LMFDB - Embedded newform 108.4.i.a.97.7

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			97.7
Character	$\chi$	$=$	108.97
Dual form			108.4.i.a.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.27095 + 4.67363i) q^{3} +(-10.0092 - 3.64305i) q^{5} +(-2.90933 + 16.4997i) q^{7} +(-16.6855 + 21.2272i) q^{9} +O(q^{10})$	\(q+(2.27095 + 4.67363i) q^{3} +(-10.0092 - 3.64305i) q^{5} +(-2.90933 + 16.4997i) q^{7} +(-16.6855 + 21.2272i) q^{9} +(3.53602 - 1.28701i) q^{11} +(-55.0460 + 46.1890i) q^{13} +(-5.70417 - 55.0525i) q^{15} +(-14.0443 - 24.3254i) q^{17} +(4.34509 - 7.52591i) q^{19} +(-83.7201 + 23.8728i) q^{21} +(4.21963 + 23.9307i) q^{23} +(-8.84313 - 7.42027i) q^{25} +(-137.100 - 29.7761i) q^{27} +(183.135 + 153.668i) q^{29} +(45.3635 + 257.269i) q^{31} +(14.0451 + 13.6033i) q^{33} +(89.2293 - 154.550i) q^{35} +(50.0527 + 86.6937i) q^{37} +(-340.877 - 152.371i) q^{39} +(177.609 - 149.031i) q^{41} +(220.317 - 80.1887i) q^{43} +(244.341 - 151.681i) q^{45} +(98.9672 - 561.271i) q^{47} +(58.5403 + 21.3069i) q^{49} +(81.7939 - 120.879i) q^{51} +368.316 q^{53} -40.0814 q^{55} +(45.0408 + 3.21632i) q^{57} +(-485.116 - 176.568i) q^{59} +(-106.741 + 605.358i) q^{61} +(-301.697 - 337.063i) q^{63} +(719.236 - 261.780i) q^{65} +(-264.013 + 221.533i) q^{67} +(-102.261 + 74.0665i) q^{69} +(496.578 + 860.098i) q^{71} +(-180.607 + 312.820i) q^{73} +(14.5972 - 58.1806i) q^{75} +(10.9477 + 62.0874i) q^{77} +(127.623 + 107.088i) q^{79} +(-172.185 - 708.374i) q^{81} +(-718.475 - 602.872i) q^{83} +(51.9533 + 294.642i) q^{85} +(-302.298 + 1204.88i) q^{87} +(-404.414 + 700.465i) q^{89} +(-601.956 - 1042.62i) q^{91} +(-1099.36 + 796.258i) q^{93} +(-70.9082 + 59.4990i) q^{95} +(1723.85 - 627.431i) q^{97} +(-31.6809 + 96.5340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	2.27095	+	4.67363i	0.437045	+	0.899440i
$3$	2.27095	+	4.67363i	0.437045	+	0.899440i
$4$		0			0
$5$	−10.0092	−	3.64305i	−0.895251	−	0.325845i	−0.146903	−	0.989151i	$-0.546930\pi$
$5$	−10.0092	−	3.64305i	−0.895251	−	0.325845i	−0.748348	+	0.663306i	$0.769153\pi$
$6$		0			0
$7$	−2.90933	+	16.4997i	−0.157089	+	0.890897i	0.799762	+	0.600318i	$0.204959\pi$
$7$	−2.90933	+	16.4997i	−0.157089	+	0.890897i	−0.956851	+	0.290580i	$0.906152\pi$
$8$		0			0
$9$	−16.6855	+	21.2272i	−0.617983	+	0.786191i
$10$		0			0
$11$	3.53602	−	1.28701i	0.0969227	−	0.0352770i	−0.293104	−	0.956081i	$-0.594688\pi$
$11$	3.53602	−	1.28701i	0.0969227	−	0.0352770i	0.390026	+	0.920804i	$0.372466\pi$
$12$		0			0
$13$	−55.0460	+	46.1890i	−1.17438	+	0.985426i	−0.174385	+	0.984678i	$0.555794\pi$
$13$	−55.0460	+	46.1890i	−1.17438	+	0.985426i	−1.00000		0.000748193i	$0.999762\pi$
$14$		0			0
$15$	−5.70417	−	55.0525i	−0.0981874	−	0.947633i
$16$		0			0
$17$	−14.0443	−	24.3254i	−0.200367	−	0.347046i	0.748280	−	0.663383i	$-0.230880\pi$
$17$	−14.0443	−	24.3254i	−0.200367	−	0.347046i	−0.948647	+	0.316338i	$0.897547\pi$
$18$		0			0
$19$	4.34509	−	7.52591i	0.0524648	−	0.0908717i	−0.838600	−	0.544747i	$-0.816626\pi$
$19$	4.34509	−	7.52591i	0.0524648	−	0.0908717i	0.891065	+	0.453876i	$0.149959\pi$
$20$		0			0
$21$	−83.7201	+	23.8728i	−0.869964	+	0.248070i
$22$		0			0
$23$	4.21963	+	23.9307i	0.0382545	+	0.216952i	0.997942	−	0.0641155i	$-0.0204226\pi$
$23$	4.21963	+	23.9307i	0.0382545	+	0.216952i	−0.959688	+	0.281068i	$0.909312\pi$
$24$		0			0
$25$	−8.84313	−	7.42027i	−0.0707451	−	0.0593622i
$26$		0			0
$27$	−137.100	−	29.7761i	−0.977218	−	0.212238i
$28$		0			0
$29$	183.135	+	153.668i	1.17267	+	0.983983i	1.00000		0.000996932i	$-0.000317333\pi$
$29$	183.135	+	153.668i	1.17267	+	0.983983i	0.172666	+	0.984980i	$0.444762\pi$
$30$		0			0
$31$	45.3635	+	257.269i	0.262823	+	1.49055i	0.775162	+	0.631762i	$0.217668\pi$
$31$	45.3635	+	257.269i	0.262823	+	1.49055i	−0.512339	+	0.858783i	$0.671221\pi$
$32$		0			0
$33$	14.0451	+	13.6033i	0.0740891	+	0.0717585i
$34$		0			0
$35$	89.2293	−	154.550i	0.430928	−	0.746390i
$36$		0			0
$37$	50.0527	+	86.6937i	0.222395	+	0.385199i	0.955535	−	0.294879i	$-0.0952793\pi$
$37$	50.0527	+	86.6937i	0.222395	+	0.385199i	−0.733140	+	0.680078i	$0.761946\pi$
$38$		0			0
$39$	−340.877	−	152.371i	−1.39959	−	0.625613i
$40$		0			0
$41$	177.609	−	149.031i	0.676531	−	0.567677i	−0.238459	−	0.971153i	$-0.576642\pi$
$41$	177.609	−	149.031i	0.676531	−	0.567677i	0.914991	+	0.403475i	$0.132198\pi$
$42$		0			0
$43$	220.317	−	80.1887i	0.781348	−	0.284387i	0.0796135	−	0.996826i	$-0.474631\pi$
$43$	220.317	−	80.1887i	0.781348	−	0.284387i	0.701735	+	0.712438i	$0.252409\pi$
$44$		0			0
$45$	244.341	−	151.681i	0.809426	−	0.502472i
$46$		0			0
$47$	98.9672	−	561.271i	0.307146	−	1.74191i	−0.306083	−	0.952005i	$-0.599019\pi$
$47$	98.9672	−	561.271i	0.307146	−	1.74191i	0.613229	−	0.789905i	$-0.289870\pi$
$48$		0			0
$49$	58.5403	+	21.3069i	0.170671	+	0.0621193i
$50$		0			0
$51$	81.7939	−	120.879i	0.224577	−	0.331892i
$52$		0			0
$53$	368.316			0.954567			0.477283	−	0.878749i	$-0.341622\pi$
$53$	368.316			0.954567			0.477283	+	0.878749i	$0.341622\pi$
$54$		0			0
$55$	−40.0814			−0.0982649
$56$		0			0
$57$	45.0408	+	3.21632i	0.104663	+	0.00747389i
$58$		0			0
$59$	−485.116	−	176.568i	−1.07045	−	0.389613i	−0.254107	−	0.967176i	$-0.581782\pi$
$59$	−485.116	−	176.568i	−1.07045	−	0.389613i	−0.816346	+	0.577563i	$0.804004\pi$
$60$		0			0
$61$	−106.741	+	605.358i	−0.224046	+	1.27063i	0.640456	+	0.767995i	$0.278746\pi$
$61$	−106.741	+	605.358i	−0.224046	+	1.27063i	−0.864501	+	0.502631i	$0.832366\pi$
$62$		0			0
$63$	−301.697	−	337.063i	−0.603337	−	0.674062i
$64$		0			0
$65$	719.236	−	261.780i	1.37246	−	0.499536i
$66$		0			0
$67$	−264.013	+	221.533i	−0.481407	+	0.403949i	−0.850935	−	0.525271i	$-0.823964\pi$
$67$	−264.013	+	221.533i	−0.481407	+	0.403949i	0.369528	+	0.929220i	$0.379520\pi$
$68$		0			0
$69$	−102.261	+	74.0665i	−0.178416	+	0.129225i
$70$		0			0
$71$	496.578	+	860.098i	0.830041	+	1.43767i	0.898005	+	0.439986i	$0.145017\pi$
$71$	496.578	+	860.098i	0.830041	+	1.43767i	−0.0679634	+	0.997688i	$0.521650\pi$
$72$		0			0
$73$	−180.607	+	312.820i	−0.289568	+	0.501546i	−0.973707	−	0.227806i	$-0.926845\pi$
$73$	−180.607	+	312.820i	−0.289568	+	0.501546i	0.684139	+	0.729352i	$0.260178\pi$
$74$		0			0
$75$	14.5972	−	58.1806i	0.0224739	−	0.0895748i
$76$		0			0
$77$	10.9477	+	62.0874i	0.0162027	+	0.0918898i
$78$		0			0
$79$	127.623	+	107.088i	0.181756	+	0.152511i	0.729126	−	0.684379i	$-0.239927\pi$
$79$	127.623	+	107.088i	0.181756	+	0.152511i	−0.547371	+	0.836890i	$0.684371\pi$
$80$		0			0
$81$	−172.185	−	708.374i	−0.236193	−	0.971706i
$82$		0			0
$83$	−718.475	−	602.872i	−0.950156	−	0.797275i	0.0291680	−	0.999575i	$-0.490714\pi$
$83$	−718.475	−	602.872i	−0.950156	−	0.797275i	−0.979324	+	0.202299i	$0.935159\pi$
$84$		0			0
$85$	51.9533	+	294.642i	0.0662956	+	0.375981i
$86$		0			0
$87$	−302.298	+	1204.88i	−0.372526	+	1.48479i
$88$		0			0
$89$	−404.414	+	700.465i	−0.481660	+	0.834260i	−0.999778	−	0.0210490i	$-0.993299\pi$
$89$	−404.414	+	700.465i	−0.481660	+	0.834260i	0.518118	+	0.855309i	$0.326633\pi$
$90$		0			0
$91$	−601.956	−	1042.62i	−0.693430	−	1.20106i
$92$		0			0
$93$	−1099.36	+	796.258i	−1.22579	+	0.887829i
$94$		0			0
$95$	−70.9082	+	59.4990i	−0.0765792	+	0.0642576i
$96$		0			0
$97$	1723.85	−	627.431i	1.80444	−	0.656762i	0.806598	−	0.591100i	$-0.201306\pi$
$97$	1723.85	−	627.431i	1.80444	−	0.656762i	0.997842	−	0.0656621i	$-0.0209160\pi$
$98$		0			0
$99$	−31.6809	+	96.5340i	−0.0321622	+	0.0980004i
$100$		0			0
$101$	−104.411	+	592.143i	−0.102864	+	0.583370i	0.889188	+	0.457542i	$0.151270\pi$
$101$	−104.411	+	592.143i	−0.102864	+	0.583370i	−0.992052	+	0.125829i	$0.959841\pi$
$102$		0			0
$103$	61.8832	+	22.5237i	0.0591994	+	0.0215468i	0.371450	−	0.928453i	$-0.378861\pi$
$103$	61.8832	+	22.5237i	0.0591994	+	0.0215468i	−0.312251	+	0.950000i	$0.601083\pi$
$104$		0			0
$105$	924.942	+	66.0493i	0.859668	+	0.0613881i
$106$		0			0
$107$	−1123.65			−1.01520			−0.507602	−	0.861591i	$-0.669468\pi$
$107$	−1123.65			−1.01520			−0.507602	+	0.861591i	$0.669468\pi$
$108$		0			0
$109$	−1790.18			−1.57310			−0.786550	−	0.617527i	$-0.788135\pi$
$109$	−1790.18			−1.57310			−0.786550	+	0.617527i	$0.788135\pi$
$110$		0			0
$111$	−291.507	+	430.805i	−0.249267	+	0.368380i
$112$		0			0
$113$	−1032.17	−	375.680i	−0.859281	−	0.312753i	−0.125462	−	0.992098i	$-0.540041\pi$
$113$	−1032.17	−	375.680i	−0.859281	−	0.312753i	−0.733818	+	0.679346i	$0.762264\pi$
$114$		0			0
$115$	44.9457	−	254.900i	0.0364453	−	0.206692i
$116$		0			0
$117$	−61.9904	−	1939.16i	−0.0489831	−	1.53227i
$118$		0			0
$119$	442.220	−	160.955i	0.340657	−	0.123989i
$120$		0			0
$121$	−1008.76	+	846.449i	−0.757895	+	0.635949i
$122$		0			0
$123$	1099.86	+	491.633i	0.806266	+	0.360399i
$124$		0			0
$125$	727.204	+	1259.55i	0.520345	+	0.901264i
$126$		0			0
$127$	1048.77	−	1816.52i	0.732782	−	1.26922i	−0.222908	−	0.974840i	$-0.571555\pi$
$127$	1048.77	−	1816.52i	0.732782	−	1.26922i	0.955690	−	0.294376i	$-0.0951118\pi$
$128$		0			0
$129$	875.101	+	847.573i	0.597274	+	0.578485i
$130$		0			0
$131$	−157.676	−	894.228i	−0.105162	−	0.596405i	−0.991155	−	0.132707i	$-0.957633\pi$
$131$	−157.676	−	894.228i	−0.105162	−	0.596405i	0.885993	−	0.463698i	$-0.153478\pi$
$132$		0			0
$133$	111.534	+	93.5878i	0.0727157	+	0.0610157i
$134$		0			0
$135$	1263.79	+	797.498i	0.805699	+	0.508427i
$136$		0			0
$137$	603.157	+	506.109i	0.376140	+	0.315619i	0.811185	−	0.584790i	$-0.198823\pi$
$137$	603.157	+	506.109i	0.376140	+	0.315619i	−0.435045	+	0.900409i	$0.643267\pi$
$138$		0			0
$139$	175.366	+	994.552i	0.107010	+	0.606883i	0.990398	+	0.138242i	$0.0441452\pi$
$139$	175.366	+	994.552i	0.107010	+	0.606883i	−0.883389	+	0.468641i	$0.844744\pi$
$140$		0			0
$141$	2847.92	−	812.084i	1.70098	−	0.485034i
$142$		0			0
$143$	−135.198	+	234.170i	−0.0790617	+	0.136939i
$144$		0			0
$145$	−1273.21	−	2205.27i	−0.729204	−	1.26302i
$146$		0			0
$147$	33.3617	+	321.982i	0.0187185	+	0.180658i
$148$		0			0
$149$	−2624.88	+	2202.54i	−1.44321	+	1.21100i	−0.505859	+	0.862616i	$0.668825\pi$
$149$	−2624.88	+	2202.54i	−1.44321	+	1.21100i	−0.937352	+	0.348383i	$0.886731\pi$
$150$		0			0
$151$	2253.91	−	820.356i	1.21471	−	0.442117i	0.346372	−	0.938097i	$-0.387413\pi$
$151$	2253.91	−	820.356i	1.21471	−	0.442117i	0.868334	+	0.495980i	$0.165191\pi$
$152$		0			0
$153$	750.695	+	107.762i	0.396667	+	0.0569417i
$154$		0			0
$155$	483.193	−	2740.32i	0.250393	−	1.42005i
$156$		0			0
$157$	−1595.55	−	580.732i	−0.811073	−	0.295207i	−0.0970061	−	0.995284i	$-0.530927\pi$
$157$	−1595.55	−	580.732i	−0.811073	−	0.295207i	−0.714067	+	0.700077i	$0.753149\pi$
$158$		0			0
$159$	836.427	+	1721.37i	0.417189	+	0.858575i
$160$		0			0
$161$	−407.125			−0.199291
$162$		0			0
$163$	1962.35			0.942966			0.471483	−	0.881875i	$-0.343719\pi$
$163$	1962.35			0.942966			0.471483	+	0.881875i	$0.343719\pi$
$164$		0			0
$165$	−91.0229	−	187.325i	−0.0429462	−	0.0883834i
$166$		0			0
$167$	−2348.59	−	854.817i	−1.08826	−	0.396094i	−0.265284	−	0.964170i	$-0.585466\pi$
$167$	−2348.59	−	854.817i	−1.08826	−	0.396094i	−0.822976	+	0.568076i	$0.807688\pi$
$168$		0			0
$169$	515.125	−	2921.42i	0.234467	−	1.32973i
$170$		0			0
$171$	87.2536	+	217.808i	0.0390202	+	0.0974046i
$172$		0			0
$173$	1234.35	−	449.268i	0.542463	−	0.197440i	−0.0562317	−	0.998418i	$-0.517909\pi$
$173$	1234.35	−	449.268i	0.542463	−	0.197440i	0.598695	+	0.800977i	$0.295686\pi$
$174$		0			0
$175$	148.159	−	124.321i	0.0639989	−	0.0537014i
$176$		0			0
$177$	−276.464	−	2668.23i	−0.117403	−	1.13309i
$178$		0			0
$179$	1735.29	+	3005.61i	0.724589	+	1.25503i	0.959143	+	0.282922i	$0.0913038\pi$
$179$	1735.29	+	3005.61i	0.724589	+	1.25503i	−0.234554	+	0.972103i	$0.575363\pi$
$180$		0			0
$181$	1010.33	−	1749.94i	0.414901	−	0.718630i	−0.580517	−	0.814248i	$-0.697149\pi$
$181$	1010.33	−	1749.94i	0.414901	−	0.718630i	0.995418	+	0.0956180i	$0.0304827\pi$
$182$		0			0
$183$	−3071.62	+	875.872i	−1.24077	+	0.353805i
$184$		0			0
$185$	−185.157	−	1050.08i	−0.0735841	−	0.417316i
$186$		0			0
$187$	−80.9677	−	67.9400i	−0.0316628	−	0.0265683i
$188$		0			0
$189$	890.165	−	2175.47i	0.342592	−	0.837261i
$190$		0			0
$191$	1101.83	+	924.547i	0.417412	+	0.350251i	0.827178	−	0.561940i	$-0.189945\pi$
$191$	1101.83	+	924.547i	0.417412	+	0.350251i	−0.409765	+	0.912191i	$0.634389\pi$
$192$		0			0
$193$	165.021	+	935.881i	0.0615465	+	0.349048i	0.999993	+	0.00362415i	$0.00115361\pi$
$193$	165.021	+	935.881i	0.0615465	+	0.349048i	−0.938447	+	0.345423i	$0.887735\pi$
$194$		0			0
$195$	2856.81	+	2766.95i	1.04913	+	1.01613i
$196$		0			0
$197$	630.410	−	1091.90i	0.227994	−	0.394898i	−0.729219	−	0.684280i	$-0.760117\pi$
$197$	630.410	−	1091.90i	0.227994	−	0.394898i	0.957214	+	0.289382i	$0.0934499\pi$
$198$		0			0
$199$	45.3986	+	78.6327i	0.0161720	+	0.0280107i	0.873998	−	0.485929i	$-0.161519\pi$
$199$	45.3986	+	78.6327i	0.0161720	+	0.0280107i	−0.857826	+	0.513940i	$0.828185\pi$
$200$		0			0
$201$	−1634.92	−	730.806i	−0.573724	−	0.256453i
$202$		0			0
$203$	−3068.28	+	2574.59i	−1.06084	+	0.890152i
$204$		0			0
$205$	−2320.65	+	844.647i	−0.790640	+	0.287769i
$206$		0			0
$207$	−578.388	−	309.726i	−0.194206	−	0.103997i
$208$		0			0
$209$	5.67842	−	32.2039i	0.00187935	−	0.0106583i
$210$		0			0
$211$	3332.78	+	1213.03i	1.08739	+	0.395776i	0.822652	−	0.568546i	$-0.192494\pi$
$211$	3332.78	+	1213.03i	1.08739	+	0.395776i	0.264734	+	0.964322i	$0.414716\pi$
$212$		0			0
$213$	−2892.07	+	4274.06i	−0.930335	+	1.37490i
$214$		0			0
$215$	−2497.33			−0.792169
$216$		0			0
$217$	−4376.83			−1.36921
$218$		0			0
$219$	−1872.15	−	133.689i	−0.577664	−	0.0412505i
$220$		0			0
$221$	1896.65	+	690.323i	0.577295	+	0.210118i
$222$		0			0
$223$	168.174	−	953.762i	0.0505012	−	0.286406i	−0.949090	−	0.315006i	$-0.897994\pi$
$223$	168.174	−	953.762i	0.0505012	−	0.286406i	0.999591	+	0.0285993i	$0.00910469\pi$
$224$		0			0
$225$	305.064	−	63.9034i	0.0903893	−	0.0189343i
$226$		0			0
$227$	−1558.12	+	567.109i	−0.455577	+	0.165816i	−0.559608	−	0.828758i	$-0.689048\pi$
$227$	−1558.12	+	567.109i	−0.455577	+	0.165816i	0.104031	+	0.994574i	$0.466826\pi$
$228$		0			0
$229$	−3824.88	+	3209.45i	−1.10373	+	0.926142i	−0.997671	−	0.0682170i	$-0.978269\pi$
$229$	−3824.88	+	3209.45i	−1.10373	+	0.926142i	−0.106063	+	0.994359i	$0.533825\pi$
$230$		0			0
$231$	−265.312	+	192.163i	−0.0755680	+	0.0547333i
$232$		0			0
$233$	1892.72	+	3278.28i	0.532171	+	0.921748i	0.999295	+	0.0375555i	$0.0119571\pi$
$233$	1892.72	+	3278.28i	0.532171	+	0.921748i	−0.467123	+	0.884192i	$0.654710\pi$
$234$		0			0
$235$	−3035.32	+	5257.33i	−0.842565	+	1.45936i
$236$		0			0
$237$	−210.665	+	839.654i	−0.0577391	+	0.230133i
$238$		0			0
$239$	−280.643	−	1591.60i	−0.0759551	−	0.430763i	−0.998944	−	0.0459369i	$-0.985373\pi$
$239$	−280.643	−	1591.60i	−0.0759551	−	0.430763i	0.922989	−	0.384826i	$-0.125738\pi$
$240$		0			0
$241$	4034.39	+	3385.25i	1.07833	+	0.904826i	0.995781	−	0.0917605i	$-0.0292494\pi$
$241$	4034.39	+	3385.25i	1.07833	+	0.904826i	0.0825491	+	0.996587i	$0.473694\pi$
$242$		0			0
$243$	2919.65	−	2413.41i	0.770764	−	0.637121i
$244$		0			0
$245$	−508.320	−	426.531i	−0.132553	−	0.111225i
$246$		0			0
$247$	108.435	+	614.966i	0.0279335	+	0.158418i
$248$		0			0
$249$	1185.98	−	4726.98i	0.301840	−	1.20305i
$250$		0			0
$251$	2000.32	−	3464.66i	0.503025	−	0.871264i	−0.496969	−	0.867768i	$-0.665554\pi$
$251$	2000.32	−	3464.66i	0.503025	−	0.871264i	0.999994	−	0.00349620i	$-0.00111288\pi$
$252$		0			0
$253$	45.7196	+	79.1887i	0.0113611	+	0.0196781i
$254$		0			0
$255$	−1259.06	+	911.928i	−0.309198	+	0.223950i
$256$		0			0
$257$	5312.76	−	4457.93i	1.28950	−	1.08202i	0.297638	−	0.954679i	$-0.403801\pi$
$257$	5312.76	−	4457.93i	1.28950	−	1.08202i	0.991859	−	0.127338i	$-0.0406432\pi$
$258$		0			0
$259$	−1576.04	+	573.630i	−0.378109	+	0.137620i
$260$		0			0
$261$	−6317.65	+	1323.39i	−1.49829	+	0.313854i
$262$		0			0
$263$	902.671	−	5119.30i	0.211639	−	1.20027i	−0.675005	−	0.737813i	$-0.735859\pi$
$263$	902.671	−	5119.30i	0.211639	−	1.20027i	0.886644	−	0.462452i	$-0.153030\pi$
$264$		0			0
$265$	−3686.55	−	1341.79i	−0.854577	−	0.311041i
$266$		0			0
$267$	−4192.12	−	299.355i	−0.960874	−	0.0686151i
$268$		0			0
$269$	−3202.65			−0.725907			−0.362953	−	0.931807i	$-0.618232\pi$
$269$	−3202.65			−0.725907			−0.362953	+	0.931807i	$0.618232\pi$
$270$		0			0
$271$	2563.49			0.574616			0.287308	−	0.957838i	$-0.407240\pi$
$271$	2563.49			0.574616			0.287308	+	0.957838i	$0.407240\pi$
$272$		0			0
$273$	3505.79	−	5181.05i	0.777217	−	1.14861i
$274$		0			0
$275$	−40.8194	−	14.8570i	−0.00895092	−	0.00325787i
$276$		0			0
$277$	−934.933	+	5302.27i	−0.202797	+	1.15012i	0.698073	+	0.716027i	$0.254041\pi$
$277$	−934.933	+	5302.27i	−0.202797	+	1.15012i	−0.900869	+	0.434090i	$0.857070\pi$
$278$		0			0
$279$	−6218.01	−	3329.74i	−1.33427	−	0.714503i
$280$		0			0
$281$	3415.67	−	1243.20i	0.725131	−	0.263926i	0.0470287	−	0.998894i	$-0.485025\pi$
$281$	3415.67	−	1243.20i	0.725131	−	0.263926i	0.678102	+	0.734967i	$0.262803\pi$
$282$		0			0
$283$	5021.18	−	4213.27i	1.05469	−	0.884993i	0.0611141	−	0.998131i	$-0.480535\pi$
$283$	5021.18	−	4213.27i	1.05469	−	0.884993i	0.993579	+	0.113138i	$0.0360902\pi$
$284$		0			0
$285$	−439.105	−	196.279i	−0.0912644	−	0.0407949i
$286$		0			0
$287$	1942.24	+	3364.06i	0.399466	+	0.691896i
$288$		0			0
$289$	2062.02	−	3571.52i	0.419706	−	0.726953i
$290$		0			0
$291$	6847.16	+	6631.77i	1.37934	+	1.33595i
$292$		0			0
$293$	88.6969	+	503.025i	0.0176851	+	0.100297i	0.992373	−	0.123274i	$-0.0393395\pi$
$293$	88.6969	+	503.025i	0.0176851	+	0.100297i	−0.974688	+	0.223571i	$0.928228\pi$
$294$		0			0
$295$	4212.38	+	3534.61i	0.831371	+	0.697603i
$296$		0			0
$297$	−523.110	+	71.1594i	−0.102202	+	0.0139027i
$298$		0			0
$299$	−1337.61	−	1122.39i	−0.258716	−	0.217088i
$300$		0			0
$301$	682.111	+	3868.44i	0.130619	+	0.740775i
$302$		0			0
$303$	−3004.57	+	856.752i	−0.569663	+	0.162439i
$304$		0			0
$305$	3273.75	−	5670.29i	0.614604	−	1.06452i
$306$		0			0
$307$	975.162	+	1689.03i	0.181288	+	0.314000i	0.942319	−	0.334715i	$-0.108640\pi$
$307$	975.162	+	1689.03i	0.181288	+	0.314000i	−0.761031	+	0.648715i	$0.775307\pi$
$308$		0			0
$309$	35.2668	+	340.369i	0.00649274	+	0.0626632i
$310$		0			0
$311$	4843.13	−	4063.87i	0.883051	−	0.740968i	−0.0837528	−	0.996487i	$-0.526691\pi$
$311$	4843.13	−	4063.87i	0.883051	−	0.740968i	0.966804	+	0.255518i	$0.0822462\pi$
$312$		0			0
$313$	472.116	−	171.836i	0.0852575	−	0.0310312i	−0.299039	−	0.954241i	$-0.596666\pi$
$313$	472.116	−	171.836i	0.0852575	−	0.0310312i	0.384297	+	0.923210i	$0.374444\pi$
$314$		0			0
$315$	1791.81	+	4472.83i	0.320499	+	0.800049i
$316$		0			0
$317$	−1665.94	+	9448.01i	−0.295169	+	1.67398i	0.371348	+	0.928494i	$0.378896\pi$
$317$	−1665.94	+	9448.01i	−0.295169	+	1.67398i	−0.666517	+	0.745490i	$0.732215\pi$
$318$		0			0
$319$	845.341	+	307.679i	0.148370	+	0.0540022i
$320$		0			0
$321$	−2551.75	−	5251.50i	−0.443690	−	0.913116i
$322$		0			0
$323$	−244.094			−0.0420488
$324$		0			0
$325$	829.514			0.141579
$326$		0			0
$327$	−4065.41	−	8366.62i	−0.687515	−	1.41491i
$328$		0			0
$329$	8972.84	+	3265.85i	1.50361	+	0.547271i
$330$		0			0
$331$	862.280	−	4890.23i	0.143188	−	0.812059i	−0.825616	−	0.564232i	$-0.809172\pi$
$331$	862.280	−	4890.23i	0.143188	−	0.812059i	0.968804	−	0.247827i	$-0.0797165\pi$
$332$		0			0
$333$	−2675.42	−	384.057i	−0.440276	−	0.0632017i
$334$		0			0
$335$	3449.62	−	1255.56i	0.562605	−	0.204771i
$336$		0			0
$337$	−350.546	+	294.143i	−0.0566632	+	0.0475460i	−0.670679	−	0.741747i	$-0.733997\pi$
$337$	−350.546	+	294.143i	−0.0566632	+	0.0475460i	0.614016	+	0.789293i	$0.289553\pi$
$338$		0			0
$339$	−588.228	−	5677.14i	−0.0942423	−	0.909558i
$340$		0			0
$341$	491.513	+	851.326i	0.0780555	+	0.135196i
$342$		0			0
$343$	−3395.21	+	5880.68i	−0.534473	+	0.925735i
$344$		0			0
$345$	1293.38	−	368.806i	0.201835	−	0.0575532i
$346$		0			0
$347$	645.039	+	3658.20i	0.0997911	+	0.565943i	0.993174	+	0.116646i	$0.0372144\pi$
$347$	645.039	+	3658.20i	0.0997911	+	0.565943i	−0.893382	+	0.449297i	$0.851675\pi$
$348$		0			0
$349$	−2640.17	−	2215.37i	−0.404943	−	0.339788i	0.417457	−	0.908696i	$-0.362921\pi$
$349$	−2640.17	−	2215.37i	−0.404943	−	0.339788i	−0.822401	+	0.568909i	$0.807366\pi$
$350$		0			0
$351$	8922.13	−	4693.46i	1.35677	−	0.713727i
$352$		0			0
$353$	−2239.14	−	1878.86i	−0.337613	−	0.283291i	0.458181	−	0.888859i	$-0.348501\pi$
$353$	−2239.14	−	1878.86i	−0.337613	−	0.283291i	−0.795793	+	0.605569i	$0.792946\pi$
$354$		0			0
$355$	−1836.97	−	10418.0i	−0.274637	−	1.55754i
$356$		0			0
$357$	1756.50	+	1701.25i	0.260403	+	0.252212i
$358$		0			0
$359$	6470.47	−	11207.2i	0.951249	−	1.64761i	0.208522	−	0.978018i	$-0.433135\pi$
$359$	6470.47	−	11207.2i	0.951249	−	1.64761i	0.742727	−	0.669594i	$-0.233532\pi$
$360$		0			0
$361$	3391.74	+	5874.67i	0.494495	+	0.856490i
$362$		0			0
$363$	−6246.83	−	2792.31i	−0.903232	−	0.403742i
$364$		0			0
$365$	2947.35	−	2473.12i	0.422662	−	0.354655i
$366$		0			0
$367$	−12298.8	+	4476.41i	−1.74930	+	0.636694i	−0.999683	−	0.0251747i	$-0.991986\pi$
$367$	−12298.8	+	4476.41i	−1.74930	+	0.636694i	−0.749620	+	0.661869i	$0.769764\pi$
$368$		0			0
$369$	200.015	+	6256.79i	0.0282178	+	0.882698i
$370$		0			0
$371$	−1071.55	+	6077.08i	−0.149952	+	0.850421i
$372$		0			0
$373$	8627.89	+	3140.29i	1.19768	+	0.435920i	0.862414	−	0.506203i	$-0.168951\pi$
$373$	8627.89	+	3140.29i	1.19768	+	0.435920i	0.335267	+	0.942123i	$0.391174\pi$
$374$		0			0
$375$	−4235.24	+	6259.07i	−0.583218	+	0.861911i
$376$		0			0
$377$	−17178.6			−2.34680
$378$		0			0
$379$	2260.05			0.306308			0.153154	−	0.988202i	$-0.451057\pi$
$379$	2260.05			0.306308			0.153154	+	0.988202i	$0.451057\pi$
$380$		0			0
$381$	10871.5	+	776.320i	1.46184	+	0.104389i
$382$		0			0
$383$	−9927.52	−	3613.32i	−1.32447	−	0.482068i	−0.419583	−	0.907717i	$-0.637824\pi$
$383$	−9927.52	−	3613.32i	−1.32447	−	0.482068i	−0.904888	+	0.425649i	$0.860046\pi$
$384$		0			0
$385$	116.610	−	661.329i	0.0154364	−	0.0875440i
$386$		0			0
$387$	−1973.93	+	6014.69i	−0.259277	+	0.790036i
$388$		0			0
$389$	−9659.45	+	3515.75i	−1.25901	+	0.458241i	−0.883436	−	0.468552i	$-0.844776\pi$
$389$	−9659.45	+	3515.75i	−1.25901	+	0.458241i	−0.375571	+	0.926793i	$0.622554\pi$
$390$		0			0
$391$	522.862	−	438.733i	0.0676273	−	0.0567460i
$392$		0			0
$393$	3821.21	−	2767.67i	0.490470	−	0.355243i
$394$		0			0
$395$	−887.276	−	1536.81i	−0.113022	−	0.195760i
$396$		0			0
$397$	1494.01	−	2587.71i	0.188873	−	0.327137i	−0.756002	−	0.654569i	$-0.772850\pi$
$397$	1494.01	−	2587.71i	0.188873	−	0.327137i	0.944875	+	0.327432i	$0.106183\pi$
$398$		0			0
$399$	−184.107	+	733.800i	−0.0230999	+	0.0920700i
$400$		0			0
$401$	1287.47	+	7301.59i	0.160332	+	0.909287i	0.953748	+	0.300607i	$0.0971894\pi$
$401$	1287.47	+	7301.59i	0.160332	+	0.909287i	−0.793416	+	0.608680i	$0.791700\pi$
$402$		0			0
$403$	−14380.1	−	12066.3i	−1.77748	−	1.49148i
$404$		0			0
$405$	−857.208	+	7717.54i	−0.105173	+	0.946883i
$406$		0			0
$407$	288.562	+	242.133i	0.0351438	+	0.0294891i
$408$		0			0
$409$	−136.025	−	771.437i	−0.0164450	−	0.0932643i	0.975481	−	0.220086i	$-0.0706337\pi$
$409$	−136.025	−	771.437i	−0.0164450	−	0.0932643i	−0.991926	+	0.126821i	$0.959523\pi$
$410$		0			0
$411$	−995.622	+	3968.28i	−0.119490	+	0.476255i
$412$		0			0
$413$	4324.67	−	7490.55i	0.515262	−	0.892460i
$414$		0			0
$415$	4995.07	+	8651.72i	0.590840	+	1.02336i
$416$		0			0
$417$	−4249.92	+	3078.18i	−0.499087	+	0.361484i
$418$		0			0
$419$	−7526.09	+	6315.14i	−0.877502	+	0.736312i	−0.965664	−	0.259794i	$-0.916345\pi$
$419$	−7526.09	+	6315.14i	−0.877502	+	0.736312i	0.0881616	+	0.996106i	$0.471901\pi$
$420$		0			0
$421$	1020.41	−	371.400i	0.118128	−	0.0429951i	−0.282280	−	0.959332i	$-0.591091\pi$
$421$	1020.41	−	371.400i	0.118128	−	0.0429951i	0.400408	+	0.916337i	$0.368868\pi$
$422$		0			0
$423$	10262.9	+	11465.9i	1.17966	+	1.31795i
$424$		0			0
$425$	−56.3056	+	319.325i	−0.00642641	+	0.0364460i
$426$		0			0
$427$	−9677.65	−	3522.38i	−1.09680	−	0.399203i
$428$		0			0
$429$	−1401.45	−	100.076i	−0.157722	−	0.0112628i
$430$		0			0
$431$	−4258.28			−0.475903			−0.237951	−	0.971277i	$-0.576476\pi$
$431$	−4258.28			−0.475903			−0.237951	+	0.971277i	$0.576476\pi$
$432$		0			0
$433$	7152.99			0.793882			0.396941	−	0.917844i	$-0.370072\pi$
$433$	7152.99			0.793882			0.396941	+	0.917844i	$0.370072\pi$
$434$		0			0
$435$	7415.20	−	10958.6i	0.817314	−	1.20787i
$436$		0			0
$437$	198.435	+	72.2244i	0.0217218	+	0.00790609i
$438$		0			0
$439$	−1804.32	+	10232.8i	−0.196162	+	1.11249i	0.714591	+	0.699542i	$0.246613\pi$
$439$	−1804.32	+	10232.8i	−0.196162	+	1.11249i	−0.910754	+	0.412950i	$0.864498\pi$
$440$		0			0
$441$	−1429.06	+	887.127i	−0.154310	+	0.0957917i
$442$		0			0
$443$	−12028.7	+	4378.09i	−1.29007	+	0.469548i	−0.893750	−	0.448565i	$-0.851935\pi$
$443$	−12028.7	+	4378.09i	−1.29007	+	0.469548i	−0.396321	+	0.918112i	$0.629713\pi$
$444$		0			0
$445$	6599.69	−	5537.80i	0.703046	−	0.589926i
$446$		0			0
$447$	−16254.8	−	7265.85i	−1.71997	−	0.768821i
$448$		0			0
$449$	3046.78	+	5277.17i	0.320237	+	0.554666i	0.980537	−	0.196336i	$-0.0629043\pi$
$449$	3046.78	+	5277.17i	0.320237	+	0.554666i	−0.660300	+	0.751002i	$0.729571\pi$
$450$		0			0
$451$	436.223	−	755.560i	0.0455453	−	0.0788868i
$452$		0			0
$453$	8952.56	+	8670.94i	0.928539	+	0.899330i
$454$		0			0
$455$	2226.79	+	12628.7i	0.229436	+	1.30120i
$456$		0			0
$457$	−5464.80	−	4585.51i	−0.559371	−	0.469368i	0.318729	−	0.947846i	$-0.396744\pi$
$457$	−5464.80	−	4585.51i	−0.559371	−	0.469368i	−0.878099	+	0.478478i	$0.841189\pi$
$458$		0			0
$459$	1201.15	+	3753.19i	0.122146	+	0.381665i
$460$		0			0
$461$	9715.80	+	8152.53i	0.981583	+	0.823646i	0.984328	−	0.176350i	$-0.0564290\pi$
$461$	9715.80	+	8152.53i	0.981583	+	0.823646i	−0.00274406	+	0.999996i	$0.500873\pi$
$462$		0			0
$463$	−2328.16	−	13203.7i	−0.233691	−	1.32533i	−0.845353	−	0.534208i	$-0.820610\pi$
$463$	−2328.16	−	13203.7i	−0.233691	−	1.32533i	0.611663	−	0.791119i	$-0.290501\pi$
$464$		0			0
$465$	13904.6	−	3964.88i	1.38668	−	0.395413i
$466$		0			0
$467$	−68.4431	+	118.547i	−0.00678195	+	0.0117467i	−0.869396	−	0.494115i	$-0.835492\pi$
$467$	−68.4431	+	118.547i	−0.00678195	+	0.0117467i	0.862615	+	0.505862i	$0.168825\pi$
$468$		0			0
$469$	−2887.12	−	5000.63i	−0.284253	−	0.492341i
$470$		0			0
$471$	−909.290	−	8775.80i	−0.0889551	−	0.858530i
$472$		0			0
$473$	675.840	−	567.097i	0.0656980	−	0.0551272i
$474$		0			0
$475$	−94.2685	+	34.3109i	−0.00910597	+	0.00331430i
$476$		0			0
$477$	−6145.55	+	7818.30i	−0.589906	+	0.750472i
$478$		0			0
$479$	599.222	−	3398.35i	0.0571589	−	0.324164i	−0.942799	−	0.333362i	$-0.891817\pi$
$479$	599.222	−	3398.35i	0.0571589	−	0.324164i	0.999958	+	0.00919797i	$0.00292785\pi$
$480$		0			0
$481$	−6759.50	−	2460.26i	−0.640762	−	0.233218i
$482$		0			0
$483$	−924.561	−	1902.75i	−0.0870993	−	0.179251i
$484$		0			0
$485$	−19540.2			−1.82943
$486$		0			0
$487$	8808.83			0.819643			0.409821	−	0.912166i	$-0.365591\pi$
$487$	8808.83			0.819643			0.409821	+	0.912166i	$0.365591\pi$
$488$		0			0
$489$	4456.41	+	9171.31i	0.412119	+	0.848141i
$490$		0			0
$491$	11912.6	+	4335.83i	1.09493	+	0.398520i	0.825443	−	0.564485i	$-0.190925\pi$
$491$	11912.6	+	4335.83i	1.09493	+	0.398520i	0.269482	+	0.963005i	$0.413147\pi$
$492$		0			0
$493$	1166.05	−	6612.99i	0.106524	−	0.604126i
$494$		0			0
$495$	668.780	−	850.814i	0.0607261	−	0.0772550i
$496$		0			0
$497$	−15636.0	+	5691.05i	−1.41121	+	0.513639i
$498$		0			0
$499$	13503.0	−	11330.4i	1.21138	−	1.01647i	0.212149	−	0.977237i	$-0.431954\pi$
$499$	13503.0	−	11330.4i	1.21138	−	1.01647i	0.999230	−	0.0392306i	$-0.0124907\pi$
$500$		0			0
$501$	−1338.44	−	12917.7i	−0.119356	−	1.15194i
$502$		0			0
$503$	3751.33	+	6497.50i	0.332532	+	0.575962i	0.983008	−	0.183565i	$-0.0587637\pi$
$503$	3751.33	+	6497.50i	0.332532	+	0.575962i	−0.650476	+	0.759527i	$0.725430\pi$
$504$		0			0
$505$	3202.28	−	5546.51i	0.282177	−	0.488745i
$506$		0			0
$507$	14823.4	−	4226.90i	1.29848	−	0.370263i
$508$		0			0
$509$	−3912.83	−	22190.7i	−0.340733	−	1.93239i	−0.360925	−	0.932595i	$-0.617539\pi$
$509$	−3912.83	−	22190.7i	−0.340733	−	1.93239i	0.0201923	−	0.999796i	$-0.493572\pi$
$510$		0			0
$511$	−4635.98	−	3890.05i	−0.401338	−	0.336762i
$512$		0			0
$513$	−819.803	+	902.422i	−0.0705559	+	0.0776665i
$514$		0			0
$515$	−537.347	−	450.888i	−0.0459774	−	0.0385796i
$516$		0			0
$517$	−372.409	−	2112.04i	−0.0316799	−	0.179666i
$518$		0			0
$519$	4902.86	+	4748.64i	0.414666	+	0.401622i
$520$		0			0
$521$	10309.3	−	17856.2i	0.866906	−	1.50153i	0.00176401	−	0.999998i	$-0.499438\pi$
$521$	10309.3	−	17856.2i	0.866906	−	1.50153i	0.865142	−	0.501527i	$-0.167228\pi$
$522$		0			0
$523$	−3362.40	−	5823.85i	−0.281123	−	0.486920i	0.690538	−	0.723296i	$-0.257374\pi$
$523$	−3362.40	−	5823.85i	−0.281123	−	0.486920i	−0.971662	+	0.236376i	$0.924040\pi$
$524$		0			0
$525$	917.491	+	410.116i	0.0762716	+	0.0340932i
$526$		0			0
$527$	5621.08	−	4716.64i	0.464626	−	0.389868i
$528$		0			0
$529$	10878.4	−	3959.40i	0.894088	−	0.325421i
$530$		0			0
$531$	11842.5	−	7351.51i	0.967833	−	0.600807i
$532$		0			0
$533$	−2893.02	+	16407.1i	−0.235104	+	1.33334i
$534$		0			0
$535$	11246.8	+	4093.50i	0.908863	+	0.330799i
$536$		0			0
$537$	−10106.3	+	14935.7i	−0.812141	+	1.20023i
$538$		0			0
$539$	234.422			0.0187333
$540$		0			0
$541$	−9213.40			−0.732190			−0.366095	−	0.930577i	$-0.619306\pi$
$541$	−9213.40			−0.732190			−0.366095	+	0.930577i	$0.619306\pi$
$542$		0			0
$543$	10473.0	+	747.866i	0.827695	+	0.0591049i
$544$		0			0
$545$	17918.3	+	6521.71i	1.40832	+	0.512586i
$546$		0			0
$547$	−1180.97	+	6697.60i	−0.0923117	+	0.523526i	0.903226	+	0.429165i	$0.141192\pi$
$547$	−1180.97	+	6697.60i	−0.0923117	+	0.523526i	−0.995538	+	0.0943612i	$0.969919\pi$
$548$		0			0
$549$	−11069.0	−	12366.5i	−0.860498	−	0.961368i
$550$		0			0
$551$	1952.23	−	710.554i	0.150940	−	0.0549376i
$552$		0			0
$553$	−2138.22	+	1794.18i	−0.164424	+	0.137968i
$554$		0			0
$555$	4487.20	−	3250.04i	0.343191	−	0.248570i
$556$		0			0
$557$	−8957.05	−	15514.1i	−0.681369	−	1.18017i	−0.974563	−	0.224113i	$-0.928052\pi$
$557$	−8957.05	−	15514.1i	−0.681369	−	1.18017i	0.293194	−	0.956053i	$-0.405282\pi$
$558$		0			0
$559$	−8423.70	+	14590.3i	−0.637361	+	1.10394i
$560$		0			0
$561$	133.652	−	532.701i	0.0100585	−	0.0400903i
$562$		0			0
$563$	1738.41	+	9859.03i	0.130134	+	0.738026i	0.978125	+	0.208016i	$0.0667007\pi$
$563$	1738.41	+	9859.03i	0.130134	+	0.738026i	−0.847992	+	0.530010i	$0.822188\pi$
$564$		0			0
$565$	8962.62	+	7520.53i	0.667363	+	0.559984i
$566$		0			0
$567$	12188.9	−	780.097i	0.902794	−	0.0577795i
$568$		0			0
$569$	−11756.4	−	9864.81i	−0.866177	−	0.726809i	0.0971124	−	0.995273i	$-0.469039\pi$
$569$	−11756.4	−	9864.81i	−0.866177	−	0.726809i	−0.963290	+	0.268464i	$0.913484\pi$
$570$		0			0
$571$	661.504	+	3751.58i	0.0484818	+	0.274954i	0.999406	−	0.0344710i	$-0.0109746\pi$
$571$	661.504	+	3751.58i	0.0484818	+	0.274954i	−0.950924	+	0.309425i	$0.899864\pi$
$572$		0			0
$573$	−1818.78	+	7249.15i	−0.132601	+	0.528513i
$574$		0			0
$575$	140.258	−	242.933i	0.0101724	−	0.0176192i
$576$		0			0
$577$	3496.19	+	6055.58i	0.252250	+	0.436910i	0.964145	−	0.265376i	$-0.0854961\pi$
$577$	3496.19	+	6055.58i	0.252250	+	0.436910i	−0.711895	+	0.702286i	$0.752163\pi$
$578$		0			0
$579$	−3999.20	+	2896.59i	−0.287049	+	0.207907i
$580$		0			0
$581$	12037.5	−	10100.6i	0.859550	−	0.721248i
$582$		0			0
$583$	1302.37	−	474.024i	0.0925192	−	0.0336742i
$584$		0			0
$585$	−6443.99	+	19635.3i	−0.455429	+	1.38772i
$586$		0			0
$587$	314.256	−	1782.23i	0.0220966	−	0.125316i	−0.971764	−	0.235954i	$-0.924178\pi$
$587$	314.256	−	1782.23i	0.0220966	−	0.125316i	0.993861	+	0.110638i	$0.0352895\pi$
$588$		0			0
$589$	2133.29	+	776.455i	0.149237	+	0.0543180i
$590$		0			0
$591$	6534.78	+	466.642i	0.454830	+	0.0324790i
$592$		0			0
$593$	−23574.5			−1.63253			−0.816265	−	0.577677i	$-0.803959\pi$
$593$	−23574.5			−1.63253			−0.816265	+	0.577677i	$0.803959\pi$
$594$		0			0
$595$	−5012.64			−0.345375
$596$		0			0
$597$	−264.402	+	390.747i	−0.0181260	+	0.0267876i
$598$		0			0
$599$	−1293.63	−	470.845i	−0.0882412	−	0.0321172i	0.297522	−	0.954715i	$-0.403840\pi$
$599$	−1293.63	−	470.845i	−0.0882412	−	0.0321172i	−0.385764	+	0.922598i	$0.626062\pi$
$600$		0			0
$601$	−2569.25	+	14571.0i	−0.174379	+	0.988955i	0.764478	+	0.644649i	$0.222997\pi$
$601$	−2569.25	+	14571.0i	−0.174379	+	0.988955i	−0.938858	+	0.344305i	$0.888114\pi$
$602$		0			0
$603$	−297.320	−	9300.64i	−0.0200793	−	0.628112i
$604$		0			0
$605$	13180.5	−	4797.32i	0.885727	−	0.322378i
$606$		0			0
$607$	−9051.09	+	7594.77i	−0.605226	+	0.507845i	−0.893121	−	0.449817i	$-0.851489\pi$
$607$	−9051.09	+	7594.77i	−0.605226	+	0.507845i	0.287894	+	0.957662i	$0.407045\pi$
$608$		0			0
$609$	−19000.6	−	8493.20i	−1.26427	−	0.565126i
$610$		0			0
$611$	20476.8	+	35466.9i	1.35582	+	2.34834i
$612$		0			0
$613$	3225.23	−	5586.27i	0.212506	−	0.368071i	−0.739992	−	0.672615i	$-0.765171\pi$
$613$	3225.23	−	5586.27i	0.212506	−	0.368071i	0.952498	+	0.304545i	$0.0985042\pi$
$614$		0			0
$615$	−9217.65	−	8927.69i	−0.604376	−	0.585365i
$616$		0			0
$617$	−2856.84	−	16201.9i	−0.186405	−	1.05716i	−0.924137	−	0.382061i	$-0.875214\pi$
$617$	−2856.84	−	16201.9i	−0.186405	−	1.05716i	0.737732	−	0.675094i	$-0.235897\pi$
$618$		0			0
$619$	−13064.5	−	10962.4i	−0.848316	−	0.711822i	0.111102	−	0.993809i	$-0.464562\pi$
$619$	−13064.5	−	10962.4i	−0.848316	−	0.711822i	−0.959418	+	0.281987i	$0.909006\pi$
$620$		0			0
$621$	134.053	−	3406.54i	0.00866240	−	0.220128i
$622$		0			0
$623$	−10380.9	−	8710.57i	−0.667576	−	0.560163i
$624$		0			0
$625$	−2439.54	−	13835.3i	−0.156131	−	0.885460i
$626$		0			0
$627$	163.404	−	46.5948i	0.0104079	−	0.00296781i
$628$		0			0
$629$	1405.91	−	2435.10i	0.0891211	−	0.154362i
$630$		0			0
$631$	7321.24	+	12680.8i	0.461892	+	0.800021i	0.999055	−	0.0434573i	$-0.0138373\pi$
$631$	7321.24	+	12680.8i	0.461892	+	0.800021i	−0.537163	+	0.843479i	$0.680504\pi$
$632$		0			0
$633$	1899.33	+	18330.9i	0.119260	+	1.15101i
$634$		0			0
$635$	−17115.1	+	14361.2i	−1.06959	+	0.897493i
$636$		0			0
$637$	−4206.55	+	1531.06i	−0.261648	+	0.0952321i
$638$		0			0
$639$	−26543.1	−	3810.27i	−1.64324	−	0.235887i
$640$		0			0
$641$	792.456	−	4494.24i	0.0488301	−	0.276929i	−0.950610	−	0.310388i	$-0.899541\pi$
$641$	792.456	−	4494.24i	0.0488301	−	0.276929i	0.999440	+	0.0334585i	$0.0106522\pi$
$642$		0			0
$643$	−4259.61	−	1550.37i	−0.261248	−	0.0950865i	0.208076	−	0.978113i	$-0.433280\pi$
$643$	−4259.61	−	1550.37i	−0.261248	−	0.0950865i	−0.469324	+	0.883026i	$0.655502\pi$
$644$		0			0
$645$	−5671.31	−	11671.6i	−0.346213	−	0.712508i
$646$		0			0
$647$	24993.3			1.51868			0.759342	−	0.650692i	$-0.225521\pi$
$647$	24993.3			1.51868			0.759342	+	0.650692i	$0.225521\pi$
$648$		0			0
$649$	−1942.62			−0.117496
$650$		0			0
$651$	−9939.57	−	20455.7i	−0.598407	−	1.23152i
$652$		0			0
$653$	−2358.00	−	858.241i	−0.141310	−	0.0514327i	0.270397	−	0.962749i	$-0.412845\pi$
$653$	−2358.00	−	858.241i	−0.141310	−	0.0514327i	−0.411707	+	0.911316i	$0.635067\pi$
$654$		0			0
$655$	−1679.50	+	9524.94i	−0.100189	+	0.568199i
$656$		0			0
$657$	−3626.76	−	9053.35i	−0.215363	−	0.537602i
$658$		0			0
$659$	24430.9	−	8892.11i	1.44415	−	0.525626i	0.503196	−	0.864172i	$-0.332157\pi$
$659$	24430.9	−	8892.11i	1.44415	−	0.525626i	0.940950	+	0.338546i	$0.109935\pi$
$660$		0			0
$661$	−4539.92	+	3809.44i	−0.267144	+	0.224161i	−0.766513	−	0.642229i	$-0.778010\pi$
$661$	−4539.92	+	3809.44i	−0.267144	+	0.224161i	0.499369	+	0.866390i	$0.333565\pi$
$662$		0			0
$663$	1080.88	+	10431.9i	0.0633153	+	0.611073i
$664$		0			0
$665$	−775.418	−	1343.06i	−0.0452171	−	0.0783184i
$666$		0			0
$667$	−2904.63	+	5030.97i	−0.168617	+	0.292054i
$668$		0			0
$669$	4839.44	−	1379.97i	0.279677	−	0.0797497i
$670$		0			0
$671$	401.661	+	2277.93i	0.0231087	+	0.131056i
$672$		0			0
$673$	22589.1	+	18954.5i	1.29383	+	1.08565i	0.991177	+	0.132547i	$0.0423156\pi$
$673$	22589.1	+	18954.5i	1.29383	+	1.08565i	0.302649	+	0.953102i	$0.402129\pi$
$674$		0			0
$675$	991.446	+	1280.63i	0.0565345	+	0.0730245i
$676$		0			0
$677$	16020.1	+	13442.5i	0.909459	+	0.763127i	0.972016	−	0.234915i	$-0.0754811\pi$
$677$	16020.1	+	13442.5i	0.909459	+	0.763127i	−0.0625569	+	0.998041i	$0.519925\pi$
$678$		0			0
$679$	5337.13	+	30268.4i	0.301650	+	1.71074i
$680$		0			0
$681$	−6188.87	−	5994.18i	−0.348249	−	0.337295i
$682$		0			0
$683$	4479.23	−	7758.25i	0.250941	−	0.434643i	−0.712844	−	0.701323i	$-0.752593\pi$
$683$	4479.23	−	7758.25i	0.250941	−	0.434643i	0.963785	+	0.266680i	$0.0859265\pi$
$684$		0			0
$685$	−4193.34	−	7263.08i	−0.233897	−	0.405121i
$686$		0			0
$687$	−23685.9	−	10587.5i	−1.31539	−	0.587976i
$688$		0			0
$689$	−20274.3	+	17012.1i	−1.12103	+	0.940655i
$690$		0			0
$691$	−23144.5	+	8423.91i	−1.27418	+	0.463764i	−0.888503	−	0.458870i	$-0.848254\pi$
$691$	−23144.5	+	8423.91i	−1.27418	+	0.463764i	−0.385677	+	0.922634i	$0.626032\pi$
$692$		0			0
$693$	−1500.61	−	803.574i	−0.0822559	−	0.0440480i
$694$		0			0
$695$	1867.93	−	10593.5i	0.101949	−	0.578182i
$696$		0			0
$697$	−6119.62	−	2227.36i	−0.332564	−	0.121044i
$698$		0			0
$699$	−11023.2	+	16290.7i	−0.596474	+	0.881501i
$700$		0			0
$701$	13936.1			0.750869			0.375435	−	0.926849i	$-0.377493\pi$
$701$	13936.1			0.750869			0.375435	+	0.926849i	$0.377493\pi$
$702$		0			0
$703$	869.932			0.0466716
$704$		0			0
$705$	−31463.9	−	2246.81i	−1.68085	−	0.120028i
$706$		0			0
$707$	−9466.38	−	3445.48i	−0.503564	−	0.183282i
$708$		0			0
$709$	2364.96	−	13412.3i	0.125272	−	0.710453i	−0.855874	−	0.517185i	$-0.826980\pi$
$709$	2364.96	−	13412.3i	0.125272	−	0.710453i	0.981146	−	0.193268i	$-0.0619088\pi$
$710$		0			0
$711$	−4402.64	+	922.245i	−0.232225	+	0.0486454i
$712$		0			0
$713$	−5965.22	+	2171.16i	−0.313323	+	0.114040i
$714$		0			0
$715$	2206.32	−	1851.32i	0.115401	−	0.0968328i
$716$		0			0
$717$	6801.23	−	4926.07i	0.354249	−	0.256580i
$718$		0			0
$719$	7771.31	+	13460.3i	0.403089	+	0.698171i	0.994097	−	0.108495i	$-0.0346032\pi$
$719$	7771.31	+	13460.3i	0.403089	+	0.698171i	−0.591008	+	0.806666i	$0.701270\pi$
$720$		0			0
$721$	−551.671	+	955.523i	−0.0284956	+	0.0493558i
$722$		0			0
$723$	−6659.50	+	26542.9i	−0.342558	+	1.36534i
$724$		0			0
$725$	−479.225	−	2717.82i	−0.0245489	−	0.139224i
$726$		0			0
$727$	323.352	+	271.325i	0.0164958	+	0.0138417i	0.650998	−	0.759079i	$-0.274351\pi$
$727$	323.352	+	271.325i	0.0164958	+	0.0138417i	−0.634502	+	0.772921i	$0.718795\pi$
$728$		0			0
$729$	17909.8	+	8164.60i	0.909910	+	0.414805i
$730$		0			0
$731$	−5044.81	−	4233.10i	−0.255252	−	0.214182i
$732$		0			0
$733$	4836.28	+	27427.9i	0.243700	+	1.38209i	0.823493	+	0.567326i	$0.192022\pi$
$733$	4836.28	+	27427.9i	0.243700	+	1.38209i	−0.579793	+	0.814764i	$0.696867\pi$
$734$		0			0
$735$	839.076	−	3344.33i	0.0421085	−	0.167833i
$736$		0			0
$737$	−648.440	+	1123.13i	−0.0324092	+	0.0561344i
$738$		0			0
$739$	6838.48	+	11844.6i	0.340403	+	0.589595i	0.984507	−	0.175343i	$-0.0561033\pi$
$739$	6838.48	+	11844.6i	0.340403	+	0.589595i	−0.644105	+	0.764937i	$0.722770\pi$
$740$		0			0
$741$	−2627.87	+	1903.34i	−0.130280	+	0.0943605i
$742$		0			0
$743$	25241.3	−	21180.0i	1.24632	−	1.04578i	0.249314	−	0.968423i	$-0.419795\pi$
$743$	25241.3	−	21180.0i	1.24632	−	1.04578i	0.997003	−	0.0773619i	$-0.0246497\pi$
$744$		0			0
$745$	34296.9	−	12483.1i	1.68663	−	0.613885i
$746$		0			0
$747$	24785.4	−	5191.94i	1.21399	−	0.254301i
$748$		0			0
$749$	3269.06	−	18539.8i	0.159478	−	0.904443i
$750$		0			0
$751$	16216.5	+	5902.33i	0.787948	+	0.286790i	0.704483	−	0.709721i	$-0.251179\pi$
$751$	16216.5	+	5902.33i	0.787948	+	0.286790i	0.0834654	+	0.996511i	$0.473401\pi$
$752$		0			0
$753$	20735.2	+	1480.68i	1.00349	+	0.0716586i
$754$		0			0
$755$	−25548.5			−1.23153
$756$		0			0
$757$	11119.9			0.533897			0.266949	−	0.963711i	$-0.413985\pi$
$757$	11119.9			0.533897			0.266949	+	0.963711i	$0.413985\pi$
$758$		0			0
$759$	−266.271	+	393.510i	−0.0127339	+	0.0188189i
$760$		0			0
$761$	−15727.2	−	5724.22i	−0.749158	−	0.272671i	−0.0609065	−	0.998143i	$-0.519399\pi$
$761$	−15727.2	−	5724.22i	−0.749158	−	0.272671i	−0.688251	+	0.725472i	$0.741621\pi$
$762$		0			0
$763$	5208.22	−	29537.3i	0.247117	−	1.40147i
$764$		0			0
$765$	−7121.28	−	3813.44i	−0.336563	−	0.180229i
$766$		0			0
$767$	34859.2	−	12687.7i	1.64106	−	0.597297i
$768$		0			0
$769$	−29314.2	+	24597.6i	−1.37464	+	1.15346i	−0.403492	+	0.914983i	$0.632204\pi$
$769$	−29314.2	+	24597.6i	−1.37464	+	1.15346i	−0.971148	+	0.238477i	$0.923352\pi$
$770$		0			0
$771$	32899.7	+	14706.1i	1.53678	+	0.686935i
$772$		0			0
$773$	−9959.54	−	17250.4i	−0.463415	−	0.802658i	0.535714	−	0.844400i	$-0.320043\pi$
$773$	−9959.54	−	17250.4i	−0.463415	−	0.802658i	−0.999128	+	0.0417417i	$0.986709\pi$
$774$		0			0
$775$	1507.85	−	2611.68i	0.0698886	−	0.121051i
$776$		0			0
$777$	−6260.04	−	6063.12i	−0.289032	−	0.279940i
$778$		0			0
$779$	−349.871	−	1984.22i	−0.0160917	−	0.0912606i
$780$		0			0
$781$	2862.86	+	2402.22i	0.131167	+	0.110062i
$782$		0			0
$783$	−20532.1	−	26521.0i	−0.937112	−	1.21045i
$784$		0			0
$785$	13854.5	+	11625.3i	0.629923	+	0.528568i
$786$		0			0
$787$	−1236.57	−	7012.96i	−0.0560090	−	0.317643i	0.943912	−	0.330197i	$-0.107115\pi$
$787$	−1236.57	−	7012.96i	−0.0560090	−	0.317643i	−0.999921	+	0.0125537i	$0.996004\pi$
$788$		0			0
$789$	25975.6	−	7406.95i	1.17206	−	0.334213i
$790$		0			0
$791$	9201.53	−	15937.5i	0.413614	−	0.716401i
$792$		0			0
$793$	−22085.3	−	38252.8i	−0.988992	−	1.71298i
$794$		0			0
$795$	−2100.94	−	20276.7i	−0.0937264	−	0.904579i
$796$		0			0
$797$	−2361.07	+	1981.18i	−0.104935	+	0.0880513i	−0.693746	−	0.720220i	$-0.744041\pi$
$797$	−2361.07	+	1981.18i	−0.104935	+	0.0880513i	0.588810	+	0.808271i	$0.299596\pi$
$798$		0			0
$799$	−15043.1	+	5475.22i	−0.666064	+	0.242427i
$800$		0			0
$801$	−8121.02	−	20272.2i	−0.358230	−	0.894236i
$802$		0			0
$803$	−236.028	+	1338.58i	−0.0103727	+	0.0588262i
$804$		0			0
$805$	4075.00	+	1483.18i	0.178416	+	0.0649380i
$806$		0			0
$807$	−7273.06	−	14968.0i	−0.317254	−	0.652909i
$808$		0			0
$809$	29146.6			1.26668			0.633338	−	0.773875i	$-0.281684\pi$
$809$	29146.6			1.26668			0.633338	+	0.773875i	$0.281684\pi$
$810$		0			0
$811$	−17449.0			−0.755509			−0.377755	−	0.925906i	$-0.623304\pi$
$811$	−17449.0			−0.755509			−0.377755	+	0.925906i	$0.623304\pi$
$812$		0			0
$813$	5821.57	+	11980.8i	0.251133	+	0.516833i
$814$		0			0
$815$	−19641.6	−	7148.96i	−0.844191	−	0.307260i
$816$		0			0
$817$	353.802	−	2006.51i	0.0151505	−	0.0859228i
$818$		0			0
$819$	32175.8	+	4618.84i	1.37279	+	0.197064i
$820$		0			0
$821$	−3391.72	+	1234.49i	−0.144180	+	0.0524773i	−0.413102	−	0.910685i	$-0.635555\pi$
$821$	−3391.72	+	1234.49i	−0.144180	+	0.0524773i	0.268922	+	0.963162i	$0.413333\pi$
$822$		0			0
$823$	−3559.55	+	2986.82i	−0.150763	+	0.126505i	−0.715050	−	0.699074i	$-0.753596\pi$
$823$	−3559.55	+	2986.82i	−0.150763	+	0.126505i	0.564286	+	0.825579i	$0.309151\pi$
$824$		0			0
$825$	−23.2627	−	224.514i	−0.000981699	−	0.00947465i
$826$		0			0
$827$	8056.05	+	13953.5i	0.338738	+	0.586711i	0.984196	−	0.177085i	$-0.0566667\pi$
$827$	8056.05	+	13953.5i	0.338738	+	0.586711i	−0.645458	+	0.763796i	$0.723333\pi$
$828$		0			0
$829$	5703.26	−	9878.33i	0.238941	−	0.413858i	−0.721470	−	0.692446i	$-0.756533\pi$
$829$	5703.26	−	9878.33i	0.238941	−	0.413858i	0.960411	+	0.278588i	$0.0898663\pi$
$830$		0			0
$831$	−26904.0	+	7671.68i	−1.12309	+	0.320250i
$832$		0			0
$833$	−303.857	−	1723.26i	−0.0126387	−	0.0716774i
$834$		0			0
$835$	20393.4	+	17112.1i	0.845201	+	0.709208i
$836$		0			0
$837$	1441.15	−	36622.3i	0.0595141	−	1.51237i
$838$		0			0
$839$	7637.59	+	6408.70i	0.314278	+	0.263710i	0.786257	−	0.617899i	$-0.212016\pi$
$839$	7637.59	+	6408.70i	0.314278	+	0.263710i	−0.471980	+	0.881609i	$0.656460\pi$
$840$		0			0
$841$	5689.31	+	32265.7i	0.233273	+	1.32296i
$842$		0			0
$843$	13567.1	+	13140.3i	0.554301	+	0.536864i
$844$		0			0
$845$	−15798.9	+	27364.4i	−0.643192	+	1.11404i
$846$		0			0
$847$	−11031.3	−	19106.8i	−0.447508	−	0.775107i
$848$		0			0
$849$	31094.1	+	13899.0i	1.25695	+	0.561851i
$850$		0			0
$851$	−1863.44	+	1563.61i	−0.0750621	+	0.0629846i
$852$		0			0
$853$	31510.1	−	11468.7i	1.26481	−	0.460355i	0.379432	−	0.925220i	$-0.376119\pi$
$853$	31510.1	−	11468.7i	1.26481	−	0.460355i	0.885382	+	0.464865i	$0.153897\pi$
$854$		0			0
$855$	−79.8538	−	2497.95i	−0.00319408	−	0.0999160i
$856$		0			0
$857$	960.939	−	5449.75i	0.0383023	−	0.217223i	−0.959649	−	0.281200i	$-0.909267\pi$
$857$	960.939	−	5449.75i	0.0383023	−	0.217223i	0.997951	+	0.0639774i	$0.0203786\pi$
$858$		0			0
$859$	−25197.0	−	9170.97i	−1.00083	−	0.364272i	−0.210924	−	0.977502i	$-0.567647\pi$
$859$	−25197.0	−	9170.97i	−1.00083	−	0.364272i	−0.789904	+	0.613231i	$0.789870\pi$
$860$		0			0
$861$	−11311.6	+	16716.9i	−0.447734	+	0.661686i
$862$		0			0
$863$	−15485.4			−0.610809			−0.305404	−	0.952223i	$-0.598792\pi$
$863$	−15485.4			−0.610809			−0.305404	+	0.952223i	$0.598792\pi$
$864$		0			0
$865$	−13991.6			−0.549975
$866$		0			0
$867$	21374.7	+	1526.35i	0.837281	+	0.0597894i
$868$		0			0
$869$	589.100	+	214.415i	0.0229964	+	0.00837000i
$870$		0			0
$871$	4300.44	−	24389.0i	0.167296	−	0.948783i
$872$		0			0
$873$	−15444.8	+	47061.5i	−0.598773	+	1.82450i
$874$		0			0
$875$	−22897.9	+	8334.15i	−0.884674	+	0.321995i
$876$		0			0
$877$	734.315	−	616.163i	0.0282737	−	0.0237245i	−0.628541	−	0.777776i	$-0.716348\pi$
$877$	734.315	−	616.163i	0.0282737	−	0.0237245i	0.656815	+	0.754052i	$0.271903\pi$
$878$		0			0
$879$	−2149.52	+	1556.88i	−0.0824820	+	0.0597410i
$880$		0			0
$881$	11851.2	+	20526.9i	0.453209	+	0.784981i	0.998583	−	0.0532115i	$-0.0169458\pi$
$881$	11851.2	+	20526.9i	0.453209	+	0.784981i	−0.545374	+	0.838193i	$0.683612\pi$
$882$		0			0
$883$	23503.0	−	40708.3i	0.895739	−	1.55147i	0.0628522	−	0.998023i	$-0.479980\pi$
$883$	23503.0	−	40708.3i	0.895739	−	1.55147i	0.832887	−	0.553443i	$-0.186686\pi$
$884$		0			0
$885$	−6953.32	+	27714.0i	−0.264105	+	1.05265i
$886$		0			0
$887$	3326.07	+	18863.1i	0.125906	+	0.714047i	0.980766	+	0.195189i	$0.0625319\pi$
$887$	3326.07	+	18863.1i	0.125906	+	0.714047i	−0.854860	+	0.518859i	$0.826357\pi$
$888$		0			0
$889$	26920.8	+	22589.2i	1.01563	+	0.852214i
$890$		0			0
$891$	−1520.53	−	2283.22i	−0.0571714	−	0.0858482i
$892$		0			0
$893$	−3794.05	−	3183.59i	−0.142176	−	0.119300i
$894$		0			0
$895$	−6419.27	−	36405.5i	−0.239746	−	1.35967i
$896$		0			0
$897$	2207.97	−	8800.38i	0.0821873	−	0.327576i
$898$		0			0
$899$	−31226.5	+	54085.9i	−1.15847	+	2.00653i
$900$		0			0
$901$	−5172.72	−	8959.42i	−0.191264	−	0.331278i
$902$		0			0
$903$	−16530.6	+	11973.0i	−0.609196	+	0.441236i
$904$		0			0
$905$	−16487.7	+	13834.8i	−0.605603	+	0.508161i
$906$		0			0
$907$	10582.7	−	3851.78i	0.387423	−	0.141010i	−0.140963	−	0.990015i	$-0.545020\pi$
$907$	10582.7	−	3851.78i	0.387423	−	0.141010i	0.528385	+	0.849005i	$0.322798\pi$
$908$		0			0
$909$	−10827.4	−	12096.6i	−0.395073	−	0.441384i
$910$		0			0
$911$	5704.27	−	32350.5i	0.207454	−	1.17653i	−0.686077	−	0.727529i	$-0.740669\pi$
$911$	5704.27	−	32350.5i	0.207454	−	1.17653i	0.893531	−	0.449002i	$-0.148220\pi$
$912$		0			0
$913$	−3316.44	−	1207.09i	−0.120217	−	0.0437555i
$914$		0			0
$915$	33935.3	+	2423.29i	1.22609	+	0.0875536i
$916$		0			0
$917$	15213.2			0.547855
$918$		0			0
$919$	−9006.48			−0.323282			−0.161641	−	0.986850i	$-0.551679\pi$
$919$	−9006.48			−0.323282			−0.161641	+	0.986850i	$0.551679\pi$
$920$		0			0
$921$	−5679.35	+	8393.25i	−0.203193	+	0.300290i
$922$		0			0
$923$	−67061.7	−	24408.5i	−2.39151	−	0.870438i
$924$		0			0
$925$	200.669	−	1138.05i	0.00713291	−	0.0404528i
$926$		0			0
$927$	−1510.67	+	937.786i	−0.0535241	+	0.0332265i
$928$		0			0
$929$	−6268.08	+	2281.40i	−0.221366	+	0.0805707i	−0.450322	−	0.892866i	$-0.648691\pi$
$929$	−6268.08	+	2281.40i	−0.221366	+	0.0805707i	0.228956	+	0.973437i	$0.426469\pi$
$930$		0			0
$931$	414.717	−	347.989i	0.0145991	−	0.0122501i
$932$		0			0
$933$	29991.5	+	13406.1i	1.05239	+	0.470415i
$934$		0			0
$935$	562.914	+	974.995i	0.0196890	+	0.0341024i
$936$		0			0
$937$	−8632.97	+	14952.7i	−0.300989	+	0.521329i	−0.976360	−	0.216149i	$-0.930650\pi$
$937$	−8632.97	+	14952.7i	−0.300989	+	0.521329i	0.675371	+	0.737478i	$0.263984\pi$
$938$		0			0
$939$	1875.25	+	1816.26i	0.0651720	+	0.0631219i
$940$		0			0
$941$	−500.873	−	2840.59i	−0.0173518	−	0.0984067i	0.974902	−	0.222635i	$-0.0714657\pi$
$941$	−500.873	−	2840.59i	−0.0173518	−	0.0984067i	−0.992254	+	0.124228i	$0.960355\pi$
$942$		0			0
$943$	4315.86	+	3621.44i	0.149039	+	0.125059i
$944$		0			0
$945$	−16835.2	+	18531.8i	−0.579523	+	0.637927i
$946$		0			0
$947$	−9699.06	−	8138.48i	−0.332816	−	0.279266i	0.461030	−	0.887385i	$-0.347480\pi$
$947$	−9699.06	−	8138.48i	−0.332816	−	0.279266i	−0.793846	+	0.608119i	$0.791925\pi$
$948$		0			0
$949$	−4507.19	−	25561.5i	−0.154172	−	0.874355i
$950$		0			0
$951$	−47939.7	+	13670.0i	−1.63465	+	0.466120i
$952$		0			0
$953$	−20384.0	+	35306.2i	−0.692868	+	1.20008i	0.278026	+	0.960573i	$0.410320\pi$
$953$	−20384.0	+	35306.2i	−0.692868	+	1.20008i	−0.970894	+	0.239509i	$0.923014\pi$
$954$		0			0
$955$	−7660.29	−	13268.0i	−0.259562	−	0.449574i
$956$		0			0
$957$	481.753	+	4649.53i	0.0162726	+	0.157051i
$958$		0			0
$959$	−10105.4	+	8479.44i	−0.340272	+	0.285522i
$960$		0			0
$961$	−36135.2	+	13152.1i	−1.21296	+	0.441481i
$962$		0			0
$963$	18748.6	−	23851.8i	0.627380	−	0.798145i
$964$		0			0
$965$	1757.73	−	9968.61i	0.0586357	−	0.332540i
$966$		0			0
$967$	20212.7	+	7356.82i	0.672179	+	0.244653i	0.655486	−	0.755208i	$-0.272464\pi$
$967$	20212.7	+	7356.82i	0.672179	+	0.244653i	0.0166931	+	0.999861i	$0.494686\pi$
$968$		0			0
$969$	−554.327	−	1140.81i	−0.0183772	−	0.0378204i
$970$		0			0
$971$	5278.90			0.174468			0.0872338	−	0.996188i	$-0.472197\pi$
$971$	5278.90			0.174468			0.0872338	+	0.996188i	$0.472197\pi$
$972$		0			0
$973$	−16920.0			−0.557481
$974$		0			0
$975$	1883.79	+	3876.84i	0.0618764	+	0.127342i
$976$		0			0
$977$	27704.0	+	10083.4i	0.907195	+	0.330192i	0.753132	−	0.657869i	$-0.228542\pi$
$977$	27704.0	+	10083.4i	0.907195	+	0.330192i	0.154063	+	0.988061i	$0.450764\pi$
$978$		0			0
$979$	−528.512	+	2997.34i	−0.0172536	+	0.0978502i
$980$		0			0
$981$	29870.1	−	38000.4i	0.972149	−	1.23676i
$982$		0			0
$983$	−20637.6	+	7511.48i	−0.669622	+	0.243722i	−0.654385	−	0.756162i	$-0.727072\pi$
$983$	−20637.6	+	7511.48i	−0.669622	+	0.243722i	−0.0152366	+	0.999884i	$0.504850\pi$
$984$		0			0
$985$	−10287.8	+	8632.46i	−0.332787	+	0.279242i
$986$		0			0
$987$	5113.55	+	49352.3i	0.164910	+	1.59159i
$988$		0			0
$989$	2848.63	+	4933.97i	0.0915885	+	0.158636i
$990$		0			0
$991$	−14802.0	+	25637.8i	−0.474470	+	0.821807i	−0.999573	−	0.0292322i	$-0.990694\pi$
$991$	−14802.0	+	25637.8i	−0.474470	+	0.821807i	0.525102	+	0.851039i	$0.324027\pi$
$992$		0			0
$993$	24813.3	−	7075.51i	0.792977	−	0.226117i
$994$		0			0
$995$	−167.941	−	952.441i	−0.00535084	−	0.0303461i
$996$		0			0
$997$	−21236.8	−	17819.8i	−0.674599	−	0.566055i	0.239824	−	0.970816i	$-0.422910\pi$
$997$	−21236.8	−	17819.8i	−0.674599	−	0.566055i	−0.914423	+	0.404761i	$0.867355\pi$
$998$		0			0
$999$	−4280.81	−	13376.1i	−0.135574	−	0.423624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.97.7	yes	54
3.2	odd	2		324.4.i.a.289.8		54
27.5	odd	18		324.4.i.a.37.8		54
27.22	even	9	inner	108.4.i.a.49.7	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.49.7	✓	54	27.22	even	9	inner
108.4.i.a.97.7	yes	54	1.1	even	1	trivial
324.4.i.a.37.8		54	27.5	odd	18
324.4.i.a.289.8		54	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.27095 + 4.67363i) q^{3} +(-10.0092 - 3.64305i) q^{5} +(-2.90933 + 16.4997i) q^{7} +(-16.6855 + 21.2272i) q^{9} +O(q^{10})\)	\(q+(2.27095 + 4.67363i) q^{3} +(-10.0092 - 3.64305i) q^{5} +(-2.90933 + 16.4997i) q^{7} +(-16.6855 + 21.2272i) q^{9} +(3.53602 - 1.28701i) q^{11} +(-55.0460 + 46.1890i) q^{13} +(-5.70417 - 55.0525i) q^{15} +(-14.0443 - 24.3254i) q^{17} +(4.34509 - 7.52591i) q^{19} +(-83.7201 + 23.8728i) q^{21} +(4.21963 + 23.9307i) q^{23} +(-8.84313 - 7.42027i) q^{25} +(-137.100 - 29.7761i) q^{27} +(183.135 + 153.668i) q^{29} +(45.3635 + 257.269i) q^{31} +(14.0451 + 13.6033i) q^{33} +(89.2293 - 154.550i) q^{35} +(50.0527 + 86.6937i) q^{37} +(-340.877 - 152.371i) q^{39} +(177.609 - 149.031i) q^{41} +(220.317 - 80.1887i) q^{43} +(244.341 - 151.681i) q^{45} +(98.9672 - 561.271i) q^{47} +(58.5403 + 21.3069i) q^{49} +(81.7939 - 120.879i) q^{51} +368.316 q^{53} -40.0814 q^{55} +(45.0408 + 3.21632i) q^{57} +(-485.116 - 176.568i) q^{59} +(-106.741 + 605.358i) q^{61} +(-301.697 - 337.063i) q^{63} +(719.236 - 261.780i) q^{65} +(-264.013 + 221.533i) q^{67} +(-102.261 + 74.0665i) q^{69} +(496.578 + 860.098i) q^{71} +(-180.607 + 312.820i) q^{73} +(14.5972 - 58.1806i) q^{75} +(10.9477 + 62.0874i) q^{77} +(127.623 + 107.088i) q^{79} +(-172.185 - 708.374i) q^{81} +(-718.475 - 602.872i) q^{83} +(51.9533 + 294.642i) q^{85} +(-302.298 + 1204.88i) q^{87} +(-404.414 + 700.465i) q^{89} +(-601.956 - 1042.62i) q^{91} +(-1099.36 + 796.258i) q^{93} +(-70.9082 + 59.4990i) q^{95} +(1723.85 - 627.431i) q^{97} +(-31.6809 + 96.5340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 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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