LMFDB - Embedded newform 108.4.i.a.97.8

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			97.8
Character	$\chi$	$=$	108.97
Dual form			108.4.i.a.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.05072 - 1.22075i) q^{3} +(11.1609 + 4.06223i) q^{5} +(-4.28132 + 24.2806i) q^{7} +(24.0196 - 12.3313i) q^{9} +O(q^{10})$	\(q+(5.05072 - 1.22075i) q^{3} +(11.1609 + 4.06223i) q^{5} +(-4.28132 + 24.2806i) q^{7} +(24.0196 - 12.3313i) q^{9} +(-9.00480 + 3.27748i) q^{11} +(6.18439 - 5.18932i) q^{13} +(61.3295 + 6.89258i) q^{15} +(-16.8131 - 29.1212i) q^{17} +(57.3341 - 99.3056i) q^{19} +(8.01668 + 127.861i) q^{21} +(29.4732 + 167.151i) q^{23} +(12.3082 + 10.3278i) q^{25} +(106.263 - 91.6038i) q^{27} +(-1.33025 - 1.11621i) q^{29} +(-26.8769 - 152.426i) q^{31} +(-41.4798 + 27.5462i) q^{33} +(-146.417 + 253.601i) q^{35} +(-143.047 - 247.765i) q^{37} +(24.9008 - 33.7594i) q^{39} +(93.7251 - 78.6447i) q^{41} +(-328.750 + 119.655i) q^{43} +(318.172 - 40.0553i) q^{45} +(-40.1073 + 227.460i) q^{47} +(-248.901 - 90.5926i) q^{49} +(-120.468 - 126.559i) q^{51} -647.947 q^{53} -113.816 q^{55} +(168.352 - 571.555i) q^{57} +(-824.149 - 299.966i) q^{59} +(126.231 - 715.889i) q^{61} +(196.576 + 636.002i) q^{63} +(90.1035 - 32.7950i) q^{65} +(-210.269 + 176.437i) q^{67} +(352.910 + 808.253i) q^{69} +(392.428 + 679.706i) q^{71} +(176.253 - 305.280i) q^{73} +(74.7732 + 37.1378i) q^{75} +(-41.0266 - 232.674i) q^{77} +(820.969 + 688.875i) q^{79} +(424.878 - 592.385i) q^{81} +(1012.90 + 849.924i) q^{83} +(-69.3525 - 393.318i) q^{85} +(-8.08135 - 4.01378i) q^{87} +(15.8047 - 27.3746i) q^{89} +(99.5222 + 172.377i) q^{91} +(-321.821 - 737.052i) q^{93} +(1043.30 - 875.434i) q^{95} +(64.2391 - 23.3811i) q^{97} +(-175.876 + 189.765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	5.05072	−	1.22075i	0.972012	−	0.234933i
$3$	5.05072	−	1.22075i	0.972012	−	0.234933i
$4$		0			0
$5$	11.1609	+	4.06223i	0.998261	+	0.363337i	0.788914	−	0.614504i	$-0.210644\pi$
$5$	11.1609	+	4.06223i	0.998261	+	0.363337i	0.209347	+	0.977841i	$0.432866\pi$
$6$		0			0
$7$	−4.28132	+	24.2806i	−0.231169	+	1.31103i	0.619363	+	0.785105i	$0.287391\pi$
$7$	−4.28132	+	24.2806i	−0.231169	+	1.31103i	−0.850533	+	0.525922i	$0.823720\pi$
$8$		0			0
$9$	24.0196	−	12.3313i	0.889613	−	0.456715i
$10$		0			0
$11$	−9.00480	+	3.27748i	−0.246823	+	0.0898361i	−0.462469	−	0.886635i	$-0.653036\pi$
$11$	−9.00480	+	3.27748i	−0.246823	+	0.0898361i	0.215646	+	0.976472i	$0.430814\pi$
$12$		0			0
$13$	6.18439	−	5.18932i	0.131942	−	0.110712i	−0.574429	−	0.818555i	$-0.694776\pi$
$13$	6.18439	−	5.18932i	0.131942	−	0.110712i	0.706370	+	0.707842i	$0.250331\pi$
$14$		0			0
$15$	61.3295	+	6.89258i	1.05568	+	0.118644i
$16$		0			0
$17$	−16.8131	−	29.1212i	−0.239870	−	0.415467i	0.720807	−	0.693136i	$-0.243771\pi$
$17$	−16.8131	−	29.1212i	−0.239870	−	0.415467i	−0.960677	+	0.277669i	$0.910438\pi$
$18$		0			0
$19$	57.3341	−	99.3056i	0.692281	−	1.19907i	−0.278807	−	0.960347i	$-0.589939\pi$
$19$	57.3341	−	99.3056i	0.692281	−	1.19907i	0.971089	−	0.238719i	$-0.0767276\pi$
$20$		0			0
$21$	8.01668	+	127.861i	0.0833040	+	1.32864i
$22$		0			0
$23$	29.4732	+	167.151i	0.267199	+	1.51536i	0.762698	+	0.646755i	$0.223874\pi$
$23$	29.4732	+	167.151i	0.267199	+	1.51536i	−0.495499	+	0.868609i	$0.665015\pi$
$24$		0			0
$25$	12.3082	+	10.3278i	0.0984660	+	0.0826228i
$26$		0			0
$27$	106.263	−	91.6038i	0.757417	−	0.652932i
$28$		0			0
$29$	−1.33025	−	1.11621i	−0.00851799	−	0.00714744i	0.638519	−	0.769606i	$-0.279548\pi$
$29$	−1.33025	−	1.11621i	−0.00851799	−	0.00714744i	−0.647037	+	0.762459i	$0.723992\pi$
$30$		0			0
$31$	−26.8769	−	152.426i	−0.155717	−	0.883115i	−0.958127	−	0.286342i	$-0.907561\pi$
$31$	−26.8769	−	152.426i	−0.155717	−	0.883115i	0.802410	−	0.596773i	$-0.203551\pi$
$32$		0			0
$33$	−41.4798	+	27.5462i	−0.218809	+	0.145309i
$34$		0			0
$35$	−146.417	+	253.601i	−0.707112	+	1.22475i
$36$		0			0
$37$	−143.047	−	247.765i	−0.635589	−	1.10087i	−0.986390	−	0.164422i	$-0.947424\pi$
$37$	−143.047	−	247.765i	−0.635589	−	1.10087i	0.350801	−	0.936450i	$-0.385909\pi$
$38$		0			0
$39$	24.9008	−	33.7594i	0.102239	−	0.138611i
$40$		0			0
$41$	93.7251	−	78.6447i	0.357010	−	0.299567i	−0.446588	−	0.894740i	$-0.647361\pi$
$41$	93.7251	−	78.6447i	0.357010	−	0.299567i	0.803598	+	0.595173i	$0.202916\pi$
$42$		0			0
$43$	−328.750	+	119.655i	−1.16590	+	0.424354i	−0.851203	−	0.524837i	$-0.824126\pi$
$43$	−328.750	+	119.655i	−1.16590	+	0.424354i	−0.314701	+	0.949191i	$0.601904\pi$
$44$		0			0
$45$	318.172	−	40.0553i	1.05401	−	0.132691i
$46$		0			0
$47$	−40.1073	+	227.460i	−0.124474	+	0.705925i	0.857146	+	0.515074i	$0.172236\pi$
$47$	−40.1073	+	227.460i	−0.124474	+	0.705925i	−0.981619	+	0.190850i	$0.938875\pi$
$48$		0			0
$49$	−248.901	−	90.5926i	−0.725659	−	0.264118i
$50$		0			0
$51$	−120.468	−	126.559i	−0.330763	−	0.347485i
$52$		0			0
$53$	−647.947			−1.67929			−0.839645	−	0.543136i	$-0.817237\pi$
$53$	−647.947			−1.67929			−0.839645	+	0.543136i	$0.817237\pi$
$54$		0			0
$55$	−113.816			−0.279034
$56$		0			0
$57$	168.352	−	571.555i	0.391205	−	1.32815i
$58$		0			0
$59$	−824.149	−	299.966i	−1.81856	−	0.661902i	−0.995589	−	0.0938171i	$-0.970093\pi$
$59$	−824.149	−	299.966i	−1.81856	−	0.661902i	−0.822970	−	0.568085i	$-0.807685\pi$
$60$		0			0
$61$	126.231	−	715.889i	0.264954	−	1.50263i	−0.504214	−	0.863579i	$-0.668218\pi$
$61$	126.231	−	715.889i	0.264954	−	1.50263i	0.769167	−	0.639048i	$-0.220671\pi$
$62$		0			0
$63$	196.576	+	636.002i	0.393114	+	1.27189i
$64$		0			0
$65$	90.1035	−	32.7950i	0.171938	−	0.0625803i
$66$		0			0
$67$	−210.269	+	176.437i	−0.383410	+	0.321719i	−0.814039	−	0.580810i	$-0.802736\pi$
$67$	−210.269	+	176.437i	−0.383410	+	0.321719i	0.430629	+	0.902529i	$0.358292\pi$
$68$		0			0
$69$	352.910	+	808.253i	0.615730	+	1.41018i
$70$		0			0
$71$	392.428	+	679.706i	0.655953	+	1.13614i	0.981654	+	0.190671i	$0.0610664\pi$
$71$	392.428	+	679.706i	0.655953	+	1.13614i	−0.325701	+	0.945473i	$0.605600\pi$
$72$		0			0
$73$	176.253	−	305.280i	0.282588	−	0.489456i	−0.689434	−	0.724349i	$-0.742141\pi$
$73$	176.253	−	305.280i	0.282588	−	0.489456i	0.972021	+	0.234893i	$0.0754739\pi$
$74$		0			0
$75$	74.7732	+	37.1378i	0.115121	+	0.0571774i
$76$		0			0
$77$	−41.0266	−	232.674i	−0.0607197	−	0.344359i
$78$		0			0
$79$	820.969	+	688.875i	1.16919	+	0.981070i	0.999990	−	0.00451148i	$-0.00143605\pi$
$79$	820.969	+	688.875i	1.16919	+	0.981070i	0.169203	+	0.985581i	$0.445880\pi$
$80$		0			0
$81$	424.878	−	592.385i	0.582823	−	0.812599i
$82$		0			0
$83$	1012.90	+	849.924i	1.33952	+	1.12399i	0.981749	+	0.190182i	$0.0609080\pi$
$83$	1012.90	+	849.924i	1.33952	+	1.12399i	0.357772	+	0.933809i	$0.383536\pi$
$84$		0			0
$85$	−69.3525	−	393.318i	−0.0884981	−	0.501897i
$86$		0			0
$87$	−8.08135	−	4.01378i	−0.00995875	−	0.00494624i
$88$		0			0
$89$	15.8047	−	27.3746i	0.0188236	−	0.0326034i	−0.856460	−	0.516213i	$-0.827341\pi$
$89$	15.8047	−	27.3746i	0.0188236	−	0.0326034i	0.875284	+	0.483610i	$0.160675\pi$
$90$		0			0
$91$	99.5222	+	172.377i	0.114646	+	0.198572i
$92$		0			0
$93$	−321.821	−	737.052i	−0.358831	−	0.821815i
$94$		0			0
$95$	1043.30	−	875.434i	1.12674	−	0.945449i
$96$		0			0
$97$	64.2391	−	23.3811i	0.0672422	−	0.0244742i	−0.308180	−	0.951328i	$-0.599720\pi$
$97$	64.2391	−	23.3811i	0.0672422	−	0.0244742i	0.375422	+	0.926854i	$0.377498\pi$
$98$		0			0
$99$	−175.876	+	189.765i	−0.178547	+	0.192647i
$100$		0			0
$101$	−111.400	+	631.783i	−0.109750	+	0.622423i	0.879466	+	0.475961i	$0.157900\pi$
$101$	−111.400	+	631.783i	−0.109750	+	0.622423i	−0.989216	+	0.146462i	$0.953211\pi$
$102$		0			0
$103$	−1465.14	−	533.267i	−1.40160	−	0.510140i	−0.472945	−	0.881092i	$-0.656809\pi$
$103$	−1465.14	−	533.267i	−1.40160	−	0.510140i	−0.928652	+	0.370952i	$0.879031\pi$
$104$		0			0
$105$	−429.927	+	1459.61i	−0.399586	+	1.35660i
$106$		0			0
$107$	−84.9771			−0.0767762			−0.0383881	−	0.999263i	$-0.512222\pi$
$107$	−84.9771			−0.0767762			−0.0383881	+	0.999263i	$0.512222\pi$
$108$		0			0
$109$	2199.34			1.93265			0.966324	−	0.257329i	$-0.0828424\pi$
$109$	2199.34			1.93265			0.966324	+	0.257329i	$0.0828424\pi$
$110$		0			0
$111$	−1024.95	−	1076.77i	−0.876431	−	0.920740i
$112$		0			0
$113$	184.357	+	67.1006i	0.153477	+	0.0558610i	0.417616	−	0.908624i	$-0.362866\pi$
$113$	184.357	+	67.1006i	0.153477	+	0.0558610i	−0.264139	+	0.964485i	$0.585088\pi$
$114$		0			0
$115$	−350.058	+	1985.28i	−0.283853	+	1.60981i
$116$		0			0
$117$	84.5552	−	200.907i	0.0668131	−	0.158751i
$118$		0			0
$119$	779.061	−	283.555i	0.600138	−	0.218432i
$120$		0			0
$121$	−949.261	+	796.524i	−0.713194	+	0.598440i
$122$		0			0
$123$	377.374	−	511.627i	0.276640	−	0.375056i
$124$		0			0
$125$	−646.907	−	1120.47i	−0.462889	−	0.801747i
$126$		0			0
$127$	697.879	−	1208.76i	0.487612	−	0.844569i	−0.512286	−	0.858815i	$-0.671201\pi$
$127$	697.879	−	1208.76i	0.487612	−	0.844569i	0.999899	+	0.0142455i	$0.00453464\pi$
$128$		0			0
$129$	−1514.35	+	1005.66i	−1.03358	+	0.686386i
$130$		0			0
$131$	−436.059	−	2473.01i	−0.290829	−	1.64937i	−0.683687	−	0.729775i	$-0.739625\pi$
$131$	−436.059	−	2473.01i	−0.290829	−	1.64937i	0.392858	−	0.919599i	$-0.371487\pi$
$132$		0			0
$133$	2165.73	+	1817.26i	1.41197	+	1.18479i
$134$		0			0
$135$	1558.10	−	590.716i	0.993334	−	0.376598i
$136$		0			0
$137$	−320.673	−	269.077i	−0.199978	−	0.167801i	0.537300	−	0.843391i	$-0.319444\pi$
$137$	−320.673	−	269.077i	−0.199978	−	0.167801i	−0.737277	+	0.675590i	$0.763889\pi$
$138$		0			0
$139$	128.625	+	729.470i	0.0784881	+	0.445128i	0.998573	+	0.0534085i	$0.0170086\pi$
$139$	128.625	+	729.470i	0.0784881	+	0.445128i	−0.920085	+	0.391720i	$0.871880\pi$
$140$		0			0
$141$	75.1002	+	1197.80i	0.0448552	+	0.715410i
$142$		0			0
$143$	−38.6813	+	66.9980i	−0.0226202	+	0.0391794i
$144$		0			0
$145$	−10.3125	−	17.8617i	−0.00590624	−	0.0102299i
$146$		0			0
$147$	−1367.72	−	153.713i	−0.767399	−	0.0862449i
$148$		0			0
$149$	165.624	−	138.975i	0.0910633	−	0.0764112i	−0.596120	−	0.802896i	$-0.703292\pi$
$149$	165.624	−	138.975i	0.0910633	−	0.0764112i	0.687183	+	0.726485i	$0.258847\pi$
$150$		0			0
$151$	−1498.00	+	545.227i	−0.807320	+	0.293841i	−0.712516	−	0.701655i	$-0.752445\pi$
$151$	−1498.00	+	545.227i	−0.807320	+	0.293841i	−0.0948039	+	0.995496i	$0.530222\pi$
$152$		0			0
$153$	−762.947	−	492.151i	−0.403141	−	0.260052i
$154$		0			0
$155$	319.221	−	1810.39i	0.165422	−	0.938156i
$156$		0			0
$157$	−340.759	−	124.026i	−0.173220	−	0.0630469i	0.253954	−	0.967216i	$-0.418269\pi$
$157$	−340.759	−	124.026i	−0.173220	−	0.0630469i	−0.427174	+	0.904169i	$0.640491\pi$
$158$		0			0
$159$	−3272.60	+	790.979i	−1.63229	+	0.394520i
$160$		0			0
$161$	−4184.70			−2.04845
$162$		0			0
$163$	−1635.53			−0.785916			−0.392958	−	0.919557i	$-0.628548\pi$
$163$	−1635.53			−0.785916			−0.392958	+	0.919557i	$0.628548\pi$
$164$		0			0
$165$	−574.850	+	138.940i	−0.271225	+	0.0655543i
$166$		0			0
$167$	1583.68	+	576.413i	0.733826	+	0.267091i	0.681784	−	0.731554i	$-0.261205\pi$
$167$	1583.68	+	576.413i	0.733826	+	0.267091i	0.0520427	+	0.998645i	$0.483427\pi$
$168$		0			0
$169$	−370.187	+	2099.44i	−0.168497	+	0.955593i
$170$		0			0
$171$	152.572	−	3092.28i	0.0682309	−	1.38288i
$172$		0			0
$173$	3073.84	−	1118.79i	1.35087	−	0.491675i	0.437648	−	0.899146i	$-0.355811\pi$
$173$	3073.84	−	1118.79i	1.35087	−	0.491675i	0.913218	+	0.407471i	$0.133589\pi$
$174$		0			0
$175$	−303.461	+	254.634i	−0.131083	+	0.109992i
$176$		0			0
$177$	−4528.73	−	508.965i	−1.92316	−	0.216137i
$178$		0			0
$179$	1379.57	+	2389.48i	0.576054	+	0.997755i	0.995926	+	0.0901720i	$0.0287417\pi$
$179$	1379.57	+	2389.48i	0.576054	+	0.997755i	−0.419872	+	0.907583i	$0.637925\pi$
$180$		0			0
$181$	1160.13	−	2009.40i	0.476418	−	0.825180i	−0.523217	−	0.852199i	$-0.675268\pi$
$181$	1160.13	−	2009.40i	0.476418	−	0.825180i	0.999635	+	0.0270195i	$0.00860161\pi$
$182$		0			0
$183$	−236.364	−	3769.85i	−0.0954784	−	1.52282i
$184$		0			0
$185$	−590.055	−	3346.37i	−0.234496	−	1.32989i
$186$		0			0
$187$	246.843	+	207.126i	0.0965292	+	0.0809976i
$188$		0			0
$189$	1769.25	+	2972.30i	0.680919	+	1.14393i
$190$		0			0
$191$	3603.66	+	3023.83i	1.36519	+	1.14553i	0.974341	+	0.225078i	$0.0722636\pi$
$191$	3603.66	+	3023.83i	1.36519	+	1.14553i	0.390851	+	0.920454i	$0.372181\pi$
$192$		0			0
$193$	−37.9402	−	215.169i	−0.0141502	−	0.0802499i	0.976915	−	0.213629i	$-0.0685284\pi$
$193$	−37.9402	−	215.169i	−0.0141502	−	0.0802499i	−0.991065	+	0.133379i	$0.957417\pi$
$194$		0			0
$195$	415.053	−	275.632i	0.152423	−	0.101223i
$196$		0			0
$197$	113.711	−	196.953i	0.0411246	−	0.0712299i	−0.844730	−	0.535192i	$-0.820239\pi$
$197$	113.711	−	196.953i	0.0411246	−	0.0712299i	0.885855	+	0.463962i	$0.153573\pi$
$198$		0			0
$199$	−501.833	−	869.199i	−0.178764	−	0.309628i	0.762694	−	0.646760i	$-0.223876\pi$
$199$	−501.833	−	869.199i	−0.178764	−	0.309628i	−0.941457	+	0.337132i	$0.890543\pi$
$200$		0			0
$201$	−846.627	+	1147.82i	−0.297097	+	0.402791i
$202$		0			0
$203$	32.7975	−	27.5204i	0.0113396	−	0.00951504i
$204$		0			0
$205$	1365.53	−	497.012i	0.465233	−	0.169331i
$206$		0			0
$207$	2769.12	+	3651.45i	0.929793	+	1.22605i
$208$		0			0
$209$	−190.810	+	1082.14i	−0.0631513	+	0.358149i
$210$		0			0
$211$	1881.22	+	684.709i	0.613785	+	0.223400i	0.630159	−	0.776466i	$-0.282990\pi$
$211$	1881.22	+	684.709i	0.613785	+	0.223400i	−0.0163734	+	0.999866i	$0.505212\pi$
$212$		0			0
$213$	2811.79	+	2953.95i	0.904512	+	0.950240i
$214$		0			0
$215$	−4155.21			−1.31806
$216$		0			0
$217$	3816.06			1.19378
$218$		0			0
$219$	517.537	−	1757.04i	0.159689	−	0.542146i
$220$		0			0
$221$	−255.098	−	92.8481i	−0.0776460	−	0.0282608i
$222$		0			0
$223$	−6.76080	+	38.3424i	−0.00203021	+	0.0115139i	−0.985806	−	0.167888i	$-0.946305\pi$
$223$	−6.76080	+	38.3424i	−0.00203021	+	0.0115139i	0.983776	+	0.179402i	$0.0574163\pi$
$224$		0			0
$225$	422.994	+	96.2935i	0.125332	+	0.0285314i
$226$		0			0
$227$	414.300	−	150.793i	0.121137	−	0.0440902i	−0.280741	−	0.959784i	$-0.590580\pi$
$227$	414.300	−	150.793i	0.121137	−	0.0440902i	0.401877	+	0.915694i	$0.368358\pi$
$228$		0			0
$229$	266.737	−	223.819i	0.0769715	−	0.0645867i	−0.603490	−	0.797370i	$-0.706224\pi$
$229$	266.737	−	223.819i	0.0769715	−	0.0645867i	0.680462	+	0.732784i	$0.261779\pi$
$230$		0			0
$231$	−491.250	−	1125.09i	−0.139921	−	0.320455i
$232$		0			0
$233$	2660.33	+	4607.83i	0.748001	+	1.29558i	0.948780	+	0.315938i	$0.102319\pi$
$233$	2660.33	+	4607.83i	0.748001	+	1.29558i	−0.200779	+	0.979637i	$0.564347\pi$
$234$		0			0
$235$	−1371.63	+	2375.73i	−0.380746	+	0.659471i
$236$		0			0
$237$	4987.43	+	2477.12i	1.36695	+	0.678929i
$238$		0			0
$239$	−266.898	−	1513.65i	−0.0722350	−	0.409665i	−0.999388	−	0.0349821i	$-0.988863\pi$
$239$	−266.898	−	1513.65i	−0.0722350	−	0.409665i	0.927153	−	0.374683i	$-0.122249\pi$
$240$		0			0
$241$	−2059.17	−	1727.85i	−0.550384	−	0.461827i	0.324687	−	0.945822i	$-0.394741\pi$
$241$	−2059.17	−	1727.85i	−0.550384	−	0.461827i	−0.875071	+	0.483995i	$0.839185\pi$
$242$		0			0
$243$	1422.79	−	3510.64i	0.375604	−	0.926780i
$244$		0			0
$245$	−2409.95	−	2022.19i	−0.628433	−	0.527318i
$246$		0			0
$247$	−160.752	−	911.669i	−0.0414105	−	0.234851i
$248$		0			0
$249$	6153.42	+	3056.23i	1.56609	+	0.777835i
$250$		0			0
$251$	1559.04	−	2700.34i	0.392055	−	0.679060i	−0.600665	−	0.799501i	$-0.705098\pi$
$251$	1559.04	−	2700.34i	0.392055	−	0.679060i	0.992720	+	0.120441i	$0.0384309\pi$
$252$		0			0
$253$	−813.234	−	1408.56i	−0.202085	−	0.350022i
$254$		0			0
$255$	−830.421	−	1901.88i	−0.203933	−	0.467059i
$256$		0			0
$257$	−2743.88	+	2302.39i	−0.665985	+	0.558828i	−0.911874	−	0.410470i	$-0.865365\pi$
$257$	−2743.88	+	2302.39i	−0.665985	+	0.558828i	0.245889	+	0.969298i	$0.420920\pi$
$258$		0			0
$259$	6628.29	−	2412.50i	1.59020	−	0.578786i
$260$		0			0
$261$	−45.7164	−	10.4072i	−0.0108421	−	0.00246816i
$262$		0			0
$263$	−653.310	+	3705.11i	−0.153174	+	0.868694i	0.807262	+	0.590194i	$0.200949\pi$
$263$	−653.310	+	3705.11i	−0.153174	+	0.868694i	−0.960436	+	0.278501i	$0.910163\pi$
$264$		0			0
$265$	−7231.66	−	2632.11i	−1.67637	−	0.610148i
$266$		0			0
$267$	46.4078	−	157.555i	0.0106371	−	0.0361131i
$268$		0			0
$269$	−1101.88			−0.249751			−0.124875	−	0.992172i	$-0.539853\pi$
$269$	−1101.88			−0.249751			−0.124875	+	0.992172i	$0.539853\pi$
$270$		0			0
$271$	−2560.66			−0.573981			−0.286991	−	0.957933i	$-0.592655\pi$
$271$	−2560.66			−0.573981			−0.286991	+	0.957933i	$0.592655\pi$
$272$		0			0
$273$	713.088	+	749.139i	0.158088	+	0.166080i
$274$		0			0
$275$	−144.683	−	52.6602i	−0.0317261	−	0.0115474i
$276$		0			0
$277$	−861.916	+	4888.17i	−0.186958	+	1.06029i	0.736455	+	0.676487i	$0.236498\pi$
$277$	−861.916	+	4888.17i	−0.186958	+	1.06029i	−0.923413	+	0.383807i	$0.874613\pi$
$278$		0			0
$279$	−2525.18	−	3329.78i	−0.541860	−	0.714512i
$280$		0			0
$281$	−7661.08	+	2788.41i	−1.62641	+	0.591966i	−0.984589	−	0.174886i	$-0.944044\pi$
$281$	−7661.08	+	2788.41i	−1.62641	+	0.591966i	−0.641824	+	0.766852i	$0.721822\pi$
$282$		0			0
$283$	−3237.19	+	2716.33i	−0.679969	+	0.570562i	−0.915997	−	0.401184i	$-0.868599\pi$
$283$	−3237.19	+	2716.33i	−0.679969	+	0.570562i	0.236028	+	0.971746i	$0.424154\pi$
$284$		0			0
$285$	4200.74	−	5695.18i	0.873090	−	1.18370i
$286$		0			0
$287$	1508.27	+	2612.40i	0.310210	+	0.537300i
$288$		0			0
$289$	1891.14	−	3275.54i	0.384925	−	0.666710i
$290$		0			0
$291$	295.911	−	196.511i	0.0596104	−	0.0395866i
$292$		0			0
$293$	1152.32	+	6535.14i	0.229759	+	1.30303i	0.853375	+	0.521297i	$0.174552\pi$
$293$	1152.32	+	6535.14i	0.229759	+	1.30303i	−0.623616	+	0.781731i	$0.714337\pi$
$294$		0			0
$295$	−7979.71	−	6695.77i	−1.57490	−	1.32150i
$296$		0			0
$297$	−656.645	+	1173.15i	−0.128291	+	0.229202i
$298$		0			0
$299$	1049.67	+	880.780i	0.203024	+	0.170357i
$300$		0			0
$301$	−1497.81	−	8494.51i	−0.286819	−	1.62663i
$302$		0			0
$303$	208.595	+	3326.95i	0.0395494	+	0.630786i
$304$		0			0
$305$	4316.96	−	7477.19i	0.810453	−	1.40375i
$306$		0			0
$307$	1427.01	+	2471.65i	0.265289	+	0.459494i	0.967639	−	0.252337i	$-0.0811993\pi$
$307$	1427.01	+	2471.65i	0.265289	+	0.459494i	−0.702350	+	0.711831i	$0.747866\pi$
$308$		0			0
$309$	−8051.00	−	904.819i	−1.48222	−	0.166580i
$310$		0			0
$311$	85.2222	−	71.5099i	0.0155386	−	0.0130384i	−0.634985	−	0.772524i	$-0.718994\pi$
$311$	85.2222	−	71.5099i	0.0155386	−	0.0130384i	0.650524	+	0.759486i	$0.274549\pi$
$312$		0			0
$313$	−1134.60	+	412.959i	−0.204892	+	0.0745745i	−0.442427	−	0.896804i	$-0.645883\pi$
$313$	−1134.60	+	412.959i	−0.204892	+	0.0745745i	0.237536	+	0.971379i	$0.423660\pi$
$314$		0			0
$315$	−389.630	+	7896.89i	−0.0696926	+	1.41251i
$316$		0			0
$317$	−897.165	+	5088.08i	−0.158958	+	0.901498i	0.796119	+	0.605140i	$0.206883\pi$
$317$	−897.165	+	5088.08i	−0.158958	+	0.901498i	−0.955077	+	0.296357i	$0.904228\pi$
$318$		0			0
$319$	15.6370	+	5.69141i	0.00274453	+	0.000998928i
$320$		0			0
$321$	−429.196	+	103.736i	−0.0746273	+	0.0180372i
$322$		0			0
$323$	−3855.86			−0.664229
$324$		0			0
$325$	129.713			0.0221391
$326$		0			0
$327$	11108.3	−	2684.84i	1.87856	−	0.454043i
$328$		0			0
$329$	−5351.14	−	1947.66i	−0.896712	−	0.326376i
$330$		0			0
$331$	1643.91	−	9323.07i	0.272983	−	1.54816i	−0.472314	−	0.881430i	$-0.656581\pi$
$331$	1643.91	−	9323.07i	0.272983	−	1.54816i	0.745297	−	0.666733i	$-0.232308\pi$
$332$		0			0
$333$	−6491.19	−	4187.24i	−1.06821	−	0.689067i
$334$		0			0
$335$	−3063.52	+	1115.03i	−0.499636	+	0.181853i
$336$		0			0
$337$	5945.60	−	4988.95i	0.961061	−	0.806426i	−0.0200644	−	0.999799i	$-0.506387\pi$
$337$	5945.60	−	4988.95i	0.961061	−	0.806426i	0.981125	+	0.193373i	$0.0619427\pi$
$338$		0			0
$339$	1013.05	+	113.853i	0.162305	+	0.0182408i
$340$		0			0
$341$	741.595	+	1284.48i	0.117770	+	0.203984i
$342$		0			0
$343$	−963.091	+	1668.12i	−0.151609	+	0.262595i
$344$		0			0
$345$	655.477	+	10454.4i	0.102289	+	1.63144i
$346$		0			0
$347$	1749.24	+	9920.45i	0.270618	+	1.53475i	0.752547	+	0.658538i	$0.228825\pi$
$347$	1749.24	+	9920.45i	0.270618	+	1.53475i	−0.481930	+	0.876210i	$0.660064\pi$
$348$		0			0
$349$	2871.58	+	2409.54i	0.440436	+	0.369570i	0.835872	−	0.548924i	$-0.184962\pi$
$349$	2871.58	+	2409.54i	0.440436	+	0.369570i	−0.395437	+	0.918493i	$0.629407\pi$
$350$		0			0
$351$	181.808	−	1117.94i	0.0276473	−	0.170004i
$352$		0			0
$353$	−6741.74	−	5656.99i	−1.01651	−	0.852950i	−0.0273217	−	0.999627i	$-0.508698\pi$
$353$	−6741.74	−	5656.99i	−1.01651	−	0.852950i	−0.989184	+	0.146677i	$0.953142\pi$
$354$		0			0
$355$	1618.73	+	9180.26i	0.242009	+	1.37250i
$356$		0			0
$357$	3588.67	−	2383.20i	0.532024	−	0.353311i
$358$		0			0
$359$	−569.401	+	986.232i	−0.0837099	+	0.144990i	−0.904841	−	0.425750i	$-0.860010\pi$
$359$	−569.401	+	986.232i	−0.0837099	+	0.144990i	0.821131	+	0.570740i	$0.193344\pi$
$360$		0			0
$361$	−3144.90	−	5447.12i	−0.458507	−	0.794157i
$362$		0			0
$363$	−3822.10	+	5181.83i	−0.552639	+	0.749244i
$364$		0			0
$365$	3207.26	−	2691.21i	0.459934	−	0.385930i
$366$		0			0
$367$	−6133.18	+	2232.29i	−0.872341	+	0.317506i	−0.739115	−	0.673579i	$-0.764756\pi$
$367$	−6133.18	+	2232.29i	−0.872341	+	0.317506i	−0.133226	+	0.991086i	$0.542534\pi$
$368$		0			0
$369$	1281.44	−	3044.76i	0.180784	−	0.429550i
$370$		0			0
$371$	2774.07	−	15732.5i	0.388200	−	2.20159i
$372$		0			0
$373$	11369.5	+	4138.17i	1.57826	+	0.574440i	0.974825	−	0.222972i	$-0.0715757\pi$
$373$	11369.5	+	4138.17i	1.57826	+	0.574440i	0.603436	+	0.797411i	$0.293798\pi$
$374$		0			0
$375$	−4635.16	−	4869.50i	−0.638290	−	0.670559i
$376$		0			0
$377$	−14.0192			−0.00191518
$378$		0			0
$379$	−13220.9			−1.79185			−0.895924	−	0.444208i	$-0.853485\pi$
$379$	−13220.9			−1.79185			−0.895924	+	0.444208i	$0.853485\pi$
$380$		0			0
$381$	2049.20	−	6957.05i	0.275548	−	0.935487i
$382$		0			0
$383$	−3370.04	−	1226.60i	−0.449611	−	0.163645i	0.107283	−	0.994229i	$-0.465785\pi$
$383$	−3370.04	−	1226.60i	−0.449611	−	0.163645i	−0.556894	+	0.830583i	$0.688007\pi$
$384$		0			0
$385$	487.280	−	2763.50i	0.0645042	−	0.365821i
$386$		0			0
$387$	−6420.92	+	6927.97i	−0.843394	+	0.909997i
$388$		0			0
$389$	4592.47	−	1671.52i	0.598580	−	0.217865i	−0.0249191	−	0.999689i	$-0.507933\pi$
$389$	4592.47	−	1671.52i	0.598580	−	0.217865i	0.623499	+	0.781824i	$0.285711\pi$
$390$		0			0
$391$	4372.10	−	3668.63i	0.565490	−	0.474502i
$392$		0			0
$393$	−5221.33	−	11958.2i	−0.670182	−	1.53489i
$394$		0			0
$395$	6364.38	+	11023.4i	0.810701	+	1.40417i
$396$		0			0
$397$	−7094.60	+	12288.2i	−0.896896	+	1.55347i	−0.0654562	+	0.997855i	$0.520850\pi$
$397$	−7094.60	+	12288.2i	−0.896896	+	1.55347i	−0.831440	+	0.555614i	$0.812483\pi$
$398$		0			0
$399$	13156.9	+	6534.68i	1.65080	+	0.819907i
$400$		0			0
$401$	617.602	+	3502.60i	0.0769117	+	0.436188i	0.998811	+	0.0487575i	$0.0155261\pi$
$401$	617.602	+	3502.60i	0.0769117	+	0.436188i	−0.921899	+	0.387430i	$0.873363\pi$
$402$		0			0
$403$	−957.205	−	803.190i	−0.118317	−	0.0992798i
$404$		0			0
$405$	7148.42	−	4885.59i	0.877057	−	0.599425i
$406$		0			0
$407$	2100.15	+	1762.24i	0.255776	+	0.214621i
$408$		0			0
$409$	2004.03	+	11365.4i	0.242281	+	1.37404i	0.826724	+	0.562607i	$0.190202\pi$
$409$	2004.03	+	11365.4i	0.242281	+	1.37404i	−0.584444	+	0.811434i	$0.698687\pi$
$410$		0			0
$411$	−1948.11	−	967.571i	−0.233803	−	0.116123i
$412$		0			0
$413$	10811.8	−	18726.5i	1.28817	−	2.23117i
$414$		0			0
$415$	7852.28	+	13600.5i	0.928803	+	1.60873i
$416$		0			0
$417$	1540.15	+	3527.33i	0.180867	+	0.414230i
$418$		0			0
$419$	−1394.94	+	1170.50i	−0.162643	+	0.136474i	−0.720477	−	0.693479i	$-0.756077\pi$
$419$	−1394.94	+	1170.50i	−0.162643	+	0.136474i	0.557834	+	0.829953i	$0.311633\pi$
$420$		0			0
$421$	683.841	−	248.898i	0.0791647	−	0.0288136i	−0.302134	−	0.953265i	$-0.597699\pi$
$421$	683.841	−	248.898i	0.0791647	−	0.0288136i	0.381299	+	0.924452i	$0.375477\pi$
$422$		0			0
$423$	1841.52	+	5958.07i	0.211673	+	0.684849i
$424$		0			0
$425$	93.8191	−	532.074i	0.0107080	−	0.0607280i
$426$		0			0
$427$	16841.8	+	6129.90i	1.90873	+	0.694723i
$428$		0			0
$429$	−113.581	+	385.608i	−0.0127826	+	0.0433971i
$430$		0			0
$431$	−10589.8			−1.18350			−0.591752	−	0.806120i	$-0.701564\pi$
$431$	−10589.8			−1.18350			−0.591752	+	0.806120i	$0.701564\pi$
$432$		0			0
$433$	8248.97			0.915520			0.457760	−	0.889076i	$-0.348652\pi$
$433$	8248.97			0.915520			0.457760	+	0.889076i	$0.348652\pi$
$434$		0			0
$435$	−73.8901	−	77.6257i	−0.00814428	−	0.00855602i
$436$		0			0
$437$	18288.8	+	6656.59i	2.00200	+	0.728668i
$438$		0			0
$439$	755.154	−	4282.69i	0.0820992	−	0.465608i	−0.915846	−	0.401530i	$-0.868478\pi$
$439$	755.154	−	4282.69i	0.0820992	−	0.465608i	0.997945	−	0.0640773i	$-0.0204104\pi$
$440$		0			0
$441$	−7095.62	+	893.281i	−0.766183	+	0.0964563i
$442$		0			0
$443$	9558.38	−	3478.97i	1.02513	−	0.373117i	0.225905	−	0.974149i	$-0.427466\pi$
$443$	9558.38	−	3478.97i	1.02513	−	0.373117i	0.799224	+	0.601033i	$0.205244\pi$
$444$		0			0
$445$	287.597	−	241.322i	0.0306368	−	0.0257074i
$446$		0			0
$447$	666.867	−	904.108i	0.0705631	−	0.0956663i
$448$		0			0
$449$	3202.24	+	5546.45i	0.336577	+	0.582969i	0.983787	−	0.179343i	$-0.0573973\pi$
$449$	3202.24	+	5546.45i	0.336577	+	0.582969i	−0.647209	+	0.762312i	$0.724064\pi$
$450$		0			0
$451$	−586.220	+	1015.36i	−0.0612062	+	0.106012i
$452$		0			0
$453$	−6900.39	+	4582.47i	−0.715692	+	0.475283i
$454$		0			0
$455$	410.519	+	2328.17i	0.0422976	+	0.239882i
$456$		0			0
$457$	−1976.70	−	1658.65i	−0.202333	−	0.169778i	0.535991	−	0.844224i	$-0.319938\pi$
$457$	−1976.70	−	1658.65i	−0.202333	−	0.169778i	−0.738324	+	0.674446i	$0.764383\pi$
$458$		0			0
$459$	−4454.22	−	1554.35i	−0.452953	−	0.158063i
$460$		0			0
$461$	−8257.79	−	6929.11i	−0.834282	−	0.700045i	0.121988	−	0.992532i	$-0.461073\pi$
$461$	−8257.79	−	6929.11i	−0.834282	−	0.700045i	−0.956270	+	0.292486i	$0.905517\pi$
$462$		0			0
$463$	−169.398	−	960.704i	−0.0170034	−	0.0964313i	0.975125	−	0.221656i	$-0.0711461\pi$
$463$	−169.398	−	960.704i	−0.0170034	−	0.0964313i	−0.992128	+	0.125224i	$0.960035\pi$
$464$		0			0
$465$	−597.735	−	9533.48i	−0.0596114	−	0.950762i
$466$		0			0
$467$	8841.29	−	15313.6i	0.876073	−	1.51740i	0.0204571	−	0.999791i	$-0.493488\pi$
$467$	8841.29	−	15313.6i	0.876073	−	1.51740i	0.855616	−	0.517612i	$-0.173179\pi$
$468$		0			0
$469$	−3383.76	−	5860.84i	−0.333150	−	0.577033i
$470$		0			0
$471$	−1872.48	−	210.441i	−0.183184	−	0.0205873i
$472$		0			0
$473$	2568.16	−	2154.94i	0.249649	−	0.209481i
$474$		0			0
$475$	1731.29	−	630.140i	0.167236	−	0.0608690i
$476$		0			0
$477$	−15563.4	+	7990.03i	−1.49392	+	0.766957i
$478$		0			0
$479$	616.357	−	3495.54i	0.0587935	−	0.333434i	−0.941197	−	0.337859i	$-0.890297\pi$
$479$	616.357	−	3495.54i	0.0587935	−	0.333434i	0.999990	+	0.00442458i	$0.00140839\pi$
$480$		0			0
$481$	−2170.39	−	789.957i	−0.205740	−	0.0748834i
$482$		0			0
$483$	−21135.7	+	5108.46i	−1.99112	+	0.481248i
$484$		0			0
$485$	811.945			0.0760176
$486$		0			0
$487$	−2435.85			−0.226651			−0.113325	−	0.993558i	$-0.536150\pi$
$487$	−2435.85			−0.226651			−0.113325	+	0.993558i	$0.536150\pi$
$488$		0			0
$489$	−8260.58	+	1996.56i	−0.763919	+	0.184637i
$490$		0			0
$491$	−16681.1	−	6071.43i	−1.53321	−	0.558044i	−0.568808	−	0.822471i	$-0.692595\pi$
$491$	−16681.1	−	6071.43i	−1.53321	−	0.558044i	−0.964406	+	0.264427i	$0.914817\pi$
$492$		0			0
$493$	−10.1398	+	57.5056i	−0.000926315	+	0.00525339i
$494$		0			0
$495$	−2733.80	+	1403.49i	−0.248233	+	0.127439i
$496$		0			0
$497$	−18183.7	+	6618.34i	−1.64115	+	0.597330i
$498$		0			0
$499$	7703.84	−	6464.29i	0.691125	−	0.579923i	−0.228108	−	0.973636i	$-0.573254\pi$
$499$	7703.84	−	6464.29i	0.691125	−	0.579923i	0.919233	+	0.393713i	$0.128810\pi$
$500$		0			0
$501$	8702.39	+	978.026i	0.776036	+	0.0872156i
$502$		0			0
$503$	5162.70	+	8942.06i	0.457641	+	0.792658i	0.998836	−	0.0482397i	$-0.0153611\pi$
$503$	5162.70	+	8942.06i	0.457641	+	0.792658i	−0.541195	+	0.840897i	$0.682028\pi$
$504$		0			0
$505$	−3809.78	+	6598.73i	−0.335709	+	0.581464i
$506$		0			0
$507$	693.169	+	11055.6i	0.0607193	+	0.968433i
$508$		0			0
$509$	1494.33	+	8474.74i	0.130127	+	0.737989i	0.978130	+	0.207996i	$0.0666942\pi$
$509$	1494.33	+	8474.74i	0.130127	+	0.737989i	−0.848002	+	0.529993i	$0.822195\pi$
$510$		0			0
$511$	6657.76	+	5586.53i	0.576364	+	0.483627i
$512$		0			0
$513$	−3004.29	−	15804.5i	−0.258563	−	1.36021i
$514$		0			0
$515$	−14186.0	−	11903.5i	−1.21381	−	1.01850i
$516$		0			0
$517$	−384.337	−	2179.68i	−0.0326946	−	0.185421i
$518$		0			0
$519$	14159.4	−	9403.07i	1.19755	−	0.795277i
$520$		0			0
$521$	11243.8	−	19474.8i	0.945486	−	1.63763i	0.190712	−	0.981646i	$-0.438920\pi$
$521$	11243.8	−	19474.8i	0.945486	−	1.63763i	0.754774	−	0.655984i	$-0.227746\pi$
$522$		0			0
$523$	2521.73	+	4367.76i	0.210837	+	0.365180i	0.951977	−	0.306171i	$-0.0990479\pi$
$523$	2521.73	+	4367.76i	0.210837	+	0.365180i	−0.741140	+	0.671351i	$0.765715\pi$
$524$		0			0
$525$	−1221.85	+	1656.54i	−0.101573	+	0.137709i
$526$		0			0
$527$	−3986.95	+	3345.45i	−0.329553	+	0.276528i
$528$		0			0
$529$	−15637.5	+	5691.58i	−1.28524	+	0.467789i
$530$		0			0
$531$	−23494.7	+	2957.79i	−1.92011	+	0.241727i
$532$		0			0
$533$	171.520	−	972.739i	0.0139388	−	0.0790506i
$534$		0			0
$535$	−948.421	−	345.197i	−0.0766426	−	0.0278956i
$536$		0			0
$537$	9884.76	+	10384.5i	0.794337	+	0.834496i
$538$		0			0
$539$	2538.22			0.202837
$540$		0			0
$541$	−8015.37			−0.636983			−0.318491	−	0.947926i	$-0.603176\pi$
$541$	−8015.37			−0.636983			−0.318491	+	0.947926i	$0.603176\pi$
$542$		0			0
$543$	3406.51	−	11565.1i	0.269222	−	0.914011i
$544$		0			0
$545$	24546.6	+	8934.23i	1.92929	+	0.702203i
$546$		0			0
$547$	2843.34	−	16125.4i	0.222253	−	1.26046i	−0.645614	−	0.763664i	$-0.723398\pi$
$547$	2843.34	−	16125.4i	0.222253	−	1.26046i	0.867867	−	0.496797i	$-0.165491\pi$
$548$		0			0
$549$	−5795.85	−	18751.9i	−0.450566	−	1.45776i
$550$		0			0
$551$	−187.115	+	68.1043i	−0.0144671	+	0.00526559i
$552$		0			0
$553$	−20241.1	+	16984.3i	−1.55649	+	1.30605i
$554$		0			0
$555$	−7065.27	−	16181.2i	−0.540367	−	1.23758i
$556$		0			0
$557$	−4603.16	−	7972.91i	−0.350166	−	0.606504i	0.636113	−	0.771596i	$-0.280541\pi$
$557$	−4603.16	−	7972.91i	−0.350166	−	0.606504i	−0.986278	+	0.165092i	$0.947208\pi$
$558$		0			0
$559$	−1412.19	+	2445.98i	−0.106850	+	0.185070i
$560$		0			0
$561$	1499.58	+	744.803i	0.112857	+	0.0560527i
$562$		0			0
$563$	−4038.40	−	22902.9i	−0.302306	−	1.71446i	−0.635921	−	0.771754i	$-0.719380\pi$
$563$	−4038.40	−	22902.9i	−0.302306	−	1.71446i	0.333615	−	0.942709i	$-0.391732\pi$
$564$		0			0
$565$	1785.01	+	1497.80i	0.132913	+	0.111528i
$566$		0			0
$567$	12564.4	+	12852.5i	0.930608	+	0.951944i
$568$		0			0
$569$	13470.6	+	11303.1i	0.992470	+	0.832781i	0.985923	−	0.167198i	$-0.0534718\pi$
$569$	13470.6	+	11303.1i	0.992470	+	0.832781i	0.00654627	+	0.999979i	$0.497916\pi$
$570$		0			0
$571$	398.268	+	2258.69i	0.0291891	+	0.165540i	0.995918	−	0.0902640i	$-0.0287711\pi$
$571$	398.268	+	2258.69i	0.0291891	+	0.165540i	−0.966729	+	0.255804i	$0.917660\pi$
$572$		0			0
$573$	21892.4	+	10873.4i	1.59611	+	0.792742i
$574$		0			0
$575$	−1363.54	+	2361.73i	−0.0988935	+	0.171288i
$576$		0			0
$577$	10473.0	+	18139.7i	0.755625	+	1.30878i	0.945063	+	0.326888i	$0.106000\pi$
$577$	10473.0	+	18139.7i	0.755625	+	1.30878i	−0.189438	+	0.981893i	$0.560667\pi$
$578$		0			0
$579$	−454.293	−	1040.45i	−0.0326075	−	0.0746795i
$580$		0			0
$581$	−24973.2	+	20955.0i	−1.78324	+	1.49632i
$582$		0			0
$583$	5834.63	−	2123.63i	0.414487	−	0.150861i
$584$		0			0
$585$	1759.84	−	1898.81i	0.124377	−	0.134199i
$586$		0			0
$587$	−2212.95	+	12550.2i	−0.155601	+	0.882459i	0.802633	+	0.596474i	$0.203432\pi$
$587$	−2212.95	+	12550.2i	−0.155601	+	0.882459i	−0.958234	+	0.285986i	$0.907679\pi$
$588$		0			0
$589$	−16677.7	−	6070.20i	−1.16671	−	0.424649i
$590$		0			0
$591$	333.891	−	1133.56i	0.0232393	−	0.0788978i
$592$		0			0
$593$	9461.47			0.655204			0.327602	−	0.944816i	$-0.393759\pi$
$593$	9461.47			0.655204			0.327602	+	0.944816i	$0.393759\pi$
$594$		0			0
$595$	9846.89			0.678459
$596$		0			0
$597$	−3595.69	−	3777.47i	−0.246502	−	0.258964i
$598$		0			0
$599$	−11410.1	−	4152.94i	−0.778305	−	0.283280i	−0.0778394	−	0.996966i	$-0.524802\pi$
$599$	−11410.1	−	4152.94i	−0.778305	−	0.283280i	−0.700466	+	0.713686i	$0.747024\pi$
$600$		0			0
$601$	−459.651	+	2606.81i	−0.0311973	+	0.176928i	−0.996425	−	0.0844819i	$-0.973076\pi$
$601$	−459.651	+	2606.81i	−0.0311973	+	0.176928i	0.965228	+	0.261410i	$0.0841876\pi$
$602$		0			0
$603$	−2874.88	+	6830.83i	−0.194153	+	0.461315i
$604$		0			0
$605$	−13830.3	+	5033.80i	−0.929389	+	0.338270i
$606$		0			0
$607$	13255.2	−	11122.4i	0.886345	−	0.743732i	−0.0811282	−	0.996704i	$-0.525852\pi$
$607$	13255.2	−	11122.4i	0.886345	−	0.743732i	0.967474	+	0.252972i	$0.0814079\pi$
$608$		0			0
$609$	132.056	−	179.035i	0.00878681	−	0.0119128i
$610$		0			0
$611$	932.323	+	1614.83i	0.0617312	+	0.106922i
$612$		0			0
$613$	1505.84	−	2608.19i	0.0992175	−	0.171850i	−0.812143	−	0.583458i	$-0.801699\pi$
$613$	1505.84	−	2608.19i	0.0992175	−	0.171850i	0.911361	+	0.411608i	$0.135033\pi$
$614$		0			0
$615$	6290.18	−	4177.23i	0.412430	−	0.273890i
$616$		0			0
$617$	−863.521	−	4897.27i	−0.0563437	−	0.319541i	0.943589	−	0.331118i	$-0.107426\pi$
$617$	−863.521	−	4897.27i	−0.0563437	−	0.319541i	−0.999933	+	0.0115772i	$0.996315\pi$
$618$		0			0
$619$	−2683.55	−	2251.77i	−0.174250	−	0.146213i	0.551492	−	0.834181i	$-0.314059\pi$
$619$	−2683.55	−	2251.77i	−0.174250	−	0.146213i	−0.725742	+	0.687967i	$0.758503\pi$
$620$		0			0
$621$	18443.5	+	15062.0i	1.19181	+	0.973299i
$622$		0			0
$623$	597.005	+	500.947i	0.0383925	+	0.0322151i
$624$		0			0
$625$	−3017.18	−	17111.3i	−0.193100	−	1.09512i
$626$		0			0
$627$	357.288	+	5698.51i	0.0227571	+	0.362961i
$628$		0			0
$629$	−4810.14	+	8331.40i	−0.304917	+	0.528132i
$630$		0			0
$631$	−15195.1	−	26318.6i	−0.958646	−	1.66042i	−0.725794	−	0.687912i	$-0.758527\pi$
$631$	−15195.1	−	26318.6i	−0.958646	−	1.66042i	−0.232852	−	0.972512i	$-0.574806\pi$
$632$		0			0
$633$	10337.4	+	1161.78i	0.649090	+	0.0729486i
$634$		0			0
$635$	12699.2	−	10655.9i	0.793628	−	0.665933i
$636$		0			0
$637$	−2009.41	+	731.367i	−0.124986	+	0.0454911i
$638$		0			0
$639$	17807.6	+	11487.1i	1.10244	+	0.711145i
$640$		0			0
$641$	367.411	−	2083.69i	0.0226394	−	0.128394i	−0.971393	−	0.237476i	$-0.923680\pi$
$641$	367.411	−	2083.69i	0.0226394	−	0.128394i	0.994033	+	0.109082i	$0.0347910\pi$
$642$		0			0
$643$	16121.2	+	5867.63i	0.988735	+	0.359870i	0.785230	−	0.619204i	$-0.212544\pi$
$643$	16121.2	+	5867.63i	0.988735	+	0.359870i	0.203505	+	0.979074i	$0.434767\pi$
$644$		0			0
$645$	−20986.8	+	5072.46i	−1.28117	+	0.309656i
$646$		0			0
$647$	−24282.8			−1.47551			−0.737756	−	0.675068i	$-0.764114\pi$
$647$	−24282.8			−1.47551			−0.737756	+	0.675068i	$0.764114\pi$
$648$		0			0
$649$	8404.43			0.508325
$650$		0			0
$651$	19273.9	−	4658.45i	1.16037	−	0.280459i
$652$		0			0
$653$	15070.7	+	5485.28i	0.903156	+	0.328722i	0.751517	−	0.659714i	$-0.229323\pi$
$653$	15070.7	+	5485.28i	0.903156	+	0.328722i	0.151639	+	0.988436i	$0.451545\pi$
$654$		0			0
$655$	5179.15	−	29372.4i	0.308956	−	1.75217i
$656$		0			0
$657$	469.029	−	9506.12i	0.0278517	−	0.564488i
$658$		0			0
$659$	12869.4	−	4684.06i	0.760727	−	0.276882i	0.0676147	−	0.997712i	$-0.478461\pi$
$659$	12869.4	−	4684.06i	0.760727	−	0.276882i	0.693112	+	0.720829i	$0.256239\pi$
$660$		0			0
$661$	2109.37	−	1769.97i	0.124123	−	0.104151i	−0.578613	−	0.815602i	$-0.696406\pi$
$661$	2109.37	−	1769.97i	0.124123	−	0.104151i	0.702736	+	0.711451i	$0.251962\pi$
$662$		0			0
$663$	−1401.77	−	157.540i	−0.0821122	−	0.00922826i
$664$		0			0
$665$	16789.3	+	29080.0i	0.979041	+	1.69575i
$666$		0			0
$667$	147.369	−	255.251i	0.00855497	−	0.0148176i
$668$		0			0
$669$	12.6595	+	201.910i	0.000731604	+	0.0116686i
$670$		0			0
$671$	1209.63	+	6860.16i	0.0695936	+	0.394685i
$672$		0			0
$673$	7306.81	+	6131.14i	0.418509	+	0.351171i	0.827596	−	0.561325i	$-0.189708\pi$
$673$	7306.81	+	6131.14i	0.418509	+	0.351171i	−0.409086	+	0.912496i	$0.634153\pi$
$674$		0			0
$675$	2253.98	−	30.0176i	0.128527	−	0.00171167i
$676$		0			0
$677$	8203.11	+	6883.23i	0.465689	+	0.390759i	0.845219	−	0.534420i	$-0.179470\pi$
$677$	8203.11	+	6883.23i	0.465689	+	0.390759i	−0.379530	+	0.925179i	$0.623914\pi$
$678$		0			0
$679$	292.679	+	1659.86i	0.0165419	+	0.0938140i
$680$		0			0
$681$	1908.43	−	1267.37i	0.107388	−	0.0713152i
$682$		0			0
$683$	−9802.23	+	16978.0i	−0.549153	+	0.951162i	0.449179	+	0.893442i	$0.351716\pi$
$683$	−9802.23	+	16978.0i	−0.549153	+	0.951162i	−0.998333	+	0.0577201i	$0.981617\pi$
$684$		0			0
$685$	−2485.95	−	4305.79i	−0.138662	−	0.240169i
$686$		0			0
$687$	1073.99	−	1456.06i	0.0596436	−	0.0808622i
$688$		0			0
$689$	−4007.15	+	3362.40i	−0.221568	+	0.185918i
$690$		0			0
$691$	5541.06	−	2016.78i	0.305053	−	0.111030i	−0.184958	−	0.982746i	$-0.559215\pi$
$691$	5541.06	−	2016.78i	0.305053	−	0.111030i	0.490011	+	0.871716i	$0.336993\pi$
$692$		0			0
$693$	−3854.61	−	5082.80i	−0.211291	−	0.278614i
$694$		0			0
$695$	−1527.70	+	8664.04i	−0.0833800	+	0.472872i
$696$		0			0
$697$	−3866.04	−	1407.12i	−0.210096	−	0.0764686i
$698$		0			0
$699$	19061.6	+	20025.3i	1.03144	+	1.08358i
$700$		0			0
$701$	−26136.5			−1.40822			−0.704109	−	0.710092i	$-0.748654\pi$
$701$	−26136.5			−1.40822			−0.704109	+	0.710092i	$0.748654\pi$
$702$		0			0
$703$	−32805.9			−1.76002
$704$		0			0
$705$	−4027.55	+	13673.6i	−0.215158	+	0.730463i
$706$		0			0
$707$	−14863.1	−	5409.73i	−0.790643	−	0.287770i
$708$		0			0
$709$	−3375.05	+	19140.9i	−0.178777	+	1.01389i	0.754917	+	0.655820i	$0.227677\pi$
$709$	−3375.05	+	19140.9i	−0.178777	+	1.01389i	−0.933694	+	0.358073i	$0.883434\pi$
$710$		0			0
$711$	28214.0	+	6422.85i	1.48820	+	0.338784i
$712$		0			0
$713$	24686.0	−	8984.98i	1.29663	−	0.471936i
$714$		0			0
$715$	−703.879	+	590.625i	−0.0368162	+	0.0308925i
$716$		0			0
$717$	−3195.81	−	7319.22i	−0.166457	−	0.381229i
$718$		0			0
$719$	11662.7	+	20200.4i	0.604930	+	1.04777i	0.992063	+	0.125745i	$0.0401322\pi$
$719$	11662.7	+	20200.4i	0.604930	+	1.04777i	−0.387133	+	0.922024i	$0.626534\pi$
$720$		0			0
$721$	19220.8	−	33291.3i	0.992813	−	1.71960i
$722$		0			0
$723$	−12509.5	−	6213.14i	−0.643478	−	0.319598i
$724$		0			0
$725$	−4.84498	−	27.4773i	−0.000248191	−	0.00140756i
$726$		0			0
$727$	−21572.4	−	18101.4i	−1.10052	−	0.923444i	−0.103058	−	0.994675i	$-0.532863\pi$
$727$	−21572.4	−	18101.4i	−1.10052	−	0.923444i	−0.997460	+	0.0712312i	$0.977307\pi$
$728$		0			0
$729$	2900.50	−	19468.1i	0.147361	−	0.989083i
$730$		0			0
$731$	9011.82	+	7561.81i	0.455970	+	0.382604i
$732$		0			0
$733$	2490.57	+	14124.7i	0.125500	+	0.711745i	0.981010	+	0.193958i	$0.0621327\pi$
$733$	2490.57	+	14124.7i	0.125500	+	0.711745i	−0.855510	+	0.517786i	$0.826756\pi$
$734$		0			0
$735$	−14640.6	−	7271.57i	−0.734728	−	0.364919i
$736$		0			0
$737$	1315.17	−	2277.93i	0.0657323	−	0.113852i
$738$		0			0
$739$	−1865.54	−	3231.22i	−0.0928622	−	0.160842i	0.815852	−	0.578260i	$-0.196268\pi$
$739$	−1865.54	−	3231.22i	−0.0928622	−	0.160842i	−0.908714	+	0.417419i	$0.862935\pi$
$740$		0			0
$741$	−1924.83	−	4408.35i	−0.0954256	−	0.218549i
$742$		0			0
$743$	−3841.35	+	3223.28i	−0.189671	+	0.159153i	−0.732678	−	0.680575i	$-0.761730\pi$
$743$	−3841.35	+	3223.28i	−0.189671	+	0.159153i	0.543007	+	0.839728i	$0.317286\pi$
$744$		0			0
$745$	2413.06	−	878.282i	0.118668	−	0.0431916i
$746$		0			0
$747$	34810.1	+	7924.42i	1.70500	+	0.388138i
$748$		0			0
$749$	363.814	−	2063.29i	0.0177483	−	0.100656i
$750$		0			0
$751$	−11741.0	−	4273.37i	−0.570485	−	0.207640i	0.0406395	−	0.999174i	$-0.487060\pi$
$751$	−11741.0	−	4273.37i	−0.570485	−	0.207640i	−0.611125	+	0.791534i	$0.709283\pi$
$752$		0			0
$753$	4577.85	−	15541.9i	0.221549	−	0.752160i
$754$		0			0
$755$	−18933.8			−0.912679
$756$		0			0
$757$	5318.20			0.255341			0.127671	−	0.991817i	$-0.459250\pi$
$757$	5318.20			0.255341			0.127671	+	0.991817i	$0.459250\pi$
$758$		0			0
$759$	−5826.92	−	6121.50i	−0.278661	−	0.292749i
$760$		0			0
$761$	−263.705	−	95.9809i	−0.0125615	−	0.00457202i	0.335732	−	0.941958i	$-0.391016\pi$
$761$	−263.705	−	95.9809i	−0.0125615	−	0.00457202i	−0.348293	+	0.937386i	$0.613239\pi$
$762$		0			0
$763$	−9416.07	+	53401.2i	−0.446769	+	2.53375i
$764$		0			0
$765$	−6515.94	−	8592.11i	−0.307953	−	0.406076i
$766$		0			0
$767$	−6653.47	+	2421.67i	−0.313224	+	0.114004i
$768$		0			0
$769$	−4855.57	+	4074.30i	−0.227693	+	0.191057i	−0.749496	−	0.662009i	$-0.769704\pi$
$769$	−4855.57	+	4074.30i	−0.227693	+	0.191057i	0.521803	+	0.853066i	$0.325260\pi$
$770$		0			0
$771$	−11047.9	+	14978.3i	−0.516058	+	0.699649i
$772$		0			0
$773$	−16590.1	−	28734.9i	−0.771934	−	1.33703i	−0.936502	−	0.350663i	$-0.885956\pi$
$773$	−16590.1	−	28734.9i	−0.771934	−	1.33703i	0.164568	−	0.986366i	$-0.447377\pi$
$774$		0			0
$775$	1243.43	−	2153.68i	0.0576325	−	0.0998225i
$776$		0			0
$777$	30532.6	−	20276.3i	1.40972	−	0.936177i
$778$		0			0
$779$	−2436.21	−	13816.4i	−0.112049	−	0.635463i
$780$		0			0
$781$	−5761.46	−	4834.44i	−0.263971	−	0.221498i
$782$		0			0
$783$	−243.606	+	3.24425i	−0.0111185	+	0.000148072i
$784$		0			0
$785$	−3299.35	−	2768.49i	−0.150011	−	0.125875i
$786$		0			0
$787$	−3540.75	−	20080.6i	−0.160374	−	0.909524i	−0.953707	−	0.300737i	$-0.902767\pi$
$787$	−3540.75	−	20080.6i	−0.160374	−	0.909524i	0.793333	−	0.608787i	$-0.208344\pi$
$788$		0			0
$789$	1223.31	+	19511.0i	0.0551977	+	0.880367i
$790$		0			0
$791$	−2418.53	+	4189.02i	−0.108714	+	0.188299i
$792$		0			0
$793$	−2934.32	−	5082.39i	−0.131401	−	0.227593i
$794$		0			0
$795$	−39738.3	−	4466.02i	−1.77279	−	0.199237i
$796$		0			0
$797$	12799.7	−	10740.3i	0.568871	−	0.477339i	−0.312400	−	0.949951i	$-0.601133\pi$
$797$	12799.7	−	10740.3i	0.568871	−	0.477339i	0.881271	+	0.472611i	$0.156689\pi$
$798$		0			0
$799$	7298.24	−	2656.34i	0.323146	−	0.117615i
$800$		0			0
$801$	42.0581	−	852.418i	0.00185524	−	0.0376014i
$802$		0			0
$803$	−586.578	+	3326.65i	−0.0257782	+	0.146195i
$804$		0			0
$805$	−46705.0	−	16999.2i	−2.04489	−	0.744278i
$806$		0			0
$807$	−5565.30	+	1345.12i	−0.242760	+	0.0586746i
$808$		0			0
$809$	−35383.0			−1.53770			−0.768851	−	0.639428i	$-0.779171\pi$
$809$	−35383.0			−1.53770			−0.768851	+	0.639428i	$0.779171\pi$
$810$		0			0
$811$	31405.6			1.35980			0.679901	−	0.733304i	$-0.262023\pi$
$811$	31405.6			1.35980			0.679901	+	0.733304i	$0.262023\pi$
$812$		0			0
$813$	−12933.2	+	3125.91i	−0.557916	+	0.134847i
$814$		0			0
$815$	−18253.9	−	6643.89i	−0.784549	−	0.285552i
$816$		0			0
$817$	−6966.15	+	39507.0i	−0.298304	+	1.69177i
$818$		0			0
$819$	4516.12	+	2913.19i	0.192681	+	0.124292i
$820$		0			0
$821$	−21704.2	+	7899.68i	−0.922633	+	0.335811i	−0.759285	−	0.650758i	$-0.774451\pi$
$821$	−21704.2	+	7899.68i	−0.922633	+	0.335811i	−0.163347	+	0.986569i	$0.552229\pi$
$822$		0			0
$823$	−10126.1	+	8496.77i	−0.428885	+	0.359877i	−0.831531	−	0.555479i	$-0.812535\pi$
$823$	−10126.1	+	8496.77i	−0.428885	+	0.359877i	0.402646	+	0.915356i	$0.368091\pi$
$824$		0			0
$825$	−795.036	−	89.3509i	−0.0335510	−	0.00377067i
$826$		0			0
$827$	−20082.7	−	34784.3i	−0.844432	−	1.46260i	−0.886113	−	0.463469i	$-0.846605\pi$
$827$	−20082.7	−	34784.3i	−0.844432	−	1.46260i	0.0416807	−	0.999131i	$-0.486729\pi$
$828$		0			0
$829$	9303.77	−	16114.6i	0.389787	−	0.675130i	−0.602634	−	0.798018i	$-0.705882\pi$
$829$	9303.77	−	16114.6i	0.389787	−	0.675130i	0.992421	+	0.122887i	$0.0392154\pi$
$830$		0			0
$831$	1613.92	+	25740.9i	0.0673722	+	1.07454i
$832$		0			0
$833$	1546.64	+	8771.45i	0.0643313	+	0.364841i
$834$		0			0
$835$	15333.8	+	12866.6i	0.635506	+	0.533253i
$836$		0			0
$837$	−16818.8	−	13735.2i	−0.694556	−	0.567213i
$838$		0			0
$839$	5456.36	+	4578.43i	0.224523	+	0.188397i	0.748109	−	0.663576i	$-0.230962\pi$
$839$	5456.36	+	4578.43i	0.224523	+	0.188397i	−0.523586	+	0.851973i	$0.675406\pi$
$840$		0			0
$841$	−4234.58	−	24015.5i	−0.173627	−	0.984686i
$842$		0			0
$843$	−35290.0	+	23435.7i	−1.44182	+	0.957495i
$844$		0			0
$845$	−12660.0	+	21927.8i	−0.515406	+	0.892709i
$846$		0			0
$847$	−15276.0	−	26458.7i	−0.619703	−	1.07336i
$848$		0			0
$849$	−13034.2	+	17671.2i	−0.526894	+	0.714340i
$850$		0			0
$851$	37198.0	−	31212.8i	1.49839	−	1.25730i
$852$		0			0
$853$	5664.58	−	2061.74i	0.227376	−	0.0827581i	−0.225820	−	0.974169i	$-0.572506\pi$
$853$	5664.58	−	2061.74i	0.227376	−	0.0827581i	0.453196	+	0.891411i	$0.350284\pi$
$854$		0			0
$855$	14264.4	−	33892.8i	0.570564	−	1.35568i
$856$		0			0
$857$	2996.65	−	16994.8i	0.119444	−	0.677400i	−0.865010	−	0.501755i	$-0.832688\pi$
$857$	2996.65	−	16994.8i	0.119444	−	0.677400i	0.984454	−	0.175645i	$-0.0562011\pi$
$858$		0			0
$859$	18113.2	+	6592.66i	0.719458	+	0.261861i	0.675695	−	0.737181i	$-0.263843\pi$
$859$	18113.2	+	6592.66i	0.719458	+	0.261861i	0.0437621	+	0.999042i	$0.486066\pi$
$860$		0			0
$861$	10806.9	+	11353.3i	0.427757	+	0.449383i
$862$		0			0
$863$	38434.6			1.51602			0.758011	−	0.652241i	$-0.226171\pi$
$863$	38434.6			1.51602			0.758011	+	0.652241i	$0.226171\pi$
$864$		0			0
$865$	38851.6			1.52716
$866$		0			0
$867$	5552.99	−	18852.5i	0.217520	−	0.738481i
$868$		0			0
$869$	−9650.44	−	3512.47i	−0.376719	−	0.137115i
$870$		0			0
$871$	−384.800	+	2182.31i	−0.0149695	+	0.0848963i
$872$		0			0
$873$	1254.67	−	1353.76i	0.0486418	−	0.0524830i
$874$		0			0
$875$	29975.4	−	10910.1i	1.15812	−	0.421520i
$876$		0			0
$877$	−7769.12	+	6519.07i	−0.299139	+	0.251007i	−0.779986	−	0.625797i	$-0.784774\pi$
$877$	−7769.12	+	6519.07i	−0.299139	+	0.251007i	0.480847	+	0.876805i	$0.340329\pi$
$878$		0			0
$879$	13797.8	+	31600.5i	0.529452	+	1.21258i
$880$		0			0
$881$	12949.0	+	22428.4i	0.495192	+	0.857698i	0.999985	−	0.00554305i	$-0.00176442\pi$
$881$	12949.0	+	22428.4i	0.495192	+	0.857698i	−0.504793	+	0.863241i	$0.668431\pi$
$882$		0			0
$883$	−11843.7	+	20513.9i	−0.451385	+	0.781822i	−0.998472	−	0.0552538i	$-0.982403\pi$
$883$	−11843.7	+	20513.9i	−0.451385	+	0.781822i	0.547087	+	0.837075i	$0.315737\pi$
$884$		0			0
$885$	−48477.1	−	24077.2i	−1.84129	−	0.914517i
$886$		0			0
$887$	1105.81	+	6271.37i	0.0418596	+	0.237398i	0.998558	−	0.0536833i	$-0.0170961\pi$
$887$	1105.81	+	6271.37i	0.0418596	+	0.237398i	−0.956698	+	0.291081i	$0.905985\pi$
$888$		0			0
$889$	26361.6	+	22120.0i	0.994532	+	0.834511i
$890$		0			0
$891$	−1884.41	+	6726.84i	−0.0708532	+	0.252927i
$892$		0			0
$893$	20288.5	+	17024.1i	0.760280	+	0.637951i
$894$		0			0
$895$	5690.58	+	32272.9i	0.212531	+	1.20532i
$896$		0			0
$897$	6376.81	+	3167.19i	0.237364	+	0.117892i
$898$		0			0
$899$	−134.387	+	232.766i	−0.00498561	+	0.00863534i
$900$		0			0
$901$	10894.0	+	18869.0i	0.402811	+	0.697688i
$902$		0			0
$903$	−17934.7	−	41074.9i	−0.660939	−	1.51372i
$904$		0			0
$905$	21110.7	−	17714.0i	0.775408	−	0.650644i
$906$		0			0
$907$	17551.1	−	6388.10i	0.642532	−	0.233862i	−0.000144890	−	1.00000i	$-0.500046\pi$
$907$	17551.1	−	6388.10i	0.642532	−	0.233862i	0.642677	+	0.766138i	$0.277824\pi$
$908$		0			0
$909$	5114.92	+	16548.9i	0.186635	+	0.603840i
$910$		0			0
$911$	−6259.33	+	35498.4i	−0.227641	+	1.29102i	0.629931	+	0.776651i	$0.283083\pi$
$911$	−6259.33	+	35498.4i	−0.227641	+	1.29102i	−0.857572	+	0.514364i	$0.828028\pi$
$912$		0			0
$913$	−11906.6	−	4333.64i	−0.431599	−	0.157089i
$914$		0			0
$915$	12676.0	−	43035.1i	0.457984	−	1.55486i
$916$		0			0
$917$	61913.0			2.22961
$918$		0			0
$919$	7124.80			0.255740			0.127870	−	0.991791i	$-0.459186\pi$
$919$	7124.80			0.255740			0.127870	+	0.991791i	$0.459186\pi$
$920$		0			0
$921$	10224.7	+	10741.6i	0.365814	+	0.384308i
$922$		0			0
$923$	5954.14	+	2167.13i	0.212332	+	0.0772827i
$924$		0			0
$925$	798.217	−	4526.92i	0.0283732	−	0.160913i
$926$		0			0
$927$	−41767.9	+	5258.24i	−1.47987	+	0.186304i
$928$		0			0
$929$	12267.6	−	4465.05i	0.433249	−	0.157690i	−0.116184	−	0.993228i	$-0.537066\pi$
$929$	12267.6	−	4465.05i	0.433249	−	0.157690i	0.549433	+	0.835538i	$0.314844\pi$
$930$		0			0
$931$	−23266.9	+	19523.2i	−0.819056	+	0.687269i
$932$		0			0
$933$	343.138	−	465.211i	0.0120406	−	0.0163240i
$934$		0			0
$935$	1913.60	+	3314.45i	0.0669319	+	0.115929i
$936$		0			0
$937$	16553.1	−	28670.9i	0.577126	−	0.999612i	−0.418681	−	0.908133i	$-0.637507\pi$
$937$	16553.1	−	28670.9i	0.577126	−	0.999612i	0.995807	−	0.0914784i	$-0.0291592\pi$
$938$		0			0
$939$	−5226.41	+	3470.79i	−0.181637	+	0.120623i
$940$		0			0
$941$	−6249.23	−	35441.1i	−0.216492	−	1.22779i	−0.878299	−	0.478113i	$-0.841321\pi$
$941$	−6249.23	−	35441.1i	−0.216492	−	1.22779i	0.661807	−	0.749675i	$-0.269790\pi$
$942$		0			0
$943$	15907.9	+	13348.3i	0.549345	+	0.460956i
$944$		0			0
$945$	7672.19	+	40360.6i	0.264102	+	1.38935i
$946$		0			0
$947$	8533.82	+	7160.73i	0.292832	+	0.245715i	0.777353	−	0.629064i	$-0.216562\pi$
$947$	8533.82	+	7160.73i	0.292832	+	0.245715i	−0.484521	+	0.874779i	$0.661006\pi$
$948$		0			0
$949$	−494.174	−	2802.60i	−0.0169037	−	0.0958655i
$950$		0			0
$951$	1679.92	+	26793.7i	0.0572821	+	0.913611i
$952$		0			0
$953$	10825.3	−	18750.0i	0.367961	−	0.637328i	−0.621285	−	0.783584i	$-0.713389\pi$
$953$	10825.3	−	18750.0i	0.367961	−	0.637328i	0.989247	+	0.146257i	$0.0467226\pi$
$954$		0			0
$955$	27936.6	+	48387.5i	0.946603	+	1.63956i
$956$		0			0
$957$	85.9260	+	9.65688i	0.00290240	+	0.000326189i
$958$		0			0
$959$	7906.24	−	6634.12i	0.266221	−	0.223386i
$960$		0			0
$961$	5483.00	−	1995.65i	0.184049	−	0.0669883i
$962$		0			0
$963$	−2041.11	+	1047.88i	−0.0683011	+	0.0350648i
$964$		0			0
$965$	450.622	−	2555.61i	0.0150322	−	0.0852517i
$966$		0			0
$967$	−24009.7	−	8738.82i	−0.798449	−	0.290612i	−0.0896056	−	0.995977i	$-0.528561\pi$
$967$	−24009.7	−	8738.82i	−0.798449	−	0.290612i	−0.708844	+	0.705366i	$0.750783\pi$
$968$		0			0
$969$	−19474.9	+	4707.04i	−0.645638	+	0.156049i
$970$		0			0
$971$	−16218.0			−0.536005			−0.268003	−	0.963418i	$-0.586364\pi$
$971$	−16218.0			−0.536005			−0.268003	+	0.963418i	$0.586364\pi$
$972$		0			0
$973$	−18262.6			−0.601719
$974$		0			0
$975$	655.146	−	158.347i	0.0215195	−	0.00520120i
$976$		0			0
$977$	−41442.9	−	15084.0i	−1.35709	−	0.493940i	−0.441936	−	0.897047i	$-0.645708\pi$
$977$	−41442.9	−	15084.0i	−1.35709	−	0.493940i	−0.915153	+	0.403107i	$0.867930\pi$
$978$		0			0
$979$	−52.5988	+	298.302i	−0.00171712	+	0.00973829i
$980$		0			0
$981$	52827.2	−	27120.7i	1.71931	−	0.882669i
$982$		0			0
$983$	47663.2	−	17348.0i	1.54651	−	0.562883i	0.578914	−	0.815389i	$-0.303477\pi$
$983$	47663.2	−	17348.0i	1.54651	−	0.562883i	0.967595	+	0.252506i	$0.0812546\pi$
$984$		0			0
$985$	2069.18	−	1736.25i	0.0669335	−	0.0561639i
$986$		0			0
$987$	−29404.7	−	3304.68i	−0.948291	−	0.106575i
$988$		0			0
$989$	−29689.8	−	51424.2i	−0.954580	−	1.65338i
$990$		0			0
$991$	−8577.07	+	14855.9i	−0.274934	+	0.476199i	−0.970118	−	0.242632i	$-0.921989\pi$
$991$	−8577.07	+	14855.9i	−0.274934	+	0.476199i	0.695185	+	0.718831i	$0.255323\pi$
$992$		0			0
$993$	−3078.19	−	49095.0i	−0.0983719	−	1.56897i
$994$		0			0
$995$	−2070.01	−	11739.6i	−0.0659535	−	0.374041i
$996$		0			0
$997$	−5448.01	−	4571.43i	−0.173060	−	0.145214i	0.552144	−	0.833749i	$-0.313810\pi$
$997$	−5448.01	−	4571.43i	−0.173060	−	0.145214i	−0.725203	+	0.688535i	$0.758254\pi$
$998$		0			0
$999$	−37896.7	−	13224.5i	−1.20020	−	0.418823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.97.8	yes	54
3.2	odd	2		324.4.i.a.289.3		54
27.5	odd	18		324.4.i.a.37.3		54
27.22	even	9	inner	108.4.i.a.49.8	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.49.8	✓	54	27.22	even	9	inner
108.4.i.a.97.8	yes	54	1.1	even	1	trivial
324.4.i.a.37.3		54	27.5	odd	18
324.4.i.a.289.3		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)

\(f(q)\)	\(=\)	\(q+(5.05072 - 1.22075i) q^{3} +(11.1609 + 4.06223i) q^{5} +(-4.28132 + 24.2806i) q^{7} +(24.0196 - 12.3313i) q^{9} +O(q^{10})\)	\(q+(5.05072 - 1.22075i) q^{3} +(11.1609 + 4.06223i) q^{5} +(-4.28132 + 24.2806i) q^{7} +(24.0196 - 12.3313i) q^{9} +(-9.00480 + 3.27748i) q^{11} +(6.18439 - 5.18932i) q^{13} +(61.3295 + 6.89258i) q^{15} +(-16.8131 - 29.1212i) q^{17} +(57.3341 - 99.3056i) q^{19} +(8.01668 + 127.861i) q^{21} +(29.4732 + 167.151i) q^{23} +(12.3082 + 10.3278i) q^{25} +(106.263 - 91.6038i) q^{27} +(-1.33025 - 1.11621i) q^{29} +(-26.8769 - 152.426i) q^{31} +(-41.4798 + 27.5462i) q^{33} +(-146.417 + 253.601i) q^{35} +(-143.047 - 247.765i) q^{37} +(24.9008 - 33.7594i) q^{39} +(93.7251 - 78.6447i) q^{41} +(-328.750 + 119.655i) q^{43} +(318.172 - 40.0553i) q^{45} +(-40.1073 + 227.460i) q^{47} +(-248.901 - 90.5926i) q^{49} +(-120.468 - 126.559i) q^{51} -647.947 q^{53} -113.816 q^{55} +(168.352 - 571.555i) q^{57} +(-824.149 - 299.966i) q^{59} +(126.231 - 715.889i) q^{61} +(196.576 + 636.002i) q^{63} +(90.1035 - 32.7950i) q^{65} +(-210.269 + 176.437i) q^{67} +(352.910 + 808.253i) q^{69} +(392.428 + 679.706i) q^{71} +(176.253 - 305.280i) q^{73} +(74.7732 + 37.1378i) q^{75} +(-41.0266 - 232.674i) q^{77} +(820.969 + 688.875i) q^{79} +(424.878 - 592.385i) q^{81} +(1012.90 + 849.924i) q^{83} +(-69.3525 - 393.318i) q^{85} +(-8.08135 - 4.01378i) q^{87} +(15.8047 - 27.3746i) q^{89} +(99.5222 + 172.377i) q^{91} +(-321.821 - 737.052i) q^{93} +(1043.30 - 875.434i) q^{95} +(64.2391 - 23.3811i) q^{97} +(-175.876 + 189.765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 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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