LMFDB - Embedded newform 117.4.q.e.82.4

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			82.4
Root			$2.04224i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.4.q.e.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76863 + 1.02112i) q^{2} +(-1.91462 - 3.31622i) q^{4} -12.0825i q^{5} +(-25.7533 + 14.8686i) q^{7} -24.1582i q^{8} +O(q^{10})$	\(q+(1.76863 + 1.02112i) q^{2} +(-1.91462 - 3.31622i) q^{4} -12.0825i q^{5} +(-25.7533 + 14.8686i) q^{7} -24.1582i q^{8} +(12.3377 - 21.3694i) q^{10} +(-24.3038 - 14.0318i) q^{11} +(-40.9717 - 22.7667i) q^{13} -60.7308 q^{14} +(9.35146 - 16.1972i) q^{16} +(25.3278 + 43.8690i) q^{17} +(91.0612 - 52.5742i) q^{19} +(-40.0681 + 23.1333i) q^{20} +(-28.6563 - 49.6342i) q^{22} +(80.2961 - 139.077i) q^{23} -20.9857 q^{25} +(-49.2164 - 82.1030i) q^{26} +(98.6155 + 56.9357i) q^{28} +(70.0525 - 121.334i) q^{29} +223.593i q^{31} +(-134.294 + 77.5348i) q^{32} +103.451i q^{34} +(179.650 + 311.163i) q^{35} +(-197.759 - 114.176i) q^{37} +214.739 q^{38} -291.890 q^{40} +(-256.259 - 147.951i) q^{41} +(96.0517 + 166.366i) q^{43} +107.462i q^{44} +(284.029 - 163.984i) q^{46} +36.9300i q^{47} +(270.653 - 468.785i) q^{49} +(-37.1160 - 21.4289i) q^{50} +(2.94589 + 179.461i) q^{52} -149.102 q^{53} +(-169.538 + 293.649i) q^{55} +(359.200 + 622.152i) q^{56} +(247.794 - 143.064i) q^{58} +(380.070 - 219.433i) q^{59} +(-143.073 - 247.809i) q^{61} +(-228.316 + 395.454i) q^{62} -466.313 q^{64} +(-275.077 + 495.038i) q^{65} +(465.166 + 268.564i) q^{67} +(96.9863 - 167.985i) q^{68} +733.777i q^{70} +(-88.9656 + 51.3643i) q^{71} +75.5209i q^{73} +(-233.175 - 403.871i) q^{74} +(-348.696 - 201.319i) q^{76} +834.535 q^{77} +17.5526 q^{79} +(-195.702 - 112.989i) q^{80} +(-302.152 - 523.342i) q^{82} -1463.08i q^{83} +(530.045 - 306.022i) q^{85} +392.322i q^{86} +(-338.983 + 587.135i) q^{88} +(290.036 + 167.453i) q^{89} +(1393.66 - 22.8773i) q^{91} -614.946 q^{92} +(-37.7100 + 65.3156i) q^{94} +(-635.225 - 1100.24i) q^{95} +(-648.442 + 374.378i) q^{97} +(957.374 - 552.740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.76863	+	1.02112i	0.625307	+	0.361021i	0.778932	−	0.627108i	$-0.215762\pi$
$2$	1.76863	+	1.02112i	0.625307	+	0.361021i	−0.153626	+	0.988129i	$0.549095\pi$
$3$		0			0
$3$		0			0
$4$	−1.91462	−	3.31622i	−0.239328	−	0.414528i
$5$		−	12.0825i		−	1.08069i	−0.841444	−	0.540344i	$-0.818294\pi$
$5$		−	12.0825i		−	1.08069i	0.841444	−	0.540344i	$-0.181706\pi$
$6$		0			0
$7$	−25.7533	+	14.8686i	−1.39055	+	0.802832i	−0.993375	−	0.114914i	$-0.963341\pi$
$7$	−25.7533	+	14.8686i	−1.39055	+	0.802832i	−0.397170	+	0.917745i	$0.630008\pi$
$8$		−	24.1582i		−	1.06765i
$9$		0			0
$10$	12.3377	−	21.3694i	0.390151	−	0.675761i
$11$	−24.3038	−	14.0318i	−0.666169	−	0.384613i	0.128454	−	0.991715i	$-0.458998\pi$
$11$	−24.3038	−	14.0318i	−0.666169	−	0.384613i	−0.794624	+	0.607102i	$0.792332\pi$
$12$		0			0
$13$	−40.9717	−	22.7667i	−0.874115	−	0.485719i
$13$	−40.9717	−	22.7667i	−0.874115	−	0.485719i
$14$	−60.7308			−1.15936
$15$		0			0
$16$	9.35146	−	16.1972i	0.146117	−	0.253081i
$17$	25.3278	+	43.8690i	0.361347	+	0.625871i	0.988183	−	0.153280i	$-0.0489838\pi$
$17$	25.3278	+	43.8690i	0.361347	+	0.625871i	−0.626836	+	0.779151i	$0.715650\pi$
$18$		0			0
$19$	91.0612	−	52.5742i	1.09952	−	0.634808i	0.163425	−	0.986556i	$-0.447746\pi$
$19$	91.0612	−	52.5742i	1.09952	−	0.634808i	0.936095	+	0.351748i	$0.114413\pi$
$20$	−40.0681	+	23.1333i	−0.447975	+	0.258639i
$21$		0			0
$22$	−28.6563	−	49.6342i	−0.277707	−	0.481002i
$23$	80.2961	−	139.077i	0.727951	−	1.26085i	−0.229796	−	0.973239i	$-0.573806\pi$
$23$	80.2961	−	139.077i	0.727951	−	1.26085i	0.957748	−	0.287610i	$-0.0928607\pi$
$24$		0			0
$25$	−20.9857			−0.167886
$26$	−49.2164	−	82.1030i	−0.371235	−	0.619297i
$27$		0			0
$28$	98.6155	+	56.9357i	0.665592	+	0.384280i
$29$	70.0525	−	121.334i	0.448566	−	0.776939i	−0.549727	−	0.835344i	$-0.685268\pi$
$29$	70.0525	−	121.334i	0.448566	−	0.776939i	0.998293	+	0.0584051i	$0.0186015\pi$
$30$		0			0
$31$			223.593i			1.29544i	0.761880	+	0.647718i	$0.224276\pi$
$31$			223.593i			1.29544i	−0.761880	+	0.647718i	$0.775724\pi$
$32$	−134.294	+	77.5348i	−0.741878	+	0.428323i
$33$		0			0
$34$			103.451i			0.521815i
$35$	179.650	+	311.163i	0.867610	+	1.50274i
$36$		0			0
$37$	−197.759	−	114.176i	−0.878684	−	0.507308i	−0.00845956	−	0.999964i	$-0.502693\pi$
$37$	−197.759	−	114.176i	−0.878684	−	0.507308i	−0.870224	+	0.492656i	$0.836026\pi$
$38$	214.739			0.916716
$39$		0			0
$40$	−291.890			−1.15380
$41$	−256.259	−	147.951i	−0.976119	−	0.563563i	−0.0750227	−	0.997182i	$-0.523903\pi$
$41$	−256.259	−	147.951i	−0.976119	−	0.563563i	−0.901096	+	0.433619i	$0.857236\pi$
$42$		0			0
$43$	96.0517	+	166.366i	0.340645	+	0.590015i	0.984553	−	0.175088i	$-0.0560211\pi$
$43$	96.0517	+	166.366i	0.340645	+	0.590015i	−0.643907	+	0.765103i	$0.722688\pi$
$44$			107.462i			0.368194i
$45$		0			0
$46$	284.029	−	163.984i	0.910386	−	0.525611i
$47$			36.9300i			0.114613i	0.998357	+	0.0573063i	$0.0182512\pi$
$47$			36.9300i			0.114613i	−0.998357	+	0.0573063i	$0.981749\pi$
$48$		0			0
$49$	270.653	−	468.785i	0.789077	−	1.36672i
$50$	−37.1160	−	21.4289i	−0.104980	−	0.0606102i
$51$		0			0
$52$	2.94589	+	179.461i	0.00785618	+	0.478591i
$53$	−149.102			−0.386429			−0.193214	−	0.981157i	$-0.561891\pi$
$53$	−149.102			−0.386429			−0.193214	+	0.981157i	$0.561891\pi$
$54$		0			0
$55$	−169.538	+	293.649i	−0.415647	+	0.719921i
$56$	359.200	+	622.152i	0.857144	+	1.48462i
$57$		0			0
$58$	247.794	−	143.064i	0.560983	−	0.323884i
$59$	380.070	−	219.433i	0.838659	−	0.484200i	−0.0181492	−	0.999835i	$-0.505777\pi$
$59$	380.070	−	219.433i	0.838659	−	0.484200i	0.856808	+	0.515635i	$0.172444\pi$
$60$		0			0
$61$	−143.073	−	247.809i	−0.300305	−	0.520143i	0.675900	−	0.736993i	$-0.263755\pi$
$61$	−143.073	−	247.809i	−0.300305	−	0.520143i	−0.976205	+	0.216850i	$0.930422\pi$
$62$	−228.316	+	395.454i	−0.467679	+	0.810044i
$63$		0			0
$64$	−466.313			−0.910768
$65$	−275.077	+	495.038i	−0.524910	+	0.944645i
$66$		0			0
$67$	465.166	+	268.564i	0.848195	+	0.489706i	0.860042	−	0.510224i	$-0.170438\pi$
$67$	465.166	+	268.564i	0.848195	+	0.489706i	−0.0118462	+	0.999930i	$0.503771\pi$
$68$	96.9863	−	167.985i	0.172961	−	0.299576i
$69$		0			0
$70$			733.777i			1.25290i
$71$	−88.9656	+	51.3643i	−0.148708	+	0.0858567i	−0.572508	−	0.819899i	$-0.694029\pi$
$71$	−88.9656	+	51.3643i	−0.148708	+	0.0858567i	0.423800	+	0.905756i	$0.360696\pi$
$72$		0			0
$73$			75.5209i			0.121083i	0.998166	+	0.0605414i	$0.0192827\pi$
$73$			75.5209i			0.121083i	−0.998166	+	0.0605414i	$0.980717\pi$
$74$	−233.175	−	403.871i	−0.366298	−	0.634446i
$75$		0			0
$76$	−348.696	−	201.319i	−0.526291	−	0.303854i
$77$	834.535			1.23512
$78$		0			0
$79$	17.5526			0.0249978			0.0124989	−	0.999922i	$-0.496021\pi$
$79$	17.5526			0.0249978			0.0124989	+	0.999922i	$0.496021\pi$
$80$	−195.702	−	112.989i	−0.273502	−	0.157906i
$81$		0			0
$82$	−302.152	−	523.342i	−0.406916	−	0.704799i
$83$		−	1463.08i		−	1.93487i	−0.253122	−	0.967434i	$-0.581457\pi$
$83$		−	1463.08i		−	1.93487i	0.253122	−	0.967434i	$-0.418543\pi$
$84$		0			0
$85$	530.045	−	306.022i	0.676371	−	0.390503i
$86$			392.322i			0.491920i
$87$		0			0
$88$	−338.983	+	587.135i	−0.410633	+	0.711236i
$89$	290.036	+	167.453i	0.345436	+	0.199438i	0.662673	−	0.748909i	$-0.269422\pi$
$89$	290.036	+	167.453i	0.345436	+	0.199438i	−0.317237	+	0.948346i	$0.602755\pi$
$90$		0			0
$91$	1393.66	−	22.8773i	1.60545	−	0.0263538i
$92$	−614.946			−0.696876
$93$		0			0
$94$	−37.7100	+	65.3156i	−0.0413776	+	0.0716680i
$95$	−635.225	−	1100.24i	−0.686029	−	1.18824i
$96$		0			0
$97$	−648.442	+	374.378i	−0.678756	+	0.391880i	−0.799386	−	0.600818i	$-0.794842\pi$
$97$	−648.442	+	374.378i	−0.678756	+	0.391880i	0.120630	+	0.992697i	$0.461508\pi$
$98$	957.374	−	552.740i	0.986830	−	0.569747i
$99$		0			0
$100$	40.1797	+	69.5933i	0.0401797	+	0.0695933i
$101$	392.001	−	678.966i	0.386194	−	0.668907i	−0.605740	−	0.795662i	$-0.707123\pi$
$101$	392.001	−	678.966i	0.386194	−	0.668907i	0.991934	+	0.126755i	$0.0404563\pi$
$102$		0			0
$103$	−396.040			−0.378864			−0.189432	−	0.981894i	$-0.560665\pi$
$103$	−396.040			−0.378864			−0.189432	+	0.981894i	$0.560665\pi$
$104$	−550.002	+	989.801i	−0.518578	+	0.933250i
$105$		0			0
$106$	−263.707	−	152.251i	−0.241636	−	0.139509i
$107$	−718.296	+	1244.12i	−0.648974	+	1.12406i	0.334394	+	0.942433i	$0.391468\pi$
$107$	−718.296	+	1244.12i	−0.648974	+	1.12406i	−0.983368	+	0.181623i	$0.941865\pi$
$108$		0			0
$109$		−	1977.92i		−	1.73807i	−0.494746	−	0.869037i	$-0.664739\pi$
$109$		−	1977.92i		−	1.73807i	0.494746	−	0.869037i	$-0.335261\pi$
$110$	−599.703	+	346.239i	−0.519813	+	0.300114i
$111$		0			0
$112$			556.175i			0.469228i
$113$	61.2026	+	106.006i	0.0509509	+	0.0882496i	0.890376	−	0.455226i	$-0.150441\pi$
$113$	61.2026	+	106.006i	0.0509509	+	0.0882496i	−0.839425	+	0.543475i	$0.817108\pi$
$114$		0			0
$115$	−1680.39	−	970.173i	−1.36258	−	0.786688i
$116$	−536.496			−0.429417
$117$		0			0
$118$	896.273			0.699225
$119$	−1304.55	−	753.180i	−1.00494	−	0.580201i
$120$		0			0
$121$	−271.718	−	470.629i	−0.204146	−	0.353591i
$122$		−	584.379i		−	0.433665i
$123$		0			0
$124$	741.484	−	428.096i	0.536994	−	0.310034i
$125$		−	1256.75i		−	0.899256i
$126$		0			0
$127$	1154.80	−	2000.18i	0.806868	−	1.39754i	−0.108154	−	0.994134i	$-0.534494\pi$
$127$	1154.80	−	2000.18i	0.806868	−	1.39754i	0.915022	−	0.403403i	$-0.132173\pi$
$128$	249.616	+	144.116i	0.172369	+	0.0995170i
$129$		0			0
$130$	−992.006	+	594.654i	−0.669266	+	0.401190i
$131$	1444.26			0.963250			0.481625	−	0.876377i	$-0.340047\pi$
$131$	1444.26			0.963250			0.481625	+	0.876377i	$0.340047\pi$
$132$		0			0
$133$	−1563.41	+	2707.91i	−1.01929	+	1.76546i
$134$	548.472	+	949.982i	0.353588	+	0.612433i
$135$		0			0
$136$	1059.80	−	611.874i	0.668212	−	0.385792i
$137$	−637.324	+	367.959i	−0.397447	+	0.229466i	−0.685382	−	0.728184i	$-0.740365\pi$
$137$	−637.324	+	367.959i	−0.397447	+	0.229466i	0.287935	+	0.957650i	$0.407031\pi$
$138$		0			0
$139$	752.571	+	1303.49i	0.459225	+	0.795400i	0.998920	−	0.0464599i	$-0.0147940\pi$
$139$	752.571	+	1303.49i	0.459225	+	0.795400i	−0.539696	+	0.841860i	$0.681461\pi$
$140$	687.923	−	1191.52i	0.415286	−	0.719297i
$141$		0			0
$142$	−209.797			−0.123984
$143$	676.309	+	1128.22i	0.395495	+	0.659767i
$144$		0			0
$145$	−1466.02	−	846.406i	−0.839629	−	0.484760i
$146$	−77.1160	+	133.569i	−0.0437134	+	0.0757139i
$147$		0			0
$148$			874.415i			0.485652i
$149$	−370.523	+	213.921i	−0.203721	+	0.117618i	−0.598390	−	0.801205i	$-0.704193\pi$
$149$	−370.523	+	213.921i	−0.203721	+	0.117618i	0.394669	+	0.918823i	$0.370859\pi$
$150$		0			0
$151$			1601.83i			0.863278i	0.902046	+	0.431639i	$0.142065\pi$
$151$			1601.83i			0.863278i	−0.902046	+	0.431639i	$0.857935\pi$
$152$	−1270.10	−	2199.87i	−0.677753	−	1.17390i
$153$		0			0
$154$	1475.99	+	852.161i	0.772327	+	0.445903i
$155$	2701.55			1.39996
$156$		0			0
$157$	−730.346			−0.371261			−0.185631	−	0.982620i	$-0.559433\pi$
$157$	−730.346			−0.371261			−0.185631	+	0.982620i	$0.559433\pi$
$158$	31.0442	+	17.9234i	0.0156313	+	0.00902473i
$159$		0			0
$160$	936.811	+	1622.60i	0.462884	+	0.801738i
$161$			4775.58i			2.33769i
$162$		0			0
$163$	−1644.03	+	949.180i	−0.790001	+	0.456107i	−0.839963	−	0.542644i	$-0.817423\pi$
$163$	−1644.03	+	949.180i	−0.790001	+	0.456107i	0.0499619	+	0.998751i	$0.484090\pi$
$164$			1133.08i			0.539505i
$165$		0			0
$166$	1493.98	−	2587.66i	0.698528	−	1.20989i
$167$	−1236.25	−	713.751i	−0.572839	−	0.330729i	0.185444	−	0.982655i	$-0.440628\pi$
$167$	−1236.25	−	713.751i	−0.572839	−	0.330729i	−0.758282	+	0.651926i	$0.773961\pi$
$168$		0			0
$169$	1160.36	+	1865.58i	0.528155	+	0.849148i
$170$	1249.94			0.563919
$171$		0			0
$172$	367.806	−	637.058i	0.163052	−	0.282414i
$173$	1022.20	+	1770.50i	0.449227	+	0.778084i	0.998336	−	0.0576667i	$-0.0183661\pi$
$173$	1022.20	+	1770.50i	0.449227	+	0.778084i	−0.549109	+	0.835751i	$0.685033\pi$
$174$		0			0
$175$	540.450	−	312.029i	0.233453	−	0.134784i
$176$	−454.552	+	262.436i	−0.194677	+	0.112397i
$177$		0			0
$178$	341.979	+	592.325i	0.144002	+	0.249419i
$179$	1944.86	−	3368.59i	0.812098	−	1.40660i	−0.0992948	−	0.995058i	$-0.531659\pi$
$179$	1944.86	−	3368.59i	0.812098	−	1.40660i	0.911393	−	0.411537i	$-0.135008\pi$
$180$		0			0
$181$	2477.02			1.01721			0.508606	−	0.861000i	$-0.330161\pi$
$181$	2477.02			1.01721			0.508606	+	0.861000i	$0.330161\pi$
$182$	2488.24	+	1382.64i	1.01341	+	0.563121i
$183$		0			0
$184$	−3359.84	−	1939.81i	−1.34615	−	0.777198i
$185$	−1379.53	+	2389.41i	−0.548242	+	0.949583i
$186$		0			0
$187$		−	1421.58i		−	0.555914i
$188$	122.468	−	70.7070i	0.0475101	−	0.0274300i
$189$		0			0
$190$		−	2594.57i		−	0.990683i
$191$	1138.40	+	1971.78i	0.431267	+	0.746977i	0.996983	−	0.0776235i	$-0.0247332\pi$
$191$	1138.40	+	1971.78i	0.431267	+	0.746977i	−0.565715	+	0.824601i	$0.691400\pi$
$192$		0			0
$193$	3396.92	+	1961.21i	1.26692	+	0.731456i	0.974404	−	0.224805i	$-0.0721744\pi$
$193$	3396.92	+	1961.21i	1.26692	+	0.731456i	0.292515	+	0.956261i	$0.405508\pi$
$194$	−1529.14			−0.565907
$195$		0			0
$196$	−2072.80			−0.755392
$197$	−4384.88	−	2531.61i	−1.58584	−	0.915584i	−0.993982	−	0.109539i	$-0.965063\pi$
$197$	−4384.88	−	2531.61i	−1.58584	−	0.915584i	−0.591855	−	0.806045i	$-0.701604\pi$
$198$		0			0
$199$	1635.03	+	2831.95i	0.582433	+	1.00880i	0.995190	+	0.0979624i	$0.0312325\pi$
$199$	1635.03	+	2831.95i	0.582433	+	1.00880i	−0.412757	+	0.910841i	$0.635434\pi$
$200$			506.977i			0.179243i
$201$		0			0
$202$	1386.61	−	800.561i	0.482979	−	0.278848i
$203$			4166.34i			1.44049i
$204$		0			0
$205$	−1787.61	+	3096.23i	−0.609035	+	1.05488i
$206$	−700.450	−	404.405i	−0.236906	−	0.136778i
$207$		0			0
$208$	−751.902	+	450.725i	−0.250649	+	0.150251i
$209$	−2950.84			−0.976622
$210$		0			0
$211$	1406.09	−	2435.42i	0.458764	−	0.794602i	−0.540132	−	0.841580i	$-0.681626\pi$
$211$	1406.09	−	2435.42i	0.458764	−	0.794602i	0.998896	+	0.0469781i	$0.0149591\pi$
$212$	285.474	+	494.455i	0.0924831	+	0.160185i
$213$		0			0
$214$	−2540.80	+	1466.93i	−0.811616	+	0.468587i
$215$	2010.12	−	1160.54i	0.637622	−	0.368131i
$216$		0			0
$217$	−3324.53	−	5758.25i	−1.04002	−	1.80136i
$218$	2019.69	−	3498.21i	0.627481	−	1.08683i
$219$		0			0
$220$	1298.41			0.397903
$221$	−38.9700	−	2374.02i	−0.0118616	−	0.722596i
$222$		0			0
$223$	794.783	+	458.868i	0.238666	+	0.137794i	0.614564	−	0.788867i	$-0.289332\pi$
$223$	794.783	+	458.868i	0.238666	+	0.137794i	−0.375897	+	0.926661i	$0.622665\pi$
$224$	2305.68	−	3993.55i	0.687743	−	1.19121i
$225$		0			0
$226$			249.981i			0.0735774i
$227$	1157.35	−	668.194i	0.338396	−	0.195373i	−0.321167	−	0.947023i	$-0.604075\pi$
$227$	1157.35	−	668.194i	0.338396	−	0.195373i	0.659562	+	0.751650i	$0.270742\pi$
$228$		0			0
$229$		−	164.820i		−	0.0475617i	−0.999717	−	0.0237808i	$-0.992430\pi$
$229$		−	164.820i		−	0.0475617i	0.999717	−	0.0237808i	$-0.00757039\pi$
$230$	−1981.33	−	3431.76i	−0.568022	−	0.983843i
$231$		0			0
$232$	−2931.22	−	1692.34i	−0.829500	−	0.478912i
$233$	−4243.42			−1.19312			−0.596558	−	0.802570i	$-0.703465\pi$
$233$	−4243.42			−1.19312			−0.596558	+	0.802570i	$0.703465\pi$
$234$		0			0
$235$	446.205			0.123860
$236$	−1455.38	−	840.264i	−0.401429	−	0.231765i
$237$		0			0
$238$	−1538.18	−	2664.20i	−0.418929	−	0.725607i
$239$			2491.07i			0.674200i	0.941469	+	0.337100i	$0.109446\pi$
$239$			2491.07i			0.674200i	−0.941469	+	0.337100i	$0.890554\pi$
$240$		0			0
$241$	−2526.54	+	1458.70i	−0.675306	+	0.389888i	−0.798084	−	0.602546i	$-0.794153\pi$
$241$	−2526.54	+	1458.70i	−0.675306	+	0.389888i	0.122778	+	0.992434i	$0.460820\pi$
$242$		−	1109.83i		−	0.294803i
$243$		0			0
$244$	−547.861	+	948.922i	−0.143743	+	0.248969i
$245$	−5664.08	−	3270.16i	−1.47700	−	0.852746i
$246$		0			0
$247$	−4927.87	+	80.8921i	−1.26944	+	0.0208382i
$248$	5401.60			1.38307
$249$		0			0
$250$	1283.29	−	2222.73i	0.324650	−	0.562310i
$251$	656.939	+	1137.85i	0.165202	+	0.286138i	0.936727	−	0.350061i	$-0.113839\pi$
$251$	656.939	+	1137.85i	0.165202	+	0.286138i	−0.771525	+	0.636199i	$0.780506\pi$
$252$		0			0
$253$	−3902.99	+	2253.39i	−0.969878	+	0.559959i
$254$	4084.85	−	2358.39i	1.00908	−	0.582593i
$255$		0			0
$256$	2159.57	+	3740.49i	0.527239	+	0.913205i
$257$	493.791	−	855.271i	0.119851	−	0.207589i	−0.799857	−	0.600190i	$-0.795091\pi$
$257$	493.791	−	855.271i	0.119851	−	0.207589i	0.919709	+	0.392601i	$0.128425\pi$
$258$		0			0
$259$	6790.57			1.62913
$260$	2168.33	−	35.5936i	0.517207	−	0.00849007i
$261$		0			0
$262$	2554.37	+	1474.77i	0.602326	+	0.347753i
$263$	−3493.23	+	6050.44i	−0.819017	+	1.41858i	0.0873899	+	0.996174i	$0.472147\pi$
$263$	−3493.23	+	6050.44i	−0.819017	+	1.41858i	−0.906407	+	0.422405i	$0.861186\pi$
$264$		0			0
$265$			1801.52i			0.417609i
$266$	−5530.22	+	3192.87i	−1.27473	+	0.735968i
$267$		0			0
$268$		−	2056.79i		−	0.468801i
$269$	−2952.17	−	5113.31i	−0.669134	−	1.15897i	−0.978147	−	0.207916i	$-0.933332\pi$
$269$	−2952.17	−	5113.31i	−0.669134	−	1.15897i	0.309013	−	0.951058i	$-0.400001\pi$
$270$		0			0
$271$	−1845.97	−	1065.77i	−0.413781	−	0.238897i	0.278632	−	0.960398i	$-0.410119\pi$
$271$	−1845.97	−	1065.77i	−0.413781	−	0.238897i	−0.692413	+	0.721501i	$0.743452\pi$
$272$	947.408			0.211195
$273$		0			0
$274$	−1502.92			−0.331368
$275$	510.032	+	294.467i	0.111840	+	0.0645710i
$276$		0			0
$277$	2016.21	+	3492.17i	0.437336	+	0.757489i	0.997483	−	0.0709046i	$-0.0225886\pi$
$277$	2016.21	+	3492.17i	0.437336	+	0.757489i	−0.560147	+	0.828393i	$0.689255\pi$
$278$			3073.86i			0.663159i
$279$		0			0
$280$	7517.12	−	4340.01i	1.60441	−	0.926305i
$281$		−	2298.29i		−	0.487916i	−0.969786	−	0.243958i	$-0.921554\pi$
$281$		−	2298.29i		−	0.487916i	0.969786	−	0.243958i	$-0.0784459\pi$
$282$		0			0
$283$	3328.40	−	5764.96i	0.699127	−	1.21092i	−0.269643	−	0.962960i	$-0.586906\pi$
$283$	3328.40	−	5764.96i	0.699127	−	1.21092i	0.968770	−	0.247963i	$-0.0797611\pi$
$284$	340.671	+	196.687i	0.0711800	+	0.0410958i
$285$		0			0
$286$	44.0914	+	2686.01i	0.00911601	+	0.555339i
$287$	8799.33			1.80978
$288$		0			0
$289$	1173.51	−	2032.57i	0.238857	−	0.413713i
$290$	−1728.57	−	2993.96i	−0.350017	−	0.606247i
$291$		0			0
$292$	250.444	−	144.594i	0.0501922	−	0.0289785i
$293$	6466.60	−	3733.49i	1.28936	−	0.744413i	0.310821	−	0.950468i	$-0.399396\pi$
$293$	6466.60	−	3733.49i	1.28936	−	0.744413i	0.978540	+	0.206055i	$0.0660627\pi$
$294$		0			0
$295$	−2651.29	−	4592.18i	−0.523269	−	0.906328i
$296$	−2758.28	+	4777.49i	−0.541628	+	0.938128i
$297$		0			0
$298$	−873.759			−0.169851
$299$	−6456.18	+	3870.14i	−1.24873	+	0.748548i
$300$		0			0
$301$	−4947.29	−	2856.32i	−0.947365	−	0.546962i
$302$	−1635.66	+	2833.05i	−0.311662	+	0.539814i
$303$		0			0
$304$		−	1966.58i		−	0.371024i
$305$	−2994.14	+	1728.67i	−0.562112	+	0.324536i
$306$		0			0
$307$			3965.99i			0.737299i	0.929568	+	0.368650i	$0.120180\pi$
$307$			3965.99i			0.737299i	−0.929568	+	0.368650i	$0.879820\pi$
$308$	−1597.82	−	2767.50i	−0.295598	−	0.511991i
$309$		0			0
$310$	4778.06	+	2758.61i	0.875405	+	0.505415i
$311$	7372.29			1.34419			0.672097	−	0.740463i	$-0.265394\pi$
$311$	7372.29			1.34419			0.672097	+	0.740463i	$0.265394\pi$
$312$		0			0
$313$	8249.55			1.48975			0.744875	−	0.667204i	$-0.232509\pi$
$313$	8249.55			1.48975			0.744875	+	0.667204i	$0.232509\pi$
$314$	−1291.72	−	745.772i	−0.232152	−	0.134033i
$315$		0			0
$316$	−33.6067	−	58.2084i	−0.00598267	−	0.0103623i
$317$			5575.26i			0.987817i	0.869514	+	0.493909i	$0.164432\pi$
$317$			5575.26i			0.987817i	−0.869514	+	0.493909i	$0.835568\pi$
$318$		0			0
$319$	−3405.08	+	1965.92i	−0.597642	+	0.345049i
$320$			5634.21i			0.984256i
$321$		0			0
$322$	−4876.44	+	8446.25i	−0.843955	+	1.46177i
$323$	4612.76	+	2663.18i	0.794615	+	0.458771i
$324$		0			0
$325$	859.819	+	477.775i	0.146751	+	0.0815452i
$326$	−3876.91			−0.658657
$327$		0			0
$328$	−3574.23	+	6190.74i	−0.601688	+	1.04215i
$329$	−549.099	−	951.068i	−0.0920146	−	0.159374i
$330$		0			0
$331$	−3600.38	+	2078.68i	−0.597870	+	0.345180i	−0.768203	−	0.640206i	$-0.778849\pi$
$331$	−3600.38	+	2078.68i	−0.597870	+	0.345180i	0.170333	+	0.985387i	$0.445516\pi$
$332$	−4851.91	+	2801.25i	−0.802057	+	0.463068i
$333$		0			0
$334$	−1457.65	−	2524.73i	−0.238800	−	0.413614i
$335$	3244.91	−	5620.35i	0.529219	−	0.916634i
$336$		0			0
$337$	−3225.18			−0.521326			−0.260663	−	0.965430i	$-0.583941\pi$
$337$	−3225.18			−0.521326			−0.260663	+	0.965430i	$0.583941\pi$
$338$	147.264	+	4484.39i	0.0236986	+	0.721653i
$339$		0			0
$340$	−2029.67	−	1171.83i	−0.323749	−	0.186916i
$341$	3137.41	−	5434.15i	0.498241	−	0.862979i
$342$		0			0
$343$			5897.11i			0.928321i
$344$	4019.11	−	2320.44i	0.629930	−	0.363690i
$345$		0			0
$346$			4175.15i			0.648721i
$347$	1645.25	+	2849.65i	0.254529	+	0.440856i	0.964767	−	0.263104i	$-0.0847464\pi$
$347$	1645.25	+	2849.65i	0.254529	+	0.440856i	−0.710239	+	0.703961i	$0.751413\pi$
$348$		0			0
$349$	−3889.77	−	2245.76i	−0.596604	−	0.344449i	0.171101	−	0.985254i	$-0.445268\pi$
$349$	−3889.77	−	2245.76i	−0.596604	−	0.344449i	−0.767704	+	0.640804i	$0.778601\pi$
$350$	1274.48			0.194639
$351$		0			0
$352$	4351.81			0.658955
$353$	5107.71	+	2948.94i	0.770130	+	0.444635i	0.832921	−	0.553392i	$-0.186667\pi$
$353$	5107.71	+	2948.94i	0.770130	+	0.444635i	−0.0627907	+	0.998027i	$0.520000\pi$
$354$		0			0
$355$	620.607	+	1074.92i	0.0927843	+	0.160707i
$356$		−	1282.43i		−	0.190924i
$357$		0			0
$358$	6879.49	−	3971.87i	1.01562	−	0.586369i
$359$		−	9277.20i		−	1.36388i	−0.731410	−	0.681938i	$-0.761137\pi$
$359$		−	9277.20i		−	1.36388i	0.731410	−	0.681938i	$-0.238863\pi$
$360$		0			0
$361$	2098.59	−	3634.87i	0.305962	−	0.529942i
$362$	4380.94	+	2529.33i	0.636069	+	0.367234i
$363$		0			0
$364$	−2744.21	−	4577.90i	−0.395152	−	0.659195i
$365$	912.477			0.130853
$366$		0			0
$367$	3287.18	−	5693.56i	0.467546	−	0.809814i	−0.531766	−	0.846891i	$-0.678471\pi$
$367$	3287.18	−	5693.56i	0.467546	−	0.809814i	0.999312	+	0.0370774i	$0.0118048\pi$
$368$	−1501.77	−	2601.14i	−0.212732	−	0.368462i
$369$		0			0
$370$	−4879.75	+	2817.33i	−0.685638	+	0.395853i
$371$	3839.86	−	2216.94i	0.537347	−	0.310237i
$372$		0			0
$373$	2672.77	+	4629.38i	0.371021	+	0.642628i	0.989723	−	0.142998i	$-0.0456743\pi$
$373$	2672.77	+	4629.38i	0.371021	+	0.642628i	−0.618702	+	0.785626i	$0.712341\pi$
$374$	1451.60	−	2514.25i	0.200697	−	0.347617i
$375$		0			0
$376$	892.162			0.122366
$377$	−5632.55	+	3376.41i	−0.769472	+	0.461258i
$378$		0			0
$379$	899.378	+	519.256i	0.121894	+	0.0703757i	0.559707	−	0.828690i	$-0.310914\pi$
$379$	899.378	+	519.256i	0.121894	+	0.0703757i	−0.437813	+	0.899066i	$0.644247\pi$
$380$	−2432.43	+	4213.10i	−0.328372	+	0.568756i
$381$		0			0
$382$			4649.80i			0.622786i
$383$	−5844.97	+	3374.59i	−0.779801	+	0.450219i	−0.836360	−	0.548181i	$-0.815321\pi$
$383$	−5844.97	+	3374.59i	−0.779801	+	0.450219i	0.0565585	+	0.998399i	$0.481987\pi$
$384$		0			0
$385$		−	10083.2i		−	1.33478i
$386$	4005.27	+	6937.33i	0.528142	+	0.914769i
$387$		0			0
$388$	2483.04	+	1433.59i	0.324890	+	0.187575i
$389$	−1246.11			−0.162417			−0.0812083	−	0.996697i	$-0.525878\pi$
$389$	−1246.11			−0.162417			−0.0812083	+	0.996697i	$0.525878\pi$
$390$		0			0
$391$	8134.89			1.05217
$392$	−11325.0	−	6538.50i	−1.45918	−	0.842459i
$393$		0			0
$394$	−5170.17	−	8954.99i	−0.661090	−	1.14504i
$395$		−	212.079i		−	0.0270148i
$396$		0			0
$397$	−7236.24	+	4177.85i	−0.914802	+	0.528161i	−0.881973	−	0.471300i	$-0.843785\pi$
$397$	−7236.24	+	4177.85i	−0.914802	+	0.528161i	−0.0328293	+	0.999461i	$0.510452\pi$
$398$			6678.25i			0.841082i
$399$		0			0
$400$	−196.247	+	339.910i	−0.0245309	+	0.0424887i
$401$	−2843.73	−	1641.83i	−0.354137	−	0.204461i	0.312369	−	0.949961i	$-0.398878\pi$
$401$	−2843.73	−	1641.83i	−0.354137	−	0.204461i	−0.666506	+	0.745500i	$0.732211\pi$
$402$		0			0
$403$	5090.47	−	9160.98i	0.629217	−	1.13236i
$404$	−3002.14			−0.369708
$405$		0			0
$406$	−4254.34	+	7368.74i	−0.520048	+	0.900749i
$407$	3204.18	+	5549.81i	0.390235	+	0.675906i
$408$		0			0
$409$	9464.72	−	5464.46i	1.14426	−	0.660636i	0.196775	−	0.980449i	$-0.436953\pi$
$409$	9464.72	−	5464.46i	1.14426	−	0.660636i	0.947481	+	0.319813i	$0.103620\pi$
$410$	−6323.26	+	3650.74i	−0.761667	+	0.439749i
$411$		0			0
$412$	758.267	+	1313.36i	0.0906726	+	0.157050i
$413$	−6525.36	+	11302.3i	−0.777462	+	1.34660i
$414$		0			0
$415$	−17677.6			−2.09099
$416$	7267.47	−	119.297i	0.856531	−	0.0140601i
$417$		0			0
$418$	−5218.96	−	3013.17i	−0.610688	−	0.352581i
$419$	3651.47	−	6324.53i	0.425742	−	0.737407i	−0.570747	−	0.821126i	$-0.693346\pi$
$419$	3651.47	−	6324.53i	0.425742	−	0.737407i	0.996489	+	0.0837185i	$0.0266796\pi$
$420$		0			0
$421$			7580.99i			0.877612i	0.898582	+	0.438806i	$0.144599\pi$
$421$			7580.99i			0.877612i	−0.898582	+	0.438806i	$0.855401\pi$
$422$	4973.71	−	2871.57i	0.573736	−	0.331247i
$423$		0			0
$424$			3602.03i			0.412571i
$425$	−531.521	−	920.622i	−0.0606649	−	0.105075i
$426$		0			0
$427$	7369.18	+	4254.60i	0.835175	+	0.482188i
$428$	5501.06			0.621270
$429$		0			0
$430$	4740.21			0.531612
$431$	−8709.40	−	5028.37i	−0.973357	−	0.561968i	−0.0730993	−	0.997325i	$-0.523289\pi$
$431$	−8709.40	−	5028.37i	−0.973357	−	0.561968i	−0.900258	+	0.435357i	$0.856622\pi$
$432$		0			0
$433$	1366.69	+	2367.18i	0.151683	+	0.262723i	0.931846	−	0.362853i	$-0.118197\pi$
$433$	1366.69	+	2367.18i	0.151683	+	0.262723i	−0.780163	+	0.625576i	$0.784864\pi$
$434$		−	13579.0i		−	1.50187i
$435$		0			0
$436$	−6559.22	+	3786.97i	−0.720481	+	0.415970i
$437$		−	16886.0i		−	1.84844i
$438$		0			0
$439$	3372.12	−	5840.68i	0.366611	−	0.634989i	−0.622422	−	0.782682i	$-0.713851\pi$
$439$	3372.12	−	5840.68i	0.366611	−	0.634989i	0.989033	+	0.147692i	$0.0471846\pi$
$440$	7094.03	+	4095.74i	0.768624	+	0.443765i
$441$		0			0
$442$	2355.24	−	4238.56i	0.253455	−	0.456126i
$443$	−8655.69			−0.928317			−0.464158	−	0.885752i	$-0.653643\pi$
$443$	−8655.69			−0.928317			−0.464158	+	0.885752i	$0.653643\pi$
$444$		0			0
$445$	2023.24	−	3504.35i	0.215530	−	0.373308i
$446$	937.120	+	1623.14i	0.0994931	+	0.172327i
$447$		0			0
$448$	12009.1	−	6933.45i	1.26646	−	0.731193i
$449$	−5648.62	+	3261.23i	−0.593708	+	0.342777i	−0.766562	−	0.642170i	$-0.778034\pi$
$449$	−5648.62	+	3261.23i	−0.593708	+	0.342777i	0.172854	+	0.984947i	$0.444701\pi$
$450$		0			0
$451$	4152.03	+	7191.53i	0.433507	+	0.750856i
$452$	234.360	−	405.923i	0.0243879	−	0.0422411i
$453$		0			0
$454$	2729.23			0.282135
$455$	−276.414	−	16838.9i	−0.0284802	−	1.73499i
$456$		0			0
$457$	−1343.40	−	775.613i	−0.137509	−	0.0793909i	0.429667	−	0.902987i	$-0.358631\pi$
$457$	−1343.40	−	775.613i	−0.137509	−	0.0793909i	−0.567176	+	0.823596i	$0.691964\pi$
$458$	168.301	−	291.507i	0.0171708	−	0.0297406i
$459$		0			0
$460$			7430.06i			0.753105i
$461$	6725.77	−	3883.12i	0.679501	−	0.392310i	−0.120166	−	0.992754i	$-0.538343\pi$
$461$	6725.77	−	3883.12i	0.679501	−	0.392310i	0.799667	+	0.600444i	$0.205009\pi$
$462$		0			0
$463$		−	2004.52i		−	0.201205i	−0.994927	−	0.100603i	$-0.967923\pi$
$463$		−	2004.52i		−	0.201205i	0.994927	−	0.100603i	$-0.0320771\pi$
$464$	−1310.19	−	2269.31i	−0.131086	−	0.227048i
$465$		0			0
$466$	−7505.06	−	4333.05i	−0.746063	−	0.430739i
$467$	18674.3			1.85042			0.925209	−	0.379458i	$-0.123889\pi$
$467$	18674.3			1.85042			0.925209	+	0.379458i	$0.123889\pi$
$468$		0			0
$469$	−15972.7			−1.57261
$470$	789.173	+	455.629i	0.0774507	+	0.0447162i
$471$		0			0
$472$	−5301.11	−	9181.80i	−0.516957	−	0.895395i
$473$		−	5391.11i		−	0.524067i
$474$		0			0
$475$	−1910.98	+	1103.31i	−0.184594	+	0.106575i
$476$			5768.22i			0.555433i
$477$		0			0
$478$	−2543.68	+	4405.79i	−0.243400	+	0.421581i
$479$	−8065.31	−	4656.51i	−0.769340	−	0.444178i	0.0632994	−	0.997995i	$-0.479838\pi$
$479$	−8065.31	−	4656.51i	−0.769340	−	0.444178i	−0.832639	+	0.553816i	$0.813171\pi$
$480$		0			0
$481$	5503.09	+	9180.28i	0.521662	+	0.870239i
$482$	−5958.03			−0.563031
$483$		0			0
$484$	−1040.47	+	1802.15i	−0.0977155	+	0.169248i
$485$	4523.41	+	7834.77i	0.423500	+	0.733523i
$486$		0			0
$487$	3062.96	−	1768.40i	0.285002	−	0.164546i	−0.350684	−	0.936494i	$-0.614051\pi$
$487$	3062.96	−	1768.40i	0.285002	−	0.164546i	0.635686	+	0.771948i	$0.280717\pi$
$488$	−5986.62	+	3456.38i	−0.555331	+	0.320621i
$489$		0			0
$490$	−6678.46	−	11567.4i	−0.615718	−	1.06646i
$491$	1680.89	−	2911.39i	0.154496	−	0.267595i	−0.778379	−	0.627794i	$-0.783958\pi$
$491$	1680.89	−	2911.39i	0.154496	−	0.267595i	0.932875	+	0.360199i	$0.117291\pi$
$492$		0			0
$493$	7097.10			0.648351
$494$	−8798.20	−	4888.88i	−0.801315	−	0.445266i
$495$		0			0
$496$	3621.58	+	2090.92i	0.327851	+	0.189285i
$497$	1527.44	−	2645.60i	0.137857	−	0.238775i
$498$		0			0
$499$		−	4027.43i		−	0.361308i	−0.983547	−	0.180654i	$-0.942179\pi$
$499$		−	4027.43i		−	0.361308i	0.983547	−	0.180654i	$-0.0578214\pi$
$500$	−4167.66	+	2406.20i	−0.372767	+	0.215217i
$501$		0			0
$502$			2683.26i			0.238565i
$503$	883.336	+	1529.98i	0.0783022	+	0.135623i	0.902518	−	0.430653i	$-0.141717\pi$
$503$	883.336	+	1529.98i	0.0783022	+	0.135623i	−0.824215	+	0.566277i	$0.808383\pi$
$504$		0			0
$505$	−8203.57	−	4736.33i	−0.722880	−	0.417355i
$506$	−9203.96			−0.808628
$507$		0			0
$508$	−8844.05			−0.772424
$509$	5903.06	+	3408.13i	0.514044	+	0.296784i	0.734495	−	0.678615i	$-0.237419\pi$
$509$	5903.06	+	3408.13i	0.514044	+	0.296784i	−0.220450	+	0.975398i	$0.570753\pi$
$510$		0			0
$511$	−1122.89	−	1944.91i	−0.0972091	−	0.168371i
$512$			6514.89i			0.562344i
$513$		0			0
$514$	1746.67	−	1008.44i	0.149888	−	0.0865378i
$515$			4785.13i			0.409433i
$516$		0			0
$517$	518.194	−	897.538i	0.0440815	−	0.0763514i
$518$	12010.0	+	6933.99i	1.01871	+	0.588151i
$519$		0			0
$520$	11959.2	+	6645.37i	1.00855	+	0.560421i
$521$	5442.27			0.457640			0.228820	−	0.973469i	$-0.426513\pi$
$521$	5442.27			0.457640			0.228820	+	0.973469i	$0.426513\pi$
$522$		0			0
$523$	−10364.3	+	17951.4i	−0.866535	+	1.50088i	−0.00101984	+	0.999999i	$0.500325\pi$
$523$	−10364.3	+	17951.4i	−0.866535	+	1.50088i	−0.865515	+	0.500883i	$0.833009\pi$
$524$	−2765.22	−	4789.49i	−0.230532	−	0.399294i
$525$		0			0
$526$	−12356.5	+	7134.01i	−1.02427	+	0.591365i
$527$	−9808.81	+	5663.12i	−0.810775	+	0.468101i
$528$		0			0
$529$	−6811.41	−	11797.7i	−0.559827	−	0.969648i
$530$	−1839.57	+	3186.22i	−0.150765	+	0.261133i
$531$		0			0
$532$	11973.4			0.975775
$533$	7130.99	+	11896.0i	0.579508	+	0.966738i
$534$		0			0
$535$	15032.1	+	8678.77i	1.21475	+	0.701339i
$536$	6488.01	−	11237.6i	0.522835	−	0.905577i
$537$		0			0
$538$		−	12058.1i		−	0.966285i
$539$	−13155.8	+	7595.50i	−1.05132	+	0.606979i
$540$		0			0
$541$		−	8577.44i		−	0.681651i	−0.940127	−	0.340825i	$-0.889294\pi$
$541$		−	8577.44i		−	0.681651i	0.940127	−	0.340825i	$-0.110706\pi$
$542$	−2176.56	−	3769.92i	−0.172493	−	0.298767i
$543$		0			0
$544$	−6802.75	−	3927.57i	−0.536150	−	0.309546i
$545$	−23898.1			−1.87832
$546$		0			0
$547$	8723.99			0.681921			0.340961	−	0.940078i	$-0.389248\pi$
$547$	8723.99			0.681921			0.340961	+	0.940078i	$0.389248\pi$
$548$	2440.47	+	1409.01i	0.190240	+	0.109835i
$549$		0			0
$550$	601.373	+	1041.61i	0.0466230	+	0.0807533i
$551$		−	14731.8i		−	1.13901i
$552$		0			0
$553$	−452.037	+	260.984i	−0.0347606	+	0.0200690i
$554$			8235.17i			0.631550i
$555$		0			0
$556$	2881.78	−	4991.39i	0.219810	−	0.380723i
$557$	835.720	+	482.503i	0.0635738	+	0.0367043i	0.531450	−	0.847090i	$-0.321647\pi$
$557$	835.720	+	482.503i	0.0635738	+	0.0367043i	−0.467876	+	0.883794i	$0.654981\pi$
$558$		0			0
$559$	−147.788	−	9003.09i	−0.0111820	−	0.681199i
$560$	6719.95			0.507089
$561$		0			0
$562$	2346.83	−	4064.83i	0.176148	−	0.305097i
$563$	7302.60	+	12648.5i	0.546657	+	0.946837i	0.998501	+	0.0547402i	$0.0174331\pi$
$563$	7302.60	+	12648.5i	0.546657	+	0.946837i	−0.451844	+	0.892097i	$0.649234\pi$
$564$		0			0
$565$	1280.81	−	739.477i	0.0953702	−	0.0550620i
$566$	11773.4	−	6797.40i	0.874337	−	0.504799i
$567$		0			0
$568$	1240.87	+	2149.25i	0.0916650	+	0.158768i
$569$	−3901.24	+	6757.15i	−0.287432	+	0.497846i	−0.973196	−	0.229977i	$-0.926135\pi$
$569$	−3901.24	+	6757.15i	−0.287432	+	0.497846i	0.685764	+	0.727824i	$0.259468\pi$
$570$		0			0
$571$	−11988.2			−0.878618			−0.439309	−	0.898336i	$-0.644777\pi$
$571$	−11988.2			−0.878618			−0.439309	+	0.898336i	$0.644777\pi$
$572$	2446.56	−	4402.91i	0.178839	−	0.321844i
$573$		0			0
$574$	15562.8	+	8985.18i	1.13167	+	0.653370i
$575$	−1685.07	+	2918.63i	−0.122213	+	0.211678i
$576$		0			0
$577$			5576.90i			0.402374i	0.979553	+	0.201187i	$0.0644798\pi$
$577$			5576.90i			0.402374i	−0.979553	+	0.201187i	$0.935520\pi$
$578$	4151.01	−	2396.58i	0.298718	−	0.172465i
$579$		0			0
$580$			6482.19i			0.464066i
$581$	21754.1	+	37679.1i	1.55337	+	2.69052i
$582$		0			0
$583$	3623.74	+	2092.17i	0.257427	+	0.148626i
$584$	1824.45			0.129274
$585$		0			0
$586$	15249.4			1.07499
$587$	23169.7	+	13377.0i	1.62916	+	0.940593i	0.984345	+	0.176251i	$0.0563969\pi$
$587$	23169.7	+	13377.0i	1.62916	+	0.940593i	0.644810	+	0.764343i	$0.276936\pi$
$588$		0			0
$589$	11755.2	+	20360.6i	0.822353	+	1.42436i
$590$		−	10829.2i		−	0.755644i
$591$		0			0
$592$	−3698.66	+	2135.42i	−0.256781	+	0.148252i
$593$		−	3589.40i		−	0.248565i	−0.992247	−	0.124283i	$-0.960337\pi$
$593$		−	3589.40i		−	0.248565i	0.992247	−	0.124283i	$-0.0396629\pi$
$594$		0			0
$595$	−9100.26	+	15762.1i	−0.627016	+	1.08602i
$596$	1418.82	+	819.158i	0.0975122	+	0.0562987i
$597$		0			0
$598$	−15370.5	+	252.310i	−1.05108	+	0.0172537i
$599$	7462.78			0.509050			0.254525	−	0.967066i	$-0.418081\pi$
$599$	7462.78			0.509050			0.254525	+	0.967066i	$0.418081\pi$
$600$		0			0
$601$	8255.52	−	14299.0i	0.560316	−	0.970495i	−0.437153	−	0.899387i	$-0.644013\pi$
$601$	8255.52	−	14299.0i	0.560316	−	0.970495i	0.997469	−	0.0711081i	$-0.0226535\pi$
$602$	−5833.30	−	10103.6i	−0.394929	−	0.684037i
$603$		0			0
$604$	5312.02	−	3066.90i	0.357853	−	0.206606i
$605$	−5686.35	+	3283.02i	−0.382121	+	0.220618i
$606$		0			0
$607$	5976.78	+	10352.1i	0.399654	+	0.692222i	0.993683	−	0.112222i	$-0.0357968\pi$
$607$	5976.78	+	10352.1i	0.399654	+	0.692222i	−0.594029	+	0.804444i	$0.702464\pi$
$608$	−8152.66	+	14120.8i	−0.543806	+	0.941900i
$609$		0			0
$610$	−7060.73			−0.468657
$611$	840.773	−	1513.08i	0.0556695	−	0.100185i
$612$		0			0
$613$	3962.63	+	2287.82i	0.261091	+	0.150741i	0.624832	−	0.780759i	$-0.285167\pi$
$613$	3962.63	+	2287.82i	0.261091	+	0.150741i	−0.363741	+	0.931500i	$0.618501\pi$
$614$	−4049.76	+	7014.38i	−0.266181	+	0.461038i
$615$		0			0
$616$		−	20160.9i		−	1.31868i
$617$	16654.6	−	9615.51i	1.08669	−	0.627400i	0.153996	−	0.988071i	$-0.450786\pi$
$617$	16654.6	−	9615.51i	1.08669	−	0.627400i	0.932693	+	0.360671i	$0.117452\pi$
$618$		0			0
$619$			11715.6i			0.760727i	0.924837	+	0.380363i	$0.124201\pi$
$619$			11715.6i			0.760727i	−0.924837	+	0.380363i	$0.875799\pi$
$620$	−5172.45	−	8958.95i	−0.335050	−	0.580323i
$621$		0			0
$622$	13038.9	+	7528.00i	0.840533	+	0.485282i
$623$	−9959.17			−0.640459
$624$		0			0
$625$	−17807.8			−1.13970
$626$	14590.4	+	8423.79i	0.931551	+	0.537831i
$627$		0			0
$628$	1398.34	+	2421.99i	0.0888531	+	0.153898i
$629$		−	11567.3i		−	0.733256i
$630$		0			0
$631$	7603.78	−	4390.04i	0.479717	−	0.276965i	−0.240581	−	0.970629i	$-0.577338\pi$
$631$	7603.78	−	4390.04i	0.479717	−	0.276965i	0.720299	+	0.693664i	$0.244005\pi$
$632$		−	424.040i		−	0.0266889i
$633$		0			0
$634$	−5693.02	+	9860.60i	−0.356623	+	0.617689i
$635$	−24167.1	−	13952.9i	−1.51030	−	0.871973i
$636$		0			0
$637$	−21761.8	+	13045.0i	−1.35359	+	0.811403i
$638$	−8029.78			−0.498279
$639$		0			0
$640$	1741.28	−	3015.98i	0.107547	−	0.186277i
$641$	−12495.9	−	21643.5i	−0.769980	−	1.33364i	−0.937573	−	0.347789i	$-0.886933\pi$
$641$	−12495.9	−	21643.5i	−0.769980	−	1.33364i	0.167593	−	0.985856i	$-0.446401\pi$
$642$		0			0
$643$	−2038.50	+	1176.93i	−0.125024	+	0.0721827i	−0.561208	−	0.827675i	$-0.689663\pi$
$643$	−2038.50	+	1176.93i	−0.125024	+	0.0721827i	0.436184	+	0.899858i	$0.356330\pi$
$644$	15836.9	−	9143.42i	0.969038	−	0.559474i
$645$		0			0
$646$	5438.85	+	9420.37i	0.331252	+	0.573745i
$647$	2955.40	−	5118.90i	0.179581	−	0.311043i	−0.762156	−	0.647393i	$-0.775859\pi$
$647$	2955.40	−	5118.90i	0.179581	−	0.311043i	0.941737	+	0.336350i	$0.109193\pi$
$648$		0			0
$649$	−12316.2			−0.744918
$650$	1032.84	+	1722.99i	0.0623251	+	0.103971i
$651$		0			0
$652$	6295.38	+	3634.64i	0.378138	+	0.218318i
$653$	2962.17	−	5130.63i	0.177517	−	0.307469i	−0.763512	−	0.645793i	$-0.776527\pi$
$653$	2962.17	−	5130.63i	0.177517	−	0.307469i	0.941029	+	0.338325i	$0.109860\pi$
$654$		0			0
$655$		−	17450.2i		−	1.04097i
$656$	−4792.79	+	2767.12i	−0.285254	+	0.164692i
$657$		0			0
$658$		−	2242.79i		−	0.132877i
$659$	−6419.77	−	11119.4i	−0.379482	−	0.657282i	0.611505	−	0.791241i	$-0.290564\pi$
$659$	−6419.77	−	11119.4i	−0.379482	−	0.657282i	−0.990987	+	0.133958i	$0.957231\pi$
$660$		0			0
$661$	8890.18	+	5132.75i	0.523129	+	0.302028i	0.738214	−	0.674567i	$-0.235670\pi$
$661$	8890.18	+	5132.75i	0.523129	+	0.302028i	−0.215085	+	0.976595i	$0.569003\pi$
$662$	−8490.35			−0.498469
$663$		0			0
$664$	−35345.4			−2.06577
$665$	32718.2	+	18889.9i	1.90791	+	1.10153i
$666$		0			0
$667$	−11249.9	−	19485.4i	−0.653069	−	1.13115i
$668$			5466.25i			0.316610i
$669$		0			0
$670$	11478.1	−	6626.89i	0.661848	−	0.382118i
$671$			8030.27i			0.462004i
$672$		0			0
$673$	4931.41	−	8541.45i	0.282454	−	0.489225i	−0.689534	−	0.724253i	$-0.742185\pi$
$673$	4931.41	−	8541.45i	0.282454	−	0.489225i	0.971989	+	0.235028i	$0.0755181\pi$
$674$	−5704.17	−	3293.30i	−0.325989	−	0.188210i
$675$		0			0
$676$	3965.03	−	7419.88i	0.225593	−	0.422160i
$677$	−32615.5			−1.85158			−0.925788	−	0.378043i	$-0.876597\pi$
$677$	−32615.5			−1.85158			−0.925788	+	0.378043i	$0.876597\pi$
$678$		0			0
$679$	11133.0	−	19282.9i	0.629227	−	1.08985i
$680$	−7392.93	−	12804.9i	−0.416921	−	0.722128i
$681$		0			0
$682$	11097.9	−	6407.35i	0.623107	−	0.359751i
$683$	−18729.9	+	10813.7i	−1.04931	+	0.605820i	−0.922456	−	0.386102i	$-0.873821\pi$
$683$	−18729.9	+	10813.7i	−1.04931	+	0.605820i	−0.126854	+	0.991921i	$0.540488\pi$
$684$		0			0
$685$	4445.85	+	7700.44i	0.247981	+	0.429516i
$686$	−6021.66	+	10429.8i	−0.335143	+	0.580485i
$687$		0			0
$688$	3592.90			0.199096
$689$	6108.95	+	3394.56i	0.337783	+	0.187696i
$690$		0			0
$691$	−12326.3	−	7116.57i	−0.678601	−	0.391790i	0.120727	−	0.992686i	$-0.461477\pi$
$691$	−12326.3	−	7116.57i	−0.678601	−	0.391790i	−0.799328	+	0.600896i	$0.794811\pi$
$692$	3914.25	−	6779.67i	0.215025	−	0.372434i
$693$		0			0
$694$			6719.98i			0.367561i
$695$	15749.4	−	9092.90i	0.859579	−	0.496278i
$696$		0			0
$697$		−	14989.1i		−	0.814566i
$698$	−4586.39	−	7943.86i	−0.248707	−	0.430773i
$699$		0			0
$700$	−2069.52	−	1194.84i	−0.111743	−	0.0645151i
$701$	−28747.0			−1.54887			−0.774437	−	0.632651i	$-0.781967\pi$
$701$	−28747.0			−1.54887			−0.774437	+	0.632651i	$0.781967\pi$
$702$		0			0
$703$	−24010.8			−1.28817
$704$	11333.2	+	6543.21i	0.606726	+	0.350293i
$705$		0			0
$706$	6022.45	+	10431.2i	0.321045	+	0.556066i
$707$			23314.1i			1.24019i
$708$		0			0
$709$	1575.00	−	909.324i	0.0834276	−	0.0481670i	−0.457706	−	0.889104i	$-0.651329\pi$
$709$	1575.00	−	909.324i	0.0834276	−	0.0481670i	0.541133	+	0.840937i	$0.317995\pi$
$710$			2534.86i			0.133988i
$711$		0			0
$712$	4045.35	−	7006.75i	0.212930	−	0.368805i
$713$	31096.6	+	17953.6i	1.63335	+	0.943014i
$714$		0			0
$715$	13631.7	−	8171.47i	0.713002	−	0.427407i
$716$	−14894.7			−0.777431
$717$		0			0
$718$	9473.15	−	16408.0i	0.492388	−	0.852841i
$719$	−13070.9	−	22639.5i	−0.677973	−	1.17428i	−0.975590	−	0.219599i	$-0.929525\pi$
$719$	−13070.9	−	22639.5i	−0.677973	−	1.17428i	0.297617	−	0.954685i	$-0.403808\pi$
$720$		0			0
$721$	10199.3	−	5888.58i	0.526827	−	0.304164i
$722$	7423.29	−	4285.84i	0.382640	−	0.220917i
$723$		0			0
$724$	−4742.55	−	8214.34i	−0.243447	−	0.421662i
$725$	−1470.10	+	2546.29i	−0.0753078	+	0.130437i
$726$		0			0
$727$	1340.10			0.0683652			0.0341826	−	0.999416i	$-0.489117\pi$
$727$	1340.10			0.0683652			0.0341826	+	0.999416i	$0.489117\pi$
$728$	−552.674	−	33668.4i	−0.0281366	−	1.71406i
$729$		0			0
$730$	1613.84	+	931.750i	0.0818231	+	0.0472406i
$731$	−4865.56	+	8427.39i	−0.246182	+	0.426400i
$732$		0			0
$733$		−	32517.1i		−	1.63854i	−0.573409	−	0.819269i	$-0.694380\pi$
$733$		−	32517.1i		−	1.63854i	0.573409	−	0.819269i	$-0.305620\pi$
$734$	11627.6	−	6713.22i	0.584719	−	0.337588i
$735$		0			0
$736$			24903.0i			1.24719i
$737$	−7536.86	−	13054.2i	−0.376694	−	0.652454i
$738$		0			0
$739$	−19200.2	−	11085.3i	−0.955741	−	0.551797i	−0.0608813	−	0.998145i	$-0.519391\pi$
$739$	−19200.2	−	11085.3i	−0.955741	−	0.551797i	−0.894860	+	0.446348i	$0.852724\pi$
$740$	10565.1			0.524838
$741$		0			0
$742$	9055.07			0.448008
$743$	−26316.6	−	15193.9i	−1.29941	−	0.750216i	−0.319110	−	0.947718i	$-0.603384\pi$
$743$	−26316.6	−	15193.9i	−1.29941	−	0.750216i	−0.980303	+	0.197502i	$0.936717\pi$
$744$		0			0
$745$	2584.70	+	4476.83i	0.127109	+	0.220159i
$746$			10916.9i			0.535786i
$747$		0			0
$748$	−4714.27	+	2721.78i	−0.230442	+	0.133046i
$749$		−	42720.3i		−	2.08407i
$750$		0			0
$751$	−8449.17	+	14634.4i	−0.410539	+	0.711074i	−0.994949	−	0.100385i	$-0.967993\pi$
$751$	−8449.17	+	14634.4i	−0.410539	+	0.711074i	0.584410	+	0.811459i	$0.301326\pi$
$752$	598.163	+	345.350i	0.0290063	+	0.0167468i
$753$		0			0
$754$	−13409.6	+	220.122i	−0.647680	+	0.0106318i
$755$	19354.0			0.932934
$756$		0			0
$757$	−16462.9	+	28514.6i	−0.790428	+	1.36906i	0.135275	+	0.990808i	$0.456808\pi$
$757$	−16462.9	+	28514.6i	−0.790428	+	1.36906i	−0.925702	+	0.378253i	$0.876525\pi$
$758$	1060.45	+	1836.75i	0.0508142	+	0.0880128i
$759$		0			0
$760$	−26579.9	+	15345.9i	−1.26862	+	0.732440i
$761$	−14542.3	+	8396.01i	−0.692718	+	0.399941i	−0.804630	−	0.593777i	$-0.797636\pi$
$761$	−14542.3	+	8396.01i	−0.692718	+	0.399941i	0.111911	+	0.993718i	$0.464303\pi$
$762$		0			0
$763$	29409.0	+	50937.8i	1.39538	+	2.41687i
$764$	4359.23	−	7550.41i	0.206429	−	0.357545i
$765$		0			0
$766$	−13783.5			−0.650153
$767$	−20567.9	+	337.626i	−0.968270	+	0.0158944i
$768$		0			0
$769$	1335.04	+	770.783i	0.0626042	+	0.0361445i	0.530975	−	0.847387i	$-0.321826\pi$
$769$	1335.04	+	770.783i	0.0626042	+	0.0361445i	−0.468371	+	0.883532i	$0.655159\pi$
$770$	10296.2	−	17833.5i	0.481882	−	0.834645i
$771$		0			0
$772$		−	15019.9i		−	0.700231i
$773$	32970.6	−	19035.6i	1.53411	−	0.885721i	0.534948	−	0.844885i	$-0.320331\pi$
$773$	32970.6	−	19035.6i	1.53411	−	0.885721i	0.999166	−	0.0408357i	$-0.0130020\pi$
$774$		0			0
$775$		−	4692.26i		−	0.217485i
$776$	9044.30	+	15665.2i	0.418391	+	0.724674i
$777$		0			0
$778$	−2203.91	−	1272.43i	−0.101560	−	0.0586358i
$779$	−31113.6			−1.43102
$780$		0			0
$781$	2882.93			0.132086
$782$	14387.6	+	8306.71i	0.657930	+	0.379856i
$783$		0			0
$784$	−5062.01	−	8767.66i	−0.230595	−	0.399401i
$785$			8824.38i			0.401217i
$786$		0			0
$787$	−17363.6	+	10024.9i	−0.786463	+	0.454065i	−0.838716	−	0.544569i	$-0.816693\pi$
$787$	−17363.6	+	10024.9i	−0.786463	+	0.454065i	0.0522528	+	0.998634i	$0.483360\pi$
$788$			19388.3i			0.876498i
$789$		0			0
$790$	216.558	−	375.090i	0.00975291	−	0.0168925i
$791$	−3152.33	−	1820.00i	−0.141699	−	0.0818100i
$792$		0			0
$793$	220.136	+	13410.5i	0.00985781	+	0.600529i
$794$	−17064.4			−0.762709
$795$		0			0
$796$	6260.93	−	10844.2i	0.278785	−	0.482869i
$797$	11200.9	+	19400.6i	0.497813	+	0.862238i	0.999997	−	0.00252302i	$-0.000803104\pi$
$797$	11200.9	+	19400.6i	0.497813	+	0.862238i	−0.502183	+	0.864761i	$0.667470\pi$
$798$		0			0
$799$	−1620.08	+	935.355i	−0.0717327	+	0.0414149i
$800$	2818.26	−	1627.12i	0.124551	−	0.0719093i
$801$		0			0
$802$	−3353.01	−	5807.59i	−0.147630	−	0.255702i
$803$	1059.69	−	1835.44i	0.0465700	−	0.0806617i
$804$		0			0
$805$	57700.7			2.52631
$806$	18357.7	−	11004.4i	0.802259	−	0.480911i
$807$		0			0
$808$	−16402.6	−	9470.04i	−0.714159	−	0.412320i
$809$	−20983.2	+	36343.9i	−0.911903	+	1.57946i	−0.100530	+	0.994934i	$0.532054\pi$
$809$	−20983.2	+	36343.9i	−0.911903	+	1.57946i	−0.811373	+	0.584528i	$0.801280\pi$
$810$		0			0
$811$		−	13029.1i		−	0.564133i	−0.959395	−	0.282067i	$-0.908980\pi$
$811$		−	13029.1i		−	0.564133i	0.959395	−	0.282067i	$-0.0910199\pi$
$812$	13816.5	−	7976.97i	0.597124	−	0.344750i
$813$		0			0
$814$			13087.4i			0.563532i
$815$	11468.4	+	19863.9i	0.492909	+	0.853744i
$816$		0			0
$817$	17493.2	+	10099.7i	0.749092	+	0.432489i
$818$	22319.5			0.954014
$819$		0			0
$820$	13690.4			0.583036
$821$	7706.01	+	4449.07i	0.327578	+	0.189127i	0.654765	−	0.755832i	$-0.272767\pi$
$821$	7706.01	+	4449.07i	0.327578	+	0.189127i	−0.327187	+	0.944960i	$0.606101\pi$
$822$		0			0
$823$	11361.8	+	19679.2i	0.481224	+	0.833504i	0.999768	−	0.0215466i	$-0.00685902\pi$
$823$	11361.8	+	19679.2i	0.481224	+	0.833504i	−0.518544	+	0.855051i	$0.673526\pi$
$824$			9567.61i			0.404494i
$825$		0			0
$826$	−23081.9	+	13326.4i	−0.972304	+	0.561360i
$827$			19073.3i			0.801989i	0.916081	+	0.400994i	$0.131335\pi$
$827$			19073.3i			0.801989i	−0.916081	+	0.400994i	$0.868665\pi$
$828$		0			0
$829$	21251.9	−	36809.4i	0.890361	−	1.54215i	0.0509178	−	0.998703i	$-0.483785\pi$
$829$	21251.9	−	36809.4i	0.890361	−	1.54215i	0.839443	−	0.543448i	$-0.182881\pi$
$830$	−31265.2	−	18051.0i	−1.30751	−	0.754891i
$831$		0			0
$832$	19105.6	+	10616.4i	0.796116	+	0.442377i
$833$	27420.2			1.14052
$834$		0			0
$835$	−8623.86	+	14937.0i	−0.357414	+	0.619060i
$836$	5649.74	+	9785.65i	0.233733	+	0.404837i
$837$		0			0
$838$	12916.2	−	7457.19i	0.532439	−	0.307404i
$839$	−16824.5	+	9713.62i	−0.692307	+	0.399704i	−0.804476	−	0.593985i	$-0.797554\pi$
$839$	−16824.5	+	9713.62i	−0.692307	+	0.399704i	0.112168	+	0.993689i	$0.464220\pi$
$840$		0			0
$841$	2379.80	+	4121.94i	0.0975768	+	0.169008i
$842$	−7741.11	+	13408.0i	−0.316836	+	0.548777i
$843$		0			0
$844$	−10768.5			−0.439180
$845$	22540.8	−	14020.0i	0.917664	−	0.570770i
$846$		0			0
$847$	13995.2	+	8080.15i	0.567747	+	0.327789i
$848$	−1394.32	+	2415.03i	−0.0564637	+	0.0977979i
$849$		0			0
$850$		−	2170.99i		−	0.0876052i
$851$	−31758.5	+	18335.8i	−1.27928	+	0.738592i
$852$		0			0
$853$		−	26851.8i		−	1.07783i	−0.842361	−	0.538914i	$-0.818835\pi$
$853$		−	26851.8i		−	1.07783i	0.842361	−	0.538914i	$-0.181165\pi$
$854$	8688.92	+	15049.7i	0.348160	+	0.603031i
$855$		0			0
$856$	30055.8	+	17352.7i	1.20010	+	0.692878i
$857$	41539.4			1.65573			0.827864	−	0.560929i	$-0.189556\pi$
$857$	41539.4			1.65573			0.827864	+	0.560929i	$0.189556\pi$
$858$		0			0
$859$	−11936.2			−0.474107			−0.237054	−	0.971497i	$-0.576182\pi$
$859$	−11936.2			−0.474107			−0.237054	+	0.971497i	$0.576182\pi$
$860$	−7697.22	−	4443.99i	−0.305201	−	0.176208i
$861$		0			0
$862$	−10269.2	−	17786.7i	−0.405765	−	0.702805i
$863$		−	41128.6i		−	1.62229i	−0.584848	−	0.811143i	$-0.698846\pi$
$863$		−	41128.6i		−	1.62229i	0.584848	−	0.811143i	$-0.301154\pi$
$864$		0			0
$865$	21392.0	−	12350.7i	0.840866	−	0.485474i
$866$			5582.22i			0.219043i
$867$		0			0
$868$	−12730.4	+	22049.7i	−0.497810	+	0.862232i
$869$	−426.595	−	246.295i	−0.0166528	−	0.00961448i
$870$		0			0
$871$	−12944.3	−	21593.8i	−0.503561	−	0.840044i
$872$	−47782.9			−1.85566
$873$		0			0
$874$	17242.7	−	29865.2i	0.667325	−	1.15584i
$875$	18686.1	+	32365.4i	0.721951	+	1.25046i
$876$		0			0
$877$	−5548.50	+	3203.43i	−0.213637	+	0.123343i	−0.603001	−	0.797741i	$-0.706028\pi$
$877$	−5548.50	+	3203.43i	−0.213637	+	0.123343i	0.389364	+	0.921084i	$0.372695\pi$
$878$	11928.1	−	6886.68i	0.458489	−	0.264709i
$879$		0			0
$880$	3170.87	+	5492.10i	0.121466	+	0.210385i
$881$	1469.04	−	2544.45i	0.0561783	−	0.0973037i	−0.836569	−	0.547862i	$-0.815442\pi$
$881$	1469.04	−	2544.45i	0.0561783	−	0.0973037i	0.892747	+	0.450559i	$0.148775\pi$
$882$		0			0
$883$	−3022.06			−0.115176			−0.0575881	−	0.998340i	$-0.518341\pi$
$883$	−3022.06			−0.115176			−0.0575881	+	0.998340i	$0.518341\pi$
$884$	−7798.16	+	4674.58i	−0.296697	+	0.177854i
$885$		0			0
$886$	−15308.8	−	8838.51i	−0.580483	−	0.335142i
$887$	−5030.22	+	8712.59i	−0.190415	+	0.329809i	−0.945388	−	0.325948i	$-0.894317\pi$
$887$	−5030.22	+	8712.59i	−0.190415	+	0.329809i	0.754973	+	0.655756i	$0.227650\pi$
$888$		0			0
$889$			68681.5i			2.59112i
$890$	7156.74	−	4131.94i	0.269544	−	0.155621i
$891$		0			0
$892$		−	3514.24i		−	0.131912i
$893$	1941.57	+	3362.89i	0.0727570	+	0.126019i
$894$		0			0
$895$	−40700.9	−	23498.7i	−1.52009	−	0.877624i
$896$	−8571.24			−0.319582
$897$		0			0
$898$	−13320.5			−0.494999
$899$	27129.5	+	15663.2i	1.00647	+	0.581088i
$900$		0			0
$901$	−3776.42	−	6540.95i	−0.139635	−	0.241854i
$902$			16958.9i			0.626020i
$903$		0			0
$904$	2560.91	−	1478.54i	0.0942197	−	0.0543978i
$905$		−	29928.4i		−	1.09929i
$906$		0			0
$907$	−21579.3	+	37376.5i	−0.789999	+	1.36832i	0.135967	+	0.990713i	$0.456586\pi$
$907$	−21579.3	+	37376.5i	−0.789999	+	1.36832i	−0.925967	+	0.377606i	$0.876748\pi$
$908$	−4431.76	−	2558.68i	−0.161975	−	0.0935163i
$909$		0			0
$910$	16705.7	−	30064.1i	0.608558	−	1.09518i
$911$	32665.9			1.18800			0.594001	−	0.804464i	$-0.297547\pi$
$911$	32665.9			1.18800			0.594001	+	0.804464i	$0.297547\pi$
$912$		0			0
$913$	−20529.7	+	35558.4i	−0.744176	+	1.28895i
$914$	−1583.99	−	2743.55i	−0.0573235	−	0.0992873i
$915$		0			0
$916$	−546.581	+	315.568i	−0.0197156	+	0.0113828i
$917$	−37194.4	+	21474.2i	−1.33944	+	0.773327i
$918$		0			0
$919$	−9494.97	−	16445.8i	−0.340816	−	0.590311i	0.643768	−	0.765221i	$-0.277370\pi$
$919$	−9494.97	−	16445.8i	−0.340816	−	0.590311i	−0.984585	+	0.174909i	$0.944037\pi$
$920$	−23437.6	+	40595.2i	−0.839909	+	1.45476i
$921$		0			0
$922$	15860.6			0.566529
$923$	4814.47	−	79.0305i	0.171690	−	0.00281833i
$924$		0			0
$925$	4150.10	+	2396.06i	0.147518	+	0.0851698i
$926$	2046.86	−	3545.27i	0.0726393	−	0.125815i
$927$		0			0
$928$			21726.0i			0.768525i
$929$	4846.98	−	2798.40i	0.171178	−	0.0988295i	−0.411963	−	0.911200i	$-0.635157\pi$
$929$	4846.98	−	2798.40i	0.171178	−	0.0988295i	0.583141	+	0.812371i	$0.301823\pi$
$930$		0			0
$931$		−	56917.6i		−	2.00365i
$932$	8124.55	+	14072.1i	0.285546	+	0.494579i
$933$		0			0
$934$	33028.1	+	19068.8i	1.15708	+	0.668040i
$935$	−17176.1			−0.600770
$936$		0			0
$937$	40294.4			1.40487			0.702433	−	0.711750i	$-0.252097\pi$
$937$	40294.4			1.40487			0.702433	+	0.711750i	$0.252097\pi$
$938$	−28249.9	−	16310.1i	−0.983360	−	0.567743i
$939$		0			0
$940$	−854.314	−	1479.72i	−0.0296432	−	0.0513436i
$941$		−	43648.8i		−	1.51213i	−0.654499	−	0.756063i	$-0.727120\pi$
$941$		−	43648.8i		−	1.51213i	0.654499	−	0.756063i	$-0.272880\pi$
$942$		0			0
$943$	−41153.1	+	23759.8i	−1.42113	+	0.820492i
$944$		−	8208.10i		−	0.282999i
$945$		0			0
$946$	5504.98	−	9534.90i	0.189199	−	0.327702i
$947$	9081.62	+	5243.28i	0.311629	+	0.179919i	0.647655	−	0.761933i	$-0.275750\pi$
$947$	9081.62	+	5243.28i	0.311629	+	0.179919i	−0.336026	+	0.941853i	$0.609083\pi$
$948$		0			0
$949$	1719.36	−	3094.22i	0.0588122	−	0.105840i
$950$	−4506.44			−0.153903
$951$		0			0
$952$	−18195.5	+	31515.5i	−0.619452	+	1.07292i
$953$	−16529.4	−	28629.7i	−0.561846	−	0.973145i	−0.997335	−	0.0729517i	$-0.976758\pi$
$953$	−16529.4	−	28629.7i	−0.561846	−	0.973145i	0.435490	−	0.900194i	$-0.356575\pi$
$954$		0			0
$955$	23823.9	−	13754.7i	0.807249	−	0.466065i
$956$	8260.93	−	4769.45i	0.279475	−	0.161355i
$957$		0			0
$958$	−9509.73	−	16471.3i	−0.320715	−	0.555495i
$959$	10942.1	−	18952.3i	0.368445	−	0.638166i
$960$		0			0
$961$	−20202.8			−0.678152
$962$	358.769	+	21855.9i	0.0120241	+	0.732497i
$963$		0			0
$964$	9674.74	+	5585.71i	0.323239	+	0.186622i
$965$	23696.2	−	41043.1i	0.790476	−	1.36914i
$966$		0			0
$967$		−	53634.9i		−	1.78364i	−0.452389	−	0.891821i	$-0.649428\pi$
$967$		−	53634.9i		−	1.78364i	0.452389	−	0.891821i	$-0.350572\pi$
$968$	−11369.5	+	6564.21i	−0.377511	+	0.217956i
$969$		0			0
$970$			18475.8i			0.611569i
$971$	−2043.40	−	3539.27i	−0.0675344	−	0.116973i	0.830281	−	0.557345i	$-0.188180\pi$
$971$	−2043.40	−	3539.27i	−0.0675344	−	0.116973i	−0.897815	+	0.440372i	$0.854847\pi$
$972$		0			0
$973$	−38762.3	−	22379.4i	−1.27715	−	0.737360i
$974$	7223.00			0.237618
$975$		0			0
$976$	−5351.76			−0.175518
$977$	12454.3	+	7190.48i	0.407827	+	0.235459i	0.689856	−	0.723947i	$-0.257674\pi$
$977$	12454.3	+	7190.48i	0.407827	+	0.235459i	−0.282028	+	0.959406i	$0.591007\pi$
$978$		0			0
$979$	−4699.32	−	8139.46i	−0.153413	−	0.265718i
$980$			25044.5i			0.816343i
$981$		0			0
$982$	5945.76	−	3432.79i	0.193215	−	0.111553i
$983$		−	12916.5i		−	0.419099i	−0.977798	−	0.209549i	$-0.932800\pi$
$983$		−	12916.5i		−	0.419099i	0.977798	−	0.209549i	$-0.0671997\pi$
$984$		0			0
$985$	−30588.1	+	52980.1i	−0.989460	+	1.71379i
$986$	12552.2	+	7247.00i	0.405418	+	0.234068i
$987$		0			0
$988$	9703.27	+	16187.0i	0.312451	+	0.521233i
$989$	30850.3			0.991893
$990$		0			0
$991$	2919.49	−	5056.71i	0.0935829	−	0.162090i	−0.815433	−	0.578851i	$-0.803501\pi$
$991$	2919.49	−	5056.71i	0.0935829	−	0.162090i	0.909016	+	0.416761i	$0.136835\pi$
$992$	−17336.2	−	30027.2i	−0.554865	−	0.961055i
$993$		0			0
$994$	5402.95	−	3119.40i	0.172406	−	0.0995385i
$995$	34217.0	−	19755.2i	1.09020	−	0.629428i
$996$		0			0
$997$	−22145.1	−	38356.4i	−0.703452	−	1.21841i	−0.967247	−	0.253835i	$-0.918308\pi$
$997$	−22145.1	−	38356.4i	−0.703452	−	1.21841i	0.263796	−	0.964579i	$-0.415026\pi$
$998$	4112.50	−	7123.05i	0.130440	−	0.225928i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.e.82.4		10
3.2	odd	2		39.4.j.c.4.2	✓	10
12.11	even	2		624.4.bv.h.433.4		10
13.6	odd	12		1521.4.a.bk.1.4		10
13.7	odd	12		1521.4.a.bk.1.7		10
13.10	even	6	inner	117.4.q.e.10.4		10
39.17	odd	6		507.4.b.i.337.4		10
39.20	even	12		507.4.a.r.1.4		10
39.23	odd	6		39.4.j.c.10.2	yes	10
39.32	even	12		507.4.a.r.1.7		10
39.35	odd	6		507.4.b.i.337.7		10
156.23	even	6		624.4.bv.h.49.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.2	✓	10	3.2	odd	2
39.4.j.c.10.2	yes	10	39.23	odd	6
117.4.q.e.10.4		10	13.10	even	6	inner
117.4.q.e.82.4		10	1.1	even	1	trivial
507.4.a.r.1.4		10	39.20	even	12
507.4.a.r.1.7		10	39.32	even	12
507.4.b.i.337.4		10	39.17	odd	6
507.4.b.i.337.7		10	39.35	odd	6
624.4.bv.h.49.2		10	156.23	even	6
624.4.bv.h.433.4		10	12.11	even	2
1521.4.a.bk.1.4		10	13.6	odd	12
1521.4.a.bk.1.7		10	13.7	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)

\(f(q)\)	\(=\)	\(q+(1.76863 + 1.02112i) q^{2} +(-1.91462 - 3.31622i) q^{4} -12.0825i q^{5} +(-25.7533 + 14.8686i) q^{7} -24.1582i q^{8} +O(q^{10})\)	\(q+(1.76863 + 1.02112i) q^{2} +(-1.91462 - 3.31622i) q^{4} -12.0825i q^{5} +(-25.7533 + 14.8686i) q^{7} -24.1582i q^{8} +(12.3377 - 21.3694i) q^{10} +(-24.3038 - 14.0318i) q^{11} +(-40.9717 - 22.7667i) q^{13} -60.7308 q^{14} +(9.35146 - 16.1972i) q^{16} +(25.3278 + 43.8690i) q^{17} +(91.0612 - 52.5742i) q^{19} +(-40.0681 + 23.1333i) q^{20} +(-28.6563 - 49.6342i) q^{22} +(80.2961 - 139.077i) q^{23} -20.9857 q^{25} +(-49.2164 - 82.1030i) q^{26} +(98.6155 + 56.9357i) q^{28} +(70.0525 - 121.334i) q^{29} +223.593i q^{31} +(-134.294 + 77.5348i) q^{32} +103.451i q^{34} +(179.650 + 311.163i) q^{35} +(-197.759 - 114.176i) q^{37} +214.739 q^{38} -291.890 q^{40} +(-256.259 - 147.951i) q^{41} +(96.0517 + 166.366i) q^{43} +107.462i q^{44} +(284.029 - 163.984i) q^{46} +36.9300i q^{47} +(270.653 - 468.785i) q^{49} +(-37.1160 - 21.4289i) q^{50} +(2.94589 + 179.461i) q^{52} -149.102 q^{53} +(-169.538 + 293.649i) q^{55} +(359.200 + 622.152i) q^{56} +(247.794 - 143.064i) q^{58} +(380.070 - 219.433i) q^{59} +(-143.073 - 247.809i) q^{61} +(-228.316 + 395.454i) q^{62} -466.313 q^{64} +(-275.077 + 495.038i) q^{65} +(465.166 + 268.564i) q^{67} +(96.9863 - 167.985i) q^{68} +733.777i q^{70} +(-88.9656 + 51.3643i) q^{71} +75.5209i q^{73} +(-233.175 - 403.871i) q^{74} +(-348.696 - 201.319i) q^{76} +834.535 q^{77} +17.5526 q^{79} +(-195.702 - 112.989i) q^{80} +(-302.152 - 523.342i) q^{82} -1463.08i q^{83} +(530.045 - 306.022i) q^{85} +392.322i q^{86} +(-338.983 + 587.135i) q^{88} +(290.036 + 167.453i) q^{89} +(1393.66 - 22.8773i) q^{91} -614.946 q^{92} +(-37.7100 + 65.3156i) q^{94} +(-635.225 - 1100.24i) q^{95} +(-648.442 + 374.378i) q^{97} +(957.374 - 552.740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) \) 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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