LMFDB - Embedded newform 117.3.j.c.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(73,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.73");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.j (of order $4$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.897122304.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 51x^{4} - 104x^{2} + 169 $ x^8 - 8x^6 + 51x^4 - 104*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.4
Root			$1.30421 + 0.752986i$ of defining polynomial
Character	$\chi$	$=$	117.73
Dual form			117.3.j.c.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.05719 + 2.05719i) q^{2} +4.46410i q^{4} +(3.01194 + 3.01194i) q^{5} +(-2.46410 + 2.46410i) q^{7} +(-0.954747 + 0.954747i) q^{8} +12.3923i q^{10} +(3.01194 - 3.01194i) q^{11} +(-12.3923 + 3.92820i) q^{13} -10.1383 q^{14} +13.9282 q^{16} -18.0717i q^{17} +(7.00000 + 7.00000i) q^{19} +(-13.4456 + 13.4456i) q^{20} +12.3923 q^{22} -20.8673i q^{23} -6.85641i q^{25} +(-33.5745 - 17.4123i) q^{26} +(-11.0000 - 11.0000i) q^{28} +26.8912 q^{29} +(-41.2487 - 41.2487i) q^{31} +(32.4720 + 32.4720i) q^{32} +(37.1769 - 37.1769i) q^{34} -14.8435 q^{35} +(-27.3923 + 27.3923i) q^{37} +28.8007i q^{38} -5.75129 q^{40} +(52.3846 + 52.3846i) q^{41} -31.4256i q^{43} +(13.4456 + 13.4456i) q^{44} +(42.9282 - 42.9282i) q^{46} +(34.3130 - 34.3130i) q^{47} +36.8564i q^{49} +(14.1050 - 14.1050i) q^{50} +(-17.5359 - 55.3205i) q^{52} -71.8541 q^{53} +18.1436 q^{55} -4.70519i q^{56} +(55.3205 + 55.3205i) q^{58} +(-74.8661 + 74.8661i) q^{59} -24.7846 q^{61} -169.713i q^{62} +77.8897i q^{64} +(-49.1564 - 25.4934i) q^{65} +(1.92820 + 1.92820i) q^{67} +80.6737 q^{68} +(-30.5359 - 30.5359i) q^{70} +(-22.6977 - 22.6977i) q^{71} +(-43.3538 + 43.3538i) q^{73} -112.703 q^{74} +(-31.2487 + 31.2487i) q^{76} +14.8435i q^{77} -79.2154 q^{79} +(41.9509 + 41.9509i) q^{80} +215.531i q^{82} +(23.8793 + 23.8793i) q^{83} +(54.4308 - 54.4308i) q^{85} +(64.6486 - 64.6486i) q^{86} +5.75129i q^{88} +(-40.7693 + 40.7693i) q^{89} +(20.8564 - 40.2154i) q^{91} +93.1540 q^{92} +141.177 q^{94} +42.1672i q^{95} +(54.0718 + 54.0718i) q^{97} +(-75.8208 + 75.8208i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7} - 16 q^{13} + 56 q^{16} + 56 q^{19} + 16 q^{22} - 88 q^{28} - 136 q^{31} + 48 q^{34} - 136 q^{37} - 240 q^{40} + 288 q^{46} - 168 q^{52} + 256 q^{55} + 304 q^{58} - 32 q^{61} - 40 q^{67} - 272 q^{70}+ \cdots + 488 q^{97}+O(q^{100}) $ 8 * q + 8 * q^7 - 16 * q^13 + 56 * q^16 + 56 * q^19 + 16 * q^22 - 88 * q^28 - 136 * q^31 + 48 * q^34 - 136 * q^37 - 240 * q^40 + 288 * q^46 - 168 * q^52 + 256 * q^55 + 304 * q^58 - 32 * q^61 - 40 * q^67 - 272 * q^70 + 152 * q^73 - 56 * q^76 - 800 * q^79 + 768 * q^85 + 56 * q^91 + 880 * q^94 + 488 * q^97

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.05719	+	2.05719i	1.02860	+	1.02860i	0.999579	+	0.0290186i	$0.00923820\pi$
$2$	2.05719	+	2.05719i	1.02860	+	1.02860i	0.0290186	+	0.999579i	$0.490762\pi$
$3$		0			0
$3$		0			0
$4$			4.46410i			1.11603i
$5$	3.01194	+	3.01194i	0.602388	+	0.602388i	0.940946	−	0.338557i	$-0.109939\pi$
$5$	3.01194	+	3.01194i	0.602388	+	0.602388i	−0.338557	+	0.940946i	$0.609939\pi$
$6$		0			0
$7$	−2.46410	+	2.46410i	−0.352015	+	0.352015i	−0.860859	−	0.508844i	$-0.830073\pi$
$7$	−2.46410	+	2.46410i	−0.352015	+	0.352015i	0.508844	+	0.860859i	$0.330073\pi$
$8$	−0.954747	+	0.954747i	−0.119343	+	0.119343i
$9$		0			0
$10$			12.3923i			1.23923i
$11$	3.01194	−	3.01194i	0.273813	−	0.273813i	−0.556820	−	0.830633i	$-0.687979\pi$
$11$	3.01194	−	3.01194i	0.273813	−	0.273813i	0.830633	+	0.556820i	$0.187979\pi$
$12$		0			0
$13$	−12.3923	+	3.92820i	−0.953254	+	0.302169i
$13$	−12.3923	+	3.92820i	−0.953254	+	0.302169i
$14$	−10.1383			−0.724162
$15$		0			0
$16$	13.9282			0.870513
$17$		−	18.0717i		−	1.06304i	−0.847046	−	0.531519i	$-0.821621\pi$
$17$		−	18.0717i		−	1.06304i	0.847046	−	0.531519i	$-0.178379\pi$
$18$		0			0
$19$	7.00000	+	7.00000i	0.368421	+	0.368421i	0.866901	−	0.498480i	$-0.166108\pi$
$19$	7.00000	+	7.00000i	0.368421	+	0.368421i	−0.498480	+	0.866901i	$0.666108\pi$
$20$	−13.4456	+	13.4456i	−0.672281	+	0.672281i
$21$		0			0
$22$	12.3923			0.563287
$23$		−	20.8673i		−	0.907276i	−0.891186	−	0.453638i	$-0.850126\pi$
$23$		−	20.8673i		−	0.907276i	0.891186	−	0.453638i	$-0.149874\pi$
$24$		0			0
$25$		−	6.85641i		−	0.274256i
$26$	−33.5745	−	17.4123i	−1.29133	−	0.669704i
$27$		0			0
$28$	−11.0000	−	11.0000i	−0.392857	−	0.392857i
$29$	26.8912			0.927284			0.463642	−	0.886023i	$-0.346542\pi$
$29$	26.8912			0.927284			0.463642	+	0.886023i	$0.346542\pi$
$30$		0			0
$31$	−41.2487	−	41.2487i	−1.33060	−	1.33060i	−0.904829	−	0.425774i	$-0.860002\pi$
$31$	−41.2487	−	41.2487i	−1.33060	−	1.33060i	−0.425774	−	0.904829i	$-0.639998\pi$
$32$	32.4720	+	32.4720i	1.01475	+	1.01475i
$33$		0			0
$34$	37.1769	−	37.1769i	1.09344	−	1.09344i
$35$	−14.8435			−0.424099
$36$		0			0
$37$	−27.3923	+	27.3923i	−0.740333	+	0.740333i	−0.972642	−	0.232309i	$-0.925372\pi$
$37$	−27.3923	+	27.3923i	−0.740333	+	0.740333i	0.232309	+	0.972642i	$0.425372\pi$
$38$			28.8007i			0.757914i
$39$		0			0
$40$	−5.75129			−0.143782
$41$	52.3846	+	52.3846i	1.27767	+	1.27767i	0.941966	+	0.335707i	$0.108975\pi$
$41$	52.3846	+	52.3846i	1.27767	+	1.27767i	0.335707	+	0.941966i	$0.391025\pi$
$42$		0			0
$43$		−	31.4256i		−	0.730829i	−0.930845	−	0.365414i	$-0.880927\pi$
$43$		−	31.4256i		−	0.730829i	0.930845	−	0.365414i	$-0.119073\pi$
$44$	13.4456	+	13.4456i	0.305582	+	0.305582i
$45$		0			0
$46$	42.9282	−	42.9282i	0.933222	−	0.933222i
$47$	34.3130	−	34.3130i	0.730063	−	0.730063i	−0.240569	−	0.970632i	$-0.577334\pi$
$47$	34.3130	−	34.3130i	0.730063	−	0.730063i	0.970632	+	0.240569i	$0.0773340\pi$
$48$		0			0
$49$			36.8564i			0.752172i
$50$	14.1050	−	14.1050i	0.282099	−	0.282099i
$51$		0			0
$52$	−17.5359	−	55.3205i	−0.337229	−	1.06386i
$53$	−71.8541			−1.35574			−0.677869	−	0.735183i	$-0.737096\pi$
$53$	−71.8541			−1.35574			−0.677869	+	0.735183i	$0.737096\pi$
$54$		0			0
$55$	18.1436			0.329884
$56$		−	4.70519i		−	0.0840212i
$57$		0			0
$58$	55.3205	+	55.3205i	0.953802	+	0.953802i
$59$	−74.8661	+	74.8661i	−1.26892	+	1.26892i	−0.322268	+	0.946649i	$0.604445\pi$
$59$	−74.8661	+	74.8661i	−1.26892	+	1.26892i	−0.946649	+	0.322268i	$0.895555\pi$
$60$		0			0
$61$	−24.7846			−0.406305			−0.203153	−	0.979147i	$-0.565119\pi$
$61$	−24.7846			−0.406305			−0.203153	+	0.979147i	$0.565119\pi$
$62$		−	169.713i		−	2.73731i
$63$		0			0
$64$			77.8897i			1.21703i
$65$	−49.1564	−	25.4934i	−0.756253	−	0.392206i
$66$		0			0
$67$	1.92820	+	1.92820i	0.0287792	+	0.0287792i	0.721350	−	0.692571i	$-0.243522\pi$
$67$	1.92820	+	1.92820i	0.0287792	+	0.0287792i	−0.692571	+	0.721350i	$0.743522\pi$
$68$	80.6737			1.18638
$69$		0			0
$70$	−30.5359	−	30.5359i	−0.436227	−	0.436227i
$71$	−22.6977	−	22.6977i	−0.319686	−	0.319686i	0.528961	−	0.848646i	$-0.322582\pi$
$71$	−22.6977	−	22.6977i	−0.319686	−	0.319686i	−0.848646	+	0.528961i	$0.822582\pi$
$72$		0			0
$73$	−43.3538	+	43.3538i	−0.593888	+	0.593888i	−0.938679	−	0.344791i	$-0.887950\pi$
$73$	−43.3538	+	43.3538i	−0.593888	+	0.593888i	0.344791	+	0.938679i	$0.387950\pi$
$74$	−112.703			−1.52301
$75$		0			0
$76$	−31.2487	+	31.2487i	−0.411167	+	0.411167i
$77$			14.8435i			0.192772i
$78$		0			0
$79$	−79.2154			−1.00273			−0.501363	−	0.865237i	$-0.667168\pi$
$79$	−79.2154			−1.00273			−0.501363	+	0.865237i	$0.667168\pi$
$80$	41.9509	+	41.9509i	0.524387	+	0.524387i
$81$		0			0
$82$			215.531i			2.62842i
$83$	23.8793	+	23.8793i	0.287702	+	0.287702i	0.836171	−	0.548469i	$-0.184789\pi$
$83$	23.8793	+	23.8793i	0.287702	+	0.287702i	−0.548469	+	0.836171i	$0.684789\pi$
$84$		0			0
$85$	54.4308	−	54.4308i	0.640362	−	0.640362i
$86$	64.6486	−	64.6486i	0.751728	−	0.751728i
$87$		0			0
$88$			5.75129i			0.0653556i
$89$	−40.7693	+	40.7693i	−0.458083	+	0.458083i	−0.898026	−	0.439943i	$-0.854999\pi$
$89$	−40.7693	+	40.7693i	−0.458083	+	0.458083i	0.439943	+	0.898026i	$0.354999\pi$
$90$		0			0
$91$	20.8564	−	40.2154i	0.229191	−	0.441927i
$92$	93.1540			1.01254
$93$		0			0
$94$	141.177			1.50188
$95$			42.1672i			0.443865i
$96$		0			0
$97$	54.0718	+	54.0718i	0.557441	+	0.557441i	0.928578	−	0.371137i	$-0.121032\pi$
$97$	54.0718	+	54.0718i	0.557441	+	0.557441i	−0.371137	+	0.928578i	$0.621032\pi$
$98$	−75.8208	+	75.8208i	−0.773682	+	0.773682i
$99$		0			0
$100$	30.6077			0.306077
$101$		−	5.59139i		−	0.0553603i	−0.999617	−	0.0276801i	$-0.991188\pi$
$101$		−	5.59139i		−	0.0553603i	0.999617	−	0.0276801i	$-0.00881199\pi$
$102$		0			0
$103$			11.5026i			0.111676i	0.998440	+	0.0558378i	$0.0177830\pi$
$103$			11.5026i			0.111676i	−0.998440	+	0.0558378i	$0.982217\pi$
$104$	8.08108	−	15.5820i	0.0777027	−	0.149827i
$105$		0			0
$106$	−147.818	−	147.818i	−1.39451	−	1.39451i
$107$	153.393			1.43358			0.716789	−	0.697290i	$-0.245611\pi$
$107$	153.393			1.43358			0.716789	+	0.697290i	$0.245611\pi$
$108$		0			0
$109$	79.3154	+	79.3154i	0.727664	+	0.727664i	0.970154	−	0.242490i	$-0.0779642\pi$
$109$	79.3154	+	79.3154i	0.727664	+	0.727664i	−0.242490	+	0.970154i	$0.577964\pi$
$110$	37.3249	+	37.3249i	0.339317	+	0.339317i
$111$		0			0
$112$	−34.3205	+	34.3205i	−0.306433	+	0.306433i
$113$	−27.3237			−0.241803			−0.120901	−	0.992665i	$-0.538579\pi$
$113$	−27.3237			−0.241803			−0.120901	+	0.992665i	$0.538579\pi$
$114$		0			0
$115$	62.8513	−	62.8513i	0.546533	−	0.546533i
$116$			120.045i			1.03487i
$117$		0			0
$118$	−308.028			−2.61041
$119$	44.5304	+	44.5304i	0.374205	+	0.374205i
$120$		0			0
$121$			102.856i			0.850053i
$122$	−50.9868	−	50.9868i	−0.417924	−	0.417924i
$123$		0			0
$124$	184.138	−	184.138i	1.48499	−	1.48499i
$125$	95.9497	−	95.9497i	0.767597	−	0.767597i
$126$		0			0
$127$		−	154.708i		−	1.21817i	−0.793105	−	0.609085i	$-0.791537\pi$
$127$		−	154.708i		−	1.21817i	0.793105	−	0.609085i	$-0.208463\pi$
$128$	−30.3463	+	30.3463i	−0.237080	+	0.237080i
$129$		0			0
$130$	−48.6795	−	153.569i	−0.374458	−	1.18130i
$131$	−188.671			−1.44024			−0.720119	−	0.693851i	$-0.755913\pi$
$131$	−188.671			−1.44024			−0.720119	+	0.693851i	$0.755913\pi$
$132$		0			0
$133$	−34.4974			−0.259379
$134$			7.93338i			0.0592043i
$135$		0			0
$136$	17.2539	+	17.2539i	0.126867	+	0.126867i
$137$	106.600	−	106.600i	0.778099	−	0.778099i	−0.201408	−	0.979507i	$-0.564552\pi$
$137$	106.600	−	106.600i	0.778099	−	0.778099i	0.979507	+	0.201408i	$0.0645518\pi$
$138$		0			0
$139$	13.1384			0.0945211			0.0472606	−	0.998883i	$-0.484951\pi$
$139$	13.1384			0.0945211			0.0472606	+	0.998883i	$0.484951\pi$
$140$		−	66.2627i		−	0.473305i
$141$		0			0
$142$		−	93.3872i		−	0.657656i
$143$	−25.4934	+	49.1564i	−0.178275	+	0.343751i
$144$		0			0
$145$	80.9948	+	80.9948i	0.558585	+	0.558585i
$146$	−178.375			−1.22174
$147$		0			0
$148$	−122.282	−	122.282i	−0.826230	−	0.826230i
$149$	−95.7334	−	95.7334i	−0.642506	−	0.642506i	0.308665	−	0.951171i	$-0.400118\pi$
$149$	−95.7334	−	95.7334i	−0.642506	−	0.642506i	−0.951171	+	0.308665i	$0.900118\pi$
$150$		0			0
$151$	98.6743	−	98.6743i	0.653472	−	0.653472i	−0.300355	−	0.953827i	$-0.597105\pi$
$151$	98.6743	−	98.6743i	0.653472	−	0.653472i	0.953827	+	0.300355i	$0.0971052\pi$
$152$	−13.3665			−0.0879373
$153$		0			0
$154$	−30.5359	+	30.5359i	−0.198285	+	0.198285i
$155$		−	248.477i		−	1.60308i
$156$		0			0
$157$	−106.000			−0.675159			−0.337580	−	0.941297i	$-0.609608\pi$
$157$	−106.000			−0.675159			−0.337580	+	0.941297i	$0.609608\pi$
$158$	−162.961	−	162.961i	−1.03140	−	1.03140i
$159$		0			0
$160$			195.608i			1.22255i
$161$	51.4193	+	51.4193i	0.319374	+	0.319374i
$162$		0			0
$163$	186.569	−	186.569i	1.14460	−	1.14460i	0.156997	−	0.987599i	$-0.449819\pi$
$163$	186.569	−	186.569i	1.14460	−	1.14460i	0.987599	−	0.156997i	$-0.0501814\pi$
$164$	−233.850	+	233.850i	−1.42592	+	1.42592i
$165$		0			0
$166$			98.2487i			0.591860i
$167$	127.467	−	127.467i	0.763275	−	0.763275i	−0.213638	−	0.976913i	$-0.568531\pi$
$167$	127.467	−	127.467i	0.763275	−	0.763275i	0.976913	+	0.213638i	$0.0685313\pi$
$168$		0			0
$169$	138.138	−	97.3590i	0.817387	−	0.576089i
$170$	223.949			1.31735
$171$		0			0
$172$	140.287			0.815623
$173$			47.3261i			0.273561i	0.990601	+	0.136781i	$0.0436755\pi$
$173$			47.3261i			0.273561i	−0.990601	+	0.136781i	$0.956324\pi$
$174$		0			0
$175$	16.8949	+	16.8949i	0.0965422	+	0.0965422i
$176$	41.9509	−	41.9509i	0.238358	−	0.238358i
$177$		0			0
$178$	−167.741			−0.942365
$179$			278.164i			1.55399i	0.629506	+	0.776996i	$0.283257\pi$
$179$			278.164i			1.55399i	−0.629506	+	0.776996i	$0.716743\pi$
$180$		0			0
$181$			277.492i			1.53311i	0.642181	+	0.766553i	$0.278030\pi$
$181$			277.492i			1.53311i	−0.642181	+	0.766553i	$0.721970\pi$
$182$	125.637	−	39.8252i	0.690311	−	0.218820i
$183$		0			0
$184$	19.9230	+	19.9230i	0.108277	+	0.108277i
$185$	−165.008			−0.891936
$186$		0			0
$187$	−54.4308	−	54.4308i	−0.291074	−	0.291074i
$188$	153.177	+	153.177i	0.814769	+	0.814769i
$189$		0			0
$190$	−86.7461	+	86.7461i	−0.456559	+	0.456559i
$191$	306.353			1.60394			0.801972	−	0.597362i	$-0.203785\pi$
$191$	306.353			1.60394			0.801972	+	0.597362i	$0.203785\pi$
$192$		0			0
$193$	−151.851	+	151.851i	−0.786794	+	0.786794i	−0.980967	−	0.194173i	$-0.937798\pi$
$193$	−151.851	+	151.851i	−0.786794	+	0.786794i	0.194173	+	0.980967i	$0.437798\pi$
$194$			222.472i			1.14677i
$195$		0			0
$196$	−164.531			−0.839443
$197$	72.5029	+	72.5029i	0.368035	+	0.368035i	0.866760	−	0.498725i	$-0.166198\pi$
$197$	72.5029	+	72.5029i	0.368035	+	0.368035i	−0.498725	+	0.866760i	$0.666198\pi$
$198$		0			0
$199$		−	119.569i		−	0.600850i	−0.953805	−	0.300425i	$-0.902871\pi$
$199$		−	119.569i		−	0.600850i	0.953805	−	0.300425i	$-0.0971286\pi$
$200$	6.54614	+	6.54614i	0.0327307	+	0.0327307i
$201$		0			0
$202$	11.5026	−	11.5026i	0.0569435	−	0.0569435i
$203$	−66.2627	+	66.2627i	−0.326417	+	0.326417i
$204$		0			0
$205$			315.559i			1.53931i
$206$	−23.6630	+	23.6630i	−0.114869	+	0.114869i
$207$		0			0
$208$	−172.603	+	54.7128i	−0.829820	+	0.263042i
$209$	42.1672			0.201757
$210$		0			0
$211$	−99.1384			−0.469850			−0.234925	−	0.972013i	$-0.575485\pi$
$211$	−99.1384			−0.469850			−0.234925	+	0.972013i	$0.575485\pi$
$212$		−	320.764i		−	1.51304i
$213$		0			0
$214$	315.559	+	315.559i	1.47457	+	1.47457i
$215$	94.6522	−	94.6522i	0.440243	−	0.440243i
$216$		0			0
$217$	203.282			0.936784
$218$			326.334i			1.49695i
$219$		0			0
$220$			80.9948i			0.368158i
$221$	70.9891	+	223.949i	0.321218	+	1.01335i
$222$		0			0
$223$	−12.2436	−	12.2436i	−0.0549038	−	0.0549038i	0.679122	−	0.734026i	$-0.262361\pi$
$223$	−12.2436	−	12.2436i	−0.0549038	−	0.0549038i	−0.734026	+	0.679122i	$0.762361\pi$
$224$	−160.029			−0.714414
$225$		0			0
$226$	−56.2102	−	56.2102i	−0.248718	−	0.248718i
$227$	−137.468	−	137.468i	−0.605586	−	0.605586i	0.336203	−	0.941790i	$-0.390857\pi$
$227$	−137.468	−	137.468i	−0.605586	−	0.605586i	−0.941790	+	0.336203i	$0.890857\pi$
$228$		0			0
$229$	154.033	−	154.033i	0.672635	−	0.672635i	−0.285688	−	0.958323i	$-0.592222\pi$
$229$	154.033	−	154.033i	0.672635	−	0.672635i	0.958323	+	0.285688i	$0.0922221\pi$
$230$	258.595			1.12432
$231$		0			0
$232$	−25.6743	+	25.6743i	−0.110665	+	0.110665i
$233$		−	386.594i		−	1.65920i	−0.558356	−	0.829602i	$-0.688568\pi$
$233$		−	386.594i		−	1.65920i	0.558356	−	0.829602i	$-0.311432\pi$
$234$		0			0
$235$	206.697			0.879563
$236$	−334.210	−	334.210i	−1.41614	−	1.41614i
$237$		0			0
$238$			183.215i			0.769813i
$239$	−199.321	−	199.321i	−0.833979	−	0.833979i	0.154079	−	0.988058i	$-0.450759\pi$
$239$	−199.321	−	199.321i	−0.833979	−	0.833979i	−0.988058	+	0.154079i	$0.950759\pi$
$240$		0			0
$241$	−196.703	+	196.703i	−0.816193	+	0.816193i	−0.985554	−	0.169361i	$-0.945830\pi$
$241$	−196.703	+	196.703i	−0.816193	+	0.816193i	0.169361	+	0.985554i	$0.445830\pi$
$242$	−211.596	+	211.596i	−0.874362	+	0.874362i
$243$		0			0
$244$		−	110.641i		−	0.453447i
$245$	−111.009	+	111.009i	−0.453099	+	0.453099i
$246$		0			0
$247$	−114.244	−	59.2487i	−0.462525	−	0.239873i
$248$	78.7642			0.317598
$249$		0			0
$250$	394.774			1.57910
$251$			107.132i			0.426822i	0.976962	+	0.213411i	$0.0684574\pi$
$251$			107.132i			0.426822i	−0.976962	+	0.213411i	$0.931543\pi$
$252$		0			0
$253$	−62.8513	−	62.8513i	−0.248424	−	0.248424i
$254$	318.264	−	318.264i	1.25301	−	1.25301i
$255$		0			0
$256$	186.703			0.729307
$257$			445.103i			1.73192i	0.500114	+	0.865960i	$0.333291\pi$
$257$			445.103i			1.73192i	−0.500114	+	0.865960i	$0.666709\pi$
$258$		0			0
$259$		−	134.995i		−	0.521216i
$260$	113.805	−	219.439i	0.437712	−	0.843997i
$261$		0			0
$262$	−388.133	−	388.133i	−1.48142	−	1.48142i
$263$	−440.377			−1.67444			−0.837218	−	0.546869i	$-0.815820\pi$
$263$	−440.377			−1.67444			−0.837218	+	0.546869i	$0.815820\pi$
$264$		0			0
$265$	−216.420	−	216.420i	−0.816681	−	0.816681i
$266$	−70.9679	−	70.9679i	−0.266797	−	0.266797i
$267$		0			0
$268$	−8.60770	+	8.60770i	−0.0321183	+	0.0321183i
$269$	43.6654			0.162325			0.0811625	−	0.996701i	$-0.474137\pi$
$269$	43.6654			0.162325			0.0811625	+	0.996701i	$0.474137\pi$
$270$		0			0
$271$	−210.608	+	210.608i	−0.777150	+	0.777150i	−0.979345	−	0.202195i	$-0.935192\pi$
$271$	−210.608	+	210.608i	−0.777150	+	0.777150i	0.202195	+	0.979345i	$0.435192\pi$
$272$		−	251.706i		−	0.925388i
$273$		0			0
$274$	438.592			1.60070
$275$	−20.6511	−	20.6511i	−0.0750949	−	0.0750949i
$276$		0			0
$277$		−	214.641i		−	0.774877i	−0.921895	−	0.387439i	$-0.873360\pi$
$277$		−	214.641i		−	0.774877i	0.921895	−	0.387439i	$-0.126640\pi$
$278$	27.0283	+	27.0283i	0.0972242	+	0.0972242i
$279$		0			0
$280$	14.1718	−	14.1718i	0.0506134	−	0.0506134i
$281$	52.3846	−	52.3846i	0.186422	−	0.186422i	−0.607725	−	0.794147i	$-0.707918\pi$
$281$	52.3846	−	52.3846i	0.186422	−	0.186422i	0.794147	+	0.607725i	$0.207918\pi$
$282$		0			0
$283$		−	2.42047i		−	0.00855290i	−0.999991	−	0.00427645i	$-0.998639\pi$
$283$		−	2.42047i		−	0.00855290i	0.999991	−	0.00427645i	$-0.00136124\pi$
$284$	101.325	−	101.325i	0.356777	−	0.356777i
$285$		0			0
$286$	−153.569	+	48.6795i	−0.536955	+	0.170208i
$287$	−258.162			−0.899519
$288$		0			0
$289$	−37.5847			−0.130051
$290$			333.244i			1.14912i
$291$		0			0
$292$	−193.536	−	193.536i	−0.662794	−	0.662794i
$293$	114.238	−	114.238i	0.389889	−	0.389889i	−0.484759	−	0.874648i	$-0.661093\pi$
$293$	114.238	−	114.238i	0.389889	−	0.389889i	0.874648	+	0.484759i	$0.161093\pi$
$294$		0			0
$295$	−450.985			−1.52876
$296$		−	52.3055i		−	0.176708i
$297$		0			0
$298$		−	393.885i		−	1.32176i
$299$	81.9712	+	258.595i	0.274151	+	0.864865i
$300$		0			0
$301$	77.4359	+	77.4359i	0.257262	+	0.257262i
$302$	405.985			1.34432
$303$		0			0
$304$	97.4974	+	97.4974i	0.320715	+	0.320715i
$305$	−74.6498	−	74.6498i	−0.244753	−	0.244753i
$306$		0			0
$307$	92.9230	−	92.9230i	0.302681	−	0.302681i	−0.539381	−	0.842062i	$-0.681342\pi$
$307$	92.9230	−	92.9230i	0.302681	−	0.302681i	0.842062	+	0.539381i	$0.181342\pi$
$308$	−66.2627			−0.215139
$309$		0			0
$310$	511.167	−	511.167i	1.64892	−	1.64892i
$311$			465.770i			1.49765i	0.662767	+	0.748826i	$0.269382\pi$
$311$			465.770i			1.49765i	−0.662767	+	0.748826i	$0.730618\pi$
$312$		0			0
$313$	−44.7077			−0.142836			−0.0714180	−	0.997446i	$-0.522752\pi$
$313$	−44.7077			−0.142836			−0.0714180	+	0.997446i	$0.522752\pi$
$314$	−218.063	−	218.063i	−0.694467	−	0.694467i
$315$		0			0
$316$		−	353.626i		−	1.11907i
$317$	158.768	+	158.768i	0.500845	+	0.500845i	0.911701	−	0.410855i	$-0.134770\pi$
$317$	158.768	+	158.768i	0.500845	+	0.500845i	−0.410855	+	0.911701i	$0.634770\pi$
$318$		0			0
$319$	80.9948	−	80.9948i	0.253902	−	0.253902i
$320$	−234.599	+	234.599i	−0.733123	+	0.733123i
$321$		0			0
$322$			211.559i			0.657015i
$323$	126.502	−	126.502i	0.391646	−	0.391646i
$324$		0			0
$325$	26.9334	+	84.9667i	0.0828719	+	0.261436i
$326$	767.618			2.35466
$327$		0			0
$328$	−100.028			−0.304964
$329$			169.101i			0.513986i
$330$		0			0
$331$	112.779	+	112.779i	0.340723	+	0.340723i	0.856639	−	0.515916i	$-0.172548\pi$
$331$	112.779	+	112.779i	0.340723	+	0.340723i	−0.515916	+	0.856639i	$0.672548\pi$
$332$	−106.600	+	106.600i	−0.321083	+	0.321083i
$333$		0			0
$334$	524.449			1.57021
$335$			11.6153i			0.0346725i
$336$		0			0
$337$			248.718i			0.738036i	0.929422	+	0.369018i	$0.120306\pi$
$337$			248.718i			0.738036i	−0.929422	+	0.369018i	$0.879694\pi$
$338$	484.464	+	83.8913i	1.43333	+	0.248199i
$339$		0			0
$340$	242.985	+	242.985i	0.714660	+	0.714660i
$341$	−248.477			−0.728673
$342$		0			0
$343$	−211.559	−	211.559i	−0.616790	−	0.616790i
$344$	30.0035	+	30.0035i	0.0872196	+	0.0872196i
$345$		0			0
$346$	−97.3590	+	97.3590i	−0.281384	+	0.281384i
$347$	88.1958			0.254167			0.127083	−	0.991892i	$-0.459438\pi$
$347$	88.1958			0.254167			0.127083	+	0.991892i	$0.459438\pi$
$348$		0			0
$349$	−103.172	+	103.172i	−0.295621	+	0.295621i	−0.839296	−	0.543675i	$-0.817032\pi$
$349$	−103.172	+	103.172i	−0.295621	+	0.295621i	0.543675	+	0.839296i	$0.317032\pi$
$350$			69.5121i			0.198606i
$351$		0			0
$352$	195.608			0.555704
$353$	144.241	+	144.241i	0.408615	+	0.408615i	0.881255	−	0.472640i	$-0.156699\pi$
$353$	144.241	+	144.241i	0.408615	+	0.408615i	−0.472640	+	0.881255i	$0.656699\pi$
$354$		0			0
$355$		−	136.728i		−	0.385150i
$356$	−181.999	−	181.999i	−0.511232	−	0.511232i
$357$		0			0
$358$	−572.238	+	572.238i	−1.59843	+	1.59843i
$359$	383.266	−	383.266i	1.06759	−	1.06759i	0.0700492	−	0.997544i	$-0.477684\pi$
$359$	383.266	−	383.266i	1.06759	−	1.06759i	0.997544	−	0.0700492i	$-0.0223156\pi$
$360$		0			0
$361$		−	263.000i		−	0.728532i
$362$	−570.856	+	570.856i	−1.57695	+	1.57695i
$363$		0			0
$364$	179.526	+	93.1051i	0.493202	+	0.255783i
$365$	−261.158			−0.715503
$366$		0			0
$367$	−558.554			−1.52194			−0.760972	−	0.648784i	$-0.775278\pi$
$367$	−558.554			−1.52194			−0.760972	+	0.648784i	$0.775278\pi$
$368$		−	290.645i		−	0.789795i
$369$		0			0
$370$	−339.454	−	339.454i	−0.917443	−	0.917443i
$371$	177.056	−	177.056i	0.477240	−	0.477240i
$372$		0			0
$373$	−431.061			−1.15566			−0.577830	−	0.816157i	$-0.696100\pi$
$373$	−431.061			−1.15566			−0.577830	+	0.816157i	$0.696100\pi$
$374$		−	223.949i		−	0.598795i
$375$		0			0
$376$			65.5204i			0.174256i
$377$	−333.244	+	105.634i	−0.883937	+	0.280197i
$378$		0			0
$379$	442.415	+	442.415i	1.16732	+	1.16732i	0.982835	+	0.184488i	$0.0590627\pi$
$379$	442.415	+	442.415i	1.16732	+	1.16732i	0.184488	+	0.982835i	$0.440937\pi$
$380$	−188.239			−0.495365
$381$		0			0
$382$	630.228	+	630.228i	1.64981	+	1.64981i
$383$	−108.963	−	108.963i	−0.284498	−	0.284498i	0.550402	−	0.834900i	$-0.314475\pi$
$383$	−108.963	−	108.963i	−0.284498	−	0.284498i	−0.834900	+	0.550402i	$0.814475\pi$
$384$		0			0
$385$	−44.7077	+	44.7077i	−0.116124	+	0.116124i
$386$	−624.775			−1.61859
$387$		0			0
$388$	−241.382	+	241.382i	−0.622119	+	0.622119i
$389$		−	643.891i		−	1.65525i	−0.561283	−	0.827624i	$-0.689692\pi$
$389$		−	643.891i		−	1.65525i	0.561283	−	0.827624i	$-0.310308\pi$
$390$		0			0
$391$	−377.108			−0.964469
$392$	−35.1886	−	35.1886i	−0.0897667	−	0.0897667i
$393$		0			0
$394$			298.305i			0.757119i
$395$	−238.592	−	238.592i	−0.604031	−	0.604031i
$396$		0			0
$397$	197.592	−	197.592i	0.497713	−	0.497713i	−0.413012	−	0.910726i	$-0.635523\pi$
$397$	197.592	−	197.592i	0.497713	−	0.497713i	0.910726	+	0.413012i	$0.135523\pi$
$398$	245.977	−	245.977i	0.618033	−	0.618033i
$399$		0			0
$400$		−	95.4974i		−	0.238744i
$401$	414.018	−	414.018i	1.03246	−	1.03246i	0.0330099	−	0.999455i	$-0.489491\pi$
$401$	414.018	−	414.018i	1.03246	−	1.03246i	0.999455	−	0.0330099i	$-0.0105093\pi$
$402$		0			0
$403$	673.200	+	349.133i	1.67047	+	0.866336i
$404$	24.9605			0.0617835
$405$		0			0
$406$	−272.631			−0.671504
$407$			165.008i			0.405425i
$408$		0			0
$409$	−207.641	−	207.641i	−0.507680	−	0.507680i	0.406134	−	0.913814i	$-0.366877\pi$
$409$	−207.641	−	207.641i	−0.507680	−	0.507680i	−0.913814	+	0.406134i	$0.866877\pi$
$410$	−649.166	+	649.166i	−1.58333	+	1.58333i
$411$		0			0
$412$	−51.3487			−0.124633
$413$		−	368.955i		−	0.893354i
$414$		0			0
$415$			143.846i			0.346617i
$416$	−529.960	−	274.846i	−1.27394	−	0.660689i
$417$		0			0
$418$	86.7461	+	86.7461i	0.207527	+	0.207527i
$419$	673.578			1.60759			0.803793	−	0.594909i	$-0.202812\pi$
$419$	673.578			1.60759			0.803793	+	0.594909i	$0.202812\pi$
$420$		0			0
$421$	422.741	+	422.741i	1.00414	+	1.00414i	0.999991	+	0.00414393i	$0.00131906\pi$
$421$	422.741	+	422.741i	1.00414	+	1.00414i	0.00414393	+	0.999991i	$0.498681\pi$
$422$	−203.947	−	203.947i	−0.483287	−	0.483287i
$423$		0			0
$424$	68.6025	−	68.6025i	0.161798	−	0.161798i
$425$	−123.907			−0.291545
$426$		0			0
$427$	61.0718	−	61.0718i	0.143025	−	0.143025i
$428$			684.761i			1.59991i
$429$		0			0
$430$	389.436			0.905665
$431$	327.753	+	327.753i	0.760449	+	0.760449i	0.976403	−	0.215955i	$-0.0692864\pi$
$431$	327.753	+	327.753i	0.760449	+	0.760449i	−0.215955	+	0.976403i	$0.569286\pi$
$432$		0			0
$433$		−	504.431i		−	1.16497i	−0.812842	−	0.582484i	$-0.802081\pi$
$433$		−	504.431i		−	1.16497i	0.812842	−	0.582484i	$-0.197919\pi$
$434$	418.191	+	418.191i	0.963573	+	0.963573i
$435$		0			0
$436$	−354.072	+	354.072i	−0.812091	+	0.812091i
$437$	146.071	−	146.071i	0.334260	−	0.334260i
$438$		0			0
$439$		−	160.210i		−	0.364944i	−0.983211	−	0.182472i	$-0.941590\pi$
$439$		−	160.210i		−	0.364944i	0.983211	−	0.182472i	$-0.0584098\pi$
$440$	−17.3226	+	17.3226i	−0.0393694	+	0.0393694i
$441$		0			0
$442$	−314.669	+	606.746i	−0.711921	+	1.37273i
$443$	−244.184			−0.551204			−0.275602	−	0.961272i	$-0.588877\pi$
$443$	−244.184			−0.551204			−0.275602	+	0.961272i	$0.588877\pi$
$444$		0			0
$445$	−245.590			−0.551887
$446$		−	50.3748i		−	0.112948i
$447$		0			0
$448$	−191.928	−	191.928i	−0.428411	−	0.428411i
$449$	−39.4719	+	39.4719i	−0.0879106	+	0.0879106i	−0.749695	−	0.661784i	$-0.769800\pi$
$449$	−39.4719	+	39.4719i	−0.0879106	+	0.0879106i	0.661784	+	0.749695i	$0.269800\pi$
$450$		0			0
$451$	315.559			0.699687
$452$		−	121.976i		−	0.269858i
$453$		0			0
$454$		−	565.597i		−	1.24581i
$455$	183.945	−	58.3081i	0.404274	−	0.128150i
$456$		0			0
$457$	210.933	+	210.933i	0.461561	+	0.461561i	0.899167	−	0.437606i	$-0.144173\pi$
$457$	210.933	+	210.933i	0.461561	+	0.461561i	−0.437606	+	0.899167i	$0.644173\pi$
$458$	633.753			1.38374
$459$		0			0
$460$	280.574	+	280.574i	0.609944	+	0.609944i
$461$	464.689	+	464.689i	1.00800	+	1.00800i	0.999968	+	0.00803355i	$0.00255718\pi$
$461$	464.689	+	464.689i	1.00800	+	1.00800i	0.00803355	+	0.999968i	$0.497443\pi$
$462$		0			0
$463$	−636.443	+	636.443i	−1.37461	+	1.37461i	−0.521132	+	0.853476i	$0.674490\pi$
$463$	−636.443	+	636.443i	−1.37461	+	1.37461i	−0.853476	+	0.521132i	$0.825510\pi$
$464$	374.547			0.807212
$465$		0			0
$466$	795.300	−	795.300i	1.70665	−	1.70665i
$467$			271.075i			0.580460i	0.956957	+	0.290230i	$0.0937318\pi$
$467$			271.075i			0.580460i	−0.956957	+	0.290230i	$0.906268\pi$
$468$		0			0
$469$	−9.50258			−0.0202614
$470$	425.217	+	425.217i	0.904716	+	0.904716i
$471$		0			0
$472$		−	142.956i		−	0.302874i
$473$	−94.6522	−	94.6522i	−0.200110	−	0.200110i
$474$		0			0
$475$	47.9948	−	47.9948i	0.101042	−	0.101042i
$476$	−198.788	+	198.788i	−0.417622	+	0.417622i
$477$		0			0
$478$		−	820.084i		−	1.71566i
$479$	−125.737	+	125.737i	−0.262499	+	0.262499i	−0.826069	−	0.563570i	$-0.809428\pi$
$479$	−125.737	+	125.737i	−0.262499	+	0.262499i	0.563570	+	0.826069i	$0.309428\pi$
$480$		0			0
$481$	231.851	−	447.056i	0.482019	−	0.929431i
$482$	−809.311			−1.67907
$483$		0			0
$484$	−459.161			−0.948681
$485$			325.722i			0.671592i
$486$		0			0
$487$	−29.1154	−	29.1154i	−0.0597853	−	0.0597853i	0.676582	−	0.736367i	$-0.263460\pi$
$487$	−29.1154	−	29.1154i	−0.0597853	−	0.0597853i	−0.736367	+	0.676582i	$0.763460\pi$
$488$	23.6630	−	23.6630i	0.0484898	−	0.0484898i
$489$		0			0
$490$	−456.736			−0.932114
$491$		−	585.583i		−	1.19263i	−0.802749	−	0.596317i	$-0.796630\pi$
$491$		−	585.583i		−	1.19263i	0.802749	−	0.596317i	$-0.203370\pi$
$492$		0			0
$493$		−	485.969i		−	0.985738i
$494$	−113.135	−	356.907i	−0.229018	−	0.722485i
$495$		0			0
$496$	−574.520	−	574.520i	−1.15831	−	1.15831i
$497$	111.859			0.225068
$498$		0			0
$499$	35.7743	+	35.7743i	0.0716920	+	0.0716920i	0.742044	−	0.670352i	$-0.233857\pi$
$499$	35.7743	+	35.7743i	0.0716920	+	0.0716920i	−0.670352	+	0.742044i	$0.733857\pi$
$500$	428.329	+	428.329i	0.856658	+	0.856658i
$501$		0			0
$502$	−220.392	+	220.392i	−0.439028	+	0.439028i
$503$	−131.861			−0.262149			−0.131075	−	0.991372i	$-0.541843\pi$
$503$	−131.861			−0.262149			−0.131075	+	0.991372i	$0.541843\pi$
$504$		0			0
$505$	16.8409	−	16.8409i	0.0333484	−	0.0333484i
$506$		−	258.595i		−	0.511056i
$507$		0			0
$508$	690.631			1.35951
$509$	11.3990	+	11.3990i	0.0223949	+	0.0223949i	0.718216	−	0.695821i	$-0.244959\pi$
$509$	11.3990	+	11.3990i	0.0223949	+	0.0223949i	−0.695821	+	0.718216i	$0.744959\pi$
$510$		0			0
$511$		−	213.656i		−	0.418114i
$512$	505.469	+	505.469i	0.987243	+	0.987243i
$513$		0			0
$514$	−915.664	+	915.664i	−1.78145	+	1.78145i
$515$	−34.6451	+	34.6451i	−0.0672720	+	0.0672720i
$516$		0			0
$517$		−	206.697i		−	0.399801i
$518$	277.711	−	277.711i	0.536121	−	0.536121i
$519$		0			0
$520$	71.2717	−	22.5922i	0.137061	−	0.0434466i
$521$	81.1062			0.155674			0.0778370	−	0.996966i	$-0.475199\pi$
$521$	81.1062			0.155674			0.0778370	+	0.996966i	$0.475199\pi$
$522$		0			0
$523$	427.969			0.818297			0.409148	−	0.912468i	$-0.365826\pi$
$523$	427.969			0.818297			0.409148	+	0.912468i	$0.365826\pi$
$524$		−	842.247i		−	1.60734i
$525$		0			0
$526$	−905.941	−	905.941i	−1.72232	−	1.72232i
$527$	−745.432	+	745.432i	−1.41448	+	1.41448i
$528$		0			0
$529$	93.5538			0.176850
$530$		−	890.438i		−	1.68007i
$531$		0			0
$532$		−	154.000i		−	0.289474i
$533$	−854.944	−	443.389i	−1.60402	−	0.831874i
$534$		0			0
$535$	462.010	+	462.010i	0.863571	+	0.863571i
$536$	−3.68189			−0.00686921
$537$		0			0
$538$	89.8282	+	89.8282i	0.166967	+	0.166967i
$539$	111.009	+	111.009i	0.205954	+	0.205954i
$540$		0			0
$541$	583.315	−	583.315i	1.07822	−	1.07822i	0.0815475	−	0.996669i	$-0.474014\pi$
$541$	583.315	−	583.315i	1.07822	−	1.07822i	0.996669	−	0.0815475i	$-0.0259862\pi$
$542$	−866.522			−1.59875
$543$		0			0
$544$	586.823	−	586.823i	1.07872	−	1.07872i
$545$			477.787i			0.876673i
$546$		0			0
$547$	502.554			0.918745			0.459373	−	0.888244i	$-0.348074\pi$
$547$	502.554			0.918745			0.459373	+	0.888244i	$0.348074\pi$
$548$	475.871	+	475.871i	0.868378	+	0.868378i
$549$		0			0
$550$		−	84.9667i		−	0.154485i
$551$	188.239	+	188.239i	0.341631	+	0.341631i
$552$		0			0
$553$	195.195	−	195.195i	0.352974	−	0.352974i
$554$	441.558	−	441.558i	0.797037	−	0.797037i
$555$		0			0
$556$			58.6513i			0.105488i
$557$	−259.877	+	259.877i	−0.466565	+	0.466565i	−0.900800	−	0.434235i	$-0.857019\pi$
$557$	−259.877	+	259.877i	−0.466565	+	0.466565i	0.434235	+	0.900800i	$0.357019\pi$
$558$		0			0
$559$	123.446	+	389.436i	0.220834	+	0.696665i
$560$	−206.743			−0.369184
$561$		0			0
$562$	215.531			0.383507
$563$		−	887.009i		−	1.57550i	−0.615992	−	0.787752i	$-0.711245\pi$
$563$		−	887.009i		−	1.57550i	0.615992	−	0.787752i	$-0.288755\pi$
$564$		0			0
$565$	−82.2975	−	82.2975i	−0.145659	−	0.145659i
$566$	4.97938	−	4.97938i	0.00879749	−	0.00879749i
$567$		0			0
$568$	43.3411			0.0763048
$569$		−	408.960i		−	0.718734i	−0.933196	−	0.359367i	$-0.882993\pi$
$569$		−	408.960i		−	0.718734i	0.933196	−	0.359367i	$-0.117007\pi$
$570$		0			0
$571$			612.102i			1.07198i	0.844223	+	0.535992i	$0.180062\pi$
$571$			612.102i			1.07198i	−0.844223	+	0.535992i	$0.819938\pi$
$572$	−219.439	−	113.805i	−0.383635	−	0.198960i
$573$		0			0
$574$	−531.090	−	531.090i	−0.925243	−	0.925243i
$575$	−143.075			−0.248826
$576$		0			0
$577$	136.215	+	136.215i	0.236075	+	0.236075i	0.815223	−	0.579148i	$-0.196614\pi$
$577$	136.215	+	136.215i	0.236075	+	0.236075i	−0.579148	+	0.815223i	$0.696614\pi$
$578$	−77.3190	−	77.3190i	−0.133770	−	0.133770i
$579$		0			0
$580$	−361.569	+	361.569i	−0.623395	+	0.623395i
$581$	−117.682			−0.202551
$582$		0			0
$583$	−216.420	+	216.420i	−0.371219	+	0.371219i
$584$		−	82.7839i		−	0.141753i
$585$		0			0
$586$	470.018			0.802078
$587$	302.044	+	302.044i	0.514555	+	0.514555i	0.915919	−	0.401364i	$-0.131464\pi$
$587$	302.044	+	302.044i	0.514555	+	0.514555i	−0.401364	+	0.915919i	$0.631464\pi$
$588$		0			0
$589$		−	577.482i		−	0.980445i
$590$	−927.763	−	927.763i	−1.57248	−	1.57248i
$591$		0			0
$592$	−381.526	+	381.526i	−0.644469	+	0.644469i
$593$	21.8327	−	21.8327i	0.0368174	−	0.0368174i	−0.688458	−	0.725276i	$-0.741712\pi$
$593$	21.8327	−	21.8327i	0.0368174	−	0.0368174i	0.725276	+	0.688458i	$0.241712\pi$
$594$		0			0
$595$			268.246i			0.450834i
$596$	427.364	−	427.364i	0.717053	−	0.717053i
$597$		0			0
$598$	−363.349	+	700.610i	−0.607606	+	1.17159i
$599$	−421.008			−0.702851			−0.351425	−	0.936216i	$-0.614303\pi$
$599$	−421.008			−0.702851			−0.351425	+	0.936216i	$0.614303\pi$
$600$		0			0
$601$	−926.277			−1.54123			−0.770613	−	0.637303i	$-0.780050\pi$
$601$	−926.277			−1.54123			−0.770613	+	0.637303i	$0.780050\pi$
$602$			318.602i			0.529239i
$603$		0			0
$604$	440.492	+	440.492i	0.729292	+	0.729292i
$605$	−309.798	+	309.798i	−0.512062	+	0.512062i
$606$		0			0
$607$	−226.000			−0.372323			−0.186161	−	0.982519i	$-0.559605\pi$
$607$	−226.000			−0.372323			−0.186161	+	0.982519i	$0.559605\pi$
$608$			454.608i			0.747711i
$609$		0			0
$610$		−	307.138i		−	0.503506i
$611$	−290.428	+	560.005i	−0.475333	+	0.916539i
$612$		0			0
$613$	241.946	+	241.946i	0.394692	+	0.394692i	0.876356	−	0.481664i	$-0.159967\pi$
$613$	241.946	+	241.946i	0.394692	+	0.394692i	−0.481664	+	0.876356i	$0.659967\pi$
$614$	382.322			0.622674
$615$		0			0
$616$	−14.1718	−	14.1718i	−0.0230061	−	0.0230061i
$617$	−243.851	−	243.851i	−0.395221	−	0.395221i	0.481322	−	0.876544i	$-0.340157\pi$
$617$	−243.851	−	243.851i	−0.395221	−	0.395221i	−0.876544	+	0.481322i	$0.840157\pi$
$618$		0			0
$619$	222.636	−	222.636i	0.359670	−	0.359670i	−0.504021	−	0.863691i	$-0.668147\pi$
$619$	222.636	−	222.636i	0.359670	−	0.359670i	0.863691	+	0.504021i	$0.168147\pi$
$620$	1109.23			1.78908
$621$		0			0
$622$	−958.179	+	958.179i	−1.54048	+	1.54048i
$623$		−	200.920i		−	0.322503i
$624$		0			0
$625$	406.580			0.650527
$626$	−91.9724	−	91.9724i	−0.146921	−	0.146921i
$627$		0			0
$628$		−	473.195i		−	0.753495i
$629$	495.024	+	495.024i	0.787002	+	0.787002i
$630$		0			0
$631$	−382.654	+	382.654i	−0.606424	+	0.606424i	−0.942010	−	0.335585i	$-0.891066\pi$
$631$	−382.654	+	382.654i	−0.606424	+	0.606424i	0.335585	+	0.942010i	$0.391066\pi$
$632$	75.6307	−	75.6307i	0.119669	−	0.119669i
$633$		0			0
$634$			653.233i			1.03034i
$635$	465.971	−	465.971i	0.733812	−	0.733812i
$636$		0			0
$637$	−144.779	−	456.736i	−0.227283	−	0.717011i
$638$	333.244			0.522327
$639$		0			0
$640$	−182.802			−0.285629
$641$			513.297i			0.800775i	0.916346	+	0.400387i	$0.131124\pi$
$641$			513.297i			0.800775i	−0.916346	+	0.400387i	$0.868876\pi$
$642$		0			0
$643$	719.113	+	719.113i	1.11837	+	1.11837i	0.991981	+	0.126391i	$0.0403393\pi$
$643$	719.113	+	719.113i	1.11837	+	1.11837i	0.126391	+	0.991981i	$0.459661\pi$
$644$	−229.541	+	229.541i	−0.356430	+	0.356430i
$645$		0			0
$646$	520.477			0.805692
$647$			450.494i			0.696281i	0.937442	+	0.348141i	$0.113187\pi$
$647$			450.494i			0.696281i	−0.937442	+	0.348141i	$0.886813\pi$
$648$		0			0
$649$			450.985i			0.694891i
$650$	−119.386	+	230.200i	−0.183671	+	0.354154i
$651$		0			0
$652$	832.864	+	832.864i	1.27740	+	1.27740i
$653$	494.159			0.756752			0.378376	−	0.925652i	$-0.376483\pi$
$653$	494.159			0.756752			0.378376	+	0.925652i	$0.376483\pi$
$654$		0			0
$655$	−568.267	−	568.267i	−0.867583	−	0.867583i
$656$	729.624	+	729.624i	1.11223	+	1.11223i
$657$		0			0
$658$	−347.874	+	347.874i	−0.528684	+	0.528684i
$659$	−668.219			−1.01399			−0.506994	−	0.861949i	$-0.669244\pi$
$659$	−668.219			−1.01399			−0.506994	+	0.861949i	$0.669244\pi$
$660$		0			0
$661$	−164.597	+	164.597i	−0.249013	+	0.249013i	−0.820565	−	0.571553i	$-0.806341\pi$
$661$	−164.597	+	164.597i	−0.249013	+	0.249013i	0.571553	+	0.820565i	$0.306341\pi$
$662$			464.019i			0.700934i
$663$		0			0
$664$	−45.5974			−0.0686708
$665$	−103.904	−	103.904i	−0.156247	−	0.156247i
$666$		0			0
$667$		−	561.149i		−	0.841302i
$668$	569.025	+	569.025i	0.851834	+	0.851834i
$669$		0			0
$670$	−23.8949	+	23.8949i	−0.0356640	+	0.0356640i
$671$	−74.6498	+	74.6498i	−0.111252	+	0.111252i
$672$		0			0
$673$			320.420i			0.476108i	0.971252	+	0.238054i	$0.0765095\pi$
$673$			320.420i			0.476108i	−0.971252	+	0.238054i	$0.923491\pi$
$674$	−511.661	+	511.661i	−0.759141	+	0.759141i
$675$		0			0
$676$	434.620	+	616.664i	0.642930	+	0.912225i
$677$	862.682			1.27427			0.637136	−	0.770752i	$-0.280119\pi$
$677$	862.682			1.27427			0.637136	+	0.770752i	$0.280119\pi$
$678$		0			0
$679$	−266.477			−0.392455
$680$			103.935i			0.152846i
$681$		0			0
$682$	−511.167	−	511.167i	−0.749511	−	0.749511i
$683$	351.965	−	351.965i	0.515322	−	0.515322i	−0.400830	−	0.916152i	$-0.631278\pi$
$683$	351.965	−	351.965i	0.515322	−	0.515322i	0.916152	+	0.400830i	$0.131278\pi$
$684$		0			0
$685$	642.144			0.937436
$686$		−	870.436i		−	1.26886i
$687$		0			0
$688$		−	437.703i		−	0.636195i
$689$	890.438	−	282.258i	1.29236	−	0.409663i
$690$		0			0
$691$	433.995	+	433.995i	0.628068	+	0.628068i	0.947582	−	0.319514i	$-0.103520\pi$
$691$	433.995	+	433.995i	0.628068	+	0.628068i	−0.319514	+	0.947582i	$0.603520\pi$
$692$	−211.268			−0.305301
$693$		0			0
$694$	181.436	+	181.436i	0.261435	+	0.261435i
$695$	39.5722	+	39.5722i	0.0569384	+	0.0569384i
$696$		0			0
$697$	946.677	−	946.677i	1.35822	−	1.35822i
$698$	−424.489			−0.608150
$699$		0			0
$700$	−75.4205	+	75.4205i	−0.107744	+	0.107744i
$701$			23.8638i			0.0340425i	0.999855	+	0.0170212i	$0.00541829\pi$
$701$			23.8638i			0.0340425i	−0.999855	+	0.0170212i	$0.994582\pi$
$702$		0			0
$703$	−383.492			−0.545508
$704$	234.599	+	234.599i	0.333238	+	0.333238i
$705$		0			0
$706$			593.464i			0.840601i
$707$	13.7778	+	13.7778i	0.0194876	+	0.0194876i
$708$		0			0
$709$	29.0282	−	29.0282i	0.0409424	−	0.0409424i	−0.686339	−	0.727282i	$-0.740783\pi$
$709$	29.0282	−	29.0282i	0.0409424	−	0.0409424i	0.727282	+	0.686339i	$0.240783\pi$
$710$	281.277	−	281.277i	0.396164	−	0.396164i
$711$		0			0
$712$		−	77.8489i		−	0.109338i
$713$	−860.751	+	860.751i	−1.20722	+	1.20722i
$714$		0			0
$715$	−224.841	+	71.2717i	−0.314463	+	0.0996807i
$716$	−1241.75			−1.73429
$717$		0			0
$718$	1576.90			2.19625
$719$		−	365.928i		−	0.508940i	−0.967081	−	0.254470i	$-0.918099\pi$
$719$		−	365.928i		−	0.508940i	0.967081	−	0.254470i	$-0.0819010\pi$
$720$		0			0
$721$	−28.3435	−	28.3435i	−0.0393114	−	0.0393114i
$722$	541.042	−	541.042i	0.749366	−	0.749366i
$723$		0			0
$724$	−1238.75			−1.71099
$725$		−	184.377i		−	0.254313i
$726$		0			0
$727$			294.728i			0.405403i	0.979241	+	0.202702i	$0.0649722\pi$
$727$			294.728i			0.405403i	−0.979241	+	0.202702i	$0.935028\pi$
$728$	18.4829	+	58.3081i	0.0253887	+	0.0800936i
$729$		0			0
$730$	−537.254	−	537.254i	−0.735964	−	0.735964i
$731$	−567.913			−0.776899
$732$		0			0
$733$	−650.664	−	650.664i	−0.887673	−	0.887673i	0.106627	−	0.994299i	$-0.465995\pi$
$733$	−650.664	−	650.664i	−0.887673	−	0.887673i	−0.994299	+	0.106627i	$0.965995\pi$
$734$	−1149.05	−	1149.05i	−1.56547	−	1.56547i
$735$		0			0
$736$	677.605	−	677.605i	0.920659	−	0.920659i
$737$	11.6153			0.0157602
$738$		0			0
$739$	−381.077	+	381.077i	−0.515666	+	0.515666i	−0.916257	−	0.400591i	$-0.868805\pi$
$739$	−381.077	+	381.077i	−0.515666	+	0.515666i	0.400591	+	0.916257i	$0.368805\pi$
$740$		−	736.613i		−	0.995423i
$741$		0			0
$742$	728.477			0.981775
$743$	−908.610	−	908.610i	−1.22289	−	1.22289i	−0.966598	−	0.256295i	$-0.917498\pi$
$743$	−908.610	−	908.610i	−1.22289	−	1.22289i	−0.256295	−	0.966598i	$-0.582502\pi$
$744$		0			0
$745$		−	576.687i		−	0.774077i
$746$	−886.777	−	886.777i	−1.18871	−	1.18871i
$747$		0			0
$748$	242.985	−	242.985i	0.324846	−	0.324846i
$749$	−377.975	+	377.975i	−0.504640	+	0.504640i
$750$		0			0
$751$			1121.47i			1.49330i	0.665215	+	0.746652i	$0.268340\pi$
$751$			1121.47i			1.49330i	−0.665215	+	0.746652i	$0.731660\pi$
$752$	477.918	−	477.918i	0.635529	−	0.635529i
$753$		0			0
$754$	−902.859	−	468.238i	−1.19743	−	0.621006i
$755$	594.403			0.787289
$756$		0			0
$757$	−1134.75			−1.49901			−0.749507	−	0.661996i	$-0.769709\pi$
$757$	−1134.75			−1.49901			−0.749507	+	0.661996i	$0.769709\pi$
$758$			1820.27i			2.40141i
$759$		0			0
$760$	−40.2590	−	40.2590i	−0.0529724	−	0.0529724i
$761$	486.305	−	486.305i	0.639034	−	0.639034i	−0.311283	−	0.950317i	$-0.600759\pi$
$761$	486.305	−	486.305i	0.639034	−	0.639034i	0.950317	+	0.311283i	$0.100759\pi$
$762$		0			0
$763$	−390.882			−0.512296
$764$			1367.59i			1.79004i
$765$		0			0
$766$		−	448.315i		−	0.585268i
$767$	633.674	−	1221.85i	0.826172	−	1.59303i
$768$		0			0
$769$	−684.395	−	684.395i	−0.889980	−	0.889980i	0.104541	−	0.994521i	$-0.466663\pi$
$769$	−684.395	−	684.395i	−0.889980	−	0.889980i	−0.994521	+	0.104541i	$0.966663\pi$
$770$	−183.945			−0.238889
$771$		0			0
$772$	−677.879	−	677.879i	−0.878082	−	0.878082i
$773$	−361.217	−	361.217i	−0.467292	−	0.467292i	0.433744	−	0.901036i	$-0.357192\pi$
$773$	−361.217	−	361.217i	−0.467292	−	0.467292i	−0.901036	+	0.433744i	$0.857192\pi$
$774$		0			0
$775$	−282.818	+	282.818i	−0.364926	+	0.364926i
$776$	−103.250			−0.133054
$777$		0			0
$778$	1324.61	−	1324.61i	1.70258	−	1.70258i
$779$			733.385i			0.941444i
$780$		0			0
$781$	−136.728			−0.175068
$782$	−775.784	−	775.784i	−0.992051	−	0.992051i
$783$		0			0
$784$			513.344i			0.654775i
$785$	−319.266	−	319.266i	−0.406708	−	0.406708i
$786$		0			0
$787$	287.010	−	287.010i	0.364689	−	0.364689i	−0.500847	−	0.865536i	$-0.666978\pi$
$787$	287.010	−	287.010i	0.364689	−	0.364689i	0.865536	+	0.500847i	$0.166978\pi$
$788$	−323.660	+	323.660i	−0.410736	+	0.410736i
$789$		0			0
$790$		−	981.661i		−	1.24261i
$791$	67.3284	−	67.3284i	0.0851181	−	0.0851181i
$792$		0			0
$793$	307.138	−	97.3590i	0.387312	−	0.122773i
$794$	812.971			1.02389
$795$		0			0
$796$	533.769			0.670564
$797$		−	899.891i		−	1.12910i	−0.825400	−	0.564549i	$-0.809050\pi$
$797$		−	899.891i		−	1.12910i	0.825400	−	0.564549i	$-0.190950\pi$
$798$		0			0
$799$	−620.092	−	620.092i	−0.776085	−	0.776085i
$800$	222.641	−	222.641i	0.278302	−	0.278302i
$801$		0			0
$802$	1703.43			2.12398
$803$			261.158i			0.325228i
$804$		0			0
$805$			309.744i			0.384775i
$806$	666.668	+	2103.14i	0.827132	+	2.60935i
$807$		0			0
$808$	5.33836	+	5.33836i	0.00660689	+	0.00660689i
$809$	−116.385			−0.143862			−0.0719311	−	0.997410i	$-0.522916\pi$
$809$	−116.385			−0.143862			−0.0719311	+	0.997410i	$0.522916\pi$
$810$		0			0
$811$	636.969	+	636.969i	0.785412	+	0.785412i	0.980738	−	0.195326i	$-0.0625766\pi$
$811$	636.969	+	636.969i	0.785412	+	0.785412i	−0.195326	+	0.980738i	$0.562577\pi$
$812$	−295.804	−	295.804i	−0.364290	−	0.364290i
$813$		0			0
$814$	−339.454	+	339.454i	−0.417019	+	0.417019i
$815$	1123.87			1.37898
$816$		0			0
$817$	219.979	−	219.979i	0.269253	−	0.269253i
$818$		−	854.316i		−	1.04440i
$819$		0			0
$820$	−1408.69			−1.71791
$821$	36.1588	+	36.1588i	0.0440424	+	0.0440424i	0.728785	−	0.684743i	$-0.240085\pi$
$821$	36.1588	+	36.1588i	0.0440424	+	0.0440424i	−0.684743	+	0.728785i	$0.740085\pi$
$822$		0			0
$823$			120.364i			0.146250i	0.997323	+	0.0731252i	$0.0232973\pi$
$823$			120.364i			0.146250i	−0.997323	+	0.0731252i	$0.976703\pi$
$824$	−10.9821	−	10.9821i	−0.0133277	−	0.0133277i
$825$		0			0
$826$	759.013	−	759.013i	0.918902	−	0.918902i
$827$	−375.396	+	375.396i	−0.453925	+	0.453925i	−0.896655	−	0.442730i	$-0.854010\pi$
$827$	−375.396	+	375.396i	−0.453925	+	0.453925i	0.442730	+	0.896655i	$0.354010\pi$
$828$		0			0
$829$		−	425.538i		−	0.513315i	−0.966502	−	0.256658i	$-0.917379\pi$
$829$		−	425.538i		−	0.513315i	0.966502	−	0.256658i	$-0.0826213\pi$
$830$	−295.919	+	295.919i	−0.356529	+	0.356529i
$831$		0			0
$832$	−305.967	−	965.233i	−0.367748	−	1.16014i
$833$	666.056			0.799587
$834$		0			0
$835$	767.846			0.919576
$836$			188.239i			0.225166i
$837$		0			0
$838$	1385.68	+	1385.68i	1.65356	+	1.65356i
$839$	−94.7836	+	94.7836i	−0.112972	+	0.112972i	−0.761333	−	0.648361i	$-0.775455\pi$
$839$	−94.7836	+	94.7836i	−0.112972	+	0.112972i	0.648361	+	0.761333i	$0.275455\pi$
$840$		0			0
$841$	−117.862			−0.140145
$842$			1739.32i			2.06570i
$843$		0			0
$844$		−	442.564i		−	0.524365i
$845$	709.305	+	122.825i	0.839414	+	0.145355i
$846$		0			0
$847$	−253.449	−	253.449i	−0.299231	−	0.299231i
$848$	−1000.80			−1.18019
$849$		0			0
$850$	−254.900	−	254.900i	−0.299882	−	0.299882i
$851$	571.605	+	571.605i	0.671686	+	0.671686i
$852$		0			0
$853$	−481.572	+	481.572i	−0.564562	+	0.564562i	−0.930600	−	0.366038i	$-0.880714\pi$
$853$	−481.572	+	481.572i	−0.564562	+	0.564562i	0.366038	+	0.930600i	$0.380714\pi$
$854$	251.273			0.294231
$855$		0			0
$856$	−146.451	+	146.451i	−0.171088	+	0.171088i
$857$		−	639.999i		−	0.746790i	−0.927672	−	0.373395i	$-0.878194\pi$
$857$		−	639.999i		−	0.746790i	0.927672	−	0.373395i	$-0.121806\pi$
$858$		0			0
$859$	−356.708			−0.415259			−0.207630	−	0.978208i	$-0.566575\pi$
$859$	−356.708			−0.415259			−0.207630	+	0.978208i	$0.566575\pi$
$860$	422.537	+	422.537i	0.491322	+	0.491322i
$861$		0			0
$862$			1348.50i			1.56439i
$863$	3.76105	+	3.76105i	0.00435811	+	0.00435811i	0.709282	−	0.704924i	$-0.249019\pi$
$863$	3.76105	+	3.76105i	0.00435811	+	0.00435811i	−0.704924	+	0.709282i	$0.749019\pi$
$864$		0			0
$865$	−142.543	+	142.543i	−0.164790	+	0.164790i
$866$	1037.71	−	1037.71i	1.19828	−	1.19828i
$867$		0			0
$868$			907.472i			1.04547i
$869$	−238.592	+	238.592i	−0.274559	+	0.274559i
$870$		0			0
$871$	−31.4693	−	16.3205i	−0.0361300	−	0.0187377i
$872$	−151.452			−0.173684
$873$		0			0
$874$	600.995			0.687637
$875$			472.859i			0.540411i
$876$		0			0
$877$	−521.249	−	521.249i	−0.594354	−	0.594354i	0.344450	−	0.938805i	$-0.388065\pi$
$877$	−521.249	−	521.249i	−0.594354	−	0.594354i	−0.938805	+	0.344450i	$0.888065\pi$
$878$	329.584	−	329.584i	0.375380	−	0.375380i
$879$		0			0
$880$	252.708			0.287168
$881$			642.192i			0.728936i	0.931216	+	0.364468i	$0.118749\pi$
$881$			642.192i			0.728936i	−0.931216	+	0.364468i	$0.881251\pi$
$882$		0			0
$883$		−	1327.26i		−	1.50313i	−0.659661	−	0.751564i	$-0.729300\pi$
$883$		−	1327.26i		−	1.50313i	0.659661	−	0.751564i	$-0.270700\pi$
$884$	−999.733	+	316.903i	−1.13092	+	0.358487i
$885$		0			0
$886$	−502.333	−	502.333i	−0.566968	−	0.566968i
$887$	1060.17			1.19523			0.597617	−	0.801782i	$-0.296114\pi$
$887$	1060.17			1.19523			0.597617	+	0.801782i	$0.296114\pi$
$888$		0			0
$889$	381.215	+	381.215i	0.428814	+	0.428814i
$890$	−505.226	−	505.226i	−0.567670	−	0.567670i
$891$		0			0
$892$	54.6565	−	54.6565i	0.0612741	−	0.0612741i
$893$	480.382			0.537941
$894$		0			0
$895$	−837.815	+	837.815i	−0.936106	+	0.936106i
$896$		−	149.553i		−	0.166911i
$897$		0			0
$898$	−162.403			−0.180849
$899$	−1109.23	−	1109.23i	−1.23385	−	1.23385i
$900$		0			0
$901$			1298.52i			1.44120i
$902$	649.166	+	649.166i	0.719696	+	0.719696i
$903$		0			0
$904$	26.0873	−	26.0873i	0.0288576	−	0.0288576i
$905$	−835.791	+	835.791i	−0.923526	+	0.923526i
$906$		0			0
$907$		−	1404.96i		−	1.54902i	−0.632560	−	0.774512i	$-0.717996\pi$
$907$		−	1404.96i		−	1.54902i	0.632560	−	0.774512i	$-0.282004\pi$
$908$	613.672	−	613.672i	0.675850	−	0.675850i
$909$		0			0
$910$	498.361	+	258.459i	0.547650	+	0.284021i
$911$	1271.84			1.39610			0.698048	−	0.716051i	$-0.254052\pi$
$911$	1271.84			1.39610			0.698048	+	0.716051i	$0.254052\pi$
$912$		0			0
$913$	143.846			0.157553
$914$			867.862i			0.949521i
$915$		0			0
$916$	687.620	+	687.620i	0.750677	+	0.750677i
$917$	464.905	−	464.905i	0.506985	−	0.506985i
$918$		0			0
$919$	−1645.98			−1.79106			−0.895530	−	0.445001i	$-0.853203\pi$
$919$	−1645.98			−1.79106			−0.895530	+	0.445001i	$0.853203\pi$
$920$			120.014i			0.130450i
$921$		0			0
$922$			1911.91i			2.07366i
$923$	370.438	+	192.116i	0.401341	+	0.208143i
$924$		0			0
$925$	187.813	+	187.813i	0.203041	+	0.203041i
$926$	−2618.58			−2.82784
$927$		0			0
$928$	873.213	+	873.213i	0.940962	+	0.940962i
$929$	219.123	+	219.123i	0.235869	+	0.235869i	0.815137	−	0.579268i	$-0.196661\pi$
$929$	219.123	+	219.123i	0.235869	+	0.235869i	−0.579268	+	0.815137i	$0.696661\pi$
$930$		0			0
$931$	−257.995	+	257.995i	−0.277116	+	0.277116i
$932$	1725.80			1.85171
$933$		0			0
$934$	−557.654	+	557.654i	−0.597060	+	0.597060i
$935$		−	327.885i		−	0.350679i
$936$		0			0
$937$	−1590.12			−1.69704			−0.848518	−	0.529166i	$-0.822505\pi$
$937$	−1590.12			−1.69704			−0.848518	+	0.529166i	$0.822505\pi$
$938$	−19.5487	−	19.5487i	−0.0208408	−	0.0208408i
$939$		0			0
$940$			922.718i			0.981615i
$941$	−813.410	−	813.410i	−0.864410	−	0.864410i	0.127437	−	0.991847i	$-0.459325\pi$
$941$	−813.410	−	813.410i	−0.864410	−	0.864410i	−0.991847	+	0.127437i	$0.959325\pi$
$942$		0			0
$943$	1093.13	−	1093.13i	1.15920	−	1.15920i
$944$	−1042.75	+	1042.75i	−1.10461	+	1.10461i
$945$		0			0
$946$		−	389.436i		−	0.411666i
$947$	−712.069	+	712.069i	−0.751921	+	0.751921i	−0.974838	−	0.222916i	$-0.928442\pi$
$947$	−712.069	+	712.069i	−0.751921	+	0.751921i	0.222916	+	0.974838i	$0.428442\pi$
$948$		0			0
$949$	366.951	−	707.557i	0.386671	−	0.745581i
$950$	197.470			0.207863
$951$		0			0
$952$	−85.0306			−0.0893178
$953$		−	873.232i		−	0.916297i	−0.888876	−	0.458149i	$-0.848513\pi$
$953$		−	873.232i		−	0.916297i	0.888876	−	0.458149i	$-0.151487\pi$
$954$		0			0
$955$	922.718	+	922.718i	0.966197	+	0.966197i
$956$	889.789	−	889.789i	0.930742	−	0.930742i
$957$		0			0
$958$	−517.331			−0.540011
$959$			525.344i			0.547804i
$960$		0			0
$961$			2441.91i			2.54101i
$962$	1396.65	−	442.719i	1.45181	−	0.460207i
$963$		0			0
$964$	−878.100	−	878.100i	−0.910892	−	0.910892i
$965$	−914.734			−0.947911
$966$		0			0
$967$	−387.557	−	387.557i	−0.400782	−	0.400782i	0.477726	−	0.878509i	$-0.341461\pi$
$967$	−387.557	−	387.557i	−0.400782	−	0.400782i	−0.878509	+	0.477726i	$0.841461\pi$
$968$	−98.2019	−	98.2019i	−0.101448	−	0.101448i
$969$		0			0
$970$	−670.074	+	670.074i	−0.690798	+	0.690798i
$971$	−1330.38			−1.37012			−0.685058	−	0.728489i	$-0.740223\pi$
$971$	−1330.38			−1.37012			−0.685058	+	0.728489i	$0.740223\pi$
$972$		0			0
$973$	−32.3744	+	32.3744i	−0.0332728	+	0.0332728i
$974$		−	119.792i		−	0.122990i
$975$		0			0
$976$	−345.205			−0.353694
$977$	−855.693	−	855.693i	−0.875837	−	0.875837i	0.117264	−	0.993101i	$-0.462588\pi$
$977$	−855.693	−	855.693i	−0.875837	−	0.875837i	−0.993101	+	0.117264i	$0.962588\pi$
$978$		0			0
$979$			245.590i			0.250858i
$980$	−495.557	−	495.557i	−0.505671	−	0.505671i
$981$		0			0
$982$	1204.66	−	1204.66i	1.22674	−	1.22674i
$983$	−1062.87	+	1062.87i	−1.08125	+	1.08125i	−0.0848560	+	0.996393i	$0.527043\pi$
$983$	−1062.87	+	1062.87i	−1.08125	+	1.08125i	−0.996393	+	0.0848560i	$0.972957\pi$
$984$		0			0
$985$			436.749i			0.443400i
$986$	999.733	−	999.733i	1.01393	−	1.01393i
$987$		0			0
$988$	264.492	−	509.995i	0.267705	−	0.516189i
$989$	−655.769			−0.663063
$990$		0			0
$991$	−16.8306			−0.0169835			−0.00849174	−	0.999964i	$-0.502703\pi$
$991$	−16.8306			−0.0169835			−0.00849174	+	0.999964i	$0.502703\pi$
$992$		−	2678.86i		−	2.70046i
$993$		0			0
$994$	230.115	+	230.115i	0.231504	+	0.231504i
$995$	360.136	−	360.136i	0.361945	−	0.361945i
$996$		0			0
$997$	927.723			0.930515			0.465257	−	0.885175i	$-0.345962\pi$
$997$	927.723			0.930515			0.465257	+	0.885175i	$0.345962\pi$
$998$			147.189i			0.147484i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.j.c.73.4	yes	8
3.2	odd	2	inner	117.3.j.c.73.1	✓	8
13.5	odd	4	inner	117.3.j.c.109.4	yes	8
39.5	even	4	inner	117.3.j.c.109.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.j.c.73.1	✓	8	3.2	odd	2	inner
117.3.j.c.73.4	yes	8	1.1	even	1	trivial
117.3.j.c.109.1	yes	8	39.5	even	4	inner
117.3.j.c.109.4	yes	8	13.5	odd	4	inner

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.05719 + 2.05719i) q^{2} +4.46410i q^{4} +(3.01194 + 3.01194i) q^{5} +(-2.46410 + 2.46410i) q^{7} +(-0.954747 + 0.954747i) q^{8} +12.3923i q^{10} +(3.01194 - 3.01194i) q^{11} +(-12.3923 + 3.92820i) q^{13} -10.1383 q^{14} +13.9282 q^{16} -18.0717i q^{17} +(7.00000 + 7.00000i) q^{19} +(-13.4456 + 13.4456i) q^{20} +12.3923 q^{22} -20.8673i q^{23} -6.85641i q^{25} +(-33.5745 - 17.4123i) q^{26} +(-11.0000 - 11.0000i) q^{28} +26.8912 q^{29} +(-41.2487 - 41.2487i) q^{31} +(32.4720 + 32.4720i) q^{32} +(37.1769 - 37.1769i) q^{34} -14.8435 q^{35} +(-27.3923 + 27.3923i) q^{37} +28.8007i q^{38} -5.75129 q^{40} +(52.3846 + 52.3846i) q^{41} -31.4256i q^{43} +(13.4456 + 13.4456i) q^{44} +(42.9282 - 42.9282i) q^{46} +(34.3130 - 34.3130i) q^{47} +36.8564i q^{49} +(14.1050 - 14.1050i) q^{50} +(-17.5359 - 55.3205i) q^{52} -71.8541 q^{53} +18.1436 q^{55} -4.70519i q^{56} +(55.3205 + 55.3205i) q^{58} +(-74.8661 + 74.8661i) q^{59} -24.7846 q^{61} -169.713i q^{62} +77.8897i q^{64} +(-49.1564 - 25.4934i) q^{65} +(1.92820 + 1.92820i) q^{67} +80.6737 q^{68} +(-30.5359 - 30.5359i) q^{70} +(-22.6977 - 22.6977i) q^{71} +(-43.3538 + 43.3538i) q^{73} -112.703 q^{74} +(-31.2487 + 31.2487i) q^{76} +14.8435i q^{77} -79.2154 q^{79} +(41.9509 + 41.9509i) q^{80} +215.531i q^{82} +(23.8793 + 23.8793i) q^{83} +(54.4308 - 54.4308i) q^{85} +(64.6486 - 64.6486i) q^{86} +5.75129i q^{88} +(-40.7693 + 40.7693i) q^{89} +(20.8564 - 40.2154i) q^{91} +93.1540 q^{92} +141.177 q^{94} +42.1672i q^{95} +(54.0718 + 54.0718i) q^{97} +(-75.8208 + 75.8208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7} - 16 q^{13} + 56 q^{16} + 56 q^{19} + 16 q^{22} - 88 q^{28} - 136 q^{31} + 48 q^{34} - 136 q^{37} - 240 q^{40} + 288 q^{46} - 168 q^{52} + 256 q^{55} + 304 q^{58} - 32 q^{61} - 40 q^{67} - 272 q^{70}+ \cdots + 488 q^{97}+O(q^{100}) \) 8 * q + 8 * q^7 - 16 * q^13 + 56 * q^16 + 56 * q^19 + 16 * q^22 - 88 * q^28 - 136 * q^31 + 48 * q^34 - 136 * q^37 - 240 * q^40 + 288 * q^46 - 168 * q^52 + 256 * q^55 + 304 * q^58 - 32 * q^61 - 40 * q^67 - 272 * q^70 + 152 * q^73 - 56 * q^76 - 800 * q^79 + 768 * q^85 + 56 * q^91 + 880 * q^94 + 488 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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