LMFDB - Embedded newform 117.4.g.d.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(55,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("117.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.g (of order $3$, degree $2$, 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:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	117.100
Dual form			117.4.g.d.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28078 + 3.95042i) q^{2} +(-6.40388 - 11.0918i) q^{4} -2.80776 q^{5} +(-4.78078 - 8.28055i) q^{7} +21.9309 q^{8} +O(q^{10})$	\(q+(-2.28078 + 3.95042i) q^{2} +(-6.40388 - 11.0918i) q^{4} -2.80776 q^{5} +(-4.78078 - 8.28055i) q^{7} +21.9309 q^{8} +(6.40388 - 11.0918i) q^{10} +(19.7116 - 34.1416i) q^{11} +(40.5270 - 23.5492i) q^{13} +43.6155 q^{14} +(1.21165 - 2.09863i) q^{16} +(1.00758 + 1.74518i) q^{17} +(30.0961 + 52.1280i) q^{19} +(17.9806 + 31.1433i) q^{20} +(89.9157 + 155.739i) q^{22} +(2.23438 - 3.87006i) q^{23} -117.116 q^{25} +(0.596118 + 213.809i) q^{26} +(-61.2311 + 106.055i) q^{28} +(70.3466 - 121.844i) q^{29} +136.155 q^{31} +(93.2505 + 161.515i) q^{32} -9.19224 q^{34} +(13.4233 + 23.2498i) q^{35} +(92.8542 - 160.828i) q^{37} -274.570 q^{38} -61.5767 q^{40} +(155.116 - 268.668i) q^{41} +(-213.735 - 370.200i) q^{43} -504.924 q^{44} +(10.1922 + 17.6535i) q^{46} +258.617 q^{47} +(125.788 - 217.872i) q^{49} +(267.116 - 462.659i) q^{50} +(-520.734 - 298.713i) q^{52} -612.656 q^{53} +(-55.3457 + 95.8615i) q^{55} +(-104.847 - 181.600i) q^{56} +(320.890 + 555.797i) q^{58} +(-258.943 - 448.502i) q^{59} +(80.6553 + 139.699i) q^{61} +(-310.540 + 537.871i) q^{62} -831.348 q^{64} +(-113.790 + 66.1205i) q^{65} +(24.9493 - 43.2135i) q^{67} +(12.9048 - 22.3518i) q^{68} -122.462 q^{70} +(139.982 + 242.455i) q^{71} +467.732 q^{73} +(423.559 + 733.626i) q^{74} +(385.464 - 667.643i) q^{76} -376.948 q^{77} +37.5379 q^{79} +(-3.40202 + 5.89247i) q^{80} +(707.568 + 1225.54i) q^{82} +76.1553 q^{83} +(-2.82904 - 4.90004i) q^{85} +1949.93 q^{86} +(432.294 - 748.754i) q^{88} +(101.403 - 175.635i) q^{89} +(-388.750 - 223.002i) q^{91} -57.2348 q^{92} +(-589.848 + 1021.65i) q^{94} +(-84.5028 - 146.363i) q^{95} +(587.184 + 1017.03i) q^{97} +(573.790 + 993.834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 5 q^{4} + 30 q^{5} - 15 q^{7} + 30 q^{8}+O(q^{10}) $ 4 * q - 5 * q^2 - 5 * q^4 + 30 * q^5 - 15 * q^7 + 30 * q^8	$ 4 q - 5 q^{2} - 5 q^{4} + 30 q^{5} - 15 q^{7} + 30 q^{8} + 5 q^{10} + 17 q^{11} + 125 q^{13} + 92 q^{14} - 57 q^{16} + 70 q^{17} + 141 q^{19} + 175 q^{20} + 170 q^{22} + 145 q^{23} + 150 q^{25} + 23 q^{26} - 80 q^{28} + 34 q^{29} - 280 q^{31} + 105 q^{32} - 78 q^{34} - 70 q^{35} + 190 q^{37} - 620 q^{38} - 370 q^{40} + 538 q^{41} - 455 q^{43} - 1360 q^{44} + 82 q^{46} - 120 q^{47} + 565 q^{49} + 450 q^{50} - 310 q^{52} - 1090 q^{53} - 510 q^{55} - 172 q^{56} + 595 q^{58} - 809 q^{59} - 502 q^{61} - 500 q^{62} - 2542 q^{64} + 555 q^{65} + 475 q^{67} - 505 q^{68} - 160 q^{70} + 127 q^{71} + 1170 q^{73} + 849 q^{74} + 140 q^{76} - 510 q^{77} + 480 q^{79} - 1065 q^{80} + 1515 q^{82} - 520 q^{83} + 1205 q^{85} + 3924 q^{86} + 1020 q^{88} + 921 q^{89} - 1287 q^{91} + 2080 q^{92} - 1040 q^{94} + 1270 q^{95} + 415 q^{97} + 1285 q^{98}+O(q^{100}) $ 4 * q - 5 * q^2 - 5 * q^4 + 30 * q^5 - 15 * q^7 + 30 * q^8 + 5 * q^10 + 17 * q^11 + 125 * q^13 + 92 * q^14 - 57 * q^16 + 70 * q^17 + 141 * q^19 + 175 * q^20 + 170 * q^22 + 145 * q^23 + 150 * q^25 + 23 * q^26 - 80 * q^28 + 34 * q^29 - 280 * q^31 + 105 * q^32 - 78 * q^34 - 70 * q^35 + 190 * q^37 - 620 * q^38 - 370 * q^40 + 538 * q^41 - 455 * q^43 - 1360 * q^44 + 82 * q^46 - 120 * q^47 + 565 * q^49 + 450 * q^50 - 310 * q^52 - 1090 * q^53 - 510 * q^55 - 172 * q^56 + 595 * q^58 - 809 * q^59 - 502 * q^61 - 500 * q^62 - 2542 * q^64 + 555 * q^65 + 475 * q^67 - 505 * q^68 - 160 * q^70 + 127 * q^71 + 1170 * q^73 + 849 * q^74 + 140 * q^76 - 510 * q^77 + 480 * q^79 - 1065 * q^80 + 1515 * q^82 - 520 * q^83 + 1205 * q^85 + 3924 * q^86 + 1020 * q^88 + 921 * q^89 - 1287 * q^91 + 2080 * q^92 - 1040 * q^94 + 1270 * q^95 + 415 * q^97 + 1285 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−2.28078	+	3.95042i	−0.806376	+	1.39668i	0.108982	+	0.994044i	$0.465241\pi$
$2$	−2.28078	+	3.95042i	−0.806376	+	1.39668i	−0.915358	+	0.402641i	$0.868092\pi$
$3$		0			0
$3$		0			0
$4$	−6.40388	−	11.0918i	−0.800485	−	1.38648i
$5$	−2.80776			−0.251134			−0.125567	−	0.992085i	$-0.540075\pi$
$5$	−2.80776			−0.251134			−0.125567	+	0.992085i	$0.540075\pi$
$6$		0			0
$7$	−4.78078	−	8.28055i	−0.258138	−	0.447108i	0.707605	−	0.706608i	$-0.249775\pi$
$7$	−4.78078	−	8.28055i	−0.258138	−	0.447108i	−0.965743	+	0.259500i	$0.916442\pi$
$8$	21.9309			0.969217
$9$		0			0
$10$	6.40388	−	11.0918i	0.202509	−	0.350755i
$11$	19.7116	−	34.1416i	0.540299	−	0.935825i	−0.458588	−	0.888649i	$-0.651645\pi$
$11$	19.7116	−	34.1416i	0.540299	−	0.935825i	0.998887	−	0.0471757i	$-0.0150221\pi$
$12$		0			0
$13$	40.5270	−	23.5492i	0.864628	−	0.502413i
$13$	40.5270	−	23.5492i	0.864628	−	0.502413i
$14$	43.6155			0.832624
$15$		0			0
$16$	1.21165	−	2.09863i	0.0189320	−	0.0327911i
$17$	1.00758	+	1.74518i	0.0143749	+	0.0248981i	0.873123	−	0.487499i	$-0.162091\pi$
$17$	1.00758	+	1.74518i	0.0143749	+	0.0248981i	−0.858748	+	0.512397i	$0.828758\pi$
$18$		0			0
$19$	30.0961	+	52.1280i	0.363396	+	0.629420i	0.988517	−	0.151107i	$-0.0482839\pi$
$19$	30.0961	+	52.1280i	0.363396	+	0.629420i	−0.625121	+	0.780528i	$0.714951\pi$
$20$	17.9806	+	31.1433i	0.201029	+	0.348193i
$21$		0			0
$22$	89.9157	+	155.739i	0.871368	+	1.50925i
$23$	2.23438	−	3.87006i	0.0202565	−	0.0350853i	−0.855719	−	0.517440i	$-0.826885\pi$
$23$	2.23438	−	3.87006i	0.0202565	−	0.0350853i	0.875976	+	0.482355i	$0.160218\pi$
$24$		0			0
$25$	−117.116			−0.936932
$26$	0.596118	+	213.809i	0.00449648	+	1.61275i
$27$		0			0
$28$	−61.2311	+	106.055i	−0.413271	+	0.715806i
$29$	70.3466	−	121.844i	0.450449	−	0.780201i	−0.547964	−	0.836502i	$-0.684597\pi$
$29$	70.3466	−	121.844i	0.450449	−	0.780201i	0.998414	+	0.0563003i	$0.0179304\pi$
$30$		0			0
$31$	136.155			0.788845			0.394423	−	0.918929i	$-0.370945\pi$
$31$	136.155			0.788845			0.394423	+	0.918929i	$0.370945\pi$
$32$	93.2505	+	161.515i	0.515141	+	0.892250i
$33$		0			0
$34$	−9.19224			−0.0463663
$35$	13.4233	+	23.2498i	0.0648272	+	0.112284i
$36$		0			0
$37$	92.8542	−	160.828i	0.412571	−	0.714594i	−0.582599	−	0.812760i	$-0.697964\pi$
$37$	92.8542	−	160.828i	0.412571	−	0.714594i	0.995170	+	0.0981657i	$0.0312975\pi$
$38$	−274.570			−1.17214
$39$		0			0
$40$	−61.5767			−0.243403
$41$	155.116	−	268.668i	0.590853	−	1.02339i	−0.403265	−	0.915083i	$-0.632125\pi$
$41$	155.116	−	268.668i	0.590853	−	1.02339i	0.994118	−	0.108304i	$-0.0345420\pi$
$42$		0			0
$43$	−213.735	−	370.200i	−0.758008	−	1.31291i	−0.943865	−	0.330331i	$-0.892840\pi$
$43$	−213.735	−	370.200i	−0.758008	−	1.31291i	0.185857	−	0.982577i	$-0.440494\pi$
$44$	−504.924			−1.73000
$45$		0			0
$46$	10.1922	+	17.6535i	0.0326688	+	0.0565840i
$47$	258.617			0.802622			0.401311	−	0.915942i	$-0.368555\pi$
$47$	258.617			0.802622			0.401311	+	0.915942i	$0.368555\pi$
$48$		0			0
$49$	125.788	−	217.872i	0.366730	−	0.635195i
$50$	267.116	−	462.659i	0.755519	−	1.30860i
$51$		0			0
$52$	−520.734	−	298.713i	−1.38871	−	0.796617i
$53$	−612.656			−1.58783			−0.793913	−	0.608031i	$-0.791960\pi$
$53$	−612.656			−1.58783			−0.793913	+	0.608031i	$0.791960\pi$
$54$		0			0
$55$	−55.3457	+	95.8615i	−0.135687	+	0.235017i
$56$	−104.847	−	181.600i	−0.250191	−	0.433344i
$57$		0			0
$58$	320.890	+	555.797i	0.726463	+	1.25827i
$59$	−258.943	−	448.502i	−0.571381	−	0.989661i	−0.996425	−	0.0844878i	$-0.973075\pi$
$59$	−258.943	−	448.502i	−0.571381	−	0.989661i	0.425044	−	0.905173i	$-0.360259\pi$
$60$		0			0
$61$	80.6553	+	139.699i	0.169293	+	0.293223i	0.938171	−	0.346171i	$-0.112518\pi$
$61$	80.6553	+	139.699i	0.169293	+	0.293223i	−0.768879	+	0.639395i	$0.779185\pi$
$62$	−310.540	+	537.871i	−0.636106	+	1.10177i
$63$		0			0
$64$	−831.348			−1.62373
$65$	−113.790	+	66.1205i	−0.217138	+	0.126173i
$66$		0			0
$67$	24.9493	−	43.2135i	0.0454933	−	0.0787966i	−0.842382	−	0.538881i	$-0.818847\pi$
$67$	24.9493	−	43.2135i	0.0454933	−	0.0787966i	0.887875	+	0.460084i	$0.152181\pi$
$68$	12.9048	−	22.3518i	0.0230138	−	0.0398611i
$69$		0			0
$70$	−122.462			−0.209100
$71$	139.982	+	242.455i	0.233982	+	0.405269i	0.958976	−	0.283486i	$-0.0914909\pi$
$71$	139.982	+	242.455i	0.233982	+	0.405269i	−0.724994	+	0.688755i	$0.758158\pi$
$72$		0			0
$73$	467.732			0.749916			0.374958	−	0.927042i	$-0.377657\pi$
$73$	467.732			0.749916			0.374958	+	0.927042i	$0.377657\pi$
$74$	423.559	+	733.626i	0.665375	+	1.15246i
$75$		0			0
$76$	385.464	−	667.643i	0.581786	−	1.00768i
$77$	−376.948			−0.557886
$78$		0			0
$79$	37.5379			0.0534600			0.0267300	−	0.999643i	$-0.491491\pi$
$79$	37.5379			0.0534600			0.0267300	+	0.999643i	$0.491491\pi$
$80$	−3.40202	+	5.89247i	−0.00475446	+	0.00823497i
$81$		0			0
$82$	707.568	+	1225.54i	0.952900	+	1.65047i
$83$	76.1553			0.100712			0.0503562	−	0.998731i	$-0.483964\pi$
$83$	76.1553			0.100712			0.0503562	+	0.998731i	$0.483964\pi$
$84$		0			0
$85$	−2.82904	−	4.90004i	−0.00361003	−	0.00625275i
$86$	1949.93			2.44496
$87$		0			0
$88$	432.294	−	748.754i	0.523666	−	0.907017i
$89$	101.403	−	175.635i	0.120772	−	0.209183i	−0.799300	−	0.600932i	$-0.794796\pi$
$89$	101.403	−	175.635i	0.120772	−	0.209183i	0.920072	+	0.391749i	$0.128130\pi$
$90$		0			0
$91$	−388.750	−	223.002i	−0.447826	−	0.256890i
$92$	−57.2348			−0.0648602
$93$		0			0
$94$	−589.848	+	1021.65i	−0.647215	+	1.12101i
$95$	−84.5028	−	146.363i	−0.0912611	−	0.158069i
$96$		0			0
$97$	587.184	+	1017.03i	0.614634	+	1.06458i	0.990449	+	0.137883i	$0.0440297\pi$
$97$	587.184	+	1017.03i	0.614634	+	1.06458i	−0.375814	+	0.926695i	$0.622637\pi$
$98$	573.790	+	993.834i	0.591445	+	1.02441i
$99$		0			0
$100$	750.000	+	1299.04i	0.750000	+	1.29904i
$101$	485.348	−	840.648i	0.478158	−	0.828194i	−0.521528	−	0.853234i	$-0.674638\pi$
$101$	485.348	−	840.648i	0.478158	−	0.828194i	0.999686	+	0.0250397i	$0.00797123\pi$
$102$		0			0
$103$	−1899.70			−1.81731			−0.908654	−	0.417550i	$-0.862889\pi$
$103$	−1899.70			−1.81731			−0.908654	+	0.417550i	$0.862889\pi$
$104$	888.792	−	516.454i	0.838012	−	0.486947i
$105$		0			0
$106$	1397.33	−	2420.25i	1.28039	−	2.21769i
$107$	−953.247	+	1651.07i	−0.861251	+	1.49173i	0.00947163	+	0.999955i	$0.496985\pi$
$107$	−953.247	+	1651.07i	−0.861251	+	1.49173i	−0.870722	+	0.491775i	$0.836348\pi$
$108$		0			0
$109$	−896.004			−0.787354			−0.393677	−	0.919249i	$-0.628797\pi$
$109$	−896.004			−0.787354			−0.393677	+	0.919249i	$0.628797\pi$
$110$	−252.462	−	437.277i	−0.218830	−	0.379025i
$111$		0			0
$112$	−23.1704			−0.0195482
$113$	−167.441	−	290.017i	−0.139394	−	0.241438i	0.787873	−	0.615837i	$-0.211182\pi$
$113$	−167.441	−	290.017i	−0.139394	−	0.241438i	−0.927267	+	0.374400i	$0.877849\pi$
$114$		0			0
$115$	−6.27361	+	10.8662i	−0.00508710	+	0.00881112i
$116$	−1801.96			−1.44231
$117$		0			0
$118$	2362.36			1.84299
$119$	9.63401	−	16.6866i	0.00742141	−	0.0128543i
$120$		0			0
$121$	−111.598	−	193.293i	−0.0838452	−	0.145224i
$122$	−735.827			−0.546054
$123$		0			0
$124$	−871.922	−	1510.21i	−0.631459	−	1.09372i
$125$	679.806			0.486430
$126$		0			0
$127$	−310.447	+	537.709i	−0.216911	+	0.375701i	−0.953862	−	0.300245i	$-0.902931\pi$
$127$	−310.447	+	537.709i	−0.216911	+	0.375701i	0.736951	+	0.675946i	$0.236265\pi$
$128$	1150.11	−	1992.06i	0.794193	−	1.37558i
$129$		0			0
$130$	−1.67376	−	600.325i	−0.00112922	−	0.405015i
$131$	1331.70			0.888180			0.444090	−	0.895982i	$-0.353527\pi$
$131$	1331.70			0.888180			0.444090	+	0.895982i	$0.353527\pi$
$132$		0			0
$133$	287.766	−	498.425i	0.187612	−	0.324954i
$134$	113.808	+	197.121i	0.0733694	+	0.127079i
$135$		0			0
$136$	22.0971	+	38.2732i	0.0139324	+	0.0241316i
$137$	311.008	+	538.681i	0.193950	+	0.335932i	0.946556	−	0.322540i	$-0.104537\pi$
$137$	311.008	+	538.681i	0.193950	+	0.335932i	−0.752606	+	0.658471i	$0.771203\pi$
$138$		0			0
$139$	−165.290	−	286.291i	−0.100861	−	0.174697i	0.811178	−	0.584799i	$-0.198827\pi$
$139$	−165.290	−	286.291i	−0.100861	−	0.174697i	−0.912040	+	0.410102i	$0.865493\pi$
$140$	171.922	−	297.778i	0.103786	−	0.179763i
$141$		0			0
$142$	−1277.07			−0.754711
$143$	−5.15196	−	1847.85i	−0.00301279	−	1.08059i
$144$		0			0
$145$	−197.517	+	342.109i	−0.113123	+	0.195935i
$146$	−1066.79	+	1847.74i	−0.604715	+	1.04740i
$147$		0			0
$148$	−2378.51			−1.32103
$149$	−905.269	−	1567.97i	−0.497735	−	0.862102i	0.502262	−	0.864716i	$-0.332501\pi$
$149$	−905.269	−	1567.97i	−0.497735	−	0.862102i	−0.999997	+	0.00261337i	$0.999168\pi$
$150$		0			0
$151$	−423.239			−0.228097			−0.114049	−	0.993475i	$-0.536382\pi$
$151$	−423.239			−0.228097			−0.114049	+	0.993475i	$0.536382\pi$
$152$	660.034	+	1143.21i	0.352209	+	0.610045i
$153$		0			0
$154$	859.734	−	1489.10i	0.449866	−	0.779190i
$155$	−382.292			−0.198106
$156$		0			0
$157$	1322.17			0.672105			0.336052	−	0.941843i	$-0.390908\pi$
$157$	1322.17			0.672105			0.336052	+	0.941843i	$0.390908\pi$
$158$	−85.6155	+	148.290i	−0.0431089	+	0.0746668i
$159$		0			0
$160$	−261.825	−	453.495i	−0.129369	−	0.224074i
$161$	−42.7283			−0.0209159
$162$		0			0
$163$	1803.20	+	3123.23i	0.866486	+	1.50080i	0.865564	+	0.500798i	$0.166960\pi$
$163$	1803.20	+	3123.23i	0.866486	+	1.50080i	0.000922205		1.00000i	$0.499706\pi$
$164$	−3973.37			−1.89188
$165$		0			0
$166$	−173.693	+	300.845i	−0.0812121	+	0.140663i
$167$	−1707.72	+	2957.85i	−0.791300	+	1.37057i	0.133863	+	0.991000i	$0.457262\pi$
$167$	−1707.72	+	2957.85i	−0.791300	+	1.37057i	−0.925162	+	0.379571i	$0.876071\pi$
$168$		0			0
$169$	1087.87	−	1908.75i	0.495163	−	0.868800i
$170$	25.8096			0.0116442
$171$		0			0
$172$	−2737.47	+	4741.44i	−1.21355	+	2.10193i
$173$	1171.11	+	2028.43i	0.514671	+	0.891436i	0.999855	+	0.0170243i	$0.00541926\pi$
$173$	1171.11	+	2028.43i	0.514671	+	0.891436i	−0.485184	+	0.874412i	$0.661247\pi$
$174$		0			0
$175$	559.908	+	969.788i	0.241857	+	0.418909i
$176$	−47.7671	−	82.7350i	−0.0204578	−	0.0354340i
$177$		0			0
$178$	462.555	+	801.169i	0.194775	+	0.337360i
$179$	−333.446	+	577.545i	−0.139234	+	0.241160i	−0.927207	−	0.374550i	$-0.877797\pi$
$179$	−333.446	+	577.545i	−0.139234	+	0.241160i	0.787973	+	0.615710i	$0.211131\pi$
$180$		0			0
$181$	−701.037			−0.287888			−0.143944	−	0.989586i	$-0.545978\pi$
$181$	−701.037			−0.287888			−0.143944	+	0.989586i	$0.545978\pi$
$182$	1767.61	−	1027.11i	0.719910	−	0.418321i
$183$		0			0
$184$	49.0019	−	84.8737i	0.0196330	−	0.0340053i
$185$	−260.713	+	451.567i	−0.103611	+	0.179459i
$186$		0			0
$187$	79.4440			0.0310670
$188$	−1656.16	−	2868.55i	−0.642487	−	1.11282i
$189$		0			0
$190$	770.928			0.294363
$191$	650.440	+	1126.59i	0.246409	+	0.426793i	0.962527	−	0.271186i	$-0.0874159\pi$
$191$	650.440	+	1126.59i	0.246409	+	0.426793i	−0.716118	+	0.697980i	$0.754083\pi$
$192$		0			0
$193$	259.667	−	449.756i	0.0968457	−	0.167742i	−0.813532	−	0.581521i	$-0.802458\pi$
$193$	259.667	−	449.756i	0.0968457	−	0.167742i	0.910377	+	0.413779i	$0.135791\pi$
$194$	−5356.94			−1.98251
$195$		0			0
$196$	−3222.14			−1.17425
$197$	1560.52	−	2702.91i	0.564379	−	0.977534i	−0.432728	−	0.901525i	$-0.642449\pi$
$197$	1560.52	−	2702.91i	0.564379	−	0.977534i	0.997107	−	0.0760091i	$-0.0242178\pi$
$198$		0			0
$199$	−618.529	−	1071.32i	−0.220333	−	0.381629i	0.734576	−	0.678527i	$-0.237381\pi$
$199$	−618.529	−	1071.32i	−0.220333	−	0.381629i	−0.954909	+	0.296898i	$0.904048\pi$
$200$	−2568.47			−0.908090
$201$		0			0
$202$	2213.94	+	3834.66i	0.771151	+	1.33567i
$203$	−1345.25			−0.465112
$204$		0			0
$205$	−435.528	+	754.356i	−0.148383	+	0.257007i
$206$	4332.78	−	7504.60i	1.46543	−	2.53821i
$207$		0			0
$208$	−0.316683	−	113.585i	−0.000105568	−	0.0378638i
$209$	2372.98			0.785369
$210$		0			0
$211$	1265.83	−	2192.49i	0.413003	−	0.715342i	−0.582214	−	0.813036i	$-0.697813\pi$
$211$	1265.83	−	2192.49i	0.413003	−	0.715342i	0.995217	+	0.0976940i	$0.0311466\pi$
$212$	3923.38	+	6795.49i	1.27103	+	2.20149i
$213$		0			0
$214$	−4348.28	−	7531.45i	−1.38898	−	2.40579i
$215$	600.118	+	1039.44i	0.190362	+	0.329716i
$216$		0			0
$217$	−650.928	−	1127.44i	−0.203631	−	0.352699i
$218$	2043.58	−	3539.59i	0.634904	−	1.09969i
$219$		0			0
$220$	1417.71			0.434463
$221$	81.9315	+	46.9991i	0.0249381	+	0.0143054i
$222$		0			0
$223$	597.766	−	1035.36i	0.179504	−	0.310910i	−0.762207	−	0.647333i	$-0.775884\pi$
$223$	597.766	−	1035.36i	0.179504	−	0.310910i	0.941711	+	0.336424i	$0.109217\pi$
$224$	891.619	−	1544.33i	0.265955	−	0.460647i
$225$		0			0
$226$	1527.58			0.449617
$227$	−434.596	−	752.742i	−0.127071	−	0.220094i	0.795469	−	0.605994i	$-0.207224\pi$
$227$	−434.596	−	752.742i	−0.127071	−	0.220094i	−0.922541	+	0.385900i	$0.873891\pi$
$228$		0			0
$229$	4684.64			1.35183			0.675916	−	0.736978i	$-0.263748\pi$
$229$	4684.64			1.35183			0.675916	+	0.736978i	$0.263748\pi$
$230$	−28.6174	−	49.5668i	−0.00820424	−	0.0142102i
$231$		0			0
$232$	1542.76	−	2672.14i	0.436583	−	0.756184i
$233$	4868.99			1.36900			0.684502	−	0.729011i	$-0.260020\pi$
$233$	4868.99			1.36900			0.684502	+	0.729011i	$0.260020\pi$
$234$		0			0
$235$	−726.137			−0.201566
$236$	−3316.48	+	5744.31i	−0.914764	+	1.58442i
$237$		0			0
$238$	43.9460	+	76.1167i	0.0119689	+	0.0207307i
$239$	−4807.53			−1.30114			−0.650572	−	0.759444i	$-0.725471\pi$
$239$	−4807.53			−1.30114			−0.650572	+	0.759444i	$0.725471\pi$
$240$		0			0
$241$	−2937.98	−	5088.73i	−0.785278	−	1.36014i	−0.928833	−	0.370499i	$-0.879187\pi$
$241$	−2937.98	−	5088.73i	−0.785278	−	1.36014i	0.143555	−	0.989642i	$-0.454147\pi$
$242$	1018.12			0.270443
$243$		0			0
$244$	1033.01	−	1789.23i	0.271033	−	0.469442i
$245$	−353.184	+	611.733i	−0.0920984	+	0.159519i
$246$		0			0
$247$	2447.28	+	1403.85i	0.630431	+	0.361640i
$248$	2986.00			0.764562
$249$		0			0
$250$	−1550.49	+	2685.52i	−0.392245	+	0.679389i
$251$	2903.13	+	5028.38i	0.730057	+	1.26450i	0.956858	+	0.290554i	$0.0938397\pi$
$251$	2903.13	+	5028.38i	0.730057	+	1.26450i	−0.226802	+	0.973941i	$0.572827\pi$
$252$		0			0
$253$	−88.0866	−	152.570i	−0.0218891	−	0.0379131i
$254$	−1416.12	−	2452.79i	−0.349823	−	0.605912i
$255$		0			0
$256$	1920.92	+	3327.12i	0.468974	+	0.812286i
$257$	−597.930	+	1035.65i	−0.145128	+	0.251369i	−0.929421	−	0.369022i	$-0.879693\pi$
$257$	−597.930	+	1035.65i	−0.145128	+	0.251369i	0.784293	+	0.620391i	$0.213026\pi$
$258$		0			0
$259$	−1775.66			−0.426001
$260$	1462.10	+	838.716i	0.348752	+	0.200058i
$261$		0			0
$262$	−3037.32	+	5260.79i	−0.716207	+	1.24051i
$263$	117.092	−	202.810i	0.0274533	−	0.0475505i	−0.851972	−	0.523587i	$-0.824594\pi$
$263$	117.092	−	202.810i	0.0274533	−	0.0475505i	0.879426	+	0.476036i	$0.157927\pi$
$264$		0			0
$265$	1720.19			0.398757
$266$	1312.66	+	2273.59i	0.302572	+	0.524071i
$267$		0			0
$268$	−639.091			−0.145667
$269$	−1334.13	−	2310.79i	−0.302393	−	0.523760i	0.674285	−	0.738471i	$-0.264452\pi$
$269$	−1334.13	−	2310.79i	−0.302393	−	0.523760i	−0.976677	+	0.214712i	$0.931119\pi$
$270$		0			0
$271$	−2850.64	+	4937.45i	−0.638982	+	1.10675i	0.346675	+	0.937985i	$0.387311\pi$
$271$	−2850.64	+	4937.45i	−0.638982	+	1.10675i	−0.985657	+	0.168763i	$0.946023\pi$
$272$	4.88331			0.00108858
$273$		0			0
$274$	−2837.35			−0.625587
$275$	−2308.56	+	3998.54i	−0.506223	+	0.876804i
$276$		0			0
$277$	3576.24	+	6194.24i	0.775725	+	1.34359i	0.934386	+	0.356261i	$0.115949\pi$
$277$	3576.24	+	6194.24i	0.775725	+	1.34359i	−0.158662	+	0.987333i	$0.550718\pi$
$278$	1507.96			0.325329
$279$		0			0
$280$	294.384	+	509.889i	0.0628316	+	0.108827i
$281$	6132.87			1.30198			0.650990	−	0.759086i	$-0.274354\pi$
$281$	6132.87			1.30198			0.650990	+	0.759086i	$0.274354\pi$
$282$		0			0
$283$	−1688.58	+	2924.70i	−0.354683	+	0.614330i	−0.987064	−	0.160328i	$-0.948745\pi$
$283$	−1688.58	+	2924.70i	−0.354683	+	0.614330i	0.632380	+	0.774658i	$0.282078\pi$
$284$	1792.85	−	3105.31i	0.374599	−	0.648824i
$285$		0			0
$286$	7311.53	+	4194.18i	1.51168	+	0.867157i
$287$	−2966.29			−0.610086
$288$		0			0
$289$	2454.47	−	4251.27i	0.499587	−	0.865310i
$290$	−900.982	−	1560.55i	−0.182440	−	0.315995i
$291$		0			0
$292$	−2995.30	−	5188.01i	−0.600297	−	1.03974i
$293$	−2352.38	−	4074.45i	−0.469037	−	0.812395i	0.530337	−	0.847787i	$-0.322065\pi$
$293$	−2352.38	−	4074.45i	−0.469037	−	0.812395i	−0.999374	+	0.0353917i	$0.988732\pi$
$294$		0			0
$295$	727.050	+	1259.29i	0.143493	+	0.248537i
$296$	2036.37	−	3527.10i	0.399871	−	0.692596i
$297$		0			0
$298$	8258.86			1.60545
$299$	−0.583991	−	209.460i	−0.000112953	−	0.0405129i
$300$		0			0
$301$	−2043.64	+	3539.69i	−0.391341	+	0.677822i
$302$	965.312	−	1671.97i	0.183932	−	0.318580i
$303$		0			0
$304$	145.863			0.0275192
$305$	−226.461	−	392.242i	−0.0425151	−	0.0736384i
$306$		0			0
$307$	5130.49			0.953787			0.476894	−	0.878961i	$-0.341763\pi$
$307$	5130.49			0.953787			0.476894	+	0.878961i	$0.341763\pi$
$308$	2413.93	+	4181.05i	0.446579	+	0.773498i
$309$		0			0
$310$	871.922	−	1510.21i	0.159748	−	0.276692i
$311$	−7948.94			−1.44933			−0.724667	−	0.689099i	$-0.758006\pi$
$311$	−7948.94			−1.44933			−0.724667	+	0.689099i	$0.758006\pi$
$312$		0			0
$313$	−8521.87			−1.53893			−0.769465	−	0.638689i	$-0.779477\pi$
$313$	−8521.87			−1.53893			−0.769465	+	0.638689i	$0.779477\pi$
$314$	−3015.57	+	5223.12i	−0.541969	+	0.938718i
$315$		0			0
$316$	−240.388	−	416.365i	−0.0427940	−	0.0741213i
$317$	6662.46			1.18044			0.590222	−	0.807241i	$-0.299040\pi$
$317$	6662.46			1.18044			0.590222	+	0.807241i	$0.299040\pi$
$318$		0			0
$319$	−2773.29	−	4803.49i	−0.486754	−	0.843083i
$320$	2334.23			0.407773
$321$		0			0
$322$	97.4536	−	168.795i	0.0168661	−	0.0292129i
$323$	−60.6483	+	105.046i	−0.0104476	+	0.0180957i
$324$		0			0
$325$	−4746.38	+	2758.00i	−0.810097	+	0.470726i
$326$	−16450.8			−2.79486
$327$		0			0
$328$	3401.82	−	5892.12i	0.572665	−	0.991884i
$329$	−1236.39	−	2141.49i	−0.207187	−	0.358858i
$330$		0			0
$331$	1955.89	+	3387.69i	0.324789	+	0.562551i	0.981470	−	0.191618i	$-0.0613733\pi$
$331$	1955.89	+	3387.69i	0.324789	+	0.562551i	−0.656681	+	0.754169i	$0.728040\pi$
$332$	−487.689	−	844.703i	−0.0806188	−	0.139636i
$333$		0			0
$334$	−7789.84	−	13492.4i	−1.27617	−	2.21039i
$335$	−70.0519	+	121.333i	−0.0114249	+	0.0197885i
$336$		0			0
$337$	−627.211			−0.101384			−0.0506919	−	0.998714i	$-0.516143\pi$
$337$	−627.211			−0.101384			−0.0506919	+	0.998714i	$0.516143\pi$
$338$	5059.18	+	8651.00i	0.814152	+	1.39217i
$339$		0			0
$340$	−36.2337	+	62.7586i	−0.00577955	+	0.0100105i
$341$	2683.84	−	4648.56i	0.426212	−	0.738221i
$342$		0			0
$343$	−5685.08			−0.894943
$344$	−4687.40	−	8118.82i	−0.734674	−	1.27249i
$345$		0			0
$346$	−10684.2			−1.66007
$347$	−1911.51	−	3310.83i	−0.295721	−	0.512204i	0.679431	−	0.733739i	$-0.262227\pi$
$347$	−1911.51	−	3310.83i	−0.295721	−	0.512204i	−0.975152	+	0.221535i	$0.928893\pi$
$348$		0			0
$349$	−1705.33	+	2953.72i	−0.261560	+	0.453035i	−0.966657	−	0.256076i	$-0.917570\pi$
$349$	−1705.33	+	2953.72i	−0.261560	+	0.453035i	0.705097	+	0.709111i	$0.250904\pi$
$350$	−5108.10			−0.780112
$351$		0			0
$352$	7352.48			1.11332
$353$	−2793.82	+	4839.03i	−0.421246	+	0.729620i	−0.996062	−	0.0886632i	$-0.971741\pi$
$353$	−2793.82	+	4839.03i	−0.421246	+	0.729620i	0.574815	+	0.818283i	$0.305074\pi$
$354$		0			0
$355$	−393.035	−	680.757i	−0.0587609	−	0.101777i
$356$	−2597.49			−0.386704
$357$		0			0
$358$	−1521.03	−	2634.50i	−0.224550	−	0.388932i
$359$	−2230.14			−0.327861			−0.163931	−	0.986472i	$-0.552417\pi$
$359$	−2230.14			−0.327861			−0.163931	+	0.986472i	$0.552417\pi$
$360$		0			0
$361$	1617.95	−	2802.37i	0.235887	−	0.408568i
$362$	1598.91	−	2769.39i	0.232146	−	0.402088i
$363$		0			0
$364$	16.0037	+	5740.04i	0.00230446	+	0.826538i
$365$	−1313.28			−0.188330
$366$		0			0
$367$	4349.57	−	7533.68i	0.618653	−	1.07154i	−0.371078	−	0.928602i	$-0.621012\pi$
$367$	4349.57	−	7533.68i	0.618653	−	1.07154i	0.989732	−	0.142938i	$-0.0456548\pi$
$368$	−5.41455	−	9.37828i	−0.000766992	−	0.00132847i
$369$		0			0
$370$	−1189.25	−	2059.85i	−0.167098	−	0.289423i
$371$	2928.97	+	5073.13i	0.409878	+	0.709929i
$372$		0			0
$373$	−5482.09	−	9495.26i	−0.760997	−	1.31809i	−0.942337	−	0.334665i	$-0.891377\pi$
$373$	−5482.09	−	9495.26i	−0.760997	−	1.31809i	0.181340	−	0.983420i	$-0.441956\pi$
$374$	−181.194	+	313.837i	−0.0250517	+	0.0433908i
$375$		0			0
$376$	5671.70			0.777914
$377$	−18.3862	−	6594.57i	−0.00251177	−	0.900895i
$378$		0			0
$379$	−6955.06	+	12046.5i	−0.942631	+	1.63269i	−0.182206	+	0.983260i	$0.558324\pi$
$379$	−6955.06	+	12046.5i	−0.942631	+	1.63269i	−0.760426	+	0.649425i	$0.775010\pi$
$380$	−1082.29	+	1874.58i	−0.146106	+	0.253064i
$381$		0			0
$382$	−5934.03			−0.794794
$383$	−247.377	−	428.469i	−0.0330035	−	0.0571638i	0.849052	−	0.528310i	$-0.177174\pi$
$383$	−247.377	−	428.469i	−0.0330035	−	0.0571638i	−0.882055	+	0.471146i	$0.843841\pi$
$384$		0			0
$385$	1058.38			0.140104
$386$	1184.48	+	2051.59i	0.156188	+	0.270526i
$387$		0			0
$388$	7520.52	−	13025.9i	0.984011	−	1.70436i
$389$	4140.47			0.539666			0.269833	−	0.962907i	$-0.413032\pi$
$389$	4140.47			0.539666			0.269833	+	0.962907i	$0.413032\pi$
$390$		0			0
$391$	9.00524			0.00116474
$392$	2758.65	−	4778.12i	0.355441	−	0.615641i
$393$		0			0
$394$	7118.41	+	12329.5i	0.910204	+	1.57652i
$395$	−105.398			−0.0134256
$396$		0			0
$397$	940.896	+	1629.68i	0.118948	+	0.206023i	0.919351	−	0.393439i	$-0.128715\pi$
$397$	940.896	+	1629.68i	0.118948	+	0.206023i	−0.800403	+	0.599462i	$0.795381\pi$
$398$	5642.90			0.710686
$399$		0			0
$400$	−141.904	+	245.784i	−0.0177380	+	0.0307231i
$401$	210.883	−	365.259i	0.0262618	−	0.0454867i	−0.852596	−	0.522571i	$-0.824973\pi$
$401$	210.883	−	365.259i	0.0262618	−	0.0454867i	0.878858	+	0.477084i	$0.158306\pi$
$402$		0			0
$403$	5517.96	−	3206.34i	0.682058	−	0.396326i
$404$	−12432.5			−1.53103
$405$		0			0
$406$	3068.20	−	5314.28i	0.375055	−	0.649615i
$407$	−3660.62	−	6340.37i	−0.445823	−	0.772188i
$408$		0			0
$409$	−1275.11	−	2208.55i	−0.154157	−	0.267007i	0.778595	−	0.627527i	$-0.215933\pi$
$409$	−1275.11	−	2208.55i	−0.154157	−	0.267007i	−0.932752	+	0.360520i	$0.882599\pi$
$410$	−1986.68	−	3441.04i	−0.239306	−	0.414489i
$411$		0			0
$412$	12165.4	+	21071.2i	1.45473	+	2.51966i
$413$	−2475.89	+	4288.37i	−0.294990	+	0.510937i
$414$		0			0
$415$	−213.826			−0.0252923
$416$	7582.69	+	4349.73i	0.893683	+	0.512651i
$417$		0			0
$418$	−5412.23	+	9374.25i	−0.633303	+	1.09691i
$419$	6192.41	−	10725.6i	0.722002	−	1.25054i	−0.238194	−	0.971218i	$-0.576555\pi$
$419$	6192.41	−	10725.6i	0.722002	−	1.25054i	0.960196	−	0.279327i	$-0.0901112\pi$
$420$		0			0
$421$	10463.0			1.21124			0.605622	−	0.795752i	$-0.292924\pi$
$421$	10463.0			1.21124			0.605622	+	0.795752i	$0.292924\pi$
$422$	5774.17	+	10001.2i	0.666071	+	1.15367i
$423$		0			0
$424$	−13436.1			−1.53895
$425$	−118.004	−	204.389i	−0.0134683	−	0.0233278i
$426$		0			0
$427$	771.190	−	1335.74i	0.0874016	−	0.151384i
$428$	24417.9			2.75767
$429$		0			0
$430$	−5474.94			−0.614012
$431$	−1981.19	+	3431.53i	−0.221417	+	0.383506i	−0.955238	−	0.295837i	$-0.904402\pi$
$431$	−1981.19	+	3431.53i	−0.221417	+	0.383506i	0.733821	+	0.679342i	$0.237735\pi$
$432$		0			0
$433$	4197.07	+	7269.54i	0.465816	+	0.806817i	0.999238	−	0.0390321i	$-0.0124275\pi$
$433$	4197.07	+	7269.54i	0.465816	+	0.806817i	−0.533422	+	0.845849i	$0.679094\pi$
$434$	5938.48			0.656812
$435$		0			0
$436$	5737.90	+	9938.34i	0.630265	+	1.09165i
$437$	268.984			0.0294446
$438$		0			0
$439$	−5087.26	+	8811.39i	−0.553079	+	0.957960i	0.444972	+	0.895545i	$0.353214\pi$
$439$	−5087.26	+	8811.39i	−0.553079	+	0.957960i	−0.998050	+	0.0624156i	$0.980120\pi$
$440$	−1213.78	+	2102.33i	−0.131510	+	0.227783i
$441$		0			0
$442$	−372.534	+	216.470i	−0.0400896	+	0.0232950i
$443$	5880.74			0.630705			0.315353	−	0.948975i	$-0.397877\pi$
$443$	5880.74			0.630705			0.315353	+	0.948975i	$0.397877\pi$
$444$		0			0
$445$	−284.716	+	493.142i	−0.0303299	+	0.0525330i
$446$	2726.74	+	4722.85i	0.289495	+	0.501420i
$447$		0			0
$448$	3974.49	+	6884.01i	0.419145	+	0.725980i
$449$	5332.43	+	9236.05i	0.560475	+	0.970771i	0.997455	+	0.0712996i	$0.0227146\pi$
$449$	5332.43	+	9236.05i	0.560475	+	0.970771i	−0.436980	+	0.899471i	$0.643952\pi$
$450$		0			0
$451$	−6115.16	−	10591.8i	−0.638474	−	1.10587i
$452$	−2144.55	+	3714.47i	−0.223166	+	0.386535i
$453$		0			0
$454$	3964.87			0.409869
$455$	1091.52	+	626.138i	0.112464	+	0.0645138i
$456$		0			0
$457$	7414.43	−	12842.2i	0.758933	−	1.31451i	−0.184462	−	0.982840i	$-0.559054\pi$
$457$	7414.43	−	12842.2i	0.758933	−	1.31451i	0.943395	−	0.331671i	$-0.107612\pi$
$458$	−10684.6	+	18506.3i	−1.09009	+	1.88808i
$459$		0			0
$460$	160.702			0.0162886
$461$	−4855.85	−	8410.58i	−0.490585	−	0.849717i	0.509357	−	0.860555i	$-0.329883\pi$
$461$	−4855.85	−	8410.58i	−0.490585	−	0.849717i	−0.999941	+	0.0108381i	$0.996550\pi$
$462$		0			0
$463$	11353.5			1.13962			0.569809	−	0.821777i	$-0.307017\pi$
$463$	11353.5			1.13962			0.569809	+	0.821777i	$0.307017\pi$
$464$	−170.470	−	295.263i	−0.0170558	−	0.0295415i
$465$		0			0
$466$	−11105.1	+	19234.6i	−1.10393	+	1.91207i
$467$	−6451.31			−0.639252			−0.319626	−	0.947544i	$-0.603557\pi$
$467$	−6451.31			−0.639252			−0.319626	+	0.947544i	$0.603557\pi$
$468$		0			0
$469$	−477.109			−0.0469741
$470$	1656.16	−	2868.55i	0.162538	−	0.281524i
$471$		0			0
$472$	−5678.84	−	9836.04i	−0.553792	−	0.959196i
$473$	−16852.3			−1.63820
$474$		0			0
$475$	−3524.75	−	6105.05i	−0.340477	−	0.589724i
$476$	−246.780			−0.0237629
$477$		0			0
$478$	10964.9	−	18991.8i	1.04921	−	1.81729i
$479$	−4783.23	+	8284.79i	−0.456266	+	0.790275i	−0.998760	−	0.0497842i	$-0.984147\pi$
$479$	−4783.23	+	8284.79i	−0.456266	+	0.790275i	0.542494	+	0.840059i	$0.317480\pi$
$480$		0			0
$481$	−24.2689	−	8704.52i	−0.00230056	−	0.825139i
$482$	26803.5			2.53292
$483$		0			0
$484$	−1429.32	+	2475.66i	−0.134234	+	0.232500i
$485$	−1648.67	−	2855.59i	−0.154356	−	0.267352i
$486$		0			0
$487$	−2458.56	−	4258.35i	−0.228764	−	0.396230i	0.728678	−	0.684856i	$-0.240135\pi$
$487$	−2458.56	−	4258.35i	−0.228764	−	0.396230i	−0.957442	+	0.288626i	$0.906802\pi$
$488$	1768.84	+	3063.72i	0.164081	+	0.284197i
$489$		0			0
$490$	−1611.07	−	2790.45i	−0.148532	−	0.257265i
$491$	1475.41	−	2555.49i	0.135610	−	0.234883i	−0.790220	−	0.612823i	$-0.790034\pi$
$491$	1475.41	−	2555.49i	0.135610	−	0.234883i	0.925830	+	0.377940i	$0.123367\pi$
$492$		0			0
$493$	283.519			0.0259007
$494$	−11127.5	+	6465.90i	−1.01346	+	0.588896i
$495$		0			0
$496$	164.972	−	285.740i	0.0149344	−	0.0258671i
$497$	1338.44	−	2318.25i	0.120799	−	0.209231i
$498$		0			0
$499$	13430.1			1.20484			0.602418	−	0.798180i	$-0.294204\pi$
$499$	13430.1			1.20484			0.602418	+	0.798180i	$0.294204\pi$
$500$	−4353.40	−	7540.30i	−0.389380	−	0.674425i
$501$		0			0
$502$	−26485.6			−2.35480
$503$	660.143	+	1143.40i	0.0585175	+	0.101355i	0.893800	−	0.448466i	$-0.148029\pi$
$503$	660.143	+	1143.40i	0.0585175	+	0.101355i	−0.835283	+	0.549821i	$0.814696\pi$
$504$		0			0
$505$	−1362.74	+	2360.34i	−0.120082	+	0.207988i
$506$	803.623			0.0706036
$507$		0			0
$508$	7952.25			0.694536
$509$	10458.2	−	18114.2i	0.910713	−	1.57740i	0.0976524	−	0.995221i	$-0.468867\pi$
$509$	10458.2	−	18114.2i	0.910713	−	1.57740i	0.813060	−	0.582180i	$-0.197800\pi$
$510$		0			0
$511$	−2236.12	−	3873.08i	−0.193582	−	0.335293i
$512$	877.105			0.0757089
$513$		0			0
$514$	−2727.49	−	4724.15i	−0.234055	−	0.405396i
$515$	5333.90			0.456388
$516$		0			0
$517$	5097.77	−	8829.60i	0.433655	−	0.751113i
$518$	4049.88	−	7014.60i	0.343517	−	0.594988i
$519$		0			0
$520$	−2495.52	+	1450.08i	−0.210453	+	0.122289i
$521$	10104.2			0.849661			0.424831	−	0.905273i	$-0.360334\pi$
$521$	10104.2			0.849661			0.424831	+	0.905273i	$0.360334\pi$
$522$		0			0
$523$	−3565.61	+	6175.82i	−0.298113	+	0.516347i	−0.975704	−	0.219092i	$-0.929691\pi$
$523$	−3565.61	+	6175.82i	−0.298113	+	0.516347i	0.677591	+	0.735439i	$0.263024\pi$
$524$	−8528.08	−	14771.1i	−0.710975	−	1.23144i
$525$		0			0
$526$	534.122	+	925.127i	0.0442753	+	0.0766871i
$527$	137.187	+	237.615i	0.0113396	+	0.0196407i
$528$		0			0
$529$	6073.52	+	10519.6i	0.499179	+	0.864604i
$530$	−3923.38	+	6795.49i	−0.321548	+	0.556938i
$531$		0			0
$532$	−7371.27			−0.600724
$533$	−40.5420	−	14541.1i	−0.00329469	−	1.18170i
$534$		0			0
$535$	2676.49	−	4635.82i	0.216289	−	0.374624i
$536$	547.161	−	947.710i	0.0440928	−	0.0763710i
$537$		0			0
$538$	12171.5			0.975369
$539$	−4958.99	−	8589.22i	−0.396287	−	0.686390i
$540$		0			0
$541$	16831.7			1.33762			0.668809	−	0.743435i	$-0.266805\pi$
$541$	16831.7			1.33762			0.668809	+	0.743435i	$0.266805\pi$
$542$	−13003.3	−	22522.5i	−1.03052	−	1.78491i
$543$		0			0
$544$	−187.914	+	325.477i	−0.0148102	+	0.0256520i
$545$	2515.77			0.197731
$546$		0			0
$547$	−9560.55			−0.747312			−0.373656	−	0.927567i	$-0.621896\pi$
$547$	−9560.55			−0.747312			−0.373656	+	0.927567i	$0.621896\pi$
$548$	3983.31	−	6899.30i	0.310508	−	0.537816i
$549$		0			0
$550$	−10530.6	−	18239.6i	−0.816412	−	1.41407i
$551$	8468.64			0.654766
$552$		0			0
$553$	−179.460	−	310.834i	−0.0138000	−	0.0239024i
$554$	−32626.5			−2.50210
$555$		0			0
$556$	−2117.00	+	3666.75i	−0.161476	+	0.279685i
$557$	−11414.0	+	19769.5i	−0.868267	+	1.50388i	−0.00450060	+	0.999990i	$0.501433\pi$
$557$	−11414.0	+	19769.5i	−0.868267	+	1.50388i	−0.863766	+	0.503893i	$0.831901\pi$
$558$		0			0
$559$	−17380.0	−	9969.82i	−1.31502	−	0.754344i
$560$	65.0571			0.00490922
$561$		0			0
$562$	−13987.7	+	24227.4i	−1.04989	+	1.81846i
$563$	10814.9	+	18731.9i	0.809578	+	1.40223i	0.913157	+	0.407609i	$0.133637\pi$
$563$	10814.9	+	18731.9i	0.809578	+	1.40223i	−0.103579	+	0.994621i	$0.533029\pi$
$564$		0			0
$565$	470.136	+	814.299i	0.0350066	+	0.0606333i
$566$	−7702.53	−	13341.2i	−0.572016	−	0.990761i
$567$		0			0
$568$	3069.92	+	5317.25i	0.226780	+	0.392794i
$569$	−5294.93	+	9171.09i	−0.390114	+	0.675698i	−0.992464	−	0.122534i	$-0.960898\pi$
$569$	−5294.93	+	9171.09i	−0.390114	+	0.675698i	0.602350	+	0.798232i	$0.294231\pi$
$570$		0			0
$571$	−1757.27			−0.128791			−0.0643954	−	0.997924i	$-0.520512\pi$
$571$	−1757.27			−0.128791			−0.0643954	+	0.997924i	$0.520512\pi$
$572$	−20463.1	+	11890.5i	−1.49581	+	0.869176i
$573$		0			0
$574$	6765.45	−	11718.1i	0.491959	−	0.852097i
$575$	−261.683	+	453.247i	−0.0189790	+	0.0328726i
$576$		0			0
$577$	−13580.6			−0.979840			−0.489920	−	0.871767i	$-0.662974\pi$
$577$	−13580.6			−0.979840			−0.489920	+	0.871767i	$0.662974\pi$
$578$	11196.2	+	19392.4i	0.805710	+	1.39553i
$579$		0			0
$580$	5059.49			0.362214
$581$	−364.081	−	630.607i	−0.0259977	−	0.0450293i
$582$		0			0
$583$	−12076.5	+	20917.0i	−0.857900	+	1.48593i
$584$	10257.8			0.726831
$585$		0			0
$586$	21461.0			1.51288
$587$	−478.663	+	829.068i	−0.0336568	+	0.0582952i	−0.882363	−	0.470569i	$-0.844049\pi$
$587$	−478.663	+	829.068i	−0.0336568	+	0.0582952i	0.848706	+	0.528864i	$0.177382\pi$
$588$		0			0
$589$	4097.75	+	7097.50i	0.286663	+	0.496515i
$590$	−6632.95			−0.462838
$591$		0			0
$592$	−225.013	−	389.734i	−0.0156216	−	0.0270573i
$593$	−6729.49			−0.466015			−0.233007	−	0.972475i	$-0.574857\pi$
$593$	−6729.49			−0.466015			−0.233007	+	0.972475i	$0.574857\pi$
$594$		0			0
$595$	−27.0500	+	46.8520i	−0.00186377	+	0.00322814i
$596$	−11594.5	+	20082.2i	−0.796859	+	1.38020i
$597$		0			0
$598$	828.785	+	475.423i	0.0566748	+	0.0325109i
$599$	−2281.52			−0.155626			−0.0778132	−	0.996968i	$-0.524794\pi$
$599$	−2281.52			−0.155626			−0.0778132	+	0.996968i	$0.524794\pi$
$600$		0			0
$601$	−3200.71	+	5543.79i	−0.217237	+	0.376266i	−0.953962	−	0.299926i	$-0.903038\pi$
$601$	−3200.71	+	5543.79i	−0.217237	+	0.376266i	0.736725	+	0.676192i	$0.236371\pi$
$602$	−9322.18	−	16146.5i	−0.631136	−	1.09316i
$603$		0			0
$604$	2710.37	+	4694.50i	0.182588	+	0.316252i
$605$	313.341	+	542.722i	0.0210564	+	0.0364707i
$606$		0			0
$607$	−1389.62	−	2406.89i	−0.0929207	−	0.160943i	0.815818	−	0.578308i	$-0.196287\pi$
$607$	−1389.62	−	2406.89i	−0.0929207	−	0.160943i	−0.908739	+	0.417365i	$0.862954\pi$
$608$	−5612.95	+	9721.92i	−0.374400	+	0.648480i
$609$		0			0
$610$	2066.03			0.137133
$611$	10481.0	−	6090.22i	0.693969	−	0.403247i
$612$		0			0
$613$	−11310.4	+	19590.2i	−0.745226	+	1.29077i	0.204863	+	0.978791i	$0.434325\pi$
$613$	−11310.4	+	19590.2i	−0.745226	+	1.29077i	−0.950089	+	0.311979i	$0.899008\pi$
$614$	−11701.5	+	20267.6i	−0.769111	+	1.33214i
$615$		0			0
$616$	−8266.80			−0.540712
$617$	10987.0	+	19030.1i	0.716889	+	1.24169i	0.962226	+	0.272250i	$0.0877679\pi$
$617$	10987.0	+	19030.1i	0.716889	+	1.24169i	−0.245337	+	0.969438i	$0.578899\pi$
$618$		0			0
$619$	7145.19			0.463957			0.231979	−	0.972721i	$-0.425480\pi$
$619$	7145.19			0.463957			0.231979	+	0.972721i	$0.425480\pi$
$620$	2448.15	+	4240.32i	0.158581	+	0.274670i
$621$		0			0
$622$	18129.8	−	31401.7i	1.16871	−	2.02426i
$623$	−1939.14			−0.124703
$624$		0			0
$625$	12730.8			0.814773
$626$	19436.5	−	33665.0i	1.24096	−	2.14940i
$627$		0			0
$628$	−8467.00	−	14665.3i	−0.538010	−	0.931861i
$629$	374.231			0.0237227
$630$		0			0
$631$	9441.62	+	16353.4i	0.595666	+	1.03172i	0.993453	+	0.114245i	$0.0364450\pi$
$631$	9441.62	+	16353.4i	0.595666	+	1.03172i	−0.397787	+	0.917478i	$0.630222\pi$
$632$	823.239			0.0518144
$633$		0			0
$634$	−15195.6	+	26319.5i	−0.951882	+	1.64871i
$635$	871.661	−	1509.76i	0.0544737	−	0.0943512i
$636$		0			0
$637$	−32.8768	−	11791.9i	−0.00204494	−	0.733457i
$638$	25301.1			1.57003
$639$		0			0
$640$	−3229.25	+	5593.22i	−0.199449	+	0.345456i
$641$	−1815.54	−	3144.61i	−0.111871	−	0.193767i	0.804653	−	0.593745i	$-0.202351\pi$
$641$	−1815.54	−	3144.61i	−0.111871	−	0.193767i	−0.916525	+	0.399978i	$0.869018\pi$
$642$		0			0
$643$	5385.98	+	9328.78i	0.330330	+	0.572148i	0.982576	−	0.185859i	$-0.0595067\pi$
$643$	5385.98	+	9328.78i	0.330330	+	0.572148i	−0.652247	+	0.758007i	$0.726173\pi$
$644$	273.627	+	473.935i	0.0167429	+	0.0289995i
$645$		0			0
$646$	−276.651	−	479.173i	−0.0168493	−	0.0291839i
$647$	7574.14	−	13118.8i	0.460232	−	0.797146i	−0.538740	−	0.842472i	$-0.681099\pi$
$647$	7574.14	−	13118.8i	0.460232	−	0.797146i	0.998972	+	0.0453265i	$0.0144328\pi$
$648$		0			0
$649$	−20416.7			−1.23487
$650$	−69.8152	−	25040.6i	−0.00421289	−	1.51103i
$651$		0			0
$652$	23094.9	−	40001.6i	1.38722	−	2.40273i
$653$	3679.45	−	6372.99i	0.220502	−	0.381921i	−0.734458	−	0.678654i	$-0.762564\pi$
$653$	3679.45	−	6372.99i	0.220502	−	0.381921i	0.954961	+	0.296733i	$0.0958971\pi$
$654$		0			0
$655$	−3739.11			−0.223052
$656$	−375.890	−	651.061i	−0.0223720	−	0.0387495i
$657$		0			0
$658$	11279.7			0.668282
$659$	14166.6	+	24537.3i	0.837411	+	1.45044i	0.892052	+	0.451932i	$0.149265\pi$
$659$	14166.6	+	24537.3i	0.837411	+	1.45044i	−0.0546414	+	0.998506i	$0.517402\pi$
$660$		0			0
$661$	−554.842	+	961.014i	−0.0326488	+	0.0565493i	−0.881888	−	0.471459i	$-0.843728\pi$
$661$	−554.842	+	961.014i	−0.0326488	+	0.0565493i	0.849239	+	0.528008i	$0.177061\pi$
$662$	−17843.8			−1.04761
$663$		0			0
$664$	1670.15			0.0976121
$665$	−807.978	+	1399.46i	−0.0471159	+	0.0816071i
$666$		0			0
$667$	−314.362	−	544.491i	−0.0182491	−	0.0316083i
$668$	43744.1			2.53369
$669$		0			0
$670$	−319.545	−	553.469i	−0.0184255	−	0.0319140i
$671$	6359.39			0.365874
$672$		0			0
$673$	−10489.5	+	18168.4i	−0.600806	+	1.04063i	0.391893	+	0.920011i	$0.371820\pi$
$673$	−10489.5	+	18168.4i	−0.600806	+	1.04063i	−0.992699	+	0.120616i	$0.961513\pi$
$674$	1430.53	−	2477.75i	0.0817535	−	0.141601i
$675$		0			0
$676$	−28138.2	+	156.905i	−1.60095	+	0.00892722i
$677$	−30941.9			−1.75656			−0.878282	−	0.478142i	$-0.841310\pi$
$677$	−30941.9			−1.75656			−0.878282	+	0.478142i	$0.841310\pi$
$678$		0			0
$679$	5614.39	−	9724.41i	0.317320	−	0.549615i
$680$	−62.0433	−	107.462i	−0.00349890	−	0.00606027i
$681$		0			0
$682$	12242.5	+	21204.6i	0.687375	+	1.19057i
$683$	2713.11	+	4699.24i	0.151997	+	0.263267i	0.931962	−	0.362557i	$-0.118096\pi$
$683$	2713.11	+	4699.24i	0.151997	+	0.263267i	−0.779964	+	0.625824i	$0.784763\pi$
$684$		0			0
$685$	−873.236	−	1512.49i	−0.0487075	−	0.0843638i
$686$	12966.4	−	22458.4i	0.721660	−	1.24995i
$687$		0			0
$688$	−1035.89			−0.0574023
$689$	−24829.1	+	14427.5i	−1.37288	+	0.797744i
$690$		0			0
$691$	16896.3	−	29265.3i	0.930199	−	1.61115i	0.147219	−	0.989104i	$-0.452968\pi$
$691$	16896.3	−	29265.3i	0.930199	−	1.61115i	0.782979	−	0.622048i	$-0.213699\pi$
$692$	14999.3	−	25979.6i	0.823973	−	1.42716i
$693$		0			0
$694$	17438.9			0.953849
$695$	464.096	+	803.838i	0.0253297	+	0.0438724i
$696$		0			0
$697$	625.164			0.0339738
$698$	−7778.97	−	13473.6i	−0.421831	−	0.730633i
$699$		0			0
$700$	7171.16	−	12420.8i	0.387206	−	0.670661i
$701$	−6905.96			−0.372089			−0.186045	−	0.982541i	$-0.559567\pi$
$701$	−6905.96			−0.372089			−0.186045	+	0.982541i	$0.559567\pi$
$702$		0			0
$703$	11178.2			0.599707
$704$	−16387.2	+	28383.5i	−0.877297	+	1.51952i
$705$		0			0
$706$	−12744.1	−	22073.5i	−0.679366	−	1.17670i
$707$	−9281.37			−0.493723
$708$		0			0
$709$	1003.56	+	1738.22i	0.0531589	+	0.0920739i	0.891380	−	0.453256i	$-0.149738\pi$
$709$	1003.56	+	1738.22i	0.0531589	+	0.0920739i	−0.838221	+	0.545330i	$0.816404\pi$
$710$	3585.70			0.189534
$711$		0			0
$712$	2223.85	−	3851.83i	0.117054	−	0.202744i
$713$	304.222	−	526.929i	0.0159793	−	0.0276769i
$714$		0			0
$715$	14.4655	+	5188.32i	0.000756613	+	0.271374i
$716$	8541.38			0.445819
$717$		0			0
$718$	5086.44	−	8809.98i	0.264379	−	0.457918i
$719$	−6393.72	−	11074.3i	−0.331635	−	0.574409i	0.651198	−	0.758908i	$-0.274267\pi$
$719$	−6393.72	−	11074.3i	−0.331635	−	0.574409i	−0.982833	+	0.184499i	$0.940934\pi$
$720$		0			0
$721$	9082.03	+	15730.5i	0.469116	+	0.812532i
$722$	7380.35	+	12783.1i	0.380427	+	0.658919i
$723$		0			0
$724$	4489.36	+	7775.80i	0.230450	+	0.399151i
$725$	−8238.74	+	14269.9i	−0.422040	+	0.730995i
$726$		0			0
$727$	−6090.70			−0.310717			−0.155359	−	0.987858i	$-0.549653\pi$
$727$	−6090.70			−0.310717			−0.155359	+	0.987858i	$0.549653\pi$
$728$	−8525.64	−	4890.64i	−0.434040	−	0.248982i
$729$		0			0
$730$	2995.30	−	5188.01i	0.151864	−	0.263037i
$731$	430.710	−	746.011i	0.0217926	−	0.0377459i
$732$		0			0
$733$	−38846.5			−1.95747			−0.978737	−	0.205117i	$-0.934243\pi$
$733$	−38846.5			−1.95747			−0.978737	+	0.205117i	$0.934243\pi$
$734$	19840.8	+	34365.3i	0.997735	+	1.72813i
$735$		0			0
$736$	833.427			0.0417399
$737$	−983.585	−	1703.62i	−0.0491599	−	0.0851474i
$738$		0			0
$739$	−7228.77	+	12520.6i	−0.359830	+	0.623245i	−0.987932	−	0.154887i	$-0.950499\pi$
$739$	−7228.77	+	12520.6i	−0.359830	+	0.623245i	0.628102	+	0.778131i	$0.283832\pi$
$740$	6678.29			0.331755
$741$		0			0
$742$	−26721.3			−1.32206
$743$	−638.901	+	1106.61i	−0.0315464	+	0.0546400i	−0.881368	−	0.472431i	$-0.843377\pi$
$743$	−638.901	+	1106.61i	−0.0315464	+	0.0546400i	0.849821	+	0.527071i	$0.176710\pi$
$744$		0			0
$745$	2541.78	+	4402.49i	0.124998	+	0.216503i
$746$	50013.7			2.45460
$747$		0			0
$748$	−508.750	−	881.181i	−0.0248687	−	0.0430738i
$749$	18229.0			0.889285
$750$		0			0
$751$	6503.93	−	11265.1i	0.316021	−	0.547364i	−0.663633	−	0.748058i	$-0.730986\pi$
$751$	6503.93	−	11265.1i	0.316021	−	0.547364i	0.979654	+	0.200694i	$0.0643197\pi$
$752$	313.353	−	542.743i	0.0151952	−	0.0263189i
$753$		0			0
$754$	26093.3	+	14968.1i	1.26029	+	0.722952i
$755$	1188.35			0.0572829
$756$		0			0
$757$	5361.61	−	9286.57i	0.257425	−	0.445874i	−0.708126	−	0.706086i	$-0.750459\pi$
$757$	5361.61	−	9286.57i	0.257425	−	0.445874i	0.965551	+	0.260212i	$0.0837926\pi$
$758$	−31725.9	−	54950.8i	−1.52023	−	2.63312i
$759$		0			0
$760$	−1853.22	−	3209.87i	−0.0884518	−	0.153203i
$761$	6810.90	+	11796.8i	0.324435	+	0.561938i	0.981398	−	0.191985i	$-0.0614925\pi$
$761$	6810.90	+	11796.8i	0.324435	+	0.561938i	−0.656963	+	0.753923i	$0.728159\pi$
$762$		0			0
$763$	4283.59	+	7419.40i	0.203246	+	0.352032i
$764$	8330.68	−	14429.2i	0.394494	−	0.683284i
$765$		0			0
$766$	2256.84			0.106453
$767$	−21056.0	−	12078.5i	−0.991250	−	0.568619i
$768$		0			0
$769$	4247.57	−	7357.01i	0.199183	−	0.344994i	−0.749081	−	0.662478i	$-0.769505\pi$
$769$	4247.57	−	7357.01i	0.199183	−	0.344994i	0.948264	+	0.317484i	$0.102838\pi$
$770$	−2413.93	+	4181.05i	−0.112977	+	0.195681i
$771$		0			0
$772$	−6651.50			−0.310094
$773$	17131.3	+	29672.2i	0.797113	+	1.38064i	0.921489	+	0.388405i	$0.126974\pi$
$773$	17131.3	+	29672.2i	0.797113	+	1.38064i	−0.124375	+	0.992235i	$0.539693\pi$
$774$		0			0
$775$	−15946.0			−0.739094
$776$	12877.5	+	22304.4i	0.595714	+	1.03181i
$777$		0			0
$778$	−9443.48	+	16356.6i	−0.435174	+	0.753743i
$779$	18673.5			0.858854
$780$		0			0
$781$	11037.1			0.505681
$782$	−20.5389	+	35.5745i	−0.000939221	+	0.00162678i
$783$		0			0
$784$	−304.822	−	527.967i	−0.0138858	−	0.0240510i
$785$	−3712.33			−0.168788
$786$		0			0
$787$	6321.29	+	10948.8i	0.286315	+	0.495912i	0.972927	−	0.231112i	$-0.0742364\pi$
$787$	6321.29	+	10948.8i	0.286315	+	0.495912i	−0.686612	+	0.727024i	$0.740903\pi$
$788$	−39973.6			−1.80711
$789$		0			0
$790$	240.388	−	416.365i	0.0108261	−	0.0187514i
$791$	−1601.00	+	2773.01i	−0.0719658	+	0.124648i
$792$		0			0
$793$	6558.51	+	3762.22i	0.293694	+	0.168474i
$794$	−8583.89			−0.383666
$795$		0			0
$796$	−7921.97	+	13721.3i	−0.352747	+	0.610976i
$797$	9542.18	+	16527.5i	0.424092	+	0.734549i	0.996335	−	0.0855350i	$-0.0272600\pi$
$797$	9542.18	+	16527.5i	0.424092	+	0.734549i	−0.572243	+	0.820084i	$0.693927\pi$
$798$		0			0
$799$	260.577	+	451.333i	0.0115376	+	0.0199837i
$800$	−10921.2	−	18916.0i	−0.482652	−	0.835978i
$801$		0			0
$802$	961.952	+	1666.15i	0.0423538	+	0.0733589i
$803$	9219.77	−	15969.1i	0.405179	−	0.701790i
$804$		0			0
$805$	119.971			0.00525269
$806$	81.1646	+	29111.2i	0.00354702	+	1.27221i
$807$		0			0
$808$	10644.1	−	18436.1i	0.463439	−	0.802700i
$809$	5805.02	−	10054.6i	0.252279	−	0.436960i	−0.711874	−	0.702307i	$-0.752153\pi$
$809$	5805.02	−	10054.6i	0.252279	−	0.436960i	0.964153	+	0.265347i	$0.0854866\pi$
$810$		0			0
$811$	9613.36			0.416240			0.208120	−	0.978103i	$-0.433266\pi$
$811$	9613.36			0.416240			0.208120	+	0.978103i	$0.433266\pi$
$812$	8614.79	+	14921.3i	0.372315	+	0.644869i
$813$		0			0
$814$	33396.2			1.43800
$815$	−5062.95	−	8769.29i	−0.217604	−	0.376901i
$816$		0			0
$817$	12865.2	−	22283.2i	0.550914	−	0.954211i
$818$	11632.9			0.497233
$819$		0			0
$820$	11156.3			0.475115
$821$	−13240.7	+	22933.6i	−0.562856	+	0.974895i	0.434390	+	0.900725i	$0.356964\pi$
$821$	−13240.7	+	22933.6i	−0.562856	+	0.974895i	−0.997246	+	0.0741699i	$0.976369\pi$
$822$		0			0
$823$	−6907.25	−	11963.7i	−0.292553	−	0.506718i	0.681859	−	0.731483i	$-0.261172\pi$
$823$	−6907.25	−	11963.7i	−0.292553	−	0.506718i	−0.974413	+	0.224766i	$0.927838\pi$
$824$	−41662.0			−1.76136
$825$		0			0
$826$	−11293.9	−	19561.6i	−0.475746	−	0.824015i
$827$	44401.0			1.86696			0.933479	−	0.358633i	$-0.116757\pi$
$827$	44401.0			1.86696			0.933479	+	0.358633i	$0.116757\pi$
$828$		0			0
$829$	−12168.7	+	21076.8i	−0.509815	+	0.883025i	0.490120	+	0.871655i	$0.336953\pi$
$829$	−12168.7	+	21076.8i	−0.509815	+	0.883025i	−0.999935	+	0.0113707i	$0.996381\pi$
$830$	487.689	−	844.703i	0.0203951	−	0.0353254i
$831$		0			0
$832$	−33692.0	+	19577.5i	−1.40392	+	0.815780i
$833$	506.966			0.0210868
$834$		0			0
$835$	4794.86	−	8304.95i	0.198722	−	0.344197i
$836$	−15196.3	−	26320.7i	−0.628677	−	1.08890i
$837$		0			0
$838$	28247.0	+	48925.2i	1.16441	+	2.01682i
$839$	−12340.0	−	21373.6i	−0.507778	−	0.879497i	−0.999959	−	0.00900472i	$-0.997134\pi$
$839$	−12340.0	−	21373.6i	−0.507778	−	0.879497i	0.492181	−	0.870493i	$-0.336200\pi$
$840$		0			0
$841$	2297.22	+	3978.90i	0.0941907	+	0.163143i
$842$	−23863.7	+	41333.1i	−0.976719	+	1.69173i
$843$		0			0
$844$	−32425.0			−1.32241
$845$	−3054.49	+	5359.33i	−0.124352	+	0.218185i
$846$		0			0
$847$	−1067.05	+	1848.18i	−0.0432872	+	0.0749757i
$848$	−742.323	+	1285.74i	−0.0300607	+	0.0520666i
$849$		0			0
$850$	1076.56			0.0434421
$851$	−414.943	−	718.702i	−0.0167145	−	0.0289504i
$852$		0			0
$853$	−10151.7			−0.407490			−0.203745	−	0.979024i	$-0.565311\pi$
$853$	−10151.7			−0.407490			−0.203745	+	0.979024i	$0.565311\pi$
$854$	3517.82	+	6093.05i	0.140957	+	0.244145i
$855$		0			0
$856$	−20905.5	+	36209.4i	−0.834739	+	1.44581i
$857$	−2028.92			−0.0808713			−0.0404357	−	0.999182i	$-0.512875\pi$
$857$	−2028.92			−0.0808713			−0.0404357	+	0.999182i	$0.512875\pi$
$858$		0			0
$859$	6655.76			0.264367			0.132184	−	0.991225i	$-0.457801\pi$
$859$	6655.76			0.264367			0.132184	+	0.991225i	$0.457801\pi$
$860$	7686.17	−	13312.8i	0.304763	−	0.527865i
$861$		0			0
$862$	−9037.32	−	15653.1i	−0.357091	−	0.618500i
$863$	−45690.8			−1.80224			−0.901121	−	0.433568i	$-0.857254\pi$
$863$	−45690.8			−1.80224			−0.901121	+	0.433568i	$0.857254\pi$
$864$		0			0
$865$	−3288.21	−	5695.35i	−0.129251	−	0.223870i
$866$	−38290.3			−1.50249
$867$		0			0
$868$	−8336.93	+	14440.0i	−0.326007	+	0.564660i
$869$	739.934	−	1281.60i	0.0288844	−	0.0500292i
$870$		0			0
$871$	−6.52092	−	2338.85i	−0.000253677	−	0.0909861i
$872$	−19650.1			−0.763117
$873$		0			0
$874$	−613.493	+	1062.60i	−0.0237434	+	0.0411248i
$875$	−3250.00	−	5629.17i	−0.125566	−	0.217486i
$876$		0			0
$877$	−15223.8	−	26368.3i	−0.586168	−	1.01527i	−0.994729	−	0.102542i	$-0.967302\pi$
$877$	−15223.8	−	26368.3i	−0.586168	−	1.01527i	0.408560	−	0.912731i	$-0.366031\pi$
$878$	−23205.8	−	40193.6i	−0.891979	−	1.54495i
$879$		0			0
$880$	134.119	+	232.300i	0.00513766	+	0.00889869i
$881$	16271.0	−	28182.2i	0.622230	−	1.07773i	−0.366840	−	0.930284i	$-0.619560\pi$
$881$	16271.0	−	28182.2i	0.622230	−	1.07773i	0.989070	−	0.147450i	$-0.0471065\pi$
$882$		0			0
$883$	27641.9			1.05348			0.526741	−	0.850026i	$-0.323414\pi$
$883$	27641.9			1.05348			0.526741	+	0.850026i	$0.323414\pi$
$884$	−3.37288	−	1209.75i	−0.000128328	−	0.0460274i
$885$		0			0
$886$	−13412.7	+	23231.4i	−0.508586	+	0.880896i
$887$	20050.0	−	34727.5i	0.758976	−	1.31458i	−0.184397	−	0.982852i	$-0.559033\pi$
$887$	20050.0	−	34727.5i	0.758976	−	1.31458i	0.943373	−	0.331733i	$-0.107633\pi$
$888$		0			0
$889$	5936.70			0.223971
$890$	−1298.75	−	2249.49i	−0.0489146	−	0.0847226i
$891$		0			0
$892$	−15312.1			−0.574761
$893$	7783.38	+	13481.2i	0.291670	+	0.505186i
$894$		0			0
$895$	936.236	−	1621.61i	0.0349664	−	0.0605636i
$896$	−21993.8			−0.820044
$897$		0			0
$898$	−48648.4			−1.80781
$899$	9578.06	−	16589.7i	0.355335	−	0.615458i
$900$		0			0
$901$	−617.299	−	1069.19i	−0.0228249	−	0.0395338i
$902$	55789.3			2.05940
$903$		0			0
$904$	−3672.13	−	6360.32i	−0.135103	−	0.234006i
$905$	1968.35			0.0722984
$906$		0			0
$907$	18412.4	−	31891.3i	0.674062	−	1.16751i	−0.302679	−	0.953092i	$-0.597881\pi$
$907$	18412.4	−	31891.3i	0.674062	−	1.16751i	0.976742	−	0.214418i	$-0.0687855\pi$
$908$	−5566.20	+	9640.95i	−0.203437	+	0.352363i
$909$		0			0
$910$	−4963.02	+	2883.88i	−0.180794	+	0.105055i
$911$	−34520.5			−1.25545			−0.627725	−	0.778435i	$-0.716014\pi$
$911$	−34520.5			−1.25545			−0.627725	+	0.778435i	$0.716014\pi$
$912$		0			0
$913$	1501.15	−	2600.06i	0.0544148	−	0.0942491i
$914$	33821.3	+	58580.2i	1.22397	+	2.11998i
$915$		0			0
$916$	−29999.9	−	51961.3i	−1.08212	−	1.87429i
$917$	−6366.58	−	11027.2i	−0.229273	−	0.397112i
$918$		0			0
$919$	−11761.4	−	20371.3i	−0.422168	−	0.731216i	0.573983	−	0.818867i	$-0.305397\pi$
$919$	−11761.4	−	20371.3i	−0.422168	−	0.731216i	−0.996151	+	0.0876506i	$0.972064\pi$
$920$	−137.586	+	238.305i	−0.00493051	+	0.00853989i
$921$		0			0
$922$	44300.4			1.58238
$923$	11382.6	+	6529.53i	0.405920	+	0.232852i
$924$		0			0
$925$	−10874.8	+	18835.6i	−0.386551	+	0.669526i
$926$	−25894.8	+	44851.2i	−0.918961	+	1.59169i
$927$		0			0
$928$	26239.4			0.928180
$929$	−12281.6	−	21272.3i	−0.433741	−	0.751262i	0.563451	−	0.826150i	$-0.309473\pi$
$929$	−12281.6	−	21272.3i	−0.433741	−	0.751262i	−0.997192	+	0.0748880i	$0.976140\pi$
$930$		0			0
$931$	15143.0			0.533073
$932$	−31180.4	−	54006.1i	−1.09587	−	1.89810i
$933$		0			0
$934$	14714.0	−	25485.4i	0.515478	−	0.892834i
$935$	−223.060			−0.00780197
$936$		0			0
$937$	−12115.6			−0.422411			−0.211206	−	0.977442i	$-0.567739\pi$
$937$	−12115.6			−0.422411			−0.211206	+	0.977442i	$0.567739\pi$
$938$	1088.18	−	1884.78i	0.0378788	−	0.0656080i
$939$		0			0
$940$	4650.09	+	8054.20i	0.161350	+	0.279467i
$941$	−14898.3			−0.516123			−0.258062	−	0.966128i	$-0.583084\pi$
$941$	−14898.3			−0.516123			−0.258062	+	0.966128i	$0.583084\pi$
$942$		0			0
$943$	−693.174	−	1200.61i	−0.0239373	−	0.0414606i
$944$	−1254.99			−0.0432695
$945$		0			0
$946$	38436.3	−	66573.7i	1.32101	−	2.28805i
$947$	3717.16	−	6438.31i	0.127552	−	0.220926i	−0.795176	−	0.606379i	$-0.792621\pi$
$947$	3717.16	−	6438.31i	0.127552	−	0.220926i	0.922727	+	0.385453i	$0.125955\pi$
$948$		0			0
$949$	18955.8	−	11014.7i	0.648399	−	0.376767i
$950$	32156.7			1.09821
$951$		0			0
$952$	211.282	−	365.951i	0.00719295	−	0.0124586i
$953$	−11764.3	−	20376.3i	−0.399877	−	0.692607i	0.593833	−	0.804588i	$-0.297614\pi$
$953$	−11764.3	−	20376.3i	−0.399877	−	0.692607i	−0.993710	+	0.111981i	$0.964280\pi$
$954$		0			0
$955$	−1826.28	−	3163.21i	−0.0618818	−	0.107182i
$956$	30786.9	+	53324.4i	1.04155	+	1.80401i
$957$		0			0
$958$	−21818.9	−	37791.5i	−0.735844	−	1.27452i
$959$	2973.72	−	5150.63i	0.100132	−	0.173433i
$960$		0			0
$961$	−11252.7			−0.377723
$962$	34441.9	+	19757.2i	1.15431	+	0.662159i
$963$		0			0
$964$	−37629.0	+	65175.3i	−1.25721	+	2.17755i
$965$	−729.083	+	1262.81i	−0.0243213	+	0.0421256i
$966$		0			0
$967$	23558.0			0.783427			0.391713	−	0.920087i	$-0.371882\pi$
$967$	23558.0			0.783427			0.391713	+	0.920087i	$0.371882\pi$
$968$	−2447.44	−	4239.09i	−0.0812642	−	0.140754i
$969$		0			0
$970$	15041.0			0.497875
$971$	−131.169	−	227.191i	−0.00433513	−	0.00750866i	0.863850	−	0.503750i	$-0.168047\pi$
$971$	−131.169	−	227.191i	−0.00433513	−	0.00750866i	−0.868185	+	0.496241i	$0.834713\pi$
$972$		0			0
$973$	−1580.43	+	2737.39i	−0.0520722	+	0.0901918i
$974$	22429.7			0.737878
$975$		0			0
$976$	390.903			0.0128202
$977$	16572.2	−	28703.9i	0.542673	−	0.939936i	−0.456077	−	0.889940i	$-0.650746\pi$
$977$	16572.2	−	28703.9i	0.542673	−	0.939936i	0.998749	−	0.0499960i	$-0.0159209\pi$
$978$		0			0
$979$	−3997.64	−	6924.11i	−0.130506	−	0.226042i
$980$	9047.00			0.294894
$981$		0			0
$982$	6730.17	+	11657.0i	0.218705	+	0.378808i
$983$	4866.80			0.157911			0.0789557	−	0.996878i	$-0.474841\pi$
$983$	4866.80			0.157911			0.0789557	+	0.996878i	$0.474841\pi$
$984$		0			0
$985$	−4381.58	+	7589.12i	−0.141735	+	0.245492i
$986$	−646.642	+	1120.02i	−0.0208857	+	0.0361751i
$987$		0			0
$988$	−100.747	−	36134.9i	−0.00324413	−	1.16357i
$989$	−1910.26			−0.0614184
$990$		0			0
$991$	−6266.97	+	10854.7i	−0.200885	+	0.347943i	−0.948814	−	0.315836i	$-0.897715\pi$
$991$	−6266.97	+	10854.7i	−0.200885	+	0.347943i	0.747929	+	0.663779i	$0.231048\pi$
$992$	12696.5	+	21991.1i	0.406367	+	0.703848i
$993$		0			0
$994$	6105.37	+	10574.8i	0.194819	+	0.337437i
$995$	1736.68	+	3008.02i	0.0553332	+	0.0958399i
$996$		0			0
$997$	1780.46	+	3083.84i	0.0565574	+	0.0979602i	0.892918	−	0.450220i	$-0.148654\pi$
$997$	1780.46	+	3083.84i	0.0565574	+	0.0979602i	−0.836361	+	0.548180i	$0.815321\pi$
$998$	−30631.0	+	53054.5i	−0.971552	+	1.68278i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.g.d.100.1		4
3.2	odd	2		13.4.c.b.9.2	yes	4
12.11	even	2		208.4.i.e.113.2		4
13.3	even	3	inner	117.4.g.d.55.1		4
13.4	even	6		1521.4.a.l.1.1		2
13.9	even	3		1521.4.a.t.1.2		2
39.2	even	12		169.4.e.g.23.4		8
39.5	even	4		169.4.e.g.147.1		8
39.8	even	4		169.4.e.g.147.4		8
39.11	even	12		169.4.e.g.23.1		8
39.17	odd	6		169.4.a.j.1.2		2
39.20	even	12		169.4.b.e.168.1		4
39.23	odd	6		169.4.c.f.146.1		4
39.29	odd	6		13.4.c.b.3.2	✓	4
39.32	even	12		169.4.b.e.168.4		4
39.35	odd	6		169.4.a.f.1.1		2
39.38	odd	2		169.4.c.f.22.1		4
156.107	even	6		208.4.i.e.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.c.b.3.2	✓	4	39.29	odd	6
13.4.c.b.9.2	yes	4	3.2	odd	2
117.4.g.d.55.1		4	13.3	even	3	inner
117.4.g.d.100.1		4	1.1	even	1	trivial
169.4.a.f.1.1		2	39.35	odd	6
169.4.a.j.1.2		2	39.17	odd	6
169.4.b.e.168.1		4	39.20	even	12
169.4.b.e.168.4		4	39.32	even	12
169.4.c.f.22.1		4	39.38	odd	2
169.4.c.f.146.1		4	39.23	odd	6
169.4.e.g.23.1		8	39.11	even	12
169.4.e.g.23.4		8	39.2	even	12
169.4.e.g.147.1		8	39.5	even	4
169.4.e.g.147.4		8	39.8	even	4
208.4.i.e.81.2		4	156.107	even	6
208.4.i.e.113.2		4	12.11	even	2
1521.4.a.l.1.1		2	13.4	even	6
1521.4.a.t.1.2		2	13.9	even	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28078 + 3.95042i) q^{2} +(-6.40388 - 11.0918i) q^{4} -2.80776 q^{5} +(-4.78078 - 8.28055i) q^{7} +21.9309 q^{8} +O(q^{10})\)	\(q+(-2.28078 + 3.95042i) q^{2} +(-6.40388 - 11.0918i) q^{4} -2.80776 q^{5} +(-4.78078 - 8.28055i) q^{7} +21.9309 q^{8} +(6.40388 - 11.0918i) q^{10} +(19.7116 - 34.1416i) q^{11} +(40.5270 - 23.5492i) q^{13} +43.6155 q^{14} +(1.21165 - 2.09863i) q^{16} +(1.00758 + 1.74518i) q^{17} +(30.0961 + 52.1280i) q^{19} +(17.9806 + 31.1433i) q^{20} +(89.9157 + 155.739i) q^{22} +(2.23438 - 3.87006i) q^{23} -117.116 q^{25} +(0.596118 + 213.809i) q^{26} +(-61.2311 + 106.055i) q^{28} +(70.3466 - 121.844i) q^{29} +136.155 q^{31} +(93.2505 + 161.515i) q^{32} -9.19224 q^{34} +(13.4233 + 23.2498i) q^{35} +(92.8542 - 160.828i) q^{37} -274.570 q^{38} -61.5767 q^{40} +(155.116 - 268.668i) q^{41} +(-213.735 - 370.200i) q^{43} -504.924 q^{44} +(10.1922 + 17.6535i) q^{46} +258.617 q^{47} +(125.788 - 217.872i) q^{49} +(267.116 - 462.659i) q^{50} +(-520.734 - 298.713i) q^{52} -612.656 q^{53} +(-55.3457 + 95.8615i) q^{55} +(-104.847 - 181.600i) q^{56} +(320.890 + 555.797i) q^{58} +(-258.943 - 448.502i) q^{59} +(80.6553 + 139.699i) q^{61} +(-310.540 + 537.871i) q^{62} -831.348 q^{64} +(-113.790 + 66.1205i) q^{65} +(24.9493 - 43.2135i) q^{67} +(12.9048 - 22.3518i) q^{68} -122.462 q^{70} +(139.982 + 242.455i) q^{71} +467.732 q^{73} +(423.559 + 733.626i) q^{74} +(385.464 - 667.643i) q^{76} -376.948 q^{77} +37.5379 q^{79} +(-3.40202 + 5.89247i) q^{80} +(707.568 + 1225.54i) q^{82} +76.1553 q^{83} +(-2.82904 - 4.90004i) q^{85} +1949.93 q^{86} +(432.294 - 748.754i) q^{88} +(101.403 - 175.635i) q^{89} +(-388.750 - 223.002i) q^{91} -57.2348 q^{92} +(-589.848 + 1021.65i) q^{94} +(-84.5028 - 146.363i) q^{95} +(587.184 + 1017.03i) q^{97} +(573.790 + 993.834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 5 q^{4} + 30 q^{5} - 15 q^{7} + 30 q^{8}+O(q^{10}) \) 4 * q - 5 * q^2 - 5 * q^4 + 30 * q^5 - 15 * q^7 + 30 * q^8	\( 4 q - 5 q^{2} - 5 q^{4} + 30 q^{5} - 15 q^{7} + 30 q^{8} + 5 q^{10} + 17 q^{11} + 125 q^{13} + 92 q^{14} - 57 q^{16} + 70 q^{17} + 141 q^{19} + 175 q^{20} + 170 q^{22} + 145 q^{23} + 150 q^{25} + 23 q^{26} - 80 q^{28} + 34 q^{29} - 280 q^{31} + 105 q^{32} - 78 q^{34} - 70 q^{35} + 190 q^{37} - 620 q^{38} - 370 q^{40} + 538 q^{41} - 455 q^{43} - 1360 q^{44} + 82 q^{46} - 120 q^{47} + 565 q^{49} + 450 q^{50} - 310 q^{52} - 1090 q^{53} - 510 q^{55} - 172 q^{56} + 595 q^{58} - 809 q^{59} - 502 q^{61} - 500 q^{62} - 2542 q^{64} + 555 q^{65} + 475 q^{67} - 505 q^{68} - 160 q^{70} + 127 q^{71} + 1170 q^{73} + 849 q^{74} + 140 q^{76} - 510 q^{77} + 480 q^{79} - 1065 q^{80} + 1515 q^{82} - 520 q^{83} + 1205 q^{85} + 3924 q^{86} + 1020 q^{88} + 921 q^{89} - 1287 q^{91} + 2080 q^{92} - 1040 q^{94} + 1270 q^{95} + 415 q^{97} + 1285 q^{98}+O(q^{100}) \) 4 * q - 5 * q^2 - 5 * q^4 + 30 * q^5 - 15 * q^7 + 30 * q^8 + 5 * q^10 + 17 * q^11 + 125 * q^13 + 92 * q^14 - 57 * q^16 + 70 * q^17 + 141 * q^19 + 175 * q^20 + 170 * q^22 + 145 * q^23 + 150 * q^25 + 23 * q^26 - 80 * q^28 + 34 * q^29 - 280 * q^31 + 105 * q^32 - 78 * q^34 - 70 * q^35 + 190 * q^37 - 620 * q^38 - 370 * q^40 + 538 * q^41 - 455 * q^43 - 1360 * q^44 + 82 * q^46 - 120 * q^47 + 565 * q^49 + 450 * q^50 - 310 * q^52 - 1090 * q^53 - 510 * q^55 - 172 * q^56 + 595 * q^58 - 809 * q^59 - 502 * q^61 - 500 * q^62 - 2542 * q^64 + 555 * q^65 + 475 * q^67 - 505 * q^68 - 160 * q^70 + 127 * q^71 + 1170 * q^73 + 849 * q^74 + 140 * q^76 - 510 * q^77 + 480 * q^79 - 1065 * q^80 + 1515 * q^82 - 520 * q^83 + 1205 * q^85 + 3924 * q^86 + 1020 * q^88 + 921 * q^89 - 1287 * q^91 + 2080 * q^92 - 1040 * q^94 + 1270 * q^95 + 415 * q^97 + 1285 * q^98

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