LMFDB - Embedded newform 108.4.i.a.97.9

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			97.9
Character	$\chi$	$=$	108.97
Dual form			108.4.i.a.49.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.17716 + 0.443910i) q^{3} +(-4.80495 - 1.74886i) q^{5} +(5.74341 - 32.5725i) q^{7} +(26.6059 + 4.59638i) q^{9} +O(q^{10})$	\(q+(5.17716 + 0.443910i) q^{3} +(-4.80495 - 1.74886i) q^{5} +(5.74341 - 32.5725i) q^{7} +(26.6059 + 4.59638i) q^{9} +(28.2317 - 10.2755i) q^{11} +(7.59849 - 6.37589i) q^{13} +(-24.0996 - 11.1871i) q^{15} +(44.7319 + 77.4779i) q^{17} +(-29.6509 + 51.3568i) q^{19} +(44.1938 - 166.083i) q^{21} +(-17.0562 - 96.7304i) q^{23} +(-75.7266 - 63.5421i) q^{25} +(135.702 + 35.6068i) q^{27} +(108.085 + 90.6938i) q^{29} +(4.10141 + 23.2603i) q^{31} +(150.721 - 40.6655i) q^{33} +(-84.5615 + 146.465i) q^{35} +(-114.087 - 197.604i) q^{37} +(42.1689 - 29.6359i) q^{39} +(-357.814 + 300.241i) q^{41} +(-10.1135 + 3.68102i) q^{43} +(-119.801 - 68.6153i) q^{45} +(-66.0561 + 374.623i) q^{47} +(-705.667 - 256.842i) q^{49} +(197.191 + 420.972i) q^{51} -202.984 q^{53} -153.622 q^{55} +(-176.305 + 252.720i) q^{57} +(766.955 + 279.149i) q^{59} +(-109.702 + 622.151i) q^{61} +(302.524 - 840.222i) q^{63} +(-47.6609 + 17.3471i) q^{65} +(-466.269 + 391.246i) q^{67} +(-45.3629 - 508.360i) q^{69} +(140.376 + 243.138i) q^{71} +(608.806 - 1054.48i) q^{73} +(-363.841 - 362.583i) q^{75} +(-172.552 - 978.592i) q^{77} +(278.680 + 233.841i) q^{79} +(686.746 + 244.582i) q^{81} +(453.825 + 380.804i) q^{83} +(-79.4366 - 450.507i) q^{85} +(519.311 + 517.516i) q^{87} +(-359.138 + 622.046i) q^{89} +(-164.037 - 284.121i) q^{91} +(10.9082 + 122.243i) q^{93} +(232.286 - 194.911i) q^{95} +(776.386 - 282.581i) q^{97} +(798.358 - 143.625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	5.17716	+	0.443910i	0.996344	+	0.0854306i
$3$	5.17716	+	0.443910i	0.996344	+	0.0854306i
$4$		0			0
$5$	−4.80495	−	1.74886i	−0.429767	−	0.156423i	0.118074	−	0.993005i	$-0.462328\pi$
$5$	−4.80495	−	1.74886i	−0.429767	−	0.156423i	−0.547841	+	0.836582i	$0.684550\pi$
$6$		0			0
$7$	5.74341	−	32.5725i	0.310115	−	1.75875i	−0.288277	−	0.957547i	$-0.593082\pi$
$7$	5.74341	−	32.5725i	0.310115	−	1.75875i	0.598392	−	0.801203i	$-0.295806\pi$
$8$		0			0
$9$	26.6059	+	4.59638i	0.985403	+	0.170236i
$10$		0			0
$11$	28.2317	−	10.2755i	0.773833	−	0.281652i	0.0752344	−	0.997166i	$-0.476029\pi$
$11$	28.2317	−	10.2755i	0.773833	−	0.281652i	0.698599	+	0.715514i	$0.253807\pi$
$12$		0			0
$13$	7.59849	−	6.37589i	0.162111	−	0.136027i	−0.558124	−	0.829758i	$-0.688479\pi$
$13$	7.59849	−	6.37589i	0.162111	−	0.136027i	0.720235	+	0.693731i	$0.244034\pi$
$14$		0			0
$15$	−24.0996	−	11.1871i	−0.414833	−	0.192566i
$16$		0			0
$17$	44.7319	+	77.4779i	0.638181	+	1.10536i	0.985832	+	0.167738i	$0.0536463\pi$
$17$	44.7319	+	77.4779i	0.638181	+	1.10536i	−0.347650	+	0.937624i	$0.613020\pi$
$18$		0			0
$19$	−29.6509	+	51.3568i	−0.358020	+	0.620108i	−0.987630	−	0.156803i	$-0.949881\pi$
$19$	−29.6509	+	51.3568i	−0.358020	+	0.620108i	0.629610	+	0.776911i	$0.283215\pi$
$20$		0			0
$21$	44.1938	−	166.083i	0.459232	−	1.72583i
$22$		0			0
$23$	−17.0562	−	96.7304i	−0.154629	−	0.876943i	−0.959124	−	0.282984i	$-0.908676\pi$
$23$	−17.0562	−	96.7304i	−0.154629	−	0.876943i	0.804496	−	0.593958i	$-0.202436\pi$
$24$		0			0
$25$	−75.7266	−	63.5421i	−0.605812	−	0.508337i
$26$		0			0
$27$	135.702	+	35.6068i	0.967257	+	0.253798i
$28$		0			0
$29$	108.085	+	90.6938i	0.692097	+	0.580738i	0.919513	−	0.393059i	$-0.128583\pi$
$29$	108.085	+	90.6938i	0.692097	+	0.580738i	−0.227416	+	0.973798i	$0.573028\pi$
$30$		0			0
$31$	4.10141	+	23.2603i	0.0237624	+	0.134764i	0.994381	−	0.105859i	$-0.0337594\pi$
$31$	4.10141	+	23.2603i	0.0237624	+	0.134764i	−0.970619	+	0.240623i	$0.922648\pi$
$32$		0			0
$33$	150.721	−	40.6655i	0.795066	−	0.214514i
$34$		0			0
$35$	−84.5615	+	146.465i	−0.408386	+	0.707345i
$36$		0			0
$37$	−114.087	−	197.604i	−0.506912	−	0.877997i	−0.999968	−	0.00799976i	$-0.997454\pi$
$37$	−114.087	−	197.604i	−0.506912	−	0.877997i	0.493056	−	0.869998i	$-0.335880\pi$
$38$		0			0
$39$	42.1689	−	29.6359i	0.173139	−	0.121681i
$40$		0			0
$41$	−357.814	+	300.241i	−1.36295	+	1.14365i	−0.387896	+	0.921703i	$0.626798\pi$
$41$	−357.814	+	300.241i	−1.36295	+	1.14365i	−0.975058	+	0.221951i	$0.928758\pi$
$42$		0			0
$43$	−10.1135	+	3.68102i	−0.0358673	+	0.0130546i	−0.359892	−	0.932994i	$-0.617186\pi$
$43$	−10.1135	+	3.68102i	−0.0358673	+	0.0130546i	0.324024	+	0.946049i	$0.394964\pi$
$44$		0			0
$45$	−119.801	−	68.6153i	−0.396865	−	0.227301i
$46$		0			0
$47$	−66.0561	+	374.623i	−0.205006	+	1.16265i	0.692424	+	0.721490i	$0.256543\pi$
$47$	−66.0561	+	374.623i	−0.205006	+	1.16265i	−0.897430	+	0.441156i	$0.854569\pi$
$48$		0			0
$49$	−705.667	−	256.842i	−2.05734	−	0.748810i
$50$		0			0
$51$	197.191	+	420.972i	0.541417	+	1.15584i
$52$		0			0
$53$	−202.984			−0.526076			−0.263038	−	0.964786i	$-0.584724\pi$
$53$	−202.984			−0.526076			−0.263038	+	0.964786i	$0.584724\pi$
$54$		0			0
$55$	−153.622			−0.376625
$56$		0			0
$57$	−176.305	+	252.720i	−0.409687	+	0.587255i
$58$		0			0
$59$	766.955	+	279.149i	1.69236	+	0.615967i	0.994919	−	0.100678i	$-0.0321013\pi$
$59$	766.955	+	279.149i	1.69236	+	0.615967i	0.697437	+	0.716646i	$0.254324\pi$
$60$		0			0
$61$	−109.702	+	622.151i	−0.230261	+	1.30587i	0.622108	+	0.782932i	$0.286277\pi$
$61$	−109.702	+	622.151i	−0.230261	+	1.30587i	−0.852368	+	0.522942i	$0.824835\pi$
$62$		0			0
$63$	302.524	−	840.222i	0.604992	−	1.68029i
$64$		0			0
$65$	−47.6609	+	17.3471i	−0.0909477	+	0.0331023i
$66$		0			0
$67$	−466.269	+	391.246i	−0.850206	+	0.713408i	−0.959835	−	0.280565i	$-0.909478\pi$
$67$	−466.269	+	391.246i	−0.850206	+	0.713408i	0.109629	+	0.993973i	$0.465034\pi$
$68$		0			0
$69$	−45.3629	−	508.360i	−0.0791457	−	0.886947i
$70$		0			0
$71$	140.376	+	243.138i	0.234642	+	0.406411i	0.959168	−	0.282835i	$-0.0912750\pi$
$71$	140.376	+	243.138i	0.234642	+	0.406411i	−0.724527	+	0.689247i	$0.757942\pi$
$72$		0			0
$73$	608.806	−	1054.48i	0.976101	−	1.69066i	0.299849	−	0.953987i	$-0.403064\pi$
$73$	608.806	−	1054.48i	0.976101	−	1.69066i	0.676252	−	0.736671i	$-0.263603\pi$
$74$		0			0
$75$	−363.841	−	362.583i	−0.560170	−	0.558233i
$76$		0			0
$77$	−172.552	−	978.592i	−0.255379	−	1.44832i
$78$		0			0
$79$	278.680	+	233.841i	0.396886	+	0.333027i	0.819289	−	0.573381i	$-0.194369\pi$
$79$	278.680	+	233.841i	0.396886	+	0.333027i	−0.422402	+	0.906408i	$0.638813\pi$
$80$		0			0
$81$	686.746	+	244.582i	0.942039	+	0.335503i
$82$		0			0
$83$	453.825	+	380.804i	0.600166	+	0.503599i	0.891499	−	0.453023i	$-0.149654\pi$
$83$	453.825	+	380.804i	0.600166	+	0.503599i	−0.291333	+	0.956622i	$0.594099\pi$
$84$		0			0
$85$	−79.4366	−	450.507i	−0.101366	−	0.574875i
$86$		0			0
$87$	519.311	+	517.516i	0.639954	+	0.637741i
$88$		0			0
$89$	−359.138	+	622.046i	−0.427737	+	0.740862i	−0.996672	−	0.0815204i	$-0.974022\pi$
$89$	−359.138	+	622.046i	−0.427737	+	0.740862i	0.568935	+	0.822383i	$0.307356\pi$
$90$		0			0
$91$	−164.037	−	284.121i	−0.188965	−	0.327297i
$92$		0			0
$93$	10.9082	+	122.243i	0.0121626	+	0.136301i
$94$		0			0
$95$	232.286	−	194.911i	0.250864	−	0.210500i
$96$		0			0
$97$	776.386	−	282.581i	0.812681	−	0.295792i	0.0979501	−	0.995191i	$-0.468771\pi$
$97$	776.386	−	282.581i	0.812681	−	0.295792i	0.714731	+	0.699400i	$0.246549\pi$
$98$		0			0
$99$	798.358	−	143.625i	0.810485	−	0.145806i
$100$		0			0
$101$	171.883	−	974.796i	0.169336	−	0.960355i	−0.775143	−	0.631785i	$-0.782322\pi$
$101$	171.883	−	974.796i	0.169336	−	0.960355i	0.944480	−	0.328569i	$-0.106566\pi$
$102$		0			0
$103$	645.975	+	235.116i	0.617959	+	0.224919i	0.631982	−	0.774983i	$-0.282242\pi$
$103$	645.975	+	235.116i	0.617959	+	0.224919i	−0.0140232	+	0.999902i	$0.504464\pi$
$104$		0			0
$105$	−502.805	+	720.733i	−0.467321	+	0.669870i
$106$		0			0
$107$	−1298.75			−1.17341			−0.586706	−	0.809800i	$-0.699576\pi$
$107$	−1298.75			−1.17341			−0.586706	+	0.809800i	$0.699576\pi$
$108$		0			0
$109$	576.373			0.506482			0.253241	−	0.967403i	$-0.418503\pi$
$109$	576.373			0.506482			0.253241	+	0.967403i	$0.418503\pi$
$110$		0			0
$111$	−502.926	−	1073.67i	−0.430051	−	0.918093i
$112$		0			0
$113$	−1844.78	−	671.443i	−1.53577	−	0.558974i	−0.570743	−	0.821129i	$-0.693345\pi$
$113$	−1844.78	−	671.443i	−1.53577	−	0.558974i	−0.965026	+	0.262155i	$0.915567\pi$
$114$		0			0
$115$	−87.2136	+	494.613i	−0.0707193	+	0.401069i
$116$		0			0
$117$	231.471	−	134.711i	0.182901	−	0.106444i
$118$		0			0
$119$	2780.57	−	1012.04i	2.14197	−	0.779612i
$120$		0			0
$121$	−328.164	+	275.362i	−0.246555	+	0.206884i
$122$		0			0
$123$	−1985.74	+	1395.56i	−1.45567	+	1.02303i
$124$		0			0
$125$	572.318	+	991.284i	0.409518	+	0.709305i
$126$		0			0
$127$	−245.983	+	426.055i	−0.171870	+	0.297687i	−0.939073	−	0.343716i	$-0.888314\pi$
$127$	−245.983	+	426.055i	−0.171870	+	0.297687i	0.767204	+	0.641403i	$0.221647\pi$
$128$		0			0
$129$	−53.9933	+	14.5677i	−0.0368515	+	0.00994275i
$130$		0			0
$131$	−377.965	−	2143.55i	−0.252084	−	1.42964i	−0.803449	−	0.595374i	$-0.797004\pi$
$131$	−377.965	−	2143.55i	−0.252084	−	1.42964i	0.551365	−	0.834264i	$-0.314107\pi$
$132$		0			0
$133$	1502.52	+	1260.77i	0.979588	+	0.821972i
$134$		0			0
$135$	−589.772	−	408.413i	−0.375996	−	0.260375i
$136$		0			0
$137$	1065.12	+	893.740i	0.664228	+	0.557353i	0.911351	−	0.411631i	$-0.135041\pi$
$137$	1065.12	+	893.740i	0.664228	+	0.557353i	−0.247123	+	0.968984i	$0.579485\pi$
$138$		0			0
$139$	191.282	+	1084.82i	0.116722	+	0.661963i	0.985883	+	0.167435i	$0.0535483\pi$
$139$	191.282	+	1084.82i	0.116722	+	0.661963i	−0.869161	+	0.494529i	$0.835341\pi$
$140$		0			0
$141$	−508.282	+	1910.16i	−0.303582	+	1.14088i
$142$		0			0
$143$	149.003	−	258.080i	0.0871344	−	0.150921i
$144$		0			0
$145$	−360.730	−	624.803i	−0.206600	−	0.357842i
$146$		0			0
$147$	−3539.33	−	1642.96i	−1.98585	−	0.921832i
$148$		0			0
$149$	1499.38	−	1258.13i	0.824388	−	0.691744i	−0.129607	−	0.991565i	$-0.541372\pi$
$149$	1499.38	−	1258.13i	0.824388	−	0.691744i	0.953995	+	0.299821i	$0.0969271\pi$
$150$		0			0
$151$	617.466	−	224.739i	0.332773	−	0.121119i	−0.170230	−	0.985404i	$-0.554451\pi$
$151$	617.466	−	224.739i	0.332773	−	0.121119i	0.503002	+	0.864285i	$0.332229\pi$
$152$		0			0
$153$	834.014	+	2266.97i	0.440693	+	1.19787i
$154$		0			0
$155$	20.9718	−	118.937i	0.0108677	−	0.0616339i
$156$		0			0
$157$	−1247.25	−	453.962i	−0.634022	−	0.230765i	0.00495878	−	0.999988i	$-0.498422\pi$
$157$	−1247.25	−	453.962i	−0.634022	−	0.230765i	−0.638981	+	0.769222i	$0.720644\pi$
$158$		0			0
$159$	−1050.88	−	90.1067i	−0.524152	−	0.0449429i
$160$		0			0
$161$	−3248.71			−1.59028
$162$		0			0
$163$	2562.11			1.23116			0.615582	−	0.788073i	$-0.288921\pi$
$163$	2562.11			1.23116			0.615582	+	0.788073i	$0.288921\pi$
$164$		0			0
$165$	−795.325	−	68.1943i	−0.375248	−	0.0321753i
$166$		0			0
$167$	−3356.67	−	1221.73i	−1.55537	−	0.566109i	−0.585703	−	0.810526i	$-0.699181\pi$
$167$	−3356.67	−	1221.73i	−1.55537	−	0.566109i	−0.969670	+	0.244417i	$0.921404\pi$
$168$		0			0
$169$	−364.420	+	2066.73i	−0.165872	+	0.940705i
$170$		0			0
$171$	−1024.94	+	1230.11i	−0.458359	+	0.550109i
$172$		0			0
$173$	−2140.09	+	778.930i	−0.940510	+	0.342318i	−0.766367	−	0.642403i	$-0.777938\pi$
$173$	−2140.09	+	778.930i	−0.940510	+	0.342318i	−0.174143	+	0.984720i	$0.555715\pi$
$174$		0			0
$175$	−2504.66	+	2101.66i	−1.08191	+	0.907830i
$176$		0			0
$177$	3846.73	+	1785.66i	1.63355	+	0.758294i
$178$		0			0
$179$	577.965	+	1001.07i	0.241336	+	0.418006i	0.961095	−	0.276218i	$-0.0890811\pi$
$179$	577.965	+	1001.07i	0.241336	+	0.418006i	−0.719759	+	0.694224i	$0.755748\pi$
$180$		0			0
$181$	1786.92	−	3095.03i	0.733815	−	1.27100i	−0.221427	−	0.975177i	$-0.571071\pi$
$181$	1786.92	−	3095.03i	0.733815	−	1.27100i	0.955241	−	0.295827i	$-0.0955952\pi$
$182$		0			0
$183$	−844.124	+	3172.27i	−0.340980	+	1.28143i
$184$		0			0
$185$	202.599	+	1149.00i	0.0805157	+	0.456627i
$186$		0			0
$187$	2058.98	+	1727.69i	0.805174	+	0.675621i
$188$		0			0
$189$	1939.20	−	4215.67i	0.746328	−	1.62246i
$190$		0			0
$191$	−615.799	−	516.717i	−0.233286	−	0.195750i	0.518649	−	0.854987i	$-0.326435\pi$
$191$	−615.799	−	516.717i	−0.233286	−	0.195750i	−0.751935	+	0.659237i	$0.770880\pi$
$192$		0			0
$193$	−155.121	−	879.737i	−0.0578543	−	0.328108i	0.942120	−	0.335276i	$-0.108829\pi$
$193$	−155.121	−	879.737i	−0.0578543	−	0.328108i	−0.999974	+	0.00716788i	$0.997718\pi$
$194$		0			0
$195$	−254.448	+	68.6517i	−0.0934432	+	0.0252115i
$196$		0			0
$197$	1162.98	−	2014.35i	0.420605	−	0.728509i	−0.575394	−	0.817876i	$-0.695151\pi$
$197$	1162.98	−	2014.35i	0.420605	−	0.728509i	0.995999	+	0.0893676i	$0.0284846\pi$
$198$		0			0
$199$	158.416	+	274.384i	0.0564311	+	0.0977415i	0.892861	−	0.450333i	$-0.148695\pi$
$199$	158.416	+	274.384i	0.0564311	+	0.0977415i	−0.836430	+	0.548074i	$0.815361\pi$
$200$		0			0
$201$	−2587.63	+	1818.56i	−0.908045	+	0.638166i
$202$		0			0
$203$	3574.90	−	2999.70i	1.23600	−	1.03713i
$204$		0			0
$205$	2244.35	−	816.878i	0.764646	−	0.278309i
$206$		0			0
$207$	−9.18465	−	2652.00i	−0.00308395	−	0.890466i
$208$		0			0
$209$	−309.377	+	1754.56i	−0.102393	+	0.580697i
$210$		0			0
$211$	−3958.48	−	1440.77i	−1.29153	−	0.470079i	−0.397302	−	0.917688i	$-0.630054\pi$
$211$	−3958.48	−	1440.77i	−1.29153	−	0.470079i	−0.894229	+	0.447609i	$0.852276\pi$
$212$		0			0
$213$	618.816	+	1321.08i	0.199064	+	0.424971i
$214$		0			0
$215$	55.0324			0.0174567
$216$		0			0
$217$	781.202			0.244384
$218$		0			0
$219$	3619.98	−	5188.97i	1.11697	−	1.60109i
$220$		0			0
$221$	833.886	+	303.510i	0.253816	+	0.0923813i
$222$		0			0
$223$	−92.7029	+	525.744i	−0.0278379	+	0.157876i	−0.995558	−	0.0941513i	$-0.969986\pi$
$223$	−92.7029	+	525.744i	−0.0278379	+	0.157876i	0.967720	+	0.252028i	$0.0810974\pi$
$224$		0			0
$225$	−1722.71	−	2038.66i	−0.510432	−	0.604048i
$226$		0			0
$227$	5420.84	−	1973.03i	1.58500	−	0.576891i	0.608713	−	0.793391i	$-0.291686\pi$
$227$	5420.84	−	1973.03i	1.58500	−	0.576891i	0.976283	+	0.216500i	$0.0694640\pi$
$228$		0			0
$229$	1142.36	−	958.554i	0.329647	−	0.276607i	−0.462909	−	0.886406i	$-0.653194\pi$
$229$	1142.36	−	958.554i	0.329647	−	0.276607i	0.792556	+	0.609799i	$0.208750\pi$
$230$		0			0
$231$	−458.923	−	5142.92i	−0.130714	−	1.46485i
$232$		0			0
$233$	225.811	+	391.116i	0.0634908	+	0.109969i	0.896024	−	0.444007i	$-0.146443\pi$
$233$	225.811	+	391.116i	0.0634908	+	0.109969i	−0.832533	+	0.553976i	$0.813110\pi$
$234$		0			0
$235$	972.558	−	1684.52i	0.269969	−	0.467600i
$236$		0			0
$237$	1338.97	+	1334.34i	0.366984	+	0.365716i
$238$		0			0
$239$	537.820	+	3050.13i	0.145559	+	0.825508i	0.966916	+	0.255093i	$0.0821062\pi$
$239$	537.820	+	3050.13i	0.145559	+	0.825508i	−0.821357	+	0.570414i	$0.806783\pi$
$240$		0			0
$241$	427.852	+	359.010i	0.114358	+	0.0959580i	0.698174	−	0.715928i	$-0.253996\pi$
$241$	427.852	+	359.010i	0.114358	+	0.0959580i	−0.583815	+	0.811886i	$0.698441\pi$
$242$		0			0
$243$	3446.82	+	1571.09i	0.909933	+	0.414756i
$244$		0			0
$245$	2941.51	+	2468.22i	0.767046	+	0.643628i
$246$		0			0
$247$	102.143	+	579.285i	0.0263127	+	0.149227i
$248$		0			0
$249$	2180.48	+	2172.94i	0.554949	+	0.553030i
$250$		0			0
$251$	−315.189	+	545.923i	−0.0792612	+	0.137284i	−0.902931	−	0.429785i	$-0.858589\pi$
$251$	−315.189	+	545.923i	−0.0792612	+	0.137284i	0.823670	+	0.567069i	$0.191923\pi$
$252$		0			0
$253$	−1475.48	−	2555.60i	−0.366650	−	0.635056i
$254$		0			0
$255$	−211.271	−	2367.61i	−0.0518835	−	0.581433i
$256$		0			0
$257$	−1711.18	+	1435.85i	−0.415333	+	0.348506i	−0.826384	−	0.563106i	$-0.809606\pi$
$257$	−1711.18	+	1435.85i	−0.415333	+	0.348506i	0.411051	+	0.911612i	$0.365162\pi$
$258$		0			0
$259$	−7091.71	+	2581.17i	−1.70138	+	0.619251i
$260$		0			0
$261$	2458.82	+	2909.79i	0.583132	+	0.690081i
$262$		0			0
$263$	115.370	−	654.298i	0.0270496	−	0.153406i	−0.968291	−	0.249824i	$-0.919627\pi$
$263$	115.370	−	654.298i	0.0270496	−	0.153406i	0.995341	+	0.0964178i	$0.0307385\pi$
$264$		0			0
$265$	975.328	+	354.990i	0.226090	+	0.0822901i
$266$		0			0
$267$	−2135.45	+	3061.00i	−0.489466	+	0.701612i
$268$		0			0
$269$	−6952.64			−1.57587			−0.787936	−	0.615757i	$-0.788850\pi$
$269$	−6952.64			−1.57587			−0.787936	+	0.615757i	$0.788850\pi$
$270$		0			0
$271$	−8783.48			−1.96885			−0.984426	−	0.175802i	$-0.943748\pi$
$271$	−8783.48			−1.96885			−0.984426	+	0.175802i	$0.943748\pi$
$272$		0			0
$273$	−723.123	−	1543.76i	−0.160313	−	0.342244i
$274$		0			0
$275$	−2790.81	−	1015.77i	−0.611972	−	0.222740i
$276$		0			0
$277$	1226.41	−	6955.33i	0.266021	−	1.50868i	−0.500089	−	0.865974i	$-0.666699\pi$
$277$	1226.41	−	6955.33i	0.266021	−	1.50868i	0.766111	−	0.642709i	$-0.222189\pi$
$278$		0			0
$279$	2.20859	+	637.712i	0.000473924	+	0.136842i
$280$		0			0
$281$	−6216.63	+	2262.67i	−1.31976	+	0.480354i	−0.903382	−	0.428837i	$-0.858923\pi$
$281$	−6216.63	+	2262.67i	−1.31976	+	0.480354i	−0.416379	+	0.909191i	$0.636701\pi$
$282$		0			0
$283$	4086.69	−	3429.14i	0.858405	−	0.720288i	−0.103218	−	0.994659i	$-0.532914\pi$
$283$	4086.69	−	3429.14i	0.858405	−	0.720288i	0.961624	+	0.274371i	$0.0884696\pi$
$284$		0			0
$285$	1289.11	−	905.973i	0.267930	−	0.188299i
$286$		0			0
$287$	7724.54	+	13379.3i	1.58873	+	2.75176i
$288$		0			0
$289$	−1545.39	+	2676.69i	−0.314551	+	0.544818i
$290$		0			0
$291$	4144.91	−	1118.32i	0.834980	−	0.225283i
$292$		0			0
$293$	−50.5304	−	286.572i	−0.0100751	−	0.0571390i	0.979356	−	0.202145i	$-0.0647911\pi$
$293$	−50.5304	−	286.572i	−0.0100751	−	0.0571390i	−0.989431	+	0.145006i	$0.953680\pi$
$294$		0			0
$295$	−3196.99	−	2682.59i	−0.630968	−	0.529445i
$296$		0			0
$297$	4196.98	−	389.168i	0.819979	−	0.0760332i
$298$		0			0
$299$	−746.344	−	626.257i	−0.144355	−	0.121128i
$300$		0			0
$301$	61.8139	+	350.564i	0.0118369	+	0.0671302i
$302$		0			0
$303$	1322.59	−	4970.37i	0.250761	−	0.942377i
$304$		0			0
$305$	1615.17	−	2797.55i	0.303227	−	0.525204i
$306$		0			0
$307$	572.764	+	992.056i	0.106480	+	0.184429i	0.914342	−	0.404943i	$-0.132709\pi$
$307$	572.764	+	992.056i	0.106480	+	0.184429i	−0.807862	+	0.589372i	$0.799375\pi$
$308$		0			0
$309$	3239.94	+	1503.98i	0.596485	+	0.276889i
$310$		0			0
$311$	−7195.48	+	6037.72i	−1.31196	+	1.10086i	−0.324011	+	0.946053i	$0.605031\pi$
$311$	−7195.48	+	6037.72i	−1.31196	+	1.10086i	−0.987945	+	0.154808i	$0.950524\pi$
$312$		0			0
$313$	−2912.59	+	1060.10i	−0.525972	+	0.191438i	−0.591339	−	0.806423i	$-0.701401\pi$
$313$	−2912.59	+	1060.10i	−0.525972	+	0.191438i	0.0653667	+	0.997861i	$0.479178\pi$
$314$		0			0
$315$	−2923.04	+	3508.15i	−0.522840	+	0.627498i
$316$		0			0
$317$	116.213	−	659.077i	0.0205905	−	0.116774i	−0.972780	−	0.231730i	$-0.925561\pi$
$317$	116.213	−	659.077i	0.0205905	−	0.116774i	0.993371	+	0.114956i	$0.0366726\pi$
$318$		0			0
$319$	3983.33	+	1449.81i	0.699134	+	0.254464i
$320$		0			0
$321$	−6723.84	−	576.529i	−1.16912	−	0.100245i
$322$		0			0
$323$	−5305.36			−0.913926
$324$		0			0
$325$	−980.545			−0.167356
$326$		0			0
$327$	2983.97	+	255.858i	0.504630	+	0.0432690i
$328$		0			0
$329$	11823.0	+	4303.23i	1.98123	+	0.721109i
$330$		0			0
$331$	50.4286	−	285.995i	0.00837404	−	0.0474915i	−0.980334	−	0.197343i	$-0.936769\pi$
$331$	50.4286	−	285.995i	0.00837404	−	0.0474915i	0.988708	+	0.149852i	$0.0478797\pi$
$332$		0			0
$333$	−2127.11	−	5781.82i	−0.350046	−	0.951476i
$334$		0			0
$335$	2924.63	−	1064.48i	0.476984	−	0.173608i
$336$		0			0
$337$	−6338.56	+	5318.68i	−1.02458	+	0.859724i	−0.990196	−	0.139685i	$-0.955391\pi$
$337$	−6338.56	+	5318.68i	−1.02458	+	0.859724i	−0.0343831	+	0.999409i	$0.510947\pi$
$338$		0			0
$339$	−9252.63	−	4295.08i	−1.48240	−	0.688132i
$340$		0			0
$341$	354.800	+	614.532i	0.0563446	+	0.0975917i
$342$		0			0
$343$	−6746.56	+	11685.4i	−1.06204	+	1.83951i
$344$		0			0
$345$	−671.083	+	2521.97i	−0.104724	+	0.393561i
$346$		0			0
$347$	−698.081	−	3959.02i	−0.107997	−	0.612482i	−0.989981	−	0.141202i	$-0.954903\pi$
$347$	−698.081	−	3959.02i	−0.107997	−	0.612482i	0.881984	−	0.471280i	$-0.156208\pi$
$348$		0			0
$349$	−6291.10	−	5278.86i	−0.964914	−	0.809659i	0.0168317	−	0.999858i	$-0.494642\pi$
$349$	−6291.10	−	5278.86i	−0.964914	−	0.809659i	−0.981745	+	0.190200i	$0.939086\pi$
$350$		0			0
$351$	1258.16	−	594.666i	0.191326	−	0.0904299i
$352$		0			0
$353$	−3542.55	−	2972.56i	−0.534139	−	0.448196i	0.335389	−	0.942080i	$-0.391132\pi$
$353$	−3542.55	−	2972.56i	−0.534139	−	0.448196i	−0.869528	+	0.493884i	$0.835577\pi$
$354$		0			0
$355$	−249.285	−	1413.76i	−0.0372694	−	0.211366i
$356$		0			0
$357$	14844.7	−	4005.18i	2.20074	−	0.593772i
$358$		0			0
$359$	6159.42	−	10668.4i	0.905521	−	1.56841i	0.0853041	−	0.996355i	$-0.472814\pi$
$359$	6159.42	−	10668.4i	0.905521	−	1.56841i	0.820217	−	0.572053i	$-0.193853\pi$
$360$		0			0
$361$	1671.15	+	2894.52i	0.243644	+	0.422004i
$362$		0			0
$363$	−1821.19	+	1279.92i	−0.263327	+	0.185064i
$364$		0			0
$365$	−4769.42	+	4002.02i	−0.683953	+	0.573905i
$366$		0			0
$367$	8080.39	−	2941.02i	1.14930	−	0.418311i	0.304036	−	0.952661i	$-0.401666\pi$
$367$	8080.39	−	2941.02i	1.14930	−	0.418311i	0.845263	+	0.534350i	$0.179444\pi$
$368$		0			0
$369$	−10900.0	+	6343.54i	−1.53775	+	0.894936i
$370$		0			0
$371$	−1165.82	+	6611.70i	−0.163144	+	0.925236i
$372$		0			0
$373$	−2385.97	−	868.421i	−0.331208	−	0.120550i	0.171063	−	0.985260i	$-0.445280\pi$
$373$	−2385.97	−	868.421i	−0.331208	−	0.120550i	−0.502271	+	0.864710i	$0.667502\pi$
$374$		0			0
$375$	2522.94	+	5386.09i	0.347424	+	0.741697i
$376$		0			0
$377$	1399.53			0.191193
$378$		0			0
$379$	11211.7			1.51955			0.759774	−	0.650187i	$-0.225309\pi$
$379$	11211.7			1.51955			0.759774	+	0.650187i	$0.225309\pi$
$380$		0			0
$381$	−1462.62	+	2096.56i	−0.196673	+	0.281916i
$382$		0			0
$383$	7480.47	+	2722.67i	0.998001	+	0.363243i	0.788813	−	0.614633i	$-0.210696\pi$
$383$	7480.47	+	2722.67i	0.998001	+	0.363243i	0.209188	+	0.977876i	$0.432918\pi$
$384$		0			0
$385$	−882.314	+	5003.85i	−0.116797	+	0.662389i
$386$		0			0
$387$	−285.998	+	51.4511i	−0.0375662	+	0.00675816i
$388$		0			0
$389$	−12432.6	+	4525.09i	−1.62045	+	0.589797i	−0.983469	−	0.181078i	$-0.942041\pi$
$389$	−12432.6	+	4525.09i	−1.62045	+	0.589797i	−0.636986	+	0.770875i	$0.719819\pi$
$390$		0			0
$391$	6731.52	−	5648.41i	0.870659	−	0.730569i
$392$		0			0
$393$	−1005.24	−	11265.3i	−0.129027	−	1.44595i
$394$		0			0
$395$	−930.091	−	1610.96i	−0.118476	−	0.205206i
$396$		0			0
$397$	6065.99	−	10506.6i	0.766859	−	1.32824i	−0.172399	−	0.985027i	$-0.555152\pi$
$397$	6065.99	−	10506.6i	0.766859	−	1.32824i	0.939258	−	0.343212i	$-0.111515\pi$
$398$		0			0
$399$	7219.13	+	7194.17i	0.905785	+	0.902654i
$400$		0			0
$401$	533.798	+	3027.32i	0.0664753	+	0.377000i	0.999837	+	0.0180626i	$0.00574981\pi$
$401$	533.798	+	3027.32i	0.0664753	+	0.377000i	−0.933362	+	0.358938i	$0.883139\pi$
$402$		0			0
$403$	179.469	+	150.593i	0.0221837	+	0.0186143i
$404$		0			0
$405$	−2872.04	−	2376.22i	−0.352377	−	0.291544i
$406$		0			0
$407$	−5251.33	−	4406.39i	−0.639555	−	0.536651i
$408$		0			0
$409$	−1787.94	−	10139.9i	−0.216156	−	1.22588i	−0.878889	−	0.477026i	$-0.841715\pi$
$409$	−1787.94	−	10139.9i	−0.216156	−	1.22588i	0.662733	−	0.748856i	$-0.269396\pi$
$410$		0			0
$411$	5117.54	+	5099.85i	0.614184	+	0.612061i
$412$		0			0
$413$	13497.5	−	23378.4i	1.60816	−	2.78541i
$414$		0			0
$415$	−1514.63	−	2623.42i	−0.179157	−	0.310310i
$416$		0			0
$417$	508.738	+	5701.18i	0.0597434	+	0.669515i
$418$		0			0
$419$	3312.78	−	2779.75i	0.386252	−	0.324104i	−0.428899	−	0.903353i	$-0.641098\pi$
$419$	3312.78	−	2779.75i	0.386252	−	0.324104i	0.815151	+	0.579248i	$0.196654\pi$
$420$		0			0
$421$	−5518.54	+	2008.58i	−0.638853	+	0.232523i	−0.641080	−	0.767474i	$-0.721513\pi$
$421$	−5518.54	+	2008.58i	−0.638853	+	0.232523i	0.00222710	+	0.999998i	$0.499291\pi$
$422$		0			0
$423$	−3479.39	+	9663.56i	−0.399938	+	1.11078i
$424$		0			0
$425$	1535.72	−	8709.50i	0.175278	−	0.994054i
$426$		0			0
$427$	19635.0	+	7146.54i	2.22530	+	0.809942i
$428$		0			0
$429$	885.974	−	1269.98i	0.0997092	−	0.142926i
$430$		0			0
$431$	−187.346			−0.0209377			−0.0104688	−	0.999945i	$-0.503332\pi$
$431$	−187.346			−0.0209377			−0.0104688	+	0.999945i	$0.503332\pi$
$432$		0			0
$433$	−313.829			−0.0348307			−0.0174153	−	0.999848i	$-0.505544\pi$
$433$	−313.829			−0.0348307			−0.0174153	+	0.999848i	$0.505544\pi$
$434$		0			0
$435$	−1590.20	−	3394.84i	−0.175274	−	0.374184i
$436$		0			0
$437$	5473.49	+	1992.19i	0.599159	+	0.218076i
$438$		0			0
$439$	2543.97	−	14427.5i	0.276576	−	1.56854i	−0.457335	−	0.889295i	$-0.651196\pi$
$439$	2543.97	−	14427.5i	0.276576	−	1.56854i	0.733911	−	0.679246i	$-0.237693\pi$
$440$		0			0
$441$	−17594.4	−	10077.0i	−1.89983	−	1.08811i
$442$		0			0
$443$	−3295.46	+	1199.45i	−0.353436	+	0.128640i	−0.512636	−	0.858606i	$-0.671331\pi$
$443$	−3295.46	+	1199.45i	−0.353436	+	0.128640i	0.159200	+	0.987246i	$0.449109\pi$
$444$		0			0
$445$	2813.51	−	2360.82i	0.299715	−	0.251491i
$446$		0			0
$447$	8321.01	−	5847.94i	0.880471	−	0.618787i
$448$		0			0
$449$	−905.931	−	1569.12i	−0.0952194	−	0.164925i	0.814481	−	0.580191i	$-0.197022\pi$
$449$	−905.931	−	1569.12i	−0.0952194	−	0.164925i	−0.909700	+	0.415266i	$0.863689\pi$
$450$		0			0
$451$	−7016.55	+	12153.0i	−0.732586	+	1.26888i
$452$		0			0
$453$	3296.48	−	889.411i	0.341904	−	0.0922477i
$454$		0			0
$455$	291.304	+	1652.07i	0.0300143	+	0.170220i
$456$		0			0
$457$	11433.8	+	9594.07i	1.17035	+	0.982039i	0.999994	−	0.00334372i	$-0.00106434\pi$
$457$	11433.8	+	9594.07i	1.17035	+	0.982039i	0.170354	+	0.985383i	$0.445509\pi$
$458$		0			0
$459$	3311.49	+	12106.7i	0.336747	+	1.23114i
$460$		0			0
$461$	−6096.59	−	5115.65i	−0.615936	−	0.516832i	0.280587	−	0.959829i	$-0.409471\pi$
$461$	−6096.59	−	5115.65i	−0.615936	−	0.516832i	−0.896523	+	0.442997i	$0.853915\pi$
$462$		0			0
$463$	2533.18	+	14366.4i	0.254270	+	1.44204i	0.797939	+	0.602738i	$0.205924\pi$
$463$	2533.18	+	14366.4i	0.254270	+	1.44204i	−0.543669	+	0.839300i	$0.682965\pi$
$464$		0			0
$465$	161.372	−	606.447i	0.0160934	−	0.0604802i
$466$		0			0
$467$	4109.70	−	7118.22i	0.407226	−	0.705336i	−0.587352	−	0.809332i	$-0.699830\pi$
$467$	4109.70	−	7118.22i	0.407226	−	0.705336i	0.994578	+	0.103996i	$0.0331629\pi$
$468$		0			0
$469$	10065.9	+	17434.6i	0.991044	+	1.71654i
$470$		0			0
$471$	−6255.70	−	2903.90i	−0.611990	−	0.284086i
$472$		0			0
$473$	−247.697	+	207.842i	−0.0240785	+	0.0202042i
$474$		0			0
$475$	5508.68	−	2004.99i	0.532117	−	0.193675i
$476$		0			0
$477$	−5400.57	−	932.993i	−0.518397	−	0.0895573i
$478$		0			0
$479$	729.906	−	4139.50i	0.0696247	−	0.394861i	−0.930002	−	0.367554i	$-0.880195\pi$
$479$	729.906	−	4139.50i	0.0696247	−	0.394861i	0.999627	−	0.0273078i	$-0.00869343\pi$
$480$		0			0
$481$	−2126.79	−	774.088i	−0.201607	−	0.0733791i
$482$		0			0
$483$	−16819.1	−	1442.14i	−1.58446	−	0.135858i
$484$		0			0
$485$	−4224.69			−0.395532
$486$		0			0
$487$	−13008.8			−1.21044			−0.605219	−	0.796059i	$-0.706914\pi$
$487$	−13008.8			−1.21044			−0.605219	+	0.796059i	$0.706914\pi$
$488$		0			0
$489$	13264.4	+	1137.34i	1.22666	+	0.105179i
$490$		0			0
$491$	−13256.1	−	4824.83i	−1.21841	−	0.443465i	−0.348797	−	0.937198i	$-0.613410\pi$
$491$	−13256.1	−	4824.83i	−1.21841	−	0.443465i	−0.869614	+	0.493733i	$0.835632\pi$
$492$		0			0
$493$	−2191.93	+	12431.1i	−0.200243	+	1.13563i
$494$		0			0
$495$	−4087.25	−	706.106i	−0.371128	−	0.0641153i
$496$		0			0
$497$	8725.86	−	3175.95i	0.787542	−	0.286642i
$498$		0			0
$499$	7229.72	−	6066.46i	0.648591	−	0.544232i	−0.258052	−	0.966131i	$-0.583081\pi$
$499$	7229.72	−	6066.46i	0.648591	−	0.544232i	0.906643	+	0.421899i	$0.138636\pi$
$500$		0			0
$501$	−16835.7	−	7815.15i	−1.50132	−	0.696916i
$502$		0			0
$503$	4547.85	+	7877.10i	0.403138	+	0.698256i	0.994103	−	0.108442i	$-0.0345861\pi$
$503$	4547.85	+	7877.10i	0.403138	+	0.698256i	−0.590965	+	0.806697i	$0.701253\pi$
$504$		0			0
$505$	−2530.67	+	4383.24i	−0.222996	+	0.386241i
$506$		0			0
$507$	−2804.10	+	10538.0i	−0.245630	+	0.923095i
$508$		0			0
$509$	1245.45	+	7063.30i	0.108455	+	0.615079i	0.989784	+	0.142576i	$0.0455384\pi$
$509$	1245.45	+	7063.30i	0.108455	+	0.615079i	−0.881329	+	0.472503i	$0.843350\pi$
$510$		0			0
$511$	−30850.6	−	25886.7i	−2.67074	−	2.24102i
$512$		0			0
$513$	−5852.35	+	5913.47i	−0.503679	+	0.508940i
$514$		0			0
$515$	−2692.69	−	2259.43i	−0.230396	−	0.193325i
$516$		0			0
$517$	1984.56	+	11255.0i	0.168822	+	0.957435i
$518$		0			0
$519$	−11425.4	+	3082.63i	−0.966316	+	0.260718i
$520$		0			0
$521$	4043.78	−	7004.04i	0.340041	−	0.588968i	−0.644399	−	0.764689i	$-0.722892\pi$
$521$	4043.78	−	7004.04i	0.340041	−	0.588968i	0.984440	+	0.175721i	$0.0562257\pi$
$522$		0			0
$523$	7678.53	+	13299.6i	0.641986	+	1.11195i	0.984989	+	0.172618i	$0.0552226\pi$
$523$	7678.53	+	13299.6i	0.641986	+	1.11195i	−0.343003	+	0.939334i	$0.611444\pi$
$524$		0			0
$525$	−13899.9	+	9768.76i	−1.15551	+	0.812083i
$526$		0			0
$527$	−1618.69	+	1358.25i	−0.133798	+	0.112270i
$528$		0			0
$529$	2367.38	−	861.657i	0.194574	−	0.0708192i
$530$		0			0
$531$	19122.4	+	10952.2i	1.56279	+	0.895077i
$532$		0			0
$533$	−804.538	+	4562.76i	−0.0653816	+	0.370798i
$534$		0			0
$535$	6240.43	+	2271.33i	0.504294	+	0.183548i
$536$		0			0
$537$	2547.83	+	5439.24i	0.204743	+	0.437096i
$538$		0			0
$539$	−22561.3			−1.80294
$540$		0			0
$541$	2309.43			0.183531			0.0917654	−	0.995781i	$-0.470749\pi$
$541$	2309.43			0.183531			0.0917654	+	0.995781i	$0.470749\pi$
$542$		0			0
$543$	10625.1	−	15230.2i	0.839714	−	1.20367i
$544$		0			0
$545$	−2769.44	−	1007.99i	−0.217669	−	0.0792252i
$546$		0			0
$547$	2461.77	−	13961.4i	0.192427	−	1.09131i	−0.723608	−	0.690212i	$-0.757517\pi$
$547$	2461.77	−	13961.4i	0.192427	−	1.09131i	0.916035	−	0.401098i	$-0.131371\pi$
$548$		0			0
$549$	−5778.36	+	16048.6i	−0.449207	+	1.24761i
$550$		0			0
$551$	−7862.54	+	2861.73i	−0.607905	+	0.221259i
$552$		0			0
$553$	9217.36	−	7734.28i	0.708792	−	0.594747i
$554$		0			0
$555$	538.837	+	6038.48i	0.0412114	+	0.461836i
$556$		0			0
$557$	11430.0	+	19797.4i	0.869489	+	1.50600i	0.862519	+	0.506024i	$0.168885\pi$
$557$	11430.0	+	19797.4i	0.869489	+	1.50600i	0.00697005	+	0.999976i	$0.497781\pi$
$558$		0			0
$559$	−53.3776	+	92.4528i	−0.00403870	+	0.00699524i
$560$		0			0
$561$	9892.72	+	9858.52i	0.744511	+	0.741937i
$562$		0			0
$563$	1033.46	+	5861.04i	0.0773626	+	0.438745i	0.998745	+	0.0500875i	$0.0159500\pi$
$563$	1033.46	+	5861.04i	0.0773626	+	0.438745i	−0.921382	+	0.388658i	$0.872939\pi$
$564$		0			0
$565$	7689.79	+	6452.50i	0.572587	+	0.480458i
$566$		0			0
$567$	11910.9	−	20964.3i	0.882207	−	1.55277i
$568$		0			0
$569$	−8500.63	−	7132.88i	−0.626301	−	0.525529i	0.273476	−	0.961879i	$-0.411826\pi$
$569$	−8500.63	−	7132.88i	−0.626301	−	0.525529i	−0.899777	+	0.436350i	$0.856271\pi$
$570$		0			0
$571$	−1804.91	−	10236.2i	−0.132282	−	0.750211i	−0.976714	−	0.214547i	$-0.931173\pi$
$571$	−1804.91	−	10236.2i	−0.132282	−	0.750211i	0.844431	−	0.535664i	$-0.179939\pi$
$572$		0			0
$573$	−2958.71	−	2948.48i	−0.215710	−	0.214964i
$574$		0			0
$575$	−4854.85	+	8408.85i	−0.352106	+	0.609866i
$576$		0			0
$577$	−10062.0	−	17427.8i	−0.725971	−	1.25742i	−0.958573	−	0.284846i	$-0.908057\pi$
$577$	−10062.0	−	17427.8i	−0.725971	−	1.25742i	0.232602	−	0.972572i	$-0.425276\pi$
$578$		0			0
$579$	−412.563	−	4623.39i	−0.0296123	−	0.331851i
$580$		0			0
$581$	15010.3	−	12595.1i	1.07183	−	0.899368i
$582$		0			0
$583$	−5730.58	+	2085.76i	−0.407095	+	0.148170i
$584$		0			0
$585$	−1347.79	+	242.468i	−0.0952554	+	0.0171365i
$586$		0			0
$587$	2679.51	−	15196.3i	0.188408	−	1.06851i	−0.733091	−	0.680131i	$-0.761923\pi$
$587$	2679.51	−	15196.3i	0.188408	−	1.06851i	0.921498	−	0.388382i	$-0.126966\pi$
$588$		0			0
$589$	−1316.18	−	479.052i	−0.0920754	−	0.0335127i
$590$		0			0
$591$	6915.14	−	9912.32i	0.481304	−	0.689913i
$592$		0			0
$593$	8549.53			0.592052			0.296026	−	0.955180i	$-0.404338\pi$
$593$	8549.53			0.592052			0.296026	+	0.955180i	$0.404338\pi$
$594$		0			0
$595$	−15130.4			−1.04250
$596$		0			0
$597$	698.340	+	1490.85i	0.0478746	+	0.102205i
$598$		0			0
$599$	−15101.5	−	5496.51i	−1.03010	−	0.374927i	−0.228983	−	0.973430i	$-0.573540\pi$
$599$	−15101.5	−	5496.51i	−1.03010	−	0.374927i	−0.801120	+	0.598504i	$0.795762\pi$
$600$		0			0
$601$	−1363.83	+	7734.68i	−0.0925656	+	0.524966i	0.902901	+	0.429849i	$0.141433\pi$
$601$	−1363.83	+	7734.68i	−0.0925656	+	0.524966i	−0.995466	+	0.0951161i	$0.969678\pi$
$602$		0			0
$603$	−14203.8	+	8266.30i	−0.959244	+	0.558258i
$604$		0			0
$605$	2058.38	−	749.189i	0.138322	−	0.0503453i
$606$		0			0
$607$	1421.95	−	1193.16i	0.0950829	−	0.0797840i	−0.594007	−	0.804460i	$-0.702455\pi$
$607$	1421.95	−	1193.16i	0.0950829	−	0.0797840i	0.689090	+	0.724676i	$0.258010\pi$
$608$		0			0
$609$	19839.4	−	13943.0i	1.32009	−	0.927746i
$610$		0			0
$611$	1886.63	+	3267.74i	0.124918	+	0.216364i
$612$		0			0
$613$	−3861.72	+	6688.70i	−0.254443	+	0.440708i	−0.964744	−	0.263190i	$-0.915225\pi$
$613$	−3861.72	+	6688.70i	−0.254443	+	0.440708i	0.710301	+	0.703898i	$0.248559\pi$
$614$		0			0
$615$	11982.0	−	3232.81i	0.785627	−	0.211967i
$616$		0			0
$617$	3164.80	+	17948.4i	0.206499	+	1.17111i	0.895063	+	0.445939i	$0.147130\pi$
$617$	3164.80	+	17948.4i	0.206499	+	1.17111i	−0.688564	+	0.725175i	$0.741759\pi$
$618$		0			0
$619$	1605.52	+	1347.19i	0.104251	+	0.0874770i	0.693423	−	0.720530i	$-0.256102\pi$
$619$	1605.52	+	1347.19i	0.104251	+	0.0874770i	−0.589172	+	0.808007i	$0.700546\pi$
$620$		0			0
$621$	1129.70	−	13733.9i	0.0730003	−	0.887474i
$622$		0			0
$623$	18198.9	+	15270.7i	1.17034	+	0.982035i
$624$		0			0
$625$	1129.38	+	6405.05i	0.0722806	+	0.409923i
$626$		0			0
$627$	−2380.56	+	8946.32i	−0.151628	+	0.569827i
$628$		0			0
$629$	10206.6	−	17678.4i	0.647004	−	1.12064i
$630$		0			0
$631$	−9208.35	−	15949.3i	−0.580948	−	1.00623i	−0.995367	−	0.0961459i	$-0.969348\pi$
$631$	−9208.35	−	15949.3i	−0.580948	−	1.00623i	0.414419	−	0.910086i	$-0.363985\pi$
$632$		0			0
$633$	−19854.1	−	9216.30i	−1.24665	−	0.578697i
$634$		0			0
$635$	1927.04	−	1616.98i	0.120429	−	0.101052i
$636$		0			0
$637$	−6999.60	+	2547.65i	−0.435376	+	0.158464i
$638$		0			0
$639$	2617.27	+	7114.13i	0.162031	+	0.440423i
$640$		0			0
$641$	−4147.90	+	23523.9i	−0.255589	+	1.44951i	0.538969	+	0.842326i	$0.318814\pi$
$641$	−4147.90	+	23523.9i	−0.255589	+	1.44951i	−0.794557	+	0.607189i	$0.792297\pi$
$642$		0			0
$643$	−3014.06	−	1097.03i	−0.184857	−	0.0672824i	0.247933	−	0.968777i	$-0.420249\pi$
$643$	−3014.06	−	1097.03i	−0.184857	−	0.0672824i	−0.432790	+	0.901495i	$0.642471\pi$
$644$		0			0
$645$	284.912	+	24.4295i	0.0173928	+	0.00149133i
$646$		0			0
$647$	−8439.89			−0.512838			−0.256419	−	0.966566i	$-0.582543\pi$
$647$	−8439.89			−0.512838			−0.256419	+	0.966566i	$0.582543\pi$
$648$		0			0
$649$	24520.8			1.48309
$650$		0			0
$651$	4044.40	+	346.783i	0.243491	+	0.0208779i
$652$		0			0
$653$	26279.5	+	9564.97i	1.57488	+	0.573210i	0.974083	−	0.226191i	$-0.0726272\pi$
$653$	26279.5	+	9564.97i	1.57488	+	0.573210i	0.600798	+	0.799401i	$0.294849\pi$
$654$		0			0
$655$	−1932.66	+	10960.6i	−0.115290	+	0.653844i
$656$		0			0
$657$	21044.6	−	25257.2i	1.24966	−	1.49981i
$658$		0			0
$659$	−4419.19	+	1608.45i	−0.261225	+	0.0950781i	−0.469313	−	0.883032i	$-0.655498\pi$
$659$	−4419.19	+	1608.45i	−0.261225	+	0.0950781i	0.208088	+	0.978110i	$0.433276\pi$
$660$		0			0
$661$	−24298.4	+	20388.8i	−1.42980	+	1.19975i	−0.483973	+	0.875083i	$0.660807\pi$
$661$	−24298.4	+	20388.8i	−1.42980	+	1.19975i	−0.945829	+	0.324664i	$0.894749\pi$
$662$		0			0
$663$	4182.43	+	1941.49i	0.244995	+	0.113727i
$664$		0			0
$665$	−5014.64	−	8685.61i	−0.292420	−	0.506486i
$666$		0			0
$667$	6929.33	−	12002.0i	0.402256	−	0.696728i
$668$		0			0
$669$	−713.320	+	2680.71i	−0.0412236	+	0.154921i
$670$		0			0
$671$	3295.83	+	18691.6i	0.189619	+	1.07538i
$672$		0			0
$673$	1397.36	+	1172.52i	0.0800358	+	0.0671580i	0.681928	−	0.731419i	$-0.261142\pi$
$673$	1397.36	+	1172.52i	0.0800358	+	0.0671580i	−0.601892	+	0.798577i	$0.705586\pi$
$674$		0			0
$675$	−8013.75	−	11319.2i	−0.456962	−	0.645446i
$676$		0			0
$677$	7383.95	+	6195.87i	0.419185	+	0.351738i	0.827853	−	0.560945i	$-0.189562\pi$
$677$	7383.95	+	6195.87i	0.419185	+	0.351738i	−0.408668	+	0.912683i	$0.634007\pi$
$678$		0			0
$679$	−4745.28	−	26911.8i	−0.268199	−	1.52103i
$680$		0			0
$681$	28940.4	−	7808.29i	1.62849	−	0.439375i
$682$		0			0
$683$	3985.79	−	6903.58i	0.223297	−	0.386762i	−0.732510	−	0.680756i	$-0.761651\pi$
$683$	3985.79	−	6903.58i	0.223297	−	0.386762i	0.955807	+	0.293994i	$0.0949847\pi$
$684$		0			0
$685$	−3554.81	−	6157.11i	−0.198281	−	0.343432i
$686$		0			0
$687$	6339.69	−	4455.48i	0.352073	−	0.247434i
$688$		0			0
$689$	−1542.37	+	1294.20i	−0.0852826	+	0.0715606i
$690$		0			0
$691$	18824.4	−	6851.54i	1.03635	−	0.377199i	0.232853	−	0.972512i	$-0.425194\pi$
$691$	18824.4	−	6851.54i	1.03635	−	0.377199i	0.803494	+	0.595313i	$0.202972\pi$
$692$		0			0
$693$	−92.9184	−	26829.4i	−0.00509333	−	1.47066i
$694$		0			0
$695$	978.087	−	5547.01i	0.0533827	−	0.302748i
$696$		0			0
$697$	−39267.8	−	14292.3i	−2.13396	−	0.776699i
$698$		0			0
$699$	995.437	+	2125.11i	0.0538639	+	0.114991i
$700$		0			0
$701$	−14959.1			−0.805987			−0.402993	−	0.915203i	$-0.632030\pi$
$701$	−14959.1			−0.805987			−0.402993	+	0.915203i	$0.632030\pi$
$702$		0			0
$703$	13531.1			0.725938
$704$		0			0
$705$	5782.86	−	8289.30i	0.308929	−	0.442827i
$706$		0			0
$707$	−30764.4	−	11197.3i	−1.63651	−	0.595641i
$708$		0			0
$709$	−1068.39	+	6059.12i	−0.0565925	+	0.320952i	−0.999941	−	0.0108511i	$-0.996546\pi$
$709$	−1068.39	+	6059.12i	−0.0565925	+	0.320952i	0.943349	+	0.331803i	$0.107657\pi$
$710$		0			0
$711$	6339.72	+	7502.46i	0.334400	+	0.395730i
$712$		0			0
$713$	2180.02	−	793.463i	0.114506	−	0.0416766i
$714$		0			0
$715$	−1167.29	+	979.477i	−0.0610550	+	0.0512313i
$716$		0			0
$717$	1430.39	+	16029.7i	0.0745036	+	0.834925i
$718$		0			0
$719$	10762.6	+	18641.4i	0.558244	+	0.966908i	0.997643	+	0.0686155i	$0.0218582\pi$
$719$	10762.6	+	18641.4i	0.558244	+	0.966908i	−0.439399	+	0.898292i	$0.644809\pi$
$720$		0			0
$721$	11368.4	−	19690.7i	0.587214	−	1.01708i
$722$		0			0
$723$	2055.69	+	2048.58i	0.105743	+	0.105377i
$724$		0			0
$725$	−2422.00	−	13735.9i	−0.124070	−	0.703637i
$726$		0			0
$727$	9630.04	+	8080.56i	0.491277	+	0.412230i	0.854484	−	0.519478i	$-0.173874\pi$
$727$	9630.04	+	8080.56i	0.491277	+	0.412230i	−0.363207	+	0.931709i	$0.618318\pi$
$728$		0			0
$729$	17147.3	+	9663.87i	0.871173	+	0.490975i
$730$		0			0
$731$	−737.594	−	618.915i	−0.0373200	−	0.0313152i
$732$		0			0
$733$	−644.806	−	3656.88i	−0.0324918	−	0.184270i	0.964242	−	0.265022i	$-0.0853791\pi$
$733$	−644.806	−	3656.88i	−0.0324918	−	0.184270i	−0.996734	+	0.0807515i	$0.974268\pi$
$734$		0			0
$735$	14133.0	+	14084.1i	0.709257	+	0.706805i
$736$		0			0
$737$	−9143.30	+	15836.7i	−0.456985	+	0.791521i
$738$		0			0
$739$	−2061.21	−	3570.13i	−0.102602	−	0.177712i	0.810154	−	0.586217i	$-0.199384\pi$
$739$	−2061.21	−	3570.13i	−0.102602	−	0.177712i	−0.912756	+	0.408505i	$0.866050\pi$
$740$		0			0
$741$	271.662	+	3044.39i	0.0134680	+	0.150929i
$742$		0			0
$743$	7603.08	−	6379.74i	0.375411	−	0.315007i	−0.435487	−	0.900195i	$-0.643424\pi$
$743$	7603.08	−	6379.74i	0.375411	−	0.315007i	0.810898	+	0.585188i	$0.198979\pi$
$744$		0			0
$745$	−9404.72	+	3423.04i	−0.462500	+	0.168336i
$746$		0			0
$747$	10324.1	+	12217.6i	0.505674	+	0.598418i
$748$		0			0
$749$	−7459.27	+	42303.6i	−0.363893	+	2.06374i
$750$		0			0
$751$	−10461.9	−	3807.83i	−0.508337	−	0.185020i	0.0751030	−	0.997176i	$-0.476071\pi$
$751$	−10461.9	−	3807.83i	−0.508337	−	0.185020i	−0.583440	+	0.812156i	$0.698294\pi$
$752$		0			0
$753$	−1874.12	+	2686.41i	−0.0906997	+	0.130011i
$754$		0			0
$755$	−3359.93			−0.161961
$756$		0			0
$757$	−32325.4			−1.55203			−0.776015	−	0.630715i	$-0.782762\pi$
$757$	−32325.4			−1.55203			−0.776015	+	0.630715i	$0.782762\pi$
$758$		0			0
$759$	−6504.31	−	13885.7i	−0.311056	−	0.664057i
$760$		0			0
$761$	13060.1	+	4753.49i	0.622114	+	0.226431i	0.633795	−	0.773501i	$-0.281496\pi$
$761$	13060.1	+	4753.49i	0.622114	+	0.226431i	−0.0116814	+	0.999932i	$0.503718\pi$
$762$		0			0
$763$	3310.35	−	18773.9i	0.157068	−	0.890775i
$764$		0			0
$765$	−42.7761	−	12351.3i	−0.00202167	−	0.583740i
$766$		0			0
$767$	7607.52	−	2768.91i	0.358138	−	0.130351i
$768$		0			0
$769$	−7019.28	+	5889.88i	−0.329157	+	0.276196i	−0.792356	−	0.610059i	$-0.791146\pi$
$769$	−7019.28	+	5889.88i	−0.329157	+	0.276196i	0.463199	+	0.886254i	$0.346701\pi$
$770$		0			0
$771$	−9496.45	+	6674.02i	−0.443588	+	0.311750i
$772$		0			0
$773$	−1545.03	−	2676.06i	−0.0718897	−	0.124517i	0.827840	−	0.560965i	$-0.189570\pi$
$773$	−1545.03	−	2676.06i	−0.0718897	−	0.124517i	−0.899729	+	0.436448i	$0.856236\pi$
$774$		0			0
$775$	1167.42	−	2022.03i	0.0541097	−	0.0937207i
$776$		0			0
$777$	−37860.7	+	10215.0i	−1.74806	+	0.471638i
$778$		0			0
$779$	−4809.95	−	27278.6i	−0.221225	−	1.25463i
$780$		0			0
$781$	6461.41	+	5421.76i	0.296040	+	0.248407i
$782$		0			0
$783$	11438.0	+	16155.9i	0.522046	+	0.737376i
$784$		0			0
$785$	5199.06	+	4362.53i	0.236385	+	0.198351i
$786$		0			0
$787$	3688.64	+	20919.3i	0.167072	+	0.947512i	0.946902	+	0.321521i	$0.104194\pi$
$787$	3688.64	+	20919.3i	0.167072	+	0.947512i	−0.779830	+	0.625991i	$0.784695\pi$
$788$		0			0
$789$	887.739	−	3336.19i	0.0400562	−	0.150534i
$790$		0			0
$791$	−32465.9	+	56232.6i	−1.45936	+	2.52769i
$792$		0			0
$793$	3133.20	+	5426.86i	0.140307	+	0.243018i
$794$		0			0
$795$	4891.84	+	2270.80i	0.218234	+	0.101304i
$796$		0			0
$797$	−16702.1	+	14014.7i	−0.742307	+	0.622870i	−0.933456	−	0.358691i	$-0.883223\pi$
$797$	−16702.1	+	14014.7i	−0.742307	+	0.622870i	0.191149	+	0.981561i	$0.438779\pi$
$798$		0			0
$799$	−31979.8	+	11639.7i	−1.41598	+	0.515373i
$800$		0			0
$801$	−12414.4	+	14899.3i	−0.547615	+	0.657232i
$802$		0			0
$803$	6352.29	−	36025.6i	0.279162	−	1.58321i
$804$		0			0
$805$	15609.9	+	5681.54i	0.683449	+	0.248755i
$806$		0			0
$807$	−35994.9	−	3086.35i	−1.57011	−	0.134628i
$808$		0			0
$809$	17728.5			0.770460			0.385230	−	0.922821i	$-0.374122\pi$
$809$	17728.5			0.770460			0.385230	+	0.922821i	$0.374122\pi$
$810$		0			0
$811$	3211.20			0.139039			0.0695194	−	0.997581i	$-0.477853\pi$
$811$	3211.20			0.139039			0.0695194	+	0.997581i	$0.477853\pi$
$812$		0			0
$813$	−45473.5	−	3899.08i	−1.96165	−	0.168200i
$814$		0			0
$815$	−12310.8	−	4480.76i	−0.529114	−	0.192582i
$816$		0			0
$817$	110.829	−	628.543i	0.00474592	−	0.0269155i
$818$		0			0
$819$	−3058.43	−	8313.28i	−0.130489	−	0.354688i
$820$		0			0
$821$	11961.2	−	4353.53i	0.508465	−	0.185066i	−0.0750324	−	0.997181i	$-0.523906\pi$
$821$	11961.2	−	4353.53i	0.508465	−	0.185066i	0.583497	+	0.812115i	$0.301684\pi$
$822$		0			0
$823$	−31351.4	+	26306.9i	−1.32787	+	1.11422i	−0.343304	+	0.939224i	$0.611546\pi$
$823$	−31351.4	+	26306.9i	−1.32787	+	1.11422i	−0.984570	+	0.174994i	$0.944009\pi$
$824$		0			0
$825$	−13997.6	−	6497.68i	−0.590706	−	0.274206i
$826$		0			0
$827$	14546.9	+	25195.9i	0.611662	+	1.05943i	0.990960	+	0.134155i	$0.0428321\pi$
$827$	14546.9	+	25195.9i	0.611662	+	1.05943i	−0.379298	+	0.925274i	$0.623835\pi$
$828$		0			0
$829$	−4034.95	+	6988.75i	−0.169047	+	0.292798i	−0.938085	−	0.346405i	$-0.887402\pi$
$829$	−4034.95	+	6988.75i	−0.169047	+	0.292798i	0.769038	+	0.639203i	$0.220736\pi$
$830$		0			0
$831$	9436.87	−	35464.4i	0.393937	−	1.48044i
$832$		0			0
$833$	−11666.3	−	66162.7i	−0.485249	−	2.75198i
$834$		0			0
$835$	13992.0	+	11740.7i	0.579896	+	0.486591i
$836$		0			0
$837$	−271.653	+	3302.51i	−0.0112183	+	0.136382i
$838$		0			0
$839$	32834.5	+	27551.4i	1.35110	+	1.13371i	0.978623	+	0.205664i	$0.0659353\pi$
$839$	32834.5	+	27551.4i	1.35110	+	1.13371i	0.372475	+	0.928042i	$0.378509\pi$
$840$		0			0
$841$	−778.180	−	4413.28i	−0.0319070	−	0.180954i
$842$		0			0
$843$	−33188.9	+	8954.55i	−1.35597	+	0.365850i
$844$		0			0
$845$	5365.43	−	9293.20i	0.218434	−	0.378338i
$846$		0			0
$847$	7084.46	+	12270.7i	0.287397	+	0.497786i
$848$		0			0
$849$	22679.7	−	15939.1i	0.916802	−	0.644320i
$850$		0			0
$851$	−17168.4	+	14406.0i	−0.691570	+	0.580296i
$852$		0			0
$853$	25788.2	−	9386.15i	1.03514	−	0.376759i	0.232103	−	0.972691i	$-0.425439\pi$
$853$	25788.2	−	9386.15i	1.03514	−	0.376759i	0.803035	+	0.595932i	$0.203217\pi$
$854$		0			0
$855$	7076.07	−	4118.11i	0.283037	−	0.164721i
$856$		0			0
$857$	3298.00	−	18703.9i	0.131456	−	0.745522i	−0.845807	−	0.533489i	$-0.820881\pi$
$857$	3298.00	−	18703.9i	0.131456	−	0.745522i	0.977263	−	0.212033i	$-0.0680083\pi$
$858$		0			0
$859$	12590.2	+	4582.47i	0.500085	+	0.182016i	0.579732	−	0.814807i	$-0.303157\pi$
$859$	12590.2	+	4582.47i	0.500085	+	0.182016i	−0.0796470	+	0.996823i	$0.525379\pi$
$860$		0			0
$861$	34051.9	+	72695.7i	1.34784	+	2.87743i
$862$		0			0
$863$	−3158.44			−0.124582			−0.0622912	−	0.998058i	$-0.519841\pi$
$863$	−3158.44			−0.124582			−0.0622912	+	0.998058i	$0.519841\pi$
$864$		0			0
$865$	11645.3			0.457747
$866$		0			0
$867$	−9188.93	+	13171.6i	−0.359945	+	0.515954i
$868$		0			0
$869$	10270.4	+	3738.13i	0.400921	+	0.145923i
$870$		0			0
$871$	−1048.40	+	5945.76i	−0.0407849	+	0.231302i
$872$		0			0
$873$	21955.3	−	3949.76i	0.851173	−	0.153126i
$874$		0			0
$875$	35575.7	−	12948.5i	1.37449	−	0.500273i
$876$		0			0
$877$	5090.44	−	4271.38i	0.196000	−	0.164463i	−0.539506	−	0.841982i	$-0.681389\pi$
$877$	5090.44	−	4271.38i	0.196000	−	0.164463i	0.735506	+	0.677518i	$0.236945\pi$
$878$		0			0
$879$	−134.391	−	1506.06i	−0.00515690	−	0.0577908i
$880$		0			0
$881$	−20849.2	−	36111.8i	−0.797305	−	1.38097i	−0.921365	−	0.388698i	$-0.872925\pi$
$881$	−20849.2	−	36111.8i	−0.797305	−	1.38097i	0.124060	−	0.992275i	$-0.460408\pi$
$882$		0			0
$883$	8379.42	−	14513.6i	0.319354	−	0.553138i	−0.660999	−	0.750387i	$-0.729867\pi$
$883$	8379.42	−	14513.6i	0.319354	−	0.553138i	0.980353	+	0.197249i	$0.0632006\pi$
$884$		0			0
$885$	−15360.5	−	15307.4i	−0.583431	−	0.581414i
$886$		0			0
$887$	−4201.60	−	23828.5i	−0.159049	−	0.902009i	−0.954991	−	0.296636i	$-0.904135\pi$
$887$	−4201.60	−	23828.5i	−0.159049	−	0.902009i	0.795942	−	0.605373i	$-0.206976\pi$
$888$		0			0
$889$	12464.9	+	10459.3i	0.470257	+	0.394593i
$890$		0			0
$891$	21901.2	−	151.703i	0.823476	−	0.00570396i
$892$		0			0
$893$	−17280.8	−	14500.3i	−0.647570	−	0.543376i
$894$		0			0
$895$	−1026.37	−	5820.84i	−0.0383328	−	0.217396i
$896$		0			0
$897$	−3585.94	−	3573.54i	−0.133479	−	0.133018i
$898$		0			0
$899$	−1666.26	+	2886.05i	−0.0618164	+	0.107069i
$900$		0			0
$901$	−9079.87	−	15726.8i	−0.335732	−	0.581504i
$902$		0			0
$903$	164.401	+	1842.36i	0.00605862	+	0.0678960i
$904$		0			0
$905$	−13998.8	+	11746.4i	−0.514183	+	0.431451i
$906$		0			0
$907$	17284.4	−	6291.01i	0.632766	−	0.230308i	−0.00566855	−	0.999984i	$-0.501804\pi$
$907$	17284.4	−	6291.01i	0.632766	−	0.230308i	0.638435	+	0.769676i	$0.279582\pi$
$908$		0			0
$909$	9053.63	−	25145.3i	0.330352	−	0.917509i
$910$		0			0
$911$	397.004	−	2251.52i	0.0144383	−	0.0818839i	−0.976737	−	0.214440i	$-0.931207\pi$
$911$	397.004	−	2251.52i	0.0144383	−	0.0818839i	0.991176	+	0.132556i	$0.0423185\pi$
$912$		0			0
$913$	16725.2	+	6087.47i	0.606268	+	0.220664i
$914$		0			0
$915$	9603.82	−	13766.4i	0.346986	−	0.497379i
$916$		0			0
$917$	−71991.5			−2.59255
$918$		0			0
$919$	4568.58			0.163986			0.0819932	−	0.996633i	$-0.473871\pi$
$919$	4568.58			0.163986			0.0819932	+	0.996633i	$0.473871\pi$
$920$		0			0
$921$	2524.90	+	5390.29i	0.0903349	+	0.192851i
$922$		0			0
$923$	2616.87	+	952.462i	0.0933209	+	0.0339660i
$924$		0			0
$925$	−3916.78	+	22213.2i	−0.139225	+	0.789584i
$926$		0			0
$927$	16106.0	+	9224.60i	0.570649	+	0.326835i
$928$		0			0
$929$	27954.9	−	10174.8i	0.987268	−	0.359336i	0.202606	−	0.979260i	$-0.435059\pi$
$929$	27954.9	−	10174.8i	0.987268	−	0.359336i	0.784662	+	0.619924i	$0.212837\pi$
$930$		0			0
$931$	34114.2	−	28625.2i	1.20091	−	1.00768i
$932$		0			0
$933$	−39932.3	+	28064.1i	−1.40121	+	0.984756i
$934$		0			0
$935$	−6871.80	−	11902.3i	−0.240355	−	0.416307i
$936$		0			0
$937$	19606.1	−	33958.8i	0.683568	−	1.18397i	−0.290317	−	0.956931i	$-0.593761\pi$
$937$	19606.1	−	33958.8i	0.683568	−	1.18397i	0.973885	−	0.227044i	$-0.0729060\pi$
$938$		0			0
$939$	−15549.5	+	4195.36i	−0.540404	+	0.145804i
$940$		0			0
$941$	−3310.43	−	18774.4i	−0.114683	−	0.650400i	−0.986907	−	0.161293i	$-0.948434\pi$
$941$	−3310.43	−	18774.4i	−0.114683	−	0.650400i	0.872223	−	0.489108i	$-0.162677\pi$
$942$		0			0
$943$	35145.4	+	29490.5i	1.21367	+	1.01839i
$944$		0			0
$945$	−16690.3	+	16864.7i	−0.574536	+	0.580537i
$946$		0			0
$947$	−4780.70	−	4011.49i	−0.164046	−	0.137651i	0.557069	−	0.830466i	$-0.311926\pi$
$947$	−4780.70	−	4011.49i	−0.164046	−	0.137651i	−0.721115	+	0.692815i	$0.756370\pi$
$948$		0			0
$949$	−2097.26	−	11894.2i	−0.0717387	−	0.406850i
$950$		0			0
$951$	894.224	−	3360.56i	0.0304913	−	0.114588i
$952$		0			0
$953$	−2401.20	+	4159.01i	−0.0816187	+	0.141368i	−0.903945	−	0.427648i	$-0.859342\pi$
$953$	−2401.20	+	4159.01i	−0.0816187	+	0.141368i	0.822327	+	0.569016i	$0.192676\pi$
$954$		0			0
$955$	2055.22	+	3559.74i	0.0696390	+	0.120618i
$956$		0			0
$957$	19978.7	+	9274.15i	0.674839	+	0.313261i
$958$		0			0
$959$	35228.8	−	29560.5i	1.18623	−	0.995367i
$960$		0			0
$961$	27470.2	−	9998.32i	0.922096	−	0.335616i
$962$		0			0
$963$	−34554.4	−	5969.56i	−1.15628	−	0.199758i
$964$		0			0
$965$	−793.184	+	4498.37i	−0.0264596	+	0.150060i
$966$		0			0
$967$	−41151.1	−	14977.8i	−1.36849	−	0.498089i	−0.449820	−	0.893119i	$-0.648512\pi$
$967$	−41151.1	−	14977.8i	−1.36849	−	0.498089i	−0.918668	+	0.395030i	$0.870734\pi$
$968$		0			0
$969$	−27466.7	−	2355.10i	−0.910584	−	0.0780772i
$970$		0			0
$971$	54379.6			1.79725			0.898623	−	0.438723i	$-0.144569\pi$
$971$	54379.6			1.79725			0.898623	+	0.438723i	$0.144569\pi$
$972$		0			0
$973$	36433.8			1.20043
$974$		0			0
$975$	−5076.43	−	435.274i	−0.166745	−	0.0142974i
$976$		0			0
$977$	11761.8	+	4280.96i	0.385153	+	0.140184i	0.527337	−	0.849656i	$-0.323190\pi$
$977$	11761.8	+	4280.96i	0.385153	+	0.140184i	−0.142184	+	0.989840i	$0.545413\pi$
$978$		0			0
$979$	−3747.25	+	21251.7i	−0.122332	+	0.693777i
$980$		0			0
$981$	15334.9	+	2649.23i	0.499089	+	0.0862217i
$982$		0			0
$983$	−4043.60	+	1471.75i	−0.131201	+	0.0477534i	−0.406786	−	0.913523i	$-0.633351\pi$
$983$	−4043.60	+	1471.75i	−0.131201	+	0.0477534i	0.275585	+	0.961277i	$0.411128\pi$
$984$		0			0
$985$	−9110.88	+	7644.93i	−0.294717	+	0.247297i
$986$		0			0
$987$	59299.4	+	27526.8i	1.91238	+	0.887730i
$988$		0			0
$989$	528.564	+	915.500i	0.0169943	+	0.0294350i
$990$		0			0
$991$	4071.74	−	7052.46i	0.130518	−	0.226063i	−0.793359	−	0.608755i	$-0.791669\pi$
$991$	4071.74	−	7052.46i	0.130518	−	0.226063i	0.923876	+	0.382691i	$0.125003\pi$
$992$		0			0
$993$	388.033	−	1458.25i	0.0124006	−	0.0466025i
$994$		0			0
$995$	−281.320	−	1595.45i	−0.00896326	−	0.0508332i
$996$		0			0
$997$	−1755.63	−	1473.15i	−0.0557687	−	0.0467955i	0.614477	−	0.788935i	$-0.289367\pi$
$997$	−1755.63	−	1473.15i	−0.0557687	−	0.0467955i	−0.670246	+	0.742139i	$0.733811\pi$
$998$		0			0
$999$	−8445.80	−	30877.6i	−0.267481	−	0.977902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.i.a.97.9	yes	54
3.2	odd	2		324.4.i.a.289.6		54
27.5	odd	18		324.4.i.a.37.6		54
27.22	even	9	inner	108.4.i.a.49.9	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.49.9	✓	54	27.22	even	9	inner
108.4.i.a.97.9	yes	54	1.1	even	1	trivial
324.4.i.a.37.6		54	27.5	odd	18
324.4.i.a.289.6		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)

\(f(q)\)	\(=\)	\(q+(5.17716 + 0.443910i) q^{3} +(-4.80495 - 1.74886i) q^{5} +(5.74341 - 32.5725i) q^{7} +(26.6059 + 4.59638i) q^{9} +O(q^{10})\)	\(q+(5.17716 + 0.443910i) q^{3} +(-4.80495 - 1.74886i) q^{5} +(5.74341 - 32.5725i) q^{7} +(26.6059 + 4.59638i) q^{9} +(28.2317 - 10.2755i) q^{11} +(7.59849 - 6.37589i) q^{13} +(-24.0996 - 11.1871i) q^{15} +(44.7319 + 77.4779i) q^{17} +(-29.6509 + 51.3568i) q^{19} +(44.1938 - 166.083i) q^{21} +(-17.0562 - 96.7304i) q^{23} +(-75.7266 - 63.5421i) q^{25} +(135.702 + 35.6068i) q^{27} +(108.085 + 90.6938i) q^{29} +(4.10141 + 23.2603i) q^{31} +(150.721 - 40.6655i) q^{33} +(-84.5615 + 146.465i) q^{35} +(-114.087 - 197.604i) q^{37} +(42.1689 - 29.6359i) q^{39} +(-357.814 + 300.241i) q^{41} +(-10.1135 + 3.68102i) q^{43} +(-119.801 - 68.6153i) q^{45} +(-66.0561 + 374.623i) q^{47} +(-705.667 - 256.842i) q^{49} +(197.191 + 420.972i) q^{51} -202.984 q^{53} -153.622 q^{55} +(-176.305 + 252.720i) q^{57} +(766.955 + 279.149i) q^{59} +(-109.702 + 622.151i) q^{61} +(302.524 - 840.222i) q^{63} +(-47.6609 + 17.3471i) q^{65} +(-466.269 + 391.246i) q^{67} +(-45.3629 - 508.360i) q^{69} +(140.376 + 243.138i) q^{71} +(608.806 - 1054.48i) q^{73} +(-363.841 - 362.583i) q^{75} +(-172.552 - 978.592i) q^{77} +(278.680 + 233.841i) q^{79} +(686.746 + 244.582i) q^{81} +(453.825 + 380.804i) q^{83} +(-79.4366 - 450.507i) q^{85} +(519.311 + 517.516i) q^{87} +(-359.138 + 622.046i) q^{89} +(-164.037 - 284.121i) q^{91} +(10.9082 + 122.243i) q^{93} +(232.286 - 194.911i) q^{95} +(776.386 - 282.581i) q^{97} +(798.358 - 143.625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 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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