LMFDB - Embedded newform 117.4.q.e.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(10,117)]

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, 5]))

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

//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);

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: 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:	$10$
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			10.1
Root			$5.04537i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.4.q.e.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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	−0.546298	+	0.837591i	$0.683963\pi$
$2$	−4.36942	+	2.52268i	−1.54482	+	0.891903i	−0.998524	+	0.0543124i	$0.982703\pi$
$3$		0			0
$3$		0			0
$4$	8.72787	−	15.1171i	1.09098	−	1.88964i
$5$		−	20.1174i		−	1.79935i	−0.436556	−	0.899677i	$-0.643802\pi$
$5$		−	20.1174i		−	1.79935i	0.436556	−	0.899677i	$-0.356198\pi$
$6$		0			0
$7$	−13.3609	−	7.71395i	−0.721423	−	0.416514i	0.0938530	−	0.995586i	$-0.470082\pi$
$7$	−13.3609	−	7.71395i	−0.721423	−	0.416514i	−0.815276	+	0.579072i	$0.803415\pi$
$8$			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	−0.784396	−	0.620261i	$-0.787027\pi$
$11$	−23.3283	+	13.4686i	−0.639432	+	0.369176i	0.144964	+	0.989437i	$0.453693\pi$
$12$		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	−0.936915	−	0.349556i	$-0.886332\pi$
$17$	−11.6167	+	20.1207i	−0.165733	+	0.287059i	0.771182	+	0.636615i	$0.219666\pi$
$18$		0			0
$19$	−39.0399	−	22.5397i	−0.471388	−	0.272156i	0.245433	−	0.969414i	$-0.421070\pi$
$19$	−39.0399	−	22.5397i	−0.471388	−	0.272156i	−0.716821	+	0.697258i	$0.754403\pi$
$20$	−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	0.984595	+	0.174848i	$0.0559434\pi$
$23$	71.0050	+	122.984i	0.643720	+	1.11496i	−0.340875	+	0.940109i	$0.610723\pi$
$24$		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	0.869669	−	0.493635i	$-0.164332\pi$
$29$	1.14534	+	1.98379i	0.00733394	+	0.0127028i	−0.862335	+	0.506338i	$0.830999\pi$
$30$		0			0
$31$			37.7740i			0.218852i	0.993995	+	0.109426i	$0.0349012\pi$
$31$			37.7740i			0.218852i	−0.993995	+	0.109426i	$0.965099\pi$
$32$	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	0.245393	−	0.969424i	$-0.421083\pi$
$37$	271.793	−	156.920i	1.20764	−	0.697228i	0.962242	+	0.272195i	$0.0877497\pi$
$38$	227.442			0.970947
$39$		0			0
$40$	959.753			3.79376
$41$	−5.08201	+	2.93410i	−0.0193580	+	0.0111763i	−0.509648	−	0.860383i	$-0.670224\pi$
$41$	−5.08201	+	2.93410i	−0.0193580	+	0.0111763i	0.490290	+	0.871559i	$0.336891\pi$
$42$		0			0
$43$	−180.449	+	312.547i	−0.639958	+	1.10844i	0.345483	+	0.938425i	$0.387715\pi$
$43$	−180.449	+	312.547i	−0.639958	+	1.10844i	−0.985441	+	0.170015i	$0.945618\pi$
$44$			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	$0.105525\pi$
$47$			209.748i			0.650956i	−0.945550	+	0.325478i	$0.894475\pi$
$48$		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	−0.118744	−	0.992925i	$-0.537887\pi$
$59$	−470.415	−	271.594i	−1.03801	−	0.599298i	−0.919270	+	0.393627i	$0.871220\pi$
$60$		0			0
$61$	−102.894	+	178.218i	−0.215971	+	0.374073i	−0.953573	−	0.301163i	$-0.902625\pi$
$61$	−102.894	+	178.218i	−0.215971	+	0.374073i	0.737601	+	0.675236i	$0.235958\pi$
$62$	−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	−0.835666	−	0.549237i	$-0.814918\pi$
$67$	−426.585	+	246.289i	−0.777846	+	0.449090i	0.0578203	+	0.998327i	$0.481585\pi$
$68$	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	−0.237073	−	0.971492i	$-0.576188\pi$
$71$	−716.081	−	413.430i	−1.19695	−	0.691057i	−0.959873	+	0.280435i	$0.909521\pi$
$72$		0			0
$73$			66.1205i			0.106011i	0.998594	+	0.0530056i	$0.0168801\pi$
$73$			66.1205i			0.106011i	−0.998594	+	0.0530056i	$0.983120\pi$
$74$	−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	$0.0298155\pi$
$83$			141.450i			0.187063i	−0.995616	+	0.0935313i	$0.970184\pi$
$84$		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	−0.792843	−	0.609426i	$-0.791400\pi$
$89$	−555.399	+	320.660i	−0.661486	+	0.381909i	0.131357	+	0.991335i	$0.458067\pi$
$90$		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	−0.0992962	−	0.995058i	$-0.531659\pi$
$97$	−965.551	−	557.461i	−1.01069	−	0.583522i	−0.911394	+	0.411536i	$0.864992\pi$
$98$	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	−0.930082	−	0.367351i	$-0.880265\pi$
$101$	−794.953	−	1376.90i	−0.783177	−	1.35650i	0.146906	−	0.989150i	$-0.453069\pi$
$102$		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	0.925073	+	0.379788i	$0.124003\pi$
$107$	875.982	+	1517.25i	0.791443	+	1.37082i	−0.133630	+	0.991031i	$0.542663\pi$
$108$		0			0
$109$		−	967.122i		−	0.849848i	−0.905229	−	0.424924i	$-0.860301\pi$
$109$		−	967.122i		−	0.849848i	0.905229	−	0.424924i	$-0.139699\pi$
$110$	−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	−0.127120	−	0.991887i	$-0.540573\pi$
$113$	955.487	−	1654.95i	0.795439	−	1.37774i	0.922560	−	0.385854i	$-0.126093\pi$
$114$		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	0.996942	−	0.0781488i	$-0.0249009\pi$
$127$	616.557	+	1067.91i	0.430792	+	0.746154i	−0.566150	+	0.824302i	$0.691568\pi$
$128$	−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	0.935446	−	0.353470i	$-0.114998\pi$
$137$	1759.18	+	1015.66i	1.09706	+	0.633385i	0.161609	+	0.986855i	$0.448332\pi$
$138$		0			0
$139$	722.832	−	1251.98i	0.441078	−	0.763969i	−0.556692	−	0.830719i	$-0.687930\pi$
$139$	722.832	−	1251.98i	0.441078	−	0.763969i	0.997770	+	0.0667498i	$0.0212629\pi$
$140$	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	0.251975	−	0.967734i	$-0.418920\pi$
$149$	−836.856	−	483.159i	−0.460120	−	0.265650i	−0.712095	+	0.702083i	$0.752253\pi$
$150$		0			0
$151$			1463.09i			0.788505i	0.919002	+	0.394252i	$0.128996\pi$
$151$			1463.09i			0.788505i	−0.919002	+	0.394252i	$0.871004\pi$
$152$	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	−0.467707	−	0.883883i	$-0.654920\pi$
$163$	−3052.95	−	1762.62i	−1.46703	−	0.846988i	−0.999319	+	0.0368953i	$0.988253\pi$
$164$			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	−0.551386	−	0.834250i	$-0.685901\pi$
$167$	−225.731	+	130.326i	−0.104596	+	0.0603887i	0.446789	+	0.894639i	$0.352567\pi$
$168$		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	−0.948640	−	0.316359i	$-0.897540\pi$
$173$	−455.876	+	789.601i	−0.200345	+	0.347007i	0.748295	+	0.663366i	$0.230873\pi$
$174$		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	−0.997346	−	0.0728016i	$-0.976806\pi$
$179$	−1345.24	−	2330.03i	−0.561721	−	0.972930i	0.435625	−	0.900128i	$-0.356527\pi$
$180$		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	−0.992412	−	0.122958i	$-0.960762\pi$
$191$	−1028.74	+	1781.82i	−0.389721	+	0.675017i	0.602691	+	0.797975i	$0.294095\pi$
$192$		0			0
$193$	632.089	−	364.937i	0.235745	−	0.136107i	−0.377475	−	0.926020i	$-0.623207\pi$
$193$	632.089	−	364.937i	0.235745	−	0.136107i	0.613219	+	0.789913i	$0.289874\pi$
$194$	5625.20			2.08178
$195$		0			0
$196$	−1832.50			−0.667822
$197$	−1473.21	+	850.557i	−0.532801	+	0.307613i	−0.742156	−	0.670227i	$-0.766197\pi$
$197$	−1473.21	+	850.557i	−0.532801	+	0.307613i	0.209355	+	0.977840i	$0.432863\pi$
$198$		0			0
$199$	−920.440	+	1594.25i	−0.327881	+	0.567906i	−0.982091	−	0.188407i	$-0.939668\pi$
$199$	−920.440	+	1594.25i	−0.327881	+	0.567906i	0.654211	+	0.756312i	$0.273001\pi$
$200$		−	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	0.854128	−	0.520063i	$-0.174091\pi$
$211$	−71.4850	−	123.816i	−0.0233234	−	0.0403972i	−0.877452	+	0.479665i	$0.840758\pi$
$212$	−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	−0.772263	−	0.635303i	$-0.780875\pi$
$223$	−2025.39	+	1169.36i	−0.608205	+	0.351148i	0.164057	+	0.986451i	$0.447542\pi$
$224$	−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	0.853986	−	0.520297i	$-0.174179\pi$
$227$	2840.01	+	1639.68i	0.830388	+	0.479425i	−0.0235973	+	0.999722i	$0.507512\pi$
$228$		0			0
$229$		−	1143.72i		−	0.330041i	−0.986290	−	0.165021i	$-0.947231\pi$
$229$		−	1143.72i		−	0.330041i	0.986290	−	0.165021i	$-0.0527690\pi$
$230$	−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	$0.147837\pi$
$239$			3310.03i			0.895849i	−0.894072	+	0.447924i	$0.852163\pi$
$240$		0			0
$241$	4938.82	+	2851.43i	1.32007	+	0.762145i	0.983740	−	0.179598i	$-0.0574798\pi$
$241$	4938.82	+	2851.43i	1.32007	+	0.762145i	0.336333	+	0.941743i	$0.390813\pi$
$242$		−	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	−0.508297	−	0.861182i	$-0.669725\pi$
$251$	1955.12	−	3386.36i	0.491657	−	0.851574i	0.999954	+	0.00960748i	$0.00305820\pi$
$252$		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	−0.884567	−	0.466413i	$-0.845546\pi$
$257$	−3486.40	−	6038.63i	−0.846209	−	1.46568i	0.0383576	−	0.999264i	$-0.487787\pi$
$258$		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	0.882064	−	0.471129i	$-0.156153\pi$
$263$	140.845	+	243.951i	0.0330224	+	0.0571965i	−0.849042	+	0.528326i	$0.822820\pi$
$264$		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	−0.508877	−	0.860839i	$-0.669939\pi$
$269$	2166.56	−	3752.60i	0.491070	−	0.850558i	0.999947	+	0.0102813i	$0.00327270\pi$
$270$		0			0
$271$	371.175	−	214.298i	0.0832003	−	0.0480357i	−0.457823	−	0.889044i	$-0.651371\pi$
$271$	371.175	−	214.298i	0.0832003	−	0.0480357i	0.541023	+	0.841008i	$0.318037\pi$
$272$	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	0.272313	−	0.962209i	$-0.412211\pi$
$277$	4469.37	−	7741.18i	0.969454	−	1.67914i	0.697140	−	0.716935i	$-0.254455\pi$
$278$			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	$-0.973757\pi$
$281$		−	775.819i		−	0.164703i	0.996603	−	0.0823514i	$-0.0262430\pi$
$282$		0			0
$283$	−2007.27	−	3476.69i	−0.421624	−	0.730274i	0.574475	−	0.818522i	$-0.305206\pi$
$283$	−2007.27	−	3476.69i	−0.421624	−	0.730274i	−0.996098	+	0.0882484i	$0.971873\pi$
$284$	−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	0.00679458	−	0.999977i	$-0.497837\pi$
$293$	−4292.21	−	2478.11i	−0.855814	−	0.494104i	−0.862608	+	0.505873i	$0.831171\pi$
$294$		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	$-0.882080\pi$
$307$		−	3894.90i		−	0.724084i	0.932162	−	0.362042i	$-0.117920\pi$
$308$	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	$0.206521\pi$
$317$			6820.62i			1.20847i	−0.796807	+	0.604233i	$0.793479\pi$
$318$		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	0.815088	−	0.579337i	$-0.196688\pi$
$331$	4341.35	+	2506.48i	0.720913	+	0.416219i	−0.0941759	+	0.995556i	$0.530022\pi$
$332$	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	−0.966231	−	0.257677i	$-0.917043\pi$
$347$	−1680.36	+	2910.46i	−0.259960	+	0.450265i	0.706271	+	0.707942i	$0.250376\pi$
$348$		0			0
$349$	3976.20	−	2295.66i	0.609859	−	0.352102i	−0.163051	−	0.986618i	$-0.552134\pi$
$349$	3976.20	−	2295.66i	0.609859	−	0.352102i	0.772910	+	0.634515i	$0.218800\pi$
$350$	−21772.4			−3.32510
$351$		0			0
$352$	−3453.54			−0.522938
$353$	−1506.96	+	870.044i	−0.227216	+	0.131183i	−0.609287	−	0.792950i	$-0.708544\pi$
$353$	−1506.96	+	870.044i	−0.227216	+	0.131183i	0.382071	+	0.924133i	$0.375211\pi$
$354$		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	$0.0334150\pi$
$359$			1425.49i			0.209567i	−0.994495	+	0.104784i	$0.966585\pi$
$360$		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	−0.936708	−	0.350111i	$-0.886144\pi$
$367$	−5424.61	−	9395.69i	−0.771559	−	1.33638i	0.165149	−	0.986269i	$-0.447189\pi$
$368$	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	−0.848345	−	0.529444i	$-0.822401\pi$
$373$	247.374	−	428.465i	0.0343393	−	0.0594774i	0.882684	+	0.469966i	$0.155734\pi$
$374$	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	0.484163	−	0.874978i	$-0.339124\pi$
$379$	10949.4	−	6321.66i	1.48400	−	0.856786i	0.999835	+	0.0181912i	$0.00579076\pi$
$380$	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	0.359855	−	0.933008i	$-0.382826\pi$
$383$	−2010.48	−	1160.75i	−0.268227	−	0.154861i	−0.628082	+	0.778147i	$0.716160\pi$
$384$		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	0.593592	−	0.804766i	$-0.297709\pi$
$397$	1530.14	+	883.424i	0.193439	+	0.111682i	−0.400152	+	0.916449i	$0.631043\pi$
$398$		−	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	−0.205424	−	0.978673i	$-0.565857\pi$
$401$	4331.55	−	2500.82i	0.539420	−	0.311434i	0.744844	+	0.667239i	$0.232524\pi$
$402$		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	−0.219025	−	0.975719i	$-0.570288\pi$
$409$	−9706.92	−	5604.29i	−1.17354	−	0.677541i	−0.954510	+	0.298178i	$0.903621\pi$
$410$	−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	0.945753	−	0.324885i	$-0.105326\pi$
$419$	1642.59	+	2845.06i	0.191518	+	0.331719i	−0.754236	+	0.656604i	$0.771992\pi$
$420$		0			0
$421$			13289.9i			1.53850i	0.638948	+	0.769250i	$0.279370\pi$
$421$			13289.9i			1.53850i	−0.638948	+	0.769250i	$0.720630\pi$
$422$	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	−0.984557	−	0.175064i	$-0.943987\pi$
$431$	−11857.8	+	6846.13i	−1.32523	+	0.765119i	−0.340668	+	0.940184i	$0.610653\pi$
$432$		0			0
$433$	−5001.26	+	8662.43i	−0.555070	+	0.961409i	0.442829	+	0.896606i	$0.353975\pi$
$433$	−5001.26	+	8662.43i	−0.555070	+	0.961409i	−0.997898	+	0.0648023i	$0.979358\pi$
$434$			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	0.961828	−	0.273656i	$-0.0882329\pi$
$439$	2243.60	+	3886.04i	0.243921	+	0.422484i	−0.717907	+	0.696139i	$0.754900\pi$
$440$	−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	0.653827	−	0.756644i	$-0.273162\pi$
$449$	3096.55	+	1787.79i	0.325468	+	0.187909i	−0.328359	+	0.944553i	$0.606496\pi$
$450$		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	−0.812672	−	0.582721i	$-0.801988\pi$
$457$	−6978.95	+	4029.30i	−0.714358	+	0.412435i	0.0983147	+	0.995155i	$0.468655\pi$
$458$	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	−0.108025	−	0.994148i	$-0.534453\pi$
$461$	−10125.7	−	5846.07i	−1.02300	−	0.590626i	−0.914970	+	0.403522i	$0.867786\pi$
$462$		0			0
$463$			1732.40i			0.173891i	0.996213	+	0.0869455i	$0.0277106\pi$
$463$			1732.40i			0.173891i	−0.996213	+	0.0869455i	$0.972289\pi$
$464$	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	−0.789824	−	0.613334i	$-0.789828\pi$
$479$	−6851.68	+	3955.82i	−0.653572	+	0.377340i	0.136251	+	0.990674i	$0.456495\pi$
$480$		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	−0.0117307	−	0.999931i	$-0.503734\pi$
$487$	−9495.78	−	5482.39i	−0.883562	−	0.510125i	−0.871831	+	0.489806i	$0.837067\pi$
$488$	−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	0.995940	−	0.0900157i	$-0.0286917\pi$
$491$	4569.69	+	7914.93i	0.420014	+	0.727486i	−0.575926	+	0.817502i	$0.695358\pi$
$492$		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	$0.190806\pi$
$499$			12577.5i			1.12835i	−0.825655	+	0.564175i	$0.809194\pi$
$500$	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	−0.409092	−	0.912493i	$-0.634155\pi$
$503$	6607.30	−	11444.2i	0.585696	−	1.01446i	0.994788	−	0.101962i	$-0.0325120\pi$
$504$		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	0.656454	−	0.754366i	$-0.272055\pi$
$509$	18809.9	−	10859.9i	1.63798	−	0.945689i	0.981527	−	0.191323i	$-0.0612779\pi$
$510$		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	−0.995907	−	0.0903788i	$-0.971192\pi$
$523$	−6891.98	−	11937.3i	−0.576224	−	0.998049i	0.419683	−	0.907671i	$-0.362141\pi$
$524$	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	$0.00575061\pi$
$541$			454.638i			0.0361302i	−0.999837	+	0.0180651i	$0.994249\pi$
$542$	−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	−0.652172	−	0.758071i	$-0.726142\pi$
$557$	−4229.61	+	2441.97i	−0.321749	+	0.185762i	0.330423	+	0.943833i	$0.392809\pi$
$558$		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	0.220793	+	0.975321i	$0.429136\pi$
$563$	−9808.67	+	16989.1i	−0.734256	+	1.27177i	−0.955049	+	0.296448i	$0.904198\pi$
$564$		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	0.694855	−	0.719150i	$-0.255469\pi$
$569$	−3737.59	−	6473.70i	−0.275374	−	0.476963i	−0.970230	+	0.242187i	$0.922135\pi$
$570$		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	$-0.842851\pi$
$577$		−	13136.1i		−	0.947771i	0.880587	−	0.473885i	$-0.157149\pi$
$578$	−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	0.360756	−	0.932660i	$-0.382519\pi$
$587$	19183.1	−	11075.3i	1.34884	−	0.778754i	0.988085	+	0.153907i	$0.0491855\pi$
$588$		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	$0.289100\pi$
$593$			22770.3i			1.57684i	−0.615138	+	0.788419i	$0.710900\pi$
$594$		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	−0.790499	−	0.612464i	$-0.790179\pi$
$601$	−13638.4	−	23622.4i	−0.925658	−	1.60329i	−0.135160	−	0.990824i	$-0.543155\pi$
$602$	−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	−0.992004	−	0.126209i	$-0.959719\pi$
$607$	−5783.08	+	10016.6i	−0.386701	+	0.669787i	0.605302	+	0.795996i	$0.293052\pi$
$608$	−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	−0.994041	−	0.109006i	$-0.965233\pi$
$613$	−21197.3	+	12238.3i	−1.39666	+	0.806362i	−0.402619	+	0.915368i	$0.631900\pi$
$614$	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	0.429969	−	0.902844i	$-0.358525\pi$
$617$	−2098.62	−	1211.64i	−0.136933	−	0.0790581i	−0.566901	+	0.823786i	$0.691858\pi$
$618$		0			0
$619$			17223.4i			1.11836i	0.829045	+	0.559182i	$0.188885\pi$
$619$			17223.4i			1.11836i	−0.829045	+	0.559182i	$0.811115\pi$
$620$	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	0.225784	−	0.974177i	$-0.427506\pi$
$631$	−8004.31	−	4621.29i	−0.504987	−	0.291554i	−0.730771	+	0.682623i	$0.760839\pi$
$632$			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	−0.630165	−	0.776461i	$-0.717013\pi$
$641$	5799.42	−	10044.9i	0.357353	−	0.618953i	0.987518	+	0.157508i	$0.0503461\pi$
$642$		0			0
$643$	21965.8	+	12682.0i	1.34720	+	0.777804i	0.987852	−	0.155401i	$-0.0496669\pi$
$643$	21965.8	+	12682.0i	1.34720	+	0.777804i	0.359345	+	0.933205i	$0.383000\pi$
$644$	−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	0.948599	−	0.316481i	$-0.102501\pi$
$647$	3295.05	+	5707.19i	0.200219	+	0.346789i	−0.748380	+	0.663270i	$0.769168\pi$
$648$		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	0.999426	−	0.0338683i	$-0.0107827\pi$
$653$	7849.12	+	13595.1i	0.470382	+	0.814726i	−0.529044	+	0.848594i	$0.677449\pi$
$654$		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	−0.820986	−	0.570948i	$-0.806576\pi$
$659$	1420.41	−	2460.22i	0.0839624	−	0.145427i	0.904949	+	0.425521i	$0.139909\pi$
$660$		0			0
$661$	18029.9	−	10409.5i	1.06094	−	0.612533i	0.135247	−	0.990812i	$-0.456817\pi$
$661$	18029.9	−	10409.5i	1.06094	−	0.612533i	0.925692	+	0.378279i	$0.123484\pi$
$662$	−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	0.833354	+	0.552740i	$0.186418\pi$
$673$	15632.3	+	27075.9i	0.895364	+	1.55082i	0.0620102	+	0.998076i	$0.480249\pi$
$674$	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	−0.958926	−	0.283655i	$-0.908453\pi$
$683$	−30059.7	−	17354.9i	−1.68404	−	0.972282i	−0.725116	−	0.688627i	$-0.758214\pi$
$684$		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	−0.189855	−	0.981812i	$-0.560802\pi$
$691$	10271.7	−	5930.39i	0.565492	−	0.326487i	0.755347	+	0.655325i	$0.227468\pi$
$692$	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	0.981394	−	0.192005i	$-0.0614990\pi$
$709$	24651.8	+	14232.7i	1.30581	+	0.753910i	0.324416	+	0.945915i	$0.394832\pi$
$710$		−	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	−0.238829	−	0.971062i	$-0.576763\pi$
$719$	13911.0	−	24094.6i	0.721550	−	1.24976i	0.960378	−	0.278699i	$-0.0899033\pi$
$720$		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	$0.197930\pi$
$733$			23120.1i			1.16502i	−0.812823	+	0.582511i	$0.802070\pi$
$734$	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	0.0195308	−	0.999809i	$-0.493783\pi$
$739$	17983.1	−	10382.6i	0.895156	−	0.516819i	0.875626	+	0.482990i	$0.160449\pi$
$740$	−110209.			−5.47482
$741$		0			0
$742$	−21552.7			−1.06634
$743$	−32039.3	+	18497.9i	−1.58198	+	0.913354i	−0.587405	+	0.809293i	$0.699850\pi$
$743$	−32039.3	+	18497.9i	−1.58198	+	0.913354i	−0.994571	+	0.104061i	$0.966816\pi$
$744$		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	−0.892851	−	0.450353i	$-0.851298\pi$
$751$	−17214.6	−	29816.5i	−0.836443	−	1.44876i	0.0564080	−	0.998408i	$-0.482035\pi$
$752$	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	0.810226	−	0.586118i	$-0.199345\pi$
$757$	−2134.44	−	3696.96i	−0.102480	−	0.177501i	−0.912706	+	0.408617i	$0.866011\pi$
$758$	−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	0.340854	−	0.940116i	$-0.389284\pi$
$761$	−6358.45	−	3671.05i	−0.302883	−	0.174869i	−0.643737	+	0.765247i	$0.722617\pi$
$762$		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	−0.170173	−	0.985414i	$-0.554433\pi$
$769$	12755.2	−	7364.23i	0.598134	−	0.345333i	0.768307	+	0.640081i	$0.221099\pi$
$770$	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	0.286235	−	0.958159i	$-0.407596\pi$
$773$	−8606.05	−	4968.71i	−0.400437	−	0.231193i	−0.686673	+	0.726967i	$0.740929\pi$
$774$		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	−0.427437	−	0.904045i	$-0.640584\pi$
$787$	−31441.1	−	18152.5i	−1.42408	−	0.822194i	−0.996645	+	0.0818508i	$0.973917\pi$
$788$			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	−0.746258	−	0.665657i	$-0.768151\pi$
$797$	4575.37	−	7924.77i	0.203347	−	0.352208i	0.949605	+	0.313449i	$0.101485\pi$
$798$		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	0.980749	+	0.195271i	$0.0625585\pi$
$809$	15174.9	+	26283.8i	0.659484	+	1.14226i	−0.321265	+	0.946989i	$0.604108\pi$
$810$		0			0
$811$			4238.72i			0.183529i	0.995781	+	0.0917643i	$0.0292506\pi$
$811$			4238.72i			0.183529i	−0.995781	+	0.0917643i	$0.970749\pi$
$812$	−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	−0.386770	−	0.922176i	$-0.626409\pi$
$821$	5139.41	−	2967.24i	0.218473	−	0.126136i	0.605243	+	0.796041i	$0.293076\pi$
$822$		0			0
$823$	−11229.8	+	19450.6i	−0.475633	+	0.823820i	−0.999610	−	0.0279120i	$-0.991114\pi$
$823$	−11229.8	+	19450.6i	−0.475633	+	0.823820i	0.523978	+	0.851732i	$0.324448\pi$
$824$		−	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	$-0.860841\pi$
$827$		−	20138.4i		−	0.846772i	0.905949	−	0.423386i	$-0.139159\pi$
$828$		0			0
$829$	2922.85	+	5062.53i	0.122455	+	0.212098i	0.920735	−	0.390188i	$-0.127590\pi$
$829$	2922.85	+	5062.53i	0.122455	+	0.212098i	−0.798281	+	0.602286i	$0.794257\pi$
$830$	−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	−0.0846986	−	0.996407i	$-0.526993\pi$
$839$	−24058.1	−	13889.9i	−0.989961	−	0.571554i	−0.905263	+	0.424852i	$0.860326\pi$
$840$		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	$0.107306\pi$
$853$			16480.5i			0.661526i	−0.943714	+	0.330763i	$0.892694\pi$
$854$	−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	$-0.997939\pi$
$863$		−	328.319i		−	0.0129503i	0.999979	−	0.00647514i	$-0.00206112\pi$
$864$		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	0.995989	−	0.0894746i	$-0.0285188\pi$
$877$	36788.7	+	21240.0i	1.41650	+	0.817815i	0.420507	+	0.907289i	$0.361852\pi$
$878$	−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	0.911614	−	0.411048i	$-0.134837\pi$
$881$	2610.47	+	4521.47i	0.0998287	+	0.172908i	−0.811785	+	0.583956i	$0.801504\pi$
$882$		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	−0.776236	−	0.630443i	$-0.782873\pi$
$887$	−24676.2	−	42740.4i	−0.934097	−	1.61790i	−0.157861	−	0.987461i	$-0.550460\pi$
$888$		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	0.916357	−	0.400362i	$-0.131116\pi$
$907$	3044.47	+	5273.17i	0.111455	+	0.193046i	−0.804902	+	0.593408i	$0.797782\pi$
$908$	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	0.366290	+	0.930501i	$0.380628\pi$
$919$	−17347.9	+	30047.4i	−0.622692	+	1.07853i	−0.988982	+	0.148034i	$0.952705\pi$
$920$	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	0.736796	−	0.676115i	$-0.236338\pi$
$929$	14714.5	+	8495.40i	0.519662	+	0.300027i	−0.217134	+	0.976142i	$0.569671\pi$
$930$		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	$0.360623\pi$
$941$			52285.3i			1.81132i	−0.424006	+	0.905659i	$0.639377\pi$
$942$		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	−0.672130	−	0.740433i	$-0.734621\pi$
$947$	−10694.1	+	6174.26i	−0.366962	+	0.211865i	0.305169	+	0.952298i	$0.401287\pi$
$948$		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	−0.561736	−	0.827317i	$-0.689866\pi$
$953$	12815.5	−	22197.1i	0.435609	−	0.754497i	0.997345	+	0.0728193i	$0.0231997\pi$
$954$		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	$0.0595494\pi$
$967$			11185.6i			0.371981i	−0.982552	+	0.185991i	$0.940451\pi$
$968$	−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	−0.992318	−	0.123714i	$-0.960519\pi$
$971$	−11770.6	+	20387.3i	−0.389019	+	0.673801i	0.603299	+	0.797515i	$0.293853\pi$
$972$		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	−0.115955	−	0.993254i	$-0.536993\pi$
$977$	20956.8	−	12099.4i	0.686251	−	0.396207i	0.802206	+	0.597047i	$0.203659\pi$
$978$		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	$0.184480\pi$
$983$			33757.4i			1.09532i	−0.836702	+	0.547658i	$0.815520\pi$
$984$		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	0.588909	−	0.808199i	$-0.299558\pi$
$991$	−12649.3	−	21909.2i	−0.405466	−	0.702288i	−0.994376	+	0.105911i	$0.966224\pi$
$992$	−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	−0.541908	−	0.840438i	$-0.682298\pi$
$997$	14383.0	−	24912.2i	0.456886	−	0.791350i	0.998794	+	0.0490874i	$0.0156313\pi$
$998$	−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.10.1		10
3.2	odd	2		39.4.j.c.10.5	yes	10
12.11	even	2		624.4.bv.h.49.5		10
13.2	odd	12		1521.4.a.bk.1.2		10
13.4	even	6	inner	117.4.q.e.82.1		10
13.11	odd	12		1521.4.a.bk.1.9		10
39.2	even	12		507.4.a.r.1.9		10
39.11	even	12		507.4.a.r.1.2		10
39.17	odd	6		39.4.j.c.4.5	✓	10
39.23	odd	6		507.4.b.i.337.2		10
39.29	odd	6		507.4.b.i.337.9		10
156.95	even	6		624.4.bv.h.433.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.5	✓	10	39.17	odd	6
39.4.j.c.10.5	yes	10	3.2	odd	2
117.4.q.e.10.1		10	1.1	even	1	trivial
117.4.q.e.82.1		10	13.4	even	6	inner
507.4.a.r.1.2		10	39.11	even	12
507.4.a.r.1.9		10	39.2	even	12
507.4.b.i.337.2		10	39.23	odd	6
507.4.b.i.337.9		10	39.29	odd	6
624.4.bv.h.49.5		10	12.11	even	2
624.4.bv.h.433.1		10	156.95	even	6
1521.4.a.bk.1.2		10	13.2	odd	12
1521.4.a.bk.1.9		10	13.11	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 $\F_{q}$

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

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

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