LMFDB - Embedded newform 117.4.q.e.82.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,4,Mod(10,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.10"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			82.1
Root			$-5.04537i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.4.q.e.10.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.36942 - 2.52268i) q^{2} +(8.72787 + 15.1171i) q^{4} +20.1174i q^{5} +(-13.3609 + 7.71395i) q^{7} -47.7076i q^{8} +(50.7498 - 87.9013i) q^{10} +(-23.3283 - 13.4686i) q^{11} +(-3.96071 - 46.7045i) q^{13} +77.8394 q^{14} +(-50.5283 + 87.5177i) q^{16} +(-11.6167 - 20.1207i) q^{17} +(-39.0399 + 22.5397i) q^{19} +(-304.117 + 175.582i) q^{20} +(67.9540 + 117.700i) q^{22} +(71.0050 - 122.984i) q^{23} -279.710 q^{25} +(-100.515 + 214.063i) q^{26} +(-233.225 - 134.653i) q^{28} +(1.14534 - 1.98379i) q^{29} -37.7740i q^{31} +(111.031 - 64.1035i) q^{32} +117.221i q^{34} +(-155.185 - 268.787i) q^{35} +(271.793 + 156.920i) q^{37} +227.442 q^{38} +959.753 q^{40} +(-5.08201 - 2.93410i) q^{41} +(-180.449 - 312.547i) q^{43} -470.209i q^{44} +(-620.501 + 358.246i) q^{46} -209.748i q^{47} +(-52.4900 + 90.9154i) q^{49} +(1222.17 + 705.619i) q^{50} +(671.469 - 467.505i) q^{52} -276.886 q^{53} +(270.953 - 469.305i) q^{55} +(368.014 + 637.419i) q^{56} +(-10.0089 + 5.77866i) q^{58} +(-470.415 + 271.594i) q^{59} +(-102.894 - 178.218i) q^{61} +(-95.2917 + 165.050i) q^{62} +161.602 q^{64} +(939.573 - 79.6791i) q^{65} +(-426.585 - 246.289i) q^{67} +(202.778 - 351.222i) q^{68} +1565.93i q^{70} +(-716.081 + 413.430i) q^{71} -66.1205i q^{73} +(-791.718 - 1371.30i) q^{74} +(-681.470 - 393.447i) q^{76} +415.584 q^{77} +317.642 q^{79} +(-1760.63 - 1016.50i) q^{80} +(14.8036 + 25.6406i) q^{82} -141.450i q^{83} +(404.777 - 233.698i) q^{85} +1820.86i q^{86} +(-642.555 + 1112.94i) q^{88} +(-555.399 - 320.660i) q^{89} +(413.195 + 593.464i) q^{91} +2478.89 q^{92} +(-529.129 + 916.478i) q^{94} +(-453.440 - 785.381i) q^{95} +(-965.551 + 557.461i) q^{97} +(458.702 - 264.832i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29}+ \cdots - 180 q^{98}+O(q^{100}) $ 10 * q + 30 * q^4 + 30 * q^7 + 40 * q^10 - 60 * q^11 + 25 * q^13 + 60 * q^14 - 250 * q^16 - 105 * q^17 + 180 * q^19 - 510 * q^20 - 290 * q^22 + 60 * q^23 - 960 * q^25 + 30 * q^26 + 150 * q^28 + 495 * q^29 - 1440 * q^32 - 60 * q^35 - 405 * q^37 + 1380 * q^38 + 2000 * q^40 - 1065 * q^41 - 370 * q^43 - 390 * q^46 + 775 * q^49 + 4320 * q^50 + 2940 * q^52 - 330 * q^53 - 260 * q^55 + 2670 * q^56 + 2040 * q^58 - 780 * q^59 - 1375 * q^61 + 780 * q^62 - 3140 * q^64 - 1605 * q^65 + 1590 * q^67 + 600 * q^68 - 1620 * q^71 - 2190 * q^74 - 5190 * q^76 + 4320 * q^77 + 1100 * q^79 - 8430 * q^80 - 2390 * q^82 + 525 * q^85 + 3170 * q^88 - 2040 * q^89 + 4770 * q^91 + 1740 * q^92 - 3230 * q^94 + 1380 * q^95 - 3750 * q^97 - 180 * q^98

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−4.36942	−	2.52268i	−1.54482	−	0.891903i	−0.998524	−	0.0543124i	$-0.982703\pi$
$2$	−4.36942	−	2.52268i	−1.54482	−	0.891903i	−0.546298	−	0.837591i	$-0.683963\pi$
$3$		0			0
$3$		0			0
$4$	8.72787	+	15.1171i	1.09098	+	1.88964i
$5$			20.1174i			1.79935i	0.436556	+	0.899677i	$0.356198\pi$
$5$			20.1174i			1.79935i	−0.436556	+	0.899677i	$0.643802\pi$
$6$		0			0
$7$	−13.3609	+	7.71395i	−0.721423	+	0.416514i	−0.815276	−	0.579072i	$-0.803415\pi$
$7$	−13.3609	+	7.71395i	−0.721423	+	0.416514i	0.0938530	+	0.995586i	$0.470082\pi$
$8$		−	47.7076i		−	2.10840i
$9$		0			0
$10$	50.7498	−	87.9013i	1.60485	−	2.77968i
$11$	−23.3283	−	13.4686i	−0.639432	−	0.369176i	0.144964	−	0.989437i	$-0.453693\pi$
$11$	−23.3283	−	13.4686i	−0.639432	−	0.369176i	−0.784396	+	0.620261i	$0.787027\pi$
$12$		0			0
$13$	−3.96071	−	46.7045i	−0.0845002	−	0.996423i
$13$	−3.96071	−	46.7045i	−0.0845002	−	0.996423i
$14$	77.8394			1.48596
$15$		0			0
$16$	−50.5283	+	87.5177i	−0.789505	+	1.36746i
$17$	−11.6167	−	20.1207i	−0.165733	−	0.287059i	0.771182	−	0.636615i	$-0.219666\pi$
$17$	−11.6167	−	20.1207i	−0.165733	−	0.287059i	−0.936915	+	0.349556i	$0.886332\pi$
$18$		0			0
$19$	−39.0399	+	22.5397i	−0.471388	+	0.272156i	−0.716821	−	0.697258i	$-0.754403\pi$
$19$	−39.0399	+	22.5397i	−0.471388	+	0.272156i	0.245433	+	0.969414i	$0.421070\pi$
$20$	−304.117	+	175.582i	−3.40013	+	1.96307i
$21$		0			0
$22$	67.9540	+	117.700i	0.658539	+	1.14062i
$23$	71.0050	−	122.984i	0.643720	−	1.11496i	−0.340875	−	0.940109i	$-0.610723\pi$
$23$	71.0050	−	122.984i	0.643720	−	1.11496i	0.984595	−	0.174848i	$-0.0559434\pi$
$24$		0			0
$25$	−279.710			−2.23768
$26$	−100.515	+	214.063i	−0.758176	+	1.61466i
$27$		0			0
$28$	−233.225	−	134.653i	−1.57412	−	0.908820i
$29$	1.14534	−	1.98379i	0.00733394	−	0.0127028i	−0.862335	−	0.506338i	$-0.830999\pi$
$29$	1.14534	−	1.98379i	0.00733394	−	0.0127028i	0.869669	+	0.493635i	$0.164332\pi$
$30$		0			0
$31$		−	37.7740i		−	0.218852i	−0.993995	−	0.109426i	$-0.965099\pi$
$31$		−	37.7740i		−	0.218852i	0.993995	−	0.109426i	$-0.0349012\pi$
$32$	111.031	−	64.1035i	0.613363	−	0.354125i
$33$		0			0
$34$			117.221i			0.591273i
$35$	−155.185	−	268.787i	−0.749456	−	1.29810i
$36$		0			0
$37$	271.793	+	156.920i	1.20764	+	0.697228i	0.962242	−	0.272195i	$-0.0877497\pi$
$37$	271.793	+	156.920i	1.20764	+	0.697228i	0.245393	+	0.969424i	$0.421083\pi$
$38$	227.442			0.970947
$39$		0			0
$40$	959.753			3.79376
$41$	−5.08201	−	2.93410i	−0.0193580	−	0.0111763i	0.490290	−	0.871559i	$-0.336891\pi$
$41$	−5.08201	−	2.93410i	−0.0193580	−	0.0111763i	−0.509648	+	0.860383i	$0.670224\pi$
$42$		0			0
$43$	−180.449	−	312.547i	−0.639958	−	1.10844i	−0.985441	−	0.170015i	$-0.945618\pi$
$43$	−180.449	−	312.547i	−0.639958	−	1.10844i	0.345483	−	0.938425i	$-0.387715\pi$
$44$		−	470.209i		−	1.61106i
$45$		0			0
$46$	−620.501	+	358.246i	−1.98887	+	1.14827i
$47$		−	209.748i		−	0.650956i	−0.945550	−	0.325478i	$-0.894475\pi$
$47$		−	209.748i		−	0.650956i	0.945550	−	0.325478i	$-0.105525\pi$
$48$		0			0
$49$	−52.4900	+	90.9154i	−0.153032	+	0.265060i
$50$	1222.17	+	705.619i	3.45681	+	1.99579i
$51$		0			0
$52$	671.469	−	467.505i	1.79069	−	1.24676i
$53$	−276.886			−0.717609			−0.358804	−	0.933413i	$-0.616815\pi$
$53$	−276.886			−0.717609			−0.358804	+	0.933413i	$0.616815\pi$
$54$		0			0
$55$	270.953	−	469.305i	0.664278	−	1.15056i
$56$	368.014	+	637.419i	0.878178	+	1.52105i
$57$		0			0
$58$	−10.0089	+	5.77866i	−0.0226593	+	0.0130823i
$59$	−470.415	+	271.594i	−1.03801	+	0.599298i	−0.919270	−	0.393627i	$-0.871220\pi$
$59$	−470.415	+	271.594i	−1.03801	+	0.599298i	−0.118744	+	0.992925i	$0.537887\pi$
$60$		0			0
$61$	−102.894	−	178.218i	−0.215971	−	0.374073i	0.737601	−	0.675236i	$-0.235958\pi$
$61$	−102.894	−	178.218i	−0.215971	−	0.374073i	−0.953573	+	0.301163i	$0.902625\pi$
$62$	−95.2917	+	165.050i	−0.195195	+	0.338087i
$63$		0			0
$64$	161.602			0.315629
$65$	939.573	−	79.6791i	1.79292	−	0.152046i
$66$		0			0
$67$	−426.585	−	246.289i	−0.777846	−	0.449090i	0.0578203	−	0.998327i	$-0.481585\pi$
$67$	−426.585	−	246.289i	−0.777846	−	0.449090i	−0.835666	+	0.549237i	$0.814918\pi$
$68$	202.778	−	351.222i	0.361625	−	0.626352i
$69$		0			0
$70$			1565.93i			2.67377i
$71$	−716.081	+	413.430i	−1.19695	+	0.691057i	−0.959873	−	0.280435i	$-0.909521\pi$
$71$	−716.081	+	413.430i	−1.19695	+	0.691057i	−0.237073	+	0.971492i	$0.576188\pi$
$72$		0			0
$73$		−	66.1205i		−	0.106011i	−0.998594	−	0.0530056i	$-0.983120\pi$
$73$		−	66.1205i		−	0.106011i	0.998594	−	0.0530056i	$-0.0168801\pi$
$74$	−791.718	−	1371.30i	−1.24372	−	2.15419i
$75$		0			0
$76$	−681.470	−	393.447i	−1.02855	−	0.593835i
$77$	415.584			0.615068
$78$		0			0
$79$	317.642			0.452374			0.226187	−	0.974084i	$-0.427374\pi$
$79$	317.642			0.452374			0.226187	+	0.974084i	$0.427374\pi$
$80$	−1760.63	−	1016.50i	−2.46055	−	1.42060i
$81$		0			0
$82$	14.8036	+	25.6406i	0.0199364	+	0.0345309i
$83$		−	141.450i		−	0.187063i	−0.995616	−	0.0935313i	$-0.970184\pi$
$83$		−	141.450i		−	0.187063i	0.995616	−	0.0935313i	$-0.0298155\pi$
$84$		0			0
$85$	404.777	−	233.698i	0.516520	−	0.298213i
$86$			1820.86i			2.28312i
$87$		0			0
$88$	−642.555	+	1112.94i	−0.778371	+	1.34818i
$89$	−555.399	−	320.660i	−0.661486	−	0.381909i	0.131357	−	0.991335i	$-0.458067\pi$
$89$	−555.399	−	320.660i	−0.661486	−	0.381909i	−0.792843	+	0.609426i	$0.791400\pi$
$90$		0			0
$91$	413.195	+	593.464i	0.475985	+	0.683648i
$92$	2478.89			2.80915
$93$		0			0
$94$	−529.129	+	916.478i	−0.580590	+	1.00561i
$95$	−453.440	−	785.381i	−0.489705	−	0.848194i
$96$		0			0
$97$	−965.551	+	557.461i	−1.01069	+	0.583522i	−0.911394	−	0.411536i	$-0.864992\pi$
$97$	−965.551	+	557.461i	−1.01069	+	0.583522i	−0.0992962	+	0.995058i	$0.531659\pi$
$98$	458.702	−	264.832i	0.472815	−	0.272980i
$99$		0			0
$100$	−2441.27	−	4228.40i	−2.44127	−	4.22840i
$101$	−794.953	+	1376.90i	−0.783177	+	1.35650i	0.146906	+	0.989150i	$0.453069\pi$
$101$	−794.953	+	1376.90i	−0.783177	+	1.35650i	−0.930082	+	0.367351i	$0.880265\pi$
$102$		0			0
$103$	−527.502			−0.504625			−0.252312	−	0.967646i	$-0.581191\pi$
$103$	−527.502			−0.504625			−0.252312	+	0.967646i	$0.581191\pi$
$104$	−2228.16	+	188.956i	−2.10086	+	0.178160i
$105$		0			0
$106$	1209.83	+	698.497i	1.10858	+	0.640038i
$107$	875.982	−	1517.25i	0.791443	−	1.37082i	−0.133630	−	0.991031i	$-0.542663\pi$
$107$	875.982	−	1517.25i	0.791443	−	1.37082i	0.925073	−	0.379788i	$-0.124003\pi$
$108$		0			0
$109$			967.122i			0.849848i	0.905229	+	0.424924i	$0.139699\pi$
$109$			967.122i			0.849848i	−0.905229	+	0.424924i	$0.860301\pi$
$110$	−2367.81	+	1367.06i	−2.05238	+	1.18494i
$111$		0			0
$112$		−	1559.09i		−	1.31536i
$113$	955.487	+	1654.95i	0.795439	+	1.37774i	0.922560	+	0.385854i	$0.126093\pi$
$113$	955.487	+	1654.95i	0.795439	+	1.37774i	−0.127120	+	0.991887i	$0.540573\pi$
$114$		0			0
$115$	2474.12	+	1428.44i	2.00620	+	1.15828i
$116$	39.9855			0.0320048
$117$		0			0
$118$	2740.59			2.13806
$119$	310.421	+	179.221i	0.239128	+	0.138061i
$120$		0			0
$121$	−302.694	−	524.281i	−0.227418	−	0.393900i
$122$			1038.28i			0.770501i
$123$		0			0
$124$	571.033	−	329.686i	0.413551	−	0.238764i
$125$		−	3112.35i		−	2.22702i
$126$		0			0
$127$	616.557	−	1067.91i	0.430792	−	0.746154i	−0.566150	−	0.824302i	$-0.691568\pi$
$127$	616.557	−	1067.91i	0.430792	−	0.746154i	0.996942	+	0.0781488i	$0.0249009\pi$
$128$	−1594.35	−	920.499i	−1.10095	−	0.635636i
$129$		0			0
$130$	−4306.39	−	2022.10i	−2.90535	−	1.36423i
$131$	1274.90			0.850292			0.425146	−	0.905125i	$-0.360223\pi$
$131$	1274.90			0.850292			0.425146	+	0.905125i	$0.360223\pi$
$132$		0			0
$133$	347.740	−	602.304i	0.226713	−	0.392679i
$134$	1242.62	+	2152.28i	0.801089	+	1.38753i
$135$		0			0
$136$	−959.913	+	554.206i	−0.605234	+	0.349432i
$137$	1759.18	−	1015.66i	1.09706	−	0.633385i	0.161609	−	0.986855i	$-0.448332\pi$
$137$	1759.18	−	1015.66i	1.09706	−	0.633385i	0.935446	+	0.353470i	$0.114998\pi$
$138$		0			0
$139$	722.832	+	1251.98i	0.441078	+	0.763969i	0.997770	−	0.0667498i	$-0.0212629\pi$
$139$	722.832	+	1251.98i	0.441078	+	0.763969i	−0.556692	+	0.830719i	$0.687930\pi$
$140$	2708.86	−	4691.88i	1.63529	−	2.83240i
$141$		0			0
$142$	4171.81			2.46542
$143$	−536.648	+	1142.88i	−0.313824	+	0.668340i
$144$		0			0
$145$	39.9086	+	23.0413i	0.0228568	+	0.0131964i
$146$	−166.801	+	288.908i	−0.0945517	+	0.163768i
$147$		0			0
$148$			5478.30i			3.04266i
$149$	−836.856	+	483.159i	−0.460120	+	0.265650i	−0.712095	−	0.702083i	$-0.752253\pi$
$149$	−836.856	+	483.159i	−0.460120	+	0.265650i	0.251975	+	0.967734i	$0.418920\pi$
$150$		0			0
$151$		−	1463.09i		−	0.788505i	−0.919002	−	0.394252i	$-0.871004\pi$
$151$		−	1463.09i		−	0.788505i	0.919002	−	0.394252i	$-0.128996\pi$
$152$	1075.32	+	1862.50i	0.573813	+	0.993874i
$153$		0			0
$154$	−1815.86	−	1048.39i	−0.950170	−	0.548581i
$155$	759.914			0.393792
$156$		0			0
$157$	−66.0424			−0.0335717			−0.0167859	−	0.999859i	$-0.505343\pi$
$157$	−66.0424			−0.0335717			−0.0167859	+	0.999859i	$0.505343\pi$
$158$	−1387.91	−	801.311i	−0.698838	−	0.403474i
$159$		0			0
$160$	1289.60	+	2233.65i	0.637197	+	1.10366i
$161$			2190.92i			1.07247i
$162$		0			0
$163$	−3052.95	+	1762.62i	−1.46703	+	0.846988i	−0.999319	−	0.0368953i	$-0.988253\pi$
$163$	−3052.95	+	1762.62i	−1.46703	+	0.846988i	−0.467707	+	0.883883i	$0.654920\pi$
$164$		−	102.434i		−	0.0487728i
$165$		0			0
$166$	−356.834	+	618.055i	−0.166842	+	0.288978i
$167$	−225.731	−	130.326i	−0.104596	−	0.0603887i	0.446789	−	0.894639i	$-0.352567\pi$
$167$	−225.731	−	130.326i	−0.104596	−	0.0603887i	−0.551386	+	0.834250i	$0.685901\pi$
$168$		0			0
$169$	−2165.63	+	369.966i	−0.985719	+	0.168396i
$170$	−2358.19			−1.06391
$171$		0			0
$172$	3149.87	−	5455.73i	1.39637	−	2.41858i
$173$	−455.876	−	789.601i	−0.200345	−	0.347007i	0.748295	−	0.663366i	$-0.230873\pi$
$173$	−455.876	−	789.601i	−0.200345	−	0.347007i	−0.948640	+	0.316359i	$0.897540\pi$
$174$		0			0
$175$	3737.18	−	2157.66i	1.61431	−	0.932023i
$176$	2357.48	−	1361.09i	1.00967	−	0.582933i
$177$		0			0
$178$	1617.85	+	2802.19i	0.681252	+	1.17996i
$179$	−1345.24	+	2330.03i	−0.561721	+	0.972930i	0.435625	+	0.900128i	$0.356527\pi$
$179$	−1345.24	+	2330.03i	−0.561721	+	0.972930i	−0.997346	+	0.0728016i	$0.976806\pi$
$180$		0			0
$181$	−4773.85			−1.96043			−0.980213	−	0.197944i	$-0.936573\pi$
$181$	−4773.85			−1.96043			−0.980213	+	0.197944i	$0.936573\pi$
$182$	−308.299	−	3635.45i	−0.125564	−	1.48065i
$183$		0			0
$184$	−5867.29	−	3387.48i	−2.35077	−	1.35722i
$185$	−3156.82	+	5467.77i	−1.25456	+	2.17296i
$186$		0			0
$187$			625.844i			0.244739i
$188$	3170.79	−	1830.66i	1.23007	−	0.710182i
$189$		0			0
$190$			4575.54i			1.74708i
$191$	−1028.74	−	1781.82i	−0.389721	−	0.675017i	0.602691	−	0.797975i	$-0.294095\pi$
$191$	−1028.74	−	1781.82i	−0.389721	−	0.675017i	−0.992412	+	0.122958i	$0.960762\pi$
$192$		0			0
$193$	632.089	+	364.937i	0.235745	+	0.136107i	0.613219	−	0.789913i	$-0.289874\pi$
$193$	632.089	+	364.937i	0.235745	+	0.136107i	−0.377475	+	0.926020i	$0.623207\pi$
$194$	5625.20			2.08178
$195$		0			0
$196$	−1832.50			−0.667822
$197$	−1473.21	−	850.557i	−0.532801	−	0.307613i	0.209355	−	0.977840i	$-0.432863\pi$
$197$	−1473.21	−	850.557i	−0.532801	−	0.307613i	−0.742156	+	0.670227i	$0.766197\pi$
$198$		0			0
$199$	−920.440	−	1594.25i	−0.327881	−	0.567906i	0.654211	−	0.756312i	$-0.273001\pi$
$199$	−920.440	−	1594.25i	−0.327881	−	0.567906i	−0.982091	+	0.188407i	$0.939668\pi$
$200$			13344.3i			4.71792i
$201$		0			0
$202$	6946.97	−	4010.83i	2.41974	−	1.39704i
$203$			35.3404i			0.0122188i
$204$		0			0
$205$	59.0265	−	102.237i	0.0201102	−	0.0348319i
$206$	2304.88	+	1330.72i	0.779555	+	0.450077i
$207$		0			0
$208$	4287.60	+	2013.27i	1.42929	+	0.671131i
$209$	1214.31			0.401894
$210$		0			0
$211$	−71.4850	+	123.816i	−0.0233234	+	0.0403972i	−0.877452	−	0.479665i	$-0.840758\pi$
$211$	−71.4850	+	123.816i	−0.0233234	+	0.0403972i	0.854128	+	0.520063i	$0.174091\pi$
$212$	−2416.63	−	4185.72i	−0.782899	−	1.35602i
$213$		0			0
$214$	−7655.06	+	4419.65i	−2.44528	+	1.41178i
$215$	6287.63	−	3630.16i	1.99448	−	1.15151i
$216$		0			0
$217$	291.386	+	504.696i	0.0911548	+	0.157885i
$218$	2439.74	−	4225.76i	0.757983	−	1.31286i
$219$		0			0
$220$	9459.37			2.89887
$221$	−893.719	+	622.246i	−0.272027	+	0.189397i
$222$		0			0
$223$	−2025.39	−	1169.36i	−0.608205	−	0.351148i	0.164057	−	0.986451i	$-0.447542\pi$
$223$	−2025.39	−	1169.36i	−0.608205	−	0.351148i	−0.772263	+	0.635303i	$0.780875\pi$
$224$	−988.982	+	1712.97i	−0.294996	+	0.510949i
$225$		0			0
$226$		−	9641.57i		−	2.83782i
$227$	2840.01	−	1639.68i	0.830388	−	0.479425i	−0.0235973	−	0.999722i	$-0.507512\pi$
$227$	2840.01	−	1639.68i	0.830388	−	0.479425i	0.853986	+	0.520297i	$0.174179\pi$
$228$		0			0
$229$			1143.72i			0.330041i	0.986290	+	0.165021i	$0.0527690\pi$
$229$			1143.72i			0.330041i	−0.986290	+	0.165021i	$0.947231\pi$
$230$	−7206.98	−	12482.9i	−2.06615	−	3.57868i
$231$		0			0
$232$	−94.6418	−	54.6415i	−0.0267825	−	0.0154629i
$233$	−4238.17			−1.19164			−0.595819	−	0.803118i	$-0.703173\pi$
$233$	−4238.17			−1.19164			−0.595819	+	0.803118i	$0.703173\pi$
$234$		0			0
$235$	4219.59			1.17130
$236$	−8211.44	−	4740.88i	−2.26491	−	1.30765i
$237$		0			0
$238$	−904.238	−	1566.19i	−0.246273	−	0.426558i
$239$		−	3310.03i		−	0.895849i	−0.894072	−	0.447924i	$-0.852163\pi$
$239$		−	3310.03i		−	0.895849i	0.894072	−	0.447924i	$-0.147837\pi$
$240$		0			0
$241$	4938.82	−	2851.43i	1.32007	−	0.762145i	0.336333	−	0.941743i	$-0.390813\pi$
$241$	4938.82	−	2851.43i	1.32007	−	0.762145i	0.983740	+	0.179598i	$0.0574798\pi$
$242$			3054.40i			0.811340i
$243$		0			0
$244$	1796.09	−	3110.92i	0.471242	−	0.816214i
$245$	−1828.98	−	1055.96i	−0.476936	−	0.275359i
$246$		0			0
$247$	1207.33	+	1734.07i	0.311015	+	0.446705i
$248$	−1802.11			−0.461427
$249$		0			0
$250$	−7851.48	+	13599.2i	−1.98629	+	3.44035i
$251$	1955.12	+	3386.36i	0.491657	+	0.851574i	0.999954	−	0.00960748i	$-0.00305820\pi$
$251$	1955.12	+	3386.36i	0.491657	+	0.851574i	−0.508297	+	0.861182i	$0.669725\pi$
$252$		0			0
$253$	−3312.85	+	1912.68i	−0.823230	+	0.475292i
$254$	−5387.99	+	3110.76i	−1.33099	+	0.768450i
$255$		0			0
$256$	3997.85	+	6924.47i	0.976037	+	1.69055i
$257$	−3486.40	+	6038.63i	−0.846209	+	1.46568i	0.0383576	+	0.999264i	$0.487787\pi$
$257$	−3486.40	+	6038.63i	−0.846209	+	1.46568i	−0.884567	+	0.466413i	$0.845546\pi$
$258$		0			0
$259$	−4841.88			−1.16162
$260$	9404.99	+	13508.2i	2.24336	+	3.22209i
$261$		0			0
$262$	−5570.56	−	3216.16i	−1.31355	−	0.758378i
$263$	140.845	−	243.951i	0.0330224	−	0.0571965i	−0.849042	−	0.528326i	$-0.822820\pi$
$263$	140.845	−	243.951i	0.0330224	−	0.0571965i	0.882064	+	0.471129i	$0.156153\pi$
$264$		0			0
$265$		−	5570.23i		−	1.29123i
$266$	−3038.84	+	1754.48i	−0.700464	+	0.404413i
$267$		0			0
$268$		−	8598.31i		−	1.95980i
$269$	2166.56	+	3752.60i	0.491070	+	0.850558i	0.999947	−	0.0102813i	$-0.00327270\pi$
$269$	2166.56	+	3752.60i	0.491070	+	0.850558i	−0.508877	+	0.860839i	$0.669939\pi$
$270$		0			0
$271$	371.175	+	214.298i	0.0832003	+	0.0480357i	0.541023	−	0.841008i	$-0.318037\pi$
$271$	371.175	+	214.298i	0.0832003	+	0.0480357i	−0.457823	+	0.889044i	$0.651371\pi$
$272$	2347.89			0.523390
$273$		0			0
$274$	−10248.8			−2.25967
$275$	6525.15	+	3767.30i	1.43084	+	0.826096i
$276$		0			0
$277$	4469.37	+	7741.18i	0.969454	+	1.67914i	0.697140	+	0.716935i	$0.254455\pi$
$277$	4469.37	+	7741.18i	0.969454	+	1.67914i	0.272313	+	0.962209i	$0.412211\pi$
$278$		−	7293.91i		−	1.57360i
$279$		0			0
$280$	−12823.2	+	7403.49i	−2.73691	+	1.58015i
$281$			775.819i			0.164703i	0.996603	+	0.0823514i	$0.0262430\pi$
$281$			775.819i			0.164703i	−0.996603	+	0.0823514i	$0.973757\pi$
$282$		0			0
$283$	−2007.27	+	3476.69i	−0.421624	+	0.730274i	−0.996098	−	0.0882484i	$-0.971873\pi$
$283$	−2007.27	+	3476.69i	−0.421624	+	0.730274i	0.574475	+	0.818522i	$0.305206\pi$
$284$	−12499.7	−	7216.71i	−2.61170	−	1.50786i
$285$		0			0
$286$	5227.97	−	3639.94i	1.08090	−	0.752566i
$287$	90.5340			0.0186204
$288$		0			0
$289$	2186.60	−	3787.31i	0.445065	−	0.770875i
$290$	−116.252	−	201.354i	−0.0235398	−	0.0407721i
$291$		0			0
$292$	999.550	−	577.091i	0.200323	−	0.115656i
$293$	−4292.21	+	2478.11i	−0.855814	+	0.494104i	−0.862608	−	0.505873i	$-0.831171\pi$
$293$	−4292.21	+	2478.11i	−0.855814	+	0.494104i	0.00679458	+	0.999977i	$0.497837\pi$
$294$		0			0
$295$	−5463.77	−	9463.53i	−1.07835	−	1.86776i
$296$	7486.27	−	12966.6i	1.47004	−	2.54618i
$297$		0			0
$298$	4875.43			0.947738
$299$	−6025.15	−	2829.15i	−1.16536	−	0.547204i
$300$		0			0
$301$	4821.94	+	2783.95i	0.923362	+	0.533103i
$302$	−3690.90	+	6392.83i	−0.703270	+	1.21810i
$303$		0			0
$304$		−	4555.58i		−	0.859474i
$305$	3585.28	−	2069.96i	0.673090	−	0.388608i
$306$		0			0
$307$			3894.90i			0.724084i	0.932162	+	0.362042i	$0.117920\pi$
$307$			3894.90i			0.724084i	−0.932162	+	0.362042i	$0.882080\pi$
$308$	3627.16	+	6282.43i	0.671029	+	1.16226i
$309$		0			0
$310$	−3320.38	−	1917.02i	−0.608338	−	0.351224i
$311$	3097.44			0.564758			0.282379	−	0.959303i	$-0.408876\pi$
$311$	3097.44			0.564758			0.282379	+	0.959303i	$0.408876\pi$
$312$		0			0
$313$	4487.36			0.810353			0.405177	−	0.914238i	$-0.367210\pi$
$313$	4487.36			0.810353			0.405177	+	0.914238i	$0.367210\pi$
$314$	288.567	+	166.604i	0.0518623	+	0.0299427i
$315$		0			0
$316$	2772.34	+	4801.83i	0.493533	+	0.854824i
$317$		−	6820.62i		−	1.20847i	−0.796807	−	0.604233i	$-0.793479\pi$
$317$		−	6820.62i		−	1.20847i	0.796807	−	0.604233i	$-0.206521\pi$
$318$		0			0
$319$	−53.4377	+	30.8523i	−0.00937911	+	0.00541503i
$320$			3251.01i			0.567928i
$321$		0			0
$322$	5526.99	−	9573.02i	0.956543	−	1.65678i
$323$	907.031	+	523.675i	0.156249	+	0.0902106i
$324$		0			0
$325$	1107.85	+	13063.7i	0.189084	+	2.22967i
$326$	17786.1			3.02173
$327$		0			0
$328$	−139.979	+	242.451i	−0.0235642	+	0.0408143i
$329$	1617.99	+	2802.44i	0.271132	+	0.469615i
$330$		0			0
$331$	4341.35	−	2506.48i	0.720913	−	0.416219i	−0.0941759	−	0.995556i	$-0.530022\pi$
$331$	4341.35	−	2506.48i	0.720913	−	0.416219i	0.815088	+	0.579337i	$0.196688\pi$
$332$	2138.32	−	1234.56i	0.353481	−	0.204082i
$333$		0			0
$334$	657.542	+	1138.90i	0.107722	+	0.186580i
$335$	4954.70	−	8581.78i	0.808071	−	1.39962i
$336$		0			0
$337$	−3220.79			−0.520616			−0.260308	−	0.965526i	$-0.583824\pi$
$337$	−3220.79			−0.520616			−0.260308	+	0.965526i	$0.583824\pi$
$338$	10395.8	+	3846.65i	1.67295	+	0.619025i
$339$		0			0
$340$	7065.68	+	4079.37i	1.12703	+	0.650691i
$341$	−508.762	+	881.202i	−0.0807948	+	0.139941i
$342$		0			0
$343$		−	6911.39i		−	1.08799i
$344$	−14910.9	+	8608.79i	−2.33703	+	1.34929i
$345$		0			0
$346$			4600.13i			0.714753i
$347$	−1680.36	−	2910.46i	−0.259960	−	0.450265i	0.706271	−	0.707942i	$-0.250376\pi$
$347$	−1680.36	−	2910.46i	−0.259960	−	0.450265i	−0.966231	+	0.257677i	$0.917043\pi$
$348$		0			0
$349$	3976.20	+	2295.66i	0.609859	+	0.352102i	0.772910	−	0.634515i	$-0.218800\pi$
$349$	3976.20	+	2295.66i	0.609859	+	0.352102i	−0.163051	+	0.986618i	$0.552134\pi$
$350$	−21772.4			−3.32510
$351$		0			0
$352$	−3453.54			−0.522938
$353$	−1506.96	−	870.044i	−0.227216	−	0.131183i	0.382071	−	0.924133i	$-0.375211\pi$
$353$	−1506.96	−	870.044i	−0.227216	−	0.131183i	−0.609287	+	0.792950i	$0.708544\pi$
$354$		0			0
$355$	−8317.12	−	14405.7i	−1.24346	−	2.15373i
$356$		−	11194.7i		−	1.66662i
$357$		0			0
$358$	11755.8	−	6787.24i	1.73552	−	1.00200i
$359$		−	1425.49i		−	0.209567i	−0.994495	−	0.104784i	$-0.966585\pi$
$359$		−	1425.49i		−	0.209567i	0.994495	−	0.104784i	$-0.0334150\pi$
$360$		0			0
$361$	−2413.42	+	4180.17i	−0.351862	+	0.609443i
$362$	20858.9	+	12042.9i	3.02851	+	1.74851i
$363$		0			0
$364$	−5365.15	+	11426.0i	−0.772555	+	1.64529i
$365$	1330.17			0.190752
$366$		0			0
$367$	−5424.61	+	9395.69i	−0.771559	+	1.33638i	0.165149	+	0.986269i	$0.447189\pi$
$367$	−5424.61	+	9395.69i	−0.771559	+	1.33638i	−0.936708	+	0.350111i	$0.886144\pi$
$368$	7175.53	+	12428.4i	1.01644	+	1.76053i
$369$		0			0
$370$	27586.9	−	15927.3i	3.87615	−	2.23789i
$371$	3699.46	−	2135.89i	0.517700	−	0.298894i
$372$		0			0
$373$	247.374	+	428.465i	0.0343393	+	0.0594774i	0.882684	−	0.469966i	$-0.155734\pi$
$373$	247.374	+	428.465i	0.0343393	+	0.0594774i	−0.848345	+	0.529444i	$0.822401\pi$
$374$	1578.81	−	2734.57i	0.218284	−	0.378078i
$375$		0			0
$376$	−10006.6			−1.37248
$377$	−97.1882	−	45.6354i	−0.0132770	−	0.00623433i
$378$		0			0
$379$	10949.4	+	6321.66i	1.48400	+	0.856786i	0.999835	−	0.0181912i	$-0.00579076\pi$
$379$	10949.4	+	6321.66i	1.48400	+	0.856786i	0.484163	+	0.874978i	$0.339124\pi$
$380$	7915.13	−	13709.4i	1.06852	−	1.85073i
$381$		0			0
$382$			10380.7i			1.39037i
$383$	−2010.48	+	1160.75i	−0.268227	+	0.154861i	−0.628082	−	0.778147i	$-0.716160\pi$
$383$	−2010.48	+	1160.75i	−0.268227	+	0.154861i	0.359855	+	0.933008i	$0.382826\pi$
$384$		0			0
$385$			8360.47i			1.10673i
$386$	−1841.24	−	3189.12i	−0.242789	−	0.420523i
$387$		0			0
$388$	−16854.4	−	9730.90i	−2.20529	−	1.27323i
$389$	−10477.6			−1.36564			−0.682821	−	0.730586i	$-0.739247\pi$
$389$	−10477.6			−1.36564			−0.682821	+	0.730586i	$0.739247\pi$
$390$		0			0
$391$	−3299.38			−0.426744
$392$	4337.36	+	2504.18i	0.558851	+	0.322653i
$393$		0			0
$394$	4291.37	+	7432.88i	0.548722	+	0.950414i
$395$			6390.14i			0.813982i
$396$		0			0
$397$	1530.14	−	883.424i	0.193439	−	0.111682i	−0.400152	−	0.916449i	$-0.631043\pi$
$397$	1530.14	−	883.424i	0.193439	−	0.111682i	0.593592	+	0.804766i	$0.297709\pi$
$398$			9287.91i			1.16975i
$399$		0			0
$400$	14133.3	−	24479.5i	1.76666	−	3.05994i
$401$	4331.55	+	2500.82i	0.539420	+	0.311434i	0.744844	−	0.667239i	$-0.232524\pi$
$401$	4331.55	+	2500.82i	0.539420	+	0.311434i	−0.205424	+	0.978673i	$0.565857\pi$
$402$		0			0
$403$	−1764.21	+	149.612i	−0.218069	+	0.0184930i
$404$	−27753.0			−3.41773
$405$		0			0
$406$	89.1526	−	154.417i	0.0108980	−	0.0188758i
$407$	−4226.98	−	7321.34i	−0.514800	−	0.891660i
$408$		0			0
$409$	−9706.92	+	5604.29i	−1.17354	+	0.677541i	−0.954510	−	0.298178i	$-0.903621\pi$
$409$	−9706.92	+	5604.29i	−1.17354	+	0.677541i	−0.219025	+	0.975719i	$0.570288\pi$
$410$	−515.822	+	297.810i	−0.0621333	+	0.0358727i
$411$		0			0
$412$	−4603.97	−	7974.31i	−0.550537	−	0.953558i
$413$	4190.13	−	7257.51i	0.499232	−	0.864695i
$414$		0			0
$415$	2845.61			0.336592
$416$	−3433.68	−	4931.73i	−0.404688	−	0.581246i
$417$		0			0
$418$	−5305.84	−	3063.33i	−0.620854	−	0.358450i
$419$	1642.59	−	2845.06i	0.191518	−	0.331719i	−0.754236	−	0.656604i	$-0.771992\pi$
$419$	1642.59	−	2845.06i	0.191518	−	0.331719i	0.945753	+	0.324885i	$0.105326\pi$
$420$		0			0
$421$		−	13289.9i		−	1.53850i	−0.638948	−	0.769250i	$-0.720630\pi$
$421$		−	13289.9i		−	1.53850i	0.638948	−	0.769250i	$-0.279370\pi$
$422$	624.695	−	360.668i	0.0720609	−	0.0416044i
$423$		0			0
$424$			13209.6i			1.51301i
$425$	3249.31	+	5627.96i	0.370858	+	0.642344i
$426$		0			0
$427$	2749.52	+	1587.44i	0.311613	+	0.179910i
$428$	30581.8			3.45380
$429$		0			0
$430$	−36631.0			−4.10815
$431$	−11857.8	−	6846.13i	−1.32523	−	0.765119i	−0.340668	−	0.940184i	$-0.610653\pi$
$431$	−11857.8	−	6846.13i	−1.32523	−	0.765119i	−0.984557	+	0.175064i	$0.943987\pi$
$432$		0			0
$433$	−5001.26	−	8662.43i	−0.555070	−	0.961409i	−0.997898	−	0.0648023i	$-0.979358\pi$
$433$	−5001.26	−	8662.43i	−0.555070	−	0.961409i	0.442829	−	0.896606i	$-0.353975\pi$
$434$		−	2940.30i		−	0.325205i
$435$		0			0
$436$	−14620.1	+	8440.91i	−1.60591	+	0.927170i
$437$			6401.73i			0.700769i
$438$		0			0
$439$	2243.60	−	3886.04i	0.243921	−	0.422484i	−0.717907	−	0.696139i	$-0.754900\pi$
$439$	2243.60	−	3886.04i	0.243921	−	0.422484i	0.961828	+	0.273656i	$0.0882329\pi$
$440$	−22389.4	−	12926.5i	−2.42585	−	1.40056i
$441$		0			0
$442$	5474.76	−	464.279i	0.589158	−	0.0499627i
$443$	−2035.35			−0.218290			−0.109145	−	0.994026i	$-0.534811\pi$
$443$	−2035.35			−0.218290			−0.109145	+	0.994026i	$0.534811\pi$
$444$		0			0
$445$	6450.84	−	11173.2i	0.687190	−	1.19025i
$446$	5899.83	+	10218.8i	0.626379	+	1.08492i
$447$		0			0
$448$	−2159.15	+	1246.59i	−0.227702	+	0.131464i
$449$	3096.55	−	1787.79i	0.325468	−	0.187909i	−0.328359	−	0.944553i	$-0.606496\pi$
$449$	3096.55	−	1787.79i	0.325468	−	0.187909i	0.653827	+	0.756644i	$0.273162\pi$
$450$		0			0
$451$	79.0365	+	136.895i	0.00825207	+	0.0142930i
$452$	−16678.7	+	28888.4i	−1.73562	+	3.00619i
$453$		0			0
$454$	−16545.6			−1.71040
$455$	−11939.0	+	8312.41i	−1.23012	+	0.856465i
$456$		0			0
$457$	−6978.95	−	4029.30i	−0.714358	−	0.412435i	0.0983147	−	0.995155i	$-0.468655\pi$
$457$	−6978.95	−	4029.30i	−0.714358	−	0.412435i	−0.812672	+	0.582721i	$0.801988\pi$
$458$	2885.25	−	4997.41i	0.294365	−	0.509855i
$459$		0			0
$460$			49868.8i			5.05466i
$461$	−10125.7	+	5846.07i	−1.02300	+	0.590626i	−0.914970	−	0.403522i	$-0.867786\pi$
$461$	−10125.7	+	5846.07i	−1.02300	+	0.590626i	−0.108025	+	0.994148i	$0.534453\pi$
$462$		0			0
$463$		−	1732.40i		−	0.173891i	−0.996213	−	0.0869455i	$-0.972289\pi$
$463$		−	1732.40i		−	0.173891i	0.996213	−	0.0869455i	$-0.0277106\pi$
$464$	115.744	+	200.475i	0.0115804	+	0.0200578i
$465$		0			0
$466$	18518.3	+	10691.6i	1.84087	+	1.06283i
$467$	10769.9			1.06718			0.533588	−	0.845745i	$-0.320843\pi$
$467$	10769.9			1.06718			0.533588	+	0.845745i	$0.320843\pi$
$468$		0			0
$469$	7599.44			0.748208
$470$	−18437.1	−	10644.7i	−1.80945	−	1.04469i
$471$		0			0
$472$	12957.1	+	22442.4i	1.26356	+	2.18855i
$473$			9721.58i			0.945029i
$474$		0			0
$475$	10919.8	−	6304.57i	1.05481	−	0.608997i
$476$			6256.88i			0.602487i
$477$		0			0
$478$	−8350.15	+	14462.9i	−0.799010	+	1.38393i
$479$	−6851.68	−	3955.82i	−0.653572	−	0.377340i	0.136251	−	0.990674i	$-0.456495\pi$
$479$	−6851.68	−	3955.82i	−0.653572	−	0.377340i	−0.789824	+	0.613334i	$0.789828\pi$
$480$		0			0
$481$	6252.37	−	13315.5i	0.592689	−	1.26223i
$482$	−28773.0			−2.71904
$483$		0			0
$484$	5283.74	−	9151.70i	0.496219	−	0.859476i
$485$	−11214.7	−	19424.4i	−1.04996	−	1.81859i
$486$		0			0
$487$	−9495.78	+	5482.39i	−0.883562	+	0.510125i	−0.871831	−	0.489806i	$-0.837067\pi$
$487$	−9495.78	+	5482.39i	−0.883562	+	0.510125i	−0.0117307	+	0.999931i	$0.503734\pi$
$488$	−8502.35	+	4908.83i	−0.788695	+	0.455353i
$489$		0			0
$490$	5327.72	+	9227.88i	0.491188	+	0.850762i
$491$	4569.69	−	7914.93i	0.420014	−	0.727486i	−0.575926	−	0.817502i	$-0.695358\pi$
$491$	4569.69	−	7914.93i	0.420014	−	0.727486i	0.995940	+	0.0900157i	$0.0286917\pi$
$492$		0			0
$493$	−53.2204			−0.00486192
$494$	−900.832	−	10622.6i	−0.0820452	−	0.967474i
$495$		0			0
$496$	3305.89	+	1908.66i	0.299272	+	0.172785i
$497$	6378.35	−	11047.6i	0.575670	−	0.997090i
$498$		0			0
$499$		−	12577.5i		−	1.12835i	−0.825655	−	0.564175i	$-0.809194\pi$
$499$		−	12577.5i		−	1.12835i	0.825655	−	0.564175i	$-0.190806\pi$
$500$	47049.8	−	27164.2i	4.20826	−	2.42964i
$501$		0			0
$502$		−	19728.6i		−	1.75404i
$503$	6607.30	+	11444.2i	0.585696	+	1.01446i	0.994788	+	0.101962i	$0.0325120\pi$
$503$	6607.30	+	11444.2i	0.585696	+	1.01446i	−0.409092	+	0.912493i	$0.634155\pi$
$504$		0			0
$505$	−27699.6	−	15992.4i	−2.44083	−	1.40921i
$506$	19300.3			1.69566
$507$		0			0
$508$	21524.9			1.87995
$509$	18809.9	+	10859.9i	1.63798	+	0.945689i	0.981527	+	0.191323i	$0.0612779\pi$
$509$	18809.9	+	10859.9i	1.63798	+	0.945689i	0.656454	+	0.754366i	$0.272055\pi$
$510$		0			0
$511$	510.050	+	883.432i	0.0441551	+	0.0764789i
$512$		−	25613.2i		−	2.21085i
$513$		0			0
$514$	30467.1	−	17590.2i	2.61449	−	1.50947i
$515$		−	10612.0i		−	0.907999i
$516$		0			0
$517$	−2825.02	+	4893.07i	−0.240317	+	0.416242i
$518$	21156.2	+	12214.5i	1.79450	+	1.03605i
$519$		0			0
$520$	−3801.30	−	44824.8i	−0.320573	−	3.78019i
$521$	4627.05			0.389088			0.194544	−	0.980894i	$-0.437677\pi$
$521$	4627.05			0.389088			0.194544	+	0.980894i	$0.437677\pi$
$522$		0			0
$523$	−6891.98	+	11937.3i	−0.576224	+	0.998049i	0.419683	+	0.907671i	$0.362141\pi$
$523$	−6891.98	+	11937.3i	−0.576224	+	0.998049i	−0.995907	+	0.0903788i	$0.971192\pi$
$524$	11127.1	+	19272.8i	0.927654	+	1.60674i
$525$		0			0
$526$	−1230.82	+	710.617i	−0.102028	+	0.0589056i
$527$	−760.040	+	438.809i	−0.0628233	+	0.0362710i
$528$		0			0
$529$	−3999.93	−	6928.07i	−0.328752	−	0.569415i
$530$	−14051.9	+	24338.7i	−1.15165	+	1.99472i
$531$		0			0
$532$	12140.1			0.989362
$533$	−116.907	+	248.974i	−0.00950061	+	0.0202331i
$534$		0			0
$535$	30523.0	+	17622.5i	2.46659	+	1.42409i
$536$	−11749.9	+	20351.4i	−0.946860	+	1.64001i
$537$		0			0
$538$		−	21862.2i		−	1.75195i
$539$	2449.01	−	1413.93i	0.195707	−	0.112992i
$540$		0			0
$541$		−	454.638i		−	0.0361302i	−0.999837	−	0.0180651i	$-0.994249\pi$
$541$		−	454.638i		−	0.0361302i	0.999837	−	0.0180651i	$-0.00575061\pi$
$542$	−1081.21	−	1872.72i	−0.0856865	−	0.148413i
$543$		0			0
$544$	−2579.62	−	1489.34i	−0.203309	−	0.117381i
$545$	−19456.0			−1.52918
$546$		0			0
$547$	11611.4			0.907621			0.453810	−	0.891098i	$-0.350064\pi$
$547$	11611.4			0.907621			0.453810	+	0.891098i	$0.350064\pi$
$548$	30707.7	+	17729.1i	2.39374	+	1.38202i
$549$		0			0
$550$	−19007.4	−	32921.8i	−1.47360	−	2.55234i
$551$			103.263i			0.00798390i
$552$		0			0
$553$	−4244.00	+	2450.28i	−0.326353	+	0.188420i
$554$		−	45099.3i		−	3.45864i
$555$		0			0
$556$	−12617.6	+	21854.3i	−0.962417	+	1.66696i
$557$	−4229.61	−	2441.97i	−0.321749	−	0.185762i	0.330423	−	0.943833i	$-0.392809\pi$
$557$	−4229.61	−	2441.97i	−0.321749	−	0.185762i	−0.652172	+	0.758071i	$0.726142\pi$
$558$		0			0
$559$	−13882.6	+	9665.69i	−1.05040	+	0.731333i
$560$	31364.9			2.36680
$561$		0			0
$562$	1957.14	−	3389.87i	0.146899	−	0.254436i
$563$	−9808.67	−	16989.1i	−0.734256	−	1.27177i	−0.955049	−	0.296448i	$-0.904198\pi$
$563$	−9808.67	−	16989.1i	−0.734256	−	1.27177i	0.220793	−	0.975321i	$-0.429136\pi$
$564$		0			0
$565$	−33293.3	+	19221.9i	−2.47905	+	1.43128i
$566$	17541.2	−	10127.4i	1.30267	−	0.752095i
$567$		0			0
$568$	19723.7	+	34162.5i	1.45702	+	2.52364i
$569$	−3737.59	+	6473.70i	−0.275374	+	0.476963i	−0.970230	−	0.242187i	$-0.922135\pi$
$569$	−3737.59	+	6473.70i	−0.275374	+	0.476963i	0.694855	+	0.719150i	$0.255469\pi$
$570$		0			0
$571$	7799.56			0.571631			0.285816	−	0.958285i	$-0.407735\pi$
$571$	7799.56			0.571631			0.285816	+	0.958285i	$0.407735\pi$
$572$	−21960.9	+	1862.36i	−1.60530	+	0.136135i
$573$		0			0
$574$	−395.581	−	228.389i	−0.0287652	−	0.0166076i
$575$	−19860.8	+	34399.9i	−1.44044	+	2.49491i
$576$		0			0
$577$			13136.1i			0.947771i	0.880587	+	0.473885i	$0.157149\pi$
$577$			13136.1i			0.947771i	−0.880587	+	0.473885i	$0.842851\pi$
$578$	−19108.4	+	11032.2i	−1.37509	+	0.793910i
$579$		0			0
$580$			804.404i			0.0575880i
$581$	1091.14	+	1889.91i	0.0779142	+	0.134951i
$582$		0			0
$583$	6459.29	+	3729.27i	0.458862	+	0.264924i
$584$	−3154.45			−0.223514
$585$		0			0
$586$	25005.9			1.76277
$587$	19183.1	+	11075.3i	1.34884	+	0.778754i	0.988085	−	0.153907i	$-0.0491855\pi$
$587$	19183.1	+	11075.3i	1.34884	+	0.778754i	0.360756	+	0.932660i	$0.382519\pi$
$588$		0			0
$589$	851.414	+	1474.69i	0.0595618	+	0.103164i
$590$			55133.4i			3.84713i
$591$		0			0
$592$	−27466.5	+	15857.8i	−1.90687	+	1.10093i
$593$		−	22770.3i		−	1.57684i	−0.615138	−	0.788419i	$-0.710900\pi$
$593$		−	22770.3i		−	1.57684i	0.615138	−	0.788419i	$-0.289100\pi$
$594$		0			0
$595$	−3605.47	+	6244.86i	−0.248420	+	0.430276i
$596$	−14607.9	−	8433.89i	−1.00397	−	0.579640i
$597$		0			0
$598$	19189.4	+	27561.3i	1.31223	+	1.88472i
$599$	7214.11			0.492088			0.246044	−	0.969259i	$-0.420869\pi$
$599$	7214.11			0.492088			0.246044	+	0.969259i	$0.420869\pi$
$600$		0			0
$601$	−13638.4	+	23622.4i	−0.925658	+	1.60329i	−0.135160	+	0.990824i	$0.543155\pi$
$601$	−13638.4	+	23622.4i	−0.925658	+	1.60329i	−0.790499	+	0.612464i	$0.790179\pi$
$602$	−14046.0	−	24328.4i	−0.950953	−	1.64710i
$603$		0			0
$604$	22117.6	−	12769.6i	1.48999	−	0.860245i
$605$	10547.2	−	6089.41i	0.708765	−	0.409206i
$606$		0			0
$607$	−5783.08	−	10016.6i	−0.386701	−	0.669787i	0.605302	−	0.795996i	$-0.293052\pi$
$607$	−5783.08	−	10016.6i	−0.386701	−	0.669787i	−0.992004	+	0.126209i	$0.959719\pi$
$608$	−2889.75	+	5005.19i	−0.192755	+	0.333861i
$609$		0			0
$610$	−20887.4			−1.38640
$611$	−9796.20	+	830.752i	−0.648628	+	0.0550059i
$612$		0			0
$613$	−21197.3	−	12238.3i	−1.39666	−	0.806362i	−0.402619	−	0.915368i	$-0.631900\pi$
$613$	−21197.3	−	12238.3i	−1.39666	−	0.806362i	−0.994041	+	0.109006i	$0.965233\pi$
$614$	9825.61	−	17018.5i	0.645813	−	1.11858i
$615$		0			0
$616$		−	19826.5i		−	1.29681i
$617$	−2098.62	+	1211.64i	−0.136933	+	0.0790581i	−0.566901	−	0.823786i	$-0.691858\pi$
$617$	−2098.62	+	1211.64i	−0.136933	+	0.0790581i	0.429969	+	0.902844i	$0.358525\pi$
$618$		0			0
$619$		−	17223.4i		−	1.11836i	−0.829045	−	0.559182i	$-0.811115\pi$
$619$		−	17223.4i		−	1.11836i	0.829045	−	0.559182i	$-0.188885\pi$
$620$	6632.42	+	11487.7i	0.429620	+	0.744124i
$621$		0			0
$622$	−13534.0	−	7813.86i	−0.872450	−	0.503709i
$623$	9894.22			0.636282
$624$		0			0
$625$	27648.7			1.76952
$626$	−19607.1	−	11320.2i	−1.25185	−	0.722757i
$627$		0			0
$628$	−576.409	−	998.370i	−0.0366262	−	0.0634384i
$629$		−	7291.57i		−	0.462216i
$630$		0			0
$631$	−8004.31	+	4621.29i	−0.504987	+	0.291554i	−0.730771	−	0.682623i	$-0.760839\pi$
$631$	−8004.31	+	4621.29i	−0.504987	+	0.291554i	0.225784	+	0.974177i	$0.427506\pi$
$632$		−	15154.0i		−	0.953786i
$633$		0			0
$634$	−17206.3	+	29802.1i	−1.07784	+	1.86687i
$635$	21483.5	+	12403.5i	1.34259	+	0.775147i
$636$		0			0
$637$	4454.06	+	2091.43i	0.277043	+	0.130087i
$638$	311.322			0.0193187
$639$		0			0
$640$	18518.0	−	32074.2i	1.14373	−	1.98100i
$641$	5799.42	+	10044.9i	0.357353	+	0.618953i	0.987518	−	0.157508i	$-0.0503461\pi$
$641$	5799.42	+	10044.9i	0.357353	+	0.618953i	−0.630165	+	0.776461i	$0.717013\pi$
$642$		0			0
$643$	21965.8	−	12682.0i	1.34720	−	0.777804i	0.359345	−	0.933205i	$-0.383000\pi$
$643$	21965.8	−	12682.0i	1.34720	−	0.777804i	0.987852	+	0.155401i	$0.0496669\pi$
$644$	−33120.3	+	19122.0i	−2.02659	+	1.17005i
$645$		0			0
$646$	−2642.13	−	4576.31i	−0.160918	−	0.278719i
$647$	3295.05	−	5707.19i	0.200219	−	0.346789i	−0.748380	−	0.663270i	$-0.769168\pi$
$647$	3295.05	−	5707.19i	0.200219	−	0.346789i	0.948599	+	0.316481i	$0.102501\pi$
$648$		0			0
$649$	14632.0			0.884985
$650$	28114.9	−	59875.5i	1.69655	−	3.61309i
$651$		0			0
$652$	−53291.4	−	30767.8i	−3.20100	−	1.84810i
$653$	7849.12	−	13595.1i	0.470382	−	0.814726i	−0.529044	−	0.848594i	$-0.677449\pi$
$653$	7849.12	−	13595.1i	0.470382	−	0.814726i	0.999426	+	0.0338683i	$0.0107827\pi$
$654$		0			0
$655$			25647.6i			1.52998i
$656$	513.571	−	296.511i	0.0305664	−	0.0176475i
$657$		0			0
$658$		−	16326.7i		−	0.967295i
$659$	1420.41	+	2460.22i	0.0839624	+	0.145427i	0.904949	−	0.425521i	$-0.139909\pi$
$659$	1420.41	+	2460.22i	0.0839624	+	0.145427i	−0.820986	+	0.570948i	$0.806576\pi$
$660$		0			0
$661$	18029.9	+	10409.5i	1.06094	+	0.612533i	0.925692	−	0.378279i	$-0.123484\pi$
$661$	18029.9	+	10409.5i	1.06094	+	0.612533i	0.135247	+	0.990812i	$0.456817\pi$
$662$	−25292.2			−1.48491
$663$		0			0
$664$	−6748.26			−0.394403
$665$	12116.8	+	6995.63i	0.706569	+	0.407938i
$666$		0			0
$667$	−162.650	−	281.718i	−0.00944202	−	0.0163541i
$668$		−	4549.87i		−	0.263532i
$669$		0			0
$670$	−43298.3	+	24998.3i	−2.49665	+	1.44144i
$671$			5543.36i			0.318925i
$672$		0			0
$673$	15632.3	−	27075.9i	0.895364	−	1.55082i	0.0620102	−	0.998076i	$-0.480249\pi$
$673$	15632.3	−	27075.9i	0.895364	−	1.55082i	0.833354	−	0.552740i	$-0.186418\pi$
$674$	14073.0	+	8125.04i	0.804260	+	0.464340i
$675$		0			0
$676$	−24494.1	−	29509.0i	−1.39361	−	1.67894i
$677$	27953.2			1.58689			0.793447	−	0.608639i	$-0.208284\pi$
$677$	27953.2			1.58689			0.793447	+	0.608639i	$0.208284\pi$
$678$		0			0
$679$	8600.46	−	14896.4i	0.486090	−	0.841933i
$680$	−11149.2	−	19310.9i	−0.628752	−	1.08903i
$681$		0			0
$682$	4445.99	−	2566.89i	0.249627	−	0.144122i
$683$	−30059.7	+	17354.9i	−1.68404	+	0.972282i	−0.725116	+	0.688627i	$0.758214\pi$
$683$	−30059.7	+	17354.9i	−1.68404	+	0.972282i	−0.958926	+	0.283655i	$0.908453\pi$
$684$		0			0
$685$	20432.4	+	35390.0i	1.13968	+	1.97399i
$686$	−17435.2	+	30198.7i	−0.970380	+	1.68075i
$687$		0			0
$688$	36471.1			2.02100
$689$	1096.67	+	12931.8i	0.0606381	+	0.715042i
$690$		0			0
$691$	10271.7	+	5930.39i	0.565492	+	0.326487i	0.755347	−	0.655325i	$-0.227468\pi$
$691$	10271.7	+	5930.39i	0.565492	+	0.326487i	−0.189855	+	0.981812i	$0.560802\pi$
$692$	7957.66	−	13783.1i	0.437146	−	0.757158i
$693$		0			0
$694$			16956.0i			0.927438i
$695$	−25186.6	+	14541.5i	−1.37465	+	0.793655i
$696$		0			0
$697$			136.338i			0.00740916i
$698$	−11582.4	−	20061.4i	−0.628083	−	1.08787i
$699$		0			0
$700$	65235.3	+	37663.6i	3.52237	+	2.03364i
$701$	16100.5			0.867486			0.433743	−	0.901037i	$-0.357193\pi$
$701$	16100.5			0.867486			0.433743	+	0.901037i	$0.357193\pi$
$702$		0			0
$703$	−14147.7			−0.759019
$704$	−3769.90	−	2176.55i	−0.201823	−	0.116523i
$705$		0			0
$706$	4389.69	+	7603.17i	0.234006	+	0.405310i
$707$		−	24528.9i		−	1.30482i
$708$		0			0
$709$	24651.8	−	14232.7i	1.30581	−	0.753910i	0.324416	−	0.945915i	$-0.394832\pi$
$709$	24651.8	−	14232.7i	1.30581	−	0.753910i	0.981394	+	0.192005i	$0.0614990\pi$
$710$			83925.9i			4.43617i
$711$		0			0
$712$	−15297.9	+	26496.8i	−0.805217	+	1.39468i
$713$	−4645.60	−	2682.14i	−0.244010	−	0.140879i
$714$		0			0
$715$	−22991.8	−	10796.0i	−1.20258	−	0.564680i
$716$	−46964.4			−2.45131
$717$		0			0
$718$	−3596.07	+	6228.57i	−0.186914	+	0.323744i
$719$	13911.0	+	24094.6i	0.721550	+	1.24976i	0.960378	+	0.278699i	$0.0899033\pi$
$719$	13911.0	+	24094.6i	0.721550	+	1.24976i	−0.238829	+	0.971062i	$0.576763\pi$
$720$		0			0
$721$	7047.93	−	4069.13i	0.364048	−	0.210183i
$722$	21090.5	−	12176.6i	1.08713	−	0.627654i
$723$		0			0
$724$	−41665.5	−	72166.7i	−2.13879	−	3.70450i
$725$	−320.363	+	554.884i	−0.0164110	+	0.0284247i
$726$		0			0
$727$	−866.153			−0.0441869			−0.0220934	−	0.999756i	$-0.507033\pi$
$727$	−866.153			−0.0441869			−0.0220934	+	0.999756i	$0.507033\pi$
$728$	28312.8	−	19712.6i	1.44140	−	1.00357i
$729$		0			0
$730$	−5812.07	−	3355.60i	−0.294677	−	0.170132i
$731$	−4192.45	+	7261.53i	−0.212125	+	0.367411i
$732$		0			0
$733$		−	23120.1i		−	1.16502i	−0.812823	−	0.582511i	$-0.802070\pi$
$733$		−	23120.1i		−	1.16502i	0.812823	−	0.582511i	$-0.197930\pi$
$734$	47404.7	−	27369.1i	2.38384	−	1.37631i
$735$		0			0
$736$		−	18206.7i		−	0.911831i
$737$	6634.34	+	11491.0i	0.331586	+	0.574324i
$738$		0			0
$739$	17983.1	+	10382.6i	0.895156	+	0.516819i	0.875626	−	0.482990i	$-0.160449\pi$
$739$	17983.1	+	10382.6i	0.895156	+	0.516819i	0.0195308	+	0.999809i	$0.493783\pi$
$740$	−110209.			−5.47482
$741$		0			0
$742$	−21552.7			−1.06634
$743$	−32039.3	−	18497.9i	−1.58198	−	0.913354i	−0.994571	−	0.104061i	$-0.966816\pi$
$743$	−32039.3	−	18497.9i	−1.58198	−	0.913354i	−0.587405	−	0.809293i	$-0.699850\pi$
$744$		0			0
$745$	−9719.90	−	16835.4i	−0.477999	−	0.827919i
$746$		−	2496.19i		−	0.122509i
$747$		0			0
$748$	−9460.95	+	5462.28i	−0.462468	+	0.267006i
$749$			27029.1i			1.31859i
$750$		0			0
$751$	−17214.6	+	29816.5i	−0.836443	+	1.44876i	0.0564080	+	0.998408i	$0.482035\pi$
$751$	−17214.6	+	29816.5i	−0.836443	+	1.44876i	−0.892851	+	0.450353i	$0.851298\pi$
$752$	18356.7	+	10598.2i	0.890159	+	0.513933i
$753$		0			0
$754$	309.532	+	444.575i	0.0149503	+	0.0214728i
$755$	29433.5			1.41880
$756$		0			0
$757$	−2134.44	+	3696.96i	−0.102480	+	0.177501i	−0.912706	−	0.408617i	$-0.866011\pi$
$757$	−2134.44	+	3696.96i	−0.102480	+	0.177501i	0.810226	+	0.586118i	$0.199345\pi$
$758$	−31895.1	−	55244.0i	−1.52834	−	2.64717i
$759$		0			0
$760$	−37468.7	+	21632.6i	−1.78833	+	1.03249i
$761$	−6358.45	+	3671.05i	−0.302883	+	0.174869i	−0.643737	−	0.765247i	$-0.722617\pi$
$761$	−6358.45	+	3671.05i	−0.302883	+	0.174869i	0.340854	+	0.940116i	$0.389284\pi$
$762$		0			0
$763$	−7460.33	−	12921.7i	−0.353974	−	0.613100i
$764$	17957.3	−	31103.0i	0.850359	−	1.47286i
$765$		0			0
$766$	11712.9			0.552484
$767$	14547.9	+	20894.8i	0.684867	+	0.983661i
$768$		0			0
$769$	12755.2	+	7364.23i	0.598134	+	0.345333i	0.768307	−	0.640081i	$-0.221099\pi$
$769$	12755.2	+	7364.23i	0.598134	+	0.345333i	−0.170173	+	0.985414i	$0.554433\pi$
$770$	21090.8	−	36530.4i	0.987092	−	1.70969i
$771$		0			0
$772$			12740.5i			0.593963i
$773$	−8606.05	+	4968.71i	−0.400437	+	0.231193i	−0.686673	−	0.726967i	$-0.740929\pi$
$773$	−8606.05	+	4968.71i	−0.400437	+	0.231193i	0.286235	+	0.958159i	$0.407596\pi$
$774$		0			0
$775$			10565.7i			0.489719i
$776$	26595.2	+	46064.2i	1.23030	+	2.13094i
$777$		0			0
$778$	45780.9	+	26431.6i	2.10967	+	1.21802i
$779$	264.535			0.0121668
$780$		0			0
$781$	22273.3			1.02049
$782$	14416.4	+	8323.29i	0.659243	+	0.380614i
$783$		0			0
$784$	−5304.47	−	9187.61i	−0.241639	−	0.418532i
$785$		−	1328.60i		−	0.0604074i
$786$		0			0
$787$	−31441.1	+	18152.5i	−1.42408	+	0.822194i	−0.996645	−	0.0818508i	$-0.973917\pi$
$787$	−31441.1	+	18152.5i	−1.42408	+	0.822194i	−0.427437	+	0.904045i	$0.640584\pi$
$788$		−	29694.2i		−	1.34240i
$789$		0			0
$790$	16120.3	−	27921.2i	0.725993	−	1.25746i
$791$	−25532.4	−	14741.2i	−1.14770	−	0.662623i
$792$		0			0
$793$	−7916.04	+	5511.49i	−0.354485	+	0.246808i
$794$	−8914.40			−0.398439
$795$		0			0
$796$	16066.9	−	27828.8i	0.715424	−	1.23915i
$797$	4575.37	+	7924.77i	0.203347	+	0.352208i	0.949605	−	0.313449i	$-0.101485\pi$
$797$	4575.37	+	7924.77i	0.203347	+	0.352208i	−0.746258	+	0.665657i	$0.768151\pi$
$798$		0			0
$799$	−4220.29	+	2436.59i	−0.186863	+	0.107885i
$800$	−31056.3	+	17930.4i	−1.37251	+	0.792418i
$801$		0			0
$802$	−12617.6	−	21854.3i	−0.555539	−	0.962221i
$803$	−890.550	+	1542.48i	−0.0391368	+	0.0677869i
$804$		0			0
$805$	−44075.5			−1.92976
$806$	8086.01	+	3796.84i	0.353372	+	0.165928i
$807$		0			0
$808$	65688.6	+	37925.4i	2.86005	+	1.65125i
$809$	15174.9	−	26283.8i	0.659484	−	1.14226i	−0.321265	−	0.946989i	$-0.604108\pi$
$809$	15174.9	−	26283.8i	0.659484	−	1.14226i	0.980749	−	0.195271i	$-0.0625585\pi$
$810$		0			0
$811$		−	4238.72i		−	0.183529i	−0.995781	−	0.0917643i	$-0.970749\pi$
$811$		−	4238.72i		−	0.183529i	0.995781	−	0.0917643i	$-0.0292506\pi$
$812$	−534.244	+	308.446i	−0.0230890	+	0.0133305i
$813$		0			0
$814$			42653.3i			1.83661i
$815$	−35459.3	−	61417.3i	−1.52403	−	2.63970i
$816$		0			0
$817$	14089.4	+	8134.53i	0.603337	+	0.348337i
$818$	56551.4			2.41721
$819$		0			0
$820$	2060.70			0.0877595
$821$	5139.41	+	2967.24i	0.218473	+	0.126136i	0.605243	−	0.796041i	$-0.293076\pi$
$821$	5139.41	+	2967.24i	0.218473	+	0.126136i	−0.386770	+	0.922176i	$0.626409\pi$
$822$		0			0
$823$	−11229.8	−	19450.6i	−0.475633	−	0.823820i	0.523978	−	0.851732i	$-0.324448\pi$
$823$	−11229.8	−	19450.6i	−0.475633	−	0.823820i	−0.999610	+	0.0279120i	$0.991114\pi$
$824$			25165.9i			1.06395i
$825$		0			0
$826$	−36616.8	+	21140.7i	−1.54245	+	0.890533i
$827$			20138.4i			0.846772i	0.905949	+	0.423386i	$0.139159\pi$
$827$			20138.4i			0.846772i	−0.905949	+	0.423386i	$0.860841\pi$
$828$		0			0
$829$	2922.85	−	5062.53i	0.122455	−	0.212098i	−0.798281	−	0.602286i	$-0.794257\pi$
$829$	2922.85	−	5062.53i	0.122455	−	0.212098i	0.920735	+	0.390188i	$0.127590\pi$
$830$	−12433.7	−	7178.58i	−0.519974	−	0.300207i
$831$		0			0
$832$	−640.058	−	7547.54i	−0.0266707	−	0.314500i
$833$	2439.05			0.101450
$834$		0			0
$835$	2621.82	−	4541.12i	0.108661	−	0.188206i
$836$	10598.4	+	18356.9i	0.438459	+	0.759434i
$837$		0			0
$838$	−14354.4	+	8287.49i	−0.591722	+	0.341631i
$839$	−24058.1	+	13889.9i	−0.989961	+	0.571554i	−0.905263	−	0.424852i	$-0.860326\pi$
$839$	−24058.1	+	13889.9i	−0.989961	+	0.571554i	−0.0846986	+	0.996407i	$0.526993\pi$
$840$		0			0
$841$	12191.9	+	21116.9i	0.499892	+	0.865839i
$842$	−33526.1	+	58069.0i	−1.37219	+	2.37671i
$843$		0			0
$844$	−2495.65			−0.101782
$845$	−7442.75	−	43566.7i	−0.303004	−	1.77366i
$846$		0			0
$847$	8088.55	+	4669.92i	0.328130	+	0.189446i
$848$	13990.6	−	24232.4i	0.566556	−	0.981304i
$849$		0			0
$850$		−	32787.9i		−	1.32308i
$851$	38597.3	−	22284.2i	1.55476	−	0.897640i
$852$		0			0
$853$		−	16480.5i		−	0.661526i	−0.943714	−	0.330763i	$-0.892694\pi$
$853$		−	16480.5i		−	0.661526i	0.943714	−	0.330763i	$-0.107306\pi$
$854$	−8009.21	−	13872.4i	−0.320925	−	0.555858i
$855$		0			0
$856$	−72384.2	−	41791.0i	−2.89024	−	1.66868i
$857$	−45445.2			−1.81141			−0.905704	−	0.423910i	$-0.860657\pi$
$857$	−45445.2			−1.81141			−0.905704	+	0.423910i	$0.860657\pi$
$858$		0			0
$859$	−28243.1			−1.12182			−0.560909	−	0.827877i	$-0.689548\pi$
$859$	−28243.1			−1.12182			−0.560909	+	0.827877i	$0.689548\pi$
$860$	109755.	+	63367.1i	4.35188	+	2.51256i
$861$		0			0
$862$	34541.2	+	59827.2i	1.36482	+	2.36395i
$863$			328.319i			0.0129503i	0.999979	+	0.00647514i	$0.00206112\pi$
$863$			328.319i			0.0129503i	−0.999979	+	0.00647514i	$0.997939\pi$
$864$		0			0
$865$	15884.7	−	9171.05i	0.624389	−	0.360491i
$866$			50466.4i			1.98027i
$867$		0			0
$868$	−5086.36	+	8809.84i	−0.198897	+	0.344499i
$869$	−7410.06	−	4278.20i	−0.289262	−	0.167006i
$870$		0			0
$871$	−9813.24	+	20898.9i	−0.381755	+	0.813012i
$872$	46139.1			1.79182
$873$		0			0
$874$	16149.5	−	27971.8i	0.625018	−	1.08256i
$875$	24008.5	+	41584.0i	0.927584	+	1.60662i
$876$		0			0
$877$	36788.7	−	21240.0i	1.41650	−	0.817815i	0.420507	−	0.907289i	$-0.361852\pi$
$877$	36788.7	−	21240.0i	1.41650	−	0.817815i	0.995989	+	0.0894746i	$0.0285188\pi$
$878$	−19606.5	+	11319.8i	−0.753629	+	0.435108i
$879$		0			0
$880$	27381.6	+	47426.4i	1.04890	+	1.81675i
$881$	2610.47	−	4521.47i	0.0998287	−	0.172908i	−0.811785	−	0.583956i	$-0.801504\pi$
$881$	2610.47	−	4521.47i	0.0998287	−	0.172908i	0.911614	+	0.411048i	$0.134837\pi$
$882$		0			0
$883$	−11790.3			−0.449349			−0.224674	−	0.974434i	$-0.572132\pi$
$883$	−11790.3			−0.449349			−0.224674	+	0.974434i	$0.572132\pi$
$884$	−17206.8	−	8079.57i	−0.654670	−	0.307404i
$885$		0			0
$886$	8893.30	+	5134.55i	0.337219	+	0.194694i
$887$	−24676.2	+	42740.4i	−0.934097	+	1.61790i	−0.157861	+	0.987461i	$0.550460\pi$
$887$	−24676.2	+	42740.4i	−0.934097	+	1.61790i	−0.776236	+	0.630443i	$0.782873\pi$
$888$		0			0
$889$			19024.4i			0.717724i
$890$	−56372.8	+	32546.9i	−2.12317	+	1.22581i
$891$		0			0
$892$		−	40823.9i		−	1.53238i
$893$	4727.67	+	8188.56i	0.177162	+	0.306853i
$894$		0			0
$895$	−46874.1	−	27062.8i	−1.75065	−	1.01074i
$896$	28402.7			1.05900
$897$		0			0
$898$	−18040.1			−0.670386
$899$	−74.9355	−	43.2640i	−0.00278002	−	0.00160505i
$900$		0			0
$901$	3216.51	+	5571.16i	0.118932	+	0.205996i
$902$		−	797.536i		−	0.0294402i
$903$		0			0
$904$	78953.9	−	45584.0i	2.90483	−	1.67710i
$905$		−	96037.3i		−	3.52750i
$906$		0			0
$907$	3044.47	−	5273.17i	0.111455	−	0.193046i	−0.804902	−	0.593408i	$-0.797782\pi$
$907$	3044.47	−	5273.17i	0.111455	−	0.193046i	0.916357	+	0.400362i	$0.131116\pi$
$908$	49574.5	+	28621.8i	1.81188	+	1.04609i
$909$		0			0
$910$	73135.8	−	6202.17i	2.66421	−	0.225934i
$911$	30301.7			1.10202			0.551010	−	0.834499i	$-0.314243\pi$
$911$	30301.7			1.10202			0.551010	+	0.834499i	$0.314243\pi$
$912$		0			0
$913$	−1905.14	+	3299.80i	−0.0690590	+	0.119614i
$914$	20329.3	+	35211.4i	0.735704	+	1.27428i
$915$		0			0
$916$	−17289.8	+	9982.27i	−0.623658	+	0.360069i
$917$	−17033.8	+	9834.49i	−0.613421	+	0.354159i
$918$		0			0
$919$	−17347.9	−	30047.4i	−0.622692	−	1.07853i	−0.988982	−	0.148034i	$-0.952705\pi$
$919$	−17347.9	−	30047.4i	−0.622692	−	1.07853i	0.366290	−	0.930501i	$-0.380628\pi$
$920$	68147.3	−	118035.i	2.44212	−	4.22988i
$921$		0			0
$922$	58991.2			2.10713
$923$	22145.2	+	31806.7i	0.789728	+	1.13427i
$924$		0			0
$925$	−76023.1	−	43892.0i	−2.70230	−	1.56017i
$926$	−4370.30	+	7569.59i	−0.155094	+	0.268631i
$927$		0			0
$928$		−	293.681i		−	0.0103885i
$929$	14714.5	−	8495.40i	0.519662	−	0.300027i	−0.217134	−	0.976142i	$-0.569671\pi$
$929$	14714.5	−	8495.40i	0.519662	−	0.300027i	0.736796	+	0.676115i	$0.236338\pi$
$930$		0			0
$931$		−	4732.44i		−	0.166594i
$932$	−36990.2	−	64068.9i	−1.30006	−	2.25177i
$933$		0			0
$934$	−47058.1	−	27169.0i	−1.64860	−	0.951817i
$935$	−12590.3			−0.440372
$936$		0			0
$937$	9307.86			0.324519			0.162260	−	0.986748i	$-0.448122\pi$
$937$	9307.86			0.324519			0.162260	+	0.986748i	$0.448122\pi$
$938$	−33205.1	−	19171.0i	−1.15585	−	0.667330i
$939$		0			0
$940$	36828.0	+	63788.0i	1.27787	+	2.21334i
$941$		−	52285.3i		−	1.81132i	−0.424006	−	0.905659i	$-0.639377\pi$
$941$		−	52285.3i		−	1.81132i	0.424006	−	0.905659i	$-0.360623\pi$
$942$		0			0
$943$	−721.697	+	416.672i	−0.0249222	+	0.0143889i
$944$		−	54892.8i		−	1.89260i
$945$		0			0
$946$	24524.5	−	42477.6i	0.842874	−	1.45990i
$947$	−10694.1	−	6174.26i	−0.366962	−	0.211865i	0.305169	−	0.952298i	$-0.401287\pi$
$947$	−10694.1	−	6174.26i	−0.366962	−	0.211865i	−0.672130	+	0.740433i	$0.734621\pi$
$948$		0			0
$949$	−3088.13	+	261.884i	−0.105632	+	0.00895797i
$950$	−63617.7			−2.17267
$951$		0			0
$952$	8550.23	−	14809.4i	0.291087	−	0.504177i
$953$	12815.5	+	22197.1i	0.435609	+	0.754497i	0.997345	−	0.0728193i	$-0.0231997\pi$
$953$	12815.5	+	22197.1i	0.435609	+	0.754497i	−0.561736	+	0.827317i	$0.689866\pi$
$954$		0			0
$955$	35845.7	−	20695.5i	1.21459	−	0.701247i
$956$	50038.0	−	28889.5i	1.69283	−	0.977356i
$957$		0			0
$958$	19958.6	+	34569.2i	0.673102	+	1.16585i
$959$	−15669.5	+	27140.4i	−0.527627	+	0.913878i
$960$		0			0
$961$	28364.1			0.952104
$962$	−60909.9	+	42408.1i	−2.04139	+	1.42130i
$963$		0			0
$964$	86210.8	+	49773.8i	2.88036	+	1.66297i
$965$	−7341.57	+	12716.0i	−0.244905	+	0.424188i
$966$		0			0
$967$		−	11185.6i		−	0.371981i	−0.982552	−	0.185991i	$-0.940451\pi$
$967$		−	11185.6i		−	0.371981i	0.982552	−	0.185991i	$-0.0595494\pi$
$968$	−25012.2	+	14440.8i	−0.830498	+	0.479488i
$969$		0			0
$970$			113164.i			3.74586i
$971$	−11770.6	−	20387.3i	−0.389019	−	0.673801i	0.603299	−	0.797515i	$-0.293853\pi$
$971$	−11770.6	−	20387.3i	−0.389019	−	0.673801i	−0.992318	+	0.123714i	$0.960519\pi$
$972$		0			0
$973$	−19315.4	−	11151.8i	−0.636408	−	0.367430i
$974$	55321.3			1.81993
$975$		0			0
$976$	20796.3			0.682041
$977$	20956.8	+	12099.4i	0.686251	+	0.396207i	0.802206	−	0.597047i	$-0.203659\pi$
$977$	20956.8	+	12099.4i	0.686251	+	0.396207i	−0.115955	+	0.993254i	$0.536993\pi$
$978$		0			0
$979$	8637.68	+	14960.9i	0.281983	+	0.488409i
$980$		−	36865.2i		−	1.20165i
$981$		0			0
$982$	−39933.7	+	23055.7i	−1.29769	+	0.749224i
$983$		−	33757.4i		−	1.09532i	−0.836702	−	0.547658i	$-0.815520\pi$
$983$		−	33757.4i		−	1.09532i	0.836702	−	0.547658i	$-0.184480\pi$
$984$		0			0
$985$	17111.0	−	29637.1i	0.553504	−	0.958697i
$986$	232.542	+	134.258i	0.00751080	+	0.00433636i
$987$		0			0
$988$	−15676.6	+	33386.1i	−0.504798	+	1.07505i
$989$	−51251.1			−1.64782
$990$		0			0
$991$	−12649.3	+	21909.2i	−0.405466	+	0.702288i	−0.994376	−	0.105911i	$-0.966224\pi$
$991$	−12649.3	+	21909.2i	−0.405466	+	0.702288i	0.588909	+	0.808199i	$0.299558\pi$
$992$	−2421.44	−	4194.06i	−0.0775009	−	0.134236i
$993$		0			0
$994$	−55739.3	+	32181.1i	−1.77862	+	1.02688i
$995$	32072.1	−	18516.8i	1.02186	−	0.589973i
$996$		0			0
$997$	14383.0	+	24912.2i	0.456886	+	0.791350i	0.998794	−	0.0490874i	$-0.0156313\pi$
$997$	14383.0	+	24912.2i	0.456886	+	0.791350i	−0.541908	+	0.840438i	$0.682298\pi$
$998$	−31729.1	+	54956.4i	−1.00638	+	1.74310i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.e.82.1		10
3.2	odd	2		39.4.j.c.4.5	✓	10
12.11	even	2		624.4.bv.h.433.1		10
13.6	odd	12		1521.4.a.bk.1.9		10
13.7	odd	12		1521.4.a.bk.1.2		10
13.10	even	6	inner	117.4.q.e.10.1		10
39.17	odd	6		507.4.b.i.337.9		10
39.20	even	12		507.4.a.r.1.9		10
39.23	odd	6		39.4.j.c.10.5	yes	10
39.32	even	12		507.4.a.r.1.2		10
39.35	odd	6		507.4.b.i.337.2		10
156.23	even	6		624.4.bv.h.49.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.5	✓	10	3.2	odd	2
39.4.j.c.10.5	yes	10	39.23	odd	6
117.4.q.e.10.1		10	13.10	even	6	inner
117.4.q.e.82.1		10	1.1	even	1	trivial
507.4.a.r.1.2		10	39.32	even	12
507.4.a.r.1.9		10	39.20	even	12
507.4.b.i.337.2		10	39.35	odd	6
507.4.b.i.337.9		10	39.17	odd	6
624.4.bv.h.49.5		10	156.23	even	6
624.4.bv.h.433.1		10	12.11	even	2
1521.4.a.bk.1.2		10	13.7	odd	12
1521.4.a.bk.1.9		10	13.6	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.36942 - 2.52268i) q^{2} +(8.72787 + 15.1171i) q^{4} +20.1174i q^{5} +(-13.3609 + 7.71395i) q^{7} -47.7076i q^{8} +(50.7498 - 87.9013i) q^{10} +(-23.3283 - 13.4686i) q^{11} +(-3.96071 - 46.7045i) q^{13} +77.8394 q^{14} +(-50.5283 + 87.5177i) q^{16} +(-11.6167 - 20.1207i) q^{17} +(-39.0399 + 22.5397i) q^{19} +(-304.117 + 175.582i) q^{20} +(67.9540 + 117.700i) q^{22} +(71.0050 - 122.984i) q^{23} -279.710 q^{25} +(-100.515 + 214.063i) q^{26} +(-233.225 - 134.653i) q^{28} +(1.14534 - 1.98379i) q^{29} -37.7740i q^{31} +(111.031 - 64.1035i) q^{32} +117.221i q^{34} +(-155.185 - 268.787i) q^{35} +(271.793 + 156.920i) q^{37} +227.442 q^{38} +959.753 q^{40} +(-5.08201 - 2.93410i) q^{41} +(-180.449 - 312.547i) q^{43} -470.209i q^{44} +(-620.501 + 358.246i) q^{46} -209.748i q^{47} +(-52.4900 + 90.9154i) q^{49} +(1222.17 + 705.619i) q^{50} +(671.469 - 467.505i) q^{52} -276.886 q^{53} +(270.953 - 469.305i) q^{55} +(368.014 + 637.419i) q^{56} +(-10.0089 + 5.77866i) q^{58} +(-470.415 + 271.594i) q^{59} +(-102.894 - 178.218i) q^{61} +(-95.2917 + 165.050i) q^{62} +161.602 q^{64} +(939.573 - 79.6791i) q^{65} +(-426.585 - 246.289i) q^{67} +(202.778 - 351.222i) q^{68} +1565.93i q^{70} +(-716.081 + 413.430i) q^{71} -66.1205i q^{73} +(-791.718 - 1371.30i) q^{74} +(-681.470 - 393.447i) q^{76} +415.584 q^{77} +317.642 q^{79} +(-1760.63 - 1016.50i) q^{80} +(14.8036 + 25.6406i) q^{82} -141.450i q^{83} +(404.777 - 233.698i) q^{85} +1820.86i q^{86} +(-642.555 + 1112.94i) q^{88} +(-555.399 - 320.660i) q^{89} +(413.195 + 593.464i) q^{91} +2478.89 q^{92} +(-529.129 + 916.478i) q^{94} +(-453.440 - 785.381i) q^{95} +(-965.551 + 557.461i) q^{97} +(458.702 - 264.832i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29}+ \cdots - 180 q^{98}+O(q^{100}) \) 10 * q + 30 * q^4 + 30 * q^7 + 40 * q^10 - 60 * q^11 + 25 * q^13 + 60 * q^14 - 250 * q^16 - 105 * q^17 + 180 * q^19 - 510 * q^20 - 290 * q^22 + 60 * q^23 - 960 * q^25 + 30 * q^26 + 150 * q^28 + 495 * q^29 - 1440 * q^32 - 60 * q^35 - 405 * q^37 + 1380 * q^38 + 2000 * q^40 - 1065 * q^41 - 370 * q^43 - 390 * q^46 + 775 * q^49 + 4320 * q^50 + 2940 * q^52 - 330 * q^53 - 260 * q^55 + 2670 * q^56 + 2040 * q^58 - 780 * q^59 - 1375 * q^61 + 780 * q^62 - 3140 * q^64 - 1605 * q^65 + 1590 * q^67 + 600 * q^68 - 1620 * q^71 - 2190 * q^74 - 5190 * q^76 + 4320 * q^77 + 1100 * q^79 - 8430 * q^80 - 2390 * q^82 + 525 * q^85 + 3170 * q^88 - 2040 * q^89 + 4770 * q^91 + 1740 * q^92 - 3230 * q^94 + 1380 * q^95 - 3750 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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