549017	+	0.835811i	$0.315002\pi$
$948$		0			0
$949$	−1404.13	+	7963.23i	−0.0480296	+	0.272389i
$950$		0			0
$951$	−35225.7	−	733.043i	−1.20113	−	0.0249953i
$952$		0			0
$953$	−21077.2	−	36506.7i	−0.716429	−	1.24089i	−0.962406	−	0.271615i	$-0.912442\pi$
$953$	−21077.2	−	36506.7i	−0.716429	−	1.24089i	0.245977	−	0.969276i	$-0.420891\pi$
$954$		0			0
$955$	−12340.3	+	21374.0i	−0.418139	+	0.724238i
$956$		0			0
$957$	3173.77	+	20482.7i	0.107203	+	0.691862i
$958$		0			0
$959$	37559.1	+	31515.8i	1.26470	+	1.06121i
$960$		0			0
$961$	−41154.1	−	14978.9i	−1.38143	−	0.502798i
$962$		0			0
$963$	39574.7	+	16298.8i	1.32428	+	0.545402i
$964$		0			0
$965$	2999.08	+	17008.6i	0.100045	+	0.567386i
$966$		0			0
$967$	−15811.2	+	5754.81i	−0.525806	+	0.191378i	−0.591265	−	0.806478i	$-0.701371\pi$
$967$	−15811.2	+	5754.81i	−0.525806	+	0.191378i	0.0654587	+	0.997855i	$0.479149\pi$
$968$		0			0
$969$	9396.27	−	47488.8i	0.311509	−	1.57437i
$970$		0			0
$971$	44445.5			1.46892			0.734461	−	0.678651i	$-0.237435\pi$
$971$	44445.5			1.46892			0.734461	+	0.678651i	$0.237435\pi$
$972$		0			0
$973$	−27494.3			−0.905886
$974$		0			0
$975$	598.310	−	3023.86i	0.0196526	−	0.0993242i
$976$		0			0
$977$	14594.3	−	5311.89i	0.477905	−	0.173943i	−0.0918251	−	0.995775i	$-0.529270\pi$
$977$	14594.3	−	5311.89i	0.477905	−	0.173943i	0.569730	+	0.821832i	$0.307048\pi$
$978$		0			0
$979$	3902.12	+	22130.0i	0.127388	+	0.722451i
$980$		0			0
$981$	−5033.35	−	2072.98i	−0.163815	−	0.0674671i
$982$		0			0
$983$	−50650.6	−	18435.3i	−1.64344	−	0.598164i	−0.655806	−	0.754929i	$-0.727671\pi$
$983$	−50650.6	−	18435.3i	−1.64344	−	0.598164i	−0.987636	+	0.156765i	$0.949893\pi$
$984$		0			0
$985$	58753.3	+	49299.9i	1.90055	+	1.59475i
$986$		0			0
$987$	−1200.95	−	7750.63i	−0.0387301	−	0.249955i
$988$		0			0
$989$	18215.5	−	31550.2i	0.585661	−	1.01440i
$990$		0			0
$991$	−14415.8	−	24969.0i	−0.462093	−	0.800369i	0.536972	−	0.843600i	$-0.319568\pi$
$991$	−14415.8	−	24969.0i	−0.462093	−	0.800369i	−0.999065	+	0.0432313i	$0.986235\pi$
$992$		0			0
$993$	8979.10	+	186.854i	0.286952	+	0.00597143i
$994$		0			0
$995$	5401.52	−	30633.5i	0.172100	−	0.976028i
$996$		0			0
$997$	−24165.5	+	20277.2i	−0.767631	+	0.644119i	−0.940101	−	0.340896i	$-0.889270\pi$
$997$	−24165.5	+	20277.2i	−0.767631	+	0.644119i	0.172470	+	0.985015i	$0.444825\pi$
$998$		0			0
$999$	−22545.8	−	45371.3i	−0.714030	−	1.43692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.49.4	✓	54
3.2	odd	2		324.4.i.a.37.2		54
27.11	odd	18		324.4.i.a.289.2		54
27.16	even	9	inner	108.4.i.a.97.4	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.49.4	✓	54	1.1	even	1	trivial
108.4.i.a.97.4	yes	54	27.16	even	9	inner
324.4.i.a.37.2		54	3.2	odd	2
324.4.i.a.289.2		54	27.11	odd	18

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.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00857 + 5.09733i) q^{3} +(13.2490 - 4.82225i) q^{5} +(3.17294 + 17.9946i) q^{7} +(-24.9656 - 10.2821i) q^{9} +O(q^{10})\)	\(q+(-1.00857 + 5.09733i) q^{3} +(13.2490 - 4.82225i) q^{5} +(3.17294 + 17.9946i) q^{7} +(-24.9656 - 10.2821i) q^{9} +(33.5576 + 12.2140i) q^{11} +(-6.15848 - 5.16757i) q^{13} +(11.2180 + 72.3982i) q^{15} +(-58.3572 + 101.078i) q^{17} +(39.9112 + 69.1281i) q^{19} +(-94.9247 - 1.97537i) q^{21} +(-15.4931 + 87.8657i) q^{23} +(56.5267 - 47.4316i) q^{25} +(77.5906 - 116.888i) q^{27} +(85.5671 - 71.7993i) q^{29} +(47.1052 - 267.147i) q^{31} +(-96.1038 + 158.735i) q^{33} +(128.813 + 223.110i) q^{35} +(180.562 - 312.742i) q^{37} +(32.5521 - 26.1799i) q^{39} +(-10.5230 - 8.82981i) q^{41} +(-383.698 - 139.655i) q^{43} +(-380.352 - 15.8370i) q^{45} +(14.3445 + 81.3518i) q^{47} +(8.57561 - 3.12127i) q^{49} +(-456.369 - 399.410i) q^{51} -28.8354 q^{53} +503.503 q^{55} +(-392.622 + 133.720i) q^{57} +(629.134 - 228.986i) q^{59} +(-16.7704 - 95.1097i) q^{61} +(105.808 - 481.870i) q^{63} +(-106.513 - 38.7676i) q^{65} +(514.271 + 431.525i) q^{67} +(-432.254 - 167.592i) q^{69} +(-47.7773 + 82.7527i) q^{71} +(-502.908 - 871.062i) q^{73} +(184.763 + 335.974i) q^{75} +(-113.309 + 642.610i) q^{77} +(780.366 - 654.805i) q^{79} +(517.559 + 513.395i) q^{81} +(-547.955 + 459.789i) q^{83} +(-285.754 + 1620.59i) q^{85} +(279.684 + 508.578i) q^{87} +(314.627 + 544.950i) q^{89} +(73.4481 - 127.216i) q^{91} +(1314.23 + 509.547i) q^{93} +(862.136 + 723.418i) q^{95} +(-1544.58 - 562.179i) q^{97} +(-712.199 - 649.969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 54 * q + 12 * q^5 - 48 * q^9	\( 54 q + 12 q^{5} - 48 q^{9} - 87 q^{11} + 234 q^{15} + 204 q^{17} - 12 q^{21} + 96 q^{23} - 216 q^{25} + 27 q^{27} + 318 q^{29} - 54 q^{31} + 63 q^{33} + 6 q^{35} + 66 q^{39} + 867 q^{41} - 513 q^{43} - 306 q^{45} - 1548 q^{47} + 594 q^{49} - 1368 q^{51} - 1068 q^{53} - 1269 q^{57} - 1218 q^{59} - 54 q^{61} + 30 q^{63} + 96 q^{65} - 2997 q^{67} + 1476 q^{69} - 120 q^{71} - 216 q^{73} + 732 q^{75} + 3480 q^{77} + 2808 q^{79} + 3348 q^{81} + 4464 q^{83} + 2160 q^{85} + 4824 q^{87} + 4029 q^{89} + 270 q^{91} + 1164 q^{93} - 1650 q^{95} - 3483 q^{97} - 5076 q^{99}+O(q^{100}) \) 54 * q + 12 * q^5 - 48 * q^9 - 87 * q^11 + 234 * q^15 + 204 * q^17 - 12 * q^21 + 96 * q^23 - 216 * q^25 + 27 * q^27 + 318 * q^29 - 54 * q^31 + 63 * q^33 + 6 * q^35 + 66 * q^39 + 867 * q^41 - 513 * q^43 - 306 * q^45 - 1548 * q^47 + 594 * q^49 - 1368 * q^51 - 1068 * q^53 - 1269 * q^57 - 1218 * q^59 - 54 * q^61 + 30 * q^63 + 96 * q^65 - 2997 * q^67 + 1476 * q^69 - 120 * q^71 - 216 * q^73 + 732 * q^75 + 3480 * q^77 + 2808 * q^79 + 3348 * q^81 + 4464 * q^83 + 2160 * q^85 + 4824 * q^87 + 4029 * q^89 + 270 * q^91 + 1164 * q^93 - 1650 * q^95 - 3483 * q^97 - 5076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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