LMFDB - Embedded newform 108.4.i.a.97.1

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			97.1
Character	$\chi$	$=$	108.97
Dual form			108.4.i.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.16735 - 0.546343i) q^{3} +(5.21695 + 1.89881i) q^{5} +(1.58868 - 9.00985i) q^{7} +(26.4030 + 5.64629i) q^{9} +O(q^{10})$	\(q+(-5.16735 - 0.546343i) q^{3} +(5.21695 + 1.89881i) q^{5} +(1.58868 - 9.00985i) q^{7} +(26.4030 + 5.64629i) q^{9} +(-67.4972 + 24.5670i) q^{11} +(-63.1985 + 53.0298i) q^{13} +(-25.9204 - 12.6621i) q^{15} +(21.0212 + 36.4097i) q^{17} +(-22.5218 + 39.0089i) q^{19} +(-13.1317 + 45.6891i) q^{21} +(12.1174 + 68.7214i) q^{23} +(-72.1445 - 60.5364i) q^{25} +(-133.349 - 43.6014i) q^{27} +(142.727 + 119.762i) q^{29} +(-46.3221 - 262.706i) q^{31} +(362.204 - 90.0696i) q^{33} +(25.3961 - 43.9873i) q^{35} +(-40.4209 - 70.0111i) q^{37} +(355.541 - 239.496i) q^{39} +(-216.792 + 181.910i) q^{41} +(-249.820 + 90.9271i) q^{43} +(127.022 + 79.5908i) q^{45} +(-10.5496 + 59.8299i) q^{47} +(243.661 + 88.6854i) q^{49} +(-88.7316 - 199.627i) q^{51} +206.241 q^{53} -398.778 q^{55} +(137.690 - 189.268i) q^{57} +(558.381 + 203.234i) q^{59} +(124.554 - 706.379i) q^{61} +(92.8181 - 228.917i) q^{63} +(-430.397 + 156.652i) q^{65} +(23.6459 - 19.8412i) q^{67} +(-25.0696 - 361.728i) q^{69} +(155.414 + 269.185i) q^{71} +(-263.889 + 457.070i) q^{73} +(339.722 + 352.229i) q^{75} +(114.113 + 647.169i) q^{77} +(-500.648 - 420.094i) q^{79} +(665.239 + 298.158i) q^{81} +(-883.108 - 741.015i) q^{83} +(40.5310 + 229.863i) q^{85} +(-672.091 - 696.832i) q^{87} +(240.988 - 417.404i) q^{89} +(377.389 + 653.656i) q^{91} +(95.8352 + 1382.80i) q^{93} +(-191.566 + 160.743i) q^{95} +(-858.230 + 312.370i) q^{97} +(-1920.84 + 267.534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−5.16735	−	0.546343i	−0.994457	−	0.105144i
$3$	−5.16735	−	0.546343i	−0.994457	−	0.105144i
$4$		0			0
$5$	5.21695	+	1.89881i	0.466618	+	0.169835i	0.564620	−	0.825351i	$-0.309023\pi$
$5$	5.21695	+	1.89881i	0.466618	+	0.169835i	−0.0980017	+	0.995186i	$0.531245\pi$
$6$		0			0
$7$	1.58868	−	9.00985i	0.0857806	−	0.486486i	−0.911405	−	0.411511i	$-0.865001\pi$
$7$	1.58868	−	9.00985i	0.0857806	−	0.486486i	0.997185	−	0.0749750i	$-0.0238877\pi$
$8$		0			0
$9$	26.4030	+	5.64629i	0.977890	+	0.209122i
$10$		0			0
$11$	−67.4972	+	24.5670i	−1.85011	+	0.673384i	−0.864918	+	0.501912i	$0.832630\pi$
$11$	−67.4972	+	24.5670i	−1.85011	+	0.673384i	−0.985189	+	0.171472i	$0.945148\pi$
$12$		0			0
$13$	−63.1985	+	53.0298i	−1.34832	+	1.13137i	−0.368911	+	0.929465i	$0.620269\pi$
$13$	−63.1985	+	53.0298i	−1.34832	+	1.13137i	−0.979405	+	0.201907i	$0.935286\pi$
$14$		0			0
$15$	−25.9204	−	12.6621i	−0.446175	−	0.217956i
$16$		0			0
$17$	21.0212	+	36.4097i	0.299905	+	0.519450i	0.976114	−	0.217259i	$-0.0697117\pi$
$17$	21.0212	+	36.4097i	0.299905	+	0.519450i	−0.676209	+	0.736710i	$0.736378\pi$
$18$		0			0
$19$	−22.5218	+	39.0089i	−0.271940	+	0.471013i	−0.969358	−	0.245650i	$-0.920998\pi$
$19$	−22.5218	+	39.0089i	−0.271940	+	0.471013i	0.697419	+	0.716664i	$0.254332\pi$
$20$		0			0
$21$	−13.1317	+	45.6891i	−0.136456	+	0.474770i
$22$		0			0
$23$	12.1174	+	68.7214i	0.109855	+	0.623018i	0.989170	+	0.146777i	$0.0468899\pi$
$23$	12.1174	+	68.7214i	0.109855	+	0.623018i	−0.879315	+	0.476241i	$0.841999\pi$
$24$		0			0
$25$	−72.1445	−	60.5364i	−0.577156	−	0.484291i
$26$		0			0
$27$	−133.349	−	43.6014i	−0.950481	−	0.310782i
$28$		0			0
$29$	142.727	+	119.762i	0.913924	+	0.766873i	0.972861	−	0.231388i	$-0.0743268\pi$
$29$	142.727	+	119.762i	0.913924	+	0.766873i	−0.0589376	+	0.998262i	$0.518771\pi$
$30$		0			0
$31$	−46.3221	−	262.706i	−0.268377	−	1.52204i	−0.759243	−	0.650807i	$-0.774431\pi$
$31$	−46.3221	−	262.706i	−0.268377	−	1.52204i	0.490866	−	0.871235i	$-0.336680\pi$
$32$		0			0
$33$	362.204	−	90.0696i	1.91065	−	0.475124i
$34$		0			0
$35$	25.3961	−	43.9873i	0.122649	−	0.212435i
$36$		0			0
$37$	−40.4209	−	70.0111i	−0.179599	−	0.311074i	0.762144	−	0.647407i	$-0.224147\pi$
$37$	−40.4209	−	70.0111i	−0.179599	−	0.311074i	−0.941743	+	0.336333i	$0.890813\pi$
$38$		0			0
$39$	355.541	−	239.496i	1.45980	−	0.983334i
$40$		0			0
$41$	−216.792	+	181.910i	−0.825787	+	0.692918i	−0.954320	−	0.298788i	$-0.903418\pi$
$41$	−216.792	+	181.910i	−0.825787	+	0.692918i	0.128533	+	0.991705i	$0.458973\pi$
$42$		0			0
$43$	−249.820	+	90.9271i	−0.885982	+	0.322471i	−0.744621	−	0.667487i	$-0.767370\pi$
$43$	−249.820	+	90.9271i	−0.885982	+	0.322471i	−0.141361	+	0.989958i	$0.545148\pi$
$44$		0			0
$45$	127.022	+	79.5908i	0.420785	+	0.263660i
$46$		0			0
$47$	−10.5496	+	59.8299i	−0.0327409	+	0.185683i	−0.996792	−	0.0800335i	$-0.974497\pi$
$47$	−10.5496	+	59.8299i	−0.0327409	+	0.185683i	0.964051	+	0.265716i	$0.0856084\pi$
$48$		0			0
$49$	243.661	+	88.6854i	0.710382	+	0.258558i
$50$		0			0
$51$	−88.7316	−	199.627i	−0.243626	−	0.548104i
$52$		0			0
$53$	206.241			0.534517			0.267258	−	0.963625i	$-0.413882\pi$
$53$	206.241			0.534517			0.267258	+	0.963625i	$0.413882\pi$
$54$		0			0
$55$	−398.778			−0.977658
$56$		0			0
$57$	137.690	−	189.268i	0.319956	−	0.439810i
$58$		0			0
$59$	558.381	+	203.234i	1.23212	+	0.448455i	0.874323	−	0.485345i	$-0.161306\pi$
$59$	558.381	+	203.234i	1.23212	+	0.448455i	0.357797	+	0.933800i	$0.383528\pi$
$60$		0			0
$61$	124.554	−	706.379i	0.261434	−	1.48266i	−0.517568	−	0.855642i	$-0.673163\pi$
$61$	124.554	−	706.379i	0.261434	−	1.48266i	0.779002	−	0.627022i	$-0.215726\pi$
$62$		0			0
$63$	92.8181	−	228.917i	0.185619	−	0.457791i
$64$		0			0
$65$	−430.397	+	156.652i	−0.821295	+	0.298927i
$66$		0			0
$67$	23.6459	−	19.8412i	0.0431164	−	0.0361790i	−0.620975	−	0.783831i	$-0.713263\pi$
$67$	23.6459	−	19.8412i	0.0431164	−	0.0361790i	0.664091	+	0.747652i	$0.268819\pi$
$68$		0			0
$69$	−25.0696	−	361.728i	−0.0437395	−	0.631115i
$70$		0			0
$71$	155.414	+	269.185i	0.259779	+	0.449950i	0.966182	−	0.257859i	$-0.0830171\pi$
$71$	155.414	+	269.185i	0.259779	+	0.449950i	−0.706404	+	0.707809i	$0.749684\pi$
$72$		0			0
$73$	−263.889	+	457.070i	−0.423094	+	0.732821i	−0.996240	−	0.0866322i	$-0.972389\pi$
$73$	−263.889	+	457.070i	−0.423094	+	0.732821i	0.573146	+	0.819453i	$0.305723\pi$
$74$		0			0
$75$	339.722	+	352.229i	0.523037	+	0.542291i
$76$		0			0
$77$	114.113	+	647.169i	0.168889	+	0.957815i
$78$		0			0
$79$	−500.648	−	420.094i	−0.713004	−	0.598281i	0.212436	−	0.977175i	$-0.431860\pi$
$79$	−500.648	−	420.094i	−0.713004	−	0.598281i	−0.925440	+	0.378893i	$0.876305\pi$
$80$		0			0
$81$	665.239	+	298.158i	0.912536	+	0.408996i
$82$		0			0
$83$	−883.108	−	741.015i	−1.16788	−	0.979964i	−0.167893	−	0.985805i	$-0.553696\pi$
$83$	−883.108	−	741.015i	−1.16788	−	0.979964i	−0.999983	+	0.00584137i	$0.998141\pi$
$84$		0			0
$85$	40.5310	+	229.863i	0.0517201	+	0.293319i
$86$		0			0
$87$	−672.091	−	696.832i	−0.828226	−	0.858716i
$88$		0			0
$89$	240.988	−	417.404i	0.287019	−	0.497132i	−0.686078	−	0.727528i	$-0.740669\pi$
$89$	240.988	−	417.404i	0.287019	−	0.497132i	0.973097	+	0.230397i	$0.0740023\pi$
$90$		0			0
$91$	377.389	+	653.656i	0.434737	+	0.752987i
$92$		0			0
$93$	95.8352	+	1382.80i	0.106856	+	1.54182i
$94$		0			0
$95$	−191.566	+	160.743i	−0.206887	+	0.173598i
$96$		0			0
$97$	−858.230	+	312.370i	−0.898351	+	0.326973i	−0.749592	−	0.661901i	$-0.769750\pi$
$97$	−858.230	+	312.370i	−0.898351	+	0.326973i	−0.148759	+	0.988873i	$0.547528\pi$
$98$		0			0
$99$	−1920.84	+	267.534i	−1.95002	+	0.271598i
$100$		0			0
$101$	−92.4446	+	524.279i	−0.0910750	+	0.516512i	0.904805	+	0.425827i	$0.140017\pi$
$101$	−92.4446	+	524.279i	−0.0910750	+	0.516512i	−0.995880	+	0.0906852i	$0.971094\pi$
$102$		0			0
$103$	303.355	+	110.412i	0.290199	+	0.105624i	0.483017	−	0.875611i	$-0.339541\pi$
$103$	303.355	+	110.412i	0.290199	+	0.105624i	−0.192819	+	0.981234i	$0.561763\pi$
$104$		0			0
$105$	−155.263	+	213.423i	−0.144305	+	0.198361i
$106$		0			0
$107$	−209.423			−0.189212			−0.0946062	−	0.995515i	$-0.530159\pi$
$107$	−209.423			−0.189212			−0.0946062	+	0.995515i	$0.530159\pi$
$108$		0			0
$109$	−196.115			−0.172334			−0.0861672	−	0.996281i	$-0.527462\pi$
$109$	−196.115			−0.172334			−0.0861672	+	0.996281i	$0.527462\pi$
$110$		0			0
$111$	170.619	+	383.855i	0.145896	+	0.328234i
$112$		0			0
$113$	203.446	+	74.0482i	0.169368	+	0.0616448i	0.425312	−	0.905047i	$-0.360164\pi$
$113$	203.446	+	74.0482i	0.169368	+	0.0616448i	−0.255945	+	0.966691i	$0.582386\pi$
$114$		0			0
$115$	−67.2731	+	381.525i	−0.0545500	+	0.309368i
$116$		0			0
$117$	−1968.05	+	1043.31i	−1.55510	+	0.824394i
$118$		0			0
$119$	361.442	−	131.554i	0.278431	−	0.101341i
$120$		0			0
$121$	2932.73	−	2460.86i	2.20341	−	1.84888i
$122$		0			0
$123$	1219.63	−	821.552i	0.894066	−	0.602251i
$124$		0			0
$125$	−608.412	−	1053.80i	−0.435344	−	0.754038i
$126$		0			0
$127$	−611.723	+	1059.53i	−0.427414	+	0.740303i	−0.996642	−	0.0818763i	$-0.973909\pi$
$127$	−611.723	+	1059.53i	−0.427414	+	0.740303i	0.569228	+	0.822180i	$0.307242\pi$
$128$		0			0
$129$	1340.59	−	333.365i	0.914977	−	0.227528i
$130$		0			0
$131$	194.741	+	1104.43i	0.129882	+	0.736599i	0.978288	+	0.207252i	$0.0664519\pi$
$131$	194.741	+	1104.43i	0.129882	+	0.736599i	−0.848405	+	0.529347i	$0.822437\pi$
$132$		0			0
$133$	315.684	+	264.891i	0.205814	+	0.172699i
$134$		0			0
$135$	−612.883	−	480.671i	−0.390730	−	0.306441i
$136$		0			0
$137$	−1967.06	−	1650.56i	−1.22670	−	1.02932i	−0.998446	−	0.0557200i	$-0.982255\pi$
$137$	−1967.06	−	1650.56i	−1.22670	−	1.02932i	−0.228252	−	0.973602i	$-0.573301\pi$
$138$		0			0
$139$	434.934	+	2466.63i	0.265400	+	1.50516i	0.767894	+	0.640577i	$0.221305\pi$
$139$	434.934	+	2466.63i	0.265400	+	1.50516i	−0.502494	+	0.864581i	$0.667584\pi$
$140$		0			0
$141$	87.2012	−	303.398i	0.0520827	−	0.181211i
$142$		0			0
$143$	2962.94	−	5131.96i	1.73268	−	3.00109i
$144$		0			0
$145$	517.194	+	895.807i	0.296211	+	0.513053i
$146$		0			0
$147$	−1210.63	−	591.391i	−0.679259	−	0.331817i
$148$		0			0
$149$	88.5089	−	74.2678i	0.0486640	−	0.0408339i	−0.618131	−	0.786075i	$-0.712110\pi$
$149$	88.5089	−	74.2678i	0.0486640	−	0.0408339i	0.666795	+	0.745241i	$0.267666\pi$
$150$		0			0
$151$	1464.39	−	532.995i	0.789209	−	0.287249i	0.0842019	−	0.996449i	$-0.473166\pi$
$151$	1464.39	−	532.995i	0.789209	−	0.287249i	0.705007	+	0.709200i	$0.250944\pi$
$152$		0			0
$153$	349.443	+	1080.02i	0.184645	+	0.570682i
$154$		0			0
$155$	257.169	−	1458.48i	0.133267	−	0.755792i
$156$		0			0
$157$	1712.19	+	623.186i	0.870367	+	0.316788i	0.738316	−	0.674455i	$-0.235621\pi$
$157$	1712.19	+	623.186i	0.870367	+	0.316788i	0.132052	+	0.991243i	$0.457844\pi$
$158$		0			0
$159$	−1065.72	−	112.678i	−0.531554	−	0.0562011i
$160$		0			0
$161$	638.420			0.312513
$162$		0			0
$163$	1785.32			0.857897			0.428948	−	0.903329i	$-0.358884\pi$
$163$	1785.32			0.857897			0.428948	+	0.903329i	$0.358884\pi$
$164$		0			0
$165$	2060.62	+	217.869i	0.972239	+	0.102795i
$166$		0			0
$167$	1097.06	+	399.298i	0.508343	+	0.185022i	0.583442	−	0.812154i	$-0.301705\pi$
$167$	1097.06	+	399.298i	0.508343	+	0.185022i	−0.0751000	+	0.997176i	$0.523928\pi$
$168$		0			0
$169$	800.382	−	4539.19i	0.364307	−	2.06609i
$170$		0			0
$171$	−814.899	+	902.788i	−0.364426	+	0.403731i
$172$		0			0
$173$	−3928.51	+	1429.86i	−1.72647	+	0.628383i	−0.998369	−	0.0570873i	$-0.981819\pi$
$173$	−3928.51	+	1429.86i	−1.72647	+	0.628383i	−0.728100	+	0.685471i	$0.759596\pi$
$174$		0			0
$175$	−660.038	+	553.838i	−0.285110	+	0.239235i
$176$		0			0
$177$	−2774.32	−	1355.25i	−1.17814	−	0.575519i
$178$		0			0
$179$	918.530	+	1590.94i	0.383543	+	0.664316i	0.991566	−	0.129604i	$-0.0413705\pi$
$179$	918.530	+	1590.94i	0.383543	+	0.664316i	−0.608023	+	0.793919i	$0.708037\pi$
$180$		0			0
$181$	−1157.45	+	2004.76i	−0.475318	+	0.823275i	−0.999600	−	0.0282697i	$-0.991000\pi$
$181$	−1157.45	+	2004.76i	−0.475318	+	0.823275i	0.524282	+	0.851544i	$0.324334\pi$
$182$		0			0
$183$	−1029.54	+	3582.06i	−0.415877	+	1.44696i
$184$		0			0
$185$	−77.9358	−	441.996i	−0.0309727	−	0.175655i
$186$		0			0
$187$	−2313.35	−	1941.13i	−0.904646	−	0.759088i
$188$		0			0
$189$	−604.691	+	1132.18i	−0.232724	+	0.435737i
$190$		0			0
$191$	1309.35	+	1098.67i	0.496027	+	0.416216i	0.856180	−	0.516677i	$-0.172831\pi$
$191$	1309.35	+	1098.67i	0.496027	+	0.416216i	−0.360153	+	0.932893i	$0.617276\pi$
$192$		0			0
$193$	−538.413	−	3053.49i	−0.200808	−	1.13884i	−0.903902	−	0.427740i	$-0.859310\pi$
$193$	−538.413	−	3053.49i	−0.200808	−	1.13884i	0.703095	−	0.711096i	$-0.251801\pi$
$194$		0			0
$195$	2309.60	−	574.330i	0.848173	−	0.210916i
$196$		0			0
$197$	−269.298	+	466.438i	−0.0973943	+	0.168692i	−0.910605	−	0.413277i	$-0.864384\pi$
$197$	−269.298	+	466.438i	−0.0973943	+	0.168692i	0.813211	+	0.581969i	$0.197717\pi$
$198$		0			0
$199$	1847.26	+	3199.55i	0.658035	+	1.13975i	0.981124	+	0.193381i	$0.0619454\pi$
$199$	1847.26	+	3199.55i	0.658035	+	1.13975i	−0.323089	+	0.946369i	$0.604721\pi$
$200$		0			0
$201$	−133.027	+	89.6078i	−0.0466814	+	0.0314450i
$202$		0			0
$203$	1305.79	−	1095.69i	0.451470	−	0.378828i
$204$		0			0
$205$	−1476.41	+	537.369i	−0.503009	+	0.183080i
$206$		0			0
$207$	−68.0839	+	1882.87i	−0.0228607	+	0.632216i
$208$		0			0
$209$	561.828	−	3186.28i	0.185945	−	1.05455i
$210$		0			0
$211$	3344.47	+	1217.29i	1.09120	+	0.397164i	0.824065	−	0.566496i	$-0.191701\pi$
$211$	3344.47	+	1217.29i	1.09120	+	0.397164i	0.267134	+	0.963660i	$0.413924\pi$
$212$		0			0
$213$	−656.012	−	1475.88i	−0.211029	−	0.474770i
$214$		0			0
$215$	−1475.95			−0.468182
$216$		0			0
$217$	−2440.53			−0.763474
$218$		0			0
$219$	1613.32	−	2217.66i	0.497801	−	0.684273i
$220$		0			0
$221$	−3259.31	−	1186.29i	−0.992058	−	0.361080i
$222$		0			0
$223$	−932.642	+	5289.28i	−0.280064	+	1.58832i	0.442337	+	0.896849i	$0.354150\pi$
$223$	−932.642	+	5289.28i	−0.280064	+	1.58832i	−0.722401	+	0.691474i	$0.756962\pi$
$224$		0			0
$225$	−1563.03	−	2005.69i	−0.463119	−	0.594279i
$226$		0			0
$227$	−1788.67	+	651.023i	−0.522988	+	0.190352i	−0.590005	−	0.807400i	$-0.700874\pi$
$227$	−1788.67	+	651.023i	−0.522988	+	0.190352i	0.0670166	+	0.997752i	$0.478652\pi$
$228$		0			0
$229$	−1969.18	+	1652.34i	−0.568240	+	0.476810i	−0.881061	−	0.473002i	$-0.843170\pi$
$229$	−1969.18	+	1652.34i	−0.568240	+	0.476810i	0.312821	+	0.949812i	$0.398726\pi$
$230$		0			0
$231$	−236.088	−	3406.49i	−0.0672443	−	0.970263i
$232$		0			0
$233$	1769.64	+	3065.11i	0.497567	+	0.861811i	0.999996	−	0.00280750i	$-0.000893656\pi$
$233$	1769.64	+	3065.11i	0.497567	+	0.861811i	−0.502429	+	0.864618i	$0.667560\pi$
$234$		0			0
$235$	−168.643	+	292.098i	−0.0468129	+	0.0810823i
$236$		0			0
$237$	2357.51	+	2444.30i	0.646146	+	0.669933i
$238$		0			0
$239$	1060.55	+	6014.68i	0.287035	+	1.62786i	0.697925	+	0.716171i	$0.254107\pi$
$239$	1060.55	+	6014.68i	0.287035	+	1.62786i	−0.410890	+	0.911685i	$0.634782\pi$
$240$		0			0
$241$	−2459.06	−	2063.40i	−0.657270	−	0.551515i	0.251997	−	0.967728i	$-0.418913\pi$
$241$	−2459.06	−	2063.40i	−0.657270	−	0.551515i	−0.909267	+	0.416213i	$0.863357\pi$
$242$		0			0
$243$	−3274.63	−	1904.14i	−0.864475	−	0.502676i
$244$		0			0
$245$	1102.77	+	925.334i	0.287565	+	0.241296i
$246$		0			0
$247$	−645.292	−	3659.63i	−0.166230	−	0.942740i
$248$		0			0
$249$	4158.48	+	4311.57i	1.05837	+	1.09733i
$250$		0			0
$251$	1804.49	−	3125.47i	0.453778	−	0.785967i	−0.544839	−	0.838541i	$-0.683409\pi$
$251$	1804.49	−	3125.47i	0.453778	−	0.785967i	0.998617	+	0.0525736i	$0.0167424\pi$
$252$		0			0
$253$	−2506.17	−	4340.82i	−0.622773	−	1.07868i
$254$		0			0
$255$	−83.8542	−	1209.93i	−0.0205928	−	0.297131i
$256$		0			0
$257$	−4944.99	+	4149.34i	−1.20023	+	1.00712i	−0.200610	+	0.979671i	$0.564292\pi$
$257$	−4944.99	+	4149.34i	−1.20023	+	1.00712i	−0.999623	+	0.0274439i	$0.991263\pi$
$258$		0			0
$259$	−695.005	+	252.961i	−0.166739	+	0.0606882i
$260$		0			0
$261$	3092.22	+	3967.97i	0.733347	+	0.941039i
$262$		0			0
$263$	−1324.95	+	7514.17i	−0.310646	+	1.76176i	0.285011	+	0.958524i	$0.408003\pi$
$263$	−1324.95	+	7514.17i	−0.310646	+	1.76176i	−0.595657	+	0.803239i	$0.703108\pi$
$264$		0			0
$265$	1075.95	+	391.613i	0.249415	+	0.0907797i
$266$		0			0
$267$	−1473.32	+	2025.21i	−0.337698	+	0.464198i
$268$		0			0
$269$	−7418.04			−1.68136			−0.840681	−	0.541531i	$-0.817845\pi$
$269$	−7418.04			−1.68136			−0.840681	+	0.541531i	$0.817845\pi$
$270$		0			0
$271$	−5946.94			−1.33303			−0.666515	−	0.745492i	$-0.732215\pi$
$271$	−5946.94			−1.33303			−0.666515	+	0.745492i	$0.732215\pi$
$272$		0			0
$273$	−1592.98	−	3583.85i	−0.353156	−	0.794523i
$274$		0			0
$275$	6356.75	+	2313.67i	1.39391	+	0.507343i
$276$		0			0
$277$	105.510	−	598.379i	0.0228863	−	0.129795i	−0.971224	−	0.238168i	$-0.923453\pi$
$277$	105.510	−	598.379i	0.0228863	−	0.129795i	0.994110	+	0.108373i	$0.0345642\pi$
$278$		0			0
$279$	260.268	−	7197.77i	0.0558489	−	1.54451i
$280$		0			0
$281$	6387.32	−	2324.79i	1.35600	−	0.493543i	0.441184	−	0.897417i	$-0.354559\pi$
$281$	6387.32	−	2324.79i	1.35600	−	0.493543i	0.914815	+	0.403874i	$0.132336\pi$
$282$		0			0
$283$	−56.9781	+	47.8103i	−0.0119682	+	0.0100425i	−0.648752	−	0.761000i	$-0.724709\pi$
$283$	−56.9781	+	47.8103i	−0.0119682	+	0.0100425i	0.636784	+	0.771042i	$0.280264\pi$
$284$		0			0
$285$	1077.71	−	725.953i	0.223993	−	0.150883i
$286$		0			0
$287$	1294.57	+	2242.26i	0.266258	+	0.461173i
$288$		0			0
$289$	1572.72	−	2724.03i	0.320114	−	0.554454i
$290$		0			0
$291$	4605.43	−	1145.24i	0.927750	−	0.230705i
$292$		0			0
$293$	−17.3041	−	98.1364i	−0.00345023	−	0.0195672i	0.983034	−	0.183423i	$-0.0587179\pi$
$293$	−17.3041	−	98.1364i	−0.00345023	−	0.0195672i	−0.986484	+	0.163856i	$0.947607\pi$
$294$		0			0
$295$	2527.14	+	2120.52i	0.498766	+	0.418514i
$296$		0			0
$297$	10071.8	−	333.002i	1.96777	−	0.0650598i
$298$		0			0
$299$	−4410.09	−	3700.50i	−0.852983	−	0.715738i
$300$		0			0
$301$	422.355	+	2395.30i	0.0808776	+	0.458680i
$302$		0			0
$303$	764.130	−	2658.63i	0.144878	−	0.504073i
$304$		0			0
$305$	1991.07	−	3448.64i	0.373798	−	0.647437i
$306$		0			0
$307$	−2496.99	−	4324.91i	−0.464204	−	0.804024i	0.534962	−	0.844876i	$-0.320326\pi$
$307$	−2496.99	−	4324.91i	−0.464204	−	0.804024i	−0.999165	+	0.0408521i	$0.986993\pi$
$308$		0			0
$309$	−1507.22	−	736.274i	−0.277484	−	0.135551i
$310$		0			0
$311$	5733.38	−	4810.88i	1.04537	−	0.877170i	0.0527712	−	0.998607i	$-0.483195\pi$
$311$	5733.38	−	4810.88i	1.04537	−	0.877170i	0.992599	+	0.121437i	$0.0387502\pi$
$312$		0			0
$313$	4171.87	−	1518.44i	0.753380	−	0.274208i	0.0633524	−	0.997991i	$-0.479821\pi$
$313$	4171.87	−	1518.44i	0.753380	−	0.274208i	0.690027	+	0.723783i	$0.257599\pi$
$314$		0			0
$315$	918.898	−	1018.00i	0.164362	−	0.182089i
$316$		0			0
$317$	−299.891	+	1700.77i	−0.0531342	+	0.301339i	−0.999781	−	0.0209343i	$-0.993336\pi$
$317$	−299.891	+	1700.77i	−0.0531342	+	0.301339i	0.946647	+	0.322273i	$0.104447\pi$
$318$		0			0
$319$	−12575.9	−	4577.25i	−2.20726	−	0.803376i
$320$		0			0
$321$	1082.16	+	114.417i	0.188164	+	0.0198945i
$322$		0			0
$323$	−1893.74			−0.326224
$324$		0			0
$325$	7769.66			1.32610
$326$		0			0
$327$	1013.40	+	107.146i	0.171379	+	0.0181199i
$328$		0			0
$329$	522.298	+	190.101i	0.0875235	+	0.0318559i
$330$		0			0
$331$	−146.572	+	831.251i	−0.0243393	+	0.138035i	−0.994556	−	0.104204i	$-0.966771\pi$
$331$	−146.572	+	831.251i	−0.0243393	+	0.138035i	0.970217	+	0.242239i	$0.0778818\pi$
$332$		0			0
$333$	−671.932	−	2076.73i	−0.110575	−	0.341754i
$334$		0			0
$335$	161.034	−	58.6116i	0.0262634	−	0.00955908i
$336$		0			0
$337$	25.8927	−	21.7265i	0.00418536	−	0.00351193i	−0.640693	−	0.767798i	$-0.721353\pi$
$337$	25.8927	−	21.7265i	0.00418536	−	0.00351193i	0.644878	+	0.764286i	$0.276908\pi$
$338$		0			0
$339$	−1010.82	−	493.784i	−0.161947	−	0.0791111i
$340$		0			0
$341$	9580.49	+	16593.9i	1.52145	+	2.63522i
$342$		0			0
$343$	2755.17	−	4772.09i	0.433717	−	0.751220i
$344$		0			0
$345$	556.067	−	1934.72i	0.0867758	−	0.301918i
$346$		0			0
$347$	−1785.27	−	10124.8i	−0.276191	−	1.56636i	−0.735154	−	0.677900i	$-0.762890\pi$
$347$	−1785.27	−	10124.8i	−0.276191	−	1.56636i	0.458963	−	0.888455i	$-0.348221\pi$
$348$		0			0
$349$	−5099.40	−	4278.91i	−0.782134	−	0.656289i	0.161651	−	0.986848i	$-0.448318\pi$
$349$	−5099.40	−	4278.91i	−0.782134	−	0.656289i	−0.943785	+	0.330559i	$0.892763\pi$
$350$		0			0
$351$	10739.6	−	4315.92i	1.63316	−	0.656316i
$352$		0			0
$353$	6159.61	+	5168.53i	0.928734	+	0.779300i	0.975590	−	0.219601i	$-0.0704756\pi$
$353$	6159.61	+	5168.53i	0.928734	+	0.779300i	−0.0468557	+	0.998902i	$0.514920\pi$
$354$		0			0
$355$	299.655	+	1699.43i	0.0448001	+	0.254074i
$356$		0			0
$357$	−1939.57	+	482.315i	−0.287543	+	0.0715037i
$358$		0			0
$359$	−1712.40	+	2965.97i	−0.251747	+	0.436039i	−0.964007	−	0.265877i	$-0.914338\pi$
$359$	−1712.40	+	2965.97i	−0.251747	+	0.436039i	0.712260	+	0.701916i	$0.247672\pi$
$360$		0			0
$361$	2415.04	+	4182.97i	0.352098	+	0.609851i
$362$		0			0
$363$	−16498.9	+	11113.8i	−2.38559	+	1.60696i
$364$		0			0
$365$	−2244.59	+	1883.43i	−0.321882	+	0.270091i
$366$		0			0
$367$	−3402.99	+	1238.59i	−0.484018	+	0.176168i	−0.572492	−	0.819910i	$-0.694023\pi$
$367$	−3402.99	+	1238.59i	−0.484018	+	0.176168i	0.0884742	+	0.996078i	$0.471801\pi$
$368$		0			0
$369$	−6751.09	+	3578.91i	−0.952433	+	0.504907i
$370$		0			0
$371$	327.651	−	1858.20i	0.0458512	−	0.260035i
$372$		0			0
$373$	−1812.31	−	659.627i	−0.251576	−	0.0915662i	0.213154	−	0.977019i	$-0.431626\pi$
$373$	−1812.31	−	659.627i	−0.251576	−	0.0915662i	−0.464730	+	0.885452i	$0.653849\pi$
$374$		0			0
$375$	2568.14	+	5777.76i	0.353649	+	0.795632i
$376$		0			0
$377$	−15371.1			−2.09988
$378$		0			0
$379$	4403.13			0.596763			0.298382	−	0.954447i	$-0.403553\pi$
$379$	4403.13			0.596763			0.298382	+	0.954447i	$0.403553\pi$
$380$		0			0
$381$	3739.85	−	5140.78i	0.502883	−	0.691260i
$382$		0			0
$383$	−10231.3	−	3723.88i	−1.36500	−	0.496819i	−0.447402	−	0.894333i	$-0.647651\pi$
$383$	−10231.3	−	3723.88i	−1.36500	−	0.496819i	−0.917596	+	0.397515i	$0.869873\pi$
$384$		0			0
$385$	−633.530	+	3592.93i	−0.0838641	+	0.475617i
$386$		0			0
$387$	−7109.41	+	990.194i	−0.933828	+	0.130063i
$388$		0			0
$389$	7053.47	−	2567.25i	0.919345	−	0.334614i	0.161367	−	0.986894i	$-0.448410\pi$
$389$	7053.47	−	2567.25i	0.919345	−	0.334614i	0.757978	+	0.652280i	$0.226187\pi$
$390$		0			0
$391$	−2247.41	+	1885.80i	−0.290681	+	0.243910i
$392$		0			0
$393$	−402.897	−	5813.37i	−0.0517136	−	0.746172i
$394$		0			0
$395$	−1814.18	−	3142.25i	−0.231091	−	0.400262i
$396$		0			0
$397$	−3635.79	+	6297.37i	−0.459635	+	0.796111i	−0.998942	−	0.0459984i	$-0.985353\pi$
$397$	−3635.79	+	6297.37i	−0.459635	+	0.796111i	0.539307	+	0.842110i	$0.318686\pi$
$398$		0			0
$399$	−1486.53	−	1541.25i	−0.186515	−	0.193381i
$400$		0			0
$401$	−2014.16	−	11422.9i	−0.250828	−	1.42252i	−0.806558	−	0.591155i	$-0.798672\pi$
$401$	−2014.16	−	11422.9i	−0.250828	−	1.42252i	0.555729	−	0.831363i	$-0.312439\pi$
$402$		0			0
$403$	16858.7	+	14146.1i	2.08385	+	1.74856i
$404$		0			0
$405$	2904.37	+	2818.64i	0.356344	+	0.345826i
$406$		0			0
$407$	4448.26	+	3732.53i	0.541750	+	0.454582i
$408$		0			0
$409$	1420.37	+	8055.31i	0.171718	+	0.973862i	0.941864	+	0.335994i	$0.109072\pi$
$409$	1420.37	+	8055.31i	0.171718	+	0.973862i	−0.770146	+	0.637868i	$0.779817\pi$
$410$		0			0
$411$	9262.74	+	9603.73i	1.11167	+	1.15260i
$412$		0			0
$413$	2718.20	−	4708.06i	0.323859	−	0.560940i
$414$		0			0
$415$	−3200.08	−	5542.70i	−0.378520	−	0.655615i
$416$		0			0
$417$	−899.829	−	12983.6i	−0.105671	−	1.52472i
$418$		0			0
$419$	−6454.20	+	5415.71i	−0.752525	+	0.631444i	−0.936169	−	0.351549i	$-0.885655\pi$
$419$	−6454.20	+	5415.71i	−0.752525	+	0.631444i	0.183644	+	0.982993i	$0.441211\pi$
$420$		0			0
$421$	4401.68	−	1602.08i	0.509560	−	0.185465i	−0.0744290	−	0.997226i	$-0.523713\pi$
$421$	4401.68	−	1602.08i	0.509560	−	0.185465i	0.583989	+	0.811762i	$0.301491\pi$
$422$		0			0
$423$	−616.358	+	1520.12i	−0.0708472	+	0.174730i
$424$		0			0
$425$	687.553	−	3899.31i	0.0784735	−	0.445045i
$426$		0			0
$427$	−6166.49	−	2244.42i	−0.698869	−	0.254368i
$428$		0			0
$429$	−18114.4	+	24899.9i	−2.03862	+	2.80228i
$430$		0			0
$431$	−8784.41			−0.981740			−0.490870	−	0.871233i	$-0.663321\pi$
$431$	−8784.41			−0.981740			−0.490870	+	0.871233i	$0.663321\pi$
$432$		0			0
$433$	−6469.85			−0.718063			−0.359031	−	0.933325i	$-0.616893\pi$
$433$	−6469.85			−0.718063			−0.359031	+	0.933325i	$0.616893\pi$
$434$		0			0
$435$	−2183.11	−	4911.51i	−0.240625	−	0.541354i
$436$		0			0
$437$	−2953.65	−	1075.04i	−0.323323	−	0.117680i
$438$		0			0
$439$	−148.990	+	844.963i	−0.0161979	+	0.0918631i	−0.991835	−	0.127528i	$-0.959296\pi$
$439$	−148.990	+	844.963i	−0.0161979	+	0.0918631i	0.975637	+	0.219391i	$0.0704070\pi$
$440$		0			0
$441$	5932.65	+	3717.34i	0.640605	+	0.401398i
$442$		0			0
$443$	412.777	−	150.239i	0.0442701	−	0.0161130i	−0.319790	−	0.947488i	$-0.603612\pi$
$443$	412.777	−	150.239i	0.0442701	−	0.0161130i	0.364060	+	0.931375i	$0.381390\pi$
$444$		0			0
$445$	2049.80	−	1719.98i	0.218359	−	0.183225i
$446$		0			0
$447$	−497.932	+	335.412i	−0.0526877	+	0.0354909i
$448$		0			0
$449$	1510.09	+	2615.54i	0.158720	+	0.274911i	0.934407	−	0.356206i	$-0.115930\pi$
$449$	1510.09	+	2615.54i	0.158720	+	0.274911i	−0.775687	+	0.631117i	$0.782597\pi$
$450$		0			0
$451$	10163.9	−	17604.4i	1.06120	−	1.83804i
$452$		0			0
$453$	−7858.23	+	1954.11i	−0.815037	+	0.202676i
$454$		0			0
$455$	727.645	+	4126.68i	0.0749726	+	0.425191i
$456$		0			0
$457$	5728.39	+	4806.69i	0.586352	+	0.492008i	0.887026	−	0.461719i	$-0.152767\pi$
$457$	5728.39	+	4806.69i	0.586352	+	0.492008i	−0.300674	+	0.953727i	$0.597212\pi$
$458$		0			0
$459$	−1215.63	−	5771.75i	−0.123618	−	0.586933i
$460$		0			0
$461$	4559.80	+	3826.13i	0.460675	+	0.386552i	0.843379	−	0.537319i	$-0.180563\pi$
$461$	4559.80	+	3826.13i	0.460675	+	0.386552i	−0.382705	+	0.923871i	$0.625007\pi$
$462$		0			0
$463$	299.450	+	1698.27i	0.0300575	+	0.170465i	0.996141	−	0.0877642i	$-0.0279722\pi$
$463$	299.450	+	1698.27i	0.0300575	+	0.170465i	−0.966084	+	0.258229i	$0.916861\pi$
$464$		0			0
$465$	−2125.71	+	7395.97i	−0.211995	+	0.737591i
$466$		0			0
$467$	7069.94	−	12245.5i	0.700552	−	1.21339i	−0.267721	−	0.963496i	$-0.586271\pi$
$467$	7069.94	−	12245.5i	0.700552	−	1.21339i	0.968273	−	0.249895i	$-0.0803961\pi$
$468$		0			0
$469$	−141.201	−	244.567i	−0.0139020	−	0.0240790i
$470$		0			0
$471$	−8507.02	−	4155.67i	−0.832235	−	0.406546i
$472$		0			0
$473$	14628.4	−	12274.7i	1.42202	−	1.19321i
$474$		0			0
$475$	3986.28	−	1450.89i	0.385059	−	0.140150i
$476$		0			0
$477$	5445.39	+	1164.50i	0.522698	+	0.111779i
$478$		0			0
$479$	467.551	−	2651.62i	0.0445991	−	0.252934i	−0.954354	−	0.298677i	$-0.903455\pi$
$479$	467.551	−	2651.62i	0.0445991	−	0.252934i	0.998953	+	0.0457434i	$0.0145656\pi$
$480$		0			0
$481$	6267.22	+	2281.08i	0.594097	+	0.216234i
$482$		0			0
$483$	−3298.94	−	348.796i	−0.310781	−	0.0328587i
$484$		0			0
$485$	−5070.47			−0.474718
$486$		0			0
$487$	12687.7			1.18056			0.590280	−	0.807199i	$-0.299017\pi$
$487$	12687.7			1.18056			0.590280	+	0.807199i	$0.299017\pi$
$488$		0			0
$489$	−9225.38	−	975.397i	−0.853142	−	0.0902024i
$490$		0			0
$491$	−5094.55	−	1854.26i	−0.468256	−	0.170431i	0.0971061	−	0.995274i	$-0.469041\pi$
$491$	−5094.55	−	1854.26i	−0.468256	−	0.170431i	−0.565362	+	0.824843i	$0.691264\pi$
$492$		0			0
$493$	−1360.22	+	7714.21i	−0.124262	+	0.704727i
$494$		0			0
$495$	−10528.9	−	2251.61i	−0.956041	−	0.204450i
$496$		0			0
$497$	2672.22	−	972.609i	0.241178	−	0.0877817i
$498$		0			0
$499$	−10451.5	+	8769.82i	−0.937619	+	0.786756i	−0.977169	−	0.212462i	$-0.931852\pi$
$499$	−10451.5	+	8769.82i	−0.937619	+	0.786756i	0.0395506	+	0.999218i	$0.487407\pi$
$500$		0			0
$501$	−5450.75	−	2662.68i	−0.486071	−	0.237445i
$502$		0			0
$503$	3966.78	+	6870.66i	0.351630	+	0.609041i	0.986535	−	0.163549i	$-0.0522942\pi$
$503$	3966.78	+	6870.66i	0.351630	+	0.609041i	−0.634905	+	0.772590i	$0.718961\pi$
$504$		0			0
$505$	−1477.79	+	2559.60i	−0.130219	+	0.225546i
$506$		0			0
$507$	−6615.80	+	23018.3i	−0.579523	+	2.01633i
$508$		0			0
$509$	−3183.90	−	18056.8i	−0.277257	−	1.57240i	−0.731700	−	0.681627i	$-0.761273\pi$
$509$	−3183.90	−	18056.8i	−0.277257	−	1.57240i	0.454443	−	0.890776i	$-0.349838\pi$
$510$		0			0
$511$	3698.89	+	3103.74i	0.320214	+	0.268691i
$512$		0			0
$513$	4704.10	−	4219.81i	0.404856	−	0.363176i
$514$		0			0
$515$	1372.94	+	1152.03i	0.117473	+	0.0985718i
$516$		0			0
$517$	−757.769	−	4297.52i	−0.0644616	−	0.365580i
$518$		0			0
$519$	21081.2	−	5242.28i	1.78297	−	0.443373i
$520$		0			0
$521$	−3020.36	+	5231.43i	−0.253982	+	0.439910i	−0.964618	−	0.263650i	$-0.915074\pi$
$521$	−3020.36	+	5231.43i	−0.253982	+	0.439910i	0.710637	+	0.703559i	$0.248407\pi$
$522$		0			0
$523$	2909.21	+	5038.90i	0.243233	+	0.421292i	0.961633	−	0.274338i	$-0.0884586\pi$
$523$	2909.21	+	5038.90i	0.243233	+	0.421292i	−0.718400	+	0.695630i	$0.755125\pi$
$524$		0			0
$525$	3713.23	−	2501.27i	0.308684	−	0.207932i
$526$		0			0
$527$	8591.29	−	7208.95i	0.710138	−	0.595876i
$528$		0			0
$529$	6857.44	−	2495.90i	0.563610	−	0.205137i
$530$		0			0
$531$	13595.4	+	8518.78i	1.11110	+	0.696202i
$532$		0			0
$533$	4054.27	−	22992.9i	0.329475	−	1.86854i
$534$		0			0
$535$	−1092.55	−	397.656i	−0.0882899	−	0.0321349i
$536$		0			0
$537$	−3877.17	−	8722.78i	−0.311568	−	0.700960i
$538$		0			0
$539$	−18625.2			−1.48839
$540$		0			0
$541$	6742.32			0.535813			0.267907	−	0.963445i	$-0.413668\pi$
$541$	6742.32			0.535813			0.267907	+	0.963445i	$0.413668\pi$
$542$		0			0
$543$	7076.23	−	9726.94i	0.559245	−	0.768735i
$544$		0			0
$545$	−1023.12	−	372.387i	−0.0804144	−	0.0292684i
$546$		0			0
$547$	996.065	−	5648.96i	0.0778586	−	0.441558i	−0.920812	−	0.390007i	$-0.872473\pi$
$547$	996.065	−	5648.96i	0.0778586	−	0.441558i	0.998670	−	0.0515507i	$-0.0164164\pi$
$548$		0			0
$549$	7277.01	−	17947.3i	0.565711	−	1.39521i
$550$		0			0
$551$	−7886.27	+	2870.37i	−0.609740	+	0.221927i
$552$		0			0
$553$	−4580.35	+	3843.37i	−0.352217	+	0.295546i
$554$		0			0
$555$	161.240	+	2326.53i	0.0123320	+	0.177938i
$556$		0			0
$557$	11916.4	+	20639.9i	0.906492	+	1.57009i	0.818902	+	0.573933i	$0.194583\pi$
$557$	11916.4	+	20639.9i	0.906492	+	1.57009i	0.0875890	+	0.996157i	$0.472084\pi$
$558$		0			0
$559$	10966.4	−	18994.4i	0.829749	−	1.43717i
$560$		0			0
$561$	10893.4	+	11294.4i	0.819818	+	0.849998i
$562$		0			0
$563$	143.937	+	816.308i	0.0107748	+	0.0611070i	0.989721	−	0.143011i	$-0.0456785\pi$
$563$	143.937	+	816.308i	0.0107748	+	0.0611070i	−0.978946	+	0.204118i	$0.934567\pi$
$564$		0			0
$565$	920.762	+	772.611i	0.0685606	+	0.0575292i
$566$		0			0
$567$	3743.21	−	5520.02i	0.277249	−	0.408852i
$568$		0			0
$569$	809.884	+	679.573i	0.0596698	+	0.0500689i	0.672135	−	0.740429i	$-0.265378\pi$
$569$	809.884	+	679.573i	0.0596698	+	0.0500689i	−0.612465	+	0.790498i	$0.709822\pi$
$570$		0			0
$571$	−4496.33	−	25499.9i	−0.329537	−	1.86890i	−0.475661	−	0.879629i	$-0.657791\pi$
$571$	−4496.33	−	25499.9i	−0.329537	−	1.86890i	0.146124	−	0.989266i	$-0.453320\pi$
$572$		0			0
$573$	−6165.62	−	6392.59i	−0.449515	−	0.466063i
$574$		0			0
$575$	3285.94	−	5691.42i	0.238319	−	0.412780i
$576$		0			0
$577$	−1489.92	−	2580.62i	−0.107498	−	0.186192i	0.807258	−	0.590199i	$-0.200951\pi$
$577$	−1489.92	−	2580.62i	−0.107498	−	0.186192i	−0.914756	+	0.404007i	$0.867617\pi$
$578$		0			0
$579$	1113.92	+	16072.6i	0.0799530	+	1.15364i
$580$		0			0
$581$	−8079.41	+	6779.43i	−0.576920	+	0.484093i
$582$		0			0
$583$	−13920.7	+	5066.72i	−0.988913	+	0.359935i
$584$		0			0
$585$	−12248.3	+	1705.93i	−0.865648	+	0.120567i
$586$		0			0
$587$	−3085.89	+	17501.0i	−0.216982	+	1.23057i	0.660452	+	0.750868i	$0.270365\pi$
$587$	−3085.89	+	17501.0i	−0.216982	+	1.23057i	−0.877434	+	0.479698i	$0.840746\pi$
$588$		0			0
$589$	11291.1	+	4109.63i	0.789884	+	0.287494i
$590$		0			0
$591$	1646.39	−	2263.12i	0.114591	−	0.157516i
$592$		0			0
$593$	−3329.70			−0.230581			−0.115290	−	0.993332i	$-0.536780\pi$
$593$	−3329.70			−0.230581			−0.115290	+	0.993332i	$0.536780\pi$
$594$		0			0
$595$	2135.42			0.147132
$596$		0			0
$597$	−7797.40	−	17542.4i	−0.534550	−	1.20262i
$598$		0			0
$599$	12799.7	+	4658.71i	0.873090	+	0.317779i	0.739418	−	0.673247i	$-0.235101\pi$
$599$	12799.7	+	4658.71i	0.873090	+	0.317779i	0.133672	+	0.991026i	$0.457323\pi$
$600$		0			0
$601$	447.186	−	2536.12i	0.0303513	−	0.172131i	−0.965864	−	0.259049i	$-0.916591\pi$
$601$	447.186	−	2536.12i	0.0303513	−	0.172131i	0.996215	+	0.0869185i	$0.0277020\pi$
$602$		0			0
$603$	736.351	−	390.357i	0.0497289	−	0.0263625i
$604$		0			0
$605$	19972.6	−	7269.45i	1.34215	−	0.488504i
$606$		0			0
$607$	−8011.80	+	6722.70i	−0.535731	+	0.449532i	−0.870075	−	0.492919i	$-0.835930\pi$
$607$	−8011.80	+	6722.70i	−0.535731	+	0.449532i	0.334344	+	0.942451i	$0.391485\pi$
$608$		0			0
$609$	−7346.09	+	4948.39i	−0.488799	+	0.329259i
$610$		0			0
$611$	−2506.05	−	4340.60i	−0.165931	−	0.287401i
$612$		0			0
$613$	−12357.4	+	21403.7i	−0.814211	+	1.41025i	0.0956826	+	0.995412i	$0.469497\pi$
$613$	−12357.4	+	21403.7i	−0.814211	+	1.41025i	−0.909893	+	0.414842i	$0.863837\pi$
$614$		0			0
$615$	7922.71	−	1970.15i	0.519470	−	0.129177i
$616$		0			0
$617$	1578.77	+	8953.67i	0.103013	+	0.584216i	0.991995	+	0.126274i	$0.0403020\pi$
$617$	1578.77	+	8953.67i	0.103013	+	0.584216i	−0.888982	+	0.457942i	$0.848587\pi$
$618$		0			0
$619$	7255.84	+	6088.37i	0.471142	+	0.395335i	0.847211	−	0.531257i	$-0.178280\pi$
$619$	7255.84	+	6088.37i	0.471142	+	0.395335i	−0.376069	+	0.926592i	$0.622725\pi$
$620$		0			0
$621$	1380.51	−	9692.26i	0.0892074	−	0.626308i
$622$		0			0
$623$	−3377.89	−	2834.39i	−0.217227	−	0.182275i
$624$		0			0
$625$	871.146	+	4940.52i	0.0557534	+	0.316193i
$626$		0			0
$627$	−4643.97	+	16157.7i	−0.295793	+	1.02915i
$628$		0			0
$629$	1699.39	−	2943.43i	0.107725	−	0.186585i
$630$		0			0
$631$	−7345.25	−	12722.3i	−0.463407	−	0.802644i	0.535721	−	0.844395i	$-0.320040\pi$
$631$	−7345.25	−	12722.3i	−0.463407	−	0.802644i	−0.999128	+	0.0417505i	$0.986707\pi$
$632$		0			0
$633$	−16617.0	−	8117.38i	−1.04339	−	0.509695i
$634$		0			0
$635$	−5203.19	+	4365.99i	−0.325169	+	0.272849i
$636$		0			0
$637$	−20102.0	+	7316.53i	−1.25035	+	0.455088i
$638$		0			0
$639$	2583.51	+	7984.82i	0.159940	+	0.494326i
$640$		0			0
$641$	−4526.38	+	25670.4i	−0.278910	+	1.58178i	0.447351	+	0.894359i	$0.352368\pi$
$641$	−4526.38	+	25670.4i	−0.278910	+	1.58178i	−0.726261	+	0.687419i	$0.758744\pi$
$642$		0			0
$643$	2079.34	+	756.817i	0.127529	+	0.0464167i	0.404996	−	0.914318i	$-0.367273\pi$
$643$	2079.34	+	756.817i	0.127529	+	0.0464167i	−0.277467	+	0.960735i	$0.589495\pi$
$644$		0			0
$645$	7626.77	+	806.376i	0.465587	+	0.0492264i
$646$		0			0
$647$	−13758.7			−0.836027			−0.418013	−	0.908441i	$-0.637273\pi$
$647$	−13758.7			−0.836027			−0.418013	+	0.908441i	$0.637273\pi$
$648$		0			0
$649$	−42682.0			−2.58154
$650$		0			0
$651$	12611.1	+	1333.36i	0.759242	+	0.0802744i
$652$		0			0
$653$	−15288.2	−	5564.44i	−0.916191	−	0.333466i	−0.159469	−	0.987203i	$-0.550978\pi$
$653$	−15288.2	−	5564.44i	−0.916191	−	0.333466i	−0.756722	+	0.653737i	$0.773200\pi$
$654$		0			0
$655$	−1081.15	+	6131.53i	−0.0644949	+	0.365769i
$656$		0			0
$657$	−9548.22	+	10578.0i	−0.566988	+	0.628140i
$658$		0			0
$659$	−10222.0	+	3720.52i	−0.604240	+	0.219925i	−0.625981	−	0.779838i	$-0.715301\pi$
$659$	−10222.0	+	3720.52i	−0.604240	+	0.219925i	0.0217411	+	0.999764i	$0.493079\pi$
$660$		0			0
$661$	316.290	−	265.399i	0.0186116	−	0.0156170i	−0.633434	−	0.773796i	$-0.718355\pi$
$661$	316.290	−	265.399i	0.0186116	−	0.0156170i	0.652046	+	0.758179i	$0.273911\pi$
$662$		0			0
$663$	16193.9	+	7910.68i	0.948594	+	0.463387i
$664$		0			0
$665$	1143.93	+	1981.35i	0.0667063	+	0.115539i
$666$		0			0
$667$	−6500.75	+	11259.6i	−0.377377	+	0.653635i
$668$		0			0
$669$	7709.04	−	26822.0i	0.445514	−	1.55007i
$670$		0			0
$671$	8946.57	+	50738.5i	0.514722	+	2.91913i
$672$		0			0
$673$	−18608.4	−	15614.3i	−1.06582	−	0.894333i	−0.0711564	−	0.997465i	$-0.522669\pi$
$673$	−18608.4	−	15614.3i	−1.06582	−	0.894333i	−0.994668	+	0.103133i	$0.967113\pi$
$674$		0			0
$675$	6980.91	+	11218.1i	0.398067	+	0.639679i
$676$		0			0
$677$	−8328.43	−	6988.38i	−0.472803	−	0.396729i	0.375013	−	0.927020i	$-0.377638\pi$
$677$	−8328.43	−	6988.38i	−0.472803	−	0.396729i	−0.847816	+	0.530291i	$0.822083\pi$
$678$		0			0
$679$	1450.95	+	8228.77i	0.0820067	+	0.465083i
$680$		0			0
$681$	9598.38	−	2386.84i	0.540104	−	0.134308i
$682$		0			0
$683$	6279.52	−	10876.5i	0.351800	−	0.609335i	−0.634765	−	0.772705i	$-0.718903\pi$
$683$	6279.52	−	10876.5i	0.351800	−	0.609335i	0.986565	+	0.163370i	$0.0522365\pi$
$684$		0			0
$685$	−7127.96	−	12346.0i	−0.397585	−	0.688637i
$686$		0			0
$687$	11078.2	−	7462.36i	0.615224	−	0.414420i
$688$		0			0
$689$	−13034.1	+	10936.9i	−0.720698	+	0.604737i
$690$		0			0
$691$	16718.3	−	6084.96i	0.920396	−	0.334997i	0.162000	−	0.986791i	$-0.448206\pi$
$691$	16718.3	−	6084.96i	0.920396	−	0.334997i	0.758396	+	0.651794i	$0.225983\pi$
$692$		0			0
$693$	−641.165	+	17731.5i	−0.0351455	+	0.971955i
$694$		0			0
$695$	−2414.65	+	13694.2i	−0.131788	+	0.747408i
$696$		0			0
$697$	−11180.5	−	4069.38i	−0.607594	−	0.221146i
$698$		0			0
$699$	−7469.76	−	16805.3i	−0.404195	−	0.909350i
$700$		0			0
$701$	21646.4			1.16629			0.583147	−	0.812367i	$-0.301821\pi$
$701$	21646.4			1.16629			0.583147	+	0.812367i	$0.301821\pi$
$702$		0			0
$703$	3641.41			0.195360
$704$		0			0
$705$	1031.02	−	1417.23i	0.0550787	−	0.0757108i
$706$		0			0
$707$	4576.81	+	1665.82i	0.243463	+	0.0886135i
$708$		0			0
$709$	3459.28	−	19618.5i	0.183238	−	1.03920i	−0.744960	−	0.667109i	$-0.767532\pi$
$709$	3459.28	−	19618.5i	0.183238	−	1.03920i	0.928198	−	0.372086i	$-0.121357\pi$
$710$		0			0
$711$	−10846.7	−	13918.5i	−0.572126	−	0.734158i
$712$		0			0
$713$	17492.2	−	6366.64i	0.918777	−	0.334407i
$714$		0			0
$715$	25202.2	−	21147.1i	1.31819	−	1.10609i
$716$		0			0
$717$	−2194.16	−	31659.4i	−0.114285	−	1.64901i
$718$		0			0
$719$	10932.0	+	18934.8i	0.567031	+	0.982126i	0.996858	+	0.0792148i	$0.0252413\pi$
$719$	10932.0	+	18934.8i	0.567031	+	0.982126i	−0.429827	+	0.902911i	$0.641425\pi$
$720$		0			0
$721$	1476.73	−	2557.77i	0.0762779	−	0.132117i
$722$		0			0
$723$	11579.5	+	12005.8i	0.595639	+	0.617566i
$724$		0			0
$725$	−3047.00	−	17280.4i	−0.156087	−	0.885211i
$726$		0			0
$727$	−25330.4	−	21254.7i	−1.29223	−	1.08431i	−0.991432	−	0.130623i	$-0.958302\pi$
$727$	−25330.4	−	21254.7i	−1.29223	−	1.08431i	−0.300799	−	0.953688i	$-0.597253\pi$
$728$		0			0
$729$	15880.8	+	11628.4i	0.806830	+	0.590784i
$730$		0			0
$731$	−8562.15	−	7184.49i	−0.433218	−	0.363513i
$732$		0			0
$733$	2985.32	+	16930.6i	0.150430	+	0.853131i	0.962846	+	0.270052i	$0.0870410\pi$
$733$	2985.32	+	16930.6i	0.150430	+	0.853131i	−0.812416	+	0.583079i	$0.801848\pi$
$734$		0			0
$735$	−5192.85	−	5384.02i	−0.260600	−	0.270194i
$736$		0			0
$737$	−1108.59	+	1920.14i	−0.0554077	+	0.0959689i
$738$		0			0
$739$	9649.35	+	16713.2i	0.480321	+	0.831940i	0.999745	−	0.0225766i	$-0.00718696\pi$
$739$	9649.35	+	16713.2i	0.480321	+	0.831940i	−0.519424	+	0.854516i	$0.673854\pi$
$740$		0			0
$741$	1335.04	+	19263.1i	0.0661859	+	0.954992i
$742$		0			0
$743$	20573.9	−	17263.5i	1.01586	−	0.852405i	0.0267555	−	0.999642i	$-0.491482\pi$
$743$	20573.9	−	17263.5i	1.01586	−	0.852405i	0.989101	+	0.147237i	$0.0470380\pi$
$744$		0			0
$745$	602.767	−	219.389i	0.0296425	−	0.0107890i
$746$		0			0
$747$	−19132.7	−	24551.3i	−0.937122	−	1.20252i
$748$		0			0
$749$	−332.707	+	1886.87i	−0.0162308	+	0.0920492i
$750$		0			0
$751$	−27645.8	−	10062.2i	−1.34329	−	0.488916i	−0.432440	−	0.901663i	$-0.642347\pi$
$751$	−27645.8	−	10062.2i	−1.34329	−	0.488916i	−0.910846	+	0.412746i	$0.864570\pi$
$752$		0			0
$753$	−11032.0	+	15164.5i	−0.533903	+	0.733899i
$754$		0			0
$755$	8651.72			0.417044
$756$		0			0
$757$	24191.8			1.16151			0.580756	−	0.814077i	$-0.302757\pi$
$757$	24191.8			1.16151			0.580756	+	0.814077i	$0.302757\pi$
$758$		0			0
$759$	10578.7	+	23799.7i	0.505905	+	1.13818i
$760$		0			0
$761$	12610.5	+	4589.85i	0.600698	+	0.218636i	0.624428	−	0.781082i	$-0.285332\pi$
$761$	12610.5	+	4589.85i	0.600698	+	0.218636i	−0.0237304	+	0.999718i	$0.507554\pi$
$762$		0			0
$763$	−311.565	+	1766.97i	−0.0147830	+	0.0838383i
$764$		0			0
$765$	−227.730	+	6297.93i	−0.0107629	+	0.297650i
$766$		0			0
$767$	−46066.3	+	16766.8i	−2.16866	+	0.789326i
$768$		0			0
$769$	16690.9	−	14005.3i	0.782689	−	0.656754i	−0.161235	−	0.986916i	$-0.551548\pi$
$769$	16690.9	−	14005.3i	0.782689	−	0.656754i	0.943924	+	0.330162i	$0.107103\pi$
$770$		0			0
$771$	27819.4	−	18739.4i	1.29947	−	0.875336i
$772$		0			0
$773$	−670.497	−	1161.34i	−0.0311981	−	0.0540367i	0.850005	−	0.526775i	$-0.176599\pi$
$773$	−670.497	−	1161.34i	−0.0311981	−	0.0540367i	−0.881203	+	0.472738i	$0.843266\pi$
$774$		0			0
$775$	−12561.4	+	21756.9i	−0.582216	+	1.00843i
$776$		0			0
$777$	3729.54	−	927.428i	0.172196	−	0.0428202i
$778$		0			0
$779$	−2213.57	−	12553.8i	−0.101809	−	0.577389i
$780$		0			0
$781$	−17103.1	−	14351.2i	−0.783607	−	0.657524i
$782$		0			0
$783$	−13810.7	−	22193.3i	−0.630338	−	1.01293i
$784$		0			0
$785$	7749.10	+	6502.26i	0.352327	+	0.295638i
$786$		0			0
$787$	−508.621	−	2884.53i	−0.0230373	−	0.130651i	0.971120	−	0.238591i	$-0.0766856\pi$
$787$	−508.621	−	2884.53i	−0.0230373	−	0.130651i	−0.994157	+	0.107940i	$0.965575\pi$
$788$		0			0
$789$	10951.8	−	38104.5i	0.494163	−	1.71934i
$790$		0			0
$791$	990.373	−	1715.38i	0.0445178	−	0.0771071i
$792$		0			0
$793$	29587.5	+	51247.1i	1.32495	+	2.29488i
$794$		0			0
$795$	−5345.85	−	2611.44i	−0.238488	−	0.116501i
$796$		0			0
$797$	−21377.1	+	17937.5i	−0.950082	+	0.797213i	−0.979311	−	0.202359i	$-0.935139\pi$
$797$	−21377.1	+	17937.5i	−0.950082	+	0.797213i	0.0292296	+	0.999573i	$0.490695\pi$
$798$		0			0
$799$	−2400.15	+	873.585i	−0.106272	+	0.0386799i
$800$		0			0
$801$	8719.60	−	9660.03i	0.384634	−	0.426118i
$802$		0			0
$803$	6582.97	−	37333.9i	0.289300	−	1.64070i
$804$		0			0
$805$	3330.61	+	1212.24i	0.145824	+	0.0530756i
$806$		0			0
$807$	38331.6	+	4052.79i	1.67204	+	0.176785i
$808$		0			0
$809$	12704.1			0.552104			0.276052	−	0.961143i	$-0.410974\pi$
$809$	12704.1			0.552104			0.276052	+	0.961143i	$0.410974\pi$
$810$		0			0
$811$	5012.10			0.217014			0.108507	−	0.994096i	$-0.465393\pi$
$811$	5012.10			0.217014			0.108507	+	0.994096i	$0.465393\pi$
$812$		0			0
$813$	30729.9	+	3249.07i	1.32564	+	0.140160i
$814$		0			0
$815$	9313.93	+	3389.99i	0.400310	+	0.145701i
$816$		0			0
$817$	2079.43	−	11793.1i	0.0890455	−	0.505002i
$818$		0			0
$819$	6273.47	+	19389.3i	0.267659	+	0.827251i
$820$		0			0
$821$	−13568.4	+	4938.51i	−0.576787	+	0.209933i	−0.613908	−	0.789378i	$-0.710403\pi$
$821$	−13568.4	+	4938.51i	−0.576787	+	0.209933i	0.0371213	+	0.999311i	$0.488181\pi$
$822$		0			0
$823$	677.888	−	568.816i	0.0287117	−	0.0240919i	−0.628319	−	0.777956i	$-0.716257\pi$
$823$	677.888	−	568.816i	0.0287117	−	0.0240919i	0.657031	+	0.753864i	$0.271812\pi$
$824$		0			0
$825$	−31583.5	−	15428.5i	−1.33284	−	0.651093i
$826$		0			0
$827$	−16997.2	−	29440.1i	−0.714693	−	1.23789i	−0.963078	−	0.269224i	$-0.913233\pi$
$827$	−16997.2	−	29440.1i	−0.714693	−	1.23789i	0.248384	−	0.968662i	$-0.420100\pi$
$828$		0			0
$829$	2235.23	−	3871.54i	0.0936463	−	0.162200i	−0.815397	−	0.578903i	$-0.803481\pi$
$829$	2235.23	−	3871.54i	0.0936463	−	0.162200i	0.909043	+	0.416703i	$0.136814\pi$
$830$		0			0
$831$	−872.129	+	3034.39i	−0.0364065	+	0.126669i
$832$		0			0
$833$	1893.03	+	10735.9i	0.0787390	+	0.446551i
$834$		0			0
$835$	4965.12	+	4166.23i	0.205779	+	0.172669i
$836$		0			0
$837$	−5277.34	+	37051.2i	−0.217935	+	1.53008i
$838$		0			0
$839$	−4716.06	−	3957.24i	−0.194060	−	0.162836i	0.540580	−	0.841292i	$-0.318205\pi$
$839$	−4716.06	−	3957.24i	−0.194060	−	0.162836i	−0.734640	+	0.678457i	$0.762649\pi$
$840$		0			0
$841$	1792.94	+	10168.3i	0.0735142	+	0.416920i
$842$		0			0
$843$	−34275.7	+	8523.36i	−1.40038	+	0.348233i
$844$		0			0
$845$	12794.6	−	22160.9i	0.520886	−	0.902201i
$846$		0			0
$847$	−17512.8	−	30333.0i	−0.710444	−	1.23052i
$848$		0			0
$849$	320.547	−	215.923i	0.0129578	−	0.00872846i
$850$		0			0
$851$	4321.46	−	3626.14i	0.174075	−	0.146066i
$852$		0			0
$853$	8837.84	−	3216.71i	0.354750	−	0.129119i	−0.158497	−	0.987360i	$-0.550665\pi$
$853$	8837.84	−	3216.71i	0.354750	−	0.129119i	0.513247	+	0.858241i	$0.328442\pi$
$854$		0			0
$855$	−5965.51	+	3162.46i	−0.238615	+	0.126496i
$856$		0			0
$857$	2250.77	−	12764.8i	0.0897141	−	0.508794i	−0.906525	−	0.422151i	$-0.861275\pi$
$857$	2250.77	−	12764.8i	0.0897141	−	0.508794i	0.996239	−	0.0866426i	$-0.0276138\pi$
$858$		0			0
$859$	22836.3	+	8311.73i	0.907059	+	0.330143i	0.753078	−	0.657931i	$-0.228568\pi$
$859$	22836.3	+	8311.73i	0.907059	+	0.330143i	0.153981	+	0.988074i	$0.450791\pi$
$860$		0			0
$861$	−5464.46	−	12293.8i	−0.216293	−	0.486612i
$862$		0			0
$863$	21125.6			0.833285			0.416643	−	0.909070i	$-0.363207\pi$
$863$	21125.6			0.833285			0.416643	+	0.909070i	$0.363207\pi$
$864$		0			0
$865$	−23209.9			−0.912323
$866$		0			0
$867$	−9615.06	+	13216.8i	−0.376637	+	0.517723i
$868$		0			0
$869$	44112.8	+	16055.7i	1.72201	+	0.626759i
$870$		0			0
$871$	−442.205	+	2507.87i	−0.0172027	+	0.0975614i
$872$		0			0
$873$	−24423.6	+	3401.70i	−0.946865	+	0.131879i
$874$		0			0
$875$	−10461.1	+	3807.55i	−0.404173	+	0.147107i
$876$		0			0
$877$	22826.9	−	19154.0i	0.878915	−	0.737498i	−0.0870404	−	0.996205i	$-0.527741\pi$
$877$	22826.9	−	19154.0i	0.878915	−	0.737498i	0.965956	+	0.258707i	$0.0832965\pi$
$878$		0			0
$879$	35.8002	+	516.559i	0.00137373	+	0.0198215i
$880$		0			0
$881$	−13196.2	−	22856.4i	−0.504643	−	0.874066i	−0.999986	−	0.00536903i	$-0.998291\pi$
$881$	−13196.2	−	22856.4i	−0.504643	−	0.874066i	0.495343	−	0.868697i	$-0.335042\pi$
$882$		0			0
$883$	8184.93	−	14176.7i	0.311942	−	0.540299i	−0.666841	−	0.745200i	$-0.732354\pi$
$883$	8184.93	−	14176.7i	0.311942	−	0.540299i	0.978783	+	0.204901i	$0.0656872\pi$
$884$		0			0
$885$	−11900.1	−	12338.2i	−0.451997	−	0.468637i
$886$		0			0
$887$	4816.38	+	27315.0i	0.182320	+	1.03399i	0.929350	+	0.369200i	$0.120368\pi$
$887$	4816.38	+	27315.0i	0.182320	+	1.03399i	−0.747030	+	0.664791i	$0.768521\pi$
$888$		0			0
$889$	8574.42	+	7194.79i	0.323483	+	0.271435i
$890$		0			0
$891$	−52226.6	−	3781.93i	−1.96370	−	0.142199i
$892$		0			0
$893$	−2096.30	−	1759.01i	−0.0785555	−	0.0659159i
$894$		0			0
$895$	1771.02	+	10044.0i	0.0661439	+	0.375121i
$896$		0			0
$897$	20766.7	+	21531.2i	0.773000	+	0.801457i
$898$		0			0
$899$	24850.8	−	43042.9i	0.921937	−	1.59684i
$900$		0			0
$901$	4335.43	+	7509.18i	0.160304	+	0.277655i
$902$		0			0
$903$	−873.806	−	12608.1i	−0.0322020	−	0.464641i
$904$		0			0
$905$	−9845.02	+	8260.96i	−0.361613	+	0.303429i
$906$		0			0
$907$	15389.5	−	5601.34i	0.563397	−	0.205060i	−0.0445917	−	0.999005i	$-0.514199\pi$
$907$	15389.5	−	5601.34i	0.563397	−	0.205060i	0.607989	+	0.793945i	$0.291976\pi$
$908$		0			0
$909$	−5401.05	+	13320.6i	−0.197075	+	0.486046i
$910$		0			0
$911$	1424.52	−	8078.83i	0.0518071	−	0.293813i	−0.947885	−	0.318612i	$-0.896783\pi$
$911$	1424.52	−	8078.83i	0.0518071	−	0.293813i	0.999692	+	0.0247988i	$0.00789451\pi$
$912$		0			0
$913$	77811.8	+	28321.2i	2.82059	+	1.02661i
$914$		0			0
$915$	−12172.7	+	16732.5i	−0.439800	+	0.604546i
$916$		0			0
$917$	10260.1			0.369486
$918$		0			0
$919$	−33771.8			−1.21222			−0.606109	−	0.795381i	$-0.707271\pi$
$919$	−33771.8			−1.21222			−0.606109	+	0.795381i	$0.707271\pi$
$920$		0			0
$921$	10539.9	+	23712.5i	0.377093	+	0.848376i
$922$		0			0
$923$	−24096.8	−	8770.52i	−0.859324	−	0.312768i
$924$		0			0
$925$	−1322.07	+	7497.85i	−0.0469941	+	0.266517i
$926$		0			0
$927$	7386.07	+	4628.05i	0.261694	+	0.163975i
$928$		0			0
$929$	−45473.2	+	16550.9i	−1.60595	+	0.584518i	−0.980633	−	0.195853i	$-0.937253\pi$
$929$	−45473.2	+	16550.9i	−1.60595	+	0.584518i	−0.625317	+	0.780371i	$0.715030\pi$
$930$		0			0
$931$	−8947.20	+	7507.60i	−0.314965	+	0.264287i
$932$		0			0
$933$	−32254.8	+	21727.1i	−1.13180	+	0.762394i
$934$		0			0
$935$	−8382.77	−	14519.4i	−0.293204	−	0.507845i
$936$		0			0
$937$	−20974.0	+	36328.0i	−0.731258	+	1.26658i	0.225087	+	0.974339i	$0.427733\pi$
$937$	−20974.0	+	36328.0i	−0.731258	+	1.26658i	−0.956346	+	0.292238i	$0.905600\pi$
$938$		0			0
$939$	−22387.1	+	5567.02i	−0.778035	+	0.193475i
$940$		0			0
$941$	−2249.89	−	12759.8i	−0.0779431	−	0.442037i	−0.998657	−	0.0518001i	$-0.983504\pi$
$941$	−2249.89	−	12759.8i	−0.0779431	−	0.442037i	0.920714	−	0.390237i	$-0.127607\pi$
$942$		0			0
$943$	−15128.1	−	12694.0i	−0.522417	−	0.438360i
$944$		0			0
$945$	−5304.45	+	4758.35i	−0.182596	+	0.163798i
$946$		0			0
$947$	−16485.1	−	13832.7i	−0.565675	−	0.474658i	0.314532	−	0.949247i	$-0.398152\pi$
$947$	−16485.1	−	13832.7i	−0.565675	−	0.474658i	−0.880208	+	0.474589i	$0.842597\pi$
$948$		0			0
$949$	−7560.92	−	42880.1i	−0.258628	−	1.46675i
$950$		0			0
$951$	2478.84	−	8624.61i	0.0845236	−	0.294082i
$952$		0			0
$953$	−17377.4	+	30098.5i	−0.590669	+	1.02307i	0.403473	+	0.914991i	$0.367803\pi$
$953$	−17377.4	+	30098.5i	−0.590669	+	1.02307i	−0.994142	+	0.108078i	$0.965531\pi$
$954$		0			0
$955$	4744.63	+	8217.94i	0.160767	+	0.278457i
$956$		0			0
$957$	62483.3	+	30523.0i	2.11055	+	1.03100i
$958$		0			0
$959$	−17996.4	+	15100.7i	−0.605978	+	0.508476i
$960$		0			0
$961$	−38874.1	+	14149.0i	−1.30489	+	0.474942i
$962$		0			0
$963$	−5529.41	−	1182.46i	−0.185029	−	0.0395684i
$964$		0			0
$965$	2989.14	−	16952.3i	0.0997139	−	0.565506i
$966$		0			0
$967$	17056.1	+	6207.92i	0.567205	+	0.206446i	0.609675	−	0.792652i	$-0.291300\pi$
$967$	17056.1	+	6207.92i	0.567205	+	0.206446i	−0.0424690	+	0.999098i	$0.513522\pi$
$968$		0			0
$969$	9785.61	+	1034.63i	0.324416	+	0.0343004i
$970$		0			0
$971$	−32473.1			−1.07324			−0.536618	−	0.843825i	$-0.680298\pi$
$971$	−32473.1			−1.07324			−0.536618	+	0.843825i	$0.680298\pi$
$972$		0			0
$973$	22914.9			0.755005
$974$		0			0
$975$	−40148.6	−	4244.90i	−1.31875	−	0.139431i
$976$		0			0
$977$	2618.73	+	953.139i	0.0857529	+	0.0312115i	0.384540	−	0.923108i	$-0.374360\pi$
$977$	2618.73	+	953.139i	0.0857529	+	0.0312115i	−0.298787	+	0.954320i	$0.596582\pi$
$978$		0			0
$979$	−6011.69	+	34094.0i	−0.196256	+	1.11302i
$980$		0			0
$981$	−5178.04	−	1107.32i	−0.168524	−	0.0360389i
$982$		0			0
$983$	54587.2	−	19868.1i	1.77117	−	0.644654i	0.771205	−	0.636587i	$-0.219654\pi$
$983$	54587.2	−	19868.1i	1.77117	−	0.644654i	0.999967	−	0.00806713i	$-0.00256788\pi$
$984$		0			0
$985$	−2290.59	+	1922.04i	−0.0740958	+	0.0621737i
$986$		0			0
$987$	−2595.04	−	1267.67i	−0.0836889	−	0.0408819i
$988$		0			0
$989$	−9275.82	−	16066.2i	−0.298235	−	0.516557i
$990$		0			0
$991$	−16680.9	+	28892.1i	−0.534698	+	0.926124i	0.464480	+	0.885584i	$0.346241\pi$
$991$	−16680.9	+	28892.1i	−0.534698	+	0.926124i	−0.999178	+	0.0405401i	$0.987092\pi$
$992$		0			0
$993$	1211.54	−	4215.28i	0.0387180	−	0.134711i
$994$		0			0
$995$	3561.72	+	20199.5i	0.113481	+	0.643585i
$996$		0			0
$997$	21033.1	+	17648.8i	0.668128	+	0.560626i	0.912511	−	0.409053i	$-0.134141\pi$
$997$	21033.1	+	17648.8i	0.668128	+	0.560626i	−0.244383	+	0.969679i	$0.578585\pi$
$998$		0			0
$999$	2337.50	+	11098.3i	0.0740292	+	0.351486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.97.1	yes	54
3.2	odd	2		324.4.i.a.289.4		54
27.5	odd	18		324.4.i.a.37.4		54
27.22	even	9	inner	108.4.i.a.49.1	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.49.1	✓	54	27.22	even	9	inner
108.4.i.a.97.1	yes	54	1.1	even	1	trivial
324.4.i.a.37.4		54	27.5	odd	18
324.4.i.a.289.4		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)

\(f(q)\)	\(=\)	\(q+(-5.16735 - 0.546343i) q^{3} +(5.21695 + 1.89881i) q^{5} +(1.58868 - 9.00985i) q^{7} +(26.4030 + 5.64629i) q^{9} +O(q^{10})\)	\(q+(-5.16735 - 0.546343i) q^{3} +(5.21695 + 1.89881i) q^{5} +(1.58868 - 9.00985i) q^{7} +(26.4030 + 5.64629i) q^{9} +(-67.4972 + 24.5670i) q^{11} +(-63.1985 + 53.0298i) q^{13} +(-25.9204 - 12.6621i) q^{15} +(21.0212 + 36.4097i) q^{17} +(-22.5218 + 39.0089i) q^{19} +(-13.1317 + 45.6891i) q^{21} +(12.1174 + 68.7214i) q^{23} +(-72.1445 - 60.5364i) q^{25} +(-133.349 - 43.6014i) q^{27} +(142.727 + 119.762i) q^{29} +(-46.3221 - 262.706i) q^{31} +(362.204 - 90.0696i) q^{33} +(25.3961 - 43.9873i) q^{35} +(-40.4209 - 70.0111i) q^{37} +(355.541 - 239.496i) q^{39} +(-216.792 + 181.910i) q^{41} +(-249.820 + 90.9271i) q^{43} +(127.022 + 79.5908i) q^{45} +(-10.5496 + 59.8299i) q^{47} +(243.661 + 88.6854i) q^{49} +(-88.7316 - 199.627i) q^{51} +206.241 q^{53} -398.778 q^{55} +(137.690 - 189.268i) q^{57} +(558.381 + 203.234i) q^{59} +(124.554 - 706.379i) q^{61} +(92.8181 - 228.917i) q^{63} +(-430.397 + 156.652i) q^{65} +(23.6459 - 19.8412i) q^{67} +(-25.0696 - 361.728i) q^{69} +(155.414 + 269.185i) q^{71} +(-263.889 + 457.070i) q^{73} +(339.722 + 352.229i) q^{75} +(114.113 + 647.169i) q^{77} +(-500.648 - 420.094i) q^{79} +(665.239 + 298.158i) q^{81} +(-883.108 - 741.015i) q^{83} +(40.5310 + 229.863i) q^{85} +(-672.091 - 696.832i) q^{87} +(240.988 - 417.404i) q^{89} +(377.389 + 653.656i) q^{91} +(95.8352 + 1382.80i) q^{93} +(-191.566 + 160.743i) q^{95} +(-858.230 + 312.370i) q^{97} +(-1920.84 + 267.534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more